File Coverage

blib/lib/Test/Number/Delta.pm

Criterion	Covered	Total	%
statement	93	93	100.0
branch	42	42	100.0
condition	12	18	66.6
subroutine	16	16	100.0
pod	4	4	100.0
total	167	173	96.5

use strict;
use warnings;

package Test::Number::Delta;
# ABSTRACT: Compare the difference between numbers against a given tolerance

our $VERSION = '1.05';

use vars qw (@EXPORT @ISA);

# Required modules
use Carp;
use Test::Builder;
use Exporter;

@ISA    = qw( Exporter );
@EXPORT = qw( delta_not_ok delta_ok delta_within delta_not_within );

#pod =head1 SYNOPSIS
#pod
#pod   # Import test functions
#pod   use Test::Number::Delta;
#pod
#pod   # Equality test with default tolerance
#pod   delta_ok( 1e-5, 2e-5, 'values within 1e-6');
#pod
#pod   # Inequality test with default tolerance
#pod   delta_not_ok( 1e-5, 2e-5, 'values not within 1e-6');
#pod
#pod   # Provide specific tolerance
#pod   delta_within( 1e-3, 2e-3, 1e-4, 'values within 1e-4');
#pod   delta_not_within( 1e-3, 2e-3, 1e-4, 'values not within 1e-4');
#pod
#pod   # Compare arrays or matrices
#pod   @a = ( 3.14, 1.41 );
#pod   @b = ( 3.15, 1.41 );
#pod   delta_ok( \@a, \@b, 'compare @a and @b' );
#pod
#pod   # Set a different default tolerance
#pod   use Test::Number::Delta within => 1e-5;
#pod   delta_ok( 1.1e-5, 2e-5, 'values within 1e-5'); # ok
#pod
#pod   # Set a relative tolerance
#pod   use Test::Number::Delta relative => 1e-3;
#pod   delta_ok( 1.01, 1.0099, 'values within 1.01e-3');
#pod
#pod
#pod =head1 DESCRIPTION
#pod
#pod At some point or another, most programmers find they need to compare
#pod floating-point numbers for equality.  The typical idiom is to test
#pod if the absolute value of the difference of the numbers is within a desired
#pod tolerance, usually called epsilon.  This module provides such a function for use
#pod with L.  Usage is similar to other test functions described in
#pod L.  Semantically, the C function replaces this kind
#pod of construct:
#pod
#pod  ok ( abs($p - $q) < $epsilon, '$p is equal to $q' ) or
#pod      diag "$p is not equal to $q to within $epsilon";
#pod
#pod While there's nothing wrong with that construct, it's painful to type it
#pod repeatedly in a test script.  This module does the same thing with a single
#pod function call.  The C function is similar, but either uses a global
#pod default value for epsilon or else calculates a 'relative' epsilon on
#pod the fly so that epsilon is scaled automatically to the size of the arguments to
#pod C.  Both functions are exported automatically.
#pod
#pod Because checking floating-point equality is not always reliable, it is not
#pod possible to check the 'equal to' boundary of 'less than or equal to
#pod epsilon'.  Therefore, Test::Number::Delta only compares if the absolute value
#pod of the difference is B epsilon (for equality tests) or
#pod B epsilon (for inequality tests).
#pod
#pod =head1 USAGE
#pod
#pod =head2 use Test::Number::Delta;
#pod
#pod With no arguments, epsilon defaults to 1e-6. (An arbitrary choice on the
#pod author's part.)
#pod
#pod =head2 use Test::Number::Delta within => 1e-9;
#pod
#pod To specify a different default value for epsilon, provide a C parameter
#pod when importing the module.  The value must be non-zero.
#pod
#pod =head2 use Test::Number::Delta relative => 1e-3;
#pod
#pod As an alternative to using a fixed value for epsilon, provide a C
#pod parameter when importing the module.  This signals that C should
#pod test equality with an epsilon that is scaled to the size of the arguments.
#pod Epsilon is calculated as the relative value times the absolute value
#pod of the argument with the greatest magnitude.  Mathematically, for arguments
#pod 'x' and 'y':
#pod
#pod  epsilon = relative * max( abs(x), abs(y) )
#pod
#pod For example, a relative value of "0.01" would mean that the arguments are equal
#pod if they differ by less than 1% of the larger of the two values.  A relative
#pod value of 1e-6 means that the arguments must differ by less than 1 millionth
#pod of the larger value.  The relative value must be non-zero.
#pod
#pod =head2 Combining with a test plan
#pod
#pod  use Test::Number::Delta 'no_plan';
#pod
#pod  # or
#pod
#pod  use Test::Number::Delta within => 1e-9, tests => 1;
#pod
#pod If a test plan has not already been specified, the optional
#pod parameter for Test::Number::Delta may be followed with a test plan (see
#pod L for details).  If a parameter for Test::Number::Delta is
#pod given, it must come first.
#pod
#pod =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, $e, $name, @indices ) = @_;
    my $epsilon;

    if ( !defined $e ) {
        $epsilon =
            $Relative
          ? $Relative * ( abs($p) > abs($q) ? abs($p) : abs($q) )
          : $Epsilon;
    }
    else {
        $epsilon = abs($e);
    }

