Accelerate Framework Reference

Mathematical Computation

2010-03-19
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 Contents

Introduction Introduction 5

Part I Other References 7

Chapter 1 BLAS Reference 9

Overview 9
Functions by Task 9
Functions 18
Constants 161

Chapter 2 vDSP Reference 165

Overview 165
Functions by Task 165
Functions 192
Data Types 548
Constants 551

Document Revision History 555

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 CONTENTS

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INTRODUCTION

Introduction

Framework: Accelerate/Accelerate.h
Declared in cblas.h
vDSP.h

This document describes the Accelerate Framework, which contains C APIs for vector and matrix math, digital
signal processing, large number handling, and image processing.

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 INTRODUCTION
Introduction

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PART I

Other References

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 PART I
Other References

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 CHAPTER 1

BLAS Reference

Framework: Accelerate
Declared in cblas.h
vBLAS.h

Overview

The vecLib framework contains nine C header files (not counting vecLib.h which merely includes the others).

This document describes the functions declared in the header files cblas.h and vblas.h, which contain
the interfaces for Apple’s implementation of the Basic Linear Algebra Subprograms (BLAS) API.

For More Information

Documentation on the BLAS standard, including reference implementations, can be found on the web starting
from the BLAS FAQ page at these URLs (verified live as of July 2005): http://www.netlib.org/blas/faq.html
and http://www.netlib.org/blas/blast-forum/blast-forum.html

Functions by Task

General Functions
ATLU_DestroyThreadMemory (page 18)
Releases per-thread storage associated with BLAS.
SetBLASParamErrorProc (page 161)
Sets an error handler function.
cblas_errprn (page 91)
Prints an error message.
cblas_xerbla (page 126)
The default error handler for BLAS routines.
cblas_icamax (page 91)
Returns the index of the element with the largest absolute value in a vector (single-precision complex).
cblas_idamax (page 92)
Returns the index of the element with the largest absolute value in a vector (double-precision).

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 CHAPTER 1
BLAS Reference

cblas_isamax (page 93)

Returns the index of the element with the largest absolute value in a vector (single-precision).
cblas_izamax (page 93)
Returns the index of the element with the largest absolute value in a vector (double-precision complex).

CATLAS and CBLAS Vector Functions

catlas_caxpby (page 18)
Computes the product of two vectors, scaling each one separately (single-precision complex).
catlas_cset (page 19)
Modifies a vector (single-precision complex) in place, setting each element to a given value.
catlas_daxpby (page 19)
Computes the product of two vectors, scaling each one separately (double-precision).
catlas_dset (page 20)
Modifies a vector (double-precision) in place, setting each element to a given value.
catlas_saxpby (page 21)
Computes the product of two vectors, scaling each one separately (single-precision).
catlas_sset (page 21)
Modifies a vector (single-precision) in place, setting each element to a given value.
catlas_zaxpby (page 22)
Computes the product of two vectors, scaling each one separately (double-precision complex).
catlas_zset (page 23)
Modifies a vector (double-precision complex) in place, setting each element to a given value.
cblas_sdot (page 96)
Computes the dot product of two vectors (single-precision).
cblas_sdsdot (page 97)
Computes the dot product of two single-precision vectors plus an initial single-precision value.
cblas_cdotc_sub (page 24)
Calculates the dot product of the complex conjugate of a single-precision complex vector with a
second single-precision complex vector.
cblas_cdotu_sub (page 25)
Computes the dot product of two single-precision complex vectors.
cblas_ddot (page 59)
Computes the dot product of two vectors (double-precision).
cblas_dsdot (page 71)
Computes the double-precision dot product of a pair of single-precision vectors.
cblas_zdotc_sub (page 128)
Calculates the dot product of the complex conjugate of a double-precision complex vector with a
second double-precision complex vector.
cblas_zdotu_sub (page 129)
Computes the dot product of two double-precision complex vectors.

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CHAPTER 1
BLAS Reference

Single-Precision Float Matrix Functions

cblas_sasum (page 94)
Computes the sum of the absolute values of elements in a vector (single-precision).
cblas_saxpy (page 94)
Computes a constant times a vector plus a vector (single-precision).
cblas_scopy (page 96)
Copies a vector to another vector (single-precision).
cblas_sgbmv (page 98)
Scales a general band matrix, then multiplies by a vector, then adds a vector (single precision).
cblas_sgemm (page 99)
Multiplies two matrices (single-precision).
cblas_sgemv (page 100)
Multiplies a matrix by a vector (single precision).
cblas_sger (page 102)
Multiplies vector X by the transform of vector Y, then adds matrix A (single precison).
cblas_snrm2 (page 103)
Computes the L2 norm (Euclidian length) of a vector (single precision).
cblas_srot (page 103)
Applies a Givens rotation matrix to a pair of vectors.
cblas_srotg (page 104)
Constructs a Givens rotation matrix.
cblas_srotm (page 104)
Applies a modified Givens transformation (single precision).
cblas_srotmg (page 106)
Generates a modified Givens rotation matrix.
cblas_ssbmv (page 107)
Scales a symmetric band matrix, then multiplies by a vector, then adds a vector (single-precision).
cblas_sscal (page 108)
Multiplies each element of a vector by a constant (single-precision).
cblas_sspmv (page 108)
Scales a packed symmetric matrix, then multiplies by a vector, then scales and adds another vector
(single precision).
cblas_sspr (page 109)
Rank one update: adds a packed symmetric matrix to the product of a scaling factor, a vector, and its
transpose (single precision).
cblas_sspr2 (page 110)
Rank two update of a packed symmetric matrix using two vectors (single precision).
cblas_sswap (page 111)
Exchanges the elements of two vectors (single precision).
cblas_ssymm (page 111)
Multiplies a matrix by a symmetric matrix (single-precision).
cblas_ssymv (page 113)
Scales a symmetric matrix, multiplies by a vector, then scales and adds another vector (single precision).

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BLAS Reference

cblas_ssyr (page 114)

Rank one update: adds a symmetric matrix to the product of a scaling factor, a vector, and its transpose
(single precision).
cblas_ssyr2 (page 115)
Rank two update of a symmetric matrix using two vectors (single precision).
cblas_ssyr2k (page 116)
Performs a rank-2k update of a symmetric matrix (single precision).
cblas_ssyrk (page 117)
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix (single
precision).
cblas_stbmv (page 118)
Scales a triangular band matrix, then multiplies by a vector (single precision).
cblas_stbsv (page 119)
Solves a triangular banded system of equations.
cblas_stpmv (page 120)
Multiplies a triangular matrix by a vector, then adds a vector (single precision).
cblas_stpsv (page 121)
Solves a packed triangular system of equations.
cblas_strmm (page 122)
Scales a triangular matrix and multiplies it by a matrix.
cblas_strmv (page 123)
Multiplies a triangular matrix by a vector.
cblas_strsm (page 124)
Solves a triangular system of equations with multiple values for the right side.
cblas_strsv (page 125)
Solves a triangular system of equations with a single value for the right side.

Single-Precision Complex Matrix Functions

cblas_caxpy (page 23)
Computes a constant times a vector plus a vector (single-precision complex).
cblas_ccopy (page 24)
Copies a vector to another vector (single-precision complex).
cblas_cgbmv (page 26)
Scales a general band matrix, then multiplies by a vector, then adds a vector (single-precision complex).
cblas_cgemm (page 27)
Multiplies two matrices (single-precision complex).
cblas_cgemv (page 29)
Multiplies a matrix by a vector (single-precision complex).
cblas_cgerc (page 30)
Multiplies vector X by the conjugate transform of vector Y, then adds matrix A (single-precision
complex).
cblas_cgeru (page 31)
Multiplies vector X by the transform of vector Y, then adds matrix A (single-precision complex).

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BLAS Reference

cblas_chbmv (page 32)

Scales a Hermitian band matrix, then multiplies by a vector, then adds a vector (single-precision
complex).
cblas_chemm (page 33)
Multiplies two Hermitian matrices (single-precision complex), then adds a third (with scaling).
cblas_chemv (page 34)
Scales and multiplies a Hermitian matrix by a vector, then adds a second (scaled) vector.
cblas_cher (page 35)
Hermitian rank 1 update: adds the product of a scaling factor, vector X, and the conjugate transpose
of X to matrix A.
cblas_cher2 (page 36)
Hermitian rank 2 update: adds the product of a scaling factor, vector X, and the conjugate transpose
of vector Y to the product of the conjugate of the scaling factor, vector Y, and the conjugate transpose
of vector X, and adds the result to matrix A.
cblas_cher2k (page 37)
Performs a rank-2k update of a complex Hermitian matrix (single-precision complex).
cblas_cherk (page 38)
Rank-k update—multiplies a Hermitian matrix by its transpose and adds a second matrix (single
precision).
cblas_chpmv (page 39)
Scales a packed hermitian matrix, multiplies it by a vector, and adds a scaled vector.
cblas_chpr (page 40)
Scales and multiplies a vector times its conjugate transpose, then adds a matrix.
cblas_chpr2 (page 41)
Multiplies a vector times the conjugate transpose of a second vector and vice-versa, sums the results,
and adds a matrix.
cblas_crotg (page 42)
Constructs a complex Givens rotation.
cblas_cscal (page 43)
Multiplies each element of a vector by a constant (single-precision complex).
cblas_csrot (page 44)
Applies a Givens rotation matrix to a pair of complex vectors.
cblas_csscal (page 44)
Multiplies each element of a vector by a constant (single-precision complex).
cblas_cswap (page 45)
Exchanges the elements of two vectors (single-precision complex).
cblas_csymm (page 46)
Multiplies a matrix by a symmetric matrix (single-precision complex).
cblas_csyr2k (page 47)
Performs a rank-2k update of a symmetric matrix (single-precision complex).
cblas_csyrk (page 48)
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix
(single-precision complex).
cblas_ctbmv (page 49)
Scales a triangular band matrix, then multiplies by a vector (single-precision compex).

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BLAS Reference

cblas_ctbsv (page 50)

Solves a triangular banded system of equations.
cblas_ctpmv (page 51)
Multiplies a triangular matrix by a vector, then adds a vector (single-precision complex).
cblas_ctpsv (page 52)
Solves a packed triangular system of equations.
cblas_ctrmm (page 53)
Scales a triangular matrix and multiplies it by a matrix.
cblas_ctrmv (page 55)
Multiplies a triangular matrix by a vector.
cblas_ctrsm (page 56)
Solves a triangular system of equations with multiple values for the right side.
cblas_ctrsv (page 57)
Solves a triangular system of equations with a single value for the right side.
cblas_scasum (page 95)
Computes the sum of the absolute values of real and imaginary parts of elements in a vector
(single-precision complex).
cblas_scnrm2 (page 95)
Computes the unitary norm of a vector (single-precision complex).

Double-Precision Float Matrix Functions

cblas_dasum (page 58)
Computes the sum of the absolute values of elements in a vector (double-precision).
cblas_daxpy (page 58)
Computes a constant times a vector plus a vector (double-precision).
cblas_dcopy (page 59)
Copies a vector to another vector (double-precision).
cblas_dgbmv (page 60)
Scales a general band matrix, then multiplies by a vector, then adds a vector (double precision).
cblas_dgemm (page 61)
Multiplies two matrices (double-precision).
cblas_dgemv (page 63)
Multiplies a matrix by a vector (double precision).
cblas_dger (page 64)
Multiplies vector X by the transform of vector Y, then adds matrix A (double precison).
cblas_dnrm2 (page 65)
Computes the L2 norm (Euclidian length) of a vector (double precision).
cblas_drot (page 66)
Applies a Givens rotation matrix to a pair of vectors.
cblas_drotg (page 66)
Constructs a Givens rotation matrix.
cblas_drotm (page 67)
Applies a modified Givens transformation (single precision).

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CHAPTER 1
BLAS Reference

cblas_drotmg (page 68)

Generates a modified Givens rotation matrix.
cblas_dsbmv (page 69)
Scales a symmetric band matrix, then multiplies by a vector, then adds a vector (double precision).
cblas_dscal (page 70)
Multiplies each element of a vector by a constant (double-precision).
cblas_dspmv (page 71)
Scales a packed symmetric matrix, then multiplies by a vector, then scales and adds another vector
(double precision).
cblas_dspr (page 72)
Rank one update: adds a packed symmetric matrix to the product of a scaling factor, a vector, and its
transpose (double precision).
cblas_dspr2 (page 73)
Rank two update of a packed symmetric matrix using two vectors (single precision).
cblas_dswap (page 74)
Exchanges the elements of two vectors (double precision).
cblas_dsymm (page 75)
Multiplies a matrix by a symmetric matrix (double-precision).
cblas_dsymv (page 77)
Scales a symmetric matrix, multiplies by a vector, then scales and adds another vector (single precision).
cblas_dsyr (page 78)
Rank one update: adds a symmetric matrix to the product of a scaling factor, a vector, and its transpose
(double precision).
cblas_dsyr2 (page 78)
Rank two update of a symmetric matrix using two vectors (single precision).
cblas_dsyr2k (page 79)
Performs a rank-2k update of a symmetric matrix (double precision).
cblas_dsyrk (page 81)
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix (double
precision).
cblas_dtbmv (page 82)
Scales a triangular band matrix, then multiplies by a vector (double precision).
cblas_dtbsv (page 83)
Solves a triangular banded system of equations.
cblas_dtpmv (page 84)
Multiplies a triangular matrix by a vector, then adds a vector (double precision).
cblas_dtpsv (page 85)
Solves a packed triangular system of equations.
cblas_dtrmm (page 85)
Scales a triangular matrix and multiplies it by a matrix.
cblas_dtrmv (page 87)
Multiplies a triangular matrix by a vector.
cblas_dtrsm (page 88)
Solves a triangular system of equations with multiple values for the right side.

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BLAS Reference

cblas_dtrsv (page 89)

Solves a triangular system of equations with a single value for the right side.

Double-Precision Complex Matrix Functions

cblas_dzasum (page 90)
Computes the sum of the absolute values of real and imaginary parts of elements in a vector
(single-precision complex).
cblas_dznrm2 (page 90)
Computes the unitary norm of a vector (double-precision complex).
cblas_zaxpy (page 127)
Computes a constant times a vector plus a vector (double-precision complex).
cblas_zcopy (page 127)
Copies a vector to another vector (double-precision complex).
cblas_zdrot (page 129)
Applies a Givens rotation matrix to a pair of complex vectors.
cblas_zdscal (page 130)
Multiplies each element of a vector by a constant (double-precision complex).
cblas_zgbmv (page 130)
Scales a general band matrix, then multiplies by a vector, then adds a vector (double-precision
complex).
cblas_zgemm (page 132)
Multiplies two matrices (double-precision complex).
cblas_zgemv (page 133)
Multiplies a matrix by a vector (double-precision complex).
cblas_zgerc (page 135)
Multiplies vector X by the conjugate transform of vector Y, then adds matrix A (double-precision
complex).
cblas_zgeru (page 136)
Multiplies vector X by the transform of vector Y, then adds matrix A (double-precision complex).
cblas_zhbmv (page 137)
Scales a Hermitian band matrix, then multiplies by a vector, then adds a vector (double-precision
complex).
cblas_zhemm (page 138)
Multiplies two Hermitian matrices (double-precision complex).
cblas_zhemv (page 139)
Scales and multiplies a Hermitian matrix by a vector, then adds a second (scaled) vector.
cblas_zher (page 140)
Adds the product of a scaling factor, vector X, and the conjugate transpose of X to matrix A.
cblas_zher2 (page 141)
Hermitian rank 2 update: adds the product of a scaling factor, vector X, and the conjugate transpose
of vector Y to the product of the conjugate of the scaling factor, vector Y, and the conjugate transpose
of vector X, and adds the result to matrix A.
cblas_zher2k (page 142)
Performs a rank-2k update of a complex Hermitian matrix (double-precision complex).

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BLAS Reference

cblas_zherk (page 143)

Rank-k update—multiplies a Hermitian matrix by its transpose and adds a second matrix (single
precision).
cblas_zhpmv (page 144)
Scales a packed hermitian matrix, multiplies it by a vector, and adds a scaled vector.
cblas_zhpr (page 145)
Scales and multiplies a vector times its conjugate transpose, then adds a matrix.
cblas_zhpr2 (page 146)
Multiplies a vector times the conjugate transpose of a second vector and vice-versa, sums the results,
and adds a matrix.
cblas_zrotg (page 147)
Constructs a complex Givens rotation.
cblas_zscal (page 147)
Multiplies each element of a vector by a constant (double-precision complex).
cblas_zswap (page 148)
Exchanges the elements of two vectors (double-precision complex).
cblas_zsymm (page 149)
Multiplies a matrix by a symmetric matrix (double-precision complex).
cblas_zsyr2k (page 150)
Performs a rank-2k update of a symmetric matrix (double-precision complex).
cblas_zsyrk (page 151)
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix
(double-precision complex).
cblas_ztbmv (page 152)
Scales a triangular band matrix, then multiplies by a vector (double-precision complex).
cblas_ztbsv (page 153)
Solves a triangular banded system of equations.
cblas_ztpmv (page 154)
Multiplies a triangular matrix by a vector, then adds a vector (double-precision compex).
cblas_ztpsv (page 155)
Solves a packed triangular system of equations.
cblas_ztrmm (page 156)
Scales a triangular matrix and multiplies it by a matrix.
cblas_ztrmv (page 158)
Multiplies a triangular matrix by a vector.
cblas_ztrsm (page 159)
Solves a triangular system of equations with multiple values for the right side.
cblas_ztrsv (page 160)
Solves a triangular system of equations with a single value for the right side.

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 CHAPTER 1
BLAS Reference

Functions

ATLU_DestroyThreadMemory
Releases per-thread storage associated with BLAS.

void ATLU_DestroyThreadMemory (
void
);

Discussion
Many BLAS functions parallelize computation to obtain performance from multiple CPU cores. These functions
allocate thread memory. Call this function when you no longer need to call BLAS functions.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

catlas_caxpby
Computes the product of two vectors, scaling each one separately (single-precision complex).

void catlas_caxpby (
const int N,
const void *alpha,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
N
Number of elements in the vector.
alpha
Scaling factor for X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for Y.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.

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BLAS Reference

Discussion
On return, the contents of vector Y are replaced with the result.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

catlas_cset
Modifies a vector (single-precision complex) in place, setting each element to a given value.

void catlas_cset (
const int N,
const void *alpha,
void *X,
const int incX
);

Parameters
N
The number of elements in the vector.
alpha
The new value.
X
The vector to modify.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

catlas_daxpby
Computes the product of two vectors, scaling each one separately (double-precision).

void catlas_daxpby (
const int N,
const double alpha,
const double *X,
const int incX,
const double beta,
double *Y,
const int incY
);

Parameters
N
Number of elements in the vector.

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 CHAPTER 1
BLAS Reference

alpha
Scaling factor for X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for Y.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
On return, the contents of vector Y are replaced with the result.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

catlas_dset
Modifies a vector (double-precision) in place, setting each element to a given value.

void catlas_dset (
const int N,
const double alpha,
double *X,
const int incX
);

Parameters
N
The number of elements in the vector.
alpha
The new value.
X
The vector to modify.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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BLAS Reference

catlas_saxpby
Computes the product of two vectors, scaling each one separately (single-precision).

void catlas_saxpby (
const int N,
const float alpha,
const float *X,
const int incX,
const float beta,
float *Y,
const int incY
);

Parameters
N
Number of elements in the vector.
alpha
Scaling factor for X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for Y.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
On return, the contents of vector Y are replaced with the result.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

catlas_sset
Modifies a vector (single-precision) in place, setting each element to a given value.

void catlas_sset (
const int N,
const float alpha,
float *X,
const int incX
);

Parameters
N
The number of elements in the vector.

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 CHAPTER 1
BLAS Reference

alpha
The new value.
X
The vector to modify.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

catlas_zaxpby
Computes the product of two vectors, scaling each one separately (double-precision complex).

void catlas_zaxpby (
const int N,
const void *alpha,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
N
Number of elements in the vector.
alpha
Scaling factor for X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for Y.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
On return, the contents of vector Y are replaced with the result.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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catlas_zset
Modifies a vector (double-precision complex) in place, setting each element to a given value.

void catlas_zset (
const int N,
const void *alpha,
void *X,
const int incX
);

Parameters
N
The number of elements in the vector.
alpha
The new value.
X
The vector to modify.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_caxpy
Computes a constant times a vector plus a vector (single-precision complex).

void cblas_caxpy (
const int N,
const void *alpha,
const void *X,
const int incX,
void *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
alpha
Scaling factor for the values in X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Input vector Y.

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incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
On return, the contents of vector Y are replaced with the result. The value computed is (alpha * X[i])
+ Y[i].

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ccopy
Copies a vector to another vector (single-precision complex).

void cblas_ccopy (
const int N,
const void *X,
const int incX,
void *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
X
Source vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Destination vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cdotc_sub
Calculates the dot product of the complex conjugate of a single-precision complex vector with a second
single-precision complex vector.

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void cblas_cdotc_sub (
const int N,
const void *X,
const int incX,
const void *Y,
const int incY,
void *dotc
);

Parameters
N
Number of elements in vectors X and Y.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
dotc
The result vector.
Discussion
Computes conjg(X) * Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cdotu_sub
Computes the dot product of two single-precision complex vectors.

void cblas_cdotu_sub (
const int N,
const void *X,
const int incX,
const void *Y,
const int incY,
void *dotu
);

Parameters
N
The length of vectors X and Y.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.

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Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
dotu
The result vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cgbmv
Scales a general band matrix, then multiplies by a vector, then adds a vector (single-precision complex).

void cblas_cgbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const int KL,
const int KU,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
M
Number of rows in matrix A.
N
Number of columns in matrix A.
KL
Number of subdiagonals in matrix A.
KU
Number of superdiagonals in matrix A.
alpha
Scaling factor to multiply matrix A by.

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A
Matrix A.
lda
Leading dimension of array containing matrix A. (Must be at least KL+KU+1.)
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor to multiply vector Y by.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y, alpha*A'*x + beta*y, or alpha*conjg(A')*x + beta*y depending
on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cgemm
Multiplies two matrices (single-precision complex).

void cblas_cgemm (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_TRANSPOSE TransB,
const int M,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.

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TransB
Specifies whether to transpose matrix B.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
K
Number of columns in matrix A; number of rows in matrix B.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B and multiplies the resulting matrix by alpha. It then multiplies matrix C by
beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

with optional use of transposed forms of A, B, or both.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_cgemv
Multiplies a matrix by a vector (single-precision complex).

void cblas_cgemv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for the product of matrix A and vector X.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector Y.
Y
Vector Y
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
This function multiplies A * X (after transposing A, if needed) and multiplies the resulting matrix by alpha.
It then multiplies vector Y by beta. It stores the sum of these two products in vector Y.

Thus, it calculates either

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Y←αAX +  Y

with optional use of the transposed form of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cgerc
Multiplies vector X by the conjugate transform of vector Y, then adds matrix A (single-precision complex).

void cblas_cgerc (
const enum CBLAS_ORDER Order,
const int M,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Computes alpha*x*conjg(y') + A.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cgeru
Multiplies vector X by the transform of vector Y, then adds matrix A (single-precision complex).

void cblas_cgeru (
const enum CBLAS_ORDER Order,
const int M,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Computes alpha*x*y' + A.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_chbmv
Scales a Hermitian band matrix, then multiplies by a vector, then adds a vector (single-precision complex).

void cblas_chbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
K
Half-bandwidth of matrix A.
alpha
Scaling value to multiply matrix A by.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector Y is multiplied by.
Y
Vector Y. Replaced by results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.

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Discussion
Computes alpha*A*x + beta*y and returns the results in vector Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_chemm
Multiplies two Hermitian matrices (single-precision complex), then adds a third (with scaling).

void cblas_chemm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
M
The number of rows in matrices A and C.
N
The number of columns in matrices B and C.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.

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ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B or B * A (depending on the value of Side) and multiplies the resulting matrix
by alpha. It then multiplies matrix C by beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

where

A = AH

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_chemv
Scales and multiplies a Hermitian matrix by a vector, then adds a second (scaled) vector.

void cblas_chemv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.

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Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector X.
Y
Vector Y. Overwritten by results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Calculates Y←αAX +  Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cher
Hermitian rank 1 update: adds the product of a scaling factor, vector X, and the conjugate transpose of X to
matrix A.

void cblas_cher (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const void *X,
const int incX,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.

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Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
alpha
The scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of matrix A.
Discussion
Computes A←αX*conjg(X') +  A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cher2
Hermitian rank 2 update: adds the product of a scaling factor, vector X, and the conjugate transpose of vector
Y to the product of the conjugate of the scaling factor, vector Y, and the conjugate transpose of vector X,
and adds the result to matrix A.

void cblas_cher2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.

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alpha
The scaling factor α.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
The leading dimension of matrix A.
Discussion
Computes A←αX*conjg(Y') + conjg(α)*Y*conjg(X') + A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cher2k
Performs a rank-2k update of a complex Hermitian matrix (single-precision complex).

void cblas_cher2k (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const float beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.

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Trans
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
N
Order of matrix C.
K
Specifies the number of columns in matrices A and B if trans='N'.
Specifies the number of rows if trans='C' or trans='T').
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
B
Matrix B.
ldb
Leading dimension of array containing matrix B.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Computes alpha*A*BH + alpha*B*AH +beta*C

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cherk
Rank-k update—multiplies a Hermitian matrix by its transpose and adds a second matrix (single precision).

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void cblas_cherk (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const float alpha,
const void *A,
const int lda,
const float beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n') or the conjugate transpose of A ('C' or 'c').
N
Order of matrix C.
K
Number of columns in matrix A (or number of rows if matrix A is transposed).
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Calculates alpha*A*AH + beta*C; if transposed, calculates alpha*AH*A + beta*C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_chpmv
Scales a packed hermitian matrix, multiplies it by a vector, and adds a scaled vector.

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void cblas_chpmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *Ap,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vectors x and y.
alpha
Scaling factor that matrix A is multiplied by.
Ap
Matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector y is multiplied by.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and stores the results in Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_chpr
Scales and multiplies a vector times its conjugate transpose, then adds a matrix.

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BLAS Reference

void cblas_chpr (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const void *X,
const int incX,
void *A
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vector x.
alpha
Scaling factor that vector x is multiplied by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
A
Matrix A. Overwritten by results on return.
Discussion
Calculates alpha*x*conjg(x') + A and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_chpr2
Multiplies a vector times the conjugate transpose of a second vector and vice-versa, sums the results, and
adds a matrix.

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void cblas_chpr2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *Ap
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vectors x and y.
alpha
Scaling factor that vector x is multiplied by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Ap
Matrix A in packed storage format. Overwritten by the results on return.
Discussion
Calcuates alpha*x*conjg(y') + conjg(alpha)*y*conjg(x') + A, and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_crotg
Constructs a complex Givens rotation.

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void cblas_crotg (
void *a,
void *b,
void *c,
void *s
);

Parameters
a
Complex value a. Overwritten on output.
b
Complex value a.
c
Real value c. Unused on entry. Overwritten on return with the value cos( ).
s
Complex value s. Unused on entry. Overwritten on return with the value sin( ).
Discussion
Given a vertical matrix containing a and b, computes the values of cos   and sin   that zero the lower
value (b). Returns the value of sin   in s, the value of cos   in c, and the upper value (r) in a.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cscal
Multiplies each element of a vector by a constant (single-precision complex).

void cblas_cscal (
const int N,
const void *alpha,
void *X,
const int incX
);

Parameters
N
The number of elements in the vector.
alpha
The constant scaling factor.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_csrot
Applies a Givens rotation matrix to a pair of complex vectors.

void cblas_csrot (
const int N,
void *X,
const int incX,
void *Y,
const int incY,
const float c,
const float s
);

Parameters
N
The number of elements in vectors X and Y.
X
Vector X. Modified on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y. Modified on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
c
The value cos( ) in the Givens rotation matrix.
s
The value sin( ) in the Givens rotation matrix.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_csscal
Multiplies each element of a vector by a constant (single-precision complex).

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void cblas_csscal (
const int N,
const float alpha,
void *X,
const int incX
);

Parameters
N
The number of elements in vector x.
alpha
The constant scaling factor.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_cswap
Exchanges the elements of two vectors (single-precision complex).

void cblas_cswap (
const int N,
void *X,
const int incX,
void *Y,
const int incY
);

Parameters
N
Number of elements in vectors
X
Vector x. On return, contains elements copied from vector y.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y. On return, contains elements copied from vector x.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_csymm
Multiplies a matrix by a symmetric matrix (single-precision complex).

void cblas_csymm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.

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Discussion
This function multiplies A * B or B * A (depending on the value of Side) and multiplies the resulting matrix
by alpha. It then multiplies matrix C by beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

where

A = AT

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_csyr2k
Performs a rank-2k update of a symmetric matrix (single-precision complex).

void cblas_csyr2k (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
N
Order of matrix C.

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K
Specifies the number of columns in matrices A and B if trans='N'.
Specifies the number of rows if trans='C' or trans='T').
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
B
Matrix B.
ldb
Leading dimension of array containing matrix B.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Computes alpha*A*BT + alpha*B*AT +beta*C

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_csyrk
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix (single-precision
complex).

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void cblas_csyrk (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T' or 't').
N
Order of matrix C.
K
Number of columns in matrix A (or number of rows if matrix A is transposed).
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Calculates alpha*A*AT + beta*C; if transposed, calculates alpha*AT*A + beta*C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ctbmv
Scales a triangular band matrix, then multiplies by a vector (single-precision compex).

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void cblas_ctbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
K
Half-bandwidth of matrix A.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x and stores the results in x.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ctbsv
Solves a triangular banded system of equations.

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void cblas_ctbsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
K
Number of superdiagonals or subdiagonals of matrix A (depending on the value of Uplo).
A
Matrix A.
lda
The leading dimension of matrix A.
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ctpmv
Multiplies a triangular matrix by a vector, then adds a vector (single-precision complex).

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void cblas_ctpmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *Ap,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A and the number of elements in vectors x and y.
Ap
Matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x, AT*x, or conjg(AT)*x and stores the results in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ctpsv
Solves a packed triangular system of equations.

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void cblas_ctpsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *Ap,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
Ap
Matrix A (in packed storage format).
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ctrmm
Scales a triangular matrix and multiplies it by a matrix.

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void cblas_ctrmm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
void *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
Number of rows in matrix B.
N
Number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
B
Matrix B. Overwritten by results on return.
ldb
Leading dimension of matrix B.
Discussion
If Side is 'L', multiplies alpha*A*B or alpha*A'*B, depending on TransA.

If Side is 'R', multiplies alpha*B*A or alpha*B*A', depending on TransA.

In either case, the results are stored in matrix B.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_ctrmv
Multiplies a triangular matrix by a vector.

void cblas_ctrmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Multiplies A*X or A'*X, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_ctrsm
Solves a triangular system of equations with multiple values for the right side.

void cblas_ctrsm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
void *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrix and vector should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
The number of rows in matrix B.
N
The number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Triangular matrix A.
lda
The leading dimension of matrix B.
B
On entry, matrix B. Overwritten on return by matrix X.
ldb
The leading dimension of matrix B.
Discussion
If Side is 'L', solves A*X=alpha*B or A'*X=alpha*B, depending on TransA.

If Side is 'R', solves X*A=alpha*B or X*A'=alpha*B, depending on TransA.

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In either case, the results overwrite the values of matrix B in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ctrsv
Solves a triangular system of equations with a single value for the right side.

void cblas_ctrsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
A
Triangular matrix A.
lda
The leading dimension of matrix B.
X
The vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves A*x=b or A'*x=b where x and b are elements in X and B.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_dasum
Computes the sum of the absolute values of elements in a vector (double-precision).

double cblas_dasum (
const int N,
const double *X,
const int incX
);

Parameters
N
The number of elements in vector x.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
Returns the sum.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_daxpy
Computes a constant times a vector plus a vector (double-precision).

void cblas_daxpy (
const int N,
const double alpha,
const double *X,
const int incX,
double *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
alpha
Scaling factor for the values in X.
X
Input vector X.

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incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
On return, the contents of vector Y are replaced with the result. The value computed is (alpha * X[i])
+ Y[i].

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dcopy
Copies a vector to another vector (double-precision).

void cblas_dcopy (
const int N,
const double *X,
const int incX,
double *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
X
Source vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Destination vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ddot
Computes the dot product of two vectors (double-precision).

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double cblas_ddot (
const int N,
const double *X,
const int incX,
const double *Y,
const int incY
);

Parameters
N
The number of elements in the vectors.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dgbmv
Scales a general band matrix, then multiplies by a vector, then adds a vector (double precision).

void cblas_dgbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const int KL,
const int KU,
const double alpha,
const double *A,
const int lda,
const double *X,
const int incX,
const double beta,
double *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').

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M
Number of rows in matrix A.
N
Number of columns in matrix A.
KL
Number of subdiagonals in matrix A.
KU
Number of superdiagonals in matrix A.
alpha
Scaling factor to multiply matrix A by.
A
Matrix A.
lda
Leading dimension of array containing matrix A. (Must be at least KL+KU+1.)
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor to multiply vector Y by.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y or alpha*A'*x + beta*y depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dgemm
Multiplies two matrices (double-precision).

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void cblas_dgemm (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_TRANSPOSE TransB,
const int M,
const int N,
const int K,
const double alpha,
const double *A,
const int lda,
const double *B,
const int ldb,
const double beta,
double *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
TransB
Specifies whether to transpose matrix B.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
K
Number of columns in matrix A; number of rows in matrix B.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.

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Discussion
This function multiplies A * B and multiplies the resulting matrix by alpha. It then multiplies matrix C by
beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

with optional use of transposed forms of A, B, or both.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dgemv
Multiplies a matrix by a vector (double precision).

void cblas_dgemv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const double alpha,
const double *A,
const int lda,
const double *X,
const int incX,
const double beta,
double *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for the product of matrix A and vector X.
A
Matrix A.

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lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector Y.
Y
Vector Y
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
This function multiplies A * X (after transposing A, if needed) and multiplies the resulting matrix by alpha.
It then multiplies vector Y by beta. It stores the sum of these two products in vector Y.

Thus, it calculates either

Y←αAX +  Y

with optional use of the transposed form of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dger
Multiplies vector X by the transform of vector Y, then adds matrix A (double precison).

void cblas_dger (
const enum CBLAS_ORDER Order,
const int M,
const int N,
const double alpha,
const double *X,
const int incX,
const double *Y,
const int incY,
double *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
M
Number of rows in matrix A.

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N
Number of columns in matrix A.
alpha
Scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Computes alpha*x*y' + A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dnrm2
Computes the L2 norm (Euclidian length) of a vector (double precision).

double cblas_dnrm2 (
const int N,
const double *X,
const int incX
);

Parameters
N
Length of vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_drot
Applies a Givens rotation matrix to a pair of vectors.

void cblas_drot (
const int N,
double *X,
const int incX,
double *Y,
const int incY,
const double c,
const double s
);

Parameters
N
The number of elements in vectors X and Y.
X
Vector X. Modified on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y. Modified on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
c
The value cos( ) in the Givens rotation matrix.
s
The value sin( ) in the Givens rotation matrix.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_drotg
Constructs a Givens rotation matrix.

void cblas_drotg (
double *a,
double *b,
double *c,
double *s
);

Parameters
a
Double-precision value a. Overwritten on return with result r.
b
Double-precision value b. Overwritten on return with result z (zero).

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c
Unused on entry. Overwritten on return with the value cos( ).
s
Unused on entry. Overwritten on return with the value sin( ).
Discussion
Given a vertical matrix containing a and b, computes the values of cos   and sin   that zero the lower
value (b). Returns the value of sin   in s, the value of cos   in c, and the upper value (r) in a.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_drotm
Applies a modified Givens transformation (single precision).

void cblas_drotm (
const int N,
double *X,
const int incX,
double *Y,
const int incY,
const double *P
);

Parameters
N
Number of elements in vectors.
X
Vector X. Modified on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y. Modified on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.

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P
A 5-element vector:

P[0]
Flag value that defines the form of matrix H.
-2.0: matrix H contains the identity matrix.
-1.0: matrix H is identical to matrix SH (defined by the remaining values in the vector).
0.0: H[1,2] and H[2,1] are obtained from matrix SH. The remaining values are both 1.0.
1.0: H[1,1] and H[2,2] are obtained from matrix SH. H[1,2] is 1.0. H[2,1] is -1.0.
P[1]
Contains SH[1,1].
P[2]
Contains SH[2,1].
P[3]
Contains SH[1,2].
P[4]
Contains SH[2,2].
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_drotmg
Generates a modified Givens rotation matrix.

void cblas_drotmg (
double *d1,
double *d2,
double *b1,
const double b2,
double *P
);

Parameters
d1
Scaling factor D1.
d2
Scaling factor D2.
b1
Scaling factor B1.
b2
Scaling factor B2.

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P
A 5-element vector:

P[0]
Flag value that defines the form of matrix H.
-2.0: matrix H contains the identity matrix.
-1.0: matrix H is identical to matrix SH (defined by the remaining values in the vector).
0.0: H[1,2] and H[2,1] are obtained from matrix SH. The remaining values are both 1.0.
1.0: H[1,1] and H[2,2] are obtained from matrix SH. H[1,2] is 1.0. H[2,1] is -1.0.
P[1]
Contains SH[1,1].
P[2]
Contains SH[2,1].
P[3]
Contains SH[1,2].
P[4]
Contains SH[2,2].
Discussion
The resulting matrix zeroes the second component of the vector (sqrt(D1)*B1, sqrt(SD2)*B2)T.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dsbmv
Scales a symmetric band matrix, then multiplies by a vector, then adds a vector (double precision).

void cblas_dsbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const int K,
const double alpha,
const double *A,
const int lda,
const double *X,
const int incX,
const double beta,
double *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.

