1 //===-- Common constants for math functions ---------------------*- C++ -*-===//
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 //===----------------------------------------------------------------------===//
9 #include "common_constants.h"
11 namespace __llvm_libc
{
13 // Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
14 const double ONE_OVER_F
[128] = {
15 0x1.0000000000000p
+0, 0x1.fc07f01fc07f0p
-1, 0x1.f81f81f81f820p
-1,
16 0x1.f44659e4a4271p
-1, 0x1.f07c1f07c1f08p
-1, 0x1.ecc07b301ecc0p
-1,
17 0x1.e9131abf0b767p
-1, 0x1.e573ac901e574p
-1, 0x1.e1e1e1e1e1e1ep
-1,
18 0x1.de5d6e3f8868ap
-1, 0x1.dae6076b981dbp
-1, 0x1.d77b654b82c34p
-1,
19 0x1.d41d41d41d41dp
-1, 0x1.d0cb58f6ec074p
-1, 0x1.cd85689039b0bp
-1,
20 0x1.ca4b3055ee191p
-1, 0x1.c71c71c71c71cp
-1, 0x1.c3f8f01c3f8f0p
-1,
21 0x1.c0e070381c0e0p
-1, 0x1.bdd2b899406f7p
-1, 0x1.bacf914c1bad0p
-1,
22 0x1.b7d6c3dda338bp
-1, 0x1.b4e81b4e81b4fp
-1, 0x1.b2036406c80d9p
-1,
23 0x1.af286bca1af28p
-1, 0x1.ac5701ac5701bp
-1, 0x1.a98ef606a63bep
-1,
24 0x1.a6d01a6d01a6dp
-1, 0x1.a41a41a41a41ap
-1, 0x1.a16d3f97a4b02p
-1,
25 0x1.9ec8e951033d9p
-1, 0x1.9c2d14ee4a102p
-1, 0x1.999999999999ap
-1,
26 0x1.970e4f80cb872p
-1, 0x1.948b0fcd6e9e0p
-1, 0x1.920fb49d0e229p
-1,
27 0x1.8f9c18f9c18fap
-1, 0x1.8d3018d3018d3p
-1, 0x1.8acb90f6bf3aap
-1,
28 0x1.886e5f0abb04ap
-1, 0x1.8618618618618p
-1, 0x1.83c977ab2beddp
-1,
29 0x1.8181818181818p
-1, 0x1.7f405fd017f40p
-1, 0x1.7d05f417d05f4p
-1,
30 0x1.7ad2208e0ecc3p
-1, 0x1.78a4c8178a4c8p
-1, 0x1.767dce434a9b1p
-1,
31 0x1.745d1745d1746p
-1, 0x1.724287f46debcp
-1, 0x1.702e05c0b8170p
-1,
32 0x1.6e1f76b4337c7p
-1, 0x1.6c16c16c16c17p
-1, 0x1.6a13cd1537290p
-1,
33 0x1.6816816816817p
-1, 0x1.661ec6a5122f9p
-1, 0x1.642c8590b2164p
-1,
34 0x1.623fa77016240p
-1, 0x1.6058160581606p
-1, 0x1.5e75bb8d015e7p
-1,
35 0x1.5c9882b931057p
-1, 0x1.5ac056b015ac0p
-1, 0x1.58ed2308158edp
-1,
36 0x1.571ed3c506b3ap
-1, 0x1.5555555555555p
-1, 0x1.5390948f40febp
-1,
37 0x1.51d07eae2f815p
-1, 0x1.5015015015015p
-1, 0x1.4e5e0a72f0539p
-1,
38 0x1.4cab88725af6ep
-1, 0x1.4afd6a052bf5bp
-1, 0x1.49539e3b2d067p
-1,
39 0x1.47ae147ae147bp
-1, 0x1.460cbc7f5cf9ap
-1, 0x1.446f86562d9fbp
-1,
40 0x1.42d6625d51f87p
-1, 0x1.4141414141414p
-1, 0x1.3fb013fb013fbp
-1,
41 0x1.3e22cbce4a902p
-1, 0x1.3c995a47babe7p
-1, 0x1.3b13b13b13b14p
-1,
42 0x1.3991c2c187f63p
-1, 0x1.3813813813814p
-1, 0x1.3698df3de0748p
-1,
43 0x1.3521cfb2b78c1p
-1, 0x1.33ae45b57bcb2p
-1, 0x1.323e34a2b10bfp
-1,
44 0x1.30d190130d190p
-1, 0x1.2f684bda12f68p
-1, 0x1.2e025c04b8097p
-1,
45 0x1.2c9fb4d812ca0p
-1, 0x1.2b404ad012b40p
-1, 0x1.29e4129e4129ep
-1,
46 0x1.288b01288b013p
-1, 0x1.27350b8812735p
-1, 0x1.25e22708092f1p
-1,
47 0x1.2492492492492p
