6 BigInteger class
6.1 Introduction
When storing integers, Java defaults to the int type, and the int type has a range of values: -2147483648 ~ 2147483647. If the number is too large, we can use the long type, but what if the long type cannot be expressed?
You need to use BigInteger, which can be understood as: a large integer.
How big is it? Theoretically, the maximum is 4.2 billion to the 2.1 billionth power
Basically, this upper limit cannot be reached until the memory bursts.
6.2 Overview
Looking at the API documentation, we can see that the definition of the BigInteger class in the API documentation is as follows:
The package where BigInteger is located is under the java.math package, so it needs to be imported when using it. We can use the BigInteger class to calculate large integers
6.3 Common methods
Construction method
public BigInteger(int num, Random rnd) //获取随机大整数，范围：[0 ~ 2的num次方-1]
public BigInteger(String val) //获取指定的大整数
public BigInteger(String val, int radix) //获取指定进制的大整数
下面这个不是构造，而是一个静态方法获取BigInteger对象
public static BigInteger valueOf(long val) //静态方法获取BigInteger的对象，内部有优化Summary of construction methods:
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If the number represented by BigInteger does not exceed the range of long, it can be obtained with a static method.
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If the value represented by BigInteger exceeds the range of long, it can be obtained with the constructor.
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Once the object is created, the value recorded inside the BigInteger cannot be changed.
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Whenever a calculation is performed, a new BigInteger object is generated
common member methods
The most used method in the BigDecimal class is the method of performing four arithmetic operations, as follows:
public BigInteger add(BigInteger val) //加法
public BigInteger subtract(BigInteger val) //减法
public BigInteger multiply(BigInteger val) //乘法
public BigInteger divide(BigInteger val) //除法
public BigInteger[] divideAndRemainder(BigInteger val) //除法，获取商和余数
public boolean equals(Object x) //比较是否相同
public BigInteger pow(int exponent) //次幂、次方
public BigInteger max/min(BigInteger val) //返回较大值/较小值
public int intValue(BigInteger val) //转为int类型整数，超出范围数据有误Code:
package com.itheima.a06bigintegerdemo;
import java.math.BigInteger;
public class BigIntegerDemo1 {
public static void main(String[] args) {
/*
public BigInteger(int num, Random rnd) 获取随机大整数，范围:[0~ 2的num次方-11
public BigInteger(String val) 获取指定的大整数
public BigInteger(String val, int radix) 获取指定进制的大整数
public static BigInteger valueOf(long val) 静态方法获取BigInteger的对象，内部有优化
细节:
对象一旦创建里面的数据不能发生改变。
*/
//1.获取一个随机的大整数
/* Random r=new Random();
for (int i = e; i < 100; i++) {
BigInteger bd1 = new BigInteger(4,r);
System.out.println(bd1);//[@ ~ 15]}
}
*/
//2.获取一个指定的大整数，可以超出long的取值范围
//细节:字符串中必须是整数，否则会报错
/* BigInteger bd2 = new BigInteger("1.1");
System.out.println(bd2);
*/
/*
BigInteger bd3 = new BigInteger("abc");
System.out.println(bd3);
*/
//3.获取指定进制的大整数
//细节:
//1.字符串中的数字必须是整数
//2.字符串中的数字必须要跟进制吻合。
//比如二进制中，那么只能写日和1，写其他的就报错。
BigInteger bd4 = new BigInteger("123", 2);
System.out.println(bd4);
//4.静态方法获取BigInteger的对象，内部有优化
//细节:
//1.能表示范围比较小，只能在long的取值范围之内，如果超出long的范围就不行了。
//2.在内部对常用的数字: -16 ~ 16 进行了优化。
// 提前把-16~16 先创建好BigInteger的对象，如果多次获取不会重新创建新的。
BigInteger bd5 = BigInteger.valueOf(16);
BigInteger bd6 = BigInteger.valueOf(16);
System.out.println(bd5 == bd6);//true
BigInteger bd7 = BigInteger.valueOf(17);
BigInteger bd8 = BigInteger.valueOf(17);
System.out.println(bd7 == bd8);//false
//5.对象一旦创建内部的数据不能发生改变
BigInteger bd9 =BigInteger.valueOf(1);
BigInteger bd10 =BigInteger.valueOf(2);
//此时，不会修改参与计算的BigInteger对象中的借，而是产生了一个新的BigInteger对象记录
BigInteger result=bd9.add(bd10);
System.out.println(result);//3
}
}
package com.itheima.a06bigintegerdemo;
import java.math.BigInteger;
public class BigIntegerDemo2 {
public static void main(String[] args) {
/*
public BigInteger add(BigInteger val) 加法
public BigInteger subtract(BigInteger val) 减法
public BigInteger multiply(BigInteger val) 乘法
public BigInteger divide(BigInteger val) 除法，获取商
public BigInteger[] divideAndRemainder(BigInteger val) 除法，获取商和余数
public boolean equals(Object x) 比较是否相同
public BigInteger pow(int exponent) 次幂
public BigInteger max/min(BigInteger val) 返回较大值/较小值
public int intValue(BigInteger val) 转为int类型整数，超出范围数据有误
*/
//1.创建两个BigInteger对象
BigInteger bd1 = BigInteger.valueOf(10);
BigInteger bd2 = BigInteger.valueOf(5);
//2.加法
BigInteger bd3 = bd1.add(bd2);
System.out.println(bd3);
//3.除法，获取商和余数
BigInteger[] arr = bd1.divideAndRemainder(bd2);
System.out.println(arr[0]);
System.out.println(arr[1]);
//4.比较是否相同
boolean result = bd1.equals(bd2);
System.out.println(result);
//5.次幂
BigInteger bd4 = bd1.pow(2);
System.out.println(bd4);
//6.max
BigInteger bd5 = bd1.max(bd2);
//7.转为int类型整数，超出范围数据有误
/* BigInteger bd6 = BigInteger.valueOf(2147483647L);
int i = bd6.intValue();
System.out.println(i);
*/
BigInteger bd6 = BigInteger.valueOf(200);
double v = bd6.doubleValue();
System.out.println(v);//200.0
}
}
6.4 Underlying storage method:
For computers, there is actually no concept of data type. They are all 0101010101. The data type is specified by the programming language itself. Therefore, when actually storing, first convert the specific number into binary, and each 32 bits is a group. , stored in an array.
The maximum number of elements that can be stored in the array: more than 2.1 billion
Numbers that can be represented by each bit in the array: more than 4.2 billion
Theoretically, the largest number that BigInteger can represent is: 4.2 billion to the 2.1 billionth power.
But before this number is reached, the memory of the computer will burst, so it is generally believed that BigInteger is infinite.
The storage method is shown in the figure:
