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/* fft/c_pass_5.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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 int
FUNCTION(fft_complex,pass_5) (const BASE in[],
const size_t istride,
BASE out[],
const size_t ostride,
const gsl_fft_direction sign,
const size_t product,
const size_t n,
const TYPE(gsl_complex) twiddle1[],
const TYPE(gsl_complex) twiddle2[],
const TYPE(gsl_complex) twiddle3[],
const TYPE(gsl_complex) twiddle4[])
{
size_t i = 0, j = 0;
size_t k, k1;
const size_t factor = 5;
const size_t m = n / factor;
const size_t q = n / product;
const size_t p_1 = product / factor;
const size_t jump = (factor - 1) * p_1;
const ATOMIC sin_2pi_by_5 = sin (2.0 * M_PI / 5.0);
const ATOMIC sin_2pi_by_10 = sin (2.0 * M_PI / 10.0);
for (k = 0; k < q; k++)
{
ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real,
w4_imag;
if (k == 0)
{
w1_real = 1.0;
w1_imag = 0.0;
w2_real = 1.0;
w2_imag = 0.0;
w3_real = 1.0;
w3_imag = 0.0;
w4_real = 1.0;
w4_imag = 0.0;
}
else
{
if (sign == gsl_fft_forward)
{
/* forward tranform */
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]);
w4_real = GSL_REAL(twiddle4[k - 1]);
w4_imag = GSL_IMAG(twiddle4[k - 1]);
}
else
{
/* backward tranform: w -> conjugate(w) */
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]);
w4_real = GSL_REAL(twiddle4[k - 1]);
w4_imag = -GSL_IMAG(twiddle4[k - 1]);
}
}
for (k1 = 0; k1 < p_1; k1++)
{
ATOMIC x0_real, x0_imag, x1_real, x1_imag, x2_real, x2_imag,
x3_real, x3_imag, x4_real, x4_imag;
const ATOMIC z0_real = REAL(in,istride,i);
const ATOMIC z0_imag = IMAG(in,istride,i);
const ATOMIC z1_real = REAL(in,istride,i + m);
const ATOMIC z1_imag = IMAG(in,istride,i + m);
const ATOMIC z2_real = REAL(in,istride,i + 2*m);
const ATOMIC z2_imag = IMAG(in,istride,i + 2*m);
const ATOMIC z3_real = REAL(in,istride,i + 3*m);
const ATOMIC z3_imag = IMAG(in,istride,i + 3*m);
const ATOMIC z4_real = REAL(in,istride,i + 4*m);
const ATOMIC z4_imag = IMAG(in,istride,i + 4*m);
/* compute x = W(5) z */
/* t1 = z1 + z4 */
const ATOMIC t1_real = z1_real + z4_real;
const ATOMIC t1_imag = z1_imag + z4_imag;
/* t2 = z2 + z3 */
const ATOMIC t2_real = z2_real + z3_real;
const ATOMIC t2_imag = z2_imag + z3_imag;
/* t3 = z1 - z4 */
const ATOMIC t3_real = z1_real - z4_real;
const ATOMIC t3_imag = z1_imag - z4_imag;
/* t4 = z2 - z3 */
const ATOMIC t4_real = z2_real - z3_real;
const ATOMIC t4_imag = z2_imag - z3_imag;
/* t5 = t1 + t2 */
const ATOMIC t5_real = t1_real + t2_real;
const ATOMIC t5_imag = t1_imag + t2_imag;
/* t6 = (sqrt(5)/4)(t1 - t2) */
const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real);
const ATOMIC t6_imag = (sqrt (5.0) / 4.0) * (t1_imag - t2_imag);
/* t7 = z0 - ((t5)/4) */
const ATOMIC t7_real = z0_real - t5_real / 4.0;
const ATOMIC t7_imag = z0_imag - t5_imag / 4.0;
/* t8 = t7 + t6 */
const ATOMIC t8_real = t7_real + t6_real;
const ATOMIC t8_imag = t7_imag + t6_imag;
/* t9 = t7 - t6 */
const ATOMIC t9_real = t7_real - t6_real;
const ATOMIC t9_imag = t7_imag - t6_imag;
/* t10 = sin(2 pi/5) t3 + sin(2 pi/10) t4 */
const ATOMIC t10_real = ((int) sign) * (sin_2pi_by_5 * t3_real +
sin_2pi_by_10 * t4_real);
const ATOMIC t10_imag = ((int) sign) * (sin_2pi_by_5 * t3_imag +
sin_2pi_by_10 * t4_imag);
/* t11 = sin(2 pi/10) t3 - sin(2 pi/5) t4 */
const ATOMIC t11_real = ((int) sign) * (sin_2pi_by_10 * t3_real -
sin_2pi_by_5 * t4_real);
const ATOMIC t11_imag = ((int) sign) * (sin_2pi_by_10 * t3_imag -
sin_2pi_by_5 * t4_imag);
/* x0 = z0 + t5 */
x0_real = z0_real + t5_real;
x0_imag = z0_imag + t5_imag;
/* x1 = t8 + i t10 */
x1_real = t8_real - t10_imag;
x1_imag = t8_imag + t10_real;
/* x2 = t9 + i t11 */
x2_real = t9_real - t11_imag;
x2_imag = t9_imag + t11_real;
/* x3 = t9 - i t11 */
x3_real = t9_real + t11_imag;
x3_imag = t9_imag - t11_real;
/* x4 = t8 - i t10 */
x4_real = t8_real + t10_imag;
x4_imag = t8_imag - t10_real;
/* apply twiddle factors */
/* to0 = 1 * x0 */
REAL(out,ostride,j) = x0_real;
IMAG(out,ostride,j) = x0_imag;
/* to1 = w1 * x1 */
REAL(out,ostride,j + p_1) = w1_real * x1_real - w1_imag * x1_imag;
IMAG(out,ostride,j + p_1) = w1_real * x1_imag + w1_imag * x1_real;
/* to2 = w2 * x2 */
REAL(out,ostride,j + 2*p_1) = w2_real * x2_real - w2_imag * x2_imag;
IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real;
/* to3 = w3 * x3 */
REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag;
IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real;
/* to4 = w4 * x4 */
REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag;
IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real;
i++;
j++;
}
j += jump;
}
return 0;
}
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