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Attached patch makes range objects precompute their length on creation. 
This speeds up indexing and len at the expense of a small increase in 
range object size. The main benefit, however is that unsupported length > 
sys.maxsize is detected early and confusing OverflowError from len(r) or 
r[i] is avoided.
See discussion starting at http://mail.python.org/pipermail/python-
3000/2008-April/013225.html .

So with this patch, range(10**100) produces an OverflowError: is that 
right?
I don't much like this aspect of the change: there are uses for
for i in range(ridiculously_large_number):
 ...
 if condition_that_occurs_early_in_practice:
 break

On Fri, Apr 25, 2008 at 12:55 PM, Mark Dickinson <report@bugs.python.org> wrote:
..
> I don't much like this aspect of the change: there are uses for
>
> for i in range(ridiculously_large_number):
For this application, I would use "for i in itertools.count():"
instead. The only caveat is that while count() lets you specify the
start, it does not provide for a step. If that is a problem, I would
rather add step to count().

I guess there needs to be a decision on whether to make range objects of 
length >= PY_SSIZE_T_MAX illegal; perhaps more discussion on python-dev 
would be worthwhile?
I can see three options, besides leaving things as they are:
(1) make large ranges illegal, as with this patch
(2) make large ranges legal, but don't allow indexing with indices
larger than PY_SSIZE_T_MAX.
(3) allow large ranges *and* large indices.
Option 3 seems to me like the ideal from the users' point of view, but I'm 
not sure whether it's easy/possible to implement it given that sq_item 
receives a Py_ssize_t for the index.
Option 2 seems messy: half of one thing and half of the other, but I 
think it would be easy to implement. This is what I'd personally prefer 
if Option 3 isn't feasible.
If Option 1 is indeed the preferred option, then the patch looks good to 
me, and works for me on OS X 10.5. (Minor nitpick: it introduces some 
extra tab characters.)
Whatever happens, we probably also need a documentation update explaining 
the limitations on range.

Option (3) would require changing both sq_item and sq_length signatures,
which is likely to have a large negative impact on performance.
Option (2) would either require a change for the sq_length signature, or
leave the problem of having valid range objects for which applying len()
would produce an OverflowError.
What are the use cases for ranges with length greater than maxsize? Note
that in 2.x all arguments to length are limited to 32 bit integers (even
on 64-bit platforms) and the main reason to support long start/stop/step
in 3.0 is because 2.x range() supports them. On the other hand, since
2.x range() produces lists, it is limited in length to a fraction of
sys.maxsize. Therefore none of the current uses of either range or
xrange require support of long length.

I am currently working on a patch that allows large ranges and large
indices. The trick is to define tp_as_mapping->mp_subscript.
Then range_item() is rarely used, only by functions calling directly the
PySequence_* functions, instead of the abstract PyObject_*.
There is still a limit with len(), which seems bound by the size_t limit.
Most of the tests in test_builtin were re-enabled.
I join the current version of the patch.
I'm still working on further simplifications, and maybe supporting
slices on ranges...
Note: I found more useful to store a "range->end" member, which is the
multiple of "step" just beyond the "stop" limit.

> What are the use cases for ranges with length greater than maxsize?
Yeah---I'm a bit short on use cases. The one that originally bit me with 
Python 2.x was when I was doing a search for a quadratic non-residue 
modulo a largeish prime;
for i in range(1, p):
 if (i_is_a_nonresidue_modulo_p):
 break
Here p might be a 200-digit prime number, and the situation is that half 
the integers between 1 and p-1 are 'quadratic residues', while the other 
half are 'quadratic nonresidues'; in practice the residues and 
nonresidues are mixed up fairly well, so the first nonresidue shows up 
pretty quickly, but there's no known small upper bound on when the first 
nonresidue appears.
Of course, it's not hard to rewrite this with a while loop instead; it 
would just be a bit annoying if that were necessary, when the code above 
is so clear and direct, and the one obvious way to do it (TM).
I'd also note that it's not completely out of the question that something 
like range(10**10) would be useful on a 32-bit machine: a long-running 
process might easily go through 10**10 iterations of something.
I agree it's a bit strange to have a semi-functional range object, that 
you can iterate over but not take the length of.

