Commit Graph

925 Commits

Author SHA1 Message Date
Warner Losh
e369c79ca0 Remove intel compiler support from math.h
The intel compiler support has badly decayed over the years. Stop
pretending that we support it. Note, I've stopped short of requiring
gcc builtin support with this commit since other compilers may be used
to build non-base software and we need to support those so more
investigation is needed before simplifying further.
2020-10-24 23:21:22 +00:00
Gordon Bergling
3d265fce43 Fix a few mandoc issues
- skipping paragraph macro: Pp after Sh
- sections out of conventional order: Sh EXAMPLES
- whitespace at end of input line
- normalizing date format
2020-10-09 19:12:44 +00:00
Stefan Eßer
fcce470c2b Apply an opimization for the kernels used by cexp(x) and cexpf(x) submitted
by Steve Kargl:

- Use sincos[f] instead of a call to cos[f] and a call to sin[f].

- While here, alphabetize declaration.

Submitted by:   sgk at troutmask.apl.washington.edu (Steve Kargl)
2020-09-20 05:32:53 +00:00
Stefan Eßer
a67cc94327 Apply fix for ld80 and ld128 submitted by Steve Kargl:
- Micro-optimization: use sincosl(x) instead of a call to cosl(x) and
  a call to sinl(x).  Argument reduction is done once not twice.

- Use a long double constant instead of an invalid double constant.

- Spell scale2 correctly

He could not test ld128, so that patch is untested.

Submitted by:	sgk at troutmask.apl.washington.edu (Steve Kargl)
2020-09-20 05:28:31 +00:00
Xin LI
941791759c Don't explicitly specify c99 or gnu99 as the default is now gnu99.
MFC after:	2 weeks
2020-08-17 05:57:02 +00:00
Mitchell Horne
2d143336de Enable long double tests on RISC-V
Some of the NetBSD contributed tests are gated behind the
__HAVE_LONG_DOUBLE flag. This flag seems to be defined only for
platforms whose long double is larger than their double. I could not
find this explicitly documented anywhere, but it is implied by the
definitions in NetBSD's sys/arch/${arch}/include/math.h headers, and the
following assertion from the UBSAN code:

  #ifdef __HAVE_LONG_DOUBLE
      long double LD;
      ASSERT(sizeof(LD) > sizeof(uint64_t));
  #endif

RISC-V has 128-bit long doubles, so enable the tests on this platform,
and update the comments to better explain the purpose of this flag.

Reviewed by:	ngie
MFC after:	1 week
Differential Revision:	https://reviews.freebsd.org/D25419
2020-06-24 13:11:19 +00:00
Eric van Gyzen
fac6dee9eb Remove tests for obsolete compilers in the build system
Assume gcc is at least 6.4, the oldest xtoolchain in the ports tree.
Assume clang is at least 6, which was in 11.2-RELEASE.  Drop conditions
for older compilers.

Reviewed by:	imp (earlier version), emaste, jhb
MFC after:	2 weeks
Sponsored by:	Dell EMC Isilon
Differential Revision:	https://reviews.freebsd.org/D24802
2020-05-12 15:22:40 +00:00
Sergio Carlavilla Delgado
d2034aedc1 Fix typo 2020-04-04 07:43:47 +00:00
Warner Losh
5310132318 Note some functions that appeared in First Edition Unix
These functions first appeared in the First Edition of Unix (or earlier in the
pdp-7 version). Just claim 1st Edition for all this. The pdp-7 code is too
fragmented at this point to extend history that far back.
2020-04-01 22:50:41 +00:00
Alfredo Dal'Ava Junior
f1343c7f67 msun: swap words order instead of bits order on BIG ENDIAN
The "for" loop on big endian was inverting all the bits instead of
just the words

Issue reported by TestSuite (msun lib nan_test case)

