Increase Accuracy of Sine/Sin function

[skondgekar]

I have Written a code for sine function but it is not much accurate

I have written a code for PI() and sin() function but it is not much accurate I want to make it more accurate can anybody tell how can I make it more accurate.
Also I dont want to use constant value of pi. I want to find it out using function to the highest accuracy.
Following is the code

#include <iostream>
#include <string>
using namespace std;


double factorial (int a);
double power (double b, int power);

double MySin(double c, int Accuracy = 100);

double MyPi(double accuracy = 50);


int main (void){


//Comment Out below code for testing factorial function
    //  int MyNumber;
    //cout << "Enter the number for which you want factorial to find out?\n";
    //cin >> MyNumber;
    //cout << "Factorial of " << MyNumber << " is " << factorial(MyNumber) << endl;
    //
    //
    //getchar();

//Comment out below code for testing power function
    //double MyNumber;
    //int NumPower;
    //cout << "Enter the number" << endl;
    //cin >> MyNumber;
    //cout << "\nEnter the power" << endl;
    //cin >> NumPower;

    //cout << power(MyNumber,NumPower);


//Comment out below code for testing Sine function
    //cout << MySin(30,1000);


//Comment out below code for testing value of pi
    //cout << MyPi(100000) << "End of line";


}


double MyPi(double accuracy){
double result = 0;
for (double index = 1+accuracy*2; index >= 3; index-=2){

    result = 2+power(index,2)/result;
}

return 4/(1+(1/result));

}

double MySin(double c, int Accuracy){
    c=c*MyPi(1000)/180;
    double result = c;
    int Minus = -1;
    for (int index = 3; index < Accuracy; index+=2 ){
        result = result + Minus * power(c,index)/factorial(index);
        Minus*=-1;  
    }
    return result;

}

double power (double b, int power){
    double result = 1;

    while (power>0){
        result *= b;
        power--;
    }
    return result;

}

double factorial (int a){
    double result;

    if(a==1){
        return 1;
    }else{

        result = a * factorial(a-1);

    }
    return result;

}

[skondgekar]

If I add calculation levels then the calculation steps becomes long and program crashes. Need to know how to do it accurately.

[mike_2000_17]

If you want better precision, you have to care about round-off error accumulation and amplification factors. Generally, things like subtracting numbers that are very close, or dividing number of wildly different magnitudes tend to make the round-off errors blow out of proportion. So, you can't really apply the mathematical formula verbatim and expect good precision all the time, you have to modify it to avoid ill-conditioned operations. I think that this sin function should work a bit better:

double MySin(double c /* in radians */, int Accuracy) {
    // you should clamp the c value within the first period around 0:
    static double pi = MyPi(1000);
    while(c > pi) c -= 2 * pi;
    while(c < -pi) c += 2 * pi;

    double result = c;
    int Minus = -1;
    double c_term = c;
    double c_sqr = c * c;
    for (int index = 3; index < Accuracy; index+=2 ) {
        c_term *= c_sqr / (index * (index - 1));
        result += Minus * c_term;
        Minus *= -1;  
    }
    return result;
}

And, of course, using the type double, you should never expect precision beyond 15 significant digits. For any precision higher than that, you will need to use a library for infinite-precision (variable-length) real number representations.