HP Prime crashes on undef-undef*i in CAS

[lyuka]

I'm sorry for the long sentence and a little sentimental.

This is what I encountered in a short period of time because of the only thing I tried
to get started with HP Prime, which my wife just gave me as a birthday present.

When explaining Widler's current source to my students, I needed Lambert's W
function to explain the change in current due to the degeneration resistor.

I wanted to plot that graph with the latest graphing calculator, HP Prime.
It's a common function for scientists and engineers, so I thought it must be
included in HP Prime, a 21st century graphing calculator with CAS.
But it didn't have Lambert's W function.

Then I wrote Lambert's W function as a programming exercise in HP Prime.
In HOME, it may be due to the size of the machine epsilon, but the behavior of
convergence by the iterative method such as Halley's method was not good.
In addition to that, I gave up using it in HOME because the standard rounding
is not an even rounding but a rounding towards zero (which accumulates errors).

I wrote the LambertW function in CAS because it is still better than HOME
because it can be used like a degraded version of IEEE 754 64-bit in CAS.
I referred to LambertW in GSL, but the initial values ​​weren't given very well,
so I decided to create another initial value approximation function.

Since the LambertW function is a multi-valued complex function, we need to
make sure that the approximation function does not jump to other branches,
not only at singularities and near zero, but also when given large values.

When I tried to plot it on HP Prime for an overview, HP Prime stalled and restarted.
As a result, the mathematical formulas I wrote experimentally were lost.

I tried to confirm by plotting instead of analytically because it is difficult to confirm
analytically when the formula to be used has not been decided yet.
What I expect from a graphing calculator is that it helps me when I think about it,
but it didn't come true.

When I was investigating to find out the reason why the plot failed, there was a place
where the required digit was temporarily doubled or tripled during the calculation.
But even though it was in the MAXREAL value range, HP Prime seemed to stall there.

When examined individually, it seems that the number of digits that can be used for
complex division is only half that of MAXREAL. I tentatively wrote a complex division
by Smith's method to deal with this.
Calculators that fail to divide complex numbers are like computer beginners trying to
make them. Fortunately, however, I found that the product of the reciprocals of
complex numbers can be used without being so bad.

HP Prime stalled and restarted when I tried to PRINT the calculated value in the
middle of each step of the calculation to see where it exceeded that digit in the formula.
I want to do my job and I don't really want to spend time doing things like these.

Apparently, HP Prime stalls and restarts when I try to PRINT what the calculation
result is undef-undef * i due to poor complex division. PRINT doesn't seem to know
how to behave with a given object. But CAT seems to know it to some extent.

As a professional in electronic circuit design, I always think it is necessary to make
sure that what I design does not behave abnormally in extreme situations, and I
always design it that way. It's a concept called failsafe or foolproof that anyone
involved in product design must know.

However, even though there are no written documents or specifications, there are
developers who say
"Please do not use it in extreme situations" or
"There is no problem because the user did not report it".
I am very sad as a technical professional.

There may be consistency issues with those developed separately, but as
development managers, we take responsibility for knowing what we are using and how.

There is no offense. But I'm disappointed as one of the generations who felt the
[(hp)] logo was a sign of trust.
HP calculators may no longer be professional tools, but more like broken educational toys.

Lyuka