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BlockedMult.pas
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BlockedMult.pas
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// ###################################################################
// #### This file is part of the mathematics library project, and is
// #### offered under the licence agreement described on
// #### http://www.mrsoft.org/
// ####
// #### Copyright:(c) 2017, Michael R. . All rights reserved.
// ####
// #### Unless required by applicable law or agreed to in writing, software
// #### distributed under the License is distributed on an "AS IS" BASIS,
// #### WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// #### See the License for the specific language governing permissions and
// #### limitations under the License.
// ###################################################################
unit BlockedMult;
interface
{$IFDEF FPC} {$MODESWITCH ADVANCEDRECORDS} {$ENDIF}
uses MatrixConst;
// ###################################################################
// #### Generic blocked multiplication routines
// blocked matrix mult + strassen multiplication functions
procedure GenericBlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble;
width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation = doNone; mem : PDouble = nil);
// calculates dest = mt1'*mt2
procedure GenericBlockMatrixMultiplicationT1(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
// calculates dest = mt1*mt2'
procedure GenericBlockMatrixMultiplicationT2(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
// this routine first performs a transposition on the second matrix before the multiplication is executed. This results
// normaly in quite a boost.
procedure BlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; op : TMatrixMultDestOperation = doNone); overload;
procedure BlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation = doNone; mem : PDouble = nil); overload;
// calculates dest = mt1'*mt2
procedure BlockMatrixMultiplicationT1(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
// calculates dest = mt1*mt2'
procedure BlockMatrixMultiplicationT2(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
// this is a blockwise matrix multiplication routine which takes a limited cache into account.
// The routine tries to tile the matrix into 256x256 blocks (which seems to be a good approximation
// for a Core2 processor) which fits into the Level1 cache thus reduces
// cache misses.
procedure BlockMatrixMultiplicationDirect(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; op : TMatrixMultDestOperation = doNone); overload;
procedure BlockMatrixMultiplicationDirect(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation = doNone); overload;
procedure BlockMatrixVectorMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; height2 : NativeInt; const LineWidth1 : NativeInt); overload;
procedure BlockMatrixVectorMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; height2 : NativeInt; const LineWidth1 : NativeInt; blockSize : NativeInt); overload;
// ################################################################
// #### Threaded versions
function UseInnerBlockMult( w, h : NativeInt) : boolean;
// calculates dest = mt1*mt2'
procedure ThrBlockMatrixMultiplicationT2(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
procedure ThrBlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; op : TMatrixMultDestOperation = doNone); overload;
procedure ThrBlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation = doNone; mem : PDouble = nil); overload;
implementation
uses BlockSizeSetup, SimpleMatrixOperations, MatrixASMStubSwitch, Math,
{$IFDEF MSWINDOWS}
Windows,
{$ENDIF}
MtxThreadPool, ThreadedMatrixOperations, MathUtilFunc;
{$I 'mrMath_CPU.inc'}
{$IFNDEF MRMATH_NOASM}
procedure YieldProcessor; {$IFDEF FPC} assembler; {$ENDIF}
asm
PAUSE;
end;
procedure MemoryBarrier; {$IFDEF FPC} assembler; {$ENDIF}
{$IFDEF x64}
asm
push rax;
XCHG [rsp],rax;
POP rax;
end;
{$ELSE}
asm
push eax;
XCHG [esp],eax;
POP eax;
end;
{$ENDIF}
{$ELSE}
// MRMATH_NOASM for FPC - need to be adjusted for non x86 cores
procedure YieldProcessor;
begin
{$IFDEF MSWINDOWS}
