xref: /llvm-project/libc/src/math/generic/common_constants.cpp (revision a0c92a3817efec51403f3129f2f6578d7625c2ce) 
1 //===-- Common constants for math functions ---------------------*- C++ -*-===//
2 //
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
6 //
7 //===----------------------------------------------------------------------===//
8 
9 #include "common_constants.h"
10 #include "src/__support/number_pair.h"
11 
12 namespace __llvm_libc {
13 
14 // Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
15 const double ONE_OVER_F[128] = {
16     0x1.0000000000000p+0, 0x1.fc07f01fc07f0p-1, 0x1.f81f81f81f820p-1,
17     0x1.f44659e4a4271p-1, 0x1.f07c1f07c1f08p-1, 0x1.ecc07b301ecc0p-1,
18     0x1.e9131abf0b767p-1, 0x1.e573ac901e574p-1, 0x1.e1e1e1e1e1e1ep-1,
19     0x1.de5d6e3f8868ap-1, 0x1.dae6076b981dbp-1, 0x1.d77b654b82c34p-1,
20     0x1.d41d41d41d41dp-1, 0x1.d0cb58f6ec074p-1, 0x1.cd85689039b0bp-1,
21     0x1.ca4b3055ee191p-1, 0x1.c71c71c71c71cp-1, 0x1.c3f8f01c3f8f0p-1,
22     0x1.c0e070381c0e0p-1, 0x1.bdd2b899406f7p-1, 0x1.bacf914c1bad0p-1,
23     0x1.b7d6c3dda338bp-1, 0x1.b4e81b4e81b4fp-1, 0x1.b2036406c80d9p-1,
24     0x1.af286bca1af28p-1, 0x1.ac5701ac5701bp-1, 0x1.a98ef606a63bep-1,
25     0x1.a6d01a6d01a6dp-1, 0x1.a41a41a41a41ap-1, 0x1.a16d3f97a4b02p-1,
26     0x1.9ec8e951033d9p-1, 0x1.9c2d14ee4a102p-1, 0x1.999999999999ap-1,
27     0x1.970e4f80cb872p-1, 0x1.948b0fcd6e9e0p-1, 0x1.920fb49d0e229p-1,
28     0x1.8f9c18f9c18fap-1, 0x1.8d3018d3018d3p-1, 0x1.8acb90f6bf3aap-1,
29     0x1.886e5f0abb04ap-1, 0x1.8618618618618p-1, 0x1.83c977ab2beddp-1,
30     0x1.8181818181818p-1, 0x1.7f405fd017f40p-1, 0x1.7d05f417d05f4p-1,
31     0x1.7ad2208e0ecc3p-1, 0x1.78a4c8178a4c8p-1, 0x1.767dce434a9b1p-1,
32     0x1.745d1745d1746p-1, 0x1.724287f46debcp-1, 0x1.702e05c0b8170p-1,
33     0x1.6e1f76b4337c7p-1, 0x1.6c16c16c16c17p-1, 0x1.6a13cd1537290p-1,
34     0x1.6816816816817p-1, 0x1.661ec6a5122f9p-1, 0x1.642c8590b2164p-1,
35     0x1.623fa77016240p-1, 0x1.6058160581606p-1, 0x1.5e75bb8d015e7p-1,
36     0x1.5c9882b931057p-1, 0x1.5ac056b015ac0p-1, 0x1.58ed2308158edp-1,
37     0x1.571ed3c506b3ap-1, 0x1.5555555555555p-1, 0x1.5390948f40febp-1,
38     0x1.51d07eae2f815p-1, 0x1.5015015015015p-1, 0x1.4e5e0a72f0539p-1,
39     0x1.4cab88725af6ep-1, 0x1.4afd6a052bf5bp-1, 0x1.49539e3b2d067p-1,
40     0x1.47ae147ae147bp-1, 0x1.460cbc7f5cf9ap-1, 0x1.446f86562d9fbp-1,
41     0x1.42d6625d51f87p-1, 0x1.4141414141414p-1, 0x1.3fb013fb013fbp-1,
42     0x1.3e22cbce4a902p-1, 0x1.3c995a47babe7p-1, 0x1.3b13b13b13b14p-1,
43     0x1.3991c2c187f63p-1, 0x1.3813813813814p-1, 0x1.3698df3de0748p-1,
44     0x1.3521cfb2b78c1p-1, 0x1.33ae45b57bcb2p-1, 0x1.323e34a2b10bfp-1,
45     0x1.30d190130d190p-1, 0x1.2f684bda12f68p-1, 0x1.2e025c04b8097p-1,
46     0x1.2c9fb4d812ca0p-1, 0x1.2b404ad012b40p-1, 0x1.29e4129e4129ep-1,
47     0x1.288b01288b013p-1, 0x1.27350b8812735p-1, 0x1.25e22708092f1p-1,
48     0x1.2492492492492p-1, 0x1.23456789abcdfp-1, 0x1.21fb78121fb78p-1,
49     0x1.20b470c67c0d9p-1, 0x1.1f7047dc11f70p-1, 0x1.1e2ef3b3fb874p-1,
50     0x1.1cf06ada2811dp-1, 0x1.1bb4a4046ed29p-1, 0x1.1a7b9611a7b96p-1,
51     0x1.19453808ca29cp-1, 0x1.1811811811812p-1, 0x1.16e0689427379p-1,
52     0x1.15b1e5f75270dp-1, 0x1.1485f0e0acd3bp-1, 0x1.135c81135c811p-1,
53     0x1.12358e75d3033p-1, 0x1.1111111111111p-1, 0x1.0fef010fef011p-1,
54     0x1.0ecf56be69c90p-1, 0x1.0db20a88f4696p-1, 0x1.0c9714fbcda3bp-1,
55     0x1.0b7e6ec259dc8p-1, 0x1.0a6810a6810a7p-1, 0x1.0953f39010954p-1,
56     0x1.0842108421084p-1, 0x1.073260a47f7c6p-1, 0x1.0624dd2f1a9fcp-1,
