From: Thomas Gleixner <tglx@linutronix.de>
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.
Signed-off-by: Andrew Morton <akpm@osdl.org>
---
25-akpm/Documentation/DocBook/Makefile | 2
25-akpm/Documentation/DocBook/librs.tmpl | 287 ++++++++++++++++++++++++++
25-akpm/include/linux/rslib.h | 105 +++++++++
25-akpm/lib/Kconfig | 18 +
25-akpm/lib/Makefile | 1
25-akpm/lib/reed_solomon/Makefile | 6
25-akpm/lib/reed_solomon/decode_rs.c | 272 +++++++++++++++++++++++++
25-akpm/lib/reed_solomon/encode_rs.c | 54 ++++
25-akpm/lib/reed_solomon/reed_solomon.c | 335 +++++++++++++++++++++++++++++++
9 files changed, 1079 insertions(+), 1 deletion(-)
diff -puN /dev/null Documentation/DocBook/librs.tmpl
--- /dev/null Thu Apr 11 07:25:15 2002
+++ 25-akpm/Documentation/DocBook/librs.tmpl Tue Oct 5 15:57:09 2004
@@ -0,0 +1,287 @@
+<!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>
diff -puN Documentation/DocBook/Makefile~shared-reed-solomon-ecc-library Documentation/DocBook/Makefile
--- 25/Documentation/DocBook/Makefile~shared-reed-solomon-ecc-library Tue Oct 5 15:57:09 2004
+++ 25-akpm/Documentation/DocBook/Makefile Tue Oct 5 15:57:09 2004
@@ -11,7 +11,7 @@ DOCBOOKS := wanbook.sgml z8530book.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):
diff -puN /dev/null include/linux/rslib.h
--- /dev/null Thu Apr 11 07:25:15 2002
+++ 25-akpm/include/linux/rslib.h Tue Oct 5 15:57:09 2004
@@ -0,0 +1,105 @@
+/*
+ * 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 1.2 2004/10/01 21:43:50 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
diff -puN lib/Kconfig~shared-reed-solomon-ecc-library lib/Kconfig
--- 25/lib/Kconfig~shared-reed-solomon-ecc-library Tue Oct 5 15:57:09 2004
+++ 25-akpm/lib/Kconfig Tue Oct 5 15:57:09 2004
@@ -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
diff -puN lib/Makefile~shared-reed-solomon-ecc-library lib/Makefile
--- 25/lib/Makefile~shared-reed-solomon-ecc-library Tue Oct 5 15:57:09 2004
+++ 25-akpm/lib/Makefile Tue Oct 5 15:57:09 2004
@@ -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
diff -puN /dev/null lib/reed_solomon/decode_rs.c
--- /dev/null Thu Apr 11 07:25:15 2002
+++ 25-akpm/lib/reed_solomon/decode_rs.c Tue Oct 5 15:57:09 2004
@@ -0,0 +1,272 @@
+/*
+ * 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 1.4 2004/10/01 21:44:39 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(®[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;
+
+}
diff -puN /dev/null lib/reed_solomon/encode_rs.c
--- /dev/null Thu Apr 11 07:25:15 2002
+++ 25-akpm/lib/reed_solomon/encode_rs.c Tue Oct 5 15:57:09 2004
@@ -0,0 +1,54 @@
+/*
+ * 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 1.2 2004/09/19 12:09:40 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;
+}
diff -puN /dev/null lib/reed_solomon/Makefile
--- /dev/null Thu Apr 11 07:25:15 2002
+++ 25-akpm/lib/reed_solomon/Makefile Tue Oct 5 15:57:09 2004
@@ -0,0 +1,6 @@
+#
+# This is a modified version of reed solomon lib,
+#
+
+obj-$(CONFIG_REED_SOLOMON) += reed_solomon.o
+
diff -puN /dev/null lib/reed_solomon/reed_solomon.c
--- /dev/null Thu Apr 11 07:25:15 2002
+++ 25-akpm/lib/reed_solomon/reed_solomon.c Tue Oct 5 15:57:09 2004
@@ -0,0 +1,335 @@
+/*
+ * 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 1.3 2004/10/01 21:44:39 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");
+
_