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+/* --------------------------------------------------------------  */
+/* (C)Copyright 2008 Free Software Foundation, Inc.                */
+/* (C)Copyright 2001,2007,                                         */
+/* International Business Machines Corporation,                    */
+/* Sony Computer Entertainment, Incorporated,                      */
+/* Toshiba Corporation,                                            */
+/*                                                                 */
+/* All Rights Reserved.                                            */
+/*                                                                 */
+/* Redistribution and use in source and binary forms, with or      */
+/* without modification, are permitted provided that the           */
+/* following conditions are met:                                   */
+/*                                                                 */
+/* - Redistributions of source code must retain the above copyright*/
+/*   notice, this list of conditions and the following disclaimer. */
+/*                                                                 */
+/* - Redistributions in binary form must reproduce the above       */
+/*   copyright notice, this list of conditions and the following   */
+/*   disclaimer in the documentation and/or other materials        */
+/*   provided with the distribution.                               */
+/*                                                                 */
+/* - Neither the name of IBM Corporation nor the names of its      */
+/*   contributors may be used to endorse or promote products       */
+/*   derived from this software without specific prior written     */
+/*   permission.                                                   */
+/*                                                                 */
+/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND          */
+/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,     */
+/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF        */
+/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE        */
+/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR            */
+/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,    */
+/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT    */
+/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;    */
+/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)        */
+/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN       */
+/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR    */
+/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,  */
+/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              */
+/* --------------------------------------------------------------  */
+/* PROLOG END TAG zYx                                              */
+
+#ifndef INCLUDED_LIBFFT_H
+#define INCLUDED_LIBFFT_H
+
+// must be defined before inclusion of fft_1d_r2.h
+#define MAX_FFT_1D_SIZE 4096
+
+/* fft_1d_r2
+ * ---------
+ * Performs a single precision, complex Fast Fourier Transform using 
+ * the DFT (Discrete Fourier Transform) with radix-2 decimation in time. 
+ * The input <in> is an array of complex numbers of length (1<<log2_size)
+ * entries. The result is returned in the array of complex numbers specified
+ * by <out>. Note: This routine can support an in-place transformation
+ * by specifying <in> and <out> to be the same array.
+ *
+ * This implementation utilizes the Cooley-Tukey algorithm consisting 
+ * of <log2_size> stages. The basic operation is the butterfly.
+ *
+ *          p --------------------------> P = p + q*Wi
+ *                        \      /
+ *                         \    /
+ *                          \  /
+ *                           \/
+ *                           /\
+ *                          /  \
+ *                         /    \
+ *               ____     /      \
+ *          q --| Wi |-----------------> Q = p - q*Wi
+ *               ----
+ *
+ * This routine also requires pre-computed twiddle values, W. W is an
+ * array of single precision complex numbers of length 1<<(log2_size-2) 
+ * and is computed as follows:
+ *
+ *     for (i=0; i<n/4; i++)
+ *         W[i].real =  cos(i * 2*PI/n);
+ *         W[i].imag = -sin(i * 2*PI/n);
+ *      }
+ *
+ * This array actually only contains the first half of the twiddle
+ * factors. Due for symmetry, the second half of the twiddle factors
+ * are implied and equal:
+ *
+ *     for (i=0; i<n/4; i++)
+ *         W[i+n/4].real =  W[i].imag =  sin(i * 2*PI/n);
+ *         W[i+n/4].imag = -W[i].real = -cos(i * 2*PI/n);
+ *      }
+ *
+ * Further symmetry allows one to generate the twiddle factor table 
+ * using half the number of trig computations as follows:
+ *
+ *      W[0].real = 1.0;
+ *      W[0].imag = 0.0;
+ *     for (i=1; i<n/4; i++)
+ *         W[i].real =  cos(i * 2*PI/n);
+ *         W[n/4 - i].imag = -W[i].real;
+ *      }
+ *
+ * The complex numbers are packed into quadwords as follows:
+ *
+ *    quadword                       complex
+ *  array element                   array elements
+ *             -----------------------------------------------------
+ *       i    |  real 2*i   |  imag 2*i  | real 2*i+1  | imag 2*i+1 | 
+ *             -----------------------------------------------------
+ *
+ */
+
+void fft_1d_r2(vector float *out, vector float *in, vector float *W, int log2_size);
+
+#endif /* INCLUDED_LIBFFT_H */