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/*
* Ezpwd Reed-Solomon -- Reed-Solomon encoder / decoder library
*
* Copyright (c) 2014, Hard Consulting Corporation.
*
* Ezpwd Reed-Solomon is free software: you can redistribute it and/or modify it under the terms of
* the GNU General Public License as published by the Free Software Foundation, either version 3 of
* the License, or (at your option) any later version. See the LICENSE file at the top of the
* source tree. Ezpwd Reed-Solomon is also available under Commercial license. The
* c++/ezpwd/rs_base file is redistributed under the terms of the LGPL, regardless of the overall
* licensing terms.
*
* Ezpwd Reed-Solomon 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.
*
* The core Reed-Solomon codec implementation in c++/ezpwd/rs_base is by Phil Karn, converted to C++
* by Perry Kundert (perry@hardconsulting.com), and may be used under the terms of the LGPL. Here
* is the terms from Phil's README file (see phil-karn/fec-3.0.1/README):
*
* COPYRIGHT
*
* This package is copyright 2006 by Phil Karn, KA9Q. It may be used
* under the terms of the GNU Lesser General Public License (LGPL). See
* the file "lesser.txt" in this package for license details.
*
* The c++/ezpwd/rs_base file is, therefore, redistributed under the terms of the LGPL, while the
* rest of Ezpwd Reed-Solomon is distributed under either the GPL or Commercial licenses.
* Therefore, even if you have obtained Ezpwd Reed-Solomon under a Commercial license, you must make
* available the source code of the c++/ezpwd/rs_base file with your product. One simple way to
* accomplish this is to include the following URL in your code or documentation:
*
* https://github.com/pjkundert/ezpwd-reed-solomon/blob/master/c++/ezpwd/rs_base
*
*
* The Linux 3.15.1 version of lib/reed_solomon was also consulted as a cross-reference, which (in
* turn) is basically verbatim copied from Phil Karn's LGPL implementation, to ensure that no new
* defects had been found and fixed; there were no meaningful changes made to Phil's implementation.
* I've personally been using Phil's implementation for years in a heavy industrial use, and it is
* rock-solid.
*
* However, both Phil's and the Linux kernel's (copy of Phil's) implementation will return a
* "corrected" decoding with impossible error positions, in some cases where the error load
* completely overwhelms the R-S encoding. These cases, when detected, are rejected in this
* implementation. This could be considered a defect in Phil's (and hence the Linux kernel's)
* implementations, which results in them accepting clearly incorrect R-S decoded values as valid
* (corrected) R-S codewords. We chose the report failure on these attempts.
*
*/
#ifndef _EZPWD_RS_BASE
#define _EZPWD_RS_BASE
#include <algorithm>
#include <array>
#include <cstdint>
#include <cstring>
#include <iostream>
#include <type_traits>
#include <vector>
//
// Preprocessor defines available:
//
// EZPWD_NO_EXCEPTS -- define to use no exceptions; return -1, or abort on catastrophic failures
// EZPWD_NO_MOD_TAB -- define to force no "modnn" Galois modulo table acceleration
// EZPWD_ARRAY_SAFE -- define to force usage of bounds-checked arrays for most tabular data
// EZPWD_ARRAY_TEST -- define to force erroneous sizing of some arrays for non-production testing
//
#if defined( DEBUG ) && DEBUG >= 2
# include "output" // ezpwd::hex... std::ostream shims for outputting containers of uint8_t data
#endif
#if defined( EZPWD_NO_EXCEPTS )
# include <cstdio> // No exceptions; don't use C++ ostream
# define EZPWD_RAISE_OR_ABORT( typ, str ) do { \
std::fputs(( str ), stderr ); std::fputc( '\n', stderr ); \
abort(); \
} while ( false )
# define EZPWD_RAISE_OR_RETURN( typ, str, ret ) return ( ret )
#else
# define EZPWD_RAISE_OR_ABORT( typ, str ) throw ( typ )( str )
# define EZPWD_RAISE_OR_RETURN( typ, str, ret ) throw ( typ )( str )
#endif
namespace ezpwd {
// ezpwd::log_<N,B> -- compute the log base B of N at compile-time
template <size_t N, size_t B=2> struct log_{ enum { value = 1 + log_<N/B, B>::value }; };
template <size_t B> struct log_<1, B>{ enum { value = 0 }; };
template <size_t B> struct log_<0, B>{ enum { value = 0 }; };
//
// reed_solomon_base - Reed-Solomon codec generic base class
//
class reed_solomon_base {
public:
virtual size_t datum() const = 0; // a data element's bits
virtual size_t symbol() const = 0; // a symbol's bits
virtual int size() const = 0; // R-S block size (maximum total symbols)
virtual int nroots() const = 0; // R-S roots (parity symbols)
virtual int load() const = 0; // R-S net payload (data symbols)
virtual ~reed_solomon_base()
{
;
}
reed_solomon_base()
{
;
}
virtual std::ostream &output(
std::ostream &lhs )
const
{
return lhs << "RS(" << this->size() << "," << this->load() << ")";
}
//
// {en,de}code -- Compute/Correct errors/erasures in a Reed-Solomon encoded container
//
/// The encoded parity symbols may be included in 'data' (len includes nroots() parity
/// symbols), or may (optionally) supplied separately in (at least nroots()-sized)
/// 'parity'.
