File indexing completed on 2024-04-28 03:40:38
0001 /************************************************************************************* 0002 * Copyright (C) 2014 by Percy Camilo T. Aucahuasi <percy.camilo.ta@gmail.com> * 0003 * * 0004 * This program is free software; you can redistribute it and/or * 0005 * modify it under the terms of the GNU General Public License * 0006 * as published by the Free Software Foundation; either version 2 * 0007 * of the License, or (at your option) any later version. * 0008 * * 0009 * This program is distributed in the hope that it will be useful, * 0010 * but WITHOUT ANY WARRANTY; without even the implied warranty of * 0011 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * 0012 * GNU General Public License for more details. * 0013 * * 0014 * You should have received a copy of the GNU General Public License * 0015 * along with this program; if not, write to the Free Software * 0016 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA * 0017 *************************************************************************************/ 0018 0019 #ifndef ADDITIONCHAINS_H 0020 #define ADDITIONCHAINS_H 0021 0022 //NOTE this code generates the whole thing ... 0023 // see seq function in 0024 // https://rosettacode.org/wiki/Addition-chain_exponentiation/Achain.c or 0025 // https://www-cs-faculty.stanford.edu/~knuth/programs/achain4.w 0026 // int main(int argc, char *argv[]) 0027 // { 0028 // const int MAX_N = 2048; 0029 // const int MAX_LEN = 15; 0030 // const int MAX_COL = MAX_LEN+1; 0031 // // seq len of max(1,2,...,MAX_N) is MAX_LEN but we need one additional slot for len (length) info (at 0) so we need MAX_COL cols 0032 // int buffer[MAX_N+1] = {0}; 0033 // 0034 // printf("static const int additionChains[%d][%d] = {\n", MAX_N+1, MAX_COL+1); 0035 // for (int k = 0; k <= MAX_N; ++k) { 0036 // int l = k==0? 0 : k==1? 0 : seq(k, 0, buffer); 0037 // printf("{%d,", l); 0038 // 0039 // for (int i = 0; i < MAX_COL; ++i) { 0040 // if (i <= l) 0041 // printf("%d%s", buffer[i], i == MAX_COL-1 ? "},\n" : ","); 0042 // else { 0043 // if (k != MAX_N) 0044 // printf("%d%s", 0, i == MAX_COL-1 ? "},\n" : ","); 0045 // else 0046 // printf("%d%s", 0, i == MAX_COL-1 ? "}};\n" : ","); 0047 // } 0048 // } 0049 // } 0050 // 0051 // return 0; 0052 // } 0053 0054 //NOTE we have cached 2049 sequences of addition chains (2048 plus a slot for zero) 0055 // e.g. additionChains[124][0] is the length of a valid sequence (without 0056 // trailing zeros) for the number 124 0057 0058 const int MAX_EXPONENT = 2048; 0059 0060 static const int additionChains[MAX_EXPONENT+1][17] = { 0061 {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, 0062 {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, 0063 {1,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, 0064 {2,1,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0}, 0065 {2,1,2,4,0,0,0,0,0,0,0,0,0,0,0,0,0}, 0066 {3,1,2,4,5,0,0,0,0,0,0,0,0,0,0,0,0}, 0067 {3,1,2,4,6,0,0,0,0,0,0,0,0,0,0,0,0}, 0068 {4,1,2,4,6,7,0,0,0,0,0,0,0,0,0,0,0}, 0069 {3,1,2,4,8,0,0,0,0,0,0,0,0,0,0,0,0}, 0070 {4,1,2,4,8,9,0,0,0,0,0,0,0,0,0,0,0}, 0071 {4,1,2,4,8,10,0,0,0,0,0,0,0,0,0,0,0}, 0072 {5,1,2,4,8,10,11,0,0,0,0,0,0,0,0,0,0}, 0073 {4,1,2,4,8,12,0,0,0,0,0,0,0,0,0,0,0}, 0074 {5,1,2,4,8,12,13,0,0,0,0,0,0,0,0,0,0}, 0075 {5,1,2,4,8,12,14,0,0,0,0,0,0,0,0,0,0}, 0076 {5,1,2,3,6,12,15,0,0,0,0,0,0,0,0,0,0}, 0077 {4,1,2,4,8,16,0,0,0,0,0,0,0,0,0,0,0}, 0078 {5,1,2,4,8,16,17,0,0,0,0,0,0,0,0,0,0}, 0079 {5,1,2,4,8,16,18,0,0,0,0,0,0,0,0,0,0}, 0080 {6,1,2,4,8,16,18,19,0,0,0,0,0,0,0,0,0}, 0081 {5,1,2,4,8,16,20,0,0,0,0,0,0,0,0,0,0}, 0082 {6,1,2,4,8,16,20,21,0,0,0,0,0,0,0,0,0}, 0083 {6,1,2,4,8,16,20,22,0,0,0,0,0,0,0,0,0}, 0084 {6,1,2,3,5,10,20,23,0,0,0,0,0,0,0,0,0}, 0085 {5,1,2,4,8,16,24,0,0,0,0,0,0,0,0,0,0}, 0086 {6,1,2,4,8,16,24,25,0,0,0,0,0,0,0,0,0}, 0087 {6,1,2,4,8,16,24,26,0,0,0,0,0,0,0,0,0}, 0088 {6,1,2,3,6,12,24,27,0,0,0,0,0,0,0,0,0}, 0089 {6,1,2,4,8,16,24,28,0,0,0,0,0,0,0,0,0}, 0090 {7,1,2,4,8,16,24,28,29,0,0,0,0,0,0,0,0}, 0091 {6,1,2,4,6,12,24,30,0,0,0,0,0,0,0,0,0}, 0092 {7,1,2,4,6,12,24,30,31,0,0,0,0,0,0,0,0}, 0093 {5,1,2,4,8,16,32,0,0,0,0,0,0,0,0,0,0}, 0094 {6,1,2,4,8,16,32,33,0,0,0,0,0,0,0,0,0}, 0095 {6,1,2,4,8,16,32,34,0,0,0,0,0,0,0,0,0}, 0096 {7,1,2,4,8,16,32,34,35,0,0,0,0,0,0,0,0}, 0097 {6,1,2,4,8,16,32,36,0,0,0,0,0,0,0,0,0}, 0098 {7,1,2,4,8,16,32,36,37,0,0,0,0,0,0,0,0}, 0099 {7,1,2,4,8,16,32,36,38,0,0,0,0,0,0,0,0}, 0100 {7,1,2,3,6,12,24,36,39,0,0,0,0,0,0,0,0}, 0101 {6,1,2,4,8,16,32,40,0,0,0,0,0,0,0,0,0}, 0102 {7,1,2,4,8,16,32,40,41,0,0,0,0,0,0,0,0}, 0103 {7,1,2,4,8,16,32,40,42,0,0,0,0,0,0,0,0}, 0104 {7,1,2,3,5,10,20,40,43,0,0,0,0,0,0,0,0}, 0105 {7,1,2,4,8,16,32,40,44,0,0,0,0,0,0,0,0}, 0106 {7,1,2,4,5,10,20,40,45,0,0,0,0,0,0,0,0}, 0107 {7,1,2,4,6,10,20,40,46,0,0,0,0,0,0,0,0}, 0108 {8,1,2,4,6,10,20,40,46,47,0,0,0,0,0,0,0}, 0109 {6,1,2,4,8,16,32,48,0,0,0,0,0,0,0,0,0}, 0110 {7,1,2,4,8,16,32,48,49,0,0,0,0,0,0,0,0}, 0111 {7,1,2,4,8,16,32,48,50,0,0,0,0,0,0,0,0}, 0112 {7,1,2,3,6,12,24,48,51,0,0,0,0,0,0,0,0}, 0113 {7,1,2,4,8,16,32,48,52,0,0,0,0,0,0,0,0}, 0114 {8,1,2,4,8,16,32,48,52,53,0,0,0,0,0,0,0}, 0115 {7,1,2,4,6,12,24,48,54,0,0,0,0,0,0,0,0}, 0116 {8,1,2,4,6,12,24,48,54,55,0,0,0,0,0,0,0}, 0117 {7,1,2,4,8,16,32,48,56,0,0,0,0,0,0,0,0}, 0118 {8,1,2,4,8,16,32,48,56,57,0,0,0,0,0,0,0}, 0119 {8,1,2,4,8,16,32,48,56,58,0,0,0,0,0,0,0}, 0120 {8,1,2,3,6,12,14,28,56,59,0,0,0,0,0,0,0}, 0121 {7,1,2,4,8,12,24,48,60,0,0,0,0,0,0,0,0}, 0122 {8,1,2,4,8,12,24,48,60,61,0,0,0,0,0,0,0}, 0123 {8,1,2,4,8,12,24,48,60,62,0,0,0,0,0,0,0}, 0124 {8,1,2,3,6,12,24,48,60,63,0,0,0,0,0,0,0}, 0125 {6,1,2,4,8,16,32,64,0,0,0,0,0,0,0,0,0}, 0126 {7,1,2,4,8,16,32,64,65,0,0,0,0,0,0,0,0}, 0127 {7,1,2,4,8,16,32,64,66,0,0,0,0,0,0,0,0}, 0128 {8,1,2,4,8,16,32,64,66,67,0,0,0,0,0,0,0}, 0129 {7,1,2,4,8,16,32,64,68,0,0,0,0,0,0,0,0}, 0130 {8,1,2,4,8,16,32,64,68,69,0,0,0,0,0,0,0}, 0131 {8,1,2,4,8,16,32,64,68,70,0,0,0,0,0,0,0}, 0132 {9,1,2,4,8,16,32,64,68,70,71,0,0,0,0,0,0}, 0133 {7,1,2,4,8,16,32,64,72,0,0,0,0,0,0,0,0}, 0134 {8,1,2,4,8,16,32,64,72,73,0,0,0,0,0,0,0}, 0135 {8,1,2,4,8,16,32,64,72,74,0,0,0,0,0,0,0}, 0136 {8,1,2,3,6,12,24,48,72,75,0,0,0,0,0,0,0}, 0137 {8,1,2,4,8,16,32,64,72,76,0,0,0,0,0,0,0}, 0138 {8,1,2,4,5,9,18,36,72,77,0,0,0,0,0,0,0}, 0139 {8,1,2,4,6,12,24,48,72,78,0,0,0,0,0,0,0}, 