rng.c

   1 /*
   2 rng.c
   3 random number generator
   4
   5 Copyright (C) 2009 Evan Rinehart
   6
   7 This software comes with no warranty.
   8 1. This software can be used for any purpose, good or evil.
   9 2. Modifications must retain this license, at least in spirit.
  10
  11
  12 Theory of Operation
  13 Lag-1024 complimentary multiply-with-carry (CMWC) generator
  14
  15 This algorithm performs the following operation
  16         ax + c
  17 where a, x, and c are numbers less than b (the base, 2^32)
  18 using the rth last products (complimented) mod b as x and the
  19 last associated carry as c. a is a constant and r is the size
  20 of the rng state.
  21
  22 Another way to explain the above is
  23    z = a*x[i-r] + c
  24 x[i] = ~(z % b)
  25    c =   z / b
  26
  27 r, a, and b must be chosen carefully or the period will be
  28 very much less than the maximum 2^(32*(r+1)). For cmwc we choose
  29 them so that p = ab^r + 1 is prime.
  30
  31 The first r x's and the initial c serve as the generator seed.
  32 For the generator to produce high quality random numbers as soon
  33 as possible, x should be prepopulated with r random numbers.
  34
  35 If the following parameters are used
  36 b = 2^32
  37 r = 1024
  38 a = 109111
  39 the resulting rng has a period of 109111*2^327652
  40
  41 The period of this rng is so large that is will effectively
  42 never repeat. It will generate high quality random numbers for
  43 the forseeable future. The state of the generator can be
  44 saved and restored in case of program interruption. Besides
  45 the initial seed the generator will never need to be reseeded.
  46
  47 When the generator is initialized for the very first time there
  48 are three options. You can reset it, which loads the state with
  49 static data stored in the module. This data was generated with
  50 a high quality RNG and should be the default initial state of the
  51 generator. You may also initialize the generator with output of
  52 the c library rand function using your desired seed. You may also
  53 initialize the generator using /dev/urandom to put it into an
  54 unpredictable state. Besides these three initialization methods you
  55 may load whatever data you wish into the state.
  56
  57 zrand - return the next number in the current sequence
  58 zseed - set the current sequence using 1024+1 numbers