On Fri, Apr 25, 2008 at 4:37 PM, Mark Dickinson <report@bugs.python.org> wrote:
..
> for i in range(1, p):
> if (i_is_a_nonresidue_modulo_p):
> break
>
> Here p might be a 200-digit prime number, and the situation is that half
> the integers between 1 and p-1 are 'quadratic residues', while the other
> half are 'quadratic nonresidues'; in practice the residues and
> nonresidues are mixed up fairly well, so the first nonresidue shows up
> pretty quickly, but there's no known small upper bound on when the first
> nonresidue appears.
Hmm, AFAIKT there is always at least one non-residue between 1 and p
and therefore you can just write
for i in itertools.count(1):
 if (i_is_a_nonresidue_modulo_p):
 break
maybe with an additional check for p > 1.

> Hmm, AFAIKT there is always at least one non-residue between 1 and p
> and therefore you can just write
>
> for i in itertools.count(1):
> if (i_is_a_nonresidue_modulo_p):
> break
>
> maybe with an additional check for p > 1.
Sure. It's just uglier that way. :-) And I feel it would be mildly 
annoying not to be able to use the obvious tool for the job, for subtle 
reasons. It's also a potential source of bugs: one might write such code 
using range and only discover later that it fails unexpectedly for large 
inputs.
These really aren't serious objections---just mild preferences. I'll stop 
being disruptive now :)

Given that range() produced a list in the 2.x series (hence limited to
available memory), and xrange() uses int internally for its values (and
hence couldn't even cope with short ranges with values greater than
sys.maxint).
So my preference is to mimic the 2.x range's behaviour in this case by
raising an overflow error if the sequence is too long.
(From Python 2.5.1)
>>> range(2**99, 2**100)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
OverflowError: range() result has too many items
>>> range(2**99, 2**99+5)
[633825300114114700748351602688L, 633825300114114700748351602689L,
633825300114114700748351602690L, 633825300114114700748351602691L,
633825300114114700748351602692L]
>>> xrange(2**99, 2**99+5)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
OverflowError: long int too large to convert to int

I've implemented range slicing and x in range(..) in range-sequence.diff 
and registered range with the Sequence ABC.

Reviewing my own patch (range-sequence.diff), I've realized that it is 
being a bit too clever in handling x in range(..) where x is not an 
integer. It seems that upon a failed PyLong_Check, range_contains should 
just do a linear search. This is easy to implement, but I will wait for 
more feedback before posting further changes.

My 2 cents: for me is more useful to have a unbound range() than to be
able to do a len() on it.
For me, range() should mimic a number generator: no limit, no length.

> For me, range() should mimic a number generator: no limit, no length.
That's itertools.count()

It also isn't what range() and xrange() are used for now in 2.x. range()
returns an actual list, hence is limited to sequences that fit in a
reasonable amount of memory, and xrange() doesn't support values greater
than sys.maxint at all (as it uses C ints for its internal storage of
the start, stop and step values).
With itertools.count() available for the unbounded iterator case, I
think making range() mimic its 2.x counterpart as closely as possible
(without the memory inefficiency) will be quite valuable.

Fair enough, specially if in the documentation of range() we put "if you
want a unbound, no limit, number generator, use itertools.count()" (or
something well written in english ;) ).
Thanks!

Has a resolution been made on this?

On the issue of whether len(range()) should be allowed to be >
sys.maxsize, I think this should be allowed. I think in the future we
should change the __len__ protocol to allow unbounded lengths. Even
today, I think range(10**100).__len__() should return 10**100 rather
than raising an OverflowError, even if len(range(10**100)) raises
OverflowError.
I also think ranges should be introspectable, exposing their start, stop
and step values just like slice objects.
Probably all those changes are for post 3.0.

Guido, does that mean we can apply this patch to get the cleaner
list-like behaviour for 3.0, and then work on the sq_item/sq_len fixes
for 3.1 as a separate issue?

This issue was missing a priority setting.
Alexander's range-sequence patch still applies cleanly to the Py3k
branch, and "make test" still runs correctly after applying it.
As Alexander notes above, range_contains does still need slightly better
handling of non-integer numbers - I suggest doing a numeric conversion
via PyNumber_Index(el) at the beginning of range_contains, and if that
conversion fails, do a conversion via PyNumber_Long(el) and immediately
return False if the result is not equal to el itself (i.e. only integer
values of non-integer types will be found in the range.
Since that explanation got kind of complicated, I've added a modified
patch that includes the above change, and adds a couple of additional
tests to ensure a non-integer floating point value won't be found in the
sequence.

