Exponentiation.cs

namespace Advanced.Algorithms.Numerical;

/// <summary>
///     A fast exponentiation algorithm implementation.
/// </summary>
public class FastExponentiation
{
    /// <summary>
    ///     Computes exponentiation using squaring.
    /// </summary>
    public static int BySquaring(int @base, int power)
    {
        while (true)
        {
            //using the algebraic result
            //a^-n  = (1/a)^n
            if (power < 0)
            {
                @base = 1 / @base;
                power = -power;
                continue;
            }

            switch (power)
            {
                case 0:
                    return 1;
                case 1:
                    return @base;
                default:
                    if (power % 2 == 0)
                    {
                        @base = @base * @base;
                        power = power / 2;
                        continue;
                    }
                    //power is odd
                    else
                    {
                        return @base * BySquaring(@base * @base, (power - 1) / 2);
                    }
            }
        }
    }
}