SwitchToThread;
{$ENDIF}
// todo other platforms
end;
procedure MemoryBarrier;
begin
// todo: MemoryBarrier is only availabel as macro in winnt.h not in windows.pas
end;
{$ENDIF}
procedure BlockMatrixVectorMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; height2 : NativeInt; const LineWidth1 : NativeInt); overload;
begin
BlockMatrixVectorMultiplication(dest, destLineWidth, mt1, mt2, width1, height1, height2, LineWidth1, BlockedVectorMatrixMultSize);
end;
procedure BlockMatrixVectorMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; height2 : NativeInt; const LineWidth1 : NativeInt; blockSize : NativeInt); overload;
var h : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pActBlk : PDouble;
pHelp : PDouble;
w1FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkHeight : NativeInt;
gammaWidth : NativeInt;
ptrMem : Pointer;
begin
if (width1 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((width1 = height2), 'Dimension error');
assert((LineWidth1 >= width1*sizeof(double)), 'Line widths do not match');
assert(BlockSize > 1, 'Error block size must be at least 2');
h1FitCacheSize := (height1 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
h := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
gamma := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
actBlk := MtxMallocAlign(2*blockSize*sizeof(double), ptrMem );
multBlk := actBlk;
inc(multBlk, blockSize);
blkHeight := blockSize;
for blkIdxY := 0 to h do
begin
if (blkIdxY = h) and not h1FitCacheSize then
blkHeight := (height1 mod blockSize);
FillChar(actBlk^, blockSize*sizeof(double), 0);
pa := mt1;
pb := mt2;
gammaWidth := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not w1FitCacheSize then
gammaWidth := width1 mod blockSize;
if gammaWidth > 1
then
MatrixMult(multBlk, sizeof(double), pa, pb, gammaWidth, blkHeight, 1, gammaWidth, LineWidth1, sizeof(double))
else
GenericMtxMult(multBlk, sizeof(double), pa, pb, gammaWidth, blkHeight, 1, gammaWidth, LineWidth1, sizeof(double));
// treat the addition as vector add:
if blkHeight > 1
then
MatrixAdd(actBlk, sizeof(double), actBlk, multBlk, blkHeight, 1, sizeof(double), sizeof(double))
else
// intersting: the normal matrix addition is a bit faster (or just a tiny bit slower) than the asm version in this case!
GenericMtxAdd(actBlk, sizeof(double), actBlk, multBlk, 1, blkHeight, sizeof(double), sizeof(double));
inc(pa, gammaWidth);
inc(pb, gammaWidth);
end;
pHelp := Dest;
pActBlk := actBlk;
for idx := 0 to blkHeight - 1 do
begin
pHelp^ := pActBlk^;
inc(PByte(pHelp), destLineWidth);
inc(pActBlk);
end;
inc(PByte(mt1), blkHeight*LineWidth1);
inc(PByte(Dest), blkHeight*destLineWidth);
end;
FreeMem(ptrMem);
end;
procedure BlockMatrixMultiplicationDirect(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; op : TMatrixMultDestOperation);
begin
BlockMatrixMultiplicationDirect(dest, destLineWidth, mt1, mt2, width1, height1, width2, height2, LineWidth1, LineWidth2, BlockMatrixCacheSize, op);
end;
procedure BlockMatrixMultiplicationDirect(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation);
var w, h : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
w2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkHeight : NativeInt;
blkWidth : NativeInt;
gammaWidth : NativeInt;
sizeVal : NativeInt;
m1, m2 : Pointer;
blockByteSize : NativeInt;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((width1 = height2), 'Dimension error');
assert((destLineWidth - Width2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
// estimate a good blocksize - one with a small number of zero columns (but as near as possible to cCacheMtxSize
if blockSize <= 0 then
begin
sizeVal := Max(width1, width2);
while sizeVal > cCacheMtxSize do
sizeVal := sizeVal shr 1;
blockSize := Min(Max(width1, width2), Max(64, sizeVal));
end;
h1FitCacheSize := (height1 mod blockSize) = 0;
w2FitCacheSize := (width2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
h := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
w := width2 div blockSize + NativeInt(not w2FitCacheSize) - 1;
gamma := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
blockByteSize := blockSize*blockSize*sizeof(double);
actBlk := MtxMallocAlign(blockByteSize, m1);
