How does your programming language handle “minus zero” (-0.0)? • Hacker News Board

Re: How does your programming language handle “minus zero” (-0.0)?

#21

Post by chrisseaton » Fri, Mar 05, 2021, 12:38 PM UTC

numlock86 wrote: post #12

chrisseaton wrote: post #7

Earlier quoted context omitted.

Computers (obviously) have to approximate the majority of actual mathematical numbers, as they do not have infinite storage. If you've got two numbers, +0.0000001 and -0.0000001, but you can't represent that precision, can you see how it's less bad to round to +0.0000 and -0.0000 rather than to just 0.0000? It's encoding strictly more information.

Ok, so what's true? -0<+0 or -0==+0

You can look these things up for yourself - they're standardised in most language's implementations in something called IEEE 754. In the cases you've asked about they're false and true. Is this what you want in all cases? No. Is this what you want in some cases? Yes. It's a tradeoff. You can still observe the difference by dividing by zero (which should be another indication that these aren't real numbers as we're conventionally understand them.)

Re: How does your programming language handle “minus zero” (-0.0)?

#22

Post by banachtarski » Fri, Mar 05, 2021, 12:38 PM UTC

croes wrote: post #13

The inverse of zero is infinity? Shouldn't it be undefined?

The limit of a function 1/x as x approaches zero from the left or right is well defined as negative or positive infinity respectively. The limit is only undefined when no approach direction is specified (as the results from the left and right do not agree)

Re: How does your programming language handle “minus zero” (-0.0)?

#23

Post by ben509 » Fri, Mar 05, 2021, 12:40 PM UTC

numlock86 wrote: post #12

chrisseaton wrote: post #7

Earlier quoted context omitted.

Computers (obviously) have to approximate the majority of actual mathematical numbers, as they do not have infinite storage. If you've got two numbers, +0.0000001 and -0.0000001, but you can't represent that precision, can you see how it's less bad to round to +0.0000 and -0.0000 rather than to just 0.0000? It's encoding strictly more information.

Ok, so what's true? -0<+0 or -0==+0

They're equal. But, copysign(1.0, -0.0) == -1.0

Re: How does your programming language handle “minus zero” (-0.0)?

#24

Post by thaumasiotes » Fri, Mar 05, 2021, 12:40 PM UTC

croes wrote: post #13

The inverse of zero is infinity? Shouldn't it be undefined?

Not if you know that it's positive or negative. The inverse of a negative infinitesimal can't be anything other than a negative infinite number, and the inverse of a positive infinitesimal can't be anything other than a positive infinite number. There's no difficulty with the definitions.

Re: How does your programming language handle “minus zero” (-0.0)?

#25

Post by thaumasiotes » Fri, Mar 05, 2021, 12:42 PM UTC

worc3131 wrote: post #15

kzemek wrote: post #6

Earlier quoted context omitted.

Isn't that true for all correct implementations of negative zero? It's still a neutral for addition

Not quite neutral. You return -0.0 only when needed. >>> 0.0+0.0 0.0 >>> 0.0+(-0.0) 0.0 >>> (-0.0)+0.0 0.0 >>> (-0.0)+(-0.0) -0.0

> Not quite neutral.

Hmm? Your examples show -0.0 being additively neutral in every case. +0.0 is the one that behaves weirdly.

Re: How does your programming language handle “minus zero” (-0.0)?

#26

Post by isolli » Fri, Mar 05, 2021, 12:44 PM UTC

bendiksolheim wrote: post #2

Does anyone have a good example of a programming problem where we _need_ signed zero? Or where it makes things significantly simpler? As far as I know, there is no distinction between -0 and +0 in math, so I have never really understood why this is a thing in computers.

A distinction can be made when considering the limit of a sequence. If a sequence converges to zero from positive values (sometimes written -> 0+), then the inverse of the sequence will diverge to +inf, while if the sequence converges to zero from negative values (-> 0-), the inverse will diverge to -inf.

As a sibling comment wrote, rounding numbers to -0 and +0 can provide extra information, though it may not be useful in all contexts.

Re: How does your programming language handle “minus zero” (-0.0)?

