# Copyright (C) 2022-2023 Exaloop Inc. <https://exaloop.io>

import sys
from math import inf as INF, sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
from bisect import bisect as _bisect
from time import time as _time

N = 624
M = 397
LOG4 = _log(4.0)
NV_MAGICCONST = 4 * _exp(-0.5) / _sqrt(2.0)
SG_MAGICCONST = 1.0 + _log(4.5)
TWOPI = 2.0 * _pi

MATRIX_A = u32(0x9908b0df)    # constant vector a
UPPER_MASK = u32(0x80000000)  # most significant w-r bits
LOWER_MASK = u32(0x7fffffff)  # least significant r bits

@tuple
class RandomGenerator:
    data: Ptr[u32]

    def __new__():
        return RandomGenerator(Ptr[u32](N + 1))

    @property
    def index(self):
        return int(self.data[0])

    @property
    def state(self):
        return self.data + 1

    def getstate(self):
        from internal.gc import sizeof
        p = Ptr[u32](N + 1)
        str.memcpy(p.as_byte(), self.data.as_byte(), (N + 1) * sizeof(u32))
        return p

    def setstate(self, state):
        from internal.gc import sizeof
        str.memcpy(self.data.as_byte(), state.as_byte(), (N + 1) * sizeof(u32))

    def genrand_int32(self) -> u32:
        mag01 = (u32(0), MATRIX_A)
        mt = self.state

        if self.index >= N:
            kk = 0

            while kk < int(N - M):
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK)
                mt[kk] = mt[kk + M] ^ (y >> u32(1)) ^ mag01[int(y & u32(1))]
                kk += 1

            while kk < int(N - 1):
                y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK)
                mt[kk] = mt[kk+(M-N)] ^ (y >> u32(1)) ^ mag01[int(y & u32(1))]
                kk += 1

            y = (mt[N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK)
            mt[N-1] = mt[M-1] ^ (y >> u32(1)) ^ mag01[int(y & u32(1))]
            self.data[0] = u32(0)

        i = self.index
        y = mt[i]
        self.data[0] = u32(i + 1)
        y ^= (y >> u32(11))
        y ^= (y << u32(7)) & u32(0x9d2c5680)
        y ^= (y << u32(15)) & u32(0xefc60000)
        y ^= (y >> u32(18))
        return y

    def genrand_res53(self) -> float:
        a = self.genrand_int32() >> u32(5)
        b = self.genrand_int32() >> u32(6)
        return (int(a) * 67108864.0 + int(b)) * (1.0 / 9007199254740992.0)

    def random(self):
        return self.genrand_res53()

    def init_u32(self, s: u32):
        mt = self.state
        mt[0] = s
        for mti in range(1, N):
            mt[mti] = (u32(1812433253) * (mt[mti-1] ^ (mt[mti-1] >> u32(30))) + u32(mti))
        self.data[0] = u32(N)

    def init_array(self, init_key: Ptr[u32], key_length: int):
        mt = self.state
        self.init_u32(u32(19650218))
        i = 1
        j = 0

        k = N if N > key_length else key_length
        while k:
            mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> u32(30))) * u32(1664525))) + init_key[j] + u32(j)
            i += 1
            j += 1
            if i >= N:
                mt[0] = mt[N - 1]
                i = 1
            if j >= key_length:
                j = 0
            k -= 1

        k = N - 1
        while k:
            mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> u32(30))) * u32(1566083941))) - u32(i)
            i += 1
            if i >= N:
                mt[0] = mt[N - 1]
                i = 1
            k -= 1

        mt[0] = u32(0x80000000)

    def init_int(self, s: int):
        init_key = (u32(s & ((1 << 32) - 1)), u32(s >> 32))
        self.init_array(Ptr[u32](__ptr__(init_key).as_byte()), 2 if init_key[1] else 1)

    def random_seed_time_pid(self):
        now = _C.seq_time() * 1000
        key = __array__[u32](5)
        key[0] = u32(now & 0xFFFFFFFF)
        key[1] = u32(now >> 32)
        key[2] = u32(_C.seq_pid())
        now = _C.seq_time_monotonic()
        key[3] = u32(now & 0xFFFFFFFF)
        key[4] = u32(now >> 32)
        self.init_array(key.ptr, len(key))

    def seed(self, s: int):
        self.init_int(s)

    def seed(self):
        self.random_seed_time_pid()

class Random:
    """
    Random number generator base class used by bound module functions.
    Used to instantiate instances of Random to get generators that don't
    share state.
    Class Random can also be subclassed if you want to use a different basic
    generator of your own devising: in that case, override the following
    methods:  random(), seed(), getstate(), and setstate().
    Optionally, implement a getrandbits() method so that randrange()
    can cover arbitrarily large ranges.
    """
    gen: RandomGenerator  # comment for another error
    gauss_next: Optional[float]

    def __init__(self, seed: Optional[int] = None):
        """
        Initialize an instance.

