Re: Calculator: no exponent, full number ?

[Emanuel Berg]

Marcin Borkowski wrote:

>> (defun hypotenuse (c1 c2)
>>   (sqrt (+ (* c1 c1) (* c2 c2))) )
>
> Just for the fun, let me mention that this is
> not a very good algorithm for computing the
> Pythagorean sum - it may happen that both the
> operands and the result lie within the bounds
> for the given type but this calculation blows
> up because of large squares overflowing.

Well, first let it be known that Marcin is
a professional mathematician, famous for his
remarkable calculations. That said, the above
comment is on the computer side of things,
right? In the math world, what would happen is
just a very large triangle, again - right?

Assuming integers, how large can they be in
Emacs Lisp? Eval us:

most-positive-fixnum ;  536870911
"Typical values are 2**29 − 1 on 32-bit and
2**61 − 1 on 64-bit platforms." [1]

most-negative-fixnum ; -536870912
"Typical values are −2**29 on 32-bit
and −2**61 on 64-bit platforms." [1]

How do you know if your "platform"
(i.e. kernel?) is 32- or 64-bit?

Tricky, but here is an incomplete guide from
the systems I have access to:

    Debian Intel:   uname -m; i686 -> 32-bit, x86_64 -> 64
    OpenBSD:        uname -m; amd64 -> 64 (same type as x86-64 BTW)
    RPi3 Raspbian:  uname -m; armv7l -> 32
    SunOS/Solaris:  'isainfo -kv' tells you

Also remember that you can have 64 HW but still
a 32 Linux kernel - but probably not the other
way around :)) (?)

Otherwise you can use Emacs to find out!

most-positive-fixnum ; 536870911

then compute 2**29 - 1:

    # /bin/zsh
    $ echo $(( 2**29 − 1 ))
    536870911

so yes, it checks out for my RPi3 :)

> Also, it is slow because of the need to
> compute square roots. Interestingly, there
> exists a clever algorithm that does not have
> these problems.

Why don't you post it in Elisp to prove my
point one can use Elisp for math, even advanced
math! <3

> It is used (among others) in Donald Knuth's
> METAFONT. The algorithm is described in the
> paper (using Emanuel's favorite format;-)):

That's true, I frekking *love* Biblatex! [2]

> @ARTICLE{5390405,
>   author={C. {Moler} and D. {Morrison}},
>   journal={IBM Journal of Research and Development},
>   title={Replacing Square Roots by Pythagorean Sums},
>   year={1983},
>   volume={27},
>   number={6},
>   pages={577-581},
>   keywords={},
>   doi={10.1147/rd.276.0577},
>   ISSN={0018-8646},
>   month={Nov},
> }

Only I keep mine much neater :)

@book{land-of-lisp,
  author     = {Conrad Barski},
  isbn       = 1593272812,
  publisher  = {No Starch},
  title      = {Land of Lisp},
  year       = 2010
}

@book{lispcraft,
  author     = {Robert Wilensky},
  isbn       = 0393954420,
  publisher  = {Norton},
  title      = {LISPcraft},
  year       = 1984
}
%% [3]


[1] (info "(elisp) Integer Basics")
[2] https://dataswamp.org/~incal/emacs-init/my-bibtex.el
[3] https://dataswamp.org/~incal//books/books.bib

-- 
underground experts united
http://user.it.uu.se/~embe8573
https://dataswamp.org/~incal