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2020-02-21math: fix __rem_pio2 in non-nearest rounding modesSzabolcs Nagy1-1/+12
Handle when after reduction |y| > pi/4+tiny. This happens in directed rounding modes because the fast round to int code does not give the nearest integer. In such cases the reduction may not be symmetric between x and -x so e.g. cos(x)==cos(-x) may not hold (but polynomial evaluation is not symmetric either with directed rounding so fixing that would require more changes with bigger performance impact). The fix only adds two predictable branches in nearest rounding mode, simple ubenchmark does not show relevant performance regression in nearest rounding mode. The code could be improved: e.g reducing the medium size threshold such that two step reduction is enough instead of three, and the single precision case can avoid the issue by doing the round to int differently, but this fix was kept minimal.
2015-11-21math: explicitly promote expressions to excess-precision typesRich Felker1-1/+1
a conforming compiler for an arch with excess precision floating point (FLT_EVAL_METHOD!=0; presently i386 is the only such arch supported) computes all intermediate results in the types float_t and double_t rather than the nominal type of the expression. some incorrect compilers, however, only keep excess precision in registers, and convert down to the nominal type when spilling intermediate results to memory, yielding unpredictable results that depend on the compiler's choices of what/when to spill. in particular, this happens on old gcc versions with -ffloat-store, which we need in order to work around bugs where the compiler wrongly keeps explicitly-dropped excess precision. by explicitly converting to double_t where expressions are expected be be evaluated in double_t precision, we can avoid depending on the compiler to get types correct when spilling; the nominal and intermediate precision now match. this commit should not change the code generated by correct compilers, or by old ones on non-i386 archs where double_t is defined as double. this fixes a serious bug in argument reduction observed on i386 with gcc 4.2: for values of x outside the unit circle, sin(x) was producing results outside the interval [-1,1]. changes made in commit 0ce946cf808274c2d6e5419b139e130c8ad4bd30 were likely responsible for breaking compatibility with this and other old gcc versions. patch by Szabolcs Nagy.
2014-10-31math: use the rounding idiom consistentlySzabolcs Nagy1-3/+10
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)
2013-11-24math: clean up __rem_pio2Szabolcs Nagy1-22/+12
- 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
2013-09-06math: remove STRICT_ASSIGN macroSzabolcs Nagy1-1/+1
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
2012-12-12math: fix comment in __rem_pio2f.cSzabolcs Nagy1-2/+2
2012-03-13first commit of the new libm!Rich Felker1-0/+78
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.