sin, cos, tan and rounding error

Question

I'm doing some trigonometry calculations in C/C++ and am running into problems with rounding errors. For example, on my Linux system:

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

int main(int argc, char *argv[]) {
    printf("%e\n", sin(M_PI));
    return 0;
}

This program gives the following output:

1.224647e-16

when the correct answer is of course 0.

How much rounding error can I expect when using trig functions? How can I best handle that error? I'm familiar with the Units in Last Place technique for comparing floating point numbers, from Bruce Dawson's Comparing Floating Point Numbers, but that doesn't seem to work here, since 0 and 1.22e-16 are quite a few ULPs apart.

Answer 1

The answer is only 0 for sin(pi) - did you include all the digits of Pi ?

-Has anyone else noticed a distinct lack of, irony/sense of humour around here?