Submitted by:	Renato Riolino <renato.riolino@eldorado.org.br>
Submitted by:	Fernando Valle <fernando.valle@eldorado.org.br>
Reviewed by:	pfg, alfredo
Approved by:	jhibbits (mentor)
Sponsored by:	Eldorado Research Institute (eldorado.org.br)
Differential Revision:	https://reviews.freebsd.org/D23926
2020-03-26 18:50:54 +00:00
Sergio Carlavilla Delgado
8e76d7909d Add HISTORY sections to log(3) man page
PR:		240265
Submitted by:	gbergling@gmail.com
Approved by:	bcr@(mentor), imp@
MFC after:	1 day
Differential Revision:	https://reviews.freebsd.org/D24148
2020-03-26 11:24:43 +00:00
Li-Wen Hsu
0fc06121ac Temporarily skip 2 failing tests after llvm10 import
PR:		244732
Sponsored by:	The FreeBSD Foundation
2020-03-11 12:43:54 +00:00
Warner Losh
a8197ad3aa Remove sparc64 specific parts of libm and fix comments
Once upon a time, sparc64 was the only ld128 architecture. However,
both aarch64 and riscv are now such architectures. Many of the
comments about how slow multiplication was on old sparc64 processors
are now no longer true. However, since no evaluation has been done for
aarch64 yet, it's unclear if they are still relevant or not. If not,
the code should be changed. If so, the comments should remove the
uncertainty.

Reviewed by: emaste@
Differential Revision: https://reviews.freebsd.org/D23658
2020-02-26 18:55:03 +00:00
Sergio Carlavilla Delgado
8209febbb3 Add some HISTORY sections to manpages
environ(7) was in AT&T Version 7
ac(8): Add a HISTORY section
sa(8): Add a HISTORY section
sqrt(3): Add the actual sqrt function to the HISTORY section

Obtained from: OpenBSD

Submitted by:	gbergling@gmail.com
Approved by:	bcr@(mentor)
MFC after:	1 week
Differential Revision:	https://reviews.freebsd.org/D23693
2020-02-19 12:49:49 +00:00
Brandon Bergren
469026a8a3 [PowerPC] Fix feholdexcept() on powerpc referencing the wrong struct member
In r355656, endianness handling of the floating point environment was fixed
in the PowerPC code to work as intended.

However, one bit got missed, causing feholdexcept() to mis-save the fenv.

Submitted by:	Renato Riolino <renato.riolino@eldorado.org.br>
Differential Revision:	https://reviews.freebsd.org/D23382
2020-02-02 19:16:52 +00:00
Pedro F. Giffuni
afced35c1d msun: drop clause 3 from the Berkeley license.
Per the University California Regents letter, drop the so-called
"advertisement" clause.

Discussed with:	bde, kargl (2017)
Differential Revision:	https://reviews.freebsd.org/D22928
2019-12-27 01:11:26 +00:00
Brandon Bergren
4f9ed3156c [PowerPC] Fix SPE floating point environment manipulation
Fix multiple problems in the powerpcspe floating point code.

* Endianness handling of the SPEFSCR in fenv.h was completely broken.
* Ensure SPEFSCR synchronization requirements are being met.

The __r.__d -> __r transformations were written by jhibbits.

Reviewed by:	jhibbits
Differential Revision:	https://reviews.freebsd.org/D22526
2019-12-12 17:12:18 +00:00
Simon J. Gerraty
2c9a9dfc18 Update Makefile.depend files
Update a bunch of Makefile.depend files as
a result of adding Makefile.depend.options files

Reviewed by:	 bdrewery
MFC after:	1 week
Sponsored by:   Juniper Networks
Differential Revision:  https://reviews.freebsd.org/D22494
2019-12-11 17:37:53 +00:00
Dimitry Andric
83fa0a287f The fdlibm hypot() implementations shouldn't potentially left-shift
negative numbers (invoking undefined behavior)

Summary:
Various paths through hypot(x, y) will multiply x and y by a power of
two, perform the calculation in a range where IEEE-754 provides greater
precision, then undo the multiplication to determine the true result.
Undoing that multiplication is implemented as t1*w, where t1=2**k.

2**k is often computed by taking the high word of 1.0, then adding k<<20
(for doubles or long doubles) or k<<23 (for floats) to it, then
overwriting that high word. But when k is negative this left-shifts a
negative value -- and that's undefined behavior in many editions of C
and C++.

This patch should fix all hypot implementations to compute 2**k without
triggering this particular bit of undefined behavior.

Test Plan: I've only very lightly tested out the hypot(double, double)
change, in SpiderMonkey's JavaScript engine, for consistency with prior
behavior.  The other functions' changes have more or less only been
eyeballed.  Careful examination appreciated!  Do note, however, that an
error in any of these changes would most likely produce a value that is
incorrect by a factor of two, so any mistake would most likely be
glaring if invoked.

