Extended Euclid Modular Inverse in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// 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++17: const vector references for inputs, mutable references for outputs, RAII workspace,
// standard lower_bound for LIS. Invalid inputs throw invalid_argument; overflow throws
// overflow_error; allocation failure propagates bad_alloc.
//
// EXAMPLE
// Expected return: 4.
// Run: g++ -std=c++17 -O2 example.cpp -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static void alg_require(bool valid) { if (!valid) throw std::invalid_argument("invalid algorithm input"); }
static int alg_checked(int64_t v) { if (v < INT32_MIN || v > INT32_MAX) throw std::overflow_error("32-bit result overflow"); return (int)v; }
static int alg_add(int a,int b) { return alg_checked((int64_t)a+b); }
static int alg_sub(int a,int b) { return alg_checked((int64_t)a-b); }
static int alg_mul(int a,int b) { return alg_checked((int64_t)a*b); }
static size_t alg_size(int n) { alg_require(n>=0 && n<=4000000); return (size_t)n; }

int modular_inverse(int a, int modulus) {
    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 = alg_sub(old_r, alg_mul(quotient, r));
        old_r = r;
        r = temp;
        temp = alg_sub(old_t, alg_mul(quotient, t));
        old_t = t;
        t = temp;
    }
    if ((old_r != 1)) {
        return alg_sub(0, 1);
    }
    return (alg_add((old_t % modulus), modulus) % modulus);
}

int main(void) {
    int a = 3;
    int modulus = 11;
    int result = modular_inverse(a, modulus);
    printf("%d\n", result);
    return 0;
}