weird optimization in sin+cos, x86 backend

[Tim Prince]

  On 02/05/2012 11:08 AM, James Courtier-Dutton wrote:
> Hi,
>
> I looked at this a bit closer.
> sin(1.0e22) is outside the +-2^63 range, so FPREM1 is used to bring it
> inside the range.
> So, I looked at FPREM1 a bit closer.
>
> #include<stdio.h>
> #include<math.h>
>
> int main (void)
> {
>   long double x, r, m;
>
>   x = 1.0e22;
> // x = 5.26300791462049950360708478127784;<- This is what the answer
> should be give or take 2PI.
>   m =  M_PIl * 2.0;
>   r = remainderl(x, m);   // Utilizes FPREM1
>
>   printf ("x = %.17Lf\n", x);
>   printf ("m = %.17Lf\n", m);
>   printf ("r = %.17Lf\n", r);
>
>   return 1;
> }
>
> This outputs:
> x = 10000000000000000000000.00000000000000000
> m = 6.28318530717958648
> r = 2.66065232182161996
>
> But, r should be
> 5.26300791462049950360708478127784... or
> -1.020177392559086973318201985281...
> according to wolfram alpha and most arbitrary maths libs I tried.
>
> I need to do a bit more digging, but this might point to a bug in the
> cpu instruction FPREM1
>
> Kind Regards
>
> James
As I recall, the remaindering instruction was documented as using a 
66-bit rounded approximation fo PI, in case that is what you refer to.

-- 
Tim Prince