I've got a problem with the precision of the random number generator.

I want if() to be true at a rate of 1/40.000, however, rand() is not precise enough and outputs 0 quite often (maybe a bit dept problem?). e.g.

I tried rand(n)-1>n-1, or using the Math::Random module but this does not improve the randomness enough.

use strict;
use warnings;

my $time = 120;
my $D=10000;                                          
my $dt=1/$D;   
my $tt=0; 
my $rateon=1;

my $count=0;

 while($time>$tt){                   
     $tt=$tt+$dt;  
     my $rand = rand($D);
     if(($rand)<=$rateon) {
                $count++;
         printf("%f > %f\n", $rateon, $rand) or die $!;
        }
 }
 print "$count total" or die $!;
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Update: This hack works, although is not ideal:

use strict;
use warnings;

my $time = 120;
my $D=10000; 
my $sqrtd=sqrt($D);
my $dt=1/$D;   
my $tt=0; 
my $rateon=40;

my $count=0;

 while($time>$tt){                   
     $tt=$tt+$dt;  
     my $rand = rand($sqrtd);
     my $rand2 = rand($sqrtd);
     if($rand<1 && $rand2<1 && rand($rateon)<1) {
                $count++;
         }
 }
 print "$count total " or die $!;
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