///
/// For decode, optionally specify some known erasure positions (up to nroots()). If
/// non-empty 'erasures' is provided, it contains the positions of each erasure. If a
/// non-zero pointer to a 'position' vector is provided, its capacity will be increased to
/// be capable of storing up to 'nroots()' ints; the actual deduced error locations will be
/// returned.
///
/// RETURN VALUE
///
/// Return -1 on error. The encode returns the number of parity symbols produced;
/// decode returns the number of symbols corrected. Both errors and erasures are included,
/// so long as they are actually different than the deduced value. In other words, if a
/// symbol is marked as an erasure but it actually turns out to be correct, it's index will
/// NOT be included in the returned count, nor the modified erasure vector!
///
//
// encode(<string>) -- extend string to contain parity, or place in supplied parity string
// encode(<vector>) -- extend vector to contain parity, or place in supplied parity vector
// encode(<array>) -- ignore 'pad' elements of array, puts nroots() parity symbols at end
// encode(pair<iter,iter>) -- encode all except the last nroots() of the data, put parity at end
// encode(pair<iter,iter>, pair<iter,iter>) -- encode data between first <iter> pair, put parity in second pair
//
int encode(
std::string &data )
const
{
typedef uint8_t uT;
typedef std::pair<uT *, uT *>
uTpair;
data.resize( data.size() + nroots() );
return encode( uTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ));
}
int encode(
const std::string &data,
std::string &parity )
const
{
typedef uint8_t uT;
typedef std::pair<const uT *, const uT *>
cuTpair;
typedef std::pair<uT *, uT *>
uTpair;
parity.resize( nroots() );
return encode( cuTpair( (const uT *)&data.front(), (const uT *)&data.front() + data.size() ),
uTpair( (uT *)&parity.front(), (uT *)&parity.front() + parity.size() ));
}
template < typename T >
int encode(
std::vector<T> &data )
const
{
typedef typename std::make_unsigned<T>::type
uT;
typedef std::pair<uT *, uT *>
uTpair;
data.resize( data.size() + nroots() );
return encode( uTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ));
}
template < typename T >
int encode(
const std::vector<T>&data,
std::vector<T> &parity )
const
{
typedef typename std::make_unsigned<T>::type
uT;
typedef std::pair<const uT *, const uT *>
cuTpair;
typedef std::pair<uT *, uT *>
uTpair;
parity.resize( nroots() );
return encode( cuTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ),
uTpair( (uT *)&parity.front(), (uT *)&parity.front() + parity.size() ));
}
template < typename T, size_t N >
int encode(
std::array<T,N> &data,
int pad = 0 ) // ignore 'pad' symbols at start of array
const
{
typedef typename std::make_unsigned<T>::type
uT;
typedef std::pair<uT *, uT *>
uTpair;
return encode( uTpair( (uT *)&data.front() + pad, (uT *)&data.front() + data.size() ));
}
virtual int encode(
const std::pair<uint8_t *, uint8_t *>
&data )
const
= 0;
virtual int encode(
const std::pair<const uint8_t *, const uint8_t *>
&data,
const std::pair<uint8_t *, uint8_t *>
&parity )
const
= 0;
virtual int encode(
const std::pair<uint16_t *, uint16_t *>
&data )
const
= 0;
virtual int encode(
const std::pair<const uint16_t *, const uint16_t *>
&data,
const std::pair<uint16_t *, uint16_t *>
&parity )
const
= 0;
virtual int encode(
const std::pair<uint32_t *, uint32_t *>
&data )
const
= 0;
virtual int encode(
const std::pair<const uint32_t *, const uint32_t *>
&data,
const std::pair<uint32_t *, uint32_t *>
&parity )
const
= 0;
int decode(
std::string &data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
typedef uint8_t uT;
typedef std::pair<uT *, uT *>
uTpair;
return decode( uTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ),
erasure, position );
}
int decode(
std::string &data,
std::string &parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
typedef uint8_t uT;
typedef std::pair<uT *, uT *>
uTpair;
return decode( uTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ),
uTpair( (uT *)&parity.front(), (uT *)&parity.front() + parity.size() ),
erasure, position );
}
template < typename T >
int decode(
std::vector<T> &data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
typedef typename std::make_unsigned<T>::type
uT;
typedef std::pair<uT *, uT *>
uTpair;
return decode( uTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ),
