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Document miller-rabin, more unit tests for some corner cases

db4
Doug Coleman 2009-05-06 16:26:06 -05:00
parent c88fc97f37
commit 6a19cae302
3 changed files with 133 additions and 19 deletions
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100
basis/math/miller-rabin/miller-rabin-docs.factor Normal file
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! Copyright (C) 2009 Doug Coleman.
! See http://factorcode.org/license.txt for BSD license.
USING: help.markup help.syntax kernel sequences math ;
IN: math.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 }
{ "?" "a boolean" }
}
{ $description "Returns true if the number is a prime. Calls " { $link miller-rabin* } " with a default of 10 Miller-Rabin tests." } ;
{ miller-rabin miller-rabin* } related-words
HELP: miller-rabin*
{ $values
{ "n" integer } { "numtrials" integer }
{ "?" "a boolean" }
}
{ $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.miller-rabin" "Miller-Rabin probabilistic primality test"
"The " { $vocab-link "math.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 } ;
ABOUT: "math.miller-rabin"

12
basis/math/miller-rabin/miller-rabin-tests.factor
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USING: math.miller-rabin tools.test kernel sequences ;
USING: math.miller-rabin tools.test kernel sequences
math.miller-rabin.private math ;
IN: math.miller-rabin.tests
[ f ] [ 473155932665450549999756893736999469773678960651272093993257221235459777950185377130233556540099119926369437865330559863 miller-rabin ] unit-test
@ -6,6 +7,9 @@ IN: math.miller-rabin.tests
[ t ] [ 3 miller-rabin ] unit-test
[ f ] [ 36 miller-rabin ] unit-test
[ t ] [ 37 miller-rabin ] 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
@ -14,6 +18,12 @@ IN: math.miller-rabin.tests
[ f ] [ 862 safe-prime? ] unit-test
[ t ] [ 7 safe-prime? ] unit-test
[ f ] [ 31 safe-prime? ] unit-test
[ t ] [ 47 safe-prime-candidate? ] unit-test
[ t ] [ 47 safe-prime? ] unit-test
[ t ] [ 863 safe-prime? ] unit-test
[ f ] [ 1000 [ drop 15 miller-rabin ] any? ] unit-test
[ 47 ] [ 31 next-safe-prime ] unit-test
[ 49 ] [ 50 random-prime log2 ] unit-test
[ 49 ] [ 50 random-bits* log2 ] unit-test

40
basis/math/miller-rabin/miller-rabin.factor
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@ -1,15 +1,20 @@
! 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 combinators.short-circuit math.bitwise ;
random sequences sets combinators.short-circuit math.bitwise
math math.order ;
IN: math.miller-rabin
<PRIVATE
: >odd ( n -- int ) dup even? [ 1 + ] when ; foldable
: >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 ;
TUPLE: positive-even-expected n ;
:: (miller-rabin) ( n trials -- ? )
@ -18,7 +23,7 @@ TUPLE: positive-even-expected n ;
0 :> a!
trials [
drop
n 1 - [1,b] random a!
2 n 2 - [a,b] random a!
a s n ^mod 1 = [
f
] [
@ -30,8 +35,6 @@ TUPLE: positive-even-expected n ;
PRIVATE>
: next-odd ( m -- n ) dup even? [ 1 + ] [ 2 + ] if ;
: miller-rabin* ( n numtrials -- ? )
over {
{ [ dup 1 <= ] [ 3drop f ] }
@ -42,11 +45,21 @@ PRIVATE>
: miller-rabin ( n -- ? ) 10 miller-rabin* ;
ERROR: prime-range-error n ;
: next-prime ( n -- p )
next-odd dup miller-rabin [ next-prime ] unless ;
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 ;
random-bits* next-prime ;
ERROR: no-relative-prime n ;
@ -80,10 +93,7 @@ ERROR: too-few-primes ;
<PRIVATE
: >safe-prime-form ( q -- p ) 2 * 1 + ;
: safe-prime-candidate? ( n -- ? )
>safe-prime-form
1 + 6 divisor? ;
: next-safe-prime-candidate ( n -- candidate )
@ -99,14 +109,8 @@ PRIVATE>
} 1&& ;
: next-safe-prime ( n -- q )
1 - >even 2 /
next-safe-prime-candidate
dup >safe-prime-form
dup miller-rabin
[ nip ] [ drop next-safe-prime ] if ;
: random-bits* ( numbits -- n )
[ random-bits ] keep set-bit ;
dup safe-prime? [ next-safe-prime ] unless ;
: random-safe-prime ( numbits -- p )
1- random-bits* next-safe-prime ;
random-bits* next-safe-prime ;