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* math: change the formula used for acos.snsz2012-05-052-20/+16
| | | | | | | | | | old: 2*atan2(sqrt(1-x),sqrt(1+x)) new: atan2(fabs(sqrt((1-x)*(1+x))),x) improvements: * all edge cases are fixed (sign of zero in downward rounding) * a bit faster (here a single call is about 131ns vs 162ns) * a bit more precise (at most 1ulp error on 1M uniform random samples in [0,1), the old formula gave some 2ulp errors as well)
* support alternate glibc name pow10 for exp10Rich Felker2012-05-013-0/+9
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* add C stub for sqrtl (already implemented in asm on i386 and x86_64)Rich Felker2012-04-301-0/+9
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* first try at writing an efficient and "correct" exp10Rich Felker2012-04-303-0/+55
| | | | | | | | | this is a nonstandard function so it's not clear what conditions it should satisfy. my intent is that it be fast and exact for positive integral exponents when the result fits in the destination type, and fast and correctly rounded for small negative integral exponents. otherwise we aim for at most 1ulp error; it seems to differ from pow by at most 1ulp and it's often 2-5 times faster than pow.
* fix typo in the x86_64 rounding asmRich Felker2012-04-294-4/+4
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* new math asm (abs/rounding) for x86_64Rich Felker2012-04-296-0/+36
| | | | untested
* math: fix x86 asin accuracynsz2012-04-042-5/+6
| | | | | use (1-x)*(1+x) instead of (1-x*x) in asin.s the later can be inaccurate with upward rounding when x is close to 1
* math: minor cleanups in ceil and floornsz2012-03-295-10/+7
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* math: remove x86 modf asmnsz2012-03-294-111/+0
| | | | | the int part was wrong when -1 < x <= -0 (+0.0 instead of -0.0) and the size and performace gain of the asm version was negligible
* math: rewrite modf.c and clean up modff.cnsz2012-03-292-72/+45
| | | | cleaner implementation with unions and unsigned arithmetic
* math: fix modfl.c bugnsz2012-03-281-1/+1
| | | | | modfl(+-inf) was wrong on ld80 because the explicit msb was not taken into account during inf vs nan check
* math: fix a regression in powl and do some cleanupsnsz2012-03-271-12/+11
| | | | | previously a division was accidentally turned into integer div (w = -i/NXT;) instead of long double div (w = -i; w /= NXT;)
* math: add dummy tgamma and tgammaf implementationsnsz2012-03-272-0/+32
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* math: remove comment about aliasing lgamma as gammansz2012-03-273-8/+4
| | | | | It is probably not worth supporting gamma. (it was already deprecated in 4.3BSD)
* math: fix typo in i386 remquof and remquol asmnsz2012-03-271-5/+5
| | | | (fldl instruction was used instead of flds and fldt)
* Merge branch 'master' of git://git.etalabs.net/muslnsz2012-03-232-0/+87
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| * asm for hypot and hypotfRich Felker2012-03-232-0/+87
| | | | | | | | | | | | | | | | | | special care is made to avoid any inexact computations when either arg is zero (in which case the exact absolute value of the other arg should be returned) and to support the special condition that hypot(±inf,nan) yields inf. hypotl is not yet implemented since avoiding overflow is nontrivial.
* | minor rintl.c fix: remove unsupported ldbl format messagensz2012-03-231-2/+0
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* | fix tgammal: don't set the signgam globalnsz2012-03-231-13/+6
|/ | | | (tgamma must be thread-safe, signgam is for lgamma* functions)
* acos.s fix: use the formula acos(x) = atan2(sqrt(1-x),sqrt(1+x))nsz2012-03-222-6/+2
| | | | | | | the old formula atan2(1,sqrt((1+x)/(1-x))) was faster but could give nan result at x=1 when the rounding mode is FE_DOWNWARD (so 1-1 == -0 and 2/-0 == -inf), the new formula gives -0 at x=+-1 with downward rounding.
* x86_64 math asm, long double functions onlyRich Felker2012-03-2017-0/+239
| | | | | | | this has not been tested heavily, but it's known to at least assemble and run in basic usage cases. it's nearly identical to the corresponding i386 code, and thus expected to be just as correct or just as incorrect.
