/* fft/c_radix2.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.
*/
int
FUNCTION(gsl_fft_complex,radix2_forward) (TYPE(gsl_complex_packed_array) data,
const size_t stride, const size_t n)
{
gsl_fft_direction sign = gsl_fft_forward;
int status = FUNCTION(gsl_fft_complex,radix2_transform) (data, stride, n, sign);
return status;
}
int
FUNCTION(gsl_fft_complex,radix2_backward) (TYPE(gsl_complex_packed_array) data,
const size_t stride, const size_t n)
{
gsl_fft_direction sign = gsl_fft_backward;
int status = FUNCTION(gsl_fft_complex,radix2_transform) (data, stride, n, sign);
return status;
}
int
FUNCTION(gsl_fft_complex,radix2_inverse) (TYPE(gsl_complex_packed_array) data,
const size_t stride, const size_t n)
{
gsl_fft_direction sign = gsl_fft_backward;
int status = FUNCTION(gsl_fft_complex,radix2_transform) (data, stride, n, sign);
if (status)
{
return status;
}
/* normalize inverse fft with 1/n */
{
const ATOMIC norm = 1.0 / n;
size_t i;
for (i = 0; i < n; i++)
{
REAL(data,stride,i) *= norm;
IMAG(data,stride,i) *= norm;
}
}
return status;
}
int
FUNCTION(gsl_fft_complex,radix2_transform) (TYPE(gsl_complex_packed_array) data,
const size_t stride,
const size_t n,
const gsl_fft_direction sign)
{
int result ;
size_t dual;
size_t bit;
size_t logn = 0;
int status;
if (n == 1) /* identity operation */
{
return 0 ;
}
/* make sure that n is a power of 2 */
result = fft_binary_logn(n) ;
if (result == -1)
{
GSL_ERROR ("n is not a power of 2", GSL_EINVAL);
}
else
{
logn = result ;
}
/* bit reverse the ordering of input data for decimation in time algorithm */
status = FUNCTION(fft_complex,bitreverse_order) (data, stride, n, logn) ;
/* apply fft recursion */
dual = 1;
for (bit = 0; bit < logn; bit++)
{
ATOMIC w_real = 1.0;
ATOMIC w_imag = 0.0;
const double theta = 2.0 * ((int) sign) * M_PI / (2.0 * (double) dual);
const ATOMIC s = sin (theta);
const ATOMIC t = sin (theta / 2.0);
const ATOMIC s2 = 2.0 * t * t;
size_t a, b;
/* a = 0 */
for (b = 0; b < n; b += 2 * dual)
{
const size_t i = b ;
const size_t j = b + dual;
const ATOMIC z1_real = REAL(data,stride,j) ;
const ATOMIC z1_imag = IMAG(data,stride,j) ;
const ATOMIC wd_real = z1_real ;
const ATOMIC wd_imag = z1_imag ;
REAL(data,stride,j) = REAL(data,stride,i) - wd_real;
IMAG(data,stride,j) = IMAG(data,stride,i) - wd_imag;
REAL(data,stride,i) += wd_real;
IMAG(data,stride,i) += wd_imag;
}
/* a = 1 .. (dual-1) */
for (a = 1; a < dual; a++)
{
/* trignometric recurrence for w-> exp(i theta) w */
{
const ATOMIC tmp_real = w_real - s * w_imag - s2 * w_real;
const ATOMIC tmp_imag = w_imag + s * w_real - s2 * w_imag;
w_real = tmp_real;
w_imag = tmp_imag;
}
for (b = 0; b < n; b += 2 * dual)
{
const size_t i = b + a;
const size_t j = b + a + dual;
const ATOMIC z1_real = REAL(data,stride,j) ;
const ATOMIC z1_imag = IMAG(data,stride,j) ;
const ATOMIC wd_real = w_real * z1_real - w_imag * z1_imag;
const ATOMIC wd_imag = w_real * z1_imag + w_imag * z1_real;
