The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic exp2m1f.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow). The
only change is to handle FLT_MAX_EXP for FE_DOWNWARD or FE_TOWARDZERO.
The benchmark inputs are based on exp2f ones.
Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1,
gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1):
Latency master patched improvement
x86_64 40.6042 48.7104 -19.96%
x86_64v2 40.7506 35.9032 11.90%
x86_64v3 35.2301 31.7956 9.75%
i686 102.094 94.6657 7.28%
aarch64 18.2704 15.1387 17.14%
power10 11.9444 8.2402 31.01%
reciprocal-throughput master patched improvement
x86_64 20.8683 16.1428 22.64%
x86_64v2 19.5076 10.4474 46.44%
x86_64v3 19.2106 10.4014 45.86%
i686 56.4054 59.3004 -5.13%
aarch64 12.0781 7.3953 38.77%
power10 6.5306 5.9388 9.06%
The generic implementation calls __ieee754_exp2f and x86_64 provides
an optimized ifunc version (built with -mfma -mavx2, not correctly
rounded). This explains the performance difference for x86_64.
Same for i686, where the ABI provides an optimized __ieee754_exp2f
version built with '-msse2 -mfpmath=sse'. When built wth same
flags, the new algorithm shows a better performance:
master patched improvement
latency 102.094 91.2823 10.59%
reciprocal-throughput 56.4054 52.7984 6.39%
Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic exp10m1f.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow). I mostly
fixed some small issues in corner cases (sNaN handling, -INFINITY,
a specific overflow check).
Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1,
gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1):
Latency master patched improvement
x86_64 45.4690 49.5845 -9.05%
x86_64v2 46.1604 36.2665 21.43%
x86_64v3 37.8442 31.0359 17.99%
i686 121.367 93.0079 23.37%
aarch64 21.1126 15.0165 28.87%
power10 12.7426 8.4929 33.35%
reciprocal-throughput master patched improvement
x86_64 19.6005 17.4005 11.22%
x86_64v2 19.6008 11.1977 42.87%
x86_64v3 17.5427 10.2898 41.34%
i686 59.4215 60.9675 -2.60%
aarch64 13.9814 7.9173 43.37%
power10 6.7814 6.4258 5.24%
The generic implementation calls __ieee754_exp10f which has an
optimized version, although it is not correctly rounded, which is
the main culprit of the the latency difference for x86_64 and
throughp for i686.
Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>
The CORE-MATH implementation is correctly rounded (for any rounding mode).
This can be checked by exhaustive tests in a few minutes since there are
less than 2^32 values to check against for example GNU MPFR.
This patch also adds some bench values for tgammaf.
Tested on x86_64 and x86 (cfarm26).
With the initial GNU libc code it gave on an Intel(R) Core(TM) i7-8700:
"tgammaf": {
"": {
"duration": 3.50188e+09,
"iterations": 2e+07,
"max": 602.891,
"min": 65.1415,
"mean": 175.094
}
}
With the new code:
"tgammaf": {
"": {
"duration": 3.30825e+09,
"iterations": 5e+07,
"max": 211.592,
"min": 32.0325,
"mean": 66.1649
}
}
With the initial GNU libc code it gave on cfarm26 (i686):
"tgammaf": {
"": {
"duration": 3.70505e+09,
"iterations": 6e+06,
"max": 2420.23,
"min": 243.154,
"mean": 617.509
}
}
With the new code:
"tgammaf": {
"": {
"duration": 3.24497e+09,
"iterations": 1.8e+07,
"max": 1238.15,
"min": 101.155,
"mean": 180.276
}
}
Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Changes in v2:
- include <math.h> (fix the linknamespace failures)
- restored original benchtests/strcoll-inputs/filelist#en_US.UTF-8 file
- restored original wrapper code (math/w_tgammaf_compat.c),
except for the dealing with the sign
- removed the tgammaf/float entries in all libm-test-ulps files
- address other comments from Joseph Myers
(https://sourceware.org/pipermail/libc-alpha/2024-July/158736.html)
Changes in v3:
- pass NULL argument for signgam from w_tgammaf_compat.c
- use of math_narrow_eval
- added more comments
Changes in v4:
- initialize local_signgam to 0 in math/w_tgamma_template.c
- replace sysdeps/ieee754/dbl-64/gamma_productf.c by dummy file
Changes in v5:
- do not mention local_signgam any more in math/w_tgammaf_compat.c
- initialize local_signgam to 1 instead of 0 in w_tgamma_template.c
and added comment
Changes in v6:
- pass NULL as 2nd argument of __ieee754_gammaf_r in
w_tgammaf_compat.c, and check for NULL in e_gammaf_r.c
Changes in v7:
- added Signed-off-by line for Alexei Sibidanov (author of the code)
Changes in v8:
- added Signed-off-by line for Paul Zimmermann (submitted of the patch)
Changes in v9:
- address comments from review by Adhemerval Zanella
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
C23 adds various <math.h> function families originally defined in TS
18661-4. Add the logp1 functions (aliases for log1p functions - the
name is intended to be more consistent with the new log2p1 and
log10p1, where clearly it would have been very confusing to name those
functions log21p and log101p). As aliases rather than new functions,
the content of this patch is somewhat different from those actually
adding new functions.
