├── .gitignore ├── LICENSE ├── Makefile ├── README.md ├── fft_complex.h ├── fft_real.h ├── fft_tb.cpp └── fft_test.cpp /.gitignore: -------------------------------------------------------------------------------- 1 | # Compiled Object files 2 | *.slo 3 | *.lo 4 | *.o 5 | *.obj 6 | 7 | # Precompiled Headers 8 | *.gch 9 | *.pch 10 | 11 | # Compiled Dynamic libraries 12 | *.so 13 | *.dylib 14 | *.dll 15 | 16 | # Fortran module files 17 | *.mod 18 | 19 | # Compiled Static libraries 20 | *.lai 21 | *.la 22 | *.a 23 | *.lib 24 | 25 | # Executables 26 | *.exe 27 | *.out 28 | *.app 29 | fft_tb 30 | fft_test 31 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 2, June 1991 3 | 4 | Copyright (C) 1989, 1991 Free Software Foundation, Inc., 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | Preamble 10 | 11 | The licenses for most software are designed to take away your 12 | freedom to share and change it. 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If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | 341 | -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- 1 | # 2 | # Huild the FFT template testbench 3 | # 4 | # Author: Tim Molteno, tim@physics.otago.ac.nz 5 | # 6 | # Copyright Tim Molteno, 2008-2015. 7 | # Licensed under the GPL v3. 8 | # 9 | all: 10 | gcc -o fft_test -O2 -ftree-vectorize -I /usr/include/eigen3/ fft_test.cpp -lstdc++ 11 | 12 | test: 13 | gcc -o fft_tb -O3 -march=native fft_tb.cpp -lstdc++ 14 | ./fft_tb 15 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Template-FFT 2 | 3 | Fast Header only C++ FFT and Inverse FFT using templates. 4 | 5 | Here is the source code for a complex FFT algorithm that uses template metaprogramming. 6 | It is quite fast (nearly as fast as fftw) and can be specialized to any type. We will be creating a fixed-point friendly FFT as well in the near future. 7 | 8 | ## Using the C++ template 9 | 10 | Create the file below, and compile it with your favourite C++ compiler. Requires Eigen for handling vectors and matrices. 11 | 12 | #include "fft_complex.h" 13 | #include 14 | using namespace std; 15 | 16 | #define LOG_LENGTH 13 17 | #define N (1< fft_complex; 20 | 21 | #include 22 | 23 | int main() 24 | { 25 | CFFT cfft; 26 | Matrix, N, 1> cdata; 27 | cdata.setRandom(); 28 | 29 | std::cout << "Perform 1000 FFT and INVERSE FFT " << endl; 30 | std::cout << "FFT Length= " << N << endl; 31 | 32 | for (int i=0;i<1000;i++) { 33 | cfft.fft(cdata); 34 | cfft.ifft(cdata); 35 | } 36 | return 0; 37 | } 38 | 39 | 40 | ## Copyright 41 | 42 | Author: Tim Molteno, tim@physics.otago.ac.nz 43 | 44 | Based on the article "A Simple and Efficient FFT Implementation in C++" by Volodymyr Myrnyy 45 | with an inverse FFT modification. 46 | 47 | Licensed under the GPL v3. -------------------------------------------------------------------------------- /fft_complex.h: -------------------------------------------------------------------------------- 1 | #ifndef _fft_complex_h_ 2 | #define _fft_complex_h_ 3 | /* 4 | A FFT and Inverse FFT C++ class library for complex arrays 5 | 6 | Author: Tim Molteno, tim@physics.otago.ac.nz 7 | 8 | Based on article "A Simple and Efficient FFT Implementation in C++" 9 | by Volodymyr Myrnyy with an Inverse FFT modification. 10 | 11 | This class uses Eigen http://eigen.tuxfamily.org 12 | as the Container class for doing its complex arrays. 13 | 14 | Copyright Tim Molteno, 2008-2015. 15 | Licensed under the GPL v3. 16 | */ 17 | 18 | 19 | #include 20 | #include 21 | #include 22 | 23 | #include 24 | using namespace Eigen; 25 | 26 | /*!\brief Radix-2 Decimation class 27 | */ 28 | template 29 | class Radix2_Decimation 30 | { 31 | enum { N2 = N>>1 }; 32 | static Radix2_Decimation next; 33 | public: 34 | /*!\brief Recursive decimation routine. 35 | \param data The array of complex numbers to decimate. 