[libmath-prime-util-perl] 03/59: Add some more implementations
Partha P. Mukherjee
ppm-guest at moszumanska.debian.org
Thu May 21 18:44:51 UTC 2015
This is an automated email from the git hooks/post-receive script.
ppm-guest pushed a commit to annotated tag v0.10
in repository libmath-prime-util-perl.
commit b728d6b7af7a5d6cfed99044d2d621a19333a49e
Author: Dana Jacobsen <dana at acm.org>
Date: Wed Jun 27 01:22:17 2012 -0600
Add some more implementations
---
examples/bench-sieve-pp.pl | 215 ++++++++++++++++++++++++++++++++++++++-------
1 file changed, 182 insertions(+), 33 deletions(-)
diff --git a/examples/bench-sieve-pp.pl b/examples/bench-sieve-pp.pl
index 6eb84d8..724351b 100644
--- a/examples/bench-sieve-pp.pl
+++ b/examples/bench-sieve-pp.pl
@@ -3,28 +3,46 @@ use strict;
use warnings;
use Benchmark qw/:all/;
+#use Devel::Size qw/total_size/;
+#use Math::Prime::Util;
+#use Math::Prime::FastSieve;
+#*mpu_erat = \&Math::Prime::Util::erat_primes;
+#*fs_erat = \&Math::Prime::FastSieve::primes;
my $upper = shift || 8192;
my $count = shift || -1;
my $countarg;
+# Shows sizes for sieving to 100k, and rate/second for sieving to 16k
my $pc_subs = {
- "Scriptol" => sub { scriptol($countarg) },
- "Shootout" => sub { shootout($countarg) },
- "In Many" => sub { inmany($countarg) },
- "Rosetta 1" => sub { rosetta1($countarg) },
- "Rosetta 2" => sub { rosetta2($countarg) },
- "Rosetta 3" => sub { rosetta3($countarg) },
- "Rosetta 4" => sub { rosetta4($countarg) },
- "DJ Vec" => sub { dj1($countarg) },
- "DJ Array" => sub { dj2($countarg) },
- "DJ String1" => sub { dj3($countarg) },
- "DJ String2" => sub { dj4($countarg) },
+ "Scriptol" => sub { scriptol($countarg) }, # 3200k 290/s
+ "Shootout" => sub { shootout($countarg) }, # 3200k 231/s
+ "In Many" => sub { inmany($countarg) }, # 2018k 666/s
+ "Rosetta 1" => sub { rosetta1($countarg) }, # 3449k 187/s
+ "Rosetta 2" => sub { rosetta2($countarg) }, # 13k 109/s
+ "Rosetta 3" => sub { rosetta3($countarg) }, # 4496k 165/s
+ "Rosetta 4" => sub { rosetta4($countarg) }, # 25k 60/s
+ "Atkin MPTA" => sub { atkin($countarg) }, # 3430k 90/s
+ "DO Array" => sub {daoswald_array($countarg)},# 3200k 306/s
+ "DO Vec" => sub {daoswald_vec($countarg)}, # 13k 112/s
+ "Merlyn" => sub { merlyn($countarg)}, # 13k 96/s
+ "DJ Vec" => sub { dj1($countarg) }, # 7k 245/s
+ "DJ Array" => sub { dj2($countarg) }, # 1494k 475/s
+ "DJ String1" => sub { dj3($countarg) }, # 50k 981/s
+ "DJ String2" => sub { dj4($countarg) }, # 50k 1682/s
+# "MPU Sieve" => sub {
+# scalar @{mpu_erat(2,$countarg)}; }, # 3k 14325/s
+# "MPFS Sieve" => sub {
+# scalar @{fs_erat($countarg)}; }, # 7k 14325/s
};
my %verify = (
10 => 4,
+ 11 => 5,
100 => 25,
+ 112 => 29,
+ 113 => 30,
+ 114 => 30,
1000 => 168,
10000 => 1229,
100000 => 9592,
@@ -48,8 +66,8 @@ cmpthese($count, $pc_subs);
# www.scriptol.com/programming/sieve.php
sub scriptol {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
my @flags = (0 .. $max);
for my $i (2 .. int(sqrt($max)) + 1)
@@ -60,6 +78,7 @@ sub scriptol {
undef $flags[$k];
}
}
+ #print "scriptol size: ", total_size(\@flags), "\n" if $max > 90000;
my $count = 0;
for my $j (2 .. $max) {
$count++ if defined $flags[$j];
