feat: add modular inv

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

@@ -0,0 +1,63 @@
+package me.hatter.math;
+
+import java.math.BigInteger;
+import java.util.Arrays;
+
+// https://zhuanlan.zhihu.com/p/426499159
+// def modular_inv(a, p):
+//    x, y, m = 1, 0, p
+//    while a > 1:
+//        q = a // m
+//        t = m
+//
+//        m = np.mod(a, m)
+//        a = t
+//        t = y
+//
+//        y, x = x - np.int64(q) * np.int64(y), t
+//
+//        if x < 0:
+//            x = np.mod(x, p)
+//    return np.mod(x, p)
+public class ModularInv {
+
+    public static void main(String[] args) {
+        for (long i = 1; i < 10000; i++) {
+            for (long j = 1; j < 10000; j++) {
+                BigInteger a = BigInteger.valueOf(i);
+                BigInteger p = BigInteger.valueOf(j);
+                if (!a.gcd(p).equals(BigInteger.ONE)) {
+                    continue;
+                }
+                BigInteger x = a.modInverse(p);
+                BigInteger y = modularInv(a, p);
+                System.out.println(Arrays.asList(a, p, a.modInverse(p), modularInv(a, p)));
+                if (!y.equals(x)) {
+                    throw new RuntimeException();
+                }
+            }
+        }
+    }
+
+    public static BigInteger modularInv(BigInteger a, BigInteger p) {
+        BigInteger x = BigInteger.ONE;
+        BigInteger y = BigInteger.ZERO;
+        BigInteger m = p;
+        while (a.compareTo(BigInteger.ONE) > 0) {
+            BigInteger q = a.divide(m);
+            BigInteger t = m;
+
+            m = a.mod(m);
+            a = t;
+            t = y;
+
+            y = x.subtract(q.multiply(y));
+            x = t;
+
+            if (x.compareTo(BigInteger.ZERO) < 0) {
+                x = x.mod(p);
+            }
+        }
+        return x.mod(p);
+    }
+}