根据标准，整数中的值表示位数？

Question

考虑以下辅助结构：

template <class T>
struct bit_count_1:
std::integral_constant<
    std::size_t,
    std::numeric_limits<typename std::make_unsigned<T>::type>::digits
> {};

template <class T>
struct bit_count_2:
std::integral_constant<
    std::size_t,
    std::numeric_limits<T>::digits + std::is_signed<T>::value
> {};

template <class T>
constexpr std::size_t compute_bit_count() {
    using type = typename std::make_unsigned<T>::type;
    constexpr type zero = 0;
    constexpr type one = 1;
    constexpr type max = ~zero;
    type current = max;
    std::size_t i = 0; 
    while (current) {
        current >>= one;
        ++i;
    }
    return i;
}

template <class T>
struct bit_count_3:
std::integral_constant<
    std::size_t,
    compute_bit_count<T>()
> {};

对于每个整数类型 T 这样 std::is_integral<T>::value 是 true 除了 bool 我是否可以保证，按照标准，

bit_count_1、bit_count_2 和 bit_count_3 具有相同的值 N
T x = 1; x <<= (N - 1)定义明确
T x = ~static_cast<T>(0); x >>= (N - 1)定义明确

我目前正在研究 C++ 提案，所以我需要确定这是否符合标准，目前我还不太清楚。

Answer 1

是的，当然有！

[basic.types] 3.9

The value representation of an object is the set of bits that hold the value of type T.

[basic.fundamental] 3.9.1

The range of non-negative values of a signed integer type is a subrange of the corresponding unsigned integer type, and the value representation of each corresponding signed/unsigned type shall be the same.

[basic.fundamental] 3.9.1

The representations of integral types shall define values by use of a pure binary numeration system.⁵⁰

⁵⁰⁾ A positional representation for integers that uses the binary digits 0 and 1, in which the values represented by successive bits are additive, begin with 1, and are multiplied by successive integral power of 2, except perhaps for the bit with the highest position. (Adapted from the American National Dictionary for Information Processing Systems.)

但这取决于 non-sign 位是什么：

[numeric.limits.members] 18.3.2.4

For integer types, the number of non-sign bits in the representation.

如果他们暗示，在所谓的 sign-and-magnitude representation 中，符号位必须是只有，那么您可以将这些表达式计算为 true：

bit_count_2<T>{} > bit_count_1<T>{} 和
bit_count_2<T>{} > bit_count_3<T>{},

对于二进制补码表示的有符号整数类型T。所以，无论如何我都会放一个 static_assert，你知道...

根据标准，整数中的值表示位数？

Number of value representation bits in a integer, according to the standard?

c++

standards

bit

language-lawyer

c++14