Errors in Bijector power

[Siva Rajesh]

I am exploring the bijector api power. I have the following example in mind. Say, X ~ N(0,1) i.e. X is sampled from a standard normal distribution. What is the distributional properties of X^3. 

This is the minimum reproducible example. 

################################

import tensorflow as tf

import tensorflow_probability as tfp

import numpy as np

tfd = tfp.distributions

tfb = tfp.bijectors

n = tfd.Normal(loc=0., scale=1.)

n_transformed = tfd.TransformedDistribution(n,bijector = tfb.Power(3))

print(n_transformed.quantile(0.10)) ## output -2.1047876 

print(n_transformed.quantile(0.90)) ## 2.1047876

print(n_transformed.cdf(-2.1047876)) ## Gives NaN as the output

print(n_transformed.cdf(2.104786)) ## 0.89999

print(n_transformed.prob(-2)) ## gives NaN

print(n_transformed.prob(2)) ## 0.037879337

#################################

Ideally, if the quantiles are correctly computed, we expect the corresponding the inverse i.e. cdfs also be computed correctly; however, it seems that specifically for negative numbers it gives NaN as the output. Similarly, for the density of computation, for positive inputs, the density is correctly computed; however, for negative inputs, it gives NaN as the output. 

Exploring further, I think it is due to the tf.math.pow function, which is used. Specifically, 

it is due to the fact that tf.math.pow gives NaN for all negative numbers raised to fractional numbers - e.g.  tf.math.pow(-8.0, 1.0/ 3.0) gives NaN

I am not sure where to report this issue. Kindly let me know if there is a way to circumvent this issue to make my reproducible example work. 

Thanks in advance. 

[Eugene Brevdo]

tf.math.pow will give a correct answer if you feed in a complex number:

tf.math.pow(-8.0+0j, 1.0/3.0)
<tf.Tensor: shape=(), dtype=complex128, numpy=(1+1.732050807568877j)>

(and obviously TF's Pow op is picking a complex branch; i'm guessing it's the line for theta=pi).  Either way the issue is probably deeper than just upcasting in a few places.

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