[Numpy-discussion] NEP for faster ufuncs

[Mark Wiebe]

Hello NumPy-ers,

After some performance analysis, I've designed and implemented a new
iterator designed to speed up ufuncs and allow for easier multi-dimensional
iteration.  The new code is fairly large, but works quite well already.  If
some people could read the NEP and give some feedback, that would be great!
 Here's a link:

https://github.com/m-paradox/numpy/blob/mw_neps/doc/neps/new-iterator-ufunc.rst

I would also love it if someone could try building the code and play around
with it a bit.  The github branch is here:

https://github.com/m-paradox/numpy/tree/new_iterator

To give a taste of the iterator's functionality, below is an example from
the NEP for how to implement a "Lambda UFunc."  With just a few lines of
code, it's possible to replicate something similar to the numexpr library
(numexpr still gets a bigger speedup, though).  In the example expression I
chose, execution time went from 138ms to 61ms.

Hopefully this is a good Christmas present for NumPy. :)

Cheers,
Mark

Here is the definition of the ``luf`` function.::

    def luf(lamdaexpr, *args, **kwargs):
        """Lambda UFunc

            e.g.
            c = luf(lambda i,j:i+j, a, b, order='K',
                                casting='safe', buffersize=8192)

            c = np.empty(...)
            luf(lambda i,j:i+j, a, b, out=c, order='K',
                                casting='safe', buffersize=8192)
        """

        nargs = len(args)
        op = args + (kwargs.get('out',None),)
        it = np.newiter(op, ['buffered','no_inner_iteration'],
                [['readonly','nbo_aligned']]*nargs +
                                [['writeonly','allocate','no_broadcast']],
                order=kwargs.get('order','K'),
                casting=kwargs.get('casting','safe'),
                buffersize=kwargs.get('buffersize',0))
        while not it.finished:
            it[-1] = lamdaexpr(*it[:-1])
            it.iternext()

        return it.operands[-1]

Then, by using ``luf`` instead of straight Python expressions, we
can gain some performance from better cache behavior.::

    In [2]: a = np.random.random((50,50,50,10))
    In [3]: b = np.random.random((50,50,1,10))
    In [4]: c = np.random.random((50,50,50,1))

    In [5]: timeit 3*a+b-(a/c)
    1 loops, best of 3: 138 ms per loop

    In [6]: timeit luf(lambda a,b,c:3*a+b-(a/c), a, b, c)
    10 loops, best of 3: 60.9 ms per loop

    In [7]: np.all(3*a+b-(a/c) == luf(lambda a,b,c:3*a+b-(a/c), a, b, c))
    Out[7]: True
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