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Re: 0.30000000000000004

#181

Post by Iburinoc »

IshKebab wrote: post #153
School-Cotton wrote: post #95

Earlier quoted context omitted.

FWIW, both of those can be expressed exactly by floating-point numbers ;)

Right all integers up to 2^53 (or something like that) can be (in double precision). I assume that's the reason they made the mantissa linear, even though having the whole thing logarithmic makes more sense.

Addition/subtraction are also much simpler/cheaper than they would be in an entirely logarithmic model. If floats were just 2^x with some 64 bit fixed point x, it's not clear to me how to do addition efficiently.

Re: 0.30000000000000004

#182

Post by jcranmer »

pmarreck wrote: post #100
saagarjha wrote: post #74

Earlier quoted context omitted.

IEEE is deterministic and (IMO) quite well thought-out. What specifically do you not like about it?

The fact that the most trivial floating-point addition of 0.1 + 0.2 = 0.300000000000004 was insufficient to make this seem HUMAN-nondeterministic to you? (I mean sure, if you thoroughly understood the entire spec, you might not be surprised by this result, but many people would be! Otherwise the original post and website would not exist, no?) It’s kind of a hallmark of bad design when you have to go into a long-winde…

⅓ to 3 decimal places is 0.333. 0.333 + 0.333 = 0.666, which is not ⅔ (to 3 decimal places, that is 0.667). That is all that is happening with the 0.1 + 0.2.

The word you're looking for is "surprising," which is a far cry from non-deterministic. IEEE 754 is so thoroughly deterministic that there exists compiler flags whose sole purpose is to say "I don't care that my result is going to be off by a couple of bits from IEEE 754."

Re: 0.30000000000000004

#183

Post by DonHopkins »

stock_toaster wrote: post #163
nothrabannosir wrote: post #132

Earlier quoted context omitted.

Storing money in floating point is always terrible. If speed is an issue, store it in integer types representing the smallest unit in the currency, e.g. pennies. Unless you’re doing, what, massively parallel GPU algos on batches of independent amounts? But even then you could use the float as an int in that way... Honestly when is float ever actually good for money? Not for speed, not for correctness, ...

> If speed is an issue, store it in integer types representing the smallest unit in the currency, e.g. pennies More typically, mills[1] (tenth of a cent). [1]: https://en.m.wikipedia.org/wiki/Mill_(currency)

Amazon's EC2 hourly prices are rounded to mils ($0.011/hour).

https://aws.amazon.com/emr/pricing/

Azure has some hourly prices with ten-thousandths of a cent ($0.0102/hour):

https://azure.microsoft.com/en-ca/pricing/details/virtual-ma...

Microsoft should use gas station 9/10 pricing conventions to just barely undercut Amazon's lowest price $0.011 with $0.0109.

https://www.marketplace.org/2018/10/11/why-do-gas-prices-end...

>“They found out that if you priced your gas 1/10 of a cent below a break point, let’s say 40 cents a gallon, ‘.399’ just looked to the public like 39 cents…”

Re: 0.30000000000000004

#184

Post by mynameisvlad »

usr1106 wrote: post #152
mynameisvlad wrote: post #124

Earlier quoted context omitted.

It's the first result for "floating point site" on Google. Sure the domain itself is impossible to remember, but you don't have to remember the actual number, just what it stands for.

Remember filter bubble. My first result is not your first result. (although in this case it happens to be, but we both probably search a lot on programming)

Also did it in an InPrivate window to confirm, which is still somewhat targeted but far less so than on my actual account. It's still first.

And, at the end of the day, even if there's a filter bubble and it's the reason I see it first, then so what? The people looking for this site are likely going to fit into the same set of targeted demographics as you and me and most people on this site. So unless you also want to cater to 65-year old retirees that don't care about computer science and what floating numbers are, then why does the filter bubble even matter?

Re: 0.30000000000000004

#185

Post by Gibbon1 »

mcv wrote: post #20

The big issue here is what you're going to use your numbers for. If you're going to do a lot of fast floating point operations for something like graphics or neural networks, these errors are fine. Speed is more important than exact accuracy. If you're handling money, or numbers representing some other real, important concern where accuracy matters, most likely any number you intend to show to the user as a number, f…

> I'd really appreciate it if Javascript had a native decimal number type like that.

