I found several article that could be used to find minimal setting for arbitrary precision, enough the chat, let my code do the talk..
Software that used:
- python ver 2.6.5 in ubuntu 10.04 64 bit
- python EPD(Enthought Python Distribution) ver 7.0-2 32 bit in windows 7 64 bit, no default mpmath installation under python epd, but its available via sympy(included ver 0.14 mpmath)
- python mpmath ver 0.17, http://code.google.com/p/mpmath/
- gmpy -> python binding for GMP
- sage version 4.7 64bit for ubuntu10.04 http://www.sagemath.org/
Below are 2 equations that could be used for searching significant setting for mpmath arbitrary precision.
1. Interval Arithmetic: Python Implementation and Applications by Stefano Taschini in SciPy2008_proceedings.pdf
2. Why and how to use arbitrary precision by Kaveh R. Ghazi, Vincent Lefèvre, Philippe Théveny, Paul Zimmermann in cise.pdf
- different BACKEND in mpmath did not effect in result and mpmath.mp context(setting for arbitrary precision), just gives an performance effect(sage faster, than gmpy, last python)
- mpmath prec value that could be gives most precision is not less than 128 bit (mpmath.mp.prec=128)
- creating a mpf object is better to converted into string data type first( mp.mpf('0.1') or mp.mpf(str(0.1)))
- better doing a arithmetic rational operation when possible see first code that solved using sympy