  59 zsrand - set the current sequence using 1 number and C srand
  60 zsrand_u - put the generator into an unpredictable state using urandom
  61 zread - return the generator state which can later be passed to zseed
  62
  63 refs:
  64 http://tbf.coe.wayne.edu/jmasm/vol2_no1.pdf
  65 http://en.wikipedia.org/wiki/Multiply-with-carry
  66 google multiply with carry generator
  67
  68 */
  69
  70 #include <stdio.h>
  71 #include <stdlib.h>
  72 #include <string.h>
  73
  74
  75 #define A 109111ULL
  76 #define R 1024
  77
  78 static unsigned x[R];
  79 static unsigned c = 0;
  80 static unsigned long long z;
  81 static int i = 0;
  82 static unsigned n;
  83
  84 static const unsigned seed[R];
  85
  86 unsigned zrand(){
  87         z = A*x[i] + c;
  88         n = ~z;
  89         x[i] = n;
  90         c = z >> 32;
  91         i = (i+1) & (R-1);
  92         return n;
  93 }
  94
  95 void zseed(unsigned data[], unsigned carry){
  96         memcpy(x, data, R*sizeof(unsigned));
  97         c = carry;
  98 }
  99
 100 void zread(unsigned data[], unsigned* carry){
 101         memcpy(data, x, R*sizeof(unsigned));
 102         *carry = c;
 103 }
 104
 105 void zreset(){
 106         memcpy(x, seed, 4*R);
 107         c = 0;
 108 }
 109
 110 void zsrand(unsigned s){
 111         int j;
 112         srand(s);
 113         for(j=0; j<R; j++){
 114                 x[j] = rand();
 115         }
 116         c = 0;
 117 }
 118
 119 void zsrand_u(){
 120         FILE* f = fopen("/dev/urandom", "r");
 121         if(fread(x, 4, R, f) < 4*R){
 122                 /* do nothing */
 123         }
 124         fclose(f);
 125         c = 0;
 126 }
 127
 128
 129
 130 static const unsigned seed[R] = {
 131 0x78ccb683,0x3481a375,0x5f9e6898,0xf9800e83,
 132 0x572d893b,0x70fff9bb,0xf70ac0ed,0x6141c9e5,
 133 0x56952454,0xe390e62b,0x506ab7f2,0xba359e85,
 134 0x9651ba89,0x2db34285,0xb9e4e900,0xc2c441bf,
 135 0xee4c1b28,0xe7b8dbb8,0x1d503c0c,0xe7b898a0,
 136 0x8973343d,0x83edcea2,0xc4594719,0x1278dfd4,
 137 0x19284537,0x93dce563,0x0f5dcba7,0x10326602,
 138 0x50622b42,0x52fd6472,0x0eab0e1c,0x86726558,
 139 0xd0e942c6,0x1b8b7f7f,0xacfdda30,0xbf546229,
 140 0x86c73055,0x1c4e38d6,0x7c9b6485,0xf1255a28,
 141 0xbf7d2776,0x245ec55a,0xa11b17da,0x5790130f,
 142 0x8aa4c429,0x7b42ce04,0x05de0f3b,0x4e5fcf14,
 143 0xbe728848,0x66309ddd,0xfdde7c99,0x7506dd9c,
 144 0x3d3dc7fe,0xd764811b,0x0fb1d105,0xf8f1f0b4,
