Brute-force equation solving

Question

I'm writing a program that uses brute-force to solve an equation. Unfortunately, I seem to have an error in my code somewhere, as my program stops at search = 0.19999. Here is the code:

#include <iostream>
#include <cmath>
#include <vector>

#define min -4.0
#define max 6.5

using namespace std;

double fx (double x){
    long double result = cos(2*x)-0.4*x;
    double scale = 0.00001;
    double value = (int)(result / scale) * scale;
    return value;
}

int sign (double a){
    if(a<0) return -1;
    if(a==0) return 0;
    else return 1;
}

int main(){
vector <double> results;
double step, interval, start, end, search; 
interval=(fabs(min)+fabs(max))/50;
step=0.00001; 

start=min;
end=min+interval;
search=start;

while(end <= max){
    if(sign(start) != sign(end)){
        search=start;
        while(search < end){
            if(fx(search) == 0) results.push_back(search);
            search=search+step;
        }
    }
    start=end;
    end=start + interval;
}

for(int i=0; i<results.size(); i++){
    cout << results[i] << endl;
}
}

I've been looking at it for quite some time now and I still can't find the error in the code. The program should check if there is a root in each given interval and, if yes, check every possibility in that interval. If it finds a root, it should push it into the results vector.

Answer 1

I've just made a run through the code again and found the error.

if(sign(start) != sign(end)) was the culprit. There will be a root if the values of f(x) for start and end have different signs. Instead, I wrote that the if the signs of start and end are different, there will be a root. Sorry for the fuss.

Answer 2

I know you already found the answer but I just spotted a problem while trying to find the bug. On line 37 you make the following comparison:

if(fx(search) == 0)

Since your fx function returns double. It's generally not advisable to test using the equal operator when dealing with double precision float numbers. Your result will probably never be exactly 0, then this test will never return true. I think you should use comparison using a maximum error margin, like this:

double maximum_error = 0.005;
if(abs(fx(search)) < maximum_error)

I think that would do the trick in your case. You may find more information on this link

Even if it's working right now, micro changes in your input numbers, CPU architecture or even compiler flags may break your program. It's highly dangerous to compare doubles in C++ like that, even though it's legal to do so.