| Commit message (Collapse) | Author | Age | Files | Lines |
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on some negative inputs (e.g. -0x1.1e6ae8p+5) acoshf failed to return
nan. ensure that negative inputs result nan without introducing new
branches. this was tried before in
commit 101e6012856918440b5d7474739c3fc22a8d3b85
math: fix acoshf on negative values
but that fix was wrong. there are 3 formulas used:
log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)))
log(2*x - 1/(x+sqrt(x*x-1)))
log(x) + 0.693147180559945309417232121458176568
the first fails on large negative inputs (may compute log1p(0) or
log1p(inf)), the second one fails on some mid range or large negative
inputs (may compute log(large) or log(inf)) and the last one fails on
-0 (returns -inf).
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this makes acosh slightly more precise around 1.0 on i386
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acosh(x) is invalid for x<1, acoshf tried to be clever using
signed comparisions to handle all x<2 the same way, but the
formula was wrong on large negative values.
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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]
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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).
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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.
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