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reedsolomon.h
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reedsolomon.h
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// This file is part of par2cmdline (a PAR 2.0 compatible file verification and
// repair tool). See http://parchive.sourceforge.net for details of PAR 2.0.
//
// Copyright (c) 2003 Peter Brian Clements
//
// par2cmdline 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 2 of the License, or
// (at your option) any later version.
//
// par2cmdline 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
#ifndef __REEDSOLOMON_H__
#define __REEDSOLOMON_H__
// The ReedSolomon object is used to calculate and store the matrix
// used during recovery block creation or data block reconstruction.
//
// During initialisation, one RSOutputRow object is created for each
// recovery block that either needs to be created or is available for
// use.
class RSOutputRow
{
public:
RSOutputRow(void) {};
RSOutputRow(bool _present, u16 _exponent) : present(_present), exponent(_exponent) {}
public:
bool present;
u16 exponent;
};
template<class g>
class ReedSolomon
{
public:
typedef g G;
ReedSolomon(void);
~ReedSolomon(void);
// Set which input blocks are present or missing
bool SetInput(const vector<bool> &present); // Some input blocks are present
bool SetInput(u32 count); // All input blocks are present
// Set which output block are available or need to be computed
bool SetOutput(bool present, u16 exponent);
bool SetOutput(bool present, u16 lowexponent, u16 highexponent);
// Compute the RS Matrix
bool Compute(CommandLine::NoiseLevel noiselevel);
// Process a block of data
bool Process(size_t size, // The size of the block of data
u32 inputindex, // The column in the RS matrix
const void *inputbuffer, // Buffer containing input data
u32 outputindex, // The row in the RS matrix
void *outputbuffer); // Buffer containing output data
private:
bool InternalProcess(const g &factor, size_t size, const void *inputbuffer, void *outputbuffer); // Optimization
protected:
// Perform Gaussian Elimination
bool GaussElim(CommandLine::NoiseLevel noiselevel,
unsigned int rows,
unsigned int leftcols,
G *leftmatrix,
G *rightmatrix,
unsigned int datamissing);
protected:
u32 inputcount; // Total number of input blocks
u32 datapresent; // Number of input blocks that are present
u32 datamissing; // Number of input blocks that are missing
u32 *datapresentindex; // The index numbers of the data blocks that are present
u32 *datamissingindex; // The index numbers of the data blocks that are missing
typename G::ValueType *database;// The "base" value to use for each input block
u32 outputcount; // Total number of output blocks
u32 parpresent; // Number of output blocks that are present
u32 parmissing; // Number of output blocks that are missing
u32 *parpresentindex; // The index numbers of the output blocks that are present
u32 *parmissingindex; // The index numbers of the output blocks that are missing
vector<RSOutputRow> outputrows; // Details of the output blocks
G *leftmatrix; // The main matrix
// When the matrices are initialised: values of the form base ^ exponent are
// stored (where the base values are obtained from database[] and the exponent
// values are obtained from outputrows[]).
#ifdef LONGMULTIPLY
GaloisLongMultiplyTable<g> *glmt; // A multiplication table used by Process()
#endif
};
template<class g>
inline ReedSolomon<g>::ReedSolomon(void)
{
inputcount = 0;
datapresent = 0;
datamissing = 0;
datapresentindex = 0;
datamissingindex = 0;
database = 0;
outputrows.empty();
outputcount = 0;
parpresent = 0;
parmissing = 0;
parpresentindex = 0;
parmissingindex = 0;
leftmatrix = 0;
#ifdef LONGMULTIPLY
glmt = new GaloisLongMultiplyTable<g>;
#endif
}
template<class g>
inline ReedSolomon<g>::~ReedSolomon(void)
{
delete [] datapresentindex;
delete [] datamissingindex;
delete [] database;
delete [] parpresentindex;
delete [] parmissingindex;
delete [] leftmatrix;
#ifdef LONGMULTIPLY
delete glmt;
#endif
}
template<class g>
inline bool ReedSolomon<g>::Process(size_t size, u32 inputindex, const void *inputbuffer, u32 outputindex, void *outputbuffer)
{
// Optimization: it occurs frequently the function exits early on, so inline the start.
// This resulted in a speed gain of approx. 8% in repairing.
// Look up the appropriate element in the RS matrix
g factor = leftmatrix[outputindex * (datapresent + datamissing) + inputindex];
// Do nothing if the factor happens to be 0
if (factor == 0)
return eSuccess;
return this->InternalProcess (factor, size, inputbuffer, outputbuffer);
}
u32 gcd(u32 a, u32 b);
// Record whether the recovery block with the specified
// exponent values is present or missing.
template<class g>
inline bool ReedSolomon<g>::SetOutput(bool present, u16 exponent)
{
// Store the exponent and whether or not the recovery block is present or missing
outputrows.push_back(RSOutputRow(present, exponent));
outputcount++;
// Update the counts.
if (present)
{
parpresent++;
}
else
{
parmissing++;
}
return true;
}
// Record whether the recovery blocks with the specified
// range of exponent values are present or missing.
