Editing Infinite loop (section)

===Rounding errors===
{| style="float:right; border: 1px solid grey;"
|-
| ''C output on an [[AMD Turion]] processor:''
|- 
|x = 0.10000000149011611938      
|- 
|x = 0.20000000298023223877      
|- 
|x = 0.30000001192092895508      
|- 
|x = 0.40000000596046447754      
|- 
|x = 0.50000000000000000000      
|- 
|x = 0.60000002384185791016      
|- 
|x = 0.70000004768371582031      
|- 
|x = 0.80000007152557373047      
|- 
|x = 0.90000009536743164062      
|- 
|x = 1.00000011920928955078      
|- 
|x = 1.10000014305114746094      
|- 
|x = 1.20000016689300537109      
|- 
| ...
|}

Unexpected behavior in evaluating the terminating condition can also cause this problem. Here is an example in [[C (programming language)|C]]:

<syntaxhighlight lang="c">
float x = 0.1;
while (x != 1.1) {
  printf("x = %22.20f\n", x);
  x += 0.1;
}
</syntaxhighlight>

On some systems, this loop will execute ten times as expected, but on other systems it will never terminate. The problem is that the loop terminating condition <code>(x != 1.1)</code> tests for exact equality of two [[floating point]] values, and the way floating point values are represented in many computers will make this test fail, because they cannot represent the value 0.1 exactly, thus introducing rounding errors on each increment (cf. box).

The same can happen in [[Python (programming language)|Python]]:
<syntaxhighlight lang="python">
x = 0.1
while x != 1:
    print(x)
    x += 0.1
</syntaxhighlight>

Because of the likelihood of tests for equality or not-equality failing unexpectedly, it is safer to use greater-than or less-than tests when dealing with floating-point values. For example, instead of testing whether <code>x</code> equals 1.1, one might test whether <code>(x <= 1.0)</code>, or <code>(x < 1.1)</code>, either of which would be certain to exit after a finite number of iterations. Another way to fix this particular example would be to use an [[integer (computer science)|integer]] as a [[control flow|loop index]], counting the number of iterations that have been performed.

A similar problem occurs frequently in [[numerical analysis]]: in order to compute a certain result, an iteration is intended to be carried out until the error is smaller than a chosen tolerance. However, because of rounding errors during the iteration, the specified tolerance can never be reached, resulting in an infinite loop.