Modular Exponentiation in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// 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++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: 24.
// 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_power(int base, int exponent, int modulus) {
    alg_require(((base >= 0) && (exponent >= 0) && (modulus > 0) && (modulus <= 46340)));
    int result = (1 % modulus);
    base = (base % modulus);
    while ((exponent > 0)) {
        if (((exponent % 2) == 1)) {
            result = (alg_mul(result, base) % modulus);
        }
        base = (alg_mul(base, base) % modulus);
        exponent = (exponent / 2);
    }
    return result;
}

int main(void) {
    int base = 2;
    int exponent = 10;
    int modulus = 1000;
    int result = modular_power(base, exponent, modulus);
    printf("%d\n", result);
    return 0;
}