'<=' operator not working properly?

I wrote a program that, among other things, utilizes a simple while loop with a '<=' operator. It malfunctioned in that it ignored the 'or equal to' part of the operator and quit the loop early. Here is an example of the part of the program that is malfunctioning, along with the output.

Code:

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#include <iostream>
using namespace std;
main(){
  double d = 0.1;
  double e = 0.02;
  double f = 0.2;
  while( d <= f ){
    cout << "d: " << d << endl;
    d += e;
  }
  cout << endl;
  double a = 0.3;
  double b = 0.05;
  double c = 0.7;
  while( a <= c ){
    cout << "a: " << a << endl;
    a += b;
  }
}

---

This program should first loop from 0.1 to 0.2 in increments of 0.02, printing every number from 0.1 to 0.2, inclusive. It then should loop from 0.3 to 0.7 in increments of 0.05, printing every number from 0.3 to 0.7, inclusive. Here is what it prints:

d: 0.1
d: 0.12
d: 0.14
d: 0.16
d: 0.18
d: 0.2

a: 0.3
a: 0.35
a: 0.4
a: 0.45
a: 0.5
a: 0.55
a: 0.6
a: 0.65

Notice that it does not print 0.7. This is my problem. The same program, executing the same loop, is behaving differently when using different values in the loop. Am I missing something blatantly obvious here? This isn't a complex piece of code here, but maybe one of you out there knows what's happening when it claims that 0.7 <= 0.7 returns false. I'd appreciate any comments.

Floating point inaccuracies. Floating point numbers cannot represent all numbers with full accuracy. What happens is that when a reaches 0.7, it's actually slightly above - 0.70000324 or something like that. Thus, the comparison fails.

Example:

Code:

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const float tolerance = 0.00001;

inline bool equal_to(float a, float b)
{
      return (+(a - b) < tolerance);
}

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Adjust the tolerance as needed, keeping in mind it introduces the possibility of precision loss.

If you are stepping from 0.3 to 0.7 in steps of 0.05, then you will take (0.7 - 0.3) / 0.05 = 8 steps. So iterate over the (already known) number of steps, instead of comparing values.

If you actually compute (0.7-0.3)/0.05, you'll get something like 7.99999, which you should obviously round to 8.

Thanks guys. I guess I shouldn't assume that any two floating point values are equal to the full precision of the computer.

Quote:

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Originally Posted by master5001

+(a - b)

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Out of curiosity, why the plus operator?

i thought the + should be an abs() ?

Yep, should be.