void _acb_poly_compose(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { if (len1 == 1) { acb_set_round(res, poly1, prec); } else if (len2 == 1) { _acb_poly_evaluate(res, poly1, len1, poly2, prec); } else if (_acb_vec_is_zero(poly2 + 1, len2 - 2)) { _acb_poly_compose_axnc(res, poly1, len1, poly2, poly2 + len2 - 1, len2 - 1, prec); } else if (len1 <= 7) { _acb_poly_compose_horner(res, poly1, len1, poly2, len2, prec); } else { _acb_poly_compose_divconquer(res, poly1, len1, poly2, len2, prec); } }
void _acb_poly_compose_series(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { if (len2 == 1) { acb_set_round(res, poly1, prec); _acb_vec_zero(res + 1, n - 1); } else if (_acb_vec_is_zero(poly2 + 1, len2 - 2)) /* poly2 is a monomial */ { slong i, j; acb_t t; acb_init(t); acb_set(t, poly2 + len2 - 1); acb_set_round(res, poly1, prec); for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1) { acb_mul(res + j, poly1 + i, t, prec); if (i + 1 < len1 && j + len2 - 1 < n) acb_mul(t, t, poly2 + len2 - 1, prec); } if (len2 != 2) for (i = 1; i < n; i++) if (i % (len2 - 1) != 0) acb_zero(res + i); acb_clear(t); } else if (len1 < 6 || n < 6) { _acb_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, prec); } else { _acb_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, prec); } }
void _acb_poly_sqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); while (hlen > 0 && acb_is_zero(h + hlen - 1)) hlen--; if (hlen <= 1) { acb_sqrt(g, h, prec); _acb_vec_zero(g + 1, len - 1); } else if (len == 2) { acb_sqrt(g, h, prec); acb_div(g + 1, h + 1, h, prec); acb_mul(g + 1, g + 1, g, prec); acb_mul_2exp_si(g + 1, g + 1, -1); } else if (_acb_vec_is_zero(h + 1, hlen - 2)) { acb_t t; acb_init(t); arf_set_si_2exp_si(arb_midref(acb_realref(t)), 1, -1); _acb_poly_binomial_pow_acb_series(g, h, hlen, t, len, prec); acb_clear(t); } else { acb_ptr t; t = _acb_vec_init(len); _acb_poly_rsqrt_series(t, h, hlen, len, prec); _acb_poly_mullow(g, t, len, h, hlen, len, prec); _acb_vec_clear(t, len); } }