-/* Correctly-rounded biased argument natural logarithm function for binary32
- value.
+/* Correctly-rounded log2(1+x) function for binary32 value.
-Copyright (c) 2022-2024 Alexei Sibidanov.
+Copyright (c) 2022-2026 Alexei Sibidanov.
This file is part of the CORE-MATH project
-project (file src/binary32/log2p1/log2p1f.c revision bc385c2).
+project (file src/binary32/log2p1/log2p1f.c revision 3fbe16be).
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
#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
__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 struct
+ {
+ float x;
+ float f, df;
+ } tb[] = {
+ { 0x1.7a13c6p+30, 0x1.e90026p+4, 0x1p-21 },
+ { -0x1.da285cp-5, -0x1.60549p-4, 0x1p-29 },
+ };
+ // the reciprocal 1/(1+j/64) is rounded to 24 bits
+ static const double ix[] = {
+ 0x1p+0, 0x1.f81f82p-1, 0x1.f07c2p-1, 0x1.e9131ap-1, 0x1.e1e1e2p-1,
+ 0x1.dae608p-1, 0x1.d41d42p-1, 0x1.cd8568p-1, 0x1.c71c72p-1, 0x1.c0e07p-1,
+ 0x1.bacf92p-1, 0x1.b4e81cp-1, 0x1.af286cp-1, 0x1.a98ef6p-1, 0x1.a41a42p-1,
+ 0x1.9ec8eap-1, 0x1.99999ap-1, 0x1.948b1p-1, 0x1.8f9c18p-1, 0x1.8acb9p-1,
+ 0x1.861862p-1, 0x1.818182p-1, 0x1.7d05f4p-1, 0x1.78a4c8p-1, 0x1.745d18p-1,
+ 0x1.702e06p-1, 0x1.6c16c2p-1, 0x1.681682p-1, 0x1.642c86p-1, 0x1.605816p-1,
+ 0x1.5c9882p-1, 0x1.58ed24p-1, 0x1.555556p-1, 0x1.51d07ep-1, 0x1.4e5e0ap-1,
+ 0x1.4afd6ap-1, 0x1.47ae14p-1, 0x1.446f86p-1, 0x1.414142p-1, 0x1.3e22ccp-1,
+ 0x1.3b13b2p-1, 0x1.381382p-1, 0x1.3521dp-1, 0x1.323e34p-1, 0x1.2f684cp-1,
+ 0x1.2c9fb4p-1, 0x1.29e412p-1, 0x1.27350cp-1, 0x1.24924ap-1, 0x1.21fb78p-1,
+ 0x1.1f7048p-1, 0x1.1cf06ap-1, 0x1.1a7b96p-1, 0x1.181182p-1, 0x1.15b1e6p-1,
+ 0x1.135c82p-1, 0x1.111112p-1, 0x1.0ecf56p-1, 0x1.0c9714p-1, 0x1.0a681p-1,
+ 0x1.08421p-1, 0x1.0624dep-1, 0x1.041042p-1, 0x1.020408p-1, 0x1p-1
+ };
+
+ // the logarithm of the reciprocal is biased by 0x1.dp-45 so log2p1_fast(x) -
+ // log2p1(x) < 0
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
+ 0x1.dp-45, -0x1.6e7966ead50c5p-6, -0x1.6bad2043a6a91p-5,
+ -0x1.0eb392fe78f6fp-4, -0x1.663f6e3b3bd32p-4, -0x1.bc841cd433853p-4,
+ -0x1.08c587b8a7d19p-3, -0x1.32aea1c2dd96p-3, -0x1.5c01a22e687e4p-3,
+ -0x1.84c2be74443dap-3, -0x1.acf5de2afbd5ap-3, -0x1.d49ee012d2a36p-3,
+ -0x1.fbc16a1ed1966p-3, -0x1.11307dc445c4cp-2, -0x1.2440796db6523p-2,
+ -0x1.37124a7b0e1dap-2, -0x1.49a7834b7d089p-2, -0x1.5c01a2e712f36p-2,
+ -0x1.6e22207523bcdp-2, -0x1.800a59ccb4b43p-2, -0x1.91bba6c447a2fp-2,
+ -0x1.a3375ec336f01p-2, -0x1.b47ebfcfdd0dap-2, -0x1.c592fb2eea99p-2,
+ -0x1.d6753b20857bp-2, -0x1.e726a9208b01ep-2, -0x1.f7a8543486f32p-2,
+ -0x1.03fda781da376p-1, -0x1.0c104f268ec39p-1, -0x1.140c9fb5a8dafp-1,
+ -0x1.1bf31371c6a2p-1, -0x1.23c41b2f88f63p-1, -0x1.2b803302a31a2p-1,
+ -0x1.3327c82828c7dp-1, -0x1.3abb40a7ec0afp-1, -0x1.423b07f511315p-1,
+ -0x1.49a785d1d0f4ap-1, -0x1.51011934bf518p-1, -0x1.584820b2f56a4p-1,
+ -0x1.5f7cfece7619p-1, -0x1.66a00716cedc6p-1, -0x1.6db194ce2d40ap-1,
+ -0x1.74b1fcac361d3p-1, -0x1.7ba1911bb9cf6p-1, -0x1.82809cff91ccap-1,
