--- /dev/null
+
+//Title: 1-d mixed radix FFT.
+//Version:
+//Copyright: Copyright (c) 1998
+//Author: Dongyan Wang
+//Company: University of Wisconsin-Milwaukee.
+//Description:
+// The number of DFT is factorized.
+//
+// Some short FFTs, such as length 2, 3, 4, 5, 8, 10, are used
+// to improve the speed.
+//
+// Prime factors are processed using DFT. In the future, we can
+// improve this part.
+// Note: there is no limit how large the prime factor can be,
+// because for a set of data of an image, the length can be
+// random, ie. an image can have size 263 x 300, where 263 is
+// a large prime factor.
+//
+// A permute() function is used to make sure FFT can be calculated
+// in place.
+//
+// A triddle() function is used to perform the FFT.
+//
+// This program is for FFT of complex data, if the input is real,
+// the program can be further improved. Because I want to use the
+// same program to do IFFT, whose input is often complex, so I
+// still use this program.
+//
+// To save the memory and improve the speed, float data are used
+// instead of double, but I do have a double version transforms.fft.
+//
+// Factorize() is done in constructor, transforms.fft() is needed to be
+// called to do FFT, this is good for use in fft2d, then
+// factorize() is not needed for each row/column of data, since
+// each row/column of a matrix has the same length.
+//
+
+
+public class fft1d {
+ // Maximum numbers of factors allowed.
+ //private int MaxFactorsNumber = 30;
+ public int MaxFactorsNumber;
+
+ // cos2to3PI = cos(2*pi/3), using for 3 point FFT.
+ // cos(2*PI/3) is not -1.5
+ public double cos2to3PI;
+ // sin2to3PI = sin(2*pi/3), using for 3 point FFT.
+ public double sin2to3PI;
+
+ // TwotoFivePI = 2*pi/5.
+ // c51, c52, c53, c54, c55 are used in fft5().
+ // c51 =(cos(TwotoFivePI)+cos(2*TwotoFivePI))/2-1.
+ public double c51;
+ // c52 =(cos(TwotoFivePI)-cos(2*TwotoFivePI))/2.
+ public double c52;
+ // c53 = -sin(TwotoFivePI).
+ public double c53;
+ // c54 =-(sin(TwotoFivePI)+sin(2*TwotoFivePI)).
+ public double c54;
+ // c55 =(sin(TwotoFivePI)-sin(2*TwotoFivePI)).
+ public double c55;
+
+ // OnetoSqrt2 = 1/sqrt(2), used in fft8().
+ public double OnetoSqrt2;
+
+ public int lastRadix;
+
+ int N; // length of N point FFT.
+ int NumofFactors; // Number of factors of N.
+ int maxFactor; // Maximum factor of N.
+
+ int factors[]; // Factors of N processed in the current stage.
+ int sofar[]; // Finished factors before the current stage.
+ int remain[]; // Finished factors after the current stage.
+
+ double inputRe[], inputIm[]; // Input of FFT.
+ double temRe[], temIm[]; // Intermediate result of FFT.
+ double outputRe[], outputIm[]; // Output of FFT.
+ boolean factorsWerePrinted;
+
+ // Constructor: FFT of Complex data.
+ public fft1d(int N) {
+ this.N = N;
+ MaxFactorsNumber = 37;
+ cos2to3PI = -1.5000f;
+ sin2to3PI = 8.6602540378444E-01f;
+ c51 = -1.25f;
+ c52 = 5.5901699437495E-01f;
+ c53 = -9.5105651629515E-01f;
+ c54 = -1.5388417685876E+00f;
+ c55 = 3.6327126400268E-01f;
+ OnetoSqrt2 = 7.0710678118655E-01f;
+ lastRadix = 0;
+ maxFactor = 20;
+ factorsWerePrinted = false;
+ outputRe = new double[N];
+ outputIm = new double[N];
+
+ factorize();
+ //printFactors();
+
+ // Allocate memory for intermediate result of FFT.
