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/* Correctly-rounded biased argument natural logarithm function for binary32
value.
Copyright (c) 2022-2024 Alexei Sibidanov.
This file is part of the CORE-MATH project
project (file src/binary32/log2p1/log2p1f.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 <errno.h>
#include <math.h>
#include <math-underflow.h>
#include <libm-alias-float.h>
#include "math_config.h"
float
__log2p1f (float x)
{
static const double ix[] =
{
0x1p+0, 0x1.fc07f01fcp-1, 0x1.f81f81f82p-1,
0x1.f44659e4ap-1, 0x1.f07c1f07cp-1, 0x1.ecc07b302p-1,
0x1.e9131abfp-1, 0x1.e573ac902p-1, 0x1.e1e1e1e1ep-1,
0x1.de5d6e3f8p-1, 0x1.dae6076bap-1, 0x1.d77b654b8p-1,
0x1.d41d41d42p-1, 0x1.d0cb58f6ep-1, 0x1.cd8568904p-1,
0x1.ca4b3055ep-1, 0x1.c71c71c72p-1, 0x1.c3f8f01c4p-1,
0x1.c0e070382p-1, 0x1.bdd2b8994p-1, 0x1.bacf914c2p-1,
0x1.b7d6c3ddap-1, 0x1.b4e81b4e8p-1, 0x1.b2036406cp-1,
0x1.af286bca2p-1, 0x1.ac5701ac6p-1, 0x1.a98ef606ap-1,
0x1.a6d01a6dp-1, 0x1.a41a41a42p-1, 0x1.a16d3f97ap-1,
0x1.9ec8e951p-1, 0x1.9c2d14ee4p-1, 0x1.99999999ap-1,
0x1.970e4f80cp-1, 0x1.948b0fcd6p-1, 0x1.920fb49dp-1,
0x1.8f9c18f9cp-1, 0x1.8d3018d3p-1, 0x1.8acb90f6cp-1,
0x1.886e5f0acp-1, 0x1.861861862p-1, 0x1.83c977ab2p-1,
0x1.818181818p-1, 0x1.7f405fd02p-1, 0x1.7d05f417ep-1,
0x1.7ad2208ep-1, 0x1.78a4c8178p-1, 0x1.767dce434p-1,
0x1.745d1745ep-1, 0x1.724287f46p-1, 0x1.702e05c0cp-1,
0x1.6e1f76b44p-1, 0x1.6c16c16c2p-1, 0x1.6a13cd154p-1,
0x1.681681682p-1, 0x1.661ec6a52p-1, 0x1.642c8590cp-1,
0x1.623fa7702p-1, 0x1.605816058p-1, 0x1.5e75bb8dp-1,
0x1.5c9882b94p-1, 0x1.5ac056b02p-1, 0x1.58ed23082p-1,
0x1.571ed3c5p-1, 0x1.555555556p-1, 0x1.5390948f4p-1,
0x1.51d07eae2p-1, 0x1.501501502p-1, 0x1.4e5e0a73p-1,
0x1.4cab88726p-1, 0x1.4afd6a052p-1, 0x1.49539e3b2p-1,
0x1.47ae147aep-1, 0x1.460cbc7f6p-1, 0x1.446f86562p-1,
0x1.42d6625d6p-1, 0x1.414141414p-1, 0x1.3fb013fbp-1,
0x1.3e22cbce4p-1, 0x1.3c995a47cp-1, 0x1.3b13b13b2p-1,
0x1.3991c2c18p-1, 0x1.381381382p-1, 0x1.3698df3dep-1,
0x1.3521cfb2cp-1, 0x1.33ae45b58p-1, 0x1.323e34a2cp-1,
0x1.30d19013p-1, 0x1.2f684bda2p-1, 0x1.2e025c04cp-1,
0x1.2c9fb4d82p-1, 0x1.2b404ad02p-1, 0x1.29e4129e4p-1,
0x1.288b01288p-1, 0x1.27350b882p-1, 0x1.25e22708p-1,
