为什么 std::totally_ordered<float> 返回 true？

Question

cpp 参考（https://en.cppreference.com/w/cpp/concepts/totally_ordered）表示std::totally_ordered<T>，仅当给定左值 a、b 和 c 类型时才进行建模const std::remove_reference_t<T>：

• bool(a < b)恰好是bool(a > b)和之一bool(a == b)；
• 如果bool(a < b)和bool(b < c)都为真，则为bool(a < c)真；
• bool(a > b) == bool(b < a)
• bool(a >= b) == !bool(a < b)
• bool(a <= b) == !bool(b < a)

于是我想了一下NaN，发现这float句话不符合bool(a > b) == bool(b < a)。但是。std::totally_ordered<float>​ true我做错了什么吗？

=======

我用这个宏来创建NaN，

#define NAN        ((float)(INFINITY * 0.0F))

这是我的代码：

#include <iostream>
#include <concepts>

using namespace std;

int main(int argc, char* argv[])
{
    /*
    1) std::totally_ordered<T> is modeled only if, given lvalues a, b and c of type const std::remove_reference_t<T>:
    Exactly one of bool(a < b), bool(a > b) and bool(a == b) is true;
    If bool(a < b) and bool(b < c) are both true, then bool(a < c) is true;
    bool(a > b) == bool(b < a)
    bool(a >= b) == !bool(a < b)
    bool(a <= b) == !bool(b < a)
    */
    constexpr bool b = totally_ordered<float>; // true
    cout << typeid(NAN).name() << endl;        // float
    cout << NAN << endl;
    cout << b << endl;

    cout << "Exactly one of bool(a < b), bool(a > b) and bool(a == b) is true;" << endl;
    cout << (NAN < NAN) << endl;
    cout << (NAN > NAN) << endl;
    cout << (NAN == NAN) << endl;

    cout << " If bool(a < b) and bool(b < c) are both true, then bool(a < c) is true;" << endl;
    cout << (1.f < 2.f) << endl;
    cout << (2.f < NAN) << endl;
    cout << (1.f < NAN) << endl;

    cout << "bool(a > b) == bool(b < a)" << endl; ////// IT IS FALSE //////
    cout << (NAN > 1.f) << endl;
    cout << (1.f < NAN) << endl;

    cout << "bool(a >= b) == !bool(a < b)" << endl;
    cout << (NAN >= 1.f) << endl;
    cout << (NAN < 1.f) << endl;

    cout << "bool(a <= b) == !bool(b < a)" << endl;
    cout << (NAN <= 1.f) << endl;
    cout << (NAN > 1.f) << endl;
    cout << endl;
}

Answer 1

概念有语法要求，即存在某些表达式集并且属于提供某些行为的类型。C++20的特性concept可以检测到这些。

概念也有语义要求，即对表达含义的要求，可能是相互关联的。该concept功能（通常）无法检测到这些。如果类型满足句法和语义要求，则可以说它“建模”了一个概念。

对于totally_ordered,float满足该概念的语法要求，但 IEEE754 浮点数 it 不满足语义要求。事实上，C++20 使用符号中的语法与语义划分totally_ordered<float>作为示例。

有些人concept试图通过要求用户明确选择语义要求来解决这个问题。但totally_ordered不是其中之一。