Please supply a rationale for better_average.

Update:I thought the code below would speak for itself, but here is my own rationale for posting it, and for questioning the better_average routine submitted above.

• The only difference between bad_average and better_average is that a division by a constant is moved inside the innermost loop.
• If this were handed to any of us as a homework problem in refactoring, would we not pull the division back out again?
• But numerical methods are for many of us an intimidating twilight zone in which paradoxical results hold true.
• Let us require at least one example in support of every numerical claim.
• I claim that better_average is worse than bad_average, and here follows my supporting example.

use strict;
use warnings;

sub bad_average {
   my $acc = 0;
   $acc += $_ for @_;
   return $acc / @_;
}

sub better_average {
   my $acc = 0;
   $acc += $_/@_ for @_;
   return $acc;
}

my @inputs = (1) x 65537; # 2**16 + 1
my $true_average = 1;

for my $adj (qw[bad better]) {
    my $func = "${adj}_average";
    no strict 'refs';
    my $average = &$func( @inputs );
    my $diff = $average - $true_average;
    print 
        "Error using $func is ", 
        $diff? "a nonzero number near $diff" : 0,
        "\n"
}
[download]

Your roundoff error may vary, but on my system I get

Error using bad_average is 0
Error using better_average is a nonzero number near 3.33066907387547e-
+015
[download]

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