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Степени КОРНЕЙ из 1 rootT≡√1 mod F4 или <rootT>F4≡1
==================================================================================== k rootk mod F4 root-k mod F4 ------------------------------------------------------------------------------------ (A-1)-арифметика A-арифметика (A-1)-арифметика A-арифметика ------------------------------------------------------------------------------------ 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 слова [ 0..+65536] [-32768..+32768] слова [ 0..+65536] [-32768..+32768] ------------------------------------------------------------------------------------ 0 0' 0. 0 = 0. 1 + 0. 1 0' 0. 0 = 0. 1 + 0. 1 1 0'255.255 = 2^16 - 0. 2 0'255.255 = 2^16 - 0. 2 =====================================================================================
Степени КОРНЕЙ из 1 rootT≡√1 mod F4 или <rootT>F4≡1
==================================================================================== k rootk mod F4 root-k mod F4 ------------------------------------------------------------------------------------ (A-1)-арифметика A-арифметика (A-1)-арифметика A-арифметика ------------------------------------------------------------------------------------ 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 слова [ 0..+65536] [-32768..+32768] слова [ 0..+65536] [-32768..+32768] ------------------------------------------------------------------------------------ 0 0' 0. 0 = 0. 1 + 0. 1 0' 0. 0 = 0. 1 + 0. 1 1 0' 0.255 = 1. 0 + 1. 0 0'255. 0 = 255. 1 - 1. 1 2 0'255.255 = 2^16 - 0. 2 0'255.255 = 2^16 - 0. 2 3 0'255. 0 = 255. 1 - 1. 1 0' 0.255 = 1. 0 + 1. 0 =====================================================================================
Степени КОРНЕЙ из 1 rootT≡√1 mod F4 или <rootT>F4≡1
==================================================================================== k rootk mod F4 root-k mod F4 ------------------------------------------------------------------------------------ (A-1)-арифметика A-арифметика (A-1)-арифметика A-арифметика ------------------------------------------------------------------------------------ 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 слова [ 0..+65536] [-32768..+32768] слова [ 0..+65536] [-32768..+32768] ------------------------------------------------------------------------------------ 0 0' 0. 0 = 0. 1 + 0. 1 0' 0. 0 = 0. 1 + 0. 1 1 0' 0. 15 = 0. 16 + 0. 16 0'240. 0 = 240. 1 - 16. 1 2 0' 0.255 = 1. 0 + 1. 0 0'255. 0 = 255. 1 - 1. 1 3 0' 15.255 = 16. 0 + 16. 0 0'255.240 = 255.241 - 0. 17 4 0'255.255 = 2^16 - 0. 2 0'255.255 = 2^16 - 0. 2 5 0'255.240 = 255.241 - 0. 17 0' 15.255 = 16. 0 + 16. 0 6 0'255. 0 = 255. 1 - 1. 1 0' 0.255 = 1. 0 + 1. 0 7 0'240. 0 = 240. 1 - 16. 1 0' 0. 15 = 0. 16 + 0. 16 =====================================================================================
