543 lines
13 KiB
C++
543 lines
13 KiB
C++
/*************************************************************************/
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/* */
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/* Centre for Speech Technology Research */
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/* University of Edinburgh, UK */
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/* Copyright (c) 1994,1995,1996 */
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/* All Rights Reserved. */
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/* */
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/* Permission is hereby granted, free of charge, to use and distribute */
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/* this software and its documentation without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of this work, and to */
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/* permit persons to whom this work is furnished to do so, subject to */
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/* the following conditions: */
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/* 1. The code must retain the above copyright notice, this list of */
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/* conditions and the following disclaimer. */
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/* 2. Any modifications must be clearly marked as such. */
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/* 3. Original authors' names are not deleted. */
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/* 4. The authors' names are not used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THE UNIVERSITY OF EDINBURGH AND THE CONTRIBUTORS TO THIS WORK */
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/* DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING */
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/* ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT */
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/* SHALL THE UNIVERSITY OF EDINBURGH NOR THE CONTRIBUTORS BE LIABLE */
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/* FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES */
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/* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN */
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/* AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, */
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/* ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF */
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/* THIS SOFTWARE. */
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/* */
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/*************************************************************************/
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/* Author : Simon King (taken from Tony Robinson) */
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/* Date : July 1994 */
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/*-----------------------------------------------------------------------*/
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/* FFT functions */
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/* */
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/*=======================================================================*/
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#include <cmath>
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//#include <iostream>
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//#include <fstream>
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#include "sigpr/EST_fft.h"
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#include "EST_math.h"
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#include "EST_error.h"
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#define PI8 0.392699081698724 /* PI / 8.0 */
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#define RT2 1.4142135623731 /* sqrt(2.0) */
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#define IRT2 0.707106781186548 /* 1.0/sqrt(2.0) */
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static void FR2TR(int, float*, float*);
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static void FR4TR(int, int, float*, float*, float*, float*);
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static void FORD1(int, float*);
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static void FORD2(int, float*);
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/*
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** FAST(b,n)
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** This routine replaces the float vector b
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** of length n with its finite discrete fourier transform.
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** DC term is returned in b[0];
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** n/2th harmonic float part in b[1].
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** jth harmonic is returned as complex number stored as
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** b[2*j] + i b[2*j + 1]
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** (i.e., remaining coefficients are as a DPCOMPLEX vector).
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**
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*/
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static int slowFFTsub(EST_FVector &real, EST_FVector &imag, float f)
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{
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// f = -1 for FFT, 1 for IFFT
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// would be nicer if we used a complex number class,
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// but we don't, so it isn't
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// taken from the FORTRAN old chestnut
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// in various sig proc books
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// FORTRAN uses 1..n arrays, so subtract 1 all over the place
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float u_real,u_imag;
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float w_real,w_imag;
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float t_real,t_imag;
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float tmp_real,tmp_imag;
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int M,N;
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int i,j,k,l;
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M = fastlog2(real.n());
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N = (int)pow(float(2.0),(float)M);
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if (N != real.n())
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{
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EST_warning("Illegal FFT order %d", real.n());
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return -1;
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}
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for(l=1;l<=M;l++){
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int le = (int)pow(float(2.0),(float)(M+1-l));
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int le1=le/2;
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u_real = 1.0;
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u_imag = 0.0;
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w_real=cos(PI/le1);
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w_imag=f * sin(PI/le1);
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for (j=1;j<=le1;j++)
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{
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for (i=j;i<=N-le1;i+=le)
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{
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int ip=i+le1;
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t_real = real.a_no_check(i-1) + real.a_no_check(ip-1);
