Fix for values near a power of two, and some tidies.
[BZ #16739]
* sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl): Correct
output when value is near a power of two. Use int64_t for lx and
remove casts. Use decimal rather than hex exponent constants.
Don't use long double multiplication when double will suffice.
* math/libm-test.inc (nextafter_test_data): Add tests.
* NEWS: Add 16739 and 16786 to bug list.
My recent exp patch introduced warnings about implicit __isinf
declarations in exp because e_exp.c didn't include <math.h>. This
patch fixes this. Because <math.h> can't be included after
<math_private.h> (because of macro definitions of __nan*), it was
necessary to put an include in sysdeps/x86_64/fpu/multiarch/e_exp.c as
well.
Tested x86_64.
* sysdeps/ieee754/dbl-64/e_exp.c: Include <math.h>.
* sysdeps/x86_64/fpu/multiarch/e_exp.c
[HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Likewise.
The dbl-64 version of exp needs round-to-nearest mode for its internal
computations, but that has the consequence of inappropriate
overflowing and underflowing results in other rounding modes. This
patch fixes this by recomputing the relevant results in cases where
the round-to-nearest result overflows to infinity or underflows to
zero (most of the diffs are actually just consequent reindentation).
Tests are enabled in all rounding modes for complex functions using
exp - but not for cexp because it turns out there are bugs causing
spurious underflows for cexp for some tests, which will need to be
fixed separately (I suspect ccos ccosh csin csinh ctan ctanh have
similar bugs, just not shown by the present set of test inputs).
Tested x86_64 and x86 and ulps updated accordingly.
[BZ #16284]
* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Use original
rounding mode to recompute results that overflow to infinity or
underflow to zero.
* math/auto-libm-test-in: Don't mark tests as expected to fail for
bug 16284.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (ccos_test): Use ALL_RM_TEST.
(ccosh_test): Likewise.
(csin_test_data): Use plus_oflow.
(csin_test): Use ALL_RM_TEST.
(csinh_test_data): Use plus_oflow.
(csinh_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
According to ISO C Annex F, log (1) should be +0 in all rounding
modes, but some implementations in glibc wrongly return -0 in
round-downward mode (mapping to log1p (x - 1) is problematic because 1
- 1 is -0 in round-downward mode, and log1p (-0) is -0). This patch
fixes this. (It helps with some implementations of other functions
such as acosh, log2 and log10 that call out to log, but not enough to
enable all-rounding-modes testing for those functions without further
fixes to other implementations of them.)
Tested x86_64 and x86 and ulps updated accordingly, and did spot tests
for mips64 for the ldbl-128 fix, and i586 for the sysdeps/i386/fpu
implementations shadowed by those in sysdeps/i386/i686/fpu.
[BZ #16731]
* sysdeps/i386/fpu/e_log.S (__ieee754_log): Take absolute value
when x - 1 is zero.
* sysdeps/i386/fpu/e_logf.S (__ieee754_logf): Likewise.
* sysdeps/i386/fpu/e_logl.S (__ieee754_logl): Likewise.
* sysdeps/i386/i686/fpu/e_logl.S (__ieee754_logl): Likewise.
* sysdeps/ieee754/dbl-64/e_log.c (__ieee754_log): Return +0 when
argument is 1.
* sysdeps/ieee754/ldbl-128/e_logl.c (__ieee754_logl): Likewise.
* sysdeps/x86_64/fpu/e_logl.S: Take absolute value when x - 1 is
zero.
* math/libm-test.inc (log_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
ISO C requires the result of nextafter to be independent of the
rounding mode, even when underflow or overflow occurs. This patch
fixes the bug in various nextafter implementations that, having done
an overflowing computation to force an overflow exception (correct),
they then return the result of that computation rather than an
infinity computed some other way (incorrect, when the overflowing
result of arithmetic with that sign and rounding mode is finite but
the correct result is infinite) - generally by falling through to
existing code to return a value that in fact is correct for this case
(but was computed by an integer increment and so without generating
the exceptions required). Having fixed the bug, the previously
deferred conversion of nextafter testing in libm-test.inc to
ALL_RM_TEST is also included.
Tested x86_64 and x86; also spot-checked results of nextafter tests
for powerpc32 and mips64 to test the ldbl-128ibm and ldbl-128
changes. (The m68k change is untested.)