Submitted by:	Jeff Walden <jwalden@mit.edu>
Obtained from:	https://github.com/freebsd/freebsd/pull/414
Reviewed by:	dim, lwhsu
MFC after:	1 week
Differential Revision: https://reviews.freebsd.org/D22354
2019-11-26 22:01:09 +00:00
Li-Wen Hsu
12c4ab4377 Get the fix in back by reverting the part accidentally included in r354491.
This brings back r354467.

MFC after:	1 week
Sponsored by:	The FreeBSD Foundation
2019-11-07 23:57:48 +00:00
Brooks Davis
a4330302f2 libcompat: build 32-bit rtld and ldd as part of "everything"
Alter bsd.compat.mk to set MACHINE and MACHINE_ARCH when included
directly so MD paths in Makefiles work. In the process centralize
setting them in LIBCOMPATWMAKEENV.

Alter .PATH and CFLAGS settings in work when the Makefile is included.

While here only support LIB32 on supported platforms rather than always
enabling it and requiring users of MK_LIB32 to filter based
TARGET/MACHINE_ARCH.

The net effect of this change is to make Makefile.libcompat only build
compatability libraries.

Changes relative to r354449:

Correct detection of the compiler type when bsd.compat.mk is used
outside Makefile.libcompat.  Previously it always matched the clang
case.

Set LDFLAGS including the linker emulation for mips where -m32 seems to
be insufficent.

Reviewed by:	imp, kib (origional version in r354449)
Obtained from:	CheriBSD (conceptually)
Sponsored by:	DARPA, AFRL
Differential Revision:	https://reviews.freebsd.org/D22251
2019-11-07 22:58:10 +00:00
Brooks Davis
271d2989ba Fix declaration of S1 by swapping misplaced ',' and ';'.
Reported by:	kargl
Obtained from:	OpenBSD (tb@openbsd.org)
MFC after:	1 week
2019-11-07 19:31:56 +00:00
Brooks Davis
1edbf0e9ba Revert change accidentally included in r354465.
Will recommit with a proper commit message shortly.
2019-11-07 19:28:03 +00:00
Brooks Davis
ccad77fe1e Revert r354449: libcompat: build 32-bit rtld and ldd as part of "everything"
Additional testing is required..
2019-11-07 19:22:51 +00:00
Dimitry Andric
f68ff1ac1c Add __isnan()/__isnanf() aliases for compatibility with glibc and CUDA
Even though clang comes with a number of internal CUDA wrapper headers,
compiling sample CUDA programs will result in errors similar to:

In file included from <built-in>:1:
In file included from /usr/lib/clang/9.0.0/include/__clang_cuda_runtime_wrapper.h:204:
/usr/home/arr/cuda/var/cuda-repo-10-0-local-10.0.130-410.48/usr/local/cuda-10.0//include/crt/math_functions.hpp:2910:7: error: no matching function for call to '__isnan'
  if (__isnan(a)) {
      ^~~~~~~
/usr/lib/clang/9.0.0/include/__clang_cuda_device_functions.h:460:16: note: candidate function not viable: call to __device__ function from __host__ function
__DEVICE__ int __isnan(double __a) { return __nv_isnand(__a); }
               ^

CUDA expects __isnan() and __isnanf() declarations to be available,
which are glibc specific extensions, equivalent to the regular isnan()
and isnanf().

To provide these, define __isnan() and __isnanf() as aliases of the
already existing static inline functions __inline_isnan() and
__inline_isnanf() from math.h.

Reported by:	arrowd
PR:		241550
MFC after:	1 week
2019-11-02 16:59:53 +00:00
Conrad Meyer
168f19a57b libm: Add missing END() directives for amd64 routines
No functional change.  Related to D22122.

Reviewed by:	emaste, kib (earlier version both)
2019-10-23 16:05:52 +00:00
Brooks Davis
e593620997 msun: Silence new harmless -Wimplicit-int-float-conversion warnings
Clang from trunk recently added a warning for when implicit int-to-float
conversions cause a loss of precision. The code in question is designed
to be able to handle that, so add explicit casts to silence this.

Submitted by:	James Clarke <jrtc27@jrtc27.com>
Reviewed by:	dim
Obtained from:	CheriBSD
MFC after:	1 week
Sponsored by:	DARPA, AFRL
Differential Revision:	https://reviews.freebsd.org/D21913
2019-10-08 21:39:51 +00:00
Dimitry Andric
5763a8cf06 Do not left-shift a negative number (inducing undefined behavior in
C/C++) in exp(3), expf(3), expm1(3) and expm1f(3) during intermediate
computations that compute the IEEE-754 bit pattern for |2**k| for
integer |k|.

