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Re: [DTB] issues with numeric casting/built-in functions

From: Sandro Hawke <sandro@w3.org>
Date: Mon, 04 May 2009 13:31:09 -0400
To: Jos de Bruijn <debruijn@inf.unibz.it>
cc: RIF <public-rif-wg@w3.org>
Message-ID: <28438.1241458269@ubehebe>

> XPath functions and operators essentially says that each implementation
> can decide for itself which length for decimals it supports.

As long as it's at least 16 digits
http://www.w3.org/TR/xmlschema11-2/#partial-implementation

> For
> example, implementation A could support decimals of length 16, while
> implementation B supports decimals of length 20.  In addition, each
> implementation can use its own rounding algorithm for representing
> numbers that need larger decimals.  For example, implementation A could
> truncate numbers, while implementation B rounds them.
> 
> this poses problems for us when defining things like casting functions
> and arithmetic operations.
> for example, according to XPath casting a string
> "0.11111111111111111111111111111111111111111111111111111111111111111111111111
> 11111111111111111111111111"
> to a decimal results either in an error or a decimal of some length
> (given by the implementation) that is obtained from the number
> corresponding to the string by some arbitrary rounding algorithm.
> 
> It is not possible for us to define this kind of behavior in DTB,
> because functions are defined as functions: you have some input values
> that define an output value.
> In addition, it is really bad for interchange, since some
> implementations do something, while other implementations do something
> else, and you get no warning.
> So, for casting, I propose to define the xs:decimal casting function
> such that the result of casting a string to a decimal is simply the
> number with the input string as lexical representation, and so we have
> no exception behavior.
> 
> We might define conformance such that implementations only need to
> support decimals of a particular length.

Am I going to be able to use an XPath number handling library for this?
Or would you be making me round numbers differently?  

I guess 0.6666666666666666 (17 digits) might reasonably round to
0.6666666666666667 (16 digits), but that wouldn't conform to the
definition you're proposing...

This functions-are-functions thing is worrying me, too.  This means list
"union", "intersect", and "except" need to be defined with stable
ordering, I think, which I believe means they're stuck with n^2
algorithms.  Is it really impossible to allow for non-determinism /
non-specification on these things?  I had been expecting the order of
lists returned from these operations to be undetermined (which would
allow an implementation to really use hash tables to b-trees behind the
scenes.)  Hmmm, I guess there are tricks one could still do -- add a
list-index field, and then sort the final result by that field -- but
ouch....

> The problem with numeric functions are similar.  With addition,
> subtraction, and multiplication we run into the same problem.  Again, I
> propose to define the functions such that the output values are simply
> the decimals which are the result of the arithmetic operations and not
> from some implementation-dependent modification.
> With division it gets a bit more complicated.  For example, there is no
> decimal that can represent the result of dividing 1 by 3, because there
> are no infinite-length decimals. If we had owl:real we could still
> properly defined the division function, although there is no syntactical
> representation for the result. I have two possible solutions for you:
> (1) We reintroduce owl:real and use it for the definition of
> numeric-divide (I think we need it only there).
> (2) We define the domain of numeric-divide such that only pairs of
> numbers a,b (if they are decimals) are included if a/b can be
> represented using a decimal. This means that if 1,3 are the arguments,
> the value of the function is not specified by DTB and is left up to the
> implementation.
> 
> I think these are crucial issues and we need to have at least an idea of
> where we want to go before DTB can go to last call. Otherwise, it will
> not be possible to make any RIF implementations.

FWIW, I don't think this is all that crucial.   *shrug*

      - Sandro
Received on Monday, 4 May 2009 17:31:17 GMT

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