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AVXMatrixMultOperations.pas
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AVXMatrixMultOperations.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) 2018, 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 AVXMatrixMultOperations;
interface
{$I 'mrMath_CPU.inc'}
{$IFNDEF x64}
// full matrix operations
procedure AVXMatrixMultAligned(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1, height1, width2, height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
procedure AVXMatrixMultUnAligned(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1, height1, width2, height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// some special types of multiplications used e.g. in QR Decomposition
// dest = mt1'*mt2; where mt2 is a lower triangular matrix and the operation is transposition
// the function assumes a unit diagonal (does not touch the real middle elements)
// width and height values are assumed to be the "original" (non transposed) ones
procedure AVXMtxMultTria2T1(dest : PDouble; LineWidthDest : NativeInt; mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// mt1 = mt1*mt2'; where mt2 is an upper triangular matrix
procedure AVXMtxMultTria2T1StoreT1(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// W = C1*V1*T -> V1 is an upper triangular matrix with assumed unit diagonal entries. Operation on V1 transposition
procedure AVXMtxMultTria2TUpperUnit(dest : PDouble; LineWidthDest : NativeInt; mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// mt1 = mt1*mt2; where mt2 is an upper triangular matrix
procedure AVXMtxMultTria2Store1(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// calculates mt1 = mt1*mt2', mt2 = lower triangular matrix. diagonal elements are assumed to be 1!
procedure AVXMtxMultLowTria2T2Store1(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// mt1 = mt1*mt2; where mt2 is an upper triangular matrix - diagonal elements are unit
procedure AVXMtxMultTria2Store1Unit(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
// performs a rank2 update in the form
// C = C - A*B' - B*A'
// N...order of C (N x N matrix)
// k... number of columns of A and B
// the lower triangle of C is not referenced
procedure AVXSymRank2UpdateUpperUnaligned( C : PDouble; LineWidthC : NativeInt; A : PDouble; LineWidthA : NativeInt;
B : PDouble; LineWidthB : NativeInt; N : NativeInt; k : NativeInt ); {$IFDEF FPC} assembler; {$ELSE} register; {$ENDIF}
{$ENDIF}
implementation
{$IFNDEF x64}
procedure AVXMatrixMultAligned(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1, height1, width2, height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt);
var bytesWidth2, destOffset : NativeInt;
iter : NativeInt;
// eax = dest; edx = destLineWidth; ecx = mtx
asm
// prolog - simulate stack
push ebx;
push edi;
push esi;
mov edi, width1;
imul edi, -8;
mov iter, edi;
sub ecx, edi;
//destOffset := destLineWidth - Width2*sizeof(double);
mov ebx, Width2;
shl ebx, 3;
sub edx, ebx;
mov destOffset, edx;
//bytesWidth2 := width2*sizeof(double);
mov bytesWidth2, ebx;
// for y := 0 to height1 - 1 do
@@foryloop:
mov esi, width2;
sub esi, 2;
