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Commit 15b54237 authored by Thomas Gleixner's avatar Thomas Gleixner Committed by David Woodhouse
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Shared Reed-Solomon ECC library 

The attached patch contains a shared Reed-Solomon Library analogous to
the shared zlib.

(N)AND FLASH is gaining popularity and there are a lot of ASIC/SoC/FPGA
controllers around which implement hardware support for Reed-Solomon
error correction. As usual they use different implementations
(polynomials etc.). So it's obvious to use a shared library for the
common tasks of error correction.

A short scan through the kernel revealed that at least the ftape driver
uses Reed-Solomon error correction. It could be easily converted to use
the shared library code. 

The encoder/decoder code is lifted from the GPL'd userspace RS-library
written by Phil Karn. I modified/wrapped it to provide the different
functions which we need in the MTD/NAND code.

The library is tested in extenso under various MTD/NAND configurations.

The lib should be usable for other purposes right out of the box.
Adjustment for currently not implemented functionality is an easy task.

I'm willing to take the maintainership of the library.
Signed-Off-By: default avatarThomas Gleixner <tglx@linutronix.de>
Signed-Off-By: default avatarDavid Woodhouse <dwmw2@infradead.org>
"No objections at all. Just keep the authorship notices." -- Phil Karn
parent a8ff8803
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Documentation/DocBook/Makefile
View file @ 15b54237
......@@ -11,7 +11,7 @@ DOCBOOKS := wanbook.sgml z8530book.sgml mcabook.sgml videobook.sgml \
mousedrivers.sgml deviceiobook.sgml procfs-guide.sgml \
tulip-user.sgml writing_usb_driver.sgml scsidrivers.sgml \
sis900.sgml kernel-api.sgml journal-api.sgml lsm.sgml usb.sgml \
gadget.sgml libata.sgml
gadget.sgml libata.sgml librs.sgml
###
# The build process is as follows (targets):
......
Documentation/DocBook/librs.tmpl 0 → 100644
View file @ 15b54237
<!DOCTYPE book PUBLIC "-//OASIS//DTD DocBook V3.1//EN"[]>
<book id="Reed-Solomon-Library-Guide">
<bookinfo>
<title>Reed-Solomon Library Programming Interface</title>
<authorgroup>
<author>
<firstname>Thomas</firstname>
<surname>Gleixner</surname>
<affiliation>
<address>
<email>tglx@linutronix.de</email>
</address>
</affiliation>
</author>
</authorgroup>
<copyright>
<year>2004</year>
<holder>Thomas Gleixner</holder>
</copyright>
<legalnotice>
<para>
This documentation is free software; you can redistribute
it and/or modify it under the terms of the GNU General Public
License version 2 as published by the Free Software Foundation.
</para>
<para>
This program is distributed in the hope that it will be
useful, but WITHOUT ANY WARRANTY; without even the implied
warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU General Public License for more details.
</para>
<para>
You should have received a copy of the GNU General Public
License along with this program; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston,
MA 02111-1307 USA
</para>
<para>
For more details see the file COPYING in the source
distribution of Linux.
</para>
</legalnotice>
</bookinfo>
<toc></toc>
<chapter id="intro">
<title>Introduction</title>
<para>
The generic Reed-Solomon Library provides encoding, decoding
and error correction functions.
</para>
<para>
Reed-Solomon codes are used in communication and storage
applications to ensure data integrity.
</para>
<para>
This documentation is provided for developers who want to utilize
the functions provided by the library.
</para>
</chapter>
<chapter id="bugs">
<title>Known Bugs And Assumptions</title>
<para>
None.
</para>
</chapter>
<chapter id="usage">
<title>Usage</title>
<para>
This chapter provides examples how to use the library.
</para>
<sect1>
<title>Initializing</title>
<para>
The init function init_rs returns a pointer to a
rs decoder structure, which holds the neccecary
information for encoding, decoding and error correction
with the given polynomial. It either uses an existing
matching decoder or creates a new one. On creation all
the lookup tables for fast en/decoding are created.
The function may take a while, so make sure not to
call it in critical code pathes.
