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- /* fft/real_pass_3.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_3) (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[])
- {
- size_t k, k1;
- const size_t factor = 3;
- const size_t m = n / factor;
- const size_t q = n / product;
- const size_t product_1 = product / factor;
- const ATOMIC tau = sqrt (3.0) / 2.0;
- 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 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 t1 = z1_real + z2_real;
- const ATOMIC x0_real = z0_real + t1;
- const ATOMIC x1_real = z0_real - t1 / 2.0;
- const ATOMIC x1_imag = -tau * (z1_real - z2_real);
- const size_t to0 = product * k1;
- const size_t to1 = to0 + 2 * product_1 - 1;
- VECTOR(out,ostride,to0) = x0_real;
- VECTOR(out,ostride,to1) = x1_real;
- VECTOR(out,ostride,to1 + 1) = x1_imag;
- }
- if (product_1 == 1)
- return;
- for (k = 1; k < (product_1 + 1) / 2; k++)
- {
- const ATOMIC w1_real = GSL_REAL(twiddle1[k - 1]);
- const ATOMIC w1_imag = -GSL_IMAG(twiddle1[k - 1]);
- const ATOMIC w2_real = GSL_REAL(twiddle2[k - 1]);
- const ATOMIC w2_imag = -GSL_IMAG(twiddle2[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 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 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;
- /* compute x = W(3) z */
- /* t1 = z1 + z2 */
- const ATOMIC t1_real = z1_real + z2_real;
- const ATOMIC t1_imag = z1_imag + z2_imag;
-
- /* t2 = z0 - t1/2 */
- const ATOMIC t2_real = z0_real - t1_real / 2;
- const ATOMIC t2_imag = z0_imag - t1_imag / 2;
-
- /* t3 = (+/-) sin(pi/3)*(z1 - z2) */
- const ATOMIC t3_real = -tau * (z1_real - z2_real);
- const ATOMIC t3_imag = -tau * (z1_imag - z2_imag);
-
- /* x0 = z0 + t1 */
- const ATOMIC x0_real = z0_real + t1_real;
- const ATOMIC x0_imag = z0_imag + t1_imag;
-
- /* x1 = t2 + i t3 */
- const ATOMIC x1_real = t2_real - t3_imag;
- const ATOMIC x1_imag = t2_imag + t3_real;
- /* x2 = t2 - i t3 */
- const ATOMIC x2_real = t2_real + t3_imag;
- const ATOMIC x2_imag = t2_imag - t3_real;
- /* apply twiddle factors */
-
- 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;
-
- /* to0 = 1 * x0 */
- VECTOR(out,ostride,to0) = x0_real;
- VECTOR(out,ostride,to0 + 1) = x0_imag;
-
- /* to1 = 1 * x1 */
- VECTOR(out,ostride,to1) = x1_real;
- VECTOR(out,ostride,to1 + 1) = x1_imag;
-
- /* to2 = 1 * x2 */
- VECTOR(out,ostride,to2) = x2_real;
- VECTOR(out,ostride,to2 + 1) = -x2_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 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 t1 = z1_real - z2_real;
- const ATOMIC x0_real = z0_real + t1 / 2.0;
- const ATOMIC x0_imag = -tau * (z1_real + z2_real);
- const ATOMIC x1_real = z0_real - t1;
- const size_t to0 = k1 * product + product_1 - 1;
- const size_t to1 = to0 + 2 * product_1;
-
- VECTOR(out,ostride,to0) = x0_real;
- VECTOR(out,ostride,to0 + 1) = x0_imag;
- VECTOR(out,ostride,to1) = x1_real;
- }
- return;
- }
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