0140 {9,1,2,4,6,12,24,48,72,78,79,0,0,0,0,0,0}, 0141 {7,1,2,4,8,16,32,64,80,0,0,0,0,0,0,0,0}, 0142 {8,1,2,4,8,16,32,64,80,81,0,0,0,0,0,0,0}, 0143 {8,1,2,4,8,16,32,64,80,82,0,0,0,0,0,0,0}, 0144 {8,1,2,3,5,10,20,40,80,83,0,0,0,0,0,0,0}, 0145 {8,1,2,4,8,16,32,64,80,84,0,0,0,0,0,0,0}, 0146 {8,1,2,4,5,10,20,40,80,85,0,0,0,0,0,0,0}, 0147 {8,1,2,4,6,10,20,40,80,86,0,0,0,0,0,0,0}, 0148 {9,1,2,4,6,10,20,40,80,86,87,0,0,0,0,0,0}, 0149 {8,1,2,4,8,16,32,64,80,88,0,0,0,0,0,0,0}, 0150 {9,1,2,4,8,16,32,64,80,88,89,0,0,0,0,0,0}, 0151 {8,1,2,4,8,10,20,40,80,90,0,0,0,0,0,0,0}, 0152 {9,1,2,4,8,10,20,40,80,90,91,0,0,0,0,0,0}, 0153 {8,1,2,4,8,12,20,40,80,92,0,0,0,0,0,0,0}, 0154 {9,1,2,4,8,12,20,40,80,92,93,0,0,0,0,0,0}, 0155 {9,1,2,4,8,12,20,40,80,92,94,0,0,0,0,0,0}, 0156 {9,1,2,3,5,10,20,23,46,92,95,0,0,0,0,0,0}, 0157 {7,1,2,4,8,16,32,64,96,0,0,0,0,0,0,0,0}, 0158 {8,1,2,4,8,16,32,64,96,97,0,0,0,0,0,0,0}, 0159 {8,1,2,4,8,16,32,64,96,98,0,0,0,0,0,0,0}, 0160 {8,1,2,3,6,12,24,48,96,99,0,0,0,0,0,0,0}, 0161 {8,1,2,4,8,16,32,64,96,100,0,0,0,0,0,0,0}, 0162 {9,1,2,4,8,16,32,64,96,100,101,0,0,0,0,0,0}, 0163 {8,1,2,4,6,12,24,48,96,102,0,0,0,0,0,0,0}, 0164 {9,1,2,4,6,12,24,48,96,102,103,0,0,0,0,0,0}, 0165 {8,1,2,4,8,16,32,64,96,104,0,0,0,0,0,0,0}, 0166 {9,1,2,4,8,16,32,64,96,104,105,0,0,0,0,0,0}, 0167 {9,1,2,4,8,16,32,64,96,104,106,0,0,0,0,0,0}, 0168 {9,1,2,3,6,12,24,26,52,104,107,0,0,0,0,0,0}, 0169 {8,1,2,4,8,12,24,48,96,108,0,0,0,0,0,0,0}, 0170 {9,1,2,4,8,12,24,48,96,108,109,0,0,0,0,0,0}, 0171 {9,1,2,4,8,12,24,48,96,108,110,0,0,0,0,0,0}, 0172 {9,1,2,3,6,12,24,48,96,108,111,0,0,0,0,0,0}, 0173 {8,1,2,4,8,16,32,64,96,112,0,0,0,0,0,0,0}, 0174 {9,1,2,4,8,16,32,64,96,112,113,0,0,0,0,0,0}, 0175 {9,1,2,4,8,16,32,64,96,112,114,0,0,0,0,0,0}, 0176 {9,1,2,3,6,12,14,28,56,112,115,0,0,0,0,0,0}, 0177 {9,1,2,3,4,7,14,28,56,112,116,0,0,0,0,0,0}, 0178 {9,1,2,4,5,10,14,28,56,112,117,0,0,0,0,0,0}, 0179 {9,1,2,4,6,12,24,28,56,112,118,0,0,0,0,0,0}, 0180 {9,1,2,4,6,7,14,28,56,112,119,0,0,0,0,0,0}, 0181 {8,1,2,4,8,16,24,48,96,120,0,0,0,0,0,0,0}, 0182 {9,1,2,4,8,16,24,48,96,120,121,0,0,0,0,0,0}, 0183 {9,1,2,4,8,16,24,48,96,120,122,0,0,0,0,0,0}, 0184 {9,1,2,3,6,12,24,48,96,120,123,0,0,0,0,0,0}, 0185 {9,1,2,4,8,16,24,48,96,120,124,0,0,0,0,0,0}, 0186 {9,1,2,4,5,10,20,40,80,120,125,0,0,0,0,0,0}, 0187 {9,1,2,4,6,12,24,48,96,120,126,0,0,0,0,0,0}, 0188 {10,1,2,4,6,12,24,48,96,120,126,127,0,0,0,0,0}, 0189 {7,1,2,4,8,16,32,64,128,0,0,0,0,0,0,0,0}, 0190 {8,1,2,4,8,16,32,64,128,129,0,0,0,0,0,0,0}, 0191 {8,1,2,4,8,16,32,64,128,130,0,0,0,0,0,0,0}, 0192 {9,1,2,4,8,16,32,64,128,130,131,0,0,0,0,0,0}, 0193 {8,1,2,4,8,16,32,64,128,132,0,0,0,0,0,0,0}, 0194 {9,1,2,4,8,16,32,64,128,132,133,0,0,0,0,0,0}, 0195 {9,1,2,4,8,16,32,64,128,132,134,0,0,0,0,0,0}, 0196 {9,1,2,3,6,12,15,30,60,120,135,0,0,0,0,0,0}, 0197 {8,1,2,4,8,16,32,64,128,136,0,0,0,0,0,0,0}, 0198 {9,1,2,4,8,16,32,64,128,136,137,0,0,0,0,0,0}, 0199 {9,1,2,4,8,16,32,64,128,136,138,0,0,0,0,0,0}, 0200 {10,1,2,4,8,16,32,64,128,136,138,139,0,0,0,0,0}, 0201 {9,1,2,4,8,16,32,64,128,136,140,0,0,0,0,0,0}, 0202 {10,1,2,4,8,16,32,64,128,136,140,141,0,0,0,0,0}, 0203 {10,1,2,4,8,16,32,64,128,136,140,142,0,0,0,0,0}, 