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math: Use exp10m1f from CORE-MATH
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>
This commit is contained in:
Adhemerval Zanella
parent
48767cbb76
commit
5fa89852fa
@ -240,3 +240,7 @@ sysdeps/ieee754/flt-32/e_gammaf_r.c
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- replace 0x1p127f * 0x1p127f by math_narrow_eval (x * 0x1p127f)
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- replace 0x1p-127f * sgn[k&1] by math_narrow_eval (0x1p-127f * sgn[k&1])
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- add libm_alias_finite (__ieee754_gammaf_r, __gammaf_r) at the end
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sysdeps/ieee754/flt-32/s_exp10m1f.c
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(file src/binary32/exp10m1/exp10m1f.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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@ -1083,22 +1083,18 @@ ldouble: 3
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Function: "exp10m1":
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double: 4
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float: 2
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ldouble: 3
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Function: "exp10m1_downward":
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double: 3
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float: 3
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ldouble: 6
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Function: "exp10m1_towardzero":
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double: 2
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float: 3
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ldouble: 6
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Function: "exp10m1_upward":
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double: 5
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float: 3
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ldouble: 6
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Function: "exp2":
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@ -789,19 +789,15 @@ float: 1
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Function: "exp10m1":
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double: 4
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float: 2
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Function: "exp10m1_downward":
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double: 3
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float: 3
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Function: "exp10m1_towardzero":
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double: 2
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float: 3
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Function: "exp10m1_upward":
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double: 5
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float: 3
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Function: "exp2":
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double: 1
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@ -194,7 +194,6 @@ float: 1
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Function: "exp10m1":
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double: 3
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float: 2
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Function: "exp2":
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double: 1
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@ -779,19 +779,15 @@ float: 1
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Function: "exp10m1":
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double: 3
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float: 2
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Function: "exp10m1_downward":
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double: 3
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float: 3
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Function: "exp10m1_towardzero":
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double: 2
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float: 3
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Function: "exp10m1_upward":
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double: 4
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float: 4
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Function: "exp2":
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double: 1
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@ -798,19 +798,15 @@ float: 1
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Function: "exp10m1":
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double: 4
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float: 2
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Function: "exp10m1_downward":
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double: 3
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float: 3
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Function: "exp10m1_towardzero":
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double: 2
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float: 3
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Function: "exp10m1_upward":
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double: 5
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float: 4
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Function: "exp2":
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double: 1
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@ -1155,25 +1155,21 @@ ldouble: 2
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Function: "exp10m1":
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double: 3
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float: 1
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float128: 3
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ldouble: 4
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Function: "exp10m1_downward":
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double: 3
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float: 3
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float128: 6
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ldouble: 6
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Function: "exp10m1_towardzero":
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double: 2
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float: 2
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float128: 6
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ldouble: 5
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Function: "exp10m1_upward":
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double: 5
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float: 3
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float128: 6
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ldouble: 6
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@ -1158,25 +1158,21 @@ ldouble: 2
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Function: "exp10m1":
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double: 3
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float: 1
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float128: 3
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ldouble: 4
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Function: "exp10m1_downward":
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double: 3
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float: 3
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float128: 6
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ldouble: 6
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Function: "exp10m1_towardzero":
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double: 2
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float: 2
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float128: 6
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ldouble: 5
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Function: "exp10m1_upward":
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double: 5
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float: 3
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float128: 6
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ldouble: 6
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225
sysdeps/ieee754/flt-32/s_exp10m1f.c
Normal file
225
sysdeps/ieee754/flt-32/s_exp10m1f.c
Normal file
@ -0,0 +1,225 @@
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/* Implementation of the exp10m1 function for binary32.
