mirror of
https://sourceware.org/git/glibc.git
synced 2025-08-07 06:43:00 +03:00
3b1c5a539b
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>
125 lines
4.4 KiB
C
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_finite (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)
|