 145 0x6b551bbb,0x59dba288,0xa2057ef2,0xb5cec6c3,
 146 0x325edf2a,0x738f018a,0xa0a1595f,0xe07e75b2,
 147 0x2ed4e01e,0xe49e9cf8,0xd81169d0,0xc33d4959,
 148 0xd3c292ef,0xa2b44c50,0x872477c9,0xbd17555a,
 149 0xca1553d9,0xbe07313f,0x98a5b066,0x0352aff0,
 150 0x26b1e8cb,0x33a579e9,0x385bc3c8,0xf0e159b5,
 151 0x7b328475,0x5e4e2476,0x826e3993,0xd2ecff8f,
 152 0x7cce1681,0x45211af5,0x465b7c0a,0xc371aeb3,
 153 0xf1955cf4,0x40ff8fda,0x4d7bf519,0xeaf544d6,
 154 0xff059143,0x97f801d1,0x9ba5d97d,0x3481e4e6,
 155 0x0a7adf1a,0x683d6419,0x1b0c23cc,0x81e96d4d,
 156 0x2d696bb8,0x5501ab1d,0xdc4d40dc,0x0a94689a,
 157 0x0b2e9d49,0x5a54142e,0xc5f53ec4,0x05b99e81,
 158 0xf6d3ad93,0xfa3a35c0,0xd824ca5a,0x9cc48f0f,
 159 0x0824427d,0x68f9ff01,0x2935fccd,0x54b3c756,
 160 0x49577f74,0x2ce4d756,0x13f28c99,0xa1f8eb08,
 161 0x25e5b692,0x146c87f7,0x2a52b5f6,0x38a167e2,
 162 0xf85e0cc5,0x0f1dcfca,0xd587d7d9,0xe670a74f,
 163 0x293cfc4f,0x441598a2,0xc33802d6,0x77611818,
 164 0x324f28ac,0xfc5e95a8,0x8d565d14,0x364cc747,
 165 0xe893601f,0x4a239063,0x4bfe992c,0xa11cccf4,
 166 0x5076fb6a,0x9f82534f,0xd55c4556,0xe67e5278,
 167 0x2713682d,0x3f67bfef,0x5e340226,0xc3827e00,
 168 0x7cb65e4d,0x96ca1fbc,0xa634377c,0xbcd99761,
 169 0xcbf9f020,0x1fe1c5f7,0x11b6c429,0xc50582a8,
 170 0x9a3d4dd6,0x08e33e56,0xc4062d25,0xc86bf8e3,
 171 0x3492f08a,0xf5a3ce2c,0x76a37a2c,0x7a03e627,
 172 0xbd08a762,0xafd09713,0x8dee4875,0xecad968c,
 173 0x1a503997,0x9079d84a,0xd47bf00d,0x8993e4b3,
 174 0x0cc997a7,0xd3692b89,0x71e6bc52,0x43f1083c,
 175 0x43ca213d,0xf55fca42,0xb8b3abff,0x9f2f07f3,
 176 0x450eb777,0x69ab46a0,0x468ef3c9,0x9a3dfded,
 177 0xb12a4324,0xbfa78f40,0x4974cd9d,0x3bd6065a,
 178 0xf22c2b23,0x9d61aab0,0x6ec63c14,0xbdb74178,
 179 0x1e79ec34,0x1ca968ce,0x46f53c5c,0xa3e7a02d,
 180 0x89116891,0xdb212284,0xf76788b0,0xc3e9b8bb,
 181 0xbe634032,0x6d4d79cc,0x19ab0387,0xca0375c7,
 182 0x6694d1a0,0xd19e9ccc,0xde2942b5,0x8eebab87,
 183 0x563942e0,0x63ab7b3a,0x3ef3b2e7,0x6fc8f783,
 184 0x76219787,0xa13e7dcd,0x4f303de9,0xc29bded4,
 185 0x1b2698d6,0x6a69d2dc,0x1a8b8baa,0x85c70b2f,
 186 0x97ca278f,0x5f688eb8,0x56ba8212,0x5bc13245,
 187 0xaaf7059b,0x4b9630bc,0x6a6cf57d,0xa6fff589,
 188 0x2c3bc80d,0x8aa32824,0xbd31bcc7,0xaba8239f,
 189 0xef1f58a5,0x85f26400,0x69f18d3c,0x4920b415,
 190 0xe43439a3,0xceadc396,0x949b2e24,0xc99ba482,
 191 0x1b94752e,0x3f0a9520,0xa5e241c3,0x7433b591,
 192 0xd84ef68e,0x24cac645,0x019b6ceb,0xb87fbbec,
 193 0x5d4b3bb0,0x6e4dc037,0xb99945c9,0xac400e3b,
