# Floating Point Compare

## 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:L/binary, _/binary>> = <<A/float>>, <<BT:L/binary, _/binary>> = <<B/float>>, 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