-1, 0x1.23456789abcdfp
-1, 0x1.21fb78121fb78p
-1,
48 0x1.20b470c67c0d9p
-1, 0x1.1f7047dc11f70p
-1, 0x1.1e2ef3b3fb874p
-1,
49 0x1.1cf06ada2811dp
-1, 0x1.1bb4a4046ed29p
-1, 0x1.1a7b9611a7b96p
-1,
50 0x1.19453808ca29cp
-1, 0x1.1811811811812p
-1, 0x1.16e0689427379p
-1,
51 0x1.15b1e5f75270dp
-1, 0x1.1485f0e0acd3bp
-1, 0x1.135c81135c811p
-1,
52 0x1.12358e75d3033p
-1, 0x1.1111111111111p
-1, 0x1.0fef010fef011p
-1,
53 0x1.0ecf56be69c90p
-1, 0x1.0db20a88f4696p
-1, 0x1.0c9714fbcda3bp
-1,
54 0x1.0b7e6ec259dc8p
-1, 0x1.0a6810a6810a7p
-1, 0x1.0953f39010954p
-1,
55 0x1.0842108421084p
-1, 0x1.073260a47f7c6p
-1, 0x1.0624dd2f1a9fcp
-1,
56 0x1.05197f7d73404p
-1, 0x1.0410410410410p
-1, 0x1.03091b51f5e1ap
-1,
57 0x1.0204081020408p
-1, 0x1.0101010101010p
-1};
59 // Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
60 const double LOG_F
[128] = {
61 0x0.0000000000000p
+0, 0x1.fe02a6b106788p
-8, 0x1.fc0a8b0fc03e3p
-7,
62 0x1.7b91b07d5b11ap
-6, 0x1.f829b0e783300p
-6, 0x1.39e87b9febd5fp
-5,
63 0x1.77458f632dcfcp
-5, 0x1.b42dd711971bep
-5, 0x1.f0a30c01162a6p
-5,
64 0x1.16536eea37ae0p
-4, 0x1.341d7961bd1d0p
-4, 0x1.51b073f06183fp
-4,
65 0x1.6f0d28ae56b4bp
-4, 0x1.8c345d6319b20p
-4, 0x1.a926d3a4ad563p
-4,
66 0x1.c5e548f5bc743p
-4, 0x1.e27076e2af2e5p
-4, 0x1.fec9131dbeabap
-4,
67 0x1.0d77e7cd08e59p
-3, 0x1.1b72ad52f67a0p
-3, 0x1.29552f81ff523p
-3,
68 0x1.371fc201e8f74p
-3, 0x1.44d2b6ccb7d1ep
-3, 0x1.526e5e3a1b437p
-3,
69 0x1.5ff3070a793d3p
-3, 0x1.6d60fe719d21cp
-3, 0x1.7ab890210d909p
-3,
70 0x1.87fa06520c910p
-3, 0x1.9525a9cf456b4p
-3, 0x1.a23bc1fe2b563p
-3,
71 0x1.af3c94e80bff2p
-3, 0x1.bc286742d8cd6p
-3, 0x1.c8ff7c79a9a21p
-3,
72 0x1.d5c216b4fbb91p
-3, 0x1.e27076e2af2e5p
-3, 0x1.ef0adcbdc5936p
-3,
73 0x1.fb9186d5e3e2ap
-3, 0x1.0402594b4d040p
-2, 0x1.0a324e27390e3p
-2,
74 0x1.1058bf9ae4ad5p
-2, 0x1.1675cababa60ep
-2, 0x1.1c898c16999fap
-2,
75 0x1.22941fbcf7965p
-2, 0x1.2895a13de86a3p
-2, 0x1.2e8e2bae11d30p
-2,
76 0x1.347dd9a987d54p
-2, 0x1.3a64c556945e9p
-2, 0x1.404308686a7e3p
-2,
77 0x1.4618bc21c5ec2p
-2, 0x1.4be5f957778a0p
-2, 0x1.51aad872df82dp
-2,
78 0x1.5767717455a6cp
-2, 0x1.5d1bdbf5809cap
-2, 0x1.62c82f2b9c795p
-2,
79 0x1.686c81e9b14aep
-2, 0x1.6e08eaa2ba1e3p
-2, 0x1.739d7f6bbd006p
-2,
80 0x1.792a55fdd47a2p
-2, 0x1.7eaf83b82afc3p
-2, 0x1.842d1da1e8b17p
-2,
81 0x1.89a3386c1425ap
-2, 0x1.8f11e873662c7p
-2, 0x1.947941c2116fap
-2,
82 0x1.99d958117e08ap
-2, 0x1.9f323ecbf984bp
-2, 0x1.a484090e5bb0ap
-2,
83 0x1.a9cec9a9a0849p
-2, 0x1.af1293247786bp
-2, 0x1.b44f77bcc8f62p
-2,
84 0x1.b9858969310fbp
-2, 0x1.beb4d9da71b7bp
-2, 0x1.c3dd7a7cdad4dp
-2,
85 0x1.c8ff7c79a9a21p
-2, 0x1.ce1af0b85f3ebp
-2, 0x1.d32fe7e00ebd5p
-2,
86 0x1.d83e7258a2f3ep
-2, 0x1.dd46a04c1c4a0p
