Exponentiation by Squaring in Java

// Exponentiation by Squaring in Java
//
// PURPOSE
// Binary exponentiation evaluates an integer power using the bits of the exponent. Squaring
// skips the repeated multiplication used by the direct method.
//
// METHOD
// When the exponent is odd, multiply the accumulator by the current base. Halve the exponent
// and square the base for the next bit. The accumulator times the remaining power stays
// equal to the answer.
//
// COMPLEXITY
// O(log exponent) multiplications and O(1) auxiliary space; arithmetic bit costs are
// excluded.
//
// CONTRACT
// Exponent is nonnegative. Returns 1 for exponent 0, including 0 to power 0 by this
// programming convention. All intermediate products must fit.
// 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: 1024.
// 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 power(int base, int exponent) {
        alg_require((exponent >= 0));
        int result = 1;
        while ((exponent > 0)) {
            if (((exponent % 2) == 1)) {
                result = Math.multiplyExact(result, base);
            }
            exponent = (exponent / 2);
            if ((exponent > 0)) {
                base = Math.multiplyExact(base, base);
            }
        }
        return result;
    }

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