The current approach tracks math maximum supported errors by explicitly
setting them per function and architecture. On newer implementations or
new compiler versions, the file is updated with newer values if it
shows higher results. The idea is to track the maximum known error, to
update the manual with the obtained values.
The constant libm-test-ulps shows little value, where it is usually a
mechanical change done by the maintainer, for past releases it is
usually ignored whether the ulp change resulted from a compiler
regression, and the math tests already have a maximum ulp error that
triggers a regression.
It was shown by a recent update after the new acosf [1] implementation
that is correctly rounded, where the libm-test-ulps was indeed from a
compiler issue.
This patch removes all arch-specific libm-test-ulps, adds system generic
libm-test-ulps where applicable, and changes its semantics. The generic
files now track specific implementation constraints, like if it is
expected to be correctly rounded, or if the system-specific has
different error expectations.
Now multiple libm-test-ulps can be defined, and system-specific
overrides generic implementation. This is for the case where
arch-specific implementation might show worse precision than generic
implementation, for instance, the cbrtf on i686.
Regressions are only reported if the implementation shows larger errors
than 9 ulps (13 for IBM long double) unless it is overridden by
libm-test-ulps and the maximum error is not printed at the end of tests.
The regen-ulps rule is also removed since it does not make sense to
update the libm-test-ulps automatically.
The manual error table is also removed, Paul Zimmermann and others have
been tracking libm precision with a more comprehensive analysis for some
releases; so link to his work instead.
[1] https://sourceware.org/git/?p=glibc.git;a=commit;h=9cc9f8e11e8fb8f54f1e84d9f024917634a78201
Single-precision remainderf() and quad-precision remainderl()
implementation derived from Sun is affected by an issue when the result
is +-0. IEEE754 requires that if remainder(x, y) = 0, its sign shall be
that of x regardless of the rounding direction.
The implementation seems to have assumed that x - x = +0 in all
rounding modes, which is not the case. When rounding direction is
roundTowardNegative the sign of an exact zero sum (or difference) is −0.
Regression tests that triggered this erroneous behavior are added to
math/libm-test-remainder.inc.
Tested for cross riscv64 and powerpc.
Original fix by: Bruce Evans <bde@FreeBSD.org> in FreeBSD's
a2ddfa5ea726c56dbf825763ad371c261b89b7c7.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
The libm size improvement built with "--enable-stack-protector=strong
--enable-bind-now=yes --enable-fortify-source=2":
Before:
text data bss dec hex filename
585192 860 12 586064 8f150 aarch64-linux-gnu/math/libm.so
960775 1068 12 961855 ead3f x86_64-linux-gnu/math/libm.so
1189174 5544 368 1195086 123c4e powerpc64le-linux-gnu/math/libm.so
After:
text data bss dec hex filename
584952 860 12 585824 8f060 aarch64-linux-gnu/math/libm.so
960615 1068 12 961695 eac9f x86_64-linux-gnu/math/libm.so
1189078 5544 368 1194990 123bee powerpc64le-linux-gnu/math/libm.so
The are small code changes for x86_64 and powerpc64le, which do not
affect performance; but on aarch64 with gcc-14 I see a slight better
code generation due the usage of ldq for floating point constant loading.
Reviewed-by: Andreas K. Huettel <dilfridge@gentoo.org>
The libm size improvement built with "--enable-stack-protector=strong
--enable-bind-now=yes --enable-fortify-source=2":
Before:
text data bss dec hex filename
587304 860 12 588176 8f990 aarch64-linux-gnu-master/math/libm.so
962855 1068 12 963935 eb55f x86_64-linux-gnu-master/math/libm.so
1191222 5544 368 1197134 12444e powerpc64le-linux-gnu-master/math/libm.so
After:
text data bss dec hex filename
585192 860 12 586064 8f150 aarch64-linux-gnu/math/libm.so
960775 1068 12 961855 ead3f x86_64-linux-gnu/math/libm.so
1189174 5544 368 1195086 123c4e powerpc64le-linux-gnu/math/libm.so
The are small code changes for x86_64 and powerpc64le, which do not
affect performance; but on aarch64 with gcc-14 I see a slight better
code generation due the usage of ldq for floating point constant loading.
Reviewed-by: Andreas K. Huettel <dilfridge@gentoo.org>
The CORE-MATH implementation is correctly rounded (for any rounding mode),
although it should worse performance than current one. The current
implementation performance comes mainly from the internal usage of
the optimize expf implementation, and shows a maximum ULPs of 2 for
FE_TONEAREST and 3 for other rounding modes.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).
