/* Implementation of the exp10m1 function for binary32.
Copyright (c) 2022-2024 Alexei Sibidanov. Paul Zimmermann.
The original version of this file was copied from the CORE-MATH
project (file src/binary32/exp10m1/exp10m1f.c, revision c46b85b).
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_config.h"
#include <libm-alias-float.h>
float
__exp10m1f (float x)
{
const double iln10h = 0x1.a934f09p+1 * 16;
const double iln10l = 0x1.e68dc57f2496p-29 * 16;
double z = x;
uint32_t ux = asuint (x);
uint32_t ax = ux & (~0u >> 1);
if (__glibc_unlikely (ux > 0xc0f0d2f1u))
{ /* x < -7.52575 */
if (ax > (0xffu << 23))
return x + x; /* nan */
return (ux == 0xff800000) ? -0x1p+0f : -0x1p+0f + 0x1p-26f;
}
else if (__glibc_unlikely (ax > 0x421a209au))
{ /* x > 38.5318 */
if (ax >= asuint (INFINITY))
return x + x; /* +Inf or NaN */
return __math_oflowf (0);
}
else if (__glibc_unlikely (ax < 0x3d89c604u))
{ /* |x| < 0.1549/log(10) */
double z2 = z * z, r;
if (__glibc_unlikely (ax < 0x3d1622fbu))
{ /* |x| < 8.44e-2/log(10) */
if (__glibc_unlikely (ax < 0x3c8b76a3u))
{ /* |x| < 3.92e-2/log(10) */
if (__glibc_unlikely (ax < 0x3bcced04u))
{ /* |x| < 1.44e-2/log(10) */
if (__glibc_unlikely (ax < 0x3acf33ebu))
{ /* |x| < 3.64e-3/log(10 */
if (__glibc_unlikely (ax < 0x395a966bu))
{ /* |x| < 4.8e-4/log(10 */
if (__glibc_unlikely (ax < 0x36fe4a4bu))
{ /* |x| < 1.745e-5/log(10) */
if (__glibc_unlikely (ax < 0x32407f39u))
{ /* |x| < 2.58e-8/log(10) */
if (__glibc_unlikely (ax < 0x245e5bd9u))
{ /* |x| < 4.82164e-17 */
r = 0x1.26bb1bbb55516p+1;
}
else
{
if (__glibc_unlikely (ux == 0x2c994b7bu))
return 0x1.60f974p-37f - 0x1p-90f;
r = 0x1.26bb1bbb55516p+1
+ z * 0x1.53524c73cea69p+1;
}
}
else
{
if (__glibc_unlikely (ux == 0xb6fa215bu))
return -0x1.1ff87ep-16 + 0x1p-68;
r = 0x1.26bb1bbb55516p+1
+ z * (0x1.53524c73ea62fp+1
+ z * 0x1.0470591de2c75p+1);
}
}
else
{
static const double cp[] =
{
0x1.26bb1bbb55515p+1, 0x1.53524c73cea69p+1,
0x1.0470595038cc2p+1, 0x1.2bd7609fe1561p+0
};
r = (cp[0] + z * cp[1])
+ z2 * (cp[2] + z * cp[3]);
}
}
else
{
static const double cp[] =
{
0x1.26bb1bbb55516p+1, 0x1.53524c73ce6dbp+1,
0x1.0470591de3024p+1, 0x1.2bd76b79060e6p+0,
0x1.1429ffd3a963dp-1
};
r = (cp[0] + z * cp[1])
+ z2 * (cp[2] + z * (cp[3] + z * cp[4]));
}
}
else
{
static const double cp[] =
{
0x1.26bb1bbb55516p+1, 0x1.53524c73cea67p+1,
0x1.0470591dc2953p+1, 0x1.2bd760a004d64p+0,
0x1.142a85da6f072p-1, 0x1.a7ed70725b00ep-3
};
r = (cp[0] + z * cp[1]) + z2
* ((cp[2] + z * cp[3])
+ z2 * (cp[4] + z * cp[5]));
}
}
else
{
static const double cp[] =
{
0x1.26bb1bbb55516p+1, 0x1.53524c73ceadep+1,
0x1.0470591de2bb4p+1, 0x1.2bd76099a9d33p+0,
0x1.1429ffd829b0bp-1, 0x1.a7f2a6a0f7dc8p-3,
0x1.16e4dfbce0f56p-4
};
r = (cp[0] + z * cp[1])
+ z2 * ((cp[2] + z * cp[3])
+ z2 * (cp[4] + z * (cp[5] + z * cp[6])));
}
}
else
{
static const double cp[] =
{
0x1.26bb1bbb55515p+1, 0x1.53524c73cea6ap+1,
0x1.0470591de476p+1, 0x1.2bd7609fd4ee2p+0,
0x1.1429ff70a9b48p-1, 0x1.a7ed71259ba5bp-3,
0x1.16f3004fb3ac1p-4, 0x1.4116b0388aa9fp-6
};
r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
+ (z2 * z2) * ((cp[4] + z * cp[5]) + z2 * (cp[6]
+ z * cp[7]));
}
}
else
{
static const double cp[] =
{
0x1.26bb1bbb55515p+1, 0x1.53524c73cea42p+1, 0x1.0470591de2d1dp+1,
0x1.2bd760a010a53p+0, 0x1.1429ffd16170cp-1, 0x1.a7ed6b2a0d97fp-3,
0x1.16e4e37fa51e4p-4, 0x1.4147fe4c1676fp-6, 0x1.4897c4b3e329ap-8
};
r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
+ (z2 * z2) * ((cp[4] + z * cp[5])
+ z2 * (cp[6] + z * (cp[7] + z * cp[8])));
}
r *= z;
return r;
}
else
{
/* -7.52575 < x < -0.1549/log(10) or 0.1549/log(10) < x < 38.5318 */
static const double tb[] =
{
0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
0x1.ea4afa2a490dap+0
};
static const double c[] =
{
0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11, 0x1.c6b08d4ad86d3p-17,
0x1.3b2ad1b1716a2p-23, 0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
};
if (__glibc_unlikely ((ux << 11) == 0))
{
uint32_t k = (ux >> 21) - 0x1fc;
if (k <= 0xb)
{
if (k == 0)
return 10.0f - 1.0f;
if (k == 4)
return 100.0f - 1.0f;
if (k == 6)
return 1000.0f - 1.0f;
if (k == 8)
return 10000.0f - 1.0f;
if (k == 9)
return 100000.0f - 1.0f;
if (k == 10)
return 1000000.0f - 1.0f;
if (k == 11)
return 10000000.0f - 1.0f;
}
}
double a = iln10h * z;
double ia = floor (a);
double h = (a - ia) + iln10l * z;
int64_t i = ia;
int64_t j = i & 0xf;
int64_t e = i - j;
e >>= 4;
double s = tb[j];
s *= asdouble ((e + 0x3ffull) << 52);
double h2 = h * h;
double c0 = c[0] + h * c[1];
double c2 = c[2] + h * c[3];
double c4 = c[4] + h * c[5];
c0 += h2 * (c2 + h2 * c4);
double w = s * h;
return (s - 1.0) + w * c0;
}
}
#ifndef __exp10m1f
libm_alias_float (__exp10m1, exp10m1)
#endif