jl @LastXColumn;
@@forxloop:
// for x := 0 to width2 div 2 - 1
// esi: mt1 - width1*sizeof(double)
// mt2: mt2
//mov ecx, mt1;
mov ebx, mt2;
mov edx, iter;
mov edi, LineWidth2;
{$IFDEF AVXSUP}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF}
{$IFDEF AVXSUP}vxorpd ymm1, ymm1, ymm1; {$ELSE}db $C5,$F5,$57,$C9;{$ENDIF}
cmp edx, -32;
jg @@Innerloop2Begin;
// for z := 0 to width1 - 1do
// AVX part:
@@InnerLoop1:
// 4x4 block
{$IFDEF AVXSUP}vmovapd xmm2, [ebx]; {$ELSE}db $C5,$F9,$28,$13;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovapd xmm4, xmm2; {$ELSE}db $C5,$F9,$29,$D4;{$ENDIF}
{$IFDEF AVXSUP}vmovapd xmm3, [ebx]; {$ELSE}db $C5,$F9,$28,$1B;{$ENDIF}
add ebx, edi;
// shuffle so we can multiply
// swap such that we can immediately multiply
{$IFDEF AVXSUP}vmovlhps xmm2, xmm2, xmm3; {$ELSE}db $C5,$E8,$16,$D3;{$ENDIF}
{$IFDEF AVXSUP}vmovhlps xmm3, xmm3, xmm4; {$ELSE}db $C5,$E0,$12,$DC;{$ENDIF}
// next 4 elements
{$IFDEF AVXSUP}vmovapd xmm4, [ebx]; {$ELSE}db $C5,$F9,$28,$23;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovapd xmm6, xmm4; {$ELSE}db $C5,$F9,$29,$E6;{$ENDIF}
{$IFDEF AVXSUP}vmovapd xmm5, [ebx]; {$ELSE}db $C5,$F9,$28,$2B;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovapd ymm7, [ecx + edx] {$ELSE}db $C5,$FD,$28,$3C,$11;{$ENDIF}
{$IFDEF AVXSUP}vmovlhps xmm4, xmm4, xmm5; {$ELSE}db $C5,$D8,$16,$E5;{$ENDIF}
{$IFDEF AVXSUP}vmovhlps xmm5, xmm5, xmm6; {$ELSE}db $C5,$D0,$12,$EE;{$ENDIF}
{$IFDEF AVXSUP}vinsertf128 ymm2, ymm2, xmm4, 1; {$ELSE}db $C4,$E3,$6D,$18,$D4,$01;{$ENDIF}
{$IFDEF AVXSUP}vinsertf128 ymm3, ymm3, xmm5, 1; {$ELSE}db $C4,$E3,$65,$18,$DD,$01;{$ENDIF}
// now multiply and add
{$IFDEF AVXSUP}vmulpd ymm2, ymm2, ymm7; {$ELSE}db $C5,$ED,$59,$D7;{$ENDIF}
{$IFDEF AVXSUP}vmulpd ymm3, ymm3, ymm7; {$ELSE}db $C5,$E5,$59,$DF;{$ENDIF}
{$IFDEF AVXSUP}vaddpd ymm0, ymm0, ymm2; {$ELSE}db $C5,$FD,$58,$C2;{$ENDIF}
{$IFDEF AVXSUP}vaddpd ymm1, ymm1, ymm3; {$ELSE}db $C5,$F5,$58,$CB;{$ENDIF}
add edx, 32;
jl @@InnerLoop1;
{$IFDEF AVXSUP}vextractf128 xmm2, ymm0, 1; {$ELSE}db $C4,$E3,$7D,$19,$C2,$01;{$ENDIF}
{$IFDEF AVXSUP}vextractf128 xmm3, ymm1, 1; {$ELSE}db $C4,$E3,$7D,$19,$CB,$01;{$ENDIF}
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm2; {$ELSE}db $C5,$F9,$7C,$C2;{$ENDIF}
{$IFDEF AVXSUP}vhaddpd xmm1, xmm1, xmm3; {$ELSE}db $C5,$F1,$7C,$CB;{$ENDIF}
test edx, edx;
jz @@InnerLoopEnd2;
@@Innerloop2Begin:
// rest in single elements
@@InnerLoop2:
{$IFDEF AVXSUP}vmovapd xmm2, [ebx]; {$ELSE}db $C5,$F9,$28,$13;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovddup xmm3, [ecx + edx]; {$ELSE}db $C5,$FB,$12,$1C,$11;{$ENDIF}
{$IFDEF AVXSUP}vmulpd xmm2, xmm2, xmm3; {$ELSE}db $C5,$E9,$59,$D3;{$ENDIF}
{$IFDEF AVXSUP}vmovhlps xmm4, xmm4, xmm2; {$ELSE}db $C5,$D8,$12,$E2;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm2; {$ELSE}db $C5,$FB,$58,$C2;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm1, xmm1, xmm4; {$ELSE}db $C5,$F3,$58,$CC;{$ENDIF}
add edx, 8;
jnz @@InnerLoop2;
@@InnerLoopEnd2:
// finall horizontal addition
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm1; {$ELSE}db $C5,$F9,$7C,$C1;{$ENDIF}
{$IFDEF AVXSUP}vmovapd [eax], xmm0; {$ELSE}db $C5,$F9,$29,$00;{$ENDIF}
// increment the pointers