multBlk := MtxMallocAlign(blockByteSize, m2);
blkHeight := blockSize;
for blkIdxY := 0 to h do
begin
if (blkIdxY = h) and not h1FitCacheSize then
blkHeight := (height1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkWidth := blockSize;
for blkIdxX := 0 to w do
begin
if (blkIdxX = w) and not w2FitCacheSize then
blkWidth := (width2 mod blockSize);
MtxMemInit(actBlk, blockByteSize, 0 );
pa := mt1;
pb := pMt2;
gammaWidth := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not w1FitCacheSize then
gammaWidth := width1 mod blockSize;
if blkWidth > 1 then
begin
MatrixMult(multBlk, blockSize*sizeof(double), pa, pb, gammaWidth, blkHeight, blkWidth, gammaWidth, LineWidth1, LineWidth2);
MatrixAdd(actBlk, blockSize*sizeof(double), actBlk, multBlk, blkWidth, blkHeight, blockSize*sizeof(double), blockSize*sizeof(double));
end
else
begin
GenericMtxMult(multBlk, blockSize*sizeof(double), pa, pb, gammaWidth, blkHeight, blkWidth, gammaWidth, LineWidth1, LineWidth2);
GenericMtxAdd(actBlk, blockSize*sizeof(double), actBlk, multBlk, blkWidth, blkHeight, blockSize*sizeof(double), blockSize*sizeof(double));
end;
inc(pa, gammaWidth);
inc(PByte(pb), gammaWidth*LineWidth2);
end;
// apply final operation such that we got the final result: Dest := Dest +- A*B ;
case op of
doNone: MatrixCopy(pDest, destLineWidth, actBlk, blockSize*sizeof(double), blkWidth, blkHeight);
doAdd: MatrixAdd(pDest, destLineWidth, pDest, actBlk, blkWidth, blkHeight, destLineWidth, blockSize*sizeof(double));
doSub: MatrixSub(pDest, destLineWidth, pDest, actBlk, blkWidth, blkHeight, destLineWidth, blockSize*sizeof(double));
end;
inc(pDest, blockSize);
inc(pMt2, blockSize);
end;
inc(PByte(mt1), blkHeight*LineWidth1);
end;
FreeMem(m1);
FreeMem(m2);
end;
procedure BlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt; op : TMatrixMultDestOperation);
begin
BlockMatrixMultiplication(dest, destLineWidth, mt1, mt2, width1, height1, width2, height2, LineWidth1, LineWidth2, BlockMatrixCacheSize, op, nil);
end;
procedure BlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
var w, h : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
transBlk, copyBlk : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
w2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkHeight : NativeInt;
blkWidth : NativeInt;
gammaWidth : NativeInt;
blockByteSize : Cardinal;
blockLineSize : Cardinal;
isAligned : boolean;
ptrMem : Pointer;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((width1 = height2), 'Dimension error');
assert((destLineWidth - Width2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
assert(blockSize > 1, 'Error blocksize must be at least 2');
if (blockSize > width1) and (not assigned(mem)) then
blockSize := Next2Pwr( width1, blockSize );
isAligned := (NativeUint(dest) and $00000001F) = 0;
h1FitCacheSize := (height1 mod blockSize) = 0;
w2FitCacheSize := (width2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
h := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
w := width2 div blockSize + NativeInt(not w2FitCacheSize) - 1;
gamma := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
blockByteSize := blockSize*blockSize*sizeof(double);
actBlk := mem;
ptrMem := nil;
if not Assigned(mem) then
actBlk := MtxMallocAlign(BlockMultMemSize(blockSize), ptrMem );
multBlk := PDouble(NativeUint(actBlk) + blockByteSize);
transBlk := PDouble(NativeUint(actBlk) + 2*blockByteSize);
copyBlk := PDouble(NativeUint(actBlk) + 3*blockByteSize);
blockLineSize := blockSize*sizeof(double);
blkHeight := blockSize;
for blkIdxY := 0 to h do
begin
if (blkIdxY = h) and not h1FitCacheSize then
blkHeight := (height1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkWidth := blockSize;
for blkIdxX := 0 to w do
begin
if (blkIdxX = w) and not w2FitCacheSize then
blkWidth := (width2 mod blockSize);
MtxMemInit(actBlk, blockByteSize, 0);
pa := mt1;
pb := pMt2;
gammaWidth := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not w1FitCacheSize then
gammaWidth := width1 mod blockSize;
if (blkWidth > 3) and (blkHeight > 3) then
begin
MatrixTranspose(transBlk, blockLineSize, pb, LineWidth2, blkWidth, gammaWidth);
// it is faster to copy the block rather then multply it unaligned!
