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math::fuzzy - Fuzzy comparison of floating-point numbers

Table Of Contents


package require Tcl ?8.3?
package require math::fuzzy ?0.2?

::math::fuzzy::teq value1 value2
::math::fuzzy::tne value1 value2
::math::fuzzy::tge value1 value2
::math::fuzzy::tle value1 value2
::math::fuzzy::tlt value1 value2
::math::fuzzy::tgt value1 value2
::math::fuzzy::tfloor value
::math::fuzzy::tceil value
::math::fuzzy::tround value
::math::fuzzy::troundn value ndigits


The package Fuzzy is meant to solve common problems with floating-point numbers in a systematic way:

The Fuzzy package is meant to help sorting out this type of problems by defining "fuzzy" comparison procedures for floating-point numbers. It does so by allowing for a small margin that is determined automatically - the margin is three times the "epsilon" value, that is three times the smallest number eps such that 1.0 and 1.0+$eps canbe distinguished. In Tcl, which uses double precision floating-point numbers, this is typically 1.1e-16.


Effectively the package provides the following procedures:


if { [teq $x $y] } { puts "x == y" }
if { [tne $x $y] } { puts "x != y" }
if { [tge $x $y] } { puts "x >= y" }
if { [tgt $x $y] } { puts "x > y" }
if { [tlt $x $y] } { puts "x < y" }
if { [tle $x $y] } { puts "x <= y" }

set fx      [tfloor $x]
set fc      [tceil  $x]
set rounded [tround $x]
set roundn  [troundn $x $nodigits]


The problems that can occur with floating-point numbers are illustrated by the test cases in the file "fuzzy.test":

The conclusion from this is that any expression should be surrounded by braces, because otherwise very awkward things can happen if you need accuracy. Furthermore, accuracy and understandable results are enhanced by using these "tolerant" or fuzzy comparisons.

Note that besides the Tcl-only package, there is also a C-based version.


Original implementation in Fortran by dr. H.D. Knoble (Penn State University).

P. E. Hagerty, "More on Fuzzy Floor and Ceiling," APL QUOTE QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5 took five years of refereed evolution (publication).

L. M. Breed, "Definitions for Fuzzy Floor and Ceiling", APL QUOTE QUAD 8(3):16-23, March 1978.

D. Knuth, Art of Computer Programming, Vol. 1, Problem 1.2.4-5.

Bugs, Ideas, Feedback

This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math :: fuzzy of the Tcllib Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.

When proposing code changes, please provide unified diffs, i.e the output of diff -u.

Note further that attachments are strongly preferred over inlined patches. Attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar.


floating-point, math, rounding