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FMAMatrixMultOperationsx64.pas
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FMAMatrixMultOperationsx64.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 FMAMatrixMultOperationsx64;
interface
{$IFDEF CPUX64}
{$DEFINE x64}
{$ENDIF}
{$IFDEF cpux86_64}
{$DEFINE x64}
{$ENDIF}
{$IFDEF x64}
uses MatrixConst;
// full matrix operations
procedure FMAMatrixMultAligned(dest : PDouble; const destLineWidth : TASMNativeInt; mt1, mt2 : PDouble; {$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt; const LineWidth1, LineWidth2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
procedure FMAMatrixMultUnAligned(dest : PDouble; const destLineWidth : TASMNativeInt; mt1, mt2 : PDouble; {$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt; const LineWidth1, LineWidth2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
// some special types of multiplications used e.g. in QR Decomposition
// dest = mt1'*mt2; where mt2 is a lower triangular matrix and the operation is transposition
// the function assumes a unit diagonal (does not touch the real middle elements)
// width and height values are assumed to be the "original" (non transposed) ones
procedure FMAMtxMultTria2T1(dest : PDouble; LineWidthDest : TASMNativeInt; mt1 : PDouble; LineWidth1 : TASMNativeInt; {$ifdef UNIX}unixMT2{$ELSE}mt2{$endif} : PDouble; {$ifdef UNIX}unixLineWidth2{$ELSE}LineWidth2{$endif} : TASMNativeInt;
width1, height1, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
// mt1 = mt1*mt2'; where mt2 is an upper triangular matrix
procedure FMAMtxMultTria2T1StoreT1(mt1 : PDouble; LineWidth1 : TASMNativeInt; mt2 : PDouble; LineWidth2 : TASMNativeInt;
{$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
// W = C1*V1*T -> V1 is an upper triangular matrix with assumed unit diagonal entries. Operation on V1 transposition
procedure FMAMtxMultTria2TUpperUnit(dest : PDouble; LineWidthDest : TASMNativeInt; mt1 : PDouble; LineWidth1 : TASMNativeInt;
{$ifdef UNIX}unixMT2{$ELSE}mt2{$endif} : PDouble; {$ifdef UNIX}unixLineWidth2{$ELSE}LineWidth2{$endif} : TASMNativeInt;
width1, height1, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
// calculates mt1 = mt1*mt2', mt2 = lower triangular matrix. diagonal elements are assumed to be 1!
procedure FMAMtxMultLowTria2T2Store1(mt1 : PDouble; LineWidth1 : TASMNativeInt; mt2 : PDouble; LineWidth2 : TASMNativeInt;
{$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
{$ENDIF}
implementation
{$IFDEF FPC} {$ASMMODE intel} {$S-} {$warnings off} {$ENDIF}
{$IFDEF x64}
procedure FMAMatrixMultAligned(dest : PDouble; const destLineWidth : TASMNativeInt; mt1, mt2 : PDouble; {$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt; const LineWidth1, LineWidth2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
var iRBX, iRSI, iRDI, iR12, iR13, iR14, iR15 : TASMNativeInt;
{$ifdef UNIX}
width1 : TASMNativeInt;
height1 : TASMNativeInt;
{$ENDIF}
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov width1, r8;
mov height1, r9;
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
// note: RCX = dest, RDX = destLineWidth, R8 = mt1, R9 = mt2
// prolog - simulate stack
mov iRBX, rbx;
mov iRSI, rsi;
mov iRDI, rdi;
mov iR12, r12;
mov iR13, r13;
