/*
-----------------------------------------------------------------------
Copyright: 2010-2016, iMinds-Vision Lab, University of Antwerp
           2014-2016, CWI, Amsterdam

Contact: astra@uantwerpen.be
Website: http://www.astra-toolbox.com/

This file is part of the ASTRA Toolbox.


The ASTRA Toolbox 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.

The ASTRA Toolbox 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 the ASTRA Toolbox. If not, see <http://www.gnu.org/licenses/>.

-----------------------------------------------------------------------
*/

#ifndef _INC_ASTRA_FOURIER
#define _INC_ASTRA_FOURIER

#include "Globals.h"

namespace astra {

/*
-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
        <case2>
            X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            ip[0] = 0; // first time only
            cdft(2*n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            cdft(2*n, -1, a, ip, w);
    [parameters]
        2*n            :data length (int)
                        n >= 1, n = power of 2
        a[0...2*n-1]   :input/output data (float32 *)
                        input data
                            a[2*j] = Re(x[j]), 
                            a[2*j+1] = Im(x[j]), 0<=j<n
                        output data
                            a[2*k] = Re(X[k]), 
                            a[2*k+1] = Im(X[k]), 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (float32 *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            cdft(2*n, -1, a, ip, w);
        is 
            cdft(2*n, 1, a, ip, w);
            for (j = 0; j <= 2 * n - 1; j++) {
                a[j] *= 1.0 / n;
            }
        .
*/
_AstraExport void cdft(int n, int isgn, float32 *a, int *ip, float32 *w);

}

#endif