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Subject: Re: [ub] Justification for < not being a total order on pointers?
From: Jeffrey Yasskin (jyasskin_at_[hidden])
Date: 2013-08-27 14:18:48


On Tue, Aug 27, 2013 at 11:59 AM, Richard Smith <richardsmith_at_[hidden]> wrote:
> On Tue, Aug 27, 2013 at 11:37 AM, John Spicer <jhs_at_[hidden]> wrote:
>>
>>
>> On Aug 27, 2013, at 1:39 PM, Jeffrey Yasskin <jyasskin_at_[hidden]> wrote:
>>
>> > On Tue, Aug 27, 2013 at 10:28 AM, Xavier Leroy <Xavier.Leroy_at_[hidden]>
>> > wrote:
>> >> On 27/08/13 17:48, Jeffrey Yasskin wrote:
>> >>>> - As a semanticist, I think it would be challenging to formalize, for
>> >>>> the general reasons given above.
>> >>>
>> >>> How do you model std::less<T*>, which already requires this total but
>> >>> unspecified order?
>> >>
>> >> No one tried, as far as I know. We (as a community) are still a long
>> >> way from formalizing the complete semantics of a "big" language like
>> >> C++, but an even longer way from formalizing specs for its standard
>> >> library...
>> >>
>> >> There are plausible ways to formalize this total order at the source
>> >> language level. But, as Gabriel wrote, the difficulty is to ensure
>> >> that your source-level semantics is not making predictions that the
>> >> compiler could invalidate later.
>> >>
>> >> In other words: at the end of the day, your pointers are just bit
>> >> patterns that the hardware compares as if they were integers. If you
>> >> could chase this hardware ordering of pointers back every compilation
>> >> pass, it should be the case that the source-level ordering you obtain
>> >> is one of those allowed by your source-level semantics. Proving this
>> >> kind of properties sounds very challenging to me.
>> >
>> > Mhmm. It sounds like you probably can't model the
>> > implementation-defined conversion to intptr_t yet either? Since
>> > T*->intptr_t->T* has to be an identity map, and intptr_t is totally
>> > ordered.
>> >
>> > If that's the case, it sounds like making operator< on T* a total
>> > order would reduce the fraction of C++ that's currently formalizable
>> > but wouldn't make it any harder to formalize the whole language?
>>
>> I think there would need to be one restriction (that may already exist,
>> I'm not sure). I think an ordering of pointers would require that all of
>> the pointers point to objects or within an object. I think we would have to
>> prohibit attempting to find the order of "one past the last element" vs.
>> another pointer as those could end up being the same even though they refer
>> to different (logical) things, except in the case that is defined by the
>> language (where the other points to an element of the array).
>>
>> With that rule, this function would provide ordering (where unsigned long
>> is replaced with the appropriate type for a given implementation):
>>
>> typedef unsigned long integral_type_large_enough_to_hold_pointer;
>> bool less(void* p1, void* p2) {
>> integral_type_large_enough_to_hold_pointer i1, i2;
>> i1 =
>> reinterpret_cast<integral_type_large_enough_to_hold_pointer>(p1);
>> i2 =
>> reinterpret_cast<integral_type_large_enough_to_hold_pointer>(p2);
>> return i1 < i2;
>> }
>>
>> The actual operator need not be implemented that way, but given that with
>> a rule such as the one above you *could* implement it that way, there does
>> not seem to be a reason not to support ordering of pointers (with such a
>> rule).
>
>
> I don't think the above implementation is guaranteed to work; I don't
> believe we have any guarantee that converting the same pointer value to an
> integral type multiple times will yield the same integral value. (For
> instance, I believe a conforming implementation could maintain a table of
> pointers, to which it adds entries each time a pointer is cast to an
> integer, and the integer value could be merely an index into that table.)

I think that particular implementation is forbidden. The rule in
[expr.reinterpret.cast]p4 is: "A pointer can be explicitly converted
to any integral type large enough to hold it. The mapping function is
implementation-defined." Since it's a "function", it has to map a
domain value to only one value in the range.

Jeffrey


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