C++标准模板（STL）- 类型支持 (数值极限，epsilon，round_error，infinity)_std::numeric_limits::epsilon()

作者：小丑西瓜9 | 2024-03-24 13:55:58

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std::numeric_limits::epsilon()

数值极限

提供查询所有基础数值类型的性质的接口

定义于头文件 <limits>

template< class T > class numeric_limits;

numeric_limits 类模板提供查询各种算术类型属性的标准化方式（例如 int 类型的最大可能值是 std::numeric_limits<int>::max() ）。

返回 1.0 与给定类型的下个可表示值的差

std::numeric_limits<T>::epsilon

static T epsilon() throw();		(C++11 前)
static constexpr T epsilon() noexcept;		(C++11 起)

返回机器 epsilon ，即 1.0 与浮点类型 T 的下个可表示值的差。它仅若 std::numeric_limits<T>::is_integer == false 才有意义。

返回值

`T`	std::numeric_limits<T>::epsilon()
/* non-specialized */	`T()`
bool	false
char	0
signed char	0
unsigned char	0
wchar_t	0
char8_t	0
char16_t	0
char32_t	0
short	0
unsigned short	0
int	0
unsigned int	0
long	0
unsigned long	0
long long	0
unsigned long long	0
float	FLT_EPSILON
double	DBL_EPSILON
long double	LDBL_EPSILON

调用示例


#include <iostream>
#include <string>
#include <limits>
#include <cstdint>
#include <cfloat>
 
struct SName
{
};
 
//偏特化
struct SPartSpec
{
};
 
namespace std
{
template<>
struct numeric_limits<SPartSpec>
{
    static _GLIBCXX_USE_CONSTEXPR bool is_specialized   = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_signed        = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_integer       = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_exact         = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_infinity     = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN    = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = true;
    static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm     = denorm_present;
    static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss  = true;
    static _GLIBCXX_USE_CONSTEXPR float_round_style round_style     = round_toward_neg_infinity;
    static _GLIBCXX_USE_CONSTEXPR bool is_iec559        = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_bounded       = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_modulo        = true;
    static _GLIBCXX_USE_CONSTEXPR int  digits           = CHAR_BIT;
    static _GLIBCXX_USE_CONSTEXPR int  digits10         = CHAR_BIT;
    static _GLIBCXX_USE_CONSTEXPR int  max_digits10     = DECIMAL_DIG;
    static _GLIBCXX_USE_CONSTEXPR int  radix            = FLT_RADIX;
    static _GLIBCXX_USE_CONSTEXPR int  min_exponent     = FLT_MIN_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  min_exponent10   = FLT_MIN_10_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  max_exponent     = FLT_MAX_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  max_exponent10   = FLT_MAX_EXP;
    static _GLIBCXX_USE_CONSTEXPR bool traps            = true;
    static _GLIBCXX_USE_CONSTEXPR bool tinyness_before  = true;
 
    static _GLIBCXX_CONSTEXPR int
    min() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MIN ; }
    static _GLIBCXX_CONSTEXPR int
    lowest() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MIN ; }
    static _GLIBCXX_CONSTEXPR int
    max() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MAX ; }
    static _GLIBCXX_CONSTEXPR int
    epsilon() _GLIBCXX_USE_NOEXCEPT { return  LDBL_EPSILON ; }
};
}
 
int main()
{
    std::cout << std::boolalpha;
    std::cout << "std::numeric_limits<bool>::epsilon():                 "
              << std::numeric_limits<bool>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<char>::epsilon():                 "
              << std::numeric_limits<char>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<signed char>::epsilon():          "
              << std::numeric_limits<signed char>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<unsigned char>::epsilon():        "
              << std::numeric_limits<unsigned char>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<wchar_t>::epsilon():              "
              << std::numeric_limits<wchar_t>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<char16_t>::epsilon():             "
              << std::numeric_limits<char16_t>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<char32_t>::epsilon():             "
              << std::numeric_limits<char32_t>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<short>::epsilon():                "
              << std::numeric_limits<short>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<unsigned short>::epsilon():       "
              << std::numeric_limits<unsigned short>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<int>::epsilon():                  "
              << std::numeric_limits<int>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<unsigned int>::epsilon():         "
              << std::numeric_limits<unsigned int>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<long>::epsilon():                 "
              << std::numeric_limits<long>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<unsigned long>::epsilon():        "
              << std::numeric_limits<unsigned long>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<long long>::epsilon():            "
              << std::numeric_limits<long long>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<unsigned long long>::epsilon():   "
              << std::numeric_limits<unsigned long long>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<float>::epsilon():                "
              << std::numeric_limits<float>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<double>::epsilon():               "
              << std::numeric_limits<double>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<long double>::epsilon():          "
              << std::numeric_limits<long double>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<std::string>::epsilon():          "
              << std::numeric_limits<std::string>::epsilon() << std::endl;
    //必须偏特化
//    std::cout << "std::numeric_limits<SName>::epsilon():                "
//              << std::numeric_limits<SName>::epsilon() << std::endl;
    std::cout << "std::numeric_limits<SPartSpec>::epsilon():            "
              << std::numeric_limits<SPartSpec>::epsilon() << std::endl;
    return 0;
}

