HP-71B Enhanced Math LEX

[J-F Garnier]

An update of the "Math 2" LEX, version 2A is available.

Since no problem was found in the test version 2a, I promoted the version to the regular 2A level, including en passant a few additional enhancements:
- complex number support extended to the decimal log LGT function, to be in line with other calculators such as the 15C, 28C/S, 42S, and later models.
- complex number support also added to the alternate keywords ASN/ACS/ATN/LOG10.
- enhancement of the complex square operation z^2, now internally computed as z*z to provide the same functionality and accuracy for complex numbers than the x^2 key on other calculators (15C, 28C/S, 42S).

Mode details on the z^2 operation enhancement:
With the Math ROM 1A, an operation such as z^2 is internally computed as exp(2*ln(z)).
With complex numbers, this can lead to modest accuracy in some cases, such as:
>(1E-9,1)^2
(-1,2.00000769645E-9)
This is not a bug, other calculators give similar results (exactly the same for the 28C/S, 42S, etc) when using the y^x key.

Now, Math 2A handles the special case when the power is the real number 2 and gives:
>(1E-9,1)^2
(-1,2E-9)
like other calculators using the x^2 function.
Actually, it is still possible to use the general involution formula by forcing a complex power:
>(1E-9,1)^(2,0)
(-1,2.00000769645E-9)
Moreover, the special case is not based on a pattern detected during the expression parsing but at execution, so an expression like
X=2 @ (1E-9,1)^X is also handled.

The weakness of the z^2 operation in the HP71 Math ROM was mentioned in this article (last pages) of W. Kahan, now it is fixed!

J-F