 ! 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


: (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|| ;


        [ (primes-between) ]
    } cond ;

: primes-upto ( n -- seq )
    2 swap primes-between ;

: nprimes ( n -- seq )
    2 swap [ [ next-prime ] keep ] replicate nip ;

: coprime? ( a b -- ? ) fast-gcd 1 = ; foldable