0204 {10,1,2,3,5,10,20,40,80,120,140,143,0,0,0,0,0}, 0205 {8,1,2,4,8,16,32,64,128,144,0,0,0,0,0,0,0}, 0206 {9,1,2,4,8,16,32,64,128,144,145,0,0,0,0,0,0}, 0207 {9,1,2,4,8,16,32,64,128,144,146,0,0,0,0,0,0}, 0208 {9,1,2,3,6,12,24,48,96,144,147,0,0,0,0,0,0}, 0209 {9,1,2,4,8,16,32,64,128,144,148,0,0,0,0,0,0}, 0210 {9,1,2,4,5,9,18,36,72,144,149,0,0,0,0,0,0}, 0211 {9,1,2,4,6,12,24,48,96,144,150,0,0,0,0,0,0}, 0212 {10,1,2,4,6,12,24,48,96,144,150,151,0,0,0,0,0}, 0213 {9,1,2,4,8,16,32,64,128,144,152,0,0,0,0,0,0}, 0214 {9,1,2,4,8,9,18,36,72,144,153,0,0,0,0,0,0}, 0215 {9,1,2,4,8,10,18,36,72,144,154,0,0,0,0,0,0}, 0216 {10,1,2,4,8,10,18,36,72,144,154,155,0,0,0,0,0}, 0217 {9,1,2,4,8,12,24,48,96,144,156,0,0,0,0,0,0}, 0218 {10,1,2,4,8,12,24,48,96,144,156,157,0,0,0,0,0}, 0219 {10,1,2,4,8,12,24,48,96,144,156,158,0,0,0,0,0}, 0220 {10,1,2,3,6,12,24,48,96,144,156,159,0,0,0,0,0}, 0221 {8,1,2,4,8,16,32,64,128,160,0,0,0,0,0,0,0}, 0222 {9,1,2,4,8,16,32,64,128,160,161,0,0,0,0,0,0}, 0223 {9,1,2,4,8,16,32,64,128,160,162,0,0,0,0,0,0}, 0224 {9,1,2,3,5,10,20,40,80,160,163,0,0,0,0,0,0}, 0225 {9,1,2,4,8,16,32,64,128,160,164,0,0,0,0,0,0}, 0226 {9,1,2,4,5,10,20,40,80,160,165,0,0,0,0,0,0}, 0227 {9,1,2,4,6,10,20,40,80,160,166,0,0,0,0,0,0}, 0228 {10,1,2,4,6,10,20,40,80,160,166,167,0,0,0,0,0}, 0229 {9,1,2,4,8,16,32,64,128,160,168,0,0,0,0,0,0}, 0230 {10,1,2,4,8,16,32,64,128,160,168,169,0,0,0,0,0}, 0231 {9,1,2,4,8,10,20,40,80,160,170,0,0,0,0,0,0}, 0232 {10,1,2,4,8,10,20,40,80,160,170,171,0,0,0,0,0}, 0233 {9,1,2,4,8,12,20,40,80,160,172,0,0,0,0,0,0}, 0234 {10,1,2,4,8,12,20,40,80,160,172,173,0,0,0,0,0}, 0235 {10,1,2,4,8,12,20,40,80,160,172,174,0,0,0,0,0}, 0236 {10,1,2,3,5,10,20,40,43,86,172,175,0,0,0,0,0}, 0237 {9,1,2,4,8,16,32,64,128,160,176,0,0,0,0,0,0}, 0238 {10,1,2,4,8,16,32,64,128,160,176,177,0,0,0,0,0}, 0239 {10,1,2,4,8,16,32,64,128,160,176,178,0,0,0,0,0}, 0240 {10,1,2,3,5,10,20,22,44,88,176,179,0,0,0,0,0}, 0241 {9,1,2,4,8,16,20,40,80,160,180,0,0,0,0,0,0}, 0242 {10,1,2,4,8,16,20,40,80,160,180,181,0,0,0,0,0}, 0243 {10,1,2,4,8,16,20,40,80,160,180,182,0,0,0,0,0}, 0244 {10,1,2,3,5,10,20,40,80,160,180,183,0,0,0,0,0}, 0245 {9,1,2,4,8,16,24,40,80,160,184,0,0,0,0,0,0}, 0246 {10,1,2,4,8,16,24,40,80,160,184,185,0,0,0,0,0}, 0247 {10,1,2,4,8,16,24,40,80,160,184,186,0,0,0,0,0}, 0248 {10,1,2,3,5,10,20,23,46,92,184,187,0,0,0,0,0}, 0249 {10,1,2,4,8,16,24,40,80,160,184,188,0,0,0,0,0}, 0250 {10,1,2,3,5,10,20,23,46,92,184,189,0,0,0,0,0}, 0251 {10,1,2,4,6,10,20,40,46,92,184,190,0,0,0,0,0}, 0252 {11,1,2,4,6,10,20,40,46,92,184,190,191,0,0,0,0}, 0253 {8,1,2,4,8,16,32,64,128,192,0,0,0,0,0,0,0}, 0254 {9,1,2,4,8,16,32,64,128,192,193,0,0,0,0,0,0}, 0255 {9,1,2,4,8,16,32,64,128,192,194,0,0,0,0,0,0}, 0256 {9,1,2,3,6,12,24,48,96,192,195,0,0,0,0,0,0}, 0257 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{14,1,2,4,8,16,32,48,56,112,224,448,896,1792,1848,1850,0}, 1912 {14,1,2,3,6,12,14,28,56,112,224,448,896,1792,1848,1851,0}, 1913 {14,1,2,3,4,7,14,28,56,112,224,448,896,1792,1848,1852,0}, 1914 {14,1,2,4,5,10,14,28,56,112,224,448,896,1792,1848,1853,0}, 1915 {14,1,2,4,6,12,24,28,56,112,224,448,896,1792,1848,1854,0}, 1916 {14,1,2,4,6,7,14,28,56,112,224,448,896,1792,1848,1855,0}, 