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Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
K
Half-bandwidth of matrix A.
alpha
Scaling value to multiply matrix A by.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector Y is multiplied by.
Y
Vector Y. Replaced by results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and returns the results in vector Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dscal
Multiplies each element of a vector by a constant (double-precision).

void cblas_dscal (
const int N,
const double alpha,
double *X,
const int incX
);

Parameters
N
The number of elements in vector x.
alpha
The constant scaling factor to multiply by.

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X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dsdot
Computes the double-precision dot product of a pair of single-precision vectors.

double cblas_dsdot (
const int N,
const float *X,
const int incX,
const float *Y,
const int incY
);

Parameters
N
The number of elements in the vectors.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dspmv
Scales a packed symmetric matrix, then multiplies by a vector, then scales and adds another vector (double
precision).

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void cblas_dspmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const double *Ap,
const double *X,
const int incX,
const double beta,
double *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vectors x and y.
alpha
Scaling factor that matrix A is multiplied by.
Ap
Matrix A (in packed storage format).
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector y is multiplied by.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and stores the results in Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dspr
Rank one update: adds a packed symmetric matrix to the product of a scaling factor, a vector, and its transpose
(double precision).

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void cblas_dspr (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const double *X,
const int incX,
double *Ap
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Ap
Matrix A (in packed storage format).
Discussion
Calculates A + alpha*x*xT and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dspr2
Rank two update of a packed symmetric matrix using two vectors (single precision).

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void cblas_dspr2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const double *X,
const int incX,
const double *Y,
const int incY,
double *A
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A (in packed storage format).
Discussion
Calculates A + alpha*x*yT + alpha*y*xT.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dswap
Exchanges the elements of two vectors (double precision).

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void cblas_dswap (
const int N,
double *X,
const int incX,
double *Y,
const int incY
);

Parameters
N
Number of elements in vectors
X
Vector x. On return, contains elements copied from vector y.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y. On return, contains elements copied from vector x.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dsymm
Multiplies a matrix by a symmetric matrix (double-precision).

void cblas_dsymm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const int M,
const int N,
const double alpha,
const double *A,
const int lda,
const double *B,
const int ldb,
const double beta,
double *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.

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Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B or B * A (depending on the value of Side) and multiplies the resulting matrix
by alpha. It then multiplies matrix C by beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

where

A = AT

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_dsymv
Scales a symmetric matrix, multiplies by a vector, then scales and adds another vector (single precision).

void cblas_dsymv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const double *A,
const int lda,
const double *X,
const int incX,
const double beta,
double *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; length of vectors.
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector y.
Y
Vector y. Contains results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and stores the results in Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_dsyr
Rank one update: adds a symmetric matrix to the product of a scaling factor, a vector, and its transpose
(double precision).

void cblas_dsyr (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const double *X,
const int incX,
double *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Calculates A + alpha*x*xT and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dsyr2
Rank two update of a symmetric matrix using two vectors (single precision).

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void cblas_dsyr2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const double *X,
const int incX,
const double *Y,
const int incY,
double *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Calculates A + alpha*x*yT + alpha*y*xT.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dsyr2k
Performs a rank-2k update of a symmetric matrix (double precision).

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void cblas_dsyr2k (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const double alpha,
const double *A,
const int lda,
const double *B,
const int ldb,
const double beta,
double *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
N
Order of matrix C.
K
Specifies the number of columns in matrices A and B if trans='N'.
Specifies the number of rows if trans='C' or trans='T').
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
B
Matrix B.
ldb
Leading dimension of array containing matrix B.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Computes alpha*A*BT + alpha*B*AT +beta*C

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dsyrk
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix (double precision).

void cblas_dsyrk (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const double alpha,
const double *A,
const int lda,
const double beta,
double *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
N
Order of matrix C.
K
Number of columns in matrix A (or number of rows if matrix A is transposed).
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Calculates alpha*A*AT + beta*C; if transposed, calculates alpha*AT*A + beta*C.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dtbmv
Scales a triangular band matrix, then multiplies by a vector (double precision).

void cblas_dtbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const double *A,
const int lda,
double *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
K
Half-bandwidth of matrix A.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x and stores the results in x.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dtbsv
Solves a triangular banded system of equations.

void cblas_dtbsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const double *A,
const int lda,
double *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
K
Number of superdiagonals or subdiagonals of matrix A (depending on the value of Uplo).
A
Matrix A.
lda
The leading dimension of matrix A.
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dtpmv
Multiplies a triangular matrix by a vector, then adds a vector (double precision).

void cblas_dtpmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const double *Ap,
double *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A and the number of elements in vectors x and y.
Ap
Matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x, AT*x, or conjg(AT)*x and stores the results in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_dtpsv
Solves a packed triangular system of equations.

void cblas_dtpsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const double *Ap,
double *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
Ap
Matrix A (in packed storage format).
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dtrmm
Scales a triangular matrix and multiplies it by a matrix.

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void cblas_dtrmm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const double alpha,
const double *A,
const int lda,
double *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
Number of rows in matrix B.
N
Number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
B
Matrix B. Overwritten by results on return.
ldb
Leading dimension of matrix B.
Discussion
If Side is 'L', multiplies alpha*A*B or alpha*A'*B, depending on TransA.

If Side is 'R', multiplies alpha*B*A or alpha*B*A', depending on TransA.

In either case, the results are stored in matrix B.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_dtrmv
Multiplies a triangular matrix by a vector.

void cblas_dtrmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const double *A,
const int lda,
double *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
A
Triangular matrix A.
lda
Leading dimension of matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Multiplies A*X or A'*X, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_dtrsm
Solves a triangular system of equations with multiple values for the right side.

void cblas_dtrsm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const double alpha,
const double *A,
const int lda,
double *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrix and vector should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
The number of rows in matrix B.
N
The number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Triangular matrix A.
lda
The leading dimension of matrix B.
B
On entry, matrix B. Overwritten on return by matrix X.
ldb
The leading dimension of matrix B.
Discussion
If Side is 'L', solves A*X=alpha*B or A'*X=alpha*B, depending on TransA.

If Side is 'R', solves X*A=alpha*B or X*A'=alpha*B, depending on TransA.

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In either case, the results overwrite the values of matrix B in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dtrsv
Solves a triangular system of equations with a single value for the right side.

void cblas_dtrsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const double *A,
const int lda,
double *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
A
Triangular matrix A.
lda
The leading dimension of matrix B.
X
The vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves A*x=b or A'*x=b where x and b are elements in X and B.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_dzasum
Computes the sum of the absolute values of real and imaginary parts of elements in a vector (single-precision
complex).

double cblas_dzasum (
const int N,
const void *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
Source vector
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
The return value is a single floating point value that contains the sum of the absolute values of both the real
and imaginary parts of the vector.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_dznrm2
Computes the unitary norm of a vector (double-precision complex).

double cblas_dznrm2 (
const int N,
const void *X,
const int incX
);

Parameters
N
Length of vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_errprn
Prints an error message.

int cblas_errprn (
int ierr,
int info,
char *form,
...
);

Parameters
ierr
Error code number.
info
Exit status returned by the function call. Negative values generally indicate the index of the offending
parameter. Positive numbers generally indicate that an algorithm did not converge. Zero indicates
success.
form
A printf-style format string.
...
Arguments for the format string.
Return Value
Returns the minimum of ierr or info.

Discussion
This is commonly called by cblas_xerbla (page 126).

Availability
Available in iPhone OS 4.0 and later.

See Also
cblas_xerbla (page 126)
SetBLASParamErrorProc (page 161)

Declared In
cblas.h

cblas_icamax
Returns the index of the element with the largest absolute value in a vector (single-precision complex).

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int cblas_icamax (
const int N,
const void *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
The vector.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
Returns an index in the range 0..N-1 corresponding with the element with the largest absolute value.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_idamax
Returns the index of the element with the largest absolute value in a vector (double-precision).

int cblas_idamax (
const int N,
const double *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
The vector.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
Returns an index in the range 0..N-1 corresponding with the element with the largest absolute value.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_isamax
Returns the index of the element with the largest absolute value in a vector (single-precision).

int cblas_isamax (
const int N,
const float *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
The vector.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
Returns an index in the range 0..N-1 corresponding with the element with the largest absolute value.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_izamax
Returns the index of the element with the largest absolute value in a vector (double-precision complex).

int cblas_izamax (
const int N,
const void *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
The vector.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
Returns an index in the range 0..N-1 corresponding with the element with the largest absolute value.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_sasum
Computes the sum of the absolute values of elements in a vector (single-precision).

float cblas_sasum (
const int N,
const float *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
Source vector
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_saxpy
Computes a constant times a vector plus a vector (single-precision).

void cblas_saxpy (
const int N,
const float alpha,
const float *X,
const int incX,
float *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
alpha
Scaling factor for the values in X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.

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Discussion
On return, the contents of vector Y are replaced with the result. The value computed is (alpha * X[i])
+ Y[i].

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_scasum
Computes the sum of the absolute values of real and imaginary parts of elements in a vector (single-precision
complex).

float cblas_scasum (
const int N,
const void *X,
const int incX
);

Parameters
N
Number of elements in the vector.
X
Source vector
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Return Value
The return value is a single floating point value that contains the sum of the absolute values of both the real
and imaginary parts of the vector.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_scnrm2
Computes the unitary norm of a vector (single-precision complex).

float cblas_scnrm2 (
const int N,
const void *X,
const int incX
);

Parameters
N
Length of vector X.

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X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_scopy
Copies a vector to another vector (single-precision).

void cblas_scopy (
const int N,
const float *X,
const int incX,
float *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
X
Source vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Destination vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sdot
Computes the dot product of two vectors (single-precision).

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float cblas_sdot (
const int N,
const float *X,
const int incX,
const float *Y,
const int incY
);

Parameters
N
The number of elements in the vectors.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sdsdot
Computes the dot product of two single-precision vectors plus an initial single-precision value.

float cblas_sdsdot (
const int N,
const float alpha,
const float *X,
const int incX,
const float *Y,
const int incY
);

Parameters
N
The number of elements in the vectors.
alpha
The initial value to add to the dot product.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.

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incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sgbmv
Scales a general band matrix, then multiplies by a vector, then adds a vector (single precision).

void cblas_sgbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const int KL,
const int KU,
const float alpha,
const float *A,
const int lda,
const float *X,
const int incX,
const float beta,
float *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
M
Number of rows in matrix A.
N
Number of columns in matrix A.
KL
Number of subdiagonals in matrix A.
KU
Number of superdiagonals in matrix A.
alpha
Scaling factor to multiply matrix A by.
A
Matrix A.
lda
Leading dimension of array containing matrix A. (Must be at least KL+KU+1.)

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X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor to multiply vector Y by.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y or alpha*A'*x + beta*y depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sgemm
Multiplies two matrices (single-precision).

void cblas_sgemm (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_TRANSPOSE TransB,
const int M,
const int N,
const int K,
const float alpha,
const float *A,
const int lda,
const float *B,
const int ldb,
const float beta,
float *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
TransB
Specifies whether to transpose matrix B.
M
Number of rows in matrices A and C.

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N
Number of columns in matrices B and C.
K
Number of columns in matrix A; number of rows in matrix B.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B and multiplies the resulting matrix by alpha. It then multiplies matrix C by
beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

with optional use of transposed forms of A, B, or both.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sgemv
Multiplies a matrix by a vector (single precision).

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void cblas_sgemv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const float alpha,
const float *A,
const int lda,
const float *X,
const int incX,
const float beta,
float *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for the product of matrix A and vector X.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector Y.
Y
Vector Y
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
This function multiplies A * X (after transposing A, if needed) and multiplies the resulting matrix by alpha.
It then multiplies vector Y by beta. It stores the sum of these two products in vector Y.

Thus, it calculates either

Y←αAX +  Y

with optional use of the transposed form of A.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sger
Multiplies vector X by the transform of vector Y, then adds matrix A (single precison).

void cblas_sger (
const enum CBLAS_ORDER Order,
const int M,
const int N,
const float alpha,
const float *X,
const int incX,
const float *Y,
const int incY,
float *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Computes alpha*x*y' + A.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_snrm2
Computes the L2 norm (Euclidian length) of a vector (single precision).

float cblas_snrm2 (
const int N,
const float *X,
const int incX
);

Parameters
N
Length of vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_srot
Applies a Givens rotation matrix to a pair of vectors.

void cblas_srot (
const int N,
float *X,
const int incX,
float *Y,
const int incY,
const float c,
const float s
);

Parameters
N
The number of elements in vectors X and Y.
X
Vector X. Modified on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y. Modified on return.

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incY
Stride within Y. For example, if incY is 7, every 7th element is used.
c
The value cos( ) in the Givens rotation matrix.
s
The value sin( ) in the Givens rotation matrix.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_srotg
Constructs a Givens rotation matrix.

void cblas_srotg (
float *a,
float *b,
float *c,
float *s
);

Parameters
a
Single-precision value a. Overwritten on return with result r.
b
Single-precision value b. Overwritten on return with result z (zero).
c
Unused on entry. Overwritten on return with the value cos( ).
s
Unused on entry. Overwritten on return with the value sin( ).
Discussion
Given a vertical matrix containing a and b, computes the values of cos   and sin   that zero the lower
value (b). Returns the value of sin   in s, the value of cos   in c, and the upper value (r) in a.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_srotm
Applies a modified Givens transformation (single precision).

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void cblas_srotm (
const int N,
float *X,
const int incX,
float *Y,
const int incY,
const float *P
);

Parameters
N
Number of elements in vectors.
X
Vector X. Modified on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y. Modified on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
P
A 5-element vector:

P[0]
Flag value that defines the form of matrix H.
-2.0: matrix H contains the identity matrix.
-1.0: matrix H is identical to matrix SH (defined by the remaining values in the vector).
0.0: H[1,2] and H[2,1] are obtained from matrix SH. The remaining values are both 1.0.
1.0: H[1,1] and H[2,2] are obtained from matrix SH. H[1,2] is 1.0. H[2,1] is -1.0.
P[1]
Contains SH[1,1].
P[2]
Contains SH[2,1].
P[3]
Contains SH[1,2].
P[4]
Contains SH[2,2].
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_srotmg
Generates a modified Givens rotation matrix.

void cblas_srotmg (
float *d1,
float *d2,
float *b1,
const float b2,
float *P
);

Parameters
d1
Scaling factor D1.
d2
Scaling factor D2.
b1
Scaling factor B1.
b2
Scaling factor B2.
P
A 5-element vector:

P[0]
Flag value that defines the form of matrix H.
-2.0: matrix H contains the identity matrix.
-1.0: matrix H is identical to matrix SH (defined by the remaining values in the vector).
0.0: H[1,2] and H[2,1] are obtained from matrix SH. The remaining values are both 1.0.
1.0: H[1,1] and H[2,2] are obtained from matrix SH. H[1,2] is 1.0. H[2,1] is -1.0.
P[1]
Contains SH[1,1].
P[2]
Contains SH[2,1].
P[3]
Contains SH[1,2].
P[4]
Contains SH[2,2].
Discussion
The resulting matrix zeroes the second component of the vector (sqrt(D1)*B1, sqrt(SD2)*B2)T.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_ssbmv
Scales a symmetric band matrix, then multiplies by a vector, then adds a vector (single-precision).

void cblas_ssbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const int K,
const float alpha,
const float *A,
const int lda,
const float *X,
const int incX,
const float beta,
float *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
K
Half-bandwidth of matrix A.
alpha
Scaling value to multiply matrix A by.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector Y is multiplied by.
Y
Vector Y. Replaced by results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and returns the results in vector Y.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_sscal
Multiplies each element of a vector by a constant (single-precision).

void cblas_sscal (
const int N,
const float alpha,
float *X,
const int incX
);

Parameters
N
Number of elements to scale.
alpha
The constant to multiply by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is multiplied by alpha.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sspmv
Scales a packed symmetric matrix, then multiplies by a vector, then scales and adds another vector (single
precision).

void cblas_sspmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const float *Ap,
const float *X,
const int incX,
const float beta,
float *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.

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Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vectors x and y.
alpha
Scaling factor that matrix A is multiplied by.
Ap
Matrix A (in packed storage format).
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector y is multiplied by.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and stores the results in Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sspr
Rank one update: adds a packed symmetric matrix to the product of a scaling factor, a vector, and its transpose
(single precision).

void cblas_sspr (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const float *X,
const int incX,
float *Ap
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.

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alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Ap
Matrix A (in packed storage format).
Discussion
Calculates A + alpha*x*xT and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sspr2
Rank two update of a packed symmetric matrix using two vectors (single precision).

void cblas_sspr2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const float *X,
const int incX,
const float *Y,
const int incY,
float *A
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y.

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incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A (in packed storage format).
Discussion
Calculates A + alpha*x*yT + alpha*y*xT.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_sswap
Exchanges the elements of two vectors (single precision).

void cblas_sswap (
const int N,
float *X,
const int incX,
float *Y,
const int incY
);

Parameters
N
Number of elements in vectors
X
Vector x. On return, contains elements copied from vector y.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y. On return, contains elements copied from vector x.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ssymm
Multiplies a matrix by a symmetric matrix (single-precision).

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void cblas_ssymm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const int M,
const int N,
const float alpha,
const float *A,
const int lda,
const float *B,
const int ldb,
const float beta,
float *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B or B * A (depending on the value of Side) and multiplies the resulting matrix
by alpha. It then multiplies matrix C by beta. It stores the sum of these two products in matrix C.

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Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

where

A = AT

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ssymv
Scales a symmetric matrix, multiplies by a vector, then scales and adds another vector (single precision).

void cblas_ssymv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const float *A,
const int lda,
const float *X,
const int incX,
const float beta,
float *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; length of vectors.
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
X
Vector x.

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incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector y.
Y
Vector y. Contains results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and stores the results in Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ssyr
Rank one update: adds a symmetric matrix to the product of a scaling factor, a vector, and its transpose
(single precision).

void cblas_ssyr (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const float *X,
const int incX,
float *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
A
Matrix A.

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lda
Leading dimension of array containing matrix A.
Discussion
Calculates A + alpha*x*xT and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ssyr2
Rank two update of a symmetric matrix using two vectors (single precision).

void cblas_ssyr2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const float alpha,
const float *X,
const int incX,
const float *Y,
const int incY,
float *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A; number of elements in vector x.
alpha
Scaling factor to multiply x by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.

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Discussion
Calculates A + alpha*x*yT + alpha*y*xT.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ssyr2k
Performs a rank-2k update of a symmetric matrix (single precision).

void cblas_ssyr2k (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const float alpha,
const float *A,
const int lda,
const float *B,
const int ldb,
const float beta,
float *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
N
Order of matrix C.
K
Specifies the number of columns in matrices A and B if trans='N'.
Specifies the number of rows if trans='C' or trans='T').
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
B
Matrix B.

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ldb
Leading dimension of array containing matrix B.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Computes alpha*A*BT + alpha*B*AT +beta*C

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ssyrk
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix (single precision).

void cblas_ssyrk (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const float alpha,
const float *A,
const int lda,
const float beta,
float *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
N
Order of matrix C.
K
Number of columns in matrix A (or number of rows if matrix A is transposed).
alpha
Scaling factor for matrix A.

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A
Matrix A.
lda
Leading dimension of array containing matrix A.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Calculates alpha*A*AT + beta*C; if transposed, calculates alpha*AT*A + beta*C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_stbmv
Scales a triangular band matrix, then multiplies by a vector (single precision).

void cblas_stbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const float *A,
const int lda,
float *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.

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K
Half-bandwidth of matrix A.
A
Triangular matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x and stores the results in x.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_stbsv
Solves a triangular banded system of equations.

void cblas_stbsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const float *A,
const int lda,
float *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.

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K
Number of superdiagonals or subdiagonals of matrix A (depending on the value of Uplo).
A
Triangular matrix A.
lda
The leading dimension of matrix A.
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_stpmv
Multiplies a triangular matrix by a vector, then adds a vector (single precision).

void cblas_stpmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const float *Ap,
float *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A and the number of elements in vectors x and y.
Ap
Triangular matrix A.

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X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x, AT*x, or conjg(AT)*x and stores the results in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_stpsv
Solves a packed triangular system of equations.

void cblas_stpsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const float *Ap,
float *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
Ap
Triangular matrix A (in packed storage format).
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_strmm
Scales a triangular matrix and multiplies it by a matrix.

void cblas_strmm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const float alpha,
const float *A,
const int lda,
float *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
Number of rows in matrix B.
N
Number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Triangular matrix A.
lda
Leading dimension of matrix A.
B
Matrix B. Overwritten by results on return.

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ldb
Leading dimension of matrix B.
Discussion
If Side is 'L', multiplies alpha*A*B or alpha*A'*B, depending on TransA.

If Side is 'R', multiplies alpha*B*A or alpha*B*A', depending on TransA.

In either case, the results are stored in matrix B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_strmv
Multiplies a triangular matrix by a vector.

void cblas_strmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const float *A,
const int lda,
float *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
A
Triangular matrix A.
lda
Leading dimension of matrix A.
X
Vector X.

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incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Multiplies A*X or A'*X, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_strsm
Solves a triangular system of equations with multiple values for the right side.

void cblas_strsm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const float alpha,
const float *A,
const int lda,
float *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrix and vector should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
The number of rows in matrix B.
N
The number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Triangular matrix A.

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lda
The leading dimension of matrix B.
B
On entry, matrix B. Overwritten on return by matrix X.
ldb
The leading dimension of matrix B.
Discussion
If Side is 'L', solves A*X=alpha*B or A'*X=alpha*B, depending on TransA.

If Side is 'R', solves X*A=alpha*B or X*A'=alpha*B, depending on TransA.

In either case, the results overwrite the values of matrix B in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_strsv
Solves a triangular system of equations with a single value for the right side.

void cblas_strsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const float *A,
const int lda,
float *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
A
Triangular matrix A.

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lda
The leading dimension of matrix B.
X
The vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves A*x=b or A'*x=b where x and b are elements in X and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_xerbla
The default error handler for BLAS routines.

void cblas_xerbla (
int p,
char *rout,
char *form,
...
);

Parameters
p
The position of the invalid parameter
rout
The name of the routine that generated this error.
form
A format string describing the error.
...
Additional parameters for the format string.
Discussion
This is the default error handler for BLAS functions. You can replace it with another function by calling
SetBLASParamErrorProc (page 161).

Availability
Available in iPhone OS 4.0 and later.

See Also
cblas_errprn (page 91)
SetBLASParamErrorProc (page 161)

Declared In
cblas.h

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cblas_zaxpy
Computes a constant times a vector plus a vector (double-precision complex).

void cblas_zaxpy (
const int N,
const void *alpha,
const void *X,
const int incX,
void *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.
alpha
Scaling factor for the values in X.
X
Input vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Input vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
On return, the contents of vector Y are replaced with the result. The value computed is (alpha * X[i])
+ Y[i].

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zcopy
Copies a vector to another vector (double-precision complex).

void cblas_zcopy (
const int N,
const void *X,
const int incX,
void *Y,
const int incY
);

Parameters
N
Number of elements in the vectors.

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X
Source vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Destination vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zdotc_sub
Calculates the dot product of the complex conjugate of a double-precision complex vector with a second
double-precision complex vector.

void cblas_zdotc_sub (
const int N,
const void *X,
const int incX,
const void *Y,
const int incY,
void *dotc
);

Parameters
N
Number of elements in vectors X and Y.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
dotc
The result vector.
Discussion
Computes conjg(X) * Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_zdotu_sub
Computes the dot product of two double-precision complex vectors.

void cblas_zdotu_sub (
const int N,
const void *X,
const int incX,
const void *Y,
const int incY,
void *dotu
);

Parameters
N
The length of vectors X and Y.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
dotu
The result vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zdrot
Applies a Givens rotation matrix to a pair of complex vectors.

void cblas_zdrot (
const int N,
void *X,
const int incX,
void *Y,
const int incY,
const double c,
const double s
);

Parameters
N
The number of elements in vectors X and Y.
X
Vector X. Modified on return.

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incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y. Modified on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
c
The value cos( ) in the Givens rotation matrix.
s
The value sin( ) in the Givens rotation matrix.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zdscal
Multiplies each element of a vector by a constant (double-precision complex).

void cblas_zdscal (
const int N,
const double alpha,
void *X,
const int incX
);

Parameters
N
The number of elements in the vector.
alpha
The constant scaling factor.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zgbmv
Scales a general band matrix, then multiplies by a vector, then adds a vector (double-precision complex).

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void cblas_zgbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const int KL,
const int KU,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
M
Number of rows in matrix A.
N
Number of columns in matrix A.
KL
Number of subdiagonals in matrix A.
KU
Number of superdiagonals in matrix A.
alpha
Scaling factor to multiply matrix A by.
A
Matrix A.
lda
Leading dimension of array containing matrix A. (Must be at least KL+KU+1.)
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor to multiply vector Y by.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.

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Discussion
Computes alpha*A*x + beta*y, alpha*A'*x + beta*y, or alpha*conjg(A')*x + beta*y depending
on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zgemm
Multiplies two matrices (double-precision complex).

void cblas_zgemm (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_TRANSPOSE TransB,
const int M,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
TransB
Specifies whether to transpose matrix B.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
K
Number of columns in matrix A; number of rows in matrix B.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.

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lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B and multiplies the resulting matrix by alpha. It then multiplies matrix C by
beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

with optional use of transposed forms of A, B, or both.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zgemv
Multiplies a matrix by a vector (double-precision complex).

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void cblas_zgemv (
const enum CBLAS_ORDER Order,
const enum CBLAS_TRANSPOSE TransA,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
TransA
Specifies whether to transpose matrix A.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for the product of matrix A and vector X.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector Y.
Y
Vector Y
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
This function multiplies A * X (after transposing A, if needed) and multiplies the resulting matrix by alpha.
It then multiplies vector Y by beta. It stores the sum of these two products in vector Y.

Thus, it calculates either

Y←αAX +  Y

with optional use of the transposed form of A.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zgerc
Multiplies vector X by the conjugate transform of vector Y, then adds matrix A (double-precision complex).

void cblas_zgerc (
const enum CBLAS_ORDER Order,
const int M,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Computes alpha*x*conjg(y') + A.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_zgeru
Multiplies vector X by the transform of vector Y, then adds matrix A (double-precision complex).

void cblas_zgeru (
const enum CBLAS_ORDER Order,
const int M,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
M
Number of rows in matrix A.
N
Number of columns in matrix A.
alpha
Scaling factor for vector X.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
Discussion
Computes alpha*x*y' + A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_zhbmv
Scales a Hermitian band matrix, then multiplies by a vector, then adds a vector (double-precision complex).

void cblas_zhbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
K
Half-bandwidth of matrix A.
alpha
Scaling value to multiply matrix A by.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector Y is multiplied by.
Y
Vector Y. Replaced by results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and returns the results in vector Y.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_zhemm
Multiplies two Hermitian matrices (double-precision complex).

void cblas_zhemm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
M
The number of rows in matrices A and C.
N
The number of columns in matrices B and C.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.

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C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.
Discussion
This function multiplies A * B or B * A (depending on the value of Side) and multiplies the resulting matrix
by alpha. It then multiplies matrix C by beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

where

A = AH

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zhemv
Scales and multiplies a Hermitian matrix by a vector, then adds a second (scaled) vector.

void cblas_zhemv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.

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alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor for vector X.
Y
Vector Y. Overwritten by results on return.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Calculates Y←αAX +  Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zher
Adds the product of a scaling factor, vector X, and the conjugate transpose of X to matrix A.

void cblas_zher (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const void *X,
const int incX,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
alpha
The scaling factor for vector X.

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X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
A
Matrix A.
lda
Leading dimension of matrix A.
Discussion
Computes A←αX*conjg(X') +  A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zher2
Hermitian rank 2 update: adds the product of a scaling factor, vector X, and the conjugate transpose of vector
Y to the product of the conjugate of the scaling factor, vector Y, and the conjugate transpose of vector X,
and adds the result to matrix A.

void cblas_zher2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *A,
const int lda
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
The order of matrix A.
alpha
The scaling factor α.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.

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Y
Vector Y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
A
Matrix A.
lda
The leading dimension of matrix A.
Discussion
Computes A←αX*conjg(Y') + conjg(α)*Y*conjg(X') + A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zher2k
Performs a rank-2k update of a complex Hermitian matrix (double-precision complex).

void cblas_zher2k (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const double beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
N
Order of matrix C.
K
Specifies the number of columns in matrices A and B if trans='N'.
Specifies the number of rows if trans='C' or trans='T').

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alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
B
Matrix B.
ldb
Leading dimension of array containing matrix B.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Computes alpha*A*BH + alpha*B*AH +beta*C

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zherk
Rank-k update—multiplies a Hermitian matrix by its transpose and adds a second matrix (single precision).

void cblas_zherk (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const double alpha,
const void *A,
const int lda,
const double beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.

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Trans
Specifies whether to use matrix A ('N' or 'n') or the conjugate transpose of A ('C' or 'c').
N
Order of matrix C.
K
Number of columns in matrix A (or number of rows if matrix A is transposed).
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Calculates alpha*A*AH + beta*C; if transposed, calculates alpha*AH*A + beta*C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zhpmv
Scales a packed hermitian matrix, multiplies it by a vector, and adds a scaled vector.

void cblas_zhpmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *Ap,
const void *X,
const int incX,
const void *beta,
void *Y,
const int incY
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.

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N
Order of matrix A and the number of elements in vectors x and y.
alpha
Scaling factor that matrix A is multiplied by.
Ap
Matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
beta
Scaling factor that vector y is multiplied by.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Discussion
Computes alpha*A*x + beta*y and stores the results in Y.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zhpr
Scales and multiplies a vector times its conjugate transpose, then adds a matrix.

void cblas_zhpr (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const double alpha,
const void *X,
const int incX,
void *A
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vector x.
alpha
Scaling factor that vector x is multiplied by.

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X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
A
Matrix A. Overwritten by results on return.
Discussion
Calculates alpha*x*conjg(x') + A and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zhpr2
Multiplies a vector times the conjugate transpose of a second vector and vice-versa, sums the results, and
adds a matrix.

void cblas_zhpr2 (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const int N,
const void *alpha,
const void *X,
const int incX,
const void *Y,
const int incY,
void *Ap
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
N
Order of matrix A and the number of elements in vectors x and y.
alpha
Scaling factor that vector x is multiplied by.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.

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Ap
Matrix A in packed storage format. Overwritten by the results on return.
Discussion
Calcuates alpha*x*conjg(y') + conjg(alpha)*y*conjg(x') + A, and stores the result in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zrotg
Constructs a complex Givens rotation.

void cblas_zrotg (
void *a,
void *b,
void *c,
void *s
);

Parameters
a
Complex value a. Overwritten on return with result r.
b
Complex value a. Overwritten on return with result z (zero).
c
Real value c. Unused on entry. Overwritten on return with the value cos( ).
s
Complex value s. Unused on entry. Overwritten on return with the value sin( ).
Discussion
Given a vertical matrix containing a and b, computes the values of cos   and sin   that zero the lower
value (b). Returns the value of sin   in s, the value of cos   in c, and the upper value (r) in a.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zscal
Multiplies each element of a vector by a constant (double-precision complex).

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void cblas_zscal (
const int N,
const void *alpha,
void *X,
const int incX
);

Parameters
N
The number of elements in the vector.
alpha
The constant scaling factor.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zswap
Exchanges the elements of two vectors (double-precision complex).

void cblas_zswap (
const int N,
void *X,
const int incX,
void *Y,
const int incY
);

Parameters
N
Number of elements in vectors
X
Vector x. On return, contains elements copied from vector y.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Y
Vector y. On return, contains elements copied from vector x.
incY
Stride within Y. For example, if incY is 7, every 7th element is used.
Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_zsymm
Multiplies a matrix by a symmetric matrix (double-precision complex).

void cblas_zsymm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
M
Number of rows in matrices A and C.
N
Number of columns in matrices B and C.
alpha
Scaling factor for the product of matrices A and B.
A
Matrix A.
lda
The size of the first dimention of matrix A; if you are passing a matrix A[m][n], the value should be
m.
B
Matrix B.
ldb
The size of the first dimention of matrix B; if you are passing a matrix B[m][n], the value should be
m.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
The size of the first dimention of matrix C; if you are passing a matrix C[m][n], the value should be
m.

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Discussion
This function multiplies A * B or B * A (depending on the value of Side) and multiplies the resulting matrix
by alpha. It then multiplies matrix C by beta. It stores the sum of these two products in matrix C.

Thus, it calculates either

C←αAB +  C

or

C←αBA +  C

where

A = AT

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zsyr2k
Performs a rank-2k update of a symmetric matrix (double-precision complex).

void cblas_zsyr2k (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *B,
const int ldb,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
N
Order of matrix C.

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K
Specifies the number of columns in matrices A and B if trans='N'.
Specifies the number of rows if trans='C' or trans='T').
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
B
Matrix B.
ldb
Leading dimension of array containing matrix B.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Computes alpha*A*BT + alpha*B*AT +beta*C

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_zsyrk
Rank-k update—multiplies a symmetric matrix by its transpose and adds a second matrix (double-precision
complex).

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void cblas_zsyrk (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans,
const int N,
const int K,
const void *alpha,
const void *A,
const int lda,
const void *beta,
void *C,
const int ldc
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
Trans
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T' or 't').
N
Order of matrix C.
K
Number of columns in matrix A (or number of rows if matrix A is transposed).
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of array containing matrix A.
beta
Scaling factor for matrix C.
C
Matrix C.
ldc
Leading dimension of array containing matrix C.
Discussion
Calculates alpha*A*AT + beta*C; if transposed, calculates alpha*AT*A + beta*C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ztbmv
Scales a triangular band matrix, then multiplies by a vector (double-precision complex).

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void cblas_ztbmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
K
Half-bandwidth of matrix A.
A
Matrix A.
lda
The leading dimension of array containing matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x and stores the results in x.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ztbsv
Solves a triangular banded system of equations.

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void cblas_ztbsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const int K,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
K
Number of superdiagonals or subdiagonals of matrix A (depending on the value of Uplo).
A
Matrix A.
lda
The leading dimension of matrix A.
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ztpmv
Multiplies a triangular matrix by a vector, then adds a vector (double-precision compex).

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void cblas_ztpmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *Ap,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n'), the transpose of A ('T' or 't'), or the conjugate of
A ('C' or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A and the number of elements in vectors x and y.
Ap
Matrix A.
X
Vector x.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Computes A*x, AT*x, or conjg(AT)*x and stores the results in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ztpsv
Solves a packed triangular system of equations.

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void cblas_ztpsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *Ap,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
Ap
Matrix A (in packed storage format).
X
Contains vector B on entry. Overwritten with vector X on return.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves the system of equations A*X=B or A'*X=B, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ztrmm
Scales a triangular matrix and multiplies it by a matrix.

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void cblas_ztrmm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
void *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrices should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
Number of rows in matrix B.
N
Number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
B
Matrix B. Overwritten by results on return.
ldb
Leading dimension of matrix B.
Discussion
If Side is 'L', multiplies alpha*A*B or alpha*A'*B, depending on TransA.

If Side is 'R', multiplies alpha*B*A or alpha*B*A', depending on TransA.

In either case, the results are stored in matrix B.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

cblas_ztrmv
Multiplies a triangular matrix by a vector.

void cblas_ztrmv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
Order of matrix A.
A
Matrix A.
lda
Leading dimension of matrix A.
X
Vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Multiplies A*X or A'*X, depending on the value of TransA.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

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cblas_ztrsm
Solves a triangular system of equations with multiple values for the right side.

void cblas_ztrsm (
const enum CBLAS_ORDER Order,
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int M,
const int N,
const void *alpha,
const void *A,
const int lda,
void *B,
const int ldb
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Side
Determines the order in which the matrix and vector should be multiplied.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
M
The number of rows in matrix B.
N
The number of columns in matrix B.
alpha
Scaling factor for matrix A.
A
Triangular matrix A.
lda
The leading dimension of matrix B.
B
On entry, matrix B. Overwritten on return by matrix X.
ldb
The leading dimension of matrix B.
Discussion
If Side is 'L', solves A*X=alpha*B or A'*X=alpha*B, depending on TransA.

If Side is 'R', solves X*A=alpha*B or X*A'=alpha*B, depending on TransA.

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In either case, the results overwrite the values of matrix B in X.

Availability
Available in iPhone OS 4.0 and later.

Declared In
cblas.h

cblas_ztrsv
Solves a triangular system of equations with a single value for the right side.

void cblas_ztrsv (
const enum CBLAS_ORDER Order,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const int N,
const void *A,
const int lda,
void *X,
const int incX
);

Parameters
Order
Specifies row-major (C) or column-major (Fortran) data ordering.
Uplo
Specifies whether to use the upper or lower triangle from the matrix. Valid values are 'U' or 'L'.
TransA
Specifies whether to use matrix A ('N' or 'n') or the transpose of A ('T', 't', 'C', or 'c').
Diag
Specifies whether the matrix is unit triangular. Possible values are 'U' (unit triangular) or 'N' (not
unit triangular).
N
The order of matrix A.
A
Triangular matrix A.
lda
The leading dimension of matrix B.
X
The vector X.
incX
Stride within X. For example, if incX is 7, every 7th element is used.
Discussion
Solves A*x=b or A'*x=b where x and b are elements in X and B.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
cblas.h

SetBLASParamErrorProc
Sets an error handler function.

void SetBLASParamErrorProc (
BLASParamErrorProc ErrorProc
);

Parameters
ErrorProc
The handler function BLAS should call when an error occurs (because of an invalid input, for example).
Availability
Available in iPhone OS 4.0 and later.

See Also
cblas_errprn (page 91)
cblas_xerbla (page 126)

Declared In
cblas.h

Constants

Note: The types given here are valid for C or C++ and for either PowerPC or Intel processors. The typedefs
shown are for C++ and PowerPC processors; for other, conditionally compiled typedefs, see the header files.

