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
6d04e1422e