+ temRe = new double[maxFactor]; //Check usage of this
+ temIm = new double[maxFactor];
+ }
+
+ public void printFactors() {
+ if (factorsWerePrinted) return;
+ factorsWerePrinted = true;
+ System.printString("factors.length = " + factors.length + "\n");
+ for (int i = 0; i < factors.length; i++)
+ System.printString("factors[i] = " + factors[i] + "\n");
+ }
+
+ public void factorize() {
+ int radices[] = new int[6];
+ radices[0] = 2;
+ radices[1] = 3;
+ radices[2] = 4;
+ radices[3] = 5;
+ radices[4] = 8;
+ radices[5] = 10;
+ int temFactors[] = new int[MaxFactorsNumber];
+
+ // 1 - point FFT, no need to factorize N.
+ if (N == 1) {
+ temFactors[0] = 1;
+ NumofFactors = 1;
+ }
+
+ // N - point FFT, N is needed to be factorized.
+ int n = N;
+ int index = 0; // index of temFactors.
+ int i = radices.length - 1;
+
+ while ((n > 1) && (i >= 0)) {
+ if ((n % radices[i]) == 0) {
+ n /= radices[i];
+ temFactors[index++] = radices[i];
+ } else
+ i--;
+ }
+
+ // Substitute 2x8 with 4x4.
+ // index>0, in the case only one prime factor, such as N=263.
+ if ((index > 0) && (temFactors[index - 1] == 2)) {
+ int test = 0;
+ for (i = index - 2; (i >= 0) && (test == 0); i--) {
+ if (temFactors[i] == 8) {
+ temFactors[index - 1] = temFactors[i] = 4;
+ // break out of for loop, because only one '2' will exist in
+ // temFactors, so only one substitutation is needed.
+ test = 1;
+ }
+ }
+ }
+
+ if (n > 1) {
+ for (int k = 2; k < Math.sqrt(n) + 1; k++)
+ while ((n % k) == 0) {
+ n /= k;
+ temFactors[index++] = k;
+ }
+ if (n > 1) {
+ temFactors[index++] = n;
+ }
+ }
+ NumofFactors = index;
+
+ // Inverse temFactors and store factors into factors[].
+ factors = new int[NumofFactors];
+ for (i = 0; i < NumofFactors; i++) {
+ factors[i] = temFactors[NumofFactors - i - 1];
+ }
+
+ // Calculate sofar[], remain[].
+ // sofar[] : finished factors before the current stage.
+ // factors[]: factors of N processed in the current stage.
+ // remain[] : finished factors after the current stage.
+
+ sofar = new int[NumofFactors];
+ remain = new int[NumofFactors];
+
+ remain[0] = N / factors[0];
+ sofar[0] = 1;
+ for (i = 1; i < NumofFactors; i++) {
+ sofar[i] = sofar[i - 1] * factors[i - 1];
+ remain[i] = remain[i - 1] / factors[i];
+ }
+ } // End of function factorize().
+} // End of class FFT1d
--- /dev/null
+public class fft2d extends Thread {
+ //Title: 2-d mixed radix FFT.
+ //Version:
+ //Copyright: Copyright (c) 1998
+ //Author: Dongyan Wang
+ //Company: University of Wisconsin-Milwaukee.
+ //Description:
+ // . Use fft1d to perform fft2d.
+ //
+ // Code borrowed from :Java Digital Signal Processing book by Lyon and Rao
+
+ public Matrix data1, data2;
+ public int x0, x1;
+
+ // Constructor: 2-d FFT of Complex data.
+ public fft2d(Matrix data1, Matrix data2, int x0, int x1) {
+ this.data1 = data1;
+ this.data2 = data2;
+ this.x0 = x0;
+ this.x1 = x1;
+ }
+
+ public void run() {
+ fft1d fft1, fft2;
+ Barrier barr;
+ barr = new Barrier("128.195.136.162");
+ double tempdataRe[][];
+ double tempdataIm[][];
+ int rowlength, columnlength;
+ int start, end;
+
+ // Calculate FFT for each row of the data.