0x1.24924924ap-1, 0x1.23456789ap-1, 0x1.21fb78122p-1,
0x1.20b470c68p-1, 0x1.1f7047dc2p-1, 0x1.1e2ef3b4p-1,
0x1.1cf06ada2p-1, 0x1.1bb4a4046p-1, 0x1.1a7b9611ap-1,
0x1.19453808cp-1, 0x1.181181182p-1, 0x1.16e068942p-1,
0x1.15b1e5f76p-1, 0x1.1485f0e0ap-1, 0x1.135c81136p-1,
0x1.12358e75ep-1, 0x1.111111112p-1, 0x1.0fef010fep-1,
0x1.0ecf56be6p-1, 0x1.0db20a89p-1, 0x1.0c9714fbcp-1,
0x1.0b7e6ec26p-1, 0x1.0a6810a68p-1, 0x1.0953f3902p-1,
0x1.084210842p-1, 0x1.073260a48p-1, 0x1.0624dd2f2p-1,
0x1.05197f7d8p-1, 0x1.041041042p-1, 0x1.03091b52p-1,
0x1.020408102p-1, 0x1.01010101p-1, 0x1p-1
};
static const double lix[] = {
0x0p+0, -0x1.6fe50b6f1eafap-7, -0x1.6e79685c160d5p-6,
-0x1.11cd1d51955bap-5, -0x1.6bad37591e03p-5, -0x1.c4dfab908ddb5p-5,
-0x1.0eb389fab4795p-4, -0x1.3aa2fdd26ae99p-4, -0x1.663f6faca846bp-4,
-0x1.918a16e4cb157p-4, -0x1.bc84240a78a13p-4, -0x1.e72ec1181cfb1p-4,
-0x1.08c588cd964e4p-3, -0x1.1dcd19759f2e3p-3, -0x1.32ae9e27627c6p-3,
-0x1.476a9f989a58ap-3, -0x1.5c01a39fa6533p-3, -0x1.70742d4eed455p-3,
-0x1.84c2bd02d6434p-3, -0x1.98edd077e9f0ap-3, -0x1.acf5e2db31eeap-3,
-0x1.c0db6cddaa82dp-3, -0x1.d49ee4c33121ap-3, -0x1.e840be751d775p-3,
-0x1.fbc16b9003e0bp-3, -0x1.0790adbae3fcp-2, -0x1.11307dad465b5p-2,
-0x1.1ac05b2924cc5p-2, -0x1.24407ab0cc41p-2, -0x1.2db10fc4ea424p-2,
-0x1.37124cea58697p-2, -0x1.406463b1d455dp-2, -0x1.49a784bcbaa37p-2,
-0x1.52dbdfc4f341dp-2, -0x1.5c01a39ff2c9bp-2, -0x1.6518fe46abaa5p-2,
-0x1.6e221cd9d6933p-2, -0x1.771d2ba7f5791p-2, -0x1.800a56315ee2ap-2,
-0x1.88e9c72df8611p-2, -0x1.91bba891d495fp-2, -0x1.9a8023920fa4dp-2,
-0x1.a33760a7fbca6p-2, -0x1.abe18797d2effp-2, -0x1.b47ebf734b923p-2,
-0x1.bd0f2e9eb2b84p-2, -0x1.c592fad2be1aap-2, -0x1.ce0a4923cf5e6p-2,
-0x1.d6753e02f4ebcp-2, -0x1.ded3fd445afp-2, -0x1.e726aa1e558fep-2,
-0x1.ef6d67325ba38p-2, -0x1.f7a8568c8aea6p-2, -0x1.ffd799a81be87p-2,
0x1.f804ae8d33c4p-2, 0x1.efec61b04af4ep-2, 0x1.e7df5fe572606p-2,
0x1.dfdd89d5b0009p-2, 0x1.d7e6c0abbd924p-2, 0x1.cffae611a74d6p-2,
0x1.c819dc2d8578cp-2, 0x1.c043859e5bdbcp-2, 0x1.b877c57b47c04p-2,
0x1.b0b67f4f29a66p-2, 0x1.a8ff97183ed07p-2, 0x1.a152f14293c74p-2,
0x1.99b072a9289cap-2, 0x1.921800927e284p-2, 0x1.8a8980ac4113p-2,
0x1.8304d90c2859dp-2, 0x1.7b89f02cbd49ap-2, 0x1.7418aceb84ab1p-2,
