C++学习笔记八：极限和数学运算<limits><cmath>

1） <limits>库：

1.1 源文档：

https://en.cppreference.com/w/cpp/types/numeric_limits

#include <limits>

1.2 库函数：

函数解释：

对于一个浮点数，lowest表示最小的可表示的负数，min表示最小的可表示的接近0的数，max表示最大的可表示的正数

对于一个有符号整数，min表示可以表示的最小的负数，max表示可以表示的最大的证书

std::cout << "The range for short is from " << std::numeric_limits<short>::min() << " to "
    << std::numeric_limits<short>::max() << std::endl;
std::cout << "The range for unsigned short is from " << std::numeric_limits<unsigned short>::min() << " to "
    << std::numeric_limits<unsigned short>::max() << std::endl;
std::cout << "The range for int is from " << std::numeric_limits<int>::min() << " to "
    << std::numeric_limits<int>::max() << std::endl;
std::cout << "The range for unsigned int is from " << std::numeric_limits<unsigned int>::min() << " to "
    << std::numeric_limits<unsigned int>::max() << std::endl;
std::cout << "The range for long is from " << std::numeric_limits<long>::min() << " to "
    << std::numeric_limits<long>::max() << std::endl;
std::cout << "The range for float is from " << std::numeric_limits<float>::min() << " to "
    << std::numeric_limits<float>::max() << std::endl;
std::cout << "The range(with lowest) for float is from " << std::numeric_limits<float>::lowest() << " to "
    << std::numeric_limits<float>::max() << std::endl;
std::cout << "The range(with lowest) for double is from " << std::numeric_limits<double>::lowest() << " to "
    << std::numeric_limits<double>::max() << std::endl;
std::cout << "The range(with lowest) for long double is from " << std::numeric_limits<long double>::lowest() << " to "
    << std::numeric_limits<long double>::max() << std::endl;

//Other facilities
//More info : https://en.cppreference.com/w/cpp/types/numeric_limits
std::cout << "int is signed : " << std::numeric_limits<int>::is_signed << std::endl;
std::cout << "int digits : " << std::numeric_limits<int>::digits << std::endl; //digits is the number of digits in base-radix that can be represented by the type T without change. For integer types, this is the number of bits not counting the sign bit and the padding bits

输出结果：

The range for short is from -32768 to 32767
The range for unsigned short is from 0 to 65535
The range for int is from -2147483648 to 2147483647
The range for float is from 1.17549e-38 to 3.40282e+38
The range(with lowest) for float is from -3.40282e+38 to 3.40282e+38
The range(with lowest) for double is from -1.79769e+308 to 1.79769e+308      
The range(with lowest) for long double is from -1.18973e+4932 to 1.18973e+4932
int is signed : 1
int digits : 31

2）<cmath>库

2.1 源文档：

#include <cmath>

https://en.cppreference.com/w/cpp/header/cmath

2.2 部分库函数：

std::abs(a): 绝对值

std::exp(a): e的乘方

std::pow(a,b): a的b次方

std::log(a): e的对数

std::log10(a): 10的对数

std::sqrt(a): 开平方根

std::round(a): 四舍五入

三角函数（单位是弧度制）：sin(), sinf(float num), sinl(long double number)

2.3 对char类型和short int类型的数学计算：

编译器无法处理小于4bytes的数据的计算，char类型占据1 Byte，short int类型占据2 Bytes， 在进行运算时会自动转换为int类型

short int var1 {10}; // 2 bytes
short int var2 {20};

char var3 {40}; //1
char var4 {50};

std::cout << "size of var1 : " << sizeof(var1) << std::endl;
std::cout << "size of var2 : " << sizeof(var2) << std::endl;
std::cout << "size of var3 : " << sizeof(var3) << std::endl;
std::cout << "size of var4 : " << sizeof(var4) << std::endl;

auto result1 = var1 + var2 ;
auto result2 = var3 + var4;

std::cout << "size of result1 : " << sizeof(result1) << std::endl; // 4
std::cout << "size of result2 : " << sizeof(result2) << std::endl; // 4