For which models was 2^3>8?

[Dieter]

(04-04-2017 06:45 PM)james summers Wrote:  Thanks for the great explanation, Dieter.

Just playing around, my MK-61, after a slight pause gives 7.9999993.
Doing [2] [ENTER] [ln] [3] [x] [e^x] also gives 7.9999993.

Interesting. Without guard digits it should be 7.9999973. What are the intermediate results you get for ln 2 and 3x this?

(04-04-2017 06:45 PM)james summers Wrote:  The 25C is more accurate, but similar, in that [2] [ENTER] [3] [y^x] and [2] [ENTER] [ln] [3] [x] [e^x] both give 8,000000002.

The 25 uses 10 digits as opposed to 8 in the MK-61.

(04-04-2017 06:45 PM)james summers Wrote:  However, my 32E, 41CV and 15C, whilst giving [2] [ENTER] [3] [y^x] as 8.000000000, for [2] [ENTER] [ln] [3] [x] [e^x] they give 8,000000003.

Why do you add an [ENTER] before the log? It's classic RPN. ;-)

The HP32/41/15 of course use the "new accuracy" since 1976 with three additional guard digits. That's why even with a manually calculated exponentional you get the correctly rounded value ...003. The difference to the HP25 result ...002 is probably due to different algorithms and/or rounding methods. In 1976 there were more improvements than just adding the guard digits, cf. the mentioned HP Journal article.

BTW, if you do not have access to the latter: most of the interesting stuff is available on hpl.hp.com.

Dieter