this is necessary to support archs where fenv is incomplete or
unavailable (presently arm). fma, fmal, and the lrint family should
work perfectly fine with this change; fmaf is slightly broken with
respect to rounding as it depends on non-default rounding modes to do
its work.
a double precision nan, when converted to extended (80-bit) precision,
will never end in 0x400, since the corresponding bits do not exist in
the original double precision value. thus there's no need to waste
time and code size on this check.
the fsqrt opcode is correctly rounded, but only in the fpu's selected
precision mode, which is 80-bit extended precision. to get a correctly
rounded double precision output, we check for the only corner cases
where two-step rounding could give different results than one-step
(extended-precision mantissa ending in 0x400) and adjust the mantissa
slightly in the opposite direction of the rounding which the fpu
already did (reported in the c1 flag of the fpu status word).
this should have near-zero cost in the non-corner cases and at worst
very low cost.
note that in order for sqrt() to get used when compiling with gcc, the
broken, non-conformant builtin sqrt must be disabled.
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.
this should not be necessary - the invalid bit patterns cannot be
created except through type punning. however, some broken gnu software
is passing them to printf and triggering dangerous stack-smashing, so
let's catch them anyway...
Rich Felker