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