/* fft/hc_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_halfcomplex,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 < product_1; k1++)
{
/* compute z = W(factor) x, for x halfcomplex */
ATOMIC dw_real = 1.0, dw_imag = 0.0;
for (e1 = 0; e1 < factor; e1++)
{
ATOMIC sum_real = 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; e2++)
{
ATOMIC z_real, z_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;
}
if (e2 == 0)
{
size_t from_idx = factor * k1 * q;
z_real = VECTOR(in,istride,from_idx);
z_imag = 0.0;
sum_real += w_real * z_real - w_imag * z_imag;
}
else if (e2 == factor - e2)
{
size_t from_idx = factor * q * k1 + 2 * e2 * q - 1;
z_real = VECTOR(in,istride,from_idx);
z_imag = 0.0;
sum_real += w_real * z_real;
}
else
{
size_t from_idx = factor * q * k1 + 2 * e2 * q - 1;
z_real = VECTOR(in,istride,from_idx);
z_imag = VECTOR(in,istride,from_idx + 1);
sum_real += 2 * (w_real * z_real - w_imag * z_imag);
}
}
{
const size_t to_idx = q * k1 + e1 * m;
VECTOR(out,ostride,to_idx) = sum_real;
}
}
}
if (q == 1)
return;
for (k = 1; k < (q + 1) / 2; k++)
{
for (k1 = 0; k1 < product_1; 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;
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 = 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;
}
if (e2 < factor - e2)
{
const size_t from0 = factor * k1 * q + 2 * k + 2 * e2 * q - 1;
z_real = VECTOR(in,istride,from0);
z_imag = VECTOR(in,istride,from0 + 1);
}
else
{
const size_t from0 = factor * k1 * q - 2 * k + 2 * (factor - e2) * q - 1;
z_real = VECTOR(in,istride,from0);
z_imag = -VECTOR(in,istride,from0 + 1);
}
sum_real += w_real * z_real - w_imag * z_imag;
sum_imag += w_real * z_imag + w_imag * z_real;
}
if (k == 0 || e1 == 0)
{
w_real = 1.0;
w_imag = 0.0;
}
else
{
size_t tskip = (q + 1) / 2 - 1;
w_real = GSL_REAL(twiddle[k - 1 + tskip * (e1 - 1)]);
w_imag = GSL_IMAG(twiddle[k - 1 + tskip * (e1 - 1)]);
}
{
const size_t to0 = k1 * q + 2 * k + e1 * m - 1;
VECTOR(out,ostride,to0) = w_real * sum_real - w_imag * sum_imag;
VECTOR(out,ostride,to0 + 1) = w_real * sum_imag + w_imag * sum_real;
}
}
}
}
if (q % 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 < product_1; k1++)
{
ATOMIC dw_real = 1.0, dw_imag = 0.0;
ATOMIC tw_real = 1.0, tw_imag = 0.0;
for (e1 = 0; e1 < factor; e1++)
{
ATOMIC w_real, w_imag, z_real, z_imag;
ATOMIC sum_real = 0.0;
if (e1 > 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;
}
w_real = tw_real;
w_imag = tw_imag;
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 - 1; e2++)
{
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;
}
if (e2 == factor - e2 - 1)
{
const size_t from0 = factor * k1 * q + q + 2 * e2 * q - 1;
z_real = VECTOR(in,istride,from0);
z_imag = 0.0;
sum_real += w_real * z_real - w_imag * z_imag;
}
else
{
const size_t from0 = factor * k1 * q + q + 2 * e2 * q - 1;
z_real = VECTOR(in,istride,from0);
z_imag = VECTOR(in,istride,from0 + 1);
sum_real += 2 * (w_real * z_real - w_imag * z_imag);
}
}
{
const size_t to0 = k1 * q + q + e1 * m - 1;
VECTOR(out,ostride,to0) = sum_real;
}
}
}
}
return;
}