Fenwick Prefix Sum in Java

// Fenwick Prefix Sum in Java
//
// PURPOSE
// A Fenwick prefix query combines disjoint stored partial sums covering the requested
// prefix.
//
// METHOD
// Starting from the exclusive prefix endpoint, add the current partial sum and clear its
// lowest set bit to move to the preceding block.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree length is n+1, 0<=end<=n. Returns sum of original values in [0,end). Empty prefix
// returns zero.
// 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 fenwick_sum(int[] tree, int end) {
        java.util.Objects.requireNonNull(tree, "tree");
        int n = Math.subtractExact(tree.length, 1);
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((tree.length == Math.addExact(n, 1)));
        alg_require(((end >= 0) && (end <= n)));
        int total = 0;
        while ((end > 0)) {
            total = Math.addExact(total, tree[end]);
            end = Math.subtractExact(end, (end & Math.negateExact(end)));
        }
        return total;
    }

    public static void main(String[] args) {
        int[] tree = new int[] {0, 1, 3, 3, 10};
        int end = 3;
        int result = fenwick_sum(tree, end);
        System.out.println(result);
    }
}