1math::fuzzy(n) Tcl Math Library math::fuzzy(n)
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8 math::fuzzy - Fuzzy comparison of floating-point numbers
9
11 package require Tcl ?8.3?
12 package require math::fuzzy ?0.2?
14 ::math::fuzzy::teq value1 value2
16 ::math::fuzzy::tne value1 value2
18 ::math::fuzzy::tge value1 value2
20 ::math::fuzzy::tle value1 value2
22 ::math::fuzzy::tlt value1 value2
24 ::math::fuzzy::tgt value1 value2
26 ::math::fuzzy::tfloor value
28 ::math::fuzzy::tceil value
30 ::math::fuzzy::tround value
32 ::math::fuzzy::troundn value ndigits
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36
38 The package Fuzzy is meant to solve common problems with floating-point
39 numbers in a systematic way:
40 • Comparing two numbers that are "supposed" to be identical, like
42 1.0 and 2.1/(1.2+0.9) is not guaranteed to give the intuitive
43 result.
44 • Rounding a number that is halfway two integer numbers can cause
46 strange errors, like int(100.0*2.8) != 28 but 27
47 The Fuzzy package is meant to help sorting out this type of problems by
49 defining "fuzzy" comparison procedures for floating-point numbers. It
50 does so by allowing for a small margin that is determined automatically
51 - the margin is three times the "epsilon" value, that is three times
52 the smallest number eps such that 1.0 and 1.0+$eps canbe distinguished.
53 In Tcl, which uses double precision floating-point numbers, this is
54 typically 1.1e-16.
55
57 Effectively the package provides the following procedures:
58 ::math::fuzzy::teq value1 value2
60 Compares two floating-point numbers and returns 1 if their val‐
61 ues fall within a small range. Otherwise it returns 0.
62 ::math::fuzzy::tne value1 value2
64 Returns the negation, that is, if the difference is larger than
65 the margin, it returns 1.
66 ::math::fuzzy::tge value1 value2
68 Compares two floating-point numbers and returns 1 if their val‐
69 ues either fall within a small range or if the first number is
70 larger than the second. Otherwise it returns 0.
71 ::math::fuzzy::tle value1 value2
73 Returns 1 if the two numbers are equal according to [teq] or if
74 the first is smaller than the second.
75 ::math::fuzzy::tlt value1 value2
77 Returns the opposite of [tge].
78 ::math::fuzzy::tgt value1 value2
80 Returns the opposite of [tle].
81 ::math::fuzzy::tfloor value
83 Returns the integer number that is lower or equal to the given
84 floating-point number, within a well-defined tolerance.
85 ::math::fuzzy::tceil value
87 Returns the integer number that is greater or equal to the given
88 floating-point number, within a well-defined tolerance.
89 ::math::fuzzy::tround value
91 Rounds the floating-point number off.
92 ::math::fuzzy::troundn value ndigits
94 Rounds the floating-point number off to the specified number of
95 decimals (Pro memorie).
96 Usage:
98 if { [teq $x $y] } { puts "x == y" }
101 if { [tne $x $y] } { puts "x != y" }
102 if { [tge $x $y] } { puts "x >= y" }
103 if { [tgt $x $y] } { puts "x > y" }
104 if { [tlt $x $y] } { puts "x < y" }
105 if { [tle $x $y] } { puts "x <= y" }
106 set fx [tfloor $x]
108 set fc [tceil $x]
109 set rounded [tround $x]
110 set roundn [troundn $x $nodigits]
111
114 The problems that can occur with floating-point numbers are illustrated
115 by the test cases in the file "fuzzy.test":
116 • Several test case use the ordinary comparisons, and they fail
118 invariably to produce understandable results
119 • One test case uses [expr] without braces ({ and }). It too
121 fails.
122 The conclusion from this is that any expression should be surrounded by
124 braces, because otherwise very awkward things can happen if you need
125 accuracy. Furthermore, accuracy and understandable results are enhanced
126 by using these "tolerant" or fuzzy comparisons.
127 Note that besides the Tcl-only package, there is also a C-based ver‐
129 sion.
130
132 Original implementation in Fortran by dr. H.D. Knoble (Penn State Uni‐
133 versity).
134 P. E. Hagerty, "More on Fuzzy Floor and Ceiling," APL QUOTE QUAD
136 8(4):20-24, June 1978. Note that TFLOOR=FL5 took five years of refereed
137 evolution (publication).
138 L. M. Breed, "Definitions for Fuzzy Floor and Ceiling", APL QUOTE QUAD
140 8(3):16-23, March 1978.
141 D. Knuth, Art of Computer Programming, Vol. 1, Problem 1.2.4-5.
143
145 This document, and the package it describes, will undoubtedly contain
146 bugs and other problems. Please report such in the category math ::
147 fuzzy of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist].
148 Please also report any ideas for enhancements you may have for either
149 package and/or documentation.
150 When proposing code changes, please provide unified diffs, i.e the out‐
152 put of diff -u.
153 Note further that attachments are strongly preferred over inlined
155 patches. Attachments can be made by going to the Edit form of the
156 ticket immediately after its creation, and then using the left-most
157 button in the secondary navigation bar.
158
160 floating-point, math, rounding
161
163 Mathematics
164tcllib 0.2 math::fuzzy(n)