1: static char help[] = "Tests `GarbageKeyAllReduceIntersect_Private()` in parallel\n\n";

  3: #include <petsc/private/garbagecollector.h>

  5: /* This program tests `GarbageKeyAllReduceIntersect_Private()`.
  6:    To test this routine in parallel, the sieve of Eratosthenes is
  7:    implemented.
  8: */

 10: /* Populate an array with Prime numbers <= n.
 11:    Primes are generated using trial division
 12: */
 13: PetscErrorCode Prime(PetscInt64 **set, PetscInt64 n)
 14: {
 15:   size_t      overestimate;
 16:   PetscBool   is_prime;
 17:   PetscInt64  ii, jj, count = 0;
 18:   PetscInt64 *prime;

 20:   PetscFunctionBeginUser;
 21:   /* There will be fewer than ceil(1.26 * n/log(n)) primes <= n */
 22:   overestimate = (size_t)PetscCeilReal(((PetscReal)n) * 1.26 / PetscLogReal((PetscReal)n));
 23:   PetscCall(PetscMalloc1(overestimate, &prime));
 24:   for (ii = 2; ii < n + 1; ii++) {
 25:     is_prime = PETSC_TRUE;
 26:     for (jj = 2; jj <= PetscFloorReal(PetscSqrtReal(ii)); jj++) {
 27:       if (ii % jj == 0) {
 28:         is_prime = PETSC_FALSE;
 29:         break;
 30:       }
 31:     }
 32:     if (is_prime) {
 33:       prime[count] = ii;
 34:       count++;
 35:     }
 36:   }

 38:   PetscCall(PetscMalloc1((size_t)count + 1, set));
 39:   (*set)[0] = count;
 40:   for (ii = 1; ii < count + 1; ii++) (*set)[ii] = prime[ii - 1];
 41:   PetscCall(PetscFree(prime));
 42:   PetscFunctionReturn(PETSC_SUCCESS);
 43: }

 45: /* Print out the contents of a set */
 46: PetscErrorCode PrintSet(MPI_Comm comm, PetscInt64 *set)
 47: {
 48:   char     text[64];
 49:   PetscInt ii;

 51:   PetscFunctionBeginUser;
 52:   PetscCall(PetscSynchronizedPrintf(comm, "["));
 53:   for (ii = 1; ii <= (PetscInt)set[0]; ii++) {
 54:     PetscCall(PetscFormatConvert(" %" PetscInt64_FMT ",", text));
 55:     PetscCall(PetscSynchronizedPrintf(comm, text, set[ii]));
 56:   }
 57:   PetscCall(PetscSynchronizedPrintf(comm, "]\n"));
 58:   PetscCall(PetscSynchronizedFlush(comm, PETSC_STDOUT));
 59:   PetscFunctionReturn(PETSC_SUCCESS);
 60: }

 62: /* Check set equality */
 63: PetscErrorCode AssertSetsEqual(PetscInt64 *set, PetscInt64 *true_set)
 64: {
 65:   PetscInt ii;

 67:   PetscFunctionBeginUser;
 68:   PetscAssert(set[0] == true_set[0], PETSC_COMM_WORLD, PETSC_ERR_ARG_INCOMP, "Sets of different sizes");
 69:   for (ii = 1; ii < set[0] + 1; ii++) PetscAssert(set[ii] == true_set[ii], PETSC_COMM_WORLD, PETSC_ERR_ARG_INCOMP, "Sets are different");
 70:   PetscFunctionReturn(PETSC_SUCCESS);
 71: }

 73: /* Parallel implementation of the sieve of Eratosthenes */
 74: PetscErrorCode test_sieve(MPI_Comm comm)
 75: {
 76:   PetscInt64  ii, local_p, maximum, n;
 77:   PetscInt64 *local_set, *cursor, *bootstrap_primes, *truth;
 78:   PetscMPIInt size, rank;
 79:   PetscReal   x;

 81:   PetscFunctionBeginUser;
 82:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
 83:   PetscCallMPI(MPI_Comm_size(comm, &size));

 85:   /* There should be at least `size + 1` primes smaller than
 86:      (size + 1)*(log(size + 1) + log(log(size + 1))
 87:     once `size` >=6
 88:     This is sufficient for each rank to create its own sieve based off
 89:     a different prime and calculate the size of the sieve.
 90:   */
 91:   x = (PetscReal)(size > 6) ? size + 1 : 7;
 92:   x = x * (PetscLogReal(x) + PetscLogReal(PetscLogReal(x)));
 93:   PetscCall(Prime(&bootstrap_primes, PetscCeilReal(x)));

 95:   /* Calculate the maximum possible prime, select a prime number for
 96:      each rank and allocate memorty for the sieve
 97:   */
 98:   maximum = bootstrap_primes[size + 1] * bootstrap_primes[size + 1] - 1;
 99:   local_p = bootstrap_primes[rank + 1];
100:   n       = maximum - local_p - (maximum / local_p) + 1 + rank + 1;
101:   PetscCall(PetscMalloc1(n + 1, &local_set));

103:   /* Populate the sieve first with all primes <= `local_p`, followed by
104:      all integers that are not a multiple of `local_p`
105:   */
106:   local_set[0] = n;
107:   cursor       = &local_set[1];
108:   for (ii = 0; ii < rank + 1; ii++) {
109:     *cursor = bootstrap_primes[ii + 1];
110:     cursor++;
111:   }
112:   for (ii = local_p + 1; ii <= maximum; ii++) {
113:     if (ii % local_p != 0) {
114:       *cursor = ii;
115:       cursor++;
116:     }
117:   }
118:   PetscCall(PetscPrintf(comm, "SIEVES:\n"));
119:   PetscCall(PrintSet(comm, local_set));

121:   PetscCall(PetscFree(bootstrap_primes));

123:   /* Perform the intersection, testing parallel intersection routine */
124:   PetscCall(GarbageKeyAllReduceIntersect_Private(PETSC_COMM_WORLD, &local_set[1], (PetscInt *)&local_set[0]));

126:   PetscCall(PetscPrintf(comm, "INTERSECTION:\n"));
127:   PetscCall(PrintSet(comm, local_set));

129:   PetscCall(Prime(&truth, maximum));
130:   PetscCall(PetscPrintf(comm, "TRUTH:\n"));
131:   PetscCall(PrintSet(comm, truth));

133:   /* Assert the intersection corresponds to primes calculated using
134:      trial division
135:   */
136:   PetscCall(AssertSetsEqual(local_set, truth));

138:   PetscCall(PetscFree(local_set));
139:   PetscCall(PetscFree(truth));
140:   PetscFunctionReturn(PETSC_SUCCESS);
141: }

143: /* Main executes the individual tests in a predefined order */
144: int main(int argc, char **argv)
145: {
146:   PetscFunctionBeginUser;
147:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));

149:   PetscCall(test_sieve(PETSC_COMM_WORLD));

151:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "ALL PASSED\n"));
152:   PetscCall(PetscFinalize());
153:   return 0;
154: }

156: /*TEST

158:    testset:
159:      test:
160:        nsize: 2
161:        suffix: 2
162:        output_file: output/ex63_2.out
163:      test:
164:        nsize: 3
165:        suffix: 3
166:        output_file: output/ex63_3.out
167:      test:
168:        nsize: 4
169:        suffix: 4
170:        output_file: output/ex63_4.out

172: TEST*/