Implementation of half-cycle trignometric functions

Steve Kargl sgk at
Thu Apr 13 17:12:54 UTC 2017

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
> 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.

While everyone is busy reviewing and testing the patch available
in bugzilla, I suspect some may be wondering about the inverse
half-cycle trignometric functions.  I have worked out an algorithm
for asinpi[fl] and have a working implemenation of asinpif(x).  
It will take a couple of weeks (due to limited available time)
before I can submit asinpi[fl], acospi[fl], and atanpi[fl], but
work is in progress.


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