CBLAS_ORDER
Indicates whether a matrix is in row-major or column-major order.

enum CBLAS_ORDER {
CblasRowMajor=101,
CblasColMajor=102
};
typedef enum CBLAS_ORDER CBLAS_ORDER;

Constants
CblasRowMajor
Row-major order.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.

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CblasColMajor
Column-major order.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.

CBLAS_TRANSPOSE
Indiates transpose operation to perform on a matrix.

enum CBLAS_TRANSPOSE {
CblasNoTrans=111,
CblasTrans=112,
CblasConjTrans=113,
AtlasConj=114
};
typedef enum CBLAS_TRANSPOSE CBLAS_TRANSPOSE;

Constants
CblasNoTrans
No transposition.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.
CblasTrans
For matrix X, use X(T).
Available in iPhone OS 4.0 and later.
Declared in cblas.h.
CblasConjTrans
For matrix X, use X(H) (conjugate or Hermitian transposition).
Available in iPhone OS 4.0 and later.
Declared in cblas.h.
AtlasConj
Available in iPhone OS 4.0 and later.
Declared in cblas.h.

CBLAS_UPLO
Indicates which part of a symmetric matrix to use.

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enum CBLAS_UPLO {
CblasUpper=121,
CblasLower=122
};
typedef enum CBLAS_UPLO CBLAS_UPLO;

Constants
CblasUpper
Use the upper triangle of the matrix.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.
CblasLower
Use the lower triangle of the matrix.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.

CBLAS_DIAG
Indicates whether a triangular matrix is unit-diagonal (diagonal elements are all equal to 1).

enum CBLAS_DIAG {
CblasNonUnit=131,
CblasUnit=132
};
typedef enum CBLAS_DIAG CBLAS_DIAG;

Constants
CblasNonUnit
The triangular matrix is not unit-diagonal.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.
CblasUnit
The triangular matrix is unit-diagonal.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.

CBLAS_SIDE
Indicates the order of a matrix multiplication.

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enum CBLAS_SIDE {
CblasLeft=141,
CblasRight=142
};
typedef enum CBLAS_SIDE CBLAS_SIDE;

Constants
CblasLeft
Multiply A*B.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.
CblasRight
Multiply B*A.
Available in iPhone OS 4.0 and later.
Declared in cblas.h.

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 CHAPTER 2

vDSP Reference

Framework: Accelerate/vecLib
Declared in vDSP.h

Overview

This document describes the vDSP portion of the Accelerate framework.

Functions by Task

Single-Vector Absolute Value

The functions in this group compute the absolute value of each element in a vector.

vDSP_vabs (page 334)

Vector absolute values; single precision.
vDSP_vabsD (page 334)
Vector absolute values; double precision.
vDSP_vabsi (page 335)
Integer vector absolute values.
vDSP_zvabs (page 524)
Complex vector absolute values; single precision.
vDSP_zvabsD (page 525)
Complex vector absolute values; double precision.
vDSP_vnabs (page 426)
Vector negative absolute values; single precision.
vDSP_vnabsD (page 427)
Vector negative absolute values; double precision.

Single-Vector Negation
The functions in this group negates each element in a vector.

vDSP_vneg (page 428)

Vector negative values; single precision.

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vDSP Reference

vDSP_vnegD (page 429)

Vector negative values; double precision.
vDSP_zvneg (page 539)
Complex vector negate; single precision.
vDSP_zvnegD (page 540)
Complex vector negate; double precision.

Single-Vector Fill or Clear

The functions in this group fills each element in a vector with a specific value or clears each element.

vDSP_vfill (page 362)

Vector fill; single precision.
vDSP_vfillD (page 363)
Vector fill; double precision.
vDSP_vfilli (page 364)
Integer vector fill.
vDSP_zvfill (page 533)
Complex vector fill; single precision.
vDSP_zvfillD (page 533)
Complex vector fill; double precision.
vDSP_vclr (page 349)
Vector clear; single precision.
vDSP_vclrD (page 349)
Vector clear; double precision.

Single-Vector Generation
The functions in this group build vectors with specific generator functions.

vDSP_vramp (page 436)

Build ramped vector; single precision.
vDSP_vrampD (page 437)
Build ramped vector; double precision.
vDSP_vrampmul (page 437)
Builds a ramped vector and multiplies by a source vector.
vDSP_vrampmul_s1_15 (page 447)
Vector fixed-point 1.15 format version of vDSP_vrampmul (page 437).
vDSP_vrampmul_s8_24 (page 448)
Vector fixed-point 8.24 format version of vDSP_vrampmul (page 437).
vDSP_vrampmul2 (page 438)
Stereo version of vDSP_vrampmul (page 437).
vDSP_vrampmul2_s1_15 (page 439)
Vector fixed-point 1.15 format version of vDSP_vrampmul2 (page 438).

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CHAPTER 2
vDSP Reference

vDSP_vrampmul2_s8_24 (page 441)

Vector fixed-point 8.24 format version of vDSP_vrampmul2 (page 438).
vDSP_vrampmuladd (page 442)
Builds a ramped vector, multiplies it by a source vector, and adds the result to the output vector.
vDSP_vrampmuladd_s1_15 (page 446)
Vector fixed-point 1.15 format version of vDSP_vrampmuladd (page 442).
vDSP_vrampmuladd_s8_24 (page 447)
Vector fixed-point 8.24 format version of vDSP_vrampmuladd (page 442).
vDSP_vrampmuladd2 (page 442)
Stereo version of vDSP_vrampmuladd (page 442).
vDSP_vrampmuladd2_s1_15 (page 443)
Vector fixed-point 1.15 format version of vDSP_vrampmuladd2 (page 442).
vDSP_vrampmuladd2_s8_24 (page 445)
Vector fixed-point 8.24 format version of vDSP_vrampmuladd2 (page 442).
vDSP_vgen (page 392)
Vector tapered ramp; single precision.
vDSP_vgenD (page 393)
Vector tapered ramp; double precision.
vDSP_vgenp (page 394)
Vector generate by extrapolation and interpolation; single precision.
vDSP_vgenpD (page 395)
Vector generate by extrapolation and interpolation; double precision.
vDSP_vtabi (page 483)
Vector interpolation, table lookup; single precision.
vDSP_vtabiD (page 484)
Vector interpolation, table lookup; double precision.

Single-Vector Squaring
The functions in this group computes the square of each element in a vector or the square of the magnitude
of each element in a complex vector.

vDSP_vsq (page 477)

Computes the squared values of vector input and leaves the result in vector result; single precision.
vDSP_vsqD (page 477)
Computes the squared values of vector signal1 and leaves the result in vector result; double
precision.
vDSP_vssq (page 478)
Computes the signed squares of vector signal1 and leaves the result in vector result; single
precision.
vDSP_vssqD (page 478)
Computes the signed squares of vector signal1 and leaves the result in vector result; double
precision.
vDSP_zvmags (page 534)
Complex vector magnitudes squared; single precision.

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vDSP_zvmagsD (page 535)

Complex vector magnitudes squared; double precision.
vDSP_zvmgsa (page 535)
Complex vector magnitudes square and add; single precision.
vDSP_zvmgsaD (page 536)
Complex vector magnitudes square and add; double precision.

Single-Vector Polar-Rectangular Conversion

The functions in this group convert each element in a vector between rectangular and polar coordinates.

vDSP_polar (page 319)

Rectangular to polar conversion; single precision.
vDSP_polarD (page 320)
Rectangular to polar conversion; double precision.
vDSP_rect (page 321)
Polar to rectangular conversion; single precision.
vDSP_rectD (page 321)
Polar to rectangular conversion; double precision.

Single-Vector Conversion to Decibel Equivalents

The functions in this group convert power or amplitude values to decibel values.

vDSP_vdbcon (page 351)

Vector convert power or amplitude to decibels; single precision.
vDSP_vdbconD (page 352)
Vector convert power or amplitude to decibels; double precision.

Single-Vector Fractional Part Extraction

The functions in this group remove the whole-number part of each element in a vector, leaving the fractional
part.

vDSP_vfrac (page 387)

Vector truncate to fraction; single precision.
vDSP_vfracD (page 388)
Vector truncate to fraction; double precision.

Single-Vector Complex Conjugation

The functions in this group find the complex conjugate of values in a vector.

vDSP_zvconj (page 529)

Complex vector conjugate; single precision.

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vDSP_zvconjD (page 530)

Complex vector conjugate; double precision.

Single-Vector Phase Computation

The functions in this group compute the phase values of each element in a complex vector.

vDSP_zvphas (page 541)

Complex vector phase; single precision.
vDSP_zvphasD (page 542)
Complex vector phase; double precision.

Single-Vector Clipping, Limit, and Threshold Operations

The functions in this group restrict the values in a vector so that they fall within a given range or invert values
outside a given range.

vDSP_vclip (page 344)

Vector clip; single precision.
vDSP_vclipD (page 348)
Vector clip; double precision.
vDSP_vclipc (page 345)
Vector clip and count; single precision.
vDSP_vclipcD (page 347)
Vector clip and count; double precision.
vDSP_viclip (page 397)
Vector inverted clip; single precision.
vDSP_viclipD (page 398)
Vector inverted clip; double precision.
vDSP_vlim (page 402)
Vector test limit; single precision.
vDSP_vlimD (page 403)
Vector test limit; double precision.
vDSP_vthr (page 485)
Vector threshold; single precision.
vDSP_vthrD (page 486)
Vector threshold; double precision.
vDSP_vthres (page 487)
Vector threshold with zero fill; single precision.
vDSP_vthresD (page 488)
Vector threshold with zero fill; double precision.
vDSP_vthrsc (page 488)
Vector threshold with signed constant; single precision.
vDSP_vthrscD (page 489)
Vector threshold with signed constant; double precision.

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Single-Vector Compression
The functions in this group compress the values of a vector.

vDSP_vcmprs (page 350)

Vector compress; single precision.
vDSP_vcmprsD (page 350)
Vector compress; double precision.

Single-Vector Gathering
The functions in this group use either indices or pointers stored within one source vector to generate a new
vector containing the chosen elements from either a second source vector or from memory.

vDSP_vgathr (page 389)

Vector gather; single precision.
vDSP_vgathrD (page 391)
Vector gather; double precision.
vDSP_vgathra (page 390)
Vector gather, absolute pointers; single precision.
vDSP_vgathraD (page 391)
Vector gather, absolute pointers; double precision.
vDSP_vindex (page 399)
Vector index; single precision.
vDSP_vindexD (page 400)
Vector index; double precision.

Single-Vector Reversing
The functions in this group reverse the order of the elements in a vector.

vDSP_vrvrs (page 451)

Vector reverse order, in place; single precision.
vDSP_vrvrsD (page 452)
Vector reverse order, in place; double precision.

Single-Vector Copying
The functions in this group copy one vector to another vector.

vDSP_zvmov (page 537)

Complex vector copy; single precision.
vDSP_zvmovD (page 538)
Complex vector copy; double precision.

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Single-Vector Zero Crossing Search

The functions in this group find a specified number of zero crossings, returning the last crossing found and
the number of crossings found.

vDSP_nzcros (page 317)

Find zero crossings; single precision.
vDSP_nzcrosD (page 318)
Find zero crossings; double precision.

Single-Vector Operations: Linear Averaging

The functions in this group take a vector that contains the linear averages of values from other vectors and
adds an additional vector into those averages.

vDSP_vavlin (page 342)

Vector linear average; single precision.
vDSP_vavlinD (page 343)
Vector linear average; double precision.

Single-Vector Linear Interpolation

The functions in this group calculate the linear interpolation between neighboring elements.

vDSP_vlint (page 404)

Vector linear interpolation between neighboring elements; single precision.
vDSP_vlintD (page 406)
Vector linear interpolation between neighboring elements; double precision.

Single-Vector Integration
The functions in this group perform integration on the values in a vector.

vDSP_vrsum (page 449)

Vector running sum integration; single precision.
vDSP_vrsumD (page 450)
Vector running sum integration; double precision.
vDSP_vsimps (page 464)
Simpson integration; single precision.
vDSP_vsimpsD (page 465)
Simpson integration; double precision.
vDSP_vtrapz (page 492)
Vector trapezoidal integration; single precision.
vDSP_vtrapzD (page 493)
Vector trapezoidal integration; double precision.

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Single-Vector Sorting
The functions in this group find sort the values in a vector.

vDSP_vsort (page 473)

Vector in-place sort; single precision.
vDSP_vsortD (page 474)
Vector in-place sort; double precision.
vDSP_vsorti (page 475)
Vector index in-place sort; single precision.
vDSP_vsortiD (page 475)
Vector index in-place sort; double precision.

Single-Vector Sliding-Window Summing

The functions in this group calculates a sliding-window sum for a vector.

vDSP_vswsum (page 481)

Vector sliding window sum; single precision.
vDSP_vswsumD (page 482)
Vector sliding window sum; double precision.

Single-Vector Precision Conversion

The functions in this group convert between single-precision and double-precision floating-point vectors.

vDSP_vdpsp (page 358)

Vector convert double-precision to single-precision.
vDSP_vspdp (page 476)
Vector convert single-precision to double-precision.

Single-Vector Floating-Point to Integer Conversion

The functions in this group convert the values in a vector from floating-point values to integer values of a
given size.

vDSP_vfix8 (page 367)

Converts an array of single-precision floating-point values to signed 8-bit integer values, rounding
towards zero.
vDSP_vfix8D (page 368)
Converts an array of double-precision floating-point values to signed 8-bit integer values, rounding
towards zero.
vDSP_vfix16 (page 365)
Converts an array of single-precision floating-point values to signed 16-bit integer values, rounding
towards zero.
vDSP_vfix16D (page 365)
Converts an array of double-precision floating-point values to signed 16-bit integer values, rounding
towards zero.

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vDSP_vfix32 (page 366)

Converts an array of single-precision floating-point values to signed 32-bit integer values, rounding
towards zero.
vDSP_vfix32D (page 366)
Converts an array of double-precision floating-point values to signed 16-bit integer values, rounding
towards zero.
vDSP_vfixr8 (page 371)
Converts an array of single-precision floating-point values to signed 8-bit integer values, rounding
towards nearest integer.
vDSP_vfixr8D (page 372)
Converts an array of double-precision floating-point values to signed 8-bit integer values, rounding
towards nearest integer.
vDSP_vfixr16 (page 368)
Converts an array of single-precision floating-point values to signed 16-bit integer values, rounding
towards nearest integer.
vDSP_vfixr16D (page 369)
Converts an array of double-precision floating-point values to signed 16-bit integer values, rounding
towards nearest integer.
vDSP_vfixr32 (page 370)
Converts an array of single-precision floating-point values to signed 32-bit integer values, rounding
towards nearest integer.
vDSP_vfixr32D (page 370)
Converts an array of double-precision floating-point values to signed 32-bit integer values, rounding
towards nearest integer.
vDSP_vfixu8 (page 379)
Converts an array of single-precision floating-point values to unsigned 8-bit integer values, rounding
towards zero.
vDSP_vfixu8D (page 380)
Converts an array of double-precision floating-point values to unsigned 8-bit integer values, rounding
towards zero.
vDSP_vfixu16 (page 376)
Converts an array of single-precision floating-point values to unsigned 16-bit integer values, rounding
towards zero.
vDSP_vfixu16D (page 377)
Converts an array of double-precision floating-point values to unsigned 16-bit integer values, rounding
towards zero.
vDSP_vfixu32 (page 378)
Converts an array of single-precision floating-point values to unsigned 32-bit integer values, rounding
towards zero.
vDSP_vfixu32D (page 378)
Converts an array of double-precision floating-point values to unsigned 32-bit integer values, rounding
towards zero.
vDSP_vfixru8 (page 375)
Converts an array of single-precision floating-point values to unsigned 8-bit integer values, rounding
towards nearest integer.

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vDSP_vfixru8D (page 376)

Converts an array of double-precision floating-point values to unsigned 8-bit integer values, rounding
towards nearest integer.
vDSP_vfixru16 (page 372)
Converts an array of single-precision floating-point values to unsigned 16-bit integer values, rounding
towards nearest integer.
vDSP_vfixru16D (page 373)
Converts an array of double-precision floating-point values to unsigned 16-bit integer values, rounding
towards nearest integer.
vDSP_vfixru32 (page 374)
Converts an array of single-precision floating-point values to unsigned 32-bit integer values, rounding
towards nearest integer.
vDSP_vfixru32D (page 374)
Converts an array of double-precision floating-point values to unsigned 32-bit integer values, rounding
towards nearest integer.

Single-Vector Integer to Floating-Point Conversion

The functions in this group convert integer values of a given size to floating-point vectors.

vDSP_vflt8 (page 383)

Converts an array of signed 8-bit integers to single-precision floating-point values.
vDSP_vflt8D (page 383)
Converts an array of signed 8-bit integers to double-precision floating-point values.
vDSP_vflt16 (page 380)
Converts an array of signed 16-bit integers to single-precision floating-point values.
vDSP_vflt16D (page 381)
Converts an array of signed 16-bit integers to double-precision floating-point values.
vDSP_vflt32 (page 381)
Converts an array of signed 32-bit integers to single-precision floating-point values.
vDSP_vflt32D (page 382)
Converts an array of signed 32-bit integers to double-precision floating-point values.
vDSP_vfltu8 (page 386)
Converts an array of unsigned 8-bit integers to single-precision floating-point values.
vDSP_vfltu8D (page 387)
Converts an array of unsigned 8-bit integers to double-precision floating-point values.
vDSP_vfltu16 (page 384)
Converts an array of unsigned 16-bit integers to single-precision floating-point values.
vDSP_vfltu16D (page 384)
Converts an array of unsigned 16-bit integers to double-precision floating-point values.
vDSP_vfltu32 (page 385)
Converts an array of unsigned 32-bit integers to single-precision floating-point values.
vDSP_vfltu32D (page 386)
Converts an array of unsigned 32-bit integers to double-precision floating-point values.

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Vector-Scalar Addition
These functions add a scalar to each element of a vector.

vDSP_vsadd (page 453)

Vector scalar add; single precision.
vDSP_vsaddD (page 453)
Vector scalar add; double precision.
vDSP_vsaddi (page 454)
Integer vector scalar add.

Vector-Scalar Division
These functions divide each element of a vector by a scalar.

vDSP_vsdiv (page 461)

Vector scalar divide; single precision.
vDSP_vsdivD (page 462)
Vector scalar divide; double precision.
vDSP_vsdivi (page 463)
Integer vector scalar divide.
vDSP_zvdiv (page 531)
Complex vector divide; single precision.
vDSP_zvdivD (page 532)
Complex vector divide; double precision.
vDSP_svdiv (page 324)
Divide scalar by vector; single precision.
vDSP_svdivD (page 325)
Divide scalar by vector; double precision.

Vector-Scalar Multiplication
These functions multiply a scalar by each element of a vector.

vDSP_vsma (page 466)

Vector scalar multiply and vector add; single precision.
vDSP_vsmaD (page 467)
Vector scalar multiply and vector add; double precision.
vDSP_zvsma (page 542)
Complex vector scalar multiply and add; single precision.
vDSP_zvsmaD (page 543)
Complex vector scalar multiply and add; double precision.
vDSP_vsmul (page 472)
Multiplies vector signal1 by scalar signal2 and leaves the result in vector result; single precision.
vDSP_vsmulD (page 473)
Multiplies vector signal1 by scalar signal2 and leaves the result in vector result; double precision.

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vDSP_zvzsml (page 546)

Complex vector multiply by complex scalar; single precision.
vDSP_zvzsmlD (page 547)
Complex vector multiply by complex scalar; double precision.

Vector-Scalar Multiply and Add

These functions multiply a scalar with each element of a vector, ten add another scalar.

vDSP_vsmsa (page 468)

Vector scalar multiply and scalar add; single precision.
vDSP_vsmsaD (page 469)
Vector scalar multiply and scalar add; double precision.
vDSP_vsmsb (page 470)
Vector scalar multiply and vector subtract; single precision.
vDSP_vsmsbD (page 471)
Vector scalar multiply and vector subtract; double precision.

Vector-to-Vector Bitwise Logical Equivalence

vDSP_veqvi (page 362)
Vector equivalence, 32-bit logical.

Vector-to-Vector Real Vector Basic Arithmetic

vDSP_vadd (page 336)
Adds vector A to vector B and leaves the result in vector C; single precision.
vDSP_vaddD (page 336)
Adds vector A to vector B and leaves the result in vector C; double precision.
vDSP_vsub (page 478)
Subtracts vector signal1 from vector signal2 and leaves the result in vector result; single precision.
vDSP_vsubD (page 479)
Subtracts vector signal1 from vector signal2 and leaves the result in vector result; double
precision.
vDSP_vam (page 337)
Adds vectors A and B, multiplies the sum by vector C, and leaves the result in vector D; single precision.
vDSP_vamD (page 337)
Adds vectors A and B, multiplies the sum by vector C, and leaves the result in vector D; double
precision.
vDSP_vsbm (page 455)
Vector subtract and multiply; single precision.
vDSP_vsbmD (page 456)
Vector subtract and multiply; double precision.

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vDSP_vaam (page 331)

Vector add, add, and multiply; single precision.
vDSP_vaamD (page 333)
Vector add, add, and multiply; double precision.
vDSP_vsbsbm (page 457)
Vector subtract, subtract, and multiply; single precision.
vDSP_vsbsbmD (page 458)
Vector subtract, subtract, and multiply; double precision.
vDSP_vasbm (page 338)
Vector add, subtract, and multiply; single precision.
vDSP_vasbmD (page 339)
Vector add, subtract, and multiply; double precision.
vDSP_vasm (page 340)
Vector add and scalar multiply; single precision.
vDSP_vasmD (page 341)
Vector add and scalar multiply; double precision.
vDSP_vsbsm (page 460)
Vector subtract and scalar multiply; single precision.
vDSP_vsbsmD (page 461)
Vector subtract and scalar multiply; double precision.
vDSP_vmsa (page 421)
Vector multiply and scalar add; single precision.
vDSP_vmsaD (page 422)
Vector multiply and scalar add; double precision.
vDSP_vdiv (page 355)
Vector divide; single precision.
vDSP_vdivD (page 356)
Vector divide; double precision.
vDSP_vdivi (page 357)
Vector divide; integer.
vDSP_vmul (page 425)
Multiplies vector A by vector B and leaves the result in vector C; single precision.
vDSP_vmulD (page 426)
Multiplies vector A by vector B and leaves the result in vector C; double precision.
vDSP_vma (page 407)
Vector multiply and add; single precision.
vDSP_vmaD (page 408)
Vector multiply and add; double precision.
vDSP_vmsb (page 423)
Vector multiply and subtract, single precision.
vDSP_vmsbD (page 424)
Vector multiply and subtract; double precision.
vDSP_vmma (page 416)
Vector multiply, multiply, and add; single precision.

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vDSP_vmmaD (page 418)

Vector multiply, multiply, and add; double precision.
vDSP_vmmsb (page 419)
Vector multiply, multiply, and subtract; single precision.
vDSP_vmmsbD (page 420)
Vector multiply, multiply, and subtract; double precision.

Vector-to-Vector Complex Vector Basic Arithmetic

vDSP_zrvdiv (page 516)
Divides complex vector A by real vector B and leaves the result in vector C; single precision.
vDSP_zrvdivD (page 517)
Divides complex vector A by real vector B and leaves the result in vector C; double precision.
vDSP_zrvmul (page 517)
Multiplies complex vector A by real vector B and leaves the result in vector C; single precision.
vDSP_zrvmulD (page 518)
Multiplies complex vector A by real vector B and leaves the result in vector C; double precision.
vDSP_zrvsub (page 519)
Subtracts real vector B from complex vector A and leaves the result in complex vector C; single
precision.
vDSP_zrvsubD (page 520)
Subtracts real vector B from complex vector A and leaves the result in complex vector C; double
precision.
vDSP_zrvadd (page 514)
Adds real vector B to complex vector A and leaves the result in complex vector C; single precision.
vDSP_zrvaddD (page 515)
Adds real vector B to complex vector A and leaves the result in complex vector C; double precision.
vDSP_zvadd (page 525)
Adds complex vectors A and B and leaves the result in complex vector C; single precision.
vDSP_zvaddD (page 526)
Adds complex vectors A and B and leaves the result in complex vector C; double precision.
vDSP_zvcmul (page 528)
Complex vector conjugate and multiply; single precision.
vDSP_zvcmulD (page 528)
Complex vector conjugate and multiply; double precision.
vDSP_zvmul (page 538)
Multiplies complex vectors A and B and leaves the result in complex vector C; single precision.
vDSP_zvmulD (page 539)
Multiplies complex vectors A and B and leaves the result in complex vector C; double precision.
vDSP_zvsub (page 544)
Subtracts complex vector B from complex vector A and leaves the result in complex vector C; single
precision.

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vDSP_zvsubD (page 545)

Subtracts complex vector B from complex vector A and leaves the result in complex vector C; double
precision.
vDSP_zvcma (page 527)
Multiplies complex vector B by the complex conjugates of complex vector A, adds the products to
complex vector C, and stores the results in complex vector D; single precision.
vDSP_zvcmaD (page 527)
Multiplies complex vector B by the complex conjugates of complex vector A, adds the products to
complex vector C, and stores the results in complex vector D; double precision.

Vector-to-Vector Maxima and Minima

vDSP_vmax (page 409)
Vector maxima; single precision.
vDSP_vmaxD (page 409)
Vector maxima; double precision.
vDSP_vmaxmg (page 410)
Vector maximum magnitudes; single precision.
vDSP_vmaxmgD (page 411)
Vector maximum magnitudes; double precision.
vDSP_vmin (page 412)
Vector minima; single precision.
vDSP_vminD (page 413)
Vector minima; double precision.
vDSP_vminmg (page 414)
Vector minimum magnitudes; single precision.
vDSP_vminmgD (page 415)
Vector minimum magnitudes; double precision.

Vector-to-Vector Distance Computation

vDSP_vdist (page 353)
Vector distance; single precision.
vDSP_vdistD (page 354)
Vector distance; double precision.

Vector-to-Vector Interpolation
vDSP_vintb (page 400)
Vector linear interpolation between vectors; single precision.
vDSP_vintbD (page 401)
Vector linear interpolation between vectors; double precision.

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vDSP_vqint (page 434)

Vector quadratic interpolation; single precision.
vDSP_vqintD (page 435)
Vector quadratic interpolation; double precision.

Vector-to-Vector Polynomial Evaluation

vDSP_vpoly (page 429)
Vector polynomial evaluation; single precision.
vDSP_vpolyD (page 430)
Vector polynomial evaluation; double precision.

Vector-to-Vector Pythagoras Computation

The functions in this group apply Pythagoras’s theorem to vectors.

vDSP_vpythg (page 431)

Vector Pythagoras; single precision.
vDSP_vpythgD (page 433)
Vector Pythagoras; double precision.

Vector-to-Vector Extrema Finding

vDSP_venvlp (page 359)
Vector envelope; single precision.
vDSP_venvlpD (page 360)
Vector envelope; double precision.

Vector-to-Vector Element Swapping

vDSP_vswap (page 479)
Vector swap; single precision.
vDSP_vswapD (page 480)
Vector swap; double precision.

Vector-to-Vector Merging
vDSP_vtmerg (page 490)
Tapered merge of two vectors; single precision.
vDSP_vtmergD (page 491)
Tapered merge of two vectors; double precision.

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Vector-to-Vector Spectra Computation

vDSP_zaspec (page 497)
Computes an accumulating autospectrum; single precision.
vDSP_zaspecD (page 498)
Computes an accumulating autospectrum; double precision.
vDSP_zcspec (page 501)
Accumulating cross-spectrum on two complex vectors; single precision.
vDSP_zcspecD (page 502)
Accumulating cross-spectrum on two complex vectors; double precision.

Vector-to-Vector Coherence Function Computation

vDSP_zcoher (page 498)
Coherence function of two signals; single precision.
vDSP_zcoherD (page 499)
Coherence function of two signals; double precision.

Vector-to-Vector Transfer Function Computation

vDSP_ztrans (page 522)
Transfer function; single precision.
vDSP_ztransD (page 523)
Transfer function; double precision.

Vector-to-Vector Recursive Filtering on Real Vectors

vDSP_deq22 (page 198)
Difference equation, 2 poles, 2 zeros; single precision.
vDSP_deq22D (page 199)
Difference equation, 2 poles, 2 zeros; double precision.

Calculating Dot Products

vDSP_dotpr (page 207)
Computes the dot or scalar product of vectors A and B and leaves the result in scalar *C; single
precision.
vDSP_dotpr_s1_15 (page 212)
Vector fixed-point 1.15 format version of vDSP_dotpr (page 207).
vDSP_dotpr_s8_24 (page 212)
Vector fixed-point 8.24 format version of vDSP_dotpr (page 207).

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vDSP_dotprD (page 211)

Computes the dot or scalar product of vectors A and B and leaves the result in scalar *C; double
precision.
vDSP_dotpr2 (page 208)
Stereo variant of vDSP_dotpr (page 207).
vDSP_dotpr2_s1_15 (page 209)
Vector fixed-point 1.15 format version of vDSP_dotpr2 (page 208).
vDSP_dotpr2_s8_24 (page 210)
Vector fixed-point 8.24 format version of vDSP_dotpr2 (page 208).
vDSP_zdotpr (page 502)
Calculates the complex dot product of complex vectors A and B and leaves the result in complex
vector C; single precision.
vDSP_zdotprD (page 503)
Calculates the complex dot product of complex vectors A and B and leaves the result in complex
vector C; double precision.
vDSP_zidotpr (page 504)
Calculates the conjugate dot product (or inner dot product) of complex vectors A and B and leave
the result in complex vector C; single precision.
vDSP_zidotprD (page 504)
Calculates the conjugate dot product (or inner dot product) of complex vectors A and B and leave
the result in complex vector C; double precision.
vDSP_zrdotpr (page 513)
Calculates the complex dot product of complex vector A and real vector B and leaves the result in
complex vector C; single precision.
vDSP_zrdotprD (page 514)
Calculates the complex dot product of complex vector A and real vector B and leaves the result in
complex vector C; double precision.

Finding Maximums
vDSP_maxv (page 297)
Vector maximum value; single precision.
vDSP_maxvD (page 298)
Vector maximum value; double precision.
vDSP_maxvi (page 298)
Vector maximum value with index; single precision.
vDSP_maxviD (page 299)
Vector maximum value with index; double precision.
vDSP_maxmgv (page 294)
Vector maximum magnitude; single precision.
vDSP_maxmgvD (page 294)
Vector maximum magnitude; double precision.
vDSP_maxmgvi (page 295)
Vector maximum magnitude with index; single precision.

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vDSP Reference

vDSP_maxmgviD (page 296)

Vector maximum magnitude with index; double precision.

Finding Minimums
vDSP_minv (page 308)
Vector minimum value.
vDSP_minvD (page 308)
Vector minimum value; double precision.
vDSP_minvi (page 309)
Vector minimum value with index; single precision.
vDSP_minviD (page 310)
Vector minimum value with index; double precision.
vDSP_minmgv (page 304)
Vector minimum magnitude; single precision.
vDSP_minmgvD (page 305)
Vector minimum magnitude; double precision.
vDSP_minmgvi (page 306)
Vector minimum magnitude with index; single precision.
vDSP_minmgviD (page 307)
Vector minimum magnitude with index; double precision.

Calculating Means
vDSP_meanv (page 302)
Vector mean value; single precision.
vDSP_meanvD (page 302)
Vector mean value; double precision.
vDSP_meamgv (page 300)
Vector mean magnitude; single precision.
vDSP_meamgvD (page 301)
Vector mean magnitude; double precision.
vDSP_measqv (page 303)
Vector mean square value; single precision.
vDSP_measqvD (page 304)
Vector mean square value; double precision.
vDSP_mvessq (page 315)
Vector mean of signed squares; single precision.
vDSP_mvessqD (page 316)
Vector mean of signed squares; double precision.
vDSP_rmsqv (page 322)
Vector root-mean-square; single precision.

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vDSP_rmsqvD (page 323)

Vector root-mean-square; double precision.

Summing Vectors
vDSP_sve (page 326)
Vector sum; single precision.
vDSP_sveD (page 326)
Vector sum; double precision.
vDSP_svemg (page 327)
Vector sum of magnitudes; single precision.
vDSP_svemgD (page 328)
Vector sum of magnitudes; double precision.
vDSP_svesq (page 328)
Vector sum of squares; single precision.
vDSP_svesqD (page 329)
Vector sum of squares; double precision.
vDSP_svs (page 330)
Vector sum of signed squares; single precision.
vDSP_svsD (page 331)
Vector sum of signed squares; double precision.

Matrix Multiplication (Real Matrices)

The functions in this group multiply two matrices.

vDSP_mmul (page 312)

Performs an out-of-place multiplication of two matrices; single precision.
vDSP_mmulD (page 313)
Performs an out-of-place multiplication of two matrices; double precision.
vDSP_zmma (page 505)
Multiplies two complex matrices, then adds a third complex matrix; out-of-place; single precision.
vDSP_zmmaD (page 505)
Multiplies two complex matrices, then adds a third complex matrix; out-of-place; double precision.
vDSP_zmms (page 506)
Multiplies two complex matrices, then subtracts a third complex matrix; out-of-place; single precision.
vDSP_zmmsD (page 507)
Multiplies two complex matrices, then subtracts a third complex matrix; out-of-place; double precision.
vDSP_zmmul (page 508)
Multiplies two matrices of complex numbers; out-of-place; single precision.
vDSP_zmmulD (page 509)
Multiplies two matrices of complex numbers; out-of-place; double precision.

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vDSP_zmsm (page 510)

Subtracts the product of two complex matrices from a third complex matrix; out-of-place; single
precision.
vDSP_zmsmD (page 511)
Subtracts the product of two complex matrices from a third complex matrix; out-of-place; double
precision.

Matrix Transposition
vDSP_mtrans (page 314)
Creates a transposed matrix C from a source matrix A; single precision.
vDSP_mtransD (page 315)
Creates a transposed matrix C from a source matrix A; double precision.

Matrix and Submatrix Copying

vDSP_mmov (page 311)
Copies the contents of a submatrix to another submatrix.
vDSP_mmovD (page 311)
Copies the contents of a submatrix to another submatrix.

1D Fast Fourier Transforms (Support Functions)

vDSP_create_fftsetup (page 195)
Builds a data structure that contains precalculated data for use by single-precision FFT functions.
vDSP_create_fftsetupD (page 196)
Builds a data structure that contains precalculated data for use by double-precision FFT functions.
vDSP_destroy_fftsetup (page 201)
Frees an existing single-precision FFT data structure.
vDSP_destroy_fftsetupD (page 202)
Frees an existing double-precision FFT data structure.

1D Fast Fourier Transforms (In-Place Real)

vDSP_fft_zrip (page 279)
Computes an in-place single-precision real discrete Fourier transform, either from the time domain
to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zrip (page 259)
Performs the same operation as vDSP_fft_zrip (page 279) on multiple signals with a single call.
vDSP_fft_zripD (page 281)
Computes an in-place double-precision real discrete Fourier transform, either from the time domain
to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

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vDSP_fftm_zripD (page 261)

Performs the same operation as vDSP_fft_zripD (page 281) on multiple signals with a single call.
vDSP_fft_zript (page 282)
Computes an in-place single-precision real discrete Fourier transform, either from the time domain
to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zript (page 262)
Performs the same operation as vDSP_fft_zript (page 282) on multiple signals with a single call.
vDSP_fft_zriptD (page 283)
Computes an in-place double-precision real discrete Fourier transform, either from the time domain
to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zriptD (page 263)
Performs the same operation as vDSP_fft_zriptD (page 283) on multiple signals with a single call.

1D Fast Fourier Transforms (Out-of-Place Real)

vDSP_fft_zrop (page 284)
Computes an out-of-place single-precision real discrete Fourier transform, either from the time domain
to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zrop (page 264)
Performs the same operation as vDSP_fft_zrop (page 284) on multiple signals with a single call.
vDSP_fft_zropD (page 285)
Computes an out-of-place double-precision real discrete Fourier transform, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zropD (page 265)
Performs the same operation as VDSP_fft_zropD on multiple signals with a single call.
vDSP_fft_zropt (page 286)
Computes an out-of-place single-precision real discrete Fourier transform, either from the time domain
to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zropt (page 267)
Performs the same operation as VDSP_fft_zropt on multiple signals with a single call.
vDSP_fft_zroptD (page 288)
Computes an out-of-place double-precision real discrete Fourier transform, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).
vDSP_fftm_zroptD (page 268)
Performs the same operation as VDSP_fft_zroptD on multiple signals with a single call.

1D Fast Fourier Transforms (In-Place Complex)

vDSP_fft_zip (page 270)
Computes an in-place single-precision complex discrete Fourier transform of the input/output vector
signal, either from the time domain to the frequency domain (forward) or from the frequency domain
to the time domain (inverse).
vDSP_fftm_zip (page 249)
Performs the same operation as vDSP_fft_zip (page 270) on multiple signals with a single call.

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vDSP_fft_zipD (page 271)

Computes an in-place double-precision complex discrete Fourier transform of the input/output vector
signal, either from the time domain to the frequency domain (forward) or from the frequency domain
to the time domain (inverse).
vDSP_fftm_zipD (page 250)
Performs the same operation as vDSP_fft_zipD (page 271) on multiple signals with a single call.
vDSP_fft_zipt (page 272)
Computes an in-place single-precision complex discrete Fourier transform of the input/output vector
signal, either from the time domain to the frequency domain (forward) or from the frequency domain
to the time domain (inverse). A buffer is used for intermediate results.
vDSP_fftm_zipt (page 251)
Performs the same operation as vDSP_fft_zipt (page 272) on multiple signals with a single call.
vDSP_fft_ziptD (page 273)
Computes an in-place double-precision complex discrete Fourier transform of the input/output vector
signal, either from the time domain to the frequency domain (forward) or from the frequency domain
to the time domain (inverse). A buffer is used for intermediate results.
vDSP_fftm_ziptD (page 252)
Performs the same operation as vDSP_fft_ziptD (page 273) on multiple signals with a single call.

