How does C compute sin() and other math functions?

For sin specifically, using Taylor expansion would give you:

sin(x) := x - x^3/3! + x^5/5! - x^7/7! + ... (1)

you would keep adding terms until either the difference between them is lower than an accepted tolerance level or just for a finite amount of steps (faster, but less precise). An example would be something like:

float sin(float x)

{

  float res=0, pow=x, fact=1;

  for(int i=0; i<5; ++i)

  {

    res+=pow/fact;

    pow=-1*x*x;

    fact*=(2*(i+1))*(2*(i+1)+1);

  }



  return res;

}

Note: (1) works because of the aproximation sin(x)=x for small angles. For bigger angles you need to calculate more and more terms to get acceptable results. You can use a while argument and continue for a certain accuracy:

double sin (double x){

    int i = 1;

    double cur = x;

    double acc = 1;

    double fact= 1;

    double pow = x;

    while (fabs(acc) > .00000001 &&   i < 100){

        fact *= ((2*i)*(2*i+1));

        pow *= -1 * xx; 

        acc =  pow / fact;

        cur += acc;

        i++;

    }

    return cur;



}

3 years ago

Yes, there are software algorithms for calculating sin too. Basically, calculating these kind of stuff with a digital computer is usually done using numerical methods like approximating the Taylor series representing the function.

Numerical methods can approximate functions to an arbitrary amount of accuracy and since the amount of accuracy you have in a floating number is finite, they suit these tasks pretty well.

3 years ago

For sin specifically, using Taylor expansion would give you:

sin(x) := x - x^3/3! + x^5/5! - x^7/7! + ... (1)

you would keep adding terms until either the difference between them is lower than an accepted tolerance level or just for a finite amount of steps (faster, but less precise). An example would be something like:

float sin(float x)

{

  float res=0, pow=x, fact=1;

  for(int i=0; i<5; ++i)

  {

    res+=pow/fact;

    pow=-1*x*x;

    fact*=(2*(i+1))*(2*(i+1)+1);

  }



  return res;

}

Note: (1) works because of the aproximation sin(x)=x for small angles. For bigger angles you need to calculate more and more terms to get acceptable results. You can use a while argument and continue for a certain accuracy:

double sin (double x){

    int i = 1;

    double cur = x;

    double acc = 1;

    double fact= 1;

    double pow = x;

    while (fabs(acc) > .00000001 &&   i < 100){

        fact *= ((2*i)*(2*i+1));

        pow *= -1 * xx; 

        acc =  pow / fact;

        cur += acc;

        i++;

    }

    return cur;

}

3 years ago