if (not isAligned) or ((LineWidth1 and $00000001F) <> 0) then
begin
MatrixCopy(copyBlk, blockLineSize, pa, LineWidth1, gammaWidth, blkHeight);
MatrixMultT2(multblk, blockLineSize, copyBlk, transBlk, gammaWidth, blkHeight, gammaWidth, blkWidth, blockLineSize, blockLineSize);
end
else
MatrixMultT2(multBlk, blockLineSize, pa, transBlk, gammaWidth, blkHeight, gammaWidth, blkWidth, LineWidth1, blockLineSize);
MatrixAdd(actBlk, blockLineSize, actBlk, multBlk, blkWidth, blkHeight, blockLineSize, blockLineSize);
end
else
begin
GenericMtxMult(multBlk, blockLineSize, pa, pb, gammaWidth, blkHeight, blkWidth, gammaWidth, LineWidth1, LineWidth2);
GenericMtxAdd(actBlk, blockLineSize, actBlk, multBlk, blkWidth, blkHeight, blockLineSize, blockLineSize);
end;
inc(pa, gammaWidth);
inc(PByte(pb), gammaWidth*LineWidth2);
end;
// apply final operation such that we got the final result: Dest := Dest +- A*B ;
case op of
doNone: MatrixCopy(pDest, destLineWidth, actBlk, blockLineSize, blkWidth, blkHeight);
doAdd: MatrixAdd(pDest, destLineWidth, pDest, actBlk, blkWidth, blkHeight, destLineWidth, blockLineSize);
doSub: MatrixSub(pDest, destLineWidth, pDest, actBlk, blkWidth, blkHeight, destLineWidth, blockLineSize);
end;
inc(pDest, blockSize);
inc(pMt2, blockSize);
end;
inc(PByte(mt1), blkHeight*LineWidth1);
end;
if Assigned(ptrMem) then
FreeMem(ptrMem);
end;
// calculates mt1'*mt2
procedure BlockMatrixMultiplicationT1(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
var w, w1 : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
transBlk1, transBlk2 : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
w2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkWidth1 : NativeInt;
blkWidth : NativeInt;
gammaHeight : NativeInt;
blockByteSize : Cardinal;
blockLineSize : Cardinal;
ptrMem : Pointer;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((height1 = height2), 'Dimension error');
assert((destLineWidth - Width2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
assert(blockSize > 1, 'Error blocksize must be at least 2');
if (blockSize > width1) and (not Assigned(mem)) then
blockSize := Next2Pwr( height1, blockSize );
h1FitCacheSize := (height1 mod blockSize) = 0;
w2FitCacheSize := (width2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
w1 := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
w := width2 div blockSize + NativeInt(not w2FitCacheSize) - 1;
gamma := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
blockByteSize := blockSize*blockSize*sizeof(double);
actBlk := mem;
ptrMem := nil;
if not Assigned(mem) then
actBlk := MtxMallocAlign(BlockMultMemSize(blockSize), ptrMem );
multBlk := PDouble(NativeUint(actBlk) + blockByteSize);
transBlk1 := PDouble(NativeUint(actBlk) + 2*blockByteSize);
transBlk2 := PDouble(NativeUint(actBlk) + 3*blockByteSize);
blockLineSize := blockSize*sizeof(double);
blkWidth1 := blockSize;
for blkIdxY := 0 to w1 do
begin
if (blkIdxY = w1) and not w1FitCacheSize then
blkWidth1 := (width1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkWidth := blockSize;
for blkIdxX := 0 to w do
begin
if (blkIdxX = w) and not w2FitCacheSize then
blkWidth := (width2 mod blockSize);
MtxMemInit(actBlk, blockByteSize, 0);
pa := mt1;
pb := pMt2;
gammaHeight := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not h1FitCacheSize then
gammaHeight := height1 mod blockSize;
if (blkWidth > 3) and (blkWidth1 > 3) then
begin
MatrixTranspose(transBlk1, blockLineSize, pa, LineWidth1, blkWidth1, gammaHeight);
MatrixTranspose(transBlk2, blockLineSize, pb, LineWidth2, blkWidth, gammaHeight);