erasure, position );
}
template < typename T >
int decode(
std::vector<T> &data,
std::vector<T> &parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
typedef typename std::make_unsigned<T>::type
uT;
typedef std::pair<uT *, uT *>
uTpair;
return decode( uTpair( (uT *)&data.front(), (uT *)&data.front() + data.size() ),
uTpair( (uT *)&parity.front(), (uT *)&parity.front() + parity.size() ),
erasure, position );
}
template < typename T, size_t N >
int decode(
std::array<T,N> &data,
int pad = 0, // ignore 'pad' symbols at start of array
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
typedef typename std::make_unsigned<T>::type
uT;
typedef std::pair<uT *, uT *>
uTpair;
return decode( uTpair( (uT *)&data.front() + pad, (uT *)&data.front() + data.size() ),
erasure, position );
}
virtual int decode(
const std::pair<uint8_t *, uint8_t *>
&data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
= 0;
virtual int decode(
const std::pair<uint8_t *, uint8_t *>
&data,
const std::pair<uint8_t *, uint8_t *>
&parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
= 0;
virtual int decode(
const std::pair<uint16_t *, uint16_t *>
&data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
= 0;
virtual int decode(
const std::pair<uint16_t *, uint16_t *>
&data,
const std::pair<uint16_t *, uint16_t *>
&parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
= 0;
virtual int decode(
const std::pair<uint32_t *, uint32_t *>
&data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
= 0;
virtual int decode(
const std::pair<uint32_t *, uint32_t *>
&data,
const std::pair<uint32_t *, uint32_t *>
&parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
= 0;
}; // class reed_solomon_base
//
// std::ostream << ezpwd::reed_solomon<...>
//
// Output a R-S codec description in standard form eg. RS(255,253)
//
inline
std::ostream &operator<<(
std::ostream &lhs,
const ezpwd::reed_solomon_base
&rhs )
{
return rhs.output( lhs );
}
//
// gfpoly - default field polynomial generator functor.
//
template < int SYM, int PLY >
struct gfpoly {
int operator() ( int sr )
const
{
if ( sr == 0 )
sr = 1;
else {
sr <<= 1;
if ( sr & ( 1 << SYM ))
sr ^= PLY;
sr &= (( 1 << SYM ) - 1);
}
return sr;
}
};
//
// class reed_solomon_tabs -- R-S tables common to all RS(NN,*) with same SYM, PRM and PLY
//
template < typename TYP, int SYM, int PRM, class PLY >
class reed_solomon_tabs
: public reed_solomon_base {
public:
typedef TYP symbol_t;
static const size_t DATUM = 8 * sizeof TYP(); // bits / TYP
static const size_t SYMBOL = SYM; // bits / symbol
static const int MM = SYM;
static const int SIZE = ( 1 << SYM ) - 1; // maximum symbols in field
static const int NN = SIZE;
static const int A0 = SIZE;
static const int MODS // modulo table: 1/2 the symbol size squared, up to 4k
#if defined( EZPWD_NO_MOD_TAB )
= 0;
#else
= SYM > 8 ? ( 1 << 12 ) : ( 1 << SYM << SYM/2 );
#endif
static int iprim; // initialized to -1, below
protected:
static std::array<TYP,
#if not defined( EZPWD_ARRAY_TEST )
NN + 1>
#else
# warning "EZPWD_ARRAY_TEST: Erroneously declaring alpha_to size!"
NN >
#endif
alpha_to;
static std::array<TYP,NN + 1>
index_of;
static std::array<TYP,MODS>
mod_of;
virtual ~reed_solomon_tabs()
{
;
}
reed_solomon_tabs()
: reed_solomon_base()
{
// Do init if not already done. We check one value which is initialized to -1; this is
// safe, 'cause the value will not be set 'til the initializing thread has completely
// initialized the structure. Worst case scenario: multiple threads will initialize
// identically. No mutex necessary.
if ( iprim >= 0 )
return;
#if defined( DEBUG ) && DEBUG >= 1
std::cout << "RS(" << SIZE << ",*): Initialize for " << NN << " symbols size, " << MODS << " modulo table." << std::endl;
#endif
// Generate Galois field lookup tables
index_of[0] = A0; // log(zero) = -inf
alpha_to[A0] = 0; // alpha**-inf = 0
PLY poly;
int sr = poly( 0 );
for ( int i = 0; i < NN; i++ ) {
index_of[sr] = i;
alpha_to[i] = sr;
sr = poly( sr );
}
// If it's not primitive, raise exception or abort
if ( sr != alpha_to[0] ) {
EZPWD_RAISE_OR_ABORT( std::runtime_error, "reed-solomon: Galois field polynomial not primitive" );
}
// Generate modulo table for some commonly used (non-trivial) values
for ( int x = NN; x < NN + MODS; ++x )
mod_of[x-NN] = _modnn( x );
// Find prim-th root of 1, index form, used in decoding.
