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2013-08-15math: fix asin, atan, log1p, tanh to raise underflow on subnormalSzabolcs Nagy-4/+2
for these functions f(x)=x for small inputs, because f(0)=0 and f'(0)=1, but for subnormal values they should raise the underflow flag (required by annex F), if they are approximated by a polynomial around 0 then spurious underflow should be avoided (not required by annex F) all these functions should raise inexact flag for small x if x!=0, but it's not required by the standard and it does not seem a worthy goal, so support for it is removed in some cases. raising underflow: - x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0 - x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0 - in case of double subnormal x, store x as float - in case of float subnormal x, store x*x as float
2013-05-15math: use double_t for temporaries to avoid stores on i386Szabolcs Nagy-1/+1
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
2012-12-16math: use 0x1p-120f and 0x1p120f for tiny and huge valuesSzabolcs Nagy-2/+2
previously 0x1p-1000 and 0x1p1000 was used for raising inexact exception like x+tiny (when x is big) or x+huge (when x is small) the rational is that these float consts are large enough (0x1p-120 + 1 raises inexact even on ld128 which has 113 mant bits) and float consts maybe smaller or easier to load on some platforms (on i386 this reduced the object file size by 4bytes in some cases)
2012-12-11math: clean up inverse trigonometric functionsSzabolcs Nagy-35/+36
modifications: * avoid unsigned->signed conversions * removed various volatile hacks * use FORCE_EVAL when evaluating only for side-effects * factor out R() rational approximation instead of manual inline * __invtrigl.h now only provides __invtrigl_R, __pio2_hi and __pio2_lo * use 2*pio2_hi, 2*pio2_lo instead of pi_hi, pi_lo otherwise the logic is not changed, long double versions will need a revisit when a genaral long double cleanup happens
2012-03-19code cleanup of named constantsnsz-5/+4
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).
2012-03-13first commit of the new libm!Rich Felker-0/+109
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.