Using standard math functions with template arguments in C++

Question

I wrote the code:

const double PI = 3.141592653589793;

namespace 
{
    const int N = 8;
    const double points[8] = {-0.9602898564975363, -0.7966664774136267, -0.5255324099163290, -0.1834346424956498,
        0.1834346424956498, 0.5255324099163290, 0.7966664774136267, 0.9602898564975363};
    const double weights[8] = {0.1012285362903706, 0.2223810344533744, 0.3137066458778874, 0.3626837833783621, 0.3626837833783621,
        0.3137066458778874, 0.2223810344533744, 0.1012285362903706};
    const double error = 1e-10;

    template <class TFunction, class TNumber>
    class ChangeOfVariables
    {
        TFunction f;
    public:
        ChangeOfVariables(TFunction f) : f(f){}
        TNumber operator() (TNumber x) { TNumber c=std::cos(x); return f(std::tan(x))/(c*c); } 
    };
}


class Quadrature
{
public:
    Quadrature(void) {};
    ~Quadrature(void) {};

    template <class TFunction, class TNumber>
    TNumber integrate(TFunction f, TNumber a, TNumber b) 
    {
        TNumber result = 0.0;
        for(int i=0; i<N; i++) 
        {
            result+= weights[i]*f(0.5*((b-a)*points[i]+(a+b)));
        }
        return 0.5*(b-a)*result;
    }

    template <class TFunction, class TNumber>
    TNumber integrateToInfty(TFunction f, TNumber a)
    {
        using std::atan; 
        return integrate<ChangeOfVariables<TFunction,TNumber>, TNumber>(ChangeOfVariables<TFunction,TNumber>(f), atan(a), PI/2); 
    }
};

which is used here:

double dampendedExp(double x) {return std::exp(-2.0*x);}
int main()
{
    Quadrature quadrature;
    cout<<"e^(-2x)="<<quadrature.integrateToInfty(dampendedExp, 0)<<endl;
}

but the compiler complains:

Error   1   error C2668: 'atan' : ambiguous call to overloaded function c:\users\ga1009\documents\dev\fouriertransform\fouriertransform\quadrature.h    48

The idea was to make it work for different number types, e.g. double and complex<double>, where atan is defined. How can I fix it?

Answer 1

Visual Studio will interpret 0 as an integer and fails at the call of std::atan because it doesn't know which floating type (float, double, long double) the integer should be cast to:

~\documents\visual studio 2010\projects\so-atan\so-atan\quadrature.h(44): error C2668: 'atan': ambiguous call to overloaded function 
          c:\program files (x86)\microsoft visual studio 10.0\vc\include\math.h(553): can be 'long double atan(long double)'
          c:\program files (x86)\microsoft visual studio 10.0\vc\include\math.h(505): or "float atan(float)"
          c:\program files (x86)\microsoft visual studio 10.0\vc\include\math.h(108): or "double atan(double)"          
          ~\documents\visual studio 2010\projects\so-atan\so-atan\main.cpp(12):
          in [...] "TNumber Quadrature::integrateToInfty(TFunction,TNumber)".
          with
          [
              TNumber=int,
              TFunction=double (__cdecl *)(double)
          ]

You can recreate this behavior yourself very easily:

#include <iostream>

float f(float x){return x;}
double f(double x){return x;}
long double f(long double x){return x;}

int main()
{
    std::cout << f(0) << std::endl;
}

This will create the very same error. To get rid of this, you should either use a specific version of std::atan, std::cos and std::tan by using static_cast<double> or static_cast<long double> in your quadrature,

template <class TFunction, class TNumber>
    TNumber integrateToInfty(TFunction f, TNumber a)
    {
        using std::atan; 
        return integrate<ChangeOfVariables<TFunction,TNumber>, TNumber>
         (ChangeOfVariables<TFunction,TNumber>(f),
              atan(static_cast<long double>(a)), PI/2); 
              /*   ^^^^^^^^^^^^^^^^^^^^^^^^^^^       */          
    }

or use a floating number instead of an integer in your call (which is much easier):

cout<<"e^(-2x)="<<quadrature.integrateToInfty(dampendedExp, 0.0)<<endl;
// cout<<"e^(-2x)="<<quadrature.integrateToInfty(dampendedExp, static_cast<double>(x))<<endl;