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@ -29,7 +29,7 @@
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*/
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/*
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* Ezpwd Reed-Solomon -- Reed-Solomon encoder / decoder library
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*
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*
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* Copyright (c) 2014, Hard Consulting Corporation.
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*
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* Ezpwd Reed-Solomon is free software: you can redistribute it and/or modify it under the terms of
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@ -38,43 +38,43 @@
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* source tree. Ezpwd Reed-Solomon is also available under Commercial license. The
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* c++/ezpwd/rs_base file is redistributed under the terms of the LGPL, regardless of the overall
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* licensing terms.
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*
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*
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* Ezpwd Reed-Solomon is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
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* without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See
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* the GNU General Public License for more details.
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*
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*
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* The core Reed-Solomon codec implementation in c++/ezpwd/rs_base is by Phil Karn, converted to C++
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* by Perry Kundert (perry@hardconsulting.com), and may be used under the terms of the LGPL. Here
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* is the terms from Phil's README file (see phil-karn/fec-3.0.1/README):
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*
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*
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* COPYRIGHT
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*
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*
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* This package is copyright 2006 by Phil Karn, KA9Q. It may be used
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* under the terms of the GNU Lesser General Public License (LGPL). See
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* the file "lesser.txt" in this package for license details.
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*
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*
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* The c++/ezpwd/rs_base file is, therefore, redistributed under the terms of the LGPL, while the
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* rest of Ezpwd Reed-Solomon is distributed under either the GPL or Commercial licenses.
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* Therefore, even if you have obtained Ezpwd Reed-Solomon under a Commercial license, you must make
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* available the source code of the c++/ezpwd/rs_base file with your product. One simple way to
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* accomplish this is to include the following URL in your code or documentation:
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*
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*
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* https://github.com/pjkundert/ezpwd-reed-solomon/blob/master/c++/ezpwd/rs_base
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*
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*
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*
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*
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* The Linux 3.15.1 version of lib/reed_solomon was also consulted as a cross-reference, which (in
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* turn) is basically verbatim copied from Phil Karn's LGPL implementation, to ensure that no new
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* defects had been found and fixed; there were no meaningful changes made to Phil's implementation.
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* I've personally been using Phil's implementation for years in a heavy industrial use, and it is
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* rock-solid.
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*
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*
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* However, both Phil's and the Linux kernel's (copy of Phil's) implementation will return a
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* "corrected" decoding with impossible error positions, in some cases where the error load
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* completely overwhelms the R-S encoding. These cases, when detected, are rejected in this
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* implementation. This could be considered a defect in Phil's (and hence the Linux kernel's)
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* implementations, which results in them accepting clearly incorrect R-S decoded values as valid
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* (corrected) R-S codewords. We chose the report failure on these attempts.
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*
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*
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*/
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#if !defined(__RS_H__)
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#define __RS_H__
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@ -91,14 +91,14 @@
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#include <type_traits>
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#include <vector>
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//
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//
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// Preprocessor defines available:
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//
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//
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// EZPWD_NO_EXCEPTS -- define to use no exceptions; return -1, or abort on catastrophic failures
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// EZPWD_NO_MOD_TAB -- define to force no "modnn" Galois modulo table acceleration
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// EZPWD_ARRAY_SAFE -- define to force usage of bounds-checked arrays for most tabular data
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// EZPWD_ARRAY_TEST -- define to force erroneous sizing of some arrays for non-production testing
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//
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//
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#if defined(EZPWD_NO_EXCEPTS)
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#include <cstdio>
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@ -114,7 +114,7 @@
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namespace edac
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{
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namespace rs
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namespace rs
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{
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// ezpwd::log_<N,B> -- compute the log base B of N at compile-time
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template <size_t N, size_t B = 2> struct log_{ enum { value = 1 + log_<N / B, B>::value }; };
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@ -147,27 +147,27 @@ namespace edac
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/// <summary></summary>
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virtual std::ostream &output(std::ostream &lhs) const { return lhs << "RS(" << this->size() << "," << this->load() << ")"; }
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//
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//
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// {en,de}code -- Compute/Correct errors/erasures in a Reed-Solomon encoded container
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//
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//
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// The encoded parity symbols may be included in 'data' (len includes nroots() parity
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// symbols), or may (optionally) supplied separately in (at least nroots()-sized)
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// 'parity'.
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//
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// 'parity'.
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//
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// For decode, optionally specify some known erasure positions (up to nroots()). If
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// non-empty 'erasures' is provided, it contains the positions of each erasure. If a
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// non-zero pointer to a 'position' vector is provided, its capacity will be increased to
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// be capable of storing up to 'nroots()' ints; the actual deduced error locations will be
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// returned.
