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more docs for math.primes, move words out of miller-rabin

db4
Doug Coleman 2009-05-10 13:47:51 -05:00
parent 18add4b769
commit 8f51f87a8f
6 changed files with 105 additions and 163 deletions
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74
basis/math/primes/miller-rabin/miller-rabin-docs.factor
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@ -3,20 +3,6 @@
USING: help.markup help.syntax kernel sequences math ;
IN: math.primes.miller-rabin
HELP: find-relative-prime
{ $values
{ "n" integer }
{ "p" integer }
}
{ $description "Returns a number that is relatively prime to " { $snippet "n" } "." } ;
HELP: find-relative-prime*
{ $values
{ "n" integer } { "guess" integer }
{ "p" integer }
}
{ $description "Returns a number that is relatively prime to " { $snippet "n" } ", starting by trying " { $snippet "guess" } "." } ;
HELP: miller-rabin
{ $values
{ "n" integer }
@ -33,68 +19,10 @@ HELP: miller-rabin*
}
{ $description "Performs " { $snippet "numtrials" } " trials of the Miller-Rabin probabilistic primality test algorithm and returns true if prime." } ;
HELP: next-prime
{ $values
{ "n" integer }
{ "p" integer }
}
{ $description "Tests consecutive numbers for primality with " { $link miller-rabin } " and returns the next prime." } ;
HELP: next-safe-prime
{ $values
{ "n" integer }
{ "q" integer }
}
{ $description "Tests consecutive numbers and returns the next safe prime. A safe prime is desirable in cryptography applications such as Diffie-Hellman and SRP6." } ;
HELP: random-bits*
{ $values
{ "numbits" integer }
{ "n" integer }
}
{ $description "Returns an integer exactly " { $snippet "numbits" } " in length, with the topmost bit set to one." } ;
HELP: random-prime
{ $values
{ "numbits" integer }
{ "p" integer }
}
{ $description "Returns a prime number exactly " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
HELP: random-safe-prime
{ $values
{ "numbits" integer }
{ "p" integer }
}
{ $description "Returns a safe prime number " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
HELP: safe-prime?
{ $values
{ "q" integer }
{ "?" "a boolean" }
}
{ $description "Tests whether the number is a safe prime. A safe prime " { $snippet "p" } " must be prime, as must " { $snippet "(p - 1) / 2" } "." } ;
HELP: unique-primes
{ $values
{ "numbits" integer } { "n" integer }
{ "seq" sequence }
}
{ $description "Generates a sequence of " { $snippet "n" } " unique prime numbers with exactly " { $snippet "numbits" } " bits." } ;
ARTICLE: "math.primes.miller-rabin" "Miller-Rabin probabilistic primality test"
"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
"The Miller-Rabin probabilistic primality test:"
{ $subsection miller-rabin }
{ $subsection miller-rabin* }
"Generating relative prime numbers:"
{ $subsection find-relative-prime }
{ $subsection find-relative-prime* }
"Generating prime numbers:"
{ $subsection next-prime }
{ $subsection random-prime }
"Generating safe prime numbers:"
{ $subsection next-safe-prime }
{ $subsection random-safe-prime } ;
{ $subsection miller-rabin* } ;
ABOUT: "math.primes.miller-rabin"

5
basis/math/primes/miller-rabin/miller-rabin-tests.factor
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@ -1,5 +1,6 @@
USING: math.primes.miller-rabin tools.test kernel sequences
math.primes.miller-rabin.private math ;
USING: kernel math math.primes math.primes.miller-rabin
math.primes.miller-rabin.private math.primes.safe
math.primes.safe.private random sequences tools.test ;
IN: math.primes.miller-rabin.tests
[ f ] [ 473155932665450549999756893736999469773678960651272093993257221235459777950185377130233556540099119926369437865330559863 miller-rabin ] unit-test

83
basis/math/primes/miller-rabin/miller-rabin.factor
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@ -1,18 +1,9 @@
! Copyright (c) 2008-2009 Doug Coleman.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators kernel locals math math.functions math.ranges
random sequences sets combinators.short-circuit math.bitwise
math math.order ;
USING: combinators combinators.short-circuit kernel locals math
math.functions math.ranges random sequences sets ;
IN: math.primes.miller-rabin
: >odd ( n -- int ) 0 set-bit ; foldable
: >even ( n -- int ) 0 clear-bit ; foldable
: next-even ( m -- n ) >even 2 + ;
: next-odd ( m -- n ) dup even? [ 1 + ] [ 2 + ] if ;
<PRIVATE
:: (miller-rabin) ( n trials -- ? )
@ -42,73 +33,3 @@ PRIVATE>
} cond ;
: miller-rabin ( n -- ? ) 10 miller-rabin* ;
ERROR: prime-range-error n ;
: next-prime ( n -- p )
dup 1 < [ prime-range-error ] when
dup 1 = [
drop 2
] [
next-odd dup miller-rabin [ next-prime ] unless
] if ;
: random-bits* ( numbits -- n )
1 - [ random-bits ] keep set-bit ;
: 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 ;
! Safe primes are of the form p = 2q + 1, p,q are prime
! See http://en.wikipedia.org/wiki/Safe_prime
<PRIVATE
: safe-prime-candidate? ( n -- ? )
1 + 6 divisor? ;
: next-safe-prime-candidate ( n -- candidate )
next-prime dup safe-prime-candidate?
[ next-safe-prime-candidate ] unless ;
PRIVATE>
: safe-prime? ( q -- ? )
{
[ 1 - 2 / dup integer? [ miller-rabin ] [ drop f ] if ]
[ miller-rabin ]
} 1&& ;
: next-safe-prime ( n -- q )
next-safe-prime-candidate
dup safe-prime? [ next-safe-prime ] unless ;
: random-safe-prime ( numbits -- p )
random-bits* next-safe-prime ;

