Exponential Search in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Exponential Search in C++
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// CONTRACT
// Ascending input; returns any matching index or -1.
// 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: 2.
// 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 exponential_search(const std::vector<int>& a, int target) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    if ((n == 0)) {
        return alg_sub(0, 1);
    }
    if ((a[0] == target)) {
        return 0;
    }
    int bound = 1;
    while (((bound < n) && (a[bound] < target))) {
        if ((bound > (n / 2))) {
            bound = n;
        } else {
            bound = alg_mul(bound, 2);
        }
    }
    int low = (bound / 2);
    int high = alg_min(bound, alg_sub(n, 1));
    int mid = 0;
    while ((low <= high)) {
        mid = alg_add(low, (alg_sub(high, low) / 2));
        if ((a[mid] == target)) {
            return mid;
        }
        if ((a[mid] < target)) {
            low = alg_add(mid, 1);
        } else {
            high = alg_sub(mid, 1);
        }
    }
    return alg_sub(0, 1);
}

int main(void) {
    std::vector<int> a = {1, 3, 5, 7};
    int target = 5;
    int result = exponential_search(a, target);
    printf("%d\n", result);
    return 0;
}