mov iR14, r14;
mov iR15, r15;
sub rsp, $30;
{$IFDEF FPC}vmovupd [rsp + $00], xmm4;{$ELSE}db $C5,$F9,$11,$24,$24;{$ENDIF}
{$IFDEF FPC}vmovupd [rsp + $10], xmm5;{$ELSE}db $C5,$F9,$11,$6C,$24,$10;{$ENDIF}
{$IFDEF FPC}vmovupd [rsp + $20], xmm6;{$ELSE}db $C5,$F9,$11,$74,$24,$20;{$ENDIF}
mov rdi, LineWidth1;
mov r10, width1;
imul r10, -8;
sub r8, r10;
mov r11, LineWidth2;
mov r12, width2;
//destOffset := destLineWidth - Width2*sizeof(double);
mov rbx, Width2;
shl rbx, 3;
mov r15, rdx;
sub r15, rbx;
//bytesWidth2 := width2*sizeof(double);
mov r14, rbx;
mov rsi, height1;
// for y := 0 to height1 - 1 do
@@foryloop:
// r12 -> counter to width2
mov r13, r12;
sub r13, 2;
jl @LastXColumn;
@@forxloop:
// for x := 0 to width2 div 2 - 1
// r8: mt1 - width1*sizeof(double)
// r9: mt2
mov rbx, r9;
mov rax, r10;
{$IFDEF FPC}vxorpd ymm0, ymm0, ymm0;{$ELSE}db $C5,$FD,$57,$C0;{$ENDIF}
{$IFDEF FPC}vxorpd ymm1, ymm1, ymm1;{$ELSE}db $C5,$F5,$57,$C9;{$ENDIF}
cmp rax, -32;
jg @@Innerloop2Begin;
// for z := 0 to width1 - 1do
// FMA part:
@@InnerLoop1:
// 4x4 block
{$IFDEF FPC}vmovapd xmm2, [rbx];{$ELSE}db $C5,$F9,$28,$13;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovapd xmm4, xmm2;{$ELSE}db $C5,$F9,$28,$E2;{$ENDIF}
{$IFDEF FPC}vmovapd xmm3, [rbx];{$ELSE}db $C5,$F9,$28,$1B;{$ENDIF}
add rbx, r11;
// shuffle so we can multiply
// swap such that we can immediately multiply
{$IFDEF FPC}vmovlhps xmm2, xmm2, xmm3;{$ELSE}db $C5,$E8,$16,$D3;{$ENDIF}
{$IFDEF FPC}vmovhlps xmm3, xmm3, xmm4;{$ELSE}db $C5,$E0,$12,$DC;{$ENDIF}
// next 4 elements
{$IFDEF FPC}vmovapd xmm4, [rbx];{$ELSE}db $C5,$F9,$28,$23;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovapd xmm6, xmm4;{$ELSE}db $C5,$F9,$28,$F4;{$ENDIF}
{$IFDEF FPC}vmovapd xmm5, [rbx];{$ELSE}db $C5,$F9,$28,$2B;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovapd ymm7, [r8 + rax]{$ELSE}db $C4,$C1,$7D,$28,$3C,$00;{$ENDIF}
{$IFDEF FPC}vmovlhps xmm4, xmm4, xmm5;{$ELSE}db $C5,$D8,$16,$E5;{$ENDIF}
{$IFDEF FPC}vmovhlps xmm5, xmm5, xmm6;{$ELSE}db $C5,$D0,$12,$EE;{$ENDIF}
{$IFDEF FPC}vinsertf128 ymm2, ymm2, xmm4, 1;{$ELSE}db $C4,$E3,$6D,$18,$D4,$01;{$ENDIF}
{$IFDEF FPC}vinsertf128 ymm3, ymm3, xmm5, 1;{$ELSE}db $C4,$E3,$65,$18,$DD,$01;{$ENDIF}
// now multiply and add
{$IFDEF FPC}vfmadd231pd ymm0, ymm7, ymm2;{$ELSE}db $C4,$E2,$C5,$B8,$C2;{$ENDIF}
{$IFDEF FPC}vfmadd231pd ymm1, ymm7, ymm3;{$ELSE}db $C4,$E2,$C5,$B8,$CB;{$ENDIF}
add rax, 32;
jl @@InnerLoop1;
{$IFDEF FPC}vextractf128 xmm2, ymm0, 1;{$ELSE}db $C4,$E3,$7D,$19,$C2,$01;{$ENDIF}
{$IFDEF FPC}vextractf128 xmm3, ymm1, 1;{$ELSE}db $C4,$E3,$7D,$19,$CB,$01;{$ENDIF}
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm2;{$ELSE}db $C5,$F9,$7C,$C2;{$ENDIF}
{$IFDEF FPC}vhaddpd xmm1, xmm1, xmm3;{$ELSE}db $C5,$F1,$7C,$CB;{$ENDIF}
test rax, rax;
jz @@InnerLoopEnd2;
@@Innerloop2Begin:
// rest in single elements
@@InnerLoop2:
{$IFDEF FPC}vmovapd xmm2, [rbx];{$ELSE}db $C5,$F9,$28,$13;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovddup xmm3, [r8 + rax];{$ELSE}db $C4,$C1,$7B,$12,$1C,$00;{$ENDIF}
{$IFDEF FPC}vmulpd xmm2, xmm2, xmm3;{$ELSE}db $C5,$E9,$59,$D3;{$ENDIF}
{$IFDEF FPC}vmovhlps xmm4, xmm4, xmm2;{$ELSE}db $C5,$D8,$12,$E2;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm2;{$ELSE}db $C5,$FB,$58,$C2;{$ENDIF}