57     0x1.05197f7d73404p-1, 0x1.0410410410410p-1, 0x1.03091b51f5e1ap-1,
58     0x1.0204081020408p-1, 0x1.0101010101010p-1};
59 
60 // Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
61 const double LOG_F[128] = {
62     0x0.0000000000000p+0, 0x1.fe02a6b106788p-8, 0x1.fc0a8b0fc03e3p-7,
63     0x1.7b91b07d5b11ap-6, 0x1.f829b0e783300p-6, 0x1.39e87b9febd5fp-5,
64     0x1.77458f632dcfcp-5, 0x1.b42dd711971bep-5, 0x1.f0a30c01162a6p-5,
65     0x1.16536eea37ae0p-4, 0x1.341d7961bd1d0p-4, 0x1.51b073f06183fp-4,
66     0x1.6f0d28ae56b4bp-4, 0x1.8c345d6319b20p-4, 0x1.a926d3a4ad563p-4,
67     0x1.c5e548f5bc743p-4, 0x1.e27076e2af2e5p-4, 0x1.fec9131dbeabap-4,
68     0x1.0d77e7cd08e59p-3, 0x1.1b72ad52f67a0p-3, 0x1.29552f81ff523p-3,
69     0x1.371fc201e8f74p-3, 0x1.44d2b6ccb7d1ep-3, 0x1.526e5e3a1b437p-3,
70     0x1.5ff3070a793d3p-3, 0x1.6d60fe719d21cp-3, 0x1.7ab890210d909p-3,
71     0x1.87fa06520c910p-3, 0x1.9525a9cf456b4p-3, 0x1.a23bc1fe2b563p-3,
72     0x1.af3c94e80bff2p-3, 0x1.bc286742d8cd6p-3, 0x1.c8ff7c79a9a21p-3,
73     0x1.d5c216b4fbb91p-3, 0x1.e27076e2af2e5p-3, 0x1.ef0adcbdc5936p-3,
74     0x1.fb9186d5e3e2ap-3, 0x1.0402594b4d040p-2, 0x1.0a324e27390e3p-2,
75     0x1.1058bf9ae4ad5p-2, 0x1.1675cababa60ep-2, 0x1.1c898c16999fap-2,
76     0x1.22941fbcf7965p-2, 0x1.2895a13de86a3p-2, 0x1.2e8e2bae11d30p-2,
77     0x1.347dd9a987d54p-2, 0x1.3a64c556945e9p-2, 0x1.404308686a7e3p-2,
78     0x1.4618bc21c5ec2p-2, 0x1.4be5f957778a0p-2, 0x1.51aad872df82dp-2,
79     0x1.5767717455a6cp-2, 0x1.5d1bdbf5809cap-2, 0x1.62c82f2b9c795p-2,
80     0x1.686c81e9b14aep-2, 0x1.6e08eaa2ba1e3p-2, 0x1.739d7f6bbd006p-2,
81     0x1.792a55fdd47a2p-2, 0x1.7eaf83b82afc3p-2, 0x1.842d1da1e8b17p-2,
82     0x1.89a3386c1425ap-2, 0x1.8f11e873662c7p-2, 0x1.947941c2116fap-2,
83     0x1.99d958117e08ap-2, 0x1.9f323ecbf984bp-2, 0x1.a484090e5bb0ap-2,
84     0x1.a9cec9a9a0849p-2, 0x1.af1293247786bp-2, 0x1.b44f77bcc8f62p-2,
85     0x1.b9858969310fbp-2, 0x1.beb4d9da71b7bp-2, 0x1.c3dd7a7cdad4dp-2,
86     0x1.c8ff7c79a9a21p-2, 0x1.ce1af0b85f3ebp-2, 0x1.d32fe7e00ebd5p-2,
87     0x1.d83e7258a2f3ep-2, 0x1.dd46a04c1c4a0p-2, 0x1.e24881a7c6c26p-2,
88     0x1.e744261d68787p-2, 0x1.ec399d2468cc0p-2, 0x1.f128f5faf06ecp-2,
89     0x1.f6123fa7028acp-2, 0x1.faf588f78f31ep-2, 0x1.ffd2e0857f498p-2,
90     0x1.02552a5a5d0fep-1, 0x1.04bdf9da926d2p-1, 0x1.0723e5c1cdf40p-1,
91     0x1.0986f4f573520p-1, 0x1.0be72e4252a82p-1, 0x1.0e44985d1cc8bp-1,
92     0x1.109f39e2d4c96p-1, 0x1.12f719593efbcp-1, 0x1.154c3d2f4d5e9p-1,
93     0x1.179eabbd899a0p-1, 0x1.19ee6b467c96ep-1, 0x1.1c3b81f713c24p-1,
94     0x1.1e85f5e7040d0p-1, 0x1.20cdcd192ab6dp-1, 0x1.23130d7bebf42p-1,
95     0x1.2555bce98f7cbp-1, 0x1.2795e1289b11ap-1, 0x1.29d37fec2b08ap-1,
96     0x1.2c0e9ed448e8bp-1, 0x1.2e47436e40268p-1, 0x1.307d7334f10bep-1,
97     0x1.32b1339121d71p-1, 0x1.34e289d9ce1d3p-1, 0x1.37117b54747b5p-1,
98     0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1,
99     0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1,
100     0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1,
101     0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1,
102     0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1,
103     0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
104     0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
105 
106 // Range reduction constants for logarithms.
107 // r(0) = 1, r(127) = 0.5
108 // r(k) = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + k*2^-7))
109 // The constants are chosen so that v = fma(r, m_x, -1) is exact in single
110 // precision, and -2^-8 <= v < 2^-7.