int iptmp = 1;
while ( iptmp % PRM != 0 )
iptmp += NN;
iprim = iptmp / PRM;
}
//
// modnn -- modulo replacement for galois field arithmetics, optionally w/ table acceleration
//
// @x: the value to reduce (will never be -'ve)
//
// where
// MM = number of bits per symbol
// NN = (2^MM) - 1
//
// Simple arithmetic modulo would return a wrong result for values >= 3 * NN
//
TYP _modnn(
int x )
const
{
while ( x >= NN ) {
x -= NN;
x = ( x >> MM ) + ( x & NN );
}
return x;
}
TYP modnn(
int x )
const
{
while ( x >= NN + MODS ) {
x -= NN;
x = ( x >> MM ) + ( x & NN );
}
if ( MODS && x >= NN )
x = mod_of[x-NN];
return x;
}
};
//
// class reed_solomon - Reed-Solomon codec
//
// @TYP: A symbol datum; {en,de}code operates on arrays of these
// @DATUM: Bits per datum (a TYP())
// @SYM{BOL}, 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
// @PRM: Primitive element, index form
// @iprim: prim-th root of 1, index form
// @PLY: The primitive generator polynominal functor
//
// All reed_solomon<T, ...> instances with the same template type parameters share a common
// (static) set of alpha_to, index_of and genpoly tables. The first instance to be constructed
// initializes the tables.
//
// Each specialized type of reed_solomon implements a specific encode/decode method
// appropriate to its datum 'TYP'. When accessed via a generic reed_solomon_base pointer, only
// access via "safe" (size specifying) containers or iterators is available.
//
template < typename TYP, int SYM, int RTS, int FCR, int PRM, class PLY >
class reed_solomon
: public reed_solomon_tabs<TYP, SYM, PRM, PLY> {
public:
typedef reed_solomon_tabs<TYP, SYM, PRM, PLY>
tabs_t;
using tabs_t::DATUM;
using tabs_t::SYMBOL;
using tabs_t::MM;
using tabs_t::SIZE;
using tabs_t::NN;
using tabs_t::A0;
using tabs_t::iprim;
using tabs_t::alpha_to;
using tabs_t::index_of;
using tabs_t::modnn;
static const int NROOTS = RTS;
static const int LOAD = SIZE - NROOTS; // maximum non-parity symbol payload
protected:
static std::array<TYP, NROOTS + 1>
genpoly;
public:
virtual size_t datum() const
{
return DATUM;
}
virtual size_t symbol() const
{
return SYMBOL;
}
virtual int size() const
{
return SIZE;
}
virtual int nroots() const
{
return NROOTS;
}
virtual int load() const
{
return LOAD;
}
using reed_solomon_base::encode;
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 );
}
virtual int encode(
const std::pair<const uint8_t *, const uint8_t *>
&data,
const std::pair<uint8_t *, uint8_t *>
&parity )
const
{
if ( parity.second - parity.first != NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1 );
}
return encode_mask( data.first, data.second - data.first, parity.first );
}
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 );
}
virtual int encode(
const std::pair<const uint16_t *, const uint16_t *>
&data,
const std::pair<uint16_t *, uint16_t *>
&parity )
const
{
if ( parity.second - parity.first != NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1 );
}
return encode_mask( data.first, data.second - data.first, parity.first );
}
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 );
}
virtual int encode(
const std::pair<const uint32_t *, const uint32_t *>
&data,
const std::pair<uint32_t *, uint32_t *>
&parity )
const
{
if ( parity.second - parity.first != NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1 );
}
return encode_mask( data.first, data.second - data.first, parity.first );
}
template < typename INP >
int encode_mask(
const INP *data,
int len,
INP *parity ) // pointer to all NROOTS parity symbols
const
{
if ( len < 1 ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: must provide space for all parity and at least one non-parity symbol", -1 );
}
const TYP *dataptr;
TYP *pariptr;
const size_t INPUT = 8 * sizeof ( INP );
if ( DATUM != SYMBOL || DATUM != INPUT ) {
// Our DATUM (TYP) size (eg. uint8_t ==> 8, uint16_t ==> 16, uint32_t ==> 32)
// doesn't exactly match our R-S SYMBOL size (eg. 6), or our INP size; Must mask and
// copy. The INP data must fit at least the SYMBOL size!
if ( SYMBOL > INPUT ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: output data type too small to contain symbols", -1 );
}
std::array<TYP,SIZE> tmp;
TYP msk = static_cast<TYP>( ~0UL << SYMBOL );
for ( int i = 0; i < len; ++i )
tmp[LOAD - len + i] = data[i] & ~msk;
dataptr = &tmp[LOAD - len];
pariptr = &tmp[LOAD];
encode( dataptr, len, pariptr );
// we copied/masked data; copy the parity symbols back (may be different sizes)
for ( int i = 0; i < NROOTS; ++i )
parity[i] = pariptr[i];
} else {
// Our R-S SYMBOL size, DATUM size and INP type size exactly matches; use in-place.
