MSVC 2010 的 <功能>（嵌套绑定）问题

Question

我有以下代码（抱歉冗长）：

double primeValue( const func1D &func,
                   const double lowerBound, const double upperBound,
                   const double pole )
{
    // check bounds
    if( lowerBound >= upperBound )
        throw runtime_error( "lowerBound must be smaller than upperBound!" );

    // C++0x way of writing: fullFunc(x) = func(x)/(x-a)
    func1D fullFunc =
            bind( divides<double>(),              // division of
                  bind(func, _1),                 // f(x), with _1 = x
                  bind(minus<double>(), _1, pole) ); // by x-a, with _1 = x

    // pole not in domain
    if( pole<lowerBound || pole>upperBound)
    {
        cout << "Case 1" << endl;
        return integrateSimpson( fullFunc, 1000, lowerBound, upperBound );
    }
    // pole closer to upper bound
    else if( upperBound-pole < pole-lowerBound  )
    {
       cout << "Case 2" << endl;
       // C++0x way of writing g(x) := [f(x)-f(2a-x)]/(x-a)
       func1D specialFirstFunc =
                bind( std::divides<double>(),                               // division of
                      bind(minus<double>(),                                 // numerator:
                           bind(func, _1),                                  // f(x) minus
                           bind(func, bind(minus<double>(), 2.*pole, _1))), //f(2a-x)
                      bind(minus<double>(), _1, pole) );                    // denominator: x-a
        const double trickyPart = integrateSimpson( specialFirstFunc, 1000, pole+.000001, upperBound );

        const double normalPart = integrateSimpson( fullFunc, 1000, lowerBound, 2.*pole-upperBound );
        cout << "Tricky part: " << trickyPart << endl;
        cout << "Normal part: " << normalPart << endl;
        return trickyPart + normalPart;
    }
    else // pole closer to lower bound
    {
        cout << "Case 3" << endl;
        // C++0x way of writing g(x) := [f(x)-f(2a-x)]/(x-a)
        func1D specialFirstFunc =
                 bind( std::divides<double>(),                               // division of
                       bind(minus<double>(),                                 // numerator:
                            bind(func, _1),                                  // f(x) minus
                            bind(func, bind(minus<double>(), 2.*pole, _1))), //f(2a-x)
                       bind(minus<double>(), _1, pole) );                    // denominator: x-a
         const double trickyPart = integrateSimpson( specialFirstFunc, 1000, lowerBound, pole-.00001 );

         const double normalPart = integrateSimpson( fullFunc, 1000, 2.*pole-lowerBound, upperBound );
         cout << "Tricky part: " << trickyPart << endl;
         cout << "Normal part: " << normalPart << endl;
         return trickyPart + normalPart;
    }
}

它使用复杂分析数学域中的主值概念对包含奇点（极点）的实轴上的函数进行积分。 bind 和 function 部分将原函数 f(x) 修改为

(f(x)-f(2*pole-x))/(x-a)

它甚至为我的简单测试用例功能提供了正确的结果。如果需要，我可以提供其他详细信息：

typedef std::function<double (double)> func1D;
double integrateSimpson( func1D, const size_t nSteps, const double lowerBound, const double upperBound);

后者使用简单的 Simpson 积分规则进行积分。可以提供代码，但与手头的问题不太相关。

这可以在 GCC 4.4+ 上正常编译（使用 4.4.5 和 4.5.2 预发行版进行测试，CFLAGS="-O2 -std=c++0x -pedantic -Wall -Wextra"），但会产生内部标头错误 (C2664 ) 在 MSVC 2010 上。（如果需要，我可以提供错误输出，我的代码完全没有引用（！））。

我在 MSVC 中发现错误了吗？

谢谢！

Answer 1

为什么不直接使用 lambda？出于这种目的，所有绑定的东西都已被弃用。

double primeValue( const func1D &func,
                   const double lowerBound, const double upperBound,
                   const double pole )
{
    // check bounds
    if( lowerBound >= upperBound )
        throw runtime_error( "lowerBound must be smaller than upperBound!" );

    // C++0x way of writing: fullFunc(x) = func(x)/(x-a)
    auto fullFunc = [=](double d) {
        return func(d) / (d - pole);
    };

    // pole not in domain
    if( pole<lowerBound || pole>upperBound)
    {
        cout << "Case 1" << endl;
        return integrateSimpson( fullFunc, 1000, lowerBound, upperBound );
    }
    // pole closer to upper bound
    else if( upperBound-pole < pole-lowerBound  )
    {
       cout << "Case 2" << endl;
       // C++0x way of writing g(x) := [f(x)-f(2a-x)]/(x-a)
       auto specialFirstFunc = [=](double x) -> double {
           double numerator = func(x) - func(2*pole - x);
           return numerator / (x - pole);
       };
        const double trickyPart = integrateSimpson( specialFirstFunc, 1000, pole+.000001, upperBound );

        const double normalPart = integrateSimpson( fullFunc, 1000, lowerBound, 2.*pole-upperBound );
        cout << "Tricky part: " << trickyPart << endl;
        cout << "Normal part: " << normalPart << endl;
        return trickyPart + normalPart;
    }
    else // pole closer to lower bound
    {
        cout << "Case 3" << endl;
        // C++0x way of writing g(x) := [f(x)-f(2a-x)]/(x-a)
       auto specialFirstFunc = [=](double x) -> double {
           double numerator = func(x) - func(2*pole - x);
           return numerator / (x - pole);
       };
         const double trickyPart = integrateSimpson( specialFirstFunc, 1000, lowerBound, pole-.00001 );

         const double normalPart = integrateSimpson( fullFunc, 1000, 2.*pole-lowerBound, upperBound );
         cout << "Tricky part: " << trickyPart << endl;
         cout << "Normal part: " << normalPart << endl;
         return trickyPart + normalPart;
    }
}

至于你是否真的在 MSVC 中发现了一个错误，我不知道，但你的解决方案绝对是不必要的 - 这段代码更干净，更容易维护。