UmbralRaptor changed the topic of #kspacademia to: https://gist.github.com/pdn4kd/164b9b85435d87afbec0c3a7e69d3e6d | Dogs are cats. Spiders are cat interferometers. | Космизм сегодня! | Document well, for tomorrow you may get mauled by a ネコバス. | <UmbralRaptor> … one of the other grad students just compared me to nomal O_o | <ferram4> I shall beat my problems to death with an engineer.
<egg>
bofh: "a"
<bofh>
egg: at least a
<egg>
bofh: yes, there's probably an inlet in the sea of numerical integration papers that's full of that
<egg>
a sound
<soundnfury>
egg: what kind of papers would accumulate in the sargasso sea?
egg is now known as egg|zzz|egg
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<egg|cell|egg>
!Wpn Fiora
* Qboid
gives Fiora a silicon Ляпунов blaster which vaguely resembles a parabola
<Fiora>
mewr?
<egg|cell|egg>
Fiora: did you see that Nice model thing
<egg|zzz|egg>
Fiora: so it starts with 3 consecutive papers published in issue 435 of Nature by people from the observatoire de Nice; the sum of the sizes of the reference lists is 69, also the last paper ends at page 469 of the issue
<egg|work|egg>
bofh: twas a helium leak, launch window now TBD :-\
<bofh>
ugh :(
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<egg|work|egg>
bofh: hmm, I still don't understand why Liouville's theorem implies that the Ляпунов spectrum is conserved by Hamiltonian flow
<bofh>
just a sec
<bofh>
since I'm having a second thought too (I know the spectrum *is* conserved, just think the proof was harder). Let me grab my dynamical systems notes.
<egg|work|egg>
bofh: the conservation of phase space volume tells us the trace vanishes, which seems reasonable
<egg|work|egg>
bofh: uh not the trace, the sum of the eggsponents, but since they are logs of eigenvalues that makes that a determinant I guess
<egg|work|egg>
(which is thus obviously related to phase space volume)
<bofh>
yes. well, log(det(A)), but yes
<bofh>
hmm
<egg|work|egg>
bofh: yes, but since for algorithmic complexities we just slap a tilde on the O we should just have dẽt for "determinant up to logs"
<bofh>
LOL. okay I am so stealing/reusing that notation.
<egg|work|egg>
bofh: the people next to me at work have "actively reducing chaos" and "embracing chaos" as mission statements, I wonder whether I should set mine to "Positive Ляпунов exponent" or something like that :-p
<egg|work|egg>
!u ／
<Qboid>
U+FF0F FULLWIDTH SOLIDUS (／)
<egg|work|egg>
!u u+f00f
<Qboid>
U+F00F PRIVATE USE-F00F ()
<bofh>
egg|work|egg: yes, of course you should. seems fitting.
<bofh>
also damn finally found my notes on my old hdd, no wonder my memory is spotty, I took this in 2012 & used its material fairly little since
<egg|work|egg>
bofh: this channel is good at nerd-sniping, er, I mean, refreshers about random topics
<kmath>
<stephentyrone> Finally have a chance to get to this question from @eggleroy: approximating functions of multiple arguments is much… https://t.co/6BwqFfIgjn
<egg|work|egg>
bofh: nice! also, hmm @ 2
<egg|work|egg>
bofh: right, I assumed that neither was exact?
<egg|work|egg>
bofh: will reply when I'm back home (or you can reply :-p)
<Qboid>
3d 0h 0m 0s left to event #2: Atlas 5 • TDRS M [at 2017-08-18 14:04:00]. Say '!kountdown 2' for details
<egg|work|egg>
bofh: also apparently my phrasing was confusing, it's not really a guideline, and it just came from my deranged mind :-p
<bofh>
egg|work|egg: does that counterexample (or a similar one) still work if you invert the inequality? but apparently.
<egg|work|egg>
bofh: that counterexample is afaict (digging through scribbles on my desk) an examlpe of something of which I was aware when I derived that (but which I then forgot): exact preprocessing is obviously fine
<egg|work|egg>
bofh: were id not exactly evaluated (yes that's a dumb id), I think the reasoning would still work
* egg|work|egg
makes a lib with an id at exactly 1 ULP error :-p
<bofh>
egg|work|egg: just invert the last bit in the integer representation of the double.