-2, 0x1.e24881a7c6c26p
-2,
87 0x1.e744261d68787p
-2, 0x1.ec399d2468cc0p
-2, 0x1.f128f5faf06ecp
-2,
88 0x1.f6123fa7028acp
-2, 0x1.faf588f78f31ep
-2, 0x1.ffd2e0857f498p
-2,
89 0x1.02552a5a5d0fep
-1, 0x1.04bdf9da926d2p
-1, 0x1.0723e5c1cdf40p
-1,
90 0x1.0986f4f573520p
-1, 0x1.0be72e4252a82p
-1, 0x1.0e44985d1cc8bp
-1,
91 0x1.109f39e2d4c96p
-1, 0x1.12f719593efbcp
-1, 0x1.154c3d2f4d5e9p
-1,
92 0x1.179eabbd899a0p
-1, 0x1.19ee6b467c96ep
-1, 0x1.1c3b81f713c24p
-1,
93 0x1.1e85f5e7040d0p
-1, 0x1.20cdcd192ab6dp
-1, 0x1.23130d7bebf42p
-1,
94 0x1.2555bce98f7cbp
-1, 0x1.2795e1289b11ap
-1, 0x1.29d37fec2b08ap
-1,
95 0x1.2c0e9ed448e8bp
-1, 0x1.2e47436e40268p
-1, 0x1.307d7334f10bep
-1,
96 0x1.32b1339121d71p
-1, 0x1.34e289d9ce1d3p
-1, 0x1.37117b54747b5p
-1,
97 0x1.393e0d3562a19p
-1, 0x1.3b68449fffc22p
-1, 0x1.3d9026a7156fap
-1,
98 0x1.3fb5b84d16f42p
-1, 0x1.41d8fe84672aep
-1, 0x1.43f9fe2f9ce67p
-1,
99 0x1.4618bc21c5ec2p
-1, 0x1.48353d1ea88dfp
-1, 0x1.4a4f85db03ebbp
-1,
100 0x1.4c679afccee39p
-1, 0x1.4e7d811b75bb0p
-1, 0x1.50913cc01686bp
-1,
101 0x1.52a2d265bc5aap
-1, 0x1.54b2467999497p
-1, 0x1.56bf9d5b3f399p
-1,
102 0x1.58cadb5cd7989p
-1, 0x1.5ad404c359f2cp
-1, 0x1.5cdb1dc6c1764p
-1,
103 0x1.5ee02a9241675p
-1, 0x1.60e32f44788d8p
-1};
105 // Range reduction constants for logarithms.
106 // r(0) = 1, r(127) = 0.5
107 // r(k) = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + k*2^-7))
108 // The constants are chosen so that v = fma(r, m_x, -1) is exact in single
109 // precision, and -2^-8 <= v < 2^-7.
110 // TODO(lntue): Add reference to how the constants are derived after the
111 // resulting paper is ready.
112 alignas(32) const float R
[128] = {
113 0x1p
0, 0x1.fcp
-1, 0x1.f8p
-1, 0x1.f4p
-1, 0x1.fp
-1, 0x1.ecp
-1, 0x1.e8p
-1,
114 0x1.e4p
-1, 0x1.ep
-1, 0x1.dep
-1, 0x1.dap
-1, 0x1.d6p
-1, 0x1.d4p
-1, 0x1.dp
-1,
115 0x1.ccp
-1, 0x1.cap
-1, 0x1.c6p
-1, 0x1.c4p
-1, 0x1.cp
-1, 0x1.bep
-1, 0x1.bap
-1,
116 0x1.b8p
-1, 0x1.b4p
-1, 0x1.b2p
-1, 0x1.aep
-1, 0x1.acp
-1, 0x1.a8p
-1, 0x1.a6p
-1,
117 0x1.a4p
-1, 0x1.ap
-1, 0x1.9ep
-1, 0x1.9cp
-1, 0x1.98p
-1, 0x1.96p
-1, 0x1.94p
-1,
118 0x1.92p
-1, 0x1.9p
-1, 0x1.8cp
-1, 0x1.8ap
-1, 0x1.88p
-1, 0x1.86p
-1, 0x1.84p
-1,
119 0x1.8p
-1, 0x1.7ep
-1, 0x1.7cp
-1, 0x1.7ap
-1, 0x1.78p
-1, 0x1.76p
-1, 0x1.74p
-1,
120 0x1.72p
-1, 0x1.7p
-1, 0x1.6ep
-1, 0x1.6cp
-1, 0x1.6ap
-1, 0x1.68p
-1, 0x1.66p
-1,
121 0x1.64p
-1, 0x1.62p
-1, 0x1.6p
-1, 0x1.5ep
-1, 0x1.5cp
-1, 0x1.5ap
-1, 0x1.58p
-1,
122 0x1.56p
-1, 0x1.54p
-1, 0x1.54p
-1, 0x1.52p
-1, 0x1.5p
-1, 0x1.4ep
-1, 0x1.4cp
-1,
123 0x1.4ap
-1, 0x1.4ap
-1, 0x1.48p
-1, 0x1.46p
-1, 0x1.44p
-1, 0x1.42p
-1, 0x1.4p
-1,
124 0x1.4p
-1, 0x1.3ep
-1, 0x1.3cp
-1, 0x1.3ap
-1, 0x1.3ap
-1, 0x1.38p
-1, 0x1.36p
-1,