Tests are shared with log1p, so this patch *does* mechanically update
all affected libm-test-ulps files to expect the same errors for both
functions.
The vector versions of log1p on aarch64 and x86_64 are *not* updated
to have logp1 aliases (and thus there are no corresponding header,
tests, abilist or ulps changes for vector functions either). It would
be reasonable for such vector aliases and corresponding changes to
other files to be made separately. For now, the log1p tests instead
avoid testing logp1 in the vector case (a Makefile change is needed to
avoid problems with grep, used in generating the .c files for vector
function tests, matching more than one ALL_RM_TEST line in a file
testing multiple functions with the same inputs, when it assumes that
the .inc file only has a single such line).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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.
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.
On running tests after from-scratch ulps regeneration, I found that
some libm tests failed with ulps in excess of those recorded in the
from-scratch regeneration, which should never happen unless those ulps
exceed the limit on ulps that can go in libm-test-ulps files.
Failure: Test: atan2_upward (inf, -inf)
Result:
is: 2.35619498e+00 0x1.2d97ccp+1
should be: 2.35619450e+00 0x1.2d97c8p+1
difference: 4.76837159e-07 0x1.000000p-21
ulp : 2.0000
max.ulp : 1.0000
Maximal error of `atan2_upward'
is : 2 ulp
accepted: 1 ulp
Failure: Test: carg_upward (-inf + inf i)
Result:
is: 2.35619498e+00 0x1.2d97ccp+1
should be: 2.35619450e+00 0x1.2d97c8p+1
difference: 4.76837159e-07 0x1.000000p-21
ulp : 2.0000
max.ulp : 1.0000
Maximal error of `carg_upward'
is : 2 ulp
accepted: 1 ulp
The problem comes from the addition of tests for the finite-math-only
versions of libm functions. Those tests share ulps with the default
function variants. make regen-ulps runs the default tests before the
finite-math-only tests, concatenating the resulting ulps before
feeding them to gen-libm-test.pl to generate a new libm-test-ulps
file. But gen-libm-test.pl always takes the last ulps value given for
any (function, type) pair. So, if the largest ulps for a function
come from non-finite inputs, a from-scratch regeneration loses those
ulps.
This patch fixes gen-libm-test.pl, in the case where there are
multiple ulps values for a (function, type) pair - which can only
happen as part of a regeneration - to take the largest ulps value
rather than the last one.
Tested for ARM / MIPS / powerpc-nofpu.
* math/gen-libm-test.pl (parse_ulps): Do not reduce
already-recorded ulps.
* sysdeps/arm/libm-test-ulps: Regenerated.
* sysdeps/mips/mips32/libm-test-ulps: Likewise.
* sysdeps/mips/mips64/libm-test-ulps: Likewise.
* sysdeps/powerpc/nofpu/libm-test-ulps: Likewise.
This patch regenerates libm-test-ulps for ARM. As before it may be
useful for someone building for a configuration with VFMA enabled to
do a followup regeneration for any additional ulps in that
configuration.
Committed.
* sysdeps/arm/libm-test-ulps: Regenerated.