MatrixMultT2(multblk, blockLineSize, transBlk1, transBlk2, gammaHeight, blkWidth1, gammaHeight, blkWidth, blockLineSize, blockLineSize);
MatrixAdd(actBlk, blockLineSize, actBlk, multBlk, blkWidth, blkWidth1, blockLineSize, blockLineSize);
end
else
begin
GenericMtxTranspose(transBlk1, blockLineSize, pa, LineWidth1, blkWidth1, gammaHeight);
GenericMtxMult(multBlk, blockLineSize, transBlk1, pb, gammaHeight, blkWidth1, blkWidth, gammaHeight, blockLineSize, LineWidth2);
GenericMtxAdd(actBlk, blockLineSize, actBlk, multBlk, blkWidth, blkWidth1, blockLineSize, blockLineSize);
end;
inc(PByte(pa), gammaHeight*LineWidth1);
inc(PByte(pb), gammaHeight*LineWidth2);
end;
// apply final operation such that we got the final result: Dest := Dest +- A*B ;
case op of
doNone: MatrixCopy(pDest, destLineWidth, actBlk, blockLineSize, blkWidth, blkWidth1);
doAdd: MatrixAdd(pDest, destLineWidth, pDest, actBlk, blkWidth, blkWidth1, destLineWidth, blockLineSize);
doSub: MatrixSub(pDest, destLineWidth, pDest, actBlk, blkWidth, blkWidth1, destLineWidth, blockLineSize);
end;
inc(pDest, blockSize);
inc(pMt2, blockSize);
end;
inc(mt1, blkWidth1);
end;
if Assigned(ptrMem) then
FreeMem(ptrMem);
end;
// calculates mt1*mt2'
procedure BlockMatrixMultiplicationT2(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
var h1, h : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
copyBlk : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
h2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkHeight : NativeInt;
blkHeight1 : NativeInt;
gammaWidth : NativeInt;
blockByteSize : Cardinal;
blockLineSize : Cardinal;
isAligned : boolean;
ptrMem : Pointer;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((width1 = width2), 'Dimension error');
assert((destLineWidth - height2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
assert(blockSize > 1, 'Error blocksize must be at least 2');
// try to take a shortcut where blocked matrix mult is hindering performance
if (op = doNone) and (width1 <= blockSize) then
begin
MatrixMultT2( dest, destLineWidth, mt1, mt2, width1, height1, width2, height2, LineWidth1, LineWidth2 );
exit;
end;
if (blockSize > width1) and (not Assigned(mem)) then
blockSize := Next2Pwr( width1, blockSize );
isAligned := (NativeUint(dest) and $0000000F) = 0;
h1FitCacheSize := (height1 mod blockSize) = 0;
h2FitCacheSize := (height2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
h := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
h1 := height2 div blockSize + NativeInt(not h2FitCacheSize) - 1;
gamma := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
blockByteSize := blockSize*blockSize*sizeof(double);
actBlk := mem;
ptrMem := nil;
if not Assigned(mem) then
actBlk := MtxMallocAlign(BlockMultMemSize(blockSize), ptrMem );
multBlk := PDouble(NativeUint(actBlk) + blockByteSize);
copyBlk := PDouble(NativeUint(actBlk) + 2*blockByteSize);
blockLineSize := blockSize*sizeof(double);
blkHeight := blockSize;
for blkIdxY := 0 to h do
begin
if (blkIdxY = h) and not h1FitCacheSize then
blkHeight := (height1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkHeight1 := blockSize;
for blkIdxX := 0 to h1 do
begin
if (blkIdxX = h1) and not h2FitCacheSize then
blkHeight1 := (height2 mod blockSize);
MtxMemInit(actBlk, blockByteSize, 0);
pa := mt1;
pb := pMt2;
gammaWidth := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not w1FitCacheSize then
gammaWidth := width1 mod blockSize;
if (blkHeight1 > 3) and (blkHeight > 3) then
begin
// it is faster to copy the block rather then multply it unaligned!
