#include #include #include #include #include static uint64_t seed = -1; static uint32_t rand32(void) { seed = 6364136223846793005ull*seed + 1; return seed >> 32; } static uint64_t rand64(void) { uint64_t u = rand32(); return u<<32 | rand32(); } static double frand(){return rand64() * 0x1p-64;} static float frandf(){return rand32() * 0x1p-32f;} static long double frandl(){return rand64() * 0x1p-64L;} /* uniform random in [0,n), n > 0 must hold */ uint64_t randn(uint64_t n) { uint64_t r, m; /* m is the largest multiple of n */ m = -1; m -= m%n; while ((r = rand64()) >= m); return r%n; } /* uniform on [a,b] */ uint64_t randint(uint64_t a, uint64_t b) { if (b < a) { uint64_t t = b; b = a; a = t; } return a + randn(b - a + 1); } int insert(uint64_t *tab, size_t len, uint64_t v) { size_t i = v & (len-1); size_t j = 1; /* 0 means empty, v > 0 must hold */ while (tab[i]) { if (tab[i] == v) return -1; i += j++; i &= len-1; } tab[i] = v; return 0; } static void shuffle2(uint64_t *p, uint64_t *q, size_t np, size_t nq) { size_t i,r,t; i = np+nq; while (i > np) { r = randn(i); i--; t = q[i-np]; if (r < np) { q[i-np] = p[r]; p[r] = t; } else { q[i-np] = q[r-np]; q[r-np] = t; } } } /* choose k unique numbers from [0,n), k <= n */ int choose(uint64_t n, size_t k, uint64_t *p) { uint64_t *tab; size_t i, j, len; if (n < k) return -1; if (n < 16) { /* no alloc */ while (k) if (randn(n--) < k) p[--k] = n; return 0; } if (k < 8) { /* no alloc, n > 15 > 2*k */ for (i = 0; i < k;) { p[i] = randn(n); for (j = 0; p[j] != p[i]; j++); if (j == i) i++; } return 0; } if (n < 5*k && (n-k)*sizeof *tab < (size_t)-1) { /* allocation is < 4*k */ tab = malloc((n-k) * sizeof *tab); if (!tab) return -1; for (i = 0; i < k; i++) p[i] = i; for (; i < n; i++) tab[i-k] = i; if (n-k < k) shuffle2(p, tab, k, n-k); else shuffle2(tab, p, n-k, k); free(tab); return 0; } /* allocation is < 4*k */ for (len = 16; len <= 2*k; len *= 2); tab = calloc(len, sizeof *tab); if (!tab) return -1; for (i = 0; i < k; i++) while (insert(tab, len, randn(n)+1)); for (i = 0; i < len; i++) if (tab[i]) *p++ = tab[i]-1; free(tab); return 0; } static int cmp64(const void *a, const void *b) { const uint64_t *ua = a, *ub = b; return *ua < *ub ? -1 : (*ua > *ub ? 1 : 0); } // todo: in place flip problem /* choose k unique uint64_t numbers */ int choose64(size_t k, uint64_t *p) { size_t i, c; /* no alloc, collisions should be very rare */ for (i = 0; i < k; i++) p[i] = rand64(); do { c = 0; qsort(p, k, sizeof *p, cmp64); for (i = 1; i < k; i++) if (p[i] == p[i-1]) { p[i-1] = rand64(); c = 1; } } while (c); return 0; } /* equidistant sampling with some randomness */ int sample(uint64_t n, size_t k, uint64_t *p) { uint64_t a = 0; uint64_t d = n/k; size_t m = n%k; size_t i, j; uint64_t *q; if (!d) return -1; q = malloc((m+1) * sizeof *q); if (!q) return -1; if (choose(k, m, q)) return -1; qsort(q, m, sizeof *q, cmp64); q[m] = k; for (i = j = 0; i < k; i++) { uint64_t t; while (q[j] < i) j++; if (q[j] == i) t = d+1; else t = d; p[i] = a + randn(t); a += t; } free(q); return 0; } /* [-inf,inf] uniform on representation */ int genall(size_t k, uint64_t *p) { size_t i; uint64_t n, d; d = 1; d <<= 52; if (sample(-2*d, k, p)) return -1; n = 0x7ff; n <<= 52; for (i = 0; i < k; i++) if (p[i] > n) p[i] += d-1; return 0; } /* [a,b) uniform on representation, 0 <= a <= b */ int genab(size_t k, uint64_t a, uint64_t b, uint64_t *p) { size_t i; if (sample(b-a, k, p)) return -1; for (i = 0; i < k; i++) p[i] += a; return 0; } #define asfloat(x) ((union{uint64_t af_i; double af_f;}){.af_i=x}.af_f) #define asint(x) ((union{uint64_t af_i; double af_f;}){.af_f=x}.af_i) int main(int argc, char *argv[]) { uint64_t k, i; uint64_t *p; double a,b,m; char *e; int opt; k = 1000; a = 0; b = 1; m = 1; while ((opt = getopt(argc, argv, "n:a:b:m:s:")) != -1) { switch(opt) { case 'n': k = strtoull(optarg,&e,0); break; case 'a': a = strtod(optarg,&e); if (a < 0) goto usage; break; case 'b': b = strtod(optarg,&e); if (b < 0) goto usage; break; case 'm': m = strtod(optarg,&e); break; case 's': seed = strtoull(optarg,&e,0); break; default: usage: fprintf(stderr, "usage: %s -n num -a absmin -b absmax -m mult -s seed\n", argv[0]); return -1; } if (*e || errno) goto usage; } if (!(a <= b)) goto usage; p = malloc(k * sizeof *p); if (!p) return -1; if (genab(k, asint(a), asint(b), p)) // if (genall(k,p)) return -1; for (i = 0; i < k; i++) // printf("0x%016llx\n", p[i]); printf("%a\n", m*asfloat(p[i])); return 0; }