malachite-q 0.14.0

The arbitrary-precision type Rational, with efficient algorithms partially derived from GMP and FLINT.
Documentation 
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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.

use malachite_base::num::arithmetic::traits::Parity;
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::logic::traits::BitAccess;
use malachite_base::num::random::random_primitive_ints;
use malachite_base::random::EXAMPLE_SEED;
use malachite_base::test_util::bench::tune::interleaved_min_pair;
use malachite_nz::integer::Integer;
use malachite_nz::natural::Natural;
use malachite_nz::platform::Limb;
use malachite_q::Rational;
use malachite_q::rational_polynomial::arithmetic::evaluate::{
    evaluate_integer_polynomial_divide_and_conquer, evaluate_integer_polynomial_horner,
};
use std::hint::black_box;

fn random_natural(seed: &str, bits: u64) -> Natural {
    use malachite_base::num::arithmetic::traits::ModPowerOf2;
    let limbs: Vec<Limb> = random_primitive_ints(EXAMPLE_SEED.fork(seed))
        .take(usize::try_from(bits.div_ceil(Limb::WIDTH)).unwrap())
        .collect();
    let mut n = Natural::from_owned_limbs_asc(limbs).mod_power_of_2(bits);
    n.set_bit(bits - 1);
    n
}

fn random_integer(seed: &str, bits: u64) -> Integer {
    let negative = random_primitive_ints::<u8>(EXAMPLE_SEED.fork(&format!("{seed}s")))
        .next()
        .unwrap()
        .odd();
    Integer::from_sign_and_abs(!negative, random_natural(seed, bits))
}

fn random_rational(seed: &str, numerator_bits: u64, denominator_bits: u64) -> Rational {
    Rational::from_integers(
        random_integer(&format!("{seed}n"), numerator_bits),
        Integer::from(random_natural(&format!("{seed}d"), denominator_bits)),
    )
}

type Inputs = Vec<(Vec<Integer>, Rational)>;

fn inputs(len: usize, coefficient_bits: u64, numerator_bits: u64, denominator_bits: u64) -> Inputs {
    (0..4)
        .map(|k| {
            let cs = (0..len)
                .map(|i| random_integer(&format!("c{k}_{i}"), coefficient_bits))
                .collect();
            (
                cs,
                random_rational(&format!("x{k}"), numerator_bits, denominator_bits),
            )
        })
        .collect()
}

// Evaluation of an IntegerPolynomial at a Rational: Horner's rule against divide and conquer. As
// with the evaluation at an Integer in malachite-nz, the crossover depends on the sizes of the
// point's numerator and denominator as well as on the length, so this prints a grid: for each
// (coefficient bits, numerator bits, denominator bits) triple, the ratio of the divide-and-conquer
// time to the Horner time at a range of lengths, and the first length from which divide and conquer
// wins at every length measured.
#[allow(clippy::print_stdout)]
fn tune_evaluate_rational() {
    let lens =
        [2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048];
    for coefficient_bits in [8u64, 64, 256, 2048] {
        for (numerator_bits, denominator_bits) in [
            (8u64, 8u64),
            (64, 64),
            (8, 64),
            (64, 8),
            (256, 256),
            (2048, 2048),
            (64, 2048),
            (2048, 64),
        ] {
            let mut line =
                format!("c {coefficient_bits:>5} a {numerator_bits:>5} b {denominator_bits:>5}:");
            let mut first_win = None;
            let mut wins = 0;
            for &len in &lens {
                let inputs = inputs(len, coefficient_bits, numerator_bits, denominator_bits);
                let (mut i, mut j) = (0usize, 0usize);
                let (th, td) = interleaved_min_pair(
                    &mut || {
                        let (cs, x) = &inputs[i % 4];
                        i += 1;
                        black_box(evaluate_integer_polynomial_horner(black_box(cs), x));
                    },
                    &mut || {
                        let (cs, x) = &inputs[j % 4];
                        j += 1;
                        black_box(evaluate_integer_polynomial_divide_and_conquer(
                            black_box(cs),
                            x,
                        ));
                    },
                );
                let ratio = td / th;
                line.push_str(&format!(" {len}:{ratio:.2}"));
                if ratio < 1.0 {
                    wins += 1;
                    first_win.get_or_insert(len);
                } else {
                    wins = 0;
                    first_win = None;
                }
                if wins >= 3 && ratio < 0.8 {
                    break;
                }
                if th > 2.0e8 {
                    break;
                }
            }
            println!(
                "{line}  => {}",
                first_win.map_or("none".to_string(), |l| l.to_string())
            );
        }
    }
}

pub fn tune(key: &str) {
    match key {
        "evaluate_rational" => tune_evaluate_rational(),
        _ => panic!("Invalid tuning key: {key}"),
    }
}