[libmath-prime-util-perl] 05/23: Use references in primes.pl for performance. Lucky primes take less memory.
Partha P. Mukherjee
ppm-guest at moszumanska.debian.org
Thu May 21 18:45:54 UTC 2015
This is an automated email from the git hooks/post-receive script.
ppm-guest pushed a commit to annotated tag v0.14
in repository libmath-prime-util-perl.
commit e3521a5df6b7931caa6c3d4063975ea11205dd67
Author: Dana Jacobsen <dana at acm.org>
Date: Wed Nov 21 16:14:47 2012 -0800
Use references in primes.pl for performance. Lucky primes take less memory.
---
bin/primes.pl | 92 +++++++++++++++++++++++++++++++++--------------------------
1 file changed, 51 insertions(+), 41 deletions(-)
diff --git a/bin/primes.pl b/bin/primes.pl
index f6c3560..9027d71 100755
--- a/bin/primes.pl
+++ b/bin/primes.pl
@@ -144,10 +144,9 @@ if ($start > $end) {
|| exists $opts{'cuban1'}
|| exists $opts{'cuban2'}
) {
- my @p = gen_and_filter($start, $end);
- print join("\n", @p), "\n" if scalar @p > 0;
+ my $p = gen_and_filter($start, $end);
+ print join("\n", @$p), "\n" if scalar @$p > 0;
} else {
- my @p;
while ($start <= $end) {
# Adjust segment sizes for some cases
@@ -164,10 +163,10 @@ if ($start > $end) {
$seg_end = $end if $end < $seg_end;
$start = $seg_end+1;
- @p = gen_and_filter($seg_start, $seg_end);
+ my $p = gen_and_filter($seg_start, $seg_end);
# print this segment
- print join("\n", @p), "\n" if scalar @p > 0;
+ print join("\n", @$p), "\n" if scalar @$p > 0;
}
}
@@ -285,9 +284,20 @@ sub lucky_primes {
# Remove the 3rd elements for k=2:
# my @lucky = grep { my $m = $_ % 6; $m == 1 || $m == 3 } (0 .. $end);
# Remove the 4th elements for k=3:
- my @lucky = grep { my $m = $_ % 21; $m != 18 && $m != 19 }
- grep { my $m = $_ % 6; $m == 1 || $m == 3 }
- map { $_*2+1 } (0 .. int(($end-1)/2));
+ # my @lucky = grep { my $m = $_ % 21; $m != 18 && $m != 19 }
+ # grep { my $m = $_ % 6; $m == 1 || $m == 3 }
+ # map { $_*2+1 } (0 .. int(($end-1)/2));
+ # This is the same k=3 sieve, but uses much less memory:
+ my @lucky;
+ my $n = 1;
+ while ($n <= $end) {
+ my $m21 = $n % 21;
+ push @lucky, $n unless $m21 == 18 || $m21 == 19;
+ push @lucky, $n+2 unless $m21 == 16 || $m21 == 17;
+ $n += 6;
+ }
+ delete $lucky[-1] if $lucky[-1] > $end;
+
for (my $k = 3; $k < scalar @lucky; $k++) {
my $skip = $lucky[$k];
my $index = $skip-1;
@@ -377,91 +387,91 @@ sub merge_primes {
sub gen_and_filter {
my ($start, $end) = @_;
my $gen;
- my @p;
+ my $p = [];
if (exists $opts{'lucas'}) {
- merge_primes(\$gen, \@p, 'lucas', lucas_primes($start, $end));
+ merge_primes(\$gen, $p, 'lucas', lucas_primes($start, $end));
}
if (exists $opts{'fibonacci'}) {
- merge_primes(\$gen, \@p, 'fibonacci', fibonacci_primes($start, $end));
+ merge_primes(\$gen, $p, 'fibonacci', fibonacci_primes($start, $end));
}
if (exists $opts{'mersenne'}) {
- merge_primes(\$gen, \@p, 'mersenne', mersenne_primes($start, $end));
+ merge_primes(\$gen, $p, 'mersenne', mersenne_primes($start, $end));
}
if (exists $opts{'euclid'}) {
- merge_primes(\$gen, \@p, 'euclid', euclid_primes($start, $end, 1));
+ merge_primes(\$gen, $p, 'euclid', euclid_primes($start, $end, 1));
}
if (exists $opts{'lucky'}) {
- merge_primes(\$gen, \@p, 'lucky', lucky_primes($start, $end));
+ merge_primes(\$gen, $p, 'lucky', lucky_primes($start, $end));
}
if (exists $opts{'cuban1'}) {
- merge_primes(\$gen, \@p, 'cuban1', cuban_primes($start, $end, 1));