dataptr = reinterpret_cast<const TYP *>( data );
pariptr = reinterpret_cast<TYP *>( parity );
encode( dataptr, len, pariptr );
}
return NROOTS;
}
using reed_solomon_base::decode;
virtual int decode(
const std::pair<uint8_t *, uint8_t *>
&data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
return decode_mask( data.first, data.second - data.first, (uint8_t *)0,
erasure, position );
}
virtual int decode(
const std::pair<uint8_t *, uint8_t *>
&data,
const std::pair<uint8_t *, uint8_t *>
&parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
if ( parity.second - parity.first != NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1 );
}
return decode_mask( data.first, data.second - data.first, parity.first,
erasure, position );
}
virtual int decode(
const std::pair<uint16_t *, uint16_t *>
&data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
return decode_mask( data.first, data.second - data.first, (uint16_t *)0,
erasure, position );
}
virtual int decode(
const std::pair<uint16_t *, uint16_t *>
&data,
const std::pair<uint16_t *, uint16_t *>
&parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
if ( parity.second - parity.first != NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1 );
}
return decode_mask( data.first, data.second - data.first, parity.first,
erasure, position );
}
virtual int decode(
const std::pair<uint32_t *, uint32_t *>
&data,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
return decode_mask( data.first, data.second - data.first, (uint32_t *)0,
erasure, position );
}
virtual int decode(
const std::pair<uint32_t *, uint32_t *>
&data,
const std::pair<uint32_t *, uint32_t *>
&parity,
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
if ( parity.second - parity.first != NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity length incompatible with number of roots", -1 );
}
return decode_mask( data.first, data.second - data.first, parity.first,
erasure, position );
}
//
// decode_mask -- mask INP data into valid SYMBOL data
//
/// Incoming data may be in a variety of sizes, and may contain information beyond the
/// R-S symbol capacity. For example, we might use a 6-bit R-S symbol to correct the lower
/// 6 bits of an 8-bit data character. This would allow us to correct common substitution
/// errors (such as '2' for '3', 'R' for 'T', 'n' for 'm').
///
template < typename INP >
int decode_mask(
INP *data,
int len,
INP *parity = 0, // either 0, or pointer to all parity symbols
const std::vector<int>
&erasure = std::vector<int>(),
std::vector<int> *position= 0 )
const
{
if ( len < ( parity ? 0 : NROOTS ) + 1 ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: must provide all parity and at least one non-parity symbol", -1 );
}
if ( ! parity ) {
len -= NROOTS;
parity = data + len;
}
TYP *dataptr;
TYP *pariptr;
const size_t INPUT = 8 * sizeof ( INP );
std::array<TYP,SIZE> tmp;
TYP msk = static_cast<TYP>( ~0UL << SYMBOL );
const bool cpy = DATUM != SYMBOL || DATUM != INPUT;
if ( cpy ) {
// Our DATUM (TYP) size (eg. uint8_t ==> 8, uint16_t ==> 16, uint32_t ==> 32)
// doesn't exactly match our R-S SYMBOL size (eg. 6), or our INP size; Must copy.
// The INP data must fit at least the SYMBOL size!
if ( SYMBOL > INPUT ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: input data type too small to contain symbols", -1 );
}
for ( int i = 0; i < len; ++i ) {
tmp[LOAD - len + i] = data[i] & ~msk;
}
dataptr = &tmp[LOAD - len];
for ( int i = 0; i < NROOTS; ++i ) {
if ( TYP( parity[i] ) & msk ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: parity data contains information beyond R-S symbol size", -1 );
}
tmp[LOAD + i] = parity[i];
}
pariptr = &tmp[LOAD];
} else {
// Our R-S SYMBOL size, DATUM size and INPUT type sizes exactly matches
dataptr = reinterpret_cast<TYP *>( data );
pariptr = reinterpret_cast<TYP *>( parity );
}
int corrects;
if ( ! erasure.size() && ! position ) {
// No erasures, and error position info not wanted.
corrects = decode( dataptr, len, pariptr );
} else {
// Either erasure location info specified, or resultant error position info wanted;
// Prepare pos (a temporary, if no position vector provided), and copy any provided
// erasure positions. After number of corrections is known, resize the position
// vector. Thus, we use any supplied erasure info, and optionally return any
// correction position info separately.
std::vector<int> _pos;
std::vector<int> &pos = position ? *position : _pos;
pos.resize( std::max( size_t( NROOTS ), erasure.size() ));
std::copy( erasure.begin(), erasure.end(), pos.begin() );
corrects = decode( dataptr, len, pariptr,
&pos.front(), erasure.size() );
if ( corrects > int( pos.size() )) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: FATAL: produced too many corrections; possible corruption!", -1 );
}
pos.resize( std::max( 0, corrects ));
}
if ( cpy && corrects > 0 ) {
for ( int i = 0; i < len; ++i ) {
data[i] &= msk;
data[i] |= tmp[LOAD - len + i];
}
for ( int i = 0; i < NROOTS; ++i ) {
parity[i] = tmp[LOAD + i];
}
}
return corrects;
}
virtual ~reed_solomon()
{
;
}
reed_solomon()
: reed_solomon_tabs<TYP, SYM, PRM, PLY>()
{
// We check one element of the array; this is safe, 'cause the value will not be
// initialized 'til the initializing thread has completely initialized the array. Worst
// case scenario: multiple threads will initialize identically. No mutex necessary.
