When is a>a true?

Question

Right, I think I really am living a dream. I have the following piece of code which I compile and run on an AIX machine:

AIX 3 5
PowerPC_POWER5 processor type
IBM XL C/C++ for AIX, V10.1
Version: 10.01.0000.0003


#include <stdio.h>
#include <math.h>

#define RADIAN(x) ((x) * acos(0.0) / 90.0)

double nearest_distance(double radius,double lon1, double lat1, double lon2, double lat2){
    double rlat1=RADIAN(lat1);
    double rlat2=RADIAN(lat2);
    double rlon1=lon1;
    double rlon2=lon2;
    double a=0,b=0,c=0;

    a = sin(rlat1)*sin(rlat2)+ cos(rlat1)*cos(rlat2)*cos(rlon2-rlon1);
    printf("%lf\n",a);
    if (a > 1) {
      printf("aaaaaaaaaaaaaaaa\n");
    }
    b = acos(a);
    c = radius * b;

    return radius*(acos(sin(rlat1)*sin(rlat2)+
        cos(rlat1)*cos(rlat2)*cos(rlon2-rlon1)));

}

int main(int argc, char** argv) {
  nearest_distance(6367.47,10,64,10,64);
  return 0;
}

Now, the value of 'a' after the calculation is reported as being '1'. And, on this AIX machine, it looks like 1 > 1 is true as my 'if' is entered !!! And my acos of what I think is '1' returns NanQ since 1 is bigger than 1. May I ask how that is even possible ? I do not know what to think anymore !

The code works just fine on other architectures where 'a' really takes the value of what I think is 1 and acos(a) is 0.

Answer 1

If you do a comparison where result and expctedResult are float types:

if (result == expectedResult)

Then it is unlikely that the comparison will be true. If the comparison is true then it is probably unstable – tiny changes in the input values, compiler, or CPU may change the result and make the comparison be false.

Comparing with epsilon – absolute error

if (fabs(result - expectedResult) < 0.00001)

From Comparing floating point numbers

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What Every Computer Scientist Should Know About Floating-Point Arithmetic