slong hypgeom_estimate_terms(const mag_t z, int r, slong prec) { double y, t; t = mag_get_d(z); if (t == 0) return 1; if (r == 0) { if (t >= 1) { flint_printf("z must be smaller than 1\n"); abort(); } y = (log(1-t) - prec * LOG2) / log(t) + 1; } else { y = (prec * LOG2) / (d_root(t, r) * EXP1 * r); y = (prec * LOG2) / (r * d_lambertw(y)) + 1; } if (y >= WORD_MAX / 2) { flint_printf("error: series will converge too slowly\n"); abort(); } return y; }
void acb_hypgeom_bessel_k(acb_t res, const acb_t nu, const acb_t z, slong prec) { mag_t zmag; mag_init(zmag); acb_get_mag(zmag, z); if (mag_cmp_2exp_si(zmag, 4) < 0 || (mag_cmp_2exp_si(zmag, 64) < 0 && 2 * mag_get_d(zmag) < prec)) acb_hypgeom_bessel_k_0f1(res, nu, z, prec); else acb_hypgeom_bessel_k_asymp(res, nu, z, prec); mag_clear(zmag); }
slong _arb_mat_exp_choose_N(const mag_t norm, slong prec) { if (mag_is_special(norm) || mag_cmp_2exp_si(norm, 30) > 0 || mag_cmp_2exp_si(norm, -prec) < 0) { return 1; } else if (mag_cmp_2exp_si(norm, -300) < 0) { slong N = -MAG_EXP(norm); return (prec + N - 1) / N; } else { double c, t; c = mag_get_d(norm); t = d_lambertw(prec * LOG2_OVER_E / c); t = c * exp(t + 1.0); return FLINT_MIN((slong) (t + 1.0), 2 * prec); } }