HP71B Enhanced Math LEX

01262020, 10:54 AM
Post: #13




RE: HP71B Enhanced Math LEX
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: >(1E9,1)^2 (1,2.00000769645E9) 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: >(1E9,1)^2 (1,2E9) like other calculators using the x^2 function. Actually, it is still possible to use the general involution formula by forcing a complex power: >(1E9,1)^(2,0) (1,2.00000769645E9) Moreover, the special case is not based on a pattern detected during the expression parsing but at execution, so an expression like X=2 @ (1E9,1)^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! JF 

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