Math-Prime-Util

Changes for version 0.72 - 2018-11-08

ADDED
- nth_semiprime(n) the nth semiprime
- nth_semiprime_approx(n) fast approximate nth semiprime
- semiprime_count_approx(n) fast approximate semiprime count
- semi_primes as primes but for semiprimes
- forsetproduct {...} \@a,\@b,... Cartesian product of list refs
FIXES
- Some platforms are extremely slow for is_pillai. Speed up tests.
- Ensure random_factored_integer factor list is sorted min->max.
- forcomposites didn't check lastfor on every callback.
- Sun's compilers, in a valid interpretation of the code, generated divide by zero code for pillai testing.
FUNCTIONALITY AND PERFORMANCE
- chebyshev_theta and chebyshev_psi redone and uses a table. Large inputs are significantly faster.
- Convert some FP functions to use quadmath if possible. Without quadmath there should be no change. With quadmath functions like LogarithmicIntegral and LambertW will be slower but more accurate.
- semiprime_count for non-trivial inputs uses a segmented sieve and precalculates primes for larger values so can run 2-3x faster.
- forsemiprimes uses a sieve so large ranges are much faster.
- ranged moebius more efficient for small intervals.
- Thanks to GRAY for his module Set::Product which has clean and clever XS code, which I used to improve my code.
- forfactored uses multicall. Up to 2x faster.
- forperm, forcomb, forderange uses multicall. 2-3x faster.
- Frobenius-Khashin algorithm changed from 2013 version to 2016/2018.

Utilities related to prime numbers, including fast sieves and factoring

Pure Perl ChaCha20 CSPRNG

Elliptic curve operations for affine points

Elliptic curve operations for projective points

Get a good random seed

An auto-free object for Math::Prime::Util

Pure Perl version of Math::Prime::Util

PP front end for Math::Prime::Util

Primality proofs and certificates

A tied array for primes

An object iterator for primes

Generate random primes

Perl Big Float versions of Riemann Zeta and R functions

Number theory utilities

To install Math::Prime::Util, copy and paste the appropriate command in to your terminal.

cpanm Math::Prime::Util

perl -MCPAN -e shell
install Math::Prime::Util

For more information on module installation, please visit the detailed CPAN module installation guide.

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