build.rs

use std::{env, fs::File, io::Write, path::PathBuf, u16};

/// The number of odd primes less than 65536.
const PRIMES_LEN: usize = 6541;

/// The number of integers that are:
///
/// * equal to 7 mod 8
/// * not divisible by any prime number less than or equal to 13.
/// * less than 8 * 3 * 5 * 7 * 11 * 13
const RESIDUES_LEN: usize = 5760;

/// The number of odd prime numbers between 13 and 65536 exclusive.
const SIEVE_INFO_LEN: usize = PRIMES_LEN - 5;

fn odd_primes_below_65536() -> Vec<usize> {
    const N: usize = 1 << 16;
    let mut sieve = vec![true; N >> 1];
    let mut q = (N as f64).powf(0.5) as usize;
    assert!(q * q <= N);
    q += 1;
    assert!(q * q > N);
    for i in (3..q).step_by(2) {
        if sieve[i >> 1] {
            for i in ((i * i >> 1)..sieve.len()).step_by(i) {
                sieve[i] = false;
            }
        }
    }
    // mega cheat ― we know the exact size of this vector
    let res: Vec<_> = (1..N / 2)
        .filter(|&i| sieve[i])
        .map(|i| 2 * i + 1)
        .collect();
    assert_eq!(res.len(), PRIMES_LEN);
    res
}

fn mod_exponentiation(base: usize, exponent: usize, modulus: usize) -> usize {
    assert!(base < u16::MAX.into());
    assert!(exponent < u16::MAX.into());
    assert!(modulus < u16::MAX.into());
    let (mut base, mut exponent, modulus) = (base as u32, exponent as u32, modulus as u32);
    let mut state = 1;
    loop {
        if exponent & 1 != 0 {
            state *= base;
            state %= modulus;
        }
        exponent >>= 1;
        if exponent == 0 {
            return state as _;
        }
        base *= base;
        base %= modulus;
    }
}

macro_rules! const_fmt {
    () => {
        "#[allow(warnings)]\nconst {}: [{}; {}] = {:#?};\n\n";
    };
}

/// A product of many small prime numbers.  We precompute the numbers between
/// `1` and `M` that are coprime to `M`.  Any number whose residue modulo `M` is
/// one of these is not divisible by any of the prime factors of `M`.  This
/// speeds up the generation of random prime numbers.
const M: usize = 8 * 3 * 5 * 7 * 11 * 13;
fn emit<T: std::fmt::Debug>(f: &mut dyn Write, name: &str, t: &str, obj: &[T]) {
    write!(f, const_fmt!(), name, t, obj.len(), obj).expect("i/o error in build script");
}

/// Write the generated code to `f`.
fn generate(f: &mut dyn Write) {
    write!(f, "const M: u32 = 8 * 3 * 5 * 7 * 11 * 13;\n\n").expect("i/o error");
    let residues: Vec<usize> = {
        let primes = [3, 5, 7, 11, 13];
        let not_divisible = |&x: &usize| primes.iter().all(|p| x % p != 0);
        (7..M).step_by(8).filter(not_divisible).collect()
    };
    assert_eq!(residues.len(), RESIDUES_LEN);
    emit(f, "RESIDUES", "u32", &residues[..]);
    let sieve_info: Vec<(usize, usize)> = odd_primes_below_65536()[5..]
        .iter()
        .map(|&i| (i, mod_exponentiation(M % i, i - 2, i)))
        .collect();
    assert_eq!(sieve_info.len(), SIEVE_INFO_LEN);
    emit(f, "SIEVE_INFO", "(u16, u16)", &sieve_info[..]);
}

fn main() {
    println!("cargo:rerun-if-changed=build.rs");
    let manifest_path = env::var("OUT_DIR").expect("cargo should have set this");
    let mut path = PathBuf::from(&manifest_path);
    path.push("constants.rs");
    let mut f = File::create(path).expect("cannot create constants.rs");
    generate(&mut f);
}