125 0x1.34p
-1, 0x1.34p
-1, 0x1.32p
-1, 0x1.3p
-1, 0x1.3p
-1, 0x1.2ep
-1, 0x1.2cp
-1,
126 0x1.2cp
-1, 0x1.2ap
-1, 0x1.28p
-1, 0x1.28p
-1, 0x1.26p
-1, 0x1.24p
-1, 0x1.24p
-1,
127 0x1.22p
-1, 0x1.2p
-1, 0x1.2p
-1, 0x1.1ep
-1, 0x1.1cp
-1, 0x1.1cp
-1, 0x1.1ap
-1,
128 0x1.1ap
-1, 0x1.18p
-1, 0x1.16p
-1, 0x1.16p
-1, 0x1.14p
-1, 0x1.14p
-1, 0x1.12p
-1,
129 0x1.1p
-1, 0x1.1p
-1, 0x1.0ep
-1, 0x1.0ep
-1, 0x1.0cp
-1, 0x1.0cp
-1, 0x1.0ap
-1,
130 0x1.0ap
-1, 0x1.08p
-1, 0x1.08p
-1, 0x1.06p
-1, 0x1.06p
-1, 0x1.04p
-1, 0x1.04p
-1,
131 0x1.02p
-1, 0x1.0p
-1};
133 alignas(64) const double RD
[128] = {
134 0x1p
0, 0x1.fcp
-1, 0x1.f8p
-1, 0x1.f4p
-1, 0x1.fp
-1, 0x1.ecp
-1, 0x1.e8p
-1,
135 0x1.e4p
-1, 0x1.ep
-1, 0x1.dep
-1, 0x1.dap
-1, 0x1.d6p
-1, 0x1.d4p
-1, 0x1.dp
-1,
136 0x1.ccp
-1, 0x1.cap
-1, 0x1.c6p
-1, 0x1.c4p
-1, 0x1.cp
-1, 0x1.bep
-1, 0x1.bap
-1,
137 0x1.b8p
-1, 0x1.b4p
-1, 0x1.b2p
-1, 0x1.aep
-1, 0x1.acp
-1, 0x1.a8p
-1, 0x1.a6p
-1,
138 0x1.a4p
-1, 0x1.ap
-1, 0x1.9ep
-1, 0x1.9cp
-1, 0x1.98p
-1, 0x1.96p
-1, 0x1.94p
-1,
139 0x1.92p
-1, 0x1.9p
-1, 0x1.8cp
-1, 0x1.8ap
-1, 0x1.88p
-1, 0x1.86p
-1, 0x1.84p
-1,
140 0x1.8p
-1, 0x1.7ep
-1, 0x1.7cp
-1, 0x1.7ap
-1, 0x1.78p
-1, 0x1.76p
-1, 0x1.74p
-1,
141 0x1.72p
-1, 0x1.7p
-1, 0x1.6ep
-1, 0x1.6cp
-1, 0x1.6ap
-1, 0x1.68p
-1, 0x1.66p
-1,
142 0x1.64p
-1, 0x1.62p
-1, 0x1.6p
-1, 0x1.5ep
-1, 0x1.5cp
-1, 0x1.5ap
-1, 0x1.58p
-1,
143 0x1.56p
-1, 0x1.54p
-1, 0x1.54p
-1, 0x1.52p
-1, 0x1.5p
-1, 0x1.4ep
-1, 0x1.4cp
-1,
144 0x1.4ap
-1, 0x1.4ap
-1, 0x1.48p
-1, 0x1.46p
-1, 0x1.44p
-1, 0x1.42p
-1, 0x1.4p
-1,
145 0x1.4p
-1, 0x1.3ep
-1, 0x1.3cp
-1, 0x1.3ap
-1, 0x1.3ap
-1, 0x1.38p
-1, 0x1.36p
-1,
146 0x1.34p
-1, 0x1.34p
-1, 0x1.32p
-1, 0x1.3p
-1, 0x1.3p
-1, 0x1.2ep
-1, 0x1.2cp
-1,
147 0x1.2cp
-1, 0x1.2ap
-1, 0x1.28p
-1, 0x1.28p
-1, 0x1.26p
-1, 0x1.24p
-1, 0x1.24p
-1,
148 0x1.22p
-1, 0x1.2p
-1, 0x1.2p
-1, 0x1.1ep
-1, 0x1.1cp
-1, 0x1.1cp
-1, 0x1.1ap
-1,
149 0x1.1ap
-1, 0x1.18p
-1, 0x1.16p
-1, 0x1.16p
-1, 0x1.14p
-1, 0x1.14p
-1, 0x1.12p
-1,
150 0x1.1p
-1, 0x1.1p
-1, 0x1.0ep
-1, 0x1.0ep
-1, 0x1.0cp
-1, 0x1.0cp
-1, 0x1.0ap
-1,
151 0x1.0ap
-1, 0x1.08p
-1, 0x1.08p
-1, 0x1.06p
-1, 0x1.06p
-1, 0x1.04p
-1, 0x1.04p
-1,
152 0x1.02p
-1, 0x1.0p
-1};
154 alignas(64) const double LOG_R
[128] = {
155 0x0.0000000000000p0
, 0x1.010157588de71p
-7, 0x1.0205658935847p
-6,
156 0x1.8492528c8cabfp
-6, 0x1.0415d89e74444p
-5, 0x1.466aed42de3eap
-5,
157 0x1.894aa149fb343p
-5, 0x1.ccb73cdddb2ccp
-5, 0x1.08598b59e3a07p
-4,
158 0x1.1973bd1465567p
-4, 0x1.3bdf5a7d1ee64p
-4, 0x1.5e95a4d9791cbp
-4,
159 0x1.700d30aeac0e1p
-4, 0x1.9335e5d594989p
-4, 0x1.b6ac88dad5b1cp
-4,
160 0x1.c885801bc4b23p
-4, 0x1.ec739830a112p
-4, 0x1.fe89139dbd566p
-4,
161 0x1.1178e8227e47cp
