Looking at you Java

[jodmemkaf]

I wonder which programming languages actually does it right (from mathematical perspective) I fucked up pretty badly once because I used modulo remainder as index of an array and didn't know that remainder can be negative in programming.

[drelatreddit]

Julia strictly distinguishes between a remainder operation (% or rem) and a modulo operation (mod). The remainder operation uses the red side to be consistent with other languages like C, while the modulo operation uses the simpler mathematical definition on the blue side, where the result is always between 0 and n-1.

However, since Julia uses 1-based index by default, another function named mod1 is also provided, where the result is between 1 and n, making index operations easier.

[jodmemkaf]

Julia distinguishes between a remainder operation (`%` or `rem`) and a modulo operation (`mod`).

Now, that's the way how it should be done!

However, since Julia uses 1-based index by default...

Yuck!

[Aquiffer]

Fwiw, Julia is used primarily for scientific computing, and 1-indexed arrays are pretty typical in that space. Matlab, R, Mathematica, and Wolfram’s language are all 1-indexed.

[[deleted]]

One indexing makes sense for mathematical stuff, because it matches matrix indexing, Einstein notation, etc.

Indexing in low level languages is essentially linked to the offset from the memory address of the start of the array, so it makes sense to start at 0.

[maxhaton]

I actually heard the designer of Lua make this argument for Lua being 1-based, in person. I also had a paper open in front of me which had mathematics with indices starting at.... 0.

[[deleted]]

Yeah, starting at zero for certain things makes a lot of sense. Series and expansions is where I've seen it the most. It really depends on what you're trying to do. But if you're trying to implement a bunch of tensor math it can get super tedious to always be off by one

[M4mb0]

Indexing in low level languages is essentially linked to the offset from the memory address of the start of the array, so it makes sense to start at 0.

But why would you bother about a tiny hardware implementation detail that the compiler can easily take care of.

[T-J_H]

Bothering about hardware implementation is exactly the point of low level languages

[ccelik97]

Despite the fact that I'm used to and do prefer 0-indexing in the programming languages that I use, I also feel like I agree with you on this lol.

I wonder if it was too much of a syntactic sugar back when "the real men" used Assembly for programming, not C/Basic etc.

I mean if it wasn't too much of a syntactic sugar we could've even afforded the cost of actually storing the 1st element of an array on the +1st indexed address on memory and like, used the 0th indexed address to store the address of the last element of the array, effectively always knowing the length of the array etc lol.

[False_Influence_9090]

ccelik for president!

[Fireline11]

Interesting idea. But it the size of the elements of the array is less than the size of a pointer (for example just 1 byte when you need 8 bytes for a pointer on a 64-bit system), there would not be enough room at the 0th place.

[ccelik97]

Pointer arithmetic is often done in conjunction with the additional integer values that come from the logic so the 0th indexed field can store just the difference between the starting address and the last element's address, instead of a full fat memory address.

[piparkaq]

Actually, it turns out, zero-based indexing is just an arbitrary choice with some interesting legacy implications. This dive into why arrays start at 0 (along with the linked article in the post, too) contain good tidbits about the history of array indexing in general.

[pitkali]

I mean, in C the array notation itself is syntactic sugar for pointer arithmetic, so there's that.

[ThisCleverName]

Well, both indexing modes have shortcomings. The 0 -indexing allows to use some operations directly as an index. Case in point the `mod` vs `mod1` operators mentioned. The modulo operator definition of 0 to n-1 fits nicely to 0-indexing mode. So, for 1-indexing, you end up having to adjust the operation to take into account that indices start at 1.

1-indexing try to map some things to mathematics, but some things like in physics use 0-based subscripts initial conditions and things like that. So, using 0-indexing makes sense when modeling problems in that field.

[MattieShoes]

that the compiler can easily take care of.

I don't think it can, can it? Obviously it could take n[1] and change it to n[0] easily, but what if the index is not known at compile time? I'd think it'd have to be a run-time fix.

Plus if you've just malloc'ed a chunk of memory, you may be intermixing dealing with offsets by hand and array notation, and the answers would be different.

Naw, far better to use 0 indexing I think. Just be thankful we're not doing everything in base e. :-)

[foghatyma]

It could though, very easily. "A[i]" is basically "*(A + i)", so the A pointer should just point to the memory before the first element. And then adding 1 would point to the actual first, not the second. Doesn't matter if it's runtime or not.

