I found the following draft in my computer, but apparently, for some reason, it has never been posted. So, with apologies to casevh, here it is:
Thank you, casevh. Your reply certainly answered my question as to the conversion from float (or double) to mpf . I failed to find the answer through googling.
With regard to my first question re/ the speed of Python relative to C++, the program that I tested is based on binary splitting which, as you know, entails recursive calls to a function from within the function itself. All operations are on integers (the largest being 9092390 decimal digits long). Then, there is a single final floating point division. The results were : python/gmpy 81.638, C++/GMP 28.800 sec.
Your comment that Python has more overhead for each function call may partly explain the relative slowness of Python. I have since come across articles that suggest that Python is significantly slower in performing simple arithmetic operations. See, for example:
http://furryland.org/~mikec/bench/
Lastly, there is a clear difference between Python and C++. Whereas in C++ the type of each operand is strictly defined at the time it is declared, Python mostly leaves the definition to the "context" during run-time. This may cause slowness and is a potential source of confusion to programmer and program alike. It is a pity because I have come to enjoy Python as a language of simple elegance as well as power and accuracy.
