124 lines
4.0 KiB
C#
124 lines
4.0 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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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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/// <summary>
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/// calculate the value of x^y
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/// </summary>
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/// <param name="x"></param>
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/// <param name="y"></param>
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/// <returns>Returns the value of x^y</returns>
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public static unsafe float Pow(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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{
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return 1;
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}
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if ((x == 1) && (y == 0))
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{
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return float.PositiveInfinity;
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}
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if ((x == 0) && (y != 0))
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{
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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 * (
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1.0f + (z * (
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0.5f + (z * (
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0.1666666667f + (z * (
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0.0416666666667f + (z *
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8.333333333e-3f)))))))));
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}
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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)
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+ 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 * (
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2.718281828f + (n * (
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1.359140914f + (n * (
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0.4530469714f + (n * (
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0.1132617429f + (n *
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0.02265234857f)))))))));
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for (int i = 0; i < m; i++)
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{
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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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{
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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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