5.2 Creating Compiled Code

Speed is crucial in mathematical computations. Though Python is a convenient very high-level language, certain calculations can be several orders of magnitude faster than in Python if they are implemented using static types in a compiled language. It is virtually impossible to write serious competitive computer algebra software if one restricts oneself to interpreted Python code.

To deal with this problem, Sage supports a compiled ``version'' of Python called Cython ([Cyt] and [Pyr]). Cython is simultaneously similar to both Python and C. Most Python constructions, including list comprehensions, conditional expressions, code like += are allowed; you can also import code that you have written in other Python modules. Moreover, one can declare arbitrary C variables and arbitrary C library calls can be made directly. The resulting code is converted to C and compiled using a C compiler.

In order to make your own compiled Sage code, give the file an .spyx extension (instead of .sage). You can attach and load compiled code exactly like with interpreted code. The actual compilation is done ``behind the scenes'' without your having to do anything explicit. See SAGE_ROOT/examples/pyrex/factorial.spyx for an example of a compiled implementation of the factorial function that directly uses the GMP C library. To try this out for yourself, cd to SAGE_ROOT/examples/pyrex/, then do the following:

sage: load "factorial.spyx"
***************************************************
                Recompiling factorial.spyx
***************************************************
sage: factorial(50)
30414093201713378043612608166064768844377641568960512000000000000L
sage: time n = factorial(10000)
CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s
Wall time: 0.03

Note that Sage will recompile factorial.spyx if you quit and restart Sage. The compiled shared object library is stored under $HOME/.sage/temp/hostname/pid/spyx. These files are deleted when you exit Sage.

NO Sage preparsing is applied to spyx files, e.g., 1/3 will result in 0 in a spyx file instead of the rational number

. If foo is a function in the Sage library, to use it from a spyx file import sage.all and use sage.all.foo.

import sage.all
def foo(n):
    return sage.all.factorial(n)