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implement Fibonacci numbers

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This commit is contained in:
Fredrik Johansson 2012-09-05 15:30:20 +02:00
parent a049873a9c
commit d992e3fb5c
2 changed files with 120 additions and 0 deletions
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3
fmprb.h
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@ -178,6 +178,9 @@ void fmprb_fac_ui(fmprb_t x, ulong n, long prec);
void fmprb_bin_ui(fmprb_t x, const fmprb_t n, ulong k, long prec);
void fmprb_bin_uiui(fmprb_t x, ulong n, ulong k, long prec);
void fmprb_fib_fmpz(fmprb_t f, const fmpz_t n, long prec);
void fmprb_fib_ui(fmprb_t f, ulong n, long prec);
void fmprb_const_pi_chudnovsky(fmprb_t x, long prec);
void fmprb_const_pi(fmprb_t x, long prec);

117
fmprb/fib.c Normal file
View file

@ -0,0 +1,117 @@
/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2012 Fredrik Johansson
******************************************************************************/
#include "fmprb.h"
/*
Fibonacci numbers using binary powering.
D. Takahashi, "A fast algorithm for computing large Fibonacci numbers",
Information Processing Letters 75 (2000) 243–246
*/
void fmprb_fib_fmpz(fmprb_t f, const fmpz_t n, long prec)
{
fmprb_t t, u;
fmpz_t mask, v;
long wp, sign, i;
if (fmpz_sgn(n) < 0)
{
fmpz_t m;
fmpz_init(m);
fmpz_neg(m, n);
fmprb_fib_fmpz(f, m, prec);
if (fmpz_is_even(m))
fmprb_neg(f, f);
fmpz_clear(m);
return;
}
if (fmpz_cmp_ui(n, 4) <= 0)
{
ulong x = fmpz_get_ui(n);
fmprb_set_ui(f, x - (x > 1));
return;
}
if (prec == FMPR_PREC_EXACT)
wp = prec;
else
wp = prec + 3 * fmpz_bits(n);
fmprb_init(u);
fmprb_init(t);
fmprb_set_ui(f, 1UL);
fmprb_set_ui(u, 1UL);
sign = -1;
for (i = fmpz_flog_ui(n, 2UL) - 1; i > 0; i--)
{
fmprb_mul(t, f, f, wp);
fmprb_add(f, f, u, wp);
fmprb_mul_2exp_si(f, f, -1);
fmprb_mul(f, f, f, wp);
fmprb_mul_2exp_si(f, f, 1);
fmprb_submul_ui(f, t, 3, wp);
fmprb_sub_si(f, f, 2 * sign, wp);
fmprb_mul_ui(u, t, 5, wp);
fmprb_add_si(u, u, 2 * sign, wp);
sign = 1;
if (fmpz_tstbit(n, i))
{
fmprb_set(t, f);
fmprb_add(f, f, u, wp);
fmprb_mul_2exp_si(f, f, -1);
fmprb_mul_2exp_si(t, t, 1);
fmprb_add(u, f, t, wp);
sign = -1;
}
}
if (fmpz_tstbit(n, 0))
{
fmprb_add(f, f, u, wp);
fmprb_mul_2exp_si(f, f, -1);
fmprb_mul(f, f, u, wp);
fmprb_sub_si(f, f, sign, prec);
}
else
{
fmprb_mul(f, f, u, prec);
}
fmprb_clear(u);
fmprb_clear(t);
}
void fmprb_fib_ui(fmprb_t f, ulong n, long prec)
{
fmpz_t t;
fmpz_init_set_ui(t, n);
fmprb_fib_fmpz(f, t, prec);
fmpz_clear(t);
}