The implementations of exp(3), expf(3), expm1(3) and expm1f(3) need to
compute IEEE-754 bit patterns for 2**k in certain places.  (k is an
integer and 2**k is exactly representable in IEEE-754.)

Currently they do things like 0x3FF0'0000+(k<<20), which is to say they
take the bit pattern representing 1 and then add directly to the
exponent field to get the desired power of two.  This is fine when k is
non-negative.

But when k<0 (and certain classes of input trigger this), this
left-shifts a negative number -- an operation with undefined behavior in
C and C++.

The desired semantics can be achieved by instead adding the
possibly-negative k to the IEEE-754 exponent bias to get the desired
exponent field, _then_ shifting that into its proper overall position.

(Note that in case of s_expm1.c and s_expm1f.c, there are SET_HIGH_WORD
and SET_FLOAT_WORD uses further down in each of these files that perform
shift operations involving k, but by these points k's range has been
restricted to 2 < k <= 56, and the shift operations under those
circumstances can't do anything that would be UB.)

Submitted by:	Jeff Walden, https://github.com/jswalden
Obtained from:	https://github.com/freebsd/freebsd/pull/411
Obtained from:	https://github.com/freebsd/freebsd/pull/412
MFC after:	3 days
2019-09-25 18:50:57 +00:00
Li-Wen Hsu
24612bfd1f Unskip test cases from netbsd-tests by defining __HAVE_FENV
This unskips:
  - lib.libc.stdlib.strtod_test.strtod_round
  - lib.msun.fe_round_test.t_nofe_round

In lib/msun/tests/Makefile only define on fe_round_test.c because
lib.msun.ilogb_test.ilogb will get wrong results and needs more examination.

MFC after:	1 week
Sponsored by:	The FreeBSD Foundation
2019-08-31 20:45:45 +00:00
Edward Tomasz Napierala
5a38af1fb8 Introduce <sys/qmath.h>, a fixed-point math library from Netflix.
This makes it possible to perform mathematical operations
on
fractional values without using floating point. It operates on Q
numbers, which are integer-sized, opaque structures initialized
to hold a chosen number of integer and fractional
bits.


For a general description of the Q number system, see the "Fixed Point
Representation & Fractional Math" whitepaper[1]; for the actual
API see the qmath(3) man page.

This is one of dependencies for the upcoming stats(3) framework[2]
that will be applied to the TCP stack in a later commit.

1. https://www.superkits.net/whitepapers/Fixed%20Point%20Representation%20&%20Fractional%20Math.pdf
2. https://reviews.freebsd.org/D20477

Reviewed by:	bcr (man pages, earlier version), sef (earlier version)
Discussed with:	cem, dteske, imp, lstewart
Sponsored By:	Klara Inc, Netflix
Obtained from:	Netflix
Differential Revision:	https://reviews.freebsd.org/D20116
2019-08-27 11:46:22 +00:00
Dimitry Andric
740890be23 Partially revert r271349, which disabled the msun cexp test #4 on i386.
Ensure the expected result is stored first in a volatile variable with
the desired type.  This makes all the tests succeed.

Slightly changed from the original pull request, but functionally the
same.

Obtained from:	https://github.com/freebsd/freebsd/pull/401
Submitted by:	Moritz Buhl <gh@moritzbuhl.de>
PR:		191676
MFC after:	3 days
2019-06-01 20:08:10 +00:00
Peter Jeremy
885bfcda11 Replace calls to sin(x) and cos(x) with a single call to sincos().
Replace calls to sinf(x) and cosf(x) with a single call to sincosf().

Submitted by:	Steve Kargl <sgk@troutmask.apl.washington.edu>
Reviewed by:	bde
Approved by:	grog
MFC after:	3 days
2019-02-10 08:46:07 +00:00
Dimitry Andric
bc8fc00705 Amend r343442, by only expecting the lib.msun.cbrt_test.cbrtl_powl and
trig_test.reduction test cases to fail, if the fixes from r343916 have
not yet been applied to the base compiler.

