* use unsigned arithmetics on the representation
* store arg reduction quotient in unsigned (so n%2 would work like n&1)
* use different convention to pass the arg reduction bit to __tan
(this argument used to be 1 for even and -1 for odd reduction
which meant obscure bithacks, the new n&1 is cleaner)
* raise inexact and underflow flags correctly for small x
(tanl(x) may still raise spurious underflow for small but normal x)
(this exception raising code increases codesize a bit, similar fixes
are needed in many other places, it may worth investigating at some
point if the inexact and underflow flags are worth raising correctly
as this is not strictly required by the standard)
* tanf manual reduction optimization is kept for now
* tanl code path is cleaned up to follow similar logic to tan and tanf
When FLT_EVAL_METHOD!=0 (only i386 with x87 fp) the excess
precision of an expression must be removed in an assignment.
(gcc needs -fexcess-precision=standard or -std=c99 for this)
This is done by extra load/store instructions which adds code
bloat when lot of temporaries are used and it makes the result
less precise in many cases.
Using double_t and float_t avoids these issues on i386 and
it makes no difference on other archs.
For now only a few functions are modified where the excess
precision is clearly beneficial (mostly polynomial evaluations
with temporaries).
object size differences on i386, gcc-4.8:
old new
__cosdf.o 123 95
__cos.o 199 169
__sindf.o 131 95
__sin.o 225 203
__tandf.o 207 151
__tan.o 605 499
erff.o 1470 1416
erf.o 1703 1649
j0f.o 1779 1745
j0.o 2308 2274
j1f.o 1602 1568
j1.o 2286 2252
tgamma.o 1431 1424
math/*.o 64164 63635
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.
