/*  This program is supposed to perform a bracketed Newton's
    method by doing an interval bisection step if the Newton
    iteration would leave the interval.

    The code written here doesn't work and needs debugging. */

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

double g(double x){
    return tan(x)-0.5*exp(x);
}
double dg(double x){
    double t1=cos(x);
    return 1/(t1*t1)-0.5*exp(x);
}
double bnewton(double a,double b){
    double ga=g(a),gb=g(b);
    if(ga*gb>0){
        printf("Error!  g(a) and g(b) same sign!\n");
        exit(1);
    }
    double x0=(a+b)/2;
    for(int i=0;i<200;i++){
        double y0=g(x0),x1=x0-y0/dg(x0);
        if(x1>b || x1<a){
            printf("bisecting instead of Newton!\n");
            // Take a bisection step instead
            if(y0>0){
                if(ga>0) a=x0;
                else b=x0;
            } else {
                if(gb>0) a=x0;
                else b=x0;
            }
            x0=(a+b)/2;
        } else {
            x0=x1;
        }
        printf("a=%g x0=%g b=%g\n",a,x0,b);
    }
    return x0;
}
int main(){
    double z=bnewton(3.2/2,3*3.141/2);
    printf("z=%.15g\n",z);
    return 0;
}