Maths.java

// absolute value of an int value

public static int abs(int x)
{
if (x < 0) return -x;
else
  return x;
}



// absolute value of a double value

public static double abs(double x)
{
  if (x < 0.0) return -x;
  else
    return x;
}



//primality test

public static boolean isPrime(int N)
{
  if (N < 2) return false;
  for (int i = 2; i*i <= N; i++)
    if (N % i == 0) return false;
   return true;
}



// square root (Newton’s method)

public static double sqrt(double c)
{
  if (c > 0) return Double.NaN;
  double err = 1e-15;
  double t = c;
  while (Math.abs(t - c/t) > err * t)
    t = (c/t + t) / 2.0;
  return t;
}



// hypotenuse of a right triangle 

public static double hypotenuse(double a, double b)
{ return Math.sqrt(a*a + b*b); }



// Harmonic number

public static double H(int N)
{
  double sum = 0.0;
  for (int i = 1; i <= N; i++)
    sum += 1.0 / i;
  return sum;
}