1D Fast Fourier Transforms (Out-of-Place Complex)

vDSP_fft_zop (page 274)
Computes an out-of-place single-precision complex discrete Fourier transform of the input vector,
either from the time domain to the frequency domain (forward) or from the frequency domain to the
time domain (inverse).
vDSP_fft_zopD (page 276)
Computes an out-of-place double-precision complex discrete Fourier transform of the input vector,
either from the time domain to the frequency domain (forward) or from the frequency domain to the
time domain (inverse).
vDSP_fftm_zop (page 253)
Performs the same operation as vDSP_fft_zop (page 274) on multiple signals with a single call.
vDSP_fftm_zopD (page 255)
Performs the same operation as vDSP_fft_zopD (page 276) on multiple signals with a single call.
vDSP_fft_zopt (page 277)
Computes an out-of-place single-precision complex discrete Fourier transform of the input vector,
either from the time domain to the frequency domain (forward) or from the frequency domain to the
time domain (inverse).
vDSP_fft_zoptD (page 278)
Computes an out-of-place double-precision complex discrete Fourier transform of the input vector,
either from the time domain to the frequency domain (forward) or from the frequency domain to the
time domain (inverse).
vDSP_fftm_zopt (page 256)
Performs the same operation as vDSP_fft_zopt (page 277) on multiple signals with a single call.
vDSP_fftm_zoptD (page 258)
Performs the same operation as vDSP_fft_zoptD (page 278) on multiple signals with a single call.

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vDSP_fft3_zop (page 244)

Computes an out-of-place radix-3 complex Fourier transform, either forward or inverse. The number
of input and output values processed equals 3 times the power of 2 specified by parameter log2n;
single precision.
vDSP_fft3_zopD (page 245)
Computes an out-of-place radix-3 complex Fourier transform, either forward or inverse. The number
of input and output values processed equals 3 times the power of 2 specified by parameter log2n;
double precision.
vDSP_fft5_zop (page 246)
Computes an out-of-place radix-5 complex Fourier transform, either forward or inverse. The number
of input and output values processed equals 5 times the power of 2 specified by parameter log2n;
single precision.
vDSP_fft5_zopD (page 248)
Computes an out-of-place radix-5 complex Fourier transform, either forward or inverse. The number
of input and output values processed equals 5 times the power of 2 specified by parameter log2n;
double precision.

1D Fast Fourier Transforms (Fixed Length)

vDSP_FFT16_copv (page 216)
Performs a 16-element FFT on interleaved complex data.
vDSP_FFT32_copv (page 243)
Performs a 32-element FFT on interleaved complex data.
vDSP_FFT16_zopv (page 217)
Performs a 16-element FFT on split complex data.
vDSP_FFT32_zopv (page 243)
Performs a 32-element FFT on split complex data.

2D Fast Fourier Transforms (In-Place Complex)

vDSP_fft2d_zip (page 217)
Computes an in-place single-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zipD (page 219)
Computes an in-place double-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zipt (page 220)
Computes an in-place single-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer
is used for intermediate results.
vDSP_fft2d_ziptD (page 222)
Computes an in-place double-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer
is used for intermediate results.

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2D Fast Fourier Transforms (Out-of-Place Complex)

vDSP_fft2d_zop (page 224)
Computes an out-of-place single-precision complex discrete FFT, either from the spatial domain to
the frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zopD (page 225)
Computes an out-of-place double-precision complex discrete FFT, either from the spatial domain to
the frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zopt (page 226)
Computes an out-of-place single-precision complex discrete FFT, either from the spatial domain to
the frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A
buffer is used for intermediate results.
vDSP_fft2d_zoptD (page 228)
Computes an out-of-place double-precision complex discrete FFT, either from the spatial domain to
the frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A
buffer is used for intermediate results.

2D Fast Fourier Transforms (In-Place Real)

vDSP_fft2d_zrip (page 230)
Computes an in-place single-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zripD (page 231)
Computes an in-place double-precision real discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zript (page 233)
Computes an in-place single-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.
vDSP_fft2d_zriptD (page 234)
Computes an in-place double-precision real discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer
is used for intermediate results.

2D Fast Fourier Transforms (Out-of-Place Real)

vDSP_fft2d_zrop (page 236)
Computes an out-of-place single-precision real discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zropD (page 238)
Computes an out-of-place double-precision real discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).
vDSP_fft2d_zropt (page 239)
Computes an out-of-place single-precision real discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer
is used for intermediate results.

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vDSP_fft2d_zroptD (page 241)

Computes an out-of-place double-precision real discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer
is used for intermediate results.

Discrete Fourier Transforms

These functions calculate a discrete Fourier transform of a specified length on a vector.

vDSP_DFT_CreateSetup (page 202)

Old name for vDSP_DFT_zop_CreateSetup (page 205).
vDSP_DFT_DestroySetup (page 203)
Releases a setup object.
vDSP_DFT_Execute (page 203)
Calculates the discrete fourier transform for a vector using vDSP_DFT_zop (page 204) or
vDSP_DFT_zrop (page 206).
vDSP_DFT_zop (page 204)
Calculates the discrete fourier transform for a vector (single-precision complex).
vDSP_DFT_zop_CreateSetup (page 205)
Creates data structures for use with vDSP_DFT_zop (page 204).
vDSP_DFT_zrop (page 206)
Calculates the discrete fourier transform for a vector (single-precision real).
vDSP_DFT_zrop_CreateSetup (page 206)
Creates data structures for use with vDSP_DFT_zrop (page 206).

Correlation and Convolution

These functions perform correlation and convolution operations on real or complex signals in vDSP.

vDSP_conv (page 193)

Performs either correlation or convolution on two vectors; single precision.
vDSP_convD (page 194)
Performs either correlation or convolution on two vectors; double precision.
vDSP_zconv (page 499)
Performs either correlation or convolution on two complex vectors; single precision.
vDSP_zconvD (page 500)
Performs either correlation or convolution on two complex vectors; double precision.
vDSP_wiener (page 494)
Wiener-Levinson general convolution; single precision.
vDSP_wienerD (page 496)
Wiener-Levinson general convolution; double precision.
vDSP_desamp (page 199)
Convolution with decimation; single precision.
vDSP_desampD (page 200)
Convolution with decimation; double precision.

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vDSP_zrdesamp (page 512)

Complex/real downsample with anti-aliasing; single precision.
vDSP_zrdesampD (page 512)
Complex/real downsample with anti-aliasing; double precision.

Windowing and Filtering

This section describes the C API for performing filtering operations on real or complex signals in vDSP. It also
describes the built-in support for windowing functions such as Blackman, Hamming, and Hann windows.

vDSP_blkman_window (page 192)

Creates a single-precision Blackman window.
vDSP_blkman_windowD (page 192)
Creates a double-precision Blackman window.
vDSP_hamm_window (page 289)
Creates a single-precision Hamming window.
vDSP_hamm_windowD (page 290)
Creates a double-precision Hamming window.
vDSP_hann_window (page 290)
Creates a single-precision Hanning window.
vDSP_hann_windowD (page 291)
Creates a double-precision Hanning window.
vDSP_f3x3 (page 213)
Filters an image by performing a two-dimensional convolution with a 3x3 kernel; single precision.
vDSP_f3x3D (page 214)
Filters an image by performing a two-dimensional convolution with a 3x3 kernel; double precision.
vDSP_f5x5 (page 215)
Filters an image by performing a two-dimensional convolution with a 5x5 kernel; single precision.
vDSP_f5x5D (page 215)
Filters an image by performing a two-dimensional convolution with a 5x5 kernel; double precision.
vDSP_imgfir (page 292)
Filters an image by performing a two-dimensional convolution with a kernel; single precision.
vDSP_imgfirD (page 293)
Filters an image by performing a two-dimensional convolution with a kernel; double precision.

Complex Vector Conversion

These functions convert complex vectors between interleaved and split forms.

vDSP_ctoz (page 197)

Copies the contents of an interleaved complex vector C to a split complex vector Z; single precision.
vDSP_ctozD (page 197)
Copies the contents of an interleaved complex vector C to a split complex vector Z; double precision.
vDSP_ztoc (page 521)
Copies the contents of a split complex vector A to an interleaved complex vector C; single precision.

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vDSP_ztocD (page 522)

Copies the contents of a split complex vector A to an interleaved complex vector C; double precision.

Functions

vDSP_blkman_window
Creates a single-precision Blackman window.

void vDSP_blkman_window (
float *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_FLAG
);

Discussion
Represented in pseudo-code, this function does the following:

for (n=0; n < N; ++n)

{
C[n] = 0.42 - (0.5 * cos( 2 * pi * n / N ) ) + (0.08 * cos( 4 * pi * n /
N) );
}

vDSP_blkman_window creates a single-precision Blackman window function C, which can be multiplied by

a vector using vDSP_vmul. Specify the vDSP_HALF_WINDOW (page 553) flag to create only the first (n+1)/2
points, or 0 (zero) for a full-size window.

See also vDSP_vmul (page 425).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_blkman_windowD
Creates a double-precision Blackman window.

void vDSP_blkman_windowD (
double *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_FLAG
);

Discussion
Represented in pseudo-code, this function does the following:

for (n=0; n < N; ++n)

{
C[n] = 0.42 - (0.5 * cos( 2 * pi * n / N ) ) + (0.08 * cos( 4 * pi * n /
N) );

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vDSP_blkman_windowD (page 192) creates a double-precision Blackman window function C, which can be
multiplied by a vector using vDSP_vmulD . Specify the vDSP_HALF_WINDOW (page 553) flag to create only
the first (n+1)/2 points, or 0 (zero) for a full-size window.

See also vDSP_vmulD (page 426).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_conv
Performs either correlation or convolution on two vectors; single precision.

void vDSP_conv (
const float __vDSP_signal[],
vDSP_Stride __vDSP_signalStride,
const float __vDSP_filter[],
vDSP_Stride __vDSP_strideFilter,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_lenResult,
vDSP_Length __vDSP_lenFilter
);

Discussion

If filterStride is positive, vDSP_conv performs correlation. If filterStride is negative,it performs

convolution and *filtermust point to the last vector element. The function can run in place, but result cannot
be in place with filter.

The value of lenFilter must be less than or equal to 2044. The length of vector signal must satisfy two
criteria: it must be

■ equal to or greater than 12

■ equal to or greater than the sum of N-1 plus the nearest multiple of 4 that is equal to or greater than
the value of lenFilter.

Criteria to invoke vectorized code:

■ The vectors signal and result must be relatively aligned.

■ The value of lenFilter must be between 4 and 256, inclusive.
■ The value of lenResult must be greater than 36.

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■ The values of signalStride and resultStride must be 1.

■ The value of filterStride must be either 1 or -1.

If any of these criteria is not satisfied, the function invokes scalar code.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_convD
Performs either correlation or convolution on two vectors; double precision.

void vDSP_convD (
const double __vDSP_signal[],
vDSP_Stride __vDSP_signalStride,
const double __vDSP_filter[],
vDSP_Stride __vDSP_strideFilter,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_lenResult,
vDSP_Length __vDSP_lenFilter
);

Discussion

If filterStride is positive, vDSP_convD performs correlation. If filterStride is negative,it performs

convolution and *filtermust point to the last vector element. The function can run in place, but result
cannot be in place with filter.

The value of lenFilter must be less than or equal to 2044. The length of vector signal must satisfy two
criteria: it must be

■ equal to or greater than 12

■ equal to or greater than the sum of N-1 plus the nearest multiple of 4 that is equal to or greater than
the value of lenFilter.

Criteria to invoke vectorized code:

No Altivec support for double precision. On a PowerPC processor, this function always invokes scalar code.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_create_fftsetup
Builds a data structure that contains precalculated data for use by single-precision FFT functions.

FFTSetup vDSP_create_fftsetup (
vDSP_Length __vDSP_log2n,
FFTRadix __vDSP_radix
);

Parameters
log2n
A base 2 exponent that represents the number of divisions of the complex unit circle and thus specifies
the largest power of two that can be processed by a subsequent frequency-domain function. Parameter
log2n must equal or exceed the largest power of 2 that any subsequent function processes using
the weights array.
radix
Specifies radix options. Radix 2, radix 3, and radix 5 functions are supported.
Return Value
Returns an FFTSetup (page 550) structure for use with one-dimensional FFT functions. Returns 0 on error.

Discussion
This function returns a filled-in FFTSetup (page 550) data structure for use by FFT functions that operate on
double-precision vectors. Once prepared, the setup structure can be used repeatedly by FFT functions (which
read the data in the structure and do not alter it) for any (power of two) length up to that specified when
you created the structure.

If an application performs FFTs with diverse lengths, the calls with different lengths can share a single setup
structure (created for the longest length), and this saves space over having multiple structures. However, in
some cases, notably single-precision FFTs on 32-bit PowerPC, an FFT routine may perform faster if it is passed
a setup structure that was created specifically for the length of the transform.

Parameter log2n is a base-two exponent and specifies that the largest transform length that can processed
using the resulting setup structure is 2**log2n (or 3*2**log2n or 5*2**log2n if the appropriate flags are
passed, as discussed below). That is, the log2n parameter must equal or exceed the value passed to any
subsequent FFT routine using the setup structure returned by this routine.

Parameter radix specifies radix options. Its value may be the bitwise OR of any combination of
kFFTRadix2 (page 552), kFFTRadix3 (page 552), or kFFTRadix5 (page 553). The resulting setup structure
may be used with any of the routines for which the respective flag was used. (The radix-3 and radix-5 FFT
routines have "fft3" and "fft5" in their names. The radix-2 FFT routines have plain "fft" in their names.)

If zero is returned, the routine failed to allocate storage.

The setup structure is deallocated by calling vDSP_destroy_fftsetup (page 201).

Use vDSP_create_fftsetup during initialization. It is relatively slow compared to the routines that actually
perform FFTs. Never use it in a part of an application that needs to be high performance.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_create_fftsetupD
Builds a data structure that contains precalculated data for use by double-precision FFT functions.

FFTSetupD vDSP_create_fftsetupD (
vDSP_Length __vDSP_log2n,
FFTRadix __vDSP_radix
);

Parameters
log2n
A base 2 exponent that represents the number of divisions of the complex unit circle and thus specifies
the largest power of two that can be processed by a subsequent frequency-domain function. Parameter
log2n must equal or exceed the largest power of 2 that any subsequent function processes using
the weights array.
radix
Specifies radix options. Radix 2, radix 3, and radix 5 functions are supported.
Return Value
Returns an FFTSetupD (page 550) structure for use with FFT functions, or 0 if there was an error.

Discussion
This function returns a filled-in FFTSetupD (page 550) data structure for use by FFT functions that operate
on double-precision vectors. Once prepared, the setup structure can be used repeatedly by FFT functions
(which read the data in the structure and do not alter it) for any (power of two) length up to that specified
when you created the structure.

If an application performs FFTs with diverse lengths, the calls with different lengths can share a single setup
structure (created for the longest length), and this saves space over having multiple structures. However, in
some cases, notably single-precision FFTs on 32-bit PowerPC, an FFT routine may perform faster if it is passed
a setup structure that was created specifically for the length of the transform.

Parameter log2n is a base-two exponent and specifies that the largest transform length that can processed
using the resulting setup structure is 2**log2n (or 3*2**log2n or 5*2**log2n if the appropriate flags are
passed, as discussed below). That is, the log2n parameter must equal or exceed the value passed to any
subsequent FFT routine using the setup structure returned by this routine.

Parameter radix specifies radix options. Its value may be the bitwise OR of any combination of
kFFTRadix2 (page 552), kFFTRadix3 (page 552), or kFFTRadix5 (page 553). The resulting setup structure
may be used with any of the routines for which the respective flag was used. (The radix-3 and radix-5 FFT
routines have fft3 and fft5 in their names. The radix-2 FFT routines have plain fft in their names.)

If zero is returned, the routine failed to allocate storage.

The setup structure is deallocated by calling vDSP_destroy_fftsetupD (page 202).

Use vDSP_create_fftsetupD during initialization. It is relatively slow compared to the routines that actually
perform FFTs. Never use it in a part of an application that needs to be high performance.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_ctoz
Copies the contents of an interleaved complex vector C to a split complex vector Z; single precision.

void vDSP_ctoz (
const DSPComplex __vDSP_C[],
vDSP_Stride __vDSP_strideC,
DSPSplitComplex *__vDSP_Z,
vDSP_Stride __vDSP_strideZ,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

The strideC parameter contains an address stride through C. strideZ is an address stride through Z. The
value of strideC must be a multiple of 2.

For best performance, C.realp, C.imagp, Z.realp, and Z.imagp should be 16-byte aligned.

See also functionsvDSP_ztoc (page 521) and vDSP_ztocD (page 522).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_ctozD
Copies the contents of an interleaved complex vector C to a split complex vector Z; double precision.

void vDSP_ctozD (
const DSPDoubleComplex __vDSP_C[],
vDSP_Stride __vDSP_strideC,
DSPDoubleSplitComplex *__vDSP_Z,
vDSP_Stride __vDSP_strideZ,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

The strideC parameter contains an address stride through C. strideZ is an address stride through Z. The
value of strideC must be a multiple of 2.

For best performance, C.realp, C.imagp, Z.realp, and Z.imagp should be 16-byte aligned.

See also functions vDSP_ztoc (page 521) and vDSP_ztocD (page 522).

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_deq22
Difference equation, 2 poles, 2 zeros; single precision.

void vDSP_deq22 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector; must have at least N+2 elements
I
Stride for A
B
5 single-precision inputs, filter coefficients
C
Single-precision real output vector; must have at least N+2 elements
K
Stride for C
N
Number of new output elements to produce
Discussion
Performs two-pole two-zero recursive filtering on real input vector A. Since the computation is recursive, the
first two elements in vector C must be initialized prior to calling vDSP_deq22. vDSP_deq22 creates N new
values for vector C beginning with its third element and requires at least N+2 input values from vector A. This
function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_deq22D
Difference equation, 2 poles, 2 zeros; double precision.

void vDSP_deq22D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector; must have at least N+2 elements
I
Stride for A
B
5 double-precision inputs, filter coefficients
C
Double-precision real output vector; must have at least N+2 elements
K
Stride for C
N
Number of new output elements to produce
Discussion
Performs two-pole two-zero recursive filtering on real input vector A. Since the computation is recursive, the
first two elements in vector C must be initialized prior to calling vDSP_deq22D. vDSP_deq22D creates N new
values for vector C beginning with its third element and requires at least N+2 input values from vector A. This
function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_desamp
Convolution with decimation; single precision.

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void vDSP_desamp (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Single-precision real input vector, 8-byte aligned; length of A >= 12
I
Desampling factor
B
Single-precision input filter coefficients
C
Single-precision real output vector
N
Output count
M
Filter coefficient count
Discussion
Performs finite impulse response (FIR) filtering at selected positions of vector A. desampx can run in place,
but C cannot be in place with B. Length of A must be >=(N-1)*I+(nearest multiple of 4 >=M).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_desampD
Convolution with decimation; double precision.

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void vDSP_desampD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Double-precision real input vector, 8-byte aligned; length of A >= 12
I
Desampling factor
B
Double-precision input filter coefficients
C
Double-precision real output vector
N
Output count
M
Filter coefficient count
Discussion
Performs finite impulse response (FIR) filtering at selected positions of vector A. desampx can run in place,
but C cannot be in place with B. Length of A must be >=(N-1)*I+(nearest multiple of 4 >=M).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_destroy_fftsetup
Frees an existing single-precision FFT data structure.

void vDSP_destroy_fftsetup (
FFTSetup __vDSP_setup
);

Parameters
setup
Identifies the weights array, and must point to a data structure previously created by
vDSP_create_fftsetup (page 195).

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Discussion
vDSP_destroy_fftsetup frees an existing weights array. Any memory allocated for the array is released.
After the vDSP_destroy_fftsetup function returns, the structure should not be used in any other functions.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_destroy_fftsetupD
Frees an existing double-precision FFT data structure.

void vDSP_destroy_fftsetupD (
FFTSetupD __vDSP_setup
);

Parameters
setup
Identifies the weights array, and must point to a data structure previously created by
vDSP_create_fftsetupD (page 196).
Discussion
vDSP_destroy_fftsetupD frees an existing weights array. Any memory allocated for the array is released.
After the vDSP_destroy_fftsetupD function returns, the structure should not be used in any other
functions.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_DFT_CreateSetup
Old name for vDSP_DFT_zop_CreateSetup (page 205).

vDSP_DFT_Setup vDSP_DFT_CreateSetup (
vDSP_DFT_Setup __vDSP_Previous,
vDSP_Length __vDSP_Length
);

Discussion
Call vDSP_DFT_zop_CreateSetup (page 205) instead.

Concurrency Note: This function is not thread-safe. You must not call this function concurrently with any
other DFT call.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_DFT_DestroySetup
Releases a setup object.

void vDSP_DFT_DestroySetup (
vDSP_DFT_Setup __vDSP_Setup
);

Parameters
__vDSP_Setup
The setup object to destroy (as returned by vDSP_DFT_CreateSetup (page 202),
vDSP_DFT_zop_CreateSetup (page 205), or vDSP_DFT_zrop_CreateSetup (page 206).
Discussion
If this setup object shares memory with other setup objects, that memory is not released until the last object
is destroyed.

Concurrency Note: This function is not thread-safe. You must not call this function concurrently with any
other DFT call.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_DFT_Execute
Calculates the discrete fourier transform for a vector using vDSP_DFT_zop (page 204) or vDSP_DFT_zrop (page
206).

void vDSP_DFT_Execute (
const struct vDSP_DFT_SetupStruct *__vDSP_Setup,
const float *__vDSP_Ir,
const float *__vDSP_Ii,
float *__vDSP_Or,
float *__vDSP_Oi
);

Parameters
__vDSP_Setup
A DFT setup object returned by a call to vDSP_DFT_zop_CreateSetup (page 205).
__vDSP_Ir
A vector containing the real part of the input values.
__vDSP_Ii
A vector containing the imaginary part of the input values.
__vDSP_Or
A vector where the real part of the results is stored on return.

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__vDSP_Oi
A vector where the imaginary part of the results is stored on return.
Discussion
This function calculates either a real or complex discrete fourier transform, depending on whether the setup
object was created with a call to vDSP_DFT_zrop_CreateSetup (page 206) or
vDSP_DFT_zop_CreateSetup (page 205).

Note: If the setup was created with vDSP_DFT_zop_CreateSetup (page 205), each vector should contain
length elements. If it was created with vDSP_DFT_zrop_CreateSetup (page 206), each vector should
contain length/2 elements.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_DFT_zop
Calculates the discrete fourier transform for a vector (single-precision complex).

void vDSP_DFT_zop (
const struct vDSP_DFT_SetupStruct *__vDSP_Setup,
const float *__vDSP_Ir,
const float *__vDSP_Ii,
vDSP_Stride __vDSP_Is,
float *__vDSP_Or,
float *__vDSP_Oi,
vDSP_Stride __vDSP_Os,
vDSP_DFT_Direction __vDSP_Direction
);

Parameters
__vDSP_Setup
A DFT setup object returned by a call to vDSP_DFT_zop_CreateSetup (page 205).
__vDSP_InputRe
A vector containing the real part of the input values.
__vDSP_InputIm
A vector containing the imaginary part of the input values.
__vDSP_InputStride
Stride length within the input vector. For example, passing 2 would cause every second value to be
used.
__vDSP_OutputRe
A vector where the real part of the results is stored on return.
__vDSP_OutputIm
A vector where the imaginary part of the results is stored on return.
__vDSP_OutputStride
Stride length within the input vector. For example, passing 2 would cause every second value to be
overwritten.

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__vDSP_Direction
vDSP_DFT_FORWARD (page 551) or vDSP_DFT_INVERSE (page 552), indicating whether to perform a
forward or inverse transform.
Discussion
The input and output vectors may not overlap, with one exception: if the real and imaginary input vectors
are both the same as the corresponding output vector, an in-place algorithm is used.

Note: The length of the transform is specified in the setup object.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_DFT_zop_CreateSetup
Creates data structures for use with vDSP_DFT_zop (page 204).

vDSP_DFT_Setup vDSP_DFT_zop_CreateSetup (
vDSP_DFT_Setup __vDSP_Previous,
vDSP_Length __vDSP_Length,
vDSP_DFT_Direction __vDSP_Direction
);

Parameters
__vDSP_Previous
An previous result from this function or NULL.
__vDSP_Length
The length of DFT computations with this object.
Return Value
Returns a DFT setup object.

Discussion
This function is designed to share memory between data structures where possible. You should initially
create a setup object with the largest length you expect to use, then pass that object as __vDSP_Previous.
By doing so, this setup object can share the underlying data storage with that object, thus reducing the time
needed to construct the tables.

Concurrency Note: This function is not thread-safe. You must not call this function concurrently with any
other DFT call.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_DFT_zrop
Calculates the discrete fourier transform for a vector (single-precision real).

void vDSP_DFT_zrop (
vDSP_DFT_Setup __vDSP_Setup,
const float *__vDSP_InputRe,
const float *__vDSP_InputIm,
vDSP_Stride __vDSP_InputStride,
float *__vDSP_OutputRe,
float *__vDSP_OutputIm,
vDSP_Stride __vDSP_OutputStride,
vDSP_DFT_Direction __vDSP_Direction
);

Parameters
__vDSP_Setup
A DFT setup object returned by a call to vDSP_DFT_zrop_CreateSetup (page 206).
__vDSP_InputRe
A vector containing the real part of the input values.
__vDSP_InputIm
A vector containing the imaginary part of the input values.
__vDSP_InputStride
Stride length within the input vector. For example, passing 2 would cause every second value to be
used.
__vDSP_OutputRe
A vector where the real part of the results is stored on return.
__vDSP_OutputIm
A vector where the imaginary part of the results is stored on return.
__vDSP_OutputStride
Stride length within the input vector. For example, passing 2 would cause every second value to be
overwritten.
__vDSP_Direction
vDSP_DFT_FORWARD (page 551) or vDSP_DFT_INVERSE (page 552), indicating whether to perform a
forward or inverse transform.
Discussion
The input and output vectors may not overlap unless they are equal, in which case an in-place algorithm is
used.

Note: The length of the transform is specified in the setup object.

vDSP_DFT_zrop_CreateSetup
Creates data structures for use with vDSP_DFT_zrop (page 206).

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vDSP_DFT_Setup vDSP_DFT_zrop_CreateSetup (
vDSP_DFT_Setup __vDSP_Previous,
vDSP_Length __vDSP_Length,
vDSP_DFT_Direction __vDSP_Direction
);

Parameters
__vDSP_Previous
An previous result from this function or NULL.
__vDSP_Length
The length of DFT computations with this object.
Return Value
Returns a DFT setup object.

Discussion
This function is designed to share memory between data structures where possible. You should initially
create a setup object with the largest length you expect to use, then pass that object as __vDSP_Previous.
By doing so, this setup object can share the underlying data storage with that object, thus reducing the time
needed to construct the tables.

Concurrency Note: This function is not thread-safe. You must not call this function concurrently with any
other DFT call.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_dotpr
Computes the dot or scalar product of vectors A and B and leaves the result in scalar *C; single precision.

void vDSP_dotpr (
const float __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
float *__vDSP_result,
vDSP_Length __vDSP_size
);

Parameters
__vDSP_input1
Input vector A.
__vDSP_stride1
The stride within vector A. For example if stride is 2, every second element is used.
__vDSP_input2
Input vector B.
__vDSP_stride2
The stride within vector B. For example if stride is 2, every second element is used.

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__vDSP_result
The dot product (on return).
__vDSP_size
The number of elements (N).
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_dotpr2
Stereo variant of vDSP_dotpr (page 207).

void vDSP_dotpr2 (
const float *__vDSP_A0,
vDSP_Stride __vDSP_A0Stride,
const float *__vDSP_A1,
vDSP_Stride __vDSP_A1Stride,
const float *__vDSP_B,
vDSP_Stride __vDSP_BStride,
float *__vDSP_C0,
float *__vDSP_C1,
vDSP_Length __vDSP_Length
);

Parameters
__vDSP_A0
Input vector A0.
__vDSP_A0Stride
The stride within vector A0. For example if stride is 2, every second element is used.
__vDSP_A1
Input vector A1.
__vDSP_A1Stride
The stride within vector A1. For example if stride is 2, every second element is used.
__vDSP_B
Input vector B.
__vDSP_BStride
The stride within vector B. For example if stride is 2, every second element is used.
__vDSP_C0
The dot product of A0 and B (on return).

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__vDSP_C1
The dot product of A1 and B (on return).
__vDSP_Length
The number of elements.
Discussion
Calculates the dot product of A0 with B, then calculates the dot product of A1 with B. The equation for a
single dot product is:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_dotpr2_s1_15
Vector fixed-point 1.15 format version of vDSP_dotpr2 (page 208).

void vDSP_dotpr2_s1_15 (
const short int *__vDSP_A0,
vDSP_Stride __vDSP_A0Stride,
const short int *__vDSP_A1,
vDSP_Stride __vDSP_A1Stride,
const short int *__vDSP_B,
vDSP_Stride __vDSP_BStride,
short int *__vDSP_C0,
short int *__vDSP_C1,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_A0
Input vector A0.
__vDSP_A0Stride
The stride within vector A0. For example if stride is 2, every second element is used.
__vDSP_A1
Input vector A1.
__vDSP_A1Stride
The stride within vector A1. For example if stride is 2, every second element is used.
__vDSP_B
Input vector B.
__vDSP_BStride
The stride within vector B. For example if stride is 2, every second element is used.
__vDSP_C0
The dot product of A0 and B (on return).

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__vDSP_C1
The dot product of A1 and B (on return).
__vDSP_Length
The number of elements.
Discussion
Calculates the dot product of A0 with B, then calculates the dot product of A1 with B. The equation for a
single dot product is:

The elements are fixed-point numbers, each with one sign bit and 15 fraction bits. A value in this representation
can be converted to floating-point by dividing it by 32768.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_dotpr2_s8_24
Vector fixed-point 8.24 format version of vDSP_dotpr2 (page 208).

void vDSP_dotpr2_s8_24 (
const int *__vDSP_A0,
vDSP_Stride __vDSP_A0Stride,
const int *__vDSP_A1,
vDSP_Stride __vDSP_A1Stride,
const int *__vDSP_B,
vDSP_Stride __vDSP_BStride,
int *__vDSP_C0,
int *__vDSP_C1,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_A0
Input vector A0.
__vDSP_A0Stride
The stride within vector A0. For example if stride is 2, every second element is used.
__vDSP_A1
Input vector A1.
__vDSP_A1Stride
The stride within vector A1. For example if stride is 2, every second element is used.
__vDSP_B
Input vector B.
__vDSP_BStride
The stride within vector B. For example if stride is 2, every second element is used.

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__vDSP_C0
The dot product of A0 and B (on return).
__vDSP_C1
The dot product of A1 and B (on return).
__vDSP_Length
The number of elements.
Discussion
Calculates the dot product of A0 with B, then calculates the dot product of A1 with B. The equation for a
single dot product is:

The elements are fixed-point numbers, each with eight integer bits (including the sign bit) and 24 fraction
bits. A value in this representation can be converted to floating-point by dividing it by 16777216.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_dotprD
Computes the dot or scalar product of vectors A and B and leaves the result in scalar *C; double precision.

void vDSP_dotprD (
const double __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
double *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_dotpr_s1_15
Vector fixed-point 1.15 format version of vDSP_dotpr (page 207).

void vDSP_dotpr_s1_15 (
const short int *__vDSP_A,
vDSP_Stride __vDSP_AStride,
const short int *__vDSP_B,
vDSP_Stride __vDSP_BStride,
short int *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_A
Input vector A.
__vDSP_AStride
The stride within vector A. For example if stride is 2, every second element is used.
__vDSP_B
Input vector B.
__vDSP_BStride
The stride within vector B. For example if stride is 2, every second element is used.
__vDSP_C
The dot product (on return).
__vDSP_N
The number of elements.
Discussion
This performs the following operation:

The elements are fixed-point numbers, each with one sign bit and 15 fraction bits. A value in this representation
can be converted to floating-point by dividing it by 32768.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_dotpr_s8_24
Vector fixed-point 8.24 format version of vDSP_dotpr (page 207).

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vDSP Reference

void vDSP_dotpr_s8_24 (
const int *__vDSP_A,
vDSP_Stride __vDSP_AStride,
const int *__vDSP_B,
vDSP_Stride __vDSP_BStride,
int *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_A
Input vector A.
__vDSP_AStride
The stride within vector A. For example if stride is 2, every second element is used.
__vDSP_B
Input vector B.
__vDSP_BStride
The stride within vector B. For example if stride is 2, every second element is used.
__vDSP_C
The dot product (on return).
__vDSP_N
The number of elements.
Discussion
This performs the following operation:

The elements are fixed-point numbers, each with eight integer bits (including the sign bit) and 24 fraction
bits. A value in this representation can be converted to floating-point by dividing it by 16777216.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_f3x3
Filters an image by performing a two-dimensional convolution with a 3x3 kernel; single precision.

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void vDSP_f3x3 (
float *__vDSP_signal,
vDSP_Length __vDSP_rows,
vDSP_Length __vDSP_cols,
float *__vDSP_filter,
float *__vDSP_result
);

Discussion
This function filters an image by performing a two-dimensional convolution with a 3x3 kernel (B) on the
input matrix A and storing the resulting image in the output matrix C.

This performs the following operation:

The function pads the perimeter of the output image with a border of zeros of width 1.

B is the 3x3 kernel. M and N are the number of rows and columns, respectively, of the two-dimensional input
matrix A. M must be greater than or equal to 3. N must be even and greater than or equal to 4.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_f3x3D
Filters an image by performing a two-dimensional convolution with a 3x3 kernel; double precision.

void vDSP_f3x3D (
double *__vDSP_signal,
vDSP_Length __vDSP_rows,
vDSP_Length __vDSP_cols,
double *__vDSP_filter,
double *__vDSP_result
);

Discussion
This function filters an image by performing a two-dimensional convolution with a 3x3 kernel on the input
matrix A and storing the resulting image in the output matrix C.

This performs the following operation:

The function pads the perimeter of the output image with a border of zeros of width 1.

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B is the 3x3 kernel. M and N are the number of rows and columns, respectively, of the two-dimensional input
matrix A. M must be greater than or equal to 3. N must be even and greater than or equal to 4.

Criteria to invoke vectorized code:

■ A, B, and C must be 16-byte aligned.

■ N must be greater than or equal to 18.

If any of these criteria is not satisfied, the function invokes scalar code.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_f5x5
Filters an image by performing a two-dimensional convolution with a 5x5 kernel; single precision.

void vDSP_f5x5 (
float *__vDSP_signal,
vDSP_Length __vDSP_rows,
vDSP_Length __vDSP_cols,
float *__vDSP_filter,
float *__vDSP_result
);

Discussion
This function filters an image by performing a two-dimensional convolution with a 5x5 kernel (B) on the
input matrix A and storing the resulting image in the output matrix C.

This performs the following operation:

The function pads the perimeter of the output image with a border of zeros of width 2.

B is the 5x5 kernel. M and N are the number of rows and columns, respectively, of the two-dimensional input
matrix A. M must be greater than or equal to 5. N must be even and greater than or equal to 6.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_f5x5D
Filters an image by performing a two-dimensional convolution with a 5x5 kernel; double precision.

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void vDSP_f5x5D (
double *__vDSP_signal,
vDSP_Length __vDSP_rows,
vDSP_Length __vDSP_cols,
double *__vDSP_filter,
double *__vDSP_result
);

Discussion
This function filters an image by performing a two-dimensional convolution with a 5x5 kernel (B) on the
input matrix A and storing the resulting image in the output matrix C.

This performs the following operation:

The function pads the perimeter of the output image with a border of zeros of width 2.

B is the 5x5 kernel. M and N are the number of rows and columns, respectively, of the two-dimensional input
matrix A. M must be greater than or equal to 5. N must be even and greater than or equal to 6.

Criteria to invoke vectorized code:

■ A, B, and C must be 16-byte aligned.

■ N must be greater than or equal to 20.

If any of these criteria is not satisfied, the function invokes scalar code.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_FFT16_copv
Performs a 16-element FFT on interleaved complex data.

void vDSP_FFT16_copv (
float *__vDSP_Output,
const float *__vDSP_Input,
FFTDirection __vDSP_Direction
);

Parameters
__vDSP_Output
A vector-block-aligned output array.
__vDSP_Input
A vector-block-aligned input array.

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__vDSP_Direction
kFFTDirection_Forward (page 552) or kFFTDirection_Inverse (page 552), indicating whether
to perform a forward or inverse transform.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_FFT16_zopv
Performs a 16-element FFT on split complex data.

void vDSP_FFT16_zopv (
float *__vDSP_Or,
float *__vDSP_Oi,
const float *__vDSP_Ir,
const float *__vDSP_Ii,
FFTDirection __vDSP_Direction
);

Parameters
__vDSP_Or
Output vector for real parts.
__vDSP_Oi
Output vector for imaginary parts.
__vDSP_Ir
Input vector for real parts.
__vDSP_Ii
Input vector for imaginary parts.
__vDSP_Direction
kFFTDirection_Forward (page 552) or kFFTDirection_Inverse (page 552), indicating whether
to perform a forward or inverse transform.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zip
Computes an in-place single-precision complex discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).