if ( genpoly[0] )
return;
#if defined( DEBUG ) && DEBUG >= 2
std::cout << "RS(" << SIZE << "," << LOAD << "): Initialize for " << NROOTS << " roots." << std::endl;
#endif
std::array<TYP, NROOTS + 1>
tmppoly; // uninitialized
// Form RS code generator polynomial from its roots. Only lower-index entries are
// consulted, when computing subsequent entries; only index 0 needs initialization.
tmppoly[0] = 1;
for ( int i = 0, root = FCR * PRM; i < NROOTS; i++, root += PRM ) {
tmppoly[i + 1] = 1;
// Multiply tmppoly[] by @**(root + x)
for ( int j = i; j > 0; j-- ) {
if ( tmppoly[j] != 0 )
tmppoly[j] = tmppoly[j - 1]
^ alpha_to[modnn(index_of[tmppoly[j]] + root)];
else
tmppoly[j] = tmppoly[j - 1];
}
// tmppoly[0] can never be zero
tmppoly[0] = alpha_to[modnn(index_of[tmppoly[0]] + root)];
}
// convert NROOTS entries of tmppoly[] to genpoly[] in index form for quicker encoding,
// in reverse order so genpoly[0] is last element initialized.
for ( int i = NROOTS; i >= 0; --i )
genpoly[i] = index_of[tmppoly[i]];
}
int encode(
const TYP *data,
int len,
TYP *parity ) // at least nroots
const
{
// Check length parameter for validity
int pad = NN - NROOTS - len;
if ( pad < 0 || pad >= NN ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: data length incompatible with block size and error correction symbols", -1 );
}
for ( int i = 0; i < NROOTS; i++ )
parity[i] = 0;
for ( int i = 0; i < len; i++ ) {
TYP feedback= index_of[data[i] ^ parity[0]];
if ( feedback != A0 )
for ( int j = 1; j < NROOTS; j++ )
parity[j] ^= alpha_to[modnn(feedback + genpoly[NROOTS - j])];
std::rotate( parity, parity + 1, parity + NROOTS );
if ( feedback != A0 )
parity[NROOTS - 1] = alpha_to[modnn(feedback + genpoly[0])];
else
parity[NROOTS - 1] = 0;
}
#if defined( DEBUG ) && DEBUG >= 2
std::cout << *this << " encode " << std::vector<TYP>( data, data + len )
<< " --> " << std::vector<TYP>( parity, parity + NROOTS ) << std::endl;
#endif
return NROOTS;
}
int decode(
TYP *data,
int len,
TYP *parity, // Requires: at least NROOTS
int *eras_pos= 0, // Capacity: at least NROOTS
int no_eras = 0, // Maximum: at most NROOTS
TYP *corr = 0 ) // Capacity: at least NROOTS
const
{
typedef std::array< TYP, NROOTS >
typ_nroots;
typedef std::array< TYP, NROOTS+1 >
typ_nroots_1;
typedef std::array< int, NROOTS >
int_nroots;
typ_nroots_1 lambda { { 0 } };
typ_nroots syn;
typ_nroots_1 b;
typ_nroots_1 t;
typ_nroots_1 omega;
int_nroots root;
typ_nroots_1 reg;
int_nroots loc;
int count = 0;
// Check length parameter and erasures for validity
int pad = NN - NROOTS - len;
if ( pad < 0 || pad >= NN ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: data length incompatible with block size and error correction symbols", -1 );
}
if ( no_eras ) {
if ( no_eras > NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: number of erasures exceeds capacity (number of roots)", -1 );
}
for ( int i = 0; i < no_eras; ++i ) {
if ( eras_pos[i] < 0 || eras_pos[i] >= len + NROOTS ) {
EZPWD_RAISE_OR_RETURN( std::runtime_error, "reed-solomon: erasure positions outside data+parity", -1 );
}
}
}
// form the syndromes; i.e., evaluate data(x) at roots of g(x)
for ( int i = 0; i < NROOTS; i++ )
syn[i] = data[0];
for ( int j = 1; j < len; j++ ) {
for ( int i = 0; i < NROOTS; i++ ) {
if ( syn[i] == 0 ) {
syn[i] = data[j];
} else {
syn[i] = data[j]
^ alpha_to[modnn(index_of[syn[i]] + ( FCR + i ) * PRM)];
}
}
}
for ( int j = 0; j < NROOTS; j++ ) {
for ( int i = 0; i < NROOTS; i++ ) {
if ( syn[i] == 0 ) {
syn[i] = parity[j];
} else {
syn[i] = parity[j]
^ alpha_to[modnn(index_of[syn[i]] + ( FCR + i ) * PRM)];
}
}
}
// Convert syndromes to index form, checking for nonzero condition
TYP syn_error = 0;
for ( int i = 0; i < NROOTS; i++ ) {
syn_error |= syn[i];
syn[i] = index_of[syn[i]];
}
int deg_lambda = 0;
int deg_omega = 0;
int r = no_eras;
int el = no_eras;
if ( ! syn_error ) {
// if syndrome is zero, data[] is a codeword and there are no errors to correct.
