Java.math包BigInteger和BigDecimal完全指南：从基础到实战

import java.math.BigInteger;

public class BigIntegerExample {
    public static void main(String[] args) {
        // 创建BigInteger对象
        BigInteger num1 = new BigInteger("12345678901234567890");
        BigInteger num2 = BigInteger.valueOf(987654321L);
        BigInteger num3 = new BigInteger("10000000000000000000");
        
        // 基本算术运算
        System.out.println("加法: " + num1.add(num2));
        System.out.println("减法: " + num1.subtract(num2));
        System.out.println("乘法: " + num1.multiply(num2));
        System.out.println("除法: " + num1.divide(num3));
        System.out.println("取余: " + num1.remainder(num3));
        
        // 比较运算
        System.out.println("比较: " + num1.compareTo(num2));
        System.out.println("是否相等: " + num1.equals(num2));
        
        // 数学运算
        System.out.println("最大值: " + num1.max(num2));
        System.out.println("最小值: " + num1.min(num2));
        System.out.println("绝对值: " + num1.abs());
        System.out.println("幂运算: " + num2.pow(3));
        System.out.println("GCD: " + num1.gcd(num3));
        
        // 位运算
        BigInteger bitNum = new BigInteger("15"); // 二进制 1111
        System.out.println("位与: " + bitNum.and(new BigInteger("7"))); // 0111
        System.out.println("位或: " + bitNum.or(new BigInteger("8")));   // 1000
        System.out.println("位非: " + bitNum.not());
        System.out.println("位异或: " + bitNum.xor(new BigInteger("10")));
        
        // 素数测试 (概率性测试)
        BigInteger primeCandidate = new BigInteger("104729"); // 第10000个素数
        System.out.println("是否为素数: " + primeCandidate.isProbablePrime(100));
    }
}

import java.math.BigDecimal;
import java.math.RoundingMode;

public class BigDecimalExample {
    public static void main(String[] args) {
        // 创建BigDecimal对象
        BigDecimal num1 = new BigDecimal("123.456789");
        BigDecimal num2 = BigDecimal.valueOf(987.654321);
        BigDecimal num3 = new BigDecimal("100.00");
        
        // 基本算术运算
        System.out.println("加法: " + num1.add(num2));
        System.out.println("减法: " + num1.subtract(num2));
        System.out.println("乘法: " + num1.multiply(num2));
        
        // 除法（需要指定精度和舍入模式）
        System.out.println("除法: " + num1.divide(num3, 4, RoundingMode.HALF_UP));
        
        // 比较运算
        System.out.println("比较: " + num1.compareTo(num2));
        System.out.println("是否相等: " + num1.equals(num2));
        
        // 数学运算
        System.out.println("最大值: " + num1.max(num2));
        System.out.println("最小值: " + num1.min(num2));
        System.out.println("绝对值: " + num1.abs());
        
        // 小数处理
        System.out.println("标度: " + num1.scale());
        System.out.println("精度: " + num1.precision());
        
        // 舍入操作
        System.out.println("四舍五入: " + num1.setScale(2, RoundingMode.HALF_UP));
        System.out.println("向上取整: " + num1.setScale(0, RoundingMode.CEILING));
        System.out.println("向下取整: " + num1.setScale(0, RoundingMode.FLOOR));
        
        // 金融计算示例
        BigDecimal principal = new BigDecimal("10000.00");
        BigDecimal rate = new BigDecimal("0.05"); // 5% 年利率
        int years = 3;
        
        // 复利计算: A = P(1 + r)^n
        BigDecimal amount = principal.multiply(
            BigDecimal.ONE.add(rate).pow(years)
        );
        System.out.println("复利总额: " + amount.setScale(2, RoundingMode.HALF_UP));
    }
}

import java.math.BigInteger;
import java.math.BigDecimal;
import java.math.RoundingMode;

public class MathPackageDemo {
    
    // 计算阶乘（使用BigInteger处理大数）
    public static BigInteger factorial(int n) {
        BigInteger result = BigInteger.ONE;
        for (int i = 2; i <= n; i++) {
            result = result.multiply(BigInteger.valueOf(i));
        }
        return result;
    }
    
    // 计算e的近似值（使用BigDecimal处理精确小数）
    public static BigDecimal calculateE(int precision) {
        BigDecimal e = BigDecimal.ONE;
        BigDecimal term = BigDecimal.ONE;
        
        for (int i = 1; i < 100; i++) {
            term = term.divide(BigDecimal.valueOf(i), precision, RoundingMode.HALF_UP);
            e = e.add(term);
        }
        
        return e;
    }
    
    public static void main(String[] args) {
        // 大数阶乘计算
        System.out.println("50的阶乘: " + factorial(50));
        
        // 精确的e值计算
        System.out.println("e的近似值: " + calculateE(20));
        
        // 金融计算：贷款月供计算
        BigDecimal loanAmount = new BigDecimal("200000.00"); // 贷款金额
        BigDecimal annualRate = new BigDecimal("0.06");      // 年利率 6%
        int loanTerm = 30;                                   // 贷款期限30年
        
        BigDecimal monthlyRate = annualRate.divide(BigDecimal.valueOf(12), 10, RoundingMode.HALF_UP);
        int numberOfPayments = loanTerm * 12;
        
        // 月供公式: P * r * (1+r)^n / ((1+r)^n - 1)
        BigDecimal onePlusR = BigDecimal.ONE.add(monthlyRate);
        BigDecimal numerator = monthlyRate.multiply(onePlusR.pow(numberOfPayments));
        BigDecimal denominator = onePlusR.pow(numberOfPayments).subtract(BigDecimal.ONE);
        
        BigDecimal monthlyPayment = loanAmount.multiply(numerator).divide(denominator, 2, RoundingMode.HALF_UP);
        System.out.println("月供: $" + monthlyPayment);
    }
}