LSD Radix Sort in C#

using System;
// LSD Radix Sort in C#
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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: [0, 1, 255, 256, 65536].
// 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 radix_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require((alg_value >= 0));
            }
            int[] output = new int[alg_size((n + 1))];
            int[] count = new int[alg_size(256)];
            int divisor = 1;
            int digit = 0;
            int pass_index = 0;
            int i = 0;
            while ((pass_index < 4)) {
                i = 0;
                while ((i < 256)) {
                    count[i] = 0;
                    i = (i + 1);
                }
                i = 0;
                while ((i < n)) {
                    digit = ((a[i] / divisor) % 256);
                    count[digit] = (count[digit] + 1);
                    i = (i + 1);
                }
                i = 1;
                while ((i < 256)) {
                    count[i] = (count[i] + count[(i - 1)]);
                    i = (i + 1);
                }
                i = (n - 1);
                while ((i >= 0)) {
                    digit = ((a[i] / divisor) % 256);
                    count[digit] = (count[digit] - 1);
                    output[count[digit]] = a[i];
                    i = (i - 1);
                }
                i = 0;
                while ((i < n)) {
                    a[i] = output[i];
                    i = (i + 1);
                }
                pass_index = (pass_index + 1);
                if ((pass_index < 4)) {
                    divisor = (divisor * 256);
                }
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {256, 1, 65536, 0, 255};
        int result = radix_sort(a);
        Console.WriteLine(result);
        // Expected a: [0, 1, 255, 256, 65536]
        Console.WriteLine("[" + string.Join(", ", a) + "]");
    }
}