// inc(mt2), inc(dest);
//add dword ptr [mt2], 8;
add mt2, 16;
add eax, 16;
// end for x := 0 to width2 div 2 - 1
sub esi, 2;
jge @@forxloop;
@LastXColumn:
cmp esi, -1;
jne @NextLine;
// last column of mt2
mov edx, iter;
mov ebx, mt2;
{$IFDEF AVXSUP}vxorpd xmm0, xmm0, xmm0; {$ELSE}db $C5,$F9,$57,$C0;{$ENDIF}
@InnerLoop2:
{$IFDEF AVXSUP}vmovsd xmm1, [ecx + edx]; {$ELSE}db $C5,$FB,$10,$0C,$11;{$ENDIF}
{$IFDEF AVXSUP}vmovsd xmm2, [ebx]; {$ELSE}db $C5,$FB,$10,$13;{$ENDIF}
{$IFDEF AVXSUP}vmulsd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm1; {$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add ebx, edi;
add edx, 8;
jnz @InnerLoop2;
{$IFDEF AVXSUP}vmovsd [eax], xmm0; {$ELSE}db $C5,$FB,$11,$00;{$ENDIF}
add eax, 8;
add mt2, 8;
@NextLine:
// dec(mt2, Width2);
// inc(PByte(mt1), LineWidth1);
// inc(PByte(dest), destOffset);
//mov ebx, bytesWidth2;
//sub dword ptr [mt2], ebx;
mov edx, bytesWidth2;
sub mt2, edx;
add eax, destOffset;
add ecx, LineWidth1;
// end for y := 0 to height1 - 1
dec height1;
jnz @@foryloop;
// epilog
{$IFDEF AVXSUP}vzeroupper; {$ELSE}db $C5,$F8,$77;{$ENDIF}
pop esi;
pop edi;
pop ebx;
end;
procedure AVXMatrixMultUnAligned(dest : PDouble; const destLineWidth : NativeInt; mt1, mt2 : PDouble; width1, height1, width2, height2 : NativeInt; const LineWidth1, LineWidth2 : NativeInt);
var bytesWidth2, destOffset : NativeInt;
iter : NativeInt;
// eax = dest; edx = destLineWidth; ecx = mtx
asm
// prolog - simulate stack
push ebx;
push edi;
push esi;
mov edi, width1;
imul edi, -8;
mov iter, edi;
sub ecx, edi;
//destOffset := destLineWidth - Width2*sizeof(double);
mov ebx, Width2;
shl ebx, 3;
sub edx, ebx;
mov destOffset, edx;
//bytesWidth2 := width2*sizeof(double);
mov bytesWidth2, ebx;
// for y := 0 to height1 - 1 do
@@foryloop:
mov esi, width2;
sub esi, 2;
jl @LastXColumn;
@@forxloop:
// for x := 0 to width2 div 2 - 1
// esi: mt1 - width1*sizeof(double)
// mt2: mt2
//mov ecx, mt1;
mov ebx, mt2;
mov edx, iter;
mov edi, LineWidth2;
{$IFDEF AVXSUP}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF}
{$IFDEF AVXSUP}vxorpd ymm1, ymm1, ymm1; {$ELSE}db $C5,$F5,$57,$C9;{$ENDIF}
cmp edx, -32;
jg @@Innerloop2Begin;
// for z := 0 to width1 - 1do
// AVX part:
@@InnerLoop1:
// 4x4 block
{$IFDEF AVXSUP}vmovupd xmm2, [ebx]; {$ELSE}db $C5,$F9,$10,$13;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovupd xmm4, xmm2; {$ELSE}db $C5,$F9,$11,$D4;{$ENDIF}
{$IFDEF AVXSUP}vmovupd xmm3, [ebx]; {$ELSE}db $C5,$F9,$10,$1B;{$ENDIF}
add ebx, edi;
// shuffle so we can multiply
// swap such that we can immediately multiply
{$IFDEF AVXSUP}vmovlhps xmm2, xmm2, xmm3; {$ELSE}db $C5,$E8,$16,$D3;{$ENDIF}
{$IFDEF AVXSUP}vmovhlps xmm3, xmm3, xmm4; {$ELSE}db $C5,$E0,$12,$DC;{$ENDIF}
// next 4 elements
{$IFDEF AVXSUP}vmovupd xmm4, [ebx]; {$ELSE}db $C5,$F9,$10,$23;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovupd xmm6, xmm4; {$ELSE}db $C5,$F9,$11,$E6;{$ENDIF}
{$IFDEF AVXSUP}vmovupd xmm5, [ebx]; {$ELSE}db $C5,$F9,$10,$2B;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovupd ymm7, [ecx + edx] {$ELSE}db $C5,$FD,$10,$3C,$11;{$ENDIF}
{$IFDEF AVXSUP}vmovlhps xmm4, xmm4, xmm5; {$ELSE}db $C5,$D8,$16,$E5;{$ENDIF}