-3, 0x1.1aa2b7e23f72ap
-3, 0x1.2d1610c86813ap
-3,
162 0x1.365fcb0159016p
-3, 0x1.4913d8333b561p
-3, 0x1.527e5e4a1b58dp
-3,
163 0x1.6574ebe8c133ap
-3, 0x1.6f0128b756abcp
-3, 0x1.823c16551a3c2p
-3,
164 0x1.8beafeb38fe8cp
-3, 0x1.95a5adcf7017fp
-3, 0x1.a93ed3c8ad9e3p
-3,
165 0x1.b31d8575bce3dp
-3, 0x1.bd087383bd8adp
-3, 0x1.d1037f2655e7bp
-3,
166 0x1.db13db0d4894p
-3, 0x1.e530effe71012p
-3, 0x1.ef5ade4dcffe6p
-3,
167 0x1.f991c6cb3b379p
-3, 0x1.07138604d5862p
-2, 0x1.0c42d676162e3p
-2,
168 0x1.1178e8227e47cp
-2, 0x1.16b5ccbacfb73p
-2, 0x1.1bf99635a6b95p
-2,
169 0x1.269621134db92p
-2, 0x1.2bef07cdc9354p
-2, 0x1.314f1e1d35ce4p
-2,
170 0x1.36b6776be1117p
-2, 0x1.3c25277333184p
-2, 0x1.419b423d5e8c7p
-2,
171 0x1.4718dc271c41bp
-2, 0x1.4c9e09e172c3cp
-2, 0x1.522ae0738a3d8p
-2,
172 0x1.57bf753c8d1fbp
-2, 0x1.5d5bddf595f3p
-2, 0x1.630030b3aac49p
-2,
173 0x1.68ac83e9c6a14p
-2, 0x1.6e60ee6af1972p
-2, 0x1.741d876c67bb1p
-2,
174 0x1.79e26687cfb3ep
-2, 0x1.7fafa3bd8151cp
-2, 0x1.85855776dcbfbp
-2,
175 0x1.8b639a88b2df5p
-2, 0x1.914a8635bf68ap
-2, 0x1.973a3431356aep
-2,
176 0x1.9d32bea15ed3bp
-2, 0x1.a33440224fa79p
-2, 0x1.a33440224fa79p
-2,
177 0x1.a93ed3c8ad9e3p
-2, 0x1.af5295248cddp
-2, 0x1.b56fa04462909p
-2,
178 0x1.bb9611b80e2fbp
-2, 0x1.c1c60693fa39ep
-2, 0x1.c1c60693fa39ep
-2,
179 0x1.c7ff9c74554c9p
-2, 0x1.ce42f18064743p
-2, 0x1.d490246defa6bp
-2,
180 0x1.dae75484c9616p
-2, 0x1.e148a1a2726cep
-2, 0x1.e148a1a2726cep
-2,
181 0x1.e7b42c3ddad73p
-2, 0x1.ee2a156b413e5p
-2, 0x1.f4aa7ee03192dp
-2,
182 0x1.f4aa7ee03192dp
-2, 0x1.fb358af7a4884p
-2, 0x1.00e5ae5b207abp
-1,
183 0x1.04360be7603adp
-1, 0x1.04360be7603adp
-1, 0x1.078bf0533c568p
-1,
184 0x1.0ae76e2d054fap
-1, 0x1.0ae76e2d054fap
-1, 0x1.0e4898611cce1p
-1,
185 0x1.11af823c75aa8p
-1, 0x1.11af823c75aa8p
-1, 0x1.151c3f6f29612p
-1,
186 0x1.188ee40f23ca6p
-1, 0x1.188ee40f23ca6p
-1, 0x1.1c07849ae6007p
-1,
187 0x1.1f8635fc61659p
-1, 0x1.1f8635fc61659p
-1, 0x1.230b0d8bebc98p
-1,
188 0x1.269621134db92p
-1, 0x1.269621134db92p
-1, 0x1.2a2786d0ec107p
-1,
189 0x1.2dbf557b0df43p
-1, 0x1.2dbf557b0df43p
-1, 0x1.315da4434068bp
-1,
190 0x1.315da4434068bp
-1, 0x1.35028ad9d8c86p
-1, 0x1.38ae2171976e7p
-1,
191 0x1.38ae2171976e7p
-1, 0x1.3c6080c36bfb5p
-1, 0x1.3c6080c36bfb5p
-1,
192 0x1.4019c2125ca93p
-1, 0x1.43d9ff2f923c5p
-1, 0x1.43d9ff2f923c5p
-1,
193 0x1.47a1527e8a2d3p
-1, 0x1.47a1527e8a2d3p
-1, 0x1.4b6fd6f970c1fp
-1,
194 0x1.4b6fd6f970c1fp
-1, 0x1.4f45a835a4e19p
-1, 0x1.4f45a835a4e19p
-1,
195 0x1.5322e26867857p
-1, 0x1.5322e26867857p
-1, 0x1.5707a26bb8c66p
-1,
196 0x1.5707a26bb8c66p
-1, 0x1.5af405c3649ep
-1, 0x1.5af405c3649ep
-1,
197 0x1.5ee82aa24192p
-1, 0x0.000000000000p0
};
199 // Lookup table for exp(m) with m = -104, ..., 89.
