in atanh exception handling was left to the called log functions,
but the argument to those functions could underflow or overflow.
use double_t and float_t to avoid some useless stores on x86
modifications:
* avoid unsigned->signed integer conversion
* do not handle special cases when they work correctly anyway
* more strict threshold values (0x1p26 instead of 0x1p28 etc)
* smaller code, cleaner branching logic
* same precision as the old code:
acosh(x) has up to 2ulp error in [1,1.125]
asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125]
atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125]
zero, one, two, half are replaced by const literals
The policy was to use the f suffix for float consts (1.0f),
but don't use suffix for long double consts (these consts
can be exactly represented as double).
thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).
based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.
various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.
Szabolcs Nagy
Rich Felker