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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.
-
-$Id$
-
-