Re: [xml] XPath numbers and exponential notation

[Bjorn Reese <breese mail1 stofanet dk>]

Thomas Broyer wrote:

> since April 21, libxml supports exponential notation of XPath numbers both
> at parsing and writing (conversion to string). In the
> xmlXPathStringEvalNumber comment was added a [30a] production, where does
> it come from? I can't find anything on W3C's site.

Out of nowhere. The production was only added to document how the actual
code behaves.

> Since then, illegal expressions such as "75.2E-12" became legal in libxml
> view and some expressions don't produce expected result anymore (the above
> example is converted to the string "7.52e-11" whereas "0.0000000000752" is
> expected)
>
> Any explaination about the why and the goal of such a transformation?

Very simple. XPath uses ANSI/IEEE Std 754 (1985) for floating point numbers.
This standard uses a fixed numbers of digits (bits, actually) to represent
numbers, which means that it cannot accurately represent, say, the number pi
as it would require an infinite number of digits. It also means that big
numbers cannot be represented accurately with the regular 9.9 floating point
notation. If we were going to try this, the least significant digit would be
garbage.

It such cases it is customary to use scientific notation instead, and this
is what we did. It is not 100% standard compliant, but the standard would
generate garbage, so we chose the lesser of the two evils. I believe that
this is a sound choice, given that W3C has realized the problem, and added
a requirement for scientific notation in XPath 2.0.

Anybody who disagrees are welcome to contribute a patch.

> I came to that while translating XML in a Nutshell's XPath Refence chapter
> where it is stated that exponential notation is allowed. That chocked me
> and I used testXPath to check, which achieved confusing my mind. I decided
> to check the XPath spec and errata and didn't find anything related.

Scientific notation is not allowed in XPath 1.0, but it has been added to
the requirements for XPath 2.0.