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The log, log2 and log10 functions share a lot of code and to a lesser
extent log1p too. A small part of the code was kept separately in
__log1p.h, but since it did not capture much of the common code and
it was inlined anyway, it did not solve the issue properly. Now the
log functions have significant code duplication, which may be resolved
later, until then they need to be modified together.
logl, log10l, log2l, log1pl:
* Fix the sign when the return value should be -inf.
* Remove the volatile hack from log10l (seems unnecessary)
log1p, log1pf:
* Change the handling of small inputs: only |x|<2^-53 is special
(then it is enough to return x with the usual subnormal handling)
this fixes the sign of log1p(0) in downward rounding.
* Do not handle the k==0 case specially (other than skipping the
elaborate argument reduction)
* Do not handle 1+x close to power-of-two specially (this code was
used rarely, did not give much speed up and the precision wasn't
better than the general)
* Fix the correction term formula (c=1-(u-x) was used incorrectly
when x<1 but (double)(x+1)==2, this was not a critical issue)
* Use the exact same method for calculating log(1+f) as in log
(except in log1p the c correction term is added to the result).
log, logf, log10, log10f, log2, log2f:
* Use double_t and float_t consistently.
* Now the first part of log10 and log2 is identical to log (until the
return statement, hopefully this makes maintainence easier).
* Most special case formulas were removed (close to power-of-two and
k==0 cases), they increase the code size without providing precision
or performance benefits (and obfuscate the code).
Only x==1 is handled specially so in downward rounding mode the
sign of zero is correct (the general formula happens to give -0).
* For x==0 instead of -1/0.0 or -two54/0.0, return -1/(x*x) to force
raising the exception at runtime.
* Arg reduction code is changed (slightly simplified)
* The thresholds for arg reduction to [sqrt(2)/2,sqrt(2)] are now
consistently the [0x3fe6a09e00000000,0x3ff6a09dffffffff] and the
[0x3f3504f3,0x3fb504f2] intervals for double and float reductions
respectively (the exact threshold values are not critical)
* Remove the obsolete comment for the FLT_EVAL_METHOD!=0 case in log2f
(The same code is used for all eval methods now, on i386 slightly
simpler code could be used, but we have asm there anyway)
all:
* Fix signed int arithmetics (using unsigned for bitmanipulation)
* Fix various comments
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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
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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
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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).
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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.
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