111 // TODO(lntue): Add reference to how the constants are derived after the
112 // resulting paper is ready.
113 alignas(32) const float R[128] = {
114     0x1p0,     0x1.fcp-1, 0x1.f8p-1, 0x1.f4p-1, 0x1.fp-1,  0x1.ecp-1, 0x1.e8p-1,
115     0x1.e4p-1, 0x1.ep-1,  0x1.dep-1, 0x1.dap-1, 0x1.d6p-1, 0x1.d4p-1, 0x1.dp-1,
116     0x1.ccp-1, 0x1.cap-1, 0x1.c6p-1, 0x1.c4p-1, 0x1.cp-1,  0x1.bep-1, 0x1.bap-1,
117     0x1.b8p-1, 0x1.b4p-1, 0x1.b2p-1, 0x1.aep-1, 0x1.acp-1, 0x1.a8p-1, 0x1.a6p-1,
118     0x1.a4p-1, 0x1.ap-1,  0x1.9ep-1, 0x1.9cp-1, 0x1.98p-1, 0x1.96p-1, 0x1.94p-1,
119     0x1.92p-1, 0x1.9p-1,  0x1.8cp-1, 0x1.8ap-1, 0x1.88p-1, 0x1.86p-1, 0x1.84p-1,
120     0x1.8p-1,  0x1.7ep-1, 0x1.7cp-1, 0x1.7ap-1, 0x1.78p-1, 0x1.76p-1, 0x1.74p-1,
121     0x1.72p-1, 0x1.7p-1,  0x1.6ep-1, 0x1.6cp-1, 0x1.6ap-1, 0x1.68p-1, 0x1.66p-1,
122     0x1.64p-1, 0x1.62p-1, 0x1.6p-1,  0x1.5ep-1, 0x1.5cp-1, 0x1.5ap-1, 0x1.58p-1,
123     0x1.56p-1, 0x1.54p-1, 0x1.54p-1, 0x1.52p-1, 0x1.5p-1,  0x1.4ep-1, 0x1.4cp-1,
124     0x1.4ap-1, 0x1.4ap-1, 0x1.48p-1, 0x1.46p-1, 0x1.44p-1, 0x1.42p-1, 0x1.4p-1,
125     0x1.4p-1,  0x1.3ep-1, 0x1.3cp-1, 0x1.3ap-1, 0x1.3ap-1, 0x1.38p-1, 0x1.36p-1,
126     0x1.34p-1, 0x1.34p-1, 0x1.32p-1, 0x1.3p-1,  0x1.3p-1,  0x1.2ep-1, 0x1.2cp-1,
127     0x1.2cp-1, 0x1.2ap-1, 0x1.28p-1, 0x1.28p-1, 0x1.26p-1, 0x1.24p-1, 0x1.24p-1,
128     0x1.22p-1, 0x1.2p-1,  0x1.2p-1,  0x1.1ep-1, 0x1.1cp-1, 0x1.1cp-1, 0x1.1ap-1,
129     0x1.1ap-1, 0x1.18p-1, 0x1.16p-1, 0x1.16p-1, 0x1.14p-1, 0x1.14p-1, 0x1.12p-1,
130     0x1.1p-1,  0x1.1p-1,  0x1.0ep-1, 0x1.0ep-1, 0x1.0cp-1, 0x1.0cp-1, 0x1.0ap-1,
131     0x1.0ap-1, 0x1.08p-1, 0x1.08p-1, 0x1.06p-1, 0x1.06p-1, 0x1.04p-1, 0x1.04p-1,
132     0x1.02p-1, 0x1.0p-1};
133 
134 alignas(64) const double RD[128] = {
135     0x1p0,     0x1.fcp-1, 0x1.f8p-1, 0x1.f4p-1, 0x1.fp-1,  0x1.ecp-1, 0x1.e8p-1,
136     0x1.e4p-1, 0x1.ep-1,  0x1.dep-1, 0x1.dap-1, 0x1.d6p-1, 0x1.d4p-1, 0x1.dp-1,
137     0x1.ccp-1, 0x1.cap-1, 0x1.c6p-1, 0x1.c4p-1, 0x1.cp-1,  0x1.bep-1, 0x1.bap-1,
138     0x1.b8p-1, 0x1.b4p-1, 0x1.b2p-1, 0x1.aep-1, 0x1.acp-1, 0x1.a8p-1, 0x1.a6p-1,
139     0x1.a4p-1, 0x1.ap-1,  0x1.9ep-1, 0x1.9cp-1, 0x1.98p-1, 0x1.96p-1, 0x1.94p-1,
140     0x1.92p-1, 0x1.9p-1,  0x1.8cp-1, 0x1.8ap-1, 0x1.88p-1, 0x1.86p-1, 0x1.84p-1,
141     0x1.8p-1,  0x1.7ep-1, 0x1.7cp-1, 0x1.7ap-1, 0x1.78p-1, 0x1.76p-1, 0x1.74p-1,
142     0x1.72p-1, 0x1.7p-1,  0x1.6ep-1, 0x1.6cp-1, 0x1.6ap-1, 0x1.68p-1, 0x1.66p-1,
143     0x1.64p-1, 0x1.62p-1, 0x1.6p-1,  0x1.5ep-1, 0x1.5cp-1, 0x1.5ap-1, 0x1.58p-1,
144     0x1.56p-1, 0x1.54p-1, 0x1.54p-1, 0x1.52p-1, 0x1.5p-1,  0x1.4ep-1, 0x1.4cp-1,
145     0x1.4ap-1, 0x1.4ap-1, 0x1.48p-1, 0x1.46p-1, 0x1.44p-1, 0x1.42p-1, 0x1.4p-1,
146     0x1.4p-1,  0x1.3ep-1, 0x1.3cp-1, 0x1.3ap-1, 0x1.3ap-1, 0x1.38p-1, 0x1.36p-1,
147     0x1.34p-1, 0x1.34p-1, 0x1.32p-1, 0x1.3p-1,  0x1.3p-1,  0x1.2ep-1, 0x1.2cp-1,
148     0x1.2cp-1, 0x1.2ap-1, 0x1.28p-1, 0x1.28p-1, 0x1.26p-1, 0x1.24p-1, 0x1.24p-1,
149     0x1.22p-1, 0x1.2p-1,  0x1.2p-1,  0x1.1ep-1, 0x1.1cp-1, 0x1.1cp-1, 0x1.1ap-1,
150     0x1.1ap-1, 0x1.18p-1, 0x1.16p-1, 0x1.16p-1, 0x1.14p-1, 0x1.14p-1, 0x1.12p-1,
151     0x1.1p-1,  0x1.1p-1,  0x1.0ep-1, 0x1.0ep-1, 0x1.0cp-1, 0x1.0cp-1, 0x1.0ap-1,
152     0x1.0ap-1, 0x1.08p-1, 0x1.08p-1, 0x1.06p-1, 0x1.06p-1, 0x1.04p-1, 0x1.04p-1,
153     0x1.02p-1, 0x1.0p-1};
154 
155 // Compensated constants for exact logarithm range reduction when FMA is not
156 // available.
157 // Generated by Sollya with the formula: CD[i] = RD[i]*(1 + i*2^-7) - 1
158 // for RD[i] defined on the table above.
