feat: add binomial theorem

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

@@ -0,0 +1,36 @@
+package me.hatter.math;
+
+import me.hatter.math.util.MathUtil;
+
+import java.math.BigDecimal;
+import java.math.RoundingMode;
+
+// https://zhuanlan.zhihu.com/p/34484169
+public class BinomialTheorem {
+
+    public static void main(String[] args) {
+        System.out.println(power(BigDecimal.valueOf(0.5), BigDecimal.valueOf(-0.3)));
+        System.out.println(Math.pow(0.5, -0.3));
+        System.out.println(power(BigDecimal.valueOf(0.6), BigDecimal.valueOf(3.1)));
+        System.out.println(Math.pow(0.6, 3.1));
+    }
+
+    public static BigDecimal power(BigDecimal x, BigDecimal u) {
+        return powerWithN(x, u, 100);
+    }
+
+    public static BigDecimal powerWithN(BigDecimal x, BigDecimal u, long n) {
+        BigDecimal result = BigDecimal.ZERO;
+        for (long i = 0; i < n; i++) {
+            BigDecimal ux = BigDecimal.ONE;
+            for (long j = 0; j < i; j++) {
+                ux = ux.multiply(u.subtract(BigDecimal.valueOf(j)));
+            }
+            result = result.add(
+                    ux.divide(new BigDecimal(MathUtil.factorial(i)), 100, RoundingMode.HALF_UP)
+                            .multiply(x.subtract(BigDecimal.ONE).pow((int) i))
+            );
+        }
+        return result.setScale(100, RoundingMode.HALF_UP);
+    }
+}