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Constraint on the lexical space of xs:float (was Re: (invalid?) floats and doubles in NIST's validation testsuite)

From: Eric van der Vlist <vdv@dyomedea.com>
Date: Thu, 25 Oct 2001 21:10:08 +0200
Message-ID: <3BD86390.8010500@dyomedea.com>
To: Anli Shundi <ashundi@tibco.com>
Cc: "'xmlschema-dev@w3.org'" <xmlschema-dev@w3.org>
Hi,

I have a question which goes along with this question kept without 
answer of this list and might be an answer.

The rec doesn't seem to put any restriction on the range of xs:float in 
its lexical space:

...............................
3.2.4.1 Lexical representation

float values have a lexical representation consisting of a mantissa 
followed, optionally, by the character "E" or "e", followed by an 
exponent. The exponent ·must· be an integer. The mantissa must be a 
decimal number. The representations for exponent and mantissa must 
follow the lexical rules for integer and decimal. If the "E" or "e" and 
the following exponent are omitted, an exponent value of 0 is assumed.

The special values positive and negative zero, positive and negative 
infinity and not-a-number have lexical representations 0, -0, INF, -INF 
and NaN, respectively.

For example, -1E4, 1267.43233E12, 12.78e-2, 12 and INF are all legal 
literals for float.
...............................

The rule given to match lexical an value spaces doesn't restrict the 
lexical space either:

...............................
A literal in the ·lexical space· representing a decimal number d maps to 
the normalized value in the ·value space· of float that is closest to d 
in the sense defined by [Clinger, WD (1990)]; if d is exactly halfway 
between two such values then the even value is chosen.
...............................

Whatever literal you take, there will allways be a "float that is 
closest to d in the sense defined by [Clinger, WD (1990)]" it will 
eventually be the maximum value of a float for an arbitrary big value in 
the lexical space, the minimum value of a float for an arbitrary big 
negative value, -0 or +0 for an arbitrary small value, but this matching 
seems to exclude the possibility of any overflow.

Is my interpretation correct and isn't it dangerous to be unable to 
detect overflows?

Thanks

Eric

Anli Shundi wrote:

> Hi,
> 
> many of the floats and doubles in the NIST validation
> testsuite at http://www.w3.org/2001/05/xmlschema-test-collection/
> are IMO out of range.  According to the spec:
> 
> float corresponds to the IEEE single-precision 32-bit floating point type
> [IEEE 754-1985]. The basic ·value space· of float consists of the values m ×
> 2^e, where m is an integer whose absolute value is less than 2^24, and e is
> an integer between -149 and 104, inclusive. 
> 
> The lexical representation uses the decimal powers
> though.  Thus the biggest representable float short of
> infinity is 2^24 * 2^104 = 3.40283E38 .  The testsuite
> uses floats such as 16777215.999999999999E104 which
> is IMO invalid, since it's out of float's value space.
> (Note that 2^24 = 16777216 in the above case)
> 
> Such floats and doubles with absolute values greater
> than 1.79E308 or smaller than 4.94E-324 are throughout
> the testsuite and they are all considered valid ?!
> 
> Question: does the E in lexical representation actually 
> stand for binary or decimal powers?
> 
> Anli Shundi                      ashundi@tibco.com
> Product Development Group        office: (919) 969-6518
> TIBCO Software Inc.              
> 
> www.extensibility.com  |  www.XMLschema.com  |  www.tibco.com
> 
> 
> 
> 
> 



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Eric van der Vlist       http://xmlfr.org            http://dyomedea.com
http://xsltunit.org      http://4xt.org           http://examplotron.org
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Received on Thursday, 25 October 2001 15:09:48 GMT

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