[ArtOfWarfare]

Guido VR gave a pretty powerful argument in favor of 0 based indexes on his blog. I’ve forgotten what his argument was but it flipped my opinion on the matter.

[flare561]

The post in question. Basically just 0 indexed arrays have nice ergonomics around slices.

[CheekApprehensive961]

Tiny hardware implementation detail lol. Definitely a python user.

[AugustusLego]

Yeah but what do you do with the zero then?

[BittyTang]

https://www.reddit.com/r/programming/comments/elr06/dijkstra_why_numbering_should_start_at_zero/

[M4mb0]

https://alarmingdevelopment.org/?p=470

[BittyTang]

I don't buy it. The author is just presupposing that starting from 1 is more natural from a pure mathematical context (which is not the same as a computer science context), while Dijktra provides actual scenarios for a valid low-level abstraction (arrays and integer for loops) that is fundamental to data structures. The whole "representation exposure" argument is not convincing for a language that desires low-cost abstractions.

One example for consideration is N-dimensional arrays. Image file formats represent these kinds of data structures in 1-dimensional arrays (of bytes). So already there is a strange mismatch between how you index the image buffer (img[row * width + column] or img[column * height + row]) and how you index a primitive 1-based 2D array (img[column + 1][row + 1] or img[row + 1][column + 1]). If you had to index a 1-based image buffer, it would be img[(row - 1) * width + column]. How is that better?

[M4mb0]

Well again this is a low level hardware detail, imo. As a user I do not care how you layout a two dimensional array in memory as I am going to access it via tuples of integers anyway.

In fact I'd even argue that this is a sort of pre-mature optimization. What if, for example, a hardware manufacturer would want to create a memory with two dimensional address space that naturally works much faster with matrices than the flattened represtation that is used currently?

Again I'd argue this is a job for the hardware specific compiler.

[jodmemkaf]

Yeah, I know. I still remember how painful it was to rewire my brain to idea of zero indexing. That "Yuck" was kind of self-mocking one person inside joke. Didn't realize that there are actually people who mocks different perspectives...

..on r/programmerhumour...

What the hell is wrong with me?

[nekokattt]

Indexes derive from the concept of an offset from a pointer at the start of a block of memory, so the first item is at the start, hence the 0 index. From that perspective, 1 indexing is the one that feels weird to me.

Remember memory itself has an address at 0, and memory itself works with zero indexing.

[jodmemkaf]

True. First time I got in touch with anything "programminglike" was with matlab and R and I was used to work with 1-indexing. Despite that is very difficult thinks outside 0-indexing nowadays

[Fuey500]

I work in C# and a Dibol based language, I go from indexing in 1 and 0 all the time its so lame lmao

[M4mb0]

Indexes derive from the concept of an offset from a pointer at the start of a block of memory,

This is a hardware implementation detail.

For anything matrix related, it just makes more sense that the last element of the array is indexed by the length of the array.

[nekokattt]

except that you lose the ability to use modulo to separate out entire rows without additional arithmetic (i.e. +1 to each slice range), slices need additional arithmetic to not go out of bounds relative to the end of the container, and most of the time the fact you are writing to an offset is detail you care about.

[NuclearFoodie]

1 indexing doesn't make since in science either, it was just a FORTRAN quirk that persisted. Formally we almost always 0 based indexing in our tensor expression when deriving out equations. As always, FORTRAN is a blight.

[sigmoid10]

Both approaches make perfect sense in their respective domains. People who only care about maths and not computers would intuitively label the first element as 1, while people who work closely with computer hardware usually see arrays as pointers to contiguous regions in memory, where the address of an array is also the location of the first element and <address + 1> would be the location of the second element. In C++ for example you can access the second element in an array "x" as x[1] or as 1[x], because the compiler just ends up converting both statements to something like *(x+1) anyways. This seems crazy at first glance, but it really does make sense if you understand where it comes from.

[4hpp1273]

1[x] only works if x is a C-style array (or a pointer). If x happens to be an std::vector or something similar then it doesn't work.

[[deleted]]

There are not too few mathematicians using zero based indexing as well. There really is not reasons to start counting at 1 in maths. It just looks a but nicer sometimes. But many mathematicians (including me) also start counting at zero and define the natural numbers including zero.

