Re: HP calculators and decimal (BCD) floating-point precision...

[Albert Chan <albertmcchan@...>]

My recollection is that all computation internally for the
built-in algorithms was performed in ** 13-digit ** registers,
and the final result was rounded to ten digits for display.

I don't know if the internal storage registers were limited to
10 digits, or if they also supported 13-digit floating-point
values.  This would have been relevant where user-defined
programs (and subroutines etc) were executed.

My recollection may be incorrect... but if not, it may explain
some of the results that people have been talking about.

cheers,

sur-behoffski etc etc

I was just reading some history of HP calculators

http://history.siam.org/\/pdfs2/Kahan_final.pdf

HP-35, HP-45 were doing math with 10 decimals (no internal precision)

HP 13 internal decimals were a response to TI full-page ad (p. 145)

    Type in you telephone numbers.

    Now, take the logarithm

    Now, hit the exponential key

    Do you get your numbers back ?

    You do on our calculator ...

Why decimal math [1] ? (page 137, For humans, decimal is best)

HP34C (HP41C too ?) NiCad leaking batteries (page 148)

History of HP12C (page 151)

Why HP15C so rare (page 158)

The HP 12C was successful enough that they were willing to take my advice about building the 15C, but not take my advice about how many to build. They wanted a third of my figure, and Harms did half again what they wanted, and that’s what they were doing. 

So they never did set up another production line. In consequence, the market was starved. There were waiting lists, and that window closed, and so I never did get the calculators into the hands of sufficiently many students to change the ways in which professors would issue assignments, and that was a bitter disappointment. It colored my relations with this particular group at HP. I continued to work with them for a couple of years, but my heart just wasn’t in it anymore. 

[1] I like decimal calculator with its WYSIWYG numbers

     Binary calculator is also OK (say, doing it in Lua)

What bugs me is mixing them together (binary + fake decimal)

This is how my Casio(s) do roundings ... total mess

_expression_             fx-115ms   fx-260solar

1e10 + .50 - 1e10        0                0

1e10 + .79 - 1e10        0                0

1e10 + .80 - 1e10        0                0.8

1e10 + .94 - 1e10        0                0.9

1e10 + .95 - 1e10        1                0.9

1e10 + .99 - 1e10        1                0.9