Eratosthenes was a clever chap!

use strict;
use warnings;

use Benchmark qw{ cmpthese };

use Test::More tests => 1;
is_deeply(
   [ primes( 10000 ) ],
   [ primes_jg( 10000 ) ],
   'same'
   );

cmpthese(
   -10,
   {
       ch => 'primes( 10000 )',
       jg => 'primes_jg( 10000 )',
   }
   );

sub primes_jg
{
    my $limit     = shift;
    my $sqrtLimit = sqrt $limit;
    
    my $sieve                = q{};
    vec( $sieve, 0, 1 )      = 1;
    vec( $sieve, 1, 1 )      = 1;
    vec( $sieve, $limit, 1 ) = 0;

    my @primes;
    my $reached = 1;
    while( $reached < $sqrtLimit )
    {
        my $prime = $reached + 1;
        ++ $prime while vec( $sieve, $prime, 1 );
    
        push @primes, $prime;
        my $fill = 2 * $prime;
        while( $fill <= $limit )
        {
            vec( $sieve, $fill, 1 ) = 1;
            $fill += $prime;
        }
        $reached = $prime;
    }
    
    foreach my $value ( $reached + 1 .. $limit )
    {
        push @primes, $value unless vec( $sieve, $value, 1 );
    }

    return @primes;
}

sub primes {
    my $n = shift;
    return if $n < 2;

    my @primes = (2);
    for my $i (3 .. $n) {
        my $sqrt = sqrt $i;
        my $notprime;
        for my $p (@primes) {
            last if $p > $sqrt;

            $notprime = 1, last if 0 == $i % $p;
        }
        push @primes, $i unless $notprime;
    }
    return @primes
}
[download]

1..1
ok 1 - same
     Rate   ch   jg
ch 71.0/s   -- -25%
jg 94.7/s  33%   --
[download]

I hope this is of interest.

"Eratosthenes was a clever chap"

I never met him. But another chap wrote some kind of shortcut:

use Math::Prime::XS qw( sieve_primes );
my @primes = sieve_primes(10_000);
[download]

I'm to tired to write the benchmarks...

Best regards, Karl

«The Crux of the Biscuit is the Apostrophe»

choroba optimezed is still little faster..


          Rate     la     di     ch     jg ch_opt
la     0.327/s     --   -99%   -99%   -99%   -99%
di      25.3/s  7628%     --   -48%   -52%   -54%
ch      48.6/s 14733%    92%     --    -7%   -13%
jg      52.3/s 15877%   107%     8%     --    -6%
ch_opt  55.6/s 16875%   120%    14%     6%     --
[download]

There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

johngg, would you please explain what you are doing with vec. I read the doc on it and got lost in the first sentence. I don't know how you are using bit vectors (this is the first time I've ever heard of them). Everything between my $sqrtLimit = sqrt $limit; to return @primes; is a big mystery to me.

You are also not eliminating numbers which end with 2, 4, 5, 6, 8, and 0 right off the bat, why?

Thanks for stopping by.

No matter how hysterical I get, my problems are not time sensitive. So, relax, have a cookie, and a very nice day!
Lady Aleena

Lady_Aleena, the Sieve of Eratosthenes is a well-known approach to generating primes. To illustrate, suppose you want to generate the primes between 2 and 20 (as neither 0 and 1 are prime, by definition).

Read more... (2 kB)

Hope that helps.

Update: 2015-04-01
Updated formatting of example lines to highlight overstrike of values.