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 11 namespace __llvm_libc { 12 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}; 58 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}; 104 105 // 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 0x1p0, 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}; 132 133 alignas(64) const double RD[128] = { 134 0x1p0, 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}; 153 154 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}; 198 199 // 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, 271 }; 272 273 // 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, 321 }; 322 323 } // namespace __llvm_libc 324