/* 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;

}