We construct pseudorandom generators for combinatorial shapes, which
substantially gener-

alize combinatorial rectangles, -biased spaces, 0/1 halfspaces, and 0/1 modular
sums.

Our generator uses seed length O(logm + log n + log^{2}(1/eps)) to get
error eps. When m = 2, this gives the fifirst generator of seed length O(log n)
which fools all weight-based tests, meaning that the distribution of the weight
of any subset is "-close to the appropriate binomial distribution in statistical
distance. Along the way, we give a generator for combinatorial rectangles with
seed length O(log^{1.5} n) and error 1/poly(n), matching Lu's bound
[ICALP 1998].

For our proof we give a simple lemma which allows us to convert closeness in
Kolmogorov

(cdf) distance to closeness in statistical distance. As a corollary of our
technique, we give an alternative proof of a powerful variant of the classical
central limit theorem showing convergence in statistical distance, instead of the
usual Kolmogorov distance.