count = 0;
goto finish;
}
lambda[0] = 1;
if ( no_eras > 0 ) {
// Init lambda to be the erasure locator polynomial. Convert erasure positions
// from index into data, to index into Reed-Solomon block.
lambda[1] = alpha_to[modnn(PRM * (NN - 1 - ( eras_pos[0] + pad )))];
for ( int i = 1; i < no_eras; i++ ) {
TYP u = modnn(PRM * (NN - 1 - ( eras_pos[i] + pad )));
for ( int j = i + 1; j > 0; j-- ) {
TYP tmp = index_of[lambda[j - 1]];
if ( tmp != A0 ) {
lambda[j] ^= alpha_to[modnn(u + tmp)];
}
}
}
}
#if DEBUG >= 1
// Test code that verifies the erasure locator polynomial just constructed
// Needed only for decoder debugging.
// find roots of the erasure location polynomial
for( int i = 1; i<= no_eras; i++ )
reg[i] = index_of[lambda[i]];
count = 0;
for ( int i = 1, k = iprim - 1; i <= NN; i++, k = modnn( k + iprim )) {
TYP q = 1;
for ( int j = 1; j <= no_eras; j++ ) {
if ( reg[j] != A0 ) {
reg[j] = modnn( reg[j] + j );
q ^= alpha_to[reg[j]];
}
}
if ( q != 0 )
continue;
// store root and error location number indices
root[count] = i;
loc[count] = k;
count++;
}
if ( count != no_eras ) {
std::cout << "ERROR: count = " << count << ", no_eras = " << no_eras
<< "lambda(x) is WRONG"
<< std::endl;
count = -1;
goto finish;
}
#if DEBUG >= 2
if ( count ) {
std::cout
<< "Erasure positions as determined by roots of Eras Loc Poly: ";
for ( int i = 0; i < count; i++ )
std::cout << loc[i] << ' ';
std::cout << std::endl;
std::cout
<< "Erasure positions as determined by roots of eras_pos array: ";
for ( int i = 0; i < no_eras; i++ )
std::cout << eras_pos[i] << ' ';
std::cout << std::endl;
}
#endif
#endif
for ( int i = 0; i < NROOTS + 1; i++ )
b[i] = index_of[lambda[i]];
//
// Begin Berlekamp-Massey algorithm to determine error+erasure locator polynomial
//
while ( ++r <= NROOTS ) { // r is the step number
// Compute discrepancy at the r-th step in poly-form
TYP discr_r = 0;
for ( int i = 0; i < r; i++ ) {
if (( lambda[i] != 0 ) && ( syn[r - i - 1] != A0 )) {
discr_r ^= alpha_to[modnn(index_of[lambda[i]] + syn[r - i - 1])];
}
}
discr_r = index_of[discr_r]; // Index form
if ( discr_r == A0 ) {
// 2 lines below: B(x) <-- x*B(x)
// Rotate the last element of b[NROOTS+1] to b[0]
std::rotate( b.begin(), b.begin()+NROOTS, b.end() );
b[0] = A0;
} else {
// 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x)
t[0] = lambda[0];
for ( int i = 0; i < NROOTS; i++ ) {
if ( b[i] != A0 ) {
t[i + 1] = lambda[i + 1]
^ alpha_to[modnn(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 ( int i = 0; i <= NROOTS; i++ ) {
b[i] = ((lambda[i] == 0)
? A0
: modnn(index_of[lambda[i]] - discr_r + NN));
}
} else {
// 2 lines below: B(x) <-- x*B(x)
std::rotate( b.begin(), b.begin()+NROOTS, b.end() );
b[0] = A0;
}
lambda = t;
}
}
// Convert lambda to index form and compute deg(lambda(x))
for ( int 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
reg = lambda;
count = 0; // Number of roots of lambda(x)
for ( int i = 1, k = iprim - 1; i <= NN; i++, k = modnn( k + iprim )) {
TYP q = 1; // lambda[0] is always 0
for ( int j = deg_lambda; j > 0; j-- ) {
if ( reg[j] != A0 ) {
reg[j] = modnn( reg[j] + j );
q ^= alpha_to[reg[j]];
}
}
if ( q != 0 )
continue; // Not a root
// store root (index-form) and error location number
#if DEBUG >= 2
std::cout << "count " << count << " root " << i << " loc " << k << std::endl;
#endif
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 ( int i = 0; i <= deg_omega; i++ ) {
TYP tmp = 0;
for ( int j = i; j >= 0; j-- ) {
if (( syn[i - j] != A0 ) && ( lambda[j] != A0 ))
tmp ^= alpha_to[modnn(syn[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 ( int j = count - 1; j >= 0; j-- ) {
TYP num1 = 0;
for ( int i = deg_omega; i >= 0; i-- ) {
if ( omega[i] != A0 )
num1 ^= alpha_to[modnn(omega[i] + i * root[j])];
}
TYP num2 = alpha_to[modnn(root[j] * ( FCR - 1 ) + NN)];
TYP den = 0;
// lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i]
for ( int i = std::min(deg_lambda, NROOTS - 1) & ~1; i >= 0; i -= 2 ) {
if ( lambda[i + 1] != A0 ) {
den ^= alpha_to[modnn(lambda[i + 1] + i * root[j])];
}
}
#if defined( DEBUG ) && DEBUG >= 1
if ( den == 0 ) {
std::cout << "ERROR: denominator = 0" << std::endl;
count = -1;
goto finish;
}
#endif
// Apply error to data. Padding ('pad' unused symbols) begin at index 0.
