CSHARP.MATH.APPROX.PI : Approximate pi Constant (C#)

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CSHARP.MATH.APPROX.PI : Approximate pi Constant (C#)

要旨

An approximate value of π is used instead of a constant provided by a math library.

Floating point operations are by nature approximated. This can introduce bugs when precise, mathematical properties are expected from inherently imprecise floating point computations. Moreover, computations that might lose precision or overflow, whose result is stored in a larger type, are suspicious since, by computing on the larger type from the beginning, one could avoid approximations and overflows.

プロパティ

例

using System;

namespace MathConstantApproxExamples
{
    public class MathConstantApprox
    {
        private double GetPI() {
            return 3.14; // Approximate pi Constant (C#) warning issued here
        }

        private double GetE()
        {
            return 2.71; // Approximate e Constant (C#) warning issued here
        }
        
        private void PrintCos180(){
            Console.WriteLine("Cos(180°) = " + Math.Cos(GetPI()));
        }
        
        private void PrintLogE(){
             Console.WriteLine("Log(e) = " + Math.Log(GetE()));
        }  
        
         static void Main(string[] args)
        {
            PrintCos180();             // prints "Cos(180°) = -0.99999873172754" (should be -1)
            PrintLogE();               // prints "Log(e) = 0.99694863489161" (should be 1)
    
        } 

    }

}

The programmer can address this program by using Math constants instead of hardcoded approximations.

using System;

namespace MathConstantApproxExamples
{
    public class MathConstantApprox
    {
        private double GetPI() {
            return Math.PI;
        }

        private double GetE()
        {
            return Math.E;
        }
        
        private void PrintCos180(){
            Console.WriteLine(Math.Cos(GetPI()));
        }
        
        private void PrintLogE(){
             Console.WriteLine(Math.Log(GetE()));
        } 
        
        static void Main(string[] args)
        {
            PrintCos180();
            PrintLogE();
        }   
    }
}

解決法

Use approximated comparisons (up to some epsilon) rather than exact comparisons. Use integral numbers instead of floating point values, whenever possible. Compute over integral numbers and translate into floating points only at the end, whenever possible. If a large type for the result of a computation is desired, compute from the beginning on that type instead of applying a type conversion at the end of the computation.

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