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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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* math: use float constants in exp10f.cSzabolcs Nagy2012-11-181-1/+1
| | | | use the 'f' suffix when a float constant is not representable
* math: expl.c cleanupSzabolcs Nagy2012-11-181-24/+19
| | | | raise overflow and underflow when necessary, fix various comments.
* math: expf.c cleanupSzabolcs Nagy2012-11-182-63/+55
| | | | | | similar to exp.c cleanup: use scalbnf, don't return excess precision, drop some optimizatoins. exp.c was changed to be more consistent with expf.c code.
* math: cleanup exp2.c exp2f.c and exp2l.cSzabolcs Nagy2012-11-173-86/+56
| | | | | | * old code relied on sign extension on right shift * exp2l ld64 wrapper was wrong * use scalbn instead of bithacks
* math: exp.c clean upSzabolcs Nagy2012-11-171-72/+49
| | | | | | | overflow and underflow was incorrect when the result was not stored. an optimization for the 0.5*ln2 < |x| < 1.5*ln2 domain was removed. did various cleanups around static constants and made the comments consistent with the code.
* math: ld80 invtrig cleanupsSzabolcs Nagy2012-11-148-110/+87
| | | | keeping only commonly used data in invtrigl
* math: simplify hypot and hypotf using scalbnSzabolcs Nagy2012-11-132-11/+4
| | | | | this also fixes overflow/underflow raising and excess precision issues (as those are handled well in scalbn)
* math: use '#pragma STDC FENV_ACCESS ON' when fenv is accessedSzabolcs Nagy2012-11-139-0/+10
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* math: excess precision fix modf, modff, scalbn, scalbnfSzabolcs Nagy2012-11-134-22/+18
| | | | | | | old code was correct only if the result was stored (without the excess precision) or musl was compiled with -ffloat-store. now we use STRICT_ASSIGN to work around the issue. (see note 160 in c11 section 6.8.6.4)
* math: fix scalbn and scalbnf on overflow/underflowSzabolcs Nagy2012-11-132-10/+24
| | | | | | old code was correct only if the result was stored (without the excess precision) or musl was compiled with -ffloat-store. (see note 160 in n1570.pdf section 6.8.6.4)
* math: fix nextafter and nexttoward on maxdbl and maxflt inputSzabolcs Nagy2012-11-134-4/+4
| | | | | old code (return x+x;) returns correct value and raises correct flags only if the result is stored as double (or float)
* math: raise flags in logl.c on <= 0 argumentsSzabolcs Nagy2012-11-132-9/+3
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* math: fix logb*.c exceptions now that ilogb raises invalidSzabolcs Nagy2012-11-133-25/+17
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* math: raise flags in log2l.c on <= 0 arguments, and fix volatileSzabolcs Nagy2012-11-131-8/+3
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* math: raise exception flags in log1pl.c on <= -1 argumentsSzabolcs Nagy2012-11-131-7/+2
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* math: raise invalid flag in ilogb*.c on +-0, +-inf and nanSzabolcs Nagy2012-11-123-6/+18
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* math: fix exception behaviour of expm1l.c on inf and nanSzabolcs Nagy2012-11-121-13/+7
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* math: fix long double constants in exp10l.cSzabolcs Nagy2012-11-121-2/+2
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* Merge remote-tracking branch 'nsz/exp'Rich Felker2012-08-132-40/+35
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| * math: fix exp.s on i386 and x86_64 so the exception flags are correctnsz2012-08-082-40/+35
| | | | | | | | exp(inf), exp(-inf), exp(nan) used to raise wrong flags
* | remove significandlRich Felker2012-08-131-7/+0
| | | | | | | | | | | | | | this function never existed historically; since the float/double functions it's based on are nonstandard and deprecated, there's really no justification for its existence except that glibc has it. it can be added back if there's ever really a need...
* | add significand[fl] math functionsRich Felker2012-08-133-0/+21
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* fix missing prototype and simplify sincosl on ld64 archsRich Felker2012-07-021-4/+2
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* fix invalid implicit pointer conversion in ld64 modflRich Felker2012-07-021-1/+1
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* math: fix fma bug on x86 (found by Bruno Haible with gnulib)nsz2012-06-201-2/+10
| | | | | | | | | | | | | | | | | | | | | | | | | | The long double adjustment was wrong: The usual check is mant_bits & 0x7ff == 0x400 before doing a mant_bits++ or mant_bits-- adjustment since this is the only case when rounding an inexact ld80 into double can go wrong. (only in nearest rounding mode) After such a check the ++ and -- is ok (the mantissa will end in 0x401 or 0x3ff). fma is a bit different (we need to add 3 numbers with correct rounding: hi_xy + lo_xy + z so we should survive two roundings at different places without precision loss) The adjustment in fma only checks for zero low bits mant_bits & 0x3ff == 0 this way the adjusted value is correct when rounded to double or *less* precision. (this is an important piece in the fma puzzle) Unfortunately in this case the -- is not a correct adjustment because mant_bits might underflow so further checks are needed and this was the source of the bug.
* support ld80 pseudo-denormal invalid bit patterns; treat them as nanRich Felker2012-06-201-2/+5
| | | | | this is silly, but it makes apps that read binary junk and interpret it as ld80 "safer", and it gets gnulib to stop replacing printf...
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