Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.lang.javascript > #38935 > unrolled thread

Loop and move within boundary "interval logic for cursored list"

Back to article view | Back to comp.lang.javascript

Contents

  Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-13 13:46 -0700
    Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-13 14:01 -0700
    Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-13 14:09 -0700
      Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-13 15:05 -0700
        Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-13 18:07 -0700
          Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-13 18:22 -0700
            Re: Loop and move within boundary "interval logic for cursored list" luserdroog <luser.droog@gmail.com> - 2020-10-13 20:36 -0700
              Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 01:34 -0700
                Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 01:37 -0700
                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 01:38 -0700
                  Re: Loop and move within boundary "interval logic for cursored list" luserdroog <luser.droog@gmail.com> - 2020-10-14 10:51 -0700
                    Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-15 18:03 +0100
                      Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-16 03:19 -0700
                        Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-16 19:30 +0100
                          Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-16 12:36 -0700
                            Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-16 19:25 -0700
                Re: Loop and move within boundary "interval logic for cursored list" luserdroog <luser.droog@gmail.com> - 2020-10-14 10:32 -0700
              Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 02:32 -0700
                Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 02:40 -0700
              Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 05:05 -0700
                Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-14 05:16 -0700
            Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-15 18:03 +0100
              Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-15 13:05 -0700
                Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-15 14:58 -0700
                Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-16 19:14 +0100
                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-16 19:23 -0700
                    Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-17 11:05 +0200
                      Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-17 03:07 -0700
                        Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-17 14:47 +0200
                          Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-17 05:59 -0700
                            Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-17 15:21 +0200
                          Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-17 15:09 +0100
                            Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-17 11:11 -0700
                              Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 01:52 -0700
                                Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-19 13:37 +0200
                                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 05:08 -0700
                                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 05:11 -0700
                                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 05:52 -0700
                                    Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-19 19:15 +0200
                                      Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 11:01 -0700
                                        Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-20 15:30 +0200
                                          Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-20 07:26 -0700
                                            Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-21 00:01 +0200
                                              Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-20 18:19 -0700
                                                Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-21 13:01 +0200
                                                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-21 15:07 -0700
                                                    Re: Loop and move within boundary "interval logic for cursored list" "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2020-10-22 01:21 +0200
                                          Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-20 07:31 -0700
                                Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-19 18:04 +0100
                                  Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 10:47 -0700
                                    Re: Loop and move within boundary "interval logic for cursored list" John G Harris <niam@jghnorth.org.uk.invalid> - 2020-10-19 19:33 +0100
                                      Re: Loop and move within boundary "interval logic for cursored list" Jonas Thörnvall <jonas.thornvall@gmail.com> - 2020-10-19 16:36 -0700
                                Re: Loop and move within boundary "interval logic for cursored list" Scott Sauyet <scott@sauyet.com> - 2020-10-20 13:36 -0700

Page 3 of 3 — ← Prev page 1 2 [3]

#39013

=?UTF-8?Q?Jonas_Th=C3=B6rnvall?= <jonas.thornvall@gmail.com> wrote on 19
Oct 2020 in comp.lang.javascript: 

>> > If you consider it sloppy writing out the exact number i could
>> > provide the shortest polynomial representing the exact value of
>> > 100000th fibonacci. 
>> 
>> You seem to fail understanding the concept of "exact" in mathematics.
> 
> Sure i do it is an answer that is not an approximation, my arithmetic is
> exact. 

In that sense even incoorect arithmetic is exact.


-- 
Evertjan.
The Netherlands.
(Please change the x'es to dots in my emailaddress)

[toc] | [prev] | [next] | [standalone]

#39014

Den tisdag 20 oktober 2020 kl. 15:30:19 UTC+2 skrev Evertjan.:
> =?UTF-8?Q?Jonas_Th=C3=B6rnvall?= <jonas.thornvall@gmail.com> wrote on 19
> Oct 2020 in comp.lang.javascript: 
> 
> >> > If you consider it sloppy writing out the exact number i could
> >> > provide the shortest polynomial representing the exact value of
> >> > 100000th fibonacci. 
> >> 
> >> You seem to fail understanding the concept of "exact" in mathematics.
> > 
> > Sure i do it is an answer that is not an approximation, my arithmetic is
> > exact. 
> 
> In that sense even incoorect arithmetic is exact.
> 
> 
> -- 
> Evertjan.
> The Netherlands.
> (Please change the x'es to dots in my emailaddress)

No it isn't using bases for math give rounding errors, even worse bases even use periodic decimal expansions in calculations.

