mirror of
https://github.com/vale981/arb
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113 lines
2.9 KiB
C
113 lines
2.9 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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/*
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Fibonacci numbers using binary powering.
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D. Takahashi, "A fast algorithm for computing large Fibonacci numbers",
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Information Processing Letters 75 (2000) 243–246
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*/
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void fmprb_fib_fmpz(fmprb_t f, const fmpz_t n, long prec)
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{
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fmprb_t t, u;
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long wp, sign, i;
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if (fmpz_sgn(n) < 0)
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{
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fmpz_t m;
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fmpz_init(m);
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fmpz_neg(m, n);
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fmprb_fib_fmpz(f, m, prec);
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if (fmpz_is_even(m))
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fmprb_neg(f, f);
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fmpz_clear(m);
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return;
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}
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if (fmpz_cmp_ui(n, 4) <= 0)
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{
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ulong x = fmpz_get_ui(n);
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fmprb_set_ui(f, x - (x > 1));
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return;
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}
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wp = FMPR_PREC_ADD(prec, 3 * fmpz_bits(n));
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fmprb_init(u);
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fmprb_init(t);
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fmprb_set_ui(f, 1UL);
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fmprb_set_ui(u, 1UL);
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sign = -1;
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for (i = fmpz_flog_ui(n, 2UL) - 1; i > 0; i--)
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{
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fmprb_mul(t, f, f, wp);
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fmprb_add(f, f, u, wp);
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fmprb_mul_2exp_si(f, f, -1);
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fmprb_mul(f, f, f, wp);
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fmprb_mul_2exp_si(f, f, 1);
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fmprb_submul_ui(f, t, 3, wp);
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fmprb_sub_si(f, f, 2 * sign, wp);
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fmprb_mul_ui(u, t, 5, wp);
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fmprb_add_si(u, u, 2 * sign, wp);
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sign = 1;
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if (fmpz_tstbit(n, i))
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{
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fmprb_set(t, f);
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fmprb_add(f, f, u, wp);
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fmprb_mul_2exp_si(f, f, -1);
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fmprb_mul_2exp_si(t, t, 1);
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fmprb_add(u, f, t, wp);
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sign = -1;
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}
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}
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if (fmpz_tstbit(n, 0))
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{
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fmprb_add(f, f, u, wp);
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fmprb_mul_2exp_si(f, f, -1);
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fmprb_mul(f, f, u, wp);
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fmprb_sub_si(f, f, sign, prec);
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}
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else
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{
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fmprb_mul(f, f, u, prec);
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}
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fmprb_clear(u);
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fmprb_clear(t);
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}
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void fmprb_fib_ui(fmprb_t f, ulong n, long prec)
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{
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fmpz_t t;
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fmpz_init_set_ui(t, n);
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fmprb_fib_fmpz(f, t, prec);
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fmpz_clear(t);
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}
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