{$IFDEF FPC}vaddsd xmm1, xmm1, xmm4;{$ELSE}db $C5,$F3,$58,$CC;{$ENDIF}
add rax, 8;
jnz @@InnerLoop2;
@@InnerLoopEnd2:
// finall horizontal addition
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm1;{$ELSE}db $C5,$F9,$7C,$C1;{$ENDIF}
{$IFDEF FPC}vmovapd [rcx], xmm0;{$ELSE}db $C5,$F9,$29,$01;{$ENDIF}
// increment the pointers
// inc(mt2), inc(dest);
//add dword ptr [mt2], 8;
add r9, 16;
add rcx, 16;
// end for x := 0 to width2 div 2 - 1
sub r13, 2;
jge @@forxloop;
@LastXColumn:
cmp r13, -1;
jne @NextLine;
// last column of mt2
mov rax, r10;
mov rbx, r9;
{$IFDEF FPC}vxorpd xmm0, xmm0, xmm0;{$ELSE}db $C5,$F9,$57,$C0;{$ENDIF}
@InnerLoop2:
{$IFDEF FPC}vmovsd xmm1, [r8 + rax];{$ELSE}db $C4,$C1,$7B,$10,$0C,$00;{$ENDIF}
{$IFDEF FPC}vmovsd xmm2, [rbx];{$ELSE}db $C5,$FB,$10,$13;{$ENDIF}
{$IFDEF FPC}vmulsd xmm1, xmm1, xmm2;{$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm1;{$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add rbx, r11;
add rax, 8;
jnz @InnerLoop2;
{$IFDEF FPC}vmovsd [rcx], xmm0;{$ELSE}db $C5,$FB,$11,$01;{$ENDIF}
add rcx, 8;
add r9, 8;
@NextLine:
// dec(mt2, Width2);
// inc(PByte(mt1), LineWidth1);
// inc(PByte(dest), destOffset);
//mov ebx, bytesWidth2;
//sub dword ptr [mt2], ebx;
sub r9, r14;
add r8, rdi;
add rcx, r15;
// end for y := 0 to height1 - 1
//dec eax;
dec rsi;
jnz @@foryloop;
// epilog
mov rbx, iRBX;
mov rsi, iRSI;
mov rdi, iRDI;
mov r12, iR12;
mov r13, iR13;
mov r14, iR14;
mov r15, iR15;
{$IFDEF FPC}vmovupd xmm4, [rsp + $00];{$ELSE}db $C5,$F9,$10,$24,$24;{$ENDIF}
{$IFDEF FPC}vmovupd xmm5, [rsp + $10];{$ELSE}db $C5,$F9,$10,$6C,$24,$10;{$ENDIF}
{$IFDEF FPC}vmovupd xmm6, [rsp + $20];{$ELSE}db $C5,$F9,$10,$74,$24,$20;{$ENDIF}
add rsp, $30;
{$IFDEF FPC}vzeroupper;{$ELSE}db $C5,$F8,$77;{$ENDIF}
end;
procedure FMAMatrixMultUnAligned(dest : PDouble; const destLineWidth : TASMNativeInt; mt1, mt2 : PDouble; {$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt; const LineWidth1, LineWidth2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
var iRBX, iRSI, iRDI, iR12, iR13, iR14, iR15 : TASMNativeInt;
{$ifdef UNIX}
width1 : TASMNativeInt;
height1 : TASMNativeInt;
{$ENDIF}
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov width1, r8;
mov height1, r9;
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
// note: RCX = dest, RDX = destLineWidth, R8 = mt1, R9 = mt2
// prolog - simulate stack
mov iRBX, rbx;
mov iRSI, rsi;
mov iRDI, rdi;
mov iR12, r12;
mov iR13, r13;
mov iR14, r14;
mov iR15, r15;
sub rsp, $30;
{$IFDEF FPC}vmovupd [rsp + $00], xmm4;{$ELSE}db $C5,$F9,$11,$24,$24;{$ENDIF}
{$IFDEF FPC}vmovupd [rsp + $10], xmm5;{$ELSE}db $C5,$F9,$11,$6C,$24,$10;{$ENDIF}
{$IFDEF FPC}vmovupd [rsp + $20], xmm6;{$ELSE}db $C5,$F9,$11,$74,$24,$20;{$ENDIF}
mov rdi, LineWidth1;
mov r10, width1;
imul r10, -8;
sub r8, r10;
mov r11, LineWidth2;
mov r12, width2;
//destOffset := destLineWidth - Width2*sizeof(double);
mov rbx, Width2;
shl rbx, 3;
mov r15, rdx;
sub r15, rbx;
//bytesWidth2 := width2*sizeof(double);
mov r14, rbx;
mov rsi, height1;
// for y := 0 to height1 - 1 do
@@foryloop:
// r12 -> counter to width2
mov r13, r12;
sub r13, 2;
jl @LastXColumn;
@@forxloop:
// for x := 0 to width2 div 2 - 1
// r8: mt1 - width1*sizeof(double)
// r9: mt2
mov rbx, r9;
mov rax, r10;
