/**
 * expt.c
 *   Code for efficient exponentiation.
 */

// +---------+-------------------------------------------------------
// | Headers |
// +---------+

#include "expt.h"

// +---------------+-------------------------------------------------
// | Local Helpers |
// +---------------+

/**
 * Compute x^n for non-negative n.
 */
double
exptkernel (double x, int n)
{
  if (0 == n)
    {
      return 1.0;
    }
  else if (0 == (n % 2))
    {
      return exptkernel (x*x, n/2);
    }
  else
    {
      return x * exptkernel (x*x, (n-1)/2);
    }
} // exptkernel

/**
 * Compute x^n for non-negative n
 */
double
expt2kernel (double X, int N)
{
  double result = 1.0;
  double x = X;
  double n = N;

  // Invariant: result * x^n = X^N
  while (n > 0)
    {
      if (0 == (n % 2))
        {
          x = x*2;
          n = n/2;
        }
      else
        {
          result = result*x;
          n = n-1;
        }
    } // while
  return result;
} // expt2kernel

// +--------------------+--------------------------------------------
// | Exported Functions |
// +--------------------+

double
exptd (double x, int n)
{
  if (n < 0)
    {
      return 1.0 / exptkernel (x, -n);
    }
  else
    {
      return exptkernel (x, n);
    }
} // exptd

double
expt2 (double x, int n)
{
  if (n < 0)
    {
      return 1.0 / expt2kernel (x, -n);
    }
  else
    {
      return expt2kernel (x, n);
    }
} // expt2