[libmath-prime-util-perl] 04/72: Turn off F&T A2, need to make sure top bit is set

[Partha P. Mukherjee]

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ppm-guest pushed a commit to annotated tag v0.32
in repository libmath-prime-util-perl.

commit 7791b3cf4303fd3c1038d7a2c7b70674f4b58d68
Author: Dana Jacobsen <dana at acm.org>
Date:   Wed Aug 14 00:59:11 2013 -0700

    Turn off F&T A2, need to make sure top bit is set
---
 lib/Math/Prime/Util.pm | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm
index 621f42d..c24f73f 100644
--- a/lib/Math/Prime/Util.pm
+++ b/lib/Math/Prime/Util.pm
@@ -838,7 +838,8 @@ sub primes {
     _validate_num($bits, 2) || _validate_positive_integer($bits, 2);
 
     # Fouque and Tobouchi (2011) Algorithm 2
-    if (1 && $bits > 256) {
+    # TODO: Make sure the top bit is set.
+    if (0 && $bits > 256) {
       if (!defined $Math::BigInt::VERSION) {
         eval { require Math::BigInt; Math::BigInt->import(try=>'GMP,Pari'); 1; }
         or do { croak "Cannot load Math::BigInt"; };
@@ -851,12 +852,13 @@ sub primes {
         my $target = $bits - $_Config{'maxbits'};
         my $beta = 2;
         $m = Math::BigInt->new(2);
+        $lambda = Math::BigInt->bone;
         while ($m->copy->blog(2)->badd(1) <= $target) {
           $beta = next_prime($beta);
           $m *= $beta;
+          $lambda = Math::BigInt::blcm($lambda, $beta-1);
         }
-        # Calculate Carmichael Lambda (used to create b) and arange.
-        $lambda = Math::BigInt::blcm( map { $_-1 } @{primes(3, $beta)} );
+        # Lambda should now equal carmichael_lambda($m)
         $arange = Math::BigInt->new(2)->bpow($bits)->bdiv($m)->bsub(1);
         my $arange_bits = $arange->copy->blog(2)->badd(1);
         die "Incorrect arange" if $arange_bits > $_Config{'maxbits'};
@@ -878,7 +880,8 @@ sub primes {
       my $loop_limit = 1_000_000;
       while ($loop_limit-- > 0) {
         my $a = $irandf->($arange);
-        my $p = $m * $a + $b;
+        # Without wrapping $a like this, Math::BigInt::GMP will segfault.
+        my $p = $m * Math::BigInt->new("$a") + $b;
         if ($_HAVE_GMP) {
           next unless Math::Prime::Util::GMP::is_prime($p);
         } else {

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