</para>
<programlisting>
/* the Reed Solomon control structure */
static struct rs_control *rs_decoder;
/* Symbolsize is 10 (bits)
* Primitve polynomial is x^10+x^3+1
* first consecutive root is 0
* primitve element to generate roots = 1
* generator polinomial degree (number of roots) = 6
*/
rs_decoder = init_rs (10, 0x409, 0, 1, 6);
</programlisting>
</sect1>
<sect1>
<title>Encoding</title>
<para>
The encoder calculates the Reed-Solomon code over
the given data length and stores the result in
the parity buffer. Note that the parity buffer must
be initialized before calling the encoder.
</para>
<para>
The expanded data can be inverted on the fly by
providing a non zero inversion mask. The expanded data is
XOR'ed with the mask. This is used e.g. for FLASH
ECC, where the all 0xFF is inverted to an all 0x00.
The Reed-Solomon code for all 0x00 is all 0x00. The
code is inverted before storing to FLASH so it is 0xFF
too. This prevent's that reading from an erased FLASH
results in ECC errors.
</para>
<para>
The databytes are expanded to the given symbolsize
on the fly. There is no support for encoding continuos
bitstreams with a symbolsize != 8 at the moment. If
it is neccecary it should be not a big deal to implement
such functionality.
</para>
<programlisting>
/* Parity buffer. Size = number of roots */
uint16_t par[6];
/* Initialize the parity buffer */
memset(par, 0, sizeof(par));
/* Encode 512 byte in data8. Store parity in buffer par */
encode_rs8 (rs_decoder, data8, 512, par, 0);
</programlisting>
</sect1>
<sect1>
<title>Decoding</title>
<para>
The decoder calculates the syndrome over
the given data length and the received parity symbols
and corrects errors in the data.
</para>
<para>
If a syndrome is available from a hardware decoder
then the syndrome calculation is skipped.
</para>
<para>
The correction of the data buffer can be suppressed
by providing a correction pattern buffer and an error
location buffer to the decoder. The decoder stores the
calculated error location and the correction bitmask
in the given buffers. This is useful for hardware
decoders which use a weird bitordering scheme.
</para>
<para>
The databytes are expanded to the given symbolsize
on the fly. There is no support for decoding continuos
bitstreams with a symbolsize != 8 at the moment. If
it is neccecary it should be not a big deal to implement
such functionality.
</para>
<sect2>
<title>
Decoding with syndrome calculation, direct data correction
</title>
<programlisting>
/* Parity buffer. Size = number of roots */
uint16_t par[6];
uint8_t data[512];
int numerr;
/* Receive data */
.....
/* Receive parity */
.....
/* Decode 512 byte in data8.*/
numerr = decode_rs8 (rs_decoder, data8, par, 512, NULL, 0, NULL, 0, NULL);
</programlisting>
</sect2>
<sect2>
<title>
Decoding with syndrome given by hardware decoder, direct data correction
</title>
<programlisting>
/* Parity buffer. Size = number of roots */
uint16_t par[6], syn[6];
uint8_t data[512];
int numerr;
/* Receive data */
.....
/* Receive parity */
.....
/* Get syndrome from hardware decoder */
.....
/* Decode 512 byte in data8.*/
numerr = decode_rs8 (rs_decoder, data8, par, 512, syn, 0, NULL, 0, NULL);
</programlisting>
</sect2>
<sect2>
<title>
Decoding with syndrome given by hardware decoder, no direct data correction.
</title>
<para>
Note: It's not neccecary to give data and recieved parity to the decoder.
</para>
<programlisting>
/* Parity buffer. Size = number of roots */
uint16_t par[6], syn[6], corr[8];
uint8_t data[512];
int numerr, errpos[8];
/* Receive data */
.....
/* Receive parity */
.....
/* Get syndrome from hardware decoder */
.....
/* Decode 512 byte in data8.*/
numerr = decode_rs8 (rs_decoder, NULL, NULL, 512, syn, 0, errpos, 0, corr);
for (i = 0; i < numerr; i++) {
do_error_correction_in_your_buffer(errpos[i], corr[i]);
}
</programlisting>
</sect2>
</sect1>
<sect1>
<title>Cleanup</title>
<para>
The function free_rs frees the allocated resources,
if the caller is the last user of the decoder.
