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-rw-r--r-- | security/nss/lib/freebl/mpi/doc/div.txt | 64 |
1 files changed, 64 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/doc/div.txt b/security/nss/lib/freebl/mpi/doc/div.txt new file mode 100644 index 0000000000..c13fb6ef18 --- /dev/null +++ b/security/nss/lib/freebl/mpi/doc/div.txt @@ -0,0 +1,64 @@ +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/. |