+ -0x1.894f76c358469p-1, -0x1.900e62e869cdfp-1, -0x1.96bdabfeb6a28p-1,
+ -0x1.9d5d9dab023d9p-1, -0x1.a3ee7f670bf3cp-1, -0x1.aa708efbac12bp-1,
+ -0x1.b0e414a155bfcp-1, -0x1.b74949237d9f7p-1, -0x1.bda06f68b3e6ep-1,
+ -0x1.c3e9ca1704a0fp-1, -0x1.ca258b4fc9ea1p-1, -0x1.d053f44c0c9e7p-1,
+ -0x1.d675400a8d4b1p-1, -0x1.dc899d687d98ep-1, -0x1.e29144ae898b8p-1,
+ -0x1.e88c6ca77b00ep-1, -0x1.ee7b44ce9bdc6p-1, -0x1.f45e05f15ca47p-1,
+ -0x1.fa34e145a695p-1, -0x1.ffffffffffe3p-1
+ };
+ static const double b[] = {
+ 0x1.7154765bab3edp+0, -0x1.71574d692522fp-1, 0x1.ec60b55c8f05p-2
+ };
+ static const double c[] = {
+ 0x1.71547652b8314p+0, -0x1.71547652b7f67p-1, 0x1.ec709db872c6dp-2,
+ -0x1.715476b06590ep-2, 0x1.277c72c128c69p-2, -0x1.ec4ff30af701bp-3
+ };
+ static const double g[] = {
+ 0x1.4ae0bf64f73a1p-26, -0x1.71547652b82fap-1, 0x1.ec709dc3bd7dep-2,
+ -0x1.71547652e6faap-2, 0x1.2776c0ff5c16ep-2, -0x1.ec70942dfbb5bp-3,
+ 0x1.a673c6b6e2fa3p-3, -0x1.71b0db8113c46p-3
};
double z = x;
uint32_t ux = asuint (x);
+ if (__glibc_unlikely (ux >= 0xbf800000u))
+ return as_special (x); // x<=-1, x=-inf, x=-nan
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])));
- }
+ if (__glibc_unlikely (ax >= 0x7f800000u))
+ return as_special (x); // x=+inf, x=+nan
+ if (__glibc_unlikely (ax < 0x3cc00000u))
+ { // |x|<0.0234375
+ if (__glibc_unlikely (ax <= 0x58b90bu))
+ { // |x|<=0x1-126*ln(2)
+ if (ax == 0)
+ return x; // log2p1(-0.0) = -0.0 and log2p1(+0.0) = +0.0
+ return z * 0x1.71547652b82fep+0;
}
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;
+ double z2 = z * z, z4 = z2 * z2;
+ double f = z
+ * ((g[0] + z * g[1]) + z2 * (g[2] + z * g[3])
+ + z4 * ((g[4] + z * g[5]) + z2 * (g[6] + z * g[7])));
+ f += z * 0x1.715476p+0; // the product is exact
+ return f;
}
- 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);
-#ifndef __FP_FAST_FMA
- /* The fma is required only for x == -0x1.da285cp-5f in FE_TONEAREST
- to provide correctly rounded results. */
- if (__glibc_likely (x != -0x1.da285cp-5f))
- z = xd * ix[j] - 1.0;
- else
-#endif
- 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;
}
+ uint64_t tp = asuint64 (z + 1.0);
+ int e = (tp >> 52) - UINT64_C(0x3ff);
+ uint64_t m = tp & (~0ull >> 12);
+ if (__glibc_unlikely (!m))
+ return e; // do not raise the inexact exception for 1+x = 2^n
+ int32_t j = (m + (1ull << (52 - 7))) >> (52 - 6);
+ double xd = asdouble (m | UINT64_C(0x3ff) << 52);
+ double d = xd * ix[j] - 1.0, d2 = d * d,
+ el = e - lix[j]; // d is exact for x < 0x1.04p+29
+ double f = (el + d * b[0]) + d2 * (b[1] + d * b[2]);
+ float lb = f, ub = f + 0x1.661p-32;
+ if (__glibc_likely (lb == ub))
+ return lb;
+ for (int i = 0; i < 2; i++)
+ if (__glibc_unlikely (ux == asuint (tb[i].x)))
+ return tb[i].f + tb[i].df;
+ double c0 = c[0] + d * c[1];
+ double c2 = c[2] + d * c[3];
+ double c4 = c[4] + d * c[5];
+ c0 += d2 * (c2 + d2 * c4);
+ f = e + (0x1.dp-45 - lix[j]) + d * c0;
+ lb = f;
+ return lb;
}
libm_alias_float (__log2p1, log2p1)
projects / thirdparty / glibc.git / commitdiff
