use num_bigint::{BigUint, BigInt, RandBigInt, Sign};
use num_traits::identities::{One, Zero};
use num_traits::Signed;
use num_integer::Integer;

use rand::Rng;
use rand::thread_rng;

use crate::error::{Error, Result};

pub const MIN_BIT_LENGTH: usize = 128;

/// Create a new prime number with size `bit_length` sourced
/// from an already-initialized `Rng`
pub fn gen_prime<R: Rng + ?Sized>(bit_length: usize, rng: &mut R) -> Result {
    if bit_length < MIN_BIT_LENGTH {
        Err(Error::BitLength(bit_length))
    } else {
        let checks = required_checks(bit_length);
        let mut candidate;

        loop {
            candidate = rng.gen_biguint(bit_length);

            //Set the top two bits and lowest bit
            candidate |= BigUint::one();

            if _is_prime(&candidate, checks, true) && lucas(&candidate) {
                return Ok(candidate)
            }
        }
    }
}

/// Constructs a new `SafePrime` with the size of `bit_length` bits, sourced
/// from an already-initialized `Rng`.
pub fn gen_safe_prime<R: Rng + ?Sized>(bit_length: usize, rng: &mut R) -> Result {
    let two = BigUint::from(2u8);
    let three = BigUint::from(3u8);
    if bit_length < MIN_BIT_LENGTH {
        Err(Error::BitLength(bit_length))
    } else {
        let mut candidate: BigUint;
        let checks = required_checks(bit_length) - 5;

        loop {
            candidate = gen_prime(bit_length, rng)?;

            if _is_safe_prime(&candidate, checks, true) &&
               lucas(&candidate) {
                break;
            }

            candidate <<= 1_usize;
            candidate += 1_usize;

            if (&candidate % &three) == two &&
                _is_prime(&candidate, checks, false) && lucas(&candidate) {
                break;
            }
        }

        Ok(candidate)
    }
}

/// Checks if number is a prime using the Baillie-PSW test
pub fn is_prime_baillie_psw(candidate: &BigUint) -> bool {
    _is_prime(candidate, required_checks(candidate.bits()), true) && lucas(candidate)
}

/// Checks if number is a safe prime using the Baillie-PSW test
pub fn is_safe_prime_baillie_psw(candidate: &BigUint) -> bool {
    _is_safe_prime(candidate, required_checks(candidate.bits()), true) && lucas(&candidate)
}

/// Checks if number is a safe prime
pub fn is_safe_prime(candidate: &BigUint) -> bool {
    _is_safe_prime(candidate, required_checks(candidate.bits()), false)
}

/// Common function for is_safe_prime
fn _is_safe_prime(candidate: &BigUint, checks: usize, force2: bool) -> bool {
    // according to https://eprint.iacr.org/2003/186.pdf
    // a safe prime is congruent to 2 mod 3
    if (candidate % &BigUint::from(3u8)) == BigUint::from(2u8) &&
        _is_prime(&candidate, checks, force2) {
            // a safe prime satisfies (p-1)/2 is prime. Since a
            // prime is odd, We just need to divide by 2
            return _is_prime(&(candidate >> 1), checks, force2);
        }

    false
}

/// Test if number is prime by
///
/// 1- Trying to divide by first 2048 primes
/// 2- Perform a Fermat Test
/// 3- Perform log2(bitlength) + 5 rounds of Miller-Rabin
///    depending on the number of bits
pub fn is_prime(candidate: &BigUint) -> bool {
    _is_prime(candidate,     required_checks(candidate.bits()), false)
}

/// Common function for is_prime
fn _is_prime(candidate: &BigUint, checks: usize, force2: bool) -> bool {
    if candidate == &BigUint::from(2u8) {
        return true;
    }

    if candidate.is_even() || candidate.is_one() {
        return false;
    }

    for p in PRIMES.iter() {
        if candidate % p == BigUint::zero() {
            return candidate == p;
        }
    }

    if !fermat(candidate) {
        return false;
    }

    // Finally, do a Miller-Rabin test
    // See https://eprint.iacr.org/2018/749.pdf for good choices on appropriate number of tests
    if !miller_rabin(candidate, checks, force2) {
        return false;
    }

    true
}

/// Minimum checks to be considered okay
fn required_checks(bits: usize) -> usize {
    ((bits as f64).log2() as usize) + 5
}