36 | \param iSign If +1 we're doing an FFT, if -1 we're doing an inverse FFT 37 | */ 38 | template 39 | static void apply(VectorType data, int iSign) { 40 | /*! Call the next-level of recursion on the first half of the data */ 41 | next.apply(data.template segment(0), iSign); 42 | 43 | /*! Call the next-level of recursion on the second half of the data */ 44 | next.apply(data.template segment(N2), iSign); 45 | 46 | T wtemp = iSign*std::sin(M_PI/N); 47 | T wpi = -iSign*std::sin(2*M_PI/N); 48 | const std::complex wp(-2.0*wtemp*wtemp, wpi); 49 | 50 | std::complex w(1.0,0.0); 51 | for (unsigned i=0; i temp(data[i+N2]*w); 53 | data[i+N2] = data[i]-temp; 54 | data[i] += temp; 55 | w += w*wp; 56 | } 57 | } 58 | }; 59 | 60 | /*!\brief N=2 case for decimation. 61 | */ 62 | template 63 | class Radix2_Decimation<2,T> 64 | { 65 | public: 66 | template 67 | static void apply(VectorType data, int iSign) { 68 | std::complex temp(data[1]); 69 | data[1] = data[0]-temp; 70 | data[0] += temp; 71 | } 72 | }; 73 | 74 | 75 | /*!\brief N=1 case for decimation. 76 | */ 77 | template 78 | class Radix2_Decimation<1,T> 79 | { 80 | public: 81 | template 82 | static void apply(VectorType data, int iSign) { } 83 | }; 84 | 85 | 86 | /*!\brief A templated FFT/Inverse FFT object 87 | 88 | \param N The length of the FFT vector. Must be a power of two. 89 | 90 | How to use this FFT..... 91 | 92 | #define LENGTH 8192 93 | 94 | CFFT cfft; 95 | Matrix, LENGTH, 1> cdata; 96 | cdata.setRandom(); 97 | 98 | cfft.fft(cdata); // Forward transform 99 | cfft.ifft(cdata); // Reverse transform 100 | */ 101 | template 102 | class CFFT { 103 | static Radix2_Decimation decimation; 104 | 105 | /*!\brief Cooley-Tukey factorization 106 | */ 107 | static void factorize(Matrix< std::complex, N, 1>& data) { 108 | unsigned j=1; 109 | for (unsigned i=1; ii) { 111 | std::swap(data[j-1], data[i-1]); 112 | } 113 | unsigned m = N/2; 114 | 115 | while (m>=2 && j>m) { 116 | j -= m; 117 | m >>= 1; 118 | } 119 | j += m; 120 | } 121 | } 122 | 123 | public: 124 | /*!\brief Replaces the complex array data[1..N] by its DFT */ 125 | static void fft(Matrix< std::complex, N, 1>& data) { 126 | factorize(data); 127 | decimation.apply(data.template segment(0),1); 128 | } 129 | 130 | /*!\brief Replaces complex array data[1..N] by its inverse DFT */ 131 | static void ifft(Matrix< std::complex, N, 1>& data) { 132 | factorize(data); 133 | decimation.apply(data.template segment(0),-1); 134 | 135 | /** Scale all results by 1/n */ 136 | T scale = static_cast(1)/N; 137 | data *= scale; 138 | } 139 | }; 140 | 141 | #endif /* _fft_complex_h_ */ 142 | -------------------------------------------------------------------------------- /fft_real.h: -------------------------------------------------------------------------------- 1 | #ifndef _fft_h_ 2 | #define _fft_h_ 3 | /* 4 | A classy FFT and Inverse FFT C++ class library 5 | 6 | Author: Tim Molteno, tim@physics.otago.ac.nz 7 | 8 | Based on the article "A Simple and Efficient FFT Implementation in C++" by Volodymyr Myrnyy 9 | with just a simple Inverse FFT modification. 10 | 11 | Licensed under the GPL v3. 12 | */ 13 | 14 | 15 | #include 16 | 17 | inline void swap(double& a, double& b) { 18 | double temp=a; 19 | a = b; 20 | b = temp; 21 | } 22 | 23 | #define TRIG_PRECALC 1 24 | 25 | #if TRIG_PRECALC 26 | ////// template class SinCosSeries 27 | // common series to compile-time calculation of sine and cosine functions 28 | 29 | template 30 | struct SinCosSeries { 31 | static double value() { 32 | return 1-(A*M_PI/B)*(A*M_PI/B)/M/(M+1) 33 | *SinCosSeries::value(); 34 | } 35 | }; 36 | 37 | template 38 | struct SinCosSeries { 39 | static double value() { return 1.; } 40 | }; 41 | 42 | ////// template class Sin 43 | // compile-time calculation of sin(A*M_PI/B) function 44 | 45 | template 46 | struct Sin; 47 | 48 | template 49 | struct Sin { 50 | static float value() { 51 | return (A*M_PI/B)*SinCosSeries<2,24,B,A>::value(); 52 | } 53 | }; 54 | template 55 | struct Sin { 56 | static double value() { 57 | return (A*M_PI/B)*SinCosSeries<2,34,B,A>::value(); 58 | } 59 | }; 60 | 61 | ////// template class Cos 62 | // compile-time calculation of cos(A*M_PI/B) function 63 | 64 | template 65 | struct Cos; 66 | 67 | template 68 | struct Cos { 69 | static float value() { 70 | return SinCosSeries<1,23,B,A>::value(); 71 | } 72 | }; 73 | template 74 | struct Cos { 75 | static double value() { 76 | return SinCosSeries<1,33,B,A>::value(); 77 | } 78 | }; 79 | 80 | #endif 81 | 82 | 83 | 84 | template 85 | class DanielsonLanczos 86 | { 87 | DanielsonLanczos next; 88 | public: 89 | void apply(T* data, int iSign) { 90 | next.apply(data, iSign); 91 | next.apply(data+N, iSign); 92 | 93 | #if TRIG_PRECALC 94 | T wtemp = iSign*Sin::value(); 95 | T wpi = -iSign*Sin::value(); 96 | #else 97 | T wtemp = iSign*std::sin(M_PI/N); 98 | T wpi = -iSign*std::sin(2*M_PI/N); 99 | #endif 100 | T wpr = -2.0*wtemp*wtemp; 101 | T wr = 1.0; 102 | T wi = 0.0; 103 | 104 | for (unsigned i=0; i 124 | class DanielsonLanczos<1,T> 125 | { 126 | public: 127 | void apply(T* data, int iSign) { } 128 | }; 129 | 130 | 131 | /*!\brief Create a templated FFT/Inverse FFT object 132 | 133 | How to use this FFT 134 | FFT gfft; 135 | 136 | unsigned long n = 1< 143 | class FFT 144 | { 145 | enum { N = 1<

recursion; 147 | 148 | // reverse-binary reindexing 149 | void scramble(T* data) { 150 | int j=1; 151 | for (int i=1; i<2*N; i+=2) { 152 | if (j>i) { 153 | swap(data[j-1], data[i-1]); 154 | swap(data[j], data[i]); 155 | } 156 | int m = N; 157 | while (m>=2 && j>m) { 158 | j -= m; 159 | m >>= 1; 160 | } 161 | j += m; 162 | } 163 | } 164 | 165 | void rescale(T* data) 166 | { 167 | /* scale all results by 1/n */ 168 | T scale = static_cast(1)/N; 169 | for (unsigned i=0; i<2*N; i++) { 170 | data[i] *= scale; 171 | } 172 | } 173 | 174 | public: 175 | /*!\brief Replaces data[1..2*N] by its discrete Fourier transform */ 176 | void fft(T* data) { 177 | scramble(data); 178 | recursion.apply(data,1); 179 | } 180 | 181 | /*!\brief Replaces data[1..2*N] by its inverse discrete Fourier transform */ 182 | void ifft(T* data) { 183 | scramble(data); 184 | recursion.apply(data,-1); 185 | rescale(data); 186 | } 187 | }; 188 | 189 | #endif /* _fft_h_ */ 190 | -------------------------------------------------------------------------------- /fft_tb.cpp: -------------------------------------------------------------------------------- 1 | /* Test code for the FFT 2 | * Author: Tim Molteno, tim@physics.otago.ac.nz 3 | * 4 | * Copyright Tim Molteno, 2008-2015. 5 | * Licensed under the GPL v3. 6 | * 7 | * Perform 1000 FFT followed by Inverse FFT. 8 | * Print out the calculated number of Megaflops from the formula 9 | * Mflops = 5 N log2(N) / t (us) 10 | * 11 | * gcc -O2 -ftree-vectorize fft_noeigen.cpp -lstdc++ 12 | * Real FFT: MFLOPS(N=16384)=1638.4 13 | * 14 | * Real FFT: MFLOPS(N=16384)=1650.19 --march=native --mtune=native 15 | */ 16 | #include "fft_real.h" 17 | #include 18 | #include 19 | using namespace std; 20 | 21 | #define LOG_LENGTH 14 22 | #define N (1< 31 | #include 32 | double secnds(void) { 33 | struct tms buffer; 34 | 35 | times(&buffer); 36 | return 1000.0 * ( (double)(buffer.tms_utime + buffer.tms_stime) ) / 37 | ( (double) sysconf(_SC_CLK_TCK) ); 38 | } 39 | 40 | typedef double fft_real; 41 | 42 | int main() 43 | { 44 | FFT gfft; 45 | 46 | unsigned long n = 1< gfft; 51 | 52 | fft_real* data = new fft_real [2*N]; 53 | for (unsigned i=0; i 12 | using namespace std; 13 | 14 | #define LOG_LENGTH 13 15 | #define N (1< fft_complex; 18 | 19 | #include 20 | 21 | int main() 22 | { 23 | CFFT cfft; 24 | Matrix, N, 1> cdata; 25 | cdata.setRandom(); 26 | 27 | std::cout << "Perform 1000 FFT and INVERSE FFT " << endl; 28 | std::cout << "FFT Length= " << N << endl; 29 | 30 | for (int i=0;i<1000;i++) { 31 | cfft.fft(cdata); 32 | cfft.ifft(cdata); 33 | } 34 | return 0; 35 | } 36 | --------------------------------------------------------------------------------