 194 0x1ba21e36,0x2827b514,0x9a519e3f,0x08113a64,
 195 0x8284e8a9,0x85269c90,0xc8002367,0xf68917be,
 196 0x35ea12f1,0x20010bc0,0xef70eaa4,0xb58d113b,
 197 0xf9c1b996,0xfb851f82,0x47d38c93,0x3f9ecf44,
 198 0x676571e8,0x4da20222,0xfb3e90d4,0x637238d5,
 199 0x133493f6,0xe6e7b50b,0x6782a425,0x89a898b6,
 200 0xe75a0349,0x07acd03f,0xe318ac70,0x68c9c705,
 201 0x24a1cfa1,0x994e441f,0xd9d7deed,0x2945eaeb,
 202 0xaaf00caf,0x9187d425,0x66ad8ade,0xc886ffa3,
 203 0xeaec9646,0x70cffcf4,0x5857f917,0x11cf60f5,
 204 0x237d5194,0x028aec76,0x2f71ef65,0x0e3dc017,
 205 0x5b57ad5b,0x2c7f8c2d,0x240c370c,0xee756fdb,
 206 0x14c42734,0xd7e72c62,0x77e74166,0x4efd0b01,
 207 0xc9db1cd2,0x44be9730,0x63f18a83,0x4f8b4338,
 208 0xa6b8b99d,0x5624b383,0xcf005b92,0xdad5b8e6,
 209 0xaf7d8e31,0xb103ee60,0x5c2d0688,0x458454ad,
 210 0x488e7e33,0x603ccf6b,0x51e2de47,0x4c47cfc0,
 211 0xa26f91bf,0xade37619,0x3f00bff2,0xab40e158,
 212 0x0255cfcb,0x86f2b7ff,0x6759c53c,0xfbef40e2,
 213 0xdd7a83ed,0xcd5347e0,0x0e106d40,0x0640608c,
 214 0x2c9ef901,0x78b76d8b,0x5e7f4eef,0xd216b10d,
 215 0x886c2275,0x8b1d0f79,0xa4b35dac,0x457abe80,
 216 0x404102d0,0x155f7659,0x94d22808,0xb44ce43f,
 217 0xfc90ca4c,0xd8632508,0xca4ae466,0x70b057b3,
 218 0x000636e1,0x43f4348b,0x2683eddd,0x06617c3f,
 219 0xa271f9a0,0x5b8fe19c,0x7f005a2e,0xa7f38cc5,
 220 0x0e35248c,0xb0b924ca,0xb4c240a2,0xc8b90031,
 221 0x146b51c8,0x763e0b09,0xc03a9944,0x9935bf09,
 222 0xfd5c6d44,0x624d91ff,0xcc165723,0xa0112178,
 223 0x56976668,0xebcd0f8b,0x5d93b3d3,0x085bd6f0,
 224 0x84543c6a,0x0ce05ee6,0x57ac79db,0xdc06d8de,
 225 0x90cfe3b1,0x8aa9a759,0xc7828fe4,0x20cf002e,
 226 0x274ec237,0x2903502c,0x9f29fa6d,0x677f044e,
 227 0xc99ed8eb,0xdbe2a291,0x6a6de59b,0x0586cf4a,
 228 0x97bdb15b,0x8f9d7a7f,0xa86f079f,0x1936774d,
 229 0xaf99474b,0x09d34689,0xcdc33564,0x1832e6bf,
 230 0x86c10bf5,0x8748f0bd,0xd261c0c4,0x9a500ba6,
 231 0xe09dbde3,0x1de20a01,0x0c31bfa7,0xef1315a4,
 232 0x4960b046,0x22247379,0xf74eb94d,0x33caf43a,
 233 0xe723c02a,0x7dfa339b,0xa3771fc2,0x60a12776,
 234 0x4fd24a1d,0x79c7180e,0xa29d4d14,0x5d3a4258,
 235 0xabd02a93,0xc74407ac,0x6de3e324,0xeb3cc2e0,
 236 0x40f67f0e,0x510aeb60,0x7e6aa493,0x8b9711f2,
 237 0x0adedf8f,0xc6d4641a,0x590f31fe,0x72944abd,
 238 0xecafecf3,0xe4a560d2,0x8c7cf2d2,0x72252c0c,
 239 0xe21d7b60,0xd12084a5,0x3cd70790,0xe06927d4,
 240 0x52cbda5b,0xaa5a4d46,0xbd0d334b,0x70079756,
 241 0x6444eff8,0x7e9aff56,0x660a5e3e,0xa231cacb,