+ atomic {
+ //
+ // Add manual prefetch for
+ // this.data1.dataRe[x0 -> x1]
+ Object o1 = this;
+ short[] offsets1 = new short[6];
+ offsets1[0] = getoffset{fft2d, data1};
+ offsets1[1] = (short) 0;
+ offsets1[2] = getoffset{Matrix, dataRe};
+ offsets1[3] = (short) 0;
+ offsets1[4] = (short) x0;
+ offsets1[5] = (short) (x1-x0-1);
+ System.rangePrefetch(o1, offsets1);
+
+ // prefetch data1.dataIm[x0 -> x1]
+ o1 = data1;
+ short[] offsets2 = new short[4];
+ offsets2[0] = getoffset{Matrix, dataIm};
+ offsets2[1] = (short) 0;
+ offsets2[2] = (short) x0;
+ offsets2[3] = (short) (x1-x0-1);
+ System.rangePrefetch(o1, offsets2);
+ ///////////////////////////// //////////
+
+ rowlength = data1.M;
+ columnlength = data1.N;
+ tempdataRe = data1.dataRe;
+ tempdataIm = data1.dataIm;
+ start = x0;
+ end = x1;
+ fft1 = new fft1d(columnlength);
+ fft2 = new fft1d(rowlength);
+ for (int i = x0; i < x1; i++) {
+ //input of FFT
+ double inputRe[] = tempdataRe[i]; //local array
+ double inputIm[] = tempdataIm[i];
+ fft(fft1, inputRe, inputIm);
+ } //end of for
+ }
+
+ //Start Barrier
+ Barrier.enterBarrier(barr);
+
+ // Tranpose data.
+ if (start == 0) {
+ atomic {
+ //
+ // Add manual prefetch
+ // prefetch data2.dataRe
+ Object o = data2;
+ short[] offsets = new short[2];
+ offsets[0] = getoffset{Matrix, dataRe};
+ offsets[1] = (short) 0;
+ System.rangePrefetch(o, offsets);
+ // prefetch data2.dataIm
+ offsets[0] = getoffset{Matrix, dataIm};
+ offsets[1] = (short) 0;
+ System.rangePrefetch(o, offsets);
+ /////////////////////
+
+ transpose(tempdataRe,tempdataIm, data2.dataRe,data2.dataIm, rowlength, columnlength);
+ }
+ }
+
+ //Start Barrier
+ Barrier.enterBarrier(barr);
+
+ // Calculate FFT for each column of the data.
+ double transtempRe[][];
+ double transtempIm[][];
+ atomic {
+ //
+ // Add manual prefetch
+ // prefetch data2.dataRe[start -> end]
+ Object o1 = data2.dataRe;
+ short[] offsets1 = new short[2];
+ offsets1[0] = (short) start;
+ offsets1[1] = (short) (start - end - 1);
+ System.rangePrefetch(o1, offsets1);
+
+ // prefetch data2.dataIm[start -> end]
+
+ o1 = data2.dataIm;
+ offsets1[0] = (short) start;
+ offsets1[1] = (short) (start - end - 1);
+ System.rangePrefetch(o1, offsets1);
+ /////////////////////
+
+ transtempRe = data2.dataRe;
+ transtempIm = data2.dataIm;
+ for (int j = start; j < end; j++) {
+ //input of FFT
+ double inputRe[] = transtempRe[j]; //local array
+ double inputIm[] = transtempIm[j];
+ fft(fft2, inputRe, inputIm);
+ } //end of fft2 for
+ }
+ } //end of run
+
+ public void transpose(double[][] tempdataRe, double[][] tempdataIm, double[][] outputRe,
+ double[][] outputIm, int rowlength, int columnlength) {
+ for(int i = 0; i<rowlength; i++) {
+ double tRe[] = tempdataRe[i];
+ double tIm[] = tempdataIm[i];
+ for(int j = 0; j<columnlength; j++) {
+ outputRe[j][i] = tRe[j];
+ outputIm[j][i] = tIm[j];
+ }
+ }
+ }
+
+ public static void main(String[] args) {
+ int NUM_THREADS = 1;
+ int SIZE = 800;
+ int inputWidth = 10;
+ if(args.length>0) {
+ NUM_THREADS=Integer.parseInt(args[0]);
+ if(args.length > 1)
+ SIZE = Integer.parseInt(args[1]);
+ }
+
