Chudnovsky-Pi

A parallel demonstration for computing Pi digits in C and Perl using the fast Chudnovsky algorithm. C code embeds OpenMP directives to consume many cores. Perl scripts pi-hobo.pl and pi-thrs.pl use MCE::Hobo and threads respectively, and pthreads for 2nd-level workers.

Content

   bin/
     pi-gmp.exe          C executable using OpenMP and GMP
     pi-hobo.pl          Perl script using Inline::C and MCE::Hobo
     pi-mpir.exe         C executable using OpenMP and MPIR
     pi-thrs.pl          Perl script using Inline::C and threads

   lib/
     Perl modules        Inline, Inline::C, MCE, MCE::Shared, and
                         Parse::RecDescent
   src/
     Makefile            For building pi-gmp.exe and pi-mpir.exe
     extra/              Parallel recursion support for mpn_get_str
     perl-chudnovsky.c   Code used by Perl via Inline::C
     pgmp-chudnovsky.c   Code containing main and OpenMP directives
     pgmp-chudnovsky.h   Common code for perl/pgmp-chudnovsky.c
     typemap             Typemap configuration used by Inline::C
     util.h              Inp & out functions supporting large data
                           E.g. mpf/mpz_inp_raw, mpf/mpz_out_raw

Dependencies

On Microsoft Windows, use 64-bit Cygwin to not have limitations. Select gcc-core, gcc-g++, libcrypt-devel, m4, make, perl, and yasm during installation.

• A C compiler, gmake or make, and m4. Yasm is required to build MPIR.
• GMP 6.2.1 or later
• MPIR 3.0.0
• YASM 1.3.0

The following modules ship with Perl typically.

• ExtUtils::MakeMaker
• Storable
• Time::HiRes

Building

• GMP

Strawberry Perl users may skip this step as GMP is included. By default, make install will install files in /usr/local. You can specify an installation prefix other than /usr/local using --prefix, for instance --prefix=$HOME.

   cd gmp-6.2.1
   ./configure --disable-static --enable-shared --enable-cxx
   make -j 4
   make check
   sudo make install

• YASM

The yasm package by the OS vendor is fine if 1.2.0 or later.

   cd yasm-1.3.0
   ./configure
   make -j 4
   sudo make install

• MPIR

MPIR may provide better performance on Microsoft Windows.

   cd mpir-3.0.0
   ./configure --disable-static --enable-shared --enable-cxx
   make -j 4
   make check
   sudo make install

• CODE

Library selection is possible via CFLAGS. The default builds against GMP. Please use gmake when available.

   CFLAGS="-O2 -DUSE_GMP"  (or)  CFLAGS="-O2 -DUSE_MPIR"
   Machines with 128 GiB: CFLAGS="-O2 -DUSE_GMP -DBIG_SIEVE=1"
     
   Strawberry Perl <  v5.26  dmake
   Strawberry Perl >= v5.26  gmake

   Cygwin    make  CFLAGS="-O2 -DUSE_MPIR"
   FreeBSD   gmake CC=clang CFLAGS="..."
   Linux     make
   Mac OS X  make
   Solaris   gmake note: src/extra supports GMP only on SPARC machines
   Other OS  make

Make without a target builds Inline C objects for Perl scripts residing in ../bin/. The C objects are stored in ../.Inline/.

   cd Chudnovsky-Pi-master/src

   make CFLAGS="-O2 -DBIG_SIEVE=0 -DUSE_GMP"    # default on all OS'es
   make CFLAGS="-O2 -DBIG_SIEVE=0 -DUSE_MPIR"   # preferred on Cygwin

   make pi-gmp    # builds the binary executable using GMP
   make pi-mpir   # builds the binary executable using MPIR

Usage

The usage is similar for pi-gmp.exe, pi-mpir.exe, and pi-thrs.pl.

   SYNOPSIS
       perl pi-hobo.pl <digits> [ <option> <threads> ]

       <digits>  digits of Pi to output

       <option>  0 - just run (default)
                 1 - output digits only
                 2 - output digits (2 columns)
                 3 - output digits (3 columns)
                 N - output digits (N columns, max 14)

       <threads> number of threads (default 1)
                 specify 'auto' to run on all cores

   EXAMPLES
       perl pi-hobo.pl 10000000 1 auto | md5sum
           bc3234ae2e3f6ec7737f037b375eabec  -

       perl pi-hobo.pl 100000000 1 auto | md5sum
           969bfe295b67da45b68086eb05a8b031  -

       perl pi-hobo.pl 100000000 5 auto > pi.txt

Limitations

The following limitations apply to 32-bit OS'es and Strawberry Perl.

• Maximum 16 threads on Windows, excluding Cygwin
• 120 million digits for 32-bit binaries, all OS'es
• 640 million digits for 64-bit Strawberry Perl

To compute more than 640 million digits on Microsoft Windows, install 64-bit Cygwin. I tested 1 and 2 billion digits, limited by available memory. In Cygwin, mutex locking using threads is noticeably slower compared to Unix during mpz/mpf_init for temporary variables by GMP/MPIR. Run pi-hobo.pl instead for best performance.

   # on Cygwin
   perl pi-hobo.pl 1000000000 1 8 | md5sum
   3901670f41a84174103bd6a8f07651c0 *-

   perl pi-hobo.pl 2000000000 1 8 | md5sum
   dcf466792a8958becbb05b74b983d8b1 *-

Acknowledgements

The code is derived from examples on the web.

• https://gmplib.org/list-archives/gmp-discuss/2008-November/003444.html
• https://gmplib.org/download/misc/gmp-chudnovsky.c

See also programs for Raspberry Pi by David Carver.

• https://github.com/davidcarver/Parallel-Chudnovsky-PI