Actual source code: ex3.c
1: static char help[] = "Run Birthday Spacing Tests for PetscRandom.\n\n";
3: #include <petscsys.h>
4: #include <petscviewer.h>
6: /* L'Ecuyer & Simard, 2001.
7: * "On the performance of birthday spacings tests with certain families of random number generators"
8: * https://doi.org/10.1016/S0378-4754(00)00253-6
9: */
11: static int PetscInt64Compare(const void *a, const void *b)
12: {
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: }
20: static PetscErrorCode PoissonTailProbability(PetscReal lambda, PetscInt Y, PetscReal *prob)
21: {
22: PetscReal p = 1.;
23: PetscReal logLambda;
24: PetscInt i;
25: PetscReal logFact = 0.;
27: PetscFunctionBegin;
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: PetscFunctionReturn(PETSC_SUCCESS);
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;
49: PetscFunctionBeginUser;
50: PetscCall(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: PetscCall(PetscOptionsInt("-t", "t, the dimension of the sample space", "ex3.c", t, &t, NULL));
56: PetscCall(PetscOptionsInt("-log2d", "The log of d, the number of bins per direction", "ex3.c", log2d, &log2d, NULL));
57: PetscCall(PetscOptionsInt("-log2n", "The log of n, the number of samples per process", "ex3.c", log2n, &log2n, NULL));
58: PetscOptionsEnd();
60: 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);
61: d = ((PetscInt64)1) << log2d;
62: k = ((PetscInt64)1) << (log2d * t);
63: 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);
64: n = ((size_t)1) << log2n;
65: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
66: N = size;
67: lambda = PetscPowRealInt(2., (3 * log2n - (2 + log2d * t)));
69: 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));
70: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Expected spacing collisions per process %g (%g total).\n", (double)lambda, (double)(N * lambda)));
71: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &random));
72: PetscCall(PetscRandomSetFromOptions(random));
73: PetscCall(PetscRandomSetInterval(random, 0.0, 1.0));
74: PetscCall(PetscRandomView(random, PETSC_VIEWER_STDOUT_WORLD));
75: PetscCall(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: PetscCall(PetscRandomGetValueReal(random, &x));
86: /* worried about precision here */
87: slot = (PetscInt64)(x * d);
88: bin += mult * slot;
89: }
90: PetscCheck(bin < k, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Generated point in bin %" PetscInt64_FMT ", but only %" PetscInt64_FMT " bins", bin, k);
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: PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &Y, 1, MPIU_INT, MPI_SUM, MPI_COMM_WORLD));
100: PetscCall(PoissonTailProbability(N * lambda, Y, &p));
101: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT " total collisions counted: that many or more should occur with probability %g.\n", Y, (double)p));
103: PetscCall(PetscFree(X));
104: PetscCall(PetscRandomDestroy(&random));
105: PetscCall(PetscFinalize());
106: return 0;
107: }
109: /*TEST
111: test:
112: args: -t 4 -log2d 7 -log2n 10
114: TEST*/