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* math: remove *_WORD64 macros from libm.hSzabolcs Nagy2013-09-051-13/+13
| | | | only fma used these macros and the explicit union is clearer
* math: long double fix (use ldshape union)Szabolcs Nagy2013-09-058-51/+24
| | | | | | * use new ldshape union consistently * add ld128 support to frexpl * simplify sqrtl comment (ld64 is not just arm)
* math: use float_t and double_t in scalbnf and scalbnSzabolcs Nagy2013-09-052-16/+20
| | | | | remove STRICT_ASSIGN (c99 semantics is assumed) and use the conventional union to prepare the scaling factor (so libm.h is no longer needed)
* math: fix remaining old long double code (erfl, fmal, lgammal, scalbnl)Szabolcs Nagy2013-09-055-93/+65
| | | | | in lgammal don't handle 1 and 2 specially, in fma use the new ldshape union instead of ld80 one.
* math: cbrt cleanup and long double fixSzabolcs Nagy2013-09-053-72/+59
| | | | | | | * use float_t and double_t * cleanup subnormal handling * bithacks according to the new convention (ldshape for long double and explicit unions for float and double)
* math: fix underflow in exp*.c and long double handling in exp2lSzabolcs Nagy2013-09-058-182/+139
| | | | | | | | | | | | * don't care about inexact flag * use double_t and float_t (faster, smaller, more precise on x86) * exp: underflow when result is zero or subnormal and not -inf * exp2: underflow when result is zero or subnormal and not exact * expm1: underflow when result is zero or subnormal * expl: don't underflow on -inf * exp2: fix incorrect comment * expm1: simplify special case handling and overflow properly * expm1: cleanup final scaling and fix negative left shift ub (twopk)
* math: long double trigonometric cleanup (cosl, sinl, sincosl, tanl)Szabolcs Nagy2013-09-058-236/+228
| | | | | | | | | | | | | | ld128 support was added to internal kernel functions (__cosl, __sinl, __tanl, __rem_pio2l) from freebsd (not tested, but should be a good start for when ld128 arch arrives) __rem_pio2l had some code cleanup, the freebsd ld128 code seems to gather the results of a large reduction with precision loss (fixed the bug but a todo comment was added for later investigation) the old copyright was removed from the non-kernel wrapper functions (cosl, sinl, sincosl, tanl) since these are trivial and the interesting parts and comments had been already rewritten.
* math: long double inverse trigonometric cleanup (acosl, asinl, atanl, atan2l)Szabolcs Nagy2013-09-056-103/+180
| | | | | | * added ld128 support from freebsd fdlibm (untested) * using new ldshape union instead of IEEEl2bits * inexact status flag is not supported
* math: rewrite hypotSzabolcs Nagy2013-09-053-324/+135
| | | | | | | | | | | | | | | | | | method: if there is a large difference between the scale of x and y then the larger magnitude dominates, otherwise reduce x,y so the argument of sqrt (x*x+y*y) does not overflow or underflow and calculate the argument precisely using exact multiplication. If the argument has less error than 1/sqrt(2) ~ 0.7 ulp, then the result has less error than 1 ulp in nearest rounding mode. the original fdlibm method was the same, except it used bit hacks instead of dekker-veltkamp algorithm, which is problematic for long double where different representations are supported. (the new hypot and hypotl code should be smaller and faster on 32bit cpu archs with fast fpu), the new code behaves differently in non-nearest rounding, but the error should be still less than 2ulps. ld80 and ld128 are supported
* math: rewrite remainder functions (remainder, remquo, fmod, modf)Szabolcs Nagy2013-09-0511-1010/+472
| | | | | | | | | * results are exact * modfl follows truncl (raises inexact flag spuriously now) * modf and modff only had cosmetic cleanup * remainder is just a wrapper around remquo now * using iterative shift+subtract for remquo and fmod * ld80 and ld128 are supported as well
* math: rewrite rounding functions (ceil, floor, trunc, round, rint)Szabolcs Nagy2013-09-0515-905/+274
| | | | | | | | | | * faster, smaller, cleaner implementation than the bit hacks of fdlibm * use arithmetics like y=(double)(x+0x1p52)-0x1p52, which is an integer neighbor of x in all rounding modes (0<=x<0x1p52) and only use bithacks when that's faster and smaller (for float it usually is) * the code assumes standard excess precision handling for casts * long double code supports both ld80 and ld128 * nearbyint is not changed (it is a wrapper around rint)
