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Sieve of eratosthene optimizations

db4
Samuel Tardieu 2007-12-22 00:28:46 +01:00
parent 8e87d56e24
commit fd8253c262
2 changed files with 19 additions and 23 deletions
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8
extra/math/erato/erato-docs.factor
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@ -1,14 +1,6 @@
USING: help.markup help.syntax ; USING: help.markup help.syntax ;
IN: math.erato IN: math.erato
HELP: <erato>
{ $values { "n" "a positive number" } { "erato" "a prime numbers generator" } }
{ $description "Build a prime numbers generator for primes between 2 and " { $snippet "n" } " (inclusive)." } ;
HELP: next-prime
{ $values { "erato" "a generator" } { "prime/f" "a prime number or f" } }
{ $description "Compute the next prime number using the given generator. If there are no more prime numbers under the limit used when building the generator, f is returned instead." } ;
HELP: lerato HELP: lerato
{ $values { "n" "a positive number" } { "lazy-list" "a lazy prime numbers generator" } } { $values { "n" "a positive number" } { "lazy-list" "a lazy prime numbers generator" } }
{ $description "Builds a lazy list containing the prime numbers between 2 and " { $snippet "n" } " (inclusive). Lazy lists are described in " { $link "lazy-lists" } "." } ; { $description "Builds a lazy list containing the prime numbers between 2 and " { $snippet "n" } " (inclusive). Lazy lists are described in " { $link "lazy-lists" } "." } ;

34
extra/math/erato/erato.factor
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@ -3,32 +3,36 @@
USING: bit-arrays kernel lazy-lists math math.functions math.ranges sequences ; USING: bit-arrays kernel lazy-lists math math.functions math.ranges sequences ;
IN: math.erato IN: math.erato
TUPLE: erato limit bits latest ;
<PRIVATE <PRIVATE
: mark-multiples ( n erato -- ) TUPLE: erato limit bits latest ;
over sqrt over erato-limit <=
[
[ erato-limit over <range> ] keep
erato-bits [ set-nth ] curry f -rot curry* each
] [
2drop
] if ;
PRIVATE> : ind ( n -- i )
2/ 1- ; inline
: is-prime ( n erato -- bool )
>r ind r> erato-bits nth ; inline
: indices ( n erato -- range )
erato-limit ind over 3 * ind swap rot <range> ;
: mark-multiples ( n erato -- )
over sq over erato-limit <=
[ [ indices ] keep erato-bits [ f -rot set-nth ] curry each ] [ 2drop ] if ;
: <erato> ( n -- erato ) : <erato> ( n -- erato )
dup 1 + <bit-array> 1 over set-bits erato construct-boa ; dup ind 1+ <bit-array> 1 over set-bits erato construct-boa ;
: next-prime ( erato -- prime/f ) : next-prime ( erato -- prime/f )
[ erato-latest 1+ ] keep [ set-erato-latest ] 2keep [ erato-latest 2 + ] keep [ set-erato-latest ] 2keep
2dup erato-limit <= 2dup erato-limit <=
[ [
2dup erato-bits nth [ dupd mark-multiples ] [ nip next-prime ] if 2dup is-prime [ dupd mark-multiples ] [ nip next-prime ] if
] [ ] [
2drop f 2drop f
] if ; ] if ;
PRIVATE>
: lerato ( n -- lazy-list ) : lerato ( n -- lazy-list )
<erato> [ next-prime ] keep [ nip next-prime ] curry lfrom-by [ ] lwhile ; <erato> 2 [ drop next-prime ] curry* lfrom-by [ ] lwhile ;