+ System.printString("Num threads = " + NUM_THREADS + " SIZE= " + SIZE + "\n");
+
+ int[] mid = new int[8];
+ mid[0] = (128<<24)|(195<<16)|(136<<8)|162; //dw-10
+ mid[1] = (128<<24)|(195<<16)|(136<<8)|163; //dw-11
+ mid[2] = (128<<24)|(195<<16)|(136<<8)|164; //dw-12
+ mid[3] = (128<<24)|(195<<16)|(136<<8)|165; //dw-13
+ mid[4] = (128<<24)|(195<<16)|(136<<8)|166; //dw-14
+ mid[5] = (128<<24)|(195<<16)|(136<<8)|167; //dw-15
+ mid[6] = (128<<24)|(195<<16)|(136<<8)|168; //dw-16
+ mid[7] = (128<<24)|(195<<16)|(136<<8)|169; //dw-17
+
+
+ // Start Barrier Server
+ BarrierServer mybarr;
+ atomic {
+ mybarr = global new BarrierServer(NUM_THREADS);
+ }
+ mybarr.start(mid[0]);
+
+ Matrix data1;
+ Matrix data2;
+
+ // Create threads to do FFT
+ fft2d[] myfft2d;
+ atomic {
+ // Set up data for FFT transform
+ data1 = global new Matrix(SIZE, SIZE);
+ data2 = global new Matrix(SIZE, SIZE);
+ data1.setValues(); //Input Matrix
+ data2.setZeros(); //Transpose Matrix
+ myfft2d = global new fft2d[NUM_THREADS];
+ int increment = SIZE/NUM_THREADS;
+ int base = 0;
+ for(int i =0 ; i<NUM_THREADS; i++) {
+ if((i+1)==NUM_THREADS)
+ myfft2d[i] = global new fft2d(data1, data2, base, SIZE);
+ else
+ myfft2d[i] = global new fft2d(data1, data2, base, base+increment);
+ base+=increment;
+ }
+ }
+
+ boolean waitfordone=true;
+ while(waitfordone) {
+ atomic {
+ if (mybarr.done)
+ waitfordone=false;
+ }
+ }
+
+ fft2d tmp;
+ //Start a thread to compute each c[l,n]
+ for(int i = 0; i<NUM_THREADS; i++) {
+ atomic {
+ tmp = myfft2d[i];
+ }
+ tmp.start(mid[i]);
+ }
+
+ //Wait for thread to finish
+ for(int i = 0; i<NUM_THREADS; i++) {
+ atomic {
+ tmp = myfft2d[i];
+ }
+ tmp.join();
+ }
+
+ System.printString("2DFFT done! \n");
+ }
+
+ public static void fft(fft1d myfft, double inputRe[], double inputIm[]) {
+ //output of FFT
+ double outputRe[] = myfft.outputRe;
+ double outputIm[] = myfft.outputIm;
+ // intermediate results
+ double temRe[] = myfft.temRe;
+ double temIm[] = myfft.temIm;
+ //Permute() operation
+ permute(myfft, outputRe, outputIm, inputRe, inputIm);
+
+ //System.printString("ready to twiddle");
+ for (int factorIndex = 0; factorIndex < myfft.NumofFactors; factorIndex++)
+ twiddle(factorIndex, myfft, temRe, temIm, outputRe, outputIm);
+
+ //System.printString("ready to copy");
+ // Copy the output[] data to input[], so the output can be
+ // returned in the input array.
+ for (int i = 0; i < myfft.N; i++) {
+ inputRe[i] = outputRe[i];
+ inputIm[i] = outputIm[i];
+ }
+ }
+
+ private static void permute(fft1d myfft, double[] outputRe, double[] outputIm, double[] inputRe, double[] inputIm) {
+ int count[] = new int[myfft.MaxFactorsNumber];
+ int j;
+ int k = 0;
+
+ for (int i = 0; i < myfft.N - 1; i++) {
+ outputRe[i] = inputRe[k];
+ outputIm[i] = inputIm[k];
+ j = 0;
+ k = k + myfft.remain[j];
+ count[0] = count[0] + 1;
+ while (count[j] >= myfft.factors[j]) {
+ count[j] = 0;
+ int tmp;
+ if(j == 0)
+ tmp = myfft.N;
+ else
+ tmp = myfft.remain[j - 1];
+ k = k - tmp + myfft.remain[j + 1];
+ j++;
+ count[j] = count[j] + 1;
+ }
+ }
+ outputRe[myfft.N - 1] = inputRe[myfft.N - 1];
+ outputIm[myfft.N - 1] = inputIm[myfft.N - 1];
+ } // End of function permute().