输出

返回给定浮点类型的最大舍入误差

std::numeric_limits<T>::round_error

static T round_error() throw();		(C++11 前)
static constexpr T round_error() noexcept;		(C++11 起)

返回以 ULP （最后位置单位）表示的最大可能舍入错误，其为 ISO 10967 定义，可以从 0.5 （舍入到最近位）变化到 1.0 （舍入到零或无穷大）。它仅若 std::numeric_limits<T>::is_integer == false 才有意义。

返回值

`T`	std::numeric_limits<T>::round_error()
/* non-specialized */	`T()`
bool	false
char	0
signed char	0
unsigned char	0
wchar_t	0
char8_t	0
char16_t	0
char32_t	0
short	0
unsigned short	0
int	0
unsigned int	0
long	0
unsigned long	0
long long	0
unsigned long long	0
float	0.5F
double	0.5
long double	0.5L

调用示例


#include <iostream>
#include <string>
#include <limits>
#include <cstdint>
#include <cfloat>
 
struct SName
{
};
 
//偏特化
struct SPartSpec
{
};
 
namespace std
{
template<>
struct numeric_limits<SPartSpec>
{
    static _GLIBCXX_USE_CONSTEXPR bool is_specialized   = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_signed        = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_integer       = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_exact         = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_infinity     = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN    = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = true;
    static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm     = denorm_present;
    static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss  = true;
    static _GLIBCXX_USE_CONSTEXPR float_round_style round_style     = round_toward_neg_infinity;
    static _GLIBCXX_USE_CONSTEXPR bool is_iec559        = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_bounded       = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_modulo        = true;
    static _GLIBCXX_USE_CONSTEXPR int  digits           = CHAR_BIT;
    static _GLIBCXX_USE_CONSTEXPR int  digits10         = CHAR_BIT;
    static _GLIBCXX_USE_CONSTEXPR int  max_digits10     = DECIMAL_DIG;
    static _GLIBCXX_USE_CONSTEXPR int  radix            = FLT_RADIX;
    static _GLIBCXX_USE_CONSTEXPR int  min_exponent     = FLT_MIN_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  min_exponent10   = FLT_MIN_10_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  max_exponent     = FLT_MAX_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  max_exponent10   = FLT_MAX_EXP;
    static _GLIBCXX_USE_CONSTEXPR bool traps            = true;
    static _GLIBCXX_USE_CONSTEXPR bool tinyness_before  = true;
 
    static _GLIBCXX_CONSTEXPR int
    min() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MIN ; }
    static _GLIBCXX_CONSTEXPR int
    lowest() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MIN ; }
    static _GLIBCXX_CONSTEXPR int
    max() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MAX ; }
    static _GLIBCXX_CONSTEXPR int
    epsilon() _GLIBCXX_USE_NOEXCEPT { return  LDBL_EPSILON ; }
    static _GLIBCXX_CONSTEXPR double
    round_error() _GLIBCXX_USE_NOEXCEPT { return  0.5F ; }
};
}
 
