Robert,
that's a tricky issue. The only bullet-proof way to get this right is=20
*not* to use floating point arithmetics when calculating the=20
auto-incremented values.
The problem is that in IEEE floating point, the neither of the following=20
equations hold:
(x_max - x_min ) / (endOffset-startOffset) =3D Dx
So no matter if we give x_min , x_max or x_min and _ Dx, we'll have=20
rounding problems. Consider this:
S_i=3DstartOffset...endOffset Dx =3D (endOffset-startOffset) =B7 Dx
Even this does not hold in floating point arithmetics. However, to=20
calculate a value x_i , it's more precise to use multiplication (like in=20
the right hand part of the equation) rather than adding things up in a=20
for loop. It avoids adding up the rounding errors. That's why I opted=20
for storing the Dx value.
The best practice when implementing it would of course be not to use=20
floating point arithmetics. Most programming languages offer a concept=20
of precise arithmetics. In Java, there's the BigDecimal class to do this.
Of course, it's important that applications write these values into the=20
AniML document without truncating them. If they truncate, there's very=20
little we can do.
Best regards,
Burkhard
Prof. Robert J. Lancashire wrote:
> Hi,
>
> I have been working through some coding for reading and writing CML
> documents and noticed that like JCAMP-DX they have followed the
> arrangement that for auto-generated X values the approach is
> provide the firstX, lastX and the number of points.
> From this deltaX is calculated.
>
> With AnIML, firstx and deltax is provided and I wonder whether this
> introduces a problem with respect to rounding errors.
> When packages give deltax in an output routine they may truncate
> to a set number of figures which would then lead to innaccuracies.
>
> I suggest it would be better to give first last and number of points
> so that deltaX is not truncated.
>
> In the case of JCAMP-DX though, I must admit to having seen numerous
> files where the ##FIRSTX=3D and ##LASTX=3D values were significantly
> trunacted by comparison to the actual values listed in the data section
> so there may be still be an issue with rounding that affects the
> calculation of delta.
>
> Any thoughts.
> Excuse me if this was covered long ago!!
>
> Robert
>
>
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