 242 0xf287ee23,0x5e286f4f,0x37b2d779,0xe8618016,
 243 0x2322f60b,0x0235ab4b,0xc788e32d,0x23788080,
 244 0xe6b7ce71,0xbdf2c30b,0xf89c28ce,0xbaa4dd64,
 245 0x7fb78637,0xf80054f2,0xda8a954b,0x53b2c79c,
 246 0x472181a0,0x55fa9f39,0x4d5a46e6,0x471ca40f,
 247 0xbb7ce1c4,0x80bdda5d,0xd6e43a9a,0xa62569b5,
 248 0x1b1ba751,0x3de2c78a,0xebcca99a,0x756ec1f5,
 249 0xb23615da,0x9bbca3c9,0x855639b6,0x13573a5a,
 250 0x90cabd4d,0xe22ac854,0xa80d9bb3,0xb93886ed,
 251 0x391930c0,0x1ab7dd5f,0x1e64bb37,0xe547b420,
 252 0x0a2e934b,0x6f017028,0xadf47a8b,0x1a3c0002,
 253 0xb56e47b0,0x7e7b953b,0x0c463808,0xd15f880b,
 254 0xf8b0f3d4,0xcd829c10,0xd7f3bd5d,0x8f773cc4,
 255 0x5aa36693,0xd08bc8b1,0xae1af81a,0x1fd7b980,
 256 0xb8666bd0,0xe3742d04,0x4c7dde81,0x5af48b8b,
 257 0x41039866,0x1e080901,0x12aafdf6,0x2b9a488f,
 258 0xccee6671,0xfe0f3664,0x1613867d,0x1925442a,
 259 0xa3d0ff13,0xc75bec5a,0x4b385188,0x5afc94c2,
 260 0x80c17d0f,0x91901bb5,0x650855c3,0xa8dace10,
 261 0xfacbb9e3,0x69d2de39,0xdd42f20a,0xf147960c,
 262 0x5a587906,0xc6e725b4,0x27d0886d,0xf462065b,
 263 0xe21bef3c,0x1fd233aa,0x99ed9b31,0xe6ec751e,
 264 0x6cb2994a,0x8131886a,0x3145e5a8,0xf558a152,
 265 0x34cb4ae8,0xa3652156,0x741e3dd5,0x5e3cb33a,
 266 0xec72dc96,0x2ebcf3d9,0x4befb0e2,0xfca149a2,
 267 0x74eee63c,0x4570a0e4,0xf9e7efd0,0x7f3d3dc4,
 268 0x211a4623,0x7fe53c8f,0x0114126b,0xc2ab46b1,
 269 0xf6fbbc22,0x07e6d02e,0x88ad479b,0x95679e16,
 270 0xb3fc5046,0xa576a264,0x471ec40c,0x4a2d62eb,
 271 0x4438e83d,0x854d650e,0xe224e45e,0x16bc6a50,
 272 0xbab37736,0x43e3ef2b,0xaf92772e,0x275da723,
 273 0xe0aea5d6,0x41e9e4fa,0x1ae44657,0x6a3a894b,
 274 0x9ae2d49f,0xe4b09222,0x2439e401,0x3c7e0cea,
 275 0x0ebd9895,0xcf5632f6,0x6030543e,0x429d9edb,
 276 0x2ff98a12,0x96c33e76,0xda74ba0f,0x2bd84112,
 277 0x20ded070,0xfadb4f71,0x70950006,0x87a5d4fb,
 278 0xc3df2020,0xa0dab835,0x4b4f4c0a,0x3358a676,
 279 0xfa02770e,0x5ba5cc28,0x2cd45d8c,0x63d0e809,
 280 0x542aa98f,0x7e024718,0xf05544fd,0x1d6483d7,
 281 0xf9955a3e,0xe063b004,0x18a8d0cb,0x83ca36c3,
 282 0x87f8af41,0x24356b37,0x87381c1e,0x2e7f8766,
 283 0x1d38e26a,0x1345efcf,0x700c8bbe,0x351d6ed1,
 284 0xbd061dec,0xa08f572d,0xd50f1cfd,0x3aa4120d,
 285 0xf751b9c8,0xc7df7503,0x54f2dacb,0x93e834bf,
 286 0x7687e44d,0x2c919332,0xf847bf8e,0x6e18cdb2,
 287 0x4ea165b1,0xb64fc741,0x655a252d,0x2be1e10c,
 288 0x81622059,0xe3efe002,0xfbd0003b,0x7f3fb5de,
 289 0x0213539a,0x19c16ab7,0xc95f0da3,0x16a3354b,