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//
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//
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// RETURN VALUE
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//
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//
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// Return -1 on error. The encode returns the number of parity symbols produced;
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// decode returns the number of symbols corrected. Both errors and erasures are included,
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// so long as they are actually different than the deduced value. In other words, if a
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// symbol is marked as an erasure but it actually turns out to be correct, it's index will
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// NOT be included in the returned count, nor the modified erasure vector!
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//
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//
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int encode(std::string &data) const
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{
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@ -180,7 +180,7 @@ namespace edac
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int encode(const std::string &data, std::string &parity) const
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{
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typedef uint8_t uT;
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typedef std::pair<const uT*, const uT*> cuTpair;
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typedef std::pair<const uT*, const uT*> cuTpair;
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typedef std::pair<uT*, uT*> uTpair;
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parity.resize(nroots());
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return encode(cuTpair((const uT*)&data.front(), (const uT*)&data.front() + data.size()),
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@ -195,10 +195,10 @@ namespace edac
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return encode(uTpair((uT*)&data.front(), (uT*)&data.front() + data.size()));
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}
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template<typename T> int encode(const std::vector<T>&data, std::vector<T> &parity) const
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template<typename T> int encode(const std::vector<T>&data, std::vector<T> &parity) const
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{
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typedef typename std::make_unsigned<T>::type uT;
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typedef std::pair<const uT*, const uT*> cuTpair;
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typedef std::pair<const uT*, const uT*> cuTpair;
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typedef std::pair<uT*, uT*> uTpair;
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parity.resize(nroots());
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return encode(cuTpair((uT*)&data.front(), (uT*)&data.front() + data.size()),
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@ -213,8 +213,8 @@ namespace edac
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}
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virtual int encode(const std::pair<uint8_t*, uint8_t*> &data) const = 0;
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virtual int encode(const std::pair<const uint8_t*, const uint8_t*> &data,
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virtual int encode(const std::pair<const uint8_t*, const uint8_t*> &data,
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const std::pair<uint8_t*, uint8_t*> &parity) const = 0;
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virtual int encode(const std::pair<uint16_t*, uint16_t*> &data) const = 0;
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virtual int encode(const std::pair<const uint16_t*, const uint16_t*> &data,
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@ -223,7 +223,7 @@ namespace edac
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virtual int encode(const std::pair<const uint32_t*, const uint32_t*> &data,
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const std::pair<uint32_t*, uint32_t*> &parity) const = 0;
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int decode(std::string &data, const std::vector<int> &erasure = std::vector<int>(),
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int decode(std::string &data, const std::vector<int> &erasure = std::vector<int>(),
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std::vector<int>* position = 0) const
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{
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typedef uint8_t uT;
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@ -231,16 +231,16 @@ namespace edac
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return decode(uTpair((uT*)&data.front(), (uT*)&data.front() + data.size()), erasure, position);
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}
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int decode(std::string &data, std::string &parity, const std::vector<int> &erasure = std::vector<int>(),
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int decode(std::string &data, std::string &parity, const std::vector<int> &erasure = std::vector<int>(),
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std::vector<int>* position = 0) const
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{
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typedef uint8_t uT;
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typedef std::pair<uT*, uT*> uTpair;
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return decode(uTpair((uT*)&data.front(), (uT*)&data.front() + data.size()),
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return decode(uTpair((uT*)&data.front(), (uT*)&data.front() + data.size()),
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uTpair((uT*)&parity.front(), (uT*)&parity.front() + parity.size()), erasure, position);
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}
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template<typename T> int decode(std::vector<T> &data, const std::vector<int> &erasure = std::vector<int>(),
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template<typename T> int decode(std::vector<T> &data, const std::vector<int> &erasure = std::vector<int>(),
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std::vector<int>* position = 0) const
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{
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typedef typename std::make_unsigned<T>::type uT;
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@ -248,7 +248,7 @@ namespace edac
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return decode(uTpair((uT*)&data.front(), (uT*)&data.front() + data.size()), erasure, position);
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}
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template<typename T> int decode(std::vector<T> &data, std::vector<T> &parity,
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template<typename T> int decode(std::vector<T> &data, std::vector<T> &parity,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const
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{
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typedef typename std::make_unsigned<T>::type uT;
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@ -257,7 +257,7 @@ namespace edac