</para>
<programlisting>
/* Release resources */
free_rs(rs_decoder);
</programlisting>
</sect1>
</chapter>
<chapter id="structs">
<title>Structures</title>
<para>
This chapter contains the autogenerated documentation of the structures which are
used in the Reed-Solomon Library and are relevant for a developer.
</para>
!Iinclude/linux/rslib.h
</chapter>
<chapter id="pubfunctions">
<title>Public Functions Provided</title>
<para>
This chapter contains the autogenerated documentation of the Reed-Solomon functions
which are exported.
</para>
!Elib/reed_solomon/reed_solomon.c
</chapter>
<chapter id="credits">
<title>Credits</title>
<para>
The library code for encoding and decoding was written by Phil Karn.
</para>
<programlisting>
Copyright 2002, Phil Karn, KA9Q
May be used under the terms of the GNU General Public License (GPL)
</programlisting>
<para>
The wrapper functions and interfaces are written by Thomas Gleixner
</para>
<para>
Many users have provided bugfixes, improvements and helping hands for testing.
Thanks a lot.
</para>
<para>
The following people have contributed to this document:
</para>
<para>
Thomas Gleixner<email>tglx@linutronix.de</email>
</para>
</chapter>
</book>
include/linux/rslib.h 0 → 100644
View file @ 15b54237
/*
* include/linux/rslib.h
*
* Overview:
* Generic Reed Solomon encoder / decoder library
*
* Copyright (C) 2004 Thomas Gleixner (tglx@linutronix.de)
*
* RS code lifted from reed solomon library written by Phil Karn
* Copyright 2002 Phil Karn, KA9Q
*
* $Id: rslib.h,v 1.3 2004/10/05 22:08:22 gleixner Exp $
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as
* published by the Free Software Foundation.
*/
#ifndef _RSLIB_H_
#define _RSLIB_H_
#include <linux/list.h>
/**
* struct rs_control - rs control structure
*
* @mm: Bits per symbol
* @nn: Symbols per block (= (1<<mm)-1)
* @alpha_to: log lookup table
* @index_of: Antilog lookup table
* @genpoly: Generator polynomial
* @nroots: Number of generator roots = number of parity symbols
* @fcr: First consecutive root, index form
* @prim: Primitive element, index form
* @iprim: prim-th root of 1, index form
* @gfpoly: The primitive generator polynominal
* @users: Users of this structure
* @list: List entry for the rs control list
*/
struct rs_control {
int mm;
int nn;
uint16_t *alpha_to;
uint16_t *index_of;
uint16_t *genpoly;
int nroots;
int fcr;
int prim;
int iprim;
int gfpoly;
int users;
struct list_head list;
};
/* General purpose RS codec, 8-bit data width, symbol width 1-15 bit */
#ifdef CONFIG_REED_SOLOMON_ENC8
int encode_rs8(struct rs_control *rs, uint8_t *data, int len, uint16_t *par,
uint16_t invmsk);
#endif
#ifdef CONFIG_REED_SOLOMON_DEC8
int decode_rs8(struct rs_control *rs, uint8_t *data, uint16_t *par, int len,
uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
uint16_t *corr);
#endif
/* General purpose RS codec, 16-bit data width, symbol width 1-15 bit */
#ifdef CONFIG_REED_SOLOMON_ENC16
int encode_rs16(struct rs_control *rs, uint16_t *data, int len, uint16_t *par,
uint16_t invmsk);
#endif
#ifdef CONFIG_REED_SOLOMON_DEC16
int decode_rs16(struct rs_control *rs, uint16_t *data, uint16_t *par, int len,
uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
uint16_t *corr);
#endif
/* Create or get a matching rs control structure */
struct rs_control *init_rs(int symsize, int gfpoly, int fcr, int prim,
int nroots);
/* Release a rs control structure */
void free_rs(struct rs_control *rs);
/** modulo replacement for galois field arithmetics
*
* @rs: the rs control structure
* @x: the value to reduce
*
* where
* rs->mm = number of bits per symbol
* rs->nn = (2^rs->mm) - 1
*
* Simple arithmetic modulo would return a wrong result for values
* >= 3 * rs->nn
*/
static inline int rs_modnn(struct rs_control *rs, int x)
{
while (x >= rs->nn) {
x -= rs->nn;
x = (x >> rs->mm) + (x & rs->nn);
}
return x;
}
#endif
lib/Kconfig
View file @ 15b54237
......@@ -39,5 +39,23 @@ config ZLIB_INFLATE
config ZLIB_DEFLATE
tristate
#
# reed solomon support is select'ed if needed
#
config REED_SOLOMON
tristate
config REED_SOLOMON_ENC8
boolean
config REED_SOLOMON_DEC8
boolean
config REED_SOLOMON_ENC16
boolean
config REED_SOLOMON_DEC16
boolean
endmenu
lib/Makefile
View file @ 15b54237
......@@ -22,6 +22,7 @@ obj-$(CONFIG_GENERIC_IOMAP) += iomap.o
obj-$(CONFIG_ZLIB_INFLATE) += zlib_inflate/
obj-$(CONFIG_ZLIB_DEFLATE) += zlib_deflate/
obj-$(CONFIG_REED_SOLOMON) += reed_solomon/
hostprogs-y := gen_crc32table
clean-files := crc32table.h
......
