Sieve of Eratosthenes in C

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Sieve of Eratosthenes in C
//
// PURPOSE
// The sieve identifies all primes up to a limit by marking multiples of smaller primes. This
// example returns their count.
//
// METHOD
// Keep a composite marker array. For each unmarked p up to the square root, mark multiples
// starting at p squared; smaller multiples were already handled. Count the remaining
// unmarked values from two onward.
//
// COMPLEXITY
// O(n log log n) time and O(n) auxiliary space.
//
// CONTRACT
// n >= 0. Returns the number of primes <= n. The marker array requires memory proportional
// to n.
// 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
// C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors
// return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result.
// Input/output arrays must not alias. No variable-length stack arrays.
//
// EXAMPLE
// Expected return: 4.
// Run: gcc -std=c99 -O2 example.c -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 int alg_checked(int64_t v, int *error) {
    if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; }
    return (int)v;
}
static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); }
static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); }
static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); }

int sieve_count(int n) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *composite = NULL;
    if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    {
        int alg_length = alg_add(n, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        composite = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*composite));
        if (!composite) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int p = 2;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int multiple = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int count = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (p <= (n / p));
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_1 = (composite[p] == 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_1) {
            multiple = alg_mul(p, p, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            while (1) {
                int alg_condition = (multiple <= n);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                if (!alg_condition) break;
                composite[multiple] = 1;
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                multiple = alg_add(multiple, p, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
        }
        p = alg_add(p, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    p = 2;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (p <= n);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_2 = (composite[p] == 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_2) {
            count = alg_add(count, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
        p = alg_add(p, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    alg_result = count;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    free(composite);
    return alg_result;
}

int main(void) {
    int n = 10;
    int result = sieve_count(n);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}