//-----------------------------------------------------------------------
//-----------------------------------------------------------------------
//     file="Pow.cs"
//     Project: StgSharp
//     AuthorGroup: Nitload Space
//     Copyright (c) Nitload Space. 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.Math
{
    public static unsafe partial class Scaler
    {

        [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 = Scaler.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;
        }

    }
}