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

//----------PROTOTYPES---------
double f(double);
double calc_rect(double,double,int);
double calc_runge(double,double,double);


int main(void){

    //----------VARIABLES---------
    double r1,r2,l1,l2,res1,res2,err=0;
    int N1,N2,i=0;
    char token=0;

    //----------TITLE---------
    for(i=1;i<30;i++) printf("=");
    printf("\nNumerical integral computation\n");
    for(i=1;i<30;i++) printf("=");
    printf("\n\nProceed with default parameters?[y/n]: ");

    //----------INPUT---------
    token=getchar();
    if (token=='y') {
        //Load default
        l1=0;
        r1=3.1415;
        l2=3.1415;
        r2=6.283;
        N1=100;
        N2=100;
        err=0.005;
    }
    else{
        //Enter parameters manually
        //Left border-integral 1
        printf("\nEnter left border for the first region: ");
        while ((!scanf("%lf", &l1)) || (!isspace(token=getchar()))) {printf("Invalid value. Enter left border: ");fflush(stdin);}
        fflush(stdin);
        //Right border-integral 1
        printf("\nEnter right border for the first region: ");
        while ((!scanf("%lf", &r1)) || (!isspace(token=getchar())) || r1<l1) {printf("Invalid value. Enter right border: ");fflush(stdin);}
        fflush(stdin);
        //Left border-integral 2
        printf("\nEnter left border for the second region: ");
        while ((!scanf("%lf", &l2)) || (!isspace(token=getchar()))) {printf("Invalid value. Enter left border: ");fflush(stdin);}
        fflush(stdin);
        //Right border-integral 2
        printf("\nEnter right border for the second region: ");
        while ((!scanf("%lf", &r2)) || (!isspace(token=getchar())) || r2<l2) {printf("Invalid value. Enter right border: ");fflush(stdin);}
        fflush(stdin);
        //Number of points-integral 1
        printf("\nEnter number of points for the first region: ");
        while ((!scanf("%d", &N1)) || (!isspace(token=getchar())) || N1<0) {printf("Invalid value. Enter number of points: ");fflush(stdin);}
        fflush(stdin);
        //Number of points
        printf("\nEnter number of points for the second region: ");
        while ((!scanf("%d", &N2)) || (!isspace(token=getchar())) || N2<0) {printf("Invalid value. Enter number of points: ");fflush(stdin);}
        fflush(stdin);
        //Estimated error
        printf("\nEnter estimated error value: ");
        while ((!scanf("%lf", &err)) || (!isspace(token=getchar()))) {printf("Invalid value. Enter estimated error value: ");fflush(stdin);}
        fflush(stdin);
    }


    //----------CALCULATIONS & OUTPUT---------
    for(i=1;i<25;i++) printf("+");
    printf("\nResults:\n");
    for(i=1;i<25;i++) printf("+");

    printf("\n::Right rectangles formula::\n--------------------------\n");
    res1=calc_rect(r1,l1,N1);
    res2=calc_rect(r2,l2,N2);
    printf("Region I: %lf; Region II: %lf; Sum: %lf\n\n", res1,res2,res1+res2);
    printf("::Runge method::\n--------------------------\n");
    res1=calc_runge(r1,l1,err);
    printf(" points for region I; ");
    res2=calc_runge(r2,l2,err);
    printf(" points for region II\n");
    printf("Region I: %lf; Region II: %lf; Sum: %lf\n\n", res1,res2,res1+res2);
    printf("\nPress return to exit...");
    getchar();
    return 0;
}

//Our function
double f(double x){

    double f;

    f=sin(x);
    return f;
}

//Right rectangles formula
double calc_rect(double r, double l, int N){

    double res=0, mul;
    int i;

    mul=(r-l)/N;
    for(i=1; i<=N; i++) res+=mul*f(l+mul*i);
    return res;
}

//Runge method
double calc_runge(double r, double l, double err){

    double res;
    int N=2;

    while(fabs(calc_rect(r,l,N)-calc_rect(r,l,N*2))>err) N*=2;
    N*=2;
    printf("%d", N);
    return calc_rect(r,l,N);
}