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floating point numbers are so wild in how they completely undermine the idea that computers are precision machines.
Don't get me wrong, they absolutely are but it's an interesting juxtaposition that one of the key building blocks of many classes of programs relies of what amounts to approximate math.
@an actual bus @XKCD Bot The trouble is, as soon as you need to represent sonething that's not a rational number, you're pretty much forced to use an approximation of some sort.
@me Fun fact: there's actually even more to it than that. Plenty of rational numbers *cannot* be represented exactly in binary. Check out this online tool and try converting simple decimals like 0.1 or anything that isn't a multiple of a negative power of two: rapidtables.com/convert/number…
(I hope this doesn't come across as mansplaining, I just want to share something I find fascinating for the benefit of anyone who might also find it interesting)
@an actual bus It can be done, just not with a floating point data structure. Many languages have a rational data type... just not all, and it could be implemented in the ones that don't. It's just more computationally expensive, and often deemed not to be worth it.
Tell me, was this written for the Data General Nova II floating point board?
(As a human assigned to watch its output, mash a remote reset button, then “smoothly” take over for one of those beastly machines, the question is ever so slightly rhetorical.)
Marcus Müller
in reply to XKCD Bot • • •Jan 🐢
in reply to XKCD Bot • • •David G. Smith
in reply to XKCD Bot • • •explain xkcd
www.explainxkcd.comJones
in reply to XKCD Bot • • •Massive Attack Pray For Rain
Borzix (YouTube)an actual bus
in reply to XKCD Bot • • •floating point numbers are so wild in how they completely undermine the idea that computers are precision machines.
Don't get me wrong, they absolutely are but it's an interesting juxtaposition that one of the key building blocks of many classes of programs relies of what amounts to approximate math.
Jonathan Lamothe likes this.
Jonathan Lamothe
in reply to an actual bus • •an actual bus
in reply to Jonathan Lamothe • • •@me Fun fact: there's actually even more to it than that. Plenty of rational numbers *cannot* be represented exactly in binary. Check out this online tool and try converting simple decimals like 0.1 or anything that isn't a multiple of a negative power of two: rapidtables.com/convert/number…
(I hope this doesn't come across as mansplaining, I just want to share something I find fascinating for the benefit of anyone who might also find it interesting)
Decimal to Binary Converter
www.rapidtables.comJonathan Lamothe
in reply to an actual bus • •Large Format Projectionist
in reply to XKCD Bot • • •Tell me, was this written for the Data General Nova II floating point board?
(As a human assigned to watch its output, mash a remote reset button, then “smoothly” take over for one of those beastly machines, the question is ever so slightly rhetorical.)
Julia Clement
in reply to Large Format Projectionist • • •Pentium FDIV bug - Wikipedia
Contributors to Wikimedia projects (Wikimedia Foundation, Inc.)Billy O'Neal
in reply to XKCD Bot • • •Token Sane Person
in reply to XKCD Bot • • •Also a favourite of mine from some time I once spent sorting out clock change bugs.