0x1.6cb0f68656c95p-2, 0x1.6552b49993dc2p-2, 0x1.5dfdcf1eacd7bp-2,
0x1.56b22e6b97c18p-2, 0x1.4f6fbb2ce6943p-2, 0x1.48365e6957b42p-2,
0x1.4106017c0dbcfp-2, 0x1.39de8e15727d9p-2, 0x1.32bfee37489bcp-2,
0x1.2baa0c34989c3p-2, 0x1.249cd2b177fd5p-2, 0x1.1d982c9d50468p-2,
0x1.169c0536677acp-2, 0x1.0fa848045f67bp-2, 0x1.08bce0d9a7c6p-2,
0x1.01d9bbcf66a2cp-2, 0x1.f5fd8a90e2d85p-3, 0x1.e857d3d3af1e5p-3,
0x1.dac22d3ec5f4ep-3, 0x1.cd3c712db459ap-3, 0x1.bfc67a7ff3c22p-3,
0x1.b2602497678f4p-3, 0x1.a5094b555a1f8p-3, 0x1.97c1cb136b96fp-3,
0x1.8a8980ac8652dp-3, 0x1.7d60496c83f66p-3, 0x1.7046031c7cdafp-3,
0x1.633a8bf460335p-3, 0x1.563dc2a08b102p-3, 0x1.494f863bbc1dep-3,
0x1.3c6fb6507a37ep-3, 0x1.2f9e32d5257ecp-3, 0x1.22dadc2a627efp-3,
0x1.1625931802e49p-3, 0x1.097e38cef9519p-3, 0x1.f9c95dc138295p-4,
0x1.e0b1ae90505f6p-4, 0x1.c7b528b5fcffap-4, 0x1.aed391abb17a1p-4,
0x1.960caf9bd35eap-4, 0x1.7d60496e3edebp-4, 0x1.64ce26bf2108ep-4,
0x1.4c560fe5b573bp-4, 0x1.33f7cde24adfbp-4, 0x1.1bb32a5ed9353p-4,
0x1.0387efbd3006ep-4, 0x1.d6ebd1f1d0955p-5, 0x1.a6f9c37a8beabp-5,
0x1.77394c9d6762cp-5, 0x1.47aa07358e1a4p-5, 0x1.184b8e4d490efp-5,
0x1.d23afc4d95c78p-6, 0x1.743ee8678a7cbp-6, 0x1.16a21e243bf78p-6,
0x1.72c7ba20c907ep-7, 0x1.720d9c0536e17p-8, 0x0p+0
};
double z = x;
uint32_t ux = asuint (x);
uint32_t ax = ux & (~0u >> 1);
if (__glibc_unlikely (ux >= 0x17fu << 23))
{ /* x <= -1 */
if (ux == (0x17fu << 23))
return __math_divzerof (1);
if (ux > (0x1ffu << 23))
return x + x; /* nan */
return __math_invalidf (x);
}
else if (__glibc_unlikely (ax >= (0xff << 23)))
{ /* +inf, nan */
if (ax > (0xff << 23))
return x + x; /* nan */
return INFINITY;
}
else if (__glibc_likely (ax < 0x3cb7aa26u))
{ /* |x| < 0x1.6f544cp-6 */
double z2 = z * z, z4 = z2 * z2;
if ( __glibc_likely (ax < 0x3b9d9d34u))
{ /* |x| < 0x1.3b3a68p-8 */
if (__glibc_likely (ax < 0x39638a7eu))
{ /* |x| < 0x1.c714fcp-13 */
if (__glibc_likely (ax < 0x329c5639u))
{ /* |x| < 0x1.38ac72p-26 */
static const double c[] =
{
0x1.71547652b82fep+0, -0x1.71547652b82ffp-1
};
return z * (c[0] + z * c[1]);
}
else
{
if (__glibc_unlikely (ux == 0x32ff7045u))
return 0x1.70851ap-25f - 0x1.8p-80f;
if (__glibc_unlikely (ux == 0xb395efbbu))