lib/reed_solomon/Makefile 0 → 100644
View file @ 15b54237
#
# This is a modified version of reed solomon lib,
#
obj-$(CONFIG_REED_SOLOMON) += reed_solomon.o
lib/reed_solomon/decode_rs.c 0 → 100644
View file @ 15b54237
/*
* lib/reed_solomon/decode_rs.c
*
* Overview:
* Generic Reed Solomon encoder / decoder library
*
* Copyright 2002, Phil Karn, KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*
* Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
*
* $Id: decode_rs.c,v 1.5 2004/10/05 22:07:53 gleixner Exp $
*
*/
/* Generic data witdh independend code which is included by the
* wrappers.
*/
{
int deg_lambda, el, deg_omega;
int i, j, r, k, pad;
int nn = rs->nn;
int nroots = rs->nroots;
int fcr = rs->fcr;
int prim = rs->prim;
int iprim = rs->iprim;
uint16_t *alpha_to = rs->alpha_to;
uint16_t *index_of = rs->index_of;
uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
/* Err+Eras Locator poly and syndrome poly The maximum value
* of nroots is 8. So the neccecary stacksize will be about
* 220 bytes max.
*/
uint16_t lambda[nroots + 1], syn[nroots];
uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1];
uint16_t root[nroots], reg[nroots + 1], loc[nroots];
int count = 0;
uint16_t msk = (uint16_t) rs->nn;
/* Check length parameter for validity */
pad = nn - nroots - len;
if (pad < 0 || pad >= nn)
return -ERANGE;
/* Deos the caller provide the syndrome ? */
if (s != NULL)
goto decode;
/* form the syndromes; i.e., evaluate data(x) at roots of
* g(x) */
for (i = 0; i < nroots; i++)
syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
for (j = 1; j < len; j++) {
for (i = 0; i < nroots; i++) {
if (syn[i] == 0) {
syn[i] = (((uint16_t) data[j]) ^
invmsk) & msk;
} else {
syn[i] = ((((uint16_t) data[j]) ^
invmsk) & msk) ^
alpha_to[rs_modnn(rs, index_of[syn[i]] +
(fcr + i) * prim)];
}
}
}
for (j = 0; j < nroots; j++) {
for (i = 0; i < nroots; i++) {
if (syn[i] == 0) {
syn[i] = ((uint16_t) par[j]) & msk;
} else {
syn[i] = (((uint16_t) par[j]) & msk) ^
alpha_to[rs_modnn(rs, index_of[syn[i]] +
(fcr+i)*prim)];
}
}
}
s = syn;
/* Convert syndromes to index form, checking for nonzero condition */
syn_error = 0;
for (i = 0; i < nroots; i++) {
syn_error |= s[i];
s[i] = index_of[s[i]];
}
if (!syn_error) {
/* if syndrome is zero, data[] is a codeword and there are no
* errors to correct. So return data[] unmodified
*/
count = 0;
goto finish;
}
decode:
memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
lambda[0] = 1;
if (no_eras > 0) {
/* Init lambda to be the erasure locator polynomial */
lambda[1] = alpha_to[rs_modnn(rs,
prim * (nn - 1 - eras_pos[0]))];
for (i = 1; i < no_eras; i++) {
u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
for (j = i + 1; j > 0; j--) {
tmp = index_of[lambda[j - 1]];
if (tmp != nn) {
lambda[j] ^=
alpha_to[rs_modnn(rs, u + tmp)];
}
}
}
}
for (i = 0; i < nroots + 1; i++)
b[i] = index_of[lambda[i]];
/*
* Begin Berlekamp-Massey algorithm to determine error+erasure
* locator polynomial
*/
r = no_eras;
el = no_eras;
while (++r <= nroots) { /* r is the step number */
/* Compute discrepancy at the r-th step in poly-form */
discr_r = 0;
for (i = 0; i < r; i++) {
if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
discr_r ^=
alpha_to[rs_modnn(rs,
index_of[lambda[i]] +
s[r - i - 1])];
}
}
discr_r = index_of[discr_r]; /* Index form */
if (discr_r == nn) {
/* 2 lines below: B(x) <-- x*B(x) */
memmove (&b[1], b, nroots * sizeof (b[0]));
b[0] = nn;
} else {
/* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
t[0] = lambda[0];
for (i = 0; i < nroots; i++) {
if (b[i] != nn) {
t[i + 1] = lambda[i + 1] ^
alpha_to[rs_modnn(rs, discr_r +
b[i])];
} else
t[i + 1] = lambda[i + 1];
}
if (2 * el <= r + no_eras - 1) {
el = r + no_eras - el;
/*
* 2 lines below: B(x) <-- inv(discr_r) *
* lambda(x)
*/
for (i = 0; i <= nroots; i++) {
b[i] = (lambda[i] == 0) ? nn :
rs_modnn(rs, index_of[lambda[i]]
- discr_r + nn);
}
} else {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1], b, nroots * sizeof(b[0]));
b[0] = nn;
}
memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
}
}
/* Convert lambda to index form and compute deg(lambda(x)) */
deg_lambda = 0;
for (i = 0; i < nroots + 1; i++) {
lambda[i] = index_of[lambda[i]];
if (lambda[i] != nn)
deg_lambda = i;
}
/* Find roots of error+erasure locator polynomial by Chien search */
memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
count = 0; /* Number of roots of lambda(x) */
for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
q = 1; /* lambda[0] is always 0 */
for (j = deg_lambda; j > 0; j--) {
if (reg[j] != nn) {
reg[j] = rs_modnn(rs, reg[j] + j);
q ^= alpha_to[reg[j]];
}
}
if (q != 0)
continue; /* Not a root */
/* store root (index-form) and error location number */
root[count] = i;
loc[count] = k;
/* If we've already found max possible roots,
* abort the search to save time
*/
if (++count == deg_lambda)
break;
}
if (deg_lambda != count) {
/*
* deg(lambda) unequal to number of roots => uncorrectable
* error detected
*/
count = -1;
goto finish;
}
/*
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
* x**nroots). in index form. Also find deg(omega).
*/
deg_omega = deg_lambda - 1;
for (i = 0; i <= deg_omega; i++) {
tmp = 0;
for (j = i; j >= 0; j--) {
if ((s[i - j] != nn) && (lambda[j] != nn))
tmp ^=
alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
}
omega[i] = index_of[tmp];
}
/*
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
* inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
*/
for (j = count - 1; j >= 0; j--) {
num1 = 0;
for (i = deg_omega; i >= 0; i--) {
if (omega[i] != nn)
num1 ^= alpha_to[rs_modnn(rs, omega[i] +
i * root[j])];
}
num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
den = 0;
/* lambda[i+1] for i even is the formal derivative
* lambda_pr of lambda[i] */
for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
if (lambda[i + 1] != nn) {
den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
i * root[j])];
}
}
/* Apply error to data */
if (num1 != 0 && loc[j] >= pad) {
uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
index_of[num2] +
nn - index_of[den])];
/* Store the error correction pattern, if a
* correction buffer is available */
if (corr) {
corr[j] = cor;
} else {
/* If a data buffer is given and the
* error is inside the message,
* correct it */
if (data && (loc[j] < (nn - nroots)))
data[loc[j] - pad] ^= cor;
}
}
}
finish:
if (eras_pos != NULL) {
for (i = 0; i < count; i++)
eras_pos[i] = loc[i] - pad;
}
return count;
}
lib/reed_solomon/encode_rs.c 0 → 100644
View file @ 15b54237
/*
* lib/reed_solomon/encode_rs.c
*
* Overview:
* Generic Reed Solomon encoder / decoder library
*
* Copyright 2002, Phil Karn, KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*
* Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
*
* $Id: encode_rs.c,v 1.3 2004/10/05 22:07:53 gleixner Exp $
*
*/
/* Generic data witdh independend code which is included by the
* wrappers.
