C++中的数值限制与类型特性

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发布时间: 2025-08-22 00:43:47 阅读量: 2 订阅数: 16

深入解析C++标准库：从入门到精通

### C++ 中的数值限制与类型特性 #### 1. 数值限制数值类型通常具有依赖于平台的限制。C++ 标准库在模板 `numeric_limits` 中提供了这些限制，它取代并补充了普通的预处理器 C 常量。这些常量在 `<climits>` 和 `<limits.h>` 中用于整数类型，在 `<cfloat>` 和 `<float.h>` 中用于浮点类型。新的数值限制概念有两个优点：一是提供了更高的类型安全性；二是使程序员能够编写评估这些限制的模板。以下是一些内置类型的最小大小： | Type | Minimum Size | | ---- | ---- | | char | 1 byte (8 bits) | | short int | 2 bytes | | int | 2 bytes | | long int | 4 bytes | | long long int | 8 bytes | | float | 4 bytes | | double | 8 bytes | | long double | 8 bytes | ##### 1.1 `numeric_limits` 类模板 - **通用模板**：为任何类型提供默认的数值。 ```cpp namespace std { // general numeric limits as default for any type template <typename T> class numeric_limits { public: // by default no specialization for any type T exists static constexpr bool is_specialized = false; // other members are meaningless for the general template }; } ``` 这个通用模板表示对于类型 T 没有可用的数值限制，通过将成员 `is_specialized` 设置为 `false` 来实现。 - **模板特化**：为每个数值类型定义数值限制。 ```cpp namespace std { // numeric limits for int // - implementation defined template<> class numeric_limits<int> { public: // yes, a specialization for numeric limits of int does exist static constexpr bool is_specialized = true; static constexpr int min() noexcept { return -2147483648; } static constexpr int max() noexcept { return 2147483647; } static constexpr int digits = 31; }; } ``` 这里，`is_specialized` 被设置为 `true`，其他成员具有特定类型的数值限制值。通用的 `numeric_limits` 模板及其标准特化在头文件 `<limits>` 中提供。特化适用于任何可以表示数值的基本类型，并且可以轻松地为用户定义的数值类型进行补充。以下是 `numeric_limits` 类的一些成员及其含义： | Member | Meaning | C Constants | | ---- | ---- | ---- | | is_specialized | Type has specialization for numeric limits | | | is_signed | Type is signed | | | is_integer | Type is integer | | | is_exact | Calculations produce no rounding errors (true for all integer types) | | | is_bounded | The set of values representable is finite (true for all built-in types) | | | is_modulo | Adding two positive numbers may wrap to a lesser result | | | is_iec559 | Conforms to standards IEC 559 and IEEE 754 | | | min() | Minimum finite value (minimum positive normalized value for floating-point types with denormalization; meaningful if is_bounded||!is_signed) | INT_MIN,FLT_MIN,CHAR_MIN,... | | max() | Maximum finite value (meaningful if is_bounded) | INT_MAX,FLT_MAX,... | | lowest() | Maximum negative finite value (meaningful if is_bounded; since C++11) | | | digits | Character/integer: number of bits, excluding sign (binary digits); Floating point: number of radix digits in the mantissa | CHAR_BIT,FLT_MANT_DIG,... | | digits10 | Number of decimal digits (meaningful if is_bounded) | FLT_DIG,... | | max_digits10 | Number of required decimal digits to ensure that values that differ are always differentiated (meaningful for all floating-point types; since C++11) | | | radix | Integer: base of the representation (almost always 2); Floating point: base of the exponent representation | FLT_RADIX | | min_exponent | Minimum negative integer exponent for base radix | FLT_MIN_EXP,... | | max_exponent | Maximum positive integer exponent for base radix | FLT_MAX_EXP,... | | min_exponent10 | Minimum negative integer exponent for base 10 | FLT_MIN_10_EXP,... | | max_exponent10 | Maximum positive integer exponent for base 10 | FLT_MAX_10_EXP,... | | epsilon() | Difference of 1 and least value greater than 1 | FLT_EPSILON,... | | round_style | Rounding style | | | round_error() | Measure of the maximum rounding error (according to standard ISO/IEC 10967 - 1) | | | has_infinity | Type has representation for positive infinity | | | infinity() | Representation of positive infinity, if available | | | has_quiet_NaN | Type has representation for nonsignaling “Not a Number” | | | quiet_NaN() | Representation of quiet “Not a Number,” if available | | 以下是 `float` 类型的完整特化示例： ```cpp namespace std { template<> class numeric_limits<float> { public: // yes, a specialization for numeric limits of float does exist static constexpr bool is_specialized = true; inline constexpr float min() noexcept { return 1.17549435E-38F; } inline constexpr float max() noexcept { return 3.40282347E+38F; } inline constexpr float lowest() noexcept { return -3.40282347E+38F; } static constexpr int digits = 24; static constexpr int digits10 = 6; static constexpr int max_digits10 = 9; static constexpr bool is_signed = true; static constexpr bool is_integer = false; static constexpr bool is_exact = false; static constexpr bool is_bounded = true; static constexpr bool is_modulo = false; static constexpr bool is_iec559 = true; static constexpr int radix = 2; inline constexpr float epsilon() noexcept { return 1.19209290E-07F; } static constexpr float_round_style round_style = round_to_nearest; ```