1917 {13,1,2,4,8,16,32,48,64,112,224,448,896,1792,1856,0,0}, 1918 {14,1,2,4,8,16,32,48,64,112,224,448,896,1792,1856,1857,0}, 1919 {14,1,2,4,8,16,32,48,64,112,224,448,896,1792,1856,1858,0}, 1920 {14,1,2,3,6,8,14,28,56,112,224,232,464,928,1856,1859,0}, 1921 {14,1,2,3,4,7,14,28,56,112,116,232,464,928,1856,1860,0}, 1922 {14,1,2,4,5,10,14,28,56,112,116,232,464,928,1856,1861,0}, 1923 {14,1,2,4,5,6,12,24,29,58,116,232,464,928,1856,1862,0}, 1924 {14,1,2,3,4,7,14,28,56,112,116,232,464,928,1856,1863,0}, 1925 {13,1,2,4,8,16,32,40,72,112,224,448,896,1792,1864,0,0}, 1926 {14,1,2,4,8,16,32,40,72,112,224,448,896,1792,1864,1865,0}, 1927 {14,1,2,4,8,16,32,40,72,112,224,448,896,1792,1864,1866,0}, 1928 {14,1,2,3,4,7,11,22,29,58,116,232,464,928,1856,1867,0}, 1929 {14,1,2,4,8,16,32,40,72,112,224,448,896,1792,1864,1868,0}, 1930 {14,1,2,4,5,9,14,28,56,112,224,233,466,932,1864,1869,0}, 1931 {14,1,2,4,6,8,14,28,56,112,224,232,464,928,1856,1870,0}, 1932 {14,1,2,4,8,12,14,15,29,58,116,232,464,928,1856,1871,0}, 1933 {13,1,2,4,8,16,32,64,80,160,224,448,896,1792,1872,0,0}, 1934 {14,1,2,4,8,16,32,64,80,160,224,448,896,1792,1872,1873,0}, 1935 {14,1,2,4,8,16,32,64,80,160,224,448,896,1792,1872,1874,0}, 1936 {14,1,2,3,6,12,24,48,96,144,288,576,1152,1728,1872,1875,0}, 1937 {14,1,2,4,8,16,32,64,80,160,224,448,896,1792,1872,1876,0}, 1938 {14,1,2,4,5,9,18,36,72,144,288,576,1152,1728,1872,1877,0}, 1939 {14,1,2,4,6,12,24,48,96,144,288,576,1152,1728,1872,1878,0}, 1940 {14,1,2,4,6,7,13,26,52,104,208,416,832,1664,1872,1879,0}, 1941 {14,1,2,3,5,8,13,26,52,104,208,416,832,1664,1872,1880,0}, 1942 {14,1,2,4,8,9,18,36,72,144,288,576,1152,1728,1872,1881,0}, 1943 {14,1,2,4,8,10,18,36,72,144,288,576,1152,1728,1872,1882,0}, 1944 {14,1,2,4,8,9,18,27,54,108,116,232,464,928,1856,1883,0}, 1945 {14,1,2,4,8,12,24,48,96,144,288,576,1152,1728,1872,1884,0}, 1946 {14,1,2,4,8,12,13,26,52,104,208,416,832,1664,1872,1885,0}, 1947 {14,1,2,4,8,12,14,26,52,104,208,416,832,1664,1872,1886,0}, 1948 {14,1,2,3,6,9,15,30,39,78,156,312,624,1248,1872,1887,0}, 1949 {13,1,2,4,8,16,32,64,96,192,384,448,896,1792,1888,0,0}, 1950 {14,1,2,4,8,16,32,64,96,192,384,448,896,1792,1888,1889,0}, 1951 {14,1,2,4,8,16,32,64,96,192,384,448,896,1792,1888,1890,0}, 1952 {14,1,2,3,6,12,14,28,56,112,224,236,472,944,1888,1891,0}, 1953 {14,1,2,3,4,7,14,28,56,59,118,236,472,944,1888,1892,0}, 1954 {14,1,2,4,5,9,18,36,41,82,118,236,472,944,1888,1893,0}, 1955 {14,1,2,4,6,12,24,28,56,112,224,448,472,944,1888,1894,0}, 1956 {14,1,2,4,6,7,14,28,56,112,118,236,472,944,1888,1895,0}, 1957 {14,1,2,4,6,8,14,28,56,112,118,236,472,944,1888,1896,0}, 1958 {14,1,2,4,8,9,17,34,42,84,118,236,472,944,1888,1897,0}, 1959 {14,1,2,4,8,10,18,36,72,82,164,236,472,944,1888,1898,0}, 1960 {14,1,2,3,6,12,24,27,54,78,156,312,624,1248,1872,1899,0}, 1961 {14,1,2,4,8,12,24,48,56,112,224,448,896,944,1888,1900,0}, 1962 {14,1,2,4,6,7,13,26,52,59,118,236,472,944,1888,1901,0}, 1963 {14,1,2,4,8,12,14,28,56,112,224,236,472,944,1888,1902,0}, 1964 {15,1,2,4,8,12,14,28,56,112,224,236,472,944,1888,1902,1903}, 1965 {13,1,2,4,8,16,32,64,96,112,224,448,896,1792,1904,0,0}, 1966 {14,1,2,4,8,16,32,64,96,112,224,448,896,1792,1904,1905,0}, 1967 {14,1,2,4,8,16,32,64,96,112,224,448,896,1792,1904,1906,0}, 1968 {14,1,2,3,6,12,14,28,56,112,224,448,896,1792,1904,1907,0}, 1969 {14,1,2,3,4,7,14,28,56,112,224,448,896,1792,1904,1908,0}, 1970 {14,1,2,4,5,10,14,28,56,112,224,448,896,1792,1904,1909,0}, 1971 {14,1,2,4,6,12,24,28,56,112,224,448,896,1792,1904,1910,0}, 1972 {14,1,2,4,6,7,14,28,56,112,224,448,896,1792,1904,1911,0}, 1973 {14,1,2,4,6,8,14,28,56,112,224,448,896,1792,1904,1912,0}, 1974 {14,1,2,4,5,9,14,28,56,112,224,448,896,1792,1904,1913,0}, 1975 {14,1,2,4,8,10,20,28,56,112,224,448,896,1792,1904,1914,0}, 1976 {14,1,2,4,5,9,18,27,54,59,118,236,472,944,1888,1915,0}, 1977 {14,1,2,4,8,12,24,48,56,112,224,448,896,1792,1904,1916,0}, 1978 {14,1,2,4,8,9,18,27,45,90,117,234,468,936,1872,1917,0}, 1979 {14,1,2,4,8,12,14,28,56,112,224,448,896,1792,1904,1918,0}, 1980 {14,1,2,3,6,12,14,28,31,59,118,236,472,944,1888,1919,0}, 1981 {12,1,2,4,8,16,32,64,128,256,384,768,1536,1920,0,0,0}, 1982 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1921,0,0}, 1983 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1922,0,0}, 1984 {13,1,2,3,6,12,24,48,96,192,384,768,1536,1920,1923,0,0}, 1985 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1924,0,0}, 1986 {13,1,2,4,5,10,20,40,80,160,320,640,1280,1920,1925,0,0}, 1987 {13,1,2,4,6,12,24,48,96,192,384,768,1536,1920,1926,0,0}, 1988 {14,1,2,4,6,12,24,48,96,192,384,768,1536,1920,1926,1927,0}, 1989 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1928,0,0}, 1990 {13,1,2,3,6,9,15,30,60,120,240,480,960,1920,1929,0,0}, 1991 {13,1,2,4,8,10,20,40,80,160,320,640,1280,1920,1930,0,0}, 1992 {14,1,2,4,8,10,20,40,80,160,320,640,1280,1920,1930,1931,0}, 1993 {13,1,2,4,8,12,24,48,96,192,384,768,1536,1920,1932,0,0}, 1994 {14,1,2,4,8,12,24,48,96,192,384,768,1536,1920,1932,1933,0}, 1995 {14,1,2,4,8,12,24,48,96,192,384,768,1536,1920,1932,1934,0}, 1996 {13,1,2,3,6,12,15,30,60,120,240,480,960,1920,1935,0,0}, 1997 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1936,0,0}, 1998 {14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1936,1937,0}, 1999 {13,1,2,4,6,12,18,30,60,120,240,480,960,1920,1938,0,0}, 2000 {14,1,2,4,6,12,18,30,60,120,240,480,960,1920,1938,1939,0}, 2001 {13,1,2,4,8,16,20,40,80,160,320,640,1280,1920,1940,0,0}, 2002 {14,1,2,4,8,16,20,40,80,160,320,640,1280,1920,1940,1941,0}, 2003 {14,1,2,4,8,16,20,40,80,160,320,640,1280,1920,1940,1942,0}, 2004 {14,1,2,3,5,10,20,40,80,160,320,640,1280,1920,1940,1943,0}, 2005 {13,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,0,0}, 2006 {14,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,1945,0}, 2007 {14,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,1946,0}, 2008 {14,1,2,3,6,12,24,48,96,192,384,768,1536,1920,1944,1947,0}, 2009 {14,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,1948,0}, 2010 {14,1,2,4,5,9,18,36,72,144,216,432,864,1728,1944,1949,0}, 2011 {13,1,2,4,6,12,24,30,60,120,240,480,960,1920,1950,0,0}, 2012 {14,1,2,4,6,12,24,30,60,120,240,480,960,1920,1950,1951,0}, 2013 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1952,0,0}, 2014 {14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1952,1953,0}, 