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/* Correctly-rounded biased argument natural logarithm function for binary32
value.
Copyright (c) 2023, 2024 Alexei Sibidanov.
This file is part of the CORE-MATH project
project (file src/binary32/log1p/log1pf.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 <stdint.h>
#include <errno.h>
#include <libm-alias-float.h>
#include "math_config.h"
static __attribute__ ((noinline)) float
as_special (float x)
{
uint32_t t = asuint (x);
if (t == 0xbf800000u)
return __math_divzerof (1);
if (t == 0x7f800000u)
return x; /* +inf */
uint32_t ax = t << 1;
if (ax > 0xff000000u)
return x + x; /* nan */
return __math_invalidf (0.0f);
}
float
__log1pf (float x)
{
static const double x0[] =
{
0x1.f81f82p-1, 0x1.e9131acp-1, 0x1.dae6077p-1, 0x1.cd85689p-1,
0x1.c0e0704p-1, 0x1.b4e81b5p-1, 0x1.a98ef6p-1, 0x1.9ec8e95p-1,
0x1.948b0fdp-1, 0x1.8acb90fp-1, 0x1.8181818p-1, 0x1.78a4c81p-1,
0x1.702e05cp-1, 0x1.6816817p-1, 0x1.605816p-1, 0x1.58ed231p-1,
0x1.51d07ebp-1, 0x1.4afd6ap-1, 0x1.446f865p-1, 0x1.3e22cbdp-1,
0x1.3813814p-1, 0x1.323e34ap-1, 0x1.2c9fb4ep-1, 0x1.27350b9p-1,
0x1.21fb781p-1, 0x1.1cf06aep-1, 0x1.1811812p-1, 0x1.135c811p-1,
0x1.0ecf56cp-1, 0x1.0a6810ap-1, 0x1.0624dd3p-1, 0x1.0204081p-1
};
static const double lixb[] =
{
0x1.fc0a8909b4218p-7, 0x1.77458f51aac89p-5, 0x1.341d793afb997p-4,
0x1.a926d3a5ebd2ap-4, 0x1.0d77e7a8a823dp-3, 0x1.44d2b6c557102p-3,
0x1.7ab89040accecp-3, 0x1.af3c94ecab3d6p-3, 0x1.e27076d54e6c9p-3,
0x1.0a324e3888ad5p-2, 0x1.22941fc0c7357p-2, 0x1.3a64c56ae3fdbp-2,
0x1.51aad874af21fp-2, 0x1.686c81d300eap-2, 0x1.7eaf83c7fa9b5p-2,
0x1.947941aa610ecp-2, 0x1.a9cec9a3f023bp-2, 0x1.beb4d9ea4156ep-2,
0x1.d32fe7f35e5c7p-2, 0x1.e7442617b817ap-2, 0x1.faf588dd5ed1p-2,
0x1.0723e5c635c39p-1, 0x1.109f39d53c99p-1, 0x1.19ee6b38a4668p-1,
0x1.23130d7f93c3bp-1, 0x1.2c0e9ec9b0b85p-1, 0x1.34e289cb35eccp-1,
0x1.3d9026ad3d3f3p-1, 0x1.4618bc1eadbbbp-1, 0x1.4e7d8127dd8a9p-1,
0x1.56bf9d5967092p-1, 0x1.5ee02a926936ep-1
};
static const double lix[] =
{
0x1.fc0a890fc03e4p-7, 0x1.77458f532dcfcp-5, 0x1.341d793bbd1d1p-4,
0x1.a926d3a6ad563p-4, 0x1.0d77e7a908e59p-3, 0x1.44d2b6c5b7d1ep-3,
0x1.7ab890410d909p-3, 0x1.af3c94ed0bff3p-3, 0x1.e27076d5af2e6p-3,
0x1.0a324e38b90e3p-2, 0x1.22941fc0f7966p-2, 0x1.3a64c56b145eap-2,
0x1.51aad874df82dp-2, 0x1.686c81d3314afp-2, 0x1.7eaf83c82afc3p-2,
0x1.947941aa916fbp-2, 0x1.a9cec9a42084ap-2, 0x1.beb4d9ea71b7cp-2,
0x1.d32fe7f38ebd5p-2, 0x1.e7442617e8788p-2, 0x1.faf588dd8f31fp-2,
