Question

I am trying to find out the precision level for various floating point formats in C (i.e. float, double and long double). Here is the code I’m using at the moment:

#include <stdio.h>
#define N 100000

int main(void)
{
   float max = 1.0, min = 0.0, test;
   int i;                              /* Counter for the conditional loop */

   for (i = 0; i < N; i++) {
      test = (max + min) / 2.0;
      if( (1.0 + test) != 1.0)         /* If too high, set max to test and try again */
     max = test;
  if( (1.0 + test) == 1.0)     /* If too low, set min to test and try again */
         min = test;
   }
   printf("The epsilon machine is %.50lf\n", max);
   return 0;
}

This gives the value of roughly ~2^-64 as expected. However when I change the decelerations to doubles or ‘long doubles’ I get the same answer I should get a smaller value but I don’t. Anybody got any ideas?

Answer 1

A guess why you’re getting the same answer:

if( (1.0 + test) != 1.0)

Here 1.0 is a double constant, so it’s promoting your float to a double and performing the addition as a double. You probably want to declare a temporary float here to perform the addition, or make those float numeric constants (1.0f IIRC).

You might also be falling into the excess-precision-in-temporary-floats problem and might need to force it to store the intermediates in memory to reduce to the correct precision.

---

Here’s a quick go at redoing your range search method but computing the test in the correct type. I get an answer that’s slightly too large, though.

#include <stdio.h>
#define N 100000
#define TYPE float

int main(void)
{
   TYPE max = 1.0, min = 0.0, test;
   int i;

   for (i = 0; i < N; i++)
   {
      TYPE one_plus_test;

      test = (max + min) / ((TYPE)2.0);
      one_plus_test = ((TYPE)1.0) + test;
      if (one_plus_test == ((TYPE)1.0))
      {
         min = test;
      }
      else
      {
         max = test;
      }
   }
   printf("The epsilon machine is %.50lf\n", max);
   return 0;
}