420 lines
13 KiB
C++
420 lines
13 KiB
C++
#include "rar.hpp"
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// We used "Screaming Fast Galois Field Arithmetic Using Intel SIMD
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// Instructions" paper by James S. Plank, Kevin M. Greenan
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// and Ethan L. Miller for fast SSE based multiplication.
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// Also we are grateful to Artem Drobanov and Bulat Ziganshin
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// for samples and ideas allowed to make Reed-Solomon codec more efficient.
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RSCoder16::RSCoder16()
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{
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Decoding=false;
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ND=NR=NE=0;
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ValidFlags=NULL;
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MX=NULL;
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DataLog=NULL;
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DataLogSize=0;
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gfInit();
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}
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RSCoder16::~RSCoder16()
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{
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delete[] gfExp;
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delete[] gfLog;
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delete[] DataLog;
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delete[] MX;
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delete[] ValidFlags;
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}
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// Initialize logarithms and exponents Galois field tables.
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void RSCoder16::gfInit()
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{
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gfExp=new uint[4*gfSize+1];
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gfLog=new uint[gfSize+1];
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for (uint L=0,E=1;L<gfSize;L++)
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{
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gfLog[E]=L;
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gfExp[L]=E;
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gfExp[L+gfSize]=E; // Duplicate the table to avoid gfExp overflow check.
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E<<=1;
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if (E>gfSize)
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E^=0x1100B; // Irreducible field-generator polynomial.
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}
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// log(0)+log(x) must be outside of usual log table, so we can set it
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// to 0 and avoid check for 0 in multiplication parameters.
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gfLog[0]= 2*gfSize;
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for (uint I=2*gfSize;I<=4*gfSize;I++) // Results for log(0)+log(x).
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gfExp[I]=0;
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}
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uint RSCoder16::gfAdd(uint a,uint b) // Addition in Galois field.
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{
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return a^b;
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}
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uint RSCoder16::gfMul(uint a,uint b) // Multiplication in Galois field.
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{
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return gfExp[gfLog[a]+gfLog[b]];
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}
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uint RSCoder16::gfInv(uint a) // Inverse element in Galois field.
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{
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return a==0 ? 0:gfExp[gfSize-gfLog[a]];
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}
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bool RSCoder16::Init(uint DataCount, uint RecCount, bool *ValidityFlags)
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{
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ND = DataCount;
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NR = RecCount;
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NE = 0;
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Decoding=ValidityFlags!=NULL;
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if (Decoding)
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{
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delete[] ValidFlags;
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ValidFlags=new bool[ND + NR];
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for (uint I = 0; I < ND + NR; I++)
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ValidFlags[I]=ValidityFlags[I];
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for (uint I = 0; I < ND; I++)
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if (!ValidFlags[I])
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NE++;
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uint ValidECC=0;
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for (uint I = ND; I < ND + NR; I++)
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if (ValidFlags[I])
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ValidECC++;
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if (NE > ValidECC || NE == 0 || ValidECC == 0)
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return false;
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}
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if (ND + NR > gfSize || NR > ND || ND == 0 || NR == 0)
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return false;
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delete[] MX;
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if (Decoding)
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{
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MX=new uint[NE * ND];
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MakeDecoderMatrix();
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InvertDecoderMatrix();
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}
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else
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{
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MX=new uint[NR * ND];
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MakeEncoderMatrix();
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}
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return true;
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}
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void RSCoder16::MakeEncoderMatrix()
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{
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// Create Cauchy encoder generator matrix. Skip trivial "1" diagonal rows,
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// which would just copy source data to destination.
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for (uint I = 0; I < NR; I++)
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for (uint J = 0; J < ND; J++)
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MX[I * ND + J] = gfInv( gfAdd( (I+ND), J) );
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}
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void RSCoder16::MakeDecoderMatrix()
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{
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// Create Cauchy decoder matrix. Skip trivial rows matching valid data
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// units and containing "1" on main diagonal. Such rows would just copy
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// source data to destination and they have no real value for us.
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// Include rows only for broken data units and replace them by first
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// available valid recovery code rows.
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for (uint Flag=0, R=ND, Dest=0; Flag < ND; Flag++)
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if (!ValidFlags[Flag]) // For every broken data unit.
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{
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while (!ValidFlags[R]) // Find a valid recovery unit.