{$IFDEF AVXSUP}vmovhlps xmm5, xmm5, xmm6; {$ELSE}db $C5,$D0,$12,$EE;{$ENDIF}
{$IFDEF AVXSUP}vinsertf128 ymm2, ymm2, xmm4, 1; {$ELSE}db $C4,$E3,$6D,$18,$D4,$01;{$ENDIF}
{$IFDEF AVXSUP}vinsertf128 ymm3, ymm3, xmm5, 1; {$ELSE}db $C4,$E3,$65,$18,$DD,$01;{$ENDIF}
// now multiply and add
{$IFDEF AVXSUP}vmulpd ymm2, ymm2, ymm7; {$ELSE}db $C5,$ED,$59,$D7;{$ENDIF}
{$IFDEF AVXSUP}vmulpd ymm3, ymm3, ymm7; {$ELSE}db $C5,$E5,$59,$DF;{$ENDIF}
{$IFDEF AVXSUP}vaddpd ymm0, ymm0, ymm2; {$ELSE}db $C5,$FD,$58,$C2;{$ENDIF}
{$IFDEF AVXSUP}vaddpd ymm1, ymm1, ymm3; {$ELSE}db $C5,$F5,$58,$CB;{$ENDIF}
add edx, 32;
jl @@InnerLoop1;
{$IFDEF AVXSUP}vextractf128 xmm2, ymm0, 1; {$ELSE}db $C4,$E3,$7D,$19,$C2,$01;{$ENDIF}
{$IFDEF AVXSUP}vextractf128 xmm3, ymm1, 1; {$ELSE}db $C4,$E3,$7D,$19,$CB,$01;{$ENDIF}
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm2; {$ELSE}db $C5,$F9,$7C,$C2;{$ENDIF}
{$IFDEF AVXSUP}vhaddpd xmm1, xmm1, xmm3; {$ELSE}db $C5,$F1,$7C,$CB;{$ENDIF}
test edx, edx;
jz @@InnerLoopEnd2;
@@Innerloop2Begin:
// rest in single elements
@@InnerLoop2:
{$IFDEF AVXSUP}vmovupd xmm2, [ebx]; {$ELSE}db $C5,$F9,$10,$13;{$ENDIF}
add ebx, edi;
{$IFDEF AVXSUP}vmovddup xmm3, [ecx + edx]; {$ELSE}db $C5,$FB,$12,$1C,$11;{$ENDIF}
{$IFDEF AVXSUP}vmulpd xmm2, xmm2, xmm3; {$ELSE}db $C5,$E9,$59,$D3;{$ENDIF}
{$IFDEF AVXSUP}vmovhlps xmm4, xmm4, xmm2; {$ELSE}db $C5,$D8,$12,$E2;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm2; {$ELSE}db $C5,$FB,$58,$C2;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm1, xmm1, xmm4; {$ELSE}db $C5,$F3,$58,$CC;{$ENDIF}
add edx, 8;
jnz @@InnerLoop2;
@@InnerLoopEnd2:
// finall horizontal addition
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm1; {$ELSE}db $C5,$F9,$7C,$C1;{$ENDIF}
{$IFDEF AVXSUP}vmovupd [eax], xmm0; {$ELSE}db $C5,$F9,$11,$00;{$ENDIF}
// increment the pointers
// inc(mt2), inc(dest);
//add dword ptr [mt2], 8;
add mt2, 16;
add eax, 16;
// end for x := 0 to width2 div 2 - 1
sub esi, 2;
jge @@forxloop;
@LastXColumn:
cmp esi, -1;
jne @NextLine;
// last column of mt2
mov edx, iter;
mov ebx, mt2;
{$IFDEF AVXSUP}vxorpd xmm0, xmm0, xmm0; {$ELSE}db $C5,$F9,$57,$C0;{$ENDIF}
@InnerLoop2:
{$IFDEF AVXSUP}vmovsd xmm1, [ecx + edx]; {$ELSE}db $C5,$FB,$10,$0C,$11;{$ENDIF}
{$IFDEF AVXSUP}vmovsd xmm2, [ebx]; {$ELSE}db $C5,$FB,$10,$13;{$ENDIF}
{$IFDEF AVXSUP}vmulsd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm1; {$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add ebx, edi;
add edx, 8;
jnz @InnerLoop2;
{$IFDEF AVXSUP}vmovsd [eax], xmm0; {$ELSE}db $C5,$FB,$11,$00;{$ENDIF}
add eax, 8;
add mt2, 8;
@NextLine:
// dec(mt2, Width2);
// inc(PByte(mt1), LineWidth1);
// inc(PByte(dest), destOffset);
//mov ebx, bytesWidth2;
//sub dword ptr [mt2], ebx;
mov edx, bytesWidth2;
sub mt2, edx;
add eax, destOffset;
add ecx, LineWidth1;
// end for y := 0 to height1 - 1
dec height1;
jnz @@foryloop;
// epilog
{$IFDEF AVXSUP}vzeroupper; {$ELSE}db $C5,$F8,$77;{$ENDIF}
pop esi;
pop edi;
pop ebx;
end;
// ###########################################
// #### Special multiplication routines (for now only used in QR Decomposition)
// ###########################################
// note the result is stored in mt1 again!
