feat: add fibonacci sequence

src/main/java/me/hatter/math/FibonacciSequence.java

@@ -0,0 +1,35 @@
+package me.hatter.math;
+
+import me.hatter.math.util.MathUtil;
+
+import java.math.BigDecimal;
+import java.math.BigInteger;
+import java.math.RoundingMode;
+import java.util.ArrayList;
+import java.util.List;
+
+public class FibonacciSequence {
+    static final BigDecimal SQRT5 = MathUtil.sqrt(BigDecimal.valueOf(5), 100);
+
+    public static void main(String[] args) {
+        List<BigInteger> nums = new ArrayList<>();
+        List<BigInteger> num2s = new ArrayList<>();
+        for (int i = 0; i < 20; i++) {
+            nums.add(fn(i));
+            num2s.add(fn2(i));
+        }
+        System.out.println(nums);
+        System.out.println(num2s);
+    }
+
+    public static BigInteger fn(int n) {
+        BigDecimal a = BigDecimal.ONE.add(SQRT5).divide(BigDecimal.valueOf(2), 100, RoundingMode.HALF_UP);
+        BigDecimal b = BigDecimal.ONE.subtract(SQRT5).divide(BigDecimal.valueOf(2), 100, RoundingMode.HALF_UP);
+        return a.pow(n).subtract(b.pow(n)).divide(SQRT5, 0, RoundingMode.HALF_UP).toBigInteger();
+    }
+
+    public static BigInteger fn2(int n) {
+        BigDecimal a = BigDecimal.ONE.add(SQRT5).divide(BigDecimal.valueOf(2), 100, RoundingMode.HALF_UP);
+        return a.pow(n).divide(SQRT5, 0, RoundingMode.HALF_UP).toBigInteger();
+    }
+}