Степени КОРНЕЙ из 1 rootT≡√1 mod F4 или <rootT>F4≡1
==================================================================================== k rootk mod F4 root-k mod F4 ------------------------------------------------------------------------------------ (A-1)-арифметика A-арифметика (A-1)-арифметика A-арифметика ------------------------------------------------------------------------------------ 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 слова [ 0..+65536] [-32768..+32768] слова [ 0..+65536] [-32768..+32768] ------------------------------------------------------------------------------------ 0 0' 0. 0 = 0. 1 + 0. 1 0' 0. 0 = 0. 1 + 0. 1 1 0' 0. 3 = 0. 4 + 0. 4 0'192. 0 = 192. 1 - 64. 1 2 0' 0. 15 = 0. 16 + 0. 16 0'240. 0 = 240. 1 - 16. 1 3 0' 0. 63 = 0. 64 + 0. 64 0'252. 0 = 252. 1 - 4. 1 4 0' 0.255 = 1. 0 + 1. 0 0'255. 0 = 255. 1 - 1. 1 5 0' 3.255 = 4. 0 + 4. 0 0'255.192 = 255.193 - 0. 65 6 0' 15.255 = 16. 0 + 16. 0 0'255.240 = 255.241 - 0. 17 7 0' 63.255 = 64. 0 + 64. 0 0'255.252 = 255.253 - 0. 5 8 0'255.255 = 2^16 - 0. 2 0'255.255 = 2^16 - 0. 2 9 0'255.252 = 255.253 - 0. 5 0' 63.255 = 64. 0 + 64. 0 10 0'255.240 = 255.241 - 0. 17 0' 15.255 = 16. 0 + 16. 0 11 0'255.192 = 255.193 - 0. 65 0' 3.255 = 4. 0 + 4. 0 12 0'255. 0 = 255. 1 - 1. 1 0' 0.255 = 1. 0 + 1. 0 13 0'252. 0 = 252. 1 - 4. 1 0' 0. 63 = 0. 64 + 0. 64 14 0'240. 0 = 240. 1 - 16. 1 0' 0. 15 = 0. 16 + 0. 16 15 0'192. 0 = 192. 1 - 64. 1 0' 0. 3 = 0. 4 + 0. 4 =====================================================================================
Степени КОРНЕЙ из 1 rootT≡√1 mod F4 или <rootT>F4≡1
==================================================================================== k rootk mod F4 root-k mod F4 ------------------------------------------------------------------------------------ (A-1)-арифметика A-арифметика (A-1)-арифметика A-арифметика ------------------------------------------------------------------------------------ 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 слова [ 0..+65536] [-32768..+32768] слова [ 0..+65536] [-32768..+32768] ------------------------------------------------------------------------------------ 0 0' 0. 0 = 0. 1 + 0. 1 0' 0. 0 = 0. 1 + 0. 1 1 0' 0. 1 = 0. 2 + 0. 2 0'128. 0 = 128. 1 -128. 1 2 0' 0. 3 = 0. 4 + 0. 4 0'192. 0 = 192. 1 - 64. 1 3 0' 0. 7 = 0. 8 + 0. 8 0'224. 0 = 224. 1 - 32. 1 4 0' 0. 15 = 0. 16 + 0. 16 0'240. 0 = 240. 1 - 16. 1 5 0' 0. 31 = 0. 32 + 0. 32 0'248. 0 = 248. 1 - 8. 1 6 0' 0. 63 = 0. 64 + 0. 64 0'252. 0 = 252. 1 - 4. 1 7 0' 0.127 = 0.128 + 0.128 0'254. 0 = 254. 1 - 2. 1 8 0' 0.255 = 1. 0 + 1. 0 0'255. 0 = 255. 1 - 1. 1 9 0' 1.255 = 2. 0 + 2. 0 0'255.128 = 255.129 - 0.129 10 0' 3.255 = 4. 0 + 4. 0 0'255.192 = 255.193 - 0. 