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Changes for version 0.50 - 2015-05-03

  • ADDED
    • harmfrac(n) (num,den) of Harmonic number
    • harmreal(n) Harmonic number as BigFloat
    • sqrtint(n) Integer square root of n
    • vecextract(\@arr, mask) Return elements from arr selected by mask
    • ramanujan_primes(lo,hi) Ramanujan primes R_n in [lo,hi]
    • nth_ramanujan_prime(n) the nth Ramanujan prime R_n
    • is_ramanujan_prime(n) 1 if n is a Ramanujan prime, 0 otherwise
  • FUNCTIONALITY AND PERFORMANCE
    • Implement single-base hashed M-R for 32-bit inputs, inspired by Forišek and Jančina 2015 as well as last year's tests with 2-base (2^49) and 3-base (2^64) hashed solutions for MPU. Primality testing is 20-40% faster for this size.
    • Small speedups for znlog.
    • PP nth_prime on 32-bit fixed for values over 2^32.
  • Misc
    • Changes to nth_prime_{lower,upper}. They use the Axler (2013) bounds, and the XS code will also use inverse prime count bounds for small values. This gives 2-10x tighter bounds.
    • Tighten prime count bounds using Axler, Kotnik, Büthe. Thanks to Charles R Greathouse IV for pointing me to these.

Modules

Utilities related to prime numbers, including fast sieves and factoring
Elliptic curve operations for affine points
Elliptic curve operations for projective points
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