1 2 static char help[] = "Run Birthday Spacing Tests for PetscRandom.\n\n"; 3 4 #include <petscsys.h> 5 #include <petscviewer.h> 6 7 /* L'Ecuyer & Simard, 2001. 8 * "On the performance of birthday spacings tests with certain families of random number generators" 9 * https://doi.org/10.1016/S0378-4754(00)00253-6 10 */ 11 12 static int PetscInt64Compare(const void *a, const void *b) 13 { 14 PetscInt64 A = *((const PetscInt64 *)a); 15 PetscInt64 B = *((const PetscInt64 *)b); 16 if (A < B) return -1; 17 if (A == B) return 0; 18 return 1; 19 } 20 21 static PetscErrorCode PoissonTailProbability(PetscReal lambda, PetscInt Y, PetscReal *prob) 22 { 23 PetscReal p = 1.; 24 PetscReal logLambda; 25 PetscInt i; 26 PetscReal logFact = 0.; 27 28 PetscFunctionBegin; 29 logLambda = PetscLogReal(lambda); 30 for (i = 0; i < Y; i++) { 31 PetscReal exponent = -lambda + i * logLambda - logFact; 32 33 logFact += PetscLogReal(i + 1); 34 35 p -= PetscExpReal(exponent); 36 } 37 *prob = p; 38 PetscFunctionReturn(0); 39 } 40 41 int main(int argc, char **argv) 42 { 43 PetscMPIInt size; 44 PetscInt log2d, log2n, t, N, Y; 45 PetscInt64 d, k, *X; 46 size_t n, i; 47 PetscReal lambda, p; 48 PetscRandom random; 49 50 PetscFunctionBeginUser; 51 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 52 t = 8; 53 log2d = 7; 54 log2n = 20; 55 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Birthday spacing test parameters", "PetscRandom"); 56 PetscCall(PetscOptionsInt("-t", "t, the dimension of the sample space", "ex3.c", t, &t, NULL)); 57 PetscCall(PetscOptionsInt("-log2d", "The log of d, the number of bins per direction", "ex3.c", log2d, &log2d, NULL)); 58 PetscCall(PetscOptionsInt("-log2n", "The log of n, the number of samples per process", "ex3.c", log2n, &log2n, NULL)); 59 PetscOptionsEnd(); 60 61 PetscCheck((size_t)log2d * t <= sizeof(PetscInt64) * 8 - 2, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "The number of bins (2^%" PetscInt_FMT ") is too big for PetscInt64.", log2d * t); 62 d = ((PetscInt64)1) << log2d; 63 k = ((PetscInt64)1) << (log2d * t); 64 PetscCheck((size_t)log2n <= sizeof(size_t) * 8 - 1, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "The number of samples per process (2^%" PetscInt_FMT ") is too big for size_t.", log2n); 65 n = ((size_t)1) << log2n; 66 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 67 N = size; 68 lambda = PetscPowRealInt(2., (3 * log2n - (2 + log2d * t))); 69 70 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Generating %zu samples (%g GB) per process in a %" PetscInt_FMT " dimensional space with %" PetscInt64_FMT " bins per dimension.\n", n, (n * 1.e-9) * sizeof(PetscInt64), t, d)); 71 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Expected spacing collisions per process %g (%g total).\n", (double)lambda, (double)(N * lambda))); 72 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &random)); 73 PetscCall(PetscRandomSetFromOptions(random)); 74 PetscCall(PetscRandomSetInterval(random, 0.0, 1.0)); 75 PetscCall(PetscRandomView(random, PETSC_VIEWER_STDOUT_WORLD)); 76 PetscCall(PetscMalloc1(n, &X)); 77 for (i = 0; i < n; i++) { 78 PetscInt j; 79 PetscInt64 bin = 0; 80 PetscInt64 mult = 1; 81 82 for (j = 0; j < t; j++, mult *= d) { 83 PetscReal x; 84 PetscInt64 slot; 85 86 PetscCall(PetscRandomGetValueReal(random, &x)); 87 /* worried about precision here */ 88 slot = (PetscInt64)(x * d); 89 bin += mult * slot; 90 } 91 PetscCheck(bin < k, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Generated point in bin %" PetscInt64_FMT ", but only %" PetscInt64_FMT " bins", bin, k); 92 X[i] = bin; 93 } 94 95 qsort(X, n, sizeof(PetscInt64), PetscInt64Compare); 96 for (i = 0; i < n - 1; i++) X[i] = X[i + 1] - X[i]; 97 qsort(X, n - 1, sizeof(PetscInt64), PetscInt64Compare); 98 for (i = 0, Y = 0; i < n - 2; i++) Y += (X[i + 1] == X[i]); 99 100 PetscCallMPI(MPI_Allreduce(MPI_IN_PLACE, &Y, 1, MPIU_INT, MPI_SUM, MPI_COMM_WORLD)); 101 PetscCall(PoissonTailProbability(N * lambda, Y, &p)); 102 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT " total collisions counted: that many or more should occur with probabilty %g.\n", Y, (double)p)); 103 104 PetscCall(PetscFree(X)); 105 PetscCall(PetscRandomDestroy(&random)); 106 PetscCall(PetscFinalize()); 107 return 0; 108 } 109 110 /*TEST 111 112 test: 113 args: -t 4 -log2d 7 -log2n 10 114 115 TEST*/ 116