security/nss/lib/freebl/mpi/doc/div.txt@6474c204b198 (annotated)
security/nss/lib/freebl/mpi/doc/div.txt
Wed, 31 Dec 2014 06:09:35 +0100
- author
- Michael Schloh von Bennewitz <michael@schloh.com>
- date
- Wed, 31 Dec 2014 06:09:35 +0100
- changeset 0
- 6474c204b198
- permissions
- -rw-r--r--
Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.
| michael@0 | 1 | Division |
| michael@0 | 2 | |
| michael@0 | 3 | This describes the division algorithm used by the MPI library. |
| michael@0 | 4 | |
| michael@0 | 5 | Input: a, b; a > b |
| michael@0 | 6 | Compute: Q, R; a = Qb + R |
| michael@0 | 7 | |
| michael@0 | 8 | The input numbers are normalized so that the high-order digit of b is |
| michael@0 | 9 | at least half the radix. This guarantees that we have a reasonable |
| michael@0 | 10 | way to guess at the digits of the quotient (this method was taken from |
| michael@0 | 11 | Knuth, vol. 2, with adaptations). |
| michael@0 | 12 | |
| michael@0 | 13 | To normalize, test the high-order digit of b. If it is less than half |
| michael@0 | 14 | the radix, multiply both a and b by d, where: |
| michael@0 | 15 | |
| michael@0 | 16 | radix - 1 |
| michael@0 | 17 | d = ----------- |
| michael@0 | 18 | bmax + 1 |
| michael@0 | 19 | |
| michael@0 | 20 | ...where bmax is the high-order digit of b. Otherwise, set d = 1. |
| michael@0 | 21 | |
| michael@0 | 22 | Given normalize values for a and b, let the notation a[n] denote the |
| michael@0 | 23 | nth digit of a. Let #a be the number of significant figures of a (not |
| michael@0 | 24 | including any leading zeroes). |
| michael@0 | 25 | |
| michael@0 | 26 | Let R = 0 |
| michael@0 | 27 | Let p = #a - 1 |
| michael@0 | 28 | |
| michael@0 | 29 | while(p >= 0) |
| michael@0 | 30 | do |
| michael@0 | 31 | R = (R * radix) + a[p] |
| michael@0 | 32 | p = p - 1 |
| michael@0 | 33 | while(R < b and p >= 0) |
| michael@0 | 34 | |
| michael@0 | 35 | if(R < b) |
| michael@0 | 36 | break |
| michael@0 | 37 | |
| michael@0 | 38 | q = (R[#R - 1] * radix) + R[#R - 2] |
| michael@0 | 39 | q = q / b[#b - 1] |
| michael@0 | 40 | |
| michael@0 | 41 | T = b * q |
| michael@0 | 42 | |
| michael@0 | 43 | while(T > L) |
| michael@0 | 44 | q = q - 1 |
| michael@0 | 45 | T = T - b |
| michael@0 | 46 | endwhile |
| michael@0 | 47 | |
| michael@0 | 48 | L = L - T |
| michael@0 | 49 | |
| michael@0 | 50 | Q = (Q * radix) + q |
| michael@0 | 51 | |
| michael@0 | 52 | endwhile |
| michael@0 | 53 | |
| michael@0 | 54 | At this point, Q is the quotient, and R is the normalized remainder. |
| michael@0 | 55 | To denormalize R, compute: |
| michael@0 | 56 | |
| michael@0 | 57 | R = (R / d) |
| michael@0 | 58 | |
| michael@0 | 59 | At this point, you are finished. |
| michael@0 | 60 | |
| michael@0 | 61 | ------------------------------------------------------------------ |
| michael@0 | 62 | This Source Code Form is subject to the terms of the Mozilla Public |
| michael@0 | 63 | # License, v. 2.0. If a copy of the MPL was not distributed with this |
| michael@0 | 64 | # file, You can obtain one at http://mozilla.org/MPL/2.0/. |