{$IFDEF FPC}vxorpd ymm0, ymm0, ymm0;{$ELSE}db $C5,$FD,$57,$C0;{$ENDIF}
{$IFDEF FPC}vxorpd ymm1, ymm1, ymm1;{$ELSE}db $C5,$F5,$57,$C9;{$ENDIF}
cmp rax, -32;
jg @@Innerloop2Begin;
// for z := 0 to width1 - 1do
// FMA part:
@@InnerLoop1:
// 4x4 block
{$IFDEF FPC}vmovupd xmm2, [rbx];{$ELSE}db $C5,$F9,$10,$13;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovapd xmm4, xmm2;{$ELSE}db $C5,$F9,$28,$E2;{$ENDIF}
{$IFDEF FPC}vmovupd xmm3, [rbx];{$ELSE}db $C5,$F9,$10,$1B;{$ENDIF}
add rbx, r11;
// shuffle so we can multiply
// swap such that we can immediately multiply
{$IFDEF FPC}vmovlhps xmm2, xmm2, xmm3;{$ELSE}db $C5,$E8,$16,$D3;{$ENDIF}
{$IFDEF FPC}vmovhlps xmm3, xmm3, xmm4;{$ELSE}db $C5,$E0,$12,$DC;{$ENDIF}
// next 4 elements
{$IFDEF FPC}vmovupd xmm4, [rbx];{$ELSE}db $C5,$F9,$10,$23;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovupd xmm6, xmm4;{$ELSE}db $C5,$F9,$10,$F4;{$ENDIF}
{$IFDEF FPC}vmovupd xmm5, [rbx];{$ELSE}db $C5,$F9,$10,$2B;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovupd ymm7, [r8 + rax]{$ELSE}db $C4,$C1,$7D,$10,$3C,$00;{$ENDIF}
{$IFDEF FPC}vmovlhps xmm4, xmm4, xmm5;{$ELSE}db $C5,$D8,$16,$E5;{$ENDIF}
{$IFDEF FPC}vmovhlps xmm5, xmm5, xmm6;{$ELSE}db $C5,$D0,$12,$EE;{$ENDIF}
{$IFDEF FPC}vinsertf128 ymm2, ymm2, xmm4, 1;{$ELSE}db $C4,$E3,$6D,$18,$D4,$01;{$ENDIF}
{$IFDEF FPC}vinsertf128 ymm3, ymm3, xmm5, 1;{$ELSE}db $C4,$E3,$65,$18,$DD,$01;{$ENDIF}
// now multiply and add
{$IFDEF FPC}vfmadd231pd ymm0, ymm7, ymm2;{$ELSE}db $C4,$E2,$C5,$B8,$C2;{$ENDIF}
{$IFDEF FPC}vfmadd231pd ymm1, ymm7, ymm3;{$ELSE}db $C4,$E2,$C5,$B8,$CB;{$ENDIF}
add rax, 32;
jl @@InnerLoop1;
{$IFDEF FPC}vextractf128 xmm2, ymm0, 1;{$ELSE}db $C4,$E3,$7D,$19,$C2,$01;{$ENDIF}
{$IFDEF FPC}vextractf128 xmm3, ymm1, 1;{$ELSE}db $C4,$E3,$7D,$19,$CB,$01;{$ENDIF}
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm2;{$ELSE}db $C5,$F9,$7C,$C2;{$ENDIF}
{$IFDEF FPC}vhaddpd xmm1, xmm1, xmm3;{$ELSE}db $C5,$F1,$7C,$CB;{$ENDIF}
test rax, rax;
jz @@InnerLoopEnd2;
@@Innerloop2Begin:
// rest in single elements
@@InnerLoop2:
{$IFDEF FPC}vmovupd xmm2, [rbx];{$ELSE}db $C5,$F9,$10,$13;{$ENDIF}
add rbx, r11;
{$IFDEF FPC}vmovddup xmm3, [r8 + rax];{$ELSE}db $C4,$C1,$7B,$12,$1C,$00;{$ENDIF}
{$IFDEF FPC}vmulpd xmm2, xmm2, xmm3;{$ELSE}db $C5,$E9,$59,$D3;{$ENDIF}
{$IFDEF FPC}vmovhlps xmm4, xmm4, xmm2;{$ELSE}db $C5,$D8,$12,$E2;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm2;{$ELSE}db $C5,$FB,$58,$C2;{$ENDIF}
{$IFDEF FPC}vaddsd xmm1, xmm1, xmm4;{$ELSE}db $C5,$F3,$58,$CC;{$ENDIF}
add rax, 8;
jnz @@InnerLoop2;
@@InnerLoopEnd2:
// finall horizontal addition
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm1;{$ELSE}db $C5,$F9,$7C,$C1;{$ENDIF}
{$IFDEF FPC}vmovupd [rcx], xmm0;{$ELSE}db $C5,$F9,$11,$01;{$ENDIF}
// increment the pointers
// inc(mt2), inc(dest);
//add dword ptr [mt2], 8;
add r9, 16;
add rcx, 16;
// end for x := 0 to width2 div 2 - 1
sub r13, 2;
jge @@forxloop;
@LastXColumn:
cmp r13, -1;
jne @NextLine;
// last column of mt2
mov rax, r10;
mov rbx, r9;
{$IFDEF FPC}vxorpd xmm0, xmm0, xmm0;{$ELSE}db $C5,$F9,$57,$C0;{$ENDIF}
@InnerLoop2:
{$IFDEF FPC}vmovsd xmm1, [r8 + rax];{$ELSE}db $C4,$C1,$7B,$10,$0C,$00;{$ENDIF}
{$IFDEF FPC}vmovsd xmm2, [rbx];{$ELSE}db $C5,$FB,$10,$13;{$ENDIF}