50
basis/math/primes/primes-docs.factor
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@ -1,10 +1,10 @@
USING: help.markup help.syntax ;
USING: help.markup help.syntax math sequences ;
IN: math.primes
{ next-prime prime? } related-words
HELP: next-prime
{ $values { "n" "an integer not smaller than 2" } { "p" "a prime number" } }
{ $values { "n" integer } { "p" "a prime number" } }
{ $description "Return the next prime number greater than " { $snippet "n" } "." } ;
HELP: prime?
@ -20,3 +20,49 @@ HELP: primes-upto
HELP: primes-between
{ $values { "low" "an integer" } { "high" "an integer" } { "seq" "a sequence" } }
{ $description "Return a sequence containing all the prime numbers between " { $snippet "low" } " and " { $snippet "high" } "." } ;
HELP: find-relative-prime
{ $values
{ "n" integer }
{ "p" integer }
}
{ $description "Returns a number that is relatively prime to " { $snippet "n" } "." } ;
HELP: find-relative-prime*
{ $values
{ "n" integer } { "guess" integer }
{ "p" integer }
}
{ $description "Returns a number that is relatively prime to " { $snippet "n" } ", starting by trying " { $snippet "guess" } "." } ;
HELP: random-prime
{ $values
{ "numbits" integer }
{ "p" integer }
}
{ $description "Returns a prime number exactly " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
HELP: unique-primes
{ $values
{ "numbits" integer } { "n" integer }
{ "seq" sequence }
}
{ $description "Generates a sequence of " { $snippet "n" } " unique prime numbers with exactly " { $snippet "numbits" } " bits." } ;
ARTICLE: "math.primes" "Prime numbers"
"The " { $vocab-link "math.primes" } " vocabulary implements words related to prime numbers." $nl
"Testing if a number is prime:"
{ $subsection prime? }
"Generating prime numbers:"
{ $subsection next-prime }
{ $subsection primes-upto }
{ $subsection primes-between }
{ $subsection random-prime }
"Generating relative prime numbers:"
{ $subsection find-relative-prime }
{ $subsection find-relative-prime* }
"Make a sequence of random prime numbers:"
{ $subsection unique-primes } ;
ABOUT: "math.primes"

13
basis/math/primes/primes-tests.factor
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@ -1,4 +1,6 @@
USING: arrays math.primes tools.test ;
USING: arrays math math.primes math.primes.miller-rabin
tools.test ;
IN: math.primes.tests
{ 1237 } [ 1234 next-prime ] unit-test
{ f t } [ 1234 prime? 1237 prime? ] unit-test
@ -7,3 +9,12 @@ USING: arrays math.primes tools.test ;
{ { 4999963 4999999 5000011 5000077 5000081 } }
[ 4999962 5000082 primes-between >array ] unit-test
[ 2 ] [ 1 next-prime ] unit-test
[ 3 ] [ 2 next-prime ] unit-test
[ 5 ] [ 3 next-prime ] unit-test
[ 101 ] [ 100 next-prime ] unit-test
[ t ] [ 2135623355842621559 miller-rabin ] unit-test
[ 100000000000031 ] [ 100000000000000 next-prime ] unit-test
[ 49 ] [ 50 random-prime log2 ] unit-test

43
basis/math/primes/primes.factor
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@ -1,8 +1,8 @@
! Copyright (C) 2007-2009 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators kernel math math.functions
math.primes.miller-rabin math.order math.primes.erato
math.ranges sequences ;
USING: combinators kernel math math.bitwise math.functions
math.order math.primes.erato math.primes.miller-rabin
math.ranges random sequences sets fry ;
IN: math.primes
<PRIVATE
@ -22,7 +22,11 @@ PRIVATE>
} cond ; foldable
: next-prime ( n -- p )
next-odd [ dup really-prime? ] [ 2 + ] until ; foldable
dup 2 < [
drop 2
] [
next-odd [ dup really-prime? ] [ 2 + ] until
] if ; foldable
: primes-between ( low high -- seq )
[ dup 3 max dup even? [ 1 + ] when ] dip
@ -32,3 +36,34 @@ PRIVATE>
: primes-upto ( n -- seq ) 2 swap primes-between ;
: coprime? ( a b -- ? ) gcd nip 1 = ; foldable
: random-prime ( numbits -- p )
random-bits* next-prime ;
: estimated-primes ( m -- n )
dup log / ; foldable
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 n numbits ;
: unique-primes ( n numbits -- seq )
2dup 2^ estimated-primes > [ too-few-primes ] when
2dup '[ _ random-prime ] replicate
dup all-unique? [ 2nip ] [ drop unique-primes ] if ;