in reply to Re (tilly) 1: In theory, theory and practice are the same...
in thread Binomial Expansion
I stand by my (quite conservative) statement. It does introduce errors for fairly small values of n. It is also at least twice as slow (it can be orders of magnitude slower).
But the greatest weakness to my mind is the following output:
Now that is quite a large error term, don't you think?200 choose 1: 200 vs. -1.#IND (1.#QNAN). Rate easy nice easy 1464/s -- -96% nice 34687/s 2270% --
Yes, there is a useful space over which its accuracy is quite good (though not always as good), and thanks for exploring that.
Here is the code I used:
- tye (but my friends call me "Tye")#!/usr/bin/perl -w use strict; use Benchmark qw( cmpthese ); sub fact { my $fact = 1; $fact *= $_ for 1..$_[0]; return $fact; } sub nice { my ($n, $r) = @_; my $res = 1; for my $i (1..$r) { $res *= $n--; $res /= $i; } return $res; } while( <> ) { my( $n, $m )= split ' '; my $nice= nice($n,$m); my $easy= fact($n)/fact($m)/fact($n-$m); print "$n choose $m: $nice vs. $easy (",abs($nice-$easy),").\n"; cmpthese( -3, { nice=>sub{nice($n,$m)}, easy=>sub{fact($n)/fact($m)/fact($n-$m)}, } ); }
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