///////////////////////////////////////////////////////////////////////////////////
// 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 <http://www.gnu.org/licenses/>. //
///////////////////////////////////////////////////////////////////////////////////
#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
};