if (not isAligned) or ((LineWidth1 and $0000001F) <> 0) then
begin
MatrixCopy(copyBlk, blockLineSize, pa, LineWidth1, gammaWidth, blkHeight);
MatrixMultT2(multblk, blockLineSize, copyBlk, pb, gammaWidth, blkHeight, gammaWidth, blkHeight1, blockLineSize, LineWidth2);
end
else
MatrixMultT2(multBlk, blockLineSize, pa, pb, gammaWidth, blkHeight, gammaWidth, blkHeight1, LineWidth1, LineWidth2);
MatrixAdd(actBlk, blockLineSize, actBlk, multBlk, blkHeight1, blkHeight, blockLineSize, blockLineSize);
end
else
begin
GenericMtxMultTransp(multBlk, blockLineSize, pa, pb, gammaWidth, blkHeight, gammaWidth, blkHeight1, LineWidth1, LineWidth2);
GenericMtxAdd(actBlk, blockLineSize, actBlk, multBlk, blkHeight1, blkHeight, blockLineSize, blockLineSize);
end;
inc(pa, gammaWidth);
inc(pb, gammaWidth);
end;
// apply final operation such that we got the final result: Dest := Dest +- A*B ;
case op of
doNone: MatrixCopy(pDest, destLineWidth, actBlk, blockLineSize, blkHeight1, blkHeight);
doAdd: MatrixAdd(pDest, destLineWidth, pDest, actBlk, blkHeight1, blkHeight, destLineWidth, blockLineSize);
doSub: MatrixSub(pDest, destLineWidth, pDest, actBlk, blkHeight1, blkHeight, destLineWidth, blockLineSize);
end;
inc(pDest, blockSize);
inc(PByte(pMt2), blockSize*LineWidth2);
end;
inc(PByte(mt1), blkHeight*LineWidth1);
end;
if Assigned(ptrMem) then
FreeMem(ptrMem);
end;
// ########################################################
// #### Generic blocked routines
// ########################################################
procedure GenericBlockMatrixMultiplication(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble;
width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation = doNone; mem : PDouble = nil);
var w, h : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
w2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkHeight : NativeInt;
blkWidth : NativeInt;
gammaWidth : NativeInt;
sizeVal : NativeInt;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((width1 = height2), 'Dimension error');
assert((destLineWidth - Width2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
// estimate a good blocksize - one with a small number of zero columns (but as near as possible to cCacheMtxSize
if blockSize <= 0 then
begin
sizeVal := Max(width1, width2);
while sizeVal > cCacheMtxSize do
sizeVal := sizeVal shr 1;
blockSize := Min(Max(width1, width2), Max(64, sizeVal));
end;
h1FitCacheSize := (height1 mod blockSize) = 0;
w2FitCacheSize := (width2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
h := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
w := width2 div blockSize + NativeInt(not w2FitCacheSize) - 1;
gamma := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
if Assigned(mem)
then
actBlk := mem
else
GetMem(actBlk, BlockMultMemSize(blockSize));
multBlk := actBlk;
inc(multBlk, blockSize*blockSize);
blkHeight := blockSize;
for blkIdxY := 0 to h do
begin
if (blkIdxY = h) and not h1FitCacheSize then
blkHeight := (height1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkWidth := blockSize;
for blkIdxX := 0 to w do
begin
if (blkIdxX = w) and not w2FitCacheSize then
blkWidth := (width2 mod blockSize);