        Optional argument x controls seeding, as for Random.seed().

        For now x is set to its default None.
        """
        self.gen = RandomGenerator()
        self.seed(seed)

    def seed(self, a: Optional[int]):
        """
        Initialize internal state from hashable object.

        None or no argument seeds from current time or from an operating
        system specific randomness source if available.

        If *a* is an int, all bits are used.

        For version 2 (the default), all of the bits are used if *a* is a str,
        bytes, or bytearray.  For version 1 (provided for reproducing random
        sequences from older versions of Python), the algorithm for str and
        bytes generates a narrower range of seeds.
        """
        if a is not None:
            self.gen.seed(abs(a))
        else:
            self.gen.seed()
        self.gauss_next = None

    def getstate(self):
        return self.gen.getstate(), self.gauss_next

    def setstate(self, state):
        gen_state, gauss_next = state
        self.gen.setstate(gen_state)
        self.gauss_next = gauss_next

    def getrandbits(self, k: int) -> int:
        """
        getrandbits(k) -> x
        Generates an int with k random bits.
        """
        if k == 0:
            return 0

        if k < 0:
            raise ValueError("number of bits must be non-negative")

        if k > 64:
            raise ValueError("number of bits cannot be greater than 64")

        if k <= 32:  # Fast path
            r = int(self.gen.genrand_int32())
            m = r >> (32 - k)
            return m

        lo = u64(int(self.gen.genrand_int32()))
        hi = u64(int(self.gen.genrand_int32()))
        mask = ~((u64(1) << u64(64 - k)) - u64(1))
        hi &= mask
        hi >>= u64(64 - k)
        return int((hi << u64(32)) | lo)

    def bit_length(self, n: int) -> int:
        """ """
        len = 0
        while n:
            len += 1
            n = int(u64(n) >> u64(1))
        return len

    def _randbelow_with_getrandbits(self, n: int) -> int:
        """
        Return a random int in the range [0,n).  Raises ValueError if n==0.
        """
        getrandbits = self.getrandbits
        k = self.bit_length(n)  # don't use (n-1) here because n can be 1
        r = getrandbits(k)  # 0 <= r < 2**k
        while r >= n:
            r = getrandbits(k)
        return r

    def randrange(self, start: int, stop: int, step: int = 1) -> int:
        """
        Choose a random item from range(start, stop[, step]).

        Return a randomly selected element from range(start, stop, step).
        This is equivalent to choice(range(start, stop, step)), but
        doesn’t actually build a range object.

        For now stop == 0 for randrange(stop) where start = stop in our parameter.
        Defaults include: stop = None, step = 1
        for now we will use default value for step.
        """
        if stop == 0:
            if start > 0:
                return self._randbelow_with_getrandbits(start)
            raise ValueError("empty range for randrange()")

        # stop argument supplied.
        width = stop - start
        if step == 1 and width > 0:
            return start + self._randbelow_with_getrandbits(width)
        if step == 1:
            raise ValueError("empty range for randrange()")

        # Non-unit step argument supplied.
        n = INF
        if step > 0:
            n = float((width + step - 1) // step)
        elif step < 0:
            n = float((width + step + 1) // step)
        else:
            raise ValueError("zero step for randrange()")

        if n <= 0:
            raise ValueError("empty range for randrange()")

        return start + step * self._randbelow_with_getrandbits(int(n))

    def randint(self, a: int, b: int):
        """
        Return random integer in range [a, b], including both end points.
        """
        return self.randrange(a, b + 1, 1)

    def random(self) -> float:
        """
        random(self) -> float

        Return the next random floating point number in the range [0.0, 1.0).
        """
        return self.gen.genrand_res53()

    def choice(self, sequence: Generator[T], T: type) -> T:
        """
        Choose a random element from a non-empty sequence.
        """
        i = 0
        l = list(sequence)
        try:
            i = self._randbelow_with_getrandbits(len(l))
        except ValueError:
            raise IndexError("Cannot choose from an empty sequence")
        return l[i]

    def shuffle(self, x):
        """
        Shuffle list x in place, and return None.

