1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/security/nss/lib/freebl/mpi/doc/div.txt Wed Dec 31 06:09:35 2014 +0100
1.3 @@ -0,0 +1,64 @@
1.4 +Division
1.5 +
1.6 +This describes the division algorithm used by the MPI library.
1.7 +
1.8 +Input: a, b; a > b
1.9 +Compute: Q, R; a = Qb + R
1.10 +
1.11 +The input numbers are normalized so that the high-order digit of b is
1.12 +at least half the radix. This guarantees that we have a reasonable
1.13 +way to guess at the digits of the quotient (this method was taken from
1.14 +Knuth, vol. 2, with adaptations).
1.15 +
1.16 +To normalize, test the high-order digit of b. If it is less than half
1.17 +the radix, multiply both a and b by d, where:
1.18 +
1.19 + radix - 1
1.20 + d = -----------
1.21 + bmax + 1
1.22 +
1.23 +...where bmax is the high-order digit of b. Otherwise, set d = 1.
1.24 +
1.25 +Given normalize values for a and b, let the notation a[n] denote the
1.26 +nth digit of a. Let #a be the number of significant figures of a (not
1.27 +including any leading zeroes).
1.28 +
1.29 + Let R = 0
1.30 + Let p = #a - 1
1.31 +
1.32 + while(p >= 0)
1.33 + do
1.34 + R = (R * radix) + a[p]
1.35 + p = p - 1
1.36 + while(R < b and p >= 0)
1.37 +
1.38 + if(R < b)
1.39 + break
1.40 +
1.41 + q = (R[#R - 1] * radix) + R[#R - 2]
1.42 + q = q / b[#b - 1]
1.43 +
1.44 + T = b * q
1.45 +
1.46 + while(T > L)
1.47 + q = q - 1
1.48 + T = T - b
1.49 + endwhile
1.50 +
1.51 + L = L - T
1.52 +
1.53 + Q = (Q * radix) + q
1.54 +
1.55 + endwhile
1.56 +
1.57 +At this point, Q is the quotient, and R is the normalized remainder.
1.58 +To denormalize R, compute:
1.59 +
1.60 + R = (R / d)
1.61 +
1.62 +At this point, you are finished.
1.63 +
1.64 +------------------------------------------------------------------
1.65 + This Source Code Form is subject to the terms of the Mozilla Public
1.66 + # License, v. 2.0. If a copy of the MPL was not distributed with this
1.67 + # file, You can obtain one at http://mozilla.org/MPL/2.0/.
