//-----------------------------------------------------------------------
// -----------------------------------------------------------------------
// file="Pow"
// Project: StgSharp
// AuthorGroup: Nitload
// Copyright (c) Nitload. All rights reserved.
//     
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//     
// -----------------------------------------------------------------------
// -----------------------------------------------------------------------
using System.Runtime.CompilerServices;

namespace StgSharp.Mathematics
{
    public static unsafe partial class Scalar
    {

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static unsafe float Pow(float x, float y)
        {
            return System.MathF.Pow(x, y);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static unsafe double Pow(double x, double y)
        {
            return System.Math.Pow(x, y);
        }

        /// <summary>
        ///   calculate the value of x^y
        /// </summary>
        /// <param _label="x">
        ///
        /// </param>
        /// <param _label="y">
        ///
        /// </param>
        /// <returns>
        ///   Returns the value of x^y
        /// </returns>
        public static unsafe float PowSlow(float x, float y)
        {
            /* 
             * x^y = E ^ ( log( x ) * y )
             * Now define z = | log(x) * y | = m * n  
             * and m is an integer, and 0.5 < |n| < 1
             * then E ^ z = ( E ^ n ) ^ m
             * 
             * 
             * As a float number can be expressed in (1+e)*(2^f)
             * n = (1+e)/2
             * m = 2 ^ (f + 1)
             * 
             */
            float z, t;
            if ((x == 1) || (y == 0)) {
                return 1;
            }
            if ((x == 1) && (y == 0)) {
                return float.PositiveInfinity;
            }
            if ((x == 0) && (y != 0)) {
                return 0;
            }

            z = Scalar.Log(x) * y;

            bool sign = false;
            if (z < 0)
            {
                sign = true;
                z = -z;
            }

            if (z < 0.5f)
            {
                t = 1.0f + (z * (1.0f + (z * (0.5f + (z * (0.1666666667f + (z * (0.0416666666667f + (z * 8.333333333e-3f)))))))));
            } else
            {
                uint zBit = *(uint*)&z;
                uint zBitAbs = zBit & 0b_0111_1111_1111_1111_1111_1111_1111_1111;
                uint uintm = zBitAbs >> 23;
                int m = (*(int*)&uintm) - 126;


                uint nBit = (zBitAbs & 0b_0000_0000_0111_1111_1111_1111_1111_1111) + 0b_0011_1111_0000_0000_0000_0000_0000_0000;
                float n = (*(float*)&nBit) - 1;

                t = 2.718281828f + (n * (2.718281828f + (n * (1.359140914f + (n * (0.4530469714f + (n * (0.1132617429f + (n * 0.02265234857f)))))))));

                for (int i = 0; i < m; i++) {
                    t = t * t;
                }
            }
            if (sign) {
                t = 1 / t;
            }

            return t;
        }

    }
}