NAME

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

VERSION

       version 1.06

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::More.  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][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 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".

SEE ALSO

       •   Number::Tolerant

       •   Test::Deep::NumberTolerant

SUPPORT

   Bugs / Feature Requests
       Please report any bugs or feature requests through the issue tracker at
       <https://github.com/dagolden/Test-Number-Delta/issues>.  You will be notified automatically of any
       progress on your issue.

   Source Code
       This is open source software.  The code repository is available for public review and contribution under
       the terms of the license.

       <https://github.com/dagolden/Test-Number-Delta>

         git clone https://github.com/dagolden/Test-Number-Delta.git

AUTHOR

       David Golden <dagolden@cpan.org>

COPYRIGHT AND LICENSE

       This software is Copyright (c) 2014 by David Golden.

       This is free software, licensed under:

         The Apache License, Version 2.0, January 2004