159 alignas(64) const double CD[128] = {
160     0.0,        -0x1p-14,   -0x1p-12,   -0x1.2p-11,  -0x1p-10,   -0x1.9p-10,
161     -0x1.2p-9,  -0x1.88p-9, -0x1p-8,    -0x1.9p-11,  -0x1.fp-10, -0x1.9cp-9,
162     -0x1p-12,   -0x1.cp-10, -0x1.bp-9,  -0x1.5p-11,  -0x1.4p-9,  0x1p-14,
163     -0x1p-9,    0x1.ap-12,  -0x1.ep-10, 0x1.8p-12,   -0x1.1p-9,  -0x1p-15,
164     -0x1.6p-9,  -0x1.ap-11, -0x1.ep-9,  -0x1.f8p-10, -0x1p-12,   -0x1.cp-9,
165     -0x1.fp-10, -0x1.cp-12, -0x1p-8,    -0x1.54p-9,  -0x1.6p-10, -0x1.4p-13,
166     0x1p-10,    -0x1.88p-9, -0x1.08p-9, -0x1.2p-10,  -0x1p-12,   0x1.2p-11,
167     -0x1p-8,    -0x1.acp-9, -0x1.6p-9,  -0x1.1cp-9,  -0x1.cp-10, -0x1.58p-10,
168     -0x1p-10,   -0x1.7p-11, -0x1p-11,   -0x1.6p-12,  -0x1p-12,   -0x1.cp-13,
169     -0x1p-12,   -0x1.6p-12, -0x1p-11,   -0x1.7p-11,  -0x1p-10,   -0x1.58p-10,
170     -0x1.cp-10, -0x1.1cp-9, -0x1.6p-9,  -0x1.acp-9,  -0x1p-8,    0x1.5p-10,
171     0x1.2p-11,  -0x1p-12,   -0x1.2p-10, -0x1.08p-9,  -0x1.88p-9, 0x1.0cp-9,
172     0x1p-10,    -0x1.4p-13, -0x1.6p-10, -0x1.54p-9,  -0x1p-8,    0x1p-10,
173     -0x1.cp-12, -0x1.fp-10, -0x1.cp-9,  0x1.68p-10,  -0x1p-12,   -0x1.f8p-10,
174     -0x1.ep-9,  0x1.1p-10,  -0x1.ap-11, -0x1.6p-9,   0x1p-9,     -0x1p-15,
175     -0x1.1p-9,  0x1.48p-9,  0x1.8p-12,  -0x1.ep-10,  0x1.6p-9,   0x1.ap-12,
176     -0x1p-9,    0x1.48p-9,  0x1p-14,    -0x1.4p-9,   0x1p-9,     -0x1.5p-11,
177     -0x1.bp-9,  0x1.1p-10,  -0x1.cp-10, 0x1.54p-9,   -0x1p-12,   -0x1.9cp-9,
178     0x1.2p-10,  -0x1.fp-10, 0x1.3p-9,   -0x1.9p-11,  -0x1p-8,    0x1p-12,
179     -0x1.88p-9, 0x1.28p-10, -0x1.2p-9,  0x1.fp-10,   -0x1.9p-10, 0x1.4cp-9,
180     -0x1p-10,   0x1.9p-9,   -0x1.2p-11, 0x1.c4p-9,   -0x1p-12,   0x1.e8p-9,
181     -0x1p-14,   -0x1p-8,
182 };
183 
184 alignas(64) const double LOG_R[128] = {
185     0x0.0000000000000p0,  0x1.010157588de71p-7, 0x1.0205658935847p-6,
186     0x1.8492528c8cabfp-6, 0x1.0415d89e74444p-5, 0x1.466aed42de3eap-5,
187     0x1.894aa149fb343p-5, 0x1.ccb73cdddb2ccp-5, 0x1.08598b59e3a07p-4,
188     0x1.1973bd1465567p-4, 0x1.3bdf5a7d1ee64p-4, 0x1.5e95a4d9791cbp-4,
189     0x1.700d30aeac0e1p-4, 0x1.9335e5d594989p-4, 0x1.b6ac88dad5b1cp-4,
190     0x1.c885801bc4b23p-4, 0x1.ec739830a112p-4,  0x1.fe89139dbd566p-4,
191     0x1.1178e8227e47cp-3, 0x1.1aa2b7e23f72ap-3, 0x1.2d1610c86813ap-3,
192     0x1.365fcb0159016p-3, 0x1.4913d8333b561p-3, 0x1.527e5e4a1b58dp-3,
193     0x1.6574ebe8c133ap-3, 0x1.6f0128b756abcp-3, 0x1.823c16551a3c2p-3,
194     0x1.8beafeb38fe8cp-3, 0x1.95a5adcf7017fp-3, 0x1.a93ed3c8ad9e3p-3,
195     0x1.b31d8575bce3dp-3, 0x1.bd087383bd8adp-3, 0x1.d1037f2655e7bp-3,
196     0x1.db13db0d4894p-3,  0x1.e530effe71012p-3, 0x1.ef5ade4dcffe6p-3,
197     0x1.f991c6cb3b379p-3, 0x1.07138604d5862p-2, 0x1.0c42d676162e3p-2,
198     0x1.1178e8227e47cp-2, 0x1.16b5ccbacfb73p-2, 0x1.1bf99635a6b95p-2,
199     0x1.269621134db92p-2, 0x1.2bef07cdc9354p-2, 0x1.314f1e1d35ce4p-2,
200     0x1.36b6776be1117p-2, 0x1.3c25277333184p-2, 0x1.419b423d5e8c7p-2,
201     0x1.4718dc271c41bp-2, 0x1.4c9e09e172c3cp-2, 0x1.522ae0738a3d8p-2,
202     0x1.57bf753c8d1fbp-2, 0x1.5d5bddf595f3p-2,  0x1.630030b3aac49p-2,
203     0x1.68ac83e9c6a14p-2, 0x1.6e60ee6af1972p-2, 0x1.741d876c67bb1p-2,
204     0x1.79e26687cfb3ep-2, 0x1.7fafa3bd8151cp-2, 0x1.85855776dcbfbp-2,
205     0x1.8b639a88b2df5p-2, 0x1.914a8635bf68ap-2, 0x1.973a3431356aep-2,
206     0x1.9d32bea15ed3bp-2, 0x1.a33440224fa79p-2, 0x1.a33440224fa79p-2,
207     0x1.a93ed3c8ad9e3p-2, 0x1.af5295248cddp-2,  0x1.b56fa04462909p-2,
208     0x1.bb9611b80e2fbp-2, 0x1.c1c60693fa39ep-2, 0x1.c1c60693fa39ep-2,
209     0x1.c7ff9c74554c9p-2, 0x1.ce42f18064743p-2, 0x1.d490246defa6bp-2,
210     0x1.dae75484c9616p-2, 0x1.e148a1a2726cep-2, 0x1.e148a1a2726cep-2,
211     0x1.e7b42c3ddad73p-2, 0x1.ee2a156b413e5p-2, 0x1.f4aa7ee03192dp-2,
212     0x1.f4aa7ee03192dp-2, 0x1.fb358af7a4884p-2, 0x1.00e5ae5b207abp-1,
213     0x1.04360be7603adp-1, 0x1.04360be7603adp-1, 0x1.078bf0533c568p-1,
214     0x1.0ae76e2d054fap-1, 0x1.0ae76e2d054fap-1, 0x1.0e4898611cce1p-1,