65 11 0' 7.255 = 8. 0 + 8. 0 0'255.224 = 255.225 - 0. 33 12 0' 15.255 = 16. 0 + 16. 0 0'255.240 = 255.241 - 0. 17 13 0' 31.255 = 32. 0 + 32. 0 0'255.248 = 255.249 - 0. 9 14 0' 63.255 = 64. 0 + 64. 0 0'255.252 = 255.253 - 0. 5 15 0'127.255 = 128. 0 2^15 0'255.254 = 255.255 - 0. 3 16 0'255.255 = 2^16 - 0. 2 0'255.255 = 2^16 - 0. 2 17 0'255.254 = 255.255 - 0. 3 0'127.255 = 128. 0 2^15 18 0'255.252 = 255.253 - 0. 5 0' 63.255 = 64. 0 + 64. 0 19 0'255.248 = 255.249 - 0. 9 0' 31.255 = 32. 0 + 32. 0 20 0'255.240 = 255.241 - 0. 17 0' 15.255 = 16. 0 + 16. 0 21 0'255.224 = 255.225 - 0. 33 0' 7.255 = 8. 0 + 8. 0 22 0'255.192 = 255.193 - 0. 65 0' 3.255 = 4. 0 + 4. 0 23 0'255.128 = 255.129 - 0.129 0' 1.255 = 2. 0 + 2. 0 24 0'255. 0 = 255. 1 - 1. 1 0' 0.255 = 1. 0 + 1. 0 25 0'254. 0 = 254. 1 - 2. 1 0' 0.127 = 0.128 + 0.128 26 0'252. 0 = 252. 1 - 4. 1 0' 0. 63 = 0. 64 + 0. 64 27 0'248. 0 = 248. 1 - 8. 1 0' 0. 31 = 0. 32 + 0. 32 28 0'240. 0 = 240. 1 - 16. 1 0' 0. 15 = 0. 16 + 0. 16 29 0'224. 0 = 224. 1 - 32. 1 0' 0. 7 = 0. 8 + 0. 8 30 0'192. 0 = 192. 1 - 64. 1 0' 0. 3 = 0. 4 + 0. 4 31 0'128. 0 = 128. 1 -128. 1 0' 0. 1 = 0. 2 + 0. 2 =====================================================================================
Степени КОРНЕЙ из 1 rootT≡√1 mod F4 или <rootT>F4≡1
==================================================================================== k rootk mod F4 root-k mod F4 ------------------------------------------------------------------------------------ (A-1)-арифметика A-арифметика (A-1)-арифметика A-арифметика ------------------------------------------------------------------------------------ 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 17-битовые ПСНВ+ mod F4 ПСАНВ± mod F4 слова [ 0..+65536] [-32768..+32768] слова [ 0..+65536] [-32768..+32768] ------------------------------------------------------------------------------------ 0 0' 0. 0 = 0. 1 + 0. 1 0' 0. 0 = 0. 1 + 0. 1 1 0' 15.239 = 15.240 + 15.240 0' 7.247 = 7.248 + 7.248 2 0' 0. 1 = 0. 2 + 0. 2 0'128. 0 = 128. 1 -128. 1 3 0' 31.223 = 31.224 + 31.224 0' 3.251 = 3.252 + 3.252 4 0' 0. 3 = 0. 4 + 0. 4 0'192. 0 = 192. 1 - 64. 1 5 0' 63.191 = 63.192 + 63.192 0' 1.253 = 1.254 + 1.254 6 0' 0. 7 = 0. 8 + 0. 8 0'224. 0 = 224. 1 - 32. 1 7 0'127.127 = 127.128 +127.128 0' 0.254 = 0.255 + 0.255 8 0' 0. 15 = 0. 16 + 0. 16 0'240. 0 = 240. 1 - 16. 1 9 0'254.255 = 255. 0 - 1. 2 0'128.127 = 128.128 -127.130 10 0' 0. 31 = 0. 32 + 0. 32 0'248. 0 = 248. 1 - 8. 1 11 0'253.254 = 253.255 - 2. 3 0' 64. 63 = 64. 64 + 64. 64 12 0' 0. 63 = 0. 64 + 0. 64 0'252. 0 = 252. 1 - 4. 1 13 0'251.252 = 251.253 - 4. 5 0' 32. 31 = 32. 32 + 32. 32 14 0' 0.127 = 0.128 + 0.128 0'254. 0 = 254. 1 - 2. 1 15 0'247.248 = 247.249 - 8. 9 0' 16. 15 = 16. 16 + 16. 16 16 0' 0.255 = 1. 0 + 1. 0 0'255. 0 = 255. 