## Comparing floating point numbers and precision problems

February 6, 2017

Our support service often receives reports on suspected bugs in Survey Solutions on the grounds of a situation similar to the one described below. These reports stem from misunderstanding of some fundamental concepts of how computations are done by a computer, and not due to an actual defect of the software.

## Problem description

Suppose you have a questionnaire containing two numeric questions X and Y, and a third question Z with an enabling condition (X*Y) == 21.6.

Some of the users report that the question Z doesn’t get enabled even for the values where it seems to hold when checked manually, e.g. for values X=18 and Y=1.2

The problem is that of comparing two floating point numbers, which is never exact. This is not a Survey Solutions problem, this is how computers work in general. One will have exactly the same situation in Stata:

``````display 18*1.2
display 18*1.2==21.6
display %21x 18*1.2
display %21x 21.6
``````

The problem is not only of division or multiplication operations, but also of addition and subtraction:

``````display 0.1+0.1+0.1==0.3
``````

As the value 21.6 can’t be stored in computer’s memory exactly, it is rounded, and it is rounded to a different value when it is obtained as a result of a mathematical operation or entered directly. Same applies to almost any programming language.

Bill Gould explains this (in the context of Stata) in a series of his blog postings here:
http://blog.stata.com/2012/04/02/the-penultimate-guide-to-precision/

Examples for C# are plentiful all over internet, see e.g. here:
http://stackoverflow.com/questions/3420812/how-do-i-find-if-two-variables-are-approximately-equals

For in-depth overview of the problems associated with the floating point representation of numbers and operations on them, see the following article:
https://docs.oracle.com/cd/E19957-01/800-7895/800-7895.pdf

## Recommendations for questionnaire designers

In most cases ask yourself first, whether you need an exact comparison. In many cases exact comparison is not required. Where it is required, ask yourself whether the values should indeed be represented as floating point numbers, or perhaps they are integers by nature. When there is no other way, compare the floating point numbers x and y as

``````Math.Abs(x-y)<\$epsilon
``````

where you define a macro \$epsilon as a sufficiently small number, for example 0.00000001.

It is also possible to instruct C# to conduct the comparison as integers, where you know you indeed intend to compare integers:

``````(long)x==(long)y
``````

You can find more about C# data types and their use in Survey Solutions by reading the article on data types.