Thomas Gleixner

tglx@linutronix.de

2004 Thomas Gleixner 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. 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. 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 For more details see the file COPYING in the source distribution of Linux. The generic Reed-Solomon Library provides encoding, decoding and error correction functions. Reed-Solomon codes are used in communication and storage applications to ensure data integrity. This documentation is provided for developers who want to utilize the functions provided by the library. None. This chapter provides examples of how to use the library. The init function init_rs returns a pointer to an rs decoder structure, which holds the necessary 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 paths. /* the Reed Solomon control structure */ static struct rs_control *rs_decoder; /* Symbolsize is 10 (bits) * Primitive polynomial is x^10+x^3+1 * first consecutive root is 0 * primitive element to generate roots = 1 * generator polynomial degree (number of roots) = 6 */ rs_decoder = init_rs (10, 0x409, 0, 1, 6); 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. 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 prevents that reading from an erased FLASH results in ECC errors. The databytes are expanded to the given symbol size on the fly. There is no support for encoding continuous bitstreams with a symbol size != 8 at the moment. If it is necessary it should be not a big deal to implement such functionality. /* 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); The decoder calculates the syndrome over the given data length and the received parity symbols and corrects errors in the data. If a syndrome is available from a hardware decoder then the syndrome calculation is skipped. 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 bit ordering scheme. The databytes are expanded to the given symbol size on the fly. There is no support for decoding continuous bitstreams with a symbolsize != 8 at the moment. If it is necessary it should be not a big deal to implement such functionality. /* 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); /* 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); Note: It's not necessary to give data and received parity to the decoder. /* 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]); } The function free_rs frees the allocated resources, if the caller is the last user of the decoder. /* Release resources */ free_rs(rs_decoder); This chapter contains the autogenerated documentation of the structures which are used in the Reed-Solomon Library and are relevant for a developer. Kernel Hackers Manual July 2017 struct rs_control 9 4.1.27 struct rs_control rs control structure 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 (* gffunc) (int); int users; struct list_head list; }; 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 gffunc Function to generate the field, if non-canonical representation users Users of this structure list List entry for the rs control list This chapter contains the autogenerated documentation of the Reed-Solomon functions which are exported. Kernel Hackers Manual July 2017 free_rs 9 4.1.27 free_rs Free the rs control structure, if it is no longer used void free_rs struct rs_control * rs rs the control structure which is not longer used by the caller Kernel Hackers Manual July 2017 init_rs 9 4.1.27 init_rs Find a matching or allocate a new rs control structure struct rs_control * init_rs int symsize int gfpoly int fcr int prim int nroots 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) Kernel Hackers Manual July 2017 init_rs_non_canonical 9 4.1.27 init_rs_non_canonical Find a matching or allocate a new rs control structure, for fields with non-canonical representation struct rs_control * init_rs_non_canonical int symsize int (*gffunc) int int fcr int prim int nroots symsize the symbol size (number of bits) gffunc pointer to function to generate the next field element, or the multiplicative identity element if given 0. Used instead of gfpoly if gfpoly is 0 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) Kernel Hackers Manual July 2017 encode_rs8 9 4.1.27 encode_rs8 Calculate the parity for data values (8bit data width) int encode_rs8 struct rs_control * rs uint8_t * data int len uint16_t * par uint16_t invmsk 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. Kernel Hackers Manual July 2017 decode_rs8 9 4.1.27 decode_rs8 Decode codeword (8bit data width) 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 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. Returns the number of corrected bits or -EBADMSG for uncorrectable errors. Kernel Hackers Manual July 2017 encode_rs16 9 4.1.27 encode_rs16 Calculate the parity for data values (16bit data width) int encode_rs16 struct rs_control * rs uint16_t * data int len uint16_t * par uint16_t invmsk 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. Kernel Hackers Manual July 2017 decode_rs16 9 4.1.27 decode_rs16 Decode codeword (16bit data width) 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 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. Returns the number of corrected bits or -EBADMSG for uncorrectable errors. The library code for encoding and decoding was written by Phil Karn. Copyright 2002, Phil Karn, KA9Q May be used under the terms of the GNU General Public License (GPL) The wrapper functions and interfaces are written by Thomas Gleixner. Many users have provided bugfixes, improvements and helping hands for testing. Thanks a lot. The following people have contributed to this document: Thomas Gleixnertglx@linutronix.de