1 - 1. 1 17 0'239.240 = 239.241 - 16. 17 0' 8. 7 = 8. 8 + 8. 8 18 0' 1.255 = 2. 0 + 2. 0 0'255.128 = 255.129 - 0.129 19 0'223.224 = 223.225 - 32. 33 0' 4. 3 = 4. 4 + 4. 4 20 0' 3.255 = 4. 0 + 4. 0 0'255.192 = 255.193 - 0. 65 21 0'191.192 = 191.193 - 64. 65 0' 2. 1 = 2. 2 + 2. 2 22 0' 7.255 = 8. 0 + 8. 0 0'255.224 = 255.225 - 0. 33 23 0'127.128 = 127.129 +127.129 0' 1. 0 = 1. 1 + 1. 1 24 0' 15.255 = 16. 0 + 16. 0 0'255.240 = 255.241 - 0. 17 25 0'255. 1 = 255. 2 - 1. 0 0'128.128 = 128.129 -127.129 26 0' 31.255 = 32. 0 + 32. 0 0'255.248 = 255.249 - 0. 9 27 0'254. 2 = 254. 3 - 1.255 0'192. 64 = 192. 65 - 63.193 28 0' 63.255 = 64. 0 + 64. 0 0'255.252 = 255.253 - 0. 5 29 0'252. 4 = 252. 5 - 3.253 0'224. 32 = 224. 33 - 31.225 30 0'127.255 = 128. 0 2^15 0'255.254 = 255.255 - 0. 3 31 0'248. 8 = 248. 9 - 7.249 0'240. 16 = 240. 17 - 15.241 32 0'255.255 = 2^16 - 0. 2 0'255.255 = 2^16 - 0. 2 33 0'240. 16 = 240. 17 - 15.241 0'248. 8 = 248. 9 - 7.249 34 0'255.254 = 255.255 - 0. 3 0'127.255 = 128. 0 2^15 35 0'224. 32 = 224. 33 - 31.225 0'252. 4 = 252. 5 - 3.253 36 0'255.252 = 255.253 - 0. 5 0' 63.255 = 64. 0 + 64. 0 37 0'192. 64 = 192. 65 - 63.193 0'254. 2 = 254. 3 - 1.255 38 0'255.248 = 255.249 - 0. 9 0' 31.255 = 32. 0 + 32. 0 39 0'128.128 = 128.129 -127.129 0'255. 1 = 255. 2 - 1. 0 40 0'255.240 = 255.241 - 0. 17 0' 15.255 = 16. 0 + 16. 0 41 0' 1. 0 = 1. 1 + 1. 1 0'127.128 = 127.129 +127.129 42 0'255.224 = 255.225 - 0. 33 0' 7.255 = 8. 0 + 8. 0 43 0' 2. 1 = 2. 2 + 2. 2 0'191.192 = 191.193 - 64. 65 44 0'255.192 = 255.193 - 0. 65 0' 3.255 = 4. 0 + 4. 0 45 0' 4. 3 = 4. 4 + 4. 4 0'223.224 = 223.225 - 32. 33 46 0'255.128 = 255.129 - 0.129 0' 1.255 = 2. 0 + 2. 0 47 0' 8. 7 = 8. 8 + 8. 8 0'239.240 = 239.241 - 16. 17 48 0'255. 0 = 255. 1 - 1. 1 0' 0.255 = 1. 0 + 1. 0 49 0' 16. 15 = 16. 16 + 16. 16 0'247.248 = 247.249 - 8. 9 50 0'254. 0 = 254. 1 - 2. 1 0' 0.127 = 0.128 + 0.128 51 0' 32. 31 = 32. 32 + 32. 32 0'251.252 = 251.253 - 4. 5 52 0'252. 0 = 252. 1 - 4. 1 0' 0. 63 = 0. 64 + 0. 64 53 0' 64. 63 = 64. 64 + 64. 64 0'253.254 = 253.255 - 2. 3 54 0'248. 0 = 248. 1 - 8. 1 0' 0. 31 = 0. 32 + 0. 32 55 0'128.127 = 128.128 -127.130 0'254.255 = 255. 0 - 1. 2 56 0'240. 0 = 240. 1 - 16. 1 0' 0. 15 = 0. 16 + 0. 16 57 0' 0.254 = 0.255 + 0.255 0'127.127 = 127.128 +127.128 58 0'224. 0 = 224. 1 - 32. 1 0' 0. 7 = 0. 8 + 0. 8 59 0' 1.253 = 1.254 + 1.254 0' 63.191 = 63.192 + 63.192 60 0'192. 0 = 192. 1 - 64. 1 0' 0. 3 = 0. 4 + 0. 4 61 0' 3.251 = 3.252 + 3.252 0' 31.223 = 31.224 + 31.224 62 0'128. 0 = 128. 1 -128. 1 0' 0. 1 = 0. 2 + 0. 2 63 0' 7.247 = 7.248 + 7.248 0' 15.239 = 15.240 + 15.240 ===================================================================================== © 2006 г., Александр Тимофеев, г.Харьков, Украина. E-mail: atimopheyev@yahoo.com |