<bofh>
:P
<egg|work|egg>
eggsactly
<egg|work|egg>
bofh: bitwise xor with 1 is best id :-p
<NonlocalRaptor>
Name would be an excuse for bird logos.
<egg>
!csharp "the context is me trying to figure out how best to evaluate some function (probably arth y/x near y/x=1), my reasoning being that errors in the evaluation of h would get amplified by an ill-conditioned g (obviously doesn't apply to an exact h).".Length
<Qboid>
244
<egg>
bofh: I am bad at the diapsid website
<egg>
also arth looks wrong; argth? arcth?
<egg>
aaargh
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<egg>
NonlocalRaptor: hah
<NonlocalRaptor>
Twitter is not the bird website because the Twitter logo is not a bird,
<NonlocalRaptor>
(check their branding guidelines)
<egg>
NonlocalRaptor: but maybe it's still a diapsid, do they explicitly deny that
<egg>
NonlocalRaptor: the logo is actually a non-avian theropod,
<NonlocalRaptor>
hah
<bofh>
egg: just split it up among two tweets
<bofh>
bird website is garbage like that
<egg>
bofh: with a character in column 6 of the second tweet? what year is this
<Fiora>
bofh: ah but the twitter branding guidelines! it's not a bird!!!1
<egg>
bofh: s/bird/diapsid/
<Qboid>
egg thinks bofh meant to say: diapsid website is garbage like that
<egg>
Fiora: of course mastodon is synapsid website
<bofh>
egg: ooh, clearly. I usually use $ for that.
<bofh>
(or a sequence number if it's a DATA statement I'm splitting up over multiple lines)
<egg>
!csharp "the context is me trying to figure out how best to evaluate some function (probably artanh y/x near y/x=1),".Length
<Qboid>
107
<egg>
!csharp "my reasoning being that errors in the evaluation of h would get amplified by an ill-conditioned g (obviously doesn't apply to an exact h)."
<Qboid>
my reasoning being that errors in the evaluation of h would get amplified by an ill-conditioned g (obviously doesn't apply to an exact h).
<egg>
!csharp "my reasoning being that errors in the evaluation of h would get amplified by an ill-conditioned g (obviously doesn't apply to an exact h).".Length
<Qboid>
138
<egg>
yay
<bofh>
also, I think atanh is what I'd call it since I *think* you specifically want the libm function, no?
<egg>
bofh: well I mean any reasonably-behaved implementation of that function in floating point, language-agnostically
<egg>
bofh: I could say Ada.Numerics.Generic_Elementary_functions.Arctanh, but :-p
<egg>
bofh: well tbh you would instantiate Generic_Elementary_Functions, so,
<egg>
bofh: ah but there are nongeneric equivalents
<egg>
for the predefined floating point types
<bofh>
let me guess, native floats vs. arbitrary precision?
<egg>
bofh: so Ada.Numerics.Long_Elementary_Functions for Long_Float
<egg>
bofh: so this is Ada, you declare your own numerical types
<bofh>
egg: I don't really feel like reimplementing MPFR tho
<egg>
bofh: this predates IEEE floating point, so it seemed a good idea for floating point too at the time
<bofh>
(that reminds me I should post those patches to mpfr Ai(x)/Bi(x) to that mailing list finally...)
<egg>
bofh: so you can declare a custom type like type T is digits 5 range 0 .. 100
<egg>
bofh: it makes a lot of sense for integers (and it's kind of bad form to use the predefined integer types too much), less so for floating point with IEEE
<egg>
bofh: see also that discussion with Fiora on how integer arithmetic works in Ada a while back
<bofh>
egg: yeah, I agree for ints it's great (also I still need to read thru that, it looks fantastically informative)
<egg>
bofh: essentially the base range isn't something you should really care about, unless you want to optimize away some range checks in intermediate variables (in that case use Animal'Base); representation clauses are just about how it's stored in memory not about the width used for computation which is up to the compiler; to force a range check assign to a variable of the right subtype, to make sure intermediate calculations
<egg>
won't raise anything make sure you derive from a type that can contain intermediate values
<egg>
bofh: in the end intermediate calculations are 1. it's up to the compiler 2. if it doesn't raise an exception the result is correct :-p
<NonlocalRaptor>
Near IR isn't very good for radial velocities.
<egg>
!wpn NonlocalRaptor
* Qboid
gives NonlocalRaptor a critical Akkadian symbol
<NonlocalRaptor>
MUL.APIN
<egg>
??
