[libmath-prime-util-perl] 27/50: Use 2 MR bases for more numbers

[Partha P. Mukherjee]

This is an automated email from the git hooks/post-receive script.

ppm-guest pushed a commit to annotated tag v0.13
in repository libmath-prime-util-perl.

commit de88bbcfe598a7d4ef0344b26068821c37a39e69
Author: Dana Jacobsen <dana at acm.org>
Date:   Sun Oct 28 04:23:06 2012 -0700

    Use 2 MR bases for more numbers
---
 Changes                |  2 ++
 factor.c               |  9 ++++++++-
 lib/Math/Prime/Util.pm | 18 +++++++++++-------
 3 files changed, 21 insertions(+), 8 deletions(-)

diff --git a/Changes b/Changes
index c49d641..b4a1784 100644
--- a/Changes
+++ b/Changes
@@ -20,6 +20,8 @@ Revision history for Perl extension Math::Prime::Util.
 
     - Some fixes and speedups for ranged primes().
 
+    - In the PP code, use 2 MR bases for more numbers when possible.
+
 0.11  23 July 2012
     - Turn off threading tests on Cygwin, as threads on some Cygwin platforms
       give random panics (my Win7 64-bit works fine, XP 32-bit does not).
diff --git a/factor.c b/factor.c
index 450da8a..a75d85e 100644
--- a/factor.c
+++ b/factor.c
@@ -256,10 +256,16 @@ int _XS_miller_rabin(UV n, const UV *bases, int nbases)
       croak("Base %"UVuf" is invalid for input %"UVuf, a, n);
 #endif
 
+    /* n is a strong pseudoprime to this base if either
+     *   -  a^d = 1 mod n
+     *   -  a^(d2^r) = -1 mod n for some r: 0 <= r <= s-1
+     */
+
     x = powmod(a, d, n);
     if ( (x == 1) || (x == (n-1)) )  continue;
 
-    for (r = 0; r < s; r++) {
+    /* cover r = 1 to s-1, r=0 was just done */
+    for (r = 1; r < s; r++) {
       x = sqrmod(x, n);
       if (x == 1) {
         return 0;
@@ -296,6 +302,7 @@ int _XS_is_prob_prime(UV n)
 #else
 #if 1
   /* Better basis from:  http://miller-rabin.appspot.com/ */
+  /* We could go up to 316_349_281 using 2 bases */
   if (n < UVCONST(9080191)) {
     bases[0] = 31;
     bases[1] = 73;
diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm
index 43eba86..940bd2a 100644
--- a/lib/Math/Prime/Util.pm
+++ b/lib/Math/Prime/Util.pm
@@ -953,14 +953,18 @@ sub is_prob_prime {
   }
 
   if ($n < 105936894253) {   # BPSW seems to be faster after this
-    # Deterministic set of Miller-Rabin tests.
+    # Deterministic set of Miller-Rabin tests.  If the MR routines can handle
+    # bases greater than n, then this can be simplified.
     my @bases;
-    if    ($n <          9080191) { @bases = (31, 73); }
-    elsif ($n <       4759123141) { @bases = (2, 7, 61); }
-    elsif ($n <     105936894253) { @bases = (2, 1005905886, 1340600841); }
-    elsif ($n <   31858317218647) { @bases = (2, 642735, 553174392, 3046413974); }
-    elsif ($n < 3071837692357849) { @bases = (2, 75088, 642735, 203659041, 3613982119); }
-    else                          { @bases = (2, 325, 9375, 28178, 450775, 9780504, 1795265022); }
+    if    ($n <          9080191) { @bases = (31,       73); }
+    elsif ($n <         19471033) { @bases = ( 2,   299417); }
+    elsif ($n <         38010307) { @bases = ( 2,  9332593); }
+    elsif ($n <        316349281) { @bases = ( 11000544, 31481107); }
+    elsif ($n <       4759123141) { @bases = ( 2, 7, 61); }
+    elsif ($n <     105936894253) { @bases = ( 2, 1005905886, 1340600841); }
+    elsif ($n <   31858317218647) { @bases = ( 2, 642735, 553174392, 3046413974); }
+    elsif ($n < 3071837692357849) { @bases = ( 2, 75088, 642735, 203659041, 3613982119); }
+    else                          { @bases = ( 2, 325, 9375, 28178, 450775, 9780504, 1795265022); }
     return Math::Prime::Util::PP::miller_rabin($n, @bases)  ?  2  :  0;
   }
 

-- 
Alioth's /usr/local/bin/git-commit-notice on /srv/git.debian.org/git/pkg-perl/packages/libmath-prime-util-perl.git