        Optional argument random is a 0-argument function returning a
        random float in [0.0, 1.0); if it is the default None, the
        standard random.random will be used.

        For now seq will use random = 0  (None = default)
        """
        random = 0
        if random == 0:
            randbelow = self._randbelow_with_getrandbits
            for i in reversed(range(1, len(x))):
                # pick an element in x[:i+1] with which to exchange x[i]
                j = randbelow(i + 1)
                x[i], x[j] = x[j], x[i]
        else:
            for i in reversed(range(1, len(x))):
                # pick an element in x[:i+1] with which to exchange x[i]
                j = int(self.random() * (i + 1))
                x[i], x[j] = x[j], x[i]

    def uniform(self, a, b) -> float:
        """
        Get a random number in the range [a, b) or [a, b] depending on rounding.
        """
        return a + (b - a) * self.random()

    def triangular(self, low: float, high: float, mode: float) -> float:
        """
        Triangular distribution.

        Continuous distribution bounded by given lower and upper limits,
        and having a given mode value in-between.

        http://en.wikipedia.org/wiki/Triangular_distribution

        For now we mode to default: mode = None
        default for low and high : low = 0.0, high = 1.0
        """
        # mode = None
        if high == low:
            return low
        u = self.random()
        c = (mode - low) / (high - low)
        if u > c:
            u = 1.0 - u
            c = 1.0 - c
            low, high = high, low
        return low + (high - low) * _sqrt(u * c)

    def gammavariate(self, alpha: float, beta: float) -> float:
        """
        Gamma distribution.  Not the gamma function!

        Conditions on the parameters are alpha > 0 and beta > 0.

        The probability distribution function is:

        ::

                    x ** (alpha - 1) * math.exp(-x / beta)
          pdf(x) =  --------------------------------------
                      math.gamma(alpha) * beta ** alpha
        """
        # alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2

        # Warning: a few older sources define the gamma distribution in terms
        # of alpha > -1.0
        if alpha <= 0.0 or beta <= 0.0:
            raise ValueError("gammavariate: alpha and beta must be > 0.0")

        if alpha > 1.0:

            # Uses R.C.H. Cheng, "The generation of Gamma
            # variables with non-integral shape parameters",
            # Applied Statistics, (1977), 26, No. 1, p71-74

            ainv = _sqrt(2.0 * alpha - 1.0)
            bbb = alpha - LOG4
            ccc = alpha + ainv

            while 1:
                u1 = self.random()
                if not 1e-7 < u1 < 0.9999999:
                    continue
                u2 = 1.0 - self.random()
                v = _log(u1 / (1.0 - u1)) / ainv
                x = alpha * _exp(v)
                z = u1 * u1 * u2
                r = bbb + ccc * v - x
                if r + SG_MAGICCONST - 4.5 * z >= 0.0 or r >= _log(z):
                    return x * beta

        elif alpha == 1.0:
            # expovariate(1/beta)
            return -_log(1.0 - self.random()) * beta

        else:  # alpha is between 0 and 1 (exclusive)

            # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
            x = 0.0
            while 1:
                u = self.random()
                b = (_e + alpha) / _e
                p = b * u
                if p <= 1.0:
                    x = p ** (1.0 / alpha)
                else:
                    x = -_log((b - p) / alpha)
                u1 = self.random()
                if p > 1.0:
                    if u1 <= x ** (alpha - 1.0):
                        break
                elif u1 <= _exp(-x):
                    break
            return x * beta

    def betavariate(self, alpha: float, beta: float) -> float:
        """
        Beta distribution.
        Conditions on the parameters are alpha > 0 and beta > 0.
        Returned values range between 0 and 1.
        """
        # This version due to Janne Sinkkonen, and matches all the std
        # texts (e.g., Knuth Vol 2 Ed 3 pg 134 "the beta distribution").
        y = self.gammavariate(alpha, 1.0)
        if y == 0:
            return 0.0
        else:
            return y / (y + self.gammavariate(beta, 1.0))

    def expovariate(self, lambd: float) -> float:
        """
        Exponential distribution.

        lambd is 1.0 divided by the desired mean.  It should be
        nonzero.