FillChar(actBlk^, blockSize*blockSize*sizeof(double), 0);
pa := mt1;
pb := pMt2;
gammaWidth := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not w1FitCacheSize then
gammaWidth := width1 mod blockSize;
GenericMtxMult(multBlk, blockSize*sizeof(double), pa, pb, gammaWidth, blkHeight, blkWidth, gammaWidth, LineWidth1, LineWidth2);
GenericMtxAdd(actBlk, blockSize*sizeof(double), actBlk, multBlk, blkWidth, blkHeight, blockSize*sizeof(double), blockSize*sizeof(double));
inc(pa, gammaWidth);
inc(PByte(pb), gammaWidth*LineWidth2);
end;
// build the result: dest = Dest +- A*B (according to the operator)
case op of
doNone: GenericMtxCopy(pDest, destLineWidth, ActBlk, blockSize*sizeof(double), blkWidth, blkHeight);
doAdd: GenericMtxAdd(pDest, destLineWidth, ActBlk, pDest, blkWidth, blkHeight, blockSize*sizeof(double), destLineWidth);
doSub: GenericMtxSub(pDest, destLineWidth, pDest, ActBlk, blkWidth, blkHeight, destLineWidth, blockSize*sizeof(double));
end;
inc(pDest, blockSize);
inc(pMt2, blockSize);
end;
inc(PByte(mt1), blkHeight*LineWidth1);
end;
if not Assigned(mem) then
FreeMem(actBlk);
end;
// calculates mt1'*mt2
procedure GenericBlockMatrixMultiplicationT1(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
var w, w1 : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
transBlk1 : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
w2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkWidth1 : NativeInt;
blkWidth : NativeInt;
gammaHeight : NativeInt;
blockByteSize : Cardinal;
blockLineSize : Cardinal;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((height1 = height2), 'Dimension error');
assert((destLineWidth - Width2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
assert(blockSize > 1, 'Error blocksize must be at least 2');
h1FitCacheSize := (height1 mod blockSize) = 0;
w2FitCacheSize := (width2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
w1 := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
w := width2 div blockSize + NativeInt(not w2FitCacheSize) - 1;
gamma := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
blockByteSize := blockSize*blockSize*sizeof(double);
actBlk := mem;
if not Assigned(mem) then
GetMem(actBlk, BlockMultMemSize(blockSize));
multBlk := PDouble(NativeUint(actBlk) + blockByteSize);
transBlk1 := PDouble(NativeUint(actBlk) + 2*blockByteSize);
blockLineSize := blockSize*sizeof(double);
blkWidth1 := blockSize;
for blkIdxY := 0 to w1 do
begin
if (blkIdxY = w1) and not w1FitCacheSize then
blkWidth1 := (width1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkWidth := blockSize;
for blkIdxX := 0 to w do
begin
if (blkIdxX = w) and not w2FitCacheSize then
blkWidth := (width2 mod blockSize);
FillChar(actBlk^, blockByteSize, 0);
pa := mt1;
pb := pMt2;
gammaHeight := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not h1FitCacheSize then
gammaHeight := height1 mod blockSize;
GenericMtxTranspose(transBlk1, blockLineSize, pa, LineWidth1, blkWidth1, gammaHeight);
GenericMtxMult(multBlk, blockLineSize, transBlk1, pb, gammaHeight, blkWidth1, blkWidth, gammaHeight, blockLineSize, LineWidth2);
