HP-71B Enhanced Math LEX
01-26-2020, 10:54 AM
Post: #13
 J-F Garnier Senior Member Posts: 749 Joined: Dec 2013
RE: HP-71B 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:
>(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
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 Messages In This Thread HP-71B Enhanced Math LEX - J-F Garnier - 01-09-2020, 07:30 PM RE: HP-71B Enhanced Math LEX - rprosperi - 01-09-2020, 10:36 PM RE: HP-71B Enhanced Math LEX - Valentin Albillo - 01-10-2020, 12:00 AM RE: HP-71B Enhanced Math LEX - charger73 - 01-10-2020, 07:23 AM RE: HP-71B Enhanced Math LEX - Raymond Del Tondo - 01-10-2020, 08:58 AM RE: HP-71B Enhanced Math LEX - Sylvain Cote - 01-10-2020, 04:16 PM RE: HP-71B Enhanced Math LEX - Albert Chan - 01-10-2020, 04:44 PM RE: HP-71B Enhanced Math LEX - Albert Chan - 01-10-2020, 05:01 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 01-10-2020, 05:40 PM RE: HP-71B Enhanced Math LEX - Albert Chan - 01-10-2020, 06:29 PM RE: HP-71B Enhanced Math LEX - Erwin - 01-13-2020, 06:10 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 01-13-2020, 07:13 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 01-26-2020 10:54 AM RE: HP-71B Enhanced Math LEX - Albert Chan - 01-26-2020, 03:08 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 01-27-2020, 08:05 AM RE: HP-71B Enhanced Math LEX - Albert Chan - 01-27-2020, 11:35 AM RE: HP-71B Enhanced Math LEX - J-F Garnier - 01-27-2020, 12:42 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 02-12-2020, 07:55 AM RE: HP-71B Enhanced Math LEX - rprosperi - 02-12-2020, 01:55 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 02-14-2020, 12:23 PM RE: HP-71B Enhanced Math LEX - rprosperi - 02-14-2020, 03:04 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 03-19-2020, 07:30 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 04-27-2020, 09:42 AM RE: HP-71B Enhanced Math LEX - Erwin - 04-27-2020, 04:50 PM RE: HP-71B Enhanced Math LEX - Albert Chan - 03-17-2021, 09:00 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 03-18-2021, 08:22 AM RE: HP-71B Enhanced Math LEX - J-F Garnier - 08-08-2020, 09:37 AM RE: HP-71B Enhanced Math LEX - Valentin Albillo - 08-08-2020, 10:14 PM RE: HP-71B Enhanced Math LEX - Paul Dale - 08-09-2020, 11:15 AM RE: HP-71B Enhanced Math LEX - John Keith - 08-09-2020, 02:16 PM RE: HP-71B Enhanced Math LEX - Valentin Albillo - 08-09-2020, 03:49 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-10-2020, 08:21 PM RE: HP-71B Enhanced Math LEX - rprosperi - 08-10-2020, 09:42 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-11-2020, 02:47 PM RE: HP-71B Enhanced Math LEX - Dave Frederickson - 08-11-2020, 04:24 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-11-2020, 05:06 PM RE: HP-71B Enhanced Math LEX - Gene - 08-09-2020, 01:49 AM RE: HP-71B Enhanced Math LEX - Paul Dale - 08-09-2020, 10:10 AM RE: HP-71B Enhanced Math LEX - John Keith - 08-09-2020, 01:04 PM RE: HP-71B Enhanced Math LEX - Dave Frederickson - 08-11-2020, 05:17 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-13-2020, 07:35 AM RE: HP-71B Enhanced Math LEX - Dave Frederickson - 08-13-2020, 03:27 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-13-2020, 04:00 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 08-14-2020, 07:53 AM RE: HP-71B Enhanced Math LEX - Dave Frederickson - 08-14-2020, 09:06 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-20-2020, 08:11 PM RE: HP-71B Enhanced Math LEX - Dave Frederickson - 08-20-2020, 08:34 PM RE: HP-71B Enhanced Math LEX - Erwin - 08-21-2020, 05:34 PM RE: HP-71B Enhanced Math LEX - J-F Garnier - 09-27-2020, 06:25 PM RE: HP-71B Enhanced Math LEX - Dave Frederickson - 09-27-2020, 06:52 PM