more docs for math.primes, move words out of miller-rabin
Doug Coleman
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18add4b769
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8f51f87a8f
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@ -3,20 +3,6 @@
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USING: help.markup help.syntax kernel sequences math ;
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IN: math.primes.miller-rabin
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HELP: find-relative-prime
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{ $values
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{ "n" integer }
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{ "p" integer }
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}
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{ $description "Returns a number that is relatively prime to " { $snippet "n" } "." } ;
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HELP: find-relative-prime*
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{ $values
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{ "n" integer } { "guess" integer }
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{ "p" integer }
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}
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{ $description "Returns a number that is relatively prime to " { $snippet "n" } ", starting by trying " { $snippet "guess" } "." } ;
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HELP: miller-rabin
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{ $values
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{ "n" integer }
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@ -33,68 +19,10 @@ HELP: miller-rabin*
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}
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{ $description "Performs " { $snippet "numtrials" } " trials of the Miller-Rabin probabilistic primality test algorithm and returns true if prime." } ;
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HELP: next-prime
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{ $values
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{ "n" integer }
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{ "p" integer }
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}
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{ $description "Tests consecutive numbers for primality with " { $link miller-rabin } " and returns the next prime." } ;
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HELP: next-safe-prime
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{ $values
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{ "n" integer }
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{ "q" integer }
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}
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{ $description "Tests consecutive numbers and returns the next safe prime. A safe prime is desirable in cryptography applications such as Diffie-Hellman and SRP6." } ;
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HELP: random-bits*
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{ $values
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{ "numbits" integer }
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{ "n" integer }
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}
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{ $description "Returns an integer exactly " { $snippet "numbits" } " in length, with the topmost bit set to one." } ;
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HELP: random-prime
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{ $values
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{ "numbits" integer }
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{ "p" integer }
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}
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{ $description "Returns a prime number exactly " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
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HELP: random-safe-prime
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{ $values
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{ "numbits" integer }
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{ "p" integer }
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}
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{ $description "Returns a safe prime number " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
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HELP: safe-prime?
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{ $values
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{ "q" integer }
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{ "?" "a boolean" }
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}
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{ $description "Tests whether the number is a safe prime. A safe prime " { $snippet "p" } " must be prime, as must " { $snippet "(p - 1) / 2" } "." } ;
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HELP: unique-primes
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{ $values
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{ "numbits" integer } { "n" integer }
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{ "seq" sequence }
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}
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{ $description "Generates a sequence of " { $snippet "n" } " unique prime numbers with exactly " { $snippet "numbits" } " bits." } ;
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ARTICLE: "math.primes.miller-rabin" "Miller-Rabin probabilistic primality test"
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"The " { $vocab-link "math.primes.miller-rabin" } " vocabulary implements the Miller-Rabin probabilistic primality test and utility words that use it in order to generate random prime numbers." $nl
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"The Miller-Rabin probabilistic primality test:"
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{ $subsection miller-rabin }
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{ $subsection miller-rabin* }
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"Generating relative prime numbers:"
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{ $subsection find-relative-prime }
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{ $subsection find-relative-prime* }
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"Generating prime numbers:"
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{ $subsection next-prime }
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{ $subsection random-prime }
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"Generating safe prime numbers:"
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{ $subsection next-safe-prime }
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{ $subsection random-safe-prime } ;
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{ $subsection miller-rabin* } ;
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ABOUT: "math.primes.miller-rabin"
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@ -1,5 +1,6 @@
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USING: math.primes.miller-rabin tools.test kernel sequences
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math.primes.miller-rabin.private math ;
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USING: kernel math math.primes math.primes.miller-rabin
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math.primes.miller-rabin.private math.primes.safe
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math.primes.safe.private random sequences tools.test ;
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IN: math.primes.miller-rabin.tests
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[ f ] [ 473155932665450549999756893736999469773678960651272093993257221235459777950185377130233556540099119926369437865330559863 miller-rabin ] unit-test
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@ -1,18 +1,9 @@
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! Copyright (c) 2008-2009 Doug Coleman.