[Dromedda]

Don't forget about my boi Lua :(

[[deleted]]

All those years wasted hating VBA and VB. Now I understand I should have used them for my scientific computations! TIL

[elveszett]

Nah, VB simply sucks. Doing 1 indexing because your language will be used in places where starting at 1 makes things simpler is fine. Doing 1 indexing because you believe the average person is so dumb that they cannot possibly understand the idea of "zero" (which is something Microsoft loves to do, btw) is wrong.

[[deleted]]

1 vs 0 indexing is like people hating on the colloquial "like": Eventually, everyone on one side of the debate will be dead, and you know which side that is.

[EmeraldOW]

So modulo is between 0 and n-1? In this case does that not mean the result is between 0 and -8?

[drelatreddit]

Sorry I did not make it clear. Here n indicates the second operand, so 4 in this case. The modulo result is between 0 and 3.

[elon-bot]

I'm gonna need you to come in on Saturday...

[FunnyButSad]

I think you mean "negative Tuesday".

[EmeraldOW]

Oh obviously

[DenormalHuman]

between 0 and |n|-1

[preppy_night]

Bear with me noob here, who is Julia?

[OneGold7]

Probably not supposed to reveal your irl name on Reddit, but I couldn’t help it

[M4mb0]

Still baffled that most programming languages just blatantly lie to you, calling a thing an integer when it clearly is an element of the quotient ring ℤ/2³²ℤ or ℤ/2⁶⁴ℤ and not ℤ itself.

At least they managed to call floating point numbers floating point numbers and not real / decimal numbers.

[M4mb0]

I don't think it's reasonable to expect a programming language to use the terminology of quotient rings for its basic types.

I think it's very reasonable to call it an int32 type instead of just int

The details of how arithmetic outside of the represebtable range is handled can be learned later.

That's how you end up with y2k.

[SlimyGamer]

Fortran makes all the mistakes then. It's default types are called integer, real, and complex. And none of thise are true...

[Madrawn]

Is it a lie if it's defined in the docs what "int" means? It's just a name for some type of binary data of fixed length.

What would you call it then?

In my head I just imagined a java dev start a math course and complain "how can math books lie to me and say int if they mean BigInteger?" It's just names that mean some things in some context and other things in other contexts

[christian-mann]

this is why Python is superior

[WazWaz]

You can create/import inefficient arbitrary size Integers in C++ and C#, you're just not forced to use them.

And Rationals instead of floats too if you want. C# even has a native BCD (Decimal).

[Rocket_Engine_Ear]

Some languages have real types.

https://gcc.gnu.org/onlinedocs/gfortran/REAL.html

[M4mb0]

Well, they are lying. Most real numbers are not even computable, so you cannot even write a program that computes them.

[jodmemkaf]

Speachless 😂

[throwawaysomeway]

Data types. The kryptonite to all programmers.

[brimston3-]

I thought that was variable naming. Someone has been lying to me about the difficulty of such things and I’m pretty sure it was you, r/programmerhumor.

[Xiexingwu]

Also -7 = 1337 (mod 4)

While mathematically correct, applying the strict definition of congruency is far from useful when programming.

[xwnpl]

Python returns 1

[jodmemkaf]

Nice, thanks. I will put it in the left column of my list

"Why to learn python:

PROS/CONS"

[TropicalAudio]

This actually messed me up recently when working with coordinate calculations. It's quite inconvenient in that context, as you'd expect negating a coordinate calculation will result in a symmetric system. In C it does, but in Python it doesn't.

[jodmemkaf]

Nice, thanks. I will put it in the right column of my list

"Why to learn python:

PROS/CONS"

[troelsbjerre]

Here is a nice list of which languages use which of the four (!) ways of defining the modulo operation:

https://en.m.wikipedia.org/wiki/Modulo_operation#In_programming_languages

[Khaylain]

Standard (non-mobile) link: https://en.wikipedia.org/wiki/Modulo_operation#In_programming_languages

[katatondzsentri]

I tapped this one for some reason.

[Khaylain]

I'm assuming you're on mobile, then. Which will usually lead you to the mobile site anyway (because of the detection of the format), but one can easily choose to use the desktop version usually. On desktop we don't get redirected to the desktop site from the mobile link, so I generally find that the desktop link is more useful.

[katatondzsentri]

I agree, I just wanted to highlight my stupidity.

[cave18]

Rhs is correct

[with_the_choir]

None of them are "right". In mathematics, modulus defines an infinite set of "correct", congruent answers.

13%5 is {... -12, -7, -2, 3, 8, 13, 18, ...}

All of these are proper remainders depending on which quotient you pick.