* nearbyint optimization (only clear inexact when necessary)nsz2012-03-203-19/+29
| | | | | | | | | | | | | | | | old code saved/restored the fenv (the new code is only as slow as that when inexact is not set before the call, but some other flag is set and the rounding is inexact, which is rare) before: bench_nearbyint_exact 5000000 N 261 ns/op bench_nearbyint_inexact_set 5000000 N 262 ns/op bench_nearbyint_inexact_unset 5000000 N 261 ns/op after: bench_nearbyint_exact 10000000 N 94.99 ns/op bench_nearbyint_inexact_set 25000000 N 65.81 ns/op bench_nearbyint_inexact_unset 10000000 N 94.97 ns/op
* remove a fixme commentnsz2012-03-203-3/+2
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* clean up pow.c and powf.cnsz2012-03-202-57/+43
| | | | fix comments about special cases
* clean up powl.cnsz2012-03-201-92/+47
| | | | fix special cases, use multiplication instead of scalbnl
* fix a cbrtl.c regression and remove x87 precision settingnsz2012-03-201-27/+6
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* optimize scalbn familyRich Felker2012-03-203-7/+46
| | | | | | | | | | | | | | | | | | the fscale instruction is slow everywhere, probably because it involves a costly and unnecessary integer truncation operation that ends up being a no-op in common usages. instead, construct a floating point scale value with integer arithmetic and simply multiply by it, when possible. for float and double, this is always possible by going to the next-larger type. we use some cheap but effective saturating arithmetic tricks to make sure even very large-magnitude exponents fit. for long double, if the scaling exponent is too large to fit in the exponent of a long double value, we simply fallback to the expensive fscale method. on atom cpu, these changes speed up scalbn by over 30%. (min rdtsc timing dropped from 110 cycles to 70 cycles.)
* remquo asm: return quotient mod 8, as intended by the specRich Felker2012-03-191-17/+26
| | | | | this is a lot more efficient and also what is generally wanted. perhaps the bit shuffling could be more efficient...
* use alternate formula for acos asm to avoid loss of precisionRich Felker2012-03-191-3/+11
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* Merge remote branch 'nsz/master'Rich Felker2012-03-1994-806/+654
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| * code cleanup of named constantsnsz2012-03-1973-623/+513
| | | | | | | | | | | | | | 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).
| * fix remainder*.c: remove useless long double castnsz2012-03-192-15/+6
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| * don't try to create non-standard denormalization signalnsz2012-03-193-7/+4
| | | | | | | | | | | | | | | | Underflow exception is only raised when the result is invalid, but fmod is always exact. x87 has a denormalization exception, but that's nonstandard. And the superflous *1.0 will be optimized away by any compiler that does not honor signaling nans.
| * new modff.c code, fix nan handling in modflnsz2012-03-192-44/+26
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| * use scalbn or *2.0 instead of ldexp, fix fmalnsz2012-03-198-101/+102
| | | | | | | | | | | | | | | | | | | | | | | | | | Some code assumed ldexp(x, 1) is faster than 2.0*x, but ldexp is a wrapper around scalbn which uses multiplications inside, so this optimization is wrong. This commit also fixes fmal which accidentally used ldexp instead of ldexpl loosing precision. There are various additional changes from the work-in-progress const cleanups.
| * fix long double const workaround in cbrtlnsz2012-03-191-5/+1
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| * don't inline __rem_pio2l so the code size is smallernsz2012-03-195-9/+1
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| * minor fix in __tanl (get sign properly)nsz2012-03-191-2/+1
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* | fix exp asmRich Felker2012-03-191-23/+22
| | | | | | | | | | | | | | | | | | | | | | | | exponents (base 2) near 16383 were broken due to (1) wrong cutoff, and (2) inability to fit the necessary range of scalings into a long double value. as a solution, we fall back to using frndint/fscale for insanely large exponents, and also have to special-case infinities here to avoid inf-inf generating nan. thankfully the costly code never runs in normal usage cases.
* | Merge remote branch 'nsz/master'Rich Felker2012-03-197-80/+3
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| * remove long double const workaroundsnsz2012-03-196-79/+2
| | | | | | | | | | | | | | | | Some long double consts were stored in two doubles as a workaround for x86_64 and i386 with the following comment: /* Long double constants are slow on these arches, and broken on i386. */ This is most likely old gcc bug related to the default x87 fpu precision setting (it's double instead of double extended on BSD).
| * fix erfl wrapper for long double==double casensz2012-03-191-1/+1
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* | bug fix: wrong opcode for writing long longRich Felker2012-03-192-2/+2
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* asm for log1pRich Felker2012-03-193-0/+45
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* asm for log2Rich Felker2012-03-193-0/+21
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* asm for remquoRich Felker2012-03-193-0/+43
| | | | | this could perhaps use some additional testing for corner cases, but it seems to be correct.
* optimize exponential asm for i386Rich Felker2012-03-192-58/+77
| | | | | | up to 30% faster exp2 by avoiding slow frndint and fscale functions. expm1 also takes a much more direct path for small arguments (the expected usage case).
* Merge remote branch 'nsz/master'Rich Felker2012-03-195-163/+208
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| * simplify scalbn*.c implementationsnsz2012-03-193-152/+65
| | | | | | | | | | The old scalbn.c was wrong and slow, the new one is just slow. (scalbn(0x1p+1023,-2097) should give 0x1p-1074, but the old code gave 0)
| * Merge branch 'master' of git://git.etalabs.net/muslnsz2012-03-199-0/+75
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