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Copyright (c) 2022-2024 Alexei Sibidanov. Paul Zimmermann.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/exp10m1/exp10m1f.c, revision c46b85b).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <math.h>
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#include "math_config.h"
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#include <libm-alias-float.h>
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float
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__exp10m1f (float x)
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{
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const double iln10h = 0x1.a934f09p+1 * 16;
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const double iln10l = 0x1.e68dc57f2496p-29 * 16;
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double z = x;
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uint32_t ux = asuint (x);
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uint32_t ax = ux & (~0u >> 1);
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if (__glibc_unlikely (ux > 0xc0f0d2f1u))
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{ /* x < -7.52575 */
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if (ax > (0xffu << 23))
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return x + x; /* nan */
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return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
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}
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else if (__glibc_unlikely (ax > 0x421a209au))
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{ /* x > 38.5318 */
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if (ax >= asuint (INFINITY))
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return x + x; /* +Inf or NaN */
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return __math_oflowf (0);
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}
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else if (__glibc_unlikely (ax < 0x3d89c604u))
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{ /* |x| < 0.1549/log(10) */
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double z2 = z * z, r;
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if (__glibc_unlikely (ax < 0x3d1622fbu))
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{ /* |x| < 8.44e-2/log(10) */
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if (__glibc_unlikely (ax < 0x3c8b76a3u))
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{ /* |x| < 3.92e-2/log(10) */
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if (__glibc_unlikely (ax < 0x3bcced04u))
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{ /* |x| < 1.44e-2/log(10) */
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if (__glibc_unlikely (ax < 0x3acf33ebu))
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{ /* |x| < 3.64e-3/log(10 */
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if (__glibc_unlikely (ax < 0x395a966bu))
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{ /* |x| < 4.8e-4/log(10 */
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if (__glibc_unlikely (ax < 0x36fe4a4bu))
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{ /* |x| < 1.745e-5/log(10) */
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if (__glibc_unlikely (ax < 0x32407f39u))
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{ /* |x| < 2.58e-8/log(10) */
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if (__glibc_unlikely (ax < 0x245e5bd9u))
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{ /* |x| < 4.82164e-17 */
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r = 0x1.26bb1bbb55516p+1;
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}
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else
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{
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if (__glibc_unlikely (ux == 0x2c994b7bu))
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return 0x1.60f974p-37f - 0x1p-90f;
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r = 0x1.26bb1bbb55516p+1
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+ z * 0x1.53524c73cea69p+1;
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}
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}
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else
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{
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if (__glibc_unlikely (ux == 0xb6fa215bu))
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return -0x1.1ff87ep-16 + 0x1p-68;
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r = 0x1.26bb1bbb55516p+1
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+ z * (0x1.53524c73ea62fp+1
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+ z * 0x1.0470591de2c75p+1);
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}
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}
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else
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{
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static const double cp[] =
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{
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0x1.26bb1bbb55515p+1, 0x1.53524c73cea69p+1,
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0x1.0470595038cc2p+1, 0x1.2bd7609fe1561p+0
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};
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r = (cp[0] + z * cp[1])
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+ z2 * (cp[2] + z * cp[3]);
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}
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}
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else
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{
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static const double cp[] =
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{
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0x1.26bb1bbb55516p+1, 0x1.53524c73ce6dbp+1,
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0x1.0470591de3024p+1, 0x1.2bd76b79060e6p+0,
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0x1.1429ffd3a963dp-1
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};
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r = (cp[0] + z * cp[1])
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+ z2 * (cp[2] + z * (cp[3] + z * cp[4]));
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}
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}
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else
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{
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static const double cp[] =
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{
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0x1.26bb1bbb55516p+1, 0x1.53524c73cea67p+1,
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0x1.0470591dc2953p+1, 0x1.2bd760a004d64p+0,
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0x1.142a85da6f072p-1, 0x1.a7ed70725b00ep-3
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};
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r = (cp[0] + z * cp[1]) + z2
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* ((cp[2] + z * cp[3])
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+ z2 * (cp[4] + z * cp[5]));
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}
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}
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else
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{
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static const double cp[] =
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{
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0x1.26bb1bbb55516p+1, 0x1.53524c73ceadep+1,
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0x1.0470591de2bb4p+1, 0x1.2bd76099a9d33p+0,
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0x1.1429ffd829b0bp-1, 0x1.a7f2a6a0f7dc8p-3,
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0x1.16e4dfbce0f56p-4
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};
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r = (cp[0] + z * cp[1])
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+ z2 * ((cp[2] + z * cp[3])
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+ z2 * (cp[4] + z * (cp[5] + z * cp[6])));
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}
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}
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else
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{
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static const double cp[] =
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{
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0x1.26bb1bbb55515p+1, 0x1.53524c73cea6ap+1,
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0x1.0470591de476p+1, 0x1.2bd7609fd4ee2p+0,
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0x1.1429ff70a9b48p-1, 0x1.a7ed71259ba5bp-3,
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0x1.16f3004fb3ac1p-4, 0x1.4116b0388aa9fp-6
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};
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r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
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+ (z2 * z2) * ((cp[4] + z * cp[5]) + z2 * (cp[6]
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+ z * cp[7]));
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}
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}
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else
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{
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static const double cp[] =
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{
