Arbitrary Precision using Python Mpmath

Mpmath is great, powerful and easy to use to calculating equation that involve floating point.
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
GMPY Backend

SAGE Backend

Python Backend

2. Why and how to use arbitrary precision by Kaveh R. Ghazi, Vincent Lefèvre, Philippe Théveny, Paul Zimmermann in cise.pdf

	#!/usr/bin/python
	import sys
	# using mpmath for arbitrary precision,
	# sympy for showing the equation in pretty way
	if sys.platform == 'linux2':
	import mpmath as mp, sympy as sm
	elif sys.platform == 'win32':
	import sympy as sm
	mp = sm.mpmath
	# just for write shorter code
	f = mp.mpf
	ms = mp.nstr
	pr = sm.pprint
	print 'Equation for testing arbitrary precision'
	# show the equation with pretty printing
	pr(173746*sm.sin(1e22) + 94228*sm.log(17.1) - 78487*sm.exp(0.42))
	# Expected value from the reference 'Why and how to use arbitrary precision'
	# by Kaveh R. Ghazi, Vincent Lefevre, Philippe Theveny, Paul Zimmermann
	expect = '-1.3418189578296195e-12'
	# show default setting for mpmath
	print '\n Default', mp.mp, '\n'
	print 'Expected value are', expect, '\n'
	print 'Searching prec value, to match the expected value', expect
	# calc -> calculate ; cpr -> for comparing with previosly calculated
	calc = cpr = 0
	# loop for searching prec setting that matched
	# expected value -1.341818958e-12'
	# by calculating f_1 function
	while calc != expect:
	mp.mp.prec +=1
	a, b, c = mp.sin(1e22), mp.log(f('17.1')), mp.exp(f('0.42'))
	r = f(173746)*(a) + f(94228)*(b) - f(78487)*(c)
	calc = mp.nstr(r, n=17)
	if cpr != calc:
	cpr = calc
	# uncomment below to find out when the calculated is changed
	# than previous when prec is changed
	#print cpr, mp.mp
	print 'Found Significand', mp.mp
	print 'Result using above setting =', calc
	print 'mpmath backend', mp.libmp.BACKEND #show mpmath backend

view raw ex_paper_mpmath2.py hosted with ❤ by GitHub

GMPY Backend

SAGE Backend

Python Backend

Conclusion

• 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

Install OpenCL and PyOpenCL in Ubuntu 10.04 LTS Lucid Lynx 64 bit

After playing with Scientific Linux 6 with OpenCL and PyOpenCL, I decided to bring it into my primary OS, and yes it is Ubuntu 10.04 LTS Lucid Lynx 64 bit.

Searching through the net, I found two ways to install OpenCL

• by using a packaged deb made by nou at AMD dev central forum -> Ubuntu package with ATI Stream SDK
• and by installing it manually using the AMD-APP-SDK-v2.4-lnx64.tgz

Because my previous experience in SL6 is worked, so i liked to doing so within my ubuntu.

Things that needed by my system for OpenCL(testing that it works by executing 'make all' in your $AMDAPPSDKROOT -> i put it on "/home/user/AMD-APP-SDK-v2.4-lnx64/", this will built samples application that included in samples folder)

• read the guide AMD_APP_SDK_Installation_Notes.pdf (it just extract and put a conf in /etc dir)
• install libglu1-mesa-dev (in my case the package(header files) that missing is only this, so might be different on your system!), this needed when build a OpenCL samples
• also add a AMDAPPSDK in your $PATH in .bashrc file like this

Below are some screenshoot to test sample applications under AMD-APP-SDK-v2.4-lnx64/samples/opencl/bin/x86_64/ directory if the installation of AMDAPPSDK and is working:
test using HelloCL

test using GlobalMemoryBandwidth

 

and notice if running an OpenCL program using all processor thread(because i didn't have a GPU capable for OpenCL

And now for PyOpenCL(made by Andreas Klöckner at http://mathema.tician.de/software/pyopencl )
To install correctly please enable the internet connectivity its needed to install required python dependency module.

In my system is need to install libboost1.40-all-dev, python-numpy and python-libxslt. (Both are available from ubuntu repository). Using command from terminal -> sudo apt-get install libboost1.40-all-dev python-numpy python-libxslt

Installing PyOpenCl:

• download PyOpenCL from PyOpenCL
• Notice when execute configure.py : python configure.py   --cl-inc-dir=$AMDAPPSDKROOT/include   --cl-lib-dir=$AMDAPPSDKROOT/lib/x86_64   --cl-libname=OpenCL
• then -> python setup.py build
• finnally -> sudo python setup.py install

test PyOpenCL using examples benchmark-all.py

BTW  I'm just noticed that python in ubuntu is faster than in Scientific Linux 6, and it same 64 bit, same laptop.