Reported by:    lwhsu
PR:		234040
Upstream PR:	https://bugs.llvm.org/show_bug.cgi?id=40206
MFC after:	1 week
2019-02-08 18:31:54 +00:00
Eric van Gyzen
50b06886a7 libm: squelch -Woverflow from gcc6
Sponsored by:	Dell EMC Isilon
2019-02-01 23:15:54 +00:00
Li-Wen Hsu
24df7b15fa Temporarily mark lib.msun.{cbrt_test.cbrtl_powl,trig_test.reduction}
expected failure after clang700-import merge

PR:		234040
Reviewed by:	ngie, markj
Approved by:	markj (mentor)
Sponsored by:	The FreeBSD Foundation
Differential Revision:	https://reviews.freebsd.org/D18938
2019-01-25 18:48:20 +00:00
Pedro F. Giffuni
76c528d350 msun: reduce diff between src/e_j0.c and src/e_j0f.c
PR:	229501
MFC after:	1 week
2019-01-14 15:48:35 +00:00
Pedro F. Giffuni
bdd8abc6d6 pow(3): Workaround possible signed shift Undefined Behavior.
j is int32_t and thus j<<31 is undefined if j==1.

Hinted by:	muusl-lib (git 688d3da0f1730daddbc954bbc2d27cc96ceee04c)
Discussed with:	freebsd-numerics (kargl)
2019-01-07 17:35:09 +00:00
Pedro F. Giffuni
50757b1452 msun: Fix some old typos.
Seen in a posting from July 27 by "CM Graff" in musl-libc.
2018-12-31 15:43:06 +00:00
Justin Hibbits
003fdafbea libm: Include float.h to get LDBL_MANT_DIG
The long double aliases of double functions are only exposed as aliases if
LDBL_MANT_DIG is 53 (same as DBL_MANT_DIG).  Without float.h included these
files were not exposing weak aliases as expected, leading to link failures
if programs use the *l functions.  This should fix editors/calligra on
targets with 64-bit long double, which uses erfl and erfcl.  Found on
powerpc64.

Reviewed by:	kargl@
2018-12-28 01:34:08 +00:00
Mateusz Piotrowski
6d080f8660 csqrt(3): Fix some typos in the manual page
Submitted by:	Steve Kargl <sgk@troutmask.apl.washington.edu>
Reviewed by:	eadler
Approved by:    krion (mentor, implicit), mat (mentor, implicit)
Differential Revision:	https://reviews.freebsd.org/D17831
2018-11-04 14:11:38 +00:00
Bruce Evans
2011986f09 In C remquol() and thus also in C remainderl(), don't clobber the sign bit
of NaNs before possible returning a NaN.

The remquo*() and remainder*() functions should now give bitwise identical
results across arches and implementations, and bitwise consistent results
(with lower precisions having truncated mantissas) across precisions.  x86
already had consistency across amd64 and i386 and precisions by using the
i387 consistently and normally not using the C versions.  Inconsistencies
for C reqmquol() were first detected on sparc64.

Remove double second clearing of the sign bit and extra blank lines.
2018-07-24 11:50:05 +00:00
Bruce Evans
daa1e39110 Fix the conversion to use nan_mix() in r336362. fmod*(x, y),
remainder*(x, y) and remquo*(x, y, quo) were broken for y = 0 by changing
multiplication by y to addition of y.  (When y is 0, the result should be
NaN but became 1 for finite x.)

Use a new macro nan_mix_op() to give more control over the mixing, and
expand comments.

Recent re-testing missed finding this bug since I only tested the macro
version on amd64 and i386 and these arches don't use the C versions (they
use either asm versions or builtins).

Reported by:	enh via freebsd-numerics
2018-07-24 10:10:16 +00:00
Dimitry Andric
5a4c3b831b Recommit r336497: Fix powl, cpow, cpowf, and cpowl imports from OpenBSD
This is a follow-up to r336299.

* lib/msun/Makefile:
  . Remove polevll.c

* lib/msun/ld80/e_powl.c:
  . Copy contents of polevll.c to here.  This is the only consumer of
    these functions.  Make functions 'static inline'.
  . Make reducl a 'static inline' function.

* lib/msun/man/exp.3:
  . Remove BUGS section that no longer applies.

* lib/msun/src/math_private.h:
  . Remove prototypes of __p1evll() and __polevll()

* lib/msun/src/s_cpow.c:
* lib/msun/src/s_cpowf.c:
* lib/msun/src/s_cpowl.c
  . Include math_private.h.
  . Use the CMPLX macro from either C99 or math_private.h (depends on
    compiler support) instead of the problematic use of complex I.

