 
 <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>
 

        [ (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


! Copyright (C) 2007-2009 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license.
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