template<class g>
inline bool ReedSolomon<g>::SetOutput(bool present, u16 lowexponent, u16 highexponent)
{
for (unsigned int exponent=lowexponent; exponent<=highexponent; exponent++)
{
if (!SetOutput(present, exponent))
return false;
}
return true;
}
// Construct the Vandermonde matrix and solve it if necessary
template<class g>
inline bool ReedSolomon<g>::Compute(CommandLine::NoiseLevel noiselevel)
{
u32 outcount = datamissing + parmissing;
u32 incount = datapresent + datamissing;
if (datamissing > parpresent)
{
cerr << "Not enough recovery blocks." << endl;
return false;
}
else if (outcount == 0)
{
cerr << "No output blocks." << endl;
return false;
}
if (noiselevel > CommandLine::nlQuiet)
cout << "Computing Reed Solomon matrix." << endl;
/* Layout of RS Matrix:
parpresent
datapresent datamissing datamissing parmissing
/ | \ / | \
parpresent | (ppi[row])| | | (ppi[row])| |
datamissing | ^ | I | | ^ | 0 |
|(dpi[col]) | | |(dmi[col]) | |
+---------------------+-------------+ +---------------------+-----------+
| (pmi[row])| | | (pmi[row])| |
parmissing | ^ | 0 | | ^ | I |
|(dpi[col]) | | |(dmi[col]) | |
\ | / \ | /
*/
// Allocate the left hand matrix
leftmatrix = new G[outcount * incount];
memset(leftmatrix, 0, outcount * incount * sizeof(G));
// Allocate the right hand matrix only if we are recovering
G *rightmatrix = 0;
if (datamissing > 0)
{
rightmatrix = new G[outcount * outcount];
memset(rightmatrix, 0, outcount *outcount * sizeof(G));
}
// Fill in the two matrices:
vector<RSOutputRow>::const_iterator outputrow = outputrows.begin();
// One row for each present recovery block that will be used for a missing data block
for (unsigned int row=0; row<datamissing; row++)
{
// Define MPDL to skip reporting and speed things up
#ifndef MPDL
if (noiselevel > CommandLine::nlQuiet)
{
int progress = row * 1000 / (datamissing+parmissing);
cout << "Constructing: " << progress/10 << '.' << progress%10 << "%\r" << flush;
}
#endif
// Get the exponent of the next present recovery block
while (!outputrow->present)
{
outputrow++;
}
u16 exponent = outputrow->exponent;
// One column for each present data block
for (unsigned int col=0; col<datapresent; col++)
{
leftmatrix[row * incount + col] = G(database[datapresentindex[col]]).pow(exponent);
}
// One column for each each present recovery block that will be used for a missing data block
for (unsigned int col=0; col<datamissing; col++)
{
leftmatrix[row * incount + col + datapresent] = (row == col) ? 1 : 0;
}
if (datamissing > 0)
{
// One column for each missing data block
for (unsigned int col=0; col<datamissing; col++)
{
rightmatrix[row * outcount + col] = G(database[datamissingindex[col]]).pow(exponent);
}
// One column for each missing recovery block
for (unsigned int col=0; col<parmissing; col++)
{
rightmatrix[row * outcount + col + datamissing] = 0;
}
}
outputrow++;
}
// One row for each recovery block being computed
outputrow = outputrows.begin();
for (unsigned int row=0; row<parmissing; row++)
{
// Define MPDL to skip reporting and speed things up
#ifndef MPDL
if (noiselevel > CommandLine::nlQuiet)
{
int progress = (row+datamissing) * 1000 / (datamissing+parmissing);
cout << "Constructing: " << progress/10 << '.' << progress%10 << "%\r" << flush;
}
#endif
// Get the exponent of the next missing recovery block
while (outputrow->present)
{
outputrow++;
}
u16 exponent = outputrow->exponent;
// One column for each present data block
for (unsigned int col=0; col<datapresent; col++)
{
leftmatrix[(row+datamissing) * incount + col] = G(database[datapresentindex[col]]).pow(exponent);
}
// One column for each each present recovery block that will be used for a missing data block
for (unsigned int col=0; col<datamissing; col++)
{
leftmatrix[(row+datamissing) * incount + col + datapresent] = 0;
}
if (datamissing > 0)
{
// One column for each missing data block
for (unsigned int col=0; col<datamissing; col++)
{
rightmatrix[(row+datamissing) * outcount + col] = G(database[datamissingindex[col]]).pow(exponent);
}
// One column for each missing recovery block
for (unsigned int col=0; col<parmissing; col++)
{
rightmatrix[(row+datamissing) * outcount + col + datamissing] = (row == col) ? 1 : 0;
}
}
outputrow++;
}
if (noiselevel > CommandLine::nlQuiet)
cout << "Constructing: done." << endl;
// Solve the matrices only if recovering data
if (datamissing > 0)
{
// Perform Gaussian Elimination and then delete the right matrix (which
// will no longer be required).