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 40.6995 49.0737 -20.58%
x86_64v2 40.5841 44.3604 -9.30%
x86_64v3 39.3879 39.7502 -0.92%
i686 112.3380 129.8570 -15.59%
aarch64 (Neoverse) 18.6914 17.0946 8.54%
power10 11.1343 9.3245 16.25%
reciprocal-throughput master patched improvement
x86_64 18.6471 24.1077 -29.28%
x86_64v2 17.7501 20.2946 -14.34%
x86_64v3 17.8262 17.1877 3.58%
i686 64.1454 86.5645 -34.95%
aarch64 (Neoverse) 9.77226 12.2314 -25.16%
power10 4.0200 5.3316 -32.63%
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>
Some CORE-MATH routines uses roundeven and most of ISA do not have
an specific instruction for the operation. In this case, the call
will be routed to generic implementation.
However, if the ISA does support round() and ctz() there is a better
alternative (as used by CORE-MATH).
This patch adds such optimization and also enables it on powerpc.
On a power10 it shows the following improvement:
expm1f master patched improvement
latency 9.8574 7.0139 28.85%
reciprocal-throughput 4.3742 2.6592 39.21%
Checked on powerpc64le-linux-gnu and aarch64-linux-gnu.
Reviewed-by: DJ Delorie <dj@redhat.com>
The k>>31 in signgam = 1 - (((k&(k>>31))&1)<<1); is not portable:
* The ISO C standard says "If E1 has a signed type and a negative
value, the resulting value is implementation-defined." (this is
still in C23).
* If the int type is larger than 32 bits (e.g. a 64-bit type),
then k = INT_MAX; line 144 will make k>>31 put 1 in bit 0
(thus signgam will be -1) while 0 is expected.
Moreover, instead of the fx >= 0x1p31f condition, testing fx >= 0
is probably better for 2 reasons:
The signgam expression has more or less a condition on the sign
of fx (the goal of k>>31, which can be dropped with this new
condition). Since fx ≥ 0 should be the most common case, one can
get signgam directly in this case (value 1). And this simplifies
the expression for the other case (fx < 0).
This new condition may be easier/faster to test on the processor
(e.g. by avoiding a load of a constant from the memory).
This is commit d41459c731865516318f813cf4c966dafa0eecbf from CORE-MATH.
Checked on x86_64-linux-gnu.
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance to the generic tanf.
The code was adapted to glibc style, to use the definition of
math_config.h, to remove errno handling, and to use a generic
128 bit routine for ABIs that do not support it natively.
Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (neoverse1,
gcc 13.2.1), and powerpc (POWER10, gcc 13.2.1):
latency master patched improvement
x86_64 82.3961 54.8052 33.49%
x86_64v2 82.3415 54.8052 33.44%
x86_64v3 69.3661 50.4864 27.22%
i686 219.271 45.5396 79.23%
aarch64 29.2127 19.1951 34.29%
power10 19.5060 16.2760 16.56%
reciprocal-throughput master patched improvement
x86_64 28.3976 19.7334 30.51%
x86_64v2 28.4568 19.7334 30.65%
x86_64v3 21.1815 16.1811 23.61%
i686 105.016 15.1426 85.58%
aarch64 18.1573 10.7681 40.70%
power10 8.7207 8.7097 0.13%
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 commit 9247f53219 triggered some regressions on loongarch and
riscv:
math/test-float-log10
math/test-float32-log10
And it is due a wrong sync with CORE-MATH for special 0.0/-0.0
inputs.
Checked on aarch64-linux-gnu and loongarch64-linux-gnu-lp64d.
On GCC 11 (x86-64), the previous code produced test failures like
this one:
Failure: Test: exp10m1_towardzero (-0x1.1p+4)
Result:
is: -1.00000000e+00 -0x1.000000p+0
should be: -9.99999940e-01 -0x1.fffffep-1
difference: 5.96046447e-08 0x1.000000p-24
ulp : 1.0000
max.ulp : 0.0000
Apply a similar fix to exp2m1f.
Co-authored-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
The CORE-MATH exp2m1f implementation showed slight worse latency
when using x86_64 baseline ABI. This patch adds a ifunc variant
with similar performance for x86_64-v3.
Reviewed-by: Noah Goldstein <goldstein.w.n@gmail.com>
Reviewed-by: DJ Delorie <dj@redhat.com>
The CORE-MATH exp10m1f implementation showed slight worse latency
when using x86_64 baseline ABI. This patch adds a ifunc variant
with similar performance for x86_64-v3.
Reviewed-by: Noah Goldstein <goldstein.w.n@gmail.com>
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 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>
Also remove the use of builtins in favor of standard names, compiler
already inline them (if supported) with current compiler options.
It also fixes and issue where __builtin_roundeven is not support on
gcc older than version 10.
Checked on x86_64-linux-gnu and i686-linux_gnu.
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>
Adhemerval Zanella
Sergei Zimmerman
Paul Eggert
Vincent Lefevre
Florian Weimer