1/*
2 * lib/reed_solomon/reed_solomon.c
3 *
4 * Overview:
5 *   Generic Reed Solomon encoder / decoder library
6 *
7 * Copyright (C) 2004 Thomas Gleixner (tglx@linutronix.de)
8 *
9 * Reed Solomon code lifted from reed solomon library written by Phil Karn
10 * Copyright 2002 Phil Karn, KA9Q
11 *
12 * $Id: rslib.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $
13 *
14 * This program is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU General Public License version 2 as
16 * published by the Free Software Foundation.
17 *
18 * Description:
19 *
20 * The generic Reed Solomon library provides runtime configurable
21 * encoding / decoding of RS codes.
22 * Each user must call init_rs to get a pointer to a rs_control
23 * structure for the given rs parameters. This structure is either
24 * generated or a already available matching control structure is used.
25 * If a structure is generated then the polynomial arrays for
26 * fast encoding / decoding are built. This can take some time so
27 * make sure not to call this function from a time critical path.
28 * Usually a module / driver should initialize the necessary
29 * rs_control structure on module / driver init and release it
30 * on exit.
31 * The encoding puts the calculated syndrome into a given syndrome
32 * buffer.
33 * The decoding is a two step process. The first step calculates
34 * the syndrome over the received (data + syndrome) and calls the
35 * second stage, which does the decoding / error correction itself.
36 * Many hw encoders provide a syndrome calculation over the received
37 * data + syndrome and can call the second stage directly.
38 *
39 */
40
41#include <linux/errno.h>
42#include <linux/kernel.h>
43#include <linux/init.h>
44#include <linux/module.h>
45#include <linux/rslib.h>
46#include <linux/slab.h>
47#include <linux/mutex.h>
48
49/* This list holds all currently allocated rs control structures */
50static LIST_HEAD (rslist);
51/* Protection for the list */
52static DEFINE_MUTEX(rslistlock);
53
54/**
55 * rs_init - Initialize a Reed-Solomon codec
56 * @symsize:	symbol size, bits (1-8)
57 * @gfpoly:	Field generator polynomial coefficients
58 * @gffunc:	Field generator function
59 * @fcr:	first root of RS code generator polynomial, index form
60 * @prim:	primitive element to generate polynomial roots
61 * @nroots:	RS code generator polynomial degree (number of roots)
62 *
63 * Allocate a control structure and the polynom arrays for faster
64 * en/decoding. Fill the arrays according to the given parameters.
65 */
66static struct rs_control *rs_init(int symsize, int gfpoly, int (*gffunc)(int),
67                                  int fcr, int prim, int nroots)
68{
69	struct rs_control *rs;
70	int i, j, sr, root, iprim;
71
72	/* Allocate the control structure */
73	rs = kmalloc(sizeof (struct rs_control), GFP_KERNEL);
74	if (rs == NULL)
75		return NULL;
76
77	INIT_LIST_HEAD(&rs->list);
78
79	rs->mm = symsize;
80	rs->nn = (1 << symsize) - 1;
81	rs->fcr = fcr;
82	rs->prim = prim;
83	rs->nroots = nroots;
84	rs->gfpoly = gfpoly;
85	rs->gffunc = gffunc;
86
87	/* Allocate the arrays */
88	rs->alpha_to = kmalloc(sizeof(uint16_t) * (rs->nn + 1), GFP_KERNEL);
89	if (rs->alpha_to == NULL)
90		goto errrs;
91
92	rs->index_of = kmalloc(sizeof(uint16_t) * (rs->nn + 1), GFP_KERNEL);
93	if (rs->index_of == NULL)
94		goto erralp;
95
96	rs->genpoly = kmalloc(sizeof(uint16_t) * (rs->nroots + 1), GFP_KERNEL);
97	if(rs->genpoly == NULL)
98		goto erridx;
99
100	/* Generate Galois field lookup tables */
101	rs->index_of[0] = rs->nn;	/* log(zero) = -inf */
102	rs->alpha_to[rs->nn] = 0;	/* alpha**-inf = 0 */
103	if (gfpoly) {
104		sr = 1;
105		for (i = 0; i < rs->nn; i++) {
106			rs->index_of[sr] = i;
107			rs->alpha_to[i] = sr;
108			sr <<= 1;
109			if (sr & (1 << symsize))
110				sr ^= gfpoly;
111			sr &= rs->nn;
112		}
113	} else {
114		sr = gffunc(0);
115		for (i = 0; i < rs->nn; i++) {
116			rs->index_of[sr] = i;
117			rs->alpha_to[i] = sr;
118			sr = gffunc(sr);
119		}
120	}
121	/* If it's not primitive, exit */
122	if(sr != rs->alpha_to[0])
123		goto errpol;
124
125	/* Find prim-th root of 1, used in decoding */
126	for(iprim = 1; (iprim % prim) != 0; iprim += rs->nn);
127	/* prim-th root of 1, index form */
128	rs->iprim = iprim / prim;
129
130	/* Form RS code generator polynomial from its roots */
131	rs->genpoly[0] = 1;
132	for (i = 0, root = fcr * prim; i < nroots; i++, root += prim) {
133		rs->genpoly[i + 1] = 1;
134		/* Multiply rs->genpoly[] by  @**(root + x) */
135		for (j = i; j > 0; j--) {
136			if (rs->genpoly[j] != 0) {
137				rs->genpoly[j] = rs->genpoly[j -1] ^
138					rs->alpha_to[rs_modnn(rs,
139					rs->index_of[rs->genpoly[j]] + root)];
140			} else
141				rs->genpoly[j] = rs->genpoly[j - 1];
142		}
143		/* rs->genpoly[0] can never be zero */
144		rs->genpoly[0] =
145			rs->alpha_to[rs_modnn(rs,
146				rs->index_of[rs->genpoly[0]] + root)];
147	}