@@ -70,8 +89,8 @@ sub scriptol {
# http://dada.perl.it/shootout/sieve.perl.html
sub shootout {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
my $count = 0;
my @flags = (0 .. $max);
@@ -82,14 +101,16 @@ sub shootout {
}
$count++;
}
+ #print "shootout size: ", total_size(\@flags), "\n" if $max > 90000;
$count;
}
# http://c2.com/cgi/wiki?SieveOfEratosthenesInManyProgrammingLanguages
sub inmany {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
+ $max++;
my @c;
for(my $t=3; $t*$t<$max; $t+=2) {
@@ -97,6 +118,7 @@ sub inmany {
for(my $s=$t*$t; $s<$max; $s+=$t*2) { $c[$s]++ }
}
}
+ #print "inmany size: ", total_size(\@c), "\n" if $max > 90000;
my $count = 1;
for(my $t=3; $t<$max; $t+=2) {
$c[$t] || $count++;
@@ -107,8 +129,8 @@ sub inmany {
# http://rosettacode.org/wiki/Sieve_of_Eratosthenes#Perl
sub rosetta1 {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
my $count = 0; #my @primes;
my @tested = (1);
@@ -120,14 +142,15 @@ sub rosetta1 {
$tested[$k-1]= 1;
}
}
+ #print "R1 size: ", total_size(\@tested), "\n" if $max > 90000;
$count; #scalar @primes;
}
# http://rosettacode.org/wiki/Sieve_of_Eratosthenes#Perl
sub rosetta2 {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
my $count = 0; #my @primes;
my $nonPrimes = '';
@@ -139,14 +162,15 @@ sub rosetta2 {
$count++; #push @primes, $p;
}
}
+ #print "R2 size: ", total_size(\$nonPrimes), "\n" if $max > 90000;
$count; #scalar @primes;
}
# http://rosettacode.org/wiki/Sieve_of_Eratosthenes#Perl
sub rosetta3 {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
my $i;
my @s;
@@ -154,14 +178,15 @@ sub rosetta3 {
grep { not $s[ $i = $_ ] and do
{ $s[ $i += $_ ]++ while $i <= $max; 1 }
} 2 .. $max;
+ #print "R3 size: ", total_size(\@s), "\n" if $max > 90000;
$count; #scalar @primes;
}
# http://rosettacode.org/wiki/Sieve_of_Eratosthenes#Perl
sub rosetta4 {
my($max) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
my $i;
my $s = '';
@@ -169,13 +194,133 @@ sub rosetta4 {
grep { not vec $s, $i = $_, 1 and do
{ (vec $s, $i += $_, 1) = 1 while $i <= $max; 1 }
} 2 .. $max;
+ #print "R4 size: ", total_size(\$s), "\n" if $max > 90000;
$count; #scalar @primes;
}
+# From Math::Primes::TiedArray
+sub atkin {
+ my($max) = @_;
+ return 0 if $max < 2;
+ return 1 if $max < 3;
+ return 2 if $max < 5;
+
+ my $sqrt = sqrt($max);
+ my %sieve;
+ foreach my $x ( 1 .. $sqrt ) {
+
+ foreach my $y ( 1 .. $sqrt ) {
+
+ my $n = 3 * $x**2 - $y**2;
+ if ( $x > $y
+ and $n <= $max
+ and $n % 12 == 11 )
+ {
+ $sieve{$n} = not $sieve{$n};
+ }
+
+ $n = 3 * $x**2 + $y**2;
+ if ( $n <= $max and $n % 12 == 7 ) {
+ $sieve{$n} = not $sieve{$n};
+ }
+
+ $n = 4 * $x**2 + $y**2;
+ if ( $n <= $max
+ and ( $n % 12 == 1 or $n % 12 == 5 ) )
+ {
+ $sieve{$n} = not $sieve{$n};
+ }
+ }
+ }
+ # eliminate composites by sieving
+ foreach my $n ( 5 .. $sqrt ) {
+
+ next unless $sieve{$n};
+
+ my $k = int(1/$n**2) * $n**2;
+ while ( $k <= $max ) {
+ $sieve{$k} = 0;
+ $k += $n**2;
+ }
+ }
+ $sieve{2} = 1;
+ $sieve{3} = 1;
+ #print "Atkin size: ", total_size(\%sieve), "\n" if $max > 90000;
+
+ # save the found primes in our cache
+ my $count = 0;
+ foreach my $n ( 2 .. $max ) {
+ next unless $sieve{$n};