[BZ #16677]
* math/s_nextafter.c (__nextafter): Do not return value from
overflowing computation.
* sysdeps/i386/fpu/s_nextafterl.c (__nextafterl): Likewise.
* sysdeps/ieee754/flt-32/s_nextafterf.c (__nextafterf): Likewise.
* sysdeps/ieee754/ldbl-128/s_nextafterl.c (__nextafterl):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl):
Likewise.
* sysdeps/m68k/m680x0/fpu/s_nextafterl.c (__nextafterl): Likewise.
* math/libm-test.inc (nextafter_test): Use ALL_RM_TEST.
In 84ba214c, I removed some redundant sign computations and in the
process, I incorrectly got rid of a temporary variable, thus passing
the absolute value of the input to bsloww1. This caused #16623.
This fix undoes the incorrect change.
The truncl assembly implementation (sysdeps/powerpc/powerpc64/fpu/s_truncl.S)
returns wrong results for some inputs where first double is a exact integer
and the precision is determined by second long double.
Checking on implementation comments and history, I am very confident the
assembly implementation was based on a version before commit
5c68d40169 that fixes BZ#2423 (Errors in
long double (ldbl-128ibm) rounding functions in glibc-2.4).
By just removing the implementation and make the build select
sysdeps/ieee754/ldbl-128ibm/s_truncl.c instead it fixes tgammal
issues regarding wrong result sign.
This patch fixes bug 16408, ldbl-128ibm expm1l returning NaN for some
large arguments.
The basic problem is that the approach of converting the exponent to
the form n * log(2) + y, where -0.5 <= y <= 0.5, then computing 2^n *
expm1(y) + (2^n - 1) falls over when 2^n overflows (starting slightly
before the point where expm1 overflows, when y is negative and n is
the least integer for which 2^n overflows). The ldbl-128 code, and
the x86/x86_64 code, make expm1l fall back to expl for large positive
arguments to avoid this issue. This patch makes the ldbl-128ibm code
do the same. (The problem appears for the particular argument in the
testsuite because the ldbl-128ibm code also uses an overflow threshold
that's for ldbl-128 and is too big for ldbl-128ibm, but the problem
described applies for large non-overflowing cases as well, although
during the freeze is not a suitable time for making the expm1 tests
cover cases close to overflow more thoroughly.)
This leaves some code for large positive arguments in expm1l that is
now dead. To keep the code for ldbl-128 and ldbl-128ibm similar, and
to avoid unnecessary changes during the freeze, the patch doesn't
remove it; instead I propose to file a bug in Bugzilla as a reminder
that this code (for overflow, including errno setting, and for
arguments of +Inf) is no longer needed and should be removed from both
those expm1l implementations.
Tested powerpc32.
* sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Use __expl
for large positive arguments.
This patch fixes bug 16407, spurious overflows from ldbl-128ibm coshl.
The implementation assumed that a high part (reinterpreted as an
integer) of the absolute value of the argument of 0x408633ce8fb9f87dLL
or more meant overflow, but the actual threshold has high part
0x408633ce8fb9f87eLL (and a negative low part). The patch adjusts the
threshold accordingly.
sinhl probably has the same issue, but I didn't get that far in adding
tests of special cases (such as just below and above overflow) before
the freeze and during the freeze is not a suitable time to add them
(as they'd require ulps to be regenerated again), so I'm not changing
that function for now; when I add more tests of special cases, we'll
discover whether sinhl indeed has this problem.
Tested powerpc32.
* sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl):
Increase overflow threshold.
This patch fixes bug 16400, spurious underflow exceptions for ldbl-128
/ ldbl-128ibm lgammal with small positive arguments, by just using
-__logl (x) as the result in the problem cases (similar to the
previous fix for problems with small negative arguments).
Tested powerpc32, and also tested on mips64 that this does not require
ulps regeneration for the ldbl-128 case.
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
Return -__logl (x) for small positive arguments without evaluating
a polynomial.
This patch fixes bug 16386, ldbl-128ibm logl inaccuracy (with
consequent inaccuracy for lgammal) for arguments where the high double
is subnormal, which showed up while attempting to regenerate ulps for
powerpc-nofpu for 2.19. The problem here is logic failing to allow
for subnormals when calculating the exponent of the argument. Tested
for powerpc-nofpu.
