mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
147 lines
4 KiB
C
147 lines
4 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012, 2013 Fredrik Johansson
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******************************************************************************/
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#include "zeta.h"
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#include "fmpcb.h"
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#include "fmpcb_poly.h"
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#include "bernoulli.h"
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static void
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bsplit(fmpcb_ptr P, fmpcb_ptr T, const fmpcb_t s, const fmpcb_t Na,
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long a, long b, int cont, long len, long prec)
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{
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long plen = FLINT_MIN(2 * (b - a) + 1, len);
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if (b - a == 1)
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{
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long j = a;
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fmpz_t t;
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fmpz_init(t);
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if (j == 0)
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{
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fmpcb_set(P, s);
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if (len > 1) fmpcb_one(P + 1);
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if (len > 2) fmpcb_zero(P + 2);
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}
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else
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{
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/* P = ((s+x)+2j-1)(s+x)+2j) */
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/* constant term = s^2 + (4j-1)s + (4j^2-2j)*/
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fmpcb_mul(P, s, s, prec);
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fmpcb_addmul_ui(P, s, 4*j-1, prec);
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fmpz_set_ui(t, 2*j);
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fmpz_mul_ui(t, t, 2*j-1);
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fmpcb_add_fmpz(P, P, t, prec);
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/* x term = (2s+4j-1) */
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if (len > 1)
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{
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fmpcb_mul_ui(P + 1, s, 2, prec);
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fmpcb_add_ui(P + 1, P + 1, 4*j-1, prec);
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}
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/* x^2 term = 1 */
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if (len > 2)
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fmpcb_one(P + 2);
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}
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/* P = P / ((2j+1)*(2j+2)) */
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fmpz_set_ui(t, 2*j+1);
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fmpz_mul_ui(t, t, 2*j+2);
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_fmpcb_vec_scalar_div_fmpz(P, P, plen, t, prec);
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/* P = P / Na or P / Na^2 */
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if (j == 0)
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fmpcb_set(T, Na);
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else
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fmpcb_mul(T, Na, Na, prec);
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_fmpcb_vec_scalar_div(P, P, plen, T, prec);
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/* T = P * B_{2j+2} */
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_fmpcb_vec_scalar_mul_fmpz(T, P, plen, fmpq_numref(bernoulli_cache + 2 * j + 2), prec);
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_fmpcb_vec_scalar_div_fmpz(T, T, plen, fmpq_denref(bernoulli_cache + 2 * j + 2), prec);
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fmpz_clear(t);
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}
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else
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{
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long m, len1, len2, alloc;
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fmpcb_ptr P1, T1, P2, T2;
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m = a + (b - a) / 2;
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len1 = FLINT_MIN(2 * (m - a) + 1, len);
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len2 = FLINT_MIN(2 * (b - m) + 1, len);
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alloc = 2 * len1 + 2 * len2;
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P1 = _fmpcb_vec_init(alloc);
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T1 = P1 + len1;
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P2 = T1 + len1;
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T2 = P2 + len2;
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bsplit(P1, T1, s, Na, a, m, 1, len, prec);
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bsplit(P2, T2, s, Na, m, b, 1, len, prec);
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/* P = P1 * P2 */
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if (cont)
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_fmpcb_poly_mullow(P, P2, len2, P1, len1, plen, prec);
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/* T = T1 + P1 * T2 */
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_fmpcb_poly_mullow(T, T2, len2, P1, len1, plen, prec);
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_fmpcb_vec_add(T, T, T1, len1, prec);
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_fmpcb_vec_clear(P1, alloc);
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}
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}
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void
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zeta_em_tail_bsplit(fmpcb_ptr z, const fmpcb_t s, const fmpcb_t Na, fmpcb_srcptr Nasx, long M, long len, long prec)
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{
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fmpcb_ptr P, T;
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if (M < 1)
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{
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_fmpcb_vec_zero(z, len);
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return;
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}
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BERNOULLI_ENSURE_CACHED(2 * M);
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P = _fmpcb_vec_init(len);
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T = _fmpcb_vec_init(len);
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bsplit(P, T, s, Na, 0, M, 0, len, prec);
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_fmpcb_poly_mullow(z, T, len, Nasx, len, len, prec);
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_fmpcb_vec_clear(P, len);
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_fmpcb_vec_clear(T, len);
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}
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