workshop 4

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

double myExp(double x, int n); // calculate exp(x) with n
double myExp(double x, double epsi); // calculate exp(x) with epsilon
double myPi(double epsi); // calculate exp(x) with epsilon
double factorial(int a); // calculate factorial of a
double mySin(double x, double epsi); // calculate sin(x) with epsilon
double myCos(double x, double epsi); // calculate cos(x) with epsilon

int main() {
    double x, epsi;
    int n;
    char ch, ch1, ch2;
    // epsi = 0.00001; n = 1000;

    /* input & check validation*/
    while (1)
    {
        printf("Enter x, epsi, n: ");
        fflush(stdin);
        scanf("%lf%c%lf%c%d%c", &x, &ch, &epsi, &ch1, &n, &ch2);
        if (ch == ' ' && ch1 == ' ' && ch2 == '\n') {
            break;
        }
        else {
            printf("Invalid input, please re-enter!\n");
        }
    }

    /*Q1*/
    printf("\nQ1:\n\n");
    printf("   myExp(%.1lf, %d) = %lf\n", x, n, myExp(x,n));
    printf("   myExp(%.1lf, %lf) = %lf\n", x, epsi, myExp(x,epsi));
    printf("   exp(%.1lf) = %lf\n", x, exp(x));

    /*Q2*/
    printf("\n--------------------------------------------------------\nQ2:\n\n");
    printf("   myPi(%lf) = %lf\n", epsi, myPi(epsi));

    /*Q3*/
    printf("\n--------------------------------------------------------\nQ3:\n\n");
    printf("   mySin(%.1lf, %lf) = %lf\n",x, epsi, mySin(x,epsi));
    printf("   sin(%.1lf) = %lf\n", x, sin(x));

    /*Q4*/
    printf("\n--------------------------------------------------------\nQ4:\n\n");
    printf("   myCos(%.1lf, %lf) = %lf\n",x, epsi, myCos(x,epsi));
    printf("   cos(%.1lf) = %lf\n", x, cos(x));

    return(0);
}

double myExp(double x, int n) { // calculate exp(x) with n
    double S, a;

    S = 1; a = 1;
    for (int i = 1; i<= n; i++) {
        a *= (x/i);
        S += a;
    }

    return (S);
}

double myExp(double x, double epsi) { // calculate exp(x) with epsilon
    double S, a; int n;

    S = 1; a = 1; n = 1;
    while (epsi < fabs(a)) {
        a *= (x/(n));
        S += a;
        n++;
    }

    return (S);
}

double myPi(double epsi) { // calculate Pi with epsilon
    double S, pi, a; int n;

    S = 0; n = 0;
    do {
        a = pow(-1,n) / (2*n+1);
        S += a;
        n++;
    } while (epsi < fabs(a));
    S *= 4;

    return (S);
}

double factorial(int a) { // calculate factorial of a
    double f = 1;

    if (a == 0) {
        return (1);
    }
    else {
        for (int i = 1; i<=a; i++) {
            f *= i;
        }
        return (f);
    }
}

double mySin(double x, double epsi) { // calculate sin(x) with epsilon
    double si, a; int n;

    si = 0; n = 0;
    do {
        a = pow(-1,n) * pow(x,2*n+1) / factorial(2*n+1);
        si += a;
        n++;
    } while (epsi < fabs(a));

    return (si);
}

double myCos(double x, double epsi) { // calculate cos(x) with epsilon
    double co, a; int n;

    co = 0; n = 0;
    do {
        a = pow(-1,n) * pow(x,2*n) / factorial(2*n);
        co += a;
        n++;
    } while (epsi < fabs(a));

    return (co);
}