hp33s and factorial timing


On my hp33s (CNA41507077), 200! is very very fast but 100! is a bit slower. Why?



Playing around a bit, 159! is fast, and 158! is slow.

157! is slow, 157.1! is fast.

My guess is that for integers 158 or less, a multiplication loop is done; for other values, some variation on Stirling's formula is used.

They could have started at 20 or so instead of 158. I do not know why this particular value was chosen.


On the original 32s, it seems that the x! is slower and slower all the way up to the overfolw limit. The Gamma function (non-integer factorial), however, is siginificantly faster---detection of the speed difference being above a threshold of around 50!



As seems evident from many of the 33s discussions, the 33s was not just a port of the 32sii but a complete rewrite. I eagerly await the 33s+ with the following:

Bug fixes.

More variables and labels (i up to 10000, multi-character labels and variables).

More readable decimal point.

(The above are the essentials; the ones below are optional)

Ability to turn off thousand's separator.

Matrix operations.

Bit fiddling (and, or, ...).

42s type graphics.

Optional bigger stack.

World peace.


Hi Martin

I would add "editability of equations" to the must have part. If it had that, then the machine would be capable of functioning like the "formula entry" machines out there--giving it a tri-functionality: RPN, old-time ALG-postfix, and Formula. To put the "answer int oa chain of formulas, I suppose you would merely send the evaluation into a variable, and use the variable in the next chain---but an "ans" button could be used, too (like, who needs the cube root feature-replace it!).

I would also change the equation writing system to eliminate the existence of the "unary minus." I find that to be an annoying business--different from machine to machine. (Much worse on the 32sii BTW because it is evaluated before y^x in most but not all circumstances!). The 17bii has no unary minus, and evaluates each minus sign to "reverse" the sign one by one, in other words, you can have 4*---7 in the equation list, and it will evaluate to -28. If you do the same on a 48GX, in 'algebraic' it will parse it to '4*-7' when it is entered to the stack. b If you try '4-*7' it will catch the error during the parsing, and tell you to fix it. These sorts of behaviors make more sense to me.




I'd make a change to the keypad.

Now that I've used the 33s for a few weeks, I find no general problems with the chevron layout. I'm barely even aware of it.

*Except* for the four way 'cursor' key, and the four function keys next to it.

Left and right are OK, and down is very good, but I often don't get the 'Up' properly.

I also find those mode/eng etc. keys a bit fiddly, but perhaps my thumb is too fat ;)


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