200 // -104 = floor(log(single precision's min denormal))
201 // 89 = ceil(log(single precision's max normal))
202 // Table is generated with Sollya as follow:
203 // > display = hexadecimal;
204 // > for i from -104 to 89 do { D(exp(i)); };
205 const double EXP_M1
[195] = {
206 0x1.f1e6b68529e33p
-151, 0x1.525be4e4e601dp
-149, 0x1.cbe0a45f75eb1p
-148,
207 0x1.3884e838aea68p
-146, 0x1.a8c1f14e2af5dp
-145, 0x1.20a717e64a9bdp
-143,
208 0x1.8851d84118908p
-142, 0x1.0a9bdfb02d240p
-140, 0x1.6a5bea046b42ep
-139,
209 0x1.ec7f3b269efa8p
-138, 0x1.4eafb87eab0f2p
-136, 0x1.c6e2d05bbc000p
-135,
210 0x1.35208867c2683p
-133, 0x1.a425b317eeacdp
-132, 0x1.1d8508fa8246ap
-130,
211 0x1.840fbc08fdc8ap
-129, 0x1.07b7112bc1ffep
-127, 0x1.666d0dad2961dp
-126,
212 0x1.e726c3f64d0fep
-125, 0x1.4b0dc07cabf98p
-123, 0x1.c1f2daf3b6a46p
-122,
213 0x1.31c5957a47de2p
-120, 0x1.9f96445648b9fp
-119, 0x1.1a6baeadb4fd1p
-117,
214 0x1.7fd974d372e45p
-116, 0x1.04da4d1452919p
-114, 0x1.62891f06b3450p
-113,
215 0x1.e1dd273aa8a4ap
-112, 0x1.4775e0840bfddp
-110, 0x1.bd109d9d94bdap
-109,
216 0x1.2e73f53fba844p
-107, 0x1.9b138170d6bfep
-106, 0x1.175af0cf60ec5p
-104,
217 0x1.7baee1bffa80bp
-103, 0x1.02057d1245cebp
-101, 0x1.5eafffb34ba31p
-100,
218 0x1.dca23bae16424p
-99, 0x1.43e7fc88b8056p
-97, 0x1.b83bf23a9a9ebp
-96,
219 0x1.2b2b8dd05b318p
-94, 0x1.969d47321e4ccp
-93, 0x1.1452b7723aed2p
-91,
220 0x1.778fe2497184cp
-90, 0x1.fe7116182e9ccp
-89, 0x1.5ae191a99585ap
-87,
221 0x1.d775d87da854dp
-86, 0x1.4063f8cc8bb98p
-84, 0x1.b374b315f87c1p
-83,
222 0x1.27ec458c65e3cp
-81, 0x1.923372c67a074p
-80, 0x1.1152eaeb73c08p
-78,
223 0x1.737c5645114b5p
-77, 0x1.f8e6c24b5592ep
-76, 0x1.571db733a9d61p
-74,
224 0x1.d257d547e083fp
-73, 0x1.3ce9b9de78f85p
-71, 0x1.aebabae3a41b5p
-70,
225 0x1.24b6031b49bdap
-68, 0x1.8dd5e1bb09d7ep
-67, 0x1.0e5b73d1ff53dp
-65,
226 0x1.6f741de1748ecp
-64, 0x1.f36bd37f42f3ep
-63, 0x1.536452ee2f75cp
-61,
227 0x1.cd480a1b74820p
-60, 0x1.39792499b1a24p
-58, 0x1.aa0de4bf35b38p
-57,
228 0x1.2188ad6ae3303p
-55, 0x1.898471fca6055p
-54, 0x1.0b6c3afdde064p
-52,
229 0x1.6b7719a59f0e0p
-51, 0x1.ee001eed62aa0p
-50, 0x1.4fb547c775da8p
-48,
230 0x1.c8464f7616468p
-47, 0x1.36121e24d3bbap
-45, 0x1.a56e0c2ac7f75p
-44,
231 0x1.1e642baeb84a0p
-42, 0x1.853f01d6d53bap
-41, 0x1.0885298767e9ap
-39,
232 0x1.67852a7007e42p
-38, 0x1.e8a37a45fc32ep
-37, 0x1.4c1078fe9228ap
-35,
233 0x1.c3527e433fab1p
-34, 0x1.32b48bf117da2p
-32, 0x1.a0db0d0ddb3ecp
-31,
234 0x1.1b48655f37267p
-29, 0x1.81056ff2c5772p
-28, 0x1.05a628c699fa1p
-26,
235 0x1.639e3175a689dp
-25, 0x1.e355bbaee85cbp
-24, 0x1.4875ca227ec38p
-22,
236 0x1.be6c6fdb01612p
-21, 0x1.2f6053b981d98p
-19, 0x1.9c54c3b43bc8bp
-18,
237 0x1.18354238f6764p
-16, 0x1.7cd79b5647c9bp
-15, 0x1.02cf22526545ap
-13,
238 0x1.5fc21041027adp
-12, 0x1.de16b9c24a98fp
-11, 0x1.44e51f113d4d6p
-9,
239 0x1.b993fe00d5376p
