/* fft/real_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_real,radix2_transform) (BASE data[], const size_t stride,  const size_t n)

{

  int result ;

  size_t p, p_1, q;

  size_t i; 

  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_real,bitreverse_order)(data, stride, n, logn) ;

  /* apply fft recursion */

  p = 1; q = n ;

  for (i = 1; i <= logn; i++)

    {

      size_t a, b;

      p_1 = p ;

      p = 2 * p ;

      q = q / 2 ;

      /* a = 0 */

      for (b = 0; b < q; b++)

        {

          ATOMIC t0_real = VECTOR(data,stride,b*p) + VECTOR(data,stride,b*p + p_1) ;

          ATOMIC t1_real = VECTOR(data,stride,b*p) - VECTOR(data,stride,b*p + p_1) ;

          VECTOR(data,stride,b*p) = t0_real ;

          VECTOR(data,stride,b*p + p_1) = t1_real ;

        }

      /* a = 1 ... p_{i-1}/2 - 1 */

      {

        ATOMIC w_real = 1.0;

        ATOMIC w_imag = 0.0;

        const double theta = - 2.0 * M_PI / p;

        const ATOMIC s = sin (theta);

        const ATOMIC t = sin (theta / 2.0);

        const ATOMIC s2 = 2.0 * t * t;

        for (a = 1; a < (p_1)/2; 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 < q; b++)

              {

                ATOMIC z0_real = VECTOR(data,stride,b*p + a) ;

                ATOMIC z0_imag = VECTOR(data,stride,b*p + p_1 - a) ;

                ATOMIC z1_real = VECTOR(data,stride,b*p + p_1 + a) ;

                ATOMIC z1_imag = VECTOR(data,stride,b*p + p - a) ;

                /* t0 = z0 + w * z1 */

                ATOMIC t0_real = z0_real + w_real * z1_real - w_imag * z1_imag;

                ATOMIC t0_imag = z0_imag + w_real * z1_imag + w_imag * z1_real;

                /* t1 = z0 - w * z1 */

                ATOMIC t1_real = z0_real - w_real * z1_real + w_imag * z1_imag;

                ATOMIC t1_imag = z0_imag - w_real * z1_imag - w_imag * z1_real;

                VECTOR(data,stride,b*p + a) = t0_real ;

                VECTOR(data,stride,b*p + p - a) = t0_imag ;

                VECTOR(data,stride,b*p + p_1 - a) = t1_real ;

                VECTOR(data,stride,b*p + p_1 + a) = -t1_imag ;

              }

          }

      }

      if (p_1 >  1) 

        {

          for (b = 0; b < q; b++) 

            {

              /* a = p_{i-1}/2 */

              VECTOR(data,stride,b*p + p - p_1/2) *= -1 ;

            }

        }

    }

  return 0;

}