+ merge_primes(\$gen, $p, 'cuban1', cuban_primes($start, $end, 1));
}
if (exists $opts{'cuban2'}) {
- merge_primes(\$gen, \@p, 'cuban2', cuban_primes($start, $end, 2));
+ merge_primes(\$gen, $p, 'cuban2', cuban_primes($start, $end, 2));
}
if (exists $opts{'palindromic'}) {
if (!defined $gen) {
foreach my $d (length($start) .. length($end)) {
- push @p, grep { $_ >= $start && $_ <= $end && is_prime($_) }
- ndig_palindromes($d);
+ push @$p, grep { $_ >= $start && $_ <= $end && is_prime($_) }
+ ndig_palindromes($d);
}
$gen = 'palindromic';
} else {
- @p = grep { $_ eq reverse $_; } @p;
+ @$p = grep { $_ eq reverse $_; } @$p;
}
}
if (exists $opts{'twin'} && !defined $gen) {
- @p = @{primes($start, $end)};
- push @p, is_prime($p[-1]+2) ? $p[-1]+2 : 0;
+ $p = primes($start, $end);
+ push @$p, is_prime($p->[-1]+2) ? $p->[-1]+2 : 0;
my @twin;
- my $prime = shift @p;
- foreach my $next (@p) {
+ my $prime = shift @$p;
+ foreach my $next (@$p) {
push @twin, $prime if $prime+2 == $next;
$prime = $next;
}
- @p = @twin;
+ $p = \@twin;
$gen = 'twin';
}
if (!defined $gen) {
- @p = @{primes($start, $end)};
+ $p = primes($start, $end);
$gen = 'primes';
}
# Apply the mod 210 pretest
if ($min_pass > 0) {
- @p = grep { $_ <= $min_pass || exists $mod_pass{$_ % 210} } @p;
+ @$p = grep { $_ <= $min_pass || exists $mod_pass{$_ % 210} } @$p;
}
if (exists $opts{'twin'} && $gen ne 'twin') {
- @p = grep { is_prime( $_+2 ); } @p;
+ @$p = grep { is_prime( $_+2 ); } @$p;
}
if (exists $opts{'triplet'}) {
- @p = grep { is_prime($_+6) && (is_prime($_+2) || is_prime($_+4)); } @p;
+ @$p = grep { is_prime($_+6) && (is_prime($_+2) || is_prime($_+4)); } @$p;
}
if (exists $opts{'quadruplet'}) {
- @p = grep { is_prime($_+2) && is_prime($_+6) && is_prime($_+8); } @p;
+ @$p = grep { is_prime($_+2) && is_prime($_+6) && is_prime($_+8); } @$p;
}
if (exists $opts{'cousin'}) {
- @p = grep { is_prime($_+4); } @p;
+ @$p = grep { is_prime($_+4); } @$p;
}
if (exists $opts{'sexy'}) {
- @p = grep { is_prime($_+6); } @p;
+ @$p = grep { is_prime($_+6); } @$p;
}
if (exists $opts{'safe'}) {
- @p = grep { is_prime( ($_-1) >> 1 ); }
- grep { ($_ <= 7) || ($_ % 12) == 11; }
- @p;
+ @$p = grep { is_prime( ($_-1) >> 1 ); }
+ grep { ($_ <= 7) || ($_ % 12) == 11; }
+ @$p;
}
if (exists $opts{'sophie'}) {
- @p = grep { is_prime( 2*$_+1 ); } @p;
+ @$p = grep { is_prime( 2*$_+1 ); } @$p;
}
#if (exists $opts{'cuban1'}) {
# @p = grep { my $n = sqrt((4*$_-1)/3); 4*$_ == int($n)*int($n)*3+1; } @p;
@@ -470,21 +480,21 @@ sub gen_and_filter {
# @p = grep { my $n = sqrt(($_-1)/3); $_ == int($n)*int($n)*3+1; } @p;
#}
if (exists $opts{'pnm1'}) {
- @p = grep { is_prime( primorial(Math::BigInt->new($_))-1 ) } @p;
+ @$p = grep { is_prime( primorial(Math::BigInt->new($_))-1 ) } @$p;
}
if (exists $opts{'pnp1'}) {
- @p = grep { is_prime( primorial(Math::BigInt->new($_))+1 ) } @p;
+ @$p = grep { is_prime( primorial(Math::BigInt->new($_))+1 ) } @$p;
}
if (exists $opts{'pillai'}) {
- @p = grep { is_pillai($_); } @p;
+ @$p = grep { is_pillai($_); } @$p;
}
if (exists $opts{'good'}) {
- @p = grep { is_good_prime($_); } @p;
+ @$p = grep { is_good_prime($_); } @$p;
}
if (exists $opts{'provable'}) {
- @p = grep { is_provable_prime($_) == 2; } @p;
+ @$p = grep { is_provable_prime($_) == 2; } @$p;
}
- @p;
+ $p;
}
sub find_mod210_restriction {
--
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