-8, 0x1.2c155b8213cf4p
-6, 0x1.97db0ccceb0afp
-5,
240 0x1.152aaa3bf81ccp
-3, 0x1.78b56362cef38p
-2, 0x1.0000000000000p
+0,
241 0x1.5bf0a8b145769p
+1, 0x1.d8e64b8d4ddaep
+2, 0x1.415e5bf6fb106p
+4,
242 0x1.b4c902e273a58p
+5, 0x1.28d389970338fp
+7, 0x1.936dc5690c08fp
+8,
243 0x1.122885aaeddaap
+10, 0x1.749ea7d470c6ep
+11, 0x1.fa7157c470f82p
+12,
244 0x1.5829dcf950560p
+14, 0x1.d3c4488ee4f7fp
+15, 0x1.3de1654d37c9ap
+17,
245 0x1.b00b5916ac955p
+18, 0x1.259ac48bf05d7p
+20, 0x1.8f0ccafad2a87p
+21,
246 0x1.0f2ebd0a80020p
+23, 0x1.709348c0ea4f9p
+24, 0x1.f4f22091940bdp
+25,
247 0x1.546d8f9ed26e1p
+27, 0x1.ceb088b68e804p
+28, 0x1.3a6e1fd9eecfdp
+30,
248 0x1.ab5adb9c43600p
+31, 0x1.226af33b1fdc1p
+33, 0x1.8ab7fb5475fb7p
+34,
249 0x1.0c3d3920962c9p
+36, 0x1.6c932696a6b5dp
+37, 0x1.ef822f7f6731dp
+38,
250 0x1.50bba3796379ap
+40, 0x1.c9aae4631c056p
+41, 0x1.370470aec28edp
+43,
251 0x1.a6b765d8cdf6dp
+44, 0x1.1f43fcc4b662cp
+46, 0x1.866f34a725782p
+47,
252 0x1.0953e2f3a1ef7p
+49, 0x1.689e221bc8d5bp
+50, 0x1.ea215a1d20d76p
+51,
253 0x1.4d13fbb1a001ap
+53, 0x1.c4b334617cc67p
+54, 0x1.33a43d282a519p
+56,
254 0x1.a220d397972ebp
+57, 0x1.1c25c88df6862p
+59, 0x1.8232558201159p
+60,
255 0x1.0672a3c9eb871p
+62, 0x1.64b41c6d37832p
+63, 0x1.e4cf766fe49bep
+64,
256 0x1.49767bc0483e3p
+66, 0x1.bfc951eb8bb76p
+67, 0x1.304d6aeca254bp
+69,
257 0x1.9d97010884251p
+70, 0x1.19103e4080b45p
+72, 0x1.7e013cd114461p
+73,
258 0x1.03996528e074cp
+75, 0x1.60d4f6fdac731p
+76, 0x1.df8c5af17ba3bp
+77,
259 0x1.45e3076d61699p
+79, 0x1.baed16a6e0da7p
+80, 0x1.2cffdfebde1a1p
+82,
260 0x1.9919cabefcb69p
+83, 0x1.160345c9953e3p
+85, 0x1.79dbc9dc53c66p
+86,
261 0x1.00c810d464097p
+88, 0x1.5d009394c5c27p
+89, 0x1.da57de8f107a8p
+90,
262 0x1.425982cf597cdp
+92, 0x1.b61e5ca3a5e31p
+93, 0x1.29bb825dfcf87p
+95,
263 0x1.94a90db0d6fe2p
+96, 0x1.12fec759586fdp
+98, 0x1.75c1dc469e3afp
+99,
264 0x1.fbfd219c43b04p
+100, 0x1.5936d44e1a146p
+102, 0x1.d531d8a7ee79cp
+103,
265 0x1.3ed9d24a2d51bp
+105, 0x1.b15cfe5b6e17bp
+106, 0x1.268038c2c0e00p
+108,
266 0x1.9044a73545d48p
+109, 0x1.1002ab6218b38p
+111, 0x1.71b3540cbf921p
+112,
267 0x1.f6799ea9c414ap
+113, 0x1.55779b984f3ebp
+115, 0x1.d01a210c44aa4p
+116,
268 0x1.3b63da8e91210p
+118, 0x1.aca8d6b0116b8p
+119, 0x1.234de9e0c74e9p
+121,
269 0x1.8bec7503ca477p
+122, 0x1.0d0eda9796b90p
+124, 0x1.6db0118477245p
+125,
270 0x1.f1056dc7bf22dp
+126, 0x1.51c2cc3433801p
+128, 0x1.cb108ffbec164p
+129,
273 // Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
274 // Table is generated with Sollya as follow:
275 // > display = hexadecimal;
276 // > for i from 0 to 127 do { D(exp(i / 128)); };
277 const double EXP_M2
[128] = {
278 0x1.0000000000000p0
, 0x1.0202015600446p0
, 0x1.04080ab55de39p0
,
279 0x1.06122436410ddp0
, 0x1.08205601127edp0
, 0x1.0a32a84e9c1f6p0
,
280 0x1.0c49236829e8cp0
, 0x1.0e63cfa7ab09dp0
