Re: weird optimization in sin+cos, x86 backend

[Michael Matz <matz at suse dot de>]

Hi,

On Thu, 9 Feb 2012, James Courtier-Dutton wrote:

> Results when compiled for 32bit x86.
> gcc -m32 -g -O0 -c -o sincos1.o sincos1.c
> gcc -m32 -static -g -o sincos1 sincos1.o -lm
> 
> ./sincos1
> sin = 4.62613040764601746e-01
> sinl = 0.46261304076460176
> sincos = 4.62613040764601746e-01
> sincosl = 0.46261304076460176
> 
> Which are all inaccurate.

Because all use hardware on x86, with unpatched glibc, not the software 
implementation.  Only on x86_64 at least the sin() implementation uses a 
software implementation while sincos (l or not) and sinl uses hardware.

I think that was said multiple times already.

> So, we have a case of the same program compiled for 32bit might give 
> different floating point results than the same source compiled for 
> 64bit.
> 
> From what I can tell, the xmm register instructions on x86_64 are using 
> 128bit precision which probably explains why the result is more 
> accurate.

That's not the reason, no.  The reason is that the reduction step of the 
software implementation is more accurate.  And it is so because it uses a 
higher precision representation of pi, for long double a 22512 bit long 
representation.  The hardware fprem simply is not as accurate.


Ciao,
Michael.