// mt1 = mt1*mt2; where mt2 is an upper triangular matrix
procedure AVXMtxMultTria2Store1(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt);
var wm1 : NativeInt;
iter : NativeInt;
aLineWidth1 : NativeInt;
// eax = mt1, edx = LineWidth1, ecx = mt2
asm
push ebx;
push edi;
push esi;
// init
mov aLineWidth1, edx;
//wm1 := width2 - 1;
mov ebx, width2;
dec ebx;
mov wm1, ebx;
// iter := -width1*sizeof(double);
mov edi, width1;
imul edi, -8;
mov iter, edi;
// inc(mt2, width2 - 1);
imul ebx, 8;
add ecx, ebx;
mov edx, LineWidth2;
// for x := 0 to width2 - 1 do
@@forxloop:
mov edi, height1;
push eax;
sub eax, iter;
// for y := 0 to height1 - 1
@@foryloop:
// tmp := 0;
{$IFDEF AVXSUP}vxorpd xmm0, xmm0, xmm0; {$ELSE}db $C5,$F9,$57,$C0;{$ENDIF}
// mt2
push ecx;
// for idx := 0 to width1 - x - 1
mov esi, iter;
// check if we have enough iterations:
test esi, esi;
jz @@foridxloopend;
@@foridxloop:
{$IFDEF AVXSUP}vmovsd xmm1, [ecx]; {$ELSE}db $C5,$FB,$10,$09;{$ENDIF}
{$IFDEF AVXSUP}vmovsd xmm2, [eax + esi] {$ELSE}db $C5,$FB,$10,$14,$30;{$ENDIF}
add ecx, edx; // + linewidth2
{$IFDEF AVXSUP}vmulsd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm1; {$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add esi, 8;
jnz @@foridxloop;
@@foridxloopend:
// PConstDoubleArr(pmt1)^[width2 - 1 - x] := tmp;
mov ecx, eax;
add ecx, iter;
mov esi, width2;
dec esi;
{$IFDEF AVXSUP}vmovsd [ecx + 8*esi], xmm0; {$ELSE}db $C5,$FB,$11,$04,$F1;{$ENDIF}
// restore mt2
pop ecx;
// inc(PByte(pmT1), LineWidth1);
add eax, aLineWidth1;
dec edi;
jnz @@foryloop;
// reduce for idx loop
add iter, 8;
pop eax;
// dec(mt2);
sub ecx, 8;
dec width2;
jnz @@forxloop;
{$IFDEF AVXSUP}vzeroupper; {$ELSE}db $C5,$F8,$77;{$ENDIF}
// cleanup stack
pop esi;
pop edi;
pop ebx;
end;
procedure AVXMtxMultTria2T1StoreT1(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt);
var iter : NativeInt;
testExitLoopVal : NativeInt;
asm
// prolog: stack
push ebx;
push edi;
push esi;
//iter := -width1*sizeof(double);
mov esi, width1;
imul esi, -8;
mov iter, esi;
// testExitLoopVal := height2*sizeof(double) + iter;
mov edi, height2;
shl edi, 3; //*8
add edi, esi;
mov testExitLoopVal, edi;
// eax := mt1
sub eax, esi; // mt1 - iter
// for y loop
@@foryloop:
mov esi, iter;
push ecx;
sub ecx, esi;
@@forxloop:
{$IFDEF AVXSUP}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF} // temp := 0
mov edi, esi; // loop counter x;
// test if height2 > width1 and loop counter > width1
test edi, edi;
jge @@foriloopend;
// in case x is odd -> handle the first element separately
test edi, $E;
jz @@foriloopAVX;
// single element handling
{$IFDEF AVXSUP}vmovsd xmm1, [eax + edi]; {$ELSE}db $C5,$FB,$10,$0C,$38;{$ENDIF}
{$IFDEF AVXSUP}vmovsd xmm2, [ecx + edi]; {$ELSE}db $C5,$FB,$10,$14,$39;{$ENDIF}
{$IFDEF AVXSUP}vmulsd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm1; {$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add edi, 8;
@@foriloopAVX:
// 4 elements at a time
add edi, 32;
jg @@foriloopAVXend;
{$IFDEF AVXSUP}vmovupd ymm1, [eax + edi - 32]; {$ELSE}db $C5,$FD,$10,$4C,$38,$E0;{$ENDIF}
{$IFDEF AVXSUP}vmovupd ymm2, [ecx + edi - 32]; {$ELSE}db $C5,$FD,$10,$54,$39,$E0;{$ENDIF}
{$IFDEF AVXSUP}vmulpd ymm1, ymm1, ymm2; {$ELSE}db $C5,$F5,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddpd ymm0, ymm0, ymm1; {$ELSE}db $C5,$FD,$58,$C1;{$ENDIF}