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R++;
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for (uint J = 0; J < ND; J++) // And place its row to matrix.
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MX[Dest*ND + J] = gfInv( gfAdd(R,J) );
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Dest++;
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R++;
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}
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}
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// Apply Gauss<73>Jordan elimination to find inverse of decoder matrix.
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// We have the square NDxND matrix, but we do not store its trivial
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// diagonal "1" rows matching valid data, so we work with NExND matrix.
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// Our original Cauchy matrix does not contain 0, so we skip search
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// for non-zero pivot.
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void RSCoder16::InvertDecoderMatrix()
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{
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uint *MI=new uint[NE * ND]; // We'll create inverse matrix here.
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memset(MI, 0, ND * NE * sizeof(*MI)); // Initialize to identity matrix.
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for (uint Kr = 0, Kf = 0; Kr < NE; Kr++, Kf++)
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{
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while (ValidFlags[Kf]) // Skip trivial rows.
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Kf++;
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MI[Kr * ND + Kf] = 1; // Set diagonal 1.
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}
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// Kr is the number of row in our actual reduced NE x ND matrix,
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// which does not contain trivial diagonal 1 rows.
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// Kf is the number of row in full ND x ND matrix with all trivial rows
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// included.
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for (uint Kr = 0, Kf = 0; Kf < ND; Kr++, Kf++) // Select pivot row.
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{
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while (ValidFlags[Kf] && Kf < ND)
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{
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// Here we process trivial diagonal 1 rows matching valid data units.
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// Their processing can be simplified comparing to usual rows.
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// In full version of elimination we would set MX[I * ND + Kf] to zero
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// after MI[..]^=, but we do not need it for matrix inversion.
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for (uint I = 0; I < NE; I++)
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MI[I * ND + Kf] ^= MX[I * ND + Kf];
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Kf++;
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}
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if (Kf == ND)
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break;
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uint *MXk = MX + Kr * ND; // k-th row of main matrix.
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uint *MIk = MI + Kr * ND; // k-th row of inversion matrix.
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uint PInv = gfInv( MXk[Kf] ); // Pivot inverse.
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// Divide the pivot row by pivot, so pivot cell contains 1.
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for (uint I = 0; I < ND; I++)
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{
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MXk[I] = gfMul( MXk[I], PInv );
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MIk[I] = gfMul( MIk[I], PInv );
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}
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for (uint I = 0; I < NE; I++)
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if (I != Kr) // For all rows except containing the pivot cell.
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{
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// Apply Gaussian elimination Mij -= Mkj * Mik / pivot.
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// Since pivot is already 1, it is reduced to Mij -= Mkj * Mik.
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uint *MXi = MX + I * ND; // i-th row of main matrix.
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uint *MIi = MI + I * ND; // i-th row of inversion matrix.
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uint Mik = MXi[Kf]; // Cell in pivot position.
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for (uint J = 0; J < ND; J++)
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{
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MXi[J] ^= gfMul(MXk[J] , Mik);
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MIi[J] ^= gfMul(MIk[J] , Mik);
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}
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}
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}
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// Copy data to main matrix.
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for (uint I = 0; I < NE * ND; I++)
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MX[I] = MI[I];
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delete[] MI;
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}
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#if 0
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// Multiply matrix to data vector. When encoding, it contains data in Data
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// and stores error correction codes in Out. When decoding it contains
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// broken data followed by ECC in Data and stores recovered data to Out.
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// We do not use this function now, everything is moved to UpdateECC.
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void RSCoder16::Process(const uint *Data, uint *Out)
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{
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uint ProcData[gfSize];
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for (uint I = 0; I < ND; I++)
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ProcData[I]=Data[I];
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if (Decoding)
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{
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// Replace broken data units with first available valid recovery codes.
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// 'Data' array must contain recovery codes after data.
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for (uint I=0, R=ND, Dest=0; I < ND; I++)
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if (!ValidFlags[I]) // For every broken data unit.
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{
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while (!ValidFlags[R]) // Find a valid recovery unit.
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R++;
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ProcData[I]=Data[R];
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R++;
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}
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}
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uint H=Decoding ? NE : NR;
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for (uint I = 0; I < H; I++)
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{
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uint R = 0; // Result of matrix row multiplication to data.
