ActiveState Code

Recipe 576707: Long period random number generator

Implements a complementary-multiply-with-carry psuedo-random-number-generator. Period is 3636507990 * 2 ** 43487 (approximately 10 ** 13101).

Python 
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import random

class CMWC(random.Random):
    'Long period random number generator: Complementary Multiply with Carry'
    # http://en.wikipedia.org/wiki/Multiply-with-carry

    a = 3636507990
    logb = 32
    b = 2 ** logb
    r = 1359

    def _gen_word(self):
        i = self.i
        xc, self.c = divmod(self.a * self.Q[i] + self.c, self.b)
        x = self.Q[i] = self.b - 1 - xc
        self.i = 0 if i + 1 == self.r else i + 1
        return x

    def getrandbits(self, k):
        while self.bits < k:
            self.f = (self.f << self.logb) | self._gen_word()
            self.bits += self.logb
        x = self.f & ((1 << k) - 1)
        self.f >>= k;  self.bits -= k
        return x

    def random(self, RECIP_BPF=random.RECIP_BPF, BPF=random.BPF):
        return self.getrandbits(BPF) * RECIP_BPF

    def seed(self, seed=None):
        seeder = random.Random(seed)
        Q = [seeder.randrange(0x100000000) for i in range(self.r)]
        c = seeder.randrange(0x100000000)
        self.setstate((0, 0, 0, c, Q))

    def getstate(self):
        return self.f, self.bits, self.i, self.c, tuple(self.Q)

    def setstate(self, (bits, f, i, c, Q)):
        self.f, self.bits, self.i, self.c, self.Q = f,  bits, i, c, list(Q)


if __name__ == '__main__':
    prng = CMWC(134123413541344)
    for i in range(20):
        print prng.random()
    print
    for i in range(20):
        print normalvariate(mu=5.0, sigma=2.2)

Discussion

Here's a fast generator version of random() optimized for parameter sets where b is an exact power-of-two. It uses the Mersenne Twister generator for seeding the Q array and the initial carry value.

def cmwc_random(seed=None, a=3636507990, b=2**32, logb=32, r=1359):
    seeder = random.Random(seed)
    Q = [seeder.randrange(b) for i in range(r)]
    c = seeder.randrange(b)
    f = bits = 0
    for i in itertools.cycle(range(r)):
        t = a * Q[i] + c
        c = t & (b - 1)
        x = Q[i] = b - 1 - (t >> logb)
        f = (f << logb) | x;  bits += logb
        if bits >= 53:            
            yield (f & (2 ** 53 - 1)) * (2 ** -53)
            f >>= 53;  bits -= 53

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