c-o

2024-06-10 15:12:08 +08:00
parent f6963b8e00
commit be6c2e6b92
305 changed files with 28336 additions and 5938 deletions
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+//-----------------------------------------------------------------------
+//-----------------------------------------------------------------------
+//     file="Sqrt.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;
+using System.Runtime.CompilerServices;
+
+namespace StgSharp.Math
+{
+    public static partial class Scaler
+    {
+
+        public static unsafe float SeedSqrt(float x)
+        {
+            /*
+             * 本方法采用分别对指数和小数处理的方法计算平方根
+             * 将指数除以2即可获得结果的指数
+             * （补充：指数最低位被加到小数位中以抵消一个多余的2 ^ 1的影响）
+             * 小数部分则统一乘以2 ^ 16后由y = Sqrt(x)在1.5 * 2 ^ 16处的切线近似
+             * 为简化操作，提高计算速度，切线左界被移动到远点
+             * 在进一步简化操作后，计算精度达到0.5%，速度约为.Net库函数的3倍
+             */
+
+            if (x < 0)
+            {
+                throw new ArgumentOutOfRangeException("Input is smaller than zero!");
+            }
+            if (x == 0)
+            {
+                return 0;
+            }
+            /*
+            * 提取指数位并减半
+            * 由于平方根仅对正数有效
+            * 故不考虑正负号
+            */
+
+            if (x < 0)
+            {
+                throw new ArgumentOutOfRangeException();
+            }
+            if (x <= 1e-12)
+            {
+                return 0;
+            }
+
+            //提取指数位并减去指数位中的127
+            //由于平方根仅对正数有效
+            //故不考虑正负号
+            uint a = *(uint*)&x;
+            uint f = a;
+            f >>= 23;
+            f /= 2;
+            f += 64;
+
+            //提取小数位
+            //由于平方根仅对正数有效
+            //故不考虑正负号
+
+            a -= 0b_0011_1111_0000_0000_0000_0000_0000_0000;
+            uint e = a << 8;
+            e >>= 8;
+
+            //线性近似
+            e *= 0b_1101_0001;
+            e >>= 24;
+            e += 0b_0000_0000_0001_0000_1010_1000_1110_0010;
+
+            //还原指数
+            f <<= 23;
+            e += f;
+
+            float result = *(float*)&e;
+            result = (result + (x / result)) / 2;
+            return (result + (x / result)) / 2;
+        }
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Sqrt(float x)
+        {
+            return MathF.Sqrt(x);
+            /**/
+        }
+
+    }
+}