[Numpy-discussion] fixed-point arithmetic

[Robert Kern]

On Mon, Sep 21, 2009 at 10:57, Neal Becker <ndbecker2 at gmail.com> wrote:
> David Cournapeau wrote:
>
>> On Mon, Sep 21, 2009 at 9:00 PM, Neal Becker <ndbecker2 at gmail.com> wrote:
>>>
>>> numpy arrays of fpi should support all numeric operations.  Also mixed
>>> fpi/integer operations.
>>>
>>> I'm not sure how to go about implementing this.  At first, I was thinking
>>> to just subclass numpy array.  But, I don't think this provides fpi
>>> scalars, and their associated operations.
>>
>> Using dtype seems more straightforward. I would first try to see how
>> far you could go using a pure python object as a dtype. For example
>> (on python 2.6):
>>
>> from decimal import Decimal
>> import numpy as np
>> a = np.array([1, 2, 3], Decimal)
>> b = np.array([2, 3, 4], Decimal)
>> a + b
>>
>> works as expected. A lot of things won't work (e.g. most transcendent
>> functions, which would require a specific implementation anyway), but
>> arithmetic, etc... would work.
>>
>> Then, you could think about implementing the class in cython. If speed
>> is an issue, then implementing your own dtype seems the way to go - I
>> don't know exactly what kind of speed increase you could hope from
>> going the object -> dtype, though.
>>
>
> We don't want to create arrays of fixed-pt objects.  That would be very
> wasteful.  What I have in mind is that integer_bits, frac_bits are
> attributes of the entire arrays, not the individual elements.  The array
> elements are just plain integers.
>
> At first I'm thinking that we could subclass numpy array, adding the
> int_bits and frac_bits attributes.  The arithmetic operators would all have
> to be overloaded.
>
> The other aspect is that accessing an element of the array would return a
> fixed-pt object (not an integer).

Actually, what you would do is create a new dtype, not a subclass of
ndarray. The new datetime dtypes are similar in that they too are
"parameterized" dtypes.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
  -- Umberto Eco