Accuracy Management of early HPs

[Matt Agajanian]

SNIP

(09-10-2022 04:49 AM)Steve Simpkin Wrote:  Dr William Kahan was directly responsible for this increased accuracy, starting with the HP-27. See page 144 of the following oral history.
http://history.siam.org/pdfs2/Kahan_final.pdf

I said, “You can do what they do, except for one thing: in order to
be honest, round every result back to ten digits even if you carry thirteen to compute it.” And I
said, “If you do that, then each operation, taken by itself, will give you a rather honest answer,
and you can explain this log exponential thing. That’s easy because when you take the log,
you’ve got the right log. It’s correct to within just a little bit worse than half a unit in the last
digit of the display. Then you can say ‘Now, it’s that error that propagates when you take the
exponential because, if we recovered your telephone number, we’d be getting the exponential not
of the number that you see before you. It would have to be the exponential of something else.’’’

SNIP

Clarify some things, please.

1--Am I to understand that to preserve and display accurate results

(Step 1) a calculation is carried out to 13 places.

(Step 2) this calculated result is displayed and rounded to 10 digits (although 13 digits are internally maintained)

(Step 3) the next calculation uses the 10 digit displayed figure, but calculated with the internal 13 digit result.

(Step 4) Go back to Step 2.

Or am I missing something?