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There are still (a few) computers in the world (Sperry Univac legacy support) using one's complement arithmetic, hence having a positive and negative zero in the architecture. https://en.wikipedia.org/wiki/Ones%27_complement
Well all computers supporting IEEE 754 floating point numbers have a positive and a negative 0. Thats quite a few. I prefer to store all my most important data in the sign bit of floats set to zero.
Isn’t that what bool is for?
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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 so…
∞ is not a number. Using it as a number is a hack invented by mathematicians.
Like many notational shortcuts, it's a hack supported by proof. ;-)
Does -0.0 == +0.0 ?
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Ok, so what's true? -0<+0 or -0==+0
You shouldn't really use equality on floating point numbers, except on very special circumstances (and I imagine the == behavior for 0 breaks things more often than it helps). But the wikipedia page on -0 has your case covered: > According to the IEEE 754 standard, negative zero and positive zero should compare as equal with the usual (numerical) comparison operators, like the == operators of C and Java. In those lan…
This is very common advice, so common that it gets cargo-culted into situations where it is really quite poor.
Information storage, retrieval, and transmission systems should faithfully deliver floating-point values that are good to the last bit. Round-trips through databases, transmission over network protocols, etc should all give values back that are exactly identical to what was put into them.
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That is not entirely correct. Schmieden and Laugwitz for example developed in the 1950s a nonstandard Analysis which adjoins an infinitely large element (called Ω) to the natural numbers. The basic idea was a formula A(Ω) was true if A(n) was true for almost all finite natural n. While it wasn't immensely useful going forward, it helped to clarify the use of infinity and infinitesimals in earlier work.
I'm well aware of nonstandard analysis, but ∞ is still not a number there, even though there are infinitely many infinitely large elements .
Same with the extended real line.
Infinity is as much a number as it is useful to define it as such.
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.
Take 2d laminar flow around a circle. The flow field splits right in the middle.
Signed zeros ensure that, along with graceful underflow, the local solution is not wonky.
Lots of complex-arithmetic examples too.
Earlier quoted context omitted.
Well all computers supporting IEEE 754 floating point numbers have a positive and a negative 0. Thats quite a few. I prefer to store all my most important data in the sign bit of floats set to zero.
Why? Isn’t that what bool is for?
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 so…
No fundamental ones, but a few practical.
32-bit numbers have 2^32 unique values, the number is even. Your approach makes the range asymmetrical like it happens with integers.
The range for 8-bit signed integers is [ -128 .. +127 ]. On ARM NEON there’re two versions of integer negate and absolute instructions, some (like vqnegq_s8 or vqabsq_s8) do saturation i.e. transform -128 into +127, others (vnegq_s8, vabsq_s8) don’t change -128. Neither of them is particularly good: the saturated version violates -(-x) == x, non-saturated version violates abs(x)>=0. Same applies to the rest of the signed integers (16, 32, 64 bits), an all modern platforms.
With IEEE floats the range is symmetrical and none of that is needed. Moreover, PCs don’t have absolute or negate instructions, but they instead have bitwise instructions processing floats, like andps, orps, xorps, andnps, they allow to flip, clear or set just the sign bit, very fast.
Another useful property of IEEE representation is that for two intervals [ 0 .. FLT_MAX ] and [-FLT_MAX .. -0.0f ] sort order of floats corresponds to [inverted] sort order of 32-bit integers.
I have a suspicion that on a fundamental level, floating point isn't actually good for games or machine learning. They're just used because existing computers are so good at floating point number crunching, especially GPUs.