/// Perform Fermat's little theorem on the candidate to determine probable
/// primality.
fn fermat(candidate: &BigUint) -> bool {
    let random = thread_rng().gen_biguint_range(&BigUint::one(), candidate);

    let result = random.modpow(&(candidate - 1u8), &candidate);

    result.is_one()
}

/// Perform miller rabin primality tests
fn miller_rabin(candidate: &BigUint, mut limit: usize, force2: bool) -> bool {
    // Perform the Miller-Rabin test on the candidate, 'limit' times.
    let (trials, d) = rewrite(candidate);

    let cand_minus_one = candidate - 1u32;

    let mut bases = ::std::collections::LinkedList::new();

    if force2 {
        bases.push_back(BigUint::from(2u8));
        limit -= 1;
    }

    for _ in 0..limit {
        bases.push_front(thread_rng().gen_biguint_range(&TWO, candidate));
    }

    'nextbasis: for basis in bases {
        let mut test = basis.modpow(&d, &candidate);

        if test.is_one() || test == cand_minus_one {
            continue;
        } else {
            for _ in 1..trials - 1 {
                test = test.modpow(&TWO, &candidate);
                if test.is_one() {
                    return false;
                } else if test == cand_minus_one {
                    break 'nextbasis;
                }
            }
            return false;
        }
    }

    true
}

/// Compute `d` and `trials`
fn rewrite(candidate: &BigUint) -> (u64, BigUint) {
    let mut d = candidate - 1u32;
    let mut trials = 0;

    while d.is_odd() {
        d >>= 1;
        trials += 1;
    }

    (trials, d)
}

fn lucas(n: &BigUint) -> bool {
    // Baillie-OEIS "method C" for choosing D, P, Q,
    // as in https://oeis.org/A217719/a217719.txt:
    // try increasing P ≥ 3 such that D = P² - 4 (so Q = 1)
    // until Jacobi(D, n) = -1.
    // The search is expected to succeed for non-square n after just a few trials.
    // After more than expected failures, check whether n is square
    // (which would cause Jacobi(D, n) = 1 for all D not dividing n).
    let mut p = 3u64;
    let n_int = BigInt::from_biguint(Sign::Plus, n.clone());

    loop {
        if p > 10000 {
            // This is widely believed to be impossible.
            // If we get a report, we'll want the exact number n.
            panic!("internal error: cannot find (D/n) = -1 for {:?}", n)
        }

        let j = jacobi(&BigInt::from(p * p - 4), &n_int);

        if j == -1 {
            break;
        }
        if j == 0 {
            // d = p²-4 = (p-2)(p+2).
            // If (d/n) == 0 then d shares a prime factor with n.
            // Since the loop proceeds in increasing p and starts with p-2==1,
            // the shared prime factor must be p+2.
            // If p+2 == n, then n is prime; otherwise p+2 is a proper factor of n.
            return n_int == BigInt::from(p as i64 + 2);
        }

        // We'll never find (d/n) = -1 if n is a square.
        // If n is a non-square we expect to find a d in just a few attempts on average.
        // After 40 attempts, take a moment to check if n is indeed a square.
        if p == 40 && (&n_int * &n_int).sqrt() == n_int {
            return false;
        }

        p += 1;
    }

    // Grantham definition of "extra strong Lucas pseudoprime", after Thm 2.3 on p. 876
    // (D, P, Q above have become Δ, b, 1):
    //
    // Let U_n = U_n(b, 1), V_n = V_n(b, 1), and Δ = b²-4.
    // An extra strong Lucas pseudoprime to base b is a composite n = 2^r s + Jacobi(Δ, n),
    // where s is odd and gcd(n, 2*Δ) = 1, such that either (i) U_s ≡ 0 mod n and V_s ≡ ±2 mod n,
    // or (ii) V_{2^t s} ≡ 0 mod n for some 0 ≤ t < r-1.
    //
    // We know gcd(n, Δ) = 1 or else we'd have found Jacobi(d, n) == 0 above.
    // We know gcd(n, 2) = 1 because n is odd.
    //
    // Arrange s = (n - Jacobi(Δ, n)) / 2^r = (n+1) / 2^r.
    let mut s = n + 1u32;
    let r = trailing_zeros(&s);
    s >>= r;
    let nm2 = n - 2u32; // n - 2

