Extended Euclid Modular Inverse in Java

// Extended Euclid Modular Inverse in Java
//
// PURPOSE
// Extended Euclid tracks a Bezout coefficient while computing the gcd. When gcd(a,m)=1, that
// coefficient is the modular inverse.
//
// METHOD
// Maintain consecutive remainders and coefficients. Update both with the Euclidean quotient;
// normalize the resulting coefficient into [0,m).
//
// COMPLEXITY
// O(log m) arithmetic steps and O(1) auxiliary space.
//
// CONTRACT
// 0 <= a < modulus, 2 <= modulus <= 10000. Returns -1 if no inverse exists. This bounded
// integer implementation is not constant time or suitable for cryptographic secrets.
// 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: 4.
// 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 modular_inverse(int a, int modulus) {
        alg_require(((modulus >= 2) && (modulus <= 10000) && (a >= 0) && (a < modulus)));
        int old_r = modulus;
        int r = a;
        int old_t = 0;
        int t = 1;
        int quotient = 0;
        int temp = 0;
        while ((r != 0)) {
            quotient = (old_r / r);
            temp = Math.subtractExact(old_r, Math.multiplyExact(quotient, r));
            old_r = r;
            r = temp;
            temp = Math.subtractExact(old_t, Math.multiplyExact(quotient, t));
            old_t = t;
            t = temp;
        }
        if ((old_r != 1)) {
            return Math.negateExact(1);
        }
        return (Math.addExact((old_t % modulus), modulus) % modulus);
    }

    public static void main(String[] args) {
        int a = 3;
        int modulus = 11;
        int result = modular_inverse(a, modulus);
        System.out.println(result);
    }
}