c - different behaviour or sqrt when compiled with 64 or 32 bits

Question

I'm using sqrt() function from math library, when I build for 64 bit using -m64 I'm getting correct result but when I build for 32 bit I have very inconsistent behaviour.

For example on 64bit

double dx = 0x1.fffffffffffffp+1023;
sqrt(dx); // => 0x1.fffffffffffffp+511
sqrt(0x1.fffffffffffffp+1023);// => 0x1.fffffffffffffp+511

(which I believe is the correctly rounded result, verified with mpfr)

But on 32 bit same input value it behaves differently.

double dx = 0x1.fffffffffffffp+1023;
sqrt(dx); // => 0x1.0p+512
sqrt(0x1.fffffffffffffp+1023); // => 0x1.fffffffffffffp+511

When the same value passed in a variable I'm getting wrong result. I checked rounding mode before and after each call and all are set to round to nearest. What the reason? I'm using gcc 4.6 on a 64bit machine, and options are -mfpmath=sse and -march=pentium for both x86 nad x64 cases.

Answer 1

Certain compilers, such as gcc, when they see certain math library functions performed on static literals, actually calculate the value during compile time, where-as with the variable, it's by necessity calculated at run-time. The compile-time value is typically calculated by the compiler using a math library like MPFR, GNU MP, etc., so the results will be more accurate, or at least as accurate as possible from platform-to-platform.