As recently discussed
<https://sourceware.org/ml/libc-alpha/2014-02/msg00670.html>, it
doesn't seem particularly useful for libm-test-ulps files to contain
huge amounts of data on ulps for individual tests; just the global
maximum observed ulps for each function, together with the
verification of exceptions, errno and special results such as
infinities and NaNs for each test, suffices to verify that a
function's behavior on the given test inputs is within the expected
accuracy. Removing this data reduces source tree churn caused by
updates to these files when libm tests are added, and reduces the
frequency with which testsuite additions actually need libm-test-ulps
changes at all.
Accordingly, this patch removes that data, so that individual tests
get checked against the global bounds for the given function and only
generate an error if those are exceeded. Tested x86_64 (including
verifying that if an ulps value is artificially reduced, the tests do
indeed fail as they should and "make regen-ulps" generates the
expected changes).
* math/libm-test.inc (struct ulp_data): Don't refer to ulps for
individual tests in comment.
(libm-test-ulps.h): Don't refer to test_ulps in #include comment.
(prev_max_error): New variable.
(prev_real_max_error): Likewise.
(prev_imag_max_error): Likewise.
(compare_ulp_data): Don't refer to test names in comment.
(find_test_ulps): Remove function.
(find_function_ulps): Likewise.
(find_complex_function_ulps): Likewise.
(init_max_error): Take function name as argument. Look up ulps
for that function.
(print_ulps): Remove function.
(print_max_error): Use prev_max_error instead of calling
find_function_ulps.
(print_complex_max_error): Use prev_real_max_error and
prev_imag_max_error instead of calling find_complex_function_ulps.
(check_float_internal): Take max_ulp parameter instead of calling
find_test_ulps. Don't call print_ulps.
(check_float): Update call to check_float_internal.
(check_complex): Update calls to check_float_internal.
(START): Pass argument to init_max_error.
* math/gen-libm-test.pl (%results): Don't include "kind"
information.
(parse_ulps): Don't handle ulps of individual tests.
(print_ulps_file): Likewise.
(output_ulps): Likewise.
* math/README.libm-test: Update.
* manual/libm-err-tab.pl (parse_ulps): Don't handle ulps of
individual tests.
* sysdeps/aarch64/libm-test-ulps: Remove individual test ulps.
* sysdeps/alpha/fpu/libm-test-ulps: Likewise.
* sysdeps/arm/libm-test-ulps: Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Likewise.
* sysdeps/ia64/fpu/libm-test-ulps: Likewise.
* sysdeps/m68k/coldfire/fpu/libm-test-ulps: Likewise.
* sysdeps/m68k/m680x0/fpu/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/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.
* sysdeps/hppa/fpu/libm-test-ulps: Remove individual test ulps.
I've moved the ARM port from ports to the main sysdeps hierarchy.
Beyond the README update, the move of the files was simply
git mv ports/sysdeps/arm sysdeps/arm
git mv ports/sysdeps/unix/arm sysdeps/unix/arm
git mv ports/sysdeps/unix/sysv/linux/arm sysdeps/unix/sysv/linux/arm
and in addition to the ChangeLog entries here, I put a note at the top
of ports/ChangeLog.arm similar to that at the top of
ChangeLog.powerpc. There is deliberately no NEWS change, as I think
it makes the most sense to put in a general note above all ports
having moved if we can achieve that for 2.20.
Tested that disassembly of installed shared libraries for arm is the
same before and after this patch, except for data (not instructions)
in ld.so (there are assertions in sysdeps/arm/dl-machine.h, and the
path by which that file is found, and so by which it appears in the
assertion message, changes as a result of the move).
* sysdeps/arm: Move directory from ports/sysdeps/arm.
* sysdeps/unix/arm: Move directory from ports/sysdeps/unix/arm.
* sysdeps/unix/sysv/linux/arm: Move directory from
ports/sysdeps/unix/sysv/linux/arm.
* README: Update listing for arm-*-linux-gnueabi.
ports/ChangeLog.arm:
* sysdeps/arm: Move directory to ../sysdeps/arm.
* sysdeps/unix/arm: Move directory to ../sysdeps.arm.
* sysdeps/unix/sysv/linux/arm: Move directory to
../sysdeps/unix/sysv/linux/arm.