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uTpair((uT*)&parity.front(), (uT*)&parity.front() + parity.size()), erasure, position);
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}
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template<typename T, size_t N> int decode(std::array<T,N> &data, int pad = 0,
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template<typename T, size_t N> int decode(std::array<T,N> &data, int pad = 0,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const
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{
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typedef typename std::make_unsigned<T>::type uT;
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@ -269,21 +269,21 @@ namespace edac
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const = 0;
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virtual int decode(const std::pair<uint8_t*, uint8_t*> &data, const std::pair<uint8_t*, uint8_t*> &parity,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const = 0;
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virtual int decode(const std::pair<uint16_t*, uint16_t*> &data,
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virtual int decode(const std::pair<uint16_t*, uint16_t*> &data,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const = 0;
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virtual int decode(const std::pair<uint16_t*, uint16_t*> &data, const std::pair<uint16_t*, uint16_t*> &parity,
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virtual int decode(const std::pair<uint16_t*, uint16_t*> &data, const std::pair<uint16_t*, uint16_t*> &parity,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const = 0;
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|
|
virtual int decode(const std::pair<uint32_t*, uint32_t*> &data,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const = 0;
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|
virtual int decode(const std::pair<uint32_t*, uint32_t*> &data, const std::pair<uint32_t*, uint32_t*> &parity,
|
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|
|
virtual int decode(const std::pair<uint32_t*, uint32_t*> &data, const std::pair<uint32_t*, uint32_t*> &parity,
|
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|
|
const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position= 0 ) const = 0;
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};
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//
|
|
|
|
|
//
|
|
|
|
|
// std::ostream << edac::rs::reed_solomon<...>
|
|
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|
|
//
|
|
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|
|
//
|
|
|
|
|
// Output a R-S codec description in standard form eg. RS(255,253)
|
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//
|
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//
|
|
|
|
|
inline std::ostream &operator<<(std::ostream &lhs, const edac::rs::reed_solomon_base &rhs) { return rhs.output(lhs); }
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// ---------------------------------------------------------------------------
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|
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|
|
@ -306,7 +306,7 @@ namespace edac
|
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|
|
return sr;
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|
}
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};
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|
// ---------------------------------------------------------------------------
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|
|
|
|
// Class Declaration
|
|
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|
|
// R-S tables common to all RS(NN,*) with same SYM, PRM and PLY.
|
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|
|
@ -324,7 +324,7 @@ namespace edac
|
|
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|
static const int SIZE = (1 << SYM) - 1; // maximum symbols in field
|
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|
static const int NN = SIZE;
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|
static const int A0 = SIZE;
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|
|
|
|
|
|
|
|
|
// modulo table: 1/2 the symbol size squared, up to 4k
|
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|
|
static const int MODS = SYM > 8 ? (1 << 12) : (1 << SYM << SYM / 2);
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|
@ -351,7 +351,7 @@ namespace edac
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|
|
// Generate Galois field lookup tables
|
|
|
|
|
index_of[0] = A0; // log(zero) = -inf
|
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|
|
alpha_to[A0] = 0; // alpha**-inf = 0
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|
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|
|
|
PLY poly;
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|
|
int sr = poly(0);
|
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|
for (int i = 0; i < NN; i++) {
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|
|
@ -380,7 +380,7 @@ namespace edac
|
|
|
|
|
/// <summary>Finalizes a instance of the reed_solomon_tabs class.</summary>
|
|
|
|
|
virtual ~reed_solomon_tabs() { /* stub */ }
|
|
|
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|
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|
|
//
|
|
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|
|
//
|
|
|
|
|
// modnn -- modulo replacement for galois field arithmetics, optionally w/ table acceleration
|
|
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|
|
//
|
|
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|
|
// @x: the value to reduce (will never be -'ve)
|
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|
|
@ -407,7 +407,7 @@ namespace edac
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|
|
x -= NN;
|
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|
|
x = (x >> MM) + (x & NN);
|
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|
}
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|
|
if ( MODS && x >= NN) {
|
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|
|
x = mod_of[x - NN];
|
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|
}
|
|
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|
|
@ -415,7 +415,7 @@ namespace edac
|
|
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|
|
}
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};
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// ---------------------------------------------------------------------------
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// Class Declaration
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// Reed-Solomon codec.
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@ -436,7 +436,7 @@ namespace edac
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// All reed_solomon<T, ...> instances with the same template type parameters share a common
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// (static) set of alpha_to, index_of and genpoly tables. The first instance to be constructed
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// initializes the tables.
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//
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//
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// Each specialized type of reed_solomon implements a specific encode/decode method
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// appropriate to its datum 'TYP'. When accessed via a generic reed_solomon_base pointer, only
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// access via "safe" (size specifying) containers or iterators is available.
