[SciPy-dev] Question about 64-bit integers being cast to double precision
Fernando Perez
Fernando.Perez at colorado.edu
Wed Oct 26 12:38:26 CDT 2005
Charles R Harris wrote:
[...]
> Now, python does the following:
>
>
>>>>from math import *
>>>>sqrt(2)
>
> 1.4142135623730951
>
> and if we are going to overload sqrt we should keep this precision. Do
> we really want to make a distinction in this case between math.sqrt and
> Numeric.sqrt ? I myself don't think so. On the other hand, it is
> reasonable that scipy not promote float types in this situation.
> Integral types remain a problem. What about uint8 vs uint64 for
> instance?
Again, I find it simplest to think about this problem in terms of
exact/approximate numbers. All integer types (of any bit-width) are exact,
all float numbers are approximate. The question is then how to handle
functions, which can be (in terms of their domain/range relation):
1. f : exact -> exact
2. f : exact -> approximate
etc.
My argument is that for #2, there should be upcasting to the widest possible
approximate type, in an attempt to preserve as much of the original
information as we can. For example, sqrt(2) should upcast to double, because
truncation to integer makes very little practical sense.
The case of accumulators is special, because they are of type 1 above, but the
result may not (and often doesn't) fit in the input type. Travis already
agreed that in this case, an upcast was a reasonable compromise.
However, for functions of the kind
3. f : approx -> approx
there should be in general no upcasting (except for accumulators, as we've
discussed). Doing a*b to two float arrays should certainly not produce an
enormous result, which may not even fit in memory.
Just my opinion.
Cheers,
f
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