+
+ private static void twiddle(int factorIndex, fft1d myfft, double[] temRe, double[] temIm,
+ double[] outputRe, double[] outputIm) {
+ // Get factor data.
+ int sofarRadix = myfft.sofar[factorIndex];
+ int radix = myfft.factors[factorIndex];
+ int remainRadix = myfft.remain[factorIndex];
+
+ double tem; // Temporary variable to do data exchange.
+
+ double W = 2 * (double) Math.setPI() / (sofarRadix * radix);
+ double cosW = (double) Math.cos(W);
+ double sinW = -(double) Math.sin(W);
+
+ double twiddleRe[] = new double[radix];
+ double twiddleIm[] = new double[radix];
+ double twRe = 1.0f, twIm = 0f;
+
+ //Initialize twiddle addBk.address variables.
+ int dataOffset = 0, groupOffset = 0, address = 0;
+
+ for (int dataNo = 0; dataNo < sofarRadix; dataNo++) {
+ //System.printString("datano="+dataNo);
+ if (sofarRadix > 1) {
+ twiddleRe[0] = 1.0f;
+ twiddleIm[0] = 0.0f;
+ twiddleRe[1] = twRe;
+ twiddleIm[1] = twIm;
+ for (int i = 2; i < radix; i++) {
+ twiddleRe[i] = twRe * twiddleRe[i - 1] - twIm * twiddleIm[i - 1];
+ twiddleIm[i] = twIm * twiddleRe[i - 1] + twRe * twiddleIm[i - 1];
+ }
+ tem = cosW * twRe - sinW * twIm;
+ twIm = sinW * twRe + cosW * twIm;
+ twRe = tem;
+ }
+ for (int groupNo = 0; groupNo < remainRadix; groupNo++) {
+ //System.printString("groupNo="+groupNo);
+ if ((sofarRadix > 1) && (dataNo > 0)) {
+ temRe[0] = outputRe[address];
+ temIm[0] = outputIm[address];
+ int blockIndex = 1;
+ do {
+ address = address + sofarRadix;
+ temRe[blockIndex] = twiddleRe[blockIndex] * outputRe[address] -
+ twiddleIm[blockIndex] * outputIm[address];
+ temIm[blockIndex] = twiddleRe[blockIndex] * outputIm[address] +
+ twiddleIm[blockIndex] * outputRe[address];
+ blockIndex++;
+ } while (blockIndex < radix);
+ } else {
+ for (int i = 0; i < radix; i++) {
+ //System.printString("temRe.length="+temRe.length);
+ //System.printString("i = "+i);
+ temRe[i] = outputRe[address];
+ temIm[i] = outputIm[address];
+ address += sofarRadix;
+ }
+ }
+ //System.printString("radix="+radix);
+ if(radix == 2) {
+ tem = temRe[0] + temRe[1];
+ temRe[1] = temRe[0] - temRe[1];
+ temRe[0] = tem;
+ tem = temIm[0] + temIm[1];
+ temIm[1] = temIm[0] - temIm[1];
+ temIm[0] = tem;
+ } else if( radix == 3) {
+ double t1Re = temRe[1] + temRe[2];
+ double t1Im = temIm[1] + temIm[2];
+ temRe[0] = temRe[0] + t1Re;
+ temIm[0] = temIm[0] + t1Im;
+
+ double m1Re = myfft.cos2to3PI * t1Re;
+ double m1Im = myfft.cos2to3PI * t1Im;
+ double m2Re = myfft.sin2to3PI * (temIm[1] - temIm[2]);
+ double m2Im = myfft.sin2to3PI * (temRe[2] - temRe[1]);
+ double s1Re = temRe[0] + m1Re;
+ double s1Im = temIm[0] + m1Im;
+
+ temRe[1] = s1Re + m2Re;
+ temIm[1] = s1Im + m2Im;
+ temRe[2] = s1Re - m2Re;
+ temIm[2] = s1Im - m2Im;
+ } else if(radix == 4) {
