lab1.cpp

#include <math.h>
#include <iostream>

using namespace std;

struct result {
    int n;
    double abs, rn;
};

result func(double x, double eps) {
    int m = 1, k = 2;

    while (x > k) {
        k = k * 2;
        m++;
    }

    double z = x / k;
    double a = (1 - z) / (1 + z);
    double ln, sum_ln = 0;
    double e4 = eps * 4;
    int n = 0;
    for (int i = 1; i != 0; i++) {
        ln = (pow(a, (2 * i - 1)) / (2 * i - 1));
        sum_ln += ln;
        if (ln < e4) {
            n = i;
            break;
        }
    }
    double rn = ln / 4;

    return { n, abs(log(x) - (m * log(2) - 2 * sum_ln - rn)), rn };
};

result func2(double xi, int n) {
    int m = 1, k = 2;
    while (xi > k) {
        k = k * 2;
        m++;
    }
    double z = xi / k;
    double a = (1 - z) / (1 + z);
    double ln, lk = 0;
    for (int i = 1; i <= n; i++) {
        ln = (pow(a, (2 * i - 1)) / (2 * i - 1));
        lk += ln;
    }

    double rn = ln / 4;

    return { n, abs(log(xi) - (m * log(2) - 2 * lk - rn)), rn };

}

int main() {
    double a = 0.1;
    double b = 15;
    double x = (a + b) * 0.5;

    cout << "_____________________________________" << endl;
    cout << "| eps  | n | Abs error |  Rem term  |" << endl;
    double eps = 1e-2;
    for (int i = 0; i < 5; i++) {
        result res = func(x, eps);

        cout << "| " << eps << " | " << res.n << " | " << res.abs << " | " << res.rn << " |" << endl;

        eps *= 1e-3;
    }

    int n = func(x, 1e-8).n;

    double h = (b - a) / 10;
    cout << "_____________________________________" << endl;
    cout << "| xi | Abs. error | Rem term |" << endl;
    for (int i = 0; i <= 10; i++) {
        double xi = a + h * i;
        result res = func2(xi, n);
        cout << "| " << xi << " | " << res.abs << " | " << res.rn << " |" << endl;
    }
}