USING: help.markup help.syntax ;
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
{ $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" } "." } ;
USING: bit-arrays kernel lazy-lists math math.functions math.ranges sequences ;
IN: math.erato
+<PRIVATE
+
TUPLE: erato limit bits latest ;
-<PRIVATE
+: ind ( n -- i )
+ 2/ 1- ; inline
-: mark-multiples ( n erato -- )
- over sqrt over erato-limit <=
- [
- [ erato-limit over <range> ] keep
- erato-bits [ set-nth ] curry f -rot curry* each
- ] [
- 2drop
- ] if ;
+: is-prime ( n erato -- bool )
+ >r ind r> erato-bits nth ; inline
-PRIVATE>
+: 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 )
- 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 )
- [ erato-latest 1+ ] keep [ set-erato-latest ] 2keep
+ [ erato-latest 2 + ] keep [ set-erato-latest ] 2keep
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
] if ;
+PRIVATE>
+
: lerato ( n -- lazy-list )
- <erato> [ next-prime ] keep [ nip next-prime ] curry lfrom-by [ ] lwhile ;
+ <erato> 2 [ drop next-prime ] curry* lfrom-by [ ] lwhile ;