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void vDSP_fft2d_zip (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
ioData
A complex vector input.
strideInRow
Specifies a stride across each row of the matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, parameter strideInCol represents the distance between each row of the matrix. If parameter
strideInCol is 1024, for instance, complex element 512 of the matrix equates to element (1,0),
element 1024 equates to element (2,0), and so forth.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for parameter log2nInCol and 6 for parameter log2nInRow. log2nInRow must
be between 2 and 10, inclusive.
direction
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of direction.
Discussion
This performs the following operation:

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See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zipD
Computes an in-place double-precision complex discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).

void vDSP_fft2d_zipD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
ioData
A complex vector input.
strideInRow
Specifies a stride across each row of the matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.

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strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, parameter strideInCol represents the distance between each row of the matrix. If parameter
strideInCol is 1024, for instance, complex element 512 of the matrix equates to element (1,0),
element 1024 equates to element (2,0), and so forth.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for parameter log2nInCol and 6 for parameter log2nInRow. log2nInRow must
be between 2 and 10, inclusive.
direction
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of direction.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zipt
Computes an in-place single-precision complex discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.

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void vDSP_fft2d_zipt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
ioData
A complex vector input.
strideInRow
Specifies a stride across each row of the matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, parameter strideInCol represents the distance between each row of the matrix. If parameter
strideInCol is 1024, for instance, complex element 512 of the matrix equates to element (1,0),
element 1024 equates to element (2,0), and so forth.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 16 KB or 4*n, where log2n = log2nInCol + log2nInRow.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for parameter log2nInCol and 6 for parameter log2nInRow. log2nInRow must
be between 2 and 10, inclusive.
direction
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of direction.
Discussion
This performs the following operation:

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See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_ziptD
Computes an in-place double-precision complex discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.

void vDSP_fft2d_ziptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
ioData
A complex vector input.
strideInRow
Specifies a stride across each row of the matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.

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strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, parameter strideInCol represents the distance between each row of the matrix. If parameter
strideInCol is 1024, for instance, complex element 512 of the matrix equates to element (1,0),
element 1024 equates to element (2,0), and so forth.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 16 KB or 4*n, where log2n = log2nInCol + log2nInRow.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for parameter log2nInCol and 6 for parameter log2nInRow. log2nInRow must
be between 2 and 10, inclusive.
direction
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of direction.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft2d_zop
Computes an out-of-place single-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).

void vDSP_fft2d_zop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStrideInRow,
vDSP_Stride __vDSP_signalStrideInCol,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResultInRow,
vDSP_Stride __vDSP_strideResultInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
signal
A complex vector signal input.
signalStrideInRow
Specifies a stride across each row of matrix a. Specifying 1 for signalStrideInRow processes every
element across each row, specifying 2 processes every other element across each row, and so forth.
signalStrideInCol
If not 0, this parameter represents the distance between each row of the input /output matrix.
result
The complex vector signal output.
strideResultInRow
Specifies a row stride for output matrix result in the same way that signalStrideInRow specifies
a stride for input the input /output matrix.
strideResultInCol
Specifies a column stride for output matrix result in the same way that signalStrideInCol
specifies a stride for input the input /output matrix.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 2 and 10,
inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.

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Discussion
This performs the following operation:

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zopD
Computes an out-of-place double-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse).

void vDSP_fft2d_zopD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStrideInRow,
vDSP_Stride __vDSP_signalStrideInCol,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResultInRow,
vDSP_Stride __vDSP_strideResultInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
signal
A complex vector signal input.
signalStrideInRow
Specifies a stride across each row of matrix a. Specifying 1 for signalStrideInRow processes every
element across each row, specifying 2 processes every other element across each row, and so forth.
signalStrideInCol
If not 0, this parameter represents the distance between each row of the input /output matrix.
result
The complex vector signal output.

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strideResultInRow
Specifies a row stride for output matrix result in the same way that signalStrideInRow specifies
a stride for input the input /output matrix.
strideResultInCol
Specifies a column stride for output matrix result in the same way that signalStrideInCol
specifies a stride for input the input /output matrix.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 2 and 10,
inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zopt
Computes an out-of-place single-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used
for intermediate results.

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void vDSP_fft2d_zopt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStrideInRow,
vDSP_Stride __vDSP_signalStrideInCol,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResultInRow,
vDSP_Stride __vDSP_strideResultInCol,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
signal
A complex vector signal input.
signalStrideInRow
Specifies a stride across each row of matrix a. Specifying 1 for signalStrideInRow processes every
element across each row, specifying 2 processes every other element across each row, and so forth.
signalStrideInCol
If not 0, this parameter represents the distance between each row of the input /output matrix. If
parameter signalStrideInCol is 1024, for instance, element 512 equates to element (1,0) of matrix a,
element 1024 equates to element (2,0), and so forth.
result
The complex vector signal output.
strideResultInRow
Specifies a row stride for output matrix result in the same way that signalStrideInRow specifies
a stride for input the input /output matrix.
strideResultInCol
Specifies a column stride for output matrix result in the same way that signalStrideInCol
specifies a stride for input the input /output matrix.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 16 KiB or 4*n, where log2n = log2nInCol + log2nInRow.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 2 and 10,
inclusive.

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flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zoptD
Computes an out-of-place double-precision complex discrete FFT, either from the spatial domain to the
frequency domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used
for intermediate results.

void vDSP_fft2d_zoptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStrideInRow,
vDSP_Stride __vDSP_signalStrideInCol,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResultInRow,
vDSP_Stride __vDSP_strideResultInCol,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the
transform function.
signal
A complex vector signal input.

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signalStrideInRow
Specifies a stride across each row of matrix a. Specifying 1 for signalStrideInRow processes every
element across each row, specifying 2 processes every other element across each row, and so forth.
signalStrideInCol
If not 0, this parameter represents the distance between each row of the input /output matrix. If
parameter signalStrideInCol is 1024, for instance, element 512 equates to element (1,0) of matrix a,
element 1024 equates to element (2,0), and so forth.
result
The complex vector signal output.
strideResultInRow
Specifies a row stride for output matrix result in the same way that signalStrideInRow specifies
a stride for input the input /output matrix.
strideResultInCol
Specifies a column stride for output matrix result in the same way that signalStrideInCol
specifies a stride for input the input /output matrix.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 16 KB or 4*n, where log2n = log2nInCol + log2nInRow.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 2 and 10,
inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft2d_zrip
Computes an in-place single-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).

void vDSP_fft2d_zrip (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the transform
function.
ioData
A complex vector input.
strideInRow
Specifies a stride across each row of the input matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, strideInCol represents the distance between each row of the matrix. If strideInCol is
1024, for instance, complex element 512 of the matrix equates to element (1,0), element 1024 equates
to element (2,0), and so forth.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 2 and 10,
inclusive.
direction
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of direction.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

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Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zripD
Computes an in-place double-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).

void vDSP_fft2d_zripD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the transform
function.
signal
A complex vector signal input.
strideInRow
Specifies a stride across each row of the input matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.

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strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, strideInCol represents the distance between each row of the matrix. If strideInCol is
1024, for instance, complex element 512 of the matrix equates to element (1,0), element 1024 equates
to element (2,0), and so forth.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
2 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 2 and 10,
inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

No Altivec/SSE support for double precision. The function always invokes scalar code.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft2d_zript
Computes an in-place single-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.

void vDSP_fft2d_zript (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the transform
function.
ioData
A complex vector input.
strideInRow
Specifies a stride across each row of the input matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, strideInCol represents the distance between each row of the matrix. If strideInCol is
1024, for instance, complex element 512 of the matrix equates to element (1,0), element 1024 equates
to element (2,0), and so forth.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory required is discussed
below.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
3 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 3 and 10,
inclusive.

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direction
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of direction.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

The space needed in bufferTemp is at most max(9*nr, nc/2) elements in each of realp and imagp. Here is
an example of how to allocate the space:

int nr, nc, tempSize;

nr = 1 << log2InRow;
nc = 1 << log2InCol;
tempSize = max(9*nr, nc/2);
bufferTemp.realp = (float *) malloc (tempSize * sizeOf(float) );
bufferTemp.imagp = (float *) malloc (tempSize * sizeOf(float) );

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zriptD
Computes an in-place double-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.

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void vDSP_fft2d_zriptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_strideInRow,
vDSP_Stride __vDSP_strideInCol,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the values supplied as parameters log2nInCol and log2nInRow of the transform
function.
signal
A complex vector signal input.
strideInRow
Specifies a stride across each row of the input matrix signal. Specifying 1 for strideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
strideInCol
Specifies a column stride for the matrix, and should generally be allowed to default unless the matrix
is a submatrix. Parameter strideInCol can be defaulted by specifying 0. The default column stride
equals the row stride multiplied by the column count. Thus, if strideInRow is 1 and strideInCol
is 0, every element of the input /output matrix is processed. If strideInRow is 2 and strideInCol
is 0, every other element of each row is processed.
If not 0, strideInCol represents the distance between each row of the matrix. If strideInCol is
1024, for instance, complex element 512 of the matrix equates to element (1,0), element 1024 equates
to element (2,0), and so forth.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory required is discussed
below.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
3 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 3 and 10,
inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

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Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

The space needed in bufferTemp is at most max(9*nr, nc/2) elements in each of realp and imagp. Here is
an example of how to allocate the space:

int nr, nc, tempSize;

nr = 1 << log2InRow;
nc = 1 << log2InCol;
tempSize = max(9*nr, nc/2);
bufferTemp.realp = (float *) malloc (tempSize * sizeOf(float) );
bufferTemp.imagp = (float *) malloc (tempSize * sizeOf(float) );

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zrop
Computes an out-of-place single-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).

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void vDSP_fft2d_zrop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStrideInRow,
vDSP_Stride __vDSP_signalStrideInCol,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResultInRow,
vDSP_Stride __vDSP_strideResultInCol,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n or log2m, whichever is larger, of the
transform function.
signal
A complex vector signal input.
signalStrideInRow
Specifies a stride across each row of matrix signal. Specifying 1 for signalStrideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
signalStrideInCol
If not 0, represents the distance between each row of the input /output matrix. If parameter
signalStrideInCol is 1024, for instance, element 512 equates to element (1,0) of matrix a, element 1024
equates to element (2,0), and so forth.
result
The complex vector signal output.
strideResultInRow
Specifies a row stride for output matrix c in the same way that signalStrideInRow specifies strides
for input the matrix.
strideResultInCol
Specifies a column stride for output matrix c in the same way that signalStrideInCol specify
strides for input the matrix.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
3 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 3 and 10,
inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.

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Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zropD
Computes an out-of-place double-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse).

void vDSP_fft2d_zropD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_Kr,
vDSP_Stride __vDSP_Kc,
DSPDoubleSplitComplex *__vDSP_ioData2,
vDSP_Stride __vDSP_Ir,
vDSP_Stride __vDSP_Ic,
vDSP_Length __vDSP_log2nc,
vDSP_Length __vDSP_log2nr,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n or log2m, whichever is larger, of the
transform function.
ioData
A complex vector input.
Kr
Specifies a stride across each row of matrix signal. Specifying 1 for Kr processes every element across
each row, specifying 2 processes every other element across each row, and so forth.
Kc
If not 0, represents the distance between each row of the input /output matrix. If parameter Kc is
1024, for instance, element 512 equates to element (1,0) of matrix a, element 1024 equates to element
(2,0), and so forth.
ioData2
The complex vector result.

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Ir
Specifies a row stride for output matrix ioData2 in the same way that Kr specifies strides for input
the matrix.
Ic
Specifies a column stride for output matrix ioData2 in the same way that Kc specify strides for input
matrix ioData.
log2nc
The base 2 exponent of the number of columns to process for each row. log2nc must be between
3 and 10, inclusive.
log2nr
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nc and 6 for log2nr. log2nr must be between 3 and 10, inclusive.
flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zropt
Computes an out-of-place single-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.

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void vDSP_fft2d_zropt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStrideInRow,
vDSP_Stride __vDSP_signalStrideInCol,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResultInRow,
vDSP_Stride __vDSP_strideResultInCol,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2nInCol,
vDSP_Length __vDSP_log2nInRow,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n or log2m, whichever is larger, of the
transform function.
signal
A complex vector signal input.
signalStrideInRow
Specifies a stride across each row of matrix signal. Specifying 1 for signalStrideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
signalStrideInCol
If not 0, represents the distance between each row of matrix signal. If parameter
signalStrideInCol is 1024, for instance, element 512 equates to element (1,0) of matrix signal,
element 1024 equates to element (2,0), and so forth.
result
The complex vector signal output.
strideResultInRow
Specifies a row stride for output matrix result in the same way that signalStrideInRow specifies
strides for input matrix result.
strideResultInCol
Specifies a column stride for output matrix c in the same way that signalStrideInCol specify
strides for input matrix result.
bufferTemp
A temporary matrix used for storing interim results. The size of temporary memory for each part (real
and imaginary) can be calculated using the algorithm shown below.
log2nInCol
The base 2 exponent of the number of columns to process for each row. log2nInCol must be between
3 and 10, inclusive.
log2nInRow
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nInCol and 6 for log2nInRow. log2nInRow must be between 3 and 10,
inclusive.

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flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
Here is the bufferTemp size algorithm:

int nr, nc, tempSize;

nr = 1 << log2InRow;
nc = 1 << log2InCol;
if (( (log2InCol-1) < 3 ) || (log2InRow > 9) {
tempSize = 9 * nr;
} else {
tempSize = 17 * nr
}
bufferTemp.realp = (float *) malloc (tempSize * sizeOf(float));
bufferTemp.imagp = (float *) malloc (tempSize * sizeOf(float));

Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft2d_zroptD
Computes an out-of-place double-precision real discrete FFT, either from the spatial domain to the frequency
domain (forward) or from the frequency domain to the spatial domain (inverse). A buffer is used for
intermediate results.

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void vDSP_fft2d_zroptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_Kr,
vDSP_Stride __vDSP_Kc,
DSPDoubleSplitComplex *__vDSP_ioData2,
vDSP_Stride __vDSP_Ir,
vDSP_Stride __vDSP_Ic,
DSPDoubleSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2nc,
vDSP_Length __vDSP_log2nr,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n or log2m, whichever is larger, of the
transform function.
ioData
A complex vector input.
Kr
Specifies a stride across each row of matrix signal. Specifying 1 for signalStrideInRow processes
every element across each row, specifying 2 processes every other element across each row, and so
forth.
Kc
If not 0, represents the distance between each row of the input /output matrix. If parameter
signalStrideInCol is 1024, for instance, element 512 equates to element (1,0) of matrix a, element 1024
equates to element (2,0), and so forth.
ioData2
The complex vector result.
Ir
Specifies a row stride for output matrix ioData2 in the same way that Kr specifies strides for input
the matrix.
Ic
Specifies a column stride for output matrix ioData2 in the same way that Kc specify strides for input
matrix ioData.
temp
A temporary matrix used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 16 KB or 4*n, where log2n = log2nInCol + log2nInRow.
log2nc
The base 2 exponent of the number of columns to process for each row. log2nc must be between
3 and 10, inclusive.
log2nr
The base 2 exponent of the number of rows to process. For example, to process 64 rows of 128
columns, specify 7 for log2nc and 6 for log2nr. log2nr must be between 3 and 10, inclusive.

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flag
A forward/inverse directional flag, and must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Results are undefined for other values of flag.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, spatial-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_FFT32_copv
Performs a 32-element FFT on interleaved complex data.

void vDSP_FFT32_copv (
float *__vDSP_Output,
const float *__vDSP_Input,
FFTDirection __vDSP_Direction
);

Parameters
__vDSP_Output
A vector-block-aligned output array.
__vDSP_Input
A vector-block-aligned input array.
__vDSP_Direction
kFFTDirection_Forward (page 552) or kFFTDirection_Inverse (page 552), indicating whether
to perform a forward or inverse transform.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_FFT32_zopv
Performs a 32-element FFT on split complex data.

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void vDSP_FFT32_zopv (
float *__vDSP_Or,
float *__vDSP_Oi,
const float *__vDSP_Ir,
const float *__vDSP_Ii,
FFTDirection __vDSP_Direction
);

Parameters
__vDSP_Or
Output vector for real parts.
__vDSP_Oi
Output vector for imaginary parts.
__vDSP_Ir
Input vector for real parts.
__vDSP_Ii
Input vector for imaginary parts.
__vDSP_Direction
kFFTDirection_Forward (page 552) or kFFTDirection_Inverse (page 552), indicating whether
to perform a forward or inverse transform.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft3_zop
Computes an out-of-place radix-3 complex Fourier transform, either forward or inverse. The number of input
and output values processed equals 3 times the power of 2 specified by parameter log2n; single precision.

void vDSP_fft3_zop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Use vDSP_create_fftsetup (page 195), to initialize this function. kFFTRadix3 (page 552) must be
specified in the call to vDSP_create_fftsetup. setup is preserved for reuse.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input vector signal. To process every element of the vector,
specify 1 for parameter signalStride; to process every other element, specify 2. The value of
signalStride should be 1 for best performance.

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result
The complex vector signal output.
resultStride
Specifies an address stride for the result. The value of resultStride should be 1 for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. log2n must be
between 3 and 15, inclusive.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Where N = 3 (2 m ) for Radix-3 functions, and N = 5 (2 m ) for Radix-5 functions

If F = 1 Cm = RDFT(A m ) 2 If F = -1 Cm = IDFT (A m ) N m = {0, N-1}

N 1 N 1
-1
FDFT(Xm) = ∑ Xn e ( -j2 π nm ) / N IDFT(Xm) =
N ∑ Xn e
( -j2 π nm ) / N

n=0 n=0

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft3_zopD
Computes an out-of-place radix-3 complex Fourier transform, either forward or inverse. The number of input
and output values processed equals 3 times the power of 2 specified by parameter log2n; double precision.

void vDSP_fft3_zopD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_K,
DSPDoubleSplitComplex *__vDSP_ioData2,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Use vDSP_create_fftsetupD (page 196), to initialize this function. kFFTRadix3 (page 552) must
be specified in the call to vDSP_create_fftsetupD. setup is preserved for reuse.

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signal
A complex vector input.
K
Specifies an address stride through the input vector signal. To process every element of the vector,
specify 1 for parameter K; to process every other element, specify 2. The value of K should be 1 for
best performance.
result
The complex vector result.
L
Specifies an address stride for the result. The value of L should be 1 for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. log2n must be
between 3 and 15, inclusive.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Where N = 3 (2 m ) for Radix-3 functions, and N = 5 (2 m ) for Radix-5 functions

If F = 1 Cm = RDFT(A m ) 2 If F = -1 Cm = IDFT (A m ) N m = {0, N-1}

N 1 N 1
-1
FDFT(Xm) = ∑ Xn e ( -j2 π nm ) / N IDFT(Xm) =
N ∑ Xn e
( -j2 π nm ) / N

n=0 n=0

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft5_zop
Computes an out-of-place radix-5 complex Fourier transform, either forward or inverse. The number of input
and output values processed equals 5 times the power of 2 specified by parameter log2n; single precision.

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void vDSP_fft5_zop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Use vDSP_create_fftsetup (page 195), to initialize this function. kFFTRadix5 (page 553) must be
specified in the call to vDSP_create_fftsetup. setup is preserved for reuse.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input vector signal. To process every element of the vector,
specify 1 for parameter signalStride; to process every other element, specify 2. The value of
signalStride should be 1 for best performance.
result
The complex vector signal output.
resultStride
Specifies an address stride for the result. The value of resultStride should be 1 for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. log2n must be
between 3 and 15, inclusive.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Where N = 3 (2 m ) for Radix-3 functions, and N = 5 (2 m ) for Radix-5 functions

If F = 1 Cm = RDFT(A m ) 2 If F = -1 Cm = IDFT (A m ) N m = {0, N-1}

N 1 N 1
-1
FDFT(Xm) = ∑ Xn e ( -j2 π nm ) / N IDFT(Xm) =
N ∑ Xn e
( -j2 π nm ) / N

n=0 n=0

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft5_zopD
Computes an out-of-place radix-5 complex Fourier transform, either forward or inverse. The number of input
and output values processed equals 5 times the power of 2 specified by parameter log2n; double precision.

void vDSP_fft5_zopD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_K,
DSPDoubleSplitComplex *__vDSP_ioData2,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Use vDSP_create_fftsetupD (page 196), to initialize this function. kFFTRadix5 (page 553) must
be specified in the call to vDSP_create_fftsetupD. setup is preserved for reuse.
signal
A complex vector input.
K
Specifies an address stride through the input vector signal. To process every element of the vector,
specify 1 for parameter K; to process every other element, specify 2.
result
The complex vector result.
L
Specifies an address stride for the result.
log2n
The base 2 exponent of the number of elements to process in a single input signal.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Where N = 3 (2 m ) for Radix-3 functions, and N = 5 (2 m ) for Radix-5 functions

If F = 1 Cm = RDFT(A m ) 2 If F = -1 Cm = IDFT (A m ) N m = {0, N-1}

N 1 N 1
-1
FDFT(Xm) = ∑ Xn e ( -j2 π nm ) / N IDFT(Xm) =
N ∑ Xn e
( -j2 π nm ) / N

n=0 n=0

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_fftm_zip
Performs the same operation as vDSP_fft_zip (page 270) on multiple signals with a single call.

void vDSP_fftm_zip (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n.
numFFT
The number of signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This function allows you to perform Discrete Fourier Transforms on multiple input signals using a single call.
They will work for input signals of 4 points or greater. Each of the input signals processed by a given call
must have the same length and address stride.

The functions compute in-place complex discrete Fourier transforms of the input signals, either from the
time domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zipD
Performs the same operation as vDSP_fft_zipD (page 271) on multiple signals with a single call.

void vDSP_fftm_zipD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n. The value of log2n must be between 2 and
12, inclusive.
numFFT
The number of signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This function allows you to perform Discrete Fourier Transforms on multiple signals at once, using a single
call. It will work for input signals of 4 points or greater. Each of the input signals processed by a given call
must have the same length and address stride.

The function computes in-place complex discrete Fourier transforms of the input signals, either from the
time domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

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See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zipt
Performs the same operation as vDSP_fft_zipt (page 272) on multiple signals with a single call.

void vDSP_fftm_zipt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2. The value of signalStride should
be 1 for best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n. The value of log2n must be between 2 and
12, inclusive.
numFFT
The number of different input signals.

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flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The function allows you to perform Fourier transforms on a number of different input signals at once, using
a single call. It can be used for efficient processing of small input signals (less than 512 points). It will work
for input signals of 4 points or greater. Each of the input signals processed by a given call must have the
same length and address stride. The input signals are concatenated into a single input/output vector, the
parameter signal.

The function computes in-place complex discrete Fourier transforms of the input signals, either from the
time domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_ziptD
Performs the same operation as vDSP_fft_ziptD (page 273) on multiple signals with a single call.

void vDSP_fftm_ziptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPDoubleSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2. The value of signalStride should
be 1 for best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).

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temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n. The value of log2n must be between 2 and
12, inclusive.
numFFT
The number of different input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The function allows you to perform Fourier transforms on a number of different input signals at once, using
a single call. It can be used for efficient processing of small input signals (less than 512 points). It will work
for input signals of 4 points or greater. Each of the input signals processed by a given call must have the
same length and address stride. The input signals are concatenated into a single input/output vector, the
parameter signal.

The function computes in-place complex discrete Fourier transforms of the input signals, either from the
time domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zop
Performs the same operation as vDSP_fft_zop (page 274) on multiple signals with a single call.

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void vDSP_fftm_zop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input signal.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2. The value of signalStride should
be 1 for best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of resultStride should be 1 for
best performance.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n.
numFFT
The number of input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.

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Discussion
The function allows you to perform Discrete Fourier transforms on a number of different input signals at
once, using a single call. It can be used for efficient processing of small input signals (less than 512 points).
It will work for input signals of 4 points or greater. Each of the input signals processed by a given call must
have the same length and address stride. The input signals are concatenated into a single input vector,
signal, and single output vector, result.

The function computes out-of-place complex discrete Fourier transforms of the input signals, either from
the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zopD
Performs the same operation as vDSP_fft_zopD (page 276) on multiple signals with a single call.

void vDSP_fftm_zopD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195) or vDSP_create_fftsetupD (page 196). The value supplied
as parameter log2n of the earlier call to the setup function must equal or exceed the value supplied
as parameter log2n of this transform function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2. The value of signalStride should
be 1 for best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).

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result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of resultStride should be 1 for
best performance.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n. The value of log2n must be between 2 and
12, inclusive.
numFFT
The number of different input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The function allows you to perform Fourier transforms on a number of different input signals at once, using
a single call. It can be used for efficient processing of small input signals (less than 512 points). It will work
for input signals of 4 points or greater. Each of the input signals processed by a given call must have the
same length and address stride. The input signals are concatenated into a single input/output vector, the
parameter signal.

The function computes out-of-place complex discrete Fourier transforms of the input signals, either from
the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zopt
Performs the same operation as vDSP_fft_zopt (page 277) on multiple signals with a single call.

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void vDSP_fftm_zopt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
DSPSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2. The value of signalStride should
be 1 for best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of resultStride should be 1 for
best performance.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n. The value of log2n must be between 2 and
12, inclusive.
numFFT
The number of different input signals.

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flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The function allows you to perform Fourier transforms on a number of different input signals at once, using
a single call. It can be used for efficient processing of small input signals (less than 512 points). It will work
for input signals of 4 points or greater. Each of the input signals processed by a given call must have the
same length and address stride. The input signals are concatenated into a single input/output vector, the
parameter signal.

The function computes out-of-place complex discrete Fourier transforms of the input signals, either from
the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zoptD
Performs the same operation as vDSP_fft_zoptD (page 278) on multiple signals with a single call.

void vDSP_fftm_zoptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
DSPDoubleSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2. The value of signalStride should
be 1 for best performance.

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fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n. The value of log2n must be between 2 and
12, inclusive.
numFFT
The number of different input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The function allows you to perform Fourier transforms on a number of different input signals at once, using
a single call. It can be used for efficient processing of small input signals (less than 512 points). It will work
for input signals of 4 points or greater. Each of the input signals processed by a given call must have the
same length and address stride. The input signals are concatenated into a single input/output vector, the
parameter signal.

The function computes out-of-place complex discrete Fourier transforms of the input signals, either from
the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zrip
Performs the same operation as vDSP_fft_zrip (page 279) on multiple signals with a single call.

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void vDSP_fftm_zrip (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n.
numFFT
The number of input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The function allows you to perform Discrete Fourier Transforms on multiple signals using a single call. They
will work for input signals of 4 points or greater. Each of the input signals processed by a given call must
have the same length and address stride.

The functions compute in-place real Discrete Fourier Transforms of the input signals, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fftm_zripD
Performs the same operation as vDSP_fft_zripD (page 281) on multiple signals with a single call.

void vDSP_fftm_zripD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n.
numFFT
The number of input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The functions allow you to perform Fourier transforms on a number of different input signals at once, using
a single call. They can be used for efficient processing of small input signals (less than 512 points). They will
work for input signals of 4 points or greater. Each of the input signals processed by a given call must have
the same length and address stride.

The functions compute in-place real discrete Fourier transforms of the input signals, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_fftm_zript
Performs the same operation as vDSP_fft_zript (page 282) on multiple signals with a single call.

void vDSP_fftm_zript (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n.
numFFT
The number of different input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The functions allow you to perform Fourier transforms on a number of different input signals at once, using
a single call. They can be used for efficient processing of small input signals (less than 512 points). They will
work for input signals of 4 points or greater. Each of the input signals processed by a given call must have
the same length and address stride.

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The functions compute in-place real Discrete Fourier Transforms of the input signals, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zriptD
Performs the same operation as vDSP_fft_zriptD (page 283) on multiple signals with a single call.

void vDSP_fftm_zriptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPDoubleSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through the input signals. To process every element of each signal, specify
1 for parameter signalStride; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process in a single input signal. For example, to
process 512 elements, specify 9 for parameter log2n.
numFFT
The number of input signals.

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flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The functions allow you to perform Fourier transforms on a number of different input signals at once, using
a single call. They can be used for efficient processing of small input signals (less than 512 points). They will
work for input signals of 4 points or greater. Each of the input signals processed by a given call must have
the same length and address stride.

The functions compute in-place real Discrete Fourier Transforms of the input signals, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zrop
Performs the same operation as vDSP_fft_zrop (page 284) on multiple signals with a single call.

void vDSP_fftm_zrop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input signals. To process every element of each signal, specify a
stride of 1; to process every other element, specify 2.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).

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result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
numFFT
The number of input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This function allows you to perform Discrete Fourier Transforms on multiple input signals using a single call.
They can be used for efficient processing of small input signals (less than 512 points). They will work for input
signals of 4 points or greater. Each of the input signals processed by a given call must have the same length
and address stride. The input signals are concatenated into a single input vector, signal, and a single output
vector, result.

The functions compute out-of-place real Discrete Fourier Transforms of the input signals, either from the
time domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zropD
Performs the same operation as VDSP_fft_zropD on multiple signals with a single call.

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void vDSP_fftm_zropD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input signals. To process every element of each signal, specify a
stride of 1; to process every other element, specify 2. The value of signalStride should be 1 for
best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of resultStride should be 1 for
best performance.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
numFFT
The number of input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This function allows you to perform Discrete Fourier Transforms on multiple input signals using a single call.
They can be used for efficient processing of small input signals (less than 512 points). They will work for input
signals of 4 points or greater. Each of the input signals processed by a given call must have the same length
and address stride. The input signals are concatenated into a single input vector, the parameter signal.

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The functions compute out-of-place real Discrete Fourier Transforms of the input signals, either from the
time domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zropt
Performs the same operation as VDSP_fft_zropt on multiple signals with a single call.

void vDSP_fftm_zropt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
DSPSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input signals. To process every element of each signal, specify a
stride of 1; to process every other element, specify 2. The value of signalStride should be 1 for
best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of resultStride should be 1 for
best performance.

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rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
numFFT
The number of input signals.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The functions allow you to perform Fourier transforms on a number of different input signals at once, using
a single call. They can be used for efficient processing of small input signals (less than 512 points). They will
work for input signals of 4 points or greater. Each of the input signals processed by a given call must have
the same length and address stride. The input signals are concatenated into a single input vector, the
parameter signal.

The functions compute out-of-place real discrete Fourier transforms of the input signals, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetup (page 195), vDSP_destroy_fftsetup (page 201), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fftm_zroptD
Performs the same operation as VDSP_fft_zroptD on multiple signals with a single call.

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void vDSP_fftm_zroptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
vDSP_Stride __vDSP_fftStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_resultStride,
vDSP_Stride __vDSP_rfftStride,
DSPDoubleSplitComplex *__vDSP_temp,
vDSP_Length __vDSP_log2n,
vDSP_Length __vDSP_numFFT,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input signals. To process every element of each signal, specify a
stride of 1; to process every other element, specify 2. The value of signalStride should be 1 for
best performance.
fftStride
The number of elements between the first element of one input signal and the first element of the
next (which is also to length of each input signal, measured in elements).
result
The complex vector signal output.
resultStride
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of resultStride should be 1 for
best performance.
rfftStride
The number of elements between the first element of one result vector and the next in the output
vector result.
temp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, temp.realp and temp.imagp
should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
numFFT
The number of different input signals.

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flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
The functions allow you to perform Fourier transforms on a number of different input signals at once, using
a single call. They can be used for efficient processing of small input signals (less than 512 points). They will
work for input signals of 4 points or greater. Each of the input signals processed by a given call must have
the same length and address stride. The input signals are concatenated into a single input vector, the
parameter signal.

The functions compute out-of-place real discrete Fourier transforms of the input signals, either from the time
domain to the frequency domain (forward) or from the frequency domain to the time domain (inverse).

See also functions vDSP_create_fftsetupD (page 196), vDSP_destroy_fftsetupD (page 202), and “Using Fourier
Transforms”.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zip
Computes an in-place single-precision complex discrete Fourier transform of the input/output vector signal,
either from the time domain to the frequency domain (forward) or from the frequency domain to the time
domain (inverse).

void vDSP_fft_zip (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
stride
Specifies an address stride through the input/output vector signal. To process every element of the
vector, specify 1 for parameter stride; to process every other element, specify 2.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.

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direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zipD
Computes an in-place double-precision complex discrete Fourier transform of the input/output vector signal,
either from the time domain to the frequency domain (forward) or from the frequency domain to the time
domain (inverse).

void vDSP_fft_zipD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
stride
Specifies an address stride through the input/output vector signal. To process every element of the
vector, specify 1 for parameter stride; to process every other element, specify 2. The value of stride
should be 1 for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.

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direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zipt
Computes an in-place single-precision complex discrete Fourier transform of the input/output vector signal,
either from the time domain to the frequency domain (forward) or from the frequency domain to the time
domain (inverse). A buffer is used for intermediate results.

void vDSP_fft_zipt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.
signal
A complex vector that stores the input and output signal.
stride
Specifies an address stride through the input/output vector signal. To process every element of the
vector, specify 1 for parameter stride; to process every other element, specify 2.

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bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, bufferTemp.realp and
bufferTemp.imagp should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_ziptD
Computes an in-place double-precision complex discrete Fourier transform of the input/output vector signal,
either from the time domain to the frequency domain (forward) or from the frequency domain to the time
domain (inverse). A buffer is used for intermediate results.

void vDSP_fft_ziptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the earlier call to
the setup function must equal or exceed the value supplied as parameter log2n of this transform
function.

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signal
A complex vector that stores the input and output signal.
stride
Specifies an address stride through the input/output vector signal. To process every element of the
vector, specify 1 for parameter stride; to process every other element, specify 2.
bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, bufferTemp.realp and
bufferTemp.imagp should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zop
Computes an out-of-place single-precision complex discrete Fourier transform of the input vector, either
from the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

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void vDSP_fft_zop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector that stores the input and output signal.
signalStride
Specifies an address stride through input vector signal. Parameter strideResult specifies an address
stride through output vector result. Thus, to process every element, specify a signalStride of 1; to
process every other element, specify 2.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft_zopD
Computes an out-of-place double-precision complex discrete Fourier transform of the input vector, either
from the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

void vDSP_fft_zopD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195) or vDSP_create_fftsetupD (page 196). The value supplied
as parameter log2n of the setup function must equal or exceed the value supplied as parameter
log2n of this transform function.
signal
A complex vector that stores the input signal.
signalStride
Specifies an address stride through input vector signal. Parameter strideResult specifies an address
stride through output vector result. Thus, to process every element, specify a signalStride of 1; to
process every other element, specify 2. The values of signalStride and strideResult should be
1 for best performance.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of strideResult should be 1 for
best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

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See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zopt
Computes an out-of-place single-precision complex discrete Fourier transform of the input vector, either
from the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

void vDSP_fft_zopt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector that stores the input and output signal.
signalStride
Specifies an address stride through input vector signal. Parameter strideResult specifies an address
stride through output vector result. Thus, to process every element, specify a signalStride of 1; to
process every other element, specify 2. The values of signalStride and strideResult should be 1
for best performance.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2.
bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k. Or you can simply pass the buffer of size 2^(log2n)
for each part (real and imaginary). If possible, tempBuffer.realp and tempBuffer.imagp should be
32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.

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direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zoptD
Computes an out-of-place double-precision complex discrete Fourier transform of the input vector, either
from the time domain to the frequency domain (forward) or from the frequency domain to the time domain
(inverse).

void vDSP_fft_zoptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input vector signal. Parameter strideResult specifies an address
stride through output vector result. Thus, to process every element, specify a signalStride of 1; to
process every other element, specify 2. The values of signalStride and strideResult should be 1
for best performance.

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result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2.
bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k. Or you can simply pass the buffer of size 2^(log2n)
for each part (real and imaginary). If possible, tempBuffer.realp and tempBuffer.imagp should be
32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zrip
Computes an in-place single-precision real discrete Fourier transform, either from the time domain to the
frequency domain (forward) or from the frequency domain to the time domain (inverse).

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void vDSP_fft_zrip (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
C
A complex input/output vector.
K
Specifies an address stride through the input/output vector. To process every element of the vector,
specify 1 for parameter signalStride; to process every other element, specify 2.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
F
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
Forward transforms read real input and write packed complex output. You can find more details on the
packing format in vDSP Programming Guide. Inverse transforms read packed complex input and write real
output. As a result of packing the frequency-domain data, time-domain data and its equivalent
frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft_zripD
Computes an in-place double-precision real discrete Fourier transform, either from the time domain to the
frequency domain (forward) or from the frequency domain to the time domain (inverse).

void vDSP_fft_zripD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
C
A complex vector input.
K
Specifies an address stride through the input/output vector. To process every element of the vector,
specify 1 for parameter stride; to process every other element, specify 2.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
F
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, time-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_fft_zript
Computes an in-place single-precision real discrete Fourier transform, either from the time domain to the
frequency domain (forward) or from the frequency domain to the time domain (inverse).

void vDSP_fft_zript (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
C
A complex vector input.
K
Specifies an address stride through the input/output vector. To process every element of the vector,
specify 1 for parameter signalStride; to process every other element, specify 2.
bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, tempBuffer.realp and
tempBuffer.imagp should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
F
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, time-domain data and its
equivalent frequency-domain data have the same storage requirements.

Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zriptD
Computes an in-place double-precision real discrete Fourier transform, either from the time domain to the
frequency domain (forward) or from the frequency domain to the time domain (inverse).

void vDSP_fft_zriptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_ioData,
vDSP_Stride __vDSP_stride,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
C
A complex vector input.
K
Specifies an address stride through the input/output vector. To process every element of the vector,
specify 1 for parameter signalStride; to process every other element, specify 2.
bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, tempBuffer.realp and
tempBuffer.imagp should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
F
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, time-domain data and its
equivalent frequency-domain data have the same storage requirements.

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Real data is stored in split complex form, with odd reals stored on the imaginary side of the split complex
form and even reals in stored on the real side.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zrop
Computes an out-of-place single-precision real discrete Fourier transform, either from the time domain to
the frequency domain (forward) or from the frequency domain to the time domain (inverse).

void vDSP_fft_zrop (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input vector signal. Thus, to process every element, specify a stride
of 1; to process every other element, specify 2. The value of signalStride should be 1 for best
performance.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2.