215     0x1.11af823c75aa8p-1, 0x1.11af823c75aa8p-1, 0x1.151c3f6f29612p-1,
216     0x1.188ee40f23ca6p-1, 0x1.188ee40f23ca6p-1, 0x1.1c07849ae6007p-1,
217     0x1.1f8635fc61659p-1, 0x1.1f8635fc61659p-1, 0x1.230b0d8bebc98p-1,
218     0x1.269621134db92p-1, 0x1.269621134db92p-1, 0x1.2a2786d0ec107p-1,
219     0x1.2dbf557b0df43p-1, 0x1.2dbf557b0df43p-1, 0x1.315da4434068bp-1,
220     0x1.315da4434068bp-1, 0x1.35028ad9d8c86p-1, 0x1.38ae2171976e7p-1,
221     0x1.38ae2171976e7p-1, 0x1.3c6080c36bfb5p-1, 0x1.3c6080c36bfb5p-1,
222     0x1.4019c2125ca93p-1, 0x1.43d9ff2f923c5p-1, 0x1.43d9ff2f923c5p-1,
223     0x1.47a1527e8a2d3p-1, 0x1.47a1527e8a2d3p-1, 0x1.4b6fd6f970c1fp-1,
224     0x1.4b6fd6f970c1fp-1, 0x1.4f45a835a4e19p-1, 0x1.4f45a835a4e19p-1,
225     0x1.5322e26867857p-1, 0x1.5322e26867857p-1, 0x1.5707a26bb8c66p-1,
226     0x1.5707a26bb8c66p-1, 0x1.5af405c3649ep-1,  0x1.5af405c3649ep-1,
227     0x1.5ee82aa24192p-1,  0x0.000000000000p0};
228 
229 // Generated by Sollya with:
230 // for i from 0 to 127 do {
231 //     r = 2^-8 * ceil( 2^8 * (1 - 2^(-8)) / (1 + i*2^-7) );
232 //     b = nearestint(log(r)*2^43) * 2^-43;
233 //     c = round(log(r) - b, D, RN);
234 //     print("{", -c, ",", -b, "},");
235 //   };
236 // We replace LOG_R[0] with log10(1.0) == 0.0
237 alignas(64) const NumberPair<double> LOG_R_DD[128] = {
238     {0.0, 0.0},
239     {-0x1.0c76b999d2be8p-46, 0x1.010157589p-7},
240     {-0x1.3dc5b06e2f7d2p-45, 0x1.0205658938p-6},
241     {-0x1.aa0ba325a0c34p-45, 0x1.8492528c9p-6},
242     {0x1.111c05cf1d753p-47, 0x1.0415d89e74p-5},
243     {-0x1.c167375bdfd28p-45, 0x1.466aed42ep-5},
244     {-0x1.97995d05a267dp-46, 0x1.894aa149fcp-5},
245     {-0x1.a68f247d82807p-46, 0x1.ccb73cdddcp-5},
246     {-0x1.7e5dd7009902cp-46, 0x1.08598b59e4p-4},
247     {-0x1.5325d560d9e9bp-45, 0x1.1973bd1466p-4},
248     {0x1.cc85ea5db4ed7p-45, 0x1.3bdf5a7d1ep-4},
249     {-0x1.c69063c5d1d1ep-45, 0x1.5e95a4d97ap-4},
250     {0x1.c1e8da99ded32p-49, 0x1.700d30aeacp-4},
251     {0x1.3115c3abd47dap-45, 0x1.9335e5d594p-4},
252     {-0x1.390802bf768e5p-46, 0x1.b6ac88dad6p-4},
253     {0x1.646d1c65aacd3p-45, 0x1.c885801bc4p-4},
254     {-0x1.dc068afe645ep-45, 0x1.ec739830a2p-4},
255     {-0x1.534d64fa10afdp-45, 0x1.fe89139dbep-4},
256     {0x1.1ef78ce2d07f2p-45, 0x1.1178e8227ep-3},
257     {0x1.ca78e44389934p-45, 0x1.1aa2b7e23fp-3},
258     {0x1.39d6ccb81b4a1p-47, 0x1.2d1610c868p-3},
259     {0x1.62fa8234b7289p-51, 0x1.365fcb0159p-3},
260     {0x1.5837954fdb678p-45, 0x1.4913d8333bp-3},
261     {0x1.633e8e5697dc7p-45, 0x1.527e5e4a1bp-3},
262     {0x1.9cf8b2c3c2e78p-46, 0x1.6574ebe8c1p-3},
263     {-0x1.5118de59c21e1p-45, 0x1.6f0128b757p-3},
264     {0x1.e0ddb9a631e83p-46, 0x1.823c16551ap-3},
265     {-0x1.73d54aae92cd1p-47, 0x1.8beafeb39p-3},
266     {0x1.7f22858a0ff6fp-47, 0x1.95a5adcf7p-3},
267     {-0x1.8724350562169p-45, 0x1.a93ed3c8aep-3},
268     {-0x1.c358d4eace1aap-47, 0x1.b31d8575bdp-3},
269     {-0x1.d4bc4595412b6p-45, 0x1.bd087383bep-3},
270     {-0x1.84a7e75b6f6e4p-47, 0x1.d1037f2656p-3},
271     {-0x1.aff2af715b035p-45, 0x1.db13db0d49p-3},
272     {0x1.212276041f43p-51, 0x1.e530effe71p-3},
273     {-0x1.a211565bb8e11p-51, 0x1.ef5ade4ddp-3},
274     {0x1.bcbecca0cdf3p-46, 0x1.f991c6cb3bp-3},
275     {0x1.89cdb16ed4e91p-48, 0x1.07138604d58p-2},
276     {0x1.7188b163ceae9p-45, 0x1.0c42d67616p-2},
277     {-0x1.c210e63a5f01cp-45, 0x1.1178e8227e8p-2},
278     {0x1.b9acdf7a51681p-45, 0x1.16b5ccbacf8p-2},
279     {0x1.ca6ed5147bdb7p-45, 0x1.1bf99635a68p-2},
280     {0x1.c93c1df5bb3b6p-45, 0x1.269621134d8p-2},
281     {0x1.a9cfa4a5004f4p-45, 0x1.2bef07cdc9p-2},
282     {-0x1.8e27ad3213cb8p-45, 0x1.314f1e1d36p-2},
283     {0x1.16ecdb0f177c8p-46, 0x1.36b6776be1p-2},
284     {0x1.83b54b606bd5cp-46, 0x1.3c25277333p-2},
285     {0x1.8e436ec90e09dp-47, 0x1.419b423d5e8p-2},
286     {-0x1.f27ce0967d675p-45, 0x1.4718dc271c8p-2},
287     {-0x1.e20891b0ad8a4p-45, 0x1.4c9e09e173p-2},
288     {0x1.ebe708164c759p-45, 0x1.522ae0738ap-2},
289     {0x1.fadedee5d40efp-46, 0x1.57bf753c8dp-2},
290     {-0x1.a0b2a08a465dcp-47, 0x1.5d5bddf596p-2},
