package Test::Number::Delta;
use strict;
#use warnings; bah -- not supported before 5.006
use vars qw ($VERSION @EXPORT @ISA);
$VERSION = "1.03";
# Required modules
use Carp;
use Test::Builder;
use Exporter;
@ISA = qw( Exporter );
@EXPORT = qw( delta_not_ok delta_ok delta_within delta_not_within );
=head1 NAME
Test::Number::Delta - Compare the difference between numbers against a given tolerance
=head1 SYNOPSIS
# Import test functions
use Test::Number::Delta;
# Equality test with default tolerance
delta_ok( 1e-5, 2e-5, 'values within 1e-6');
# Inequality test with default tolerance
delta_not_ok( 1e-5, 2e-5, 'values not within 1e-6');
# Provide specific tolerance
delta_within( 1e-3, 2e-3, 1e-4, 'values within 1e-4');
delta_not_within( 1e-3, 2e-3, 1e-4, 'values not within 1e-4');
# Compare arrays or matrices
@a = ( 3.14, 1.41 );
@b = ( 3.15, 1.41 );
delta_ok( \@a, \@b, 'compare @a and @b' );
# Set a different default tolerance
use Test::Number::Delta within => 1e-5;
delta_ok( 1.1e-5, 2e-5, 'values within 1e-5'); # ok
# Set a relative tolerance
use Test::Number::Delta relative => 1e-3;
delta_ok( 1.01, 1.0099, 'values within 1.01e-3');
=head1 DESCRIPTION
At some point or another, most programmers find they need to compare
floating-point numbers for equality. The typical idiom is to test
if the absolute value of the difference of the numbers is within a desired
tolerance, usually called epsilon. This module provides such a function for use
with L<Test::Harness>. Usage is similar to other test functions described in
L<Test::More>. Semantically, the C<delta_within> function replaces this kind
of construct:
ok ( abs($p - $q) < $epsilon, '$p is equal to $q' ) or
diag "$p is not equal to $q to within $epsilon";
While there's nothing wrong with that construct, it's painful to type it
repeatedly in a test script. This module does the same thing with a single
function call. The C<delta_ok> function is similar, but either uses a global
default value for epsilon or else calculates a 'relative' epsilon on
the fly so that epsilon is scaled automatically to the size of the arguments to
C<delta_ok>. Both functions are exported automatically.
Because checking floating-point equality is not always reliable, it is not
possible to check the 'equal to' boundary of 'less than or equal to
epsilon'. Therefore, Test::Number::Delta only compares if the absolute value
of the difference is B<less than> epsilon (for equality tests) or
B<greater than> epsilon (for inequality tests).
=head1 USAGE
=head2 use Test::Number::Delta;
With no arguments, epsilon defaults to 1e-6. (An arbitrary choice on the
author's part.)
=head2 use Test::Number::Delta within => 1e-9;
To specify a different default value for epsilon, provide a C<within> parameter
when importing the module. The value must be non-zero.
=head2 use Test::Number::Delta relative => 1e-3;
As an alternative to using a fixed value for epsilon, provide a C<relative>
parameter when importing the module. This signals that C<delta_ok> should
test equality with an epsilon that is scaled to the size of the arguments.
Epsilon is calculated as the relative value times the absolute value
of the argument with the greatest magnitude. Mathematically, for arguments
'x' and 'y':
epsilon = relative * max( abs(x), abs(y) )
For example, a relative value of "0.01" would mean that the arguments are equal
if they differ by less than 1% of the larger of the two values. A relative
value of 1e-6 means that the arguments must differ by less than 1 millionth
of the larger value. The relative value must be non-zero.
=head2 Combining with a test plan
use Test::Number::Delta 'no_plan';
# or
use Test::Number::Delta within => 1e-9, tests => 1;
If a test plan has not already been specified, the optional
parameter for Test::Number::Delta may be followed with a test plan (see
L<Test::More> for details). If a parameter for Test::Number::Delta is
given, it must come first.
