//! Implements core functionality of the prime factorization.
//!
//! The complete factorization algorithm consists of
//! - Trial division with the first 1006 primes.
//! - Fermat's factorization method, useful if the integer is of the form n=(a+b)*(a-b).
//! - Primality test, consisting of Miller-Rabin and strong Baillie-PSW tests.
//! - Lenstra elliptic-curve factorization with multiple of OS threads. Module `elliptic`
//! implements elliptic curve arithmetic needed during factorization.
//!
//! Constants `MAX_THREADS_` define the maximal thread counts. These values must be at least two and preferably
//! below the number of CPU cores. In terms of performance, lower value (2-5) seems to be the best but large
//! 128 bit semiprimes could be factorized faster with larger thread count based on benchmarking.
//!
//! First thread will actually run wheel factorization targeting smaller prime factors whereas other threads
//! run the actual elliptic-curve factorization method. Thus, if the thread count has been set to one,
//! only the wheel factorization will run.
//!
//! Factorization algorithm stops when the factored number equals one.
//!
use std::cmp::Ordering;
use std::fmt::{Display, Formatter, Result};
use std::sync::{mpsc, Arc, Mutex};
use std::thread;

use num::integer;

use crate::{arith::Arith, elliptic::EllipticCurve, prime, UInt};

/// Thread count for elliptic curve factorization. Currently, optimal count seems to be between 2 and 5.
const MAX_THREADS_SMALL: usize = 2;
const MAX_THREADS_LARGE: usize = 3;

/// Max count of elliptic curves during single elliptic factorization run.
const MAX_ELLIPTIC_CURVES: usize = 125;

const SMALL_PRIMES_COUNT: usize = 1006;
/// First 1006 primes as 32 bit unsigned integers.
static SMALL_PRIMES: [u32; SMALL_PRIMES_COUNT] = [
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
    197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307,
    311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
    431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
    557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
    661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
    809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
    937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039,
    1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
    1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
    1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409,
    1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499,
    1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613,
    1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
    1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873,
    1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
    2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113,
    2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251,
    2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
    2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477,
    2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647,
    2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731,
    2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857,
    2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
    3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163,
    3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299,
    3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
    3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
    3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
    3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793,
    3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919,
    3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051,
    4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201,
    4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
    4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463,
    4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603,
    4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733,
    4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
    4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009,
    5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153,
    5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303,
    5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441,
    5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569,
    5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701,
    5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843,
    5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987,
    6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131,
    6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269,
    6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
    6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553,
    6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691,
    6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829,
    6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967,
    6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109,
    7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247,
    7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451,
    7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559,
    7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687,
    7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841,
    7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963,
];

struct MaybeFactors<T: UInt> {
    num: T,
    factors: Vec<(T, bool)>,
}

#[derive(Debug)]
pub struct Factorization<T: UInt> {
    pub num: T,
    pub is_prime: bool,
    pub factors: Vec<T>,
}

impl<T: 'static + UInt> Factorization<T> {
    /// Factorize a positive natural number `num` to its prime factors.
    ///
    /// After the call, `factors` field of the struct contains
    /// all the prime factors, smallest prime being the first
    /// element in the container. Field `num` has the original number
    /// and field `is_prime` indicates whether the number is prime.
    ///
    /// # Examples
    ///
    /// Factorize natural number 1729
    ///
    /// ```
    /// use prime_factorization::Factorization;
    ///
    /// let factor_repr = Factorization::<u32>::run(1729);
    ///
    /// assert_eq!(factor_repr.factors, vec![7, 13, 19]);
    /// ```
    ///
    /// Check whether 1801 is a prime number (no other factors than it itself)
    ///
    /// ```
    /// use prime_factorization::Factorization;
    ///
    /// let num = 1801u32;
    /// let factor_repr = Factorization::run(num);
    ///
    /// assert_eq!(factor_repr.is_prime, true);
    ///
    /// assert_eq!(factor_repr.factors, vec![num]);
    /// ```
    pub fn run(num: T) -> Self {
        let mut factorization = Factorization {
            num,
            is_prime: false,
            factors: Vec::<T>::new(),
        };

        if num <= T::one() {
            return factorization;
        }

        let num = factorization.factorize_trial(num);
        factorization.factorize_until_completed(num);

        if factorization.factors.len() > 1 {
            factorization.prune_duplicate_factors();
        } else {
            factorization.is_prime = true;
        }

