numpy arbitrary precision linear algebra

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I have a numpy 2d array [medium/large sized - say 500x500]. I want to find the eigenvalues of the element-wise exponent of it. The problem is that some of the values are quite negative (-800,-1000, etc), and their exponents underflow (meaning they are so close to zero, so that numpy treats them as zero). Is there anyway to use arbitrary precision in numpy?

The way I dream it:

import numpy as np

np.set_precision('arbitrary') # <--- Missing part
a = np.array([[-800.21,-600.00],[-600.00,-1000.48]])
ex = np.exp(a)  ## Currently warns about underflow
eigvals, eigvecs = np.linalg.eig(ex)

I have searched for a solution with gmpy and mpmath to no avail. Any idea will be welcome.

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