int main()
{
    std::cout << std::boolalpha;
    std::cout << "std::numeric_limits<bool>::round_error():                 "
              << std::numeric_limits<bool>::round_error() << std::endl;
    std::cout << "std::numeric_limits<char>::round_error():                 "
              << std::numeric_limits<char>::round_error() << std::endl;
    std::cout << "std::numeric_limits<signed char>::round_error():          "
              << std::numeric_limits<signed char>::round_error() << std::endl;
    std::cout << "std::numeric_limits<unsigned char>::round_error():        "
              << std::numeric_limits<unsigned char>::round_error() << std::endl;
    std::cout << "std::numeric_limits<wchar_t>::round_error():              "
              << std::numeric_limits<wchar_t>::round_error() << std::endl;
    std::cout << "std::numeric_limits<char16_t>::round_error():             "
              << std::numeric_limits<char16_t>::round_error() << std::endl;
    std::cout << "std::numeric_limits<char32_t>::round_error():             "
              << std::numeric_limits<char32_t>::round_error() << std::endl;
    std::cout << "std::numeric_limits<short>::round_error():                "
              << std::numeric_limits<short>::round_error() << std::endl;
    std::cout << "std::numeric_limits<unsigned short>::round_error():       "
              << std::numeric_limits<unsigned short>::round_error() << std::endl;
    std::cout << "std::numeric_limits<int>::round_error():                  "
              << std::numeric_limits<int>::round_error() << std::endl;
    std::cout << "std::numeric_limits<unsigned int>::round_error():         "
              << std::numeric_limits<unsigned int>::round_error() << std::endl;
    std::cout << "std::numeric_limits<long>::round_error():                 "
              << std::numeric_limits<long>::round_error() << std::endl;
    std::cout << "std::numeric_limits<unsigned long>::round_error():        "
              << std::numeric_limits<unsigned long>::round_error() << std::endl;
    std::cout << "std::numeric_limits<long long>::round_error():            "
              << std::numeric_limits<long long>::round_error() << std::endl;
    std::cout << "std::numeric_limits<unsigned long long>::round_error():   "
              << std::numeric_limits<unsigned long long>::round_error() << std::endl;
    std::cout << "std::numeric_limits<float>::round_error():                "
              << std::numeric_limits<float>::round_error() << std::endl;
    std::cout << "std::numeric_limits<double>::round_error():               "
              << std::numeric_limits<double>::round_error() << std::endl;
    std::cout << "std::numeric_limits<long double>::round_error():          "
              << std::numeric_limits<long double>::round_error() << std::endl;
    std::cout << "std::numeric_limits<std::string>::round_error():          "
              << std::numeric_limits<std::string>::round_error() << std::endl;
    //必须偏特化
//    std::cout << "std::numeric_limits<SName>::round_error():                "
//              << std::numeric_limits<SName>::round_error() << std::endl;
    std::cout << "std::numeric_limits<SPartSpec>::round_error():            "
              << std::numeric_limits<SPartSpec>::round_error() << std::endl;
    return 0;
}

输出

返回给定类型的正无穷大值

std::numeric_limits<T>::infinity

static T infinity() throw();		(C++11 前)
static constexpr T infinity() noexcept;		(C++11 起)

返回浮点类型 T 所表示的特殊值“正无穷大”。仅若 std::numeric_limits<T>::has_infinity == true 才有意义。在最常见的浮点数二进制表示 IEEE 754 中，正无穷大是所有指数位为 1 而所有尾数位为 0 的值。

返回值

`T`	std::numeric_limits<T>::infinity()
/* non-specialized */	`T()`
bool	false
char	0
signed char	0
unsigned char	0
wchar_t	0
char8_t	0
char16_t	0
char32_t	0
short	0
unsigned short	0
int	0
unsigned int	0
long	0
unsigned long	0
long long	0
unsigned long long	0
float	HUGE_VALF
double	HUGE_VAL
long double	HUGE_VALL

调用示例


#include <iostream>
#include <string>
#include <limits>
#include <cstdint>
#include <cfloat>
#include <cmath>
 
struct SName
{
};
 
//偏特化
struct SPartSpec
{
};
 
namespace std
{
template<>
struct numeric_limits<SPartSpec>
{
    static _GLIBCXX_USE_CONSTEXPR bool is_specialized   = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_signed        = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_integer       = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_exact         = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_infinity     = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN    = true;
    static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = true;
    static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm     = denorm_present;
    static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss  = true;
    static _GLIBCXX_USE_CONSTEXPR float_round_style round_style     = round_toward_neg_infinity;
    static _GLIBCXX_USE_CONSTEXPR bool is_iec559        = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_bounded       = true;
    static _GLIBCXX_USE_CONSTEXPR bool is_modulo        = true;
    static _GLIBCXX_USE_CONSTEXPR int  digits           = CHAR_BIT;
    static _GLIBCXX_USE_CONSTEXPR int  digits10         = CHAR_BIT;
    static _GLIBCXX_USE_CONSTEXPR int  max_digits10     = DECIMAL_DIG;
    static _GLIBCXX_USE_CONSTEXPR int  radix            = FLT_RADIX;
    static _GLIBCXX_USE_CONSTEXPR int  min_exponent     = FLT_MIN_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  min_exponent10   = FLT_MIN_10_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  max_exponent     = FLT_MAX_EXP;
    static _GLIBCXX_USE_CONSTEXPR int  max_exponent10   = FLT_MAX_EXP;
    static _GLIBCXX_USE_CONSTEXPR bool traps            = true;
    static _GLIBCXX_USE_CONSTEXPR bool tinyness_before  = true;
 
