# NAME

Test::Number::Delta - Compare the difference between numbers against a given tolerance

# 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');

``````

# 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 (for equality tests) or greater than epsilon (for inequality tests).

# 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. The value must be non-zero.

## 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. The relative value must be non-zero.

## 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 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 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 : 1.4100000 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 function tests for equality within a default epsilon value. See "USAGE" for details on changing the default. Otherwise, this function works the same as `delta_within`.

## 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 greater than epsilon. For array or matrix comparisons, the test is true if any pair of values differs by more than epsilon. Otherwise, this function works the same as `delta_within`.

## 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 "USAGE" for details on changing the default. Otherwise, this function works the same as `delta_not_within`.

# 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 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.

# AUTHOR

David A Golden (DAGOLDEN)

dagolden@cpan.org

http://dagolden.com/

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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