        factorization
    }

    /// Get the prime factor representation for the natural number `num`:
    /// num = prm_1^k_1 * prm_2^k_2 * ... * prm_n^k_n.
    ///
    /// Representation is returned such that each element of the container
    /// is a tuple with the prime factor `prm_i` and its count `k_i` as
    /// its two elements, ordered s.t. the first tuple has the smallest prime.
    ///
    /// This method assumes that the `factors` field has the correct prime
    /// factors sorted from smallest to largest and as such the representation
    /// can be directly produced from them.
    ///
    /// Hence, always call the `run` associated function first.
    ///
    /// # Examples
    ///
    /// ```
    /// use prime_factorization::Factorization;
    ///
    /// let num = 491_520u32;
    ///
    /// // Run first the factorization, which is 2^15 * 3 * 5 for `num`
    /// let factor_repr = Factorization::run(num);
    ///
    /// assert_eq!(factor_repr.prime_factor_repr(), vec![(2, 15), (3, 1), (5, 1)]);
    /// ```
    pub fn prime_factor_repr(&self) -> Vec<(T, u32)> {
        let mut prm_factor_repr = Vec::<(T, u32)>::new();

        let mut k = self.num;
        let mut count = 0;
        let mut prev_factor = T::zero();

        for factor in self.factors.iter().rev() {
            let curr_factor = *factor;

            if curr_factor != prev_factor && count > 0 {
                prm_factor_repr.push((prev_factor, count));
                count = 0;
            }

            count += 1;
            k = k / curr_factor;

            prev_factor = curr_factor;

            if k == T::one() {
                prm_factor_repr.push((prev_factor, count));
                break;
            }
        }
        prm_factor_repr.reverse();

        prm_factor_repr
    }

    fn factorize_trial(&mut self, mut num: T) -> T {
        for prm in SMALL_PRIMES.iter() {
            let prime = (*prm).into();

            while num % prime == T::zero() {
                self.factors.push(prime);
                num = num / prime;
            }

            if num == T::one() {
                break;
            }
        }

        num
    }

    fn factorize_until_completed(&mut self, mut num: T) {
        while num > T::one() {
            num = self.factorize_fermat(num, 2);

            if num == T::one() {
                break;
            }

            if prime::is_odd_prime_factor(num) {
                self.factors.push(num);
                break;
            }

            num = self.factorize_elliptic(num);
        }
    }

    fn factorize_fermat(&mut self, num: T, level: usize) -> T {
        let mut a = integer::sqrt(num);
        let mut a_square = T::trunc_square(a);

        if a_square == num {
            if prime::is_odd_prime_factor(a) {
                for _ in 0..level {
                    self.factors.push(a);
                }
                return T::one();
            }
            // a not yet prime, start recursive search
            let mut num_back = self.factorize_fermat(a, level << 1);

            if num_back > T::one() {
                // Factoring not completed, return the original num
                num_back = num;
            }
            return num_back;
        }

        a = a + T::one();
        a_square = T::trunc_square(a);

        if a_square == T::zero() {
            return num;
        }

        for _ in 0..10 {
            let b_square = a_square - num;
            let b = integer::sqrt(b_square);

            if T::trunc_square(b) == b_square {
                let rounds = level >> 1;

                for _ in 0..rounds {
                    self.factors.push(a - b);
                    self.factors.push(a + b);
                }
                return T::one();
            }

            a = a + T::one();
            a_square = T::trunc_square(a);

            if a_square == T::zero() {
                return num;
            }
        }

        num
    }

    fn factorize_elliptic(&mut self, mut num: T) -> T {
        let mut ec_factors: Vec<(T, bool)> = Vec::new();

        num = self.spawn_and_run(num, &mut ec_factors);

        for (ec_factor, is_sure_prime) in ec_factors {
            if is_sure_prime || prime::is_odd_prime_factor(ec_factor) {
                self.factors.push(ec_factor);
            } else {
                // Factor is a power of prime or product of several primes
                let mut factorization_inner = Factorization {
                    num: ec_factor,
                    is_prime: false,
                    factors: Vec::<T>::new(),
                };

                factorization_inner.factorize_until_completed(ec_factor);

                for new_factor in factorization_inner.factors {
                    self.factors.push(new_factor);
                }
            }
        }

        num
    }

    fn spawn_and_run(&self, num: T, factors: &mut Vec<(T, bool)>) -> T {
        let (sender, receiver) = mpsc::channel();

        let maybe_factors_mtx = Arc::new(Mutex::new(MaybeFactors {
            num,
            factors: Vec::new(),
        }));

        let max_threads = if num.into() <= u64::MAX as u128 {
            MAX_THREADS_SMALL
        } else {
            MAX_THREADS_LARGE
        };

        for thread in 0..max_threads {
            let sender = sender.clone();
            let maybe_factors_mtx_clone = Arc::clone(&maybe_factors_mtx);

            thread::spawn(move || {
                if thread == 0 {
                    // Try to find smaller factors with wheel factorization
                    Self::wheel_runner(maybe_factors_mtx_clone, num, sender);
                } else {
                    Self::elliptic_runner(maybe_factors_mtx_clone, num, sender);
                }
            });
        }

        match receiver.recv() {
            Ok(completed) => {
                let maybe_factors_guard = match maybe_factors_mtx.lock() {
                    Ok(mtx_guard) => mtx_guard,
                    _ => {
                        eprintln!("Error: maybe_factors_mtx.lock() panicked.");
                        return num;
                    }
                };