* sysdeps/ieee754/ldbl-128ibm/e_logl.c (__ieee754_logl): Adjust
numbers with subnormal high part when calculating exponent.
This patch fixes bug 16385, ldbl-128ibm asinhl inaccuracy, which
showed up while attempting to regenerate ulps for powerpc-nofpu for
2.19. The problem here was use of fabs instead of fabsl meaning large
arguments were reduced to the precision of double. Tested for
powerpc-nofpu.
* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Use fabsl not
fabs.
This patch fixes bug 16384, ldbl-128ibm acoshl inaccuracy, which
showed up while attempting to regenerate ulps for powerpc-nofpu for
2.19. There were two separate problems, use of __log1p instead of
__log1pl and an insufficiently accurate constant value for log 2
(which this patch replaces by use of M_LN2l), each of which could
cause substantial inaccuracy in affected cases.
Tested for powerpc-nofpu.
* sysdeps/ieee754/ldbl-128ibm/e_acoshl.c (ln2): Initialize with
M_LN2l.
(__ieee754_acoshl): Use __log1pl not __log1p.
This patch fixes bug 16337, ldbl-128 lgammal spurious overflows for
small negative arguments (the arguments in question are already in the
testsuite). The implementation uses the reflection formula to compute
lgamma of negative x from lgamma of -x, effectively resulting in a
calculation -log(x^2) + log(-x); cancellation isn't problematic in
this case (bugs for problematic cancellation in lgamma are 2542, 2543,
2558), but the x^2 calculation can underflow (in which case there is
spurious logic to return an overflowing value - lgamma can only ever
correctly overflow for large positive arguments, though tgamma can
overflow for small arguments of either sign as well as large positive
arguments). The fix is simply to calculate the result directly with
logl when the argument is a small enough negative number.
Tested mips64.
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
Calculate results for small negative arguments directly rather
than using reflection formula with special underflow handling.
This patch consolidates the multiple copies of code that looks up sin
and cos of a number from the lookup table and computes the final
value, into static functions. This does not have a noticeable
performance impact since the functions are inlined by gcc.
There is further scope for consolidation in the functions but they
cause a more noticable impact on performance (>5%) due to which I have
held back on them.
Removed more redundant computations in the slow paths of the sin and
cos functions. The notable change is the passing of the most
significant bits of X to the slow functions to check if X is positive
so that just the absolute value of x can be passed and the repeated
ABS() operation is avoided.
There are multiple points in the code where the absolute value of a
number is computed multiple times or is computed even though the value
can only be positive. This change removes those redundant
computations. Tested on x86_64 to verify that there were no
regressions in the testsuite.
This patch fixes bug 16338, ldbl-128 logl not handling subnormals
(with consequent inaccuracy for lgammal as well). The fix is simply
to use __frexpl when determining the exponent, as done already in
log2l and log10l. Given the lack of testing of small arguments to any
of the log* functions, appropriate tests are added for all of them.
Tested x86_64 and x86 and ulps updated accordingly, and spot tests
also run for mips64 to confirm the ldbl-128 fix.
Note that while this fixes lgammal inaccuracy for small positive
arguments, I suspect that there will still be problems with spurious
underflows in that case.
* sysdeps/ieee754/ldbl-128/e_logl.c (__ieee754_logl): Use __frexpl
to determine exponent and adjust argument to have exponent of -1.
* math/auto-libm-test-in: Add more tests of log, log10, log1p and
log2.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
- Remove redundant mynumber union definitions
- Clean up a clumsy ternary operator
- Rename TAYLOR_SINCOS to TAYLOR_SIN since we're only expanding the
sin Taylor series in it.
This patch helps some math functions performance by adding the libc_fexxx
variant of inline functions to handle both FPU round and exception set/restore
and by using them on the libc_fexxx_ctx functions. It is based on already coded
fexxx family functions for PPC with fpu.