<egg>
"Even though the Babylonians used a luni-solar calendar, which added an occasional thirteenth month to the calendar, MUL.APIN, like most texts of Babylonian astrology, uses an ‘ideal’ year composed of 12 ‘ideal’ months each of which was composed of an ‘ideal’ 30 days. In this scheme the equinoxes were set on the 15th day of the first and seventh month, and the solstices on the 15th day of the fourt
<egg>
h and tenth month."
<egg>
NonlocalRaptor: bofh: ^ D:
<NonlocalRaptor>
;c 365.2422/360*86400
<kmath>
NonlocalRaptor: 87658.12800000001
<NonlocalRaptor>
^seconds in an ideal day
<egg>
NonlocalRaptor: is that the right kind of year
* egg
pokes the 141345 astronomical definitions of year
<egg>
yeah, 365.24219 seems to be the tropical year
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<bofh>
yeah, that's the tropical year (sadly I can tell by the seconds in a day)
<NonlocalRaptor>
Oops?
<egg>
NonlocalRaptor: no, that seems to be the right year
<egg>
NonlocalRaptor: since they have the solstices and equinoxes at fixed dates
<egg>
bofh: why sadly :-p
<NonlocalRaptor>
right number of days and seconds?
<egg>
bofh: I know that, Atlas tweeted about it a while back
<bofh>
and wait, doesn't what you just asked boil down to a simple application of Sterbenz?
<egg>
bofh: but my question is x^2-y^2, y/x~1; however upon reflection, I think just (x+y)(x-y) is very good in that case, since the subtraction is eggsact, yes
<bofh>
yep, that's exactly how I'd do it assuming you've got y and x within a factor of ~2
<egg>
bofh: now maybe you could fma the hell out of it to get a correctly rounded result, but it seems tricky
<bofh>
(or heck, prolly even greater than that, tho not sure where the breakway point is)
<bofh>
(...right, exactly within a factor of two)
<egg>
Sterbenz is a factor of two, see #floatingpointwithatlas
<egg>
!csharp "(in the specific example of artanh y/x with y/x≈1, I think arsinh y/((x-y)(x+y)) ends up being well-behaved)".Length
<Qboid>
108
<egg>
bofh: I thought I might clarify what I meant with my artanh
<egg>
bofh: did I put the right thing in that arsinh though
<bofh>
hell if I know, literally my most-visited webpage is wikipedia List of Trigonometric Identities.
<egg>
bofh: I mean in our case where x~y, the sum is really nicely conditioned too, the thing is two operations is still two operations, and they're probably not exact, right?
<bofh>
hmm... okay, I'm kind of mentally restricting to the problem domain where both (x-y) and (x+y) are small enough for their product to be exact but not underflow.
<bofh>
that is indeed a bad assumption to make and now I'm not sure.
<egg>
bofh: hm, under what conditions is a product exact?
<egg>
we need an Atlas episode about that
<bofh>
...that's actually a *really good* question
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<egg>
uh
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<kmath>
YouTube - Solar Eclipse - The Science Behind Eye Damage & More
<egg>
bofh: like, it seems to me that this should be scale-free except for over/gradual under/underflow, so there's no reason to believe that a particular product should be exact just based on the relative size of its factors?
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<soundnfury>
egg: shirley a product is exact iff the mantissas between them have enough trailing zeros?
<soundnfury>
though only in binary (and other prime bases), not decimal
egg is now known as egg|zzz|egg
<egg|cell|egg>
Bofh: have you found that proof of conservation of the Ляпунов exponents?
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<bofh>
egg|cell|egg: oh, got distracted by lab work I needed to do. poke me in like an hour, I think I found the chapter at least.
<bofh>
also, hmm. that's a good point, actually no I only agree that based on the relative size of the factors you cannot say that a product will be exact, but you should be able to say that it will not be for others.
<bofh>
hmm.
<bofh>
I'm tempted to ask this to Atlas
<egg|cell|egg>
Do it! Σ:3
<egg|cell|egg>
Also I should zzz
<bofh>
let me first skim IEEE754-2008 to make sure it's not already in there
<kmath>
<bofh453> @stephentyrone Okay, this is possibly a *very* dumb question: under what input constraints can we say * (float64 mu… https://t.co/3oZteptCja