/* fft/real_pass_4.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_4) (const BASE in[],
const size_t istride,
BASE out[],
const size_t ostride,
const size_t product,
const size_t n,
const TYPE(gsl_complex) twiddle1[],
const TYPE(gsl_complex) twiddle2[],
const TYPE(gsl_complex) twiddle3[])
{
size_t k, k1;
const size_t factor = 4;
const size_t m = n / factor;
const size_t q = n / product;
const size_t product_1 = product / factor;
for (k1 = 0; k1 < q; k1++)
{
const size_t from0 = k1 * product_1;
const size_t from1 = from0 + m;
const size_t from2 = from1 + m;
const size_t from3 = from2 + m;
const ATOMIC z0_real = VECTOR(in,istride,from0);
const ATOMIC z1_real = VECTOR(in,istride,from1);
const ATOMIC z2_real = VECTOR(in,istride,from2);
const ATOMIC z3_real = VECTOR(in,istride,from3);
/* compute x = W(4) z */
/* t1 = z0 + z2 */
const ATOMIC t1_real = z0_real + z2_real;
/* t2 = z1 + z3 */
const ATOMIC t2_real = z1_real + z3_real;
/* t3 = z0 - z2 */
const ATOMIC t3_real = z0_real - z2_real;
/* t4 = - (z1 - z3) */
const ATOMIC t4_real = -(z1_real - z3_real);
/* x0 = t1 + t2 */
const ATOMIC x0_real = t1_real + t2_real;
/* x1 = t3 + i t4 */
const ATOMIC x1_real = t3_real;
const ATOMIC x1_imag = t4_real;
/* x2 = t1 - t2 */
const ATOMIC x2_real = t1_real - t2_real;
const size_t to0 = product * k1;
const size_t to1 = to0 + 2 * product_1 - 1;
const size_t to2 = to1 + 2 * product_1;
VECTOR(out,ostride,to0) = x0_real;
VECTOR(out,ostride,to1) = x1_real;
VECTOR(out,ostride,to1 + 1) = x1_imag;
VECTOR(out,ostride,to2) = x2_real;
}
if (product_1 == 1)
return;
for (k = 1; k < (product_1 + 1) / 2; k++)
{
ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag;
w1_real = GSL_REAL(twiddle1[k - 1]);
w1_imag = -GSL_IMAG(twiddle1[k - 1]);
w2_real = GSL_REAL(twiddle2[k - 1]);
w2_imag = -GSL_IMAG(twiddle2[k - 1]);
w3_real = GSL_REAL(twiddle3[k - 1]);
w3_imag = -GSL_IMAG(twiddle3[k - 1]);
for (k1 = 0; k1 < q; k1++)
{
const size_t from0 = k1 * product_1 + 2 * k - 1;
const size_t from1 = from0 + m;
const size_t from2 = from1 + m;
const size_t from3 = from2 + m;
const ATOMIC f0_real = VECTOR(in,istride,from0);
const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1);
const ATOMIC f1_real = VECTOR(in,istride,from1);
const ATOMIC f1_imag = VECTOR(in,istride,from1 + 1);
const ATOMIC f2_real = VECTOR(in,istride,from2);
const ATOMIC f2_imag = VECTOR(in,istride,from2 + 1);
const ATOMIC f3_real = VECTOR(in,istride,from3);
const ATOMIC f3_imag = VECTOR(in,istride,from3 + 1);
const ATOMIC z0_real = f0_real;
const ATOMIC z0_imag = f0_imag;
const ATOMIC z1_real = w1_real * f1_real - w1_imag * f1_imag;
const ATOMIC z1_imag = w1_real * f1_imag + w1_imag * f1_real;
const ATOMIC z2_real = w2_real * f2_real - w2_imag * f2_imag;
const ATOMIC z2_imag = w2_real * f2_imag + w2_imag * f2_real;
const ATOMIC z3_real = w3_real * f3_real - w3_imag * f3_imag;
const ATOMIC z3_imag = w3_real * f3_imag + w3_imag * f3_real;
/* compute x = W(4) z */
/* t1 = z0 + z2 */
const ATOMIC t1_real = z0_real + z2_real;
const ATOMIC t1_imag = z0_imag + z2_imag;
/* t2 = z1 + z3 */
const ATOMIC t2_real = z1_real + z3_real;
const ATOMIC t2_imag = z1_imag + z3_imag;
/* t3 = z0 - z2 */
const ATOMIC t3_real = z0_real - z2_real;
const ATOMIC t3_imag = z0_imag - z2_imag;
/* t4 = - (z1 - z3) */
const ATOMIC t4_real = -(z1_real - z3_real);
const ATOMIC t4_imag = -(z1_imag - z3_imag);
/* x0 = t1 + t2 */
const ATOMIC x0_real = t1_real + t2_real;
const ATOMIC x0_imag = t1_imag + t2_imag;
/* x1 = t3 + i t4 */
const ATOMIC x1_real = t3_real - t4_imag;
const ATOMIC x1_imag = t3_imag + t4_real;
/* x2 = t1 - t2 */
const ATOMIC x2_real = t1_real - t2_real;
const ATOMIC x2_imag = t1_imag - t2_imag;
/* x3 = t3 - i t4 */
const ATOMIC x3_real = t3_real + t4_imag;
const ATOMIC x3_imag = t3_imag - t4_real;
const size_t to0 = k1 * product + 2 * k - 1;
const size_t to1 = to0 + 2 * product_1;
const size_t to2 = 2 * product_1 - 2 * k + k1 * product - 1;
const size_t to3 = to2 + 2 * product_1;
VECTOR(out,ostride,to0) = x0_real;
VECTOR(out,ostride,to0 + 1) = x0_imag;
VECTOR(out,ostride,to1) = x1_real;
VECTOR(out,ostride,to1 + 1) = x1_imag;
VECTOR(out,ostride,to3) = x2_real;
VECTOR(out,ostride,to3 + 1) = -x2_imag;
VECTOR(out,ostride,to2) = x3_real;
VECTOR(out,ostride,to2 + 1) = -x3_imag;
}
}
if (product_1 % 2 == 1)
return;
for (k1 = 0; k1 < q; k1++)
{
const size_t from0 = k1 * product_1 + product_1 - 1;
const size_t from1 = from0 + m;
const size_t from2 = from1 + m;
const size_t from3 = from2 + m;
const ATOMIC x0 = VECTOR(in,istride,from0);
const ATOMIC x1 = VECTOR(in,istride,from1);
const ATOMIC x2 = VECTOR(in,istride,from2);
const ATOMIC x3 = VECTOR(in,istride,from3);
const ATOMIC t1 = (1.0 / sqrt (2.0)) * (x1 - x3);
const ATOMIC t2 = (1.0 / sqrt (2.0)) * (x1 + x3);
const size_t to0 = k1 * product + 2 * k - 1;
const size_t to1 = to0 + 2 * product_1;
VECTOR(out,ostride,to0) = x0 + t1;
VECTOR(out,ostride,to0 + 1) = -x2 - t2;
VECTOR(out,ostride,to1) = x0 - t1;
VECTOR(out,ostride,to1 + 1) = x2 - t2;
}
return;
}