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authorMatt A. Tobin <mattatobin@localhost.localdomain>2018-02-02 04:16:08 -0500
committerMatt A. Tobin <mattatobin@localhost.localdomain>2018-02-02 04:16:08 -0500
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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.
+
+------------------------------------------------------------------
+ This Source Code Form is subject to the terms of the Mozilla Public
+ # License, v. 2.0. If a copy of the MPL was not distributed with this
+ # file, You can obtain one at http://mozilla.org/MPL/2.0/.