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102 lines
3.0 KiB
Plaintext
102 lines
3.0 KiB
Plaintext
Division
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This describes the division algorithm used by the MPI library.
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Input: a, b; a > b
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Compute: Q, R; a = Qb + R
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The input numbers are normalized so that the high-order digit of b is
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at least half the radix. This guarantees that we have a reasonable
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way to guess at the digits of the quotient (this method was taken from
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Knuth, vol. 2, with adaptations).
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To normalize, test the high-order digit of b. If it is less than half
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the radix, multiply both a and b by d, where:
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radix - 1
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d = -----------
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bmax + 1
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...where bmax is the high-order digit of b. Otherwise, set d = 1.
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Given normalize values for a and b, let the notation a[n] denote the
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nth digit of a. Let #a be the number of significant figures of a (not
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including any leading zeroes).
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Let R = 0
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Let p = #a - 1
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while(p >= 0)
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do
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R = (R * radix) + a[p]
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p = p - 1
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while(R < b and p >= 0)
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if(R < b)
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break
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q = (R[#R - 1] * radix) + R[#R - 2]
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q = q / b[#b - 1]
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T = b * q
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while(T > L)
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q = q - 1
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T = T - b
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endwhile
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L = L - T
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Q = (Q * radix) + q
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endwhile
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At this point, Q is the quotient, and R is the normalized remainder.
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To denormalize R, compute:
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R = (R / d)
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At this point, you are finished.
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------------------------------------------------------------------
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***** BEGIN LICENSE BLOCK *****
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Version: MPL 1.1/GPL 2.0/LGPL 2.1
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The contents of this file are subject to the Mozilla Public License Version
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1.1 (the "License"); you may not use this file except in compliance with
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the License. You may obtain a copy of the License at
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http://www.mozilla.org/MPL/
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Software distributed under the License is distributed on an "AS IS" basis,
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WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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for the specific language governing rights and limitations under the
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License.
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The Original Code is the MPI Arbitrary Precision Integer Arithmetic
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library.
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The Initial Developer of the Original Code is
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Michael J. Fromberger <sting@linguist.dartmouth.edu>
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Portions created by the Initial Developer are Copyright (C) 1998, 2000
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the Initial Developer. All Rights Reserved.
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Contributor(s):
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Alternatively, the contents of this file may be used under the terms of
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either the GNU General Public License Version 2 or later (the "GPL"), or
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the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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in which case the provisions of the GPL or the LGPL are applicable instead
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of those above. If you wish to allow use of your version of this file only
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under the terms of either the GPL or the LGPL, and not to allow others to
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use your version of this file under the terms of the MPL, indicate your
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decision by deleting the provisions above and replace them with the notice
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and other provisions required by the GPL or the LGPL. If you do not delete
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the provisions above, a recipient may use your version of this file under
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the terms of any one of the MPL, the GPL or the LGPL.
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***** END LICENSE BLOCK *****
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$Id: div.txt,v 1.2 2005/02/02 22:28:22 gerv%gerv.net Exp $
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