glibc/sysdeps/ieee754/flt-32/s_expm1f.c
Adhemerval Zanella bbd578b38d math: Use expm1f from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic expm1f.

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                      96.7402        36.4026        62.37%
x86_64v2                    97.5391        33.4625        65.69%
x86_64v3                    82.1778        30.8668        62.44%
i686                         120.58        94.8302        21.35%
aarch64                     32.3558        12.8881        60.17%
power10                     23.5087        9.8574         58.07%
powerpc                     23.4776        9.06325        61.40%

reciprocal-throughput        master        patched   improvement
x86_64                      27.8224        15.9255        42.76%
x86_64v2                    27.8364        9.6438         65.36%
x86_64v3                    20.3227        9.6146         52.69%
i686                        63.5629        59.4718         6.44%
aarch64                     17.4838        7.1082         59.34%
power10                     12.4644        8.7829         29.54%
powerpc                     14.2152        5.94765        58.16%

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>
2024-11-01 11:27:35 -03:00

125 lines
4.4 KiB
C

/* Correctly-rounded natural exponent function biased by 1 for binary32 value.
Copyright (c) 2022-2024 Alexei Sibidanov.
This file is part of the CORE-MATH project
project (file src/binary32/expm1/expm1f.c, revision bc385c2).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#include <math.h>
#include <math-underflow.h>
#include <libm-alias-float.h>
#include "math_config.h"
float
__expm1f (float x)
{
static const double c[] =
{
1, 0x1.62e42fef4c4e7p-6, 0x1.ebfd1b232f475p-13, 0x1.c6b19384ecd93p-20
};
static const double ch[] =
{
0x1.62e42fefa39efp-6, 0x1.ebfbdff82c58fp-13, 0x1.c6b08d702e0edp-20,
0x1.3b2ab6fb92e5ep-27, 0x1.5d886e6d54203p-35, 0x1.430976b8ce6efp-43
};
static const double td[] =
{
0x1p+0, 0x1.059b0d3158574p+0, 0x1.0b5586cf9890fp+0,
0x1.11301d0125b51p+0, 0x1.172b83c7d517bp+0, 0x1.1d4873168b9aap+0,
0x1.2387a6e756238p+0, 0x1.29e9df51fdee1p+0, 0x1.306fe0a31b715p+0,
0x1.371a7373aa9cbp+0, 0x1.3dea64c123422p+0, 0x1.44e086061892dp+0,
0x1.4bfdad5362a27p+0, 0x1.5342b569d4f82p+0, 0x1.5ab07dd485429p+0,
0x1.6247eb03a5585p+0, 0x1.6a09e667f3bcdp+0, 0x1.71f75e8ec5f74p+0,
0x1.7a11473eb0187p+0, 0x1.82589994cce13p+0, 0x1.8ace5422aa0dbp+0,
0x1.93737b0cdc5e5p+0, 0x1.9c49182a3f09p+0, 0x1.a5503b23e255dp+0,
0x1.ae89f995ad3adp+0, 0x1.b7f76f2fb5e47p+0, 0x1.c199bdd85529cp+0,
0x1.cb720dcef9069p+0, 0x1.d5818dcfba487p+0, 0x1.dfc97337b9b5fp+0,
0x1.ea4afa2a490dap+0, 0x1.f50765b6e454p+0
};
const double iln2 = 0x1.71547652b82fep+5;
const double big = 0x1.8p52;
double z = x;
uint32_t ux = asuint (x);
uint32_t ax = ux << 1;
if (__glibc_likely (ax < 0x7c400000u))
{ /* |x| < 0.15625 */
if (__glibc_unlikely (ax < 0x676a09e8u))
{ /* |x| < 0x1.6a09e8p-24 */
if (__glibc_unlikely (ax == 0x0u))
return x; /* x = +-0 */
return fmaf (fabsf (x), 0x1p-25f, x);
}
static const double b[] =
{
0x1.fffffffffffc2p-2, 0x1.55555555555fep-3, 0x1.555555559767fp-5,
0x1.1111111098dc1p-7, 0x1.6c16bca988aa9p-10, 0x1.a01a07658483fp-13,
0x1.a05b04d2c3503p-16, 0x1.71de3a960b5e3p-19
};
double z2 = z * z, z4 = z2 * z2;
double r = z + z2
* ((b[0] + z * b[1]) + z2 * (b[2] + z * b[3])
+ z4 * ((b[4] + z * b[5]) + z2 * (b[6] + z * b[7])));
return r;
}
if (__glibc_unlikely (ax >= 0x8562e430u))
{ /* |x| > 88.72 */
if (ax > (0xffu << 24))
return x + x; /* nan */
if (__glibc_unlikely (ux >> 31))
{ /* x < 0 */
if (ax == (0xffu << 24))
return -1.0f;
return -1.0f + 0x1p-26f;
}
if (ax == (0xffu << 24))
return INFINITY;
return __math_oflowf (0);
}
double a = iln2 * z;
double ia = roundeven (a);
double h = a - ia;
double h2 = h * h;
uint64_t u = asuint64 (ia + big);
double c2 = c[2] + h * c[3], c0 = c[0] + h * c[1];
const uint64_t *tdl = (uint64_t *) ((void *) td);
double sv = asdouble (tdl[u & 0x1f] + ((u >> 5) << 52));
double r = (c0 + h2 * c2) * sv - 1.0;
float ub = r, lb = r - sv * 0x1.3b3p-33;
if (__glibc_unlikely (ub != lb))
{
if (__glibc_unlikely (ux > 0xc18aa123u)) /* x < -17.32 */
return -1.0f + 0x1p-26f;
const double iln2h = 0x1.7154765p+5;
const double iln2l = 0x1.5c17f0bbbe88p-26;
double s = sv;
h = (iln2h * z - ia) + iln2l * z;
h2 = h * h;
double w = s * h;
r = (s - 1) + w
* ((ch[0] + h * ch[1])
+ h2 * ((ch[2] + h * ch[3]) + h2 * (ch[4] + h * ch[5])));
ub = r;
}
return ub;
}
libm_alias_float (__expm1, expm1)