+ $count++;
+ }
+ $count;
+}
+
+# https://github.com/daoswald/Inline-C-Perl-Mongers-Talk/blob/master/primesbench.pl
+sub daoswald_array {
+ my($top) = @_;
+ return 0 if $top < 2;
+ return 1 if $top < 3;
+
+ my @primes = (1) x $top;
+ my $i_times_j;
+ for my $i ( 2 .. sqrt $top ) {
+ if ( $primes[$i] ) {
+ for ( my $j = $i; ( $i_times_j = $i * $j ) < $top; $j++ ) {
+ undef $primes[$i_times_j];
+ }
+ }
+ }
+ #print "do_array size: ", total_size(\@primes), "\n" if $top > 90000;
+ my $count = scalar grep { $primes[$_] } 2 .. $#primes;
+ $count;
+}
+
+sub daoswald_vec {
+ my($top) = @_;
+ return 0 if $top < 2;
+ return 1 if $top < 3;
+
+ my $primes = '';
+ vec( $primes, $top, 1 ) = 0;
+ my $i_times_j;
+ for my $i ( 2 .. sqrt $top ) {
+ if ( !vec( $primes, $i, 1 ) ) {
+ for ( my $j = $i; ( $i_times_j = $i * $j ) < $top; $j++ ) {
+ vec( $primes, $i_times_j, 1 ) = 1;
+ }
+ }
+ }
+ #print "do_vec size: ", total_size(\$primes), "\n" if $top > 90000;
+ my $count = scalar grep { !vec( $primes, $_, 1 ) } 2 .. $top-1 ;
+ $count;
+}
+
+# Merlyn's Unix Review Column 26, June 1999
+# http://www.stonehenge.com/merlyn/UnixReview/col26.html
+sub merlyn {
+ my($UPPER) = @_;
+ return 0 if $UPPER < 2;
+ return 1 if $UPPER < 3;
+
+ my $count = 0;
+ my $sieve = "";
+ GUESS: for (my $guess = 2; $guess <= $UPPER; $guess++) {
+ next GUESS if vec($sieve,$guess,1);
+ $count++;
+ for (my $mults = $guess * $guess; $mults <= $UPPER; $mults += $guess) {
+ vec($sieve,$mults,1) = 1;
+ }
+ }
+ #print "Merlyn size: ", total_size(\$sieve), "\n" if $UPPER > 90000;
+ $count;
+}
+
+
sub dj1 {
my($end) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $end < 2;
+ return 1 if $end < 3;
# vector
my $sieve = '';
@@ -188,6 +333,7 @@ sub dj1 {
}
do { $n += 2 } while vec($sieve, $n >> 1, 1) != 0;
}
+ #print "DJ1 size: ", total_size(\$sieve), "\n" if $end > 90000;
my $count = 1;
$n = 3;
while ($n <= $end) {
@@ -199,8 +345,8 @@ sub dj1 {
sub dj2 {
my($end) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $end < 2;
+ return 1 if $end < 3;
# array
my @sieve;
@@ -213,6 +359,7 @@ sub dj2 {
}
do { $n += 2 } while $sieve[$n>>1];
}
+ #print "DJ2 size: ", total_size(\@sieve), "\n" if $end > 90000;
my $count = 1;
$n = 3;
while ($n <= $end) {
@@ -226,8 +373,8 @@ sub dj2 {
# which is just this code with a presieve added.
sub dj3 {
my($end) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $end < 2;
+ return 1 if $end < 3;
$end-- if ($end & 1) == 0;
# string
@@ -243,6 +390,7 @@ sub dj3 {
}
do { $n += 2 } while substr($sieve, $n>>1, 1);
}
+ #print "DJ3 size: ", total_size(\$sieve), "\n" if $end > 90000;
my $count = 1 + $sieve =~ tr/0//;
$count;
}
@@ -250,8 +398,8 @@ sub dj3 {
# 2-3x faster than inmany, 6-7x faster than any of the other non-DJ methods.
sub dj4 {
my($end) = @_;
- return 0 if $upper < 2;
- return 1 if $upper < 3;
+ return 0 if $end < 2;
+ return 1 if $end < 3;
$end-- if ($end & 1) == 0;
# string with prefill
@@ -269,6 +417,7 @@ sub dj4 {
}
do { $n += 2 } while substr($sieve, $n>>1, 1);
}
+ #print "DJ4 size: ", total_size(\$sieve), "\n" if $end > 90000;
my $count = 1 + $sieve =~ tr/0//;
$count;
}
--
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