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t_imag = imag.a_no_check(i-1) + imag.a_no_check(ip-1);
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tmp_real = real.a_no_check(i-1) - real.a_no_check(ip-1);
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tmp_imag = imag.a_no_check(i-1) - imag.a_no_check(ip-1);
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real.a_no_check(ip-1) = tmp_real*u_real - tmp_imag*u_imag;
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imag.a_no_check(ip-1) = tmp_real*u_imag + tmp_imag*u_real;
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real.a_no_check(i-1) = t_real;
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imag.a_no_check(i-1) = t_imag;
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}
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tmp_real = u_real*w_real - u_imag*w_imag;
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tmp_imag = u_real*w_imag + u_imag*w_real;
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u_real=tmp_real;
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u_imag=tmp_imag;
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}
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}
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int NV2=N/2;
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int NM1=N-1;
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j=1;
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for (i=1; i<=NM1;i++)
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{
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if (i < j)
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{
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t_real=real(j-1);
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t_imag=imag(j-1);
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real[j-1] = real(i-1);
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imag[j-1] = imag(i-1);
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real[i-1] = t_real;
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imag[i-1] = t_imag;
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}
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k=NV2;
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while(k < j)
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{
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j=j-k;
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k=k/2;
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}
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j=j+k;
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}
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return 0;
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}
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int slowFFT(EST_FVector &real, EST_FVector &imag)
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{
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return slowFFTsub(real,imag,-1.0);
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}
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int slowIFFT(EST_FVector &real, EST_FVector &imag)
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{
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int N=real.n();
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if (N <=0 )
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return -1;
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if (slowFFTsub(real,imag,1.0) != 0)
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return -1;
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for(int i=1;i<=N;i++){
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real[i-1] /= (float)N;
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imag[i-1] /= (float)N;
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}
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return 0;
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}
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int energy_spectrum(EST_FVector &real, EST_FVector &imag)
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{
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if (slowFFT(real, imag) != 0)
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return -1;
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int i;
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for(i=0;i<real.n();i++)
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real[i] = imag[i] = (real(i)*real(i) + imag(i)*imag(i));
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return 0;
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}
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int power_spectrum_slow(EST_FVector &real, EST_FVector &imag)
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{
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if (slowFFT(real,imag) != 0)
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return -1;
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int i;
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for(i=0;i<real.n();i++)
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real[i] = imag[i] = sqrt((real(i)*real(i) + imag(i)*imag(i)));
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return 0;
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}
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int power_spectrum(EST_FVector &real, EST_FVector &imag)
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{
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if (fastFFT(real) == 0)
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return -1;
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int i,j,k;
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int n=real.n();
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for(i=0,j=0, k=1;i<n;i+=2,j++,k+=2)
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real.a_no_check(j)
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= imag.a_no_check(j)
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= sqrt((real.a_no_check(i)*real.a_no_check(i)
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+ real.a_no_check(k)*real.a_no_check(k)));
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return 0;
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}
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// the following code is not by Simon King, as you can see
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/*
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** Discrete Fourier analysis routine
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** from IEEE Programs for Digital Signal Processing
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** G. D. Bergland and M. T. Dolan, original authors
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** Translated from the FORTRAN with some changes by Paul Kube
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**
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** Modified to return the power spectrum by Chuck Wooters
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**
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** Modified again by Tony Robinson (ajr@eng.cam.ac.uk) Dec 92
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**
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** Modified to use EST_FVector class Simon King (simonk@cstr.ed.ac.uk) Nov 96
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**
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*/
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#define signum(i) (i < 0 ? -1 : i == 0 ? 0 : 1)
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int fastFFT(EST_FVector &invec)
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{
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// Tony Robinsons
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float fn;
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int i, in, nn, n2pow, n4pow, nthpo;
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// we could modify all the code to use vector classes ....
