HP-35’s x^y Why?

[robve]

(11-03-2021 03:43 PM)J-F Garnier Wrote:  

(11-03-2021 02:38 PM)robve Wrote:  Wow. This is even worse,

Rob, I can be interested by comparing math algorithms, but not by systematic denigrating.

Math, logic and engineering people are not subject to critique or discussion here.

Justly criticizing a machine or a technology is not denigrating. There is no rationale to anthropomorphize objects or algorithms. There is no systematic aspect to that either. Really strange to hear accusations to intentionally repeatedly criticizing the same thing. I've never posted anything negative about the HP 35s before in my life.

I hold the (former) engineers at HP (and other brands) in high esteem for technical prowess and innovation.

It is not uncommon to find poor decisions with respect to handling roundoff in the past. It is a tradeoff. Increasing the fp accuracy by adding roundoff "correction" digits or increasing the algorithmic complexity of an arithmetic operation is not without manufacturing cost. Consider for example Sharp PC-1500 3^2 does not equal 9 exactly. At least they did not hide it. It's in the manual with an explanation. I don't care what machine or brand we're talking about.

Algorithms and implementation decisions can be poor, often in hindsight. That is why we fix em and continually innovate. If someone defends a poor implementation then that's open to debate, critique, or correction. In self-reflection, I like to hear if something is not working as documented so it can be fixed. You want to build something solid from the get-go. Unfortunately, to avoid any algorithmic mistakes requires algorithm proofs, think axiomatic or denotational semantics to provide such strong assurances. This can still go wrong if the assumptions (weakest preconditions in axiomatic semantics) are not met in practice. The Ariane 5 disaster comes to mind.

(11-03-2021 03:43 PM)J-F Garnier Wrote:  It can also be fooled to get it wrong

(-128)^(1÷6.999) = 2.00019808 ???

That's why I was thinking that there would be a calculator that returns (-128)^(.1428571429)=-2 perhaps, but did not find yet it though I'm sure there is a value close enough to 1/7 that will trip it up. (-128)^(1/6.999)=2.00019808 is a good one! I suspect that moving to smaller integer reciprocals beyond 1/7 could produce some interesting artifacts.

So no, I wouldn't use this Casio either to launch rockets See? I fixed it: this sure sounds better than "it is even worse"!

- Rob