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uint *MXi=MX + I * ND;
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for (uint J = 0; J < ND; J++)
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R ^= gfMul(MXi[J], ProcData[J]);
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Out[I] = R;
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}
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}
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#endif
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// We update ECC in blocks by applying every data block to all ECC blocks.
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// This function applies one data block to one ECC block.
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void RSCoder16::UpdateECC(uint DataNum, uint ECCNum, const byte *Data, byte *ECC, size_t BlockSize)
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{
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if (DataNum==0) // Init ECC data.
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memset(ECC, 0, BlockSize);
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bool DirectAccess;
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#ifdef LITTLE_ENDIAN
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// We can access data and ECC directly if we have little endian 16 bit uint.
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DirectAccess=sizeof(ushort)==2;
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#else
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DirectAccess=false;
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#endif
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#ifdef USE_SSE
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if (DirectAccess && SSE_UpdateECC(DataNum,ECCNum,Data,ECC,BlockSize))
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return;
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#endif
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if (ECCNum==0)
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{
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if (DataLogSize!=BlockSize)
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{
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delete[] DataLog;
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DataLog=new uint[BlockSize];
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DataLogSize=BlockSize;
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}
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if (DirectAccess)
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for (size_t I=0; I<BlockSize; I+=2)
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DataLog[I] = gfLog[ *(ushort*)(Data+I) ];
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else
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for (size_t I=0; I<BlockSize; I+=2)
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{
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uint D=Data[I]+Data[I+1]*256;
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DataLog[I] = gfLog[ D ];
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}
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}
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uint ML = gfLog[ MX[ECCNum * ND + DataNum] ];
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if (DirectAccess)
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for (size_t I=0; I<BlockSize; I+=2)
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*(ushort*)(ECC+I) ^= gfExp[ ML + DataLog[I] ];
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else
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for (size_t I=0; I<BlockSize; I+=2)
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{
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uint R=gfExp[ ML + DataLog[I] ];
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ECC[I]^=byte(R);
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ECC[I+1]^=byte(R/256);
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}
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}
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#ifdef USE_SSE
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// Data and ECC addresses must be properly aligned for SSE.
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// AVX2 did not provide a noticeable speed gain on i7-6700K here.
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bool RSCoder16::SSE_UpdateECC(uint DataNum, uint ECCNum, const byte *Data, byte *ECC, size_t BlockSize)
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{
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// Check data alignment and SSSE3 support.
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if ((size_t(Data) & (SSE_ALIGNMENT-1))!=0 || (size_t(ECC) & (SSE_ALIGNMENT-1))!=0 ||
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_SSE_Version<SSE_SSSE3)
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return false;
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uint M=MX[ECCNum * ND + DataNum];
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// Prepare tables containing products of M and 4, 8, 12, 16 bit length
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// numbers, which have 4 high bits in 0..15 range and other bits set to 0.
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// Store high and low bytes of resulting 16 bit product in separate tables.
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__m128i T0L,T1L,T2L,T3L; // Low byte tables.
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__m128i T0H,T1H,T2H,T3H; // High byte tables.
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for (uint I=0;I<16;I++)
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{
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((byte *)&T0L)[I]=gfMul(I,M);
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((byte *)&T0H)[I]=gfMul(I,M)>>8;
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((byte *)&T1L)[I]=gfMul(I<<4,M);
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((byte *)&T1H)[I]=gfMul(I<<4,M)>>8;
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((byte *)&T2L)[I]=gfMul(I<<8,M);
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((byte *)&T2H)[I]=gfMul(I<<8,M)>>8;
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((byte *)&T3L)[I]=gfMul(I<<12,M);
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((byte *)&T3H)[I]=gfMul(I<<12,M)>>8;
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}
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size_t Pos=0;
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__m128i LowByteMask=_mm_set1_epi16(0xff); // 00ff00ff...00ff
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__m128i Low4Mask=_mm_set1_epi8(0xf); // 0f0f0f0f...0f0f
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__m128i High4Mask=_mm_slli_epi16(Low4Mask,4); // f0f0f0f0...f0f0
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for (; Pos+2*sizeof(__m128i)<=BlockSize; Pos+=2*sizeof(__m128i))
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{
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// We process two 128 bit chunks of source data at once.
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__m128i *D=(__m128i *)(Data+Pos);
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// Place high bytes of both chunks to one variable and low bytes to
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// another, so we can use the table lookup multiplication for 16 values
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// 4 bit length each at once.
