korobovcoeff.c

The CUBA library provides new implementation of four general-purpose multidimensional integration al

#define KOROBOV_MINDIM 2
#define KOROBOV_MAXDIM 33
#define MAXPRIME 9689

#define Hash(x) ((19945 - x)*(-47 + x))/121634

static int prime[] = {
   FIRST,47,53,59,67,71,79,83,89,97,103,109,113,127,131,137,139,149,151,
   157,163,173,179,181,191,193,199,211,223,227,229,233,239,241,251,257,263,
   269,277,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,
   389,397,401,409,419,421,431,433,439,443,449,457,461,467,479,487,491,499,
   503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,
   619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,
   743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,
   863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,
   997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,
   1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,
   1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,
   1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,
   1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,
   1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,
   1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,
   1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,
   1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,
   1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,
   2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,
   2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,
   2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,
   2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,
   2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,
   2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,
   2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,
   2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,
   2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,
   3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,
   3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,
   3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,
   3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,
   3511,3517,3527,3529,3533,3539,3547,3557,3571,3581,3583,3593,3607,3613,
   3623,3631,3643,3659,3671,3673,3677,3691,3701,3709,3719,3733,3739,3761,
   3767,3769,3779,3793,3797,3803,3821,3833,3847,3851,3853,3863,3877,3889,
   3907,3911,3917,3929,3943,3947,3967,3989,4001,4003,4007,4013,4019,4027,
   4049,4051,4057,4073,4079,4091,4099,4111,4127,4133,4139,4153,4159,4177,
   4201,4211,4217,4219,4229,4231,4243,4259,4271,4283,4289,4297,4327,4337,
   4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4451,4463,4481,
   4483,4493,4507,4517,4523,4547,4549,4561,4567,4583,4597,4603,4621,4637,
   4639,4651,4663,4673,4691,4703,4721,4723,4733,4751,4759,4783,4787,4789,
   4801,4813,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4943,4957,
   4969,4987,4993,5003,5021,5023,5039,5051,5059,5077,5087,5101,5119,5147,
   5153,5167,5171,5179,5189,5209,5227,5231,5237,5261,5273,5281,5297,5309,
   5323,5333,5347,5351,5381,5387,5399,5413,5431,5437,5449,5471,5479,5501,
   5507,5519,5531,5557,5563,5573,5591,5623,5639,5641,5647,5657,5669,5683,
   5701,5711,5737,5743,5749,5779,5783,5801,5813,5827,5843,5857,5869,5881,
   5903,5923,5927,5953,5981,5987,6007,6011,6029,6037,6053,6067,6089,6101,
   6113,6131,6151,6163,6173,6197,6211,6229,6247,6257,6277,6287,6311,6323,
   6343,6359,6373,6389,6421,6427,6449,6469,6481,6491,6521,6529,6547,6563,
   6581,6599,6619,6637,6653,6673,6691,6709,6733,6737,6763,6781,6803,6823,
   6841,6863,6883,6899,6917,6947,6961,6983,7001,7019,7043,7057,7079,7103,
   7127,7151,7159,7187,7211,7229,7253,7283,7297,7321,7349,7369,7393,7417,
   7433,7459,7487,7507,7537,7561,7583,7607,7639,7669,7687,7717,7741,7759,
   7793,7823,7853,7883,7907,7937,7963,7993,8039,8059,8093,8123,8161,8191,
   8221,8263,8297,8329,8369,8419,8447,8501,8527,8563,8609,8663,8699,8747,
   8803,8849,8893,8963,9029,9091,9157,9239,9319,9413,9533,MarkLast(9689)
};

