Extended Euclid Modular Inverse in C#

using System;
// Extended Euclid Modular Inverse in C#
//
// PURPOSE
// Extended Euclid tracks a Bezout coefficient while computing the gcd. When gcd(a,m)=1, that
// coefficient is the modular inverse.
//
// METHOD
// Maintain consecutive remainders and coefficients. Update both with the Euclidean quotient;
// normalize the resulting coefficient into [0,m).
//
// COMPLEXITY
// O(log m) arithmetic steps and O(1) auxiliary space.
//
// CONTRACT
// 0 <= a < modulus, 2 <= modulus <= 10000. Returns -1 if no inverse exists. This bounded
// integer implementation is not constant time or suitable for cryptographic secrets.
// 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: 4.
// 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_inverse(int a, int modulus) {
        checked {
            alg_require(((modulus >= 2) && (modulus <= 10000) && (a >= 0) && (a < modulus)));
            int old_r = modulus;
            int r = a;
            int old_t = 0;
            int t = 1;
            int quotient = 0;
            int temp = 0;
            while ((r != 0)) {
                quotient = (old_r / r);
                temp = (old_r - (quotient * r));
                old_r = r;
                r = temp;
                temp = (old_t - (quotient * t));
                old_t = t;
                t = temp;
            }
            if ((old_r != 1)) {
                return (-1);
            }
            return (((old_t % modulus) + modulus) % modulus);
        }
    }

    static void Main() {
        int a = 3;
        int modulus = 11;
        int result = modular_inverse(a, modulus);
        Console.WriteLine(result);
    }
}