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Add "cancellation of significant digits" example
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7 files changed

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‎NumericalCalculation/BasicWithCSharp/BasicWithCSharp.sln‎

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@@ -7,6 +7,8 @@ Project("{8BB2217D-0F2D-49D1-97BC-3654ED321F3B}") = "MachineEpsilon", "MachineEp
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EndProject
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Project("{8BB2217D-0F2D-49D1-97BC-3654ED321F3B}") = "LossOfTrailingDigits", "LossOfTrailingDigits\LossOfTrailingDigits.xproj", "{528DBCCD-69CC-4599-B0F6-3CF203FC098A}"
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EndProject
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Project("{8BB2217D-0F2D-49D1-97BC-3654ED321F3B}") = "CancellationOfSignificantDigits", "CancellationOfSignificantDigits\CancellationOfSignificantDigits.xproj", "{29AECCDE-8736-4B28-A0E3-5B3F36751283}"
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
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Debug|Any CPU = Debug|Any CPU
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{528DBCCD-69CC-4599-B0F6-3CF203FC098A}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{528DBCCD-69CC-4599-B0F6-3CF203FC098A}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{528DBCCD-69CC-4599-B0F6-3CF203FC098A}.Release|Any CPU.Build.0 = Release|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Release|Any CPU.Build.0 = Release|Any CPU
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EndGlobalSection
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GlobalSection(SolutionProperties) = preSolution
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HideSolutionNode = FALSE

‎NumericalCalculation/BasicWithCSharp/CancellationOfSignificantDigits/CancellationOfSignificantDigits.cs‎

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using System;
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namespace CancellationOfSignificantDigits
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{
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public class CancellationOfSignificantDigits
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{
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public static void Main(string[] args)
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{
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CheckCancellation();
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}
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static Tuple<float, float> NormalSolver(float a, float b, float c)
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{
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float det = (float)Math.Sqrt(b * b - 4 * a * c);
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float x_1 = (-b + det) / 2.0f / a;
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float x_2 = (-b - det) / 2.0f / a;
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return Tuple.Create(x_1, x_2);
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}
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static Tuple<float, float> CaredSolver(float a, float b, float c)
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{
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float det = (float)Math.Sqrt(b * b - 4 * a * c);
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float x_1, x_2;
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if (b > 0)
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{
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x_2 = (-b - det) / 2.0f / a;
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x_1 = c / (a * x_2);
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}
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else
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{
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x_1 = (-b + det) / 2.0f / a;
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x_2 = c / (a * x_1);
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}
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return Tuple.Create(x_1, x_2);
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}
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static void CheckCancellation()
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{
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float a = 1.0f, b = -1000.0f, c = 1.0f; // x^2 - 1000x + c = 0
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var normal = NormalSolver(a, b, c);
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var cared = CaredSolver(a, b, c);
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Console.WriteLine($"normal: x_1= {normal.Item1:F8}, x_2= {normal.Item2:F8}");
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Console.WriteLine($"x_2 -> {(a * normal.Item2 * normal.Item2 + b * normal.Item2 + c):F8}");
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Console.WriteLine($"cared : x_1= {cared.Item1:F8}, x_2= {cared.Item2:F8}");
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Console.WriteLine($"x_2 -> {(a * cared.Item2 * cared.Item2 + b * cared.Item2 + c):F8}");
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}
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}
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}

‎NumericalCalculation/BasicWithCSharp/CancellationOfSignificantDigits/CancellationOfSignificantDigits.xproj‎

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<?xml version="1.0" encoding="utf-8"?>
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<Project ToolsVersion="14.0" DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
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<PropertyGroup>
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<VisualStudioVersion Condition="'$(VisualStudioVersion)' == ''">14.0</VisualStudioVersion>
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<VSToolsPath Condition="'$(VSToolsPath)' == ''">$(MSBuildExtensionsPath32)\Microsoft\VisualStudio\v$(VisualStudioVersion)</VSToolsPath>
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</PropertyGroup>
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<Import Project="$(VSToolsPath)\DotNet\Microsoft.DotNet.Props" Condition="'$(VSToolsPath)' != ''" />
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<PropertyGroup Label="Globals">
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<ProjectGuid>29aeccde-8736-4b28-a0e3-5b3f36751283</ProjectGuid>
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<RootNamespace>CancellationOfSignificantDigits</RootNamespace>
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<BaseIntermediateOutputPath Condition="'$(BaseIntermediateOutputPath)'=='' ">.\obj</BaseIntermediateOutputPath>
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<OutputPath Condition="'$(OutputPath)'=='' ">.\bin\</OutputPath>
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<TargetFrameworkVersion>v4.5.2</TargetFrameworkVersion>
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</PropertyGroup>
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<PropertyGroup>
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<SchemaVersion>2.0</SchemaVersion>
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</PropertyGroup>
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<Import Project="$(VSToolsPath)\DotNet\Microsoft.DotNet.targets" Condition="'$(VSToolsPath)' != ''" />
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</Project>

‎NumericalCalculation/BasicWithCSharp/CancellationOfSignificantDigits/Properties/launchSettings.json‎

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{
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"profiles": {
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"CancellationOfSignificantDigits": {
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"commandName": "Project",
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"commandLineArgs": "> result.txt"
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}
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}
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}

‎NumericalCalculation/BasicWithCSharp/CancellationOfSignificantDigits/project.json‎

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{
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"version": "1.0.0-*",
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"buildOptions": {
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"emitEntryPoint": true
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},
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"dependencies": {
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"Microsoft.NETCore.App": {
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"type": "platform",
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"version": "1.0.0"
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}
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},
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"frameworks": {
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"netcoreapp1.0": {
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"imports": "dnxcore50"
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}
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}
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}

‎NumericalCalculation/BasicWithCSharp/CancellationOfSignificantDigits/result.txt‎

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normal: x_1= 999.99900000, x_2= 0.00100708
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x_2 -> -0.00707901
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cared : x_1= 999.99900000, x_2= 0.00100000
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x_2 -> 0.00000006

‎NumericalCalculation/BasicWithCSharp/LossOfTrailingDigits/LossOfTrailingDigits.cs‎

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using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Threading.Tasks;
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namespace LossOfTrailingDigits
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{

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