        Returned values range from 0 to
        positive infinity if lambd is positive, and from negative
        infinity to 0 if lambd is negative.
        """
        if lambd == 0.0:
            raise ZeroDivisionError("Cannot divide by zero")
        # lambd: rate lambd = 1/mean
        # we use 1-random() instead of random() to preclude the
        # possibility of taking the log of zero.
        return -_log(1.0 - self.random()) / lambd

    def gauss(self, mu: float = 0.0, sigma: float = 1.0) -> float:
        """
        Gaussian distribution.

        mu is the mean, and sigma is the standard deviation.  This is
        slightly faster than the normalvariate() function.
        Not thread-safe without a lock around calls.
        """
        z = self.gauss_next
        self.gauss_next = None
        if z is None:
            x2pi = self.random() * TWOPI
            g2rad = _sqrt(-2.0 * _log(1.0 - self.random()))
            z = _cos(x2pi) * g2rad
            self.gauss_next = _sin(x2pi) * g2rad
        return mu + z * sigma

    def paretovariate(self, alpha: float) -> float:
        """
        Pareto distribution.  alpha is the shape parameter."""
        u = 1.0 - self.random()
        return 1.0 / u ** (1.0 / alpha)

    def weibullvariate(self, alpha: float, beta: float) -> float:
        """
        Weibull distribution.

        alpha is the scale parameter and beta is the shape parameter.
        """
        u = 1.0 - self.random()
        return alpha * (-_log(u)) ** (1.0 / beta)

    def normalvariate(self, mu: float = 0.0, sigma: float = 1.0) -> float:
        """
        Normal distribution.

        mu is the mean, and sigma is the standard deviation.
        """
        z = 0.0
        while 1:
            u1 = self.random()
            u2 = 1.0 - self.random()
            z = NV_MAGICCONST * (u1 - 0.5) / u2
            zz = z * z / 4.0
            if zz <= -_log(u2):
                break
        return mu + z * sigma

    def lognormvariate(self, mu: float, sigma: float) -> float:
        """
        Log normal distribution.

        If you take the natural logarithm of this distribution, you'll get a
        normal distribution with mean mu and standard deviation sigma.
        mu can have any value, and sigma must be greater than zero.
        """
        return _exp(self.normalvariate(mu, sigma))

    def vonmisesvariate(self, mu: float, kappa: float) -> float:
        """
        Circular data distribution.

        mu is the mean angle, expressed in radians between 0.0 and 2*pi, and
        kappa is the concentration parameter, which must be greater than or
        equal to zero.  If kappa is equal to zero, this distribution reduces
        to a uniform random angle over the range 0.0 to 2*pi.
        """
        def _mod(a: float, b: float):
            @pure
            @llvm
            def _truediv_float_float(self: float, other: float) -> float:
                %0 = fdiv double %self, %other
                ret double %0

            @pure
            @llvm
            def _mod_float_float(self: float, other: float) -> float:
                %0 = frem double %self, %other
                ret double %0

            mod = _mod_float_float(a, b)
            div = _truediv_float_float(a - mod, b)
            if mod:
                if (b < 0) != (mod < 0):
                    mod += b
                    div -= 1.0
            else:
                mod = (0.0).copysign(b)
            return mod

        z = 0.0
        theta = 0.0

        if kappa <= 1e-6:
            return TWOPI * self.random()

        s = 0.5 / kappa
        r = s + _sqrt(1.0 + s * s)

        while 1:
            u1 = self.random()
            z = _cos(_pi * u1)

            d = z / (r + z)
            u2 = self.random()
            if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d):
                break

        q = 1.0 / r
        f = (q + z) / (1.0 + q * z)
        u3 = self.random()
        if u3 > 0.5:
            theta = _mod(mu + _acos(f), TWOPI)
        else:
            theta = _mod(mu - _acos(f), TWOPI)

        return theta

    def sample(self, population: List[T], k: int, T: type):
        """
        Chooses k unique random elements from a population sequence or set.

        Returns a new list containing elements from the population while
        leaving the original population unchanged.  The resulting list is
        in selection order so that all sub-slices will also be valid random
        samples.  This allows raffle winners (the sample) to be partitioned
        into grand prize and second place winners (the subslices).

