/* fft/real_pass_n.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
*
* This program 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 3 of the License, or (at
* your option) any later version.
*
* This program 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 this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
static void
FUNCTION(fft_real,pass_n) (const BASE in[],
const size_t istride,
BASE out[],
const size_t ostride,
const size_t factor,
const size_t product,
const size_t n,
const TYPE(gsl_complex) twiddle[])
{
size_t k, k1;
const size_t m = n / factor;
const size_t q = n / product;
const size_t product_1 = product / factor;
size_t e1, e2;
const double d_theta = 2.0 * M_PI / ((double) factor);
const ATOMIC cos_d_theta = cos (d_theta);
const ATOMIC sin_d_theta = sin (d_theta);
for (k1 = 0; k1 < q; k1++)
{
/* compute x = W(factor) z, for z real */
ATOMIC dw_real = 1.0, dw_imag = 0.0;
for (e1 = 0; e1 <= factor - e1; e1++)
{
ATOMIC sum_real = 0.0;
ATOMIC sum_imag = 0.0;
ATOMIC w_real = 1.0, w_imag = 0.0;
if (e1 > 0)
{
ATOMIC tmp_real = dw_real * cos_d_theta + dw_imag * sin_d_theta;
ATOMIC tmp_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta;
dw_real = tmp_real;
dw_imag = tmp_imag;
}
for (e2 = 0; e2 < factor; e2++)
{
ATOMIC z_real = VECTOR(in,istride,k1 * product_1 + e2 * m);
if (e2 > 0)
{
ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;
ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;
w_real = tmp_real;
w_imag = tmp_imag;
}
sum_real += w_real * z_real;
sum_imag += w_imag * z_real;
}
if (e1 == 0)
{
const size_t to0 = product * k1;
VECTOR(out,ostride,to0) = sum_real;
}
else if (e1 < factor - e1)
{
const size_t to0 = k1 * product + 2 * e1 * product_1 - 1;
VECTOR(out,ostride,to0) = sum_real;
VECTOR(out,ostride,to0 + 1) = sum_imag;
}
else if (e1 == factor - e1)
{
const size_t to0 = k1 * product + 2 * e1 * product_1 - 1;
VECTOR(out,ostride,to0) = sum_real;
}
}
}
if (product_1 == 1)
return;
for (k = 1; k < (product_1 + 1) / 2; k++)
{
for (k1 = 0; k1 < q; k1++)
{
ATOMIC dw_real = 1.0, dw_imag = 0.0;
for (e1 = 0; e1 < factor; e1++)
{
ATOMIC sum_real = 0.0, sum_imag = 0.0;
ATOMIC w_real = 1.0, w_imag = 0.0;
if (e1 > 0)
{
const ATOMIC tmp_real = dw_real * cos_d_theta + dw_imag * sin_d_theta;
const ATOMIC tmp_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta;
dw_real = tmp_real;
dw_imag = tmp_imag;
}
for (e2 = 0; e2 < factor; e2++)
{
int tskip = (product_1 + 1) / 2 - 1;
const size_t from0 = k1 * product_1 + 2 * k + e2 * m - 1;
ATOMIC tw_real, tw_imag;
ATOMIC z_real, z_imag;
if (e2 == 0)
{
tw_real = 1.0;
tw_imag = 0.0;
}
else
{
const size_t t_index = (k - 1) + (e2 - 1) * tskip;
tw_real = GSL_REAL(twiddle[t_index]);
tw_imag = -GSL_IMAG(twiddle[t_index]);
}
{
const ATOMIC f0_real = VECTOR(in,istride,from0);
const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1);
z_real = tw_real * f0_real - tw_imag * f0_imag;
z_imag = tw_real * f0_imag + tw_imag * f0_real;
}
if (e2 > 0)
{
const ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;
const ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;
w_real = tmp_real;
w_imag = tmp_imag;
}
sum_real += w_real * z_real - w_imag * z_imag;
sum_imag += w_real * z_imag + w_imag * z_real;
}
if (e1 < factor - e1)
{
const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k;
VECTOR(out,ostride,to0) = sum_real;
VECTOR(out,ostride,to0 + 1) = sum_imag;
}
else
{
const size_t to0 = k1 * product - 1 + 2 * (factor - e1) * product_1 - 2 * k;
VECTOR(out,ostride,to0) = sum_real;
VECTOR(out,ostride,to0 + 1) = -sum_imag;
}
}
}
}
if (product_1 % 2 == 1)
return;
{
double tw_arg = M_PI / ((double) factor);
ATOMIC cos_tw_arg = cos (tw_arg);
ATOMIC sin_tw_arg = -sin (tw_arg);
for (k1 = 0; k1 < q; k1++)
{
ATOMIC dw_real = 1.0, dw_imag = 0.0;
for (e1 = 0; e1 < factor; e1++)
{
ATOMIC z_real, z_imag;
ATOMIC sum_real = 0.0;
ATOMIC sum_imag = 0.0;
ATOMIC w_real = 1.0, w_imag = 0.0;
ATOMIC tw_real = 1.0, tw_imag = 0.0;
if (e1 > 0)
{
ATOMIC t_real = dw_real * cos_d_theta + dw_imag * sin_d_theta;
ATOMIC t_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta;
dw_real = t_real;
dw_imag = t_imag;
}
for (e2 = 0; e2 < factor; e2++)
{
if (e2 > 0)
{
ATOMIC tmp_real = tw_real * cos_tw_arg - tw_imag * sin_tw_arg;
ATOMIC tmp_imag = tw_real * sin_tw_arg + tw_imag * cos_tw_arg;
tw_real = tmp_real;
tw_imag = tmp_imag;
}
if (e2 > 0)
{
ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;
ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;
w_real = tmp_real;
w_imag = tmp_imag;
}
{
const size_t from0 = k1 * product_1 + 2 * k + e2 * m - 1;
const ATOMIC f0_real = VECTOR(in,istride,from0);
z_real = tw_real * f0_real;
z_imag = tw_imag * f0_real;
}
sum_real += w_real * z_real - w_imag * z_imag;
sum_imag += w_real * z_imag + w_imag * z_real;
}
if (e1 + 1 < factor - e1)
{
const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k;
VECTOR(out,ostride,to0) = sum_real;
VECTOR(out,ostride,to0 + 1) = sum_imag;
}
else if (e1 + 1 == factor - e1)
{
const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k;
VECTOR(out,ostride,to0) = sum_real;
}
else
{
const size_t to0 = k1 * product - 1 + 2 * (factor - e1) * product_1 - 2 * k;
VECTOR(out,ostride,to0) = sum_real;
VECTOR(out,ostride,to0 + 1) = -sum_imag;
}
}
}
}
return;
}