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Laurence Rowe | 3 Jan 21:53
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Re: number() floated?

On 16 December 2011 17:06, Konrad Korzeniowski <konrad <at> pandur.net> wrote:
> Hi there,
>
> I'm using 1.1.26-6 version of libxslt (Debian Lenny), and cannot find any
> explanation regarding described below behaviour.
>
> I got following simple xslt file:
>
> <?xml version="1.0" encoding="UTF-8"?>
>
> <xsl:stylesheet version="1.0"
> xmlns:xsl='http://www.w3.org/1999/XSL/Transform'>
>     <xsl:template match="/">
>     <xsl:value-of select="number('8.95')"/>
>     </xsl:template>
> </xsl:stylesheet>
>
>
> running xsltproc with this xsl against any xml gives:
> 8.949999999999999
>
> Is this expected? Shouldn't this be 8.85?
>
> Thanks for any explanation.

Not all decimals may be exactly represented in binary floating point.
See: http://en.wikipedia.org/wiki/Floating_point#Representable_numbers.2C_conversion_and_rounding

Laurence
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Vincent Lefevre | 3 Jan 23:00

Re: number() floated?

On 2012-01-03 20:53:40 +0000, Laurence Rowe wrote:
> On 16 December 2011 17:06, Konrad Korzeniowski <konrad <at> pandur.net> wrote:
> > I got following simple xslt file:
> >
> > <?xml version="1.0" encoding="UTF-8"?>
> >
> > <xsl:stylesheet version="1.0"
> > xmlns:xsl='http://www.w3.org/1999/XSL/Transform'>
> >     <xsl:template match="/">
> >     <xsl:value-of select="number('8.95')"/>
> >     </xsl:template>
> > </xsl:stylesheet>
> >
> >
> > running xsltproc with this xsl against any xml gives:
> > 8.949999999999999
> >
> > Is this expected? Shouldn't this be 8.85?
> >
> > Thanks for any explanation.
> 
> Not all decimals may be exactly represented in binary floating point.
> See: http://en.wikipedia.org/wiki/Floating_point#Representable_numbers.2C_conversion_and_rounding

Except that this seems to be a bug here:

$ /usr/bin/printf "%a\n" 8.95
0x8.f33333333333333p+0

This is the binary value represented internally.
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Vincent Lefevre | 3 Jan 23:33

Re: number() floated?

On 2012-01-03 23:00:16 +0100, Vincent Lefevre wrote:
> On 2012-01-03 20:53:40 +0000, Laurence Rowe wrote:
> > On 16 December 2011 17:06, Konrad Korzeniowski <konrad <at> pandur.net> wrote:
[...]
> > >     <xsl:value-of select="number('8.95')"/>
[...]
> 
> Except that this seems to be a bug here:

After looking at the spec, I confirm this is a bug. The XPath spec
says for number(): "a string that consists of optional whitespace
followed by an optional minus sign followed by a Number followed
by whitespace is converted to the IEEE 754 number that is nearest
(according to the IEEE 754 round-to-nearest rule) to the mathematical
value represented by the string"

The nearest value X is the following one (represented exactly in
radix 16, thanks to %a):

> $ /usr/bin/printf "%a\n" 8.95
> 0x8.f33333333333333p+0

But actually (see below) the internal representation doesn't matter
here.

Concerning xsl:value-of, the XSLT spec says that for a number, the
XPath string() fucntion is used, and the XPath spec says for the
above value: "otherwise, the number is represented in decimal form
as a Number including [...]; beyond the one required digit after
the decimal point there must be as many, but only as many, more
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Laurence Rowe | 4 Jan 01:33
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Re: number() floated?

On 3 January 2012 22:33, Vincent Lefevre <vincent+gnome <at> vinc17.org> wrote:
> On 2012-01-03 23:00:16 +0100, Vincent Lefevre wrote:
>> On 2012-01-03 20:53:40 +0000, Laurence Rowe wrote:
>> > On 16 December 2011 17:06, Konrad Korzeniowski <konrad <at> pandur.net> wrote:
> [...]
>> > >     <xsl:value-of select="number('8.95')"/>
> [...]
>>
>> Except that this seems to be a bug here:
>
> After looking at the spec, I confirm this is a bug. The XPath spec
> says for number(): "a string that consists of optional whitespace
> followed by an optional minus sign followed by a Number followed
> by whitespace is converted to the IEEE 754 number that is nearest
> (according to the IEEE 754 round-to-nearest rule) to the mathematical
> value represented by the string"
>
> The nearest value X is the following one (represented exactly in
> radix 16, thanks to %a):
>
>> $ /usr/bin/printf "%a\n" 8.95
>> 0x8.f33333333333333p+0
>
> But actually (see below) the internal representation doesn't matter
> here.
>
> Concerning xsl:value-of, the XSLT spec says that for a number, the
> XPath string() fucntion is used, and the XPath spec says for the
> above value: "otherwise, the number is represented in decimal form
> as a Number including [...]; beyond the one required digit after
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Vincent Lefevre | 4 Jan 03:01

Re: number() floated?

On 2012-01-04 00:33:44 +0000, Laurence Rowe wrote:
> On 3 January 2012 22:33, Vincent Lefevre <vincent+gnome <at> vinc17.org> wrote:
> > As a consequence, the output value should be "8.95" (like the input)
> > because 8.95 rounds to X and has less than 17 digits.
> 
> You're right, xpath.c just prints DBL_DIG digits (a constant from
> float.h).

At least, this guarantees that when the value is read back in decimal,
this will give the same floating-point number.

BTW, I've just noticed that my examples with printf were incorrect:
I didn't pay attention to the fact that /usr/bin/printf uses the
long double type, and not the double type (this doesn't seem to be
documented).

> However, doing this properly is difficult, see:
> http://bugs.python.org/issue1580.

The reference I have is

@InProceedings{BurgerDybvig1996,
  author = {R.~G. Burger and R.~Kent Dybvig},
  title = {Printing Floating-Point Numbers Quickly and Accurately},
  booktitle =    {Proceedings of the {SIGPLAN'96} Conference on  Programming Languages Design and Implementation},
  year =         1996,
  pages =      {108--116},
  month =        jun,
}
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Phil Shafer | 4 Jan 06:38
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Re: number() floated?

Konrad Korzeniowski writes:
>running xsltproc with this xsl against any xml gives:
>8.949999999999999

You may be hitting this rounding error:

https://bugzilla.gnome.org/show_bug.cgi?id=629325

Thanks,
 Phil
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