Here is the summary of performance improvements due this patch (measured on a
POWER7 machine):
Before:
cos(): ITERS:9.5895e+07: TOTAL:5116.03Mcy, MAX:77.6cy, MIN:49.792cy, 18744 calls/Mcy
exp(): ITERS:2.827e+07: TOTAL:5187.15Mcy, MAX:494.018cy, MIN:38.422cy, 5450.01 calls/Mcy
pow(): ITERS:6.1705e+07: TOTAL:5144.26Mcy, MAX:171.95cy, MIN:29.935cy, 11994.9 calls/Mcy
sin(): ITERS:8.6898e+07: TOTAL:5117.06Mcy, MAX:83.841cy, MIN:46.582cy, 16982 calls/Mcy
tan(): ITERS:2.9473e+07: TOTAL:5115.39Mcy, MAX:191.017cy, MIN:172.352cy, 5761.63 calls/Mcy
After:
cos(): ITERS:2.05265e+08: TOTAL:5111.37Mcy, MAX:78.754cy, MIN:24.196cy, 40158.5 calls/Mcy
exp(): ITERS:3.341e+07: TOTAL:5170.84Mcy, MAX:476.317cy, MIN:15.574cy, 6461.23 calls/Mcy
pow(): ITERS:7.6153e+07: TOTAL:5129.1Mcy, MAX:147.5cy, MIN:30.916cy, 14847.2 calls/Mcy
sin(): ITERS:1.58816e+08: TOTAL:5115.11Mcy, MAX:1490.39cy, MIN:22.341cy, 31048.4 calls/Mcy
tan(): ITERS:3.4964e+07: TOTAL:5114.18Mcy, MAX:177.422cy, MIN:146.115cy, 6836.68 calls/Mcy
Autoconf has been deprecating configure.in for quite a long time.
Rename all our configure.in and preconfigure.in files to .ac.
Signed-off-by: Mike Frysinger <vapier@gentoo.org>
Add systemtap probes to various slow paths in libm so that application
developers may use systemtap to find out if their applications are
hitting these slow paths. We have added probes for pow, exp, log,
tan, atan and atan2.
http://sourceware.org/ml/libc-alpha/2013-07/msg00197.html
A rewrite to make this code correct for little-endian.
* sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c (mynumber): Replace
union 32-bit int array member with 64-bit int array.
(t515, tm256): Double rather than long double.
(__ieee754_sqrtl): Rewrite using 64-bit arithmetic.
http://sourceware.org/ml/libc-alpha/2013-08/msg00085.html
Rid ourselves of ieee854.
* sysdeps/ieee754/ldbl-128ibm/ieee754.h (union ieee854_long_double):
Delete.
(IEEE854_LONG_DOUBLE_BIAS): Delete.
* sysdeps/ieee754/ldbl-128ibm/math_ldbl.h: Don't include ieee854
version of math_ldbl.h.
http://sourceware.org/ml/libc-alpha/2013-08/msg00084.html
Another batch of ieee854 macros and union replacement. These four
files also have bugs fixed with this patch. The fact that the two
doubles in an IBM long double may have different signs means that
negation and absolute value operations can't just twiddle one sign bit
as you can with ieee864 style extended double. fmodl, remainderl,
erfl and erfcl all had errors of this type. erfl also returned +1 for
large magnitude negative input where it should return -1. The hypotl
error is innocuous since the value adjusted twice is only used as a
flag. The e_hypotl.c tests for large "a" and small "b" are mutually
exclusive because we've already exited when x/y > 2**120. That allows
some further small simplifications.
[BZ #15734], [BZ #15735]
* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c (__ieee754_fmodl): Rewrite
all uses of ieee875 long double macros and unions. Simplify test
for 0.0L. Correct |x|<|y| and |x|=|y| test. Use
ldbl_extract_mantissa value for ix,iy exponents. Properly
normalize after ldbl_extract_mantissa, and don't add hidden bit
already handled. Don't treat low word of ieee854 mantissa like
low word of IBM long double and mask off bit when testing for
zero.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl): Rewrite
all uses of ieee875 long double macros and unions. Simplify tests
for 0.0L and inf. Correct double adjustment of k. Delete dead code
adjusting ha,hb. Simplify code setting kld. Delete two600 and
two1022, instead use their values. Recognise that tests for large
"a" and small "b" are mutually exclusive. Rename vars. Comment.
* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c (__ieee754_remainderl):
Rewrite all uses of ieee875 long double macros and unions. Simplify
test for 0.0L and nan. Correct negation.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Rewrite all uses of
ieee875 long double macros and unions. Correct output for large
magnitude x. Correct absolute value calculation.
(__erfcl): Likewise.
* math/libm-test.inc: Add tests for errors discovered in IBM long
double versions of fmodl, remainderl, erfl and erfcl.
