table and the requirement on trailing zero bits.
* Remove the __aligned() compiler directives as these were found
to have a negative effect on the produced code.
Submitted by: bde
Approved by: das (mentor)
. Change the API for the LD80C by removing the explicit passing
of the sign bit. The sign can be determined from the last
parameter of the macro.
. On i386, load long double by bit manipulations to work around
at least a gcc compiler issue. On non-i386 ld80 architectures,
use a simple assignment.
* ld80/s_expl.c:
. Update the only consumer of LD80C.
Submitted by: bde
Approved by: das (mentor)
. Fix the threshold for expl(x) where |x| is small.
. Also update the previously incorrect comment to match the
new threshold.
* ld128/s_expl.c:
. Re-order logic in exceptional cases to match the logic used in
other long double functions.
. Fix the threshold for expl(x) where is |x| is small.
. Also update the previously incorrect comment to match the
new threshold.
Submitted by: bde
Approved by: das (mentor)
. Guard a comment from reformatting by indent(1).
. Re-order variables in declarations to alphabetical order.
. Remove a banal comment.
* ld128/s_expl.c:
. Add a comment to point to ld80/s_expl.c for implementation details.
. Move the #define of INTERVAL to reduce the diff with ld80/s_expl.c.
. twom10000 does not need to be volatile, so move its declaration.
. Re-order variables in declarations to alphabetical order.
. Add a comment that describes the argument reduction.
. Remove the same banal comment found in ld80/s_expl.c.
Reviewed by: bde
Approved by: das (mentor)
Also, update the comment to describe the choice of using
a high and low decomposition of 2^(i/INTERNVAL) for
0 <= i <= INTERVAL in preparation for an implementation of
expm1l.
* Move the #define of INTERVAL above the comment, because the
comment refers to INTERVAL.
Reviewed by: bde
Approved by: das (mentor)
only affects i386. The double case was intentionally left broken
as an optimization, but we are getting closer to supporting
applications and/or kernels that change the (FreeBSD i386) default
rounding precision from FP_PD to FP_PE and never change it back,
and this requires the STRICT_ALIGN()s that were added to support
FP_PE to actually work in all precisions.
* Remove an extraneous semicolon at the end of a macro that was
supposed to be function-like.
Submitted by: bde
Approved by: das (mentor)
they need to refer to static constants, which C99 does not allow for
extern inline functions.
While here, change a comment in e_rem_pio2f.c to mention the correct
number of bits.
Reviewed by: bde
MFC after: 1 week
compatibility with the INTERVALS macro used in the soon-to-be-commmitted
expm1l() and someday-to-be-committed log*l() functions.
Add a comment into ld128/s_expl.c noting at gcc issue that was
deleted when rewriting ld80/e_expl.c as ld128/s_expl.c.
Requested by: bde
Approved by: das (mentor)
. Remove a few #ifdefs that should have been removed in the initial
commit.
. Sort fpmath.h to its rightful place.
* ld128/s_expl.c:
. Replace EXPMASK with its actual value.
. Sort fpmath.h to its rightful place.
Requested by: bde
Approved by: das (mentor)
format. These implementations are based on
PTP Tang, "Table-driven implementation of the exponential function
in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15,
144-157 (1989).
PR: standards/152415
Submitted by: kargl
Reviewed by: bde, das
Approved by: das (mentor)
quotation. Also make sure we have the same amount of columns in each row as
the number of columns we specify in the head arguments.
Reviewed by: brueffer
correct sign when the remainder was 0.
Fix a separate bug in remquo alone, in which the remainder and
quotient were both off by a bit in certain cases involving subnormal
remainders.
The bugs affected all platforms except amd64 and i386, on which the
routines are implemented in assembly.
PR: 166463
Submitted by: Ilya Burylov
MFC after: 2 weeks
the function bodies require only 2 to 10 instructions. However, it
leads to application binaries that refer to a private ABI, namely, the
softfloat innards in libc. This could complicate future changes in
the implementation of the floating-point emulation layer, so it seems
best to have programs refer to the official fe* entry points in libm.
use softfloat.
Thanks to Ian Lepore for testing and debugging this patch. The fenv
regression tests pass (at least for Ian's arm chip) with this change.
- Handle cases where exp(x) would overflow, but ccosh(x) ~= exp(x) / 2
shouldn't.
- Use the ccosh(x) ~= exp(x) / 2 approximation to simplify the calculation
when x is large.
