Ln(x) and Sqrtaï(x) function added

2023-01-23 20:38:57 +08:00
parent c14b7ae7f8
commit 4c5dfb4828
39 changed files with 254 additions and 40 deletions
@@ -5,7 +5,7 @@ VisualStudioVersion = 17.3.32825.248
 MinimumVisualStudioVersion = 10.0.40219.1
 Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "StgSharp", "StgSharp\StgSharp.csproj", "{EEC1D075-F8F4-43EA-914A-02B1339D2305}"
 EndProject
-Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "StgSharpDebug", "StgSharpDebug\StgSharpDebug.csproj", "{467F2A1A-D7E2-4904-AAAD-A5998EE45C71}"
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "StgSharpDebug", "StgSharpDebug\StgSharpDebug.csproj", "{467F2A1A-D7E2-4904-AAAD-A5998EE45C71}"
 EndProject
 Global
 	GlobalSection(SolutionConfigurationPlatforms) = preSolution
@@ -1,11 +1,35 @@
 using System;
 using System.Collections.Generic;
+using System.Net.Sockets;
 using System.Text;
+using static System.Net.WebRequestMethods;

 namespace StgSharp
 {
+
+
+
    public static partial class Math
    {
+
+        static private readonly float[] logArray =
+        {
+            0f, 0.00995033085316809f,   0.0198026272961797f,    0.0295588022415444f,    0.0392207131532813f,    0.048790164169432f, 0.0582689081239758f,    0.0676586484738149f,    0.0769610411361284f,    0.0861776962410524f,
+            0.0953101798043249f,    0.104360015324243f, 0.113328685307003f, 0.122217632724249f, 0.131028262406404f, 0.139761942375159f, 0.148420005118273f, 0.157003748809665f, 0.165514438477573f, 0.173953307123438f,
+            0.182321556793955f, 0.19062035960865f,  0.198850858745165f, 0.207014169384326f, 0.215111379616945f, 0.22314355131421f,  0.231111720963387f, 0.2390169004705f,   0.246860077931526f, 0.254642218373581f,
+            0.262364264467491f, 0.27002713721306f,  0.27763173659828f,  0.285178942233662f, 0.29266961396282f,  0.300104592450338f, 0.307484699747961f, 0.314810739840034f, 0.322083499169113f, 0.3293037471426f,
+            0.336472236621213f, 0.343589704390077f, 0.350656871613169f, 0.357674444271816f, 0.364643113587909f, 0.371563556432483f, 0.378436435720245f, 0.385262400790645f, 0.392042087776024f, 0.398776119957368f,
+            0.405465108108164f, 0.412109650826833f, 0.418710334858185f, 0.425267735404344f, 0.431782416425538f, 0.438254930931155f, 0.444685821261446f, 0.451075619360217f, 0.457424847038875f, 0.46373401623214f,
+            0.470003629245736f, 0.476234178996372f, 0.482426149244293f, 0.488580014818671f, 0.494696241836107f, 0.500775287912489f, 0.506817602368452f, 0.512823626428664f, 0.518793793415168f, 0.524728528934982f,
+            0.53062825106217f,  0.536493370514568f, 0.542324290825362f, 0.548121408509688f, 0.553885113226438f, 0.559615787935423f, 0.56531380905006f,  0.570979546585738f, 0.576613364303994f, 0.582215619852664f,
+            0.587786664902119f, 0.593326845277734f, 0.598836501088704f, 0.60431596685333f,  0.609765571620894f, 0.615185639090233f, 0.62057648772511f,  0.625938430866495f, 0.631271776841858f, 0.636576829071551f,
+            0.641853886172395f, 0.647103242058538f, 0.65232518603969f,  0.657520002916794f, 0.662687973075237f, 0.667829372575655f, 0.672944473242426f, 0.678033542749897f, 0.683096844706444f, 0.688134638736401f,
+
+
+
+
+        };
+
        /// <summary>
        /// 
        /// </summary>
@@ -13,9 +37,31 @@ namespace StgSharp
        /// <returns>
        /// Returns the value of ln(x).
        /// </returns>
-        public static float Log(float x)
+        public unsafe static float Log(float x)
        {
-            
+
+            uint input = *(uint*)&x;
+
+            uint f = input;
+            f >>= 23;
+            f -= 127;
+            input <<= 9;
+            input >>= 9;
+            input += 0b_0011_1111_1000_0000_0000_0000_0000_0000;
+            float result = *(float*)&input;
+            int order = (int)(result * 100)-100;
+
+            float cache = (result) / (1f + 0.01f * order) -1 ;
+            result = cache * -0.25f + 0.3333333333333f;
+            result = result * cache - 0.5f;
+            result = result * cache + 1.0f;
+            result *= cache;
+
+            return 
+                f*0.6931471806f + 
+                result + 
+                logArray[order];
        }
+        
    }
 }
@@ -0,0 +1,65 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics.CodeAnalysis;
+using System.Text;
+
+namespace StgSharp
+{
+    public static partial class Math
+    {
+        /*本方法将小数部分统一提升至2^16处后进行线性近似
+         
+        const uint sqmov = 0b_0100_0111_1000_0000_0000_0000_0000_0000;
+        const float sqmov1 = 0.0015947f;
+        const float sqmov2 = 156.7673435f;
+        const float sqmov3 = 261.2776027f;
+        /**/
+        public static unsafe float Sqrt(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1.8倍
+             */
+
+            /*
+             * 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;
+        }
+        
+
+    }
+}
@@ -4,5 +4,14 @@
        <name>StgSharp</name>
    </assembly>
    <members>
+        <member name="M:StgSharp.Math.Log(System.Single)">
+            <summary>
+            
+            </summary>
+            <param name="x"></param>
+            <returns>
+            Returns the value of ln(x).
+            </returns>
+        </member>
    </members>
 </doc>
@@ -1 +1 @@
-ffe0859de4666337fddb22395a629f5b2a7223e3
+9f6c1da9ad577916e70408e10ff0292581a33dcb
@@ -4,5 +4,14 @@
        <name>StgSharp</name>
    </assembly>
    <members>
+        <member name="M:StgSharp.Math.Log(System.Single)">
+            <summary>
+            
+            </summary>
+            <param name="x"></param>
+            <returns>
+            Returns the value of ln(x).
+            </returns>
+        </member>
    </members>
 </doc>
@@ -1,54 +1,78 @@
 using StgSharp;
 using System;
+using System.Diagnostics;