0x1.0723e5c64df4p-1, 0x1.109f39d554c97p-1, 0x1.19ee6b38bc96fp-1,
0x1.23130d7fabf43p-1, 0x1.2c0e9ec9c8e8cp-1, 0x1.34e289cb4e1d3p-1,
0x1.3d9026ad556fbp-1, 0x1.4618bc1ec5ec2p-1, 0x1.4e7d8127f5bb1p-1,
0x1.56bf9d597f399p-1, 0x1.5ee02a9281675p-1
};
static const double b[] =
{
0x1p+0,
-0x1p-1,
0x1.5555555556f6bp-2,
-0x1.00000000029b9p-2,
0x1.9999988d176e4p-3,
-0x1.55555418889a7p-3,
0x1.24adeca50e2bcp-3,
-0x1.001ba33bf57cfp-3
};
double z = x;
uint32_t ux = asuint (x);
uint32_t ax = ux & (~0u >> 1);
if (__glibc_likely (ax < 0x3c880000))
{
if (__glibc_unlikely (ax < 0x33000000))
{
if (!ax)
return x;
return fmaf (x, -x, x);
}
double z2 = z * z, z4 = z2 * z2;
double f = z2
* ((b[1] + z * b[2]) + z2 * (b[3] + z * b[4])
+ z4 * ((b[5] + z * b[6]) + z2 * b[7]));
double r = z + f;
if (__glibc_unlikely ((asuint64 (r) & 0xfffffffll) == 0))
r += 0x1p14 * (f + (z - r));
return r;
}
else
{
if (__glibc_unlikely (ux >= 0xbf800000u || ax >= 0x7f800000))
return as_special (x);
uint64_t tp = asuint64 (z + 1);
int e = tp >> 52;
uint64_t m52 = tp & (~(uint64_t) 0 >> 12);
unsigned int j = (tp >> (52 - 5)) & 31;
e -= 0x3ff;
double xd = asdouble (m52 | ((uint64_t) 0x3ff << 52));
z = xd * x0[j] - 1;
static const double c[] =
{
-0x1.3902c33434e7fp-43, 0x1.ffffffe1cbed5p-1, -0x1.ffffff7d1b014p-2,
0x1.5564e0ed3613ap-2, -0x1.0012232a00d4ap-2
};
const double ln2 = 0x1.62e42fefa39efp-1;
double z2 = z * z,
r = (ln2 * e + lixb[j])
+ z * ((c[1] + z * c[2]) + z2 * (c[3] + z * c[4]));
float ub = r;
float lb = r + 2.2e-11;
if (__glibc_unlikely (ub != lb))
{
double z4 = z2 * z2,
f = z
* ((b[0] + z * b[1]) + z2 * (b[2] + z * b[3])
+ z4 * ((b[4] + z * b[5]) + z2 * (b[6] + z * b[7])));
const double ln2l = 0x1.7f7d1cf79abcap-20, ln2h = 0x1.62e4p-1;
double Lh = ln2h * e;
double Ll = ln2l * e;
double rl = f + Ll + lix[j];
double tr = rl + Lh;
if (__glibc_unlikely ((asuint64 (tr) & 0xfffffffll) == 0))
{
if (x == -0x1.247ab0p-6)
return -0x1.271f0ep-6f - 0x1p-31f;
if (x == -0x1.3a415ep-5)
return -0x1.407112p-5f + 0x1p-30f;
if (x == 0x1.fb035ap-2)
return 0x1.9bddc2p-2f + 0x1p-27f;
tr += 64 * (rl + (Lh - tr));
}
else if (rl + (Lh - tr) == 0.0)
{
if (x == 0x1.b7fd86p-4)
return 0x1.a1ece2p-4f + 0x1p-29f;
if (x == -0x1.3a415ep-5)
return -0x1.407112p-5f + 0x1p-30f;
if (x == 0x1.43c7e2p-6)
return 0x1.409f80p-6f + 0x1p-31f;
}
ub = tr;
}
return ub;
}
}
libm_alias_float (__log1p, log1p)
strong_alias (__log1pf, __logp1f)
libm_alias_float (__logp1, logp1)
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