Step by Step solution about How to resolve the algorithm Exponentiation operator step by step in the C++ programming language

The provided C++ code implements the power function using a technique called iterative binary exponentiation. This technique is often used to efficiently compute the power of a number by reducing the number of multiplications required.

Here's how the code works:

1. Template Declaration: The code starts with a template declaration, which allows the power function to be used with different numeric data types (e.g., integers, floating-point numbers). The template parameter Number represents the numerical type that will be used.

2. Initialization: The function initializes several variables:

   • zerodir: This variable determines whether the base is being raised to a positive or negative exponent. It is set to 1 for negative exponents and -1 for positive exponents.
   • factor: This variable stores the base raised to the power of 1. It is set to 1/base for negative exponents and base for positive exponents.
   • result: This variable stores the result of the power operation. It is initialized to 1.

3. Loop for Exponentiation: The code enters a loop that continues as long as the exponent is not equal to 0. Inside the loop:

   • If the exponent is odd (i.e., exponent % 2 != 0), the result is multiplied by the factor. The exponent is then incremented or decremented by zerodir, depending on whether the exponent is positive or negative.
   • If the exponent is even (i.e., exponent % 2 == 0), the factor is squared (i.e., multiplied by itself). The exponent is then divided by 2.

4. Returning the Result: After the loop completes, the function returns the value of result, which contains the computed power of the base.

5. Usage: You can use the power function by passing the base and exponent as arguments. For example, to compute 2 raised to the power of 10, you could call power<int>(2, 10).

In summary, this code provides an efficient implementation of the power function using iterative binary exponentiation, which reduces the number of multiplications required to compute the result.

template<typename Number>
 Number power(Number base, int exponent)
{
  int zerodir;
  Number factor;
  if (exponent < 0)
  {
    zerodir = 1;
    factor = Number(1)/base;
  }
  else
  {
    zerodir = -1;
    factor = base;
  }

  Number result(1);
  while (exponent != 0)
  {
    if (exponent % 2 != 0)
    {
      result *= factor;
      exponent += zerodir;
    }
    else
    {
      factor *= factor;
      exponent /= 2;
    }
  }
  return result;
}