+ fft4(temRe, temIm);
+ } else if(radix == 5) {
+ fft5(myfft, temRe, temIm);
+ } else if(radix == 8) {
+ fft8(myfft, temRe, temIm);
+ } else if(radix == 10) {
+ fft10(myfft, temRe, temIm);
+ } else {
+ fftPrime(radix, temRe, temIm);
+ }
+ address = groupOffset;
+ for (int i = 0; i < radix; i++) {
+ outputRe[address] = temRe[i];
+ outputIm[address] = temIm[i];
+ address += sofarRadix;
+ }
+ groupOffset += sofarRadix * radix;
+ address = groupOffset;
+ }
+ groupOffset = ++dataOffset;
+ address = groupOffset;
+ }
+ } //twiddle operation
+
+ // The two arguments dataRe[], dataIm[] are mainly for using in fft8();
+ private static void fft4(double dataRe[], double dataIm[]) {
+ double t1Re,t1Im, t2Re,t2Im;
+ double m2Re,m2Im, m3Re,m3Im;
+
+ t1Re = dataRe[0] + dataRe[2];
+ t1Im = dataIm[0] + dataIm[2];
+ t2Re = dataRe[1] + dataRe[3];
+ t2Im = dataIm[1] + dataIm[3];
+
+ m2Re = dataRe[0] - dataRe[2];
+ m2Im = dataIm[0] - dataIm[2];
+ m3Re = dataIm[1] - dataIm[3];
+ m3Im = dataRe[3] - dataRe[1];
+
+ dataRe[0] = t1Re + t2Re;
+ dataIm[0] = t1Im + t2Im;
+ dataRe[2] = t1Re - t2Re;
+ dataIm[2] = t1Im - t2Im;
+ dataRe[1] = m2Re + m3Re;
+ dataIm[1] = m2Im + m3Im;
+ dataRe[3] = m2Re - m3Re;
+ dataIm[3] = m2Im - m3Im;
+ } // End of function fft4().
+
+ // The two arguments dataRe[], dataIm[] are mainly for using in fft10();
+ private static void fft5(fft1d myfft, double dataRe[], double dataIm[]) {
+ double t1Re,t1Im, t2Re,t2Im, t3Re,t3Im, t4Re,t4Im, t5Re,t5Im;
+ double m1Re,m1Im, m2Re,m2Im, m3Re,m3Im, m4Re,m4Im, m5Re,m5Im;
+ double s1Re,s1Im, s2Re,s2Im, s3Re,s3Im, s4Re,s4Im, s5Re,s5Im;
+
+ t1Re = dataRe[1] + dataRe[4];
+ t1Im = dataIm[1] + dataIm[4];
+ t2Re = dataRe[2] + dataRe[3];
+ t2Im = dataIm[2] + dataIm[3];
+ t3Re = dataRe[1] - dataRe[4];
+ t3Im = dataIm[1] - dataIm[4];
+ t4Re = dataRe[3] - dataRe[2];
+ t4Im = dataIm[3] - dataIm[2];
+ t5Re = t1Re + t2Re;
+ t5Im = t1Im + t2Im;
+
+ dataRe[0] = dataRe[0] + t5Re;
+ dataIm[0] = dataIm[0] + t5Im;
+
+ m1Re = myfft.c51 * t5Re;
+ m1Im = myfft.c51 * t5Im;
+ m2Re = myfft.c52 * (t1Re - t2Re);
+ m2Im = myfft.c52 * (t1Im - t2Im);
+ m3Re = -(myfft.c53) * (t3Im + t4Im);
+ m3Im = myfft.c53 * (t3Re + t4Re);
+ m4Re = -(myfft.c54) * t4Im;
+ m4Im = myfft.c54 * t4Re;
+ m5Re = -(myfft.c55) * t3Im;
+ m5Im = myfft.c55 * t3Re;
+
+ s3Re = m3Re - m4Re;
+ s3Im = m3Im - m4Im;
+ s5Re = m3Re + m5Re;
+ s5Im = m3Im + m5Im;
+ s1Re = dataRe[0] + m1Re;
+ s1Im = dataIm[0] + m1Im;
+ s2Re = s1Re + m2Re;
+ s2Im = s1Im + m2Im;
+ s4Re = s1Re - m2Re;
+ s4Im = s1Im - m2Im;
+
+ dataRe[1] = s2Re + s3Re;
+ dataIm[1] = s2Im + s3Im;
+ dataRe[2] = s4Re + s5Re;
+ dataIm[2] = s4Im + s5Im;
+ dataRe[3] = s4Re - s5Re;
+ dataIm[3] = s4Im - s5Im;
+ dataRe[4] = s2Re - s3Re;
+ dataIm[4] = s2Im - s3Im;
+ } // End of function fft5().