jmp @@foriloopAVX;
@@foriloopAVXend:
{$IFDEF AVXSUP}vextractf128 xmm2, ymm0, 1; {$ELSE}db $C4,$E3,$7D,$19,$C2,$01;{$ENDIF}
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm2; {$ELSE}db $C5,$F9,$7C,$C2;{$ENDIF}
sub edi, 32;
jz @@foriloopend;
// for i := x to width1 - 1
@@foriloop:
// two elements at a time:
{$IFDEF AVXSUP}vmovupd xmm1, [eax + edi]; {$ELSE}db $C5,$F9,$10,$0C,$38;{$ENDIF}
{$IFDEF AVXSUP}vmovupd xmm2, [ecx + edi]; {$ELSE}db $C5,$F9,$10,$14,$39;{$ENDIF}
{$IFDEF AVXSUP}vmulpd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F1,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddpd xmm0, xmm0, xmm1; {$ELSE}db $C5,$F9,$58,$C1;{$ENDIF}
add edi, 16;
jnz @@foriloop;
@@foriloopend:
// final result
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm0; {$ELSE}db $C5,$F9,$7C,$C0;{$ENDIF}
{$IFDEF AVXSUP}vmovsd [eax + esi], xmm0; {$ELSE}db $C5,$FB,$11,$04,$30;{$ENDIF}
add ecx, LineWidth2;
add esi, 8;
cmp esi, testExitLoopVal;
jne @@forxloop;
// restore mt2
pop ecx;
add eax, edx;
dec height1;
jnz @@foryloop;
// epilog
{$IFDEF AVXSUP}vzeroupper; {$ELSE}db $C5,$F8,$77;{$ENDIF}
pop esi;
pop edi;
pop ebx;
end;
procedure AVXMtxMultTria2TUpperUnit(dest : PDouble; LineWidthDest : NativeInt; mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt);
var iter, testExitLoopVal : NativeInt;
asm
// prolog: stack
push ebx;
push edi;
push esi;
// init
//iter := -width1*sizeof(double);
mov ebx, width1;
imul ebx, -8;
mov iter, ebx;
sub mt2, ebx;
// ecx := mt1
sub eax, ebx;
sub ecx, ebx; // mt1 - iter
// testExitLoopVal := height2*sizeof(double) + iter;
mov edi, height2;
shl edi, 3; //*8
add edi, ebx;
mov testExitLoopVal, edi;
// for y loop
@@foryloop:
mov ebx, mt2;
//sub ebx, iter;
mov esi, iter;
@@forxloop:
{$IFDEF AVXSUP}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF} // temp := 0
mov edi, esi; // loop counter x;
// test if height2 > width1 and loop counter > width1
test edi, edi;
jge @@foriloopend;
// in case x is odd -> handle the first element separately
//and esi, $E;
test edi, $E;
jz @@foriloopinit;
// single element handling -> mt1 first element is assumed unit!
{$IFDEF AVXSUP}vmovsd xmm0, [ecx + edi]; {$ELSE}db $C5,$FB,$10,$04,$39;{$ENDIF}
add edi, 8;
jmp @@AfterLoopInit;
@@foriloopinit:
test edi, edi;
jz @@foriloopend;
// two elements init at a time:
{$IFDEF AVXSUP}vmovsd xmm0, [ecx + edi]; {$ELSE}db $C5,$FB,$10,$04,$39;{$ENDIF}
{$IFDEF AVXSUP}vmovsd xmm1, [ecx + edi + 8]; {$ELSE}db $C5,$FB,$10,$4C,$39,$08;{$ENDIF}
{$IFDEF AVXSUP}vmovsd xmm2, [ebx + edi + 8]; {$ELSE}db $C5,$FB,$10,$54,$3B,$08;{$ENDIF}
{$IFDEF AVXSUP}vmulsd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm1; {$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add edi, 16;
@@AfterLoopInit:
// in case the last single x element was handled we do not need further looping
test edi, edi;
jz @@finalizeloop;
// for i := x to width1 - 1
@@foriloop:
add edi, 32;
jg @@foriloopend;
// 4 elements at a time:
{$IFDEF AVXSUP}vmovupd ymm1, [ecx + edi - 32]; {$ELSE}db $C5,$FD,$10,$4C,$39,$E0;{$ENDIF}
{$IFDEF AVXSUP}vmovupd ymm2, [ebx + edi - 32]; {$ELSE}db $C5,$FD,$10,$54,$3B,$E0;{$ENDIF}
