[Cython] Lisp inspired transforms

[Martin C. Martin]

Hi all,




http://wiki.cython.org/enhancements/metaprogramming


"deriv" which means you can write:

def eggs(a, b):
   return deriv(5*a+b, a)

and it is translated at compile time to:

def eggs(a, b):
   return (((5 * 1) + (0 * a)) + 0)



>>> TestTrans.myfunct(10.0)
(4990.0, 1500.0)
>>> TestTrans.newtons(TestTrans.myfunct, 10.0)
f( 10.0 ) = 4990.0 , f'( 10.0 ) = 1500.0
f( 6.67333333333 ) = 1475.93037185 , f'( 6.67333333333 ) = 668.000666667
f( 4.46385893383 ) = 434.735082042 , f'( 4.46385893383 ) = 298.890548717
f( 3.00936301916 ) = 126.267956666 , f'( 3.00936301916 ) = 135.843986716
f( 2.07985587115 ) = 34.9852072625 , f'( 2.07985587115 ) = 64.8870066716
f( 1.54068464016 ) = 8.28568621842 , f'( 1.54068464016 ) = 35.6056374064
f( 1.3079774954 ) = 1.18847303518 , f'( 1.3079774954 ) = 25.6620769269
f( 1.26166506953 ) = 0.0415843883547 , f'( 1.26166506953 ) = 23.8769812152
f( 1.25992345957 ) = 5.73769235945e-05 , f'( 1.25992345957 ) = 23.8111068596
f( 1.2599210499 ) = 1.09734443754e-10 , f'( 1.2599210499 ) = 23.8110157797
f( 1.25992104989 ) = 0.0 , f'( 1.25992104989 ) = 23.8110157795
1.2599210498948732



There are many other use cases as well.



Best,
Martin

I've been doing some thinking and prototyping of a transform system inspired by Common Lisp macros. You can see the results as the newest CEP: Briefly, it allows you to define a transform in the Cython source code. The transform runs at compile time, and takes the *parse trees* of its arguments. In the examples, I define a simple symbolic differentiator You can use this, for example, with numerical optimization techniques like Newton's method. An example which differentiates 5 * x**3 - 10 and finds it's root is given on the above wiki page, here's the output: It's also useful for moving computation from run time to compile time, and makes it easy for the programmer to specify what should happen where. I'm attaching a patch that implements the examples. It's very proof-of-concept, which means its really rough. :) I also implemented the bar minimum to get the examples working, but it gives you an idea.

CythonMetaprogramming.tar.gz
Description: application/gzip

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