    static _GLIBCXX_CONSTEXPR int
    min() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MIN ; }
    static _GLIBCXX_CONSTEXPR int
    lowest() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MIN ; }
    static _GLIBCXX_CONSTEXPR int
    max() _GLIBCXX_USE_NOEXCEPT { return  CHAR_MAX ; }
    static _GLIBCXX_CONSTEXPR int
    epsilon() _GLIBCXX_USE_NOEXCEPT { return  LDBL_EPSILON ; }
    static _GLIBCXX_CONSTEXPR double
    round_error() _GLIBCXX_USE_NOEXCEPT { return  0.5F ; }
    static _GLIBCXX_CONSTEXPR double
    infinity() _GLIBCXX_USE_NOEXCEPT { return  HUGE_VAL ; }
};
}
 
int main()
{
    std::cout << std::boolalpha;
    std::cout << "std::numeric_limits<bool>::infinity():                 "
              << std::numeric_limits<bool>::infinity() << std::endl;
    std::cout << "std::numeric_limits<char>::infinity():                 "
              << std::numeric_limits<char>::infinity() << std::endl;
    std::cout << "std::numeric_limits<signed char>::infinity():          "
              << std::numeric_limits<signed char>::infinity() << std::endl;
    std::cout << "std::numeric_limits<unsigned char>::infinity():        "
              << std::numeric_limits<unsigned char>::infinity() << std::endl;
    std::cout << "std::numeric_limits<wchar_t>::infinity():              "
              << std::numeric_limits<wchar_t>::infinity() << std::endl;
    std::cout << "std::numeric_limits<char16_t>::infinity():             "
              << std::numeric_limits<char16_t>::infinity() << std::endl;
    std::cout << "std::numeric_limits<char32_t>::infinity():             "
              << std::numeric_limits<char32_t>::infinity() << std::endl;
    std::cout << "std::numeric_limits<short>::infinity():                "
              << std::numeric_limits<short>::infinity() << std::endl;
    std::cout << "std::numeric_limits<unsigned short>::infinity():       "
              << std::numeric_limits<unsigned short>::infinity() << std::endl;
    std::cout << "std::numeric_limits<int>::infinity():                  "
              << std::numeric_limits<int>::infinity() << std::endl;
    std::cout << "std::numeric_limits<unsigned int>::infinity():         "
              << std::numeric_limits<unsigned int>::infinity() << std::endl;
    std::cout << "std::numeric_limits<long>::infinity():                 "
              << std::numeric_limits<long>::infinity() << std::endl;
    std::cout << "std::numeric_limits<unsigned long>::infinity():        "
              << std::numeric_limits<unsigned long>::infinity() << std::endl;
    std::cout << "std::numeric_limits<long long>::infinity():            "
              << std::numeric_limits<long long>::infinity() << std::endl;
    std::cout << "std::numeric_limits<unsigned long long>::infinity():   "
              << std::numeric_limits<unsigned long long>::infinity() << std::endl;
    std::cout << "std::numeric_limits<float>::infinity():                "
              << std::numeric_limits<float>::infinity() << std::endl;
    std::cout << "std::numeric_limits<double>::infinity():               "
              << std::numeric_limits<double>::infinity() << std::endl;
    std::cout << "std::numeric_limits<long double>::infinity():          "
              << std::numeric_limits<long double>::infinity() << std::endl;
    std::cout << "std::numeric_limits<std::string>::infinity():          "
              << std::numeric_limits<std::string>::infinity() << std::endl;
    //必须偏特化
//    std::cout << "std::numeric_limits<SName>::infinity():                "
//              << std::numeric_limits<SName>::infinity() << std::endl;
    std::cout << "std::numeric_limits<SPartSpec>::infinity():            "
              << std::numeric_limits<SPartSpec>::infinity() << std::endl;
    return 0;
}

输出

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