Fast Doubling Fibonacci in C#

using System;
// Fast Doubling Fibonacci in C#
//
// PURPOSE
// Fast doubling computes Fibonacci numbers using identities for doubling an index, reducing
// the number of recurrence steps logarithmically.
//
// METHOD
// Read n bits from most significant to least. Derive F(2k) and F(2k+1) from F(k),F(k+1),
// then advance one extra position for a set bit.
//
// COMPLEXITY
// O(log n) arithmetic operations, O(1) auxiliary space under bounded integer arithmetic.
//
// CONTRACT
// 0 <= n <= 45 so all intermediates fit signed 32-bit. Returns F(n), with F(0)=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.
// 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 fast_fibonacci(int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((n >= 0) && (n <= 45)));
            int a = 0;
            int b = 1;
            int c = 0;
            int d = 0;
            int bit = 1;
            while ((bit <= (n / 2))) {
                bit = (bit * 2);
            }
            while ((bit > 0)) {
                c = (a * ((2 * b) - a));
                d = ((a * a) + (b * b));
                if ((((n / bit) % 2) == 0)) {
                    a = c;
                    b = d;
                } else {
                    a = d;
                    b = (c + d);
                }
                bit = (bit / 2);
            }
            return a;
        }
    }

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