Why (1.1-1.0)*10 isn't 1.0?

Question

Why result of this code is false? I can't solve this problem.

#include <stdio.h>
int main(int argc, char **argv)
{
if ( (1.1 - 1.0)*10.0 - 1.0 == 0.0 )
    printf("True");
else
    printf("False");
return 0;
}

Answer 1

Chasing equality in floating point is mostly a fools game.

Best you can do is decide upon a delta that's 'close enough' and compare with that.

google told me to read this for more information: http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

Answer 2

But this works as you wanted:

int main(int argc, char **argv)
{
    float x,y;
    x=0.0;
    y=0.0;

    x=1.1 - 1.0;
    x=x*10.0;
    x=x-1.0;

    if (   x==y )
        printf("True");
    else
        printf("False");
    return 0;
}

Answer 3

Most double math uses a binary floating point representation. So 1.1 is not exactly representable - just something close to it. Consider the following which uses volatile to prevent compiler optimizations.

#include <stdio.h>
int main(void) {
  volatile double wpw = 1.1;
  volatile double one = 1.0;
  volatile double ten = 10.0;
  printf("%.20e\n", wpw);
  printf("%.20e\n", wpw - one);
  printf("%.20e\n", (wpw - one) * ten);
  printf("%.20e\n", (wpw - one) * ten - one);
  return 0;
}

And it output below. 1.1 - 1.0 is only approximately 0.1.

1.10000000000000008882e+00
1.00000000000000088818e-01
1.00000000000000088818e+00
8.88178419700125232339e-16