It looks like your range_subscript() forgets to compute the length field...

My initial patch had a few problems - I removed it and uploaded a
corrected version.

Good catch Antoine (I missed that in Alexander's patch) - working on
that now.

v2 of my updated patch attached to fix the issue Antoine noted.
Also gets rid of some tab-instead-of-spaces indenting issues in the
file, and avoids hardcoding PyRange_Type when creating new instances.
However, the patch still has issues, as can be seen with the new tests I
added to test_range to actually exercise some of the functionality
beyond the sys.maxsize limit.

By the way, why is this release blocker? do we have performance numbers?

I wonder if we shouldn't hold off on this. It's a substantial amount of
new code. I'd be fine with it going into 3.0.1 since it's pure
optimization (IIUC!). But right now we want burn-in, not new features.

Given the problems with it, I'm dropping this to normal priority and
punting to 3.1.
(the release blocker status was just temporary to ensure we got a
decision on it before rc1 - it previously didn't have a priority set)

@Nick, would you have time to work on this for 3.2, or should we target 3.3, or could somebody else take this over?

I'd still like to have another look at this before beta 1, but can't promise I'll get to it. Unassigning in case someone else has some roundtuits to spare over the next few weeks.

I brought the patch up to date for the Py3k branch, but realised just before checking it in that it may run afoul of the language moratorium (since it alters the behaviour of builtin range objects).
However, the .count() and .index() methods (along with the Sequence ABC registration) as well as the O(1) containment testing for integers were already put in place. (I also noticed that the new methods from issue #9213 are not mentioned in the range() docs, unlike the O(1) optimisation)
I've gone ahead and checked it in as r86970, as I see this patch as filling out the promise of the Sequence ABC registration by adding support for slicing and negative indices (with the length caching as more of an implementation detail).
However, I'm also leaving the tracker issue open and assigning to Georg in case he wants to revert it before the beta goes out.
Note that I also fixed the patch so that OverflowError occurs only when encountering an affected operation (primarily indexing and retrieval of the length). If you don't do any of those things, you can make your ranges as large as you like. (The indexing could fairly easily be fixed to eliminate the overflow errors - I just didn't do it in this patch, since it is a separate problem).

> (I also noticed that the new methods from issue #9213 are not mentioned
> in the range() docs
Wasn't that fixed in Issue9746?

On Sat, Dec 4, 2010 at 2:26 AM, Daniel Stutzbach <report@bugs.python.org> wrote:
>
> Daniel Stutzbach <stutzbach@google.com> added the comment:
>
>> (I also noticed that the new methods from issue #9213 are not mentioned
>> in the range() docs
>
> Wasn't that fixed in Issue9746?
Ah, I see what you mean. I was more referring to the lack of a
versionchanged note on the range() documentation itself, rather than
the mentioning of range() under the sequence types documentation.
Some of my new additions to the range documentation could probably be
deleted and replaced with a reference to that part of the docs.
Cheers,
Nick.

Daniel Stutzbach pointed out that range() is also mentioned under:
http://docs.python.org/dev/library/stdtypes.html#sequence-types-str-bytes-bytearray-list-tuple-range
The descriptions of range's limitations there is no longer accurate (slicing is supported following this patch and containment testing is now efficient)

> The descriptions of range's limitations there is no longer accurate
> (slicing is supported following this patch and containment testing is
> now efficient)
Want to open a new issue for that? (or is there one already?)

(Oops, didn't mean to reclose this yet)
I want to wait for Georg's verdict on including the functionality in 3.2 before stressing too much about correct documentation of it :)

I'm fine with it: as with the other changes for .count and .index, consistency with the protocols/ABCs the types are members of is not exclusively a new feature.

The descriptions of range's limitations in the docs still needs an update.

Not sure this worth a patch, to me it looks like a removal of a single word. But here it goes anyway.

Applied in r87162 

The other major change for ranges is that "in" and "not in" are no longer inefficient for actual instances of int (it does an arithmetic calculation instead of a linear search).

Is the in/not-in fast path in 2.7?

No, I believe it was added as part of the .index() and .count() implementation.
Checking the source, there's definitely no sq_contains implementation in 3.1 or 2.7.

here is the patch for the py3k docs.

Doc change committed to py3k in r87346. Thanks, SilentGhost!
I also committed r87349 to reverse r87162 (which was in the wrong branch).