#include <stdint.h> // to make sure I get 8-byte integers
#include <iostream>
#include <iomanip>
#include <fstream>
#include <cmath>
using namespace std;

int main() {
	ofstream outfil("output.txt");
	int64_t cic[4],resold[4]; // cic[i] and resold[i] are the sums of the  cic stages and the sums 1024 samples earlier
// I use int64_t to be sure that 64-bit integers are used. you can use long also
// typically, long is typecast to int64_t but that is not garantueed
	double result=0; // the result after 1024*n steps
	int64_t res;
	int input;
	int time=0;
	double rms[2]; // the rms can be calculated
	for (int i=0; i<4; i++) cic[i]=resold[i]=0;
	rms[0]=rms[1]=0;
	int totval=0;
// in c++, cin returns 0 if the operation did not go right.
	while (cin >> input) {
		time ++;
		cic[0]+=input;
		for (int i=0; i<3; i++) cic[i+1]+=cic[i]; 
		if (time%1024==0) {
// every 1024 steps, decimate the results. check the values of the
// 4-stage cic filters and the values of the previous steps 
			int64_t res=cic[3];
			for (int j=0; j<4; j++) {
				int64_t delay=resold[j]; // store the previous result in delay
				resold[j]=res; // update the result with the current value of the result
				res -= delay; // subtract the previous value from the result 
			}
			result=res/pow(1024,4); // normalize the double-precision result

// the true signal equals 2.7 sin(17t)
			double sig=2.7*sin(17*time/1024000.0);
			outfil << setprecision(9) << time/1024000.0 << " " << sig << " " << result << " " << input << endl;
			if (time/1024>1) {
				rms[1]+=pow(input-sig,2);
				sig=2.7*sin(17*(time-2048)/1024000.0);
				rms[0]+=pow(result-sig,2);
				totval++;
			}
		}
	}
	cout << "RMS of the input minus the signal : " << sqrt(rms[1]/totval) << " RMS of the CIC-filtered result : " << sqrt(rms[0]/totval) << endl;
	return 0;
}