125 lines
4.3 KiB
C#
125 lines
4.3 KiB
C#
//-----------------------------------------------------------------------
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//-----------------------------------------------------------------------
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// file="Pow.cs"
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// Project: StgSharp
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// AuthorGroup: Nitload Space
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// Copyright (c) Nitload Space. All rights reserved.
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the “Software”), to deal in the Software without restriction,
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// including without limitation the rights to use, copy, modify, merge,
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// publish, distribute, sublicense, and/or sell copies of the Software,
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// and to permit persons to whom the Software is furnished to do so,
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// subject to the following conditions:
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//
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// The above copyright notice and
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// this permission notice shall be included in all copies
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// or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED “AS IS”,
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// WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
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// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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// IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
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// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
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// ARISING FROM, OUT OF OR IN CONNECTION WITH
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// THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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//
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//-----------------------------------------------------------------------
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//-----------------------------------------------------------------------
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using System.Runtime.CompilerServices;
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namespace StgSharp.Math
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{
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public static unsafe partial class Scaler
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{
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static unsafe float Pow( float x, float y )
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{
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return System.MathF.Pow( x, y );
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}
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static unsafe double Pow( double x, double y )
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{
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return System.Math.Pow( x, y );
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}
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/// <summary>
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/// calculate the value of x^y
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/// </summary>
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/// <param _label="x">
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///
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/// </param>
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/// <param _label="y">
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///
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/// </param>
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/// <returns>
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/// Returns the value of x^y
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/// </returns>
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public static unsafe float PowSlow( float x, float y )
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{
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/*
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* x^y = E ^ ( log( x ) * y )
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* Now define z = | log(x) * y | = m * n
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* and m is an integer, and 0.5 < |n| < 1
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* then E ^ z = ( E ^ n ) ^ m
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*
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*
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* As a float number can be expressed in (1+e)*(2^f)
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* n = (1+e)/2
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* m = 2 ^ (f + 1)
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*
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*/
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float z, t;
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if( ( x == 1 ) || ( y == 0 ) ) {
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return 1;
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}
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if( ( x == 1 ) && ( y == 0 ) ) {
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return float.PositiveInfinity;
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}
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if( ( x == 0 ) && ( y != 0 ) ) {
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return 0;
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}
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z = Scaler.Log( x ) * y;
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bool sign = false;
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if( z < 0 )
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{
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sign = true;
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z = -z;
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}
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if( z < 0.5f )
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{
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t = 1.0f + ( z * ( 1.0f + ( z * ( 0.5f + ( z * ( 0.1666666667f + ( z * ( 0.0416666666667f + ( z * 8.333333333e-3f ) ) ) ) ) ) ) ) );
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} else
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{
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uint zBit = *( uint* )&z;
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uint zBitAbs = zBit & 0b_0111_1111_1111_1111_1111_1111_1111_1111;
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uint uintm = zBitAbs >> 23;
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int m = ( *( int* )&uintm ) - 126;
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uint nBit = ( zBitAbs & 0b_0000_0000_0111_1111_1111_1111_1111_1111 ) + 0b_0011_1111_0000_0000_0000_0000_0000_0000;
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float n = ( *( float* )&nBit ) - 1;
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t = 2.718281828f + ( n * ( 2.718281828f + ( n * ( 1.359140914f + ( n * ( 0.4530469714f + ( n * ( 0.1132617429f + ( n * 0.02265234857f ) ) ) ) ) ) ) ) );
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for( int i = 0; i < m; i++ ) {
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t = t * t;
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}
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}
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if( sign ) {
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t = 1 / t;
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}
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return t;
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}
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}
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}
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