291     {-0x1.db623e731aep-45, 0x1.630030b3abp-2},
292     {0x1.0a0d32756ebap-45, 0x1.68ac83e9c68p-2},
293     {0x1.721657c222d87p-46, 0x1.6e60ee6af18p-2},
294     {0x1.d8b0949dc60b3p-45, 0x1.741d876c678p-2},
295     {0x1.9ec7d2efd1778p-45, 0x1.79e26687cf8p-2},
296     {-0x1.72090c812566ap-45, 0x1.7fafa3bd818p-2},
297     {0x1.fd56f3333778ap-45, 0x1.85855776dc8p-2},
298     {-0x1.05ae1e5e7047p-45, 0x1.8b639a88b3p-2},
299     {-0x1.766b52ee6307dp-46, 0x1.914a8635bf8p-2},
300     {-0x1.52313a502d9fp-46, 0x1.973a3431358p-2},
301     {-0x1.6279e10d0c0bp-45, 0x1.9d32bea15fp-2},
302     {0x1.3c6457f9d79f5p-45, 0x1.a33440224f8p-2},
303     {0x1.3c6457f9d79f5p-45, 0x1.a33440224f8p-2},
304     {0x1.e36f2bea77a5dp-46, 0x1.a93ed3c8ad8p-2},
305     {-0x1.17cc552774458p-45, 0x1.af5295248dp-2},
306     {0x1.095252d841995p-46, 0x1.b56fa044628p-2},
307     {0x1.7d85bf40a666dp-45, 0x1.bb9611b80ep-2},
308     {0x1.cec807fe8e18p-45, 0x1.c1c60693fap-2},
309     {0x1.cec807fe8e18p-45, 0x1.c1c60693fap-2},
310     {-0x1.9b6ddc15249aep-45, 0x1.c7ff9c74558p-2},
311     {-0x1.797c33ec7a6bp-47, 0x1.ce42f180648p-2},
312     {0x1.35bafe9a767a8p-45, 0x1.d490246def8p-2},
313     {-0x1.ea42d60dc616ap-46, 0x1.dae75484c98p-2},
314     {-0x1.326b207322938p-46, 0x1.e148a1a2728p-2},
315     {-0x1.326b207322938p-46, 0x1.e148a1a2728p-2},
316     {-0x1.465505372bd08p-45, 0x1.e7b42c3ddbp-2},
317     {0x1.f27f45a470251p-45, 0x1.ee2a156b41p-2},
318     {0x1.2cde56f014a8bp-46, 0x1.f4aa7ee0318p-2},
319     {0x1.2cde56f014a8bp-46, 0x1.f4aa7ee0318p-2},
320     {0x1.085fa3c164935p-47, 0x1.fb358af7a48p-2},
321     {-0x1.53ba3b1727b1cp-47, 0x1.00e5ae5b208p-1},
322     {-0x1.4c45fe79539ep-47, 0x1.04360be7604p-1},
323     {-0x1.4c45fe79539ep-47, 0x1.04360be7604p-1},
324     {0x1.6812241edf5fdp-45, 0x1.078bf0533c4p-1},
325     {0x1.f486b887e7e27p-46, 0x1.0ae76e2d054p-1},
326     {0x1.f486b887e7e27p-46, 0x1.0ae76e2d054p-1},
327     {0x1.c299807801742p-46, 0x1.0e4898611ccp-1},
328     {-0x1.58647bb9ddcb2p-45, 0x1.11af823c75cp-1},
329     {-0x1.58647bb9ddcb2p-45, 0x1.11af823c75cp-1},
330     {-0x1.edd97a293ae49p-45, 0x1.151c3f6f298p-1},
331     {0x1.4cc4ef8ab465p-46, 0x1.188ee40f23cp-1},
332     {0x1.4cc4ef8ab465p-46, 0x1.188ee40f23cp-1},
333     {0x1.cacdeed70e667p-51, 0x1.1c07849ae6p-1},
334     {-0x1.a7242c9fe81d3p-45, 0x1.1f8635fc618p-1},
335     {-0x1.a7242c9fe81d3p-45, 0x1.1f8635fc618p-1},
336     {0x1.2fc066e48667bp-46, 0x1.230b0d8bebcp-1},
337     {-0x1.b61f10522625p-47, 0x1.269621134dcp-1},
338     {-0x1.b61f10522625p-47, 0x1.269621134dcp-1},
339     {0x1.06d2be797882dp-45, 0x1.2a2786d0ecp-1},
340     {-0x1.7a6e507b9dc11p-46, 0x1.2dbf557b0ep-1},
341     {-0x1.7a6e507b9dc11p-46, 0x1.2dbf557b0ep-1},
342     {-0x1.74e93c5a0ed9cp-45, 0x1.315da443408p-1},
343     {-0x1.74e93c5a0ed9cp-45, 0x1.315da443408p-1},
344     {0x1.0b83f9527e6acp-46, 0x1.35028ad9d8cp-1},
345     {-0x1.18b7abb5569a4p-45, 0x1.38ae2171978p-1},
346     {-0x1.18b7abb5569a4p-45, 0x1.38ae2171978p-1},
347     {-0x1.2b7367cfe13c2p-47, 0x1.3c6080c36cp-1},
348     {-0x1.2b7367cfe13c2p-47, 0x1.3c6080c36cp-1},
349     {-0x1.6ce7930f0c74cp-45, 0x1.4019c2125ccp-1},
350     {-0x1.d984f481051f7p-48, 0x1.43d9ff2f924p-1},
351     {-0x1.d984f481051f7p-48, 0x1.43d9ff2f924p-1},
352     {-0x1.2cb6af94d60aap-45, 0x1.47a1527e8a4p-1},
353     {-0x1.2cb6af94d60aap-45, 0x1.47a1527e8a4p-1},
354     {0x1.f7115ed4c541cp-49, 0x1.4b6fd6f970cp-1},
355     {0x1.f7115ed4c541cp-49, 0x1.4b6fd6f970cp-1},
356     {-0x1.e6c516d93b8fbp-45, 0x1.4f45a835a5p-1},
357     {-0x1.e6c516d93b8fbp-45, 0x1.4f45a835a5p-1},
358     {0x1.5ccc45d257531p-47, 0x1.5322e268678p-1},
359     {0x1.5ccc45d257531p-47, 0x1.5322e268678p-1},
360     {0x1.9980bff3303ddp-47, 0x1.5707a26bb8cp-1},
361     {0x1.9980bff3303ddp-47, 0x1.5707a26bb8cp-1},
362     {0x1.dfa63ac10c9fbp-45, 0x1.5af405c3648p-1},
363     {0x1.dfa63ac10c9fbp-45, 0x1.5af405c3648p-1},
364     {0x1.202380cda46bep-45, 0x1.5ee82aa2418p-1},
365     {0.0, 0.0},
366 };
367 
368 // Lookup table for exp(m) with m = -104, ..., 89.
