Non-linear equation solving using bisection method. (Automated guessing)

bisectionWithAutomatedGuess.cpp

/*******************************
 * Bisection Method:
 * @author nootanghimire
 *******************************/

/******************************
 *
 * TODO: Dynamic function loading and solving..
 *     : see github/nootanghimire/calc-cpp
 *     :    function: addSpace(char[], *char[])
 *     :            : basically, doesn't care spaces and put things into array for eval.

/************************
 * Algorithm
 *
 * f(x) = x sin(x) + cos(x) = 0
 *
 * Guess x1, x2
 *
 * check if f(x1)*f(x2) > 0 ?
 *
 *   -- Yes: Guess incorrect! Re-guess
 *   -- No: Guess correct! Yay!
 *
 * Calculate xo = (x1+x2)/2
 *
 * Calculate f(x0), f(x1), f(x2)
 *
 * check if f(x1)*f(x0)<0 ?
 *
 *
 *   -- Yes: Set x1 = x1, and x2 = x0 ;
 *   -- No : Set x1 = x0, and x2 = x2 ;
 *
 * Loop until the stopping criteria is found or f(x) = 0
 *
 ************************/

 /***********
  *
  * Stopping criteria, (x2-x1)/x2 < e
  *
  ********/

#include <iostream>
#include <cmath>
using namespace std;


//The funcitons

/*float func(float x){
    return x*sin(x) + cos(x);
}*/



float func(float x){
    return (x*x + x - 3.75);
}


/*float func(float x){
    return (x*x + 3*x - 2) ;
}*/

/*float func(float x){
	return (log(x)+exp(x*x));
}*/



//Global
//put the guess apart

float gx1 = 1;
float gx2 = 0;

//on first iteration, it would be 0 to 1 
//on next iteration
//the guess would be -1 to 2 

void getGuess(){
    gx1--; gx2++;
}

bool isCorrectGuess(float x1, float x2){
    return ((func(x1)*func(x2))>0) ? false : true;
}

int main(){
    int countItr=0;
    float x1, x2, x0;
    float fx1, fx2, fx0;
    float error;
    float permissibleError = 0.000001;
    //Step 1: Get guess.

    do{
        getGuess();
    }while(!isCorrectGuess(gx1,gx2));
    x1 = gx1; x2 = gx2;

    //yay! Correct guess.
    cout<<"\n[i] Bracket Value guessed! X1 = "<<x1<<" and X2 = "<<x2;

    do {
        //compute x0
        x0 = (x1 + x2)/2;
        cout<<"\n[i] Iteration "<<++countItr<<": Xo = "<<x0;
        if((func(x1)*func(x0))<0){
            x2 = x0;
        } else {
            x1 = x0;
        }
        error = (x2 - x1)/x2;
        error = (error<0) ? -error : error; //Making abs
        if(error<permissibleError) {
            cout<<"\n[!] Nah! Not anymore! I am low with my stamina! :(";
            break;
        }

    }while((func(x0))!=0.0);

    //The above while is almost useless : P 
    //See: http://www.parashift.com/c++-faq/floating-point-arith.html
    
    
    cout<<"\n\n[i] Most probably, the solution is: "<<x0;
    cout<<"\n[i] Just for check, The value is: "<<func(x0);
    cout<<"\n";
    return 0;
}