factor: trim using lists

[factor.git] / basis / math / primes / primes.factor

diff --git a/basis/math/primes/primes.factor b/basis/math/primes/primes.factor
index e3985fc6000107e5dcc450baed6f6469b2de95b5..dce69fe67fa42a62ae435d786aab12e40228d8da 100644 (file)
--- a/basis/math/primes/primes.factor
+++ b/basis/math/primes/primes.factor
@@ -1,62 +1,96 @@
 ! Copyright (C) 2007-2009 Samuel Tardieu.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: combinators kernel math math.bitwise math.functions
-math.order math.primes.erato math.primes.miller-rabin
-math.ranges random sequences sets fry ;
+USING: combinators combinators.short-circuit kernel
+math math.bitwise math.functions math.order math.primes.erato
+math.primes.erato.private math.primes.miller-rabin ranges
+literals random sequences sets vectors ;
 IN: math.primes
 
 <PRIVATE
 
-: look-in-bitmap ( n -- ? ) >index 4999999 sieve nth ;
+: look-in-bitmap ( n -- ? )
+    integer>fixnum $[ 8,999,999 sieve ] marked-unsafe? ; inline
 
-: really-prime? ( n -- ? )
-    dup 5000000 < [ look-in-bitmap ] [ miller-rabin ] if ; foldable
+: (prime?) ( n -- ? )
+    dup 8,999,999 <= [ look-in-bitmap ] [ miller-rabin ] if ;
+
+: simple? ( n -- ? )
+    { [ even? ] [ 3 divisor? ] [ 5 divisor? ] } 1|| ;
 
 PRIVATE>
 
 : prime? ( n -- ? )
     {
-        { [ dup 2 < ] [ drop f ] }
-        { [ dup even? ] [ 2 = ] }
-        [ really-prime? ]
+        { [ dup 7 < ] [ { 2 3 5 } member? ] }
+        { [ dup simple? ] [ drop f ] }
+        [ (prime?) ]
     } cond ; foldable
 
 : next-prime ( n -- p )
     dup 2 < [
         drop 2
     ] [
-        next-odd [ dup really-prime? ] [ 2 + ] until
+        next-odd [ dup prime? ] [ 2 + ] until
     ] if ; foldable
 
+<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 )
+    [ <primes-range> ] [ <primes-vector> ] 2bi
+    [ '[ [ prime? ] _ push-if ] each ] keep ;
+
+PRIVATE>
+
 : primes-between ( low high -- seq )
-    [ dup 3 max dup even? [ 1 + ] when ] dip
-    2 <range> [ prime? ] filter
-    swap 3 < [ 2 prefix ] when ;
+    [ ceiling >integer ] [ floor >integer ] bi*
+    {
+        { [ 2dup > ] [ 2drop V{ } clone ] }
+        { [ dup 2 = ] [ 2drop V{ 2 } clone ] }
+        { [ dup 2 < ] [ 2drop V{ } clone ] }
+        [ (primes-between) ]
+    } cond ;
 
-: primes-upto ( n -- seq ) 2 swap primes-between ;
+: primes-upto ( n -- seq )
+    2 swap primes-between ;
 
-: coprime? ( a b -- ? ) gcd nip 1 = ; foldable
+: nprimes ( n -- seq )
+    2 swap [ [ next-prime ] keep ] replicate nip ;
+
+: coprime? ( a b -- ? ) simple-gcd 1 = ; foldable
 
 : random-prime ( numbits -- p )
-    random-bits* next-prime ;
+    [ ] [ 2^ ] [ random-bits* next-prime ] tri
+    2dup < [ 2drop random-prime ] [ 2nip ] if ;
 
 : estimated-primes ( m -- n )
     dup log / ; foldable
 
 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 gcd nip 1 > [ 2 + (find-relative-prime) ] [ nip ] if ;
-
-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* ;
@@ -65,5 +99,5 @@ ERROR: too-few-primes n numbits ;
 
 : unique-primes ( n numbits -- seq )
     2dup 2^ estimated-primes > [ too-few-primes ] when
-    2dup '[ _ random-prime ] replicate
+    2dup [ random-prime ] curry replicate
     dup all-unique? [ 2nip ] [ drop unique-primes ] if ;