GenericMtxAdd(actBlk, blockLineSize, actBlk, multBlk, blkWidth, blkWidth1, blockLineSize, blockLineSize);
inc(PByte(pa), gammaHeight*LineWidth1);
inc(PByte(pb), gammaHeight*LineWidth2);
end;
// apply final operation such that we got the final result: Dest := Dest +- A*B ;
case op of
doNone: GenericMtxCopy(pDest, destLineWidth, actBlk, blockLineSize, blkWidth, blkWidth1);
doAdd: GenericMtxAdd(pDest, destLineWidth, pDest, actBlk, blkWidth, blkWidth1, destLineWidth, blockLineSize);
doSub: GenericMtxSub(pDest, destLineWidth, pDest, actBlk, blkWidth, blkWidth1, destLineWidth, blockLineSize);
end;
inc(pDest, blockSize);
inc(pMt2, blockSize);
end;
inc(mt1, blkWidth1);
end;
if not Assigned(mem) then
FreeMem(actBlk);
end;
// calculates mt1*mt2'
procedure GenericBlockMatrixMultiplicationT2(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1 : NativeInt; height1 : NativeInt; width2 : NativeInt; height2 : NativeInt;
const LineWidth1, LineWidth2 : NativeInt; blockSize : NativeInt; op : TMatrixMultDestOperation; mem : Pdouble);
var h1, h : NativeInt;
blkIdxX : NativeInt;
actBlk : PDouble;
multBlk : PDouble;
pA, pB : PDouble;
blkIdxY : NativeInt;
idx : NativeInt;
gamma : NativeInt;
pDest : PDouble;
pMt2 : PDouble;
w1FitCacheSize : boolean;
h2FitCacheSize : boolean;
h1FitCacheSize : boolean;
blkHeight : NativeInt;
blkHeight1 : NativeInt;
gammaWidth : NativeInt;
blockByteSize : Cardinal;
blockLineSize : Cardinal;
begin
if (width1 = 0) or (width2 = 0) or (height1 = 0) or (height2 = 0) then
exit;
assert((width1 = width2), 'Dimension error');
assert((destLineWidth - height2*sizeof(double) >= 0) and (LineWidth1 >= width1*sizeof(double)) and (LineWidth2 >= width2*sizeof(double)), 'Line widths do not match');
assert(blockSize > 1, 'Error blocksize must be at least 2');
h1FitCacheSize := (height1 mod blockSize) = 0;
h2FitCacheSize := (height2 mod blockSize) = 0;
w1FitCacheSize := (width1 mod blockSize) = 0;
h := height1 div blockSize + NativeInt(not h1FitCacheSize) - 1;
h1 := height2 div blockSize + NativeInt(not h2FitCacheSize) - 1;
gamma := width1 div blockSize + NativeInt(not w1FitCacheSize) - 1;
blockByteSize := blockSize*blockSize*sizeof(double);
actBlk := mem;
if not Assigned(mem) then
GetMem(actBlk, BlockMultMemSize(blockSize));
multBlk := PDouble(NativeUint(actBlk) + blockByteSize);
blockLineSize := blockSize*sizeof(double);
blkHeight := blockSize;
for blkIdxY := 0 to h do
begin
if (blkIdxY = h) and not h1FitCacheSize then
blkHeight := (height1 mod blockSize);
pDest := dest;
inc(PByte(pDest), blkIdxY*blockSize*destLineWidth);
pMt2 := mt2;
blkHeight1 := blockSize;
for blkIdxX := 0 to h1 do
begin
if (blkIdxX = h1) and not h2FitCacheSize then
blkHeight1 := (height2 mod blockSize);
FillChar(actBlk^, blockByteSize, 0);
pa := mt1;
pb := pMt2;
gammaWidth := blockSize;
for idx := 0 to gamma do
begin
if (idx = gamma) and not w1FitCacheSize then
gammaWidth := width1 mod blockSize;
GenericMtxMultTransp(multBlk, blockLineSize, pa, pb, gammaWidth, blkHeight, gammaWidth, blkHeight1, LineWidth1, LineWidth2);
GenericMtxAdd(actBlk, blockLineSize, actBlk, multBlk, blkHeight1, blkHeight, blockLineSize, blockLineSize);
inc(pa, gammaWidth);
inc(pb, gammaWidth);