, 0x1.1082b577d34edp0
,
281 0x1.12a5dd543ccc5p0
, 0x1.14cd4fc989cd6p0
, 0x1.16f9157587069p0
,
282 0x1.192937074e0cdp0
, 0x1.1b5dbd3f68122p0
, 0x1.1d96b0eff0e79p0
,
283 0x1.1fd41afcba45ep0
, 0x1.2216045b6f5cdp0
, 0x1.245c7613b8a9bp0
,
284 0x1.26a7793f60164p0
, 0x1.28f7170a755fdp0
, 0x1.2b4b58b372c79p0
,
285 0x1.2da4478b620c7p0
, 0x1.3001ecf601af7p0
, 0x1.32645269ea829p0
,
286 0x1.34cb8170b5835p0
, 0x1.373783a722012p0
, 0x1.39a862bd3c106p0
,
287 0x1.3c1e2876834aap0
, 0x1.3e98deaa11dccp0
, 0x1.41188f42c3e32p0
,
288 0x1.439d443f5f159p0
, 0x1.462707b2bac21p0
, 0x1.48b5e3c3e8186p0
,
289 0x1.4b49e2ae5ac67p0
, 0x1.4de30ec211e60p0
, 0x1.50817263c13cdp0
,
290 0x1.5325180cfacf7p0
, 0x1.55ce0a4c58c7cp0
, 0x1.587c53c5a7af0p0
,
291 0x1.5b2fff3210fd9p0
, 0x1.5de9176045ff5p0
, 0x1.60a7a734ab0e8p0
,
292 0x1.636bb9a983258p0
, 0x1.663559cf1bc7cp0
, 0x1.690492cbf9433p0
,
293 0x1.6bd96fdd034a2p0
, 0x1.6eb3fc55b1e76p0
, 0x1.719443a03acb9p0
,
294 0x1.747a513dbef6ap0
, 0x1.776630c678bc1p0
, 0x1.7a57ede9ea23ep0
,
295 0x1.7d4f946f0ba8dp0
, 0x1.804d30347b546p0
, 0x1.8350cd30ac390p0
,
296 0x1.865a7772164c5p0
, 0x1.896a3b1f66a0ep0
, 0x1.8c802477b0010p0
,
297 0x1.8f9c3fd29beafp0
, 0x1.92be99a09bf00p0
, 0x1.95e73e6b1b75ep0
,
298 0x1.99163ad4b1dccp0
, 0x1.9c4b9b995509bp0
, 0x1.9f876d8e8c566p0
,
299 0x1.a2c9bda3a3e78p0
, 0x1.a61298e1e069cp0
, 0x1.a9620c6cb3374p0
,
300 0x1.acb82581eee54p0
, 0x1.b014f179fc3b8p0
, 0x1.b3787dc80f95fp0
,
301 0x1.b6e2d7fa5eb18p0
, 0x1.ba540dba56e56p0
, 0x1.bdcc2cccd3c85p0
,
302 0x1.c14b431256446p0
, 0x1.c4d15e873c193p0
, 0x1.c85e8d43f7cd0p0
,
303 0x1.cbf2dd7d490f2p0
, 0x1.cf8e5d84758a9p0
, 0x1.d3311bc7822b4p0
,
304 0x1.d6db26d16cd67p0
, 0x1.da8c8d4a66969p0
, 0x1.de455df80e3c0p0
,
305 0x1.e205a7bdab73ep0
, 0x1.e5cd799c6a54ep0
, 0x1.e99ce2b397649p0
,
306 0x1.ed73f240dc142p0
, 0x1.f152b7a07bb76p0
, 0x1.f539424d90f5ep0
,
307 0x1.f927a1e24bb76p0
, 0x1.fd1de6182f8c9p0
, 0x1.008e0f64294abp1
,
308 0x1.02912df5ce72ap1
, 0x1.049856cd84339p1
, 0x1.06a39207f0a09p1
,
309 0x1.08b2e7d2035cfp1
, 0x1.0ac6606916501p1
, 0x1.0cde041b0e9aep1
,
310 0x1.0ef9db467dcf8p1
, 0x1.1119ee5ac36b6p1
, 0x1.133e45d82e952p1
,
311 0x1.1566ea50201d7p1
, 0x1.1793e4652cc50p1
, 0x1.19c53ccb3fc6bp1
,
312 0x1.1bfafc47bda73p1
, 0x1.1e352bb1a74adp1
, 0x1.2073d3f1bd518p1
,
313 0x1.22b6fe02a3b9cp1
, 0x1.24feb2f105cb8p1
, 0x1.274afbdbba4a6p1
,
314 0x1.299be1f3e7f1cp1
, 0x1.2bf16e7d2a38cp1
, 0x1.2e4baacdb6614p1
,
315 0x1.30aaa04e80d05p1
, 0x1.330e587b62b28p1
, 0x1.3576dce33feadp1
,
316 0x1.37e437282d4eep1
, 0x1.3a5670ff972edp1
, 0x1.3ccd9432682b4p1
,
317 0x1.3f49aa9d30590p1
, 0x1.41cabe304cb34p1
, 0x1.4450d8f00edd4p1
,
318 0x1.46dc04f4e5338p1
, 0x1.496c4c6b832dap1
, 0x1.4c01b9950a111p1
,
319 0x1.4e9c56c731f5dp1
, 0x1.513c2e6c731d7p1
, 0x1.53e14b042f9cap1
,
320 0x1.568bb722dd593p1
, 0x1.593b7d72305bbp1
,
323 } // namespace __llvm_libc
