#include <stdio.h>
#include <math.h>
long double f(long double x)
{
    return cos(x);
}
long double fp1(long double x)
{
    return -sinl(x);
}
long double fp2(long double x)
{
    return -cosl(x);
}
long double power(long double x, int n)
{
    long double mult = 1;
    if (n == 0)
    {
        return 1;
    }
    int i = 0;
    for (i = 1; i <= n; i++)
    {
        mult *= x;
    }
    return mult;
}
void Simple_Iteration(int kmax, long double eps, long double x0, long double *x1,
                      int *k)
{
    long double tau;
    printf("\nMethod simple iteration\n");
    *x1 = x0;
    tau = -1.0 / fp1(x0);
    *k = 0;
    do
    {
        x0 = *x1;
        *x1 = x0 + tau * f(x0);
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x1 - x0) <= eps) && !(fabsl(f(*x1)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x1);
        printf("With iteration %d\n", *k);
    }
}
void Method_Newton(int kmax, long double eps, long double x0, long double *x1, int *k)
{
    printf("\nMethod Newton\n");
    *x1 = x0;
    *k = 0;
    do
    {
        x0 = *x1;
        *x1 = x0 - f(x0) / fp1(x0);
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x1 - x0) <= eps) && !(fabsl(f(*x1)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x1);
        printf("With iteration %d\n", *k);
    }
}
void Method_Chebysheva(int kmax, long double eps, long double x0, long double *x1,
                       int *k)
{
    printf("\nMethod Chebusheva\n");
    *x1 = x0;
    *k = 0;
    do
    {
        x0 = *x1;
        *x1 =
            x0 - f(x0) / fp1(x0) - 0.5 * power(f(x0), 2) * fp2(x0) / power(fp1(x0), 3);
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x1 - x0) <= eps) && !(fabsl(f(*x1)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x1);
        printf("With iteration %d\n", *k);
    }
}
void Method_Hord(int kmax, long double eps, long double x0, long double *x2, int *k)
{
    long double tau, x1;
    printf("\nMethod Hord\n");
    *k = 0;
    tau = -1.0 / fp1(x0);
    x1 = x0 + tau * f(x0);
    *x2 = x1;
    x1 = x0;
    do
    {
        x0 = x1;
        x1 = *x2;
        *x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0));
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x2 - x1) <= eps) && !(fabsl(f(*x2)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x2);
        printf("With iteration %d\n", *k);
    }
}
long double rr(long double x0, long double x1)
{
    long double res = (f(x1) - f(x0)) / (x1 - x0);
    return res;
}
long double delta(long double x1, long double x2, long double root, long double rr1, long double rr2, int ind)
{
    long double res;
    if (ind == 0)
    {
        res = (-((x2 - x1) * rr2 + rr1) + root) / (2 * rr2);
    }
    if (ind == 1)
    {
        res = (-((x2 - x1) * rr2 + rr1) - root) / (2 * rr2);
    }
    return res;
}
void Method_Parabol(int kmax, long double eps, long double x0, long double *x3,
                    int *k)
{
    long double x1, x2, delta0, delta1, delta2, rr1, rr2, root, tau;
    printf("\nMethod parabol\n");
    *k = 0;
    tau = -1.0 / fp1(x0);
    x1 = x0 + tau * f(x0);
    x2 = x1 + tau * f(x1);
    *x3 = x2;
    x2 = x1;
    x1 = x0;
    do
    {
        x0 = x1;
        x1 = x2;
        x2 = *x3;
        rr1 = rr(x1, x2);
        rr2 = (rr(x1, x2) - rr(x0, x1)) / (x2 - x0);
        root = sqrtl(power((x2 - x1) * rr2 + rr1, 2) - 4 * rr2 * f(x2));
        delta1 = delta(x1, x2, root, rr1, rr2, 0);
        delta2 = delta(x1, x2, root, rr1, rr2, 1);
        if (fabsl(delta1) < fabsl(delta2))
        {
            delta0 = delta1;
        }
        else
        {
            delta0 = delta2;
        }
        *x3 = x2 + delta0;
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x3 - x2) <= eps) && !(fabsl(f(*x3)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x3);
        printf("With iteration %d\n", *k);
    }
}
void Method_Reverse_Interpolation(int kmax, long double eps, long double x0, long double *x2, int *k)
{
    printf("\nMethod_reverse_interpolation\n");
    long double x1, tau;
    *k = 0;
    tau = -1.0 / fp1(x0);
    x1 = x0 + tau * f(x0);
    *x2 = x1;
    x1 = x0;
    do
    {
        x0 = x1;
        x1 = *x2;
        *x2 = -x0 * f(x1) / (f(x0) - f(x1)) - x1 * f(x0) / (f(x1) - f(x0));
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x2 - x1) <= eps) && !(fabsl(f(*x2)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x2);
        printf("With iteration %d\n", *k);
    }
}
void Method_Eitkena(int kmax, long double eps, long double x0, long double *x3,
                    int *k)
{
    printf("\nMethod Eitkena\n");
    long double x2, x1, tau;
    tau = -1.0 / fp1(x0);
    *x3 = x0;
    *k = 0;
    do
    {
        x0 = *x3;
        x1 = x0 + tau * f(x0);
        x2 = x1 + tau * f(x1);
        *x3 = x2 + power(x2 - x1, 2) / (2 * x1 - x2 - x0);
        *k += 1;
        if (*k > kmax)
        {
            break;
        }
    } while (!(fabsl(*x3 - x2) <= eps) && !(fabsl(f(*x3)) <= eps));
    if (*k > kmax)
    {
        printf("Solution not found\n");
    }
    else
    {
        printf("Solution = %Le\n", *x3);
        printf("With iteration %d\n", *k);
    }
}
int main()
{
    FILE *output = fopen("result.txt", "w");
    long double x0, x1, x2, x3;
    long double eps = 1e-10;
    int k;
    int k_max = 1e+4;
    x0 = 5;
    Simple_Iteration(k_max, eps, x0, &x1, &k);
    fprintf(output, "\nSimple_Iteration\n");
    fprintf(output, "Solution = %Le\n", x1);
    fprintf(output, "With iteration %d\n", k);
    Method_Newton(k_max, eps, x0, &x1, &k);
    fprintf(output, "\nMethod_Newton\n");
    fprintf(output, "Solution = %Le\n", x1);
    fprintf(output, "With iteration %d\n", k);
    Method_Chebysheva(k_max, eps, x0, &x1, &k);
    fprintf(output, "\nMethod_Chebysheva\n");
    fprintf(output, "Solution = %Le\n", x1);
    fprintf(output, "With iteration %d\n", k);
    Method_Hord(k_max, eps, x0, &x2, &k);
    fprintf(output, "\nMethod_Hord\n");
    fprintf(output, "Solution = %Le\n", x2);
    fprintf(output, "With iteration %d\n", k);
    Method_Parabol(k_max, eps, x0, &x3, &k);
    fprintf(output, "\nMethod_Parabol\n");
    fprintf(output, "Solution = %Le\n", x3);
    fprintf(output, "With iteration %d\n", k);
    Method_Reverse_Interpolation(k_max, eps, x0, &x2, &k);
    fprintf(output, "\nMethod_Reverse_Interpolation\n");
    fprintf(output, "Solution = %Le\n", x2);
    fprintf(output, "With iteration %d\n", k);
    Method_Eitkena(k_max, eps, x0, &x3, &k);
    fprintf(output, "\nMethod_Eitkena\n");
    fprintf(output, "Solution = %Le\n", x3);
    fprintf(output, "With iteration %d\n", k);
    return 0;
}