Implement vectorized log2/log2f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector log2/log2f with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized log10/log10f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector log10/log10f with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized atan2/atan2f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector atan2/atan2f with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized cbrt/cbrtf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector cbrt/cbrtf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized sinh/sinhf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector sinh/sinhf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized expm1/expm1f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector expm1/expm1f with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized cosh/coshf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector cosh/coshf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized exp10/exp10f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector exp10/exp10f with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized exp2/exp2f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector exp2/exp2f with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized hypot/hypotf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector hypot/hypotf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized asin/asinf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector asin/asinf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized atan/atanf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector atan/atanf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
Implement vectorized acos/acosf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI. It also contains
accuracy and ABI tests for vector acos/acosf with regenerated ulps.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
On x86_64, when configuring glibc with CFLAGS="-O2 -g -march=native",
some tests fail. After this patch, "make check" succeeds.
Tested on Intel Core i5-4590 with gcc 10.2.1.
With this patch, the maximal known error for tgamma is now reduced to 9 ulps
for dbl-64, for all rounding modes. Since exhaustive testing is not possible
for dbl-64, it might be that there are still cases with an error larger than
9 ulps, but all known cases are fixed (intensive tests were done to find cases
with large errors).
Tested on x86_64 and powerpc (and by Adhemerval Zanella on aarch64, arm,
s390x, sparc, and i686).
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
For j0f/j1f/y0f/y1f, the largest error for all binary32
inputs is reduced to at most 9 ulps for all rounding modes.
The new code is enabled only when there is a cancellation at the very end of
the j0f/j1f/y0f/y1f computation, or for very large inputs, thus should not
give any visible slowdown on average. Two different algorithms are used:
* around the first 64 zeros of j0/j1/y0/y1, approximation polynomials of
degree 3 are used, computed using the Sollya tool (https://www.sollya.org/)
* for large inputs, an asymptotic formula from [1] is used
[1] Fast and Accurate Bessel Function Computation,
John Harrison, Proceedings of Arith 19, 2009.
Inputs yielding the new largest errors are added to auto-libm-test-in,
and ulps are regenerated for various targets (thanks Adhemerval Zanella).
Tested on x86_64 with --disable-multi-arch and on powerpc64le-linux-gnu.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
This patch series removes all remaining slow paths and related code.
First asin/acos, tan, atan, atan2 implementations are updated, and the final
patch removes the unused mpa files, headers and probes. Passes buildmanyglibc.
Remove slow paths from asin/acos. Add ULP annotations based on previous slow
path checks (which are approximate). Update AArch64 and x86_64 libm-test-ulps.
Reviewed-By: Paul Zimmermann <Paul.Zimmermann@inria.fr>
The corner cases included were generated using exhaustive search
for all float/binary32 values on x86_64 (comparing to MPFR for
correct rounding to nearest).
For the j0/j1/y0 functions, only cases with ulp error <= 9 were
included.
Reviewed-by: Carlos O'Donell <carlos@redhat.com>
With mathinline removal there is no need to keep building and testing
inline math tests.
The gen-libm-tests.py support to generate ULP_I_* is removed and all
libm-test-ulps files are updated to longer have the
i{float,double,ldouble} entries. The support for no-test-inline is
also removed from both gen-auto-libm-tests and the
auto-libm-test-out-* were regenerated.
Checked on x86_64-linux-gnu and i686-linux-gnu.
Optimized exp and exp2 implementations using a lookup table for
fractional powers of 2. There are several variants, see e_exp_data.c,
they can be selected by modifying math_config.h allowing different
tradeoffs.
The default selection should be acceptable as generic libm code.
Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on
aarch64 the rodata size is 2160 bytes, shared between exp and exp2.
On aarch64 .text + .rodata size decreased by 24912 bytes.
The non-nearest rounding error is less than 1 ULP even on targets
without efficient round implementation (although the error rate is
higher in that case). Targets with single instruction, rounding mode
independent, to nearest integer rounding and conversion can use them
by setting TOINT_INTRINSICS and adding the necessary code to their
math_private.h.
The __exp1 code uses the same algorithm, so the error bound of pow
increased a bit.
New double precision error handling code was added following the
style of the single precision error handling code.
