The London Perl and Raku Workshop takes place on 26th Oct 2024. If your company depends on Perl, please consider sponsoring and/or attending.


Number::Tolerant - tolerance ranges for inexact numbers


version 1.710


 use Number::Tolerant;

 my $range  = tolerance(10 => to => 12);
 my $random = 10 + rand(2);

 die "I shouldn't die" unless $random == $range;

 print "This line will always print.\n";


Number::Tolerant creates a number-like object whose value refers to a range of possible values, each equally acceptable. It overloads comparison operations to reflect this.

I use this module to simplify the comparison of measurement results to specified tolerances.

 reject $product unless $measurement == $specification;


This library should run on perls released even a long time ago. It should work on any version of perl released in the last five years.

Although it may work on older versions of perl, no guarantee is made that the minimum required version will not be increased. The version may be increased for any reason, and there is no promise that patches will be accepted to lower the minimum required perl.





There is a new method on the Number::Tolerant class, but it also exports a simple function, tolerance, which will return an object of the Number::Tolerant class. Both use the same syntax:

 my $range = Number::Tolerant->new( $x => $method => $y);

 my $range = tolerance( $x => $method => $y);

The meaning of $x and $y are dependent on the value of $method, which describes the nature of the tolerance. Tolerances can be defined in five ways, at present:

  method              range
  plus_or_minus     | x +/- y
  plus_or_minus_pct | x +/- (y% of x)
  or_more           | x to Inf
  or_less           | x to -Inf
  more_than         | x to Inf, not x
  less_than         | x to -Inf, not x
  to                | x to y
  infinite          | -Inf to Inf
  offset            | (x + y1) to (x + y2)

For or_less and or_more, $y is ignored if passed. For infinite, neither $x nor $y is used; "infinite" should be the sole argument. The first two arguments can be reversed for more_than and less_than, to be more English-like.

Offset tolerances are slightly unusual. Here is an example:

  my $offset_tolerance = tolerance(10 => offset => (-3, 5));
  # stringifies to: 10 (-3 +5)

An offset is very much like a plus_or_minus tolerance, but its center value is not necessarily the midpoint between its extremes. This is significant for comparisons and numifications of the tolerance. Given the following two tolerances:

  my $pm_dice = tolerance(10.5 => plus_or_minus => 7.5);
  my $os_dice = tolerance(11 => offset => (-8, 7));

The first will sort as numerically less than the second.

If the given arguments can't be formed into a tolerance, an exception will be raised.


A new tolerance can be instantiated from the stringification of an old tolerance. For example:

 my $range = Number::Tolerant->from_string("10 to 12");

 die "Everything's OK!" if 11 == $range; # program dies of joy

This will not yet parse stringified unions, but that will be implemented in the future. (I just don't need it yet.)

If a string can't be parsed, an exception is raised.


  my $string = $tolerance->stringify_as($type);

This method does nothing! Someday, it will stringify the given tolerance as a different type, if possible. "10 +/- 1" will stringify_as('plus_or_minus_pct') to "10 +/- 10%" for example.


  my $n = $tolerance->numify;

This returns the numeric form of a tolerance. If a tolerance has both a minimum and a maximum, and they are the same, then that is the numification. Otherwise, numify returns undef.


Tolerances overload a few operations, mostly comparisons.


Tolerances are always true.


Most tolerances numify to undef; see "numify".


A tolerance stringifies to a short description of itself, generally something like "m < x < n"

 infinite  - "any number"
 to        - "m <= x <= n"
 or_more   - "m <= x"
 or_less   - "x <= n"
 more_than - "m < x"
 less_than - "x < n"
 offset    - "x (-y1 +y2)"
 constant  - "x"
 plus_or_minus     - "x +/- y"
 plus_or_minus_pct - "x +/- y%"

A number is equal to a tolerance if it is neither less than nor greater than it. (See below).

smart match

Same as equality.


A number is greater than a tolerance if it is greater than its maximum value.

A number is less than a tolerance if it is less than its minimum value.

No number is greater than an "or_more" tolerance or less than an "or_less" tolerance.

"...or equal to" comparisons include the min/max values in the permissible range, as common sense suggests.

tolerance intersection

A tolerance & a tolerance or number is the intersection of the two ranges. Intersections allow you to quickly narrow down a set of tolerances to the most stringent intersection of values.

 tolerance(5 => to => 6) & tolerance(5.5 => to => 6.5);
 # this yields: tolerance(5.5 => to => 6)

If the given values have no intersection, () is returned.

An intersection with a normal number will yield that number, if it is within the tolerance.

tolerance union

A tolerance | a tolerance or number is the union of the two. Unions allow multiple tolerances, whether they intersect or not, to be treated as one. See Number::Tolerant::Union for more information.


This feature is slighly experimental, but it's here.

New tolerance types may be written as subclasses of Number::Tolerant::Type, providing the interface described in its documentation. They can then be enabled or disabled with the following methods:



This method enables the named class, so that attempts to create new tolerances will check against this class. Classes are checked against "validate_plugin" before being enabled. An exception is thrown if the class does not appear to provide the Number::Tolerant::Type interface.



This method will disable the named class, so that future attempts to create new tolerances will not check against this class.



This method checks (naively) that the given class provides the interface defined in Number::Tolerant::Type. If it does not, an exception is thrown.


  • Extend from_string to cover unions.

  • Extend from_string to include Number::Range-type specifications.

  • Allow translation into forms not originally used:

     my $range    = tolerance(9 => to => 17);
     my $range_pm = $range->convert_to('plus_minus');
  • Create a factory so that you can simultaneously work with two sets of plugins.

    This one is very near completion. There will now be two classes that should be used: Number::Tolerant::Factory, which produces tolerances, and Number::Tolerant::Tolerance, which is a tolerance. Both will inherit from N::T, for supporting old code, and N::T will dispatch construction methods to a default factory.


The module Number::Range provides another way to deal with ranges of numbers. The major differences are: N::R is set-like, not range-like; N::R does not overload any operators. Number::Tolerant will not (like N::R) attempt to parse a textual range specification like "1..2,5,7..10" unless specifically instructed to. (The valid formats for strings passed to from_string does not match Number::Range exactly. See TODO.)

The Number::Range code:

 $range = Number::Range->new("10..15","20..25");

Is equivalent to the Number::Tolerant code:

 $range = Number::Tolerant::Union->new(10..15,20..25);

...while the following code expresses an actual range:

 $range = tolerance(10 => to => 15) | tolerance(20 => to => 25);


Thanks to Yuval Kogman and #perl-qa for helping find the bizarre bug that drove the minimum required perl up to 5.8

Thanks to Tom Freedman, who reminded me that this code was fun to work on, and also provided the initial implementation for the offset type.


Ricardo Signes <>


  • Alexandre Mestiashvili <>

  • Karen Etheridge <>

  • Michael Carman <>

  • Ricardo SIGNES <>

  • Ricardo Signes <>

  • Smylers <>


This software is copyright (c) 2004 by Ricardo Signes.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.