math.primes: little bit more cleanup.

db4
John Benediktsson 2015-05-13 15:17:15 -07:00
parent ab50fc818f
commit 40b699cc1e
1 changed files with 29 additions and 33 deletions

View File

@ -1,7 +1,7 @@
! Copyright (C) 2007-2009 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators combinators.short-circuit fry kernel math
math.bitwise math.functions math.order math.primes.erato
USING: combinators combinators.short-circuit fry kernel locals
math math.bitwise math.functions math.order math.primes.erato
math.primes.erato.private math.primes.miller-rabin math.ranges
literals random sequences sets vectors ;
IN: math.primes
@ -14,21 +14,6 @@ IN: math.primes
: (prime?) ( n -- ? )
dup 8999999 <= [ look-in-bitmap ] [ miller-rabin ] if ;
! In order not to reallocate large vectors, we compute the upper bound
! of the number of primes in a given interval. We use a double inequality given
! by Pierre Dusart in http://www.ams.org/mathscinet-getitem?mr=99d:11133
! for x > 598. Under this limit, we know that there are at most 108 primes.
: upper-pi ( x -- y )
dup log [ / ] [ 1.2762 swap / 1 + ] bi * ceiling ;
: lower-pi ( x -- y )
dup log [ / ] [ 0.992 swap / 1 + ] bi * floor ;
: <primes-vector> ( low high -- vector )
swap [ [ upper-pi ] [ lower-pi ] bi* - >integer
108 max 10000 min <vector> ] keep
3 < [ 2 suffix! ] when ;
: simple? ( n -- ? ) { [ even? ] [ 3 divisor? ] [ 5 divisor? ] } 1|| ;
PRIVATE>
@ -49,10 +34,27 @@ PRIVATE>
<PRIVATE
: <primes-range> ( low high -- range )
[ 3 max dup even? [ 1 + ] when ] dip 2 <range> ;
! In order not to reallocate large vectors, we compute the upper bound
! of the number of primes in a given interval. We use a double inequality given
! by Pierre Dusart in http://www.ams.org/mathscinet-getitem?mr=99d:11133
! for x > 598. Under this limit, we know that there are at most 108 primes.
: upper-pi ( x -- y )
dup log [ / ] [ 1.2762 swap / 1 + ] bi * ceiling ;
: lower-pi ( x -- y )
dup log [ / ] [ 0.992 swap / 1 + ] bi * floor ;
:: <primes-vector> ( low high -- vector )
high upper-pi low lower-pi - >integer
108 10000 clamp <vector>
low 3 < [ 2 suffix! ] when ;
: (primes-between) ( low high -- seq )
[ [ 3 max dup even? [ 1 + ] when ] dip 2 <range> ]
[ <primes-vector> ] 2bi
[ '[ [ prime? ] _ push-if ] each ] keep clone ;
[ <primes-range> ] [ <primes-vector> ] 2bi
[ '[ [ prime? ] _ push-if ] each ] keep ;
PRIVATE>
@ -65,9 +67,11 @@ PRIVATE>
[ (primes-between) ]
} cond ;
: primes-upto ( n -- seq ) 2 swap primes-between ;
: primes-upto ( n -- seq )
2 swap primes-between ;
: nprimes ( n -- seq ) 2 swap [ [ next-prime ] keep ] replicate nip ;
: nprimes ( n -- seq )
2 swap [ [ next-prime ] keep ] replicate nip ;
: coprime? ( a b -- ? ) fast-gcd 1 = ; foldable
@ -80,18 +84,10 @@ PRIVATE>
ERROR: no-relative-prime n ;
<PRIVATE
: (find-relative-prime) ( n guess -- p )
over 1 <= [ over no-relative-prime ] when
dup 1 <= [ drop 3 ] when
[ 2dup coprime? ] [ 2 + ] until nip ;
PRIVATE>
: find-relative-prime* ( n guess -- p )
#! find a prime relative to n with initial guess
>odd (find-relative-prime) ;
[ dup 1 <= [ no-relative-prime ] when ]
[ >odd dup 1 <= [ drop 3 ] when ] bi*
[ 2dup coprime? ] [ 2 + ] until nip ;
: find-relative-prime ( n -- p )
dup random find-relative-prime* ;