Iterative Segment Tree Range Sum in C#

using System;
// Iterative Segment Tree Range Sum in C#
//
// PURPOSE
// A segment tree range query combines the small number of disjoint nodes covering a half-
// open interval.
//
// METHOD
// Move both endpoints to leaves. Include a left endpoint when it is a right child and a
// right endpoint when it is about to cross a left child, then move both up.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree has 2*n entries; n>=1, 0<=left<=right<=n. Returns sum in [left,right). Empty range
// 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
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 5.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int segment_sum(ReadOnlySpan<int> tree, int left, int right) {
        checked {
            int n = (tree.Length / 2);
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((tree.Length == (2 * n)));
            alg_require(((n >= 1) && (left >= 0) && (left <= right) && (right <= n)));
            left = (left + n);
            right = (right + n);
            int total = 0;
            while ((left < right)) {
                if (((left % 2) == 1)) {
                    total = (total + tree[left]);
                    left = (left + 1);
                }
                if (((right % 2) == 1)) {
                    right = (right - 1);
                    total = (total + tree[right]);
                }
                left = (left / 2);
                right = (right / 2);
            }
            return total;
        }
    }

    static void Main() {
        int[] tree = new int[] {0, 10, 3, 7, 1, 2, 3, 4};
        int left = 1;
        int right = 3;
        int result = segment_sum(tree, left, right);
        Console.WriteLine(result);
    }
}