Improvements on Cortex-A72 compared to current glibc master:
exp thruput: 1.61x in [-9.9 9.9]
exp latency: 1.53x in [-9.9 9.9]
exp thruput: 1.13x in [0.5 1]
exp latency: 1.30x in [0.5 1]
exp2 thruput: 2.03x in [-9.9 9.9]
exp2 latency: 1.64x in [-9.9 9.9]
For small (< 1) inputs the current exp code uses a separate algorithm
so the speed up there is less.
Was tested on
aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and
arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and
x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) and
powerpc64le-linux-gnu (!TOINT_INTRINSICS, fma contraction) targets,
only non-nearest rounding ulp errors increase and they are within
acceptable bounds (ulp updates are in separate patches).
* NEWS: Mention exp and exp2 improvements.
* math/Makefile (libm-support): Remove t_exp.
(type-double-routines): Add math_err and e_exp_data.
* sysdeps/aarch64/libm-test-ulps: Update.
* sysdeps/arm/libm-test-ulps: Update.
* sysdeps/i386/fpu/e_exp_data.c: New file.
* sysdeps/i386/fpu/math_err.c: New file.
* sysdeps/i386/fpu/t_exp.c: Remove.
* sysdeps/ia64/fpu/e_exp_data.c: New file.
* sysdeps/ia64/fpu/math_err.c: New file.
* sysdeps/ia64/fpu/t_exp.c: Remove.
* sysdeps/ieee754/dbl-64/e_exp.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_exp_data.c: New file.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound.
* sysdeps/ieee754/dbl-64/eexp.tbl: Remove.
* sysdeps/ieee754/dbl-64/math_config.h: New file.
* sysdeps/ieee754/dbl-64/math_err.c: New file.
* sysdeps/ieee754/dbl-64/t_exp.c: Remove.
* sysdeps/ieee754/dbl-64/t_exp2.h: Remove.
* sysdeps/ieee754/dbl-64/uexp.h: Remove.
* sysdeps/ieee754/dbl-64/uexp.tbl: Remove.
* sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file.
* sysdeps/m68k/m680x0/fpu/math_err.c: New file.
* sysdeps/m68k/m680x0/fpu/t_exp.c: Remove.
* sysdeps/powerpc/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
Fix a few missing spaces, it's now identical to the regenerated version.
Passes GLIBC tests on x64.
* sysdeps/x86_64/fpu/libm-test-ulps: Regenerate to fix spaces.
The second patch improves performance of sinf and cosf using the same
algorithms and polynomials. The returned values are identical to sincosf
for the same input. ULP definitions for AArch64 and x64 are updated.
sinf/cosf througput gains on Cortex-A72:
* |x| < 0x1p-12 : 1.2x
* |x| < M_PI_4 : 1.8x
* |x| < 2 * M_PI: 1.7x
* |x| < 120.0 : 2.3x
* |x| < Inf : 3.0x
* NEWS: Mention sinf, cosf, sincosf.
* sysdeps/aarch64/libm-test-ulps: Update ULP for sinf, cosf, sincosf.
* sysdeps/x86_64/fpu/libm-test-ulps: Update ULP for sinf and cosf.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Add definitions of
constants rather than including generic sincosf.h.
* sysdeps/x86_64/fpu/s_sincosf_data.c: Remove.
* sysdeps/ieee754/flt-32/s_cosf.c (cosf): Rewrite.
* sysdeps/ieee754/flt-32/s_sincosf.h (reduced_sin): Remove.
(reduced_cos): Remove.
(sinf_poly): New function.
* sysdeps/ieee754/flt-32/s_sinf.c (sinf): Rewrite.
This series of patches removes the slow patchs from sin, cos and sincos.
Besides greatly simplifying the implementation, the new version is also much
faster for inputs up to PI (41% faster) and for large inputs needing range
reduction (27% faster).
ULP is ~0.55 with no errors found after testing 1.6 billion inputs across most
of the range with mpsin and mpcos. The number of incorrectly rounded results
(ie. ULP >0.5) is at most ~2750 per million inputs between 0.125 and 0.5,
the average is ~850 per million between 0 and PI.
Tested on AArch64 and x86_64 with no regressions.
The first patch removes the slow paths for the cases where the input is small
and doesn't require range reduction. Update ULP tables for sin, cos and sincos
on AArch64 and x86_64.
* sysdeps/aarch64/libm-test-ulps: Update ULP for sin, cos, sincos.
* sysdeps/ieee754/dbl-64/s_sin.c (__sin): Remove slow paths for small
inputs.
