math::fuzzy(n)                 Tcl Math Library                 math::fuzzy(n)



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

SYNOPSIS
       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

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

       o      Comparing two numbers that are "supposed" to be identical, like
              1.0 and 2.1/(1.2+0.9) is not guaranteed to give the intuitive
              result.

       o      Rounding a number that is halfway two integer numbers can cause
              strange errors, like int(100.0*2.8) != 28 but 27

       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.

PROCEDURES
       Effectively the package provides the following procedures:

       ::math::fuzzy::teq value1 value2
              Compares two floating-point numbers and returns 1 if their
              values fall within a small range. Otherwise it returns 0.

       ::math::fuzzy::tne value1 value2
              Returns the negation, that is, if the difference is larger than
              the margin, it returns 1.

       ::math::fuzzy::tge value1 value2
              Compares two floating-point numbers and returns 1 if their
              values either fall within a small range or if the first number
              is larger than the second. Otherwise it returns 0.

       ::math::fuzzy::tle value1 value2
              Returns 1 if the two numbers are equal according to [teq] or if
              the first is smaller than the second.

       ::math::fuzzy::tlt value1 value2
              Returns the opposite of [tge].

       ::math::fuzzy::tgt value1 value2
              Returns the opposite of [tle].

       ::math::fuzzy::tfloor value
              Returns the integer number that is lower or equal to the given
              floating-point number, within a well-defined tolerance.

       ::math::fuzzy::tceil value
              Returns the integer number that is greater or equal to the given
              floating-point number, within a well-defined tolerance.

       ::math::fuzzy::tround value
              Rounds the floating-point number off.

       ::math::fuzzy::troundn value ndigits
              Rounds the floating-point number off to the specified number of
              decimals (Pro memorie).

       Usage:


              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]


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

       o      Several test case use the ordinary comparisons, and they fail
              invariably to produce understandable results

       o      One test case uses [expr] without braces ({ and }). It too
              fails.

       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.

REFERENCES
       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 SF Trackers
       [http://sourceforge.net/tracker/?group_id=12883].  Please also report
       any ideas for enhancements you may have for either package and/or
       documentation.

KEYWORDS
       floating-point, math, rounding

CATEGORY
       Mathematics



math                                  0.2                       math::fuzzy(n)