[toc] | [prev] | [next] | [standalone]

#39019

<jonas.thornvall@gmail.com> wrote on 20 Oct 2020 in comp.lang.javascript: 

>> > Sure i do it is an answer that is not an approximation, my arithmetic
>> > is exact. 
>> 
>> In that sense even incorrect arithmetic is exact.
> 
> No it isn't using bases for math give rounding errors, even worse bases
> even use periodic decimal expansions in calculations. 

Can you explain in plain and ***correct** language,
what you mean with this last sentense,
please. 



-- 
Evertjan.
The Netherlands.
(Please change the x'es to dots in my emailaddress)

[toc] | [prev] | [next] | [standalone]

#39020

Den onsdag 21 oktober 2020 kl. 00:01:17 UTC+2 skrev Evertjan.:
> <jonas.thornvall@gmail.com> wrote on 20 Oct 2020 in comp.lang.javascript: 
> 
> >> > Sure i do it is an answer that is not an approximation, my arithmetic
> >> > is exact. 
> >> 
> >> In that sense even incorrect arithmetic is exact.
> > 
> > No it isn't using bases for math give rounding errors, even worse bases
> > even use periodic decimal expansions in calculations. 
> 
> Can you explain in plain and ***correct** language,
> what you mean with this last sentense,
> please. 
> 
> 
> 
> -- 
> Evertjan.
> The Netherlands.
> (Please change the x'es to dots in my emailaddress)

You have to try harder, put in some comas.

[toc] | [prev] | [next] | [standalone]

#39021

=?UTF-8?Q?Jonas_Th=C3=B6rnvall?= <jonas.thornvall@gmail.com> wrote on 21
Oct 2020 in comp.lang.javascript: 

> Den onsdag 21 oktober 2020 kl. 00:01:17 UTC+2 skrev Evertjan.:
>> <jonas.thornvall@gmail.com> wrote on 20 Oct 2020 in
>> comp.lang.javascript: 
>> 
>> >> > Sure i do it is an answer that is not an approximation, my
>> >> > arithmetic is exact. 
>> >> 
>> >> In that sense even incorrect arithmetic is exact.
>> > 
>> > No it isn't using bases for math give rounding errors, even worse
>> > bases even use periodic decimal expansions in calculations. 
>> 
>> Can you explain in plain and ***correct** language,
>> what you mean with this last sentense,
>> please. 
> 
> You have to try harder,

I don't have to do anything, why are you such a rude little boy?

> put in some comas.

Are you permanently in a coma?

-- 
Evertjan.
The Netherlands.
(Please change the x'es to dots in my emailaddress)

[toc] | [prev] | [next] | [standalone]

#39023

Den onsdag 21 oktober 2020 kl. 13:10:11 UTC+2 skrev Evertjan.:
> =?UTF-8?Q?Jonas_Th=C3=B6rnvall?= <jonas.thornvall@gmail.com> wrote on 21
> Oct 2020 in comp.lang.javascript: 
> 
> > Den onsdag 21 oktober 2020 kl. 00:01:17 UTC+2 skrev Evertjan.:
> >> <jonas.thornvall@gmail.com> wrote on 20 Oct 2020 in
> >> comp.lang.javascript: 
> >> 
> >> >> > Sure i do it is an answer that is not an approximation, my
> >> >> > arithmetic is exact. 
> >> >> 
> >> >> In that sense even incorrect arithmetic is exact.
> >> > 
> >> > No it isn't using bases for math give rounding errors, even worse
> >> > bases even use periodic decimal expansions in calculations. 
> >> 
> >> Can you explain in plain and ***correct** language,
> >> what you mean with this last sentense,
> >> please. 
> > 
> > You have to try harder,
> 
> I don't have to do anything, why are you such a rude little boy?
> 
> > put in some comas.
> 
> Are you permanently in a coma?
> 
> -- 
> Evertjan.
> The Netherlands.
> (Please change the x'es to dots in my emailaddress)

Well they said to until i factored RSA on an Atari with a Mac emulator.
http://www.stcarchiv.de/stc1988/11/aladin-version-2-1

[toc] | [prev] | [next] | [standalone]

#39024

<jonas.thornvall@gmail.com> wrote on 22 Oct 2020 in comp.lang.javascript:

>>> put in some comas.
> 
>> Are you permanently in a coma?
> 
> Well they said to until i factored RSA on an Atari with a Mac emulator.
> http://www.stcarchiv.de/stc1988/11/aladin-version-2-1


"they said to .." ???

