Two points. I found that if I used Math::BigFloat in the
choose function, I got round off errors; errors I didn't
get when using Math::BigInt.
Second, I got a much better performance for the choose function if I didn't calculate 3 factorials, but just one,
and did some multiplication myself. The further the second
argument is away from half of the first argument, the bigger
the advantage. Here's a benchmark:
#!/usr/bin/perl
use strict;
use warnings;
use Math::BigFloat;
use Benchmark qw /timethese cmpthese/;
#
# choose (n, k) == n! / ((n  k)! * k!) == n! / (n  k)! / k!
# == n * (n  1) * ... * (n  k + 1) / k!
sub choose_fac {
my ($n, $k) = @_;
Math::BigInt > new ($n) > bfac /
Math::BigInt > new ($n  $k) > bfac /
Math::BigInt > new ($k) > bfac
}
sub choose_mul {
my ($n, $k) = @_;
$k = $n  $k if $k > $n  $k; # Make the loop smaller;
# we can do this because
# choose (n, k) == choose (n, n  k
+).
my $p = Math::BigInt > new (1);
my $start = $n  $k + 1;
for (my $i = $start; $i <= $n; $i ++) {
$p *= $i;
}
$p / Math::BigInt > new ($k) > bfac;
}
our (@r1, @r2);
our @pairs = map {[/(\d+)\s+(\d+)/]} <DATA>;
cmpthese 10 => {
fac => '@r1 = map {choose_fac @$_} @pairs',
mul => '@r2 = map {choose_mul @$_} @pairs',
};
die "Unequal" unless "@r1" eq "@r2";
__DATA__
1000 0
1000 100
1000 500
1000 1000
s/iter fac mul
fac 2.08  89%
mul 0.226 824% 
Abigail
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