=cut
my $Test = Test::Builder->new;
my $Epsilon = 1e-6;
my $Relative = undef;
sub import {
my $self = shift;
my $pack = caller;
my $found = grep /within|relative/, @_;
croak "Can't specify more than one of 'within' or 'relative'"
if $found > 1;
if ($found) {
my ($param,$value) = splice @_, 0, 2;
croak "'$param' parameter must be non-zero"
if $value == 0;
if ($param eq 'within') {
$Epsilon = abs($value);
}
elsif ($param eq 'relative') {
$Relative = abs($value);
}
else {
croak "Test::Number::Delta parameters must come first";
}
}
$Test->exported_to($pack);
$Test->plan(@_);
$self->export_to_level(1, $self, $_) for @EXPORT;
}
#--------------------------------------------------------------------------#
# _check -- recursive function to perform comparison
#--------------------------------------------------------------------------#
sub _check {
my ($p, $q, $epsilon, $name, @indices) = @_;
my ($ok, $diag) = ( 1, q{} ); # assume true
if ( ref $p eq 'ARRAY' || ref $q eq 'ARRAY' ) {
if ( @$p == @$q ) {
for my $i ( 0 .. $#{$p} ) {
my @new_indices;
($ok, $diag, @new_indices) = _check(
$p->[$i],
$q->[$i],
$epsilon,
$name,
scalar @indices ? @indices : (),
$i,
);
if ( not $ok ) {
@indices = @new_indices;
last;
}
}
}
else {
$ok = 0;
$diag = "Got an array of length " . scalar(@$p) .
", but expected an array of length " . scalar(@$q);
}
}
else {
$ok = abs($p - $q) < $epsilon;
if ( ! $ok ) {
my ($ep, $dp) = _ep_dp( $epsilon );
$diag = sprintf("%.${dp}f and %.${dp}f are not equal" .
" to within %.${ep}f", $p, $q, $epsilon
);
}
}
return ( $ok, $diag, scalar(@indices) ? @indices : () );
}
sub _ep_dp {
my $epsilon = shift;
my ($exp) = sprintf("%e",$epsilon) =~ m/e(.+)/;
my $ep = $exp < 0 ? -$exp : 1;
my $dp = $ep + 1;
return ($ep, $dp);
}
=head1 FUNCTIONS
=cut
#--------------------------------------------------------------------------#
# delta_within()
#--------------------------------------------------------------------------#
=head2 delta_within
delta_within( $p, $q, $epsilon, '$p and $q are equal within $epsilon' );
delta_within( \@p, \@q, $epsilon, '@p and @q are equal within $epsilon' );
This function tests for equality within a given value of epsilon. The test is
true if the absolute value of the difference between $p and $q is B<less than>
epsilon. If the test is true, it prints an "OK" statement for use in testing.
If the test is not true, this function prints a failure report and diagnostic.
Epsilon must be non-zero.
The values to compare may be scalars or references to arrays. If the values
are references to arrays, the comparison is done pairwise for each index value
of the array. The pairwise comparison is recursive, so matrices may
be compared as well.
For example, this code sample compares two matrices:
my @a = ( [ 3.14, 6.28 ],
[ 1.41, 2.84 ] );
my @b = ( [ 3.14, 6.28 ],
[ 1.42, 2.84 ] );
delta_within( \@a, \@b, 1e-6, 'compare @a and @b' );
The sample prints the following:
not ok 1 - compare @a and @b
# At [1][0]: 1.4100000 and 1.4200000 are not equal to within 0.000001
=cut
sub delta_within($$$;$) {
my ($p, $q, $epsilon, $name) = @_;
croak "Value of epsilon to delta_within must be non-zero"
if $epsilon == 0;
$epsilon = abs($epsilon);
my ($ok, $diag, @indices) = _check( $p, $q, $epsilon, $name );
if ( @indices ) {
$diag = "At [" . join( "][", @indices ) . "]: $diag";
}
return $Test->ok($ok,$name) || $Test->diag( $diag );
}
#--------------------------------------------------------------------------#
# delta_ok()
#--------------------------------------------------------------------------#
=head2 delta_ok
delta_ok( $p, $q, '$p and $q are close enough to equal' );
delta_ok( \@p, \@q, '@p and @q are close enough to equal' );
This function tests for equality within a default epsilon value. See L</USAGE>
for details on changing the default. Otherwise, this function works the same
as C<delta_within>.