369 //   -104 = floor(log(single precision's min denormal))
370 //     89 = ceil(log(single precision's max normal))
371 // Table is generated with Sollya as follow:
372 // > display = hexadecimal;
373 // > for i from -104 to 89 do { D(exp(i)); };
374 const double EXP_M1[195] = {
375     0x1.f1e6b68529e33p-151, 0x1.525be4e4e601dp-149, 0x1.cbe0a45f75eb1p-148,
376     0x1.3884e838aea68p-146, 0x1.a8c1f14e2af5dp-145, 0x1.20a717e64a9bdp-143,
377     0x1.8851d84118908p-142, 0x1.0a9bdfb02d240p-140, 0x1.6a5bea046b42ep-139,
378     0x1.ec7f3b269efa8p-138, 0x1.4eafb87eab0f2p-136, 0x1.c6e2d05bbc000p-135,
379     0x1.35208867c2683p-133, 0x1.a425b317eeacdp-132, 0x1.1d8508fa8246ap-130,
380     0x1.840fbc08fdc8ap-129, 0x1.07b7112bc1ffep-127, 0x1.666d0dad2961dp-126,
381     0x1.e726c3f64d0fep-125, 0x1.4b0dc07cabf98p-123, 0x1.c1f2daf3b6a46p-122,
382     0x1.31c5957a47de2p-120, 0x1.9f96445648b9fp-119, 0x1.1a6baeadb4fd1p-117,
383     0x1.7fd974d372e45p-116, 0x1.04da4d1452919p-114, 0x1.62891f06b3450p-113,
384     0x1.e1dd273aa8a4ap-112, 0x1.4775e0840bfddp-110, 0x1.bd109d9d94bdap-109,
385     0x1.2e73f53fba844p-107, 0x1.9b138170d6bfep-106, 0x1.175af0cf60ec5p-104,
386     0x1.7baee1bffa80bp-103, 0x1.02057d1245cebp-101, 0x1.5eafffb34ba31p-100,
387     0x1.dca23bae16424p-99,  0x1.43e7fc88b8056p-97,  0x1.b83bf23a9a9ebp-96,
388     0x1.2b2b8dd05b318p-94,  0x1.969d47321e4ccp-93,  0x1.1452b7723aed2p-91,
389     0x1.778fe2497184cp-90,  0x1.fe7116182e9ccp-89,  0x1.5ae191a99585ap-87,
390     0x1.d775d87da854dp-86,  0x1.4063f8cc8bb98p-84,  0x1.b374b315f87c1p-83,
391     0x1.27ec458c65e3cp-81,  0x1.923372c67a074p-80,  0x1.1152eaeb73c08p-78,
392     0x1.737c5645114b5p-77,  0x1.f8e6c24b5592ep-76,  0x1.571db733a9d61p-74,
393     0x1.d257d547e083fp-73,  0x1.3ce9b9de78f85p-71,  0x1.aebabae3a41b5p-70,
394     0x1.24b6031b49bdap-68,  0x1.8dd5e1bb09d7ep-67,  0x1.0e5b73d1ff53dp-65,
395     0x1.6f741de1748ecp-64,  0x1.f36bd37f42f3ep-63,  0x1.536452ee2f75cp-61,
396     0x1.cd480a1b74820p-60,  0x1.39792499b1a24p-58,  0x1.aa0de4bf35b38p-57,
397     0x1.2188ad6ae3303p-55,  0x1.898471fca6055p-54,  0x1.0b6c3afdde064p-52,
398     0x1.6b7719a59f0e0p-51,  0x1.ee001eed62aa0p-50,  0x1.4fb547c775da8p-48,
399     0x1.c8464f7616468p-47,  0x1.36121e24d3bbap-45,  0x1.a56e0c2ac7f75p-44,
400     0x1.1e642baeb84a0p-42,  0x1.853f01d6d53bap-41,  0x1.0885298767e9ap-39,
401     0x1.67852a7007e42p-38,  0x1.e8a37a45fc32ep-37,  0x1.4c1078fe9228ap-35,
402     0x1.c3527e433fab1p-34,  0x1.32b48bf117da2p-32,  0x1.a0db0d0ddb3ecp-31,
403     0x1.1b48655f37267p-29,  0x1.81056ff2c5772p-28,  0x1.05a628c699fa1p-26,
404     0x1.639e3175a689dp-25,  0x1.e355bbaee85cbp-24,  0x1.4875ca227ec38p-22,
405     0x1.be6c6fdb01612p-21,  0x1.2f6053b981d98p-19,  0x1.9c54c3b43bc8bp-18,
406     0x1.18354238f6764p-16,  0x1.7cd79b5647c9bp-15,  0x1.02cf22526545ap-13,
407     0x1.5fc21041027adp-12,  0x1.de16b9c24a98fp-11,  0x1.44e51f113d4d6p-9,
408     0x1.b993fe00d5376p-8,   0x1.2c155b8213cf4p-6,   0x1.97db0ccceb0afp-5,
409     0x1.152aaa3bf81ccp-3,   0x1.78b56362cef38p-2,   0x1.0000000000000p+0,
410     0x1.5bf0a8b145769p+1,   0x1.d8e64b8d4ddaep+2,   0x1.415e5bf6fb106p+4,
411     0x1.b4c902e273a58p+5,   0x1.28d389970338fp+7,   0x1.936dc5690c08fp+8,
412     0x1.122885aaeddaap+10,  0x1.749ea7d470c6ep+11,  0x1.fa7157c470f82p+12,
413     0x1.5829dcf950560p+14,  0x1.d3c4488ee4f7fp+15,  0x1.3de1654d37c9ap+17,
414     0x1.b00b5916ac955p+18,  0x1.259ac48bf05d7p+20,  0x1.8f0ccafad2a87p+21,
415     0x1.0f2ebd0a80020p+23,  0x1.709348c0ea4f9p+24,  0x1.f4f22091940bdp+25,
416     0x1.546d8f9ed26e1p+27,  0x1.ceb088b68e804p+28,  0x1.3a6e1fd9eecfdp+30,
417     0x1.ab5adb9c43600p+31,  0x1.226af33b1fdc1p+33,  0x1.8ab7fb5475fb7p+34,
418     0x1.0c3d3920962c9p+36,  0x1.6c932696a6b5dp+37,  0x1.ef822f7f6731dp+38,
419     0x1.50bba3796379ap+40,  0x1.c9aae4631c056p+41,  0x1.370470aec28edp+43,
420     0x1.a6b765d8cdf6dp+44,  0x1.1f43fcc4b662cp+46,  0x1.866f34a725782p+47,
421     0x1.0953e2f3a1ef7p+49,  0x1.689e221bc8d5bp+50,  0x1.ea215a1d20d76p+51,
422     0x1.4d13fbb1a001ap+53,  0x1.c4b334617cc67p+54,  0x1.33a43d282a519p+56,
423     0x1.a220d397972ebp+57,  0x1.1c25c88df6862p+59,  0x1.8232558201159p+60,
424     0x1.0672a3c9eb871p+62,  0x1.64b41c6d37832p+63,  0x1.e4cf766fe49bep+64,
425     0x1.49767bc0483e3p+66,  0x1.bfc951eb8bb76p+67,  0x1.304d6aeca254bp+69,
426     0x1.9d97010884251p+70,  0x1.19103e4080b45p+72,  0x1.7e013cd114461p+73,
427     0x1.03996528e074cp+75,  0x1.60d4f6fdac731p+76,  0x1.df8c5af17ba3bp+77,
428     0x1.45e3076d61699p+79,  0x1.baed16a6e0da7p+80,  0x1.2cffdfebde1a1p+82,
429     0x1.9919cabefcb69p+83,  0x1.160345c9953e3p+85,  0x1.79dbc9dc53c66p+86,
430     0x1.00c810d464097p+88,  0x1.5d009394c5c27p+89,  0x1.da57de8f107a8p+90,
431     0x1.425982cf597cdp+92,  0x1.b61e5ca3a5e31p+93,  0x1.29bb825dfcf87p+95,
432     0x1.94a90db0d6fe2p+96,  0x1.12fec759586fdp+98,  0x1.75c1dc469e3afp+99,
433     0x1.fbfd219c43b04p+100, 0x1.5936d44e1a146p+102, 0x1.d531d8a7ee79cp+103,
434     0x1.3ed9d24a2d51bp+105, 0x1.b15cfe5b6e17bp+106, 0x1.268038c2c0e00p+108,
435     0x1.9044a73545d48p+109, 0x1.1002ab6218b38p+111, 0x1.71b3540cbf921p+112,
436     0x1.f6799ea9c414ap+113, 0x1.55779b984f3ebp+115, 0x1.d01a210c44aa4p+116,
437     0x1.3b63da8e91210p+118, 0x1.aca8d6b0116b8p+119, 0x1.234de9e0c74e9p+121,
438     0x1.8bec7503ca477p+122, 0x1.0d0eda9796b90p+124, 0x1.6db0118477245p+125,
439     0x1.f1056dc7bf22dp+126, 0x1.51c2cc3433801p+128, 0x1.cb108ffbec164p+129,
440 };
441 
442 // Lookup table for exp(m * 2^(-7)) with m = 0, ..., 127.
