【JavaBigDecimal练习】利用BigDecimal精确计算欧拉数

利用BigDecimal精确计算欧拉数小数点后面1000位

相信大家对于泰勒展开已经稔熟于心，接下来我们就利用下列的泰勒展开： $$e^x=1+\frac{1}{1!}x+\frac{1}{2!}{x}^2+\frac{1}{3!}{x}^3+.......+\frac{1}{n!}{x}^n$$
当展开式满足下列条件时：$$x=1$$

可推出如下结论：
$$e^1=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+..........+\frac{1}{(n-1)!}+\frac{1}{n!}$$

用代码进行实现

// An highlighted block
package Exe5;

import java.math.BigDecimal;

public class Demo {

    /** main-method */

    public static void main(String[] args) {
        int num1 = 10000;
        BigDecimal temp1 = new BigDecimal(num1);
        System.out.println(valueOfEuler(temp1));
        System.out.println("===============================");
        int num2 = 20000;
        BigDecimal temp2 = new BigDecimal(num2);
        System.out.println(valueOfEuler(temp2));
        System.out.println("===============================");
        int num3 = 30000;
        BigDecimal temp3 = new BigDecimal(num3);
        System.out.println(valueOfEuler(temp3));
    }
    /**
     * approximately value of nature Euler scale
     *
     * @param num
     * @return value of Euler
     */
    public static BigDecimal valueOfEuler(BigDecimal num) {
        //初始化自然对数也就是欧拉数
        double euler = 0;
        //初始化赋值1 用来和num比较以便控制累加次数
        double temp = -1;
        //temp2作用为提供 num个1来累加
        double temp2 = 1;
        //将double型欧拉数字转化为BigDecimal
        //将temp也转化为BigDecimal
        //将temp2也转化为BigDecimal
        BigDecimal newEuler = new BigDecimal(euler);
        BigDecimal newTemp = new BigDecimal(temp);
        BigDecimal newTemp2 = new BigDecimal(temp2);
        //运用compareTo（）方法控制累加次数
        do {
            // newTemp++
            newTemp = newTemp.add(newTemp2);
            // e = 1/0！+ 1/1!+1/2!+......+1/num!
            newEuler = newEuler.add(newTemp2.divide(ComputeFactorial(newTemp), 1000, BigDecimal.ROUND_UP));
            //直到newTemp自己加到与num相等后
        } while (newTemp.compareTo(num) == -1);
        //返回欧拉数
        return newEuler;
    }

    /**
     * 大数阶乘方法
     */
    public static BigDecimal ComputeFactorial(BigDecimal num) {
        //初始变量 值为1
        int s = 1;
        //改变数据类型
        BigDecimal begin = new BigDecimal(s);
        //如果导入的参数num > begin，则返回1
        if (num.compareTo(begin) == 1) {
            //结果result = num*（num-1)
            BigDecimal result = num.multiply(num.subtract(begin));
            //返回结果 result = num * (num - 1) * (num - 2) * (num -3) .....* 1 两两一组以此递归
            return result.multiply(ComputeFactorial(num.subtract(begin.add(begin))));
        }
        //如果相等过后返回begin begin的值为1
        else {
            return begin;
        }
    }
}

输出语句

由于计算量很大目前只展示

int num = 10000;
BigDecimal newNum = new BigDecimal(num);
System.out.println(ValueOfEuler(newNum));

结果展示