arb/fmprb_poly/log_series.c
2013-10-21 15:30:19 +02:00

103 lines
3.1 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, 2013 Fredrik Johansson
******************************************************************************/
#include "fmprb_poly.h"
void
_fmprb_poly_log_series(fmprb_ptr res, fmprb_srcptr f, long flen, long n, long prec)
{
flen = FLINT_MIN(flen, n);
if (flen == 1)
{
fmprb_log(res, f, prec);
_fmprb_vec_zero(res + 1, n - 1);
}
else if (n == 2)
{
fmprb_div(res + 1, f + 1, f + 0, prec); /* safe since hlen >= 2 */
fmprb_log(res, f, prec);
}
else if (_fmprb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
long i, j, d = flen - 1;
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
fmprb_div(res + j, f + d, f + 0, prec);
else
fmprb_mul(res + j, res + j - d, res + d, prec);
_fmprb_vec_zero(res + j - d + 1, flen - 2);
}
_fmprb_vec_zero(res + j - d + 1, n - (j - d + 1));
for (i = 2, j = 2 * d; j < n; j += d, i++)
fmprb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
fmprb_log(res, f, prec); /* done last to allow aliasing */
}
else
{
fmprb_ptr f_diff, f_inv;
fmprb_t a;
long alloc;
alloc = n + flen - 1;
f_inv = _fmprb_vec_init(alloc);
f_diff = f_inv + n;
fmprb_init(a);
fmprb_log(a, f, prec);
_fmprb_poly_derivative(f_diff, f, flen, prec);
_fmprb_poly_inv_series(f_inv, f, flen, n, prec);
_fmprb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_fmprb_poly_integral(res, res, n, prec);
fmprb_swap(res, a);
fmprb_clear(a);
_fmprb_vec_clear(f_inv, alloc);
}
}
void
fmprb_poly_log_series(fmprb_poly_t res, const fmprb_poly_t f, long n, long prec)
{
if (n == 0)
{
fmprb_poly_zero(res);
return;
}
fmprb_poly_fit_length(res, n);
if (f->length == 0)
_fmprb_vec_indeterminate(res->coeffs, n);
else
_fmprb_poly_log_series(res->coeffs, f->coeffs, f->length, n, prec);
_fmprb_poly_set_length(res, n);
_fmprb_poly_normalise(res);
}