Re: 2button, 1op RPN calculator, again

This is just a curiosity.  I thought I'd point out its uselessness
for encoding computation of scientific use.

What is the precision and accuracy of eml?

If it is not specified, it should be clear that it is useless.

 If it is specified, then examples for which the result
is arbitrarily incorrect can be devised.

If eml were used (say) for plotting, the picture could be arbitrarily wrong.

Maybe the original author addresses this?
RJF

On Tue, May 5, 2026 at 1:12 PM Stavros Macrakis <[email protected]> wrote:

> It has to have some way of entering other inputs if you want to denote
> anything but constants. Or maybe you pre-push the inputs onto the stack, in
> general multiple instances of them so that they'll be available at the
> right place.
>
> On Tue, May 5, 2026 at 12:14 PM Henry Baker <[email protected]> wrote:
>
>> I just realized that this calculator doesn't have any 'regular' buttons
>> at all; the only 2 buttons are the parentheses '(' and ')'.
>>
>> The '(' button pushes '1' onto the stack; the ')' replaces the top 2 elts
>> of the stack with the single object eml(x,y), where x,y were the top two
>> elements of the stack.
>>
>> Clearly '(' increments the stack length by 1, while ')' decrements the
>> stack length by 1, so we have a *parenthesis language*, and only properly
>> paired parentheses are allowed.
>>
>> The stack comes initialized with a single object '1', because *every*
>> legal computation has to start with a push, and the only constant that can
>> be pushed onto the stack is a '1', so we needn't bother with that first
>> push instruction at all !
>>
>> The number of legal instruction sequences of length 2n is Catalan(n) =
>> binomial(2*n,n)/(n+1).
>>
>> This means that the fraction of legal instruction sequences approaches
>> zero as the length of the sequence grows, so the bit efficiency of ANY
>> RPN-type representation isn't going to be particularly good.
>>
>>
>>
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