import random
import matplotlib.pyplot as plt

def rnd5():
    while True:
        yield random.randint(1,5)

# idea behind this:
# fold sufficiently large (size affects precision)
# string of base5 numbers to a [0.0, 1.0) range,
# then unfold it into a base7 number and take its
# integral part
#
# takes fixed point base5 number in an
# array ordered most-significant digit first
# (0 . b5[0] b5[1] ... b5[-1])
# returns first digit after the point of base7 number
def b5tob7d1(b5):
    fp = 0.0
    for d in b5:
        fp = fp * 5.0 + d
    fp /= pow(5, len(b5))
    return int(fp * 7)

def rnd7(rnd5, precision):
    source = [rnd5.next()-1 for i in range(precision)]
    while True:
        yield b5tob7d1(source)+1
        source.pop(0)
        source.append(rnd5.next()-1)



# visual 'proof'

r5 = rnd5()
gens = [(r5, 5, ''),
        (rnd7(r5, 1), 7, ' d=1'),
        (rnd7(r5, 2), 7, ' d=2'),
        (rnd7(r5, 3), 7, ' d=3'),
        (rnd7(r5, 4), 7, ' d=4'),
]

def samples(gen):
    sample_sizes = [100, 1000, 10000]
    return [([gen.next() for i in range(s)], s) for s in sample_sizes]

samples = [(samples(g), r, t) for (g, r, t) in gens]

plt.interactive(True)

for i in range(len(samples)):
    ss, r, t = samples[i]
    for j in range(len(ss)):
        s, n = ss[j]
        plt.subplot(len(ss), len(samples), j*len(samples)+i+1)
        plt.hist(s, range(1,r+2), normed=True)
        plt.title('1..%d %s n=%d'%(r, t, n))

plt.subplots_adjust(hspace=0.3, wspace=0.4)
plt.draw()
plt.waitforbuttonpress()