* math: fix logb(-0.0) in downward rounding modeSzabolcs Nagy2013-09-053-6/+6
| | | | | use -1/(x*x) instead of -1/(x+0) to return -inf, -0+0 is -0 in downward rounding mode
* math: ilogb cleanupSzabolcs Nagy2013-09-053-16/+43
| | | | | | | * consistent code style * explicit union instead of typedef for double and float bit access * turn FENV_ACCESS ON to make 0/0.0f raise invalid flag * (untested) ld128 version of ilogbl (used by logbl which has ld128 support)
* long double cleanup, initial commitSzabolcs Nagy2013-09-056-70/+61
| | | | | | | | new ldshape union, ld128 support is kept, code that used the old ldshape union was rewritten (IEEEl2bits union of freebsd libm is not touched yet) ld80 __fpclassifyl no longer tries to handle invalid representation
* some initial math asm for armhf (fabs[f] and sqrt[f])Rich Felker2013-08-1612-0/+32
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* fix build of x86_64 expl assemblyRich Felker2013-08-161-1/+1
| | | | | apparently this label change was not carried over when adapting the changes from the i386 version.
* math: fix pow(x,-1) to raise underflow properlySzabolcs Nagy2013-08-151-2/+14
| | | | | | if FLT_EVAL_METHOD!=0 check if (double)(1/x) is subnormal and not a power of 2 (if 1/x is power of 2 then either it is exact or the long double to double rounding already raised inexact and underflow)
* math: fix i386 atan2.s to raise underflow for subnormal resultsSzabolcs Nagy2013-08-152-2/+24
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* math: clean up atan2.cSzabolcs Nagy2013-08-154-103/+73
| | | | | | | | | * remove volatile hacks * don't care about inexact flag for now (removed all the +-tiny) * fix atanl to raise underflow properly * remove signed int arithmetics * use pi/2 instead of pi_o_2 (gcc generates the same code, which is not correct, but it does not matter: we mainly care about nearest rounding)
* math: fix x86 asin, atan, exp, log1p to raise underflowSzabolcs Nagy2013-08-156-3/+98
| | | | | | underflow is raised by an inexact subnormal float store, since subnormal operations are slow, check the underflow flag and skip the store if it's already raised
* math: fix x86 expl.s to raise underflow and clean up special case handlingSzabolcs Nagy2013-08-152-45/+31
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* math: fix asin, atan, log1p, tanh to raise underflow on subnormalSzabolcs Nagy2013-08-159-26/+39
| | | | | | | | | | | | | | | | | | 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
* math: fix tgamma to raise underflow for large negative valuesSzabolcs Nagy2013-08-151-0/+1
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* math: fix pow(0,-inf) to raise divbyzero flagSzabolcs Nagy2013-08-152-2/+2
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* math: minor scalbn*.c simplificationSzabolcs Nagy2013-08-153-18/+10
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* add missing erfcl wrapper for archs where long double is plain doubleRich Felker2013-07-281-0/+4
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* math: add fma TODO comments about the underflow issueSzabolcs Nagy2013-05-193-2/+14
| | | | | | | | | The underflow exception is not raised correctly in some cornercases (see previous fma commit), added comments with examples for fmaf, fmal and non-x86 fma. In fmaf store the result before returning so it has the correct precision when FLT_EVAL_METHOD!=0
* math: fix two fma issues (only affects non-nearest rounding mode, x86)Szabolcs Nagy2013-05-191-4/+38
| | | | | | | | | | | | | | | | | | | | | | 1) in downward rounding fma(1,1,-1) should be -0 but it was 0 with gcc, the code was correct but gcc does not support FENV_ACCESS ON so it used common subexpression elimination where it shouldn't have. now volatile memory access is used as a barrier after fesetround. 2) in directed rounding modes there is no double rounding issue so the complicated adjustments done for nearest rounding mode are not needed. the only exception to this rule is raising the underflow flag: assume "small" is an exactly representible subnormal value in double precision and "verysmall" is a much smaller value so that (long double)(small plus verysmall) == small then (double)(small plus verysmall) raises underflow because the result is an inexact subnormal, but (double)(long double)(small plus verysmall) does not because small is not a subnormal in long double precision and it is exact in double precision. now this problem is fixed by checking inexact using fenv when the result is subnormal
