Changing Of The Guard

[jte]

’Mike Morrow’ pid=’9614’ dateline=’1398 Wrote:⋮
⋮ lots of good stuff snipped…
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TI machines used three guard digits at least as early as the SR-50 in 1974. Those non-displayed digits still exist when the value is presented for display. Subtracting a manually keyed-in value that appears identical to the displayed value will generally show the presence of the guard digits in the original value.

Last month I was (in connection with a bug ticket filed for the HP Prime) writing an email to a teacher about hidden guard digits and why the HP Prime differs from other calculators commonly used in classrooms when punching in 1/3*3. I thought I’d use a very simple calculation with a TI-84 to reveal its hidden guard digits — simply 1/3*3-1. But that didn’t reveal that the apparent “1” from 1/3*3 wasn’t actually 1 (“1/3*3-1” had “0” showing up on the display).

So I wholeheartedly agree with the “generally” above! (I.e., not always!) (Using the TI’s floor function revealed that 1/3*3 wasn’t actually 1, as did raising the apparent “1” to the power of 10^10.)

Quote:Most Casio machines (like the fx-115ES Plus) show the same behavior, except that the 115ES has five guard digits! I personally always preferred TI’s use of guard digits to HP’s refusal to improve the precision of calculations on their machines. HP always bizarrely maintained that their failure to provide guard digits was a positive characteristic, compared to TI. That was pure HP BS. For example, I always got far better accuracy of results, due to far better precision, from a fourth-order Runge-Kutta program on a TI-59 than I ever got from the same program executed on a HP-67 or HP-97 or 41C.

To me, at least theoretically, hidden guard digits and precision are two distinct choices. (“Theoretically” as practical computation limits may well have the two decisions connected.) From a debugging / understanding perspective, it is nice to be able to easily see the exact state of a machine. Perhaps a compromise is possible: have the default display mode show less than full precision (hide digits) yet let the user get the calculator to display the numbers as actually stored by changing a setting.