        Members of the population need not be hashable or unique.  If the
        population contains repeats, then each occurrence is a possible
        selection in the sample.

        To choose a sample in a range of integers, use range as an argument.
        This is especially fast and space efficient for sampling from a
        large population:   sample(range(10000000), 60)

        For now seq will deal with only lists.
        """
        randbelow = self._randbelow_with_getrandbits
        n = len(population)
        if not 0 <= k <= n:
            raise ValueError("Sample larger than population or is negative")
        result = [T() for _ in range(k)]
        setsize = 21.0  # size of a small set minus size of an empty list
        if k > 5:
            # Should be _log(k * 3, 4)
            setsize += 4 ** _ceil(_log(float(k * 3)))  # table size for big sets
        if n <= setsize:
            # An n-length list is smaller than a k-length set
            pool = list(population)
            for i in range(k):  # invariant:  non-selected at [0,n-i)
                j = randbelow(n - i)
                result[i] = pool[j]
                pool[j] = pool[n - i - 1]  # move non-selected item into vacancy
        else:
            selected = Set[int]()
            selected_add = selected.add
            for i in range(k):
                j = randbelow(n)
                while j in selected:
                    j = randbelow(n)
                selected_add(j)
                result[i] = population[j]
        return result

    def choices(
        self,
        population,
        weights: Optional[List[int]],
        cum_weights: Optional[List[int]],
        k: int,
    ):
        """
        Return a k sized list of population elements chosen with replacement.

        If the relative weights or cumulative weights are not specified,
        the selections are made with equal probability.

        Since weights and cum_weights is assumed to be positive, we will replace None with [-1].
        """

        def accumulate(weights: List[int]) -> List[int]:
            """
            Calculate cum_weights
            """
            n = len(weights)
            cum_weight = List[int](n)
            accum = 0
            if n > 0:
                for i in range(n):
                    accum += weights[i]
                    cum_weight.append(accum)

            return cum_weight

        n = len(population)
        if cum_weights is None:
            if weights is None:
                return [population[int(self.random() * n)] for i in range(k)]
            cum_weights = accumulate(weights)
        elif weights is not None:
            raise TypeError("Cannot specify both weights and cumulative weights")
        if len(cum_weights) != n:
            raise ValueError("The number of weights does not match the population")

        total = float(cum_weights[-1])  # convert to float
        hi = n - 1
        return [
            population[_bisect(cum_weights, int(self.random() * total), 0, hi)]
            for i in range(k)
        ]

_rnd = Random()

def seed(a: int):
    _rnd.seed(a)

def getrandbits(k: int):
    return _rnd.getrandbits(k)

def randrange(start: int, stop: Optional[int] = None, step: int = 1):
    return _rnd.randrange(start, stop, step) if stop is not None else _rnd.randrange(0, start, step)

def randint(a: int, b: int):
    return _rnd.randint(a, b)

def choice(s):
    return _rnd.choice(s)

def choices(
    population,
    weights: Optional[List[int]] = None,
    cum_weights: Optional[List[int]] = None,
    k: int = 1,
):
    return _rnd.choices(population, weights, cum_weights, k)

def shuffle(s):
    _rnd.shuffle(s)

def sample(population, k: int):
    return _rnd.sample(population, k)

def random():
    return _rnd.random()

def uniform(a, b):
    return _rnd.uniform(a, b)

def triangular(low: float = 0.0, high: float = 1.0, mode: Optional[float] = None):
    return _rnd.triangular(low, high, mode if mode is not None else (low + high) / 2)

def betavariate(alpha: float, beta: float):
    return _rnd.betavariate(alpha, beta)

def expovariate(lambd: float):
    return _rnd.expovariate(lambd)

def gammavariate(alpha: float, beta: float):
    return _rnd.gammavariate(alpha, beta)

def gauss(mu: float, sigma: float):
    return _rnd.gauss(mu, sigma)

def lognormvariate(mu: float, sigma: float):
    return _rnd.lognormvariate(mu, sigma)

def normalvariate(mu: float, sigma: float):
    return _rnd.normalvariate(mu, sigma)

def vonmisesvariate(mu: float, kappa: float):
    return _rnd.vonmisesvariate(mu, kappa)

def paretovariate(alpha: float):
    return _rnd.paretovariate(alpha)

def weibullvariate(alpha: float, beta: float):
    return _rnd.weibullvariate(alpha, beta)