=cut
sub delta_ok($$;$) {
my ($p, $q, $name) = @_;
{
local $Test::Builder::Level = $Test::Builder::Level + 1;
my $e = $Relative
? $Relative * (abs($p) > abs($q) ? abs($p) : abs($q))
: $Epsilon;
delta_within( $p, $q, $e, $name );
}
}
#--------------------------------------------------------------------------#
# delta_not_ok()
#--------------------------------------------------------------------------#
=head2 delta_not_within
delta_not_within( $p, $q, '$p and $q are different' );
delta_not_within( \@p, \@q, $epsilon, '@p and @q are different' );
This test compares inequality in excess of a given value of epsilon. The test
is true if the absolute value of the difference between $p and $q is B<greater
than> epsilon. For array or matrix comparisons, the test is true if I<any>
pair of values differs by more than epsilon. Otherwise, this function works
the same as C<delta_within>.
=cut
sub delta_not_within($$$;$) {
my ($p, $q, $epsilon, $name) = @_;
croak "Value of epsilon to delta_not_within must be non-zero"
if $epsilon == 0;
$epsilon = abs($epsilon);
my ($ok, undef, @indices) = _check( $p, $q, $epsilon, $name );
$ok = !$ok;
my ($ep, $dp) = _ep_dp( $epsilon );
my $diag = sprintf("Arguments are equal to within %.${ep}f", $epsilon);
return $Test->ok($ok,$name) || $Test->diag( $diag );
}
=head2 delta_not_ok
delta_not_ok( $p, $q, '$p and $q are different' );
delta_not_ok( \@p, \@q, '@p and @q are different' );
This function tests for inequality in excess of a default epsilon value. See
L</USAGE> for details on changing the default. Otherwise, this function works
the same as C<delta_not_within>.
=cut
sub delta_not_ok($$;$) {
my ($p, $q, $name) = @_;
{
local $Test::Builder::Level = $Test::Builder::Level + 1;
my $e = $Relative
? $Relative * (abs($p) > abs($q) ? abs($p) : abs($q))
: $Epsilon;
delta_not_within( $p, $q, $e, $name );
}
}
1; #this line is important and will help the module return a true value
__END__
=head1 SEE ALSO
L<Test::More>, L<Test::Harness>, L<Test::Builder>
=head1 BUGS
Please report any bugs or feature using the CPAN Request Tracker.
Bugs can be submitted by email to C<bug-Test-Number-Delta@rt.cpan.org> or
through the web interface at
L<http://rt.cpan.org/Dist/Display.html?Queue=Test-Number-Delta>
When submitting a bug or request, please include a test-file or a patch to an
existing test-file that illustrates the bug or desired feature.
=head1 AUTHOR
David A Golden (DAGOLDEN)
dagolden@cpan.org
L<http://dagolden.com/>
=head1 COPYRIGHT
Copyright (c) 2005, 2006 by David A. Golden
This program is free software; you can redistribute
it and/or modify it under the same terms as Perl itself.
The full text of the license can be found in the
LICENSE file included with this module.
=head1 DISCLAIMER OF WARRANTY
BECAUSE THIS SOFTWARE IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
FOR THE SOFTWARE, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
PROVIDE THE SOFTWARE "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER
EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE
ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE SOFTWARE IS WITH
YOU. SHOULD THE SOFTWARE PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL
NECESSARY SERVICING, REPAIR, OR CORRECTION.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
REDISTRIBUTE THE SOFTWARE AS PERMITTED BY THE ABOVE LICENCE, BE
LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL,
OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE
THE SOFTWARE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING
RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A
FAILURE OF THE SOFTWARE TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF
SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.
=cut