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 PetscInt64 A = *((const PetscInt64 *)a); 14 PetscInt64 B = *((const PetscInt64 *)b); 15 if (A < B) return -1; 16 if (A == B) return 0; 17 return 1; 18 } 19 20 static PetscErrorCode PoissonTailProbability(PetscReal lambda, PetscInt Y, PetscReal *prob) { 21 PetscReal p = 1.; 22 PetscReal logLambda; 23 PetscInt i; 24 PetscReal logFact = 0.; 25 26 PetscFunctionBegin; 27 logLambda = PetscLogReal(lambda); 28 for (i = 0; i < Y; i++) { 29 PetscReal exponent = -lambda + i * logLambda - logFact; 30 31 logFact += PetscLogReal(i + 1); 32 33 p -= PetscExpReal(exponent); 34 } 35 *prob = p; 36 PetscFunctionReturn(0); 37 } 38 39 int main(int argc, char **argv) { 40 PetscMPIInt size; 41 PetscInt log2d, log2n, t, N, Y; 42 PetscInt64 d, k, *X; 43 size_t n, i; 44 PetscReal lambda, p; 45 PetscRandom random; 46 47 PetscFunctionBeginUser; 48 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 49 t = 8; 50 log2d = 7; 51 log2n = 20; 52 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Birthday spacing test parameters", "PetscRandom"); 53 PetscCall(PetscOptionsInt("-t", "t, the dimension of the sample space", "ex3.c", t, &t, NULL)); 54 PetscCall(PetscOptionsInt("-log2d", "The log of d, the number of bins per direction", "ex3.c", log2d, &log2d, NULL)); 55 PetscCall(PetscOptionsInt("-log2n", "The log of n, the number of samples per process", "ex3.c", log2n, &log2n, NULL)); 56 PetscOptionsEnd(); 57 58 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); 59 d = ((PetscInt64)1) << log2d; 60 k = ((PetscInt64)1) << (log2d * t); 61 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); 62 n = ((size_t)1) << log2n; 63 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 64 N = size; 65 lambda = PetscPowRealInt(2., (3 * log2n - (2 + log2d * t))); 66 67 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)); 68 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Expected spacing collisions per process %g (%g total).\n", (double)lambda, (double)(N * lambda))); 69 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &random)); 70 PetscCall(PetscRandomSetFromOptions(random)); 71 PetscCall(PetscRandomSetInterval(random, 0.0, 1.0)); 72 PetscCall(PetscRandomView(random, PETSC_VIEWER_STDOUT_WORLD)); 73 PetscCall(PetscMalloc1(n, &X)); 74 for (i = 0; i < n; i++) { 75 PetscInt j; 76 PetscInt64 bin = 0; 77 PetscInt64 mult = 1; 78 79 for (j = 0; j < t; j++, mult *= d) { 80 PetscReal x; 81 PetscInt64 slot; 82 83 PetscCall(PetscRandomGetValueReal(random, &x)); 84 /* worried about precision here */ 85 slot = (PetscInt64)(x * d); 86 bin += mult * slot; 87 } 88 PetscCheck(bin < k, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Generated point in bin %" PetscInt64_FMT ", but only %" PetscInt64_FMT " bins", bin, k); 89 X[i] = bin; 90 } 91 92 qsort(X, n, sizeof(PetscInt64), PetscInt64Compare); 93 for (i = 0; i < n - 1; i++) X[i] = X[i + 1] - X[i]; 94 qsort(X, n - 1, sizeof(PetscInt64), PetscInt64Compare); 95 for (i = 0, Y = 0; i < n - 2; i++) Y += (X[i + 1] == X[i]); 96 97 PetscCallMPI(MPI_Allreduce(MPI_IN_PLACE, &Y, 1, MPIU_INT, MPI_SUM, MPI_COMM_WORLD)); 98 PetscCall(PoissonTailProbability(N * lambda, Y, &p)); 99 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT " total collisions counted: that many or more should occur with probabilty %g.\n", Y, (double)p)); 100 101 PetscCall(PetscFree(X)); 102 PetscCall(PetscRandomDestroy(&random)); 103 PetscCall(PetscFinalize()); 104 return 0; 105 } 106 107 /*TEST 108 109 test: 110 args: -t 4 -log2d 7 -log2n 10 111 112 TEST*/ 113