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304 lines
8.5 KiB
304 lines
8.5 KiB
/* |
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* qrencode - QR Code encoder |
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* |
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* Reed solomon encoder. This code is taken from Phil Karn's libfec then |
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* editted and packed into a pair of .c and .h files. |
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* |
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* Copyright (C) 2002, 2003, 2004, 2006 Phil Karn, KA9Q |
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* (libfec is released under the GNU Lesser General Public License.) |
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* |
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* Copyright (C) 2006, 2007, 2008, 2009 Kentaro Fukuchi <fukuchi@megaui.net> |
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* |
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* This library is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Lesser General Public |
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* License as published by the Free Software Foundation; either |
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* version 2.1 of the License, or any later version. |
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* |
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* This library is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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* Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public |
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* License along with this library; if not, write to the Free Software |
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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*/ |
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#include <stdlib.h> |
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#include <string.h> |
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#include "rscode.h" |
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/* Stuff specific to the 8-bit symbol version of the general purpose RS codecs |
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* |
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*/ |
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typedef unsigned char data_t; |
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/** |
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* Reed-Solomon codec control block |
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*/ |
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struct _RS { |
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int mm; /* Bits per symbol */ |
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int nn; /* Symbols per block (= (1<<mm)-1) */ |
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data_t *alpha_to; /* log lookup table */ |
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data_t *index_of; /* Antilog lookup table */ |
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data_t *genpoly; /* Generator polynomial */ |
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int nroots; /* Number of generator roots = number of parity symbols */ |
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int fcr; /* First consecutive root, index form */ |
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int prim; /* Primitive element, index form */ |
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int iprim; /* prim-th root of 1, index form */ |
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int pad; /* Padding bytes in shortened block */ |
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int gfpoly; |
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struct _RS *next; |
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}; |
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static RS *rslist = NULL; |
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static inline int modnn(RS *rs, int x){ |
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while (x >= rs->nn) { |
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x -= rs->nn; |
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x = (x >> rs->mm) + (x & rs->nn); |
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} |
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return x; |
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} |
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#define MODNN(x) modnn(rs,x) |
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#define MM (rs->mm) |
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#define NN (rs->nn) |
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#define ALPHA_TO (rs->alpha_to) |
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#define INDEX_OF (rs->index_of) |
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#define GENPOLY (rs->genpoly) |
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#define NROOTS (rs->nroots) |
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#define FCR (rs->fcr) |
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#define PRIM (rs->prim) |
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#define IPRIM (rs->iprim) |
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#define PAD (rs->pad) |
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#define A0 (NN) |
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/* Initialize a Reed-Solomon codec |
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* symsize = symbol size, bits |
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* gfpoly = Field generator polynomial coefficients |
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* fcr = first root of RS code generator polynomial, index form |
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* prim = primitive element to generate polynomial roots |
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* nroots = RS code generator polynomial degree (number of roots) |
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* pad = padding bytes at front of shortened block |
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*/ |
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static RS *init_rs_char(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad) |
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{ |
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RS *rs; |
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/* Common code for intializing a Reed-Solomon control block (char or int symbols) |
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* Copyright 2004 Phil Karn, KA9Q |
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* May be used under the terms of the GNU Lesser General Public License (LGPL) |
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*/ |
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//#undef NULL |
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//#define NULL ((void *)0) |
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int i, j, sr,root,iprim; |
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rs = NULL; |
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/* Check parameter ranges */ |
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if(symsize < 0 || symsize > (int)(8*sizeof(data_t))){ |
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goto done; |
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} |
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if(fcr < 0 || fcr >= (1<<symsize)) |
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goto done; |
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if(prim <= 0 || prim >= (1<<symsize)) |
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goto done; |
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if(nroots < 0 || nroots >= (1<<symsize)) |
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goto done; /* Can't have more roots than symbol values! */ |
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if(pad < 0 || pad >= ((1<<symsize) -1 - nroots)) |
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goto done; /* Too much padding */ |
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rs = (RS *)calloc(1,sizeof(RS)); |
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if(rs == NULL) |
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goto done; |
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rs->mm = symsize; |
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rs->nn = (1<<symsize)-1; |
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rs->pad = pad; |
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rs->alpha_to = (data_t *)malloc(sizeof(data_t)*(rs->nn+1)); |
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if(rs->alpha_to == NULL){ |
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free(rs); |
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rs = NULL; |
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goto done; |
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} |
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rs->index_of = (data_t *)malloc(sizeof(data_t)*(rs->nn+1)); |
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if(rs->index_of == NULL){ |
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free(rs->alpha_to); |
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free(rs); |
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rs = NULL; |
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goto done; |
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} |
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/* Generate Galois field lookup tables */ |
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rs->index_of[0] = A0; /* log(zero) = -inf */ |
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rs->alpha_to[A0] = 0; /* alpha**-inf = 0 */ |
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sr = 1; |
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for(i=0;i<rs->nn;i++){ |
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rs->index_of[sr] = i; |
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rs->alpha_to[i] = sr; |
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sr <<= 1; |
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if(sr & (1<<symsize)) |
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sr ^= gfpoly; |
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sr &= rs->nn; |
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} |
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if(sr != 1){ |
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/* field generator polynomial is not primitive! */ |
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free(rs->alpha_to); |
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free(rs->index_of); |
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free(rs); |
