Comparisons with zero on HP-65

[Mark Hardman]

(08-30-2017 06:43 PM)Dieter Wrote:  Let me see if I understand this.

For x > ln 2 the e^x command returns a value > 2. So DSZ decrements this to a value >1 and the next step is not skipped.

For 0 < x < ln 2 the e^x command returns a value between 1 and less than 2. So DSZ decrements this to something between 0 and 0,999... and the next step is skipped.

For x < 0 the e^x command returns a value between 0 and less than 1. So DSZ decrements this to something between -1 and 0. I assume that this causes the next step to be skipped.

Somewhere between x=–23 and x=–24 the e^x result is so close to 0 that DSZ decrements this to a plain –1. I don't know how if the HP65 then skipped the next step or not, but I can say that the HP67 does not (!).

But this way the threshold for skip/no-skip is not 0, but ln 2 = 0,6931...
And maybe there is a second threshold somewhere below –20 (not sure).

Did I miss something here?

Dieter

DSZ only skips 2 steps if the value in R8 is exactly zero after being decremented by 1. After posting I realized that there are underflow conditions that will result in e^x returning a value of exactly 1. Results of e^x where -1e-11 <= x <= 1e-10 will also return exactly 1.

I concede that it is not the best solution, but it might have some value in limited cases.

Mark Hardman