(******************************************************************* This file was generated automatically by the Mathematica front end. It contains Initialization cells from a Notebook file, which typically will have the same name as this file except ending in ".nb" instead of ".m". This file is intended to be loaded into the Mathematica kernel using the package loading commands Get or Needs. Doing so is equivalent to using the Evaluate Initialization Cells menu command in the front end. DO NOT EDIT THIS FILE. This entire file is regenerated automatically each time the parent Notebook file is saved in the Mathematica front end. Any changes you make to this file will be overwritten. ***********************************************************************) (* LFSR-- A Mathematica package for symbolic representation and computation of Linear Feedback Shift Registers. http://modp.com/release/mma_lfsr/ Version 2.0.0, 23-Aug-2005 Nick Galbreath, nickg [at] modp [dot] com Copyright (c) 2005 Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. *) BeginPackage["modp`lfsr`"]; LFSR::usage = \ "LFSR[complexity, polynomial] represents an abstract, stateless, linear feedback shift register. For example LFSR[4, 1 + t + t^2]. See LFSRGenerate for more details.";\ LFSRGenerate::ussage = \ "LFSRGenerate[LFSR, numbits, initialstate_List] generates a sequence of bits using the inital state. LFSRGenerate[LFSR, numbits, initstate_Symbol] does the same thing except the variable initialstate is update";\ LinearComplexity::usage = \ "Returns the linear complexity of a binary sequence. This uses a different implementation than LinearComplexityProfile and is 10x faster";\ LinearComplexityProfile::usage = \ "LinearComplexityProfile[bits_Lists] determines the minimal LFSR that could generate the input sequence. Also compute the 'linear complexity profile'";\ Begin["`Private`"]; (* Generate bits and save state *) LFSRGenerate[LFSR[l_Integer, cd_], n_Integer, state_Symbol] := Module[{coef, output, newbit}, coef = PadRight[Drop[CoefficientList[cd, Variables[cd][[1]]],1], l]; Table[ output = state[[1]]; newbit = Mod[Dot[coef, Reverse[state]],2]; Unevaluated[state] = Append[Rest[state], newbit]; output, {n}] ] (* Generate bits, use given state, but dont save it *) LFSRGenerate[LFSR[l_Integer, cd_], n_Integer, stateOrig_List] := Module[{coef, output, newbit, state= stateOrig}, coef = PadRight[Drop[CoefficientList[cd, Variables[cd][[1]]],1], l]; Table[ output = state[[1]]; newbit = Mod[Dot[coef, Reverse[state]],2]; state = Append[Rest[state], newbit]; output, {n}] ] SetAttributes[LFSRGenerate, HoldRest] (* c-style implementation. compiling gives a 10x boost! *) LinearComplexity = Compile[{{u, _Integer, 1}}, Module[{len = Length[u], b,c,d,p,tmp, l=0, m=0, }, c=ReplacePart[Table[0, {len}], 1,1]; b=ReplacePart[Table[0, {len}], 1,1]; Do[ d= Mod[u[[n]] + Dot[ Take[c, {2, l+1}],Reverse[Take[u,{n-l , n-1 }]]], 2]; If[d\[Equal]1, tmp = c; p = Table[0, {len}]; Do[ If[b[[i]] \[Equal]1,p[[i+n-m]] = 1], {i,1, l+1}]; c = Mod[c+p, 2]; If[2*l \[LessEqual] n, l = n -l; m = n; b = tmp; ]; ], {n, 1, len}]; l ] ]; (* very symbolic implementation *) LinearComplexityProfile[u_List, t_Symbol] := Module[{ phi = 1, psi = 1 , (* last feedback polynomial *) eta = 0, (* new feedback polynomial *) l = 0, (* linear complexity up to actual index *) r = -1, \ (* last index *) d = 0, (* discrepancy between predicted and actual *) b, feedbacklist, lcp (* auxiliary variables *) }, lcp = Table[ b = Reverse[Take[u,{n-l+1,n}]]; feedbacklist = PadRight[Drop[CoefficientList[phi, t],1], l]; d = Mod[u[[n+1]] + feedbacklist . b, 2]; If[d\[Equal] 1, eta = PolynomialMod[phi + ( t^(n-r ) )psi, 2]; If[2l \[LessEqual] n, l = n +1-l; psi = phi; r = n ]; phi = eta ]; l, {n, 0,Length[u]-1}]; {LFSR[l,phi], lcp} ]; (* Slight conflict. Mathematica uses array who's first index is 1, while in we need to do deal polynomials whose first index is 0. This is the \ Berklekamp-Massey algorithm, but iterates starting from 1. (same algorithm, different implementations) *) bma2[u_List] := Module[{ phi = 1, psi = 1 , (* last feedback polynomial *) eta = 0, (* new feedback polynomial *) l = 0, (* linear complexity up to actual index *) r = 0, \ (* last index *) d = 0, (* discrepancy between predicted bit and *) \ (* true bit -- always 0 or 1 in F_2 *) b, feedbacklist (* auxiliary variables *) }, linprof = Table[ b = Reverse[Take[u,{n-l,n-1}]]; feedbacklist = PadRight[Drop[CoefficientList[phi, T],1], l]; d = Mod[u[[n]] + feedbacklist . b, 2]; If[d\[Equal] 1, eta = PolynomialMod[phi + ( T^(n-r ) )psi, 2]; If[2*l < n, l = n -l; psi = phi; r = n ]; phi = eta ]; l, {n, 1,Length[u]}]; {LFSR[l, phi], linprof} ] End[]; EndPackage[];