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__m128i HighBytes0=_mm_srli_epi16(D[0],8);
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__m128i LowBytes0=_mm_and_si128(D[0],LowByteMask);
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__m128i HighBytes1=_mm_srli_epi16(D[1],8);
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__m128i LowBytes1=_mm_and_si128(D[1],LowByteMask);
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__m128i HighBytes=_mm_packus_epi16(HighBytes0,HighBytes1);
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__m128i LowBytes=_mm_packus_epi16(LowBytes0,LowBytes1);
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// Multiply bits 0..3 of low bytes. Store low and high product bytes
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// separately in cumulative sum variables.
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__m128i LowBytesLow4=_mm_and_si128(LowBytes,Low4Mask);
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__m128i LowBytesMultSum=_mm_shuffle_epi8(T0L,LowBytesLow4);
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__m128i HighBytesMultSum=_mm_shuffle_epi8(T0H,LowBytesLow4);
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// Multiply bits 4..7 of low bytes. Store low and high product bytes separately.
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__m128i LowBytesHigh4=_mm_and_si128(LowBytes,High4Mask);
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LowBytesHigh4=_mm_srli_epi16(LowBytesHigh4,4);
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__m128i LowBytesHigh4MultLow=_mm_shuffle_epi8(T1L,LowBytesHigh4);
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__m128i LowBytesHigh4MultHigh=_mm_shuffle_epi8(T1H,LowBytesHigh4);
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// Add new product to existing sum, low and high bytes separately.
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LowBytesMultSum=_mm_xor_si128(LowBytesMultSum,LowBytesHigh4MultLow);
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HighBytesMultSum=_mm_xor_si128(HighBytesMultSum,LowBytesHigh4MultHigh);
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// Multiply bits 0..3 of high bytes. Store low and high product bytes separately.
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__m128i HighBytesLow4=_mm_and_si128(HighBytes,Low4Mask);
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__m128i HighBytesLow4MultLow=_mm_shuffle_epi8(T2L,HighBytesLow4);
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__m128i HighBytesLow4MultHigh=_mm_shuffle_epi8(T2H,HighBytesLow4);
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// Add new product to existing sum, low and high bytes separately.
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LowBytesMultSum=_mm_xor_si128(LowBytesMultSum,HighBytesLow4MultLow);
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HighBytesMultSum=_mm_xor_si128(HighBytesMultSum,HighBytesLow4MultHigh);
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// Multiply bits 4..7 of high bytes. Store low and high product bytes separately.
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__m128i HighBytesHigh4=_mm_and_si128(HighBytes,High4Mask);
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HighBytesHigh4=_mm_srli_epi16(HighBytesHigh4,4);
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__m128i HighBytesHigh4MultLow=_mm_shuffle_epi8(T3L,HighBytesHigh4);
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__m128i HighBytesHigh4MultHigh=_mm_shuffle_epi8(T3H,HighBytesHigh4);
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// Add new product to existing sum, low and high bytes separately.
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LowBytesMultSum=_mm_xor_si128(LowBytesMultSum,HighBytesHigh4MultLow);
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HighBytesMultSum=_mm_xor_si128(HighBytesMultSum,HighBytesHigh4MultHigh);
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// Combine separate low and high cumulative sum bytes to 16-bit words.
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__m128i HighBytesHigh4Mult0=_mm_unpacklo_epi8(LowBytesMultSum,HighBytesMultSum);
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__m128i HighBytesHigh4Mult1=_mm_unpackhi_epi8(LowBytesMultSum,HighBytesMultSum);
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// Add result to ECC.
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__m128i *StoreECC=(__m128i *)(ECC+Pos);
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StoreECC[0]=_mm_xor_si128(StoreECC[0],HighBytesHigh4Mult0);
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StoreECC[1]=_mm_xor_si128(StoreECC[1],HighBytesHigh4Mult1);
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}
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// If we have non 128 bit aligned data in the end of block, process them
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// in a usual way. We cannot do the same in the beginning of block,
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// because Data and ECC can have different alignment offsets.
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for (; Pos<BlockSize; Pos+=2)
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*(ushort*)(ECC+Pos) ^= gfMul( M, *(ushort*)(Data+Pos) );
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return true;
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}
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#endif
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