NAME

       Math::Prime::Util::PP - Pure Perl version of Math::Prime::Util

VERSION

       Version 0.57

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

       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 2012-2016 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.