I don't believe you ever got out of that coma.

Are you experienced in comas?

Why did you "put in comas" in the first place?


-- 
Evertjan.
The Netherlands.
(Please change the x'es to dots in my emailaddress)

[toc] | [prev] | [next] | [standalone]

#39015

Den tisdag 20 oktober 2020 kl. 15:30:19 UTC+2 skrev Evertjan.:
> =?UTF-8?Q?Jonas_Th=C3=B6rnvall?= <jonas.thornvall@gmail.com> wrote on 19
> Oct 2020 in comp.lang.javascript: 
> 
> >> > If you consider it sloppy writing out the exact number i could
> >> > provide the shortest polynomial representing the exact value of
> >> > 100000th fibonacci. 
> >> 
> >> You seem to fail understanding the concept of "exact" in mathematics.
> > 
> > Sure i do it is an answer that is not an approximation, my arithmetic is
> > exact. 
> 
> In that sense even incoorect arithmetic is exact.
> 
> 
> -- 
> Evertjan.
> The Netherlands.
> (Please change the x'es to dots in my emailaddress)

If you feel confused you probably should read this.
http://wiki.math.se/wikis/2009/bridgecourse1-ImperialCollege/index.php/1.1_Different_types_of_numbers

Especially you shold look at example 8

[toc] | [prev] | [next] | [standalone]

#39003

On Mon, 19 Oct 2020 01:52:55 -0700 (PDT), Jonas Thörnvall
<jonas.thornvall@gmail.com> wrote:

  <snip>
>In fact my methods do not need any approximations, always exact on spot given any values because i "have/and would calculate any decimals into continued fractions".

Why do I have to say it again. Your value for root 2 will always be an
approximation, no matter how big a fraction you build. 

Also, a continued fraction is an expression that hasn't been evaluated
yet. When you do evaluate it you get a simple fraction, which will
still not be accurate for some numbers.

  John

[toc] | [prev] | [next] | [standalone]

#39005

Den måndag 19 oktober 2020 kl. 19:04:31 UTC+2 skrev John G Harris:
> On Mon, 19 Oct 2020 01:52:55 -0700 (PDT), Jonas Thörnvall
> <jonas.thornvall@gmail.com> wrote:
> 
>   <snip>
> >In fact my methods do not need any approximations, always exact on spot given any values because i "have/and would calculate any decimals into continued fractions".
> 
> Why do I have to say it again. Your value for root 2 will always be an
> approximation, no matter how big a fraction you build. 
> 
> Also, a continued fraction is an expression that hasn't been evaluated
> yet. When you do evaluate it you get a simple fraction, which will
> still not be accurate for some numbers.
> 
>   John

You are just confused or misinformed, i say my calculations do not degrade like decimal calculations do as you add more and more terms.

[toc] | [prev] | [next] | [standalone]

#39007

On Mon, 19 Oct 2020 10:47:32 -0700 (PDT), Jonas Thörnvall
<jonas.thornvall@gmail.com> wrote:

  <snip>
>You are just confused or misinformed, i say my calculations do not degrade like decimal calculations do as you add more and more ter

Have a look at the continued fraction for root 2 given in Wikipedia :
  <https://en.wikipedia.org/wiki/Square_root_of_2#Continued_fraction>

It goes on for ever. You can't calculate it exactly.

  John

[toc] | [prev] | [next] | [standalone]

#39009

Den måndag 19 oktober 2020 kl. 20:33:13 UTC+2 skrev John G Harris:
> On Mon, 19 Oct 2020 10:47:32 -0700 (PDT), Jonas Thörnvall
> <jonas.thornvall@gmail.com> wrote:
> 
>   <snip>
> >You are just confused or misinformed, i say my calculations do not degrade like decimal calculations do as you add more and more ter
> 
> Have a look at the continued fraction for root 2 given in Wikipedia :
>   <https://en.wikipedia.org/wiki/Square_root_of_2#Continued_fraction>
> 
> It goes on for ever. You can't calculate it exactly.
> 
>   John

Even overly confused people should understand that the accuarcy of any calculation never can get better then the "estimation/approximation" you provide.

