Before I begin, I'd like to thank you in advance for any help I get with
this question. I'm currently working with some heavy computation and
decided to cython-ize my code. Because of what I'm doing in my math
research, I will need to make MILLIONS of calls to pretty high level
complex functions such as gamma, eta, and the list goes on. I've gotten
stuck with a curiosity concerning the MPComplexNumber and the ComplexNumber
types in sage.
I would like to make a function, f, which takes sage ComplexNumber types
and does something with it. In the end, I'd like to return a sage
ComplexNumber type. Should I use MPComplexNumber so that within the
function in order to use the GNU mpc library or would it be better to use
the mpfr library that is given to me by ComplexNumber and use Sage
directly? In other words, would it be better for me to use mpc to square a
complex number or would it be better for me to just square the number using
the built-in sage code that does it with MPFR? I tend to believe that it
would be best for me to use MPComplexNumbers and directly use GNU mpc.
If I'm right, how do I convert MPComplexNumber into a ComplexNumber in
cython? How do I initialize a variable in cython with the type
MPComplexNumber? I am quite the novice in cython.
The last question I have concerns weather I should just install the mpfr
and mpc libraries, and use the header file directly. Would this result in
faster computation?
Below is a code snippet of an example of what I'm trying to do...
Should I:
from sage.rings.complex_number cimport ComplexNumber
def Square(ComplexNumber x):
return x^2
or should I use the following pseudo-code:
#IMPORT GNU MPC USING mpc.h
from sage.rings.complex_number cimport ComplexNumber
def Square(ComplexNumber x):
Square The number using mpc, by extracting the real and imaginary
parts
Convert back to ComplexNumber type (if so..how?)
or should I:
from sage.rings.complex_mpc cimport MPComplexNumber
from sage.rings.complex_number cimport ComplexNumber
def Square(ComplexNumber x):
Initialize MPComplexNumber variable
Extract the real and imaginary part of x, make them have type mpfr_t
square the result using mpc's multiply function
Build the ComplexNumber from the real and imaginary parts
again...(again, if so...how?)
Very sorry if I'm not making a lot of sense. Thank you for any help!
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