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

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

--- Comment #36 from commit-hook@FreeBSD.org ---
A commit in branch main references this bug:

URL:
https://cgit.FreeBSD.org/src/commit/?id=6d04e1422e70ca0a77552782c01c291f90716773

commit 6d04e1422e70ca0a77552782c01c291f90716773
Author:     Steve Kargl <kargl@FreeBSD.org>
AuthorDate: 2021-11-02 08:54:10 +0000
Commit:     Konstantin Belousov <kib@FreeBSD.org>
CommitDate: 2021-11-02 08:54:10 +0000

    cosl(): fix polynomial approximation coefficients for ld128 version

    As mention previously, the minmax polynomial approximation
    in the kernel for cosl() seem to have a bad set of coefficients.

    In testing, cosl() in the interval [0.785, pi/4] for 1 million
    values and pi/4 written to 37 decimal digits.  The old version
    on an aarch64 system gave

    % tlibm/tlibm_lmath -l -x 0.78 -X
    7.85398163397448309615660845819875721e-1L cos
    Interval tested for cosl: [0.78,0.785398]
    count: 1000000
      xm =  7.80213913234863919029058821396125599e-01L
      libm =  7.10763080972549562455058499280609083e-01L
      mpfr =  7.10763080972549562455058499280608983e-01L
      ULP = 1.04431

    The max ULP exceeds 1, which is not good.  So, I rinsed off a 10
    year code and recomputed coefficients.  The new minmax polynomial
    now yields

    % tlibm/tlibm_lmath -l -x 0.78 -X
    7.85398163397448309615660845819875721e-1L cos
    Interval tested for cosl: [0.78,0.785398]
    count: 1000000
      xm =  7.82916198746768272588844890973704219e-01L
      libm =  7.08859615479571058183956453286628396e-01L
      mpfr =  7.08859615479571058183956453286628469e-01L
      ULP = 0.75407

    which is very good.

    PR:     218514
    MFC after:      1 week

 lib/msun/ld128/k_cosl.c | 32 +++++++++++++++-----------------
 1 file changed, 15 insertions(+), 17 deletions(-)

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