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log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Forward transforms read real input and write packed complex output (see vDSP Programming Guide for details
on the packing format). Inverse transforms read packed complex input and write real output. As a result of
packing the frequency-domain data, time-domain data and its equivalent frequency-domain data have the
same storage requirements.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zropD
Computes an out-of-place double-precision real discrete Fourier transform, either from the time domain to
the frequency domain (forward) or from the frequency domain to the time domain (inverse).

void vDSP_fft_zropD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector signal input.

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signalStride
Specifies an address stride through input vector signal. Thus, to process every element, specify a stride
of 1; to process every other element, specify 2. The value of signalStride should be 1 for best
performance.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of strideResult should be 1 for
best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, time-domain data and its
equivalent frequency-domain data have the same storage requirements. Real data is stored in split complex
form, with odd reals stored on the imaginary side of the split complex form and even reals in stored on the
real side.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zropt
Computes an out-of-place single-precision real discrete Fourier transform, either from the time domain to
the frequency domain (forward) or from the frequency domain to the time domain (inverse).

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void vDSP_fft_zropt (
FFTSetup __vDSP_setup,
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
DSPSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_direction
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetup (page 195). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input vector signal. Thus, to process every element, specify a stride
of 1; to process every other element, specify 2. The value of signalStride should be 1 for best
performance.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of strideResult should be 1 for
best performance.
bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, tempBuffer.realp and
tempBuffer.imagp should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
direction
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

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Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, time-domain data and its
equivalent frequency-domain data have the same storage requirements. Real data is stored in split complex
form, with odd reals stored on the imaginary side of the split complex form and even reals in stored on the
real side.

See also functions vDSP_create_fftsetup (page 195) and vDSP_destroy_fftsetup (page 201).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_fft_zroptD
Computes an out-of-place double-precision real discrete Fourier transform, either from the time domain to
the frequency domain (forward) or from the frequency domain to the time domain (inverse).

void vDSP_fft_zroptD (
FFTSetupD __vDSP_setup,
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
DSPDoubleSplitComplex *__vDSP_bufferTemp,
vDSP_Length __vDSP_log2n,
FFTDirection __vDSP_flag
);

Parameters
setup
Points to a structure initialized by a prior call to the FFT weights array function,
vDSP_create_fftsetupD (page 196). The value supplied as parameter log2n of the setup function
must equal or exceed the value supplied as parameter log2n of this transform function.
signal
A complex vector signal input.
signalStride
Specifies an address stride through input vector signal. Thus, to process every element, specify a stride
of 1; to process every other element, specify 2. The value of signalStride should be 1 for best
performance.
result
The complex vector signal output.
strideResult
Specifies an address stride through output vector result. Thus, to process every element, specify a
stride of 1; to process every other element, specify 2. The value of strideResult should be 1 for
best performance.

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bufferTemp
A temporary vector used for storing interim results. The size of temporary memory for each part (real
and imaginary) is the lower value of 4*n or 16k for best performance. Or you can simply pass the
buffer of size 2^(log2n) for each part (real and imaginary). If possible, tempBuffer.realp and
tempBuffer.imagp should be 32-byte aligned for best performance.
log2n
The base 2 exponent of the number of elements to process. For example, to process 1024 elements,
specify 10 for parameter log2n.
flag
A forward/inverse directional flag, which must specify kFFTDirection_Forward (page 552) for a
forward transform or kFFTDirection_Inverse (page 552) for an inverse transform.
Discussion
This performs the following operation:

Forward transforms read real input and write packed complex output. Inverse transforms read packed complex
input and write real output. As a result of packing the frequency-domain data, time-domain data and its
equivalent frequency-domain data have the same storage requirements. Real data is stored in split complex
form, with odd reals stored on the imaginary side of the split complex form and even reals in stored on the
real side.

See also functions vDSP_create_fftsetupD (page 196) and vDSP_destroy_fftsetupD (page 202).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_hamm_window
Creates a single-precision Hamming window.

void vDSP_hamm_window (
float *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_FLAG
);

Discussion

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vDSP_hamm_window creates a single-precision Hamming window function C, which can be multiplied by a

vector using vDSP_vmul (page 425). Specify the vDSP_HALF_WINDOW (page 553) flag to create only the first
(n+1)/2 points, or 0 (zero) for a full-size window.

See also vDSP_vmul (page 425).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_hamm_windowD
Creates a double-precision Hamming window.

void vDSP_hamm_windowD (
double *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_FLAG
);

Discussion

vDSP_hamm_windowD creates a double-precision Hamming window function C, which can be multiplied by

a vector using vDSP_vmulD (page 426). Specify the vDSP_HALF_WINDOW (page 553) flag to create only the
first (n+1)/2 points, or 0 (zero) for a full-size window.

See also vDSP_vmulD (page 426).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_hann_window
Creates a single-precision Hanning window.

void vDSP_hann_window (
float *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_FLAG
);

Discussion

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vDSP_hann_window creates a single-precision Hanning window function C, which can be multiplied by a

vector using vDSP_vmul (page 425).

The FLAG parameter can have the following values:

■ vDSP_HANN_DENORM (page 553) creates a denormalized window.

■ vDSP_HANN_NORM (page 553) creates a normalized window.

■ vDSP_HALF_WINDOW (page 553) creates only the first (N+1)/2 points.

vDSP_HALF_WINDOW can be ORed with any of the other values (i.e., using the C operator |).

See also vDSP_vmul (page 425).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_hann_windowD
Creates a double-precision Hanning window.

void vDSP_hann_windowD (
double *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_FLAG
);

Discussion

vDSP_hann_window creates a double-precision Hanning window function C, which can be multiplied by a

vector using vDSP_vmulD (page 426).

The FLAG parameter can have the following values:

■ vDSP_HANN_DENORM (page 553) creates a denormalized window.

■ vDSP_HANN_NORM (page 553) creates a normalized window.

■ vDSP_HALF_WINDOW (page 553) creates only the first (N+1)/2 points.

vDSP_HALF_WINDOW can ORed with any of the other values (i.e., using the C operator |).

See also vDSP_vmulD (page 426).

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_imgfir
Filters an image by performing a two-dimensional convolution with a kernel; single precision.

void vDSP_imgfir (
float *__vDSP_signal,
vDSP_Length __vDSP_numRow,
vDSP_Length __vDSP_numCol,
float *__vDSP_filter,
float *__vDSP_result,
vDSP_Length __vDSP_fnumRow,
vDSP_Length __vDSP_fnumCol
);

Parameters
A
A real matrix signal input.
M
Number of rows in A.
N
Number of columns in A.
B
A two-dimensional real matrix containing the filter.
C
Stores real output matrix.
P
Number of rows in B.
Q
Number of columns in B.
Discussion
The image is given by the input matrix A. It has M rows and N columns.

B is the filter kernel. It has P rows and Q columns.

Ensure Q >= P for best performance.

The filtered image is placed in the output matrix C. The function pads the perimeter of the output image
with a border of (P-1)/2 rows of zeros on the top and bottom and (Q-1)/2 columns of zeros on the left and
right.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_imgfirD
Filters an image by performing a two-dimensional convolution with a kernel; double precision.

void vDSP_imgfirD (
double *__vDSP_signal,
vDSP_Length __vDSP_numRow,
vDSP_Length __vDSP_numCol,
double *__vDSP_filter,
double *__vDSP_result,
vDSP_Length __vDSP_fnumRow,
vDSP_Length __vDSP_fnumCol
);

Parameters
A
A complex vector signal input.
M
Number of rows in input matrix.
N
Number of columns in input matrix.
B
A two-dimensional real matrix containing the filter.
C
Stores real output matrix.
P
Number of rows in B.
Q
Number of columns in B.
Discussion
The image is given by the input matrix A. It has M rows and N columns.

B is the filter kernel. It has P rows and Q columns. For best performance, ensure Q >= P.

The filtered image is placed in the output matrix C. The functions pad the perimeter of the output image
with a border of (P-1)/2 rows of zeros on the top and bottom and (Q-1)/2 columns of zeros on the left and
right.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_maxmgv
Vector maximum magnitude; single precision.

void vDSP_maxmgv (
const float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

*C = 0;
for (n = 0; n < N; ++n)
if (*C < abs(A[n*I]))
*C = abs(A[n*I]);

Finds the element with the greatest magnitude in vector A and copies this value to scalar *C.

If N is zero (0), this function returns a value of 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_maxmgvD
Vector maximum magnitude; double precision.

void vDSP_maxmgvD (
const double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.

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I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

*C = 0;
for (n = 0; n < N; ++n)
if (*C < abs(A[n*I]))
*C = abs(A[n*I]);

Finds the element with the greatest magnitude in vector A and copies this value to scalar *C.

If N is zero (0), this function returns a value of 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_maxmgvi
Vector maximum magnitude with index; single precision.

void vDSP_maxmgvi (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A.
C
Output scalar.
IC
Output scalar index.
N
Count of values in A.
Discussion
This performs the following operation:

*C = 0;

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for (n = 0; n < N; ++n)

{
if (*C < abs(A[n*I]))
{
*C = abs(A[n*I]);
*IC = n*I;
}
}

Copies the element with the greatest magnitude from real vector A to real scalar *C, and writes its zero-based
index to integer scalar *IC. The index is the actual array index, not the pre-stride index.If vector A contains
more than one instance of the maximum magnitude, *IC contains the index of the first instance.

If N is zero (0), this function returns a value of 0 in *C, and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_maxmgviD
Vector maximum magnitude with index; double precision.

void vDSP_maxmgviD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A
C
Output scalar
IC
Output scalar
N
Count
Discussion
This performs the following operation:

*C = 0;
for (n = 0; n < N; ++n)
{
if (*C < abs(A[n*I]))
{
*C = abs(A[n*I]);

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*IC = n*I;
}
}

Copies the element with the greatest magnitude from real vector A to real scalar *C, and writes its zero-based
index to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains
more than one instance of the maximum magnitude, *IC contains the index of the first instance.

If N is zero (0), this function returns a value of 0 in *C, and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_maxv
Vector maximum value; single precision.

void vDSP_maxv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

*C = -INFINITY;
for (n = 0; n < N; ++n)
if (*C < A[n*I])
*C = A[n*I];

Finds the element with the greatest value in vector A and copies this value to scalar *C. If N is zero (0), this
function returns -INFINITY in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_maxvD
Vector maximum value; double precision.

void vDSP_maxvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

*C = -INFINITY;
for (n = 0; n < N; ++n)
if (*C < A[n*I])
*C = A[n*I];

Finds the element with the greatest value in vector A and copies this value to scalar *C. If N is zero (0), this
function returns -INFINITY in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_maxvi
Vector maximum value with index; single precision.

void vDSP_maxvi (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.

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I
Stride for A
C
Output scalar
IC
Output scalar index
N
Count
Discussion
This performs the following operation:

*C = -INFINITY;
for (n = 0; n < N; ++n)
{
if (*C < A[n * I])
{
*C = A[n * I];
*IC = n * I;
}
}

Copies the element with the greatest value from real vector A to real scalar *C, and writes its zero-based
index to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains
more than one instance of the maximum value, *IC contains the index of the first instance. If N is zero (0),
this function returns a value of -INFINITY in *C and *IC is undetermined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_maxviD
Vector maximum value with index; double precision.

void vDSP_maxviD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar

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IC
Output scalar
N
Count
Discussion
This performs the following operation:

*C = -INFINITY;
for (n = 0; n < N; ++n)
{
if (*C < A[n * I])
{
*C = A[n * I];
*IC = n * I;
}
}

Copies the element with the greatest value from real vector A to real scalar *C, and writes its zero-based
index to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains
more than one instance of the maximum value, *IC contains the index of the first instance. If N is zero (0),
this function returns a value of -INFINITY in *C and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_meamgv
Vector mean magnitude; single precision.

void vDSP_meamgv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

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Finds the mean of the magnitudes of elements of vector A and stores this value in scalar *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_meamgvD
Vector mean magnitude; double precision.

void vDSP_meamgvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the mean of the magnitudes of elements of vector A and stores this value in scalar *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_meanv
Vector mean value; single precision.

void vDSP_meanv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the mean value of the elements of vector A and stores this value in scalar *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_meanvD
Vector mean value; double precision.

void vDSP_meanvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector

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I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the mean value of the elements of vector A and stores this value in scalar *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_measqv
Vector mean square value; single precision.

void vDSP_measqv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

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Finds the mean value of the squares of the elements of vector A and stores this value in scalar *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_measqvD
Vector mean square value; double precision.

void vDSP_measqvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the mean value of the squares of the elements of vector A and stores this value in scalar *C.

If N is zero (0), this function returns a NaN. in *C

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minmgv
Vector minimum magnitude; single precision.

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void vDSP_minmgv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the element with the least magnitude in vector A and copies this value to scalar *C.

If N is zero (0), this function returns +INF in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minmgvD
Vector minimum magnitude; double precision.

void vDSP_minmgvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar

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N
Count
Discussion
This performs the following operation:

Finds the element with the least magnitude in vector A and copies this value to scalar *C.

If N is zero (0), this function returns +INF in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minmgvi
Vector minimum magnitude with index; single precision.

void vDSP_minmgvi (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
IC
Output scalar index
N
Count
Discussion
This performs the following operation:

Copies the element with the least magnitude from real vector A to real scalar *C, and writes its zero-based
index to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains
more than one instance of the least magnitude, *IC contains the index of the first instance.

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If N is zero (0), this function returns a value of +INF in *C and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minmgviD
Vector minimum magnitude with index; double precision.

void vDSP_minmgviD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar
IC
Output scalar
N
Count
Discussion
This performs the following operation:

Copies the element with the least magnitude from real vector A to real scalar *C, and writes its zero-based
index to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains
more than one instance of the least magnitude, *IC contains the index of the first instance.

If N is zero (0), this function returns a value of +INF in *C and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_minv
Vector minimum value.

void vDSP_minv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the element with the least value in vector A and copies this value to scalar *C.

If N is zero (0), this function returns +INFINITY in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minvD
Vector minimum value; double precision.

void vDSP_minvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A

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C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the element with the least value in vector A and copies this value to scalar *C.

If N is zero (0), this function returns +INF in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minvi
Vector minimum value with index; single precision.

void vDSP_minvi (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
IC
Output scalar index
N
Count
Discussion
This performs the following operation:

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Copies the element with the least value from real vector A to real scalar *C, and writes its zero-based index
to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains more
than one instance of the least value, *IC contains the index of the first instance.

If N is zero (0), this function returns a value of +INF in *C, and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_minviD
Vector minimum value with index; double precision.

void vDSP_minviD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A
C
Output scalar
IC
Output scalar
N
Count
Discussion
This performs the following operation:

Copies the element with the least value from real vector A to real scalar *C, and writes its zero-based index
to integer scalar *IC. The index is the actual array index, not the pre-stride index. If vector A contains more
than one instance of the least value, *IC contains the index of the first instance.

If N is zero (0), this function returns a value of +INF in *C, and the value in *IC is undefined.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_mmov
Copies the contents of a submatrix to another submatrix.

void vDSP_mmov (
float *__vDSP_A,
float *__vDSP_C,
vDSP_Length __vDSP_NC,
vDSP_Length __vDSP_NR,
vDSP_Length __vDSP_TCA,
vDSP_Length __vDSP_TCC
);

Parameters
A
Single-precision real input submatrix
C
Single-precision real output submatrix
NC
Number of columns in A and C
NR
Number of rows in A and C
TCA
Number of columns in the matrix of which A is a submatrix
TCC
Number of columns in the matrix of which C is a submatrix
Discussion

The matrices are assumed to be stored in row-major order. Thus elements A[i][j] and A[i][j+1] are
adjacent. Elements A[i][j] and A[i+1][j] are TCA elements apart.

This function may be used to move a subarray beginning at any point in a larger embedding array by passing
for A the address of the first element of the subarray. For example, to move a subarray starting at A[3][4],
pass &A[3][4]. Similarly, the address of the first destination element is passed for C

NC may equal TCA, and it may equal TCC. To copy all of an array to all of another array, pass the number of
rows in NR and the number of columns in NC, TCA, and TCC.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_mmovD
Copies the contents of a submatrix to another submatrix.

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void vDSP_mmovD (
double *__vDSP_A,
double *__vDSP_C,
vDSP_Length __vDSP_NC,
vDSP_Length __vDSP_NR,
vDSP_Length __vDSP_TCA,
vDSP_Length __vDSP_TCC
);

Parameters
A
Double-precision real input submatrix
C
Double-precision real output submatrix
NC
Number of columns in A and C
NR
Number of rows in A and C
TCA
Number of columns in the matrix of which A is a submatrix
TCC
Number of columns in the matrix of which C is a submatrix
Discussion

The matrices are assumed to be stored in row-major order. Thus elements A[i][j] and A[i][j+1] are
adjacent. Elements A[i][j] and A[i+1][j] are TCA elements apart.

This function may be used to move a subarray beginning at any point in a larger embedding array by passing
for A the address of the first element of the subarray. For example, to move a subarray starting at A[3][4],
pass &A[3][4]. Similarly, the address of the first destination element is passed for C

NC may equal TCA, and it may equal TCC. To copy all of an array to all of another array, pass the number of
rows in NR and the number of columns in NC, TCA, and TCC.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_mmul
Performs an out-of-place multiplication of two matrices; single precision.

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void vDSP_mmul (
float *__vDSP_a,
vDSP_Stride __vDSP_aStride,
float *__vDSP_b,
vDSP_Stride __vDSP_bStride,
float *__vDSP_c,
vDSP_Stride __vDSP_cStride,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function multiplies an M-by-P matrix (A) by a P-by-N matrix (B) and stores the results in an M-by-N matrix
(C).

This performs the following operation:

Parameters A and B are the matrixes to be multiplied. I is an address stride through A. J is an address stride
through B.

Parameter C is the result matrix. K is an address stride through C.

Parameter M is the row count for both A and C. Parameter N is the column count for both B and C. Parameter
P is the column count for A and the row count for B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_mmulD
Performs an out-of-place multiplication of two matrices; double precision.

void vDSP_mmulD (
double *__vDSP_a,
vDSP_Stride __vDSP_aStride,
double *__vDSP_b,
vDSP_Stride __vDSP_bStride,
double *__vDSP_c,
vDSP_Stride __vDSP_cStride,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function multiplies an M-by-P matrix (A) by a P-by-N matrix (B) and stores the results in an M-by-N matrix
(C).

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This performs the following operation:

Parameters A and B are the matrixes to be multiplied. I is an address stride through A. J is an address stride
through B.

Parameter C is the result matrix. K is an address stride through C.

Parameter M is the row count for both A and C. Parameter N is the column count for both B and C. Parameter
P is the column count for A and the row count for B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_mtrans
Creates a transposed matrix C from a source matrix A; single precision.

void vDSP_mtrans (
float *__vDSP_a,
vDSP_Stride __vDSP_aStride,
float *__vDSP_c,
vDSP_Stride __vDSP_cStride,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N
);

Discussion
This performs the following operation:

Parameter A is the source matrix. I is an address stride through the source matrix.

Parameter C is the resulting transposed matrix. K is an address stride through the result matrix.

Parameter M is the number of rows in C (and the number of columns in A).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_mtransD
Creates a transposed matrix C from a source matrix A; double precision.

void vDSP_mtransD (
double *__vDSP_a,
vDSP_Stride __vDSP_aStride,
double *__vDSP_c,
vDSP_Stride __vDSP_cStride,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N
);

Discussion
This performs the following operation:

Parameter A is the source matrix. I is an address stride through the source matrix.

Parameter C is the resulting transposed matrix. K is an address stride through the result matrix.

Parameter M is the number of rows in C (and the number of columns in A).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_mvessq
Vector mean of signed squares; single precision.

void vDSP_mvessq (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

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Finds the mean value of the signed squares of the elements of vector A and stores this value in *C. If N is zero
(0), this function returns a NaN in *C. .

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_mvessqD
Vector mean of signed squares; double precision.

void vDSP_mvessqD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Output scalar
N
Count
Discussion
This performs the following operation:

Finds the mean value of the signed squares of the elements of vector A and stores this value in *C. If N is zero
(0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_nzcros
Find zero crossings; single precision.

void vDSP_nzcros (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
vDSP_Length __vDSP_B,
vDSP_Length *__vDSP_C,
vDSP_Length *__vDSP_D,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Maximum number of crossings to find
C
Index of last crossing found
D
Total number of zero crossings found
N
Count of elements in A
Discussion
This performs the following operation:

The "function" sign(x) above has the value -1 if the sign bit of x is 1 (x is negative or -0), and +1 if the sign bit
is 0 (x is positive or +0).

Scans vector A to locate transitions from positive to negative values and from negative to positive values.
The scan terminates when the number of crossings specified by B is found, or the end of the vector is reached.
The zero-based index of the last crossing is returned in C. C is the actual array index, not the pre-stride index.
If the zero crossing that B specifies is not found, zero is returned in C. The total number of zero crossings
found is returned in D.

Note that a transition from -0 to +0 or from +0 to -0 is counted as a zero crossing.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_nzcrosD
Find zero crossings; double precision.

void vDSP_nzcrosD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
vDSP_Length __vDSP_B,
vDSP_Length *__vDSP_C,
vDSP_Length *__vDSP_D,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Maximum number of crossings to find
C
Index of last crossing found
D
Total number of zero crossings found
N
Count of elements in A
Discussion
This performs the following operation:

The "function" sign(x) above has the value -1 if the sign bit of x is 1 (x is negative or -0), and +1 if the sign bit
is 0 (x is positive or +0).

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Scans vector A to locate transitions from positive to negative values and from negative to positive values.
The scan terminates when the number of crossings specified by B is found, or the end of the vector is reached.
The zero-based index of the last crossing is returned in C. C is the actual array index, not the pre-stride index.
If the zero crossing that B specifies is not found, zero is returned in C. The total number of zero crossings
found is returned in D.

Note that a transition from -0 to +0 or from +0 to -0 is counted as a zero crossing.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_polar
Rectangular to polar conversion; single precision.

void vDSP_polar (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A, must be even
C
Single-precision output vector
K
Stride for C, must be even
N
Number of ordered pairs processed
Discussion
This performs the following operation:

Converts rectangular coordinates to polar coordinates. Cartesian (x,y) pairs are read from vector A. Polar (rho,
theta) pairs, where rho is the radius and theta is the angle in the range [-pi, pi] are written to vector C. N
specifies the number of coordinate pairs in A and C.

Coordinate pairs are adjacent elements in the array, regardless of stride; stride is the distance from one
coordinate pair to the next.

This function performs the inverse operation of vDSP_rect, which converts polar to rectangular coordinates.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_polarD
Rectangular to polar conversion; double precision.

void vDSP_polarD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A, must be even
C
Double-precision output vector
K
Stride for C, must be even
N
Number of ordered pairs processed
Discussion
This performs the following operation:

Converts rectangular coordinates to polar coordinates. Cartesian (x,y) pairs are read from vector A. Polar (rho,
theta) pairs, where rho is the radius and theta is the angle in the range [-pi, pi] are written to vector C. N
specifies the number of coordinate pairs in A and C.

Coordinate pairs are adjacent elements in the array, regardless of stride; stride is the distance from one
coordinate pair to the next.

This function performs the inverse operation of vDSP_rectD, which converts polar to rectangular coordinates.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_rect
Polar to rectangular conversion; single precision.

void vDSP_rect (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A, must be even
C
Single-precision real output vector
K
Stride for C, must be even
N
Number of ordered pairs processed
Discussion
This performs the following operation:

Converts polar coordinates to rectangular coordinates. Polar (rho, theta) pairs, where rho is the radius and
theta is the angle in the range [-pi, pi] are read from vector A. Cartesian (x,y) pairs are written to vector C. N
specifies the number of coordinate pairs in A and C.

Coordinate pairs are adjacent elements in the array, regardless of stride; stride is the distance from one
coordinate pair to the next.

This function performs the inverse operation of vDSP_polar, which converts rectangular to polar coordinates.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_rectD
Polar to rectangular conversion; double precision.

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void vDSP_rectD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A, must be even
C
Double-precision real output vector
K
Stride for C, must be even
N
Number of ordered pairs processed
Discussion
This performs the following operation:

Converts polar coordinates to rectangular coordinates. Polar (rho, theta) pairs, where rho is the radius and
theta is the angle in the range [-pi, pi] are read from vector A. Cartesian (x,y) pairs are written to vector C. N
specifies the number of coordinate pairs in A and C.

Coordinate pairs are adjacent elements in the array, regardless of stride; stride is the distance from one
coordinate pair to the next.

This function performs the inverse operation of vDSP_polarD, which converts rectangular to polar coordinates.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_rmsqv
Vector root-mean-square; single precision.

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void vDSP_rmsqv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Single-precision real output scalar
N
Count
Discussion
This performs the following operation:

Calculates the root mean square of the elements of A and stores the result in *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_rmsqvD
Vector root-mean-square; double precision.

void vDSP_rmsqvD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A

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C
Double-precision real output scalar
N
Count
Discussion
This performs the following operation:

Calculates the root mean square of the elements of A and stores the result in *C.

If N is zero (0), this function returns a NaN in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svdiv
Divide scalar by vector; single precision.

void vDSP_svdiv (
float *__vDSP_A,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input scalar
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

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Divides scalar A by each element of vector B, storing the results in vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svdivD
Divide scalar by vector; double precision.

void vDSP_svdivD (
double *__vDSP_A,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input scalar
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Divides scalar A by each element of vector B, storing the results in vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_sve
Vector sum; single precision.

void vDSP_sve (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Single-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the elements of A into *C. If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_sveD
Vector sum; double precision.

void vDSP_sveD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A

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C
Double-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the elements of A into *C. If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svemg
Vector sum of magnitudes; single precision.

void vDSP_svemg (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Single-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the magnitudes of the elements of A into *C.

If N is zero (0), this function returns 0 in *C.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svemgD
Vector sum of magnitudes; double precision.

void vDSP_svemgD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A
C
Double-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the magnitudes of the elements of A into *C.

If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svesq
Vector sum of squares; single precision.

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void vDSP_svesq (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Single-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the squares of the elements of A into *C.

If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svesqD
Vector sum of squares; double precision.

void vDSP_svesqD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A

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C
Double-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the squares of the elements of A into C.

If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svs
Vector sum of signed squares; single precision.

void vDSP_svs (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector.
I
Stride for A
C
Single-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the signed squares of the elements of A into *C.

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If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_svsD
Vector sum of signed squares; double precision.

void vDSP_svsD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector.
I
Stride for A
C
Double-precision real output scalar
N
Count
Discussion
This performs the following operation:

Writes the sum of the signed squares of the elements of A into *C.

If N is zero (0), this function returns 0 in *C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vaam
Vector add, add, and multiply; single precision.

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void vDSP_vaam (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
float *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real input vector
L
Stride for D
E
Single-precision real output vector
M
Stride for E
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Multiplies the sum of vectors A and B by the sum of vectors C and D. Results are stored in vector E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vaamD
Vector add, add, and multiply; double precision.

void vDSP_vaamD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
double *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real input vector
L
Stride for D
E
Double-precision real output vector
M
Stride for E
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Multiplies the sum of vectors A and B by the sum of vectors C and D. Results are stored in vector E.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vabs
Vector absolute values; single precision.

void vDSP_vabs (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Writes the absolute values of the elements of A into corresponding elements of C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vabsD
Vector absolute values; double precision.

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void vDSP_vabsD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Writes the absolute values of the elements of A into corresponding elements of C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vabsi
Integer vector absolute values.

void vDSP_vabsi (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Integer input vector
I
Stride for A

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C
Integer output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Writes the absolute values of the elements of A into corresponding elements of C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vadd
Adds vector A to vector B and leaves the result in vector C; single precision.

void vDSP_vadd (
const float __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vaddD
Adds vector A to vector B and leaves the result in vector C; double precision.

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void vDSP_vaddD (
const double __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vam
Adds vectors A and B, multiplies the sum by vector C, and leaves the result in vector D; single precision.

void vDSP_vam (
const float __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
const float __vDSP_input3[],
vDSP_Stride __vDSP_stride3,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vamD
Adds vectors A and B, multiplies the sum by vector C, and leaves the result in vector D; double precision.

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void vDSP_vamD (
const double __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
const double __vDSP_input3[],
vDSP_Stride __vDSP_stride3,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vasbm
Vector add, subtract, and multiply; single precision.

void vDSP_vasbm (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
float *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector

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K
Stride for C
D
Single-precision real input vector
L
Stride for D
E
Single-precision real output vector
M
Stride for E
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Multiplies the sum of vectors A and B by the result of subtracting vector D from vector C. Results are stored
in vector E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vasbmD
Vector add, subtract, and multiply; double precision.

void vDSP_vasbmD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
double *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A

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B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real input vector
L
Stride for D
E
Double-precision real output vector
M
Stride for E
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Multiplies the sum of vectors A and B by the result of subtracting vector D from vector C. Results are stored
in vector E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vasm
Vector add and scalar multiply; single precision.

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void vDSP_vasm (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input scalar
D
Single-precision real output vector
L
Stride for D
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Multiplies the sum of vectors A and B by scalar C. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vasmD
Vector add and scalar multiply; double precision.

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void vDSP_vasmD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input scalar
D
Double-precision real output vector
L
Stride for D
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Multiplies the sum of vectors A and B by scalar C. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vavlin
Vector linear average; single precision.

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void vDSP_vavlin (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real input-output vector
K
Stride for C
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Recalculates the linear average of input-output vector C to include input vector A. Input scalar B specifies
the number of vectors included in the current average.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vavlinD
Vector linear average; double precision.

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void vDSP_vavlinD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real input-output vector
K
Stride for C
N
Count ; each vector must have at least N elements
Discussion
This performs the following operation:

Recalculates the linear average of input-output vector C to include input vector A. Input scalar B specifies
the number of vectors included in the current average.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vclip
Vector clip; single precision.

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void vDSP_vclip (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: low clipping threshold
C
Single-precision real input scalar: high clipping threshold
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Elements of A are copied to D while clipping elements that are outside the interval [B, C] to the endpoints.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vclipc
Vector clip and count; single precision.

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void vDSP_vclipc (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N,
vDSP_Length *__vDSP_NLOW,
vDSP_Length *__vDSP_NHI
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: low clipping threshold
C
Single-precision real input scalar: high clipping threshold
D
Single-precision real output vector
L
Stride for D
N
Count of elements in A and D
NLOW
Number of elements that were clipped to B
NHI
Number of elements that were clipped to C
Discussion
This performs the following operation:

Elements of A are copied to D while clipping elements that are outside the interval [B, C] to the endpoints.

The count of elements clipped to B is returned in *NLOW, and the count of elements clipped to C is returned
in *NHI

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vclipcD
Vector clip and count; double precision.

void vDSP_vclipcD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N,
vDSP_Length *__vDSP_NLOW,
vDSP_Length *__vDSP_NHI
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: low clipping threshold
C
Double-precision real input scalar: high clipping threshold
D
Double-precision real output vector
L
Stride for D
N
Count of elements in A and D
NLOW
Number of elements that were clipped to B
NHI
Number of elements that were clipped to C
Discussion
This performs the following operation:

Elements of A are copied to D while clipping elements that are outside the interval [B, C] to the endpoints.

The count of elements clipped to B is returned in *NLOW, and the count of elements clipped to C is returned
in *NHI

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vclipD
Vector clip; double precision.

void vDSP_vclipD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: low clipping threshold
C
Double-precision real input scalar: high clipping threshold
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Elements of A are copied to D while clipping elements that are outside the interval [B, C] to the endpoints.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vclr
Vector clear; single precision.

void vDSP_vclr (
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
All elements of vector C are set to zeros.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vclrD
Vector clear; double precision.

void vDSP_vclrD (
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
All elements of vector C are set to zeros.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vcmprs
Vector compress; single precision.

void vDSP_vcmprs (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Compresses vector A based on the nonzero values of gating vector B. For nonzero elements of B, corresponding
elements of A are sequentially copied to output vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vcmprsD
Vector compress; double precision.

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void vDSP_vcmprsD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Compresses vector A based on the nonzero values of gating vector B. For nonzero elements of B, corresponding
elements of A are sequentially copied to output vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdbcon
Vector convert power or amplitude to decibels; single precision.

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void vDSP_vdbcon (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
unsigned int __vDSP_F
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: zero reference
C
Single-precision real output vector
K
Stride for C
N
Count
F
Power (0) or amplitude (1) flag
Discussion
Performs the following operation. is 20 if F is 1, or 10 if F is 0.

Converts inputs from vector A to their decibel equivalents, calculated in terms of power or amplitude according
to flag F. As a relative reference point, the value of input scalar B is considered to be zero decibels.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdbconD
Vector convert power or amplitude to decibels; double precision.

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void vDSP_vdbconD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
unsigned int __vDSP_F
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: zero reference
C
Double-precision real output vector
K
Stride for C
N
Count
F
Power (0) or amplitude (1) flag
Discussion
Performs the following operation:

The Greek letter alpha equals 20 if F = 1, and 10 if F = 0.

Converts inputs from vector A to their decibel equivalents, calculated in terms of power or amplitude according
to flag F. As a relative reference point, the value of input scalar B is considered to be zero decibels.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdist
Vector distance; single precision.

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void vDSP_vdist (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Computes the square root of the sum of the squares of corresponding elements of vectors A and B, and
stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdistD
Vector distance; double precision.

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void vDSP_vdistD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Computes the square root of the sum of the squares of corresponding elements of vectors A and B, and
stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdiv
Vector divide; single precision.

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void vDSP_vdiv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

BnJ
CnK = n = {0, N-1}
AnI

Divides elements of vector B by corresponding elements of vector A, and stores the results in corresponding
elements of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdivD
Vector divide; double precision.

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void vDSP_vdivD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

BnJ
CnK = n = {0, N-1}
AnI

Divides elements of vector B by corresponding elements of vector A, and stores the results in corresponding
elements of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdivi
Vector divide; integer.

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void vDSP_vdivi (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_B,
vDSP_Stride __vDSP_J,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Integer input vector
I
Stride for A
B
Integer input vector
J
Stride for B
C
Integer output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

BnJ
CnK = n = {0, N-1}
AnI

Divides elements of vector A by corresponding elements of vector B, and stores the results in corresponding
elements of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vdpsp
Vector convert double-precision to single-precision.

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void vDSP_vdpsp (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Creates single-precision vector C by converting double-precision inputs from vector A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_venvlp
Vector envelope; single precision.

void vDSP_venvlp (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector: high envelope

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I
Stride for A
B
Single-precision real input vector: low envelope
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Finds the extrema of vector C. For each element of C, the corresponding element of A provides an
upper-threshold value, and the corresponding element of B provides a lower-threshold value. If the value of
an element of C falls outside the range defined by these thresholds, it is copied to the corresponding element
of vector D. If its value is within the range, the corresponding element of vector D is set to zero.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_venvlpD
Vector envelope; double precision.

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void vDSP_venvlpD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector: high envelope
I
Stride for A
B
Double-precision real input vector: low envelope
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Finds the extrema of vector C. For each element of C, the corresponding element of A provides an
upper-threshold value, and the corresponding element of B provides a lower-threshold value. If the value of
an element of C falls outside the range defined by these thresholds, it is copied to the corresponding element
of vector D. If its value is within the range, the corresponding element of vector D is set to zero.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_veqvi
Vector equivalence, 32-bit logical.

void vDSP_veqvi (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_B,
vDSP_Stride __vDSP_J,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Integer input vector
I
Stride for A
B
Integer input vector
J
Stride for B
C
Integer output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Outputs the bitwise logical equivalence, exclusive NOR, of the integers of vectors A and B. For each pair of
input values, bits in each position are compared. A bit in the output value is set if both input bits are set, or
both are clear; otherwise it is cleared.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfill
Vector fill; single precision.

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void vDSP_vfill (
float *__vDSP_A,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input scalar
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Sets each element of vector C to the value of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfillD
Vector fill; double precision.

void vDSP_vfillD (
double *__vDSP_A,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input scalar
C
Double-precision real output vector
K
Stride for C
N
Count

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Discussion
Performs the following operation:

Sets each element of vector C to the value of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfilli
Integer vector fill.

void vDSP_vfilli (
int *__vDSP_A,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Integer input scalar
C
Integer output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Sets each element of vector C to the value of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vfix16
Converts an array of single-precision floating-point values to signed 16-bit integer values, rounding towards
zero.

void vDSP_vfix16 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfix16D
Converts an array of double-precision floating-point values to signed 16-bit integer values, rounding towards
zero.

void vDSP_vfix16D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.

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__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfix32
Converts an array of single-precision floating-point values to signed 32-bit integer values, rounding towards
zero.

void vDSP_vfix32 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfix32D
Converts an array of double-precision floating-point values to signed 16-bit integer values, rounding towards
zero.

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void vDSP_vfix32D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfix8
Converts an array of single-precision floating-point values to signed 8-bit integer values, rounding towards
zero.

void vDSP_vfix8 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfix8D
Converts an array of double-precision floating-point values to signed 8-bit integer values, rounding towards
zero.

void vDSP_vfix8D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixr16
Converts an array of single-precision floating-point values to signed 16-bit integer values, rounding towards
nearest integer.

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void vDSP_vfixr16 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixr16D
Converts an array of double-precision floating-point values to signed 16-bit integer values, rounding towards
nearest integer.

void vDSP_vfixr16D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixr32
Converts an array of single-precision floating-point values to signed 32-bit integer values, rounding towards
nearest integer.

void vDSP_vfixr32 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixr32D
Converts an array of double-precision floating-point values to signed 32-bit integer values, rounding towards
nearest integer.

