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

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

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A commit in branch main references this bug:

URL:
https://cgit.FreeBSD.org/src/commit/?id=4f889260c33c163ab28e0e082b4d7e7562d9c647

commit 4f889260c33c163ab28e0e082b4d7e7562d9c647
Author:     Steve Kargl <kargl@FreeBSD.org>
AuthorDate: 2021-10-31 22:26:20 +0000
Commit:     Konstantin Belousov <kib@FreeBSD.org>
CommitDate: 2021-11-01 02:38:19 +0000

    sinpi[fl] etc: 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.

    PR:     218514
    MFC after:      1 week

 lib/msun/ld128/s_cospil.c | 31 +++++++++++++++++--------------
 lib/msun/ld128/s_sinpil.c | 29 ++++++++++++++++-------------
 lib/msun/ld128/s_tanpil.c | 23 +++++++++++++----------
 3 files changed, 46 insertions(+), 37 deletions(-)

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