2015 {14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1952,1954,0}, 2016 {14,1,2,3,6,12,24,48,96,98,196,392,488,976,1952,1955,0}, 2017 {13,1,2,4,8,12,24,36,60,120,240,480,960,1920,1956,0,0}, 2018 {14,1,2,4,8,12,24,36,60,120,240,480,960,1920,1956,1957,0}, 2019 {14,1,2,4,8,12,24,36,60,120,240,480,960,1920,1956,1958,0}, 2020 {14,1,2,3,6,12,24,36,60,120,240,480,960,1920,1956,1959,0}, 2021 {13,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,0,0}, 2022 {14,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,1961,0}, 2023 {14,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,1962,0}, 2024 {14,1,2,3,5,10,20,40,80,160,320,640,1280,1920,1960,1963,0}, 2025 {14,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,1964,0}, 2026 {14,1,2,4,5,10,20,40,80,160,320,640,1280,1920,1960,1965,0}, 2027 {14,1,2,4,6,10,20,40,80,160,320,640,1280,1920,1960,1966,0}, 2028 {14,1,2,4,5,10,15,30,60,120,240,244,488,976,1952,1967,0}, 2029 {13,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,0,0}, 2030 {14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1969,0}, 2031 {14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1970,0}, 2032 {14,1,2,3,6,12,24,48,96,192,384,768,1536,1920,1968,1971,0}, 2033 {14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1972,0}, 2034 {14,1,2,4,5,10,20,40,80,160,164,328,656,1312,1968,1973,0}, 2035 {14,1,2,4,6,12,24,48,96,192,384,768,1536,1920,1968,1974,0}, 2036 {14,1,2,4,5,10,15,30,60,120,240,480,490,980,1960,1975,0}, 2037 {14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1976,0}, 2038 {14,1,2,4,5,9,18,36,41,82,164,328,656,1312,1968,1977,0}, 2039 {14,1,2,4,8,10,20,40,80,160,320,328,656,1312,1968,1978,0}, 2040 {15,1,2,4,8,10,20,40,80,160,320,328,656,1312,1968,1978,1979}, 2041 {13,1,2,4,8,12,24,48,60,120,240,480,960,1920,1980,0,0}, 2042 {14,1,2,4,8,12,24,48,60,120,240,480,960,1920,1980,1981,0}, 2043 {14,1,2,4,8,12,24,48,60,120,240,480,960,1920,1980,1982,0}, 2044 {14,1,2,3,6,12,24,48,60,120,240,480,960,1920,1980,1983,0}, 2045 {13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1984,0,0}, 2046 {14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1984,1985,0}, 2047 {14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1984,1986,0}, 2048 {14,1,2,3,6,12,24,48,50,100,200,248,496,992,1984,1987,0}, 2049 {14,1,2,3,4,7,14,28,31,62,124,248,496,992,1984,1988,0}, 2050 {14,1,2,4,5,10,20,40,80,84,168,248,496,992,1984,1989,0}, 2051 {14,1,2,4,6,12,24,48,96,100,200,400,496,992,1984,1990,0}, 2052 {14,1,2,4,6,7,14,28,56,62,124,248,496,992,1984,1991,0}, 2053 {13,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,0,0}, 2054 {14,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,1993,0}, 2055 {14,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,1994,0}, 2056 {14,1,2,3,6,12,24,48,72,120,240,480,960,1920,1992,1995,0}, 2057 {14,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,1996,0}, 2058 {14,1,2,3,5,10,20,40,80,83,166,332,664,1328,1992,1997,0}, 2059 {14,1,2,4,6,12,24,48,72,120,240,480,960,1920,1992,1998,0}, 2060 {14,1,2,4,5,10,15,30,60,120,124,248,496,992,1984,1999,0}, 2061 {13,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,0,0}, 2062 {14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2001,0}, 2063 {14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2002,0}, 2064 {14,1,2,3,5,10,20,40,80,160,320,640,1280,1920,2000,2003,0}, 2065 {14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2004,0}, 2066 {14,1,2,4,5,10,20,40,80,160,320,640,1280,1920,2000,2005,0}, 2067 {14,1,2,4,6,10,20,40,80,160,320,640,1280,1920,2000,2006,0}, 2068 {14,1,2,3,6,9,15,30,60,120,240,249,498,996,1992,2007,0}, 2069 {14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2008,0}, 2070 {14,1,2,4,8,9,17,25,50,100,200,400,800,1600,2000,2009,0}, 2071 {14,1,2,4,8,10,20,40,80,160,320,640,1280,1920,2000,2010,0}, 2072 {14,1,2,4,8,9,18,27,54,62,124,248,496,992,1984,2011,0}, 2073 {14,1,2,4,8,12,20,40,80,160,320,640,1280,1920,2000,2012,0}, 2074 {14,1,2,4,8,12,13,25,50,100,200,400,800,1600,2000,2013,0}, 2075 {14,1,2,4,8,10,20,30,60,120,240,248,496,992,1984,2014,0}, 2076 {14,1,2,4,5,10,15,25,50,100,200,400,800,1600,2000,2015,0}, 2077 {13,1,2,4,8,16,32,64,96,192,384,768,1536,1920,2016,0,0}, 2078 {14,1,2,4,8,16,32,64,96,192,384,768,1536,1920,2016,2017,0}, 2079 {14,1,2,4,8,16,32,64,96,192,384,768,1536,1920,2016,2018,0}, 2080 {14,1,2,3,6,12,24,48,96,192,384,768,1536,1920,2016,2019,0}, 2081 {14,1,2,3,4,7,14,28,56,112,224,448,896,1792,2016,2020,0}, 2082 {14,1,2,4,5,10,14,28,56,112,224,448,896,1792,2016,2021,0}, 2083 {14,1,2,4,6,12,24,48,96,192,384,768,1536,1920,2016,2022,0}, 2084 {14,1,2,4,6,7,14,28,56,112,224,448,896,1792,2016,2023,0}, 2085 {14,1,2,4,6,8,14,28,56,112,224,448,896,1792,2016,2024,0}, 2086 {14,1,2,4,5,9,14,28,56,112,224,448,896,1792,2016,2025,0}, 2087 {14,1,2,4,8,10,20,28,56,112,224,448,896,1792,2016,2026,0}, 2088 {14,1,2,4,8,10,11,21,42,84,168,336,672,1344,2016,2027,0}, 2089 {14,1,2,3,6,9,12,21,42,84,168,336,672,1344,2016,2028,0}, 2090 {14,1,2,3,5,8,13,21,42,84,168,336,672,1344,2016,2029,0}, 2091 {14,1,2,4,8,12,14,28,56,112,224,448,896,1792,2016,2030,0}, 2092 {14,1,2,3,6,12,15,30,42,84,168,336,672,1344,2016,2031,0}, 2093 {14,1,2,4,8,12,16,28,56,112,224,448,896,1792,2016,2032,0}, 2094 {14,1,2,4,8,16,17,34,68,84,168,336,672,1344,2016,2033,0}, 2095 {14,1,2,4,8,10,18,28,56,112,224,448,896,1792,2016,2034,0}, 2096 {14,1,2,3,5,10,20,40,43,83,166,332,664,1328,1992,2035,0}, 2097 {14,1,2,4,8,16,20,40,56,112,224,448,896,1792,2016,2036,0}, 2098 {14,1,2,4,8,16,20,21,42,84,168,336,672,1344,2016,2037,0}, 2099 {14,1,2,4,8,16,20,22,42,84,168,336,672,1344,2016,2038,0}, 2100 {14,1,2,3,5,10,20,23,43,63,126,252,504,1008,2016,2039,0}, 2101 {13,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,0,0}, 2102 {14,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,2041,0}, 2103 {14,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,2042,0}, 2104 {14,1,2,3,6,12,24,48,96,120,240,480,960,1920,2040,2043,0}, 2105 {14,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,2044,0}, 2106 {14,1,2,4,5,10,20,40,80,120,240,480,960,1920,2040,2045,0}, 2107 {14,1,2,4,6,12,24,48,96,120,240,480,960,1920,2040,2046,0}, 2108 {15,1,2,4,6,12,24,48,96,120,240,480,960,1920,2040,2046,2047}, 2109 {11,1,2,4,8,16,32,64,128,256,512,1024,2048,0,0,0,0}}; 2110 2111 #endif // ADDITIONCHAINS_H