 290 0x591b7289,0xa8762dcf,0x07669c50,0x4bdbcbda,
 291 0xa3f833d2,0xb0e453d3,0x62ad9e76,0x96d63c01,
 292 0x2dc71a74,0xc2700652,0xaf812ed8,0x58bdb8ee,
 293 0x31194cbd,0x6cc94a8c,0xdbd6721b,0x0b47b413,
 294 0x032f62d4,0x662b8d44,0xe22709fb,0xf391ab6a,
 295 0x75205ed0,0xae56f40d,0xe4a38906,0xde446c0a,
 296 0xcbe7633f,0x15eb029b,0xe483fd69,0x53169fca,
 297 0xf11c2dc7,0x50923fee,0x17091a3e,0x618dc7c0,
 298 0x33494049,0x56a7c2d6,0x3ee64506,0x7b38446f,
 299 0xc16e318f,0xda219fab,0xb8220def,0xdb6e5cff,
 300 0x193dd0f1,0xa3205a84,0xa12a6c53,0x8c802cf5,
 301 0x600f80ff,0xe91425ec,0xfca8dbfa,0x3a284a25,
 302 0xd3ebda03,0x32d8ec03,0x63ef3e64,0x1611e012,
 303 0x5dd8ef17,0x3e9b0525,0x23802863,0xabe1bbbb,
 304 0xc062c84e,0x22191bef,0x6678f71b,0xced7fa52,
 305 0x7d16ab68,0x46b53255,0xb6b4b754,0x585ee57f,
 306 0xad004ebd,0x8d0eb7ba,0x496a4358,0x003a76da,
 307 0x45d8a5f5,0xc7d457c6,0x38f47353,0xe6cf9032,
 308 0x0e22692e,0x617c53d2,0x9d8d4905,0x7b3c48fc,
 309 0x20179377,0xeee8a0a8,0xa1505f61,0x5579ee38,
 310 0xc70f8dab,0x1030ff8f,0x0235bdc7,0xa2435abd,
 311 0x42be7ad0,0x95340af8,0x2c5eecc9,0xc6377722,
 312 0x2df31134,0xe27e7de0,0x11e053f7,0x7395aa54,
 313 0x15ca6f6a,0xc6f999b5,0x3c4e4ba5,0xea34d68e,
 314 0xf5427a59,0xce5c4d06,0xe16d2494,0x3ae219ee,
 315 0x80c2ef1b,0x3259e75d,0x67127bfb,0x0f3163c5,
 316 0xdc6d34a1,0xaa4b95ed,0x7487ac64,0x413df8a8,
 317 0xdebc5b26,0xb5011148,0xd899ec53,0xb093c566,
 318 0x889ad5e7,0x5ddfa97d,0xa1cb7749,0xc3e31de8,
 319 0xaaec178a,0x4ff11de5,0x8942cc38,0x52dd5db6,
 320 0x4789b3c7,0x7e52610b,0xa41fbcc3,0xf8081823,
 321 0x54420030,0x46c27d0e,0x1a67966d,0xa66e320a,
 322 0xd3be6dee,0x0ec03c4e,0xc9bd6e7b,0xe87e5b7b,
 323 0x58c22e12,0x9fd0a92a,0x5095127e,0xf9434224,
 324 0x0a4a9fc6,0x50b37439,0x11451b9e,0x69a59028,
 325 0x00366203,0xf816c308,0x620173d0,0x9fc4dd84,
 326 0x497a7f1f,0xaaba033b,0x8fd4c439,0x1868ee3d,
 327 0xb222ba46,0xa0c3a09a,0x5fa25e0b,0x5a21f132,
 328 0xc12dba9b,0x855f8b4d,0x67009272,0x11f2e885,
 329 0xc455b065,0x44aa4ae4,0xc61b6fb4,0x84cd83b0,
 330 0x0dadacef,0xcf01c1f4,0x992d49f3,0x6f19c165,
 331 0xf8f819ee,0x0094daae,0x7f123269,0xa83ef1fb,
 332 0x38b5fb9b,0xa1094c7f,0x78b880cd,0x4c8c8d12,
 333 0xe6b7b0de,0x1bcc790e,0x2c43ae95,0xa8921cd1,
 334 0x2d97286e,0x844dcfd0,0xf2825de7,0x0d357b5c,
 335 0x63259e87,0x46cbb174,0x7bf4ea7f,0xb16f9c2d,
 336 0x55c138cb,0x33a02270,0xa2b84686,0x19cbe730,
 337 0x37bb8813,0x00e4e6c8,0xde365a1a,0x5e90e5d3,
 338 0xc206f6cd,0x26a56e98,0x6f6de8b3,0x4aed90ca,
