Modular Exponentiation in Java

// Modular Exponentiation in Java
//
// PURPOSE
// Modular exponentiation computes a power while reducing every intermediate product modulo
// m. It is widely used in number theory, though this teaching version is not constant time.
//
// METHOD
// Reduce the base, then process exponent bits by squaring. Multiply the result on odd bits
// and reduce after each product.
//
// COMPLEXITY
// O(log exponent) modular multiplications, O(1) auxiliary space.
//
// CONTRACT
// base and exponent are nonnegative, modulus > 0. Products of two residues must fit the
// integer type; this is not a cryptographic implementation.
// 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: 24.
// 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_power(int base, int exponent, int modulus) {
        alg_require(((base >= 0) && (exponent >= 0) && (modulus > 0) && (modulus <= 46340)));
        int result = (1 % modulus);
        base = (base % modulus);
        while ((exponent > 0)) {
            if (((exponent % 2) == 1)) {
                result = (Math.multiplyExact(result, base) % modulus);
            }
            base = (Math.multiplyExact(base, base) % modulus);
            exponent = (exponent / 2);
        }
        return result;
    }

    public static void main(String[] args) {
        int base = 2;
        int exponent = 10;
        int modulus = 1000;
        int result = modular_power(base, exponent, modulus);
        System.out.println(result);
    }
}