443 // Table is generated with Sollya as follow:
444 // > display = hexadecimal;
445 // > for i from 0 to 127 do { D(exp(i / 128)); };
446 const double EXP_M2[128] = {
447     0x1.0000000000000p0, 0x1.0202015600446p0, 0x1.04080ab55de39p0,
448     0x1.06122436410ddp0, 0x1.08205601127edp0, 0x1.0a32a84e9c1f6p0,
449     0x1.0c49236829e8cp0, 0x1.0e63cfa7ab09dp0, 0x1.1082b577d34edp0,
450     0x1.12a5dd543ccc5p0, 0x1.14cd4fc989cd6p0, 0x1.16f9157587069p0,
451     0x1.192937074e0cdp0, 0x1.1b5dbd3f68122p0, 0x1.1d96b0eff0e79p0,
452     0x1.1fd41afcba45ep0, 0x1.2216045b6f5cdp0, 0x1.245c7613b8a9bp0,
453     0x1.26a7793f60164p0, 0x1.28f7170a755fdp0, 0x1.2b4b58b372c79p0,
454     0x1.2da4478b620c7p0, 0x1.3001ecf601af7p0, 0x1.32645269ea829p0,
455     0x1.34cb8170b5835p0, 0x1.373783a722012p0, 0x1.39a862bd3c106p0,
456     0x1.3c1e2876834aap0, 0x1.3e98deaa11dccp0, 0x1.41188f42c3e32p0,
457     0x1.439d443f5f159p0, 0x1.462707b2bac21p0, 0x1.48b5e3c3e8186p0,
458     0x1.4b49e2ae5ac67p0, 0x1.4de30ec211e60p0, 0x1.50817263c13cdp0,
459     0x1.5325180cfacf7p0, 0x1.55ce0a4c58c7cp0, 0x1.587c53c5a7af0p0,
460     0x1.5b2fff3210fd9p0, 0x1.5de9176045ff5p0, 0x1.60a7a734ab0e8p0,
461     0x1.636bb9a983258p0, 0x1.663559cf1bc7cp0, 0x1.690492cbf9433p0,
462     0x1.6bd96fdd034a2p0, 0x1.6eb3fc55b1e76p0, 0x1.719443a03acb9p0,
463     0x1.747a513dbef6ap0, 0x1.776630c678bc1p0, 0x1.7a57ede9ea23ep0,
464     0x1.7d4f946f0ba8dp0, 0x1.804d30347b546p0, 0x1.8350cd30ac390p0,
465     0x1.865a7772164c5p0, 0x1.896a3b1f66a0ep0, 0x1.8c802477b0010p0,
466     0x1.8f9c3fd29beafp0, 0x1.92be99a09bf00p0, 0x1.95e73e6b1b75ep0,
467     0x1.99163ad4b1dccp0, 0x1.9c4b9b995509bp0, 0x1.9f876d8e8c566p0,
468     0x1.a2c9bda3a3e78p0, 0x1.a61298e1e069cp0, 0x1.a9620c6cb3374p0,
469     0x1.acb82581eee54p0, 0x1.b014f179fc3b8p0, 0x1.b3787dc80f95fp0,
470     0x1.b6e2d7fa5eb18p0, 0x1.ba540dba56e56p0, 0x1.bdcc2cccd3c85p0,
471     0x1.c14b431256446p0, 0x1.c4d15e873c193p0, 0x1.c85e8d43f7cd0p0,
472     0x1.cbf2dd7d490f2p0, 0x1.cf8e5d84758a9p0, 0x1.d3311bc7822b4p0,
473     0x1.d6db26d16cd67p0, 0x1.da8c8d4a66969p0, 0x1.de455df80e3c0p0,
474     0x1.e205a7bdab73ep0, 0x1.e5cd799c6a54ep0, 0x1.e99ce2b397649p0,
475     0x1.ed73f240dc142p0, 0x1.f152b7a07bb76p0, 0x1.f539424d90f5ep0,
476     0x1.f927a1e24bb76p0, 0x1.fd1de6182f8c9p0, 0x1.008e0f64294abp1,
477     0x1.02912df5ce72ap1, 0x1.049856cd84339p1, 0x1.06a39207f0a09p1,
478     0x1.08b2e7d2035cfp1, 0x1.0ac6606916501p1, 0x1.0cde041b0e9aep1,
479     0x1.0ef9db467dcf8p1, 0x1.1119ee5ac36b6p1, 0x1.133e45d82e952p1,
480     0x1.1566ea50201d7p1, 0x1.1793e4652cc50p1, 0x1.19c53ccb3fc6bp1,
481     0x1.1bfafc47bda73p1, 0x1.1e352bb1a74adp1, 0x1.2073d3f1bd518p1,
482     0x1.22b6fe02a3b9cp1, 0x1.24feb2f105cb8p1, 0x1.274afbdbba4a6p1,
483     0x1.299be1f3e7f1cp1, 0x1.2bf16e7d2a38cp1, 0x1.2e4baacdb6614p1,
484     0x1.30aaa04e80d05p1, 0x1.330e587b62b28p1, 0x1.3576dce33feadp1,
485     0x1.37e437282d4eep1, 0x1.3a5670ff972edp1, 0x1.3ccd9432682b4p1,
486     0x1.3f49aa9d30590p1, 0x1.41cabe304cb34p1, 0x1.4450d8f00edd4p1,
487     0x1.46dc04f4e5338p1, 0x1.496c4c6b832dap1, 0x1.4c01b9950a111p1,
488     0x1.4e9c56c731f5dp1, 0x1.513c2e6c731d7p1, 0x1.53e14b042f9cap1,
489     0x1.568bb722dd593p1, 0x1.593b7d72305bbp1,
490 };
491 
492 } // namespace __llvm_libc
493