[Bug 218514] [LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl]

https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=218514

--- Comment #30 from Steve Kargl <kargl@FreeBSD.org> ---
Created attachment 229180
  --> https://bugs.freebsd.org/bugzilla/attachment.cgi?id=229180&action=edit
Fix the ld128 implementations

Mark Murray graciously provided access to an aarch64 system
to test the ld128 implementations.  This patch address

* Misuses of copysignl() in sinpil() and tanpil().

* Redo the splitting of argument 'x' into an integer part and
  remainder.  The remainder must satify 0 <= r < 1.

* Update the reduction of the integer part to something that can
  easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r)
  with n <= 2^112 and we an reduce n by subtracting integer powers
  of 2.

* In s_cospil.c, fix typos where 'x' is used where 'ax', the 
  remainder, is required.

* In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax),
  ax should be x in fabsl().

One item of note, in the limited tested on aarch64, the max ULP
for sinpil() and cospil() were less than 1.1 ULP, which is higher
that the desired max ULP less than 1.  This was traced to the
kernel for cosl() in the fundamental interval [0,pi/4].  The 
coefficients in the minmax polynomial likely need refinement.

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