floating point - How do I fix this Perl code so that 1.1 + 2.2 == 3.3?

Question

How do I fix this code so that 1.1 + 2.2 == 3.3? What is actually happening here that's causing this behavior? I'm vaguely familiar with rounding problems and floating point math, but I thought that applied to division and multiplication only and would be visible in the output.

[me@unixbox1:~/perltests]> cat testmathsimple.pl 
#!/usr/bin/perl

use strict;
use warnings;

check_math(1, 2, 3);
check_math(1.1, 2.2, 3.3);

sub check_math {
        my $one = shift;
        my $two = shift;
        my $three = shift;

        if ($one + $two == $three) {
                print "$one + $two == $three
";
        } else {
                print "$one + $two != $three
";
        }
}

[me@unixbox1:~/perltests]> perl testmathsimple.pl 
1 + 2 == 3
1.1 + 2.2 != 3.3

Edit:

Most of the answers thus far are along the lines of "it's a floating point problem, duh" and are providing workarounds for it. I already suspect that to be the problem. How do I demonstrate it? How do I get Perl to output the long form of the variables? Storing the $one + $two computation in a temp variable and printing it doesn't demonstrate the problem.

Edit:

Using the sprintf technique demonstrated by aschepler, I'm now able to "see" the problem. Further, using bignum, as recommended by mscha and rafl, fixes the problem of the comparison not being equal. However, the sprintf output still indicates that the numbers aren't "correct". That's leaving a modicum of doubt about this solution.

Is bignum a good way to resolve this? Are there any possible side effects of bignum that we should look out for when integrating this into a larger, existing, program?

Answer 1

See What Every Computer Scientist Should Know About Floating-Point Arithmetic.

None of this is Perl specific: There are an uncountably infinite number of real numbers and, obviously, all of them cannot be represented using only a finite number of bits.

The specific "solution" to use depends on your specific problem. Are you trying to track monetary amounts? If so, use the arbitrary precision numbers (use more memory and more CPU, get more accurate results) provided by bignum. Are you doing numeric analysis? Then, decide on the precision you want to use, and use sprintf (as shown below) and eq to compare.

You can always use:

use strict; use warnings;

check_summation(1, $_) for [1, 2, 3], [1.1, 2.2, 3.3];

sub check_summation {
    my $precision = shift;
    my ($x, $y, $expected) = @{ $_[0] };
    my $result = $x + $y;

    for my $n ( $x, $y, $expected, $result) {
        $n = sprintf('%.*f', $precision, $n);
    }

    if ( $expected eq $result ) {
        printf "%s + %s = %s
", $x, $y, $expected;
    }
    else {
        printf "%s + %s != %s
", $x, $y, $expected;
    }
    return;
}

Output:

1.0 + 2.0 = 3.0
1.1 + 2.2 = 3.3