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@ -480,7 +480,7 @@ namespace edac
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#if DEBUG_RS
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LogDebug(LOG_HOST, "reed_solomon::reed_solomon() RS(%d,%d): initialized for %d roots", SIZE, LOAD, NROOTS);
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#endif
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std::array<TYP, NROOTS + 1> tmppoly; // uninitialized
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// Form RS code generator polynomial from its roots. Only lower-index entries are
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@ -488,7 +488,7 @@ namespace edac
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tmppoly[0] = 1;
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for (int i = 0, root = FCR * PRM; i < NROOTS; i++, root += PRM) {
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tmppoly[i + 1] = 1;
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// Multiply tmppoly[] by @**(root + x)
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for (int j = i; j > 0; j--) {
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if (tmppoly[j] != 0) {
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@ -497,7 +497,7 @@ namespace edac
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tmppoly[j] = tmppoly[j - 1];
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}
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}
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// tmppoly[0] can never be zero
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tmppoly[0] = alpha_to[modnn(index_of[tmppoly[0]] + root)];
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}
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@ -524,18 +524,18 @@ namespace edac
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using reed_solomon_base::encode;
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virtual int encode(const std::pair<uint8_t*, uint8_t*> &data) const { return encode_mask(data.first, data.second - data.first - NROOTS, data.second - NROOTS); }
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virtual int encode(const std::pair<const uint8_t*, const uint8_t*> &data,
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virtual int encode(const std::pair<const uint8_t*, const uint8_t*> &data,
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const std::pair<uint8_t*, uint8_t*> &parity) const
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{
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if (parity.second - parity.first != NROOTS) {
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EZPWD_RAISE_OR_RETURN(std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1);
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}
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return encode_mask(data.first, data.second - data.first, parity.first);
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}
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virtual int encode(const std::pair<uint16_t*, uint16_t*> &data) const { return encode_mask(data.first, data.second - data.first - NROOTS, data.second - NROOTS); }
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virtual int encode(const std::pair<const uint16_t*, const uint16_t*> &data,
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virtual int encode(const std::pair<const uint16_t*, const uint16_t*> &data,
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const std::pair<uint16_t*, uint16_t*> &parity) const
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{
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if (parity.second - parity.first != NROOTS) {
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@ -546,7 +546,7 @@ namespace edac
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}
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virtual int encode(const std::pair<uint32_t*, uint32_t*> &data) const { return encode_mask(data.first, data.second - data.first - NROOTS, data.second - NROOTS); }
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virtual int encode(const std::pair<const uint32_t*, const uint32_t*> &data,
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virtual int encode(const std::pair<const uint32_t*, const uint32_t*> &data,
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const std::pair<uint32_t*, uint32_t*> &parity) const
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{
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if (parity.second - parity.first != NROOTS) {
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@ -574,7 +574,7 @@ namespace edac
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if (SYMBOL > INPUT) {
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EZPWD_RAISE_OR_RETURN(std::runtime_error, "reed-solomon: output data type too small to contain symbols", -1);
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}
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std::array<TYP, SIZE> tmp;
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TYP msk = static_cast<TYP>(~0UL << SYMBOL);
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for (int i = 0; i < len; ++i) {
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@ -600,7 +600,7 @@ namespace edac
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return NROOTS;
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}
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using reed_solomon_base::decode;
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virtual int decode(const std::pair<uint8_t*, uint8_t*> &data,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const
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@ -608,7 +608,7 @@ namespace edac
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return decode_mask(data.first, data.second - data.first, (uint8_t*)0, erasure, position);
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}
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virtual int decode(const std::pair<uint8_t*, uint8_t*> &data, const std::pair<uint8_t*, uint8_t*> &parity,
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virtual int decode(const std::pair<uint8_t*, uint8_t*> &data, const std::pair<uint8_t*, uint8_t*> &parity,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const
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{
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if (parity.second - parity.first != NROOTS) {
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@ -618,7 +618,7 @@ namespace edac
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return decode_mask(data.first, data.second - data.first, parity.first, erasure, position);
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}
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virtual int decode(const std::pair<uint16_t*, uint16_t*> &data,
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virtual int decode(const std::pair<uint16_t*, uint16_t*> &data,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const
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{
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return decode_mask(data.first, data.second - data.first, (uint16_t*)0, erasure, position);
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@ -634,13 +634,13 @@ namespace edac
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return decode_mask(data.first, data.second - data.first, parity.first, erasure, position);
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}
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virtual int decode(const std::pair<uint32_t*, uint32_t*> &data,
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virtual int decode(const std::pair<uint32_t*, uint32_t*> &data,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position = 0) const
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{
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return decode_mask(data.first, data.second - data.first, (uint32_t*)0, erasure, position);
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}
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virtual int decode(const std::pair<uint32_t*, uint32_t*> &data, const std::pair<uint32_t*, uint32_t*> &parity,
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virtual int decode(const std::pair<uint32_t*, uint32_t*> &data, const std::pair<uint32_t*, uint32_t*> &parity,
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const std::vector<int> &erasure = std::vector<int>(), std::vector<int>* position= 0 ) const
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{
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if (parity.second - parity.first != NROOTS) {
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@ -650,14 +650,14 @@ namespace edac
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return decode_mask(data.first, data.second - data.first, parity.first, erasure, position);
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}
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//
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//
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// decode_mask -- mask INP data into valid SYMBOL data
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//
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//
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// Incoming data may be in a variety of sizes, and may contain information beyond the
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// R-S symbol capacity. For example, we might use a 6-bit R-S symbol to correct the lower
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// 6 bits of an 8-bit data character. This would allow us to correct common substitution
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// errors (such as '2' for '3', 'R' for 'T', 'n' for 'm').