 internal class Program
 {
-    private static void Main(string[] args)
+    private unsafe static void Main(string[] args)
    {
-        Console.WriteLine("Hello, World!");
-        a asd = new a();
-        ase a01 = new ase(asd.cwc);
-        ase a02 = a01;
-        a01 -= asd.cwc;
-        a01 += asd.cwb;
-        a01.Invoke();
-        a02.Invoke();
-
-        a fff = new a();
-        fff._a = 10;
-        a ggg = fff;
-        fff._a = 15;
-        Console.WriteLine(ggg._a);
-
-        Point p = new Point();
-        Point p2 = new Point();
-        ContainerNode<Point> pC = new ContainerNode<Point>(p);
-        ContainerNode<Point> pC02 = new ContainerNode<Point>(p2);
-        pC.Next=pC02;
-
+        /*
+        int cc = 3;
+        Console.WriteLine(cc/2);
+        /**/

+        /*
+        float aa = 261.2776027f;
+        uint bb = *(uint*)&aa;
+        Console.WriteLine(Convert.ToString(bb,toBase:2));
+        Console.WriteLine(StgSharp.Math.Log(3.5f));
+        /**/

        
+        for (int wasd = 0; wasd < 100; wasd++)
+        {
+            float time = 1000000;
+            double a = 114514;
+            System.Diagnostics.Stopwatch stopwatch = new Stopwatch();
+            stopwatch.Start(); //  开始监视代码运行时间
+            for (float i = 2; i < time; i++)
+            {
+                a = StgSharp.Math.Log(i);
+            }
+            stopwatch.Stop(); //  停止监视
+            TimeSpan timespan = stopwatch.Elapsed; //  获取当前实例测量得出的总时间
+            double milliseconds = timespan.TotalMilliseconds;  //  总毫秒数
+            Console.WriteLine($"{milliseconds},{a}");


