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Look at what they need to mimic a fraction inaccurately.
The fundamental mathematical nature of how binary floating point values are stored means that extremely straightforward and rational (in the mathematical sense of the term) base-10 arithmetic can surprisingly often yield results that are irrational (again, mathematically) in binary - hence why you’ll sometimes see a result of 3.000000000101325 or something like that in places where you’d expect the result to be simply 3.0
It’d be more correct to say round or unround.
Irrational specifically means infinite non-repeating decimal values, or equivalently that a number can’t be represented as any fraction. This is independent of number system.
Sometimes “more irrational” is used as a way of saying further from those small-integer fractions by some measure, but that doesn’t really work here.
Yep. Open your browser’s console and do
.1 + .2and you get0.30000000000000004.One of the reasons not to use floating point when working with money.
What’s the right way to do money math without floats?
There is also Decimal floating-point arithmetic which has a larger range and better memory safety. Java, C#, Python, Ruby, etc. have built in support for it via Decimal.
Banks and big companies have to worry about round-off and fractions of a penny, so Decimal is a better solution for them. But the great unwashed like you and me will never have to worry about that, so either works.
Also known as “if you ain’t storing cents, you ain’t making sense.”
As other people mentioned, things like the decimal structure works well, but you can also just use an int to store how many pennies something costs and convert it to dollars for display.
The same IEEE spec that introduced base-2 floating point models was updated in 2008 to include some base-10 models that eliminate these issues. Many languages already support them natively, as well as most database engines. Otherwise, you can probably find third-party-library support.
If you don’t have access to an IEEE decimal implementation, or if you just wanna be a rulebreaker, the common strategy is to just store only plain integers, and the precision level you want. So, say, if you’re just dealing with simple american dollars, you’d just make sure to always interpret the integer value as “cents”. If you need more precision than that, you might do “millicents”.
Use a dedicated data type or library. Some languages also have something like python’s Decimal type
>>> .1 + .2 0.30000000000000004 >>> Decimal(".1") + Decimal(".2") Decimal('0.3')
i see what you’re trying to say, but that’s not what rational and irrational means (mathematically).
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Look what they need to mimic a fraction of a fraction.
Don’t be irrational.
You like math jokes and guys with fast cars? Well, you’re in luck because I drive a bmw √-64
Edit: I know nothing about cars. Don’t judge me.
I do enjoy how many number sets are referred to as “normal numbers”:
- Natural numbers
- Rational numbers
- Real numbers
- “Integer” is Latin for “hasn’t been fucked with”
- And of course, the most normal numbers: https://en.wikipedia.org/wiki/Normal_number
Cause fractions can be figured out in context. You can store the numerators and have the denominator as a constant in the code.
You can also have a type which does it. Raku has a Rational type for this.
Python has the Fraction type, and there are many more
Part of my first programming courses in the 90s in C were creating a native fraction type.
unrelated but the image shows so low res (86x96) that it’s unreadable, is this different for everyone else?
what mine shows - https://eviltoast.org/pictrs/image/44915c44-8836-4961-bd06-a45bba04408a.jpeg
The link you gave shows hires for me. Can you try loading in incognito?
just pict-rs things I guess 🤷
hmm very weird. i also tried wget and it grabs the same 86x96 file. https://termbin.com/gvg9
Weird. My wget gives full resolution. No redirect options or anything. Only difference is the IP resolve for you is in Korea and mine is in the US. Likely just closest server resolve.
Try curl with -L set?
Or I’d be curious if something like gallery-dl resolves the image in finding the higher resolution and what the difference is if it does.
Maybe it’s a DNS issue if not a redirect issue.
My guess is DNS. Try with another provider?
It’s not “mimicking” a fraction. It is a fraction.
It’s also the most compact fraction representation around.
Show how 1/3 can be precisely represented in floating point.
fl_numerator = 1
fl_denominator = 3
And division is a “stretch goal” once we get funding.
How many decimal places can it be stretched?
As usual, the best jokes are in the comments. (Though goddamn I chuckled at the meme.)
Do you have a computer type that can represent the entire rational set?
Yes. Have a structure with 2 BigInts. Treat one as the numerator. The other as denominators.
It might not be efficient or fast. But it is possible.
No. They all need to mimic certain numbers.
Agreed, but in terms of efficiency wouldn’t it make more sense to put the sign bit right before the mantissa in order to keep the memory layout more consistent with powers of two?
I doubt the layout is relevant there as the FPU should be just physically wired to handle it.
Having the sign bit in front, makes them compare like sign-bit-integers and if they are compared/sorted like 2s-complement integers, the negatives are reversed but still come after the positives.
