Re: [PATCH 1/4] Add a routine for accurate reduction mod (2pi), for j0f/j1f/y0f/y1f.

[Paul Zimmermann <Paul.Zimmermann@inria.fr>]

       Dear Wilco,

> Do we really need another range reducer here? Would it be possible to use
> the
> much faster reduce_fast and reduce_large in
> sysdeps/ieee754/flt-32/s_sincosf.h?
> Given that returns a 62-bit modulo of PI/4, it should be more accurate as
> well.

yes indeed I was wondering, and too lazy so far. Your mail forced me to try.

reduce_fast is clearly not accurate enough: for x=0x1.96d666p+7, it gives
y=0x1.947b0da22168cp+8 (and n=-128), and we clearly see that y is not in
[-PI/4,PI/4] as advertized. What happens is that in the #else part of
the code that is executed on my machine, r is larger than 2^31, thus the
cast (int32_t) r overflows, the value of n is wrong, and thus the returned
value x - n * p->hpi. Maybe a comment should be added about this limitation
of reduce_fast?

As for reduce_large, I need to run again the exhaustive tests for all four
functions (j0, j1, y0, y1) and all four rounding modes to see if it is accurate
enough.

Paul