#27

Post by bombcar » Fri, Mar 05, 2021, 12:44 PM UTC

majewsky wrote: post #17

portmanteaufu wrote: post #9

Earlier quoted context omitted.

Sometimes the sign is used to indicate which "direction" the temperature is moving. If it was -10° overnight and it's -0° now, the puddles outside will still be frozen. If it was 10° overnight and it's 0° now, the puddles will still be liquid. (Edit: no idea whether this applies to the Apple watch, it's just a use case for -0 with regards to temperature.)

Your predictions about the state of the puddle are most likely right, but not for the reasons that you think. Air temperature is commonly measured at 2m above ground. An measurement of 0° air temperature does not imply 0° ground temperature. The more significant effect is that the ground has a higher thermal capacity than the air, so it changes temperature more slowly throughout the day. If it's been colder before an…

The thermal capacity of the ground is also why, if you're insulating a basement or slab, you want to insulate the edges and DOWN - but you don't need to insulate in the center of the slab (as eventually the ground reaches the ambient temperature and acts as a huge thermal mass).

Re: How does your programming language handle “minus zero” (-0.0)?

#28

Post by ben509 » Fri, Mar 05, 2021, 12:49 PM UTC

thaumasiotes wrote: post #24

croes wrote: post #13

The inverse of zero is infinity? Shouldn't it be undefined?

Not if you know that it's positive or negative. The inverse of a negative infinitesimal can't be anything other than a negative infinite number, and the inverse of a positive infinitesimal can't be anything other than a positive infinite number. There's no difficulty with the definitions.

There is the difficulty that you don't actually have zero, you have postive and negative infinitesimal.

Re: How does your programming language handle “minus zero” (-0.0)?

#29

Post by bendiksolheim » Fri, Mar 05, 2021, 12:50 PM UTC

chrisseaton wrote: post #7

bendiksolheim wrote: post #2

Does anyone have a good example of a programming problem where we _need_ signed zero? Or where it makes things significantly simpler? As far as I know, there is no distinction between -0 and +0 in math, so I have never really understood why this is a thing in computers.

Computers (obviously) have to approximate the majority of actual mathematical numbers, as they do not have infinite storage. If you've got two numbers, +0.0000001 and -0.0000001, but you can't represent that precision, can you see how it's less bad to round to +0.0000 and -0.0000 rather than to just 0.0000? It's encoding strictly more information.

> it`s less bad

Really good point. My approach to this was "if it’s not used in any mathematical algorithms, why do we need it in computers?". But in your example, you retain some information even though you can’t represent the whole truth. Thanks!

Re: How does your programming language handle “minus zero” (-0.0)?

#30

Post by patrec » Fri, Mar 05, 2021, 12:52 PM UTC

bendiksolheim wrote: post #2

Does anyone have a good example of a programming problem where we _need_ signed zero? Or where it makes things significantly simpler? As far as I know, there is no distinction between -0 and +0 in math, so I have never really understood why this is a thing in computers.

When does this need arise? Well, otherwise inverting a value can change it's sign and in particular inverting -∞ twice will give you +∞, and being off by "2∞" is a pretty large error for a lot of computations ;)

You can end up with zeros and infinities pretty easily because you overflow or underflow the range of floating point precision, and generally you want something sensible to happen in typical cases, even if some common arithmetic identities necessarily break down.

I would actually like a true signed zero (or rather "epsilon" value ), so -0 and +0 as distinct from "normal" 0 which is truly unsigned, neither positive nor negative. The former two would only arise from underflow, and the reason this is useful that if you underflow from below zero and invert that you want to get -∞ and if you underflow from above zero and invert that you want to get +∞. Inverting a signless zero should give NaN (instead it gives +∞, which is nonsense in basically any case where the domain is not inherently the non-negative reals already and the 0 did not come about by and underflow; in particular 1/0 should be NaN).

If anyone knows why this design was not chosen and what fundamental downsides it has, I'd love to hear it. Obviously representing three zeros is a tad more annoying, but IEEE754 has a lot of stuff that's annoying implementation wise but was added for nicer numerical behavior (e.g. denormals, and of course various "global" rounding modes etc. which probably qualify as a mistake in retrospect).