+            System.Diagnostics.Stopwatch stopwatch1 = new Stopwatch();
+            double b = 114514;
+            double time2 = time;
+            stopwatch1.Start();
+            for (double i = 2; i < time2; i++)
+            {
+                b = System.Math.Log(i);
+            }
+            stopwatch1.Stop();
+            timespan = stopwatch1.Elapsed;
+            double milliseconds2 = timespan.TotalMilliseconds;
+            Console.WriteLine($"{milliseconds2},{b}");
+            Console.WriteLine("");
+        }
+        /**/

+        /*
+        double accuracy = 0;
+        for (float i = 1.001f; i < 4; i += 0.001f)
+        {
+            double r1 = StgSharp.Math.Log(i);
+            double r2 = System.Math.Log(i);
+            double ac = ( System.Math.Max(r1,r2)- System.Math.Min(r1, r2) ) / System.Math.Max(r1, r2);
+            if (ac>accuracy)
+            {
+                accuracy = ac;
+                Console.WriteLine(i);
+                Console.WriteLine(ac);
+                Console.WriteLine(r1);
+                Console.WriteLine(r2);
+                Console.WriteLine("");
+            }
+        }
+        Console.WriteLine(accuracy);
+        /**/
    }

-    public delegate void ase();

    
 }

-class a
-{
-    public int _a;
-
-    public void cwc()
-    {
-        Console.WriteLine("c");
-    }
-    public void cwb()
-    {
-        Console.WriteLine("b");
-    }
-}
@@ -5,6 +5,7 @@
    <TargetFramework>net6.0</TargetFramework>
    <ImplicitUsings>enable</ImplicitUsings>
    <Nullable>enable</Nullable>
+    <AllowUnsafeBlocks>True</AllowUnsafeBlocks>
  </PropertyGroup>

  <ItemGroup>
@@ -4,5 +4,14 @@
        <name>StgSharp</name>
    </assembly>
    <members>
+        <member name="M:StgSharp.Math.Log(System.Single)">
+            <summary>
+            
+            </summary>
+            <param name="x"></param>
+            <returns>
+            Returns the value of ln(x).
+            </returns>
+        </member>
    </members>
 </doc>
@@ -0,0 +1,31 @@
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <PropertyGroup>
+    <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
+    <SchemaVersion>2.0</SchemaVersion>
+    <ProjectGuid>E439935D-B2A2-46AE-856D-2AA408428F33</ProjectGuid>
+    <!--457858db-8f6d-45ae-8571-166818eeb6f7-->
+    <ProjectHome>.</ProjectHome>
+    <StartupFile>
+    </StartupFile>
+    <SearchPath>
+    </SearchPath>
+    <WorkingDirectory>.</WorkingDirectory>
+    <OutputPath>.</OutputPath>
+    <Name>calc</Name>
+    <RootNamespace>calc</RootNamespace>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)' == 'Debug' ">
+    <DebugSymbols>true</DebugSymbols>
+    <EnableUnmanagedDebugging>false</EnableUnmanagedDebugging>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)' == 'Release' ">
+    <DebugSymbols>true</DebugSymbols>
+    <EnableUnmanagedDebugging>false</EnableUnmanagedDebugging>
+  </PropertyGroup>
+  <ItemGroup>
+    <Compile Include="file1.lua">
+      <SubType>Code</SubType>
+    </Compile>
+  </ItemGroup>
+  <Import Project="$(MSBuildToolsPath)\Microsoft.Common.targets" />
+</Project>
@@ -0,0 +1,20 @@
+--region *.lua
+--Date
+--This file is automatically generated by the 【BabeLua】 plugin
+
+ a = 1;
+ b = 0.001;
+ c = 0;
+
+
+
+while a-b > 0.0001*a do
+    c= (a+b)/2
+    b = math.sqrt( a*b )
+    a = c;
+end
+
+
+print(a,b)
+
+--endregion