mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
109 lines
2.9 KiB
C
109 lines
2.9 KiB
C
/*=============================================================================
|
|
|
|
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 "fmpcb.h"
|
|
|
|
void
|
|
fmpcb_root_exp(fmpcb_t r, const fmpcb_t a, long m, long index, long prec)
|
|
{
|
|
if (m == 1)
|
|
fmpcb_set_round(r, a, prec);
|
|
else if (m == -1)
|
|
fmpcb_inv(r, a, prec);
|
|
else
|
|
{
|
|
fmpcb_log(r, a, prec);
|
|
|
|
if (index != 0)
|
|
{
|
|
fmprb_t t;
|
|
fmprb_init(t);
|
|
fmprb_const_pi(t, prec);
|
|
fmprb_mul_2exp_si(t, t, 1);
|
|
fmprb_mul_si(t, t, index, prec);
|
|
fmprb_add(fmpcb_imagref(r), fmpcb_imagref(r), t, prec);
|
|
fmprb_clear(t);
|
|
}
|
|
|
|
fmpcb_div_si(r, r, m, prec);
|
|
fmpcb_exp(r, r, prec);
|
|
}
|
|
}
|
|
|
|
void
|
|
fmpcb_root_newton(fmpcb_t r, const fmpcb_t a, long m, long index, long prec)
|
|
{
|
|
if (m == 1)
|
|
fmpcb_set_round(r, a, prec);
|
|
else if (m == -1)
|
|
fmpcb_inv(r, a, prec);
|
|
else
|
|
{
|
|
long startprec;
|
|
fmpcb_t t;
|
|
|
|
fmpcb_init(t);
|
|
|
|
startprec = 100;
|
|
fmpcb_root_exp(t, a, -FLINT_ABS(m), index, startprec);
|
|
|
|
/* note: should check isolation first */
|
|
fmpcb_invroot_newton(t, a, FLINT_ABS(m), t, startprec, prec);
|
|
|
|
if (m < 0)
|
|
{
|
|
fmpcb_set(r, t);
|
|
}
|
|
else
|
|
{
|
|
if (fmpcb_is_one(a))
|
|
fmpcb_conj(r, t);
|
|
else if (m == 2)
|
|
fmpcb_mul(r, t, a, prec);
|
|
else
|
|
fmpcb_inv(r, t, prec);
|
|
}
|
|
|
|
fmpcb_clear(t);
|
|
}
|
|
}
|
|
|
|
void
|
|
fmpcb_root(fmpcb_t r, const fmpcb_t a, long m, long index, long prec)
|
|
{
|
|
if (m == 1)
|
|
fmpcb_set_round(r, a, prec);
|
|
else if (m == -1)
|
|
fmpcb_inv(r, a, prec);
|
|
else if (m == 2)
|
|
fmpcb_sqrt(r, a, prec);
|
|
else if (m == -2)
|
|
fmpcb_rsqrt(r, a, prec);
|
|
else if (prec < 300 || !fmpcb_is_exact(a) || (m == LONG_MIN))
|
|
fmpcb_root_exp(r, a, m, index, prec);
|
|
else
|
|
fmpcb_root_newton(r, a, m, index, prec);
|
|
}
|
|
|