* math: sin cos cleanupSzabolcs Nagy2013-05-1810-112/+128
| | | | | | | | * use unsigned arithmetics * use unsigned to store arg reduction quotient (so n&3 is understood) * remove z=0.0 variables, use literal 0 * raise underflow and inexact exceptions properly when x is small * fix spurious underflow in tanl
* math: tan cleanupsSzabolcs Nagy2013-05-186-106/+80
| | | | | | | | | | | | | | | | * use unsigned arithmetics on the representation * store arg reduction quotient in unsigned (so n%2 would work like n&1) * use different convention to pass the arg reduction bit to __tan (this argument used to be 1 for even and -1 for odd reduction which meant obscure bithacks, the new n&1 is cleaner) * raise inexact and underflow flags correctly for small x (tanl(x) may still raise spurious underflow for small but normal x) (this exception raising code increases codesize a bit, similar fixes are needed in many other places, it may worth investigating at some point if the inexact and underflow flags are worth raising correctly as this is not strictly required by the standard) * tanf manual reduction optimization is kept for now * tanl code path is cleaned up to follow similar logic to tan and tanf
* math: use double_t for temporaries to avoid stores on i386Szabolcs Nagy2013-05-1521-28/+31
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 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
* math: erf and erfc cleanupSzabolcs Nagy2013-01-073-297/+207
| | | | | | | | | | | | common part of erf and erfc was put in a separate function which saved some space and the new code is using unsigned arithmetics erfcf had a bug: for some inputs in [7.95,8] the result had more than 60ulp error: in expf(-z*z - 0.5625f) the argument must be exact but not enough lowbits of z were zeroed, -SET_FLOAT_WORD(z, ix&0xfffff000); +SET_FLOAT_WORD(z, ix&0xffffe000); fixed the issue
* math: bessel cleanup (jn.c and jnf.c)Szabolcs Nagy2013-01-012-164/+161
| | | | | | | | | | | | | | | | | | | | | | | | both jn and yn functions had integer overflow issues for large and small n to handle these issues nm1 (== |n|-1) is used instead of n and -n in the code and some loops are changed to make sure the iteration counter does not overflow (another solution could be to use larger integer type or even double but that has more size and runtime cost, on x87 loading int64_t or even uint32_t into an fpu register is more than two times slower than loading int32_t, and using double for n slows down iteration logic) yn(-1,0) now returns inf posix2008 specifies that on overflow and at +-0 all y0,y1,yn functions return -inf, this is not consistent with math when n<0 odd integer in yn (eg. when x->0, yn(-1,x)->inf, but historically yn(-1,0) seems to be special cased and returned -inf) some threshold values in jnf and ynf were fixed that seems to be incorrectly copy-pasted from the double version
* math: bessel cleanup (j1.c and j1f.c)Szabolcs Nagy2013-01-012-187/+138
| | | | | | | | | | | | | | | a common code path in j1 and y1 was factored out so the resulting object code is a bit smaller unsigned int arithmetics is used for bit manipulation j1(-inf) now returns 0 instead of -0 an incorrect threshold in the common code of j1f and y1f got fixed (this caused spurious overflow and underflow exceptions) the else branch in pone and pzero functions are fixed (so code analyzers dont warn about uninitialized values)
* math: bessel cleanup (j0.c and j0f.c)Szabolcs Nagy2013-01-012-203/+161
| | | | | | | | | | | | | a common code path in j0 and y0 was factored out so the resulting object code is smaller unsigned int arithmetics is used for bit manipulation the logic of j0 got a bit simplified (x < 1 case was handled separately with a bit higher precision than now, but there are large errors in other domains anyway so that branch has been removed) some threshold values were adjusted in j0f and y0f
* math: use 0x1p-120f and 0x1p120f for tiny and huge valuesSzabolcs Nagy2012-12-1610-27/+27
| | | | | | | | | | 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)
* math: tgammal.c fixesSzabolcs Nagy2012-12-161-28/+23
