Implementation of half-cycle trignometric functions

[Steve Kargl]

On Sun, Apr 09, 2017 at 03:08:09PM -0700, Steve Kargl wrote:
> Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle
> trignometric functions cospi, sinpi, and tanpi.  The attached
> patch implements cospi[fl], sinpi[fl], and tanpi[fl].  Limited
> testing on the cospi and sinpi reveal a max ULP less than 0.89;
> while tanpi is more problematic with a max ULP less than 2.01 
> in the interval [0,0.5].  The algorithms used in these functions
> are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c.
> 
> Note 1.  ISO/IEC TS 18661-4 says these funstions are guarded by
> a predefine macro.  I have no idea or interest in what clang and
> gcc do with regards to this macro.  I've put the functions behind
> __BSD_VISIBLE.
> 
> Note 2.  I no longer have access to a system with ld128 and 
> adequate support to compile and test the ld128 implementations
> of these functions.  Given the almost complete lack of input from
> others on improvements to libm, I doubt that anyone cares.  If 
> someone does care, the ld128 files contain a number of FIXME comments,
> and in particular, while the polynomial coefficients are given
> I did not update the polynomial algorithms to properly use the
> coefficients.
> 
> The code is attached the bug reportr.
> 
> https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=218514
> 

I have attached a new diff to the bugzilla report.  The 
diff is 3090 lines and won't be broadcast the mailing list.

This diff includes fixes for a few inconsequential bugs
and implements modified Estrin's method for sum a few
ploynomials.  If you want the previous Horner's method
then add -DHORNER to your CFLAGS.

-- 
Steve
20170425 https://www.youtube.com/watch?v=VWUpyCsUKR4
20161221 https://www.youtube.com/watch?v=IbCHE-hONow