My favorite FP Fun Fact is that float comparisons can (almost) use integer comparisons. To determine if a > b, reinterpret a and b as signed ints and just compare those like any old ints. It (almost) works!
The implication is that the next biggest float is (almost) always what you get when you reinterpret its bits as an integer, and add one. For example, start with the zero float: all bits zero. Add one using integer arithmetic. In int-speak it's just one; in float-speak it's a tiny-mantissa denormal. But that's the next float; and `nextafter` is implemented using integer arithmetic.
Learning that floats are ordered according to integer comparisons makes it feel way more natural. But of course there's the usual asterisks: this fails with NaNs, infinities, and negative zero. We get a few nice things, but only a few.
splicer · 5m ago
Thanks for HexFiend man! I use several times a week.
Sniffnoy · 47m ago
This isn't accurate. It's true for positive numbers, and when comparing a positive to a negative, but false for comparisons between negative numbers. Standard floating point uses sign-magnitude representation, while signed integers these days use 2s-complement. On negative numbers, comparisons are reversed between these two encodings. Incrementing a float as if it were an integer will, in ordinary circumstances, get you the next one larger in magnitude, but with the same sign -- i.e., you go up for positives but down for negatives. Whereas with signed integers, you always go up except when there's an overflow into the sign bit.
A more correct version of the statement would be that comparison is the same as on sign-magnitude integers. Of course, this still has the caveats you already mentioned.
adgjlsfhk1 · 42m ago
One of the unambiguously nice things about Posits (unlike floats) is that they use a 2s compliment scheme which makes it actually true for all values that they sort like integers.
Sniffnoy · 38m ago
I was going to say "well, you've still got NaR", but apparently that's been defined to sort less than all other posits? Huh, OK.
omoikane · 1h ago
Previously I was using this site to explore floating point representations:
This one has the extra feature of showing the conversion error, but it doesn't support double precision.
SomaticPirate · 1h ago
This came during my OMSCS Game AI course as an example of the dangers of using floats to represent game object location. If you get further from the origin point (or another game element you are referencing from) you are losing precision as the float needs to use more of the significand to store the larger value.
mwkaufma · 1h ago
Define boundary conditions -- how much precision do you need? Then you can compute the min/max distances. If the "world" needs to be larger, then prepare to divide it into sectors, and have separate global/local coordinates (e.g. No Man's Sky works this way).
Really though, games are theater tech, not science. Double-Precision will be more than enough for anything but the most exotic use-case.
The most important thing is just to remember not to add very-big and very-small numbers together.
slater · 4h ago
Why tf is there a .exposed TLD?
shoo · 2h ago
> THE .EXPOSED TLD This TLD is attractive and useful to end-users as it better facilitates search, self-expression, information sharing and the provision of legitimate goods and services. Along with the other TLDs in the Donuts family, this TLD will provide Internet users with opportunities for online identities and expression that do not currently exist. In doing so, the TLD will introduce significant consumer choice and competition to the Internet namespace – the very purpose of ICANN’s new TLD program.
> .EXPOSED will be utilized by registrants seeking new avenues for expression on the Internet. There is a deep history of progressivity and societal advancement resulting from the online free expressions of criticism. Individuals and groups will register names in .EXPOSED when interested in editorializing, providing input, revealing new facts or views, interacting with other communities, and publishing commentary.
For the same reason there's a .sucks TLD. There's a market for it.
magackame · 1h ago
So windows.sucks and linux.sucks are available and 2000 USD/year, emacs.sucks is 200 USD/year and vi.sucks is already registered (but no website unfortunately)!
On the other hand linux.rocks and windows.rocks are taken (no website), vi.rocks is 200 USD/year and emacs.rocks is just 14 USD/year.
microsoft.sucks redirects to microsoft.com, but microsoft.rocks is just taken :thinking:
8cvor6j844qw_d6 · 1h ago
Pretty sure there's a domain monitoring service for similarly or something along these lines that buys up domains like these to prevent usage.
On that note, I've been trying to see if GoDaddy will buy a domain and resell for higher price by searching for some plausibly nice domain names on their site. They haven't took the "bait" yet.
The implication is that the next biggest float is (almost) always what you get when you reinterpret its bits as an integer, and add one. For example, start with the zero float: all bits zero. Add one using integer arithmetic. In int-speak it's just one; in float-speak it's a tiny-mantissa denormal. But that's the next float; and `nextafter` is implemented using integer arithmetic.
Learning that floats are ordered according to integer comparisons makes it feel way more natural. But of course there's the usual asterisks: this fails with NaNs, infinities, and negative zero. We get a few nice things, but only a few.
A more correct version of the statement would be that comparison is the same as on sign-magnitude integers. Of course, this still has the caveats you already mentioned.
https://www.h-schmidt.net/FloatConverter/IEEE754.html
This one has the extra feature of showing the conversion error, but it doesn't support double precision.
Really though, games are theater tech, not science. Double-Precision will be more than enough for anything but the most exotic use-case.
The most important thing is just to remember not to add very-big and very-small numbers together.
> .EXPOSED will be utilized by registrants seeking new avenues for expression on the Internet. There is a deep history of progressivity and societal advancement resulting from the online free expressions of criticism. Individuals and groups will register names in .EXPOSED when interested in editorializing, providing input, revealing new facts or views, interacting with other communities, and publishing commentary.
-- https://icannwiki.org/.exposed
On the other hand linux.rocks and windows.rocks are taken (no website), vi.rocks is 200 USD/year and emacs.rocks is just 14 USD/year.
microsoft.sucks redirects to microsoft.com, but microsoft.rocks is just taken :thinking:
On that note, I've been trying to see if GoDaddy will buy a domain and resell for higher price by searching for some plausibly nice domain names on their site. They haven't took the "bait" yet.