{$IFDEF FPC}vmulsd xmm1, xmm1, xmm2;{$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm1;{$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add rbx, r11;
add rax, 8;
jnz @InnerLoop2;
{$IFDEF FPC}vmovsd [rcx], xmm0;{$ELSE}db $C5,$FB,$11,$01;{$ENDIF}
add rcx, 8;
add r9, 8;
@NextLine:
// dec(mt2, Width2);
// inc(PByte(mt1), LineWidth1);
// inc(PByte(dest), destOffset);
//mov ebx, bytesWidth2;
//sub dword ptr [mt2], ebx;
sub r9, r14;
add r8, rdi;
add rcx, r15;
// end for y := 0 to height1 - 1
//dec eax;
dec rsi;
jnz @@foryloop;
// epilog
mov rbx, iRBX;
mov rsi, iRSI;
mov rdi, iRDI;
mov r12, iR12;
mov r13, iR13;
mov r14, iR14;
mov r15, iR15;
{$IFDEF FPC}vmovupd xmm4, [rsp + $00];{$ELSE}db $C5,$F9,$10,$24,$24;{$ENDIF}
{$IFDEF FPC}vmovupd xmm5, [rsp + $10];{$ELSE}db $C5,$F9,$10,$6C,$24,$10;{$ENDIF}
{$IFDEF FPC}vmovupd xmm6, [rsp + $20];{$ELSE}db $C5,$F9,$10,$74,$24,$20;{$ENDIF}
add rsp, $30;
{$IFDEF FPC}vzeroupper;{$ELSE}db $C5,$F8,$77;{$ENDIF}
end;
// ###########################################
// #### Special multiplication routines (for now only used in QR Decomposition)
// ###########################################
procedure FMAMtxMultTria2T1StoreT1(mt1 : PDouble; LineWidth1 : TASMNativeInt; mt2 : PDouble; LineWidth2 : TASMNativeInt;
{$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
var iRBX, iRDI, iRSI : TASMNativeInt;
{$ifdef UNIX}
width1 : TASMNativeInt;
height1 : TASMNativeInt;
{$ENDIF}
// rcx = mt1, rdx = LineWidth1, r8 = mt2, r9 = LineWidth2
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov width1, r8;
mov height1, r9;
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
// prolog: stack
mov iRBX, rbx;
mov iRDI, rdi;
mov iRSI, rsi;
//iter := -width1*sizeof(double);
mov r10, width1;
imul r10, -8;
// testExitLoopVal := height2*sizeof(double) + iter;
mov r11, height2;
shl r11, 3; //*8
add r11, r10;
// rcx := mt1
sub rcx, r10; // mt1 - iter
// for y loop
@@foryloop:
mov rbx, r8;
sub rbx, r10;
mov rsi, r10;
@@forxloop:
{$IFDEF FPC}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF} // temp := 0
mov rax, rsi; // loop counter x;
// test if height2 > width1 and loop counter > width1
mov rdi, rax;
test rdi, rdi;
jge @@foriloopend;
// in case x is odd -> handle the first element separately
and rdi, $E;
jz @@foriloopFMA;
// single element handling
{$IFDEF FPC}vmovsd xmm1, [rcx + rax];{$ELSE}db $C5,$FB,$10,$0C,$01;{$ENDIF}
{$IFDEF FPC}vmovsd xmm2, [rbx + rax];{$ELSE}db $C5,$FB,$10,$14,$03;{$ENDIF}
{$IFDEF FPC}vmulsd xmm1, xmm1, xmm2;{$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm1;{$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add rax, 8;
@@foriloopFMA:
// 4 elements at a time
add rax, 32;
jg @@foriloopFMAend;
{$IFDEF FPC}vmovupd ymm1, [rcx + rax - 32];{$ELSE}db $C5,$FD,$10,$4C,$01,$E0;{$ENDIF}
{$IFDEF FPC}vmovupd ymm2, [rbx + rax - 32];{$ELSE}db $C5,$FD,$10,$54,$03,$E0;{$ENDIF}
{$IFDEF FPC}vfmadd231pd ymm0, ymm1, ymm2;{$ELSE}db $C4,$E2,$F5,$B8,$C2;{$ENDIF}
jmp @@foriloopFMA;
@@foriloopFMAend:
{$IFDEF FPC}vextractf128 xmm2, ymm0, 1;{$ELSE}db $C4,$E3,$7D,$19,$C2,$01;{$ENDIF}
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm2;{$ELSE}db $C5,$F9,$7C,$C2;{$ENDIF}
sub rax, 32;
jz @@foriloopend;
// for i := x to width1 - 1
@@foriloop:
// two elements at a time:
{$IFDEF FPC}vmovupd xmm1, [rcx + rax];{$ELSE}db $C5,$F9,$10,$0C,$01;{$ENDIF}