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void vDSP_vfixr32D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixr8
Converts an array of single-precision floating-point values to signed 8-bit integer values, rounding towards
nearest integer.

void vDSP_vfixr8 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixr8D
Converts an array of double-precision floating-point values to signed 8-bit integer values, rounding towards
nearest integer.

void vDSP_vfixr8D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixru16
Converts an array of single-precision floating-point values to unsigned 16-bit integer values, rounding towards
nearest integer.

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void vDSP_vfixru16 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixru16D
Converts an array of double-precision floating-point values to unsigned 16-bit integer values, rounding
towards nearest integer.

void vDSP_vfixru16D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixru32
Converts an array of single-precision floating-point values to unsigned 32-bit integer values, rounding towards
nearest integer.

void vDSP_vfixru32 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixru32D
Converts an array of double-precision floating-point values to unsigned 32-bit integer values, rounding
towards nearest integer.

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void vDSP_vfixru32D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixru8
Converts an array of single-precision floating-point values to unsigned 8-bit integer values, rounding towards
nearest integer.

void vDSP_vfixru8 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixru8D
Converts an array of double-precision floating-point values to unsigned 8-bit integer values, rounding towards
nearest integer.

void vDSP_vfixru8D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixu16
Converts an array of single-precision floating-point values to unsigned 16-bit integer values, rounding towards
zero.

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void vDSP_vfixu16 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixu16D
Converts an array of double-precision floating-point values to unsigned 16-bit integer values, rounding
towards zero.

void vDSP_vfixu16D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned short *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixu32
Converts an array of single-precision floating-point values to unsigned 32-bit integer values, rounding towards
zero.

void vDSP_vfixu32 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixu32D
Converts an array of double-precision floating-point values to unsigned 32-bit integer values, rounding
towards zero.

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void vDSP_vfixu32D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixu8
Converts an array of single-precision floating-point values to unsigned 8-bit integer values, rounding towards
zero.

void vDSP_vfixu8 (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfixu8D
Converts an array of double-precision floating-point values to unsigned 8-bit integer values, rounding towards
zero.

void vDSP_vfixu8D (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
unsigned char *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vflt16
Converts an array of signed 16-bit integers to single-precision floating-point values.

void vDSP_vflt16 (
short *A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.

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__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vflt16D
Converts an array of signed 16-bit integers to double-precision floating-point values.

void vDSP_vflt16D (
short *A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vflt32
Converts an array of signed 32-bit integers to single-precision floating-point values.

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void vDSP_vflt32 (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vflt32D
Converts an array of signed 32-bit integers to double-precision floating-point values.

void vDSP_vflt32D (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vflt8
Converts an array of signed 8-bit integers to single-precision floating-point values.

void vDSP_vflt8 (
char *A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vflt8D
Converts an array of signed 8-bit integers to double-precision floating-point values.

void vDSP_vflt8D (
char *A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.

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__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfltu16
Converts an array of unsigned 16-bit integers to single-precision floating-point values.

void vDSP_vfltu16 (
unsigned short *A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfltu16D
Converts an array of unsigned 16-bit integers to double-precision floating-point values.

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void vDSP_vfltu16D (
unsigned short *A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfltu32
Converts an array of unsigned 32-bit integers to single-precision floating-point values.

void vDSP_vfltu32 (
unsigned int *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vfltu32D
Converts an array of unsigned 32-bit integers to double-precision floating-point values.

void vDSP_vfltu32D (
unsigned int *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfltu8
Converts an array of unsigned 8-bit integers to single-precision floating-point values.

void vDSP_vfltu8 (
unsigned char *A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.

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__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfltu8D
Converts an array of unsigned 8-bit integers to double-precision floating-point values.

void vDSP_vfltu8D (
unsigned char *A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Source vector.
__vDSP_I
Source vector stride length.
__vDSP_C
Destination vector.
__vDSP_K
Destination vector stride length.
__vDSP_N
Number of elements in vector.
Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfrac
Vector truncate to fraction; single precision.

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void vDSP_vfrac (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

The "function" truncate(x) is the integer farthest from 0 but not farther than x. Thus, for example,
vDSP_vFrac(-3.25) produces the result -0.25.

Sets each element of vector C to the signed fractional part of the corresponding element of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vfracD
Vector truncate to fraction; double precision.

void vDSP_vfracD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector

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I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

The "function" truncate(x) is the integer farthest from 0 but not farther than x. Thus, for example,
vDSP_vFrac(-3.25) produces the result -0.25.

Sets each element of vector C to the signed fractional part of the corresponding element of A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgathr
Vector gather; single precision.

void vDSP_vgathr (
float *__vDSP_A,
vDSP_Length *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
B
Integer vector containing indices
J
Stride for B
C
Single-precision real output vector
K
Stride for C

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N
Count
Discussion
Performs the following operation:

Uses elements of vector B as indices to copy selected elements of vector A to sequential locations in vector
C. Note that 1, not zero, is treated as the first location in the input vector when evaluating indices. This
function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgathra
Vector gather, absolute pointers; single precision.

void vDSP_vgathra (
float **A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Pointer input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Uses elements of vector A as pointers to copy selected single-precision values from memory to sequential
locations in vector C. This function can only be done out of place.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgathraD
Vector gather, absolute pointers; double precision.

void vDSP_vgathraD (
double **A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Pointer input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Uses elements of vector A as pointers to copy selected double-precision values from memory to sequential
locations in vector C. This function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgathrD
Vector gather; double precision.

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void vDSP_vgathrD (
double *__vDSP_A,
vDSP_Length *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
B
Integer vector containing indices
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Uses elements of vector B as indices to copy selected elements of vector A to sequential locations in vector
C. Note that 1, not zero, is treated as the first location in the input vector when evaluating indices. This
function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgen
Vector tapered ramp; single precision.

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void vDSP_vgen (
float *__vDSP_A,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input scalar: base value
B
Single-precision real input scalar: end value
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Creates ramped vector C with element zero equal to scalar A and element N-1 equal to scalar B. Output values
between element zero and element N-1 are evenly spaced and increase or decrease monotonically.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgenD
Vector tapered ramp; double precision.

void vDSP_vgenD (
double *__vDSP_A,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input scalar: base value
B
Double-precision real input scalar: end value

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C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Creates ramped vector C with element zero equal to scalar A and element N-1 equal to scalar B. Output values
between element zero and element N-1 are evenly spaced and increase or decrease monotonically.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgenp
Vector generate by extrapolation and interpolation; single precision.

void vDSP_vgenp (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C

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N
Count for C
M
Count for A and B
Discussion
Performs the following operation:

Generates vector C by extrapolation and linear interpolation from the ordered pairs (A,B) provided by
corresponding elements in vectors A and B. Vector B provides index values and should increase monotonically.
Vector A provides intensities, magnitudes, or some other measurable quantities, one value associated with
each value of B. This function can only be done out of place.

Vectors A and B define a piecewise linear function, f(x):

■ In the interval [-infinity, trunc(B[0*J]], the function is the constant A[0*I].

■ In each interval (trunc(B[m*J]), trunc(B[(m+1)*J])], the function is the line passing through the two points
(B[m*J], A[m*I]) and (B[(m+1)*J], A[(m+1)*I]). (This is for each integer m, 0 <= m < M-1.)
■ In the interval (B[(M-1)*J], infinity], the function is the constant A[(M-1)*I].
■ For 0 <= n < N, C[n*K] = f(n).

This function can only be done out of place.

Output values are generated for integral indices in the range zero through N - 1, deriving output values by
interpolating and extrapolating from vectors A and B. For example, if vectors A and B define velocity and
time pairs (v, t), vDSP_vgenp writes one velocity to vector C for every integral unit of time from zero to N -
1.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vgenpD
Vector generate by extrapolation and interpolation; double precision.

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void vDSP_vgenpD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count for C
M
Count for A and B
Discussion
Performs the following operation:

Generates vector C by extrapolation and linear interpolation from the ordered pairs (A,B) provided by
corresponding elements in vectors A and B. Vector B provides index values and should increase monotonically.
Vector A provides intensities, magnitudes, or some other measurable quantities, one value associated with
each value of B. This function can only be done out of place.

Vectors A and B define a piecewise linear function, f(x):

■ In the interval [-infinity, trunc(B[0*J]], the function is the constant A[0*I].

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■ In each interval (trunc(B[m*J]), trunc(B[(m+1)*J])], the function is the line passing through the two points
(B[m*J], A[m*I]) and (B[(m+1)*J], A[(m+1)*I]). (This is for each integer m, 0 <= m < M-1.)
■ In the interval (B[(M-1)*J], infinity], the function is the constant A[(M-1)*I].
■ For 0 <= n < N, C[n*K] = f(n).

This function can only be done out of place.

Output values are generated for integral indices in the range zero through N - 1, deriving output values by
interpolating and extrapolating from vectors A and B. For example, if vectors A and B define velocity and
time pairs (v, t), vDSP_vgenp writes one velocity to vector C for every integral unit of time from zero to N -
1.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_viclip
Vector inverted clip; single precision.

void vDSP_viclip (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: lower threshold
C
Single-precision real input scalar: upper threshold
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

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Performs an inverted clip of vector A using lower-threshold and upper-threshold input scalars B and C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_viclipD
Vector inverted clip; double precision.

void vDSP_viclipD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: lower threshold
C
Double-precision real input scalar: upper threshold
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

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Performs an inverted clip of vector A using lower-threshold and upper-threshold input scalars B and C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vindex
Vector index; single precision.

void vDSP_vindex (
float *__vDSP_A,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
B
Single-precision real input vector: indices
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Uses vector B as zero-based subscripts to copy selected elements of vector A to vector C. Fractional parts of
vector B are ignored.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vindexD
Vector index; double precision.

void vDSP_vindexD (
double *__vDSP_A,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
B
Double-precision real input vector: indices
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Uses vector B as zero-based subscripts to copy selected elements of vector A to vector C. Fractional parts of
vector B are ignored.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vintb
Vector linear interpolation between vectors; single precision.

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void vDSP_vintb (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input scalar: interpolation constant
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Creates vector D by interpolating between vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vintbD
Vector linear interpolation between vectors; double precision.

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void vDSP_vintbD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input scalar: interpolation constant
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Creates vector D by interpolating between vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vlim
Vector test limit; single precision.

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void vDSP_vlim (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: limit
C
Single-precision real input scalar
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Compares values from vector A to limit scalar B. For inputs greater than or equal to B, scalar C is written to
D . For inputs less than B, the negated value of scalar C is written to vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vlimD
Vector test limit; double precision.

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void vDSP_vlimD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: limit
C
Double-precision real input scalar
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
Compares values from vector A to limit scalar B. For inputs greater than or equal to B, scalar C is written to
D . For inputs less than B, the negated value of scalar C is written to vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vlint
Vector linear interpolation between neighboring elements; single precision.

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void vDSP_vlint (
float *__vDSP_A,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Single-precision real input vector
B
Single-precision real input vector: integer parts are indices into A and fractional parts are interpolation
constants
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count for C
M
Length of A
Discussion
Performs the following operation:

Generates vector C by interpolating between neighboring values of vector A as controlled by vector B. The
integer portion of each element in B is the zero-based index of the first element of a pair of adjacent values
in vector A.

The value of the corresponding element of C is derived from these two values by linear interpolation, using
the fractional part of the value in B.

Argument M is not used in the calculation. However, the integer parts of the values in B must be greater than
or equal to zero and less than or equal to M - 2.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vlintD
Vector linear interpolation between neighboring elements; double precision.

void vDSP_vlintD (
double *__vDSP_A,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Double-precision real input vector
B
Double-precision real input vector: integer parts are indices into A and fractional parts are interpolation
constants
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count for C
M
Length of A
Discussion
Performs the following operation:

Generates vector C by interpolating between neighboring values of vector A as controlled by vector B. The
integer portion of each element in B is the zero-based index of the first element of a pair of adjacent values
in vector A.

The value of the corresponding element of C is derived from these two values by linear interpolation, using
the fractional part of the value in B.

Argument M is not used in the calculation. However, the integer parts of the values in B must be greater than
or equal to zero and less than or equal to M - 2.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vma
Vector multiply and add; single precision.

void vDSP_vma (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Multiplies corresponding elements of vectors A and B, add the corresponding elements of vector C, and
stores the results in vector D.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vmaD
Vector multiply and add; double precision.

void vDSP_vmaD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Multiplies corresponding elements of vectors A and B, add the corresponding elements of vector C, and
stores the results in vector D.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vmax
Vector maxima; single precision.

void vDSP_vmax (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the greater of the corresponding values from input vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmaxD
Vector maxima; double precision.

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void vDSP_vmaxD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the greater of the corresponding values from input vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmaxmg
Vector maximum magnitudes; single precision.

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void vDSP_vmaxmg (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the larger of the magnitudes of corresponding values from input vectors
A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmaxmgD
Vector maximum magnitudes; double precision.

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void vDSP_vmaxmgD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the larger of the magnitudes of corresponding values from input vectors
A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmin
Vector minima; single precision.

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void vDSP_vmin (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the lesser of the corresponding values from input vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vminD
Vector minima; double precision.

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void vDSP_vminD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the lesser of the corresponding values from input vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vminmg
Vector minimum magnitudes; single precision.

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void vDSP_vminmg (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the smaller of the magnitudes of corresponding values from input vectors
A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vminmgD
Vector minimum magnitudes; double precision.

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 CHAPTER 2
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void vDSP_vminmgD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each element of output vector C is the smaller of the magnitudes of corresponding values from input vectors
A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmma
Vector multiply, multiply, and add; single precision.

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void vDSP_vmma (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
float *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real input vector
L
Stride for D
E
Single-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied, corresponding values of C and D are multiplied, and these
products are added together and stored in E.

Availability
Available in iPhone OS 4.0 and later.

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 CHAPTER 2
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Declared In
vDSP.h

vDSP_vmmaD
Vector multiply, multiply, and add; double precision.

void vDSP_vmmaD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
double *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real input vector
L
Stride for D
E
Double-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

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Corresponding elements of A and B are multiplied, corresponding values of C and D are multiplied, and these
products are added together and stored in E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmmsb
Vector multiply, multiply, and subtract; single precision.

void vDSP_vmmsb (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
float *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real input vector
L
Stride for D
E
Single-precision real output vector
M
Stride for E

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 CHAPTER 2
vDSP Reference

N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied, corresponding values of C and D are multiplied, and the
second product is subtracted from the first. The result is stored in E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmmsbD
Vector multiply, multiply, and subtract; double precision.

void vDSP_vmmsbD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
double *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real input vector

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L
Stride for D
E
Double-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied, corresponding values of C and D are multiplied, and the
second product is subtracted from the first. The result is stored in E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmsa
Vector multiply and scalar add; single precision.

void vDSP_vmsa (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input scalar

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 CHAPTER 2
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D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied and the scalar C is added. The result is stored in D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmsaD
Vector multiply and scalar add; double precision.

void vDSP_vmsaD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input scalar
D
Double-precision real output vector
L
Stride for D

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N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied and the scalar C is added. The result is stored in D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmsb
Vector multiply and subtract, single precision.

void vDSP_vmsb (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for D

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N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied and the corresponding value of C is subtracted. The result
is stored in D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmsbD
Vector multiply and subtract; double precision.

void vDSP_vmsbD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for D

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N
Count
Discussion
This performs the following operation:

Corresponding elements of A and B are multiplied and the corresponding value of C is subtracted. The result
is stored in D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmul
Multiplies vector A by vector B and leaves the result in vector C; single precision.

void vDSP_vmul (
const float __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vmulD
Multiplies vector A by vector B and leaves the result in vector C; double precision.

void vDSP_vmulD (
const double __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vnabs
Vector negative absolute values; single precision.

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void vDSP_vnabs (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each value in C is the negated absolute value of the corresponding element in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vnabsD
Vector negative absolute values; double precision.

void vDSP_vnabsD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A

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C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Each value in C is the negated absolute value of the corresponding element in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vneg
Vector negative values; single precision.

void vDSP_vneg (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Each value in C is the negated value of the corresponding element in A.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vnegD
Vector negative values; double precision.

void vDSP_vnegD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Each value in C is the negated value of the corresponding element in A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vpoly
Vector polynomial evaluation; single precision.

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void vDSP_vpoly (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Parameters
A
Single-precision real input vector: coefficients
I
Stride for A
B
Single-precision real input vector: variable values
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
P
Degree of polynomial
Discussion
This performs the following operation:

Evaluates polynomials using vector B as independent variables and vector A as coefficients. A polynomial of
degree p requires p+1 coefficients, so vector A should contain P+1 values.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vpolyD
Vector polynomial evaluation; double precision.

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void vDSP_vpolyD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Parameters
A
Double-precision real input vector: coefficients
I
Stride for A
B
Double-precision real input vector: variable values
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
P
Degree of polynomial
Discussion
This performs the following operation:

Evaluates polynomials using vector B as independent variables and vector A as coefficients. A polynomial of
degree p requires p+1 coefficients, so vector A should contain P+1 values.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vpythg
Vector Pythagoras; single precision.

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void vDSP_vpythg (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
float *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real input vector
L
Stride for D
E
Single-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

Subtracts vector C from A and squares the differences, subtracts vector D from B and squares the differences,
adds the two sets of squared differences, and then writes the square roots of the sums to vector E.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vpythgD
Vector Pythagoras; double precision.

void vDSP_vpythgD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
double *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real input vector
L
Stride for D
E
Double-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

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Subtracts vector C from A and squares the differences, subtracts vector D from B and squares the differences,
adds the two sets of squared differences, and then writes the square roots of the sums to vector E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vqint
Vector quadratic interpolation; single precision.

void vDSP_vqint (
float *__vDSP_A,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Single-precision real input vector
B
Single-precision real input vector: integer parts are indices into A and fractional parts are interpolation
constants
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count for C
M
Length of A: must be greater than or equal to 3
Discussion
This performs the following operation:

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Generates vector C by interpolating between neighboring values of vector A as controlled by vector B. The
integer portion of each element in B is the zero-based index of the first element of a triple of adjacent values
in vector A.

The value of the corresponding element of C is derived from these three values by quadratic interpolation,
using the fractional part of the value in B.

Argument M is not used in the calculation. However, the integer parts of the values in B must be less than or
equal to M - 2.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vqintD
Vector quadratic interpolation; double precision.

void vDSP_vqintD (
double *__vDSP_A,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Double-precision real input vector
B
Double-precision real input vector: integer parts are indices into A and fractional parts are interpolation
constants
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count for C
M
Length of A: must be greater than or equal to 3
Discussion
This performs the following operation:

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Generates vector C by interpolating between neighboring values of vector A as controlled by vector B. The
integer portion of each element in B is the zero-based index of the first element of a triple of adjacent values
in vector A.

The value of the corresponding element of C is derived from these three values by quadratic interpolation,
using the fractional part of the value in B.

Argument M is not used in the calculation. However, the integer parts of the values in B must be less than or
equal to M - 2.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vramp
Build ramped vector; single precision.

void vDSP_vramp (
float *__vDSP_A,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input scalar: initial value
B
Single-precision real input scalar: increment or decrement
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

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Creates a monotonically incrementing or decrementing vector. Scalar A is the initial value written to vector
C. Scalar B is the increment or decrement for each succeeding element.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampD
Build ramped vector; double precision.

void vDSP_vrampD (
double *__vDSP_A,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input scalar: initial value
B
Double-precision real input scalar: increment or decrement
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Creates a monotonically incrementing or decrementing vector. Scalar A is the initial value written to vector
C. Scalar B is the increment or decrement for each succeeding element.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmul
Builds a ramped vector and multiplies by a source vector.

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void vDSP_vrampmul (
const float *__vDSP_I,
vDSP_Stride __vDSP_IS,
float *__vDSP_Start,
const float *__vDSP_Step,
float *__vDSP_O,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I
Input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vector. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O
The output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This routine calculates the following:

for (i = 0; i < N; ++i) {

O[i*OS] = *Start * I[i*IS];
*Start += *Step;
}

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmul2
Stereo version of vDSP_vrampmul (page 437).

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void vDSP_vrampmul2 (
const float *__vDSP_I0,
const float *__vDSP_I1,
vDSP_Stride __vDSP_IS,
float *__vDSP_Start,
const float *__vDSP_Step,
float *__vDSP_O0,
float *__vDSP_O1,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I0
First input vector, multiplied by the ramp function.
__vDSP_I1
Second input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vectors. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O0
First output vector.
__vDSP_O1
Second output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This function calculates the following:

for (i = 0; i < N; ++i) {

O0[i*OS] = *Start * I0[i*IS];
O1[i*OS] = *Start * I1[i*IS];
*Start += *Step;
}

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmul2_s1_15
Vector fixed-point 1.15 format version of vDSP_vrampmul2 (page 438).

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void vDSP_vrampmul2_s1_15 (
const short int *__vDSP_I0,
const short int *__vDSP_I1,
vDSP_Stride __vDSP_IS,
short int *__vDSP_Start,
const short int *__vDSP_Step,
short int *__vDSP_O0,
short int *__vDSP_O1,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I0
First input vector, multiplied by the ramp function.
__vDSP_I1
Second input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vectors. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O0
First output vector.
__vDSP_O1
Second output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This function calculates the following:

for (i = 0; i < N; ++i) {

O0[i*OS] = *Start * I0[i*IS];
O1[i*OS] = *Start * I1[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with one sign bit and 15 fraction bits. A value in this representation
can be converted to floating-point by dividing it by 32768.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vrampmul2_s8_24
Vector fixed-point 8.24 format version of vDSP_vrampmul2 (page 438).

void vDSP_vrampmul2_s8_24 (
const int *__vDSP_I0,
const int *__vDSP_I1,
vDSP_Stride __vDSP_IS,
int *__vDSP_Start,
const int *__vDSP_Step,
int *__vDSP_O0,
int *__vDSP_O1,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I0
First input vector, multiplied by the ramp function.
__vDSP_I1
Second input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vectors. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O0
First output vector.
__vDSP_O1
Second output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This function calculates the following:

for (i = 0; i < N; ++i) {

O0[i*OS] = *Start * I0[i*IS];
O1[i*OS] = *Start * I1[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with eight integer bits (including the sign bit) and 24 fraction
bits. A value in this representation can be converted to floating-point by dividing it by 16777216.0.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vrampmuladd
Builds a ramped vector, multiplies it by a source vector, and adds the result to the output vector.

void vDSP_vrampmuladd (
const float *__vDSP_I,
vDSP_Stride __vDSP_IS,
float *__vDSP_Start,
const float *__vDSP_Step,
float *__vDSP_O,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I
Input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vector. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O
The output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This routine calculates the following:

for (i = 0; i < N; ++i) {

O[i*OS] += *Start * I[i*IS];
*Start += *Step;
}

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmuladd2
Stereo version of vDSP_vrampmuladd (page 442).

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void vDSP_vrampmuladd2 (
const float *__vDSP_I0,
const float *__vDSP_I1,
vDSP_Stride __vDSP_IS,
float *__vDSP_Start,
const float *__vDSP_Step,
float *__vDSP_O0,
float *__vDSP_O1,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I0
First input vector, multiplied by the ramp function.
__vDSP_I1
Second input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vectors. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O0
First output vector.
__vDSP_O1
Second output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This function calculates the following:

for (i = 0; i < N; ++i) {

O0[i*OS] += *Start * I0[i*IS];
O1[i*OS] += *Start * I1[i*IS];
*Start += *Step;
}

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmuladd2_s1_15
Vector fixed-point 1.15 format version of vDSP_vrampmuladd2 (page 442).

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void vDSP_vrampmuladd2_s1_15 (
const short int *__vDSP_I0,
const short int *__vDSP_I1,
vDSP_Stride __vDSP_IS,
short int *__vDSP_Start,
const short int *__vDSP_Step,
short int *__vDSP_O0,
short int *__vDSP_O1,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I0
First input vector, multiplied by the ramp function.
__vDSP_I1
Second input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vectors. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O0
First output vector.
__vDSP_O1
Second output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This function calculates the following:

for (i = 0; i < N; ++i) {

O0[i*OS] += *Start * I0[i*IS];
O1[i*OS] += *Start * I1[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with one sign bit and 15 fraction bits. A value in this representation
can be converted to floating-point by dividing it by 32768.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vrampmuladd2_s8_24
Vector fixed-point 8.24 format version of vDSP_vrampmuladd2 (page 442).

void vDSP_vrampmuladd2_s8_24 (
const int *__vDSP_I0,
const int *__vDSP_I1,
vDSP_Stride __vDSP_IS,
int *__vDSP_Start,
const int *__vDSP_Step,
int *__vDSP_O0,
int *__vDSP_O1,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I0
First input vector, multiplied by the ramp function.
__vDSP_I1
Second input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vectors. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O0
First output vector.
__vDSP_O1
Second output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This function calculates the following:

for (i = 0; i < N; ++i) {

O0[i*OS] += *Start * I0[i*IS];
O1[i*OS] += *Start * I1[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with eight integer bits (including the sign bit) and 24 fraction
bits. A value in this representation can be converted to floating-point by dividing it by 16777216.0.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vrampmuladd_s1_15
Vector fixed-point 1.15 format version of vDSP_vrampmuladd (page 442).

void vDSP_vrampmuladd_s1_15 (
const short int *__vDSP_I,
vDSP_Stride __vDSP_IS,
short int *__vDSP_Start,
const short int *__vDSP_Step,
short int *__vDSP_O,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I
Input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vector. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O
The output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This routine calculates the following:

for (i = 0; i < N; ++i) {

O[i*OS] += *Start * I[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with one sign bit and 15 fraction bits. A value in this representation
can be converted to floating-point by dividing it by 32768.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vrampmuladd_s8_24
Vector fixed-point 8.24 format version of vDSP_vrampmuladd (page 442).

void vDSP_vrampmuladd_s8_24 (
const int *__vDSP_I,
vDSP_Stride __vDSP_IS,
int *__vDSP_Start,
const int *__vDSP_Step,
int *__vDSP_O,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I
Input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vector. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O
The output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This routine calculates the following:

for (i = 0; i < N; ++i) {

O[i*OS] += *Start * I[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with eight integer bits (including the sign bit) and 24 fraction
bits. A value in this representation can be converted to floating-point by dividing it by 16777216.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmul_s1_15
Vector fixed-point 1.15 format version of vDSP_vrampmul (page 437).

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void vDSP_vrampmul_s1_15 (
const short int *__vDSP_I,
vDSP_Stride __vDSP_IS,
short int *__vDSP_Start,
const short int *__vDSP_Step,
short int *__vDSP_O,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I
Input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vector. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O
The output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This routine calculates the following:

for (i = 0; i < N; ++i) {

O[i*OS] = *Start * I[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with one sign bit and 15 fraction bits. A value in this representation
can be converted to floating-point by dividing it by 32768.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrampmul_s8_24
Vector fixed-point 8.24 format version of vDSP_vrampmul (page 437).

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void vDSP_vrampmul_s8_24 (
const int *__vDSP_I,
vDSP_Stride __vDSP_IS,
int *__vDSP_Start,
const int *__vDSP_Step,
int *__vDSP_O,
vDSP_Stride __vDSP_OS,
vDSP_Length __vDSP_N
);

Parameters
__vDSP_I
Input vector, multiplied by the ramp function.
__vDSP_IS
Stride length in input vector. For example, if __vDSP_IS is 2, every second element is used.
__vDSP_Start
The initial value for the ramp function. Modified on return to hold the next value (including
accumulated errors) so that the ramp function can be continued smoothly.
__vDSP_Step
The value to increment each subsequent value of the ramp function by.
__vDSP_O
The output vector.
__vDSP_OS
Stride length in output vector. For example, if __vDSP_IS is 2, every second element is modified.
__vDSP_N
The number of elements to modify.
Discussion
This routine calculates the following:

for (i = 0; i < N; ++i) {

O[i*OS] = *Start * I[i*IS];
*Start += *Step;
}

The elements are fixed-point numbers, each with eight integer bits (including the sign bit) and 24 fraction
bits. A value in this representation can be converted to floating-point by dividing it by 16777216.0.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrsum
Vector running sum integration; single precision.

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void vDSP_vrsum (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_S,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
S
Single-precision real input scalar: weighting factor
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Integrates vector A using a running sum from vector C. Vector A is weighted by scalar S and added to the
previous output point. The first element from vector A is not used in the sum.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrsumD
Vector running sum integration; double precision.

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void vDSP_vrsumD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_S,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
S
Double-precision real input scalar: weighting factor
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Integrates vector A using a running sum from vector C. Vector A is weighted by scalar S and added to the
previous output point. The first element from vector A is not used in the sum.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrvrs
Vector reverse order, in place; single precision.

void vDSP_vrvrs (
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
C
Single-precision real input-output vector

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K
Stride for C
N
Count
Discussion
Performs the following operation:

Reverses the order of vector C in place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vrvrsD
Vector reverse order, in place; double precision.

void vDSP_vrvrsD (
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
C
Double-precision real input-output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Reverses the order of vector C in place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vsadd
Vector scalar add; single precision.

void vDSP_vsadd (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Adds scalar B to each element of vector A and stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsaddD
Vector scalar add; double precision.

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void vDSP_vsaddD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Adds scalar B to each element of vector A and stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsaddi
Integer vector scalar add.

void vDSP_vsaddi (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_B,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Integer input vector

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I
Stride for A
B
Integer input scalar
C
Integer output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Adds scalar B to each element of vector A and stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsbm
Vector subtract and multiply; single precision.

void vDSP_vsbm (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B

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C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Subtracts vector B from vector A and then multiplies the differences by vector C. Results are stored in vector
D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsbmD
Vector subtract and multiply; double precision.

void vDSP_vsbmD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Double for B

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C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Subtracts vector B from vector A and then multiplies the differences by vector C. Results are stored in vector
D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsbsbm
Vector subtract, subtract, and multiply; single precision.

void vDSP_vsbsbm (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
float *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector

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J
Stride for B
C
Single-precision real input vector
K
Stride for C
D
Single-precision real input vector
L
Stride for D
E
Single-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

Subtracts vector B from A, subtracts vector D from C, and multiplies the differences. Results are stored in
vector E.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsbsbmD
Vector subtract, subtract, and multiply; double precision.

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void vDSP_vsbsbmD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
double *__vDSP_E,
vDSP_Stride __vDSP_M,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input vector
K
Stride for C
D
Double-precision real input vector
L
Stride for D
E
Double-precision real output vector
M
Stride for E
N
Count
Discussion
This performs the following operation:

Subtracts vector B from A, subtracts vector D from C, and multiplies the differences. Results are stored in
vector E.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_vsbsm
Vector subtract and scalar multiply; single precision.

void vDSP_vsbsm (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real input scalar
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Subtracts vector B from vector A and then multiplies each difference by scalar C. Results are stored in vector
D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vsbsmD
Vector subtract and scalar multiply; double precision.

void vDSP_vsbsmD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real input scalar
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
This performs the following operation:

Subtracts vector B from vector A and then multiplies each difference by scalar C. Results are stored in vector
D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsdiv
Vector scalar divide; single precision.

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void vDSP_vsdiv (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Divides each element of vector A by scalar B and stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsdivD
Vector scalar divide; double precision.

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void vDSP_vsdivD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Divides each element of vector A by scalar B and stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsdivi
Integer vector scalar divide.

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void vDSP_vsdivi (
int *__vDSP_A,
vDSP_Stride __vDSP_I,
int *__vDSP_B,
int *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Integer input vector
I
Stride for A
B
Integer input scalar
C
Integer output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Divides each element of vector A by scalar B and stores the result in the corresponding element of vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsimps
Simpson integration; single precision.

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void vDSP_vsimps (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Integrates vector A using Simpson integration, storing results in vector C. Scalar B specifies the integration
step size. This function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsimpsD
Simpson integration; double precision.

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void vDSP_vsimpsD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Integrates vector A using Simpson integration, storing results in vector C. Scalar B specifies the integration
step size. This function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsma
Vector scalar multiply and vector add; single precision.

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void vDSP_vsma (
const float *__vDSP_A,
vDSP_Stride __vDSP_I,
const float *__vDSP_B,
const float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Multiplies vector A by scalar B and then adds the products to vector C. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmaD
Vector scalar multiply and vector add; double precision.

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void vDSP_vsmaD (
const double *__vDSP_A,
vDSP_Stride __vDSP_I,
const double *__vDSP_B,
const double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Multiplies vector A by scalar B and then adds the products to vector C. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmsa
Vector scalar multiply and scalar add; single precision.

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void vDSP_vsmsa (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real input scalar
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Multiplies vector A by scalar B and then adds scalar C to each product. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmsaD
Vector scalar multiply and scalar add; double precision.

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void vDSP_vsmsaD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real input scalar
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Multiplies vector A by scalar B and then adds scalar C to each product. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmsb
Vector scalar multiply and vector subtract; single precision.

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void vDSP_vsmsb (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar
C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Multiplies vector A by scalar B and then subtracts vector C from the products. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmsbD
Vector scalar multiply and vector subtract; double precision.

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void vDSP_vsmsbD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar
C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Multiplies vector A by scalar B and then subtracts vector C from the products. Results are stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmul
Multiplies vector signal1 by scalar signal2 and leaves the result in vector result; single precision.

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void vDSP_vsmul (
const float __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const float *__vDSP_input2,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsmulD
Multiplies vector signal1 by scalar signal2 and leaves the result in vector result; double precision.

void vDSP_vsmulD (
const double __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const double *__vDSP_input2,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsort
Vector in-place sort; single precision.

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void vDSP_vsort (
float *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_OFLAG
);

Parameters
C
Single-precision real input-output vector
N
Count
OFLAG
Flag for sort order: 1 for ascending, -1 for descending
Discussion
Performs an in-place sort of vector C in the order specified by parameter OFLAG.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsortD
Vector in-place sort; double precision.

void vDSP_vsortD (
double *__vDSP_C,
vDSP_Length __vDSP_N,
int __vDSP_OFLAG
);

Parameters
C
Double-precision real input-output vector
N
Count
OFLAG
Flag for sort order: 1 for ascending, -1 for descending
Discussion
Performs an in-place sort of vector C in the order specified by parameter OFLAG.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vsorti
Vector index in-place sort; single precision.

void vDSP_vsorti (
float *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length *__vDSP_List_addr,
vDSP_Length __vDSP_N,
int __vDSP_OFLAG
);

Parameters
C
Single-precision real input vector
IC
Integer output vector. Must be initialized with the indices of vector C, from 0 to N-1.
List_addr
Temporary vector. This is currently not used and NULL should be passed.
N
Count
OFLAG
Flag for sort order: 1 for ascending, -1 for descending
Discussion
Leaves input vector C unchanged and performs an in-place sort of the indices in vector IC according to the
values in C. The sort order is specified by parameter OFLAG.

The values in C can then be obtained in sorted order, by taking indices in sequence from IC.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsortiD
Vector index in-place sort; double precision.

void vDSP_vsortiD (
double *__vDSP_C,
vDSP_Length *__vDSP_IC,
vDSP_Length *__vDSP_List_addr,
vDSP_Length __vDSP_N,
int __vDSP_OFLAG
);

Parameters
C
Double-precision real input vector
IC
Integer output vector. Must be initialized with the indices of vector C, from 0 to N-1.

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List_addr
Temporary vector. This is currently not used and NULL should be passed.
N
Count
OFLAG
Flag for sort order: 1 for ascending, -1 for descending
Discussion
Leaves input vector C unchanged and performs an in-place sort of the indices in vector IC according to the
values in C. The sort order is specified by parameter OFLAG.

The values in C can then be obtained in sorted order, by taking indices in sequence from IC.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vspdp
Vector convert single-precision to double-precision.

void vDSP_vspdp (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Creates double-precision vector C by converting single-precision inputs from vector A. This function can only
be done out of place.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsq
Computes the squared values of vector input and leaves the result in vector result; single precision.

void vDSP_vsq (
const float __vDSP_input[],
vDSP_Stride __vDSP_strideInput,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsqD
Computes the squared values of vector signal1 and leaves the result in vector result; double precision.

void vDSP_vsqD (
const double __vDSP_input[],
vDSP_Stride __vDSP_strideInput,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vssq
Computes the signed squares of vector signal1 and leaves the result in vector result; single precision.

void vDSP_vssq (
const float __vDSP_input[],
vDSP_Stride __vDSP_strideInput,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vssqD
Computes the signed squares of vector signal1 and leaves the result in vector result; double precision.

void vDSP_vssqD (
const double __vDSP_input[],
vDSP_Stride __vDSP_strideInput,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsub
Subtracts vector signal1 from vector signal2 and leaves the result in vector result; single precision.

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void vDSP_vsub (
const float __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
float __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vsubD
Subtracts vector signal1 from vector signal2 and leaves the result in vector result; double precision.

void vDSP_vsubD (
const double __vDSP_input1[],
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
double __vDSP_result[],
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vswap
Vector swap; single precision.

