83 lines
2.0 KiB
Factor
Executable File
83 lines
2.0 KiB
Factor
Executable File
USING: combinators combinators.lib io locals kernel math
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math.functions math.ranges namespaces random sequences
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hashtables sets ;
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IN: math.miller-rabin
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SYMBOL: a
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SYMBOL: n
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SYMBOL: r
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SYMBOL: s
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SYMBOL: count
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SYMBOL: trials
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: >even ( n -- int )
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dup even? [ 1- ] unless ; foldable
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: >odd ( n -- int )
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dup even? [ 1+ ] when ; foldable
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: next-odd ( m -- n )
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dup even? [ 1+ ] [ 2 + ] if ;
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TUPLE: positive-even-expected n ;
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: (factor-2s) ( r s -- r s )
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dup even? [ -1 shift >r 1+ r> (factor-2s) ] when ;
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: factor-2s ( n -- r s )
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#! factor an integer into s * 2^r
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0 swap (factor-2s) ;
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:: (miller-rabin) ( n prime?! -- ? )
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n 1- factor-2s s set r set
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trials get [
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n 1- [1,b] random a set
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a get s get n ^mod 1 = [
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0 count set
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r get [
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2^ s get * a get swap n ^mod n - -1 = [
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count [ 1+ ] change
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r get +
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] when
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] each
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count get zero? [
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f prime?!
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trials get +
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] when
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] unless
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drop
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] each prime? ;
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TUPLE: miller-rabin-bounds ;
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: miller-rabin* ( n numtrials -- ? )
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over {
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{ [ dup 1 <= ] [ 3drop f ] }
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{ [ dup 2 = ] [ 3drop t ] }
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{ [ dup even? ] [ 3drop f ] }
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[ [ drop trials set t (miller-rabin) ] with-scope ]
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} cond ;
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: miller-rabin ( n -- ? ) 10 miller-rabin* ;
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: next-prime ( n -- p )
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next-odd dup miller-rabin [ next-prime ] unless ;
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: random-prime ( numbits -- p )
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random-bits next-prime ;
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: (find-relative-prime) ( n guess -- p )
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2dup gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
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: find-relative-prime* ( n guess -- p )
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#! find a prime relative to n with initial guess
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>odd (find-relative-prime) ;
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: find-relative-prime ( n -- p )
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dup random find-relative-prime* ;
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: unique-primes ( numbits n -- seq )
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#! generate two primes
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over 5 < [ "not enough primes below 5 bits" throw ] when
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[ [ drop random-prime ] with map ] [ all-unique? ] generate ;
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