Task: Numeric error propagation


C++: #pragma once

#include <cmath>
#include <string>
#include <sstream>
#include <iomanip>

class Approx {
public:
    Approx(double _v, double _s = 0.0) : v(_v), s(_s) {}

    operator std::string() const {
        std::ostringstream os("");
        os << std::setprecision(15) << v << " ±" << std::setprecision(15) << s << std::ends;
        return os.str();
    }

    Approx operator +(const Approx& a) const { return Approx(v + a.v, sqrt(s * s + a.s * a.s)); }
    Approx operator +(double d) const { return Approx(v + d, s); }
    Approx operator -(const Approx& a) const { return Approx(v - a.v, sqrt(s * s + a.s * a.s)); }
    Approx operator -(double d) const { return Approx(v - d, s); }

    Approx operator *(const Approx& a) const {
        const double t = v * a.v;
        return Approx(v, sqrt(t * t * s * s / (v * v) + a.s * a.s / (a.v * a.v)));
    }

    Approx operator *(double d) const { return Approx(v * d, fabs(d * s)); }

    Approx operator /(const Approx& a) const {
        const double t = v / a.v;
        return Approx(t, sqrt(t * t * s * s / (v * v) + a.s * a.s / (a.v * a.v)));
    }

    Approx operator /(double d) const { return Approx(v / d, fabs(d * s)); }

    Approx pow(double d) const {
        const double t = ::pow(v, d);
        return Approx(t, fabs(t * d * s / v));
    }

private:
    double v, s;
};




Java: public class Approx {
    private double value;
    private double error;
    
    public Approx(){this.value = this.error = 0;}
    
    public Approx(Approx b){
        this.value = b.value;
        this.error = b.error;
    }
    
    public Approx(double value, double error){
        this.value = value;
        this.error = error;
    }
    
    public Approx add(Approx b){
        value+= b.value;
        error = Math.sqrt(error * error + b.error * b.error);
        return this;
    }
    
    public Approx add(double b){
        value+= b;
        return this;
    }
    
    public Approx sub(Approx b){
        value-= b.value;
        error = Math.sqrt(error * error + b.error * b.error);
        return this;
    }
    
    public Approx sub(double b){
        value-= b;
        return this;
    }
    
    public Approx mult(Approx b){
        double oldVal = value;
        value*= b.value;
        error = Math.sqrt(value * value * (error*error) / (oldVal*oldVal) +
                                  (b.error*b.error) / (b.value*b.value));
        return this;
    }

    public Approx mult(double b){
        value*= b;
        error = Math.abs(b * error);
        return this;
    }
    
    public Approx div(Approx b){
        double oldVal = value;
        value/= b.value;
        error = Math.sqrt(value * value * (error*error) / (oldVal*oldVal) +
                                  (b.error*b.error) / (b.value*b.value));
        return this;
    }

    public Approx div(double b){
        value/= b;
        error = Math.abs(b * error);
        return this;
    }
    
    public Approx pow(double b){
        double oldVal = value;
        value = Math.pow(value, b);
        error = Math.abs(value * b * (error / oldVal));
        return this;
    }
    
    @Override
    public String toString(){return value+"±"+error;}
    
    public static void main(String[] args){
        Approx x1 = new Approx(100, 1.1);
        Approx y1 = new Approx(50, 1.2);
        Approx x2 = new Approx(200, 2.2);
        Approx y2 = new Approx(100, 2.3);
        
        x1.sub(x2).pow(2).add(y1.sub(y2).pow(2)).pow(0.5);
        
        System.out.println(x1);
    }
}