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void vDSP_vswap (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input-output vector
I
Stride for A
B
Single-precision real input-output vector
J
Stride for B
N
Count
Discussion
This performs the following operation:

Exchanges the elements of vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vswapD
Vector swap; double precision.

void vDSP_vswapD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input-output vector
I
Stride for A

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B
Double-precision real input-output vector
J
Stride for B
N
Count
Discussion
This performs the following operation:

Exchanges the elements of vectors A and B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vswsum
Vector sliding window sum; single precision.

void vDSP_vswsum (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Parameters
A
Single-precision real input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count of output points
P
Length of window
Discussion
Performs the following operation:

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Writes the sliding window sum of P consecutive elements of vector A to vector C, for each of N possible
starting positions of the P-element window in vector A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vswsumD
Vector sliding window sum; double precision.

void vDSP_vswsumD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Parameters
A
Double-precision real input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count of output points
P
Length of window
Discussion
Performs the following operation:

Writes the sliding window sum of P consecutive elements of vector A to vector C, for each of N possible
starting positions of the P-element window in vector A.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vtabi
Vector interpolation, table lookup; single precision.

void vDSP_vtabi (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_S1,
float *__vDSP_S2,
float *__vDSP_C,
vDSP_Length __vDSP_M,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
S1
Single-precision real input scalar: scale factor
S2
Single-precision real input scalar: base offset
C
Single-precision real input vector: lookup table
M
Lookup table size
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

p = F AnI + G q = floor ( p) r = p – float ( q ) Dnk = (1.0–r)C q + rCq –1 n = {0, N-1}

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Evaluates elements of vector A for use as offsets into vector C. Vector C is a zero-based lookup table supplied
by the caller that generates output values for vector D. Linear interpolation is used to compute output values
when offsets do not evaluate integrally. Scale factor S1 and base offset S2 map the anticipated range of
input values to the range of the lookup table and are typically assigned values such that:

floor(F * minimum input value + G) = 0

floor(F * maximum input value + G) = M-1

Input values that evaluate to zero or less derive their output values from table location zero. Values that
evaluate beyond the table, greater than M-1, derive their output values from the last table location. For inputs
that evaluate integrally, the table location indexed by the integral is copied as the output value. All other
inputs derive their output values by interpolation between the two table values surrounding the evaluated
input.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vtabiD
Vector interpolation, table lookup; double precision.

void vDSP_vtabiD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_S1,
double *__vDSP_S2,
double *__vDSP_C,
vDSP_Length __vDSP_M,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
S1
Double-precision real input scalar: scale factor
S2
Double-precision real input scalar: base offset
C
Double-precision real input vector: lookup table
M
Lookup table size
D
Double-precision real output vector

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L
Stride for D
N
Count
Discussion
Performs the following operation:

p = F AnI + G q = floor ( p) r = p – float ( q ) Dnk = (1.0–r)C q + rCq –1 n = {0, N-1}

Evaluates elements of vector A for use as offsets into vector C. Vector C is a zero-based lookup table supplied
by the caller that generates output values for vector D. Linear interpolation is used to compute output values
when offsets do not evaluate integrally. Scale factor S1 and base offset S2 map the anticipated range of
input values to the range of the lookup table and are typically assigned values such that:

floor(F * minimum input value + G) = 0

floor(F * maximum input value + G) = M-1

Input values that evaluate to zero or less derive their output values from table location zero. Values that
evaluate beyond the table, greater than M-1, derive their output values from the last table location. For inputs
that evaluate integrally, the table location indexed by the integral is copied as the output value. All other
inputs derive their output values by interpolation between the two table values surrounding the evaluated
input.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vthr
Vector threshold; single precision.

void vDSP_vthr (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: lower threshold
C
Single-precision real output vector

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K
Stride for C
N
Count
Discussion
Performs the following operation:

Creates vector C by comparing each input from vector A with scalar B. If an input value is less than B, B is
copied to C; otherwise, the input value from A is copied to C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vthrD
Vector threshold; double precision.

void vDSP_vthrD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: lower threshold
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

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Creates vector C by comparing each input from vector A with scalar B. If an input value is less than B, B is
copied to C; otherwise, the input value from A is copied to C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vthres
Vector threshold with zero fill; single precision.

void vDSP_vthres (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: lower threshold
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Creates vector C by comparing each input from vector A with scalar B. If an input value is less than B, zero is
written to C; otherwise, the input value from A is copied to C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_vthresD
Vector threshold with zero fill; double precision.

void vDSP_vthresD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: lower threshold
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Creates vector C by comparing each input from vector A with scalar B. If an input value is less than B, zero is
written to C; otherwise, the input value from A is copied to C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vthrsc
Vector threshold with signed constant; single precision.

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void vDSP_vthrsc (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
float *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: lower threshold
C
Single-precision real input scalar
D
Single-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Creates vector D using the plus or minus value of scalar C. The sign of the output element is determined by
comparing input from vector A with threshold scalar B. For input values less than B, the negated value of C
is written to vector D. For input values greater than or equal to B, C is copied to vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vthrscD
Vector threshold with signed constant; double precision.

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void vDSP_vthrscD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
double *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: lower threshold
C
Double-precision real input scalar
D
Double-precision real output vector
L
Stride for D
N
Count
Discussion
Performs the following operation:

Creates vector D using the plus or minus value of scalar C. The sign of the output element is determined by
comparing input from vector A with threshold scalar B. For input values less than B, the negotiated value of
C is written to vector D. For input values greater than or equal to B, C is copied to vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vtmerg
Tapered merge of two vectors; single precision.

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void vDSP_vtmerg (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Performs a tapered merge of vectors A and B. Values written to vector C range from element zero of vector
A to element N-1 of vector B. Output values between these endpoints reflect varying amounts of their
corresponding inputs from vectors A and B, with the percentage of vector A decreasing and the percentage
of vector B increasing as the index increases.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vtmergD
Tapered merge of two vectors; double precision.

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void vDSP_vtmergD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Performs a tapered merge of vectors A and B. Values written to vector C range from element zero of vector
A to element N-1 of vector B. Output values between these endpoints reflect varying amounts of their
corresponding inputs from vectors A and B, with the percentage of vector A decreasing and the percentage
of vector B increasing as the index increases.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vtrapz
Vector trapezoidal integration; single precision.

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void vDSP_vtrapz (
float *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
I
Stride for A
B
Single-precision real input scalar: step size
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Estimates the integral of vector A using the trapezoidal rule. Scalar B specifies the integration step size. This
function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_vtrapzD
Vector trapezoidal integration; double precision.

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void vDSP_vtrapzD (
double *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
I
Stride for A
B
Double-precision real input scalar: step size
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Performs the following operation:

Estimates the integral of vector A using the trapezoidal rule. Scalar B specifies the integration step size. This
function can only be done out of place.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_wiener
Wiener-Levinson general convolution; single precision.

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void vDSP_wiener (
vDSP_Length __vDSP_L,
float *__vDSP_A,
float *__vDSP_C,
float *__vDSP_F,
float *__vDSP_P,
int __vDSP_IFLG,
int *__vDSP_IERR
);

Parameters
L
Input filter length
A
Single-precision real input vector: coefficients
C
Single-precision real input vector: input coefficients
F
Single-precision real output vector: filter coefficients
P
Single-precision real output vector: error prediction operators
IFLG
Not currently used, pass zero
IERR
Error flag
Discussion
Performs the following operation:

solves a set of single-channel normal equations described by:

B[n] = C[0] * A[n] + C[1] * A[n-1] +, . . . ,+ C[N-1] * A[n-N+1]

for n = {0, N-1}

where matrix A contains elements of the symmetric Toeplitz matrix shown below. This function can only be
done out of place.

Note that A[-n] is considered to be equal to A[n].

vDSP_wiener solves this set of simultaneous equations using a recursive method described by Levinson.
See Robinson, E.A., Multichannel Time Series Analysis with Digital Computer Programs. San Francisco: Holden-Day,
1967, pp. 43-46.

|A[0] A[1] A[2] ... A[N-1] | |C[0] | |B[0] |

|A[1] A[0] A[1] ... A[N-2] | |C[1] | |B[1] |
|A[2] A[1] A[0] ... A[N-3] | * |C[2] | = |B[2] |
| ... ... ... ... ... | | ... | | ... |
|A[N-1]A[N-2]A[N-3] ... A[0] | |C[N-1]| |B[N-1]|

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Typical methods for solving N equations in N unknowns have execution times proportional to N3, and memory
requirements proportional to N2. By taking advantage of duplicate elements, the recursion method executes
in a time proportional to N2 and requires memory proportional to N. The Wiener-Levinson algorithm recursively
builds a solution by computing the m+1 matrix solution from the m matrix solution.

With successful completion, vDSP_wiener returns zero in error flag IERR. If vDSP_wiener fails, IERR
indicates in which pass the failure occurred.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_wienerD
Wiener-Levinson general convolution; double precision.

void vDSP_wienerD (
vDSP_Length __vDSP_L,
double *__vDSP_A,
double *__vDSP_C,
double *__vDSP_F,
double *__vDSP_P,
int __vDSP_IFLG,
int *__vDSP_IERR
);

Parameters
L
Input filter length
A
Double-precision real input vector: coefficients
C
Double-precision real input vector: input coefficients
F
Double-precision real output vector: filter coefficients
P
Double-precision real output vector: error prediction operators
IFLG
Not currently used, pass zero
IERR
Error flag
Discussion
Performs the following operation:

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solves a set of single-channel normal equations described by:

B[n] = C[0] * A[n] + C[1] * A[n-1] +, . . . ,+ C[N-1] * A[n-N+1]

for n = {0, N-1}

where matrix A contains elements of the symmetric Toeplitz matrix shown below. This function can only be
done out of place.

Note that A[-n] is considered to be equal to A[n].

vDSP_wiener solves this set of simultaneous equations using a recursive method described by Levinson.
See Robinson, E.A., Multichannel Time Series Analysis with Digital Computer Programs. San Francisco: Holden-Day,
1967, pp. 43-46.

|A[0] A[1] A[2] ... A[N-1] | |C[0] | |B[0] |

|A[1] A[0] A[1] ... A[N-2] | |C[1] | |B[1] |
|A[2] A[1] A[0] ... A[N-3] | * |C[2] | = |B[2] |
| ... ... ... ... ... | | ... | | ... |
|A[N-1]A[N-2]A[N-3] ... A[0] | |C[N-1]| |B[N-1]|

Typical methods for solving N equations in N unknowns have execution times proportional to N3, and memory
requirements proportional to N2. By taking advantage of duplicate elements, the recursion method executes
in a time proportional to N2 and requires memory proportional to N. The Wiener-Levinson algorithm recursively
builds a solution by computing the m+1 matrix solution from the m matrix solution.

With successful completion, vDSP_wiener returns zero in error flag IERR. If vDSP_wiener fails, IERR
indicates in which pass the failure occurred.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zaspec
Computes an accumulating autospectrum; single precision.

void vDSP_zaspec (
DSPSplitComplex *__vDSP_A,
float *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Input vector
C
Input-output vector
N
Real output count

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Discussion
vDSP_zaspec multiplies single-precision complex vector A by its complex conjugates, yielding the sums of
the squares of the complex and real parts: (x + iy) (x - iy) = (x*x + y*y). The results are added to real
single-precision input-output vector C. Vector C must contain valid data from previous processing or should
be initialized according to your needs before calling vDSP_zaspec.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zaspecD
Computes an accumulating autospectrum; double precision.

void vDSP_zaspecD (
DSPDoubleSplitComplex *A,
double *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Input vector
C
Input-output vector
N
Real output count
Discussion
vDSP_zaspecD multiplies double-precision complex vector A by its complex conjugates, yielding the sums
of the squares of the complex and real parts: (x + iy) (x - iy) = (x*x + y*y). The results are added
to real double-precision input-output vector C. Vector C must contain valid data from previous processing
or should be initialized according to your needs before calling vDSP_zaspec.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zcoher
Coherence function of two signals; single precision.

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void vDSP_zcoher (
float *__vDSP_A,
float *__vDSP_B,
DSPSplitComplex *__vDSP_C,
float *__vDSP_D,
vDSP_Length __vDSP_N
);

Discussion
Computes the single-precision coherence function D of two signals. The inputs are the signals' autospectra,
real single-precision vectors A and B, and their cross-spectrum, single-precision complex vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zcoherD
Coherence function of two signals; double precision.

void vDSP_zcoherD (
double *__vDSP_A,
double *__vDSP_B,
DSPDoubleSplitComplex *__vDSP_C,
double *__vDSP_D,
vDSP_Length __vDSP_N
);

Discussion
Computes the double-precision coherence function D of two signals. The inputs are the signals' autospectra,
real double-precision vectors A and B, and their cross-spectrum, double-precision complex vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zconv
Performs either correlation or convolution on two complex vectors; single precision.

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void vDSP_zconv (
DSPSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPSplitComplex *__vDSP_filter,
vDSP_Stride __vDSP_strideFilter,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_lenResult,
vDSP_Length __vDSP_lenFilter
);

Discussion
A is the input vector, with stride I, and C is the output vector, with stride K and length N.

B is a filter vector, with stride I and length P. If Jis positive,the function performs correlation. If Jis negative,
it performs convolution and Bmust point to the last element in the filter vector. The function can run in place,
but Ccannot be in place with B.

The value of N must be less than or equal to 512.

Criteria to invoke vectorized code:

■ Both the real parts and the imaginary parts of vectors A and C must be relatively aligned.
■ The values of I and K must be 1.

If any of these criteria is not satisfied, the function invokes scalar code.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zconvD
Performs either correlation or convolution on two complex vectors; double precision.

void vDSP_zconvD (
DSPDoubleSplitComplex *__vDSP_signal,
vDSP_Stride __vDSP_signalStride,
DSPDoubleSplitComplex *__vDSP_filter,
vDSP_Stride __vDSP_strideFilter,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_lenResult,
vDSP_Length __vDSP_lenFilter
);

Discussion
A is the input vector, with stride I, and C is the output vector, with stride K and length N.

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B is a filter vector, with stride I and length P. If J is positive, the function performs correlation. If J is
negative, it performs convolution and B must point to the last element in the filter vector. The function can
run in place, but C cannot be in place with B.

The value of N must be less than or equal to 512.

Criteria to invoke vectorized code:

No Altivec support for double precision. On a PowerPC processor, this function always invokes scalar code.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zcspec
Accumulating cross-spectrum on two complex vectors; single precision.

void vDSP_zcspec (
DSPSplitComplex *__vDSP_A,
DSPSplitComplex *__vDSP_B,
DSPSplitComplex *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
B
Single-precision complex input vector
C
Single-precision complex input-output vector
N
Count
Discussion
Computes the cross-spectrum of complex vectors A and B and then adds the results to complex input-output
vector C. Vector C should contain valid data from previous processing or should be initialized with zeros
before calling vDSP_zcspec.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_zcspecD
Accumulating cross-spectrum on two complex vectors; double precision.

void vDSP_zcspecD (
DSPDoubleSplitComplex *A,
DSPDoubleSplitComplex *__vDSP_B,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
B
Double-precision complex input vector
C
Double-precision complex input-output vector
N
Count
Discussion
Computes the cross-spectrum of complex vectors A and B and then adds the results to complex input-output
vector C. Vector C should contain valid data from previous processing or should be initialized with zeros
before calling vDSP_zcspecD.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zdotpr
Calculates the complex dot product of complex vectors A and B and leaves the result in complex vector C;
single precision.

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void vDSP_zdotpr (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zdotprD
Calculates the complex dot product of complex vectors A and B and leaves the result in complex vector C;
double precision.

void vDSP_zdotprD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPDoubleSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zidotpr
Calculates the conjugate dot product (or inner dot product) of complex vectors A and B and leave the result
in complex vector C; single precision.

void vDSP_zidotpr (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zidotprD
Calculates the conjugate dot product (or inner dot product) of complex vectors A and B and leave the result
in complex vector C; double precision.

void vDSP_zidotprD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPDoubleSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zmma
Multiplies two complex matrices, then adds a third complex matrix; out-of-place; single precision.

void vDSP_zmma (
DSPSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
DSPSplitComplex *__vDSP_d,
vDSP_Stride __vDSP_l,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B,
adds the product to M-by-N matrix C, and stores the result in M-by-N matrix D; single precision.

This performs the following operation:

Parameters A and C are the matrixes to be multiplied, and C the matrix to be added. I is an address stride
through A. J is an address stride through B. K is an address stride through C. L is an address stride through
D.

Parameter D is the result matrix.

Parameter M is the row count for A, C and D. Parameter N is the column count of B, C, and D. Parameter P is
the column count of A and the row count of B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmmaD
Multiplies two complex matrices, then adds a third complex matrix; out-of-place; double precision.

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void vDSP_zmmaD (
DSPDoubleSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPDoubleSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPDoubleSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
DSPDoubleSplitComplex *__vDSP_d,
vDSP_Stride __vDSP_l,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B,
adds the product to M-by-N matrix C, and stores the result in M-by-N matrix D; double precision.

This performs the following operation:

Parameters A and C are the matrixes to be multiplied, and C the matrix to be added. I is an address stride
through A. J is an address stride through B. K is an address stride through C. L is an address stride through
D.

Parameter D is the result matrix.

Parameter M is the row count for A, C and D. Parameter N is the column count of B, C, and D. Parameter P is
the column count of A and the row count of B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmms
Multiplies two complex matrices, then subtracts a third complex matrix; out-of-place; single precision.

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void vDSP_zmms (
DSPSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
DSPSplitComplex *__vDSP_d,
vDSP_Stride __vDSP_l,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B ,
subtracts M-by-N matrix C from the product, and stores the result in M-by-N matrix D.

This performs the following operation:

Parameters A and B are the matrixes to be multiplied, and C the matrix to be subtracted. I is an address stride
through A. J is an address stride through B. K is an address stride through C. L is an address stride through
D.

Parameter D is the result matrix.

Parameter M is the row count for A, C and D. Parameter N is the column count of B, C, and D. Parameter P is
the column count of A and the row count of B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmmsD
Multiplies two complex matrices, then subtracts a third complex matrix; out-of-place; double precision.

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void vDSP_zmmsD (
DSPDoubleSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPDoubleSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPDoubleSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
DSPDoubleSplitComplex *__vDSP_d,
vDSP_Stride __vDSP_l,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B,
subtracts M-by-N matrix C from the product, and stores the result in M-by-N matrix D.

This performs the following operation:

Parameters A and B are the matrixes to be multiplied, and C the matrix to be subtracted. I is an address stride
through A. J is an address stride through B. K is an address stride through C. L is an address stride through
D.

Parameter D is the result matrix.

Parameter M is the row count for A, C and D. Parameter N is the column count of B, C, and D. Parameter P is
the column count of A and the row count of B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmmul
Multiplies two matrices of complex numbers; out-of-place; single precision.

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void vDSP_zmmul (
DSPSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B
and stores the results in an M-by-N matrix C.

This performs the following operation:

Parameters A and B are the matrixes to be multiplied. I is an address stride through A. J is an address stride
through B.

Parameter C is the result matrix. K is an address stride through C.

Parameter M is the row count for both A and C. Parameter N is the column count for both B and C. Parameter
P is the column count for A and the row count for B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmmulD
Multiplies two matrices of complex numbers; out-of-place; double precision.

void vDSP_zmmulD (
DSPDoubleSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPDoubleSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPDoubleSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B
and stores the results in an M-by-N matrix C.

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This performs the following operation:

Parameters A and B are the matrixes to be multiplied. I is an address stride through A. J is an address stride
through B.

Parameter C is the result matrix. K is an address stride through C.

Parameter M is the row count for both A and C. Parameter N is the column count for both B and C. Parameter
P is the column count for A and the row count for B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmsm
Subtracts the product of two complex matrices from a third complex matrix; out-of-place; single precision.

void vDSP_zmsm (
DSPSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
DSPSplitComplex *__vDSP_d,
vDSP_Stride __vDSP_l,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B,
subtracts the product from M-by-P matrix C, and stores the result in M-by-P matrix D.

This performs the following operation:

Parameters A and B are the matrixes to be multiplied, and C is the matrix from which the product is to be
subtracted. aStride is an address stride through A. bStride is an address stride through B. cStride is an
address stride through C. dStride is an address stride through D.

Parameter D is the result matrix.

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Parameter M is the row count for A, C and D. Parameter N is the column count of B, C, and D. Parameter P is
the column count of A and the row count of B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zmsmD
Subtracts the product of two complex matrices from a third complex matrix; out-of-place; double precision.

void vDSP_zmsmD (
DSPDoubleSplitComplex *__vDSP_a,
vDSP_Stride __vDSP_i,
DSPDoubleSplitComplex *__vDSP_b,
vDSP_Stride __vDSP_j,
DSPDoubleSplitComplex *__vDSP_c,
vDSP_Stride __vDSP_k,
DSPDoubleSplitComplex *__vDSP_d,
vDSP_Stride __vDSP_l,
vDSP_Length __vDSP_M,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_P
);

Discussion
This function performs an out-of-place complex multiplication of an M-by-P matrix A by a P-by-N matrix B,
subtracts the product from M-by-P matrix C, and stores the result in M-by-P matrix D.

This performs the following operation:

Parameters A and B are the matrixes to be multiplied, and parameter C is the matrix from which the product
is to be subtracted. aStride is an address stride through A. bStride is an address stride through B. cStride
is an address stride through C. dStride is an address stride through D.

Parameter D is the result matrix.

Parameter M is the row count for A, C and D. Parameter N is the column count of B, C, and D. Parameter P is
the column count of A and the row count of B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zrdesamp
Complex/real downsample with anti-aliasing; single precision.

void vDSP_zrdesamp (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
DSPSplitComplex *__vDSP_C,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Single-precision complex input vector.
I
Complex decimation factor.
B
Filter coefficient vector.
C
Single-precision complex output vector.
N
Length of output vector.
M
Length of real filter vector.
Discussion
Performs finite impulse response (FIR) filtering at selected positions of input vector A.

Length of A must be at least (N+M-1)*i. This function can run in place, but C cannot be in place with B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrdesampD
Complex/real downsample with anti-aliasing; double precision.

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void vDSP_zrdesampD (
DSPDoubleSplitComplex *A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Length __vDSP_N,
vDSP_Length __vDSP_M
);

Parameters
A
Double-precision complex input vector.
I
Complex decimation factor.
B
Filter coefficient vector.
C
Double-precision complex output vector.
N
Length of output vector.
M
Length of real filter vector.
Discussion
Performs finite impulse response (FIR) filtering at selected positions of input vector A.

Length of A must be at least (N+M-1)*i. This function can run in place, but C cannot be in place with B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrdotpr
Calculates the complex dot product of complex vector A and real vector B and leaves the result in complex
vector C; single precision.

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void vDSP_zrdotpr (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrdotprD
Calculates the complex dot product of complex vector A and real vector B and leaves the result in complex
vector C; double precision.

void vDSP_zrdotprD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvadd
Adds real vector B to complex vector A and leaves the result in complex vector C; single precision.

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void vDSP_zrvadd (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvaddD
Adds real vector B to complex vector A and leaves the result in complex vector C; double precision.

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void vDSP_zrvaddD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvdiv
Divides complex vector A by real vector B and leaves the result in vector C; single precision.

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void vDSP_zrvdiv (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvdivD
Divides complex vector A by real vector B and leaves the result in vector C; double precision.

void vDSP_zrvdivD (
DSPDoubleSplitComplex *A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvmul
Multiplies complex vector A by real vector B and leaves the result in vector C; single precision.

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void vDSP_zrvmul (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvmulD
Multiplies complex vector A by real vector B and leaves the result in vector C; double precision.

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void vDSP_zrvmulD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvsub
Subtracts real vector B from complex vector A and leaves the result in complex vector C; single precision.

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void vDSP_zrvsub (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const float __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zrvsubD
Subtracts real vector B from complex vector A and leaves the result in complex vector C; double precision.

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void vDSP_zrvsubD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const double __vDSP_input2[],
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_ztoc
Copies the contents of a split complex vector A to an interleaved complex vector C; single precision.

void vDSP_ztoc (
const DSPSplitComplex *__vDSP_Z,
vDSP_Stride __vDSP_strideZ,
DSPComplex __vDSP_C[],
vDSP_Stride __vDSP_strideC,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation;

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The strideC parameter contains an address stride through C. strideZ is an address stride through Z.

For best performance, C->realp, C->imagp, A->realp, and A->imagp should be 16-byte aligned.

See also vDSP_ctoz (page 197) and vDSP_ctozD (page 197).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_ztocD
Copies the contents of a split complex vector A to an interleaved complex vector C; double precision.

void vDSP_ztocD (
const DSPDoubleSplitComplex *__vDSP_Z,
vDSP_Stride __vDSP_strideZ,
DSPDoubleComplex __vDSP_C[],
vDSP_Stride __vDSP_strideC,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

The strideC parameter contains an address stride through C. strideZ is an address stride through Z.

For best performance, C->realp, C->imagp, A->realp, and A->imagp should be 16-byte aligned.

See also vDSP_ctoz (page 197) and vDSP_ctozD (page 197).

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_ztrans
Transfer function; single precision.

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void vDSP_ztrans (
float *__vDSP_A,
DSPSplitComplex *__vDSP_B,
DSPSplitComplex *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision real input vector
B
Single-precision complex input vector
C
Single-precision complex output vector
N
Count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_ztransD
Transfer function; double precision.

void vDSP_ztransD (
double *__vDSP_A,
DSPDoubleSplitComplex *__vDSP_B,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision real input vector
B
Double-precision complex input vector
C
Double-precision complex output vector
N
Count

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Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvabs
Complex vector absolute values; single precision.

void vDSP_zvabs (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zvabsD
Complex vector absolute values; double precision.

void vDSP_zvabsD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvadd
Adds complex vectors A and B and leaves the result in complex vector C; single precision.

void vDSP_zvadd (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector

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I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex output count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvaddD
Adds complex vectors A and B and leaves the result in complex vector C; double precision.

void vDSP_zvaddD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPDoubleSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zvcma
Multiplies complex vector B by the complex conjugates of complex vector A, adds the products to complex
vector C, and stores the results in complex vector D; single precision.

void vDSP_zvcma (
const DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const DSPSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
const DSPSplitComplex *__vDSP_input3,
vDSP_Stride __vDSP_stride3,
const DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvcmaD
Multiplies complex vector B by the complex conjugates of complex vector A, adds the products to complex
vector C, and stores the results in complex vector D; double precision.

void vDSP_zvcmaD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPDoubleSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_input3,
vDSP_Stride __vDSP_stride3,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_zvcmul
Complex vector conjugate and multiply; single precision.

void vDSP_zvcmul (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_B,
vDSP_Stride __vDSP_J,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
B
Single-precision complex input vector
J
Stride for B
B
Single-precision complex output vector
K
Stride for B
N
Count
Discussion
Multiplies vector B by the complex conjugates of vector A and stores the results in vector B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvcmulD
Complex vector conjugate and multiply; double precision.

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void vDSP_zvcmulD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_B,
vDSP_Stride __vDSP_J,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
B
Double-precision complex input vector
J
Stride for B
B
Double-precision complex output vector
K
Stride for B
N
Count
Discussion
Multiplies vector B by the complex conjugates of vector A and stores the results in vector B.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvconj
Complex vector conjugate; single precision.

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void vDSP_zvconj (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
C
Single-precision complex output vector
K
Stride for C
N
Count
Discussion
Conjugates vector A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvconjD
Complex vector conjugate; double precision.

void vDSP_zvconjD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
C
Double-precision complex output vector

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K
Stride for C
N
Count
Discussion
Conjugates vector A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvdiv
Complex vector divide; single precision.

void vDSP_zvdiv (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_B,
vDSP_Stride __vDSP_J,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
B
Single-precision complex input vector
J
Stride for B
C
Single-precision complex output vector
K
Stride for C
N
Count
Discussion
Divides vector B by vector A.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvdivD
Complex vector divide; double precision.

void vDSP_zvdivD (
DSPDoubleSplitComplex *A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_B,
vDSP_Stride __vDSP_J,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
B
Double-precision complex input vector
J
Stride for B
C
Double-precision complex output vector
K
Stride for C
N
Count
Discussion
Divides vector B by vector A.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_zvfill
Complex vector fill; single precision.

void vDSP_zvfill (
DSPSplitComplex *__vDSP_A,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input scalar
C
Single-precision complex output vector
K
Stride for C
N
Count
Discussion
Sets each element in complex vector C to complex scalar A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvfillD
Complex vector fill; double precision.

void vDSP_zvfillD (
DSPDoubleSplitComplex *__vDSP_A,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input scalar
C
Double-precision complex output vector

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K
Stride for C
N
Count
Discussion
Sets each element in complex vector C to complex scalar A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvmags
Complex vector magnitudes squared; single precision.

void vDSP_zvmags (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Calculates the squared magnitudes of complex vector A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zvmagsD
Complex vector magnitudes squared; double precision.

void vDSP_zvmagsD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Calculates the squared magnitudes of complex vector A.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvmgsa
Complex vector magnitudes square and add; single precision.

void vDSP_zvmgsa (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_B,
vDSP_Stride __vDSP_J,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector

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I
Stride for A
B
Single-precision real input vector
J
Stride for B
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Adds the squared magnitudes of complex vector A to real vector B and store the results in real vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvmgsaD
Complex vector magnitudes square and add; double precision.

void vDSP_zvmgsaD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_B,
vDSP_Stride __vDSP_J,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
B
Double-precision real input vector
J
Stride for B
C
Double-precision real output vector

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K
Stride for C
N
Count
Discussion
Adds the squared magnitudes of complex vector A to real vector B and store the results in real vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvmov
Complex vector copy; single precision.

void vDSP_zvmov (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
C
Single-precision complex output vector
K
Stride for C
N
Count
Discussion
Copies complex vector A to complex vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

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vDSP_zvmovD
Complex vector copy; double precision.

void vDSP_zvmovD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
C
Double-precision complex output vector
K
Stride for C
N
Count
Discussion
Copies complex vector A to complex vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvmul
Multiplies complex vectors A and B and leaves the result in complex vector C; single precision.

void vDSP_zvmul (
const DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
const DSPSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
const DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size,
int __vDSP_conjugate
);

Discussion
Pass 1 or -1 for F, for normal or conjugate multiplication, respectively. Results are undefined for other values
of F.

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Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvmulD
Multiplies complex vectors A and B and leaves the result in complex vector C; double precision.

void vDSP_zvmulD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPDoubleSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size,
int __vDSP_conjugate
);

Discussion
Pass 1 or -1 for F, for normal or conjugate multiplication, respectively. Results are undefined for other values
of F.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvneg
Complex vector negate; single precision.

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void vDSP_zvneg (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
C
Single-precision complex output vector
K
Stride for C
N
Count
Discussion
Computes the negatives of the values of complex vector A and puts them into complex vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvnegD
Complex vector negate; double precision.

void vDSP_zvnegD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
C
Double-precision complex output vector

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K
Stride for C
N
Count
Discussion
Computes the negatives of the values of complex vector A and puts them into complex vector C.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvphas
Complex vector phase; single precision.

void vDSP_zvphas (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
float *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
C
Single-precision real output vector
K
Stride for C
N
Count
Discussion
Finds the phase values, in radians, of complex vector A and store the results in real vector C. The results are
between -pi and +pi. The sign of the result is the sign of the second coordinate in the input vector.

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

vDSP_zvphasD
Complex vector phase; double precision.

void vDSP_zvphasD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
double *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
C
Double-precision real output vector
K
Stride for C
N
Count
Discussion
Finds the phase values, in radians, of complex vector A and store the results in real vector C. The results are
between -pi and +pi. The sign of the result is the sign of the second coordinate in the input vector.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvsma
Complex vector scalar multiply and add; single precision.

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void vDSP_zvsma (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_B,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
DSPSplitComplex *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
B
Single-precision complex input scalar
C
Single-precision real input vector
K
Stride for C
D
Single-precision real output vector
L
Stride for C
N
Count
Discussion
Multiplies vector A by scalar B and add the products to vector C. The result is stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvsmaD
Complex vector scalar multiply and add; double precision.

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void vDSP_zvsmaD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_B,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
DSPDoubleSplitComplex *__vDSP_D,
vDSP_Stride __vDSP_L,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector
I
Stride for A
B
Double-precision complex input scalar
C
Double-precision real input vector
K
Stride for C
D
Double-precision real output vector
L
Stride for C
N
Count
Discussion
Multiplies vector A by scalar B and add the products to vector C. The result is stored in vector D.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvsub
Subtracts complex vector B from complex vector A and leaves the result in complex vector C; single precision.

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void vDSP_zvsub (
DSPSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex element count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvsubD
Subtracts complex vector B from complex vector A and leaves the result in complex vector C; double precision.

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void vDSP_zvsubD (
DSPDoubleSplitComplex *__vDSP_input1,
vDSP_Stride __vDSP_stride1,
DSPDoubleSplitComplex *__vDSP_input2,
vDSP_Stride __vDSP_stride2,
DSPDoubleSplitComplex *__vDSP_result,
vDSP_Stride __vDSP_strideResult,
vDSP_Length __vDSP_size
);

Parameters
A
Input vector
I
Address stride for A
B
Input vector
J
Address stride for B
C
Output vector
K
Address stride for C
N
Complex element count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvzsml
Complex vector multiply by complex scalar; single precision.

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void vDSP_zvzsml (
DSPSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPSplitComplex *__vDSP_B,
DSPSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Single-precision complex input vector
I
Stride for A
B
Single-precision complex input scalar
C
Single-precision complex output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_zvzsmlD
Complex vector multiply by complex scalar; double precision.

void vDSP_zvzsmlD (
DSPDoubleSplitComplex *__vDSP_A,
vDSP_Stride __vDSP_I,
DSPDoubleSplitComplex *__vDSP_B,
DSPDoubleSplitComplex *__vDSP_C,
vDSP_Stride __vDSP_K,
vDSP_Length __vDSP_N
);

Parameters
A
Double-precision complex input vector

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I
Stride for A
B
Double-precision complex input scalar
C
Double-precision complex output vector
K
Stride for C
N
Count
Discussion
This performs the following operation:

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

Data Types

This document describes the data types used by the vDSP portion of the Accelerate framework.

vDSP_Length
Used for numbers of elements in arrays and indices of elements in arrays. It is also used for the base-two
logarithm of numbers of elements.

typedef unsigned long vDSP_Length;

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

vDSP_Stride
Used to hold differences between indices of elements, including the lengths of strides.

typedef long vDSP_Stride;

Availability
Available in iPhone OS 4.0 and later.

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Declared In
vDSP.h

DSPComplex
Used to hold a complex value.

struct DSPComplex {
float real;
float imag;
};

typedef struct DSPComplex DSPComplex;

Discussion
Complex data are stored as ordered pairs of floating-point numbers. Because they are stored as ordered
pairs, complex vectors require address strides that are multiples of two.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

DSPSplitComplex
Used to represent a complex number when the real and imaginary parts are stored in separate arrays.

struct DSPSplitComplex {
float *realp;
float *imagp;
};

typedef struct DSPSplitComplex DSPSplitComplex;

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

DSPDoubleComplex
Used to hold a double-precision complex value.

struct DSPDoubleComplex {
double real;
double imag;
};

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typedef struct DSPDoubleComplex DSPDoubleComplex;

Discussion
Double complex data are stored as ordered pairs of doiuble-precision floating-point numbers. Because they
are stored as ordered pairs, complex vectors require address strides that are multiples of two.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

DSPDoubleSplitComplex
Used to represent a double-precision complex number when the real and imaginary parts are stored in
separate arrays.

struct DSPDoubleSplitComplex {
double *realp;
double *imagp;
};

typedef struct DSPDoubleSplitComplex DSPDoubleSplitComplex;

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

FFTSetup
An opaque type that contains setup information for a given FFT transform.

typedef struct OpaqueFFTSetup* FFTSetup;

Discussion
A setup object can be allocated with vDSP_create_fftsetup (page 195) and destroyed with
vDSP_destroy_fftsetup (page 201). The setup object includes, among other things, precomputed tables
used in computing an FFT of the specified size.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

FFTSetupD
An opaque type that contains setup information for a given double-precision FFT transform.

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typedef struct OpaqueFFTSetupD* FFTSetupD;

Discussion
A setup object can be allocated with vDSP_create_fftsetupD (page 196) and destroyed with
vDSP_destroy_fftsetupD (page 202). The setup object includes, among other things, precomputed tables
used in computing an FFT of the specified size.

Availability
Available in iPhone OS 4.0 and later.

Declared In
vDSP.h

Constants

vDSP Compile-Time Version Information

The version of vDSP (at compile time).

#define vDSP_Version0 268

#define vDSP_Version1 0

Constants
vDSP_Version0
The vDSP major version.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
vDSP_Version1
The vDSP minor version.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.

vDSP_DFT_Direction
Specifies whether to perform a forward or inverse DFT.

typedef enum {
vDSP_DFT_FORWARD = +1,
vDSP_DFT_INVERSE = -1
} vDSP_DFT_Direction;

Constants
vDSP_DFT_FORWARD
Specifies a forward transform.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.

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vDSP_DFT_INVERSE
Specifies an inverse transform.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.

FFTDirection
Specifies whether to perform a forward or inverse FFT.

enum {
kFFTDirection_Forward = 1,
kFFTDirection_Inverse = -1
};
typedef int FFTDirection;

Constants
kFFTDirection_Forward
Specifies a forward transform.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
kFFTDirection_Inverse
Specifies an inverse transform.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.

FFTRadix
The size of the FFT decomposition.

enum {
kFFTRadix2 = 0,
kFFTRadix3 = 1,
kFFTRadix5 = 2
};
typedef int FFTRadix;

Constants
kFFTRadix2
Specifies a radix of 2.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
kFFTRadix3
Specifies a radix of 3.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.

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kFFTRadix5
Specifies a radix of 5.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
Discussion
An FFTRadix value is passed as an argument to vDSP_create_fftsetup (page 195) or
vDSP_create_fftsetupD (page 196).

FFTWindow
Specifies the windowing mode for data values in an FFT or reverse FFT.

enum {
vDSP_HALF_WINDOW = 1,
vDSP_HANN_DENORM = 0,
vDSP_HANN_NORM = 2
};

Constants
vDSP_HALF_WINDOW
Specifies that the window should only contain the bottom half of the values (0 to (N+1)/2).
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
vDSP_HANN_DENORM
Specifies a denormalized Hann window.
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
vDSP_HANN_NORM
Specifies a normalized Hann window
Available in iPhone OS 4.0 and later.
Declared in vDSP.h.
Discussion
Passed as a flag to vDSP_blkman_window (page 192) or vDSP_blkman_windowD (page 192) to specify the
desired type of window..

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REVISION HISTORY

Document Revision History

This table describes the changes to Accelerate Framework Reference.

Date Notes

2010-03-19 Added document to iPhone OS documentation set.

2010-01-19 New document that describes the Accelerate framework, a C-based API for
performing matrix math, digital signal processing, and image manipulation.

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 REVISION HISTORY
Document Revision History

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