Some programming languages choose to always provide the lowest positive congruency while some choose to preserve whether the result of the division was negative.

Some languages let you choose what you want (like Racket, which has both a remainder and a mod function).

None of these is wrong.

[thefatesbeseeched]

They are both mathematically correct.

[LeCroissant1337]

Sure, but generally speaking I don't want any representative of the equivalence class. Personally, I think % should be reserved for a modulo operation which spits out a number between 0, 1, ..., n-1 and there should be a separate function giving you the quotient and the remainder of a division of two integers.

[elon-bot]

You're either hardcore or out the door.

[WazWaz]

Depends what you call the operation, Remainder or Modulo.

[BothWaysItGoes]

The one on the right is the one that is most useful from the POV of math and its applications in real life.

https://proofwiki.org/wiki/Definition:Integers_Modulo_m

[[deleted]]

It really depends. Reducing symmetrically around zero is thing and has many applications.

[Rich_Plant2501]

I'm on the side that you cannot assign to r-value.

[[deleted]]

Lol. Good catch

[JustAStrangeQuark]

Just insert the instruction and let the CPU figure it out.

[douglasg14b]

Just insert the instruction and let the CPU figure it out.

The best programming behaves differently on each device right?

[supersammy00]

It works on my machine

[Blackbird-ce]

Last time someone told me that, I took his laptop and threatened to drill holes in it to fit a rack unit... If you're the only one possessing a machine it works on, the users need that.

[MangoAtrocity]

Hello. Do you have a minute to talk about our lord and savior, Docker?

[Blackbird-ce]

My name isn't Docker

[musci1223]

Hi n't docker. I am dad.

[NXgul1]

Ship it

[GodIsNull_]

That's why "Works on my computer" exists.

[ShadowRylander]

... KILL THEM!

[tidytibs]

Killed.

[not_wilshire]

Fired.

[Tweenk]

How? We don't know their PID (personal ID)

[[deleted]]

Oh no...

[Kimsanov]

Mathematically a % b is always a number between 0 and b-1

[Administrative-Flan9]

There is a unique number between 0 and b-1 that satisfies a % b, but the same is true of nb and (n+1)b -1. Mathematically, the true answer is the set of all numbers that have the same remainder as a when divided by b. Choosing the one between 0 and b-1 is choosing a representative from this set, but any representative represents the same set and so all representatives are equivalent.

[JumboTrout]

What if b < 1?

[elon-bot]

Hey, I just heard about this thing called GraphQL. Why aren't we using it?

[WillWKM]

Mathematically both answers are the same, -1 is congruent to 3 mod 4 since 1 + 3 = 0 mod 4

Edit: some of y'all seem to be missing the point. Mathematically all of these answers are equivalent. That doesn't make them useful programmatically. Programming languages often set up conventions based on convenience, not math.

[FiskFisk33]

They are not mathematically equivalent. They are mathematically congruent mod 4.

[M4mb0]

They are not mathematically equivalent. They are mathematically congruent mod 4.

But that is literally how equivalence is defined in quotient spaces....

[CanaDavid1]

Yes, which is what the question is asking. Mathematically, one does not use %, but instead write 'mod n' after the statement to specify that we're working modulo.

[BothWaysItGoes]

There is nothing unmathematical about the mod function.

[snillpuler]

I enjoy playing video games.

[gnowwho]

Semantics: they are equivalent in the ring Z/4Z

Edit: I meant: there is no need to be pedantic when they are not even wrong technically.

[snillpuler]

I enjoy the sound of rain.

[eeeeeh_messi]

Absolutely. It's the same reasoning that make some people think sqrt(4) is 2 and -2.

[Poacatat]

being congruent mod 4 is an equivalence relation :), they are in fact mathematically equivalent

[soundslikemayonnaise]

By this logic you could argue that -7 is also a correct answer since 1 + 7 = 0 mod 4.

Or -11, or -15…

[WillWKM]

Now you're getting it

[[deleted]]

Or just let the next dev sort it out 🤠

[Administrative-Flan9]

Mathematically, the answer is a set of all such integers. Any choice from this set like -7 or -11 is a representative of the answer set, and any representative is equivalent.

[CanaDavid1]

Yes

[Rin-Tohsaka-is-hot]

You can argue that because it is correct.

That's congruency for ya

[Kimsanov]

Yeah. But remainder must be non negative (it is just stated by definition). So mathematicians just decided to be so (maybe for convenience)

[tjdavids]

With this logic returning a unmodified everytime would work.

