c-o

2024-06-10 15:12:08 +08:00
parent f6963b8e00
commit be6c2e6b92
305 changed files with 28336 additions and 5938 deletions
@@ -0,0 +1,123 @@
+//-----------------------------------------------------------------------
+//-----------------------------------------------------------------------
+//     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.
+//     
+//-----------------------------------------------------------------------
+//-----------------------------------------------------------------------
+namespace StgSharp.Math
+{
+    public static unsafe partial class Scaler
+    {
+
+        /// <summary>
+        /// calculate the value of x^y
+        /// </summary>
+        /// <param name="x"></param>
+        /// <param name="y"></param>
+        /// <returns>Returns the value of x^y</returns>
+        public static unsafe float Pow(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;
+        }
+
+    }
+}