Loop cannot reach the limit

Question

I want to understand why this for doesn't stop its execution to 10. See the code:

#include <stdio.h>

int main()
{
  float i;
  for (i = 0.0; i <= 10; i += 0.01)
    printf("Iteration %g\n", i);

  return 0;
}

The latest iterations are:

Iteration 9.96013
Iteration 9.97013
Iteration 9.98013
Iteration 9.99013

Why this behaviour ?

Please see [Is floating point math broken?](http://stackoverflow.com/questions/588004/is-floating-point-math-broken) — Weather Vane, Mar 09 '16 at 13:02
You accumulate rounding errors because you add a small number which is not exactly representable as a IEEE floating point number (0.01) many times to another float. Additionally you make an exact comparison which is almost always wrong with floating points. The detailed rules how to compute with and compare floating point numbers are difficult (and I don't know them). You can avoid accumulating rounding errors by obtaining the steps through multiplication: `for(int=0; i<101; i++) { printf("Iteration %lg\n", i*0.01);`. Comparisons usually involve FLT_EPSILON from `float.h`. — Peter - Reinstate Monica, Mar 09 '16 at 13:05
As a comparison, you could try to add (1.0/128) 128 times... — Peter - Reinstate Monica, Mar 09 '16 at 13:13
Thinking in decimal: what happens if you add one third (0.333333~) 3 times? You don't get `1.0`. One hundredth is exactly representable in decimal (by definition) but one third is not. — Weather Vane, Mar 09 '16 at 13:24

score 0 · Answer 1 · edited May 23 '17 at 11:50

0

In the last iteration, you see Iteration 9.99013 because if the loop iterated again, i would equal 10.00013, which is greater than 10, your looping condition. The for loop only continues as long as the condition is satisfied.

As @WeatherVane pointed out, you should take a look at this question, which explains why you see the additional 0.00013 at the end of your i variable.

edited May 23 '17 at 11:50

Community

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answered Mar 09 '16 at 12:50

TayTay

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I think OP is asking why sum 0.01 to 0 many times gives X.XXX13 at the end of iterations. – LPs Mar 09 '16 at 13:04
I don't think that necessarily warranted the downvote, but I edited. – TayTay Mar 09 '16 at 13:06
I'm not the downvoter. Well done, about the edit. – LPs Mar 09 '16 at 13:07

score 0 · Answer 2 · answered Mar 09 '16 at 12:56

0

10.00013 <= 10 condition false so control goes out of for loop

answered Mar 09 '16 at 12:56

Abhishek

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Loop cannot reach the limit

2 Answers2