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Why do arrays start at 0?

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Re: Why do arrays start at 0?

#491

Post by schoen »

jccalhoun wrote: post #241
ajuc wrote: post #219

Earlier quoted context omitted.

The ground floor is 0. The floor above 0 is 1. The floor below 0 is -1. Anything else is crazy TBH, the whole point of integer numbers is to count things that start at a defined point and go opposite ways. Why shift it and then reinvent weird pseudo-negative numbers like S1? But then again people measure distance in feet and write dates as month day year :)

It would be nice if this was the case. In grad school I taught in a building that was on a hill and had once been separate buildings so different entrances were on different floor and the transition between the former separate buildings was 4 stairs. So there was a floor with rooms numbered 1xx and 0xx. There was also a floor below the 0xx floor. They just numbered it 00xx. And you could enter the building on any of…

Could this be Dwinelle Hall at UC Berkeley?

Re: Why do arrays start at 0?

#492

Post by oh_my_goodness »

kazinator wrote: post #74
hougaard wrote: post #14

It really comes down to a choice between a machine-focused (0) or human-focused (1) approach. The 0 makes a lot of sense in a C pointer world where memcpy and other alike functions can be written very thight. The 1 makes a lot of sense in a human world, when we count, we start at 1, we talk about the "1st", counting on finger starts with 1, etc. I once were at a Lua (1 indexed language) conference where this was disc…

In Western music theory, intervals are one based. No pitch change is "unison"; one diatonic step is a "major second" and so on. As a result of this silly state of affairs, an octave occurs every 7 notes, even though the root "oct" means eight. Furthermore, a "rule of nines" is needed to invert an interval: e.g. inversion of minor 3rd is a major 6th (exchange major/minor, subtract from 9).

True, and it's a great example of how this whole drama is about a practical trade-off, not about a unique Right Answer. If you play piano, the second is the second finger; the fifth is the fifth finger, and it all makes sense. No problem. On the other hand trying to actually count that way (two thirds make a fifth and so forth) is maddening.

Re: Why do arrays start at 0?

#493

Post by ZephyrBlu »

TillE wrote: post #372
just_boost_it wrote: post #324

Earlier quoted context omitted.

We're 20 years past the point where you can expect everyone in tech to trace every instruction down to machine instructions. Higher level languages abstract away the need for it, and for the most part, we can rely on the authors of those languages to make many of the decisions that impact performance. The rest of us learn about these details on posts like this. It's not a sad fact, in fact it's probably one of the mo…

I barely touch assembly in my day to day work, but I do understand on a fairly deep level how a computer works , which I feel is extremely important and very frequently influences how I write high-level code. Certainly one can bang out code their entire career without ever having a clue how machine code works, but I really wouldn't advise it. At worst it leads to total ignorance, and at best you accumulate a disconne…

What do you consider "high-level code" and in what way does deeply understanding how a computer works influence your approach?

Re: Why do arrays start at 0?

#494

Post by salty_biscuits »

JadeNB wrote: post #471
salty_biscuits wrote: post #441

Earlier quoted context omitted.

I'm not arguing that the natural numbers should start from one, rather that the usual path for developing the natural numbers starting with set theory is that zero is the size of a set with nothing in it. In maths they always talk about the first element in a vector, not the zeroth. It is a bad argument to point to mathematics for using zero based indices. It is not at all common to use zero based indexing there.

I'm a mathematician, and 0-based indexing makes way more sense to me. Dijkstra's argument ( https://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF ) is that we count the number of predecessors. This fits well with the mathematical usage, at least among mathematicians who care to dig into the order-theoretic foundations: the von Neumann construction of ordinals (and of cardinals as least ordinals of a fixed, well, car…

I'm a mathematician too, and it doesn't make sense to me. It seems somewhat arbitrary depending on the application, i.e. I think it is a type problem. We use an Int to mean something special about array elements. I'd be happier with first() and last() methods really, I don't care for coming up with meanings based on implementation details.

Re: Why do arrays start at 0?

#495

Post by Koshkin »

anigbrowl wrote: post #359
marak830 wrote: post #357

Earlier quoted context omitted.

