Exponential Search in Java

// Exponential Search in Java
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// CONTRACT
// Ascending input; returns any matching index or -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: 2.
// 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 exponential_search(int[] a, int target) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        if ((n == 0)) {
            return Math.negateExact(1);
        }
        if ((a[0] == target)) {
            return 0;
        }
        int bound = 1;
        while (((bound < n) && (a[bound] < target))) {
            if ((bound > (n / 2))) {
                bound = n;
            } else {
                bound = Math.multiplyExact(bound, 2);
            }
        }
        int low = (bound / 2);
        int high = Math.min(bound, Math.subtractExact(n, 1));
        int mid = 0;
        while ((low <= high)) {
            mid = Math.addExact(low, (Math.subtractExact(high, low) / 2));
            if ((a[mid] == target)) {
                return mid;
            }
            if ((a[mid] < target)) {
                low = Math.addExact(mid, 1);
            } else {
                high = Math.subtractExact(mid, 1);
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 3, 5, 7};
        int target = 5;
        int result = exponential_search(a, target);
        System.out.println(result);
    }
}