static short coeff[][32] = {
   {13,11,10,3,9,2,2,2,2,9,2,2,7,2,2,2,2,2,2,6,2,2,2,13,11,10,3,9,2,2,2,2},
   {23,17,12,11,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,12,12,12,14,14,14},
   {18,14,5,14,2,2,19,19,25,25,18,18,18,2,2,2,2,2,2,2,2,2,2,2,25,6,2,2,2,18,14,5},
   {18,13,23,5,2,12,6,12,12,12,10,10,16,2,16,16,2,2,2,2,2,2,2,10,2,2,2,2,10,2,2,2},
   {21,22,7,21,2,20,20,2,2,2,2,22,2,2,2,2,2,2,2,6,6,21,2,2,2,2,2,2,2,2,6,6},
   {29,19,27,32,6,8,2,2,2,2,2,8,8,2,2,2,2,9,9,9,9,2,2,2,2,2,2,2,9,9,2,2},
   {30,19,24,16,22,8,2,2,22,5,9,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {34,28,13,28,27,27,2,4,2,2,2,16,16,4,20,20,36,20,36,5,5,5,36,36,5,5,5,7,5,7,7,2},
   {35,19,33,8,21,30,8,2,4,2,4,4,2,2,2,2,2,2,2,2,2,17,2,2,11,25,11,17,17,17,17,17},
   {37,21,35,29,27,19,19,2,2,2,5,15,2,2,15,15,19,19,19,19,19,2,2,2,2,2,19,2,2,2,2,2},
   {45,44,13,25,17,47,30,2,30,2,2,2,2,2,2,2,2,2,19,19,19,17,17,2,2,2,2,2,2,2,2,2},
   {35,22,37,9,35,12,35,8,2,2,50,50,2,2,32,32,32,31,13,8,8,8,2,22,50,9,9,9,22,22,22,10},
   {29,24,43,36,49,2,2,8,4,25,49,25,2,2,8,10,10,10,5,5,5,40,10,33,40,40,2,27,10,25,25,25},
   {50,18,32,39,21,2,2,2,4,4,36,36,14,14,14,14,2,2,2,17,17,17,16,16,2,14,14,14,14,2,2,2},
   {31,28,45,20,18,43,43,13,28,2,2,2,31,31,31,31,31,2,2,2,43,43,2,2,2,2,2,2,2,2,30,2},
   {39,15,41,7,24,2,2,30,40,2,2,25,25,25,25,2,2,2,2,2,2,6,6,2,25,2,5,2,2,25,2,2},
   {44,20,29,39,7,21,21,21,2,2,45,2,2,2,49,49,49,49,49,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {56,20,22,13,18,35,35,6,2,4,2,4,2,2,2,23,16,16,4,23,2,34,52,2,34,2,4,2,2,2,23,16},
   {46,32,17,18,29,27,31,31,31,2,2,4,15,2,2,2,2,2,2,2,2,2,2,2,2,2,23,32,32,32,15,15},
   {62,42,43,17,23,13,13,2,2,13,2,2,2,2,2,2,2,10,2,2,2,2,9,10,2,2,2,19,9,9,9,9},
   {64,34,16,28,16,51,47,2,2,2,6,18,39,39,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,12,12,2},
   {74,26,44,25,50,24,54,39,58,42,2,42,42,2,2,2,2,2,2,2,2,33,33,2,2,39,11,2,2,58,39,58},
   {70,22,50,22,16,9,25,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {74,21,17,25,35,33,10,2,10,20,20,57,57,57,2,2,57,2,2,2,2,2,2,2,13,2,2,2,2,2,2,2},
   {81,18,10,11,47,38,71,37,2,37,2,2,2,2,2,26,26,26,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {55,30,85,42,16,36,45,67,2,2,68,2,2,2,2,2,2,2,68,10,2,2,2,2,2,2,2,2,2,2,2,2},
   {64,17,24,26,49,12,10,39,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,59,2,2},
   {68,57,23,38,61,38,13,13,8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,68,15,2,44,44,44,2,2,2},
   {94,28,58,29,13,5,15,8,66,2,2,2,39,39,15,66,2,2,6,6,2,2,66,66,66,66,2,2,2,2,2,66},
   {94,85,9,41,41,37,29,29,17,2,2,2,7,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,8,8},
   {89,32,75,77,77,13,2,30,30,2,2,2,2,2,2,2,2,2,2,67,67,2,2,2,2,2,2,2,2,8,19,32},
   {70,45,58,63,67,10,72,72,70,6,2,36,2,70,70,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {101,33,76,13,45,63,2,2,6,19,2,2,32,32,32,32,32,65,2,63,63,11,11,11,19,19,19,19,9,63,63,63},
   {70,89,44,37,19,45,2,2,2,8,10,8,54,54,80,80,80,80,80,2,116,2,116,2,2,80,40,51,100,100,8,2},
   {71,54,83,51,42,98,2,2,8,8,14,30,93,22,15,15,30,30,30,44,44,44,2,2,22,22,22,117,44,11,11,11},