148	/* convert rs->genpoly[] to index form for quicker encoding */
149	for (i = 0; i <= nroots; i++)
150		rs->genpoly[i] = rs->index_of[rs->genpoly[i]];
151	return rs;
152
153	/* Error exit */
154errpol:
155	kfree(rs->genpoly);
156erridx:
157	kfree(rs->index_of);
158erralp:
159	kfree(rs->alpha_to);
160errrs:
161	kfree(rs);
162	return NULL;
163}
164
165
166/**
167 *  free_rs - Free the rs control structure, if it is no longer used
168 *  @rs:	the control structure which is not longer used by the
169 *		caller
170 */
171void free_rs(struct rs_control *rs)
172{
173	mutex_lock(&rslistlock);
174	rs->users--;
175	if(!rs->users) {
176		list_del(&rs->list);
177		kfree(rs->alpha_to);
178		kfree(rs->index_of);
179		kfree(rs->genpoly);
180		kfree(rs);
181	}
182	mutex_unlock(&rslistlock);
183}
184
185/**
186 * init_rs_internal - Find a matching or allocate a new rs control structure
187 *  @symsize:	the symbol size (number of bits)
188 *  @gfpoly:	the extended Galois field generator polynomial coefficients,
189 *		with the 0th coefficient in the low order bit. The polynomial
190 *		must be primitive;
191 *  @gffunc:	pointer to function to generate the next field element,
192 *		or the multiplicative identity element if given 0.  Used
193 *		instead of gfpoly if gfpoly is 0
194 *  @fcr:  	the first consecutive root of the rs code generator polynomial
195 *		in index form
196 *  @prim:	primitive element to generate polynomial roots
197 *  @nroots:	RS code generator polynomial degree (number of roots)
198 */
199static struct rs_control *init_rs_internal(int symsize, int gfpoly,
200                                           int (*gffunc)(int), int fcr,
201                                           int prim, int nroots)
202{
203	struct list_head	*tmp;
204	struct rs_control	*rs;
205
206	/* Sanity checks */
207	if (symsize < 1)
208		return NULL;
209	if (fcr < 0 || fcr >= (1<<symsize))
210    		return NULL;
211	if (prim <= 0 || prim >= (1<<symsize))
212    		return NULL;
213	if (nroots < 0 || nroots >= (1<<symsize))
214		return NULL;
215
216	mutex_lock(&rslistlock);
217
218	/* Walk through the list and look for a matching entry */
219	list_for_each(tmp, &rslist) {
220		rs = list_entry(tmp, struct rs_control, list);
221		if (symsize != rs->mm)
222			continue;
223		if (gfpoly != rs->gfpoly)
224			continue;
225		if (gffunc != rs->gffunc)
226			continue;
227		if (fcr != rs->fcr)
228			continue;
229		if (prim != rs->prim)
230			continue;
231		if (nroots != rs->nroots)
232			continue;
233		/* We have a matching one already */
234		rs->users++;
235		goto out;
236	}
237
238	/* Create a new one */
239	rs = rs_init(symsize, gfpoly, gffunc, fcr, prim, nroots);
240	if (rs) {
241		rs->users = 1;
242		list_add(&rs->list, &rslist);
243	}
244out:
245	mutex_unlock(&rslistlock);
246	return rs;
247}
248
249/**
250 * init_rs - Find a matching or allocate a new rs control structure
251 *  @symsize:	the symbol size (number of bits)
252 *  @gfpoly:	the extended Galois field generator polynomial coefficients,
253 *		with the 0th coefficient in the low order bit. The polynomial
254 *		must be primitive;
255 *  @fcr:  	the first consecutive root of the rs code generator polynomial
256 *		in index form
257 *  @prim:	primitive element to generate polynomial roots
258 *  @nroots:	RS code generator polynomial degree (number of roots)
259 */
260struct rs_control *init_rs(int symsize, int gfpoly, int fcr, int prim,
261                           int nroots)
262{
263	return init_rs_internal(symsize, gfpoly, NULL, fcr, prim, nroots);
264}
265
266/**
267 * init_rs_non_canonical - Find a matching or allocate a new rs control
268 *                         structure, for fields with non-canonical
269 *                         representation
270 *  @symsize:	the symbol size (number of bits)
271 *  @gffunc:	pointer to function to generate the next field element,
272 *		or the multiplicative identity element if given 0.  Used
273 *		instead of gfpoly if gfpoly is 0
274 *  @fcr:  	the first consecutive root of the rs code generator polynomial
275 *		in index form
276 *  @prim:	primitive element to generate polynomial roots
277 *  @nroots:	RS code generator polynomial degree (number of roots)
278 */
279struct rs_control *init_rs_non_canonical(int symsize, int (*gffunc)(int),
280                                         int fcr, int prim, int nroots)
281{
282	return init_rs_internal(symsize, 0, gffunc, fcr, prim, nroots);
283}
284
285#ifdef CONFIG_REED_SOLOMON_ENC8
286/**
287 *  encode_rs8 - Calculate the parity for data values (8bit data width)
288 *  @rs:	the rs control structure
289 *  @data:	data field of a given type
290 *  @len:	data length
291 *  @par:	parity data, must be initialized by caller (usually all 0)
292 *  @invmsk:	invert data mask (will be xored on data)
293 *
294 *  The parity uses a uint16_t data type to enable
295 *  symbol size > 8. The calling code must take care of encoding of the
296 *  syndrome result for storage itself.
