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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

____________________________________________________________________________________________________________

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

       •      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.

       •      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 num-ber number
       ber eps such that 1.0 and 1.0+$eps canbe distinguished. In Tcl, which uses double precision floating-point floatingpoint
       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":

       •      Several  test  case  use  the ordinary comparisons, and they fail invariably to produce under-
              standable results

       •      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://source -
       forge.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)