| | | | | | | | | this is not a full rewrite just fixes to the special case logic: +-0 and non-integer x<INT_MIN inputs incorrectly raised invalid exception and for +-0 the return value was wrong so integer test and odd/even test for negative inputs are changed and a useless overflow test was removed
* math: tanh.c cleanup similar to sinh, coshSzabolcs Nagy2012-12-163-173/+83
| | | | | | | | | | | | | | | | | | | | comments are kept in the double version of the function compared to fdlibm/freebsd we partition the domain into one more part and select different threshold points: now the [log(5/3)/2,log(3)/2] and [log(3)/2,inf] domains should have <1.5ulp error (so only the last bit may be wrong, assuming good exp, expm1) (note that log(3)/2 and log(5/3)/2 are the points where tanh changes resolution: tanh(log(3)/2)=0.5, tanh(log(5/3)/2)=0.25) for some x < log(5/3)/2 (~=0.2554) the error can be >1.5ulp but it should be <2ulp (the freebsd code had some >2ulp errors in [0.255,1]) even with the extra logic the new code produces smaller object files
* math: sinh.c cleanup similar to the cosh oneSzabolcs Nagy2012-12-163-171/+72
| | | | comments are kept in the double version of the function
* math: finished cosh.c cleanupSzabolcs Nagy2012-12-163-142/+49
| | | | | | | | | | | | | | | | | changed the algorithm: large input is not special cased (when exp(-x) is small compared to exp(x)) and the threshold values are reevaluated (fdlibm code had a log(2)/2 cutoff for which i could not find justification, log(2) seems to be a better threshold and this was verified empirically) the new code is simpler, makes smaller binaries and should be faster for common cases the old comments were removed as they are no longer true for the new algorithm and the fdlibm copyright was dropped as well because there is no common code or idea with the original anymore except for trivial ones.
* math: x86_64 version of expl, fixed some comments in the i386 versionSzabolcs Nagy2012-12-164-4/+112
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* math: move x86_64 exp2l implementation to exp2l.s from expl.sSzabolcs Nagy2012-12-163-85/+76
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* math: fix i386/expl.s with more precise x*log2eSzabolcs Nagy2012-12-142-7/+107
| | | | | | | | | with naive exp2l(x*log2e) the last 12bits of the result was incorrect for x with large absolute value with hi + lo = x*log2e is caluclated to 128 bits precision and then expl(x) = exp2l(hi) + exp2l(hi) * f2xm1(lo) this gives <1.5ulp measured error everywhere in nearest rounding mode
* math: add a non-dummy tgamma implementationSzabolcs Nagy2012-12-122-20/+215
| | | | | | | | | | | | uses the lanczos approximation method with the usual tweaks. same parameters were selected as in boost and python. (avoides some extra work and special casing found in boost so the precision is not that good: measured error is <5ulp for positive x and <10ulp for negative) an alternative lgamma_r implementation is also given in the same file which is simpler and smaller than the current one, but less precise so it's ifdefed out for now.
* math: cosh cleanupSzabolcs Nagy2012-12-123-70/+63
| | | | do fabs by hand, don't check for nan and inf separately
* math: fix comment in __rem_pio2f.cSzabolcs Nagy2012-12-121-2/+2
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* math: add empty __invtrigl.s to i386 and x86_64Szabolcs Nagy2012-12-122-0/+0
| | | | | __invtrigl is not needed when acosl, asinl, atanl have asm implementations
* math: clean up inverse trigonometric functionsSzabolcs Nagy2012-12-1112-377/+258
| | | | | | | | | | | | | 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
* math: rewrite inverse hyperbolic functions to be simpler/smallerSzabolcs Nagy2012-12-119-406/+149
| | | | | | | | | | | | modifications: * avoid unsigned->signed integer conversion * do not handle special cases when they work correctly anyway * more strict threshold values (0x1p26 instead of 0x1p28 etc) * smaller code, cleaner branching logic * same precision as the old code: acosh(x) has up to 2ulp error in [1,1.125] asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125] atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125]
* fix trailing whitespace issues that crept in here and thereRich Felker2012-12-071-1/+1
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