libs5BigNumbersAndMath

1package pkg13libs;2 3import java.math.BigDecimal;4import java.math.BigInteger;5import java.math.MathContext;6import java.math.RoundingMode;7 8/*9 * libs5BigNumbersAndMath.java10 * ---------------------------11 * Arbitrary-precision numbers (BigInteger/BigDecimal) and the Math utilities.12 *13 * DEFINITION:14 *   BigInteger holds integers of unlimited size; BigDecimal holds exact decimal15 *   numbers (no binary floating-point error). Use them for cryptography, money,16 *   and anywhere precision matters.17 *18 * KEY POINTS:19 *   - double/float are binary and inexact (0.1 + 0.2 != 0.3) — never use for money.20 *   - BigDecimal is exact; control scale + RoundingMode explicitly.21 *   - BigInteger supports modPow/gcd/isProbablePrime — crypto building blocks.22 *   - These types are immutable; operations return new instances.23 */24public class libs5BigNumbersAndMath {25 26    public static void main(String[] args) {27        // The classic floating-point trap28        System.out.println("double 0.1 + 0.2 = " + (0.1 + 0.2) + "  <- not 0.3!");29        System.out.println("BigDecimal       = " + new BigDecimal("0.1").add(new BigDecimal("0.2")));30 31        // BigInteger: factorial of 50 (overflows long instantly)32        BigInteger fact = BigInteger.ONE;33        for (int i = 1; i <= 50; i++) fact = fact.multiply(BigInteger.valueOf(i));34        System.out.println("\n50! = " + fact);35 36        // BigInteger crypto helpers37        BigInteger a = BigInteger.valueOf(1071), b = BigInteger.valueOf(462);38        System.out.println("\ngcd(1071,462)    = " + a.gcd(b));39        System.out.println("2^10 mod 1000    = " + BigInteger.TWO.modPow(BigInteger.TEN, BigInteger.valueOf(1000)));40        System.out.println("is 7919 prime?   = " + BigInteger.valueOf(7919).isProbablePrime(20));41 42        // BigDecimal: money math with explicit rounding43        BigDecimal price = new BigDecimal("19.99");44        BigDecimal qty   = new BigDecimal("3");45        BigDecimal total = price.multiply(qty).setScale(2, RoundingMode.HALF_UP);46        System.out.println("\n3 x $19.99       = $" + total);47        BigDecimal third = BigDecimal.ONE.divide(new BigDecimal(3), new MathContext(10));48        System.out.println("1/3 (10 digits)  = " + third);49 50        // Math utilities51        System.out.println("\nMath.sqrt(2)     = " + Math.sqrt(2));52        System.out.println("Math.pow(2,10)   = " + Math.pow(2, 10));53        System.out.println("Math.floorMod(-7,3) = " + Math.floorMod(-7, 3));54        System.out.println("Math.addExact OK    = " + Math.addExact(2, 3));55        try { Math.addExact(Integer.MAX_VALUE, 1); }56        catch (ArithmeticException e) { System.out.println("addExact overflow caught: " + e.getMessage()); }57    }58}