00│ │ 89r144│
> > >> │0.61802575107296143│ │ 144r233│
> > >> │0.61803713527851456│ │ 233r377│
> > >> │0.61803278688524588│ │ 377r610│
> > >> │0.61803444782168182│ │ 610r987│
> > >> │0.6180338134001252000
On Mon, Apr 8, 2019 at 12:37 PM William Tanksley, Jr
wrote:
> Raul Miller wrote:
> > They can, which is disturbing.
> > However, they don't have to (and they have some other advantages, also...).
>
> They do have to (round and otherwise display non-arithmetic behavior).
> All floats are actually
Raul Miller wrote:
> They can, which is disturbing.
> However, they don't have to (and they have some other advantages, also...).
They do have to (round and otherwise display non-arithmetic behavior).
All floats are actually rational numbers which follow a specific
format and truncate in specific
0.61538461538461542│ │ 8r13│
> > >> │0.61904761904761907│ │ 13r21│
> > >> │0.61764705882352944│ │ 21r34│
> > >> │0.61818181818181817│ │ 34r55│
> > >> │0.61797752808988760│ │ 55r89│
> > >> │0.61805555555580000│ │ 89r144│
>
1808│ │ 89r144│
> >> │0.61802575107296143│ │ 144r233│
> >> │0.61803713527851456│ │ 233r377│
> >> │0.61803278688524588│ │ 377r610│
> >> │0.618034447821681820000│ │ 610r987│
> >> │0.61803381340012520│ │ 987r1597│
> >> │0.61
84│
>> │0.61803396316670656│ │ 2584r4181│
>> │0.618033998521803410000│ │ 4181r6765│
>> │0.61803398501735796│ │6765r10946│
>> └───┴─┴──┘
>>
>> Linda
>>
>>
>>
>> -Original Message---
65r10946│
> └───┴─┴──┘
>
> Linda
>
>
>
> -----Original Message-
> From: Programming On Behalf Of
> William Tanksley, Jr
> Sent: Friday, March 29, 2019 12:23 PM
> To: Programming forum
> Subject: Re: [Jprogramming]
To: Programming forum
Subject: Re: [Jprogramming] converting from 'floating' to 'rational'
Ian Clark wrote:
> But why should I feel obliged to carry on using lossy methods when
> I've just discovered I don't need to? Methods such as floating point
> arithmetic, pl
I see what you are doing and for many things using rational numbers is
very useful (i.e. I've used 1r3p1)and the internal representation is a
few bits better than a floating point number. Is this important
considering that often numbers that aren't rational or involve
operations that may requi
@William -- I've bought Wildberger's book, on your recommendation. Right up
my street!
> Do keep us posted -- I for one would love to see the result.
If I get results with this (and I am getting results already) you won't be
able to shut me up! :-)
On Sun, 31 Mar 2019 at 23:29, William Tanksley,
Ian Clark wrote:
> accurate timing for GPS satellites. Both require significant relativistic
> corrections: not Special relativistic but General relativistic. When it's
OK, you have GOT to check out Wildberger's rational trig -- especially
his "universal hyperbolic geometry", which extends the w
Don Kelly wrote
> Of some interest, looking at
the sine problem one can note that a =sin(a) =1.23e_5 from the first
term of the series and the second term is of the order of 10e_16. The
cosine series has a first term of 1 and a second of -7.56e-11.
That's the very problem which has triggered my fo
Fair enough. I graduated in Electrical Engineering in '54, then MSc, 56
and PhD in mid 60's. I have used a slide rule and also 6 figure log
tables, where needed, in the 50's. I was aware of sig figs from the
first day of lectures. First programming was in '61 (using MAD (Michigan
Algorithmic De
Ian Clark wrote:
> But why should I feel obliged to carry on using lossy methods when I've
> just discovered I don't need to? Methods such as floating point arithmetic,
> plus truncation of infinite series at some arbitrary point. The fact that
> few practical measurements are made to an accuracy
[This post contains no code. If you feel inclined to compose a
response with similar characteristics, that probably means it's time
to move this thread to the chat forum. I haven't done that here,
because I felt that a hint should be left behind in the old forum when
moving a thread across forums.]
@Devon - thanks for drawing my attention to a method of formatting I've
been overlooking in favour of dyadic (":). Though it isn't actually a
"display problem" I've got: more a choice of facilities I want to offer.
Anyway 8!:0 is another arrow in my quiver.
@Don - If your point concerning the Chur
Ian - could your display problem be solved by always formatting displays
but retaining arbitrary internal precision? You probably already do this
but thought I'd mention it because I just had to format a correlation
matrix to show only two digits of precision, but was annoyed that my
rounding fnc
Probalbly the main problem, as exemplified in the "sine(a) problem is
that a and sine a are the same within 10e-16 and the cosine is 1-7.5e-5
but the display is only 6 figures and so the displayed result is rounded
to 1. as it is closer to 1 than 0.99. This is grade 8
rounding.Increasing
Raul wrote:
> So I am curious about the examples driving your concern here.
I'm in the throes of converting TABULA (
https://code.jsoftware.com/wiki/TABULA ) to work with rationals instead of
floats. Or more accurately, the engines CAL and UU which TABULA uses.
No, I don't need to offer the speed
On Tue, Mar 26, 2019 at 7:38 PM Ian Clark wrote:
> I will still employ my "mickey-mouse" method, because it's easily checked
> once it's coded. I need built-into TABULA a number of physical constants
> which the SI defines exactly, e.g.
> • The thermodynamic temperature of the triple point of wate
Thanks, folks.
I had a senior moment here. I was browsing my code (TABULA in fact) and
posted my question based on a morning's head-scratching. Then I discovered
2 weeks ago I'd written up a literature search I'd done on rational
precision -- and there was (x:) and what it could and could not do f
Good point, Raul. Depending on what you're doing, there are more or
less unconventional ways to compute triangle geometry. Probably the
one best supported by the existing library is the best one to use :) .
Found some links:
Here's a link to Wildberger's own intro (I personally recommend
ignoring
If you haven't already seen it the following essay on the Jwiki may be of
interest:
https://code.jsoftware.com/wiki/Essays/Extended_Precision_Functions
On Tue, Mar 26, 2019 at 8:08 PM Ian Clark wrote:
> I'm doing trigonometry with very small angles and I want to keep all my
> calculations in ra
Or often you can avoid using angles entirely and use mechanisms based
on cross product for contexts that demand "sine" and dot product for
cosine...
(Not always, though - especially if you're working through someone
else's math notes which were explicitly about angles.)
Thanks,
--
Raul
On Tue,
Does J provide rational trig functions? If not, you'll want to check
out N.J. Wildberger's rational trigonometry, based on "quadrance" (an
unsquare-rooted distance) and "spread" (like a relative slope of
quadrances). That way your rational numbers will stay rational until
it's time to convert them
The x: verb makes a best effort, converting floating point to rational.
x:3.14
157r50
It's limited, of course, by both floating point precision and its own
internal concepts of epsilon.
I hope this helps,
--
Raul
On Tue, Mar 26, 2019 at 3:08 PM Ian Clark wrote:
>
> I'm doing trigonometry
I'm doing trigonometry with very small angles and I want to keep all my
calculations in rational precision. Is there a J-supported way of
converting from floating-point precision to rational, or reasonably speedy
verbs to do the job routinely?
My problem is this. Let PIa be π expressed as a ration
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