+
+ private static void fft8(fft1d myfft, double[] temRe, double[] temIm) {
+ double data1Re[] = new double[4];
+ double data1Im[] = new double[4];
+ double data2Re[] = new double[4];
+ double data2Im[] = new double[4];
+ double tem;
+
+ // To improve the speed, use direct assaignment instead for loop here.
+ data1Re[0] = temRe[0];
+ data2Re[0] = temRe[1];
+ data1Re[1] = temRe[2];
+ data2Re[1] = temRe[3];
+ data1Re[2] = temRe[4];
+ data2Re[2] = temRe[5];
+ data1Re[3] = temRe[6];
+ data2Re[3] = temRe[7];
+
+ data1Im[0] = temIm[0];
+ data2Im[0] = temIm[1];
+ data1Im[1] = temIm[2];
+ data2Im[1] = temIm[3];
+ data1Im[2] = temIm[4];
+ data2Im[2] = temIm[5];
+ data1Im[3] = temIm[6];
+ data2Im[3] = temIm[7];
+
+ fft4(data1Re, data1Im);
+ fft4(data2Re, data2Im);
+
+ tem = myfft.OnetoSqrt2 * (data2Re[1] + data2Im[1]);
+ data2Im[1] = myfft.OnetoSqrt2 * (data2Im[1] - data2Re[1]);
+ data2Re[1] = tem;
+ tem = data2Im[2];
+ data2Im[2] = -data2Re[2];
+ data2Re[2] = tem;
+ tem = myfft.OnetoSqrt2 * (data2Im[3] - data2Re[3]);
+ data2Im[3] = -(myfft.OnetoSqrt2) * (data2Re[3] + data2Im[3]);
+ data2Re[3] = tem;
+
+ temRe[0] = data1Re[0] + data2Re[0];
+ temRe[4] = data1Re[0] - data2Re[0];
+ temRe[1] = data1Re[1] + data2Re[1];
+ temRe[5] = data1Re[1] - data2Re[1];
+ temRe[2] = data1Re[2] + data2Re[2];
+ temRe[6] = data1Re[2] - data2Re[2];
+ temRe[3] = data1Re[3] + data2Re[3];
+ temRe[7] = data1Re[3] - data2Re[3];
+
+ temIm[0] = data1Im[0] + data2Im[0];
+ temIm[4] = data1Im[0] - data2Im[0];
+ temIm[1] = data1Im[1] + data2Im[1];
+ temIm[5] = data1Im[1] - data2Im[1];
+ temIm[2] = data1Im[2] + data2Im[2];
+ temIm[6] = data1Im[2] - data2Im[2];
+ temIm[3] = data1Im[3] + data2Im[3];
+ temIm[7] = data1Im[3] - data2Im[3];
+ } // End of function fft8().
+
+ private static void fft10(fft1d myfft, double[] temRe, double[] temIm) {
+ double data1Re[] = new double[5];
+ double data1Im[] = new double[5];
+ double data2Re[] = new double[5];
+ double data2Im[] = new double[5];
+
+ // To improve the speed, use direct assaignment instead for loop here.