                for tuple in maybe_factors_guard.factors.iter() {
                    factors.push(*tuple);
                }

                if completed {
                    T::one()
                } else {
                    maybe_factors_guard.num
                }
            }
            Err(_) => {
                eprintln!("Error: all elliptic threads disconnected, channel closed.");

                let maybe_factors_guard = maybe_factors_mtx.lock().unwrap();

                for tuple in maybe_factors_guard.factors.iter() {
                    factors.push(*tuple);
                }

                maybe_factors_guard.num
            }
        }
    }

    fn elliptic_runner(
        maybe_factors: Arc<Mutex<MaybeFactors<T>>>,
        mut num: T,
        sender: mpsc::Sender<bool>,
    ) {
        let mut curve_count = 1;

        while num > T::one() && curve_count <= MAX_ELLIPTIC_CURVES {
            let maybe_factor = EllipticCurve::compute_maybe_factor_from_curve(num);

            if maybe_factor > T::one() && maybe_factor < num {
                let mut factors_guard = match maybe_factors.lock() {
                    Ok(mtx_guard) => mtx_guard,
                    _ => {
                        curve_count += 1;
                        continue;
                    }
                };

                if maybe_factor > factors_guard.num {
                    num = factors_guard.num;
                } else {
                    num = num / maybe_factor;
                    factors_guard.num = num;
                    factors_guard.factors.push((maybe_factor, false));

                    if prime::is_odd_prime_factor(num) {
                        factors_guard.factors.push((num, true));
                        num = T::one();
                        factors_guard.num = num;
                    }
                }
            } else if maybe_factor == num && prime::is_odd_prime_factor(maybe_factor) {
                let mut factors_guard = match maybe_factors.lock() {
                    Ok(mtx_guard) => mtx_guard,
                    _ => {
                        curve_count += 1;
                        continue;
                    }
                };

                if maybe_factor == factors_guard.num {
                    num = T::one();
                    factors_guard.num = num;
                    factors_guard.factors.push((maybe_factor, true));
                } else {
                    num = factors_guard.num;
                }
            } else if curve_count & 31 == 0 {
                // Update factored number `num`
                if let Ok(mtx_guard) = maybe_factors.lock() {
                    num = mtx_guard.num;
                }
            }

            curve_count += 1;
        }

        if sender.send(num == T::one()).is_err() {}
    }

    fn wheel_runner(
        maybe_factors: Arc<Mutex<MaybeFactors<T>>>,
        mut num: T,
        sender: mpsc::Sender<bool>,
    ) {
        // Use basis {2, 3, 5, 7}
        let wheel_inc: [u32; 48] = [
            2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 6,
            2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2, 10,
        ];

        let mut k = 7991.into(); // Start search from 1007th prime 7993

        for wheel in wheel_inc.iter().cycle() {
            k = k + (*wheel).into();

            if k > num / k {
                if let Ok(mut factors_guard) = maybe_factors.lock() {
                    factors_guard.factors.push((num, false));
                    num = T::one();
                    factors_guard.num = num;
                }
                break;
            }

            if num % k == T::zero() {
                let mut factors_guard = match maybe_factors.lock() {
                    Ok(mtx_guard) => mtx_guard,
                    _ => break,
                };

                if k > factors_guard.num || factors_guard.factors.iter().any(|&e| e.0 == k) {
                    // Maybe factor `k` already larger than the active number or it has already been found
                    num = factors_guard.num;
                    break;
                }

                loop {
                    num = num / k;

                    factors_guard.num = num;
                    factors_guard.factors.push((k, true));

                    if num % k != T::zero() {
                        break;
                    }
                }
            }
        }

        if sender.send(num == T::one()).is_err() {}
    }

    fn prune_duplicate_factors(&mut self) {
        self.factors.sort();

        let mut unique_factors: Vec<T> = vec![];
        let mut k = self.num;

        for factor in self.factors.iter().rev() {
            if k % *factor == T::zero() {
                unique_factors.push(*factor);
                k = k / *factor;
            }
        }

        unique_factors.reverse();
        self.factors = unique_factors;
    }
}

impl<T: UInt> Display for Factorization<T> {
    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
        let flen = self.factors.len();

        match flen.cmp(&1) {
            Ordering::Less => write!(f, "Not factorized yet!"),
            Ordering::Equal => write!(f, "factors: {}", self.factors[0]),
            Ordering::Greater => {
                let k = self.factors.len() - 1;
                let str_prefix = self
                    .factors
                    .iter()
                    .take(k)
                    .fold(String::new(), |acc, &e| acc + &e.to_string() + ", ");

                write!(f, "factors: {}{}", str_prefix, self.factors[k])
            }
        }
    }
}

#[cfg(test)]
mod tests;