On 2010-11-23 08:25:24 +0200, Nikos Chantziaras wrote:
> I have a problem figuring out the precision of floating point operations.
> Basically, DBL_EPSILON seems to give a wrong value.
>
> Consider this small C program which tries to detect the smallest possible
> value of a double that still makes a difference in a "1 + x > 1" floating
> point comparison (some people refer to that value as "machine epsilon"):
>
> #include <stdio.h>
> #include <float.h>
>
> int main(void)
> {
> double epsilon = 1.0;
>
> while (1.0 + (epsilon / 2.0) > 1.0) {
> epsilon /= 2.0;
> }
> printf("epsilon = %e\n", epsilon);
> printf("DBL_EPSILON: %e\n", DBL_EPSILON);
> return 0;
> }
Since the C standard allows intermediate computations to be carried
out with a higher range and precision (and GCC uses that), your
program is buggy. :)
Basically, the result of each operation should be stored in a variable
or cast to double. And you should compile with -std=c99 or any other
option that would remove the excess precision, such as
-fexcess-precision=standard
I think you need GCC 4.5 or higher. Otherwise you should store the
values to variables and use -ffloat-store.
> The values don't match and DBL_EPSILON gives a much bigger value then the
> detected one. Why is that? It would seem that compiling on 32bit with -O0
> yields higher precision. Is this a result of the FPU being used (or not
> used)?
The extended precision is provided by the processor in 32-bit mode
(FPU instead of SSE).
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