FasterPrime

This is an alternative implementation to the standard lib/prime.rb. It is (almost) comapatible and faster than lib/prime.rb.

Usage

• Install faster_prime gem.
• Replace require "prime" with require "faster_prime".
• Replace Prime with FasterPrime.

If you want to use this without the core extension, you can use require "faster_prime/base" and FasterPrime.prime?(num) instead of Integer#prime?.

Benchmark

Integer#prime?

test	Prime	FasterPrime
(2**31-1).prime?	0.00355 s	0.000035 s
(10**100+267).prime?	n/a	0.7003 s

Integer#prime_division

test	Prime	FasterPrime
(2**59-1).prime_division	0.1293 s	0.01259 s
(2**256+1).prime_division	n/a	71.71 s

Prime.each

test	Prime	FasterPrime
Prime.each until 10**7	0.6039 s	0.4855 s
Prime.each until 10**9	57.21 s	49.75 s

Internal

• Integer#prime? uses APR-CL primality test.
• Integer#prime_division uses Pollard's rho algorithm and Multiple Polynomial Quadratic Sieve.
• Prime.each uses the sieve of Atkin.

Caveat

• This library is not intended for practical use because it is written only in Ruby. If you are serious about enjoying number theory, use PARI/GP.
• I have never evaluated the library throughout. It may be slower than lib/prime.rb in some range.
• The author does not understand the algorithms. I just read and implemented some papers. If you find a bug, I'd appreciate if you could give me a patch :-)

License

The MIT License (MIT)

Copyright (c) 2017 Yusuke Endoh

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.