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Diffstat (limited to 'security/nss/lib/freebl/mpi/doc/sqrt.txt')
| -rw-r--r-- | security/nss/lib/freebl/mpi/doc/sqrt.txt | 87 |
1 files changed, 0 insertions, 87 deletions
diff --git a/security/nss/lib/freebl/mpi/doc/sqrt.txt b/security/nss/lib/freebl/mpi/doc/sqrt.txt deleted file mode 100644 index c709217a5..000000000 --- a/security/nss/lib/freebl/mpi/doc/sqrt.txt +++ /dev/null @@ -1,87 +0,0 @@ -Square Root - -A simple iterative algorithm is used to compute the greatest integer -less than or equal to the square root. Essentially, this is Newton's -linear approximation, computed by finding successive values of the -equation: - - x[k]^2 - V -x[k+1] = x[k] - ------------ - 2 x[k] - -...where V is the value for which the square root is being sought. In -essence, what is happening here is that we guess a value for the -square root, then figure out how far off we were by squaring our guess -and subtracting the target. Using this value, we compute a linear -approximation for the error, and adjust the "guess". We keep doing -this until the precision gets low enough that the above equation -yields a quotient of zero. At this point, our last guess is one -greater than the square root we're seeking. - -The initial guess is computed by dividing V by 4, which is a heuristic -I have found to be fairly good on average. This also has the -advantage of being very easy to compute efficiently, even for large -values. - -So, the resulting algorithm works as follows: - - x = V / 4 /* compute initial guess */ - - loop - t = (x * x) - V /* Compute absolute error */ - u = 2 * x /* Adjust by tangent slope */ - t = t / u - - /* Loop is done if error is zero */ - if(t == 0) - break - - /* Adjust guess by error term */ - x = x - t - end - - x = x - 1 - -The result of the computation is the value of x. - ------------------------------------------------------------------- -***** 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 ***** - -$Id$ - - |