A journey with Perl, MCE, Inline::C (and more) to count, sum, and generate prime numbers.
The sandbox has the minimum required to run the practical sieve demonstration. Perl MCE and Inline::C modules are pre-installed under the lib directory. ExtUtils::MakeMaker and Time::HiRes, possibly missing in Perl 8 and 10, are required on the system.
.Inline/ Where Inline::C is configured to cache C object files.
bin/
algorithm3.pl Practical sieve based on Algorithm3 from Xuedong Luo [1].
primesieve.pl Calls the primesieve.org C API for generating primes.
primeutil.pl Utilizes the Math::Prime::Util module for primes.
demos/
primes1.c Algorithm3 in C with OpenMP directives.
primes2.codon Algorithm3 in Codon, a Python-like language.
primes3.c Using libprimesieve C API in C
primes4.codon Using libprimesieve C API in Codon
examples/ Progressive demonstrations.
practicalsieve.c single big loop
segmentsieve.c segmented variant, faster
rangesieve.c process range; start stop
prangesieve.c parallel rangesieve in C
cpusieve.codon parallel rangesieve in Codon (CPU)
gpusieve.codon parallel rangesieve in Codon (GPU)
pgpusieve.codon using Codon @par(gpu=True) syntax
cudasieve.cu using NVIDIA CUDA Toolkit
lib/
Sandbox.pm Common code for the bin scripts.
CpuAffinity.pm CPU Affinity support on Linux.
src/
algorithm3.c Inline::C code for algorithm3.pl.
bits.h Utility functions for byte array.
output.h Fast printing of primes to a file descriptor.
primesieve.c Inline::C code for primesieve.pl.
sandbox.h Header file, includes bits.h, output.h, sprintull.h.
sprintull.h Fast base10 to string conversion.
typemap Type-map file for Inline::C.
Algorithm3 is something I tried early on. It will run out of the box, granted you have a C compiler installed. Some OS environments may need to update ExtUtils::MakeMaker manually for Inline::C to function properly; e.g Cygwin.
There is a one time delay the first time running algorithm3 and primesieve.
The delay comes from Inline::C building the relevant C files. Note: Inline::C
will not know of subsequent edits to the header files. If necessary, remove the
.Inline folder manually to clear the cache.
More variants using Math::Prime::Util and libprimesieve were created next. They run faster than algorithm3.
The demos folder is how I learned Codon,
a Python-like language that compiles to native machine code. They run with
limited usage, accepting one or two integers and -p options. Usage can be
found at the top of the file.
The examples folder provides progressive demonstrations in C including parallel range variants in Codon.
The primesieve.pl and primeutil.pl Perl examples have additional dependencies.
For example, on Ubuntu Linux:
sudo apt install libmath-prime-util-gmp-perl libmath-prime-util-perl
sudo apt install libprimesieve-dev
Refer to primesieve's home page.
Change the base path in primesieve.pl (lines 187 and 188) if installing
the development files elsewhere, other than /usr or /usr/local.
The Math::Prime::Util demonstration requires also, Perl::Unsafe::Signals. This enables workers, running a long XS function, to stop immediately upon receiving a signal.
Using 32-bit Perl, finding prime numbers above 2^32-1 requires bigint.
Uncomment the line use bigint in the following files. Leave commented
for 64-bit Perl.
bin/algorithm3.pl
bin/primesieve.pl
bin/primeutil.pl
lib/Sandbox.pm
The following usage is taken from algorithm3.pl, similar for primesieve.pl
and primeutil.pl.
The base10 to string conversion and buffered IO logic provides efficient printing of primes. Please be careful with the --print/-p options. It can quickly fill your disk. A suggestion is specifying a range instead.
NAME
algorithm3.pl -- count, sum, or generate prime numbers in order
SYNOPISIS
algorithm3.pl [options] [[ FROM ] NUMBER ]
DESCRIPTION
The algorithm3.pl utility is a parallel sieve generator based off the
3rd sieve extension from Xuedong Luo (Algorithm3) [1].
It generates 50,847,534 primes in little time. Notice the file size for
primes.out. This will obviously consume lots of space; e.g. running with
1e+11 requires 45.5 GB. The upper limit for number is 2^64-1-6.
algorithm3.pl 1e9 --print > primes.out # file size 479 MB
algorithm3.pl 4294967296 # default, count primes
203280221
algorithm3.pl 4294967296 --sum # sum primes otherwise
425649736193687430
The following options are available:
--maxworkers=<val> specify the number of workers (default 100%)
--threads=<val> alias for --maxworkers
--usethreads spawn workers via threads if available (not fork)
--help, -h display this help and exit
--print, -p print primes (ignored if sum is specified)
--quiet, -q suppress progress including extra output
--sum, -s sum primes (maximum N allowed 29505444490)
EXAMPLES
algorithm3.pl 18446744073000000000 18446744073709551609
algorithm3.pl --maxworkers=8 1000000000
algorithm3.pl --threads=50% 1e+16 1.00001e+16
algorithm3.pl 22801763489 --sum
algorithm3.pl 1e5 3e5 --print
EXIT STATUS
The algorithm3.pl utility exits with one of the following values:
0 a prime was found
1 a prime was not found
>1 an error occurred
This sandbox includes Inline::C and Parse::RecDescent. Both work reasonably well across many environments in which MCE runs on. The popcount function (in bits.h) is based on popcnt in Math::Prime::Util. I learned a trick in POE to export variables without having to require Exporter.
Thank you, Xuedong Luo for the wonderful sieve algorithm. This repository provides parallel implementations, based on Algorithm3.
- ** Xuedong Luo. A practical sieve algorithm for finding prime numbers. ACM Volume 32 Issue 3, March 1989, Pages 344-346: https://dl.acm.org/doi/pdf/10.1145/62065.62072 https://dl.acm.org/citation.cfm?doid=62065.62072