forwarded 530381 http://code.google.com/p/mpmath/issues/detail?id=148 thanks
Hi Sanjoy, Thanks for the report; I've forwarded it upstream so they can have a look at it. On Sun, May 24, 2009 at 16:23, Sanjoy Mahajan <[email protected]> wrote: > Package: python-mpmath > Version: 0.11-2 > Severity: normal > > The following Python code uses mpmath to implement Salamin's algorithm > for computing pi (using arithmetic and geometric means). The number > of digits of accuracy should roughly double with each iteration, and > it does so if mp.dps=1000 (the number of digits is printed at the end > of each swing through the loop). > > However, if mp.dps=4000, then the number of digits doubles for a few > iterations, then goes to infinity: > > 3.0 > 8.1 > 18.7 > 40.3 > 83.6 > inf > inf > inf > > Somehow the estimate became exactly equal to pi. It seems strange to > me and I wonder if it's a bug in one of the math functions like sqrt > or whether it's a feature. Or perhaps mpmath computes pi using the > same algorithm? > > > from mpmath import * > > mp.dps = 4000 > > # a sequence is successive arithmetic means; > # g sequence is successive geometric means > a, b = 1, sqrt(0.5) > n = 1 > sum = 0 > factor = 2 > while n < mp.dps-10: > n = -log(a*a-b*b)/log(10) > a,b = (a+b)/2, sqrt(a*b) > factor *= 2 > sum += factor * (a*a-b*b) > M = (a+b)/2 > estimate = 4*M*M/(1-sum) > digits = -log(abs(estimate-pi))/log(10) > print "%7.1f" % digits > > > -- System Information: > Debian Release: squeeze/sid > APT prefers unstable > APT policy: (500, 'unstable'), (1, 'experimental') > Architecture: i386 (i686) > > Kernel: Linux 2.6.29-2-686 (SMP w/2 CPU cores) > Locale: LANG=en_US.utf8, LC_CTYPE=en_US.utf8 (charmap=UTF-8) > Shell: /bin/sh linked to /bin/bash > > Versions of packages python-mpmath depends on: > ii python-support 1.0.3 automated rebuilding support for > P > > python-mpmath recommends no packages. > > Versions of packages python-mpmath suggests: > ii python-gmpy 1.03.ds-1 Interfaces GMP to Python for > fast, > ii python-matplotlib 0.98.3-5 Python based plotting system in a > ii python-mpmath-doc 0.11-2 library for arbitrary-precision > fl > > -- no debconf information > > > > _______________________________________________ > Python-modules-team mailing list > [email protected] > http://lists.alioth.debian.org/mailman/listinfo/python-modules-team > -- Sandro Tosi (aka morph, morpheus, matrixhasu) My website: http://matrixhasu.altervista.org/ Me at Debian: http://wiki.debian.org/SandroTosi -- To UNSUBSCRIBE, email to [email protected] with a subject of "unsubscribe". Trouble? Contact [email protected]
