Implementation of half-cycle trignometric functions

Steve Kargl sgk at
Sun Apr 9 22:08:15 UTC 2017

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

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

The code is attached the bug reportr.


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