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clang-format and clang-tidy fixes for a6594c85
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@ -1,70 +1,75 @@
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/**
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* @file
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* @brief [A fast Fourier transform (FFT)](https://medium.com/@aiswaryamathur/understanding-fast-fouriertransform-from-scratch-to-solve-polynomial-multiplication-8018d511162f) is an algorithm that computes the
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* discrete Fourier transform (DFT) of a sequence , or its inverse (IDFT) , this algorithm
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* has application in use case scenario where a user wants to find points of a function
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* in short period time by just using the coefficents of the polynomial function.
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* @brief [A fast Fourier transform
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(FFT)](https://medium.com/@aiswaryamathur/understanding-fast-fouriertransform-from-scratch-to-solve-polynomial-multiplication-8018d511162f)
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is an algorithm that computes the
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* discrete Fourier transform (DFT) of a sequence , or its inverse (IDFT) , this
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algorithm
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* has application in use case scenario where a user wants to find points of a
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function
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* in short period time by just using the coefficents of the polynomial
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function.
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* @details
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* https://medium.com/@aiswaryamathur/understanding-fast-fourier-transform-from-scratch-to
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-solve-polynomial-multiplication-8018d511162f
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* @author [Ameya Chawla](https://github.com/ameyachawlaggsipu)
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*/
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#include <iostream> /// for IO operations
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#include <cassert> /// for assert
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#include <cmath> /// for mathematical-related functions
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#include <complex> /// for storing points and coefficents
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#include <cassert> /// for assert
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#include <iostream> /// for IO operations
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#include <vector> /// for storing test cases
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/**
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* @brief FastFourierTransform is a recursive function which returns list of complex numbers
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* @brief FastFourierTransform is a recursive function which returns list of
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* complex numbers
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* @param p List of Coefficents in form of complex numbers
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* @param n Count of elements in list p
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* @returns p if n==1
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* @returns y if n!=1
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*/
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std::complex<double>* FastFourierTransform(std::complex<double>*p ,uint64_t n)
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{
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std::complex<double> *FastFourierTransform(std::complex<double> *p,
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uint64_t n) {
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double pi = 2 * asin(1.0); /// Declaring value of pi
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if(n==1) return p; ///Base Case To return
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if (n == 1)
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return p; /// Base Case To return
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std::complex<double> om=std::complex<double>(cos(2*pi/n),sin(2*pi/n)); ///Calculating value of omega
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std::complex<double> om = std::complex<double>(
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cos(2 * pi / n), sin(2 * pi / n)); /// Calculating value of omega
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std::complex<double> *pe= new std::complex<double>[n/2]; /// Coefficents of even power
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auto *pe = new std::complex<double>[n / 2]; /// Coefficents of even power
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std::complex<double> *po= new std::complex<double>[n/2]; ///Coefficents of odd power
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auto *po = new std::complex<double>[n / 2]; /// Coefficents of odd power
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uint64_t k1 = 0, k2 = 0;
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for(uint64_t j=0;j<n;j++)
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{
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for (uint64_t j = 0; j < n; j++) {
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if (j % 2 == 0) {
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pe[k1++] = p[j]; /// Assigning values of even coefficents
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}
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else po[k2++]=p[j]; ///Assigning value of odd coefficents
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} else
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po[k2++] = p[j]; /// Assigning value of odd coefficents
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}
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std::complex<double>*ye=FastFourierTransform(pe,n/2);///Recursive Call
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std::complex<double> *ye =
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FastFourierTransform(pe, n / 2); /// Recursive Call
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std::complex<double>*yo=FastFourierTransform(po,n/2);///Recursive Call
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std::complex<double> *yo =
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FastFourierTransform(po, n / 2); /// Recursive Call
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std::complex<double>*y=new std::complex<double>[n];///Final value representation list
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auto *y = new std::complex<double>[n]; /// Final value representation list
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for(uint64_t i=0;i<n/2;i++)
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{
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for (uint64_t i = 0; i < n / 2; i++) {
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y[i] = ye[i] + pow(om, i) * yo[i]; /// Updating the first n/2 elements
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y[i+n/2]=ye[i]-pow(om,i)*yo[i];///Updating the last n/2 elements
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y[i + n / 2] =
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ye[i] - pow(om, i) * yo[i]; /// Updating the last n/2 elements
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}
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delete[] ye;
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delete[] yo;
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delete[] pe;
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delete[] po;
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return y; /// Returns the list
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}
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/**
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@ -76,40 +81,41 @@ std::complex<double>* FastFourierTransform(std::complex<double>*p ,uint64_t n)
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static void test() {
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/* descriptions of the following test */
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std::complex<double> *t1= new std::complex<double>[2];///Test case 1
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auto *t1 = new std::complex<double>[2]; /// Test case 1
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t1[0] = {1, 0};
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t1[1] = {2, 0};
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std::complex<double> *t2=new std::complex<double>[4];///Test case 2
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auto *t2 = new std::complex<double>[4]; /// Test case 2
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t2[0] = {1, 0};
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t2[1] = {2, 0};
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t2[2] = {3, 0};
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t2[3] = {4, 0};
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uint8_t n1 = sizeof(t1) / sizeof(std::complex<double>);
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uint8_t n2 = sizeof(t2) / sizeof(std::complex<double>);
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std::vector<std::complex<double>> r1 = {
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{3, 0}, {-1, 0}}; /// True Answer for test case 1
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std::vector<std::complex<double>> r1={{3,0},{-1,0} };///True Answer for test case 1
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std::vector<std::complex<double>> r2={{10,0},{-2,-2},{-2,0},{-2,2} };///True Answer for test case 2
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std::vector<std::complex<double>> r2 = {
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{10, 0}, {-2, -2}, {-2, 0}, {-2, 2}}; /// True Answer for test case 2
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std::complex<double> *o1 = FastFourierTransform(t1, n1);
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std::complex<double> *o2 = FastFourierTransform(t2, n2);
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for(uint8_t i=0;i<n1;i++)
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{
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assert((r1[i].real()-o1->real()<0.000000000001 ) && (r1[i].imag()-o1->imag()<0.000000000001 ));/// Comparing for both real and imaginary values for test case 1
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for (uint8_t i = 0; i < n1; i++) {
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assert((r1[i].real() - o1->real() < 0.000000000001) &&
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(r1[i].imag() - o1->imag() <
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0.000000000001)); /// Comparing for both real and imaginary
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/// values for test case 1
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o1++;
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}
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for(uint8_t i=0;i<n2;i++)
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{
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assert((r2[i].real()-o2->real()<0.000000000001 ) && ( r2[i].imag()-o2->imag()<0.000000000001 ));/// Comparing for both real and imaginary values for test case 2
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for (uint8_t i = 0; i < n2; i++) {
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assert((r2[i].real() - o2->real() < 0.000000000001) &&
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(r2[i].imag() - o2->imag() <
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0.000000000001)); /// Comparing for both real and imaginary
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/// values for test case 2
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o2++;
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}
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@ -117,7 +123,6 @@ static void test() {
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delete[] o2;
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delete[] t1;
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delete[] t2;
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}
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/**
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@ -127,8 +132,7 @@ static void test() {
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* calls automated test function to test the working of fast fourier transform.
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* @returns 0 on exit
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*/
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int main(int argc, char const *argv[])
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{
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int main(int argc, char const *argv[]) {
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test(); // run self-test implementations
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return 0;
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}
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