REAL(data,stride,j) = REAL(data,stride,i) - wd_real;
IMAG(data,stride,j) = IMAG(data,stride,i) - wd_imag;
REAL(data,stride,i) += wd_real;
IMAG(data,stride,i) += wd_imag;
}
}
dual *= 2;
}
return 0;
}
int
FUNCTION(gsl_fft_complex,radix2_dif_forward) (TYPE(gsl_complex_packed_array) data,
const size_t stride,
const size_t n)
{
gsl_fft_direction sign = gsl_fft_forward;
int status = FUNCTION(gsl_fft_complex,radix2_dif_transform) (data, stride, n, sign);
return status;
}
int
FUNCTION(gsl_fft_complex,radix2_dif_backward) (TYPE(gsl_complex_packed_array) data,
const size_t stride,
const size_t n)
{
gsl_fft_direction sign = gsl_fft_backward;
int status = FUNCTION(gsl_fft_complex,radix2_dif_transform) (data, stride, n, sign);
return status;
}
int
FUNCTION(gsl_fft_complex,radix2_dif_inverse) (TYPE(gsl_complex_packed_array) data,
const size_t stride,
const size_t n)
{
gsl_fft_direction sign = gsl_fft_backward;
int status = FUNCTION(gsl_fft_complex,radix2_dif_transform) (data, stride, n, sign);
if (status)
{
return status;
}
/* normalize inverse fft with 1/n */
{
const ATOMIC norm = 1.0 / n;
size_t i;
for (i = 0; i < n; i++)
{
REAL(data,stride,i) *= norm;
IMAG(data,stride,i) *= norm;
}
}
return status;
}
int
FUNCTION(gsl_fft_complex,radix2_dif_transform) (TYPE(gsl_complex_packed_array) data,
const size_t stride,
const size_t n,
const gsl_fft_direction sign)
{
int result ;
size_t dual;
size_t bit;
size_t logn = 0;
int status;
if (n == 1) /* identity operation */
{
return 0 ;
}
/* make sure that n is a power of 2 */
result = fft_binary_logn(n) ;
if (result == -1)
{
GSL_ERROR ("n is not a power of 2", GSL_EINVAL);
}
else
{
logn = result ;
}
/* apply fft recursion */
dual = n / 2;
for (bit = 0; bit < logn; bit++)
{
ATOMIC w_real = 1.0;
ATOMIC w_imag = 0.0;
const double theta = 2.0 * ((int) sign) * M_PI / ((double) (2 * dual));
const ATOMIC s = sin (theta);
const ATOMIC t = sin (theta / 2.0);
const ATOMIC s2 = 2.0 * t * t;
size_t a, b;
for (b = 0; b < dual; b++)
{
for (a = 0; a < n; a+= 2 * dual)
{
const size_t i = b + a;
const size_t j = b + a + dual;
const ATOMIC t1_real = REAL(data,stride,i) + REAL(data,stride,j);
const ATOMIC t1_imag = IMAG(data,stride,i) + IMAG(data,stride,j);
const ATOMIC t2_real = REAL(data,stride,i) - REAL(data,stride,j);
const ATOMIC t2_imag = IMAG(data,stride,i) - IMAG(data,stride,j);
REAL(data,stride,i) = t1_real;
IMAG(data,stride,i) = t1_imag;
REAL(data,stride,j) = w_real*t2_real - w_imag * t2_imag;
IMAG(data,stride,j) = w_real*t2_imag + w_imag * t2_real;
}
/* trignometric recurrence for w-> exp(i theta) w */
{
const ATOMIC tmp_real = w_real - s * w_imag - s2 * w_real;
const ATOMIC tmp_imag = w_imag + s * w_real - s2 * w_imag;
w_real = tmp_real;
w_imag = tmp_imag;
}
}
dual /= 2;
}
/* bit reverse the ordering of output data for decimation in
frequency algorithm */
status = FUNCTION(fft_complex,bitreverse_order)(data, stride, n, logn) ;
return 0;
}