{$IFDEF FPC}vmovupd xmm2, [rbx + rax];{$ELSE}db $C5,$F9,$10,$14,$03;{$ENDIF}
{$IFDEF FPC}vfmadd231pd xmm0, xmm1, xmm2;{$ELSE}db $C4,$E2,$F1,$B8,$C2;{$ENDIF}
add rax, 16;
jnz @@foriloop;
@@foriloopend:
// final result
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm0;{$ELSE}db $C5,$F9,$7C,$C0;{$ENDIF}
{$IFDEF FPC}vmovsd [rcx + rsi], xmm0;{$ELSE}db $C5,$FB,$11,$04,$31;{$ENDIF}
add rbx, r9;
add rsi, 8;
mov rax, r11;
cmp rsi, rax;
jne @@forxloop;
add rcx, rdx;
dec height1;
jnz @@foryloop;
// epilog
mov rbx, iRBX;
mov rdi, iRDI;
mov rsi, iRSI;
{$IFDEF FPC}vzeroupper;{$ELSE}db $C5,$F8,$77;{$ENDIF}
end;
procedure FMAMtxMultTria2TUpperUnit(dest : PDouble; LineWidthDest : TASMNativeInt; mt1 : PDouble; LineWidth1 : TASMNativeInt;
{$ifdef UNIX}unixMT2{$ELSE}mt2{$endif} : PDouble; {$ifdef UNIX}unixLineWidth2{$ELSE}LineWidth2{$endif} : TASMNativeInt;
width1, height1, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
var iRBX, iRDI, iRSI, iR12, iR13 : TASMNativeInt;
{$IFDEF UNIX}
mt2 : PDouble;
LineWidth2 : TASMNativeInt;
{$ENDIF}
// rcx = dest, rdx = LineWidthDest, r8 = mt1, r9 = LineWidth1
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov mt2, r8;
mov LineWidth2, r9;
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
// prolog: stack
mov iRBX, rbx;
mov iRDI, rdi;
mov iRSI, rsi;
mov iR12, r12;
mov iR13, r13;
// r12: mt2
mov r12, mt2;
// r13: LineWidth2
mov r13, LineWidth2;
//iter := -width1*sizeof(double);
mov r10, width1;
imul r10, -8;
// testExitLoopVal := height2*sizeof(double) + iter;
mov r11, height2;
shl r11, 3; //*8
add r11, r10;
// r8 := mt1
sub r8, r10; // mt1 - iter
sub rcx, r10;
// for y loop
@@foryloop:
mov rbx, r12;
sub rbx, r10;
mov rsi, r10;
@@forxloop:
{$IFDEF FPC}vxorpd ymm0, ymm0, ymm0; {$ELSE}db $C5,$FD,$57,$C0;{$ENDIF} // temp := 0
mov rax, rsi; // loop counter x;
// test if height2 > width1 and loop counter > width1
mov rdi, rax;
test rdi, rdi;
jge @@foriloopend;
// in case x is odd -> handle the first element separately
and rdi, $E;
jz @@foriloopinit;
// single element handling -> mt1 first element is assumed unit!
{$IFDEF FPC}vmovsd xmm0, [r8 + rax];{$ELSE}db $C4,$C1,$7B,$10,$04,$00;{$ENDIF}
add rax, 8;
jmp @@AfterLoopInit;
@@foriloopinit:
test rax, rax;
jz @@foriloopend;
// two elements init at a time:
{$IFDEF FPC}vmovsd xmm0, [r8 + rax];{$ELSE}db $C4,$C1,$7B,$10,$04,$00;{$ENDIF}
{$IFDEF FPC}vmovsd xmm1, [r8 + rax + 8];{$ELSE}db $C4,$C1,$7B,$10,$4C,$00,$08;{$ENDIF}
{$IFDEF FPC}vmovsd xmm2, [rbx + rax + 8];{$ELSE}db $C5,$FB,$10,$54,$03,$08;{$ENDIF}
{$IFDEF FPC}vmulsd xmm1, xmm1, xmm2;{$ELSE}db $C5,$F3,$59,$CA;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm1;{$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
add rax, 16;
@@AfterLoopInit:
// in case the last single x element was handled we do not need further looping
test rax, rax;
jz @@finalizeloop;
// for i := x to width1 - 1
@@foriloop:
add rax, 32;
jg @@foriloopend;
// two elements at a time:
{$IFDEF FPC}vmovupd ymm1, [r8 + rax - 32];{$ELSE}db $C4,$C1,$7D,$10,$4C,$00,$E0;{$ENDIF}
{$IFDEF FPC}vmovupd ymm2, [rbx + rax - 32];{$ELSE}db $C5,$FD,$10,$54,$03,$E0;{$ENDIF}
{$IFDEF FPC}vfmadd231pd ymm0, ymm1, ymm2;{$ELSE}db $C4,$E2,$F5,$B8,$C2;{$ENDIF}
jmp @@foriloop;
@@foriloopend:
