Re^6: [OT] The statistics of hashing. (odd)

[tye]

in reply to Re^5: [OT] The statistics of hashing.
in thread [OT] The statistics of hashing.

I suspect you need to start $toggle reversed for odd values (or for even values, though you note that you verified against the two even cases). Though, I would have expected that particular mistake to lead to negative values (but you don't show most of the code so I didn't go much further in looking). The numbers are supposed to be f(...)**$P where f() is positive (and monotonic), so, yes, odd values of $P should give you results between the results for $P-1 and $P+1, not like the results you posted.

Sorry for the wrapping.

You might want to put the big tables into READMORE tags so that they don't impact the rendering of the whole thread (though that should only happen for people who have code wrapping badly configured).

[BrowserUk]

I suspect you need to start $toggle reversed for odd values

Indeed. Using my $toggle = $P & 1 ? 1 : -1;, the output makes much more sense:

<Reveal this spoiler or all in this thread>

you don't show most of the code so I didn't go much further in looking

The entire code looks like this:

#! perl -slw
use strict;

sub PTn {
    my @row;
    for( 1 .. shift ) {
        push @row, 1;
        $row [$_] += $row [$_ - 1] for reverse 1 .. @row - 2;
    }
    return @row;
}

sub expN {
    my( $P, $N, $X ) = @_;
    my $xDIVn = $X / $N;
    my @coefs = PTn( $P+1 );
    my $rv = 0;
    my $toggle = $P & 1 ? 1 : -1;
    for my $p ( reverse 1 .. $P ) {
        $rv += $toggle * $coefs[ $p ] * $N / $p * exp( -$p * $xDIVn );
        $toggle *= -1;
    }
    return $rv + $X;
}

our $H //= 10;
our $B //= 32;

print "Using N x 2**$B vectors:";

for my $inserts ( map{ 2**$_*3/4, 2**$_ } 4 .. $B ) {
    printf "%10d : ", $inserts;
    for my $h ( 1 .. $H ) {
        printf "%6d ", expN( $h, 2**$B, $inserts ) - expN( $h, 2**$B, 
+0 );
    }
    print '';
}