factor/basis/math/miller-rabin/miller-rabin.factor

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Factor
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! Copyright (C) 2008 Doug Coleman.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators kernel locals math math.functions math.ranges
random sequences sets ;
IN: math.miller-rabin
<PRIVATE
: >odd ( n -- int ) dup even? [ 1+ ] when ; foldable
TUPLE: positive-even-expected n ;
:: (miller-rabin) ( n trials -- ? )
[let | r [ n 1- factor-2s drop ]
s [ n 1- factor-2s nip ]
prime?! [ t ]
a! [ 0 ]
count! [ 0 ] |
trials [
n 1- [1,b] random a!
a s n ^mod 1 = [
0 count!
r [
2^ s * a swap n ^mod n - -1 =
[ count 1+ count! r + ] when
] each
count zero? [ f prime?! trials + ] when
] unless drop
] each prime? ] ;
PRIVATE>
: next-odd ( m -- n ) dup even? [ 1+ ] [ 2 + ] if ;
: miller-rabin* ( n numtrials -- ? )
over {
{ [ dup 1 <= ] [ 3drop f ] }
{ [ dup 2 = ] [ 3drop t ] }
{ [ dup even? ] [ 3drop f ] }
[ drop (miller-rabin) ]
} cond ;
: miller-rabin ( n -- ? ) 10 miller-rabin* ;
: next-prime ( n -- p )
next-odd dup miller-rabin [ next-prime ] unless ;
: random-prime ( numbits -- p )
random-bits next-prime ;
ERROR: no-relative-prime n ;
<PRIVATE
: (find-relative-prime) ( n guess -- p )
over 1 <= [ over no-relative-prime ] when
dup 1 <= [ drop 3 ] when
2dup gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
PRIVATE>
: find-relative-prime* ( n guess -- p )
#! find a prime relative to n with initial guess
>odd (find-relative-prime) ;
: find-relative-prime ( n -- p )
dup random find-relative-prime* ;
ERROR: too-few-primes ;
: unique-primes ( numbits n -- seq )
#! generate two primes
swap
dup 5 < [ too-few-primes ] when
2dup [ random-prime ] curry replicate
dup all-unique? [ 2nip ] [ drop unique-primes ] if ;