Euler Totient by Factorization in Java

// Euler Totient by Factorization in Java
//
// PURPOSE
// Euler totient counts positive integers up to n that are coprime with n.
//
// METHOD
// For each distinct prime divisor p, remove all factors p from a working value and replace
// result with result-result/p. Handle any remaining prime factor.
//
// COMPLEXITY
// O(sqrt(n)) trial-division time and O(1) space.
//
// CONTRACT
// n >= 1. phi(1)=1.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 6.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int totient(int n) {
        alg_require((n >= 1));
        int result = n;
        int p = 2;
        while ((p <= (n / p))) {
            if (((n % p) == 0)) {
                while (((n % p) == 0)) {
                    n = (n / p);
                }
                result = Math.subtractExact(result, (result / p));
            }
            p = Math.addExact(p, 1);
        }
        if ((n > 1)) {
            result = Math.subtractExact(result, (result / n));
        }
        return result;
    }

    public static void main(String[] args) {
        int n = 9;
        int result = totient(n);
        System.out.println(result);
    }
}