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Why do arrays start at 0?

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Re: Why do arrays start at 0?

#511

Post by samatman »

Tagbert wrote: post #87
randomdata wrote: post #19

Earlier quoted context omitted.

> when we count, we start at 1, we talk about the "1st" Although often with an implicit zero. Under typical North American culture, your 1st birthday, for example, is more accurately the first anniversary of your birthday. Your birth is zero indexed.

Birthdays are anniversaries. Anniversaries are annual activities when we celebrate/honor past events. They do not include the event itself. The first anniversary is 1 year after the initial event.

Ok then everyone must do it like us, right?

There's no culture where you're born at 1 year old and turn 2 on New Years when everyone gets older?

You sure?

Re: Why do arrays start at 0?

#512

Post by codebje »

kitkat_new wrote: post #449
dboreham wrote: post #434

Earlier quoted context omitted.

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

would it? or would it be just a differently wired circuit?

Well, maybe, if the specific use case of 1-based arrays was all that got supported.

It'd be a pretty huge waste of processor design space to do that, though: if an HLL wants to support n-based arrays for n != 0 it can just store the base pointer with the initial index offset already applied.

Early 8-bit processors had a pretty poor set of addressing modes: you couldn't even expect [R1 + R2] let alone [R1 + R2 * scale + displacement], so random access into an array would be a multi-instruction task. By the time of the 80386 base scaled index addressing with displacement was in the CPU core, but it's not _free_ - there's an additional byte in the instruction encoding for the displacement, so even if the CPU computes the displacement with no additional clock cycles you'll have a latency cost for fetching the byte.

Re: Why do arrays start at 0?

#513

Post by quickthrower2 »

divbzero wrote: post #283
diego_sandoval wrote: post #273

Because otherwise you would be wasting a perfectly good number for no reason, which means you need to use more bits to do the same thing. To write 4 numbers (including zero) you only need two bits 0: 00 1: 01 2: 10 3: 11 To write 4 numbers if you avoid using the number zero, you need three bits 1: 001 2: 010 3: 011 4: 100 If you extrapolate that a little bit, you'll realize that you'll need two bytes (1 Byte + 1 bit…

The same applies to counting in other bases too. For instance, in 1-indexed counting grids for kids, the last column always feels out of place. 0-indexed decimal grid: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 8…

Neither looks like the canonical choice to me. They are both just as good.

Re: Why do arrays start at 0?

#514

Post by quickthrower2 »

diego_sandoval wrote: post #273

Because otherwise you would be wasting a perfectly good number for no reason, which means you need to use more bits to do the same thing. To write 4 numbers (including zero) you only need two bits 0: 00 1: 01 2: 10 3: 11 To write 4 numbers if you avoid using the number zero, you need three bits 1: 001 2: 010 3: 011 4: 100 If you extrapolate that a little bit, you'll realize that you'll need two bytes (1 Byte + 1 bit…

Fron the article:

> It's not the reason you think. No, it's not that reason either.

Indexing is a language level concern, it has nothing to do with the generated code.

Unless you write machine code I guess.

Re: Why do arrays start at 0?

#515

Post by samatman »

throwaway821909 wrote: post #218
drewzero1 wrote: post #194

Earlier quoted context omitted.

Oddly(?) though, most parents of young children don't refer to a baby as being "zero years old." Rather, we break them down into smaller units: two days old, six weeks old, four months old.

It helps that change happens particularly fast at that age, so the difference between newborn and 6 months is worth mentioning. Later on the units go up again and we just say "I'm in my 30s" :P On the other hand a computer/car/house can also be 10 years old but not 0.

Duration only ever departs from 0, it can never arrive there.

That's why zero-based indexing is good!

Re: Why do arrays start at 0?

#516

Post by tuatoru »

xg15 wrote: post #235

I don't quite understand the argument "0-based being easier for pointer arithmetic is nonsense because the language doesn't have pointers". Whether or not the language presents the concept of "pointer" to the user is independent of whether or not it uses pointers internally. And if it exposes arrays as a concept, it has to implement them somehow. The simplest possible implementation of arrays is having a start addres…

I would be fine with it all if 0-based was called "offset", with "index" reserved for 1-based.

The element at offset 0 is the first element.

Precision in naming is important.

Re: Why do arrays start at 0?

#519

Post by samatman »

themacks wrote: post #49
randomdata wrote: post #29

Earlier quoted context omitted.

The moment you are born you are 0 years old (or perhaps 0.75 years old, but we don't usually recognize that). We count from zero in this case, at least implicitly. In some cultures you are considered 1 the moment you are born, so the zero indexing isn't universal here, but typical in North America as noted earlier.

Typical counting of things starts from 0. If you count apples you implicitly start at zero and add 1 for each apple. If you count age, you start at birth (0) and count years; one for each birthday. That isn't zero based. The difference is the index of the item between the starting point and the next item. In zero based this item is number 0, in one based, this item is number 1. The first year of life is generally con…

This is a philosophically deep point which took me a long time to grasp.

There is a narrowing from "nothing at all" to "zero apples" which doesn't happen 'in the world' but is a necessary precondition to counting apples. The existence of any apple is a requirement for there to be zero of them before you put anything in the basket.

Re: Why do arrays start at 0?

#520

Post by dathinab »

Ignoring the past; 0 indexing is:

- closer to hardware

- makes index == element wise offset from the first element

- there are both algorithm which are (very slightly) easier to implement with 0 and 1 indexing, AFIK more of the "bread and butter" algorithm are easier with 0 then 1 (e.g. indexing of C-style arrays used all the time, heaps etc.)

- 0 is not special => less bounds checks in typed languages (if you have an unsigned int index you only have to check the upper bounds, with 1-index you also have to check for 0)

- 0 is not special => with signed integer you can have negative indices (from the end) in which case all signed integers are valid (but potential out of bounds), with 1 indexing you have a "gap" in the middle which for some (rare) use cases can be very painful to handle

So independent of what the history was. It's just much more pragmatic to use 0-indexing in many common use-cases. Especially given that 1-indexing produces more special cases for very common use-cases makes it sub-optimal for both usability and performance.

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