NAME
Test::Number::Delta - Compare if the difference between numbers is less
than a given tolerance
SYNOPSIS
# Default tolerance
use Test::Number::Delta;
delta_ok( 1e-5, 2e-5, 'values within 1e-6'); # not ok
# Specific tolerance for a single test
delta_within( 1e-3, 2e-3, 1e-4, 'values within 1e-4'); not ok
# 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'); # ok
# Compare arrays or matrices
@a = ( 3.14, 1.41 );
@b = ( 3.15, 1.41 );
delta_ok( \@a, \@b, 'compare @a and @b' );
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 Test::Harness. Usage is similar to other test functions
described in Test::More. Semantically, the "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 "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 "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 less than epsilon.
USAGE
use Test::Number::Delta;
With no arguments, epsilon defaults to 1e-6. (An arbitrary choice on the
author's part.)
use Test::Number::Delta within => 1e-9;
To specify a different default value for epsilon, provide a "within"
parameter when importing the module.
use Test::Number::Delta relative => 1e-3;
As an alternative to using a fixed value for epsilon, provide a
"relative" parameter when importing the module. This signals that
"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.
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 Test::More
for details). If a parameter for Test::Number::Delta is given, it must
come first.
FUNCTIONS
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 test compares equality within a given value of epsilon. The test is
true if the absolute value of the difference between $p and $q is 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.
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
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 test compares equality using one of two pre-set approaches for
determining epsilon. (See "USAGE") If a "within" parameter was provided
during "use", that value is the default for epsilon. If a "relative"
parameter was provided, that value is multiplied by the larger absolute
value of the arguments to "delta_ok" to determine epsilon for that
comparison. If neither parameter was specified, the default epsilon is
1e-6.
The test is true if the absolute value of the difference between $p and
$q is 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.
As with "delta_within", the values to compare may be scalars or
references to arrays.
SEE ALSO
Test::More, Test::Harness, Test::Builder
BUGS
Please report any bugs or feature using the CPAN Request Tracker. Bugs
can be submitted by email to "bug-Test-Number-Delta@rt.cpan.org" or
through the web interface at
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.
AUTHOR
David A Golden (DAGOLDEN)
dagolden@cpan.org
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.
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