But the calculation will not degrade the way it does using a base...

[toc] | [prev] | [next] | [standalone]

#39018

Jonas Thörnvall <jonas.thornvall@gmail.com> wrote:
> Jonas Thörnvall <jonas.thornvall@gmail.com> wrote:

>> I just saying i probably could do alot better and more accurate 
>> calculations using continued fractions then anyone of you, oh not 
>> probably surely would be the correct term. 
>> 
>> https://jonasth.github.io/Fibonacci/fibonacci15.html

Calculating the expansion of a finite continued fraction or of a
finite prefix of an infinite one is a trivial problem, where for
i > 0, n_i represents the numerator, and d_i the denominator of
the ith approximation to the value:

    n_k = a_k * n_(k - 1) + n_(k - 2)
    d_k = a_k * d_(k - 1) + d_(k - 2) 

with appropriate initial values of n_-1 = 0, n_0 = 1, d_-1 = 1, d_0 = 0.

If the value is rational, then the continued fraction representation
will be finite.  If the value is quadratic, then the representation 
will eventually fall into a repeating sequence.

And these prefixes have the wonderful quality of representing all the
best rational approximations to a value.

But I know of no useful algorithms to do calculations with continued
fraction representations of numbers, except for one single calculation:
it's easy to find the reciprocal of a positive continued fraction.

Addition, multiplication, exponentiation all seem to require you to
initially calculate the rational representation and then perform the
calculation before converting back to a continued fraction 
representation.  So, while they have their uses, they do not offer
any sort of panacea for calculations.

> How come Wolfram have to approximate something that i can calculate 
> exact... 
> Within a second or two... 

For Fibonacci, they are presumably using the exact formula involving
the golden ratio, but then to express the result in decimal, they are
using some approximation.  There are clearly other ways, but doing such
Big Decimal handling quickly gets ill-performant.


> In fact my methods do not need any approximations, always exact on 
> spot given any values because i "have/and would calculate any 
> decimals into continued fractions".

If you have exact decimals, then you can do exact calculations.  But
much real-world work does not give you exact values.  Would you convert
0.33333333333333333333 into 

33333333333333333333 / 100000000000000000000

?  Because that's the true value of that fraction, but in practice,
such a decimal is much more likely to actually represent 1 / 3. And
then your calculations will be slightly off.

Much worse is when you deal with irrational numbers.  The quadratics
aren't bad.  The Golden Ratio can be beautifually expressed as

    [1; 1, 1, 1, 1, 1, 1, 1, ...>, which represents (1 + sqrt(5)) / 2]

And there are some numbers, such as `e`, the base of the natural
logarithms, which, though not repeating, still have beatiful patterns.
In a slightly non-standard expression, we can say that e is represented
by

    [1; 0, 1, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, ...]

That zero is non-standard; more traditionally, but less elegantly, we
would write that as

    [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, ...]

Nontheless, there is an elegant pattern there.  

But then we come to pi.  Here is the beginning of it:

    [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, ...]

And it proceeds without much pattern at all.

We can learn some nice things about approximations to pi from this.

3/1 is the best approximation with a numerator less than 7.  22/7 (which
is represented by [3; 7]) is a reasonably good approximation, as the 
next best one requires a numerator of 106 - 333/106 ([3; 7, 15]).  But
that one is not so useful since there is another one very close:
355/113 ([3; 7, 15, 1]).  But that is quite a good approximation, since
the next best on is 103993 / 33102 ([3, 7, 15, 1, 292]).  (The higher
the following term in the continued fraction is, the better the current
approximation is.  292 is quite high.)

But that's about all we can get from these representations.  It's not
nothing.  It's actually quite useful.  But I don't see doing any
serious calculations with them.

  -- Scott

[toc] | [prev] | [standalone]

Page 3 of 3 — ← Prev page 1 2 [3]

Back to top | Article view | comp.lang.javascript

csiph-web