void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi) { slong hlen = h->length; if (n == 0) { arb_poly_zero(s); arb_poly_zero(c); return; } if (hlen == 0) { arb_poly_zero(s); arb_poly_one(c); return; } arb_poly_fit_length(s, n); arb_poly_fit_length(c, n); _arb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi); _arb_poly_set_length(s, n); _arb_poly_normalise(s); _arb_poly_set_length(c, n); _arb_poly_normalise(c); }
void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_sin_cos_pi(s, c, h, prec); _arb_vec_zero(s + 1, n - 1); _arb_vec_zero(c + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_const_pi(t, prec); arb_mul(t, t, h + 1, prec); arb_sin_cos_pi(s, c, h, prec); arb_mul(s + 1, c, t, prec); arb_neg(t, t); arb_mul(c + 1, s, t, prec); arb_clear(t); } else if (hlen < TANGENT_CUTOFF) _arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 1); else _arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 1); }
void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_sin_cos(s, c, h, prec); _arb_vec_zero(s + 1, n - 1); _arb_vec_zero(c + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_set(t, h + 1); arb_sin_cos(s, c, h, prec); arb_mul(s + 1, c, t, prec); arb_neg(t, t); arb_mul(c + 1, s, t, prec); arb_clear(t); } else { slong cutoff; if (prec <= 128) { cutoff = 1400; } else { cutoff = 100000 / pow(log(prec), 3); cutoff = FLINT_MIN(cutoff, 700); } if (hlen < cutoff) _arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 0); else _arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 0); } }