From 50191588e43c8930bb960f0d9f1d6cfa89c9c8e7 Mon Sep 17 00:00:00 2001
From: Samuel Tardieu <sam@rfc1149.net>
Date: Wed, 24 Jun 2009 15:27:58 +0200
Subject: [PATCH] Get rid of vector reallocation by preallocating it
---
basis/math/primes/primes.factor | 26 +++++++++++++++++++++-----
1 file changed, 21 insertions(+), 5 deletions(-)
diff --git a/basis/math/primes/primes.factor b/basis/math/primes/primes.factor
index ea8c60508d..5dc6a51334 100644
--- a/basis/math/primes/primes.factor
+++ b/basis/math/primes/primes.factor
@@ -1,8 +1,9 @@
! Copyright (C) 2007-2009 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license.
-USING: combinators kernel math math.bitwise math.functions
+USING: combinators fry kernel math math.bitwise math.functions
math.order math.primes.erato math.primes.erato.private
-math.primes.miller-rabin math.ranges literals random sequences sets ;
+math.primes.miller-rabin math.ranges literals random sequences sets
+vectors ;
IN: math.primes
<PRIVATE
@@ -12,6 +13,21 @@ 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 swap push ] keep ] when ;
+
PRIVATE>
: prime? ( n -- ? )
@@ -29,9 +45,9 @@ PRIVATE>
] if ; foldable
: primes-between ( low high -- seq )
- [ dup 3 max dup even? [ 1 + ] when ] dip
- 2 <range> [ prime? ] filter
- swap 3 < [ 2 prefix ] when ;
+ [ [ 3 max dup even? [ 1 + ] when ] dip 2 <range> ]
+ [ <primes-vector> ] 2bi
+ [ '[ [ prime? ] _ push-if ] each ] keep clone ;
: primes-upto ( n -- seq ) 2 swap primes-between ;