    // We apply the "almost extra strong" test, which checks the above conditions
    // except for U_s ≡ 0 mod n, which allows us to avoid computing any U_k values.
    // Jacobsen points out that maybe we should just do the full extra strong test:
    // "It is also possible to recover U_n using Crandall and Pomerance equation 3.13:
    // U_n = D^-1 (2V_{n+1} - PV_n) allowing us to run the full extra-strong test
    // at the cost of a single modular inversion. This computation is easy and fast in GMP,
    // so we can get the full extra-strong test at essentially the same performance as the
    // almost extra strong test."

    // Compute Lucas sequence V_s(b, 1), where:
    //
    //	V(0) = 2
    //	V(1) = P
    //	V(k) = P V(k-1) - Q V(k-2).
    //
    // (Remember that due to method C above, P = b, Q = 1.)
    //
    // In general V(k) = α^k + β^k, where α and β are roots of x² - Px + Q.
    // Crandall and Pomerance (p.147) observe that for 0 ≤ j ≤ k,
    //
    //	V(j+k) = V(j)V(k) - V(k-j).
    //
    // So in particular, to quickly double the subscript:
    //
    //	V(2k) = V(k)² - 2
    //	V(2k+1) = V(k) V(k+1) - P
    //
    // We can therefore start with k=0 and build up to k=s in log₂(s) steps.
    let mut vk = BigUint::from(2u8);
    let mut vk1 = BigUint::from(p);

    for i in (0..s.bits()).rev() {
        if is_bit_set(&s, i) {
            // k' = 2k+1
            // V(k') = V(2k+1) = V(k) V(k+1) - P
            let t1 = (&vk * &vk1) + n - p;
            vk = &t1 % n;
            // V(k'+1) = V(2k+2) = V(k+1)² - 2
            let t1 = (&vk1 * &vk1) + &nm2;
            vk1 = &t1 % n;
        } else {
            // k' = 2k
            // V(k'+1) = V(2k+1) = V(k) V(k+1) - P
            let t1 = (&vk * &vk1) + n - p;
            vk1 = &t1 % n;
            // V(k') = V(2k) = V(k)² - 2
            let t1 = (&vk * &vk) + &nm2;
            vk = &t1 % n;
        }
    }

    // Now k=s, so vk = V(s). Check V(s) ≡ ±2 (mod n).
    if vk == BigUint::from(2u8) || vk == nm2 {
        // Check U(s) ≡ 0.
        // As suggested by Jacobsen, apply Crandall and Pomerance equation 3.13:
        //
        //	U(k) = D⁻¹ (2 V(k+1) - P V(k))
        //
        // Since we are checking for U(k) == 0 it suffices to check 2 V(k+1) == P V(k) mod n,
        // or P V(k) - 2 V(k+1) == 0 mod n.
        let mut t1 = &vk * p;
        let mut t2 = &vk1 << 1;

        if t1 < t2 {
            ::std::mem::swap(&mut t1, &mut t2);
        }

        t1 -= t2;

        if (t1 % n).is_zero() {
            return true;
        }
    }

    // Check V(2^t s) ≡ 0 mod n for some 0 ≤ t < r-1.
    for _ in 0..r - 1 {
        if vk.is_zero() {
            return true;
        }

        // Optimization: V(k) = 2 is a fixed point for V(k') = V(k)² - 2,
        // so if V(k) = 2, we can stop: we will never find a future V(k) == 0.
        if vk == BigUint::from(2u8) {
            return false;
        }

