Exponentiation by Squaring in C#

using System;
// Exponentiation by Squaring in C#
//
// PURPOSE
// Binary exponentiation evaluates an integer power using the bits of the exponent. Squaring
// skips the repeated multiplication used by the direct method.
//
// METHOD
// When the exponent is odd, multiply the accumulator by the current base. Halve the exponent
// and square the base for the next bit. The accumulator times the remaining power stays
// equal to the answer.
//
// COMPLEXITY
// O(log exponent) multiplications and O(1) auxiliary space; arithmetic bit costs are
// excluded.
//
// CONTRACT
// Exponent is nonnegative. Returns 1 for exponent 0, including 0 to power 0 by this
// programming convention. All intermediate products must fit.
// 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: 1024.
// 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 power(int base_value, int exponent) {
        checked {
            alg_require((exponent >= 0));
            int result = 1;
            while ((exponent > 0)) {
                if (((exponent % 2) == 1)) {
                    result = (result * base_value);
                }
                exponent = (exponent / 2);
                if ((exponent > 0)) {
                    base_value = (base_value * base_value);
                }
            }
            return result;
        }
    }

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