mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
129 lines
No EOL
3.4 KiB
C
129 lines
No EOL
3.4 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 Fredrik Johansson
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******************************************************************************/
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#include "fmprb.h"
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#define CONST_A 13591409UL
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#define CONST_B 545140134UL
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#define CONST_C 640320UL
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#define CONST_D 12UL
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#define BITS_PER_TERM 47.1104131382158 /* log2(640320^3 / (2^6 * 3^3)) */
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void
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chudnovsky_bsplit(fmprb_t G, fmprb_t P, fmprb_t Q, long a, long b, long wp, int cont)
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{
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if (b - a == 1)
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{
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/* g = (6*b-5)*(2*b-1)*(6*b-1) */
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fmprb_set_si(G, 6*b - 5);
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fmprb_mul_si(G, G, 2*b-1, FMPR_PREC_EXACT);
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fmprb_mul_si(G, G, 6*b-1, FMPR_PREC_EXACT);
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/* p = C^3 * b^3 / 24 */
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#if FLINT_BITS == 64
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fmprb_set_si(P, CONST_C * CONST_C * CONST_C / 24);
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#else
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fmprb_set_ui(P, CONST_C / 24);
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fmprb_mul_ui(P, P, CONST_C, FMPR_PREC_EXACT);
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fmprb_mul_ui(P, P, CONST_C, FMPR_PREC_EXACT);
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#endif
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fmprb_mul_ui(P, P, b, FMPR_PREC_EXACT);
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fmprb_mul_ui(P, P, b, FMPR_PREC_EXACT);
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fmprb_mul_ui(P, P, b, FMPR_PREC_EXACT);
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/* (-1)^b * g * (A + B*b) */
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{
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fmpz_t t;
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fmpz_init(t);
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fmpz_set_ui(t, CONST_B);
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fmpz_mul_ui(t, t, b);
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fmpz_add_ui(t, t, CONST_A);
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fmprb_mul_fmpz(Q, G, t, FMPR_PREC_EXACT);
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fmpz_clear(t);
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}
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if (b % 2)
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fmprb_neg(Q, Q);
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}
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else
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{
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long m;
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fmprb_t G2, P2, Q2;
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m = (a + b) / 2;
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fmprb_init(G2);
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fmprb_init(P2);
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fmprb_init(Q2);
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chudnovsky_bsplit(G, P, Q, a, m, wp, 1);
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chudnovsky_bsplit(G2, P2, Q2, m, b, wp, 1);
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fmprb_mul(Q, Q, P2, wp);
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fmprb_addmul(Q, Q2, G, wp);
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fmprb_mul(P, P, P2, wp);
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if (cont)
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fmprb_mul(G, G, G2, wp);
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fmprb_clear(G2);
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fmprb_clear(P2);
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fmprb_clear(Q2);
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}
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}
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void
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fmprb_const_pi_chudnovsky(fmprb_t x, long prec)
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{
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long wp, N;
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fmprb_t G, P, Q;
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wp = prec + 32;
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N = wp / BITS_PER_TERM + 1;
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fmprb_init(G);
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fmprb_init(P);
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fmprb_init(Q);
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chudnovsky_bsplit(G, P, Q, 0, N, wp, 0);
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fmprb_sqrt_ui(G, CONST_C, wp);
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fmprb_mul_si(G, G, CONST_C, wp);
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fmprb_mul(G, G, P, wp);
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fmprb_mul_si(P, P, CONST_A, wp);
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fmprb_add(Q, Q, P, wp);
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fmprb_mul_si(Q, Q, CONST_D, wp);
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fmprb_div(x, G, Q, wp);
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/* TODO: add error term */
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fmprb_clear(G);
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fmprb_clear(P);
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fmprb_clear(Q);
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} |