* int encode_rsX (struct rs_control *rs, uintX_t *data, int len, uintY_t *par)
*/
{
int i, j, pad;
int nn = rs->nn;
int nroots = rs->nroots;
uint16_t *alpha_to = rs->alpha_to;
uint16_t *index_of = rs->index_of;
uint16_t *genpoly = rs->genpoly;
uint16_t fb;
uint16_t msk = (uint16_t) rs->nn;
/* Check length parameter for validity */
pad = nn - nroots - len;
if (pad < 0 || pad >= nn)
return -ERANGE;
for (i = 0; i < len; i++) {
fb = index_of[((((uint16_t) data[i])^invmsk) & msk) ^ par[0]];
/* feedback term is non-zero */
if (fb != nn) {
for (j = 1; j < nroots; j++) {
par[j] ^= alpha_to[rs_modnn(rs, fb +
genpoly[nroots - j])];
}
}
/* Shift */
memmove(&par[0], &par[1], sizeof(uint16_t) * (nroots - 1));
if (fb != nn) {
par[nroots - 1] = alpha_to[rs_modnn(rs,
fb + genpoly[0])];
} else {
par[nroots - 1] = 0;
}
}
return 0;
}
lib/reed_solomon/reed_solomon.c 0 → 100644
View file @ 15b54237
/*
* lib/reed_solomon/rslib.c
*
* Overview:
* Generic Reed Solomon encoder / decoder library
*
* Copyright (C) 2004 Thomas Gleixner (tglx@linutronix.de)
*
* Reed Solomon code lifted from reed solomon library written by Phil Karn
* Copyright 2002 Phil Karn, KA9Q
*
* $Id: rslib.c,v 1.4 2004/10/05 22:07:53 gleixner Exp $
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as
* published by the Free Software Foundation.
*
* Description:
*
* The generic Reed Solomon library provides runtime configurable
* encoding / decoding of RS codes.
* Each user must call init_rs to get a pointer to a rs_control
* structure for the given rs parameters. This structure is either
* generated or a already available matching control structure is used.
* If a structure is generated then the polynominal arrays for
* fast encoding / decoding are built. This can take some time so
* make sure not to call this function from a timecritical path.
* Usually a module / driver should initialize the neccecary
* rs_control structure on module / driver init and release it
* on exit.
* The encoding puts the calculated syndrome into a given syndrom
* buffer.
* The decoding is a two step process. The first step calculates
* the syndrome over the received (data + syndrom) and calls the
* second stage, which does the decoding / error correction itself.
* Many hw encoders provide a syndrom calculation over the received
* data + syndrom and can call the second stage directly.