Similarly for csinh(). Also fixed the return value of csinh(-Inf +- 0i).
exp(x) scaled down by some factor, and the challenge is doing this
accurately when exp(x) would overflow. This change replaces all of
the tricks we've been using with common __ldexp_exp() and
__ldexp_cexp() routines that handle all the scaling.
bde plans to improve on this further by moving the guts of exp() into
k_exp.c and handling the scaling in a more direct manner. But the
current approach is simple and adequate for now.
library," since complex.h, tgmath.h, and fenv.h are also part of the
math library. Replace the outdated sentence with some references to
the other parts.
- Rename __kernel_log() to k_log1p().
- Move some of the work that was previously done in the kernel log into
the callers. This enables further refactoring to improve accuracy or
speed, although I don't recall the details.
- Use extra precision when adding the final scaling term, which improves
accuracy.
- Describe and work around compiler problems that break some of the
multiprecision calculations.
A fix for a small bug is also included:
- Add a special case for log*(1). This is needed to ensure that log*(1) == +0
instead of -0, even when the rounding mode is FE_DOWNWARD.
Submitted by: bde
no longer "fast" on sparc64. (It really wasn't to begin with, since
the old implementation was using long doubles, and long doubles are
emulated in software on sparc64.)
round-to-nearest mode when the result, rounded to twice machine
precision, was exactly halfway between two machine-precision
values. The essence of the fix is to simulate a "sticky bit" in
the pathological cases, which is how hardware implementations
break the ties.
MFC after: 1 month
fenv.h that are currently inlined.
The definitions are provided in fenv.c via 'extern inline'
declaractions. This assumes the compiler handles 'extern inline' as
specified in C99, which has been true under FreeBSD since 8.0.
The goal is to eventually remove the 'static' keyword from the inline
definitions in fenv.h, so that non-inlined references all wind up
pointing to the same external definition like they're supposed to.
I am deferring the second step to provide a window where
newly-compiled apps will still link against old math libraries.
(This isn't supported, but there's no need to cause undue breakage.)
Reviewed by: stefanf, bde
on i386-class hardware for sinl and cosl. The hand-rolled argument
reduction have been replaced by e_rem_pio2l() implementations. To
preserve history the following commands have been executed:
svn cp src/e_rem_pio2.c ld80/e_rem_pio2l.h
mv ${HOME}/bde/ld80/e_rem_pio2l.c ld80/e_rem_pio2l.h
svn cp src/e_rem_pio2.c ld128/e_rem_pio2l.h
mv ${HOME}/bde/ld128/e_rem_pio2l.c ld128/e_rem_pio2l.h
The ld80 version has been tested by bde, das, and kargl over the
last few years (bde, das) and few months (kargl). An older ld128
version was tested by das. The committed version has only been
compiled tested via 'make universe'.
Approved by: das (mentor)
Obtained from: bde
with r219571 and re-enable building of cbrtl.
Implement the long double version for the cube root function, cbrtl.
The algorithm uses Newton's iterations with a crude estimate of the
cube root to converge to a result.
Reviewed by: bde
Approved by: das
implementing accurate logarithms in different bases. This is based
on an approach bde coded up years ago.
This function should always be inlined; it will be used in only a few
places, and rudimentary tests show a 40% performance improvement in
implementations of log2() and log10() on amd64.
The kernel takes a reduced argument x and returns the same polynomial
approximation as e_log.c, but omitting the low-order term. The low-order
term is much larger than the rest of the approximation, so the caller of
the kernel function can scale it to the appropriate base in extra precision
and obtain a much more accurate answer than by using log(x)/log(b).
Explanation by Steve:
jn[f](n,x) for certain ranges of x uses downward recursion to compute
the value of the function. The recursion sequence that is generated is
proportional to the actual desired value, so a normalization step is
taken. This normalization is j0[f](x) divided by the zeroth sequence
member. As Bruce notes, near the zeros of j0[f](x) the computed value
can have giga-ULP inaccuracy. I found for the 1st zero of j0f(x) only
the leading decimal digit is correct. The solution to the issue is
fairly straight forward. The zeros of j0(x) and j1(x) never coincide,
so as j0(x) approaches a zero, the normalization constant switches to
j1[f](x) divided by the 2nd sequence member. The expectation is that
j1[f](x) is a more accurately computed value.
PR: bin/144306
Submitted by: Steven G. Kargl <kargl@troutmask.apl.washington.edu>
Reviewed by: bde
MFC after: 7 days
and one under lib/msun/amd64. This avoids adding the identifiers to the
.text section, and moves them to the .comment section instead.
Suggested by: bde
Approved by: rpaulo (mentor)
macro expand to __isnanf() instead of isnanf() for float arguments.
This change is needed because isnanf() isn't declared in strict POSIX
or C99 mode.
Compatibility note: Apps using isnan(float) that are compiled after
this change won't link against an older libm.
Reported by: Florian Forster <octo@verplant.org>