(__cos): Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Update ULP for sin, cos, sincos.
Remove the slow paths from pow. Like several other double precision math
functions, pow is exactly rounded. This is not required from math functions
and causes major overheads as it requires multiple fallbacks using higher
precision arithmetic if a result is close to 0.5ULP. Ridiculous slowdowns
of up to 100000x have been reported when the highest precision path triggers.
All GLIBC math tests pass on AArch64 and x64 (with ULP of pow set to 1).
The worst case error is ~0.506ULP. A simple test over a few hundred million
values shows pow is 10% faster on average. This fixes BZ #13932.
[BZ #13932]
* sysdeps/ieee754/dbl-64/uexp.h (err_1): Remove.
* benchtests/pow-inputs: Update comment for slow path cases.
* manual/probes.texi (slowpow_p10): Delete removed probe.
(slowpow_p10): Likewise.
* math/Makefile: Remove halfulp.c and slowpow.c.
* sysdeps/aarch64/libm-test-ulps: Set ULP of pow to 1.
* sysdeps/generic/math_private.h (__exp1): Remove error argument.
(__halfulp): Remove.
(__slowpow): Remove.
* sysdeps/i386/fpu/halfulp.c: Delete file.
* sysdeps/i386/fpu/slowpow.c: Likewise.
* sysdeps/ia64/fpu/halfulp.c: Likewise.
* sysdeps/ia64/fpu/slowpow.c: Likewise.
* sysdeps/ieee754/dbl-64/e_exp.c (__exp1): Remove error argument,
improve comments and add error analysis.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Add error analysis.
(power1): Remove function:
(log1): Remove error argument, add error analysis.
(my_log2): Remove function.
* sysdeps/ieee754/dbl-64/halfulp.c: Delete file.
* sysdeps/ieee754/dbl-64/slowpow.c: Likewise.
* sysdeps/m68k/m680x0/fpu/halfulp.c: Likewise.
* sysdeps/m68k/m680x0/fpu/slowpow.c: Likewise.
* sysdeps/powerpc/power4/fpu/Makefile: Remove CPPFLAGS-slowpow.c.
* sysdeps/x86_64/fpu/libm-test-ulps: Set ULP of pow to 1.
* sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowpow-fma.c,
slowpow-fma4.c, halfulp-fma.c, halfulp-fma4.c.
* sysdeps/x86_64/fpu/multiarch/e_pow-fma.c (__slowpow): Remove define.
* sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c (__slowpow): Likewise.
* sysdeps/x86_64/fpu/multiarch/halfulp-fma.c: Delete file.
* sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowpow-fma.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c: Likewise.
This patch obsoletes the pow10, pow10f and pow10l functions (makes
them into compat symbols, not available for new ports or static
linking). The exp10 names for these functions are standardized (in TS
18661-4) and were added in the same glibc version (2.1) as pow10 so
source code can change to use them without any loss of portability.
Since pow10 is deliberately not provided for _Float128, only exp10,
this slightly simplifies moving to the new wrapper templates in the
!LIBM_SVID_COMPAT case, by avoiding needing to arrange for pow10,
pow10f and pow10l to be defined by those templates.
Tested for x86_64, and with build-many-glibcs.py.
* manual/math.texi (pow10): Do not document.
(pow10f): Likewise.
(pow10l): Likewise.
* math/bits/mathcalls.h [__USE_GNU] (pow10): Do not declare.
* math/bits/math-finite.h [__USE_GNU] (pow10): Likewise.
* math/libm-test-exp10.inc (pow10_test): Remove.
(do_test): Do not call pow10.
* math/w_exp10_compat.c (pow10): Make into compat symbol.
[NO_LONG_DOUBLE] (pow10l): Likewise.
* math/w_exp10f_compat.c (pow10f): Likewise.
* math/w_exp10l_compat.c (pow10l): Likewise.
* sysdeps/ia64/fpu/e_exp10.S: Include <shlib-compat.h>.
(pow10): Make into compat symbol.
* sysdeps/ia64/fpu/e_exp10f.S: Include <shlib-compat.h>.
(pow10f): Make into compat symbol.
* sysdeps/ia64/fpu/e_exp10l.S: Include <shlib-compat.h>.
(pow10l): Make into compat symbol.
* sysdeps/ieee754/ldbl-opt/Makefile (libnldbl-calls): Remove
pow10.
(CFLAGS-nldbl-pow10.c): Remove variable..
