Sieve of eratosthene optimizations
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USING: help.markup help.syntax ;
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IN: math.erato
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HELP: <erato>
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{ $values { "n" "a positive number" } { "erato" "a prime numbers generator" } }
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{ $description "Build a prime numbers generator for primes between 2 and " { $snippet "n" } " (inclusive)." } ;
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HELP: next-prime
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{ $values { "erato" "a generator" } { "prime/f" "a prime number or f" } }
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{ $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." } ;
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HELP: lerato
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{ $values { "n" "a positive number" } { "lazy-list" "a lazy prime numbers generator" } }
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{ $description "Builds a lazy list containing the prime numbers between 2 and " { $snippet "n" } " (inclusive). Lazy lists are described in " { $link "lazy-lists" } "." } ;
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@ -3,32 +3,36 @@
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USING: bit-arrays kernel lazy-lists math math.functions math.ranges sequences ;
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IN: math.erato
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TUPLE: erato limit bits latest ;
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<PRIVATE
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: mark-multiples ( n erato -- )
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over sqrt over erato-limit <=
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[
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[ erato-limit over <range> ] keep
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erato-bits [ set-nth ] curry f -rot curry* each
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] [
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2drop
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] if ;
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TUPLE: erato limit bits latest ;
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PRIVATE>
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: ind ( n -- i )
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2/ 1- ; inline
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: is-prime ( n erato -- bool )
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>r ind r> erato-bits nth ; inline
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: indices ( n erato -- range )
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erato-limit ind over 3 * ind swap rot <range> ;
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: mark-multiples ( n erato -- )
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over sq over erato-limit <=
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[ [ indices ] keep erato-bits [ f -rot set-nth ] curry each ] [ 2drop ] if ;
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: <erato> ( n -- erato )
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dup 1 + <bit-array> 1 over set-bits erato construct-boa ;
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dup ind 1+ <bit-array> 1 over set-bits erato construct-boa ;
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: next-prime ( erato -- prime/f )
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[ erato-latest 1+ ] keep [ set-erato-latest ] 2keep
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[ erato-latest 2 + ] keep [ set-erato-latest ] 2keep
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2dup erato-limit <=
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[
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2dup erato-bits nth [ dupd mark-multiples ] [ nip next-prime ] if
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2dup is-prime [ dupd mark-multiples ] [ nip next-prime ] if
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] [
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2drop f
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] if ;
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PRIVATE>
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: lerato ( n -- lazy-list )
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<erato> [ next-prime ] keep [ nip next-prime ] curry lfrom-by [ ] lwhile ;
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<erato> 2 [ drop next-prime ] curry* lfrom-by [ ] lwhile ;
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