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ppm-guest pushed a commit to annotated tag v0.13
in repository libmath-prime-util-perl.
commit 32c0cf3067f28f7d66188bf2e33e6319c1b54e2a
Author: Dana Jacobsen <d...@acm.org>
Date: Sat Oct 20 03:31:30 2012 -0600
Minor issues with huge inputs
---
lib/Math/Prime/Util.pm | 57 ++++++++++++++++++++++++++++-------------------
lib/Math/Prime/Util/PP.pm | 7 +++---
2 files changed, 37 insertions(+), 27 deletions(-)
diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm
index b858b03..43eba86 100644
--- a/lib/Math/Prime/Util.pm
+++ b/lib/Math/Prime/Util.pm
@@ -197,7 +197,8 @@ sub _validate_positive_integer {
sub _upgrade_to_float {
my($n) = @_;
return $n unless defined $Math::BigInt::VERSION || defined
$Math::BigFloat::VERSION;
- do { require Math::BigFloat; Math::BigFloat->import; } if defined
$Math::BigInt::VERSION && !defined $Math::BigFloat::VERSION;
+ do { require Math::BigFloat; Math::BigFloat->import(try=>'GMP,Pari') }
+ if defined $Math::BigInt::VERSION && !defined $Math::BigFloat::VERSION;
return Math::BigFloat->new($n);
}
@@ -239,7 +240,8 @@ sub primes {
if ($_HAVE_GMP) {
$sref = Math::Prime::Util::GMP::primes($low,$high);
# Convert the returned strings into BigInts
- croak "Internal error: large value without bigint loaded." unless
defined $Math::BigInt::VERSION;
+ croak "Internal error: large value without bigint loaded."
+ unless defined $Math::BigInt::VERSION;
@$sref = map { Math::BigInt->new("$_") } @$sref;
return $sref;
}
@@ -566,8 +568,8 @@ sub primes {
return random_nbit_prime($k) if $k <= $p0;
eval {
- require Math::BigInt; Math::BigInt->import();
- require Math::BigFloat; Math::BigFloat->import();
+ require Math::BigInt; Math::BigInt->import( try=>'GMP,Pari' );
+ require Math::BigFloat; Math::BigFloat->import( try=>'GMP,Pari' );
1;
} or do {
croak "Cannot load Math::BigInt and Math::BigFloat";
@@ -913,6 +915,8 @@ sub miller_rabin {
#############################################################################
+ # Oct 2012 note: these numbers are old.
+ #
# Timings for various combinations, given the current possibilities of:
# 1) XS MR optimized (either x86-64, 32-bit on 64-bit mach, or half-word)
# 2) XS MR non-optimized (big input not on 64-bit machine)
@@ -990,11 +994,11 @@ sub prime_count_approx {
#
# Also consider: http://trac.sagemath.org/sage_trac/ticket/8135
- # return int( (prime_count_upper($x) + prime_count_lower($x)) / 2);
+ # my $result = int( (prime_count_upper($x) + prime_count_lower($x)) / 2);
- # return int( LogarithmicIntegral($x) );
+ # my $result = int( LogarithmicIntegral($x) );
- # return int( LogarithmicIntegral($x) - LogarithmicIntegral(sqrt($x))/2 );
+ # my $result = int(LogarithmicIntegral($x) -
LogarithmicIntegral(sqrt($x))/2);
my $result = RiemannR($x) + 0.5;
@@ -1240,7 +1244,7 @@ sub RiemannZeta {
my($n) = @_;
croak("Invalid input to ReimannZeta: x must be > 0") if $n <= 0;
- #return Math::Prime::Util::PP::RiemannZeta($n, 1e-30) if defined
$bignum::VERSION || ref($n) eq 'Math::BigFloat';
+ #return Math::Prime::Util::PP::RiemannZeta($n) if defined $bignum::VERSION
|| ref($n) eq 'Math::BigFloat';
return Math::Prime::Util::PP::RiemannZeta($n) if !$_Config{'xs'};
return _XS_RiemannZeta($n);
}
@@ -1249,7 +1253,7 @@ sub RiemannR {
my($n) = @_;
croak("Invalid input to ReimannR: x must be > 0") if $n <= 0;
- return Math::Prime::Util::PP::RiemannR($n, 1e-30) if defined
$bignum::VERSION || ref($n) eq 'Math::BigFloat';
+ return Math::Prime::Util::PP::RiemannR($n) if defined $bignum::VERSION ||
ref($n) eq 'Math::BigFloat';
return Math::Prime::Util::PP::RiemannR($n) if !$_Config{'xs'};
return _XS_RiemannR($n);
@@ -1264,7 +1268,7 @@ sub ExponentialIntegral {
my($n) = @_;
croak "Invalid input to ExponentialIntegral: x must be != 0" if $n == 0;
- return Math::Prime::Util::PP::ExponentialIntegral($n, 1e-30) if defined
$bignum::VERSION || ref($n) eq 'Math::BigFloat';
+ return Math::Prime::Util::PP::ExponentialIntegral($n) if defined
$bignum::VERSION || ref($n) eq 'Math::BigFloat';
return Math::Prime::Util::PP::ExponentialIntegral($n) if !$_Config{'xs'};
return _XS_ExponentialIntegral($n);
}
@@ -1476,21 +1480,28 @@ is less than a millisecond, it's really not important
in general (also, a
future implementation may find a way to speed this up without the option).
