HP-71B: 1^Inf Error

[Albert Chan]

The HP-71B is the first handheld to implement the proposed IEEE floating-point math standard.
Back then, IEEE treatment 1^Inf is not defined yet.

Current IEEE treatment of powers edge cases:

(−1.)^(anything, except  NaN) = 1.
(+1.)^(anything, *even* NaN) = 1.

https://en.cppreference.com/w/cpp/numeric/math/pow

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But, HP71B IEEE implementation is not perfect ...

>E=1e-9 @ Z=0.
>acos((2,E))
(5.7735026919E-10,-1.31695789692)
>acos((2,Z))
(0,1.31695789692)      ! ???
>acos((2,-Z))
(0,1.31695789692)
>acos((2,-E))
(5.7735026919E-10,1.31695789692)

IEEE correctly implemented, it should be like this:

>>> from cmath import *
>>> E, Z = 1e-9, 0.
>>> acos(complex(2,E))
(5.7735026918962588e-10-1.3169578969248166j)
>>> acos(complex(2,Z))
-1.3169578969248166j
>>> acos(complex(2,-Z))
1.3169578969248166j
>>> acos(complex(2,-E))
(5.7735026918962588e-10+1.3169578969248166j)