Created attachment 23670 [details]
c code to produce the output above

I am not sure if this is a "good" bug to submit to gcc, since it involves the math library. I have found it occurs on my own machine (Intel Core i7) with gcc4.5 and gcc4.6, as well as on other machines I have access to that use gcc. 

Again, I apologize if this is either not a real error, or if it is related to other floating point errors that people report. I have tried to look through the database. The error below appears even without optimization flags.

In any case, I am finding that fmod, given a double precision set of inputs, produces answers that are only good to (approximately) single precision. In other words, the output of fmod is a double, but the answer is not accurate. It seems to show up for large values of x in fmod(x,y).

Below I compare the outputs to Mathematica (which can handle arbitrary precision.)

10^9 mod 2pi:      0.5773954624831035
Mathematica value: 0.5773954235013852
[this is accurate only to 10^-8]

sin(10^9 mod 2pi): 0.5458434821109812
sin(10^9):         0.5458434494486994
Mathematica value: 0.5458434494486996
[the sin function handles the large number gracefully to give standard 10^-16 precision]

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

#define TWOPI 6.2831853071795864769252867665590057683943387987502

int main() {
	double big, twopi;

	big=1000000000.0;

	printf("10^9 mod 2pi:      %#17.16g\n",  fmod(big, TWOPI));
	printf("Mathematica value: 0.5773954235013852\n");
	printf("\n");
	printf("sin(10^9 mod 2pi): %#17.16g\nsin(10^9):         %#17.16g\n", sin(fmod(big, TWOPI)), sin(big));
	printf("Mathematica value: 0.5458434494486996\n");
}