div.txt
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- Division
- This describes the division algorithm used by the MPI library.
- Input: a, b; a > b
- Compute: Q, R; a = Qb + R
- The input numbers are normalized so that the high-order digit of b is
- at least half the radix. This guarantees that we have a reasonable
- way to guess at the digits of the quotient (this method was taken from
- Knuth, vol. 2, with adaptations).
- To normalize, test the high-order digit of b. If it is less than half
- the radix, multiply both a and b by d, where:
- radix - 1
- d = -----------
- bmax + 1
- ...where bmax is the high-order digit of b. Otherwise, set d = 1.
- Given normalize values for a and b, let the notation a[n] denote the
- nth digit of a. Let #a be the number of significant figures of a (not
- including any leading zeroes).
- Let R = 0
- Let p = #a - 1
- while(p >= 0)
- do
- R = (R * radix) + a[p]
- p = p - 1
- while(R < b and p >= 0)
- if(R < b)
- break
- q = (R[#R - 1] * radix) + R[#R - 2]
- q = q / b[#b - 1]
- T = b * q
- while(T > L)
- q = q - 1
- T = T - b
- endwhile
- L = L - T
- Q = (Q * radix) + q
- endwhile
- At this point, Q is the quotient, and R is the normalized remainder.
- To denormalize R, compute:
- R = (R / d)
- At this point, you are finished.
- ------------------------------------------------------------------
- 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 Michael J. Fromberger are
- Copyright (C) 1998, 2000 Michael J. Fromberger. All Rights Reserved.
- Contributor(s):
- Alternatively, the contents of this file may be used under the
- terms of the GNU General Public License Version 2 or later (the
- "GPL"), in which case the provisions of the GPL are applicable
- instead of those above. If you wish to allow use of your
- version of this file only under the terms of the GPL and not to
- allow others to use your version of this file under the MPL,
- indicate your decision by deleting the provisions above and
- replace them with the notice and other provisions required by
- the GPL. If you do not delete the provisions above, a recipient
- may use your version of this file under either the MPL or the GPL.
- $Id: div.txt,v 1.1 2000/07/14 00:44:32 nelsonb%netscape.com Exp $