{$IFDEF AVXSUP}vmulpd ymm1, ymm1, ymm2; {$ELSE}db $C5,$F5,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddpd ymm0, ymm0, ymm1; {$ELSE}db $C5,$FD,$58,$C1;{$ENDIF}
jmp @@foriloop;
@@foriloopend:
{$IFDEF AVXSUP}vextractf128 xmm1, ymm0, 1; {$ELSE}db $C4,$E3,$7D,$19,$C1,$01;{$ENDIF}
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm1; {$ELSE}db $C5,$F9,$7C,$C1;{$ENDIF}
sub edi, 32;
// test if we missed 2 elements
jz @@finalizeloop;
// need to process two more elements:
{$IFDEF AVXSUP}vmovupd xmm1, [ecx + edi]; {$ELSE}db $C5,$F9,$10,$0C,$39;{$ENDIF}
{$IFDEF AVXSUP}vmovupd xmm2, [ebx + edi]; {$ELSE}db $C5,$F9,$10,$14,$3B;{$ENDIF}
{$IFDEF AVXSUP}vmulpd xmm1, xmm1, xmm2; {$ELSE}db $C5,$F1,$59,$CA;{$ENDIF}
{$IFDEF AVXSUP}vaddpd xmm0, xmm0, xmm1; {$ELSE}db $C5,$F9,$58,$C1;{$ENDIF}
@@finalizeloop:
// final result
{$IFDEF AVXSUP}vhaddpd xmm0, xmm0, xmm0; {$ELSE}db $C5,$F9,$7C,$C0;{$ENDIF}
{$IFDEF AVXSUP}vmovsd [eax + esi], xmm0; {$ELSE}db $C5,$FB,$11,$04,$30;{$ENDIF}
add ebx, LineWidth2;
add esi, 8;
cmp esi, testExitLoopVal;
jne @@forxloop;
add ecx, LineWidth1;
add eax, edx;
dec height1;
jnz @@foryloop;
// epilog
{$IFDEF AVXSUP}vzeroupper; {$ELSE}db $C5,$F8,$77;{$ENDIF}
pop esi;
pop edi;
pop ebx;
end;
// note the result is stored in mt2 again!
// dest = mt1'*mt2; where mt2 is a lower triangular matrix and the operation is transposition
// the function assumes a unit diagonal (does not touch the real middle elements)
// width and height values are assumed to be the "original" (non transposed) ones
procedure AVXMtxMultTria2T1(dest : PDouble; LineWidthDest : NativeInt; mt1 : PDouble; LineWidth1 : NativeInt;
mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt);
var pMt2 : PDouble;
width2D2 : NativeInt;
aLineWidthDest : NativeInt;
asm
// Prolog
push ebx;
push esi;
push edi;
mov aLineWidthDest, edx;
// width2D2 := width2 div 2;
mov ebx, width2;
shr ebx, 1;
mov width2D2, ebx;
// for x := 0 to width1 - 1 do
@@forxloop:
// pMT2 := mt2;
// pDest := dest;
push eax; // eax is pDest
mov ebx, mt2;
mov pMT2, ebx;
// for y := 0 to width2D2 - 1 do
mov edx, width2D2;
test edx, edx;
jz @@foryloopend;
xor edx, edx;
@@foryloop:
// valCounter1 := PConstDoubleArr(mt1);
// inc(PByte(valCounter1), 2*y*LineWidth1);
mov esi, mt1;
mov ebx, edx;
add ebx, ebx;
imul ebx, LineWidth1;
add esi, ebx;
// valCounter2 := PConstDoubleArr(pMT2);
// inc(PByte(valCounter2), (2*y + 1)*LineWidth2);
mov edi, pMt2;
mov ebx, edx;
add ebx, ebx;
imul ebx, LineWidth2;
add ebx, LineWidth2;
add edi, ebx;
// tmp[0] := valCounter1^[0];
// inc(PByte(valCounter1), LineWidth1);
{$IFDEF AVXSUP}vmovsd xmm0, [esi]; {$ELSE}db $C5,$FB,$10,$06;{$ENDIF}
add esi, LineWidth1;
// if height2 - 2*y - 1 > 0 then
mov ebx, edx;
add ebx, ebx;
inc ebx;
cmp ebx, height2;
jnl @@PreInnerLoop;
// tmp[0] := tmp[0] + valCounter1^[0]*valCounter2^[0];
// tmp[1] := valCounter1^[0];
{$IFDEF AVXSUP}vmovsd xmm1, [esi]; {$ELSE}db $C5,$FB,$10,$0E;{$ENDIF}
{$IFDEF AVXSUP}vmovlhps xmm0, xmm0, xmm1; {$ELSE}db $C5,$F8,$16,$C1;{$ENDIF}
{$IFDEF AVXSUP}vmulsd xmm1, xmm1, [edi]; {$ELSE}db $C5,$F3,$59,$0F;{$ENDIF}
{$IFDEF AVXSUP}vaddsd xmm0, xmm0, xmm1; {$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
//inc(PByte(valCounter1), LineWidth1);
//inc(PByte(valCounter2), LineWidth2);
add esi, LineWidth1;
add edi, LineWidth2;
@@PreInnerLoop:
// rest is a double column!
