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