bool success = GaussElim(noiselevel, outcount, incount, leftmatrix, rightmatrix, datamissing);
delete [] rightmatrix;
return success;
}
return true;
}
// Use Gaussian Elimination to solve the matrices
template<class g>
inline bool ReedSolomon<g>::GaussElim(CommandLine::NoiseLevel noiselevel, unsigned int rows, unsigned int leftcols, G *leftmatrix, G *rightmatrix, unsigned int datamissing)
{
if (noiselevel == CommandLine::nlDebug)
{
for (unsigned int row=0; row<rows; row++)
{
cout << ((row==0) ? "/" : (row==rows-1) ? "\\" : "|");
for (unsigned int col=0; col<leftcols; col++)
{
cout << " "
<< hex << setw(G::Bits>8?4:2) << setfill('0')
<< (unsigned int)leftmatrix[row*leftcols+col];
}
cout << ((row==0) ? " \\ /" : (row==rows-1) ? " / \\" : " | |");
for (unsigned int col=0; col<rows; col++)
{
cout << " "
<< hex << setw(G::Bits>8?4:2) << setfill('0')
<< (unsigned int)rightmatrix[row*rows+col];
}
cout << ((row==0) ? " \\" : (row==rows-1) ? " /" : " | |");
cout << endl;
cout << dec << setw(0) << setfill(' ');
}
}
// Because the matrices being operated on are Vandermonde matrices
// they are guaranteed not to be singular.
// Additionally, because Galois arithmetic is being used, all calulations
// involve exact values with no loss of precision. It is therefore
// not necessary to carry out any row or column swapping.
// Solve one row at a time
int progress = 0;
// For each row in the matrix
for (unsigned int row=0; row<datamissing; row++)
{
// NB Row and column swapping to find a non zero pivot value or to find the largest value
// is not necessary due to the nature of the arithmetic and construction of the RS matrix.
// Get the pivot value.
G pivotvalue = rightmatrix[row * rows + row];
assert(pivotvalue != 0);
if (pivotvalue == 0)
{
cerr << "RS computation error." << endl;
return false;
}
// If the pivot value is not 1, then the whole row has to be scaled
if (pivotvalue != 1)
{
for (unsigned int col=0; col<leftcols; col++)
{
if (leftmatrix[row * leftcols + col] != 0)
{
leftmatrix[row * leftcols + col] /= pivotvalue;
}
}
rightmatrix[row * rows + row] = 1;
for (unsigned int col=row+1; col<rows; col++)
{
if (rightmatrix[row * rows + col] != 0)
{
rightmatrix[row * rows + col] /= pivotvalue;
}
}
}
// For every other row in the matrix
for (unsigned int row2=0; row2<rows; row2++)
{
// Define MPDL to skip reporting and speed things up
#ifndef MPDL
if (noiselevel > CommandLine::nlQuiet)
{
int newprogress = (row*rows+row2) * 1000 / (datamissing*rows);
if (progress != newprogress)
{
progress = newprogress;
cout << "Solving: " << progress/10 << '.' << progress%10 << "%\r" << flush;
}
}
#endif
if (row != row2)
{
// Get the scaling factor for this row.
G scalevalue = rightmatrix[row2 * rows + row];
if (scalevalue == 1)
{
// If the scaling factor happens to be 1, just subtract rows
for (unsigned int col=0; col<leftcols; col++)
{
if (leftmatrix[row * leftcols + col] != 0)
{
leftmatrix[row2 * leftcols + col] -= leftmatrix[row * leftcols + col];
}
}
for (unsigned int col=row; col<rows; col++)
{
if (rightmatrix[row * rows + col] != 0)
{
rightmatrix[row2 * rows + col] -= rightmatrix[row * rows + col];
}
}
}
else if (scalevalue != 0)
{
// If the scaling factor is not 0, then compute accordingly.
for (unsigned int col=0; col<leftcols; col++)
{
if (leftmatrix[row * leftcols + col] != 0)
{
leftmatrix[row2 * leftcols + col] -= leftmatrix[row * leftcols + col] * scalevalue;
}
}
for (unsigned int col=row; col<rows; col++)
{
if (rightmatrix[row * rows + col] != 0)
{
rightmatrix[row2 * rows + col] -= rightmatrix[row * rows + col] * scalevalue;
}
}
}
}
}
}
if (noiselevel > CommandLine::nlQuiet)
cout << "Solving: done." << endl;
if (noiselevel == CommandLine::nlDebug)
{
for (unsigned int row=0; row<rows; row++)
{
cout << ((row==0) ? "/" : (row==rows-1) ? "\\" : "|");
for (unsigned int col=0; col<leftcols; col++)
{
cout << " "
<< hex << setw(G::Bits>8?4:2) << setfill('0')
<< (unsigned int)leftmatrix[row*leftcols+col];
}
cout << ((row==0) ? " \\ /" : (row==rows-1) ? " / \\" : " | |");
for (unsigned int col=0; col<rows; col++)
{
cout << " "
<< hex << setw(G::Bits>8?4:2) << setfill('0')
<< (unsigned int)rightmatrix[row*rows+col];
}
cout << ((row==0) ? " \\" : (row==rows-1) ? " /" : " | |");
cout << endl;
cout << dec << setw(0) << setfill(' ');
}
}
return true;
}
#endif // __REEDSOLOMON_H__