Actual source code: ex3.c
2: static char help[] = "Run Birthday Spacing Tests for PetscRandom.\n\n";
4: #include <petscsys.h>
5: #include <petscviewer.h>
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: */
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: }
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.;
28: logLambda = PetscLogReal(lambda);
29: for (i = 0; i < Y; i++) {
30: PetscReal exponent = -lambda + i * logLambda - logFact;
32: logFact += PetscLogReal(i + 1);
34: p -= PetscExpReal(exponent);
35: }
36: *prob = p;
37: return 0;
38: }
40: int main(int argc, char **argv)
41: {
42: PetscMPIInt size;
43: PetscInt log2d, log2n, t, N, Y;
44: PetscInt64 d, k, *X;
45: size_t n, i;
46: PetscReal lambda, p;
47: PetscRandom random;
50: PetscInitialize(&argc, &argv, NULL, help);
51: t = 8;
52: log2d = 7;
53: log2n = 20;
54: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Birthday spacing test parameters", "PetscRandom");
55: PetscOptionsInt("-t", "t, the dimension of the sample space", "ex3.c", t, &t, NULL);
56: PetscOptionsInt("-log2d", "The log of d, the number of bins per direction", "ex3.c", log2d, &log2d, NULL);
57: PetscOptionsInt("-log2n", "The log of n, the number of samples per process", "ex3.c", log2n, &log2n, NULL);
58: PetscOptionsEnd();
61: d = ((PetscInt64)1) << log2d;
62: k = ((PetscInt64)1) << (log2d * t);
64: n = ((size_t)1) << log2n;
65: MPI_Comm_size(PETSC_COMM_WORLD, &size);
66: N = size;
67: lambda = PetscPowRealInt(2., (3 * log2n - (2 + log2d * t)));
69: 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);
70: PetscPrintf(PETSC_COMM_WORLD, "Expected spacing collisions per process %g (%g total).\n", (double)lambda, (double)(N * lambda));
71: PetscRandomCreate(PETSC_COMM_WORLD, &random);
72: PetscRandomSetFromOptions(random);
73: PetscRandomSetInterval(random, 0.0, 1.0);
74: PetscRandomView(random, PETSC_VIEWER_STDOUT_WORLD);
75: PetscMalloc1(n, &X);
76: for (i = 0; i < n; i++) {
77: PetscInt j;
78: PetscInt64 bin = 0;
79: PetscInt64 mult = 1;
81: for (j = 0; j < t; j++, mult *= d) {
82: PetscReal x;
83: PetscInt64 slot;
85: PetscRandomGetValueReal(random, &x);
86: /* worried about precision here */
87: slot = (PetscInt64)(x * d);
88: bin += mult * slot;
89: }
91: X[i] = bin;
92: }
94: qsort(X, n, sizeof(PetscInt64), PetscInt64Compare);
95: for (i = 0; i < n - 1; i++) X[i] = X[i + 1] - X[i];
96: qsort(X, n - 1, sizeof(PetscInt64), PetscInt64Compare);
97: for (i = 0, Y = 0; i < n - 2; i++) Y += (X[i + 1] == X[i]);
99: MPI_Allreduce(MPI_IN_PLACE, &Y, 1, MPIU_INT, MPI_SUM, MPI_COMM_WORLD);
100: PoissonTailProbability(N * lambda, Y, &p);
101: PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT " total collisions counted: that many or more should occur with probability %g.\n", Y, (double)p);
103: PetscFree(X);
104: PetscRandomDestroy(&random);
105: PetscFinalize();
106: return 0;
107: }
109: /*TEST
111: test:
112: args: -t 4 -log2d 7 -log2n 10
114: TEST*/