/////////////////////////////////////////////////////////////////////////////////// // Copyright (C) 2018 F4EXB // // written by Edouard Griffiths // // // // This program is free software; you can redistribute it and/or modify // // it under the terms of the GNU General Public License as published by // // the Free Software Foundation as version 3 of the License, or // // (at your option) any later version. // // // // This program is distributed in the hope that it will be useful, // // but WITHOUT ANY WARRANTY; without even the implied warranty of // // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // // GNU General Public License V3 for more details. // // // // You should have received a copy of the GNU General Public License // // along with this program. If not, see . // /////////////////////////////////////////////////////////////////////////////////// #include "fixedtraits.h" // 1.0 = 2^28 internal representation // ln(1/2^n), n = index+1 then list is reversed const int64_t FixedTraits<28>::log_two_power_n_reversed[35] = { 0x18429946ELL, 0x1791272EFLL, 0x16DFB516FLL, 0x162E42FF0LL, 0x157CD0E70LL, 0x14CB5ECF1LL, 0x1419ECB71LL, 0x13687A9F2LL, 0x12B708872LL, 0x1205966F3LL, 0x115424573LL, 0x10A2B23F4LL, 0xFF140274LL, 0xF3FCE0F5LL, 0xE8E5BF75LL, 0xDDCE9DF6LL, 0xD2B77C76LL, 0xC7A05AF7LL, 0xBC893977LL, 0xB17217F8LL, 0xA65AF679LL, 0x9B43D4F9LL, 0x902CB379LL, 0x851591FaLL, 0x79FE707bLL, 0x6EE74EFbLL, 0x63D02D7BLL, 0x58B90BFcLL, 0x4DA1EA7CLL, 0x428AC8FdLL, 0x3773A77DLL, 0x2C5C85FeLL, 0x2145647ELL, 0x162E42FfLL, 0xB17217FLL }; // ln(1+2^-n), n = index+1 const int64_t FixedTraits<28>::log_one_plus_two_power_minus_n[28] = { 0x67CC8FBLL, 0x391FEF9LL, 0x1E27077LL, 0xF85186LL, 0x7E0A6CLL, 0x3F8151LL, 0x1FE02ALL, 0xFF805LL, 0x7FE01LL, 0x3FF80LL, 0x1FFE0LL, 0xFFF8LL, 0x7FFELL, 0x4000LL, 0x2000LL, 0x1000LL, 0x800LL, 0x400LL, 0x200LL, 0x100LL, 0x80LL, 0x40LL, 0x20LL, 0x10LL, 0x8LL, 0x4LL, 0x2LL, 0x1LL }; // ln(1/1-2^-n), n = index+1 const int64_t FixedTraits<28>::log_one_over_one_minus_two_power_minus_n[28] = { 0xB172180LL, 0x49A5884LL, 0x222F1D0LL, 0x108598BLL, 0x820AECLL, 0x408159LL, 0x20202BLL, 0x100805LL, 0x80201LL, 0x40080LL, 0x20020LL, 0x10008LL, 0x8002LL, 0x4001LL, 0x2000LL, 0x1000LL, 0x800LL, 0x400LL, 0x200LL, 0x100LL, 0x80LL, 0x40LL, 0x20LL, 0x10LL, 0x8LL, 0x4LL, 0x2LL, 0x1LL }; const int64_t FixedTraits<28>::arctantab[32] = { 297197971, 210828714, 124459457, 65760959, 33381290, 16755422, 8385879, 4193963, 2097109, 1048571, 524287, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0, 0 }; // 1.0 = 2^16 internal representation const int64_t FixedTraits<16>::log_two_power_n_reversed[47] = { 2135026LL, 2089600LL, 2044174LL, 1998748LL, 1953322LL, 1907896LL, 1862470LL, 1817044LL, 1771618LL, 1726192LL, 1680765LL, 1635339LL, 1589913LL, 1544487LL, 1499061LL, 1453635LL, 1408209LL, 1362783LL, 1317357LL, 1271931LL, 1226505LL, 1181078LL, 1135652LL, 1090226LL, 1044800LL, 999374LL, 953948LL, 908522LL, 863096LL, 817670LL, 772244LL, 726817LL, 681391LL, 635965LL, 590539LL, 545113LL, 499687LL, 454261LL, 408835LL, 363409LL, 317983LL, 272557LL, 227130LL, 181704LL, 136278LL, 90852LL, 45426LL }; const int64_t FixedTraits<16>::log_one_plus_two_power_minus_n[16] = { 26573LL, 14624LL, 7719LL, 3973LL, 2017LL, 1016LL, 510LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL }; const int64_t FixedTraits<16>::log_one_over_one_minus_two_power_minus_n[16] = { 45426LL, 18854LL, 8751LL, 4230LL, 2081LL, 1032LL, 514LL, 257LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL }; const int64_t FixedTraits<16>::arctantab[32] = { 72558LL, 51471LL, 30385LL, 16054LL, 8149LL, 4090LL, 2047LL, 1023LL, 511LL, 255LL, 127LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL }; // 1.0 = 2^23 internal representation const int64_t FixedTraits<23>::log_two_power_n_reversed[40] = { 232581599LL, 226767059LL, 220952519LL, 215137979LL, 209323439LL, 203508899LL, 197694359LL, 191879819LL, 186065279LL, 180250740LL, 174436200LL, 168621660LL, 162807120LL, 156992580LL, 151178040LL, 145363500LL, 139548960LL, 133734420LL, 127919880LL, 122105340LL, 116290800LL, 110476260LL, 104661720LL, 98847180LL, 93032640LL, 87218100LL, 81403560LL, 75589020LL, 69774480LL, 63959940LL, 58145400LL, 52330860LL, 46516320LL, 40701780LL, 34887240LL, 29072700LL, 23258160LL, 17443620LL, 11629080LL, 5814540LL }; const int64_t FixedTraits<23>::log_one_plus_two_power_minus_n[23] = { 3401288LL, 1871864LL, 988036LL, 508556LL, 258131LL, 130059LL, 65281LL, 32704LL, 16368LL, 8188LL, 4095LL, 2048LL, 1024LL, 512LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL }; const int64_t FixedTraits<23>::log_one_over_one_minus_two_power_minus_n[23] = { 5814540LL, 2413252LL, 1120143LL, 541388LL, 266327LL, 132107LL, 65793LL, 32832LL, 16400LL, 8196LL, 4097LL, 2048LL, 1024LL, 512LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL }; const int64_t FixedTraits<23>::arctantab[32] = { 9287436LL, 6588397LL, 3889358LL, 2055029LL, 1043165LL, 523606LL, 262058LL, 131061LL, 65534LL, 32767LL, 16383LL, 8192LL, 4096LL, 2048LL, 1024LL, 512LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL }; // 1.0 = 2^24 internal representation const int64_t FixedTraits<24>::log_two_power_n_reversed[39] = { 453534119LL, 441905039LL, 430275959LL, 418646879LL, 407017799LL, 395388719LL, 383759639LL, 372130559LL, 360501479LL, 348872399LL, 337243319LL, 325614239LL, 313985159LL, 302356079LL, 290726999LL, 279097919LL, 267468839LL, 255839759LL, 244210679LL, 232581599LL, 220952519LL, 209323439LL, 197694359LL, 186065279LL, 174436200LL, 162807120LL, 151178040LL, 139548960LL, 127919880LL, 116290800LL, 104661720LL, 93032640LL, 81403560LL, 69774480LL, 58145400LL, 46516320LL, 34887240LL, 23258160LL, 11629080LL }; const int64_t FixedTraits<24>::log_one_plus_two_power_minus_n[24] = { 6802576LL, 3743728LL, 1976071LL, 1017112LL, 516263LL, 260117LL, 130563LL, 65408LL, 32736LL, 16376LL, 8190LL, 4096LL, 2048LL, 1024LL, 512LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL }; const int64_t FixedTraits<24>::log_one_over_one_minus_two_power_minus_n[24] = { 11629080LL, 4826504LL, 2240285LL, 1082777LL, 532655LL, 264214LL, 131587LL, 65664LL, 32800LL, 16392LL, 8194LL, 4097LL, 2048LL, 1024LL, 512LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL }; const int64_t FixedTraits<24>::arctantab[32] = { 18574873LL, 13176794LL, 7778716LL, 4110059LL, 2086330LL, 1047213LL, 524117LL, 262122LL, 131069LL, 65535LL, 32767LL, 16384LL, 8192LL, 4096LL, 2048LL, 1024LL, 512LL, 256LL, 128LL, 64LL, 32LL, 16LL, 8LL, 4LL, 2LL, 1LL, 0LL, 0LL, 0LL, 0LL, 0LL, 0LL };