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