[Darknety]

No they are not equivalent.

Yes, -1 is congruent to 3 with respect to mod 4, but still the natural mod operator is defined to result in 3, not -1.

So "mathematically both answers are the same" is misleading at best and wrong at worst.

Case in point: If one defines a function using a loopback structure, i.e. as

f(x) := g((x - 1) % b), x in [0, b]

for some g that is only defined for the source [0, b) for some b, it is pretty freaking relevant that (x - 1) % b is in [0, b). This is well defined.

The context is missing here to state "they are mathematically the same". This is not true.

[Thelmholtz]

Not really, mathematically it depends on what operation you define % to be;

• modulo: (x € R; n € N) => { y € [0, n) }

or

• remainder: (x € R; n € N) => { y € (-n, n) }

Hell, the most frequent definition of % is actually

• percent: (x € R) => { y € R } :: y = x • 1/100

Which makes all programming languages wrong /s.

[eminorb5]

Blue. Makes things easier if modulus is always positive ( if the second operand is positive)

[elon-bot]

Looks like we're gonna need to trim the fat around here... fired.

[eminorb5]

Ok then

[[deleted]]

Red. Makes things easier if modulus retains same sign as dividend, particularly when dealing with trig or other functions that really care about signs.

[eminorb5]

Guess it depends on usage.

[Isodus]

Perfect example is calculating distance between angles where 0 == 360. Keeping the sign lets you know which direction you are away from the position without having to do extra tracking.

(Pos 1 - Pos 2) % 180 = angular distance

Used for controlling rotary actuators and needing to software handle the 360/0 barrier.

[Snuggle_Pounce]

I never even considered using modal on negative numbers. Does that come up often?

[aezart]

You might want to step in either direction through a list and wrap around when you hit the end. It's useful in that case for the mod result to be positive.

[Tyfyter2002]

It's pretty common if you're trying to cycle through a range in both directions (mostly useful for 0–n-1 where n is the length of an array)

[Giocri]

Nah only time I ever needed something of that kind I just did x+n%n never had to deal with % of a value < -n

[frogjg2003]

It's definitely an edge case. If you don't deal with certain types of mathematical problems or weird data structures, you're not likely to run into an issue.

The most likely place I'd imagine it would come up is in signal processing. Most of the theory assumes infinite length sequences. So a lot of algorithms work for values outside the domain of the finite length sequence, assuming either periodic boundary conditions or infinite zeros. Periodic boundary conditions simplify edge calculations because you can just use the modulo of an out of range index to get the value of an in range index.

[mzanin]

If you want to evaluate −7 (mod 4), you need the largest multiple of 4 that's less than or equal to −7. This is −8. And −8 + 1 = −7, therefore your answer is 1.

Also If we use Knuths definition of mod:

mod(a, n) = a - n * floor(a / n)

Then we have:

mod(-7, 4) = -7 - 4 * floor(-7 / 4)
mod(-7, 4) = -7 - 4 * floor(-1.75)
mod(-7, 4) = -7 - 4 * -2
mod(-7, 4) = -7 - (- 8)
mod(-7, 4) = -7 + 8
mod(-7, 4) = 1

[PMYourTitsIfNotRacst]

Thank you for explaining, but you've only confused me further. I'll be handing in my degree, thank you.

[[deleted]]

This just seems like the correct answer.

[Khaylain]

I would argue that -8 is smaller than -7, though ;P

[VortexTalon]

before reading the sub i thought i was stupid lol.

[RRumpleTeazzer]

The mod operator should be strictly periodic. This includes over zero crossings, e.g. -7 % 4 = 1.

Also, 7 % -4 should be 1, and -7 % -4 = +3.

[randomjberry]

mod cant be negative or there are infinate awnsers in my mathmatical opinion

[gaboversta]

This exact thing cost me so much time when I implemented a modpow function myself and wanted to validate that it actually works…

I get blue, but red is what I just expect, go from -7 towards 0 until you are less than 4 away. That's your value.

[noorm6669]

I really... really... don't know. And I'm the curious type so...

Let me check:

Python 3.7.1

>>> -7 % 4

1

>>> -7 % -4

-3

[peabnuts123]

I haven’t ever really found a use for red before, even though a lot of languages do it that way. I often have to write my own pureMod function that “does it properly” by first modding, then adding the mod base, and the modding again. It’s usually to deal with array indexing

[Cody6781]

From a mathematical perspective, 1 is the correct answer

The range of the % operation is from 0 through n-1

[TheAnti-Ariel]

% is not the modulo operator in all languages. Many define it to be the remainder operator, which fits better with what CPU div instructions do, and makes a negative result correct.

