NAME¶
Math::Prime::Util::PP - Pure Perl version of Math::Prime::Util
VERSION¶
Version 0.46
SYNOPSIS¶
The functionality is basically identical to Math::Prime::Util, as this module is
just the Pure Perl implementation. This documentation will only note
differences.
# Normally you would just import the functions you are using.
# Nothing is exported by default.
use Math::Prime::Util ':all';
DESCRIPTION¶
Pure Perl implementations of prime number utilities that are normally handled
with XS or GMP. Having the Perl implementations (1) provides examples, (2)
allows the functions to run even if XS isn't available, and (3) gives big
number support if Math::Prime::Util::GMP isn't available. This is a subset of
Math::Prime::Util's functionality.
All routines should work with native integers or multi-precision numbers. To
enable big numbers, use bigint or bignum:
use bigint;
say prime_count_approx(1000000000000000000000000)'
# says 18435599767347543283712
This is still experimental, and some functions will be very slow. The
Math::Prime::Util::GMP module has much faster versions of many of these
functions. Alternately, Math::Pari has a lot of these types of functions.
FUNCTIONS¶
euler_phi¶
Takes a
single integer input and returns the Euler totient.
euler_phi_range¶
Takes two values defining a range "low" to "high" and
returns an array with the totient of each value in the range, inclusive.
moebius¶
Takes a
single integer input and returns the Moebius function.
moebius_range¶
Takes two values defining a range "low" to "high" and
returns an array with the Moebius function of each value in the range,
inclusive.
LIMITATIONS¶
The SQUFOF and Fermat factoring algorithms are not implemented yet.
Some of the prime methods use more memory than they should, as the segmented
sieve is not properly used in "primes" and "prime_count".
Performance compared to the XS/C code is quite poor for many operations. Some
operations that are relatively close for small and medium-size values:
next_prime / prev_prime
is_prime / is_prob_prime
is_strong_pseudoprime
ExponentialIntegral / LogarithmicIntegral / RiemannR
primearray
Operations that are slower include:
primes
random_prime / random_ndigit_prime
factor / factor_exp / divisors
nth_prime
prime_count
is_aks_prime
Performance improvement in this code is still possible. The prime sieve is over
2x faster than anything I was able to find online, but it is still has room
for improvement.
Math::Prime::Util::GMP offers "C+XS+GMP" support for most of the
important functions, and will be vastly faster for most operations. If you
install that module, Math::Prime::Util will load it automatically, meaning you
should not have to think about what code is actually being used (C, GMP, or
Perl).
Memory use will generally be higher for the PP code, and in some cases
much higher. Some of this may be addressed in a later release.
For small values (e.g. primes and prime counts under 10M) most of this will not
matter.
SEE ALSO¶
Math::Prime::Util
Math::Prime::Util::GMP
AUTHORS¶
Dana Jacobsen <dana@acm.org>
COPYRIGHT¶
Copyright 2012-2014 by Dana Jacobsen <dana@acm.org>
This program is free software; you can redistribute it and/or modify it under
the same terms as Perl itself.