 339 0xdedcc216,0xedcb8b04,0x4cd2e06b,0x135d765b,
 340 0xcbdab903,0x1e8623bc,0xf4dd5959,0x58f72256,
 341 0x0cc68c76,0x9385e695,0x0df07923,0x25780fa6,
 342 0xf9aa17d3,0x79ca3daa,0x7de341f3,0x858ebe32,
 343 0x113164a5,0x39bd5133,0xd4e5ae8a,0xe3b00fc0,
 344 0x7b07df0d,0xd3a3b026,0xd576a9a1,0x8bfac055,
 345 0xfa4ee836,0xfa708691,0x5b46911b,0x44e1f903,
 346 0x0eb679e1,0xbc945613,0x977d7ed7,0x1a305f22,
 347 0x0c9bc435,0xada73b62,0x7bb53db9,0x3e7dfc20,
 348 0xb36c4434,0x37075fa0,0x6a5cfc72,0x497abcca,
 349 0x4922d0ab,0xd6cc674b,0xdfaaa1c7,0x09f7e0b0,
 350 0xe9150218,0x53c661d9,0xe24d095b,0xbf9b03c4,
 351 0x9aaeee7e,0x335b206a,0xf60b8e4a,0x996b7933,
 352 0xc4adfbcb,0x588a2ccb,0x80757000,0x1e895e88,
 353 0x4d73fb03,0x65ed62f0,0x03448eb0,0xf349d162,
 354 0xe849f8b7,0xebe423b1,0xc81187a7,0x201e4c9a,
 355 0x1afaa893,0x7803d25b,0xb4f1e9e7,0x6b6eadec,
 356 0xcaef703e,0x3361407d,0x7014c8b6,0x9edeb022,
 357 0xd4b9a3ba,0xbc74f0ad,0x3d00f7f5,0x6e556e31,
 358 0x4ab88abc,0xeae0f853,0xb2d4039d,0xf38f1441,
 359 0xa1ce980e,0x99f874e3,0x894d41be,0xc474fb9f,
 360 0x05af1e82,0xde824b66,0xfc86f0f5,0x93d9f6f3,
 361 0xcd4f6d72,0x9d52f00b,0x87418c3d,0x661689a5,
 362 0x6abd7ce1,0x79890d4f,0x9ddb73b8,0xd19d251c,
 363 0xe2527680,0xef92f5d7,0xd3c94750,0xe0d5a177,
 364 0xbbab5e1e,0xd24b75d2,0x08a46507,0x9e4ecbb5,
 365 0x9e3d0c0f,0x8258ec58,0x6a289d70,0xf58bfe7e,
 366 0x1db04252,0x1e27c93e,0x7f269ba3,0x031e994a,
 367 0x61d00429,0x563751b4,0x0a89cdc6,0x6dfece7a,
 368 0x889611b0,0x86a215e5,0xbcbca365,0x4191770a,
 369 0x60dcc19e,0x607f5121,0x49611e62,0x30a04b14,
 370 0xad538ef1,0x0a48c1ae,0xdc2fd80d,0xf48e5375,
 371 0xc8f7d9fb,0x964c0d8e,0x252641be,0xe552ca6a,
 372 0x3a806a22,0x78c6788f,0x0eb9a73c,0x5cf8eba4,
 373 0xee4ce76e,0xca24d902,0xd81d4257,0xba4f4373,
 374 0xa4e6d2fc,0xcdff8c5d,0xf04452a0,0xd24ed156,
 375 0xe3135ea0,0xfdb8846e,0x54cdd95c,0x3285f5f0,
 376 0x8a5aefe3,0x6c68d56b,0x1e9b5109,0xf34f2aef,
 377 0x84e3071b,0x46b82e1d,0xd970b8ba,0x08bee27d,
 378 0x7408b4ef,0x2a9e6edc,0x3cbf57bb,0xfe3c8cf9,
 379 0x44c2dbfe,0x45206d53,0x5ace5ff5,0x099bf422,
 380 0xbf99926c,0x5aaaf1b7,0xbecee19b,0x878d8917,
 381 0xa4e6b59c,0x181d373d,0x9926d5d1,0x9c79a6b9,
 382 0x21f94776,0xa8fce4be,0x9eb14285,0x5709faa5,
 383 0x9a72dec5,0x2dcbef6c,0xb00e107c,0x635c25d3,
 384 0xf9c6a9c5,0x94fb2617,0x99bf9c4a,0x36b717cd,
 385 0x1e5af761,0x224336ab,0x3d928cdb,0x8104788b,
 386 0x3caa7ea5,0x31eec558,0xc0cf133e,0x787100a9
 387 };