codon/stdlib/random.codon at develop · strider4560/codon · GitHub

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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:

gen: RandomGenerator

gauss_next: Optional[float]

def __init__(self, seed: Optional[int] = None):

self.gen = RandomGenerator()

self.seed(seed)

def seed(self, a: Optional[int]):

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:

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:

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:

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 self.randrange(a, b + 1, 1)

def random(self) -> float:

return self.gen.genrand_res53()

def choice(self, sequence: Generator[T], T: type) -> T:

return self.choice(list(sequence))

@overload

def choice(self, sequence: List[T], T: type) -> T:

if not sequence:

raise IndexError("Cannot choose from an empty sequence")

i = self._randbelow_with_getrandbits(len(sequence))

return sequence._get(i)

def shuffle(self, x):

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:

return a + (b - a) * self.random()

def triangular(self, low: float, high: float, mode: float) -> float:

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:

# 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:

# 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:

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:

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:

u = 1.0 - self.random()

return 1.0 / u ** (1.0 / alpha)

def weibullvariate(self, alpha: float, beta: float) -> float:

u = 1.0 - self.random()

return alpha * (-_log(u)) ** (1.0 / beta)

def normalvariate(self, mu: float = 0.0, sigma: float = 1.0) -> float:

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:

return _exp(self.normalvariate(mu, sigma))

def vonmisesvariate(self, mu: float, kappa: float) -> float:

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, k: int):

randbelow = self._randbelow_with_getrandbits

n = len(population)

if not 0 <= k <= n:

raise ValueError("Sample larger than population or is negative")

result = [population[0] 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[T]],

cum_weights: Optional[List[T]],

k: int,

T: type

def accumulate(weights: list[T], T: type) -> list[T]:

n = len(weights)

cum_weight = list[T](n)

accum = T(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, 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[T]] = None,

cum_weights: Optional[List[T]] = None,

k: int = 1,

T: type = int

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)

codon/stdlib/random.codon at develop · strider4560/codon · GitHub

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