   {109,37,51,113,17,10,2,2,17,17,55,2,55,55,55,55,55,55,2,2,2,57,48,48,55,55,2,2,55,2,2,55},
   {75,38,68,89,11,52,2,2,81,39,2,38,2,2,2,2,2,2,2,2,2,2,2,19,2,2,2,2,2,2,2,2},
   {81,84,35,34,20,93,2,12,12,12,2,96,2,96,96,2,96,2,2,2,2,2,2,2,2,2,2,2,2,56,56,56},
   {104,32,56,46,77,11,35,35,24,56,19,2,2,2,78,2,2,75,2,2,2,2,78,2,2,2,2,2,2,2,2,2},
   {81,103,25,35,28,15,20,20,20,2,2,2,2,20,20,20,107,107,2,2,2,2,2,2,2,2,2,2,2,2,13,13},
   {119,75,42,29,74,23,54,36,39,2,2,4,4,19,19,2,2,2,2,2,2,2,2,54,2,2,2,2,2,2,2,54},
   {115,73,22,102,75,138,16,73,50,16,2,50,2,2,2,133,2,2,2,2,2,2,2,2,2,2,2,2,2,33,33,33},
   {119,48,66,51,14,22,20,20,2,2,2,2,2,60,2,2,2,2,2,2,2,2,60,2,2,2,2,2,2,60,2,65},
   {121,94,80,29,51,69,42,36,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,17,2,2},
   {129,123,41,79,43,34,24,11,2,2,4,2,2,2,2,75,16,16,16,75,75,75,16,16,16,25,2,99,2,2,75,16},
   {128,33,35,68,22,8,62,94,2,2,2,62,62,2,98,2,2,4,98,2,2,32,81,32,32,32,98,98,98,98,98,98},
   {101,109,154,15,57,6,27,36,2,2,37,37,2,2,2,2,2,2,2,107,2,2,2,107,107,2,2,2,2,2,2,2},
   {106,40,24,38,61,118,106,106,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {149,111,58,79,127,13,41,33,27,16,30,2,61,2,72,2,2,2,2,2,2,2,2,2,2,2,2,75,75,2,2,2},
   {105,92,43,156,25,53,57,115,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {99,40,62,67,66,29,99,99,99,78,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,79},
   {109,42,96,95,66,41,103,84,13,103,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {111,72,16,89,25,86,117,29,14,14,2,2,2,2,2,60,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {106,72,49,94,140,44,97,157,75,2,2,4,123,123,2,2,123,123,123,123,2,2,2,2,2,2,2,2,2,2,2,2},
   {115,67,74,32,43,50,21,36,135,36,85,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {151,71,157,42,41,37,80,27,18,2,2,2,2,2,2,2,2,2,2,2,2,2,115,128,128,128,128,128,32,2,128,80},
   {119,91,38,30,92,44,32,76,22,2,34,2,2,2,2,2,2,2,2,2,2,2,2,2,2,129,2,2,129,2,2,2},
   {121,126,31,52,120,37,57,10,171,2,2,2,2,35,35,35,2,2,97,97,97,97,97,97,97,35,35,35,97,97,97,2},
   {155,86,49,104,87,94,64,45,61,91,91,91,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {164,121,44,166,47,33,7,15,13,2,2,122,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {128,120,133,17,71,52,25,107,42,21,21,2,2,2,2,4,4,96,2,9,9,2,9,94,94,94,94,94,94,94,94,96},
   {179,82,157,76,61,35,13,90,197,2,69,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,39,39},
   {136,136,148,63,66,10,169,95,95,163,30,28,28,2,41,130,2,2,2,21,2,2,2,2,2,2,2,2,2,2,2,36},
   {131,40,112,63,55,30,53,79,79,79,2,79,2,2,2,2,2,79,2,2,2,2,14,36,2,21,21,21,21,2,2,91},
   {165,81,92,48,9,110,12,40,40,34,2,2,2,107,107,107,2,107,2,2,2,2,2,2,2,2,2,2,2,15,41,41},
   {169,66,170,97,35,56,55,86,32,32,2,2,2,2,14,2,40,2,37,2,2,37,40,40,40,2,2,2,37,37,37,37},
   {135,63,126,156,70,18,49,143,6,117,2,109,109,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {193,59,51,68,68,15,170,170,170,143,143,12,2,2,2,63,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
   {145,101,56,65,23,76,110,2,4,4,4,146,146,146,2,146,2,2,2,2,2,2,2,2,2,2,2,2,2,2,146,146},