    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], $e, $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
      or return;
    $epsilon = abs($epsilon);
    my ($exp) = sprintf( "%e", $epsilon ) =~ m/e(.+)/;
    my $ep = $exp < 0 ? -$exp : 1;
    my $dp = $ep + 1;
    return ( $ep, $dp );
}

sub _diag_default {
    my ($ep) = _ep_dp( abs( $Relative || $Epsilon ) );
    my $diag = "Arguments are equal to within ";
    $diag .=
      $Relative
      ? sprintf( "relative tolerance %.${ep}f", abs($Relative) )
      : sprintf( "%.${ep}f",                    abs($Epsilon) );
    return $diag;
}

#pod =head1 FUNCTIONS
#pod
#pod =cut

#--------------------------------------------------------------------------#
# delta_within()
#--------------------------------------------------------------------------#

#pod =head2 delta_within
#pod
#pod  delta_within(  $p,  $q, $epsilon, '$p and $q are equal within $epsilon' );
#pod  delta_within( \@p, \@q, $epsilon, '@p and @q are equal within $epsilon' );
#pod
#pod This function tests for equality within a given value of epsilon. The test is
#pod true if the absolute value of the difference between $p and $q is B
#pod epsilon.  If the test is true, it prints an "OK" statement for use in testing.
#pod If the test is not true, this function prints a failure report and diagnostic.
#pod Epsilon must be non-zero.
#pod
#pod The values to compare may be scalars or references to arrays.  If the values
#pod are references to arrays, the comparison is done pairwise for each index value
#pod of the array.  The pairwise comparison is recursive, so matrices may
#pod be compared as well.
#pod
#pod For example, this code sample compares two matrices:
#pod
#pod     my @a = (   [ 3.14, 6.28 ],
#pod                 [ 1.41, 2.84 ]   );
#pod
#pod     my @b = (   [ 3.14, 6.28 ],
#pod                 [ 1.42, 2.84 ]   );
#pod
#pod     delta_within( \@a, \@b, 1e-6, 'compare @a and @b' );
#pod
#pod The sample prints the following:
#pod
#pod     not ok 1 - compare @a and @b
#pod     # At [1][0]: 1.4100000 and 1.4200000 are not equal to within 0.000001
#pod
#pod =cut

sub delta_within($$$;$) { ## no critic
    my ( $p, $q, $epsilon, $name ) = @_;
    croak "Value of epsilon to delta_within must be non-zero"
      if !defined($epsilon) || $epsilon == 0;
    {
        local $Test::Builder::Level = $Test::Builder::Level + 1;
        _delta_within( $p, $q, $epsilon, $name );
    }
}

sub _delta_within {
    my ( $p, $q, $epsilon, $name ) = @_;
    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()
#--------------------------------------------------------------------------#

#pod =head2 delta_ok
#pod
#pod  delta_ok(  $p,  $q, '$p and $q are close enough to equal' );
#pod  delta_ok( \@p, \@q, '@p and @q are close enough to equal' );
#pod
#pod This function tests for equality within a default epsilon value.  See L
#pod for details on changing the default.  Otherwise, this function works the same
#pod as C.
#pod
#pod =cut

sub delta_ok($$;$) { ## no critic
    my ( $p, $q, $name ) = @_;
    {
        local $Test::Builder::Level = $Test::Builder::Level + 1;
        _delta_within( $p, $q, undef, $name );
    }
}

#--------------------------------------------------------------------------#
# delta_not_ok()
#--------------------------------------------------------------------------#

#pod =head2 delta_not_within
#pod
#pod  delta_not_within(  $p,  $q, '$p and $q are different' );
#pod  delta_not_within( \@p, \@q, $epsilon, '@p and @q are different' );
#pod
#pod This test compares inequality in excess of a given value of epsilon. The test
#pod is true if the absolute value of the difference between $p and $q is B
#pod than> epsilon.  For array or matrix comparisons, the test is true if I
#pod pair of values differs by more than epsilon.  Otherwise, this function works
#pod the same as C.
#pod
#pod =cut

sub delta_not_within($$$;$) { ## no critic
    my ( $p, $q, $epsilon, $name ) = @_;
    croak "Value of epsilon to delta_not_within must be non-zero"
      if !defined($epsilon) || $epsilon == 0;
    {
        local $Test::Builder::Level = $Test::Builder::Level + 1;
        _delta_not_within( $p, $q, $epsilon, $name );
    }
}

sub _delta_not_within($$$;$) { ## no critic
    my ( $p, $q, $epsilon, $name ) = @_;
    my ( $ok, undef, @indices ) = _check( $p, $q, $epsilon, $name );
    $ok = !$ok;
    my ( $ep, $dp ) = _ep_dp($epsilon);
    my $diag =
      defined($epsilon)
      ? sprintf( "Arguments are equal to within %.${ep}f", abs($epsilon) )
      : _diag_default();
    return $Test->ok( $ok, $name ) || $Test->diag($diag);
}

#pod =head2 delta_not_ok
#pod
#pod  delta_not_ok(  $p,  $q, '$p and $q are different' );
#pod  delta_not_ok( \@p, \@q, '@p and @q are different' );
#pod
#pod This function tests for inequality in excess of a default epsilon value.  See
#pod L for details on changing the default.  Otherwise, this function works
#pod the same as C.
#pod
#pod =cut

sub delta_not_ok($$;$) { ## no critic
    my ( $p, $q, $name ) = @_;
    {
        local $Test::Builder::Level = $Test::Builder::Level + 1;
        _delta_not_within( $p, $q, undef, $name );
    }
}

1;

__END__