{$IFDEF FPC}vextractf128 xmm1, ymm0, 1;{$ELSE}db $C4,$E3,$7D,$19,$C1,$01;{$ENDIF}
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm1;{$ELSE}db $C5,$F9,$7C,$C1;{$ENDIF}
sub rax, 32;
// test if we missed 2 elements
jz @@finalizeloop;
// need to process two more elements:
{$IFDEF FPC}vmovupd xmm1, [r8 + rax];{$ELSE}db $C4,$C1,$79,$10,$0C,$00;{$ENDIF}
{$IFDEF FPC}vmovupd xmm2, [rbx + rax];{$ELSE}db $C5,$F9,$10,$14,$03;{$ENDIF}
{$IFDEF FPC}vfmadd231pd xmm0, xmm1, xmm2;{$ELSE}db $C4,$E2,$F1,$B8,$C2;{$ENDIF}
@@finalizeloop:
// final result
{$IFDEF FPC}vhaddpd xmm0, xmm0, xmm0;{$ELSE}db $C5,$F9,$7C,$C0;{$ENDIF}
{$IFDEF FPC}vmovsd [rcx + rsi], xmm0;{$ELSE}db $C5,$FB,$11,$04,$31;{$ENDIF}
add rbx, r13;
add rsi, 8;
mov rax, r11;
cmp rsi, rax;
jne @@forxloop;
add r8, r9;
add rcx, rdx;
dec height1;
jnz @@foryloop;
// epilog
mov rbx, iRBX;
mov rdi, iRDI;
mov rsi, iRSI;
mov r12, iR12;
mov r13, iR13;
{$IFDEF FPC}vzeroupper;{$ELSE}db $C5,$F8,$77;{$ENDIF}
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 FMAMtxMultTria2T1(dest : PDouble; LineWidthDest : TASMNativeInt; mt1 : PDouble; LineWidth1 : TASMNativeInt;
{$ifdef UNIX}unixMT2{$ELSE}mt2{$endif} : PDouble; {$ifdef UNIX}unixLineWidth2{$ELSE}LineWidth2{$endif} : TASMNativeInt;
width1, height1, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
var pMt2 : PDouble;
iRBX, iRSI, iRDI, iR12, iR13, iR14, iR15 : TASMNativeInt;
{$IFDEF UNIX}
mt2 : PDouble;
LineWidth2 : TASMNativeInt;
{$ENDIF}
// note: RCX = dest, RDX = destLineWidth, R8 = mt1, R9 = LineWidth1
// prolog - simulate stack
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov mt2, r8;
mov LineWidth2, r9;
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
mov iR12, r12;
mov iR13, r13;
mov iR14, r14;
mov iR15, r15;
mov iRSI, rsi;
mov iRDI, rdi;
mov iRBX, rbx;
mov r15, LineWidth2; // Linewidth2 is on the stack -> use it in local register
// width2D2 := width2 div 2;
mov r14, width2;
shr r14, 1;
// for x := 0 to width1 - 1 do
mov rax, width1;
@@forxloop:
// pMT2 := mt2;
// pDest := dest;
mov rbx, mt2;
mov pMT2, rbx;
mov r13, rcx; // r13 is pDest
// for y := 0 to width2D2 - 1 do
mov r12, r14;
test r12, r12;
jz @@foryloopend;
xor r12, r12;
@@foryloop:
// valCounter1 := PConstDoubleArr(mt1);
// inc(PByte(valCounter1), 2*y*LineWidth1);
mov rsi, r8;
mov rbx, r12;
add rbx, rbx;
imul rbx, r9;
add rsi, rbx;
// valCounter2 := PConstDoubleArr(pMT2);
// inc(PByte(valCounter2), (2*y + 1)*LineWidth2);
mov rdi, pMt2;
mov rbx, r12;
add rbx, rbx;
imul rbx, r15;
add rbx, r15;
add rdi, rbx;
// tmp[0] := valCounter1^[0];
// inc(PByte(valCounter1), LineWidth1);
{$IFDEF FPC}vmovsd xmm0, [rsi];{$ELSE}db $C5,$FB,$10,$06;{$ENDIF}
add rsi, r9;
// if height2 - 2*y - 1 > 0 then
mov rbx, r12;
add rbx, rbx;
inc rbx;
cmp rbx, height2;
jnl @@PreInnerLoop;
// tmp[0] := tmp[0] + valCounter1^[0]*valCounter2^[0];
// tmp[1] := valCounter1^[0];
{$IFDEF FPC}vmovsd xmm1, [rsi];{$ELSE}db $C5,$FB,$10,$0E;{$ENDIF}
{$IFDEF FPC}vmovlhps xmm0, xmm0, xmm1;{$ELSE}db $C5,$F8,$16,$C1;{$ENDIF}
{$IFDEF FPC}vmulsd xmm1, xmm1, [rdi];{$ELSE}db $C5,$F3,$59,$0F;{$ENDIF}
{$IFDEF FPC}vaddsd xmm0, xmm0, xmm1;{$ELSE}db $C5,$FB,$58,$C1;{$ENDIF}
//inc(PByte(valCounter1), LineWidth1);
//inc(PByte(valCounter2), LineWidth2);
add rsi, r9;
add rdi, r15;
@@PreInnerLoop:
// rest is a double column!
