mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
125 lines
3 KiB
C
125 lines
3 KiB
C
/*
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Copyright (C) 2013 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "arb_poly.h"
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void
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_arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
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arb_srcptr h, slong hlen, slong len, slong prec, int times_pi)
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{
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arb_ptr t, u, v;
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arb_t s0, c0;
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hlen = FLINT_MIN(hlen, len);
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if (hlen == 1)
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{
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if (times_pi)
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arb_sin_cos_pi(s, c, h, prec);
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else
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arb_sin_cos(s, c, h, prec);
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_arb_vec_zero(s + 1, len - 1);
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_arb_vec_zero(c + 1, len - 1);
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return;
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}
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/*
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sin(x) = 2*tan(x/2)/(1+tan(x/2)^2)
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cos(x) = (1-tan(x/2)^2)/(1+tan(x/2)^2)
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*/
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arb_init(s0);
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arb_init(c0);
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t = _arb_vec_init(3 * len);
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u = t + len;
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v = u + len;
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/* sin, cos of h0 */
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if (times_pi)
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arb_sin_cos_pi(s0, c0, h, prec);
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else
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arb_sin_cos(s0, c0, h, prec);
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/* t = tan((h-h0)/2) */
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arb_zero(u);
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_arb_vec_scalar_mul_2exp_si(u + 1, h + 1, hlen - 1, -1);
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if (times_pi)
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{
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arb_const_pi(t, prec);
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_arb_vec_scalar_mul(u + 1, u + 1, hlen - 1, t, prec);
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}
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_arb_poly_tan_series(t, u, hlen, len, prec);
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/* v = 1 + t^2 */
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_arb_poly_mullow(v, t, len, t, len, len, prec);
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arb_add_ui(v, v, 1, prec);
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/* u = 1/(1+t^2) */
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_arb_poly_inv_series(u, v, len, len, prec);
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/* sine */
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_arb_poly_mullow(s, t, len, u, len, len, prec);
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_arb_vec_scalar_mul_2exp_si(s, s, len, 1);
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/* cosine */
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arb_sub_ui(v, v, 2, prec);
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_arb_vec_neg(v, v, len);
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_arb_poly_mullow(c, v, len, u, len, len, prec);
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/* sin(h0 + h1) = cos(h0) sin(h1) + sin(h0) cos(h1)
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cos(h0 + h1) = cos(h0) cos(h1) - sin(h0) sin(h1) */
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if (!arb_is_zero(s0))
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{
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_arb_vec_scalar_mul(t, s, len, c0, prec);
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_arb_vec_scalar_mul(u, c, len, s0, prec);
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_arb_vec_scalar_mul(v, s, len, s0, prec);
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_arb_vec_add(s, t, u, len, prec);
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_arb_vec_scalar_mul(t, c, len, c0, prec);
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_arb_vec_sub(c, t, v, len, prec);
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}
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_arb_vec_clear(t, 3 * len);
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arb_clear(s0);
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arb_clear(c0);
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}
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void
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arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
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const arb_poly_t h, slong n, slong prec, int times_pi)
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{
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slong hlen = h->length;
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if (n == 0)
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{
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arb_poly_zero(s);
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arb_poly_zero(c);
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return;
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}
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if (hlen == 0)
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{
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arb_poly_zero(s);
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arb_poly_one(c);
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return;
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}
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arb_poly_fit_length(s, n);
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arb_poly_fit_length(c, n);
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_arb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs,
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h->coeffs, hlen, n, prec, times_pi);
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_arb_poly_set_length(s, n);
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_arb_poly_normalise(s);
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_arb_poly_set_length(c, n);
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_arb_poly_normalise(c);
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}
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