Was proposed in the late 90's Mike Cowlishaw but the rest of the standards committee would have none of it.

Re: 0.30000000000000004

#187

Post by dnautics »

Koshkin wrote: post #32
_bxg1 wrote: post #17

I remember in college when we learned about this and I had the thought, "Why don't we just store the numerator and denominator?", and threw together a little C++ class complete with (then novel, to me) operator-overloads, which implemented the concept. I felt very proud of myself. Then years later I learned that it's a thing people actually use: https://en.wikipedia.org/wiki/Rational_data_type

But rationals are more expensive to compute with (compared to floating-point; this is another example of the trade-off between performance and accuracy.)

it's not just that they are expensive, it's that there is a nondetermistic compute time.

Let's say we need to do a comparison. Set

    a = 34241432415/344425151233
and

    b = 45034983295/453218433828
Which is greater?

Or even more feindish, Set

    a = 14488683657616/14488641242046
and

    b = 10733594563328/10733563140768
which is greater?

By what algorithm would you do the computation, and could you guarantee me the same compute time as comparing 2/3 and 4/5?

Re: 0.30000000000000004

#188

Post by dang »

School-Cotton wrote: post #95
dang wrote: post #71

A thread from 2017.00000000000: https://news.ycombinator.com/item?id=14018450 2015.000000000000: https://news.ycombinator.com/item?id=10558871

FWIW, both of those can be expressed exactly by floating-point numbers ;)

Whew. I almost put some non-zeros in there.

Re: 0.30000000000000004

#189

Post by TeMPOraL »

ehvatum wrote: post #167
nothrabannosir wrote: post #132

Earlier quoted context omitted.

Storing money in floating point is always terrible. If speed is an issue, store it in integer types representing the smallest unit in the currency, e.g. pennies. Unless you’re doing, what, massively parallel GPU algos on batches of independent amounts? But even then you could use the float as an int in that way... Honestly when is float ever actually good for money? Not for speed, not for correctness, ...

My day job is high performance financial model implementation. Floats storing dollar amounts are the norm for predictions. Operating on values that are linear combinations of integer fractions multiplied by irrational constants (such as Euler’s number) is perfectly possible, but it’s much more performant to be aware of floating point epsilon when writing modeling code.

Financial models are predictive, they don't have to be accurate to a penny, right? Unlike processing actual money people own.

(I do some work with predictive simulations about money, but outside finance, and there we care that the result has accurate order of magnitude. Floats were used extensively in the project; I actually upgraded them to doubles for the sake of handling larger order of magnitude spans.)

Re: 0.30000000000000004

#190

Post by mffnbs »

4ntonius8lock wrote: post #85
jonny_eh wrote: post #36

> It's actually pretty simple The explanation then goes on to be very complex. e.g. "it can only express fractions that use a prime factor of the base". Please don't say things like this when explaining things to people, it makes them feel stupid if it doesn't click with the first explanation. I suggest instead "It's actually rather interesting".

For including words in a sale pitch, I'd agree. But this isn't a sales pitch. Some people are just bad at things. The explanation on that page require grade school levels of math. I think math that's taught in grade school can be objectively called simple. Some people suck at math. That's ok. I'm very geeky. I get geeky things. Many times geeky things can be very simple to me. I went to a dance lesson. I'm terribly u…

When faced with criticism about your lack of inclusivity, what's to gain by doubling down in order to intentionally exclude people? The argument you are presenting always feels disingenuous because you imply that there is something lost in the efforts to be more inclusive.

The idea that you care about the growth of people you are actively excluding doesn't make a whole lot of sense. In this example we're talking about word choice. The over-sensitivity from my point of view is in the person who takes offense that someone criticized their language and refuses to adapt out of some feigned interest for the disadvantaged party. The parent succinctly critiqued the word choice of the author and offered an alternative that doesn't detract from the message in the slightest.

The lowest common denominator is the person who throws their arms up when offered valid criticism.

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