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators kernel locals math math.functions math.ranges
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random sequences sets combinators.short-circuit math.bitwise
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math math.order ;
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USING: combinators combinators.short-circuit kernel locals math
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math.functions math.ranges random sequences sets ;
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IN: math.primes.miller-rabin
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: >odd ( n -- int ) 0 set-bit ; foldable
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: >even ( n -- int ) 0 clear-bit ; foldable
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: next-even ( m -- n ) >even 2 + ;
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: next-odd ( m -- n ) dup even? [ 1 + ] [ 2 + ] if ;
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<PRIVATE
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:: (miller-rabin) ( n trials -- ? )
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@ -42,73 +33,3 @@ PRIVATE>
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} cond ;
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: miller-rabin ( n -- ? ) 10 miller-rabin* ;
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ERROR: prime-range-error n ;
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: next-prime ( n -- p )
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dup 1 < [ prime-range-error ] when
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dup 1 = [
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drop 2
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] [
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next-odd dup miller-rabin [ next-prime ] unless
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] if ;
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: random-bits* ( numbits -- n )
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1 - [ random-bits ] keep set-bit ;
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: random-prime ( numbits -- p )
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random-bits* next-prime ;
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ERROR: no-relative-prime n ;
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<PRIVATE
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: (find-relative-prime) ( n guess -- p )
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over 1 <= [ over no-relative-prime ] when
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dup 1 <= [ drop 3 ] when
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2dup gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
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PRIVATE>
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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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ERROR: too-few-primes ;
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: unique-primes ( numbits n -- seq )
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#! generate two primes
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swap
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dup 5 < [ too-few-primes ] when
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2dup [ random-prime ] curry replicate
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dup all-unique? [ 2nip ] [ drop unique-primes ] if ;
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! Safe primes are of the form p = 2q + 1, p,q are prime
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! See http://en.wikipedia.org/wiki/Safe_prime
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<PRIVATE
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: safe-prime-candidate? ( n -- ? )
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1 + 6 divisor? ;
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: next-safe-prime-candidate ( n -- candidate )
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next-prime dup safe-prime-candidate?
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[ next-safe-prime-candidate ] unless ;
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PRIVATE>
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: safe-prime? ( q -- ? )
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{
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[ 1 - 2 / dup integer? [ miller-rabin ] [ drop f ] if ]
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[ miller-rabin ]
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} 1&& ;
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: next-safe-prime ( n -- q )
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next-safe-prime-candidate
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dup safe-prime? [ next-safe-prime ] unless ;
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: random-safe-prime ( numbits -- p )
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random-bits* next-safe-prime ;
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@ -1,10 +1,10 @@
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USING: help.markup help.syntax ;
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USING: help.markup help.syntax math sequences ;
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IN: math.primes
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{ next-prime prime? } related-words
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HELP: next-prime
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{ $values { "n" "an integer not smaller than 2" } { "p" "a prime number" } }
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{ $values { "n" integer } { "p" "a prime number" } }
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{ $description "Return the next prime number greater than " { $snippet "n" } "." } ;
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HELP: prime?
