1 ! Copyright (C) 2008 Doug Coleman.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: combinators combinators.lib io locals kernel math
4 math.functions math.ranges namespaces random sequences
8 : >even ( n -- int ) dup even? [ 1- ] unless ; foldable
9 : >odd ( n -- int ) dup even? [ 1+ ] when ; foldable
10 : next-odd ( m -- n ) dup even? [ 1+ ] [ 2 + ] if ;
12 TUPLE: positive-even-expected n ;
14 :: (miller-rabin) ( n trials -- ? )
15 [let | r [ n 1- factor-2s drop ]
16 s [ n 1- factor-2s nip ]
25 2^ s * a swap n ^mod n - -1 =
26 [ count 1+ count! r + ] when
28 count zero? [ f prime?! trials + ] when
32 : miller-rabin* ( n numtrials -- ? )
34 { [ dup 1 <= ] [ 3drop f ] }
35 { [ dup 2 = ] [ 3drop t ] }
36 { [ dup even? ] [ 3drop f ] }
37 [ [ drop (miller-rabin) ] with-scope ]
40 : miller-rabin ( n -- ? ) 10 miller-rabin* ;
42 : next-prime ( n -- p )
43 next-odd dup miller-rabin [ next-prime ] unless ;
45 : random-prime ( numbits -- p )
46 random-bits next-prime ;
48 ERROR: no-relative-prime n ;
50 : (find-relative-prime) ( n guess -- p )
51 over 1 <= [ over no-relative-prime ] when
52 dup 1 <= [ drop 3 ] when
53 2dup gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
55 : find-relative-prime* ( n guess -- p )
56 #! find a prime relative to n with initial guess
57 >odd (find-relative-prime) ;
59 : find-relative-prime ( n -- p )
60 dup random find-relative-prime* ;
62 ERROR: too-few-primes ;
64 : unique-primes ( numbits n -- seq )
65 #! generate two primes
66 over 5 < [ too-few-primes ] when
67 [ [ drop random-prime ] with map ] [ all-unique? ] generate ;