I’m not 100% clear on what you are asking, but integer addition is associative, right? (With quibbles about over/underflow of course). If you have some limited range of decimal numbers that you care about, you can always just use integers and account for the shifted decimal places as needed.
Floats are mostly for when you need that dynamic range.
It could also be that a lot of languages don't actually have integer types and just use a 64bit floating point number instead - ala JavaScript etc.
worth mentioning - js has had a built-in bigint type for quite a while now:
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...
the problem is it's marginally useful, since everyone expects number
Really? That seems nuts. How do they index an array?
They index them with doubles, they do the same with loop variables. As long as your integer is less (in absolute value) than about 2^53 (because they have 53 bit mantisas) you can represent it exactly with a double. 2^53 is 2^(10*5+3) so even if you're indexing individual bytes that many indexes works until you need to index into an array with 8 petabytes of data in it, at which point you're probably not using javascript anymore.
Like many things in javascript it's a bit cursed but it does work.
Plus 53-bit indices exceed the amount of memory that many 64-bit architectures can address (x86_64 is 48 bits, ARM is either 48 or 52 bits).
x86-64 is 57 bits these days https://en.wikipedia.org/wiki/Intel_5-level_paging
Thanks for the correction! TIL.
Tbf, it's not commonly run because it increases TLB miss latency for rarely any benefit (why are you mmap-ing so much? How can you afford to keep that much data around...).
In practice, JavaScript has 32-bit signed integers and 64-bit floating-point numbers as distinct types (look into any JS engine, and you'll see a distinction between the two being made), even if they both surface as a single "number" type. You can also see the distinction in the way that bitwise operators coerce numbers to integers, even though the arithmetic operators coerce to floats in theory.
The spec describes the behavior of converting to and from 32-bit signed for the purposes of the bitwise operators. https://tc39.es/ecma262/#sec-toint32
floor() enters the chat
It would be quite funny if that was how it worked, but it just checks to see if the exponent is 0 and then uses the mantisa as the index if so.