Earlier quoted context omitted.
One-based is not better for iterating backwards. Zero-based indexing is naturally coupled with using only half-open ranges. When using zero-based indexing and half-open ranges, accessing an array forwards, backwards or circularly is equally easy. In this case you can also do like in the language Icon, where non-negative indices access the array forwards, while negative indices access the array backwards (i.e. -1 is t…
The problem is that half-open ranges work best when you the start is closed and the ending is open. In forward iteration we use [0,n) but for backwards iteration we have to use (-1, n-1] or [0,n-1], both of which are kinda clunky.
The whole point here is to use a single kind of range, without exceptions, in order to avoid the errors caused by using the wrong type of range for the context.
For backwards iteration the right range is [-1,-1-n), i.e. none of those listed by you.
Like for any such range, the number of accessed elements is the difference of the range limits, i.e. n, which is how you check that you have written the correct limits. When the end of the range is less than the start, that means that the index must be decremented. In some programming languages specifying a range selects automatically incrementing or decrementing based on the relationship between the limits. In less clever languages, like C/C++, you have to select yourself between incrementing and decrementing (i.e. between "i=0;i-1-n;i--").
It is easy to remember the backwards range, as it is obtained by the conversion rules: 0 => -1 (i.e. first element => last element) and n => -n (i.e. forwards => backwards).
To a negative index, the length of the array must be added, unless you use a programming language where that is done implicitly.
In the C language, instead of adding the length of the array, one can use a negative index into an array together with a pointer pointing to one element past the array, e.g. obtained as the address of the element indexed by the length of the array. Such a pointer is valid in C, even if accessing memory directly through it would generate an out-of-range error, like also taking the address of any element having an index greater than the length of the array. The validity of such a pointer is specified in the standard exactly for allowing the access of an array backwards, using negative indices.