// prepare loop
mov ebx, height2;
sub ebx, edx;
sub ebx, edx;
sub ebx, 2;
test ebx, ebx;
jle @@InnerLoopEnd;
@@InnerLoop:
// tmp[0] := tmp[0] + valCounter1^[0]*valCounter2^[0];
// tmp[1] := tmp[1] + valCounter1^[0]*valCounter2^[1];
{$IFDEF AVXSUP}vmovddup xmm1, [esi]; {$ELSE}db $C5,$FB,$12,$0E;{$ENDIF}
{$IFDEF AVXSUP}vmovupd xmm2, [edi]; {$ELSE}db $C5,$F9,$10,$17;{$ENDIF}
{$IFDEF AVXSUP}vmulpd xmm2, xmm2, xmm1; {$ELSE}db $C5,$E9,$59,$D1;{$ENDIF}
{$IFDEF AVXSUP}vaddpd xmm0, xmm0, xmm2; {$ELSE}db $C5,$F9,$58,$C2;{$ENDIF}
//inc(PByte(valCounter1), LineWidth1);
//inc(PByte(valCounter2), LineWidth2);
add esi, LineWidth1;
add edi, LineWidth2;
dec ebx;
jnz @@InnerLoop;
@@InnerLoopEnd:
// write back result
// pDest^ := tmp[0];
// PDouble(NativeUint(pDest) + sizeof(double))^ := tmp[1];
{$IFDEF AVXSUP}vmovupd [eax], xmm0; {$ELSE}db $C5,$F9,$11,$00;{$ENDIF}
// inc(pDest, 2);
// inc(pMT2, 2);
add pMT2, 16;
add eax, 16;
// end foryloop
inc edx;
cmp edx, width2D2;
jne @@foryloop;
@@foryloopend:
//if (width2 and $01) = 1 then
mov edx, width2;
and edx, 1;
jz @@ifend1;
// special handling of last column (just copy the value)
// valCounter1 := PConstDoubleArr(mt1);
mov edx, ecx;
//inc(PByte(valCounter1), LineWidth1*(height1 - 1));
mov ebx, height1;
dec ebx;
imul ebx, LineWidth1;
// pDest^ := valCounter1^[0];
{$IFDEF AVXSUP}vmovsd xmm0, [edx + ebx]; {$ELSE}db $C5,$FB,$10,$04,$1A;{$ENDIF}
{$IFDEF AVXSUP}vmovsd [eax], xmm0; {$ELSE}db $C5,$FB,$11,$00;{$ENDIF}
@@ifend1:
//inc(mt1);
//inc(PByte(dest), LineWidthDest);
pop eax;
add ecx, 8;
add eax, aLineWidthDest;
// end for loop
dec Width1;
jnz @@forxloop;
// epilog
{$IFDEF AVXSUP}vzeroupper; {$ELSE}db $C5,$F8,$77;{$ENDIF}
pop edi;
pop esi;
pop ebx;
end;
// calculates mt1 = mt1*mt2', mt2 = lower triangular matrix. diagonal elements are assumed to be 1!
procedure AVXMtxMultLowTria2T2Store1(mt1 : PDouble; LineWidth1 : NativeInt; mt2 : PDouble; LineWidth2 : NativeInt;
width1, height1, width2, height2 : NativeInt);
var aLineWidth1 : NativeInt;
aMt1 : PDouble;
// eax = mt1, edx = LineWidth1, ecx = mt2
asm
push ebx;
push edi;
push esi;
// init
mov aMt1, eax;
mov aLineWidth1, edx;
// iter := -(width2 - 1)*sizeof(double);
mov edx, width2;
dec edx;
imul edx, -8;
// start from bottom
// ebx: mt2
// inc(PByte(mt2),(height2 - 1)*LineWidth2);
mov esi, height2;
dec esi;
imul esi, LineWidth2;
add ecx, esi;
sub ecx, edx;
// for x := 0 to width2 - 2
dec width2;
jz @@endproc;
@@forxloop:
mov eax, aMt1;
sub eax, edx;
// for y := 0 to height1 - 1
mov esi, height1;
@@foryloop:
{$IFDEF AVXSUP}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF}
// for idx := 0 to width2 - x - 2
mov edi, edx;
test edi, edi;
jz @@foridxloopend;