ckormanyos/pi-crunch-metal computes up to a million digits of $\pi$ on a bare-metal RaspberryPi(R)-Zero (and other systems).

This fascinating, educational and fun project combines the domain of high-performance numerical computing with the raw simplicity of bare-metal embedded microcontroller systems.

ckormanyos/pi-crunch-metal exihbits the utmost in portability and is realized primarily through modern, header-only C++14, 17, 20, 23 (and beyond) template code.

The application software is intended to run out of the box on both PC/host systems as well as selected bare-metal microcontroller targets.

The wide-decimal multiprecision float back end provides the big-number engine for pi-crunch-metal. Computation progress can be displayed on either the console (for PC systems) or on a simple industry-standard LCD character display.

The backbone real-time operating system is taken directly from the OSEK-like OS implemented in Chalandi/OSEK_Raspberry_Pi_Zero

In this variation of the project, up to $1,000,001$ decmal digits of $\pi$ (i.e., one-million-and-1) are computed with a quadratically converging Gauss arithmetic geometric mean iteration.

Multiplication is the hot-spot of this program. The multiplication implementation uses a combination of school multiplication for low precision and Karatsuba multiplication for medium percision, switching directly over to an FFT multiplication scheme for higher precision.

The microcontroller boots and performs static initialization via self-written startup code. Hardware setup including clock initialization, FPU enable, instruction caching, etc. is carried out with self-written hybrid assembly/C++ code shortly after reaching main().

Compact code size is in focus and the entire project easily fits within 40k of program code, with slight variations depending on the optimization settings, compiler and target system selected. The calculation does, however, require ample RAM of about 16 Mbyte.

GNU/GCC gcc-arm-non-eabi is used for the target system. Cross development with Win* and/or *nix host is supported. Build tools, the build system and the compilers are essentially the same as those used in the real-time-cpp project. These can also be found within a coherent collection of toolchains in the real-time-cpp-toolchains repository.

In addition to the AGM algorithm mentioned above, a slower quadratic pi-spigot algorithm of order $N^2$ is also supported in this alternate variation of the project. Switching to use the (interchangeable) file pi_spigot.cpp instead of the default pi_agm.cpp alternately uses the pi-spigot algorithm.

The spigot calculation is slower than the AGM calculation and requires sightly more time to compute a count of $100,001$ decimal digits, a factor of ten fewer.

This repo features a fully-worked-out pi-crunch-metal prototype example project running on a RaspberryPi(R)-Zero. This powerful single-board computer is driven in OS-less, bare-metal mode directly out-of-the-box.

The build system is set up to use GCC, making use of the arm-none-eabi compiler taken directly from the real-time-cpp-toolchains repository.

The default optimization setting is -Os and the million-and-one decimal digit pi calculation takes slightly under 30 minutes on this target system with the above-mentioned compiler.

The hardware setup is pictured in the image below. In this image, the system has successfully completed one full mega-digit pi calculation and is almost done with a second one.

Traditional wire-wrapping techniques connect the pins on a self-made breakout board to a solderless prototyping breadboard. Double and quadruple strands of skinny wire are used on the power and ground pins, as these might typically carry up to $150mA$ of current in this setup.

Bit banging is used to implement an all-software SPI-compatible driver which controls a port expander chip. The port expander chip is used to control the pins on an industry-standard LCD character display.

A classic logic AND-gate converts $3.3V$ to TTL $5V$ level. A little sawed-out, semi-hollow aluminum chunk is used as a heat-sink to cool the processor.

The output pin connections from the Rpi-Zero to the logic-AND gate are shown in the table below.

The LCD pin connections and the input/output connections of the port expander chip are clearly identifiable in the image. The port expander chip uses hardware addressing and is hard-wired to address 2.