Modular Exponentiation in C#

using System;
// Modular Exponentiation in C#
//
// PURPOSE
// Modular exponentiation computes a power while reducing every intermediate product modulo
// m. It is widely used in number theory, though this teaching version is not constant time.
//
// METHOD
// Reduce the base, then process exponent bits by squaring. Multiply the result on odd bits
// and reduce after each product.
//
// COMPLEXITY
// O(log exponent) modular multiplications, O(1) auxiliary space.
//
// CONTRACT
// base and exponent are nonnegative, modulus > 0. Products of two residues must fit the
// integer type; this is not a cryptographic implementation.
// 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: 24.
// 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 modular_power(int base_value, int exponent, int modulus) {
        checked {
            alg_require(((base_value >= 0) && (exponent >= 0) && (modulus > 0) && (modulus <= 46340)));
            int result = (1 % modulus);
            base_value = (base_value % modulus);
            while ((exponent > 0)) {
                if (((exponent % 2) == 1)) {
                    result = ((result * base_value) % modulus);
                }
                base_value = ((base_value * base_value) % modulus);
                exponent = (exponent / 2);
            }
            return result;
        }
    }

    static void Main() {
        int base_value = 2;
        int exponent = 10;
        int modulus = 1000;
        int result = modular_power(base_value, exponent, modulus);
        Console.WriteLine(result);
    }
}