*
*/
#include <linux/errno.h>
#include <linux/kernel.h>
#include <linux/init.h>
#include <linux/module.h>
#include <linux/rslib.h>
#include <linux/slab.h>
#include <asm/semaphore.h>
/* This list holds all currently allocated rs control structures */
static LIST_HEAD (rslist);
/* Protection for the list */
static DECLARE_MUTEX(rslistlock);
/**
* rs_init - Initialize a Reed-Solomon codec
*
* @symsize: symbol size, bits (1-8)
* @gfpoly: Field generator polynomial coefficients
* @fcr: first root of RS code generator polynomial, index form
* @prim: primitive element to generate polynomial roots
* @nroots: RS code generator polynomial degree (number of roots)
*
* Allocate a control structure and the polynom arrays for faster
* en/decoding. Fill the arrays according to the given parameters
*/
static struct rs_control *rs_init(int symsize, int gfpoly, int fcr,
int prim, int nroots)
{
struct rs_control *rs;
int i, j, sr, root, iprim;
/* Allocate the control structure */
rs = kmalloc(sizeof (struct rs_control), GFP_KERNEL);
if (rs == NULL)
return NULL;
INIT_LIST_HEAD(&rs->list);
rs->mm = symsize;
rs->nn = (1 << symsize) - 1;
rs->fcr = fcr;
rs->prim = prim;
rs->nroots = nroots;
rs->gfpoly = gfpoly;
/* Allocate the arrays */
rs->alpha_to = kmalloc(sizeof(uint16_t) * (rs->nn + 1), GFP_KERNEL);
if (rs->alpha_to == NULL)
goto errrs;
rs->index_of = kmalloc(sizeof(uint16_t) * (rs->nn + 1), GFP_KERNEL);
if (rs->index_of == NULL)
goto erralp;
rs->genpoly = kmalloc(sizeof(uint16_t) * (rs->nroots + 1), GFP_KERNEL);
if(rs->genpoly == NULL)
goto erridx;
/* Generate Galois field lookup tables */
rs->index_of[0] = rs->nn; /* log(zero) = -inf */
rs->alpha_to[rs->nn] = 0; /* alpha**-inf = 0 */
sr = 1;
for (i = 0; i < rs->nn; i++) {
rs->index_of[sr] = i;
rs->alpha_to[i] = sr;
sr <<= 1;
if (sr & (1 << symsize))
sr ^= gfpoly;
sr &= rs->nn;
}
/* If it's not primitive, exit */
if(sr != 1)
goto errpol;
/* Find prim-th root of 1, used in decoding */
for(iprim = 1; (iprim % prim) != 0; iprim += rs->nn);
/* prim-th root of 1, index form */
rs->iprim = iprim / prim;
/* Form RS code generator polynomial from its roots */
rs->genpoly[0] = 1;
for (i = 0, root = fcr * prim; i < nroots; i++, root += prim) {
rs->genpoly[i + 1] = 1;
/* Multiply rs->genpoly[] by @**(root + x) */
for (j = i; j > 0; j--) {
if (rs->genpoly[j] != 0) {
rs->genpoly[j] = rs->genpoly[j -1] ^
rs->alpha_to[rs_modnn(rs,
rs->index_of[rs->genpoly[j]] + root)];
} else
rs->genpoly[j] = rs->genpoly[j - 1];
}
/* rs->genpoly[0] can never be zero */
rs->genpoly[0] =
rs->alpha_to[rs_modnn(rs,
rs->index_of[rs->genpoly[0]] + root)];
}
/* convert rs->genpoly[] to index form for quicker encoding */
for (i = 0; i <= nroots; i++)
rs->genpoly[i] = rs->index_of[rs->genpoly[i]];
return rs;
/* Error exit */
errpol:
kfree(rs->genpoly);
erridx:
kfree(rs->index_of);
erralp:
kfree(rs->alpha_to);
errrs:
kfree(rs);
return NULL;
}
/**
* free_rs - Free the rs control structure, if its not longer used
*
* @rs: the control structure which is not longer used by the
* caller
*/
void free_rs(struct rs_control *rs)
{
down(&rslistlock);
rs->users--;
if(!rs->users) {
list_del(&rs->list);
kfree(rs->alpha_to);
kfree(rs->index_of);
kfree(rs->genpoly);
kfree(rs);
}
up(&rslistlock);
}
/**
* init_rs - Find a matching or allocate a new rs control structure
*
* @symsize: the symbol size (number of bits)
* @gfpoly: the extended Galois field generator polynomial coefficients,
* with the 0th coefficient in the low order bit. The polynomial
* must be primitive;
* @fcr: the first consecutive root of the rs code generator polynomial
* in index form
* @prim: primitive element to generate polynomial roots
* @nroots: RS code generator polynomial degree (number of roots)
*/
struct rs_control *init_rs(int symsize, int gfpoly, int fcr, int prim,
int nroots)
{
struct list_head *tmp;
struct rs_control *rs;
/* Sanity checks */
if (symsize < 1)
return NULL;
if (fcr < 0 || fcr >= (1<<symsize))
return NULL;
if (prim <= 0 || prim >= (1<<symsize))
return NULL;
if (nroots < 0 || nroots >= (1<<symsize) || nroots > 8)
return NULL;
down(&rslistlock);
/* Walk through the list and look for a matching entry */
list_for_each(tmp, &rslist) {
rs = list_entry(tmp, struct rs_control, list);
if (symsize != rs->mm)
continue;
if (gfpoly != rs->gfpoly)
continue;
if (fcr != rs->fcr)
continue;
if (prim != rs->prim)
continue;
if (nroots != rs->nroots)
continue;
/* We have a matching one already */
rs->users++;
goto out;
}
/* Create a new one */
rs = rs_init(symsize, gfpoly, fcr, prim, nroots);
if (rs) {
rs->users = 1;
list_add(&rs->list, &rslist);
}
out:
up(&rslistlock);
return rs;
}
#ifdef CONFIG_REED_SOLOMON_ENC8
/**
* encode_rs8 - Calculate the parity for data values (8bit data width)
*
* @rs: the rs control structure
* @data: data field of a given type
* @len: data length
* @par: parity data, must be initialized by caller (usually all 0)
* @invmsk: invert data mask (will be xored on data)
*
* The parity uses a uint16_t data type to enable
* symbol size > 8. The calling code must take care of encoding of the
* syndrome result for storage itself.