+ data1Re[0] = temRe[0];
+ data2Re[0] = temRe[5];
+ data1Re[1] = temRe[2];
+ data2Re[1] = temRe[7];
+ data1Re[2] = temRe[4];
+ data2Re[2] = temRe[9];
+ data1Re[3] = temRe[6];
+ data2Re[3] = temRe[1];
+ data1Re[4] = temRe[8];
+ data2Re[4] = temRe[3];
+
+ data1Im[0] = temIm[0];
+ data2Im[0] = temIm[5];
+ data1Im[1] = temIm[2];
+ data2Im[1] = temIm[7];
+ data1Im[2] = temIm[4];
+ data2Im[2] = temIm[9];
+ data1Im[3] = temIm[6];
+ data2Im[3] = temIm[1];
+ data1Im[4] = temIm[8];
+ data2Im[4] = temIm[3];
+
+ fft5(myfft, data1Re, data1Im);
+ fft5(myfft, data2Re, data2Im);
+
+ temRe[0] = data1Re[0] + data2Re[0];
+ temRe[5] = data1Re[0] - data2Re[0];
+ temRe[6] = data1Re[1] + data2Re[1];
+ temRe[1] = data1Re[1] - data2Re[1];
+ temRe[2] = data1Re[2] + data2Re[2];
+ temRe[7] = data1Re[2] - data2Re[2];
+ temRe[8] = data1Re[3] + data2Re[3];
+ temRe[3] = data1Re[3] - data2Re[3];
+ temRe[4] = data1Re[4] + data2Re[4];
+ temRe[9] = data1Re[4] - data2Re[4];
+
+ temIm[0] = data1Im[0] + data2Im[0];
+ temIm[5] = data1Im[0] - data2Im[0];
+ temIm[6] = data1Im[1] + data2Im[1];
+ temIm[1] = data1Im[1] - data2Im[1];
+ temIm[2] = data1Im[2] + data2Im[2];
+ temIm[7] = data1Im[2] - data2Im[2];
+ temIm[8] = data1Im[3] + data2Im[3];
+ temIm[3] = data1Im[3] - data2Im[3];
+ temIm[4] = data1Im[4] + data2Im[4];
+ temIm[9] = data1Im[4] - data2Im[4];
+ } // End of function fft10().
+
+ private static void fftPrime(int radix, double[] temRe, double[] temIm) {
+ // Initial WRe, WIm.
+ double W = 2 * (double) Math.setPI() / radix;
+ double cosW = (double) Math.cos(W);
+ double sinW = -(double) Math.sin(W);
+ double WRe[] = new double[radix];
+ double WIm[] = new double[radix];
+
+ WRe[0] = 1;
+ WIm[0] = 0;
+ WRe[1] = cosW;
+ WIm[1] = sinW;
+
+ for (int i = 2; i < radix; i++) {
+ WRe[i] = cosW * WRe[i - 1] - sinW * WIm[i - 1];
+ WIm[i] = sinW * WRe[i - 1] + cosW * WIm[i - 1];
+ }
+
+ // FFT of prime length data, using DFT, can be improved in the future.
+ double rere, reim, imre, imim;
+ int j, k;
+ int max = (radix + 1) / 2;
+
+ double tem1Re[] = new double[max];
+ double tem1Im[] = new double[max];
+ double tem2Re[] = new double[max];
+ double tem2Im[] = new double[max];
+
+ for (j = 1; j < max; j++) {
+ tem1Re[j] = temRe[j] + temRe[radix - j];
+ tem1Im[j] = temIm[j] - temIm[radix - j];
+ tem2Re[j] = temRe[j] - temRe[radix - j];
+ tem2Im[j] = temIm[j] + temIm[radix - j];
+ }
+
+ for (j = 1; j < max; j++) {
+ temRe[j] = temRe[0];
+ temIm[j] = temIm[0];
+ temRe[radix - j] = temRe[0];
+ temIm[radix - j] = temIm[0];
+ k = j;
+ for (int i = 1; i < max; i++) {
+ rere = WRe[k] * tem1Re[i];
+ imim = WIm[k] * tem1Im[i];
+ reim = WRe[k] * tem2Im[i];
+ imre = WIm[k] * tem2Re[i];
+
+ temRe[radix - j] += rere + imim;
+ temIm[radix - j] += reim - imre;
+ temRe[j] += rere - imim;
+ temIm[j] += reim + imre;
+
+ k = k + j;
+ if (k >= radix)
+ k = k - radix;
+ }
+ }
+ for (j = 1; j < max; j++) {
+ temRe[0] = temRe[0] + tem1Re[j];
+ temIm[0] = temIm[0] + tem2Im[j];
+ }
+ } // End of function fftPrime().
+}
projects / IRC.git / commitdiff