-If you are using bigints, there are two performance suggestions. The first
-is to install L<Math::Prime::Util::GMP>, as that will vastly increase the speed
-for many of the functions. This does require the L<GMP|gttp://gmplib.org>
-library be installed on your system, but this increasingly comes pre-installed
-or easily available using the OS vendor package installation tool. If you
-do not want to use that, I recommend L<Math::BigInt::GMP> or
-L<Math::BigInt::Pari> and then writing C<use bigint try =E<gt> 'GMP,Pari'>.
-Large modular exponentiation is much faster using the GMP or Pari backends.
-This is not so important if you installed L<Math::Prime::Util::GMP>, but it can
-still speed up large random Maurer primes.
+If you are using bigints, here are some performance suggestions:
+
+=over 4
+
+=item Install L<Math::Prime::Util::GMP>, as that will vastly increase the
+ speed of many of the functions. This does require the
+ L<GMP|gttp://gmplib.org> library be installed on your system, but this
+ increasingly comes pre-installed or easily available using the OS vendor
+ package installation tool.
+
+=item Install and use L<Math::BigInt::GMP> or L<Math::BigInt::Pari>, then use
+ C<use bigint try =E<gt> 'GMP,Pari'> in your script, or on the command
+ line C<-Mbigint=lib,GMP>. Large modular exponentiation is much faster
+ using the GMP or Pari backends, as are the math and approximation
+ functions when called with very large inputs.
+=item Having run these functions on many versions of Perl, if you're using
+ anything older than Perl 5.14, I would recommend you upgrade if you
+ are using bignums a lot. There are some brittle behaviors on
+ 5.12.4 and earlier with bignums.
-Having run these functions on many versions of Perl, if you're using anything
-older than Perl 5.14, I would recommend you upgrade if you are using bignums
-a lot. There are some brittle behaviors on 5.12.4 and earlier with bignums.
+=back
=head1 FUNCTIONS
diff --git a/lib/Math/Prime/Util/PP.pm b/lib/Math/Prime/Util/PP.pm
index 0750638..515b9fb 100644
--- a/lib/Math/Prime/Util/PP.pm
+++ b/lib/Math/Prime/Util/PP.pm
@@ -1281,14 +1281,13 @@ sub RiemannZeta {
for my $k (2 .. 1000000) {
my $term = (2*$k+1) ** -$x;
$y = $term-$c; $t = $sum+$y; $c = ($t-$sum)-$y; $sum = $t;
- last if abs($term/$sum) < $tol;
+ last if $term < abs($tol*$sum);
}
my $term = 3 ** -$x;
$y = $term-$c; $t = $sum+$y; $c = ($t-$sum)-$y; $sum = $t;
$t = 1.0 / (1.0 - (2 ** -$x));
$sum *= $t;
- $term = $t - 1.0;
- $y = $term-$c; $t = $sum+$y; $c = ($t-$sum)-$y; $sum = $t;
+ $sum += ($t - 1.0);
$sum;
}
@@ -1316,7 +1315,7 @@ sub RiemannR {
$part_term *= $flogx / $k;
my $term = $part_term / ($k + $k * $zeta);
$y = $term-$c; $t = $sum+$y; $c = ($t-$sum)-$y; $sum = $t;
- last if abs($term) < $tol;
+ last if abs($term/$sum) < $tol;
}
$sum;
}
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