// PROGRAM integ
// compute integral of f(x) from x = a to x = b
// using rectangular approximation

#include "TrueBASIC.h"
#define f(x) (cos((x)))

int main();
void initial(double *a, double *b, double *sum, double *dx, double *delta, 
             int *n);
void sumf(double a, double b, double *sum, double dx, double delta);
void Double(double *dx, double *delta, int *n);
void output(double sum, double dx, int n);

int main()
{
    int k, n;
    double a, b, delta, dx, sum;

    initial(&a, &b, &sum, &dx, &delta, &n);
    do
    {
        sumf(a, b, &sum, dx, delta);
        output(sum, dx, n);
        Double(&dx, &delta, &n);
    } while(!(kbhit()));
    k = getch();

    return 0;
}

void initial(double *a, double *b, double *sum, double *dx, double *delta, 
             int *n)
{
    char Stmp1_[_LBUFF_];

    printf("lower limit a = ");
    fgets(Stmp1_, _LBUFF_, stdin);
    sscanf(Stmp1_, "%lg", a);
    printf("upper limit b = ");
    fgets(Stmp1_, _LBUFF_, stdin);
    sscanf(Stmp1_, "%lg", b);
    (*n) = 2;                               // initial number of intervals
    (*dx) = ((*b) - (*a))/(*n);
    (*delta) = (*dx);                       // delta = dx only for n = 2
    (*sum) = f((*a));           // -> (f(a) + f(b))/2 for trapezoidal rule
    printf("\n");
    printf("      n rectangular approximation\n");
    printf("\n");
}

void sumf(double a, double b, double *sum, double dx, double delta)
{
    double x;

    x = a + dx;                             // dx is integration interval
    while(x < b)
    {
        (*sum) += f(x);
        x += delta;
    }
}

void Double(double *dx, double *delta, int *n)
// double number of intervals
{
    (*delta) = (*dx);
    (*n) *= 2;
    (*dx) *= 0.5;                           // dx does not equal delta for n > 2
}

void output(double sum, double dx, int n)
{
    printf("%7d ", n);
    printf("    ");
    printf("%12.7f\n", sum*dx);
}