        // k' = 2k
        // V(k') = V(2k) = V(k)² - 2
        let t1 = (&vk * &vk) - 2u32;
        vk = &t1 % n;
    }

    false
}

/// Returns the number of least-significant bits that are zero
fn trailing_zeros<B: Clone + Integer + std::ops::ShrAssign<usize>>(n: &B) -> usize {
    let mut i = 0usize;
    let mut t = n.clone();
    while t.is_even() {
        i += 1;
        t >>= 1_usize;
    }
    i
}

/// Jacobi returns the Jacobi symbol (x/y), either +1, -1, or 0.
/// The y argument must be an odd integer.
#[allow(clippy::many_single_char_names)]
fn jacobi(x: &BigInt, y: &BigInt) -> isize {
    if !y.is_odd() {
        panic!(
            "invalid arguments, y must be an odd integer,but got {:?}",
            y
        );
    }

    let mut a = x.clone();
    let mut b = y.clone();
    let mut j = 1;

    if b.is_negative() {
        if a.is_negative() {
            j = -1;
        }
        b = -b;
    }

    loop {
        if b.is_one() {
            return j;
        }
        if a.is_zero() {
            return 0;
        }

        a = a.mod_floor(&b);
        if a.is_zero() {
            return 0;
        }

        // a > 0

        // handle factors of 2 in a
        let s = trailing_zeros(&a);
        if s & 1 != 0 {
            let bmod8 = &b & BigInt::from(7);
            if bmod8 == BigInt::from(3) ||
               bmod8 == BigInt::from(5) {
                j = -j;
            }
        }

        let c = &a >> s; // a = 2^s*c

        // swap numerator and denominator
        if &b & BigInt::from(3) == BigInt::from(3) &&
           &c & BigInt::from(3) == BigInt::from(3) {
            j = -j
        }

        a = b;
        b = c.clone();
    }
}

/// Checks if the i-th bit is set
#[inline]
fn is_bit_set(x: &BigUint, i: usize) -> bool {
    if i >= x.bits() {
        return false;
    }
    let res = x >> i;
    res.is_odd()
}

lazy_static! {
    static ref PRIMES: Vec<BigUint> = gen_primes();
}
lazy_static! {
    static ref TWO: BigUint = BigUint::from(2u8);
}
lazy_static! {
    static ref THREE: BigUint = BigUint::from(3u8);
}

fn gen_primes() -> Vec<BigUint> {
    [
        3u32, 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, 7993, 8009,
        8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087,
        8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161,
        8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231,
        8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
        8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369,
        8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443,
        8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537,
        8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609,
        8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
        8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731,
        8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803,
        8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861,
        8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941,
        8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011,
        9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091,
        9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161,
        9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227,
        9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311,
        9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377,
        9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433,
        9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491,
        9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587,
        9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649,
        9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
        9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791,
        9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857,
        9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929,
        9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037,
        10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099,
        10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163,
        10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247,
        10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303,
        10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369,
        10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459,
        10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531,
        10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627,
        10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691,
        10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771,
        10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859,
        10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937,
        10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003,
        11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087,
        11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161,
        11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251,
        11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317,
        11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399,
        11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483,
        11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551,
        11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657,
        11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731,
        11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813,
        11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887,
        11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941,
        11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011,
        12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101,
        12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161,
        12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251,
        12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323,
        12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401,
        12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473,
        12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527,
        12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589,
        12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653,
        12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739,
        12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821,
        12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907,
        12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967,
        12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033,
        13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109,
        13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177,
        13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259,
        13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337,
        13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421,
        13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499,
        13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597,
        13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681,
        13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723,
        13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799,
        13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879,
        13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933,
        13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033,
        14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143,
        14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221,
        14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323,
        14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407,
        14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461,
        14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549,
        14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627,
        14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699,
        14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753,
        14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821,
        14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887,
        14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957,
        14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073,
        15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137,
        15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217,
        15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277,
        15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331,
        15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401,
        15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473,
        15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569,
        15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643,
        15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727,
        15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773,
        15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859,
        15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919,
        15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007,
        16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087,
        16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183,
        16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249,
        16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349,
        16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427,
        16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493,
        16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603,
        16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661,
        16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747,
        16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843,
        16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927,
        16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993,
        17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053,
        17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159,
        17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231,
        17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327,
        17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389,
        17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467,
        17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519,
        17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599,
        17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683,
        17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783,
        17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863
    ].iter().map(|x| BigUint::from(*x)).collect()
}