if ( num1 != 0 ) {
if ( loc[j] < pad ) {
// If the computed error position is in the 'pad' (the unused portion of the
// R-S data capacity), then our solution has failed -- we've computed a
// correction location outside of the data and parity we've been provided!
#if DEBUG >= 2
std::cout
<< "ERROR: RS(" << SIZE <<"," << LOAD
<< ") computed error location: " << loc[j]
<< " within " << pad << " pad symbols, not within "
<< LOAD - pad << " data or " << NROOTS << " parity"
<< std::endl;
#endif
count = -1;
goto finish;
}
TYP cor = alpha_to[modnn(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;
// If a data/parity buffer is given and the error is inside the message or
// parity data, correct it
if ( loc[j] < ( NN - NROOTS )) {
if ( data ) {
data[loc[j] - pad] ^= cor;
}
} else if ( loc[j] < NN ) {
if ( parity )
parity[loc[j] - ( NN - NROOTS )] ^= cor;
}
}
}
finish:
#if defined( DEBUG ) && DEBUG > 0
if ( count > NROOTS )
std::cout << "ERROR: Number of corrections: " << count << " exceeds NROOTS: " << NROOTS << std::endl;
#endif
#if defined( DEBUG ) && DEBUG > 1
std::cout << "data x" << std::setw( 3 ) << len << ": " << std::vector<uint8_t>( data, data + len ) << std::endl;
std::cout << "parity x" << std::setw( 3 ) << NROOTS << ": " << std::string( len * 2, ' ' ) << std::vector<uint8_t>( parity, parity + NROOTS ) << std::endl;
if ( count > 0 ) {
std::string errors( 2 * ( len + NROOTS ), ' ' );
for ( int i = 0; i < count; ++i ) {
errors[2*(loc[i]-pad)+0] = 'E';
errors[2*(loc[i]-pad)+1] = 'E';
}
for ( int i = 0; i < no_eras; ++i ) {
errors[2*(eras_pos[i])+0] = 'e';
errors[2*(eras_pos[i])+1] = 'e';
}
std::cout << "e)ra,E)rr x" << std::setw( 3 ) << count << ": " << errors << std::endl;
}
#endif
if ( eras_pos != NULL ) {
for ( int i = 0; i < count; i++)
eras_pos[i] = loc[i] - pad;
}
return count;
}
}; // class reed_solomon
//
// Define the static reed_solomon...<...> members; allowed in header for template types.
//
// The reed_solomon_tags<...>::iprim < 0 is used to indicate to the first instance that the
// static tables require initialization.
//
template < typename TYP, int SYM, int PRM, class PLY >
int reed_solomon_tabs< TYP, SYM, PRM, PLY >::iprim = -1;
template < typename TYP, int SYM, int PRM, class PLY >
std::array< TYP, reed_solomon_tabs< TYP, SYM, PRM, PLY >
#if not defined( EZPWD_ARRAY_TEST )
::NN + 1 >
#else
# warning "EZPWD_ARRAY_TEST: Erroneously defining alpha_to size!"
::NN >
#endif
reed_solomon_tabs< TYP, SYM, PRM, PLY >::alpha_to;
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;
template < typename TYP, int SYM, int PRM, class PLY >
std::array< TYP, reed_solomon_tabs< TYP, SYM, PRM, PLY >::MODS >
reed_solomon_tabs< TYP, SYM, PRM, PLY >::mod_of;
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;
} // namespace ezpwd
#endif // _EZPWD_RS_BASE
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