I asked my son to show me zero fingers(after show me 2 fingers and 5 fingers), he closed his fists.

My point exactly - there isn't an identifiable zeroth finger.

Of course there is - I can write “0” on it!

Re: Why do arrays start at 0?

#496

Post by dahart »

Jtsummers wrote: post #444
dboreham wrote: post #434

Earlier quoted context omitted.

"just subtract one" would take a long time 50-60 years ago.

If you did this, you'd subtract one once at array creation. Or subtract whatever the offset is (really, you'd subtract 1 * data type size). Under the hood, using C syntax instead of assembly: int foo[n]; // what the user wrote // what happens behind the scenes, after a fashion int* foo = malloc(n * sizeof(int); // or sp - n * sizeof(int) if stack allocated; subtraction since stacks usually grow "down" foo = foo - 1;…

The well known “Numerical Recipes in C 2nd ed.” talks about how the first edition promoted exactly this - offset the pointer after allocation and you can use any indexing origin you want. And they promoted 1-indexing and wrote all the algorithms as such, before switching everything to 0-indexing for the 2nd edition.

I agree with you the subtraction instruction is not exorbitant, especially considering malloc is much more expensive and always has been.

Re: Why do arrays start at 0?

#497

Post by ithinkso »

javajosh wrote: post #470
ajuc wrote: post #219

Earlier quoted context omitted.

The ground floor is 0. The floor above 0 is 1. The floor below 0 is -1. Anything else is crazy TBH, the whole point of integer numbers is to count things that start at a defined point and go opposite ways. Why shift it and then reinvent weird pseudo-negative numbers like S1? But then again people measure distance in feet and write dates as month day year :)

This is how it should be, but the only country in the world, AFAIK, that does it that way is Germany.

Not german here, this is standard and I'm a bit confused by your comment.

0 is ground floor.

Re: Why do arrays start at 0?

#499

Post by samatman »

salty_biscuits wrote: post #494
JadeNB wrote: post #471

Earlier quoted context omitted.

I'm a mathematician, and 0-based indexing makes way more sense to me. Dijkstra's argument ( https://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF ) is that we count the number of predecessors. This fits well with the mathematical usage, at least among mathematicians who care to dig into the order-theoretic foundations: the von Neumann construction of ordinals (and of cardinals as least ordinals of a fixed, well, car…

I'm a mathematician too, and it doesn't make sense to me. It seems somewhat arbitrary depending on the application, i.e. I think it is a type problem. We use an Int to mean something special about array elements. I'd be happier with first() and last() methods really, I don't care for coming up with meanings based on implementation details.

The question is whether 0 is a valid ordinal. If it is, why skip it?

If you allow 0 as a valid ordinal, it unifies ordination and measure. That's the best reason to do so.

There. Djikstra as haiku.

Re: Why do arrays start at 0?

#500

Post by samatman »

armchairhacker wrote: post #489
twanvl wrote: post #45

Other advantages of zero based indexing, beyond being 'closer to the machine': It works better with the modulo operator: `array[i%length]` vs `array[(i+length-1)%length+1]`. Or you would have to define a modulo-like operator that maps ℕ to [1..n]. It works better if you have a multi-dimensional index, for example the pixels in an image. With 0 based indexing, pixel `(x,y)` is at `array[x+width y]`. With 1 based index…

Another advantage is with ranges: 0-based indexing and exclusive ranges work well. This is apparent with cursor position in text selection Consider: Characters h e l l o Cursor index 0 1 2 3 4 5 Char index 0 1 2 3 4 Range [0,3) [0,1,2] Range [2,5) [2,3,4] Range [1,1) [] If we used 1-based indexing and exclusive ranges, it leads to ranges where the end index is greater than the string's length... Characters h e l l o…

This is the bane of my existence working with Lua.

Iterating an array or adding to the end are fine, we have ipairs and insert for that, but ranges on strings I'm constantly having to think harder and write more code than necessary.

I love the language, wouldn't trade it for another, but the 1-based indexing on strings, which represents an empty string at position 3 as (3,2), it's egregious.

Not as egregious as a dynamic language where 0 is false though.

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