Shell Sort in C#

using System;
// Shell Sort in C#
//
// PURPOSE
// Shell sort applies insertion sort to elements separated by a gap. Early passes move values
// over long distances before a final gap-one pass.
//
// METHOD
// Start at n/2 and halve the gap. For each gap, insert each value into its gap-separated
// sorted subsequence. Gap one finishes the full ordering.
//
// COMPLEXITY
// O(n squared) worst-case time for this halving gap sequence; O(1) auxiliary space. Not
// stable.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0. Complexity depends on the chosen gap
// sequence.
// 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: 0.
// Expected a after call: [1, 1, 3, 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 shell_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int gap = (n / 2);
            int i = 0;
            int j = 0;
            int key = 0;
            while ((gap > 0)) {
                i = gap;
                while ((i < n)) {
                    key = a[i];
                    j = i;
                    while (((j >= gap) && (a[(j - gap)] > key))) {
                        a[j] = a[(j - gap)];
                        j = (j - gap);
                    }
                    a[j] = key;
                    i = (i + 1);
                }
                gap = (gap / 2);
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {5, 1, 3, 1};
        int result = shell_sort(a);
        Console.WriteLine(result);
        Console.WriteLine("[" + string.Join(", ", a) + "]");
        // Expected a: [1, 1, 3, 5]
    }
}