I should point out that Bharath is using Numpy, so if anyone knows of
a solution using that, that will work too.

Aaron Meurer

On Jun 1, 2012, at 2:01 AM, Joachim Durchholz <[email protected]> wrote:

> Am 01.06.2012 09:45, schrieb Chris Smith:
>> On Fri, Jun 1, 2012 at 1:25 PM, Joachim Durchholz<[email protected]>  wrote:
>>> Am 01.06.2012 09:25, schrieb Chris Smith:
>>>>
>>>> How about round down and then add your interval width?
>>>
>>> You'll add a rounding unit if the input value happens to be exact.
>>>
>>
>> Can the interval have zero width?
>
> It could, but that doesn't affect the outcome - you're working on the upper 
> bound.
>
> > If so then, yes, and b could then be
>> calculated as
>>
>> b=(a+10**-3).round(3) if a!=n else a
>
> Not sure what n is here.
> Also, you'd want to add half of the step size to cover the round-down case.
>
> I'm not sure what Python's rounding mode is. IEEE defines some rounding modes 
> that won't do what you expect (such as rounding up or down depending on the 
> parity of the mantissa - I heard that's helpful to improve the stability of 
> some numeric algorithm, that's why IEEE defines it).
> The scary thing here is that C code might actually have changed the rounding 
> mode. And if you're doing numeric work, I'd expect that some people will 
> indeed use a C module that does exactly this together with SymPy.
>
> So my proposal would be to stick with floor() and ceil(). These are 
> well-defined operations.
>
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