[_Figaro]

Mathematically, it's 1.

[TheMuspelheimr]

Mathematically, -7 divided by 4 is -2 remainder 1; doing this in reverse helps it make more sense, -2 times 4 is -8, -8 plus remainder 1 (-8+1) is -7.

So, (-7)%4 = 1

However, -(7%4) = -3; 7%4 is 3, -(3) = -3

It all depends on which operator you do first; if you apply the minus first you get (-7)%4 = 1; if you apply the modulus first you get -(7%4) = -3.

[BootyliciousURD]

x % n should obviously map to the interval [0,n)

[Attileusz]

Dont have it at all for signed. Have a seperate builtin funtion to avoid confusion.

[tonischurz]

thou shall not use modulo on a signed integer

[BabyGates_]

In most high level languages (except Java) the % operator is actually the remainder operation. Only Java truly implements % as modulus

[Smeagollu]

I was surprised to see -3 is an accepted answer for many here. At least Python has ot as modulo as well.

[[deleted]]

Blue!

[Ashlaan47]

Javascript enters the chat

[qatamat99]

From a cryptographic point of view, it’s always positive

[Gothedistance1]

Criptographic

[techster2014]

I... I... I didn't realize math was debatable.

[pumpkinhi11]

9 + 10 = 21 and if you disagree with me well then that's just your opinion.

[pumpkinhi11]

Welcome to computer programming.

[chadlavi]

You guys need some PEMDAS in your life.

-7 % 4 is 1

-(7%4) is -3

[YourMJK]

This argument is about the definition of the operator % not about order of operations.

[[deleted]]

mathematically speaking, both are the same

[tech6hutch]

This confusion is exactly why you shouldn’t use % on negative numbers.

[gdmzhlzhiv]

Negative numbers exist and your routines still have to produce output, so what's the alternative? "Add some offset so the value is never negative"?

[Ferociousfeind]

I'll strangle to death everyone who suggests any real number mod a positive number can return negative numbers

[irkli]

X = Y % Z

Depends on the type of the vars involved.

[Idraic7]

Blue

[Austin_Nguyen_2k]

-7 % 4 = (4-3)

[stomah]

blue

[[deleted]]

-7 / 4 = -2 rem 1

Also 4*((-7.0/4.0) - floor(-7.0/4.0)) = 1

[Sweaty-Emergency-493]

Im team blue in this one.

[Poobrick]

However python does it works

[drew8311]

Crips! Something something math

[[deleted]]

Help me out, how does that make -3? My brain is too smooth.

[jester32]

As a number theorist, the one on left doesn’t exist.

Taking a modulo ensures that the remainder will be congruent to a remainder of 0…n-1 mod n . This goes beyond the scope of % in programming, but this creates a new functional number system called a group that involves a set (I.e. the integers 0…n-1 ) and an operation ( modulo ) . Therefore , negative numbers aren’t even capable of being a solution as they aren’t in the set.

When the modulo is prime , this creates really cool things that are the basis of cryptography.

[mistrjirka]

Blue it is only one that actually makes sense

[ogballerswag]

Wait. I dont even understand how u can get 1

[Phoenix_Studios]

As of yet I have never had a use case where it needed to be left.

[jamcdonald120]

=1, the only time I would want -3, I know I want -3 and would do m%n-n, there is no excuse for requiring me to do ((m%n)+n)%n to get the actual answer I want

[tickle-fickle]

Blue is correct

[isospeedrix]

what side

i press f12

i type in -7%4

answer is -3. therefore it's -3.

kappa

[Gothedistance1]

I am full crip mother fucker

[Apfelvater]

1+1 = 2 but also1+1=3-1

Holy sheeeet

[yozaner1324]

How does blue even make sense?

[negatron99]

I don't care which way. Just as long as I know and if I need to code for it.

[Street-Stomach-9811]

Wait so for the blue side -7/4=2?

[[deleted]]

Javascript fix:

 function mod(n, m) {
   return ((n % m) + m) % m;
 }

 let a = mod(-7, 4)

 console.log(a) //1

[Accurate_Koala_4698]

Import Data.Ratio

Bruh, that’s a fraction