Iterative Factorial in C#

using System;
// Iterative Factorial in C#
//
// PURPOSE
// Factorial counts permutations of n distinct objects. Iterative multiplication avoids
// recursion and its call-stack overhead.
//
// METHOD
// Start with the empty product one. Multiply successively by every integer from two through
// n. After each multiplication the accumulator is the factorial of the current index.
//
// COMPLEXITY
// O(n) multiplications and O(1) auxiliary space; arbitrary-precision arithmetic costs are
// excluded.
//
// CONTRACT
// n >= 0. For a portable signed 32-bit result use n <= 12. Factorial grows quickly.
// 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: 1.
// 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 factorial(int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((n >= 0) && (n <= 12)));
            int result = 1;
            int i = 2;
            while ((i <= n)) {
                result = (result * i);
                i = (i + 1);
            }
            return result;
        }
    }

    static void Main() {
        int n = 0;
        int result = factorial(n);
        Console.WriteLine(result);
    }
}