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0x1.26bb1bbb55515p+1, 0x1.53524c73cea42p+1, 0x1.0470591de2d1dp+1,
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0x1.2bd760a010a53p+0, 0x1.1429ffd16170cp-1, 0x1.a7ed6b2a0d97fp-3,
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0x1.16e4e37fa51e4p-4, 0x1.4147fe4c1676fp-6, 0x1.4897c4b3e329ap-8
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};
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r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
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+ (z2 * z2) * ((cp[4] + z * cp[5])
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+ z2 * (cp[6] + z * (cp[7] + z * cp[8])));
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}
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r *= z;
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return r;
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}
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else
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{
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/* -7.52575 < x < -0.1549/log(10) or 0.1549/log(10) < x < 38.5318 */
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static const double tb[] =
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{
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0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
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0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
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0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
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0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
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0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
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0x1.ea4afa2a490dap+0
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};
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static const double c[] =
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{
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0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11, 0x1.c6b08d4ad86d3p-17,
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0x1.3b2ad1b1716a2p-23, 0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
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};
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if (__glibc_unlikely ((ux << 11) == 0))
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{
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uint32_t k = (ux >> 21) - 0x1fc;
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if (k <= 0xb)
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{
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if (k == 0)
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return 10.0f - 1.0f;
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if (k == 4)
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return 100.0f - 1.0f;
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if (k == 6)
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return 1000.0f - 1.0f;
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if (k == 8)
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return 10000.0f - 1.0f;
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if (k == 9)
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return 100000.0f - 1.0f;
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if (k == 10)
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return 1000000.0f - 1.0f;
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if (k == 11)
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return 10000000.0f - 1.0f;
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}
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}
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double a = iln10h * z;
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double ia = floor (a);
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double h = (a - ia) + iln10l * z;
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int64_t i = ia;
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int64_t j = i & 0xf;
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int64_t e = i - j;
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e >>= 4;
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double s = tb[j];
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s *= asdouble ((e + 0x3ffull) << 52);
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double h2 = h * h;
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double c0 = c[0] + h * c[1];
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double c2 = c[2] + h * c[3];
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double c4 = c[4] + h * c[5];
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c0 += h2 * (c2 + h2 * c4);
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double w = s * h;
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return (s - 1.0) + w * c0;
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}
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}
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libm_alias_float (__exp10m1, exp10m1)
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@ -977,22 +977,18 @@ ldouble: 3
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Function: "exp10m1":
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double: 4
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float: 2
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ldouble: 3
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Function: "exp10m1_downward":
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double: 3
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float: 3
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ldouble: 6
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Function: "exp10m1_towardzero":
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double: 2
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float: 3
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ldouble: 6
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Function: "exp10m1_upward":
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double: 5
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float: 3
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ldouble: 6
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Function: "exp2":
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@ -882,19 +882,15 @@ ldouble: 3
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Function: "exp10m1":
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double: 1
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float: 1
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Function: "exp10m1_downward":
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double: 1
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float: 1
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Function: "exp10m1_towardzero":
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double: 1
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float: 1
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Function: "exp10m1_upward":
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||||
double: 3
|
||||
float: 1
|
||||
|
||||
Function: "exp2":
|
||||
double: 1
|
||||
|
||||
@ -779,19 +779,15 @@ float: 1
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 3
|
||||
float: 2
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 4
|
||||
float: 4
|
||||
|
||||
Function: "exp2":
|
||||
double: 1
|
||||
|
||||
@ -978,22 +978,18 @@ ldouble: 3
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 3
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp2":
|
||||
|
||||
@ -1186,25 +1186,21 @@ ldouble: 4
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 4
|
||||
float: 2
|
||||
float128: 3
|
||||
ldouble: 4
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
float128: 6
|
||||
ldouble: 9
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
float128: 6
|
||||
ldouble: 9
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 5
|
||||
float: 3
|
||||
float128: 6
|
||||
ldouble: 8
|
||||
|
||||
|
||||
@ -987,22 +987,18 @@ ldouble: 4
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 3
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 9
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
ldouble: 9
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 10
|
||||
|
||||
Function: "exp2":
|
||||
|
||||
@ -974,7 +974,6 @@ ldouble: 3
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 2
|
||||
float: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "exp2":
|
||||
|
||||
@ -977,22 +977,18 @@ ldouble: 3
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 4
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 5
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp2":
|
||||
|
||||
@ -978,22 +978,18 @@ ldouble: 3
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 4
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 5
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp2":
|
||||
|
||||
@ -978,22 +978,18 @@ ldouble: 3
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 3
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 4
|
||||
float: 4
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp2":
|
||||
|
||||
@ -1431,25 +1431,21 @@ float: 1
|
||||
|
||||
Function: "exp10m1":
|
||||
double: 4
|
||||
float: 2
|
||||
float128: 3
|
||||
ldouble: 4
|
||||
|
||||
Function: "exp10m1_downward":
|
||||
double: 3
|
||||
float: 3
|
||||
float128: 6
|
||||
ldouble: 6
|
||||
|
||||
Function: "exp10m1_towardzero":
|
||||
double: 2
|
||||
float: 3
|
||||
float128: 6
|
||||
ldouble: 5
|
||||
|
||||
Function: "exp10m1_upward":
|
||||
double: 5
|
||||
float: 4
|
||||
float128: 6
|
||||
ldouble: 6
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user