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Diffstat (limited to 'security/nss/lib/freebl/mpi/doc/pi.txt')
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diff --git a/security/nss/lib/freebl/mpi/doc/pi.txt b/security/nss/lib/freebl/mpi/doc/pi.txt deleted file mode 100644 index 01c82abe9..000000000 --- a/security/nss/lib/freebl/mpi/doc/pi.txt +++ /dev/null @@ -1,90 +0,0 @@ -This file describes how pi is computed by the program in 'pi.c' (see -the utils subdirectory). - -Basically, we use Machin's formula, which is what everyone in the -world uses as a simple method for computing approximations to pi. -This works for up to a few thousand digits without too much effort. -Beyond that, though, it gets too slow. - -Machin's formula states: - - pi := 16 * arctan(1/5) - 4 * arctan(1/239) - -We compute this in integer arithmetic by first multiplying everything -through by 10^d, where 'd' is the number of digits of pi we wanted to -compute. It turns out, the last few digits will be wrong, but the -number that are wrong is usually very small (ordinarly only 2-3). -Having done this, we compute the arctan() function using the formula: - - 1 1 1 1 1 - arctan(1/x) := --- - ----- + ----- - ----- + ----- - ... - x 3 x^3 5 x^5 7 x^7 9 x^9 - -This is done iteratively by computing the first term manually, and -then iteratively dividing x^2 and k, where k = 3, 5, 7, ... out of the -current figure. This is then added to (or subtracted from) a running -sum, as appropriate. The iteration continues until we overflow our -available precision and the current figure goes to zero under integer -division. At that point, we're finished. - -Actually, we get a couple extra bits of precision out of the fact that -we know we're computing y * arctan(1/x), by setting up the multiplier -as: - - y * 10^d - -... instead of just 10^d. There is also a bit of cleverness in how -the loop is constructed, to avoid special-casing the first term. -Check out the code for arctan() in 'pi.c', if you are interested in -seeing how it is set up. - -Thanks to Jason P. for this algorithm, which I assembled from notes -and programs found on his cool "Pile of Pi Programs" page, at: - - http://www.isr.umd.edu/~jasonp/pipage.html - -Thanks also to Henrik Johansson <Henrik.Johansson@Nexus.Comm.SE>, from -whose pi program I borrowed the clever idea of pre-multiplying by x in -order to avoid a special case on the loop iteration. - ------------------------------------------------------------------- -***** BEGIN LICENSE BLOCK ***** -Version: MPL 1.1/GPL 2.0/LGPL 2.1 - -The contents of this file are subject to the Mozilla Public License Version -1.1 (the "License"); you may not use this file except in compliance with -the License. You may obtain a copy of the License at -http://www.mozilla.org/MPL/ - -Software distributed under the License is distributed on an "AS IS" basis, -WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License -for the specific language governing rights and limitations under the -License. - -The Original Code is the MPI Arbitrary Precision Integer Arithmetic -library. - -The Initial Developer of the Original Code is -Michael J. Fromberger <sting@linguist.dartmouth.edu> -Portions created by the Initial Developer are Copyright (C) 1998, 2000 -the Initial Developer. All Rights Reserved. - -Contributor(s): - -Alternatively, the contents of this file may be used under the terms of -either the GNU General Public License Version 2 or later (the "GPL"), or -the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), -in which case the provisions of the GPL or the LGPL are applicable instead -of those above. If you wish to allow use of your version of this file only -under the terms of either the GPL or the LGPL, and not to allow others to -use your version of this file under the terms of the MPL, indicate your -decision by deleting the provisions above and replace them with the notice -and other provisions required by the GPL or the LGPL. If you do not delete -the provisions above, a recipient may use your version of this file under -the terms of any one of the MPL, the GPL or the LGPL. - -***** END LICENSE BLOCK ***** - -$Id$ - - |