Submitted by:	Steve Kargl <sgk@troutmask.apl.washington.edu>
PR:		229876
MFC after:	1 week
2018-07-20 18:27:30 +00:00
Bruce Evans
27aa844253 Centralize the complications for special efficient rounding to integers.
This was open-coded in range reduction for trig and exp functions.  Now
there are 3 static inline functions rnint[fl]() that replace open-coded
expressions, and type-generic irint() and i64rint() macros that hide the
complications for efficiently using non-generic irint() and irintl()
functions and casts.

Special details:

ld128/e_rem_pio2l.h needs to use i64rint() since it needs a 46-bit integer
result.  Everything else only needs a (less than) 32-bit integer result so
uses irint().

Float and double cases now use float_t and double_t locally instead of
STRICT_ASSIGN() to avoid bugs in extra precision.

On amd64, inline asm is now only used for irint() on long doubles.  The SSE
asm for irint() on amd64 only existed because the ifdef tangles made the
correct method of simply casting to int for this case non-obvious.
2018-07-20 12:42:24 +00:00
Dimitry Andric
c422fbac00 Revert r336497 for now, as it breaks on architectures using gcc, with:
cc1: warnings being treated as errors
/usr/src/lib/msun/src/s_cpow.c: In function 'cpow':
/usr/src/lib/msun/src/s_cpow.c:63: warning: implicit declaration of function 'CMPLX'
2018-07-19 19:07:25 +00:00
Dimitry Andric
2ae9055f49 Fix powl, cpow, cpowf, and cpowl imports from OpenBSD
This is a follow-up to r336299.

* lib/msun/Makefile:
  . Remove polevll.c

* lib/msun/ld80/e_powl.c:
  . Copy contents of polevll.c to here.  This is the only consumer of
    these functions.  Make functions 'static inline'.
  . Make reducl a 'static inline' function.

* lib/msun/man/exp.3:
  . Remove BUGS section that no longer applies.

* lib/msun/src/math_private.h:
  . Remove prototypes of __p1evll() and __polevll()

* lib/msun/src/s_cpow.c:
* lib/msun/src/s_cpowf.c:
* lib/msun/src/s_cpowl.c
  . Use the CMPLX macro from either C99 or math_private.h (depends of
    compiler support) instead of the problematic use of complex I.

Submitted by:	Steve Kargl <sgk@troutmask.apl.washington.edu>
PR:		229876
MFC after:	1 week
2018-07-19 18:44:10 +00:00
Bruce Evans
b7092eef4d Fix spurious and extra underflows and resulting inaccuracies for some cases
with 1 huge component and 1 tiny (but nowhere near denormal) component.
Rescale earlier so that a scale factor of 2 can be combined with a non-
scale divisor of 2, so that the division doesn't shift out a bit.  In the
usual case where the scale factor is just 1, the division may shift out a
bit, but then the underflow is not spurious and the inaccuracies are harder
to fix.
2018-07-19 15:04:10 +00:00
Bruce Evans
50c8bd4e53 Oops, r336412 undid the fix of the overflow threshold in r323003. Restore
the previous overflow threshold and adjust comments.
2018-07-19 14:24:48 +00:00
Bruce Evans
1693fd03d9 Minor cleanups to csqrt*(), mostly in comments.
Remove the STDC CX_LIMITED_RANGE pragma and its verbose comment.  We still
don't have any C99 compilers (that support fenv pragmas), and if we did
then there are thousands of other places in libm that would need to use
them more than here.

The other cleanups are smaller.
2018-07-17 12:01:59 +00:00
Bruce Evans
9d7dc13615 Fix scaling bugs which gave innaccuracies and spurious underflows in csqrt()
and csqrtl().

When one component is huge and the other is tiny, scaling down the tiny
component gave spurious underflow.

When both components are denormal, not scaling them up gave inaccuracies
of 34+ ulps on not very carefully selected args.  Fixing this reduces the
maximum error to 1.6 ulps on the same set of args (mosly not denormal ones).

The scaling used multiplication of a complex variable by 2, but clang messes
this on amd64 up by losing the sign of -0.0.  Calculate the components
separately, as is well known to be needed for operations on more exceptional
values.
2018-07-17 10:44:16 +00:00