Hi all,

Sylvain's descriptions and rational are very good, I think. I am wondering, 
however, if we are making too bold claims about accuracy when we have no 
control over the interpolation method's implementation.  A  user's technique 
may differ from the creator's (that's OK), but if one technique was  
numerically ill-conditioned and the other not, even using the same precision 
could lead to  inaccurate results.

With that in mind, here's another suggestion (I think I prefer the 
one-paragraph approach, as the it helps connect the constituent points, but I 
don't have a strong opinion on that):

---

The accuracy of the reconstituted coordinates depends mainly on the degree of 
subsampling and the choice of interpolation method, both of which are set by 
the creator of the dataset. The accuracy will also depend, however, on how the 
interpolation method is implemented and on the computer platform carrying out 
the computations .There are no restrictions on the choice of interpolation 
method implementation, for neither the data creator nor the data user, but the 
floating-point arithmetic precision used by the data creator during the 
preparation and validation of the compressed coordinates must be specified by 
setting the interpolation variable’s **`computational_precision`** attribute to 
one of the following values: 

(table)
"32": 32-bit floating-point arithmetic, comparable to the binary32 standard in 
[IEEE_754]
"64": 64-bit floating-point arithmetic, comparable to the binary64 standard in 
[IEEE_754]

Using the given computational precision in the interpolation computations is a 
necessary, but not sufficient, condition for the data user to be able to 
reconstitute the coordinates to an accuracy comparable to that intended by the 
data creator. For instance, a **`computational_precision`** value of "`64`" 
would specify that, using the same software and hardware as the creator of the 
compressed dataset, sufficient accuracy could not be reached when using a 
floating-point precision lower than 64-bit floating-point arithmetic in the 
interpolation computations required to reconstitute the coordinates.

---

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