On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel <baruc...@gmx.com> wrote:
> From time to time it is asked on forums how to extend precision of > computation on Numpy array. The most common answer > given to this question is: use the dtype=object with some arbitrary > precision module like mpmath or gmpy. > See > http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra > or http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath > or > http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values > > While this is obviously the most relevant answer for many users because it > will allow them to use Numpy arrays exactly > as they would have used them with native types, the wrong thing is that > from some point of view "true" vectorization > will be lost. > > With years I got very familiar with the extended double-double type which > has (for usual architectures) about 32 accurate > digits with faster arithmetic than "arbitrary precision types". I even > used it for research purpose in number theory and > I got convinced that it is a very wonderful type as long as such precision > is suitable. > > I often implemented it partially under Numpy, most of the time by trying > to vectorize at a low-level the libqd library. > > But I recently thought that a very nice and portable way of implementing > it under Numpy would be to use the existing layer > of vectorization on floats for computing the arithmetic operations by > "columns containing half of the numbers" rather than > by "full numbers". As a proof of concept I wrote the following file: > https://gist.github.com/baruchel/c86ed748939534d8910d > > I converted and vectorized the Algol 60 codes from > http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf > (Dekker, 1971). > > A test is provided at the end; for inverting 100,000 numbers, my type is > about 3 or 4 times faster than GMPY and almost > 50 times faster than MPmath. It should be even faster for some other > operations since I had to create another np.ones > array for testing this type because inversion isn't implemented here > (which could of course be done). You can run this file by yourself > (maybe you will have to discard mpmath or gmpy if you don't have it). > > I would like to discuss about the way to make available something related > to that. > > a) Would it be relevant to include that in Numpy ? (I would think to some > "contribution"-tool rather than including it in > the core of Numpy because it would be painful to code all ufuncs; on the > other hand I am pretty sure that many would be happy > to perform several arithmetic operations by knowing that they can't use > cos/sin/etc. on this type; in other words, I am not > sure it would be a good idea to embed it as an every-day type but I think > it would be nice to have it quickly available > in some way). If you agree with that, in which way should I code it (the > current link only is a "proof of concept"; I would > be very happy to code it in some cleaner way)? > > b) Do you think such attempt should remain something external to Numpy > itself and be released on my Github account without being > integrated to Numpy? > I think astropy does something similar for time and dates. There has also been some talk of adding a user type for ieee 128 bit doubles. I've looked once for relevant code for the latter and, IIRC, the available packages were GPL :(. Chuck
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