return -0x1.b0a00ap-24f + 0x1p-76f;
if (__glibc_unlikely (ux == 0x35a14df7u))
return 0x1.d16d2p-20f + 0x1p-72f;
if (__glibc_unlikely (ux == 0x3841cb81u))
return 0x1.17949ep-14f + 0x1p-67f;
static const double c[] =
{
0x1.71547652b82fep+0, -0x1.71547652b82fdp-1,
0x1.ec709ead0c9a7p-2, -0x1.7154773c1cb29p-2
};
return z * ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]));
}
}
else
{
if (__glibc_unlikely (ux == 0xbac9363du))
return -0x1.2282aap-9f + 0x1p-61f;
static const double c[] =
{
0x1.71547652b82fep+0, -0x1.71547652b83p-1,
0x1.ec709dc28f51bp-2, -0x1.7154765157748p-2,
0x1.2778a510a3682p-2, -0x1.ec745df1551fcp-3
};
return z
* ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3])
+ z4 * ((c[4] + z * c[5])));
}
}
else
{
static const double c[] =
{
0x1.71547652b82fep+0, -0x1.71547652b82fbp-1,
0x1.ec709dc3b6a73p-2, -0x1.71547652dc09p-2,
0x1.2776c1a88901p-2, -0x1.ec7095bd4d208p-3,
0x1.a66bec7fc8f7p-3, -0x1.71a900fc3f3f9p-3
};
return z
* ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3])
+ z4 * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7])));
}
}
else
{ /* |x| >= 0x1.6f544cp-6 */
float h, l;
/* With gcc 6.3.0, if we return 0x1.e90026p+4f + 0x1.fp-21
in the second exceptional case, with rounding up it yields
0x1.e90026p+4 which is incorrect, thus we use this workaround. See
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=112367. */
if (__glibc_unlikely (ux == 0x52928e33u))
{
h = 0x1.318ffap+5f;
l = 0x1.fp-20f;
return h + l;
}
if (__glibc_unlikely (ux == 0x4ebd09e3u))
{
h = 0x1.e90026p+4f;
l = 0x1.fp-21;
return h + l;
}
uint64_t tp = asuint64 (z + 1.0);
uint64_t m = tp & (~(uint64_t) 0 >> 12);
int e = (tp >> 52) - 0x3ff;
int j = (m + ((int64_t) 1 << (52 - 8))) >> (52 - 7), k = j > 53;
e += k;
double xd = asdouble (m | (uint64_t) 0x3ff << 52);
z = fma (xd, ix[j], -1.0);
static const double c[] =
{
0x1.71547652b82fep+0, -0x1.71547652b82ffp-1, 0x1.ec709dc32988bp-2,
-0x1.715476521ec2bp-2, 0x1.277801a1ad904p-2, -0x1.ec731704d6a88p-3
};
double z2 = z * z;
double c0 = c[0] + z * c[1];
double c2 = c[2] + z * c[3];
double c4 = c[4] + z * c[5];
c0 += z2 * (c2 + z2 * c4);
return (z * c0 - lix[j]) + e;
}
}
libm_alias_float (__log2p1, log2p1)
|