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//
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//
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template<typename INP>
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int decode_mask(INP *data, int len, INP *parity = 0, const std::vector<int> &erasure = std::vector<int>(),
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@ -870,7 +870,7 @@ namespace edac
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#if DEBUG_RS
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// Test code that verifies the erasure locator polynomial just constructed
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// Needed only for decoder debugging.
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// find roots of the erasure location polynomial
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for (int i = 1; i<= no_eras; i++) {
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reg[i] = index_of[lambda[i]];
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@ -955,7 +955,7 @@ namespace edac
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if (2 * el <= r + no_eras - 1) {
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el = r + no_eras - el;
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// 2 lines below: B(x) <-- inv(discr_r) * lambda(x)
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for (int i = 0; i <= NROOTS; i++) {
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b[i] = ((lambda[i] == 0) ? A0 : modnn(index_of[lambda[i]] - discr_r + NN));
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@ -1067,7 +1067,7 @@ namespace edac
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// correction location outside of the data and parity we've been provided!
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#if DEBUG_RS
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std::stringstream ss;
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ss << "reed_solomon::decode(): ERROR: RS(" << SIZE <<"," << LOAD << ") computed error location: " << loc[j] <<
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ss << "reed_solomon::decode(): ERROR: RS(" << SIZE <<"," << LOAD << ") computed error location: " << loc[j] <<
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" within " << pad << " pad symbols, not within " << LOAD - pad << " data or " << NROOTS << " parity";
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LogDebug(LOG_HOST, "%s", ss.str().c_str());
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#endif
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@ -1113,7 +1113,7 @@ finish:
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errors[2 * (eras_pos[i]) + 0] = 'e';
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errors[2 * (eras_pos[i]) + 1] = 'e';
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}
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std::stringstream ss;
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ss << "reed_solomon::decode(): e)rase, E)rror; count = " << count << ": " << std::endl << errors;
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LogDebug(LOG_HOST, "%s", ss.str().c_str());
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@ -1129,12 +1129,12 @@ finish:
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}
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};
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//
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//
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// Define the static reed_solomon...<...> members; allowed in header for template types.
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//
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//
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// The reed_solomon_tags<...>::iprim < 0 is used to indicate to the first instance that the
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// static tables require initialization.
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//
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//
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template<typename TYP, int SYM, int PRM, class PLY> int reed_solomon_tabs<TYP, SYM, PRM, PLY>::iprim = -1;
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template<typename TYP, int SYM, int PRM, class PLY> std::array<TYP, reed_solomon_tabs<TYP, SYM, PRM, PLY>::NN + 1> reed_solomon_tabs<TYP, SYM, PRM, PLY>::alpha_to;
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template<typename TYP, int SYM, int PRM, class PLY> std::array<TYP, reed_solomon_tabs<TYP, SYM, PRM, PLY>::NN + 1> reed_solomon_tabs<TYP, SYM, PRM, PLY>::index_of;
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@ -1142,5 +1142,5 @@ finish:
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template<typename TYP, int SYM, int RTS, int FCR, int PRM, class PLY> std::array<TYP, reed_solomon< TYP, SYM, RTS, FCR, PRM, PLY>::NROOTS + 1> reed_solomon<TYP, SYM, RTS, FCR, PRM, PLY>::genpoly;
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} // namespace rs
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} // namespace edac
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#endif // __RS_H__
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Bryan Biedenkapp
3 years ago