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// ... or we could do this:
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// TO DO
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// use FSimpleVector::copy_section here
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// quick fix
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int n=invec.n(); // order
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#if 0
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float *b = new float[n];
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for(i=0; i<n; i++)
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b[i] = invec(i);
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#endif
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float *b=invec.memory();
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n2pow = fastlog2(n);
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if (n2pow <= 0) return 0;
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nthpo = n;
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fn = nthpo;
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n4pow = n2pow / 2;
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/* radix 2 iteration required; do it now */
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if (n2pow % 2)
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{
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nn = 2;
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in = n / nn;
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FR2TR(in, b, b + in );
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}
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else nn = 1;
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/* perform radix 4 iterations */
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for(i = 1; i <= n4pow; i++) {
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nn *= 4;
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in = n / nn;
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FR4TR(in, nn, b, b + in, b + 2 * in, b + 3 * in);
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}
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/* perform inplace reordering */
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FORD1(n2pow, b);
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FORD2(n2pow, b);
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/* take conjugates */
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for(i = 3; i < n; i += 2) b[i] = -b[i];
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#if 0
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// copy back
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for(i=0; i<n; i++)
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invec[i] = b[i];
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#endif
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return 1;
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}
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/* radix 2 subroutine */
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void FR2TR(int in, float *b0, float *b1)
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{
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int k;
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float t;
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for (k = 0; k < in; k++)
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{
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t = b0[k] + b1[k];
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b1[k] = b0[k] - b1[k];
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b0[k] = t;
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}
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}
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/* radix 4 subroutine */
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void FR4TR(int in, int nn, float *b0, float *b1, float *b2, float* b3) {
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float arg, piovn, th2;
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float *b4 = b0, *b5 = b1, *b6 = b2, *b7 = b3;
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float t0, t1, t2, t3, t4, t5, t6, t7;
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float r1, r5, pr, pi;
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float c1, c2, c3, s1, s2, s3;
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int j, k, jj, kk, jthet, jlast, ji, jl, jr, int4;
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int L[16], L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15;
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int j0, j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12, j13, j14;
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int k0, kl;
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L[1] = nn / 4;
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for(k = 2; k < 16; k++) { /* set up L's */
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switch (signum(L[k-1] - 2)) {
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case -1:
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L[k-1]=2;
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case 0:
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L[k]=2;
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break;
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case 1:
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L[k]=L[k-1]/2;
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}
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}
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L15=L[1]; L14=L[2]; L13=L[3]; L12=L[4]; L11=L[5]; L10=L[6]; L9=L[7];
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L8=L[8]; L7=L[9]; L6=L[10]; L5=L[11]; L4=L[12]; L3=L[13]; L2=L[14];
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L1=L[15];
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piovn = PI / nn;
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ji=3;
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jl=2;
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jr=2;
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for(j1=2;j1<=L1;j1+=2)
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for(j2=j1;j2<=L2;j2+=L1)
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for(j3=j2;j3<=L3;j3+=L2)
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for(j4=j3;j4<=L4;j4+=L3)
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for(j5=j4;j5<=L5;j5+=L4)
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for(j6=j5;j6<=L6;j6+=L5)
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for(j7=j6;j7<=L7;j7+=L6)
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for(j8=j7;j8<=L8;j8+=L7)
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for(j9=j8;j9<=L9;j9+=L8)
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for(j10=j9;j10<=L10;j10+=L9)
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for(j11=j10;j11<=L11;j11+=L10)
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for(j12=j11;j12<=L12;j12+=L11)
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for(j13=j12;j13<=L13;j13+=L12)
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for(j14=j13;j14<=L14;j14+=L13)
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for(jthet=j14;jthet<=L15;jthet+=L14)
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{
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th2 = jthet - 2;
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if(th2<=0.0)
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{
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for(k=0;k<in;k++)
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{
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t0 = b0[k] + b2[k];
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t1 = b1[k] + b3[k];
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b2[k] = b0[k] - b2[k];