#[cfg(test)]
mod tests {
    use super::{is_prime, is_safe_prime, is_prime_baillie_psw, is_safe_prime_baillie_psw, gen_prime, gen_safe_prime, PRIMES};
    use crate::error::Error;
    use num_bigint::BigUint;
    use num_traits::Num;
    use rand::thread_rng;

    #[test]
    fn gen_safe_prime_tests() {
        let mut rng = thread_rng();
        match gen_prime(16, &mut rng) {
            Ok(_) => assert!(false, "No primes allowed under 16 bits"),
            Err(e) => match e {
                Error::BitLength(l) => assert_eq!(l, 16),
                _ => assert!(false, "Unexpected error")
            }
        };

        for bits in [128, 256, 384].iter() {
            let n = gen_safe_prime(*bits, &mut rng).unwrap();
            assert!(is_safe_prime_baillie_psw(&n));
        }
    }

    #[test]
    fn gen_prime_tests() {
        let mut rng = thread_rng();
        match gen_prime(16, &mut rng) {
            Ok(_) => assert!(false, "No primes allowed under 16 bits"),
            Err(e) => match e {
                Error::BitLength(l) => assert_eq!(l, 16),
                _ => assert!(false, "Unexpected error")
            }
        };

        for bits in [256, 512, 1024, 2048].iter() {
            let n = gen_prime(*bits, &mut rng).unwrap();
            assert!(is_prime(&n));
        }
    }

    #[test]
    fn is_prime_tests() {
        for prime in PRIMES.iter() {
            assert!(is_prime(&prime));
        }

        let mut n = BigUint::from(18088387217903330459u64);
        assert!(!is_prime(&(n.clone() >> 1)));
        assert!(is_prime_baillie_psw(&n));
        for _ in 0..5 {
            n <<= 1;
            n += 1u8;
            assert!(is_safe_prime(&n));
            assert!(is_prime_baillie_psw(&n));
        }

        n = BigUint::from_str_radix("33376463607021642560387296949", 10).unwrap();
        assert!(!is_prime(&(n.clone() >> 1)));
        assert!(is_prime_baillie_psw(&n));
        for _ in 0..5 {
            n <<= 1;
            n += 1u8;
            assert!(is_safe_prime(&n));
        }

        n = BigUint::from_str_radix("170141183460469231731687303717167733089", 10).unwrap();
        assert!(!is_prime(&(n.clone() >> 1)));
        assert!(is_prime_baillie_psw(&n));
        for _ in 0..5 {
            n <<= 1;
            n += 1u8;
            assert!(is_safe_prime(&n));
        }

        n = BigUint::from_str_radix("113910913923300788319699387848674650656041243163866388656000063249848353322899", 10).unwrap();
        assert!(!is_prime(&(n.clone() >> 1)));
        assert!(is_prime_baillie_psw(&n));
        for _ in 0..4 {
            n <<= 1;
            n += 1u8;
            assert!(is_safe_prime(&n));
        }

        n = BigUint::from_str_radix("1675975991242824637446753124775730765934920727574049172215445180465220503759193372100234287270862928461253982273310756356719235351493321243304213304923049", 10).unwrap();
        assert!(!is_prime(&(n.clone() >> 1)));
        assert!(is_prime(&n));
        for _ in 0..4 {
            n <<= 1;
            n += 1u8;
            assert!(is_safe_prime(&n));
        }
        n = BigUint::from_str_radix("153739637779647327330155094463476939112913405723627932550795546376536722298275674187199768137486929460478138431076223176750734095693166283451594721829574797878338183845296809008576378039501400850628591798770214582527154641716248943964626446190042367043984306973709604255015629102866732543697075866901827761489", 10).unwrap();

        assert!(!is_prime(&(n.clone() >> 1)));
        assert!(is_prime_baillie_psw(&n));
        for _ in 0..3 {
            n <<= 1;
            n += 1u8;
            assert!(is_safe_prime(&n));
        }
    }
}