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Bug in sample()

Kellie Ottoboni 
Dear all,

Philip Stark and I think we have found a problem with how R generates
random samples, resulting from how it generates random integers between 1
and n. (If we are reading the code correctly, the method is to multiply a
pseudo-random binary fraction by n, take the floor, and add 1; this suffers
from quantization effects that can get quite large when n is just below
2^31).

A better method, used in Python, is to generate ceil(log_2(n))
pseudo-random bits, add 1, and discard values bigger than n.

Attached is a short document explaining the issue in more detail.

Best,
Kellie