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b3[k] = b1[k] - b3[k];
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b0[k] = t0 + t1;
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b1[k] = t0 - t1;
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}
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if(nn-4>0)
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{
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k0 = in*4 + 1;
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kl = k0 + in - 1;
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for (k=k0;k<=kl;k++)
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{
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kk = k-1;
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pr = IRT2 * (b1[kk]-b3[kk]);
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pi = IRT2 * (b1[kk]+b3[kk]);
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b3[kk] = b2[kk] + pi;
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b1[kk] = pi - b2[kk];
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b2[kk] = b0[kk] - pr;
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b0[kk] = b0[kk] + pr;
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}
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}
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}
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else
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{
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arg = th2*piovn;
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c1 = cos(arg);
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s1 = sin(arg);
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c2 = c1*c1 - s1*s1;
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s2 = c1*s1 + c1*s1;
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c3 = c1*c2 - s1*s2;
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s3 = c2*s1 + s2*c1;
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int4 = in*4;
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j0=jr*int4 + 1;
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k0=ji*int4 + 1;
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jlast = j0+in-1;
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for(j=j0;j<=jlast;j++)
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{
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k = k0 + j - j0;
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kk = k-1; jj = j-1;
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r1 = b1[jj]*c1 - b5[kk]*s1;
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r5 = b1[jj]*s1 + b5[kk]*c1;
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t2 = b2[jj]*c2 - b6[kk]*s2;
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t6 = b2[jj]*s2 + b6[kk]*c2;
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t3 = b3[jj]*c3 - b7[kk]*s3;
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t7 = b3[jj]*s3 + b7[kk]*c3;
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t0 = b0[jj] + t2;
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t4 = b4[kk] + t6;
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t2 = b0[jj] - t2;
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t6 = b4[kk] - t6;
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t1 = r1 + t3;
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t5 = r5 + t7;
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t3 = r1 - t3;
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t7 = r5 - t7;
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b0[jj] = t0 + t1;
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b7[kk] = t4 + t5;
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b6[kk] = t0 - t1;
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b1[jj] = t5 - t4;
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b2[jj] = t2 - t7;
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b5[kk] = t6 + t3;
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b4[kk] = t2 + t7;
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b3[jj] = t3 - t6;
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}
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jr += 2;
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ji -= 2;
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if(ji-jl <= 0) {
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ji = 2*jr - 1;
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jl = jr;
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}
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}
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}
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}
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/* an inplace reordering subroutine */
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void FORD1(int m, float *b) {
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int j, k = 4, kl = 2, n = 0x1 << m;
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float t;
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for(j = 4; j <= n; j += 2) {
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if (k - j>0) {
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t = b[j-1];
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b[j - 1] = b[k - 1];
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b[k - 1] = t;
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}
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k -= 2;
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if (k - kl <= 0) {
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k = 2*j;
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kl = j;
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}
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}
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}
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/* the other inplace reordering subroutine */
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void FORD2(int m, float *b)
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{
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float t;
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int n = 0x1<<m, k, ij, ji, ij1, ji1;
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int l[16], l1, l2, l3, l4, l5, l6, l7, l8, l9, l10, l11, l12, l13, l14, l15;
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int j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12, j13, j14;
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l[1] = n;
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for(k=2;k<=m;k++) l[k]=l[k-1]/2;
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for(k=m;k<=14;k++) l[k+1]=2;
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l15=l[1];l14=l[2];l13=l[3];l12=l[4];l11=l[5];l10=l[6];l9=l[7];
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l8=l[8];l7=l[9];l6=l[10];l5=l[11];l4=l[12];l3=l[13];l2=l[14];l1=l[15];
|
|
|
|
ij = 2;
|
|
|
|
for(j1=2;j1<=l1;j1+=2)
|
|
for(j2=j1;j2<=l2;j2+=l1)
|
|
for(j3=j2;j3<=l3;j3+=l2)
|
|
for(j4=j3;j4<=l4;j4+=l3)
|
|
for(j5=j4;j5<=l5;j5+=l4)
|
|
for(j6=j5;j6<=l6;j6+=l5)
|
|
for(j7=j6;j7<=l7;j7+=l6)
|
|
for(j8=j7;j8<=l8;j8+=l7)
|
|
for(j9=j8;j9<=l9;j9+=l8)
|
|
for(j10=j9;j10<=l10;j10+=l9)
|
|
for(j11=j10;j11<=l11;j11+=l10)
|
|
for(j12=j11;j12<=l12;j12+=l11)
|
|
for(j13=j12;j13<=l13;j13+=l12)
|
|
for(j14=j13;j14<=l14;j14+=l13)
|
|
for(ji=j14;ji<=l15;ji+=l14) {
|
|
ij1 = ij-1; ji1 = ji - 1;
|
|
if(ij-ji<0) {
|
|
t = b[ij1-1];
|
|
b[ij1-1]=b[ji1-1];
|
|
b[ji1-1] = t;
|
|
|
|
t = b[ij1];
|
|
b[ij1]=b[ji1];
|
|
b[ji1] = t;
|
|
}
|
|
ij += 2;
|
|
}
|
|
}
|
|
|
|
int fastlog2(int n) {
|
|
int num_bits, power = 0;
|
|
|
|
if ((n < 2) || (n % 2 != 0)) return(0);
|
|
num_bits = sizeof(int) * 8; /* How big are ints on this machine? */
|
|
|
|
while(power <= num_bits) {
|
|
n >>= 1;
|
|
power += 1;
|
|
if (n & 0x01) {
|
|
if (n > 1) return(0);
|
|
else return(power);
|
|
}
|
|
}
|
|
return(0);
|
|
}
|