16 cdf(x) = 0.5 + 0.5 * sgn(x) * [1 - {alpha/(alpha + |x|)} ^ beta]
18 For a given beta and a given probability of the 1-node, the alpha
19 is first solved, and then the {alpha, beta} pair is used to generate
30 def cdf_spareto(x, xm, beta):  argument
31   p = 1 - (xm / (np.abs(x) + xm))**beta
36 def get_spareto(p, beta):  argument
40     return ((cdf(1.5, x, beta) - cdf(0.5, x, beta)) /
41             (1 - cdf(0.5, x, beta)) - p)**2
45   parray[0] = 2 * (cdf(0.5, alpha, beta) - 0.5)
46   parray[1] = (2 * (cdf(1.5, alpha, beta) - cdf(0.5, alpha, beta)))
47   parray[2] = (2 * (cdf(2.5, alpha, beta) - cdf(1.5, alpha, beta)))
48   parray[3] = (2 * (cdf(3.5, alpha, beta) - cdf(2.5, alpha, beta)))
49   parray[4] = (2 * (cdf(4.5, alpha, beta) - cdf(3.5, alpha, beta)))
50   parray[5] = (2 * (cdf(6.5, alpha, beta) - cdf(4.5, alpha, beta)))
51   parray[6] = (2 * (cdf(10.5, alpha, beta) - cdf(6.5, alpha, beta)))
52   parray[7] = (2 * (cdf(18.5, alpha, beta) - cdf(10.5, alpha, beta)))
53   parray[8] = (2 * (cdf(34.5, alpha, beta) - cdf(18.5, alpha, beta)))
54   parray[9] = (2 * (cdf(66.5, alpha, beta) - cdf(34.5, alpha, beta)))
55   parray[10] = 2 * (1. - cdf(66.5, alpha, beta))
96 def get_quantized_spareto(p, beta, bits, first_token):  argument
97   parray = get_spareto(p, beta)
107   beta = 8
109     parray = get_quantized_spareto(q / 256., beta, bits, first_token)