Floating Point Compare

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Revision as of 15:22, 24 September 2006 (edit)
Ayrnieu (Talk | contribs)
(remove irritating angsting, remove bogus reference to 'imaginary' Erlang bignums and its consequent reasoning (hint: Erlang has bignums.))
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Ayrnieu (Talk | contribs)
(Actually implement the "fuzzy match".)
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In these cases, you can use floating-point byte strings to represent and compare numbers: In these cases, you can use floating-point byte strings to represent and compare numbers:
<code> <code>
-1> Aval = 8.001e-3 * 9.001e5.+fuzzy_match(A,B,L) ->
 + <<AT:L/binary, _/binary>> = <<A/float>>,
 + <<BT:L/binary, _/binary>> = <<B/float>>,
 + AT == BT.
 +1> A = 8.001e-3 * 9.001e5.
7201.70 7201.70
-2> Bval = 8.0011e-3 * 9.001e5.+2> B = 8.0011e-3 * 9.001e5.
7201.79 7201.79
-3> Aval == Bval.+3> A == B.
false false
-4> ABin = << Aval/float >>.+4> fuzzy_match(A,B,3).
-<<64,188,33,179,57,192,235,237>>+
-5> BBin = << Bval/float >>.+
-<<64,188,33,202,68,166,34,63>>+
-6> << ABinTest:3/binary, ARest:5/binary >> = ABin.+
-<<64,188,33,179,57,192,235,237>>+
-7> ABinTest.+
-<<64,188,33>>+
-8> << BBinTest:3/binary, BRest:5/binary >> = BBin.+
-<<64,188,33,202,68,166,34,63>>+
-9> BBinTest.+
-<<64,188,33>>+
-10> BinTest == BinTest2.+
true true
-11> << ABinTest2:4/binary, ARest2:4/binary >> = ABin.+5> fuzzy_match(A,B,4).
-<<64,188,33,179,57,192,235,237>>+
-12> << BBinTest2:4/binary, BRest2:4/binary >> = BBin. +
-<<64,188,33,202,68,166,34,63>>+
-13> ABinTest2 == BBinTest2.+
false false
</code> </code>
Line 39: Line 27:
Another option is to convert the numbers into strings and then compare the portions of the numbers of interest: Another option is to convert the numbers into strings and then compare the portions of the numbers of interest:
<code> <code>
-14> [Nsa]=io_lib:format("~.12f", [Aval]).+equal_to_digit(A,B,D) ->
-["7201.700099999999"]+ [As0,Bs0] = io_lib:fwrite("~.*f~.*f", [D+1,A-trunc(A),D+1,B-trunc(B)]),
-15> [NSB]=io_lib:format("~.12f", [Bval]). + As = string:substr(As0,1,D+2), Bs = string:substr(Bs0,1,D+2),
-["7201.790110000001"]+ As == Bs.
-16> string:substr(NSAa, 1, 6) == string:substr(NSB, 1, 6).+5> equal_to_digit(7201.700099999999, 7201.790110000001,1).
-true+
-</code>+
- +
-A final thought: +
-<code>+
-20> Equal_to_digit = fun(Digit, Numa, Numb) -> +
-20> [N_a] = io_lib:format("~.12f", [Numa]), +
-20> [N_b] = io_lib:format("~.12f", [Numb]), +
-20> string:substr(N_a, 1, Digit) == string:substr(N_b,1,Digit) end.+
-#Fun<erl_eval.18.83214871>+
-21> Equal_to_digit(6, Aval, Bval).+
true true
 +6> equal_to_digit(7201,700099999999, 7201.790110000001,2).
 +false
</code> </code>

Revision as of 15:48, 24 September 2006

Problem

You want to compare two floating-point numbers and know if they are equal. Unfortunately, floating-point arithmetic is not precise so very few results will match exactly. Consequently, we usually want to compare floating point values up to a certain number of decimal places.

Solution

Implement a "fuzzy match" on two real numbers where the difference is below some epsilon threshhold.

In these cases, you can use floating-point byte strings to represent and compare numbers: 

fuzzy_match(A,B,L) ->
    <> = <>,
    <> = <>,
    AT == BT.
1> A = 8.001e-3 * 9.001e5.
7201.70
2> B = 8.0011e-3 * 9.001e5.
7201.79
3> A == B.
false
4> fuzzy_match(A,B,3).
true
5> fuzzy_match(A,B,4).
false

Another option is to convert the numbers into strings and then compare the portions of the numbers of interest: 

equal_to_digit(A,B,D) ->
    [As0,Bs0] = io_lib:fwrite("~.*f~.*f", [D+1,A-trunc(A),D+1,B-trunc(B)]),
    As = string:substr(As0,1,D+2), Bs = string:substr(Bs0,1,D+2),
    As == Bs.
5> equal_to_digit(7201.700099999999, 7201.790110000001,1).
true
6> equal_to_digit(7201,700099999999, 7201.790110000001,2).
false

Note: Some error handling would obviously be necessary to handle cases where the digits are insufficient for the match.

See Also

Volume 2, Section 4.2.2 of The Art of Computer Programming

Retrieved from "http://www.trapexit.org/Floating_Point_Compare"
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