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/*=============================================================================
This file is part of FLINT.
FLINT 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.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include "fmpz.h"
#include "arith.h"
static void
sum_of_two_squares(fmpz_t r, const fmpz_t n)
{
fmpz_factor_t fac;
slong i;
fmpz_factor_init(fac);
fmpz_factor(fac, n);
fmpz_one(r);
for (i = 0; i < fac->num; i++)
{
const int res = fmpz_fdiv_ui(fac->p + i, 4);
if (res == 1)
{
fac->exp[i]++;
fmpz_mul_ui(r, r, fac->exp[i]);
}
else if (res == 3)
{
if (fac->exp[i] % 2)
{
fmpz_zero(r);
break;
}
}
}
fmpz_mul_ui(r, r, 4);
fmpz_factor_clear(fac);
}
static void
sum_of_four_squares(fmpz_t r, const fmpz_t n)
{
const mp_bitcnt_t v = fmpz_val2(n);
if (v == 0)
{
arith_divisor_sigma(r, n, 1);
fmpz_mul_ui(r, r, 8);
}
else
{
fmpz_tdiv_q_2exp(r, n, v);
arith_divisor_sigma(r, r, 1);
fmpz_mul_ui(r, r, 24);
}
}
static void
sum_of_squares_recursive(fmpz_t r, slong k, ulong n)
{
fmpz_t t, u;
slong i, j;
fmpz_init(t);
fmpz_init(u);
fmpz_zero(r);
for (i = j = 0; j <= n; i++)
{
fmpz_set_ui(u, n - j);
arith_sum_of_squares(t, k - 1, u);
if (j > 0)
fmpz_mul_ui(t, t, 2);
fmpz_add(r, r, t);
j += 2 * i + 1;
}
fmpz_clear(t);
fmpz_clear(u);
}
static void
sum_of_squares_series(fmpz_t r, ulong k, slong n)
{
fmpz * t;
t = _fmpz_vec_init(n + 1);
arith_sum_of_squares_vec(t, k, n + 1);
fmpz_set(r, t + n);
_fmpz_vec_clear(t, n + 1);
}
void
arith_sum_of_squares(fmpz_t r, ulong k, const fmpz_t n)
{
if (fmpz_sgn(n) <= 0 || k == 0)
fmpz_set_ui(r, fmpz_is_zero(n) != 0);
else if (k == 1)
fmpz_set_ui(r, 2 * (fmpz_is_square(n) != 0));
else if (k == 2)
sum_of_two_squares(r, n);
else if (k == 4)
sum_of_four_squares(r, n);
else if (k == 3 || k == 5)
sum_of_squares_recursive(r, k, fmpz_get_ui(n));
else if (fmpz_fits_si(n))
sum_of_squares_series(r, k, fmpz_get_ui(n));
else
{
flint_printf("Exception (arith_sum_of_squares). n is too large.\n");
abort();
}
}
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