SageX hacking example --- fix the mangled pow() function

Some useful links:

Pyrex has an unfortunate bug in the way it handles the power function for cdef integers. Namely

   1 %pyrex
   3 def foo(int n):
   4     return 2**n


Looking at the c source code we see the the error on line 85

  __pyx_1 = PyFloat_FromDouble(pow(2, __pyx_v_n)); if (!__pyx_1) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 7; goto __pyx_L1;}

Here the c function pow() is being used, which only operates on doubles. This is fine if the return type is a float, but if it is, say, a python object, then this code (potentially) violates two principles: (1) Behave like python when possible and (2) arithmatic on two cdef ints (longs, etc.) should return an int (long, etc.)

Expand the sagex spkg found in SAGE_ROOT/spkg/standard (tar xvfj sagex-20070126.spkg). Now the all the code we want to look at (for this problem) is in Pyrex/Compiler/. Most of the time you will want to look at (for parsing) and (for code generation). Read the comments at the top of those files, but don't be worried if you don't underand them right away.

The relavent code is in the PowNode.compute_c_result_type() function (line 2514).

    def compute_c_result_type(self, type1, type2):
        if self.c_types_okay(type1, type2):
            return PyrexTypes.c_double_type
            return None

The questions now becomes, what is the best way of fixing this issue.