297 */
298int encode_rs8(struct rs_control *rs, uint8_t *data, int len, uint16_t *par,
299	       uint16_t invmsk)
300{
301#include "encode_rs.c"
302}
303EXPORT_SYMBOL_GPL(encode_rs8);
304#endif
305
306#ifdef CONFIG_REED_SOLOMON_DEC8
307/**
308 *  decode_rs8 - Decode codeword (8bit data width)
309 *  @rs:	the rs control structure
310 *  @data:	data field of a given type
311 *  @par:	received parity data field
312 *  @len:	data length
313 *  @s:		syndrome data field (if NULL, syndrome is calculated)
314 *  @no_eras:	number of erasures
315 *  @eras_pos:	position of erasures, can be NULL
316 *  @invmsk:	invert data mask (will be xored on data, not on parity!)
317 *  @corr:	buffer to store correction bitmask on eras_pos
318 *
319 *  The syndrome and parity uses a uint16_t data type to enable
320 *  symbol size > 8. The calling code must take care of decoding of the
321 *  syndrome result and the received parity before calling this code.
322 *  Returns the number of corrected bits or -EBADMSG for uncorrectable errors.
323 */
324int decode_rs8(struct rs_control *rs, uint8_t *data, uint16_t *par, int len,
325	       uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
326	       uint16_t *corr)
327{
328#include "decode_rs.c"
329}
330EXPORT_SYMBOL_GPL(decode_rs8);
331#endif
332
333#ifdef CONFIG_REED_SOLOMON_ENC16
334/**
335 *  encode_rs16 - Calculate the parity for data values (16bit data width)
336 *  @rs:	the rs control structure
337 *  @data:	data field of a given type
338 *  @len:	data length
339 *  @par:	parity data, must be initialized by caller (usually all 0)
340 *  @invmsk:	invert data mask (will be xored on data, not on parity!)
341 *
342 *  Each field in the data array contains up to symbol size bits of valid data.
343 */
344int encode_rs16(struct rs_control *rs, uint16_t *data, int len, uint16_t *par,
345	uint16_t invmsk)
346{
347#include "encode_rs.c"
348}
349EXPORT_SYMBOL_GPL(encode_rs16);
350#endif
351
352#ifdef CONFIG_REED_SOLOMON_DEC16
353/**
354 *  decode_rs16 - Decode codeword (16bit data width)
355 *  @rs:	the rs control structure
356 *  @data:	data field of a given type
357 *  @par:	received parity data field
358 *  @len:	data length
359 *  @s:		syndrome data field (if NULL, syndrome is calculated)
360 *  @no_eras:	number of erasures
361 *  @eras_pos:	position of erasures, can be NULL
362 *  @invmsk:	invert data mask (will be xored on data, not on parity!)
363 *  @corr:	buffer to store correction bitmask on eras_pos
364 *
365 *  Each field in the data array contains up to symbol size bits of valid data.
366 *  Returns the number of corrected bits or -EBADMSG for uncorrectable errors.
367 */
368int decode_rs16(struct rs_control *rs, uint16_t *data, uint16_t *par, int len,
369		uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
370		uint16_t *corr)
371{
372#include "decode_rs.c"
373}
374EXPORT_SYMBOL_GPL(decode_rs16);
375#endif
376
377EXPORT_SYMBOL_GPL(init_rs);
378EXPORT_SYMBOL_GPL(init_rs_non_canonical);
379EXPORT_SYMBOL_GPL(free_rs);
380
381MODULE_LICENSE("GPL");
382MODULE_DESCRIPTION("Reed Solomon encoder/decoder");
383MODULE_AUTHOR("Phil Karn, Thomas Gleixner");
384
385