// prepare loop
mov rbx, height2;
sub rbx, r12;
sub rbx, r12;
sub rbx, 2;
test rbx, rbx;
jle @@InnerLoopEnd;
@@InnerLoop:
// tmp[0] := tmp[0] + valCounter1^[0]*valCounter2^[0];
// tmp[1] := tmp[1] + valCounter1^[0]*valCounter2^[1];
{$IFDEF FPC}vmovddup xmm1, [rsi];{$ELSE}db $C5,$FB,$12,$0E;{$ENDIF}
{$IFDEF FPC}vmovupd xmm2, [rdi];{$ELSE}db $C5,$F9,$10,$17;{$ENDIF}
{$IFDEF FPC}vfmadd231pd xmm0, xmm1, xmm2;{$ELSE}db $C4,$E2,$F1,$B8,$C2;{$ENDIF}
//inc(PByte(valCounter1), LineWidth1);
//inc(PByte(valCounter2), LineWidth2);
add rsi, r9;
add rdi, r15;
dec rbx;
jnz @@InnerLoop;
@@InnerLoopEnd:
// write back result
// pDest^ := tmp[0];
// PDouble(TASMNativeUInt(pDest) + sizeof(double))^ := tmp[1];
{$IFDEF FPC}vmovupd [r13], xmm0;{$ELSE}db $C4,$C1,$79,$11,$45,$00;{$ENDIF}
// inc(pDest, 2);
// inc(pMT2, 2);
add r13, 16;
add pMT2, 16;
// end foryloop
inc r12;
cmp r12, r14;
jne @@foryloop;
@@foryloopend:
//if (width2 and $01) = 1 then
mov r12, width2;
and r12, 1;
jz @@ifend1;
// special handling of last column (just copy the value)
// valCounter1 := PConstDoubleArr(mt1);
mov r12, r8;
//inc(PByte(valCounter1), LineWidth1*(height1 - 1));
mov rbx, height1;
dec rbx;
imul rbx, r9;
// pDest^ := valCounter1^[0];
{$IFDEF FPC}vmovsd xmm0, [r12 + rbx];{$ELSE}db $C4,$C1,$7B,$10,$04,$1C;{$ENDIF}
{$IFDEF FPC}vmovsd [r13], xmm0;{$ELSE}db $C4,$C1,$7B,$11,$45,$00;{$ENDIF}
@@ifend1:
//inc(mt1);
//inc(PByte(dest), LineWidthDest);
add r8, 8;
add rcx, rdx; // note: this can be done since dest is rcx
// end for loop
dec rax;
jnz @@forxloop;
// epilog
mov r12, iR12;
mov r13, iR13;
mov r14, iR14;
mov r15, iR15;
mov rsi, iRSI;
mov rdi, iRDI;
mov rbx, iRBX;
{$IFDEF FPC}vzeroupper;{$ELSE}db $C5,$F8,$77;{$ENDIF}
end;
// calculates mt1 = mt1*mt2', mt2 = lower triangular matrix. diagonal elements are assumed to be 1!
procedure FMAMtxMultLowTria2T2Store1(mt1 : PDouble; LineWidth1 : TASMNativeInt; mt2 : PDouble; LineWidth2 : TASMNativeInt;
{$ifdef UNIX}unixWidth1{$ELSE}width1{$ENDIF}, {$ifdef UNIX}unixHeight1{$ELSE}height1{$ENDIF}, width2, height2 : TASMNativeInt); {$IFDEF FPC}assembler;{$ENDIF}
var iRBX, iRDI, iRSI : TASMNativeInt;
{$ifdef UNIX}
width1 : TASMNativeInt;
height1 : TASMNativeInt;
{$ENDIF}
// rcx: mt1, rdx: LineWidth1, r8 : mt2, r9 : LineWidth2
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov width1, r8;
mov height1, r9;
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
// prolog - stack
mov iRBX, rbx;
mov iRDI, rdi;
mov iRSI, rsi;
// r11 : height1
mov r11, height1;
// r10 = iter := -(width2 - 1)*sizeof(double);
mov r10, width2;
dec r10;
imul r10, -8;