void mag_exp_tail(mag_t z, const mag_t x, ulong N) { if (N == 0 || mag_is_inf(x)) { mag_exp(z, x); } else if (mag_is_zero(x)) { mag_zero(z); } else { mag_t t; mag_init(t); mag_set_ui_2exp_si(t, N, -1); /* bound by geometric series when N >= 2*x <=> N/2 >= x */ if (mag_cmp(t, x) >= 0) { /* 2 c^N / N! */ mag_pow_ui(t, x, N); mag_rfac_ui(z, N); mag_mul(z, z, t); mag_mul_2exp_si(z, z, 1); } else { mag_exp(z, x); } mag_clear(t); } }
int main() { slong iter; flint_rand_t state; flint_printf("rfac_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++) { fmpr_t x, y; fmpz_t f; mag_t xb; ulong n; fmpr_init(x); fmpr_init(y); fmpz_init(f); mag_init(xb); mag_randtest_special(xb, state, 80); n = n_randtest(state) % 2000; mag_rfac_ui(xb, n); fmpz_fac_ui(f, n); fmpr_one(x); fmpr_div_fmpz(x, x, f, 2 * MAG_BITS, FMPR_RND_UP); mag_get_fmpr(y, xb); MAG_CHECK_BITS(xb) if (!(fmpr_cmpabs(y, x) >= 0)) { flint_printf("FAIL\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpz_clear(f); mag_clear(xb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
static __inline__ long rec_fac_bound_2exp_si(slong n) { if (n < TABSIZE) { return rec_fac_bound_2exp_si_tab[n]; } else { mag_t t; mag_init(t); mag_rfac_ui(t, n); /* todo: check for overflow */ return MAG_EXP(t); } }
/* Given T(K), compute bound for T(n) z^n. We need to multiply by z^n * 1/rf(K+1,m)^r * (rf(K+1,m)/rf(K+1-A,m)) * (rf(K+1-B,m)/rf(K+1-2B,m)) where m = n - K. This is equal to z^n * (K+A)! (K-2B)! (K-B+m)! ----------------------- * ((K+m)! / K!)^(1-r) (K-B)! (K-A+m)! (K-2B+m)! */ void hypgeom_term_bound(mag_t Tn, const mag_t TK, slong K, slong A, slong B, int r, const mag_t z, slong n) { mag_t t, u, num; slong m; mag_init(t); mag_init(u); mag_init(num); m = n - K; if (m < 0) { flint_printf("hypgeom term bound\n"); abort(); } /* TK * z^n */ mag_pow_ui(t, z, n); mag_mul(num, TK, t); /* numerator: (K+A)! (K-2B)! (K-B+m)! */ mag_fac_ui(t, K+A); mag_mul(num, num, t); mag_fac_ui(t, K-2*B); mag_mul(num, num, t); mag_fac_ui(t, K-B+m); mag_mul(num, num, t); /* denominator: (K-B)! (K-A+m)! (K-2B+m)! */ mag_rfac_ui(t, K-B); mag_mul(num, num, t); mag_rfac_ui(t, K-A+m); mag_mul(num, num, t); mag_rfac_ui(t, K-2*B+m); mag_mul(num, num, t); /* ((K+m)! / K!)^(1-r) */ if (r == 0) { mag_fac_ui(t, K+m); mag_mul(num, num, t); mag_rfac_ui(t, K); mag_mul(num, num, t); } else if (r != 1) { mag_fac_ui(t, K); mag_rfac_ui(u, K+m); mag_mul(t, t, u); mag_pow_ui(t, t, r-1); mag_mul(num, num, t); } mag_set(Tn, num); mag_clear(t); mag_clear(u); mag_clear(num); }