*/
int encode_rs8(struct rs_control *rs, uint8_t *data, int len, uint16_t *par,
uint16_t invmsk)
{
#include "encode_rs.c"
}
EXPORT_SYMBOL_GPL(encode_rs8);
#endif
#ifdef CONFIG_REED_SOLOMON_DEC8
/**
* decode_rs8 - Decode codeword (8bit data width)
*
* @rs: the rs control structure
* @data: data field of a given type
* @par: received parity data field
* @len: data length
* @s: syndrome data field (if NULL, syndrome is calculated)
* @no_eras: number of erasures
* @eras_pos: position of erasures, can be NULL
* @invmsk: invert data mask (will be xored on data, not on parity!)
* @corr: buffer to store correction bitmask on eras_pos
*
* The syndrome and parity uses a uint16_t data type to enable
* symbol size > 8. The calling code must take care of decoding of the
* syndrome result and the received parity before calling this code.
*/
int decode_rs8(struct rs_control *rs, uint8_t *data, uint16_t *par, int len,
uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
uint16_t *corr)
{
#include "decode_rs.c"
}
EXPORT_SYMBOL_GPL(decode_rs8);
#endif
#ifdef CONFIG_REED_SOLOMON_ENC16
/**
* encode_rs16 - Calculate the parity for data values (16bit data width)
*
* @rs: the rs control structure
* @data: data field of a given type
* @len: data length
* @par: parity data, must be initialized by caller (usually all 0)
* @invmsk: invert data mask (will be xored on data, not on parity!)
*
* Each field in the data array contains up to symbol size bits of valid data.
*/
int encode_rs16(struct rs_control *rs, uint16_t *data, int len, uint16_t *par,
uint16_t invmsk)
{
#include "encode_rs.c"
}
EXPORT_SYMBOL_GPL(encode_rs16);
#endif
#ifdef CONFIG_REED_SOLOMON_DEC16
/**
* decode_rs16 - Decode codeword (16bit data width)
*
* @rs: the rs control structure
* @data: data field of a given type
* @par: received parity data field
* @len: data length
* @s: syndrome data field (if NULL, syndrome is calculated)
* @no_eras: number of erasures
* @eras_pos: position of erasures, can be NULL
* @invmsk: invert data mask (will be xored on data, not on parity!)
* @corr: buffer to store correction bitmask on eras_pos
*
* Each field in the data array contains up to symbol size bits of valid data.
*/
int decode_rs16(struct rs_control *rs, uint16_t *data, uint16_t *par, int len,
uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
uint16_t *corr)
{
#include "decode_rs.c"
}
EXPORT_SYMBOL_GPL(decode_rs16);
#endif
EXPORT_SYMBOL_GPL(init_rs);
EXPORT_SYMBOL_GPL(free_rs);
MODULE_LICENSE("GPL");
MODULE_DESCRIPTION("Reed Solomon encoder/decoder");
MODULE_AUTHOR("Phil Karn, Thomas Gleixner");
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