* sysdeps/ieee754/ldbl-opt/nldbl-pow10.c: Remove file.
* sysdeps/ieee754/ldbl-opt/w_exp10_compat.c (pow10l): Condition on
[SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_27)].
* sysdeps/ieee754/ldbl-opt/w_exp10l_compat.c (compat_symbol):
Undefine and redefine.
(pow10l): Make into compat symbol.
* sysdeps/aarch64/libm-test-ulps: Remove pow10 ulps.
* sysdeps/alpha/fpu/libm-test-ulps: Likewise.
* sysdeps/arm/libm-test-ulps: Likewise.
* sysdeps/hppa/fpu/libm-test-ulps: Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Likewise.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/microblaze/libm-test-ulps: Likewise.
* sysdeps/mips/mips32/libm-test-ulps: Likewise.
* sysdeps/mips/mips64/libm-test-ulps: Likewise.
* sysdeps/nios2/libm-test-ulps: Likewise.
* sysdeps/powerpc/fpu/libm-test-ulps: Likewise.
* sysdeps/powerpc/nofpu/libm-test-ulps: Likewise.
* sysdeps/s390/fpu/libm-test-ulps: Likewise.
* sysdeps/sh/libm-test-ulps: Likewise.
* sysdeps/sparc/fpu/libm-test-ulps: Likewise.
* sysdeps/tile/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Update libm-test-ulps for AVX512 mathvec tests by running
“make regen-ulps” on Intel Xeon processor with AVX512.
* sysdeps/x86_64/fpu/libm-test-ulps: Regenerated.
This patch enables float128 support for x86_64 and x86. All GCC
versions that can build glibc provide the required support, but since
GCC 6 and before don't provide __builtin_nanq / __builtin_nansq, sNaN
tests and some tests of NaN payloads need to be disabled with such
compilers (this does not affect the generated glibc binaries at all,
just the tests). bits/floatn.h declares float128 support to be
available for GCC versions that provide the required libgcc support
(4.3 for x86_64, 4.4 for i386 GNU/Linux, 4.5 for i386 GNU/Hurd);
compilation-only support was present some time before then, but not
really useful without the libgcc functions.
fenv_private.h needed updating to avoid trying to put _Float128 values
in registers. I make no assertion of optimality of the
math_opt_barrier / math_force_eval definitions for this case; they are
simply intended to be sufficient to work correctly.
Tested for x86_64 and x86, with GCC 7 and GCC 6. (Testing for x32 was
compilation tests only with build-many-glibcs.py to verify the ABI
baseline updates. I have not done any testing for Hurd, although the
float128 support is enabled there as for GNU/Linux.)
* sysdeps/i386/Implies: Add ieee754/float128.
* sysdeps/x86_64/Implies: Likewise.
* sysdeps/x86/bits/floatn.h: New file.
* sysdeps/x86/float128-abi.h: Likewise.
* manual/math.texi (Mathematics): Document support for _Float128
on x86_64 and x86.
* sysdeps/i386/fpu/fenv_private.h: Include <bits/floatn.h>.
(math_opt_barrier): Do not put _Float128 values in floating-point
registers.
(math_force_eval): Likewise.
[__x86_64__] (SET_RESTORE_ROUNDF128): New macro.
* sysdeps/x86/fpu/Makefile [$(subdir) = math] (CPPFLAGS): Append
to Makefile variable.
* sysdeps/x86/fpu/e_sqrtf128.c: New file.
* sysdeps/x86/fpu/sfp-machine.h: Likewise. Based on libgcc.
* sysdeps/x86/math-tests.h: New file.
* math/libm-test-support.h (XFAIL_FLOAT128_PAYLOAD): New macro.
* math/libm-test-getpayload.inc (getpayload_test_data): Use
XFAIL_FLOAT128_PAYLOAD.
* math/libm-test-setpayload.inc (setpayload_test_data): Likewise.
* math/libm-test-totalorder.inc (totalorder_test_data): Likewise.
* math/libm-test-totalordermag.inc (totalordermag_test_data):
Likewise.
* sysdeps/unix/sysv/linux/i386/libc.abilist: Update.
* sysdeps/unix/sysv/linux/i386/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/x86_64/64/libc.abilist: Likewise.
* sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/x86_64/x32/libc.abilist: Likewise.
* sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Likewise.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of catan and catanh with finite inputs (other
than the divide-by-zero cases producing an exact infinity) to using
the auto-libm-test machinery. Each of auto-libm-test-out-catan and
auto-libm-test-out-catanh takes about three seconds to generate on my
system (so in fact it wasn't necessary after all to defer the move to
auto-libm-test-* until the output files were split up by function).
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of catan and catanh.
* math/auto-libm-test-out-catan: New generated file.
* math/auto-libm-test-out-catanh: Likewise.
* math/libm-test-catan.inc (catan_test_data): Use AUTO_TESTS_c_c.
Move tests with finite inputs, except divide-by-zero cases, to
auto-libm-test-in.
* math/libm-test-catanh.inc (catanh_test_data): Likewise.
* math/Makefile (libm-test-funcs-auto): Add catan and catanh.
(libm-test-funcs-noauto): Remove catan and catanh.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of casin and casinh with finite inputs to using
the auto-libm-test machinery. Each of auto-libm-test-out-casin and
auto-libm-test-out-casinh takes about 38 minutes to generate on my
system because of MPC slowness on special cases that appear in the
tests (with MPC 1.0.3; I don't know to what extent current MPC master
might speed it up).
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of casin and casinh.
* math/auto-libm-test-out-casin: New generated file.
* math/auto-libm-test-out-casinh: Likewise.
* math/libm-test-casin.inc (casin_test_data): Use AUTO_TESTS_c_c.
Move tests with finite inputs to auto-libm-test-in.
* math/libm-test-casinh.inc (casinh_test_data): Likewise.
* math/Makefile (libm-test-funcs-auto): Add casin and casinh.
(libm-test-funcs-noauto): Remove casin and casinh.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of cacos and cacosh with finite inputs to using
the auto-libm-test machinery. Each of auto-libm-test-out-cacos and
auto-libm-test-out-cacosh takes about 80 minutes to generate on my
system because of MPC slowness on special cases that appear in the
tests (with MPC 1.0.3; I don't know to what extent current MPC master
might speed it up).
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of cacos and cacosh.
* math/auto-libm-test-out-cacos: New generated file.
* math/auto-libm-test-out-cacosh: Likewise.
* math/libm-test-cacos.inc (cacos_test_data): Use AUTO_TESTS_c_c.
Move tests with finite inputs to auto-libm-test-in.
* math/libm-test-cacosh.inc (cacosh_test_data): Likewise.
* math/Makefile (libm-test-funcs-auto): Add cacos and cacosh.
(libm-test-funcs-noauto): Remove cacos and cacosh.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Bug 19848 reports cases where powl on x86 / x86_64 has error
accumulation, for small integer exponents, larger than permitted by
glibc's accuracy goals, at least in some rounding modes. This patch
further restricts the exponent range for which the
small-integer-exponent logic is used to limit the possible error
accumulation.
Tested for x86_64 and x86 and ulps updated accordingly.
[BZ #19848]
* sysdeps/i386/fpu/e_powl.S (p3): Rename to p2 and change value
from 8 to 4.
(__ieee754_powl): Compare integer exponent against 4 not 8.
* sysdeps/x86_64/fpu/e_powl.S (p3): Rename to p2 and change value
from 8 to 4.
(__ieee754_powl): Compare integer exponent against 4 not 8.
* math/auto-libm-test-in: Add more tests of pow.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch improves test coverage of the real libm functions [a-e]*,
ensuring that special cases and ranges of input values of potential
significance (such as close to overflow and underflow thresholds) are
more systematically covered.
This is a followup to
<https://sourceware.org/ml/libc-alpha/2013-12/msg00757.html> which
covered [a-c]* (however, I found more weaknesses in the coverage of
those functions when preparing this patch, hence the additional tests
being added for them here).
Addition of a test for acosh (-qNaN) is temporarily deferred, to be
included as part of a fix for bug 19032 which was discovered in the
course of adding these tests (and which illustrates the use of testing
-qNaN as well as +qNaN as input even to functions for which the sign
of a NaN isn't meant to be significant).
Tested for x86_64 and x86.
* math/auto-libm-test-in: Add more tests of acos, acosh, asin,
atan, atan2, atanh, cbrt, cos, cosh, erf, erfc, exp, exp10, exp2
and expm1.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (acos_test_data): Add more tests.
(asin_test_data): Likewise.
(asinh_test_data): Likewise.
(atan_test_data): Likewise.
(atanh_test_data): Likewise.
(atan2_test_data): Likewise.