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rs = NULL; |
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goto done; |
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} |
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/* Form RS code generator polynomial from its roots */ |
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rs->genpoly = (data_t *)malloc(sizeof(data_t)*(nroots+1)); |
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if(rs->genpoly == NULL){ |
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free(rs->alpha_to); |
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free(rs->index_of); |
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free(rs); |
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rs = NULL; |
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goto done; |
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} |
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rs->fcr = fcr; |
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rs->prim = prim; |
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rs->nroots = nroots; |
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rs->gfpoly = gfpoly; |
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/* Find prim-th root of 1, used in decoding */ |
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for(iprim=1;(iprim % prim) != 0;iprim += rs->nn) |
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; |
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rs->iprim = iprim / prim; |
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rs->genpoly[0] = 1; |
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for (i = 0,root=fcr*prim; i < nroots; i++,root += prim) { |
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rs->genpoly[i+1] = 1; |
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/* Multiply rs->genpoly[] by @**(root + x) */ |
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for (j = i; j > 0; j--){ |
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if (rs->genpoly[j] != 0) |
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rs->genpoly[j] = rs->genpoly[j-1] ^ rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[j]] + root)]; |
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else |
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rs->genpoly[j] = rs->genpoly[j-1]; |
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} |
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/* rs->genpoly[0] can never be zero */ |
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rs->genpoly[0] = rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[0]] + root)]; |
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} |
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/* convert rs->genpoly[] to index form for quicker encoding */ |
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for (i = 0; i <= nroots; i++) |
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rs->genpoly[i] = rs->index_of[rs->genpoly[i]]; |
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done:; |
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return rs; |
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} |
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RS *init_rs(int symsize, int gfpoly, int fcr, int prim, int nroots, int pad) |
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{ |
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RS *rs; |
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for(rs = rslist; rs != NULL; rs = rs->next) { |
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if(rs->pad != pad) continue; |
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if(rs->nroots != nroots) continue; |
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if(rs->mm != symsize) continue; |
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if(rs->gfpoly != gfpoly) continue; |
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if(rs->fcr != fcr) continue; |
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if(rs->prim != prim) continue; |
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goto DONE; |
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} |
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rs = init_rs_char(symsize, gfpoly, fcr, prim, nroots, pad); |
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if(rs == NULL) goto DONE; |
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rs->next = rslist; |
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rslist = rs; |
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DONE: |
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return rs; |
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} |
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void free_rs_char(RS *rs) |
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{ |
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free(rs->alpha_to); |
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free(rs->index_of); |
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free(rs->genpoly); |
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free(rs); |
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} |
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void free_rs_cache(void) |
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{ |
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RS *rs, *next; |
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rs = rslist; |
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while(rs != NULL) { |
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next = rs->next; |
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free_rs_char(rs); |
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rs = next; |
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} |
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} |
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/* The guts of the Reed-Solomon encoder, meant to be #included |
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* into a function body with the following typedefs, macros and variables supplied |
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* according to the code parameters: |
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* data_t - a typedef for the data symbol |
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* data_t data[] - array of NN-NROOTS-PAD and type data_t to be encoded |
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* data_t parity[] - an array of NROOTS and type data_t to be written with parity symbols |
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* NROOTS - the number of roots in the RS code generator polynomial, |
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* which is the same as the number of parity symbols in a block. |
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Integer variable or literal. |
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* |
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* NN - the total number of symbols in a RS block. Integer variable or literal. |
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* PAD - the number of pad symbols in a block. Integer variable or literal. |
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* ALPHA_TO - The address of an array of NN elements to convert Galois field |
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* elements in index (log) form to polynomial form. Read only. |
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* INDEX_OF - The address of an array of NN elements to convert Galois field |
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* elements in polynomial form to index (log) form. Read only. |
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* MODNN - a function to reduce its argument modulo NN. May be inline or a macro. |
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* GENPOLY - an array of NROOTS+1 elements containing the generator polynomial in index form |
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* The memset() and memmove() functions are used. The appropriate header |
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* file declaring these functions (usually <string.h>) must be included by the calling |
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* program. |
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* Copyright 2004, Phil Karn, KA9Q |
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* May be used under the terms of the GNU Lesser General Public License (LGPL) |
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*/ |
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#undef A0 |
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#define A0 (NN) /* Special reserved value encoding zero in index form */ |
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void encode_rs_char(RS *rs, const data_t *data, data_t *parity) |
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{ |
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int i, j; |
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data_t feedback; |
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memset(parity,0,NROOTS*sizeof(data_t)); |
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for(i=0;i<NN-NROOTS-PAD;i++){ |
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feedback = INDEX_OF[data[i] ^ parity[0]]; |
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if(feedback != A0){ /* feedback term is non-zero */ |
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#ifdef UNNORMALIZED |
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/* This line is unnecessary when GENPOLY[NROOTS] is unity, as it must |
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* always be for the polynomials constructed by init_rs() |
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*/ |
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feedback = MODNN(NN - GENPOLY[NROOTS] + feedback); |
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#endif |
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for(j=1;j<NROOTS;j++) |
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parity[j] ^= ALPHA_TO[MODNN(feedback + GENPOLY[NROOTS-j])]; |
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} |
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/* Shift */ |
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memmove(&parity[0],&parity[1],sizeof(data_t)*(NROOTS-1)); |
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if(feedback != A0) |
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parity[NROOTS-1] = ALPHA_TO[MODNN(feedback + GENPOLY[0])]; |
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else |
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parity[NROOTS-1] = 0; |
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} |
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}
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