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# mpmath in Sage to become 3x faster

*February 1, 2010*

I’ve blogged previously about the potential speedups attainable by rewriting core parts of mpmath in Cython (here and here), but all I had back then was some standalone classes and functions that couldn’t easily be integrated. Well, I now finally have a fully working, fully integrated Cython implementation of the `mpf` and `mpc` types (plus related utility functions) — and it successfully runs the entire mpmath test suite!

On my computer (Ubuntu 64 bit, AMD Athlon 64 3700+), running `import mpmath; mpmath.runtests()` in Sage takes this much time:

Before [mpmath (svn trunk) + Sage 4.3.1]: **62.75 seconds**

After [mpmath (svn trunk with modifications) + Cython mpmath types + Sage 4.3.1 + a Sage performance patch by Robert Bradshaw]: **19.87 seconds**

I have essentially only implemented arithmetic operations and conversions, so core transcendental functions (as well as square roots and powers) still fall back to the Python code, and they account for the majority of the running time. According to cProfile, about 20% of the total time is spent in `exp()` and `gamma()` alone. Hypergeometric series evaluation is also still done in Python. Replacing these functions with Cython versions should give a significant boost, and will be very easy to do in the future (in terms of code infrastructure). So realistically, the running time for the unit tests can be cut much further, probably in half.

The code isn’t public yet. I will soon commit the changes to the mpmath svn repository and create a patch for Sage with the Cython extensions. The code just needs a little more cleanup, and there are no doubt a couple of subtle issues (such as corner-case memory leaks) that need fixing… but essentially, it’s working, and the tests pass, so I expect it to be releasable quite soon.

*Update: after adding just a little more Cythonized wrapper code, the time is now down to 17.64 seconds. I have still not touched exp, log, cos, sin, gamma, or any other core transcendental functions. Expect further improvements.*

*Update 2 (2010-02-03): preliminary version of the Cython code here*