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the idiomatic rounding of x is
n = x + toint - toint;
where toint is either 1/EPSILON (x is non-negative) or 1.5/EPSILON
(x may be negative and nearest rounding mode is assumed) and EPSILON is
according to the evaluation precision (the type of toint is not very
important, because single precision float can represent the 1/EPSILON of
ieee binary128).
in case of FLT_EVAL_METHOD!=0 this avoids a useless store to double or
float precision, and the long double code became cleaner with
1/LDBL_EPSILON instead of ifdefs for toint.
__rem_pio2f and __rem_pio2 functions slightly changed semantics:
on i386 a double-rounding is avoided so close to half-way cases may
get evaluated differently eg. as sin(pi/4-eps) instead of cos(pi/4+eps)
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- remove the HAVE_EFFICIENT_IRINT case: fn is an exact integer, so
it can be converted to int32_t a bit more efficiently than with a
cast (the rounding mode change can be avoided), but musl does not
support this case on any arch.
- __rem_pio2: use double_t where possible
- __rem_pio2f: use less assignments to avoid stores on i386
- use unsigned int bit manipulation (and union instead of macros)
- use hexfloat literals instead of named constants
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gcc did not always drop excess precision according to c99 at assignments
before version 4.5 even if -std=c99 was requested which caused badly
broken mathematical functions on i386 when FLT_EVAL_METHOD!=0
but STRICT_ASSIGN was not used consistently and it is worked around for
old compilers with -ffloat-store so it is no longer needed
the new convention is to get the compiler respect c99 semantics and when
excess precision is not harmful use float_t or double_t or to specialize
code using FLT_EVAL_METHOD
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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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