Re: [Caml-list] How much optimized is the 'a option type ?

[Alain Frisch <alain@frisch.fr>]

Revised description:  there is no need to keep the tag on B or C values 
when applying the A constructor, and one can skip the 0 integer as the 
second field when applying the B/C constructor.

    B (x, y)   ---->   b0 = 1:(id_t,x, y)
A (B (x, y))  ---->   b1 = 0:(id_t, b0)

    C          ---->   c0 = 2:(id_t)
A  C          ---->   c1 = 0:(id_t, c0)


This simplifies the criterion for checking if a value of type t has the 
B/C constructor (tag = 1 or 2) or the A constructor (tag = 0, and the 
argument is the second field of the block if the first is id_t, and the 
value itself otherwise).

-- Alain


On 01/24/2014 11:06 AM, Alain Frisch wrote:
> On 01/17/2014 10:10 AM, Gabriel Scherer wrote:
>> There have been recurrent discussions of optimizing `'a option` to
>> avoid allocation in some cases, which is interesting when it is used
>> as a default value for example. (The nice recent blog post by Thomas
>> Leonard also seems to assume that `'a option` is somehow optimized.)
>>
>> My strictly personal opinion is that I doubt this would be a good
>> idea, because I expect a fair share of the programming practice that
>> currently use ('a option) to move to something like (('a,
>> error-description) either) later in their lifetime, and I wouldn't
>> want people to avoid to do that for performance concerns.
>> Historically, we've rather come to see special-case representation
>> optimizations (eg. array of floats) as a mistake -- but on the other
>> hand there is not much downside to record of floats.
>
> It could be argued the role of option types is important enough to
> justify a special treatment for them.  But maybe one could think (just
> for the fun of it) about a more general optimized representation for sum
> types where one constructor should behave (mostly) as the identity at
> runtime.
>
> To take an example, consider a type:
>
>    type ('a, 'b) t =
>       | A of 'a
>       | B of 'b * 'b
>       | C
>
> with some marker to tell the compiler to optimize the representation of A.
>
> If one wants the constructor A to be the identity at runtime (in most
> cases), we still need to distinguish C from A C, A (A C), A (A (A C)),
> etc,  and B (x, y) from A (B (x, y)), A (A (B (x, y))), etc.  Here is
> one possible implementation:  let's allocate a fresh value to represent
> the identity of the t type:
>
>    id_t = 0:(0)
>
> that is, a block of size 1, tag 0, with a single 0 field (equivalent to:
> id_t = ref ()).  (This value would be generated by the compiler and
> passed along in modules which re-export the type t.)
>
> The value (B (x, y)) would be represented as a block b0 = 1:(id_t, 0, x,
> y)  (block with tag 1 and 4 fields).  Applying the A constructor to such
> a block b0 would return a new block b1 = 1:(id_t, b0).  Applying again
> the A constructor to b1 would return b2 = 1:(id_t, b1).
>
> Similarly, the value C would be represented as a block c0 = 2:(id_t, 0).
>   Applying A to such a value would return a block c1 = 1:(id_t, c0), and
> then c2 = 1:(id_t, c1).
>
> So, in general, applying the A constructor to a value x requires to
> check if its argument is a block whose first field is equal to id_t, and
> in this case, it returns a new block with the same tag and the two
> fields id_t and x.  In other cases, the constructors simply returns its
> argument.
>
> With this representation, it is not difficult to deconstruct the three
> constructors.  For a value of type t:
>
>   - If the value is a block whose first field is equal to id_t and its
> second field is 0, then the value comes from the B or C constructor
> (according to the block tag) and the arguments can be found in the block.
>
>   - If the value is a block whose first first is equal to id_t and its
> second field is not 0, then the value comes from the A constructor, and
> the argument is the second field of the block.
>
>   - Otherwise, the value comes from the A constructor and its argument
> is represented by the same value.
>
>
> There is one correctness problem with this representation, though:
> applying the A constructor to a float value cannot be the identity,
> because of the specific representation for float arrays (which is
> triggered by checking if the value is a float block).  This means we
> must also have a special representation for A x, A (A x), etc, where x
> is a float.  The scheme above extends naturally to support this
> representation:  a0 = 0:(id_t, 0, x), a1 = 0:(id_t, a0), etc.
>
>
> Another drawback is related to the use of the id_t block, which does not
> work well with the generic marshaling, and requires extra plumbing to
> make this value available where the type t can be constructed or
> deconstructed.  It's possible to do better for a type with a "global name".
>
>
> In case of a constant constructor such as C, one can of course
> pre-allocate the block c0 = 2:(id_t, 0).  To avoid passing an extra
> value around, one could store it within id_t itself (id_t = 0:(c0)
> instead of id_t = 0:(0)).
>
> Another optimization is to avoid the allocation when applying the A
> constructor several times to the same B or C value.  This can be done by
> memoization.  One can add an extra field to all the blocks described
> above, initialized to 0, and updated to point to the "next" application
> of A when requested.
>
> So, we would have:
>
>    c0 = 2:(id_t, 0, 0)
>
> When applying A to it, one create c1
>
>    c1 = 2:(id_t, c0, 0)
>
> and update the last field of c0 to be c1:
>
>    c0 = 2:(id_t, 0, c1)
>
> If one needs to apply A again to c0, one can reuse the existing value.
> The same applies to non-constant constructors as well.
>
>
>
> -- Alain
>