[PATCH][BZ #14412] Define __sincos_finite as a fast version of sincos

[Rich Felker]

On Mon, Apr 29, 2013 at 03:53:00PM +0100, Andrew Haley wrote:
> On 04/29/2013 03:15 PM, Ondřej Bílka wrote:
> > On Mon, Apr 29, 2013 at 01:34:42PM +0000, Joseph S. Myers wrote:
> >> On Mon, 29 Apr 2013, Siddhesh Poyarekar wrote:
> >>
> >>> This patch brings back the assembly implementation of sincos (with
> >>> some changes) to give a fast alternative to the default sincos
> >>> implementation.  This is defined as __sincos_finite and is used if the
> >>> implementing program is compiled with the -ffinite-math-only gcc flag.
> >>
> >> The changes don't seem to include accurate range reduction.  Without that, 
> >> I think this is inappropriate, as it will result in wildly inaccurate 
> >> results for large but finite inputs.
> >>
> > These inputs contain zero significant digits. You cannot expect any
> > accuracty from them.
> 
> You can't possibly know that.  If the caller asks for sin(2^80) you should
> return a close approximation to sin(2^80), not garbage.

Ondřej is simply repeating the standard fallacy from people who think
floating point numbers represent intervals or some sort of
approximation with a distribution of possible "actual values" centered
on the nominal value. These views are all incorrect. Floating point
values are always exact values. Floating point _calculations_,
including conversion from decimal strings, can be inexact, but the
values represented, and used as inputs to floating point functions and
operators, are exact.

Rich