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@ -20,3 +20,49 @@ HELP: primes-upto
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HELP: primes-between
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{ $values { "low" "an integer" } { "high" "an integer" } { "seq" "a sequence" } }
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{ $description "Return a sequence containing all the prime numbers between " { $snippet "low" } " and " { $snippet "high" } "." } ;
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HELP: find-relative-prime
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{ $values
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{ "n" integer }
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{ "p" integer }
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}
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{ $description "Returns a number that is relatively prime to " { $snippet "n" } "." } ;
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HELP: find-relative-prime*
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{ $values
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{ "n" integer } { "guess" integer }
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{ "p" integer }
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}
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{ $description "Returns a number that is relatively prime to " { $snippet "n" } ", starting by trying " { $snippet "guess" } "." } ;
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HELP: random-prime
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{ $values
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{ "numbits" integer }
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{ "p" integer }
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}
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{ $description "Returns a prime number exactly " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
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HELP: unique-primes
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{ $values
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{ "numbits" integer } { "n" integer }
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{ "seq" sequence }
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}
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{ $description "Generates a sequence of " { $snippet "n" } " unique prime numbers with exactly " { $snippet "numbits" } " bits." } ;
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ARTICLE: "math.primes" "Prime numbers"
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"The " { $vocab-link "math.primes" } " vocabulary implements words related to prime numbers." $nl
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"Testing if a number is prime:"
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{ $subsection prime? }
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"Generating prime numbers:"
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{ $subsection next-prime }
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{ $subsection primes-upto }
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{ $subsection primes-between }
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{ $subsection random-prime }
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"Generating relative prime numbers:"
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{ $subsection find-relative-prime }
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{ $subsection find-relative-prime* }
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"Make a sequence of random prime numbers:"
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{ $subsection unique-primes } ;
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ABOUT: "math.primes"
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@ -1,4 +1,6 @@
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USING: arrays math.primes tools.test ;
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USING: arrays math math.primes math.primes.miller-rabin
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tools.test ;
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IN: math.primes.tests
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{ 1237 } [ 1234 next-prime ] unit-test
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{ f t } [ 1234 prime? 1237 prime? ] unit-test
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@ -7,3 +9,12 @@ USING: arrays math.primes tools.test ;
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{ { 4999963 4999999 5000011 5000077 5000081 } }
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[ 4999962 5000082 primes-between >array ] unit-test
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[ 2 ] [ 1 next-prime ] unit-test
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[ 3 ] [ 2 next-prime ] unit-test
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[ 5 ] [ 3 next-prime ] unit-test
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[ 101 ] [ 100 next-prime ] unit-test
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[ t ] [ 2135623355842621559 miller-rabin ] unit-test
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[ 100000000000031 ] [ 100000000000000 next-prime ] unit-test
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[ 49 ] [ 50 random-prime log2 ] unit-test
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@ -1,8 +1,8 @@
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! Copyright (C) 2007-2009 Samuel Tardieu.
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators kernel math math.functions
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math.primes.miller-rabin math.order math.primes.erato
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math.ranges sequences ;
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USING: combinators kernel math math.bitwise math.functions
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math.order math.primes.erato math.primes.miller-rabin
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math.ranges random sequences sets fry ;
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IN: math.primes
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<PRIVATE
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@ -22,7 +22,11 @@ PRIVATE>
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} cond ; foldable
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: next-prime ( n -- p )
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next-odd [ dup really-prime? ] [ 2 + ] until ; foldable
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dup 2 < [
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drop 2
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] [
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next-odd [ dup really-prime? ] [ 2 + ] until
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] if ; foldable
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: primes-between ( low high -- seq )
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[ dup 3 max dup even? [ 1 + ] when ] dip
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@ -32,3 +36,34 @@ PRIVATE>
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: primes-upto ( n -- seq ) 2 swap primes-between ;
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: coprime? ( a b -- ? ) gcd nip 1 = ; foldable
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: random-prime ( numbits -- p )
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random-bits* next-prime ;
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: estimated-primes ( m -- n )
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dup log / ; foldable
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ERROR: no-relative-prime n ;
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<PRIVATE
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: (find-relative-prime) ( n guess -- p )
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over 1 <= [ over no-relative-prime ] when
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dup 1 <= [ drop 3 ] when
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2dup gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
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PRIVATE>
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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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ERROR: too-few-primes n numbits ;
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: unique-primes ( n numbits -- seq )
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2dup 2^ estimated-primes > [ too-few-primes ] when
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2dup '[ _ random-prime ] replicate
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dup all-unique? [ 2nip ] [ drop unique-primes ] if ;
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