(cbrt_test_data): Likewise.
(ceil_test_data): Likewise.
(copysign_test_data): Likewise.
(cos_test_data): Likewise.
(cosh_test_data): Likewise.
(erf_test_data): Likewise.
(erfc_test_data): Likewise.
(exp_test_data): Likewise.
(exp10_test_data): Likewise.
(exp2_test_data): Likewise.
(expm1_test_data): Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
For arguments with X^2 + Y^2 close to 1, clog and clog10 avoid large
errors from log(hypot) by computing X^2 + Y^2 - 1 in a way that avoids
cancellation error and then using log1p.
However, the thresholds for using that approach still result in log
being used on argument as large as sqrt(13/16) > 0.9, leading to
significant errors, in some cases above the 9ulp maximum allowed in
glibc libm. This patch arranges for the approach using log1p to be
used in any cases where |X|, |Y| < 1 and X^2 + Y^2 >= 0.5 (with the
existing allowance for cases where one of X and Y is very small),
adjusting the __x2y2m1 functions to work with the wider range of
inputs. This way, log only gets used on arguments below sqrt(1/2) (or
substantially above 1), where the error involved is much less.
Tested for x86_64, x86, mips64 and powerpc. For the ulps regeneration
I removed the existing clog and clog10 ulps before regenerating to
allow any reduced ulps to appear. Tests added include those found by
random test generation to produce large ulps either before or after
the patch, and some found by trying inputs close to the (0.75, 0.5)
threshold where the potential errors from using log are largest.
[BZ #19016]
* sysdeps/generic/math_private.h (__x2y2m1f): Update comment to
allow more cases with X^2 + Y^2 >= 0.5.
* sysdeps/ieee754/dbl-64/x2y2m1.c (__x2y2m1): Likewise. Add -1 as
normal element in sum instead of special-casing based on values of
arguments.
* sysdeps/ieee754/dbl-64/x2y2m1f.c (__x2y2m1f): Update comment.
* sysdeps/ieee754/ldbl-128/x2y2m1l.c (__x2y2m1l): Likewise. Add
-1 as normal element in sum instead of special-casing based on
values of arguments.
* sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c (__x2y2m1l): Likewise.
* sysdeps/ieee754/ldbl-96/x2y2m1.c [FLT_EVAL_METHOD != 0]
(__x2y2m1): Update comment.
* sysdeps/ieee754/ldbl-96/x2y2m1l.c (__x2y2m1l): Likewise. Add -1
as normal element in sum instead of special-casing based on values
of arguments.
* math/s_clog.c (__clog): Handle more cases using log1p without
hypot.
* math/s_clog10.c (__clog10): Likewise.
* math/s_clog10f.c (__clog10f): Likewise.
* math/s_clog10l.c (__clog10l): Likewise.
* math/s_clogf.c (__clogf): Likewise.
* math/s_clogl.c (__clogl): Likewise.
* math/auto-libm-test-in: Add more tests of clog and clog10.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The flt-32 version of powf can be inaccurate because of bugs in the
extra-precision calculation of (x-1)/(x+1) or (x-1.5)/(x+1.5) as part
of calculating log(x) with extra precision: a constant used (as part
of adding 1 or 1.5 through integer arithmetic) is incorrect, and then
the code fails to mask a computed high part before using it in
arithmetic that relies on s_h*t_h being exactly representable. This
patch fixes these bugs.
Tested for x86_64 and x86. x86_64 ulps for powf removed and
regenerated to reflect reduced ulps from the increased accuracy for
existing tests.
[BZ #18956]
* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Add 0x00400000
not 0x0040000 for high bit of mantissa. Mask with 0xfffff000 when
extracting high part.
* math/auto-libm-test-in: Add another test of pow.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
This patch adds more libm test inputs found through random test
generation to increase previously known ulps. This particular test
generation was run for mips64, so most of the increased ulps are for
ldbl-128 (float and double having been fairly well covered by such
testing for x86_64), but there's the odd ulps increase for other
formats.
Tested for x86_64, x86 and mips64.
* math/auto-libm-test-in: Add more tests of acos, acosh, asin,
asinh, atan, atan2, atanh, cabs, carg, cos, csqrt, erfc, exp,
exp10, exp2, log, log1p, log2, pow, sin, sincos, sinh, tan and
tanh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/mips/mips32/libm-test-ulps: Likewise.
* sysdeps/mips/mips64/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
