arb/acb_dirichlet/arb_theta_smallorder.c
2016-10-08 22:46:00 +02:00

77 lines
2.3 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) 2016 Pascal Molin
******************************************************************************/
#include "acb_dirichlet.h"
#include "acb_poly.h"
/* small order, multiply by chi at the end */
void
acb_dirichlet_arb_theta_smallorder(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_powers_t z, slong len, slong prec)
{
slong k;
ulong order = z->order;
arb_t xk2, kxk2, dx, x2;
acb_ptr t;
arb_init(xk2);
arb_init(dx);
arb_init(x2);
arb_init(kxk2);
arb_set(dx, x);
arb_set(xk2, x);
arb_mul(x2, x, x, prec);
t = _acb_vec_init(order);
_acb_vec_zero(t, order);
arb_set(acb_realref(t + 0), xk2);
/* TODO: reduce precision at each step */
for (k = 2; k < len; k++)
{
arb_mul(dx, dx, x2, prec);
arb_mul(xk2, xk2, dx, prec);
if (a[k] != ACB_DIRICHLET_CHI_NULL)
{
if (parity)
{
arb_mul_si(kxk2, xk2, k, prec);
arb_add(acb_realref(t + a[k]), acb_realref(t + a[k]), kxk2, prec);
}
else
{
arb_add(acb_realref(t + a[k]), acb_realref(t + a[k]), xk2, prec);
}
}
}
/* now Hörner */
_acb_poly_evaluate(res, t, order, z->z + 1, prec);
_acb_vec_clear(t, order);
arb_clear(xk2);
arb_clear(x2);
arb_clear(dx);
}