factor/basis/math/primes/erato/erato.factor

60 lines
1.7 KiB
Factor

! Copyright (C) 2009 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel kernel.private locals math math.bitwise
math.functions math.order math.private math.ranges sequences
sequences.private ;
IN: math.primes.erato
<PRIVATE
! This is a compressed Sieve of Eratosthenes that uses the
! 2-3-5 wheel to check groups of 8 candidates starting with
! { 1 7 11 13 17 19 23 29 } allowing us to use a byte-array
! to store each group of booleans in a byte.
CONSTANT: masks
{ f 128 f f f f f 64 f f f 32 f 16 f f f 8 f 4 f f f 2 f f f f f 1 }
: bit-pos ( n -- byte mask/f )
{ fixnum } declare
30 /mod masks nth-unsafe
{ maybe{ fixnum } } declare ; inline
:: marked-unsafe? ( n sieve -- ? )
n bit-pos [
[ sieve nth-unsafe ] [ mask zero? not ] bi*
] [ drop f ] if* ; inline
:: unmark ( n sieve -- )
n bit-pos [
swap sieve [ swap unmask ] change-nth-unsafe
] [ drop ] if* ; inline
: upper-bound ( sieve -- n ) length 30 * 1 - ; inline
:: unmark-multiples ( i upper sieve -- )
i 2 fixnum*fast :> step
i i fixnum*fast
[ dup upper <= ] [
[ sieve unmark ] [ step fixnum+fast ] bi
] while drop ; inline
: init-sieve ( n -- sieve )
30 /i 1 + [ 255 ] B{ } replicate-as ; inline
PRIVATE>
:: sieve ( n -- sieve )
n integer>fixnum-strict init-sieve :> sieve
sieve upper-bound >fixnum :> upper
3 upper sqrt 2 <range> [| i |
i sieve marked-unsafe? [
i upper sieve unmark-multiples
] when
] each sieve ;
: marked-prime? ( n sieve -- ? )
[ integer>fixnum-strict ] dip
2dup upper-bound 2 swap between? [ bounds-error ] unless
over { 2 3 5 } member? [ 2drop t ] [ marked-unsafe? ] if ;