ferram4 changed the topic of #RO to: Welcome to the discussion channel for the Realism Overhaul (meta)mod for KSP! Realism Overhaul Main Thread https://goo.gl/wH7Dzb ! RO Spreadsheet http://goo.gl/Oem3g0 ! Code of Conduct http://goo.gl/wOSv2M ! | Maximal & soundnfury's RP-1 Race Into Space Signup: http://bit.ly/2DEVm2i [15:01] <soundnfury> Straight Eight Stronk (and) RP-0/1 is basically "Space Agency Spreadsheet Simulator"
<github>
[RP-0] pap1723 pushed 1 new commit to SatellitePayloadFixes: https://git.io/fhWWI
<github>
RP-0/SatellitePayloadFixes 0cac522 Dan Paplaczyk: Delete Class1.cs...
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<github>
RP-0/master 819d459 siimav: Another fix to maintenance costs, changed first level pad to be lvl 1 instead of 0
<soundnfury>
egg: what's the condition number of a function that passes through (0,0), such as ln(1 + x)? Is it just undefined there, or can we do something a bit l'hôpitish?
<soundnfury>
but that's basically the same thing :P
<egg>
aha, but it is not
<soundnfury>
?
<egg>
you are not talking about the function that maps x to log(1+x), but rather about the composition of the rounded addition with the log (the division by 20 is boring, let us disregard it)
<soundnfury>
ah, this is true
<soundnfury>
for very small d you just get 0, because d + 1.0 == 1.0 yes?
<egg>
yes
<egg>
but there the log is well-conditioned and does not make things worse
<egg>
but if you looked at the condition of log(1+x), you have seen that the scary part is at -1
<egg>
where it greatly amplifies any error fed into it
<egg>
Fortunately, Sterbenz says there is none from the addition if x is near -1 and denormals are not flushed
<egg>
unfortunately, we must now ask whence x comes
<egg>
for any error therein will still get amplified ad infinitum
<soundnfury>
egg: yes, I think the querent already understands that the pole at -1 is nasty
<egg>
(now we are indeed just looking at log(1+x), not log and the sum in isolation, but I think it bears eggsplaining the intervening step)
<egg>
the interesting part is that given a half-decent log, implementing log(1+x) as log(1+x) will yield a half-decent log(1+x) at x=-1
<egg>
because Sterbenz
<egg>
Note: this is not the case if denormals are flushed
<soundnfury>
egg: as you say, interesting.
<soundnfury>
(not sarcastic at all, how could you suggest such a thing)
<egg>
By Sterbenz, 1+x will be eggsact for x between minus two and minus a half, thus the error will be the error from the log
<soundnfury>
I shall remember that next time I need to calculate log(1+eggs)
<egg>
admittedly this is actually very boring because the log is arbitrarily well-conditioned at 0.
<egg>
<egg> Note: this is not the case if denormals are flushed << yeah, given the log that part isn't true, because the condition of the log might just eat that up
<soundnfury>
so, not _necessarily_ the case, rather than certainly not the case?
<egg>
well, Sterbenz requires denormals not to be flushed
<egg>
the question is: can you live without Sterbenz?
<egg>
also, do you feel lucky?
* soundnfury
has no idea whether he can live without Sterbenz or not
* soundnfury
tries to stick to situations where condition and stabbity and other floaty things don't matter
<egg>
honestly just don't flush denormals, Sterbenz is your friend
<egg>
also don't evaluate 1-x² as (1-x) ** 2
<egg>
um
<egg>
yes
<egg>
but
<soundnfury>
???
<egg>
also don't evaluate 1-x² as 1-x*x, more interestingly
<egg>
soundnfury: look i'm tired
<soundnfury>
what about (1-x)(1+x), is that ok?
<egg>
yes
<egg>
that is the only correct way to do it
<soundnfury>
\o/
<egg>
1-x*x is horrible
<egg>
eggsercise: why
<soundnfury>
hmm. It's either gonna be x close to 0 or x close to ±1 that's bad, let me think
<soundnfury>
condition number of f:x→x² is 2... condition number of f:x→(1-x) is x/(x-1) which explodes at x=1
<soundnfury>
so you want to do the x→(1-x) first
<soundnfury>
get the ill-conditioner out of the way asap
<soundnfury>
am I close?
<egg>
indeed
<soundnfury>
yay
<egg>
more formally, the rounding error from x*x will get arbitrarily amplified by the ill-conditioned subtraction near x=1
<soundnfury>
yep
<soundnfury>
I miss these conversations. Am I still banned from #kspacademia?
<soundnfury>
yes :(
<Mike`>
what did you do? :D
<soundnfury>
Mike`: I'm not entirely sure. I suggested that someone (I think it was whitequark) who was repeatedly pushing all my most obvious buttons wasn't engaging in good faith.
<soundnfury>
because I felt that I, as a right-winger, was being used as an object of amusement and derision.
<Mike`>
hehe
<soundnfury>
And apparently I'm the one in the wrong.
<soundnfury>
But I guess I'm used to that kind of treatment. Like when alternatehistory.com banned me for quoting Thomas Sowell.
<soundnfury>
(Then when I challenged it, they changed their story and accused me of being a conspiracy theorist instead, for having the gall to believe in the existence of the Soviet dezinformatsiya campaign that both the KGB and the CIA say existed.)