Das ganze ist ideal für OpenGL-Freunde. Es läuft mit 32 und 64Bit Intel/AMD-CPUs.
Code: Alles auswählen
Type
TVector4f = array[0..3] of Single;
TMatrix = array [0..3, 0..3] of SingleCode: Alles auswählen
operator * (const mat0, mat1: TMatrix) Res: TMatrix;
var
i, j, k: integer;
begin
for i := 0 to 3 do begin
for j := 0 to 3 do begin
Res[i, j] := 0.0;
for k := 0 to 3 do begin
Res[i, j] += mat1[i, k] * mat0[k, j];
end;
end;
end;
end; Code: Alles auswählen
function VectorMultiplySSE(const mat: TMatrix; const vec: TVector4f): TVector4f; assembler;
{$asmmode intel}
asm
// pointer to the first 4 elements of the array:
// Move Unaligned Parallel Scalars
// load the registers with matrix values:
Movups Xmm4, [mat+$30] // xmm4 contains 1,5, 9,13
Movups Xmm5, [mat+$20] // +16 (4 bytes x 4 elements)
// xmm5 contains 2,6,10,14
Movups Xmm6, [mat+$10] // +32 (8 bytes x 4 elements)
// xmm6 contains 3,7,11,15
Movups Xmm7, [mat+$00] // +48 (12 bytes x 4
// esi contains the starting address of the vec array
// [2, 3, 4, 5], so load this vector into xmm0:
Movups Xmm0, [vec] // xmm0 contains 2, 3, 4, 5
// we'll store the final result in xmm2, initialize it to 0:
Xorps Xmm2, Xmm2 // xmm2 contains 4x32
// bits with zeros
// now we need to multiply first column (xmm4)
// by the vector (xmm0) and add it to the total (xmm2)
// copy content of xmm0 into xmm1:
Movups Xmm1, Xmm0 // xmm1 now contains
// [2, 3, 4, 5]
// each value in xmm1 has the following mask representation:
// mask value: 11 10 01 00
// register value: [ 2, 3, 4, 5 ]
// Shuffle Parallel Scalars
Shufps Xmm1, Xmm1, $FF // FF mask is 11 11 11 11
// xmm1 contains 2, 2, 2, 2
// Multiply Parallel Scalars
Mulps Xmm1, Xmm4 // multiply xmm1 (2,2,2,2)
// and xmm4 (1,5,9,13)
// [ 2*1, 2*5, 2*9, 2*13 ]
// save it in xmm1
// Add Parallel Scalars
Addps Xmm2, Xmm1 // add xmm2 (0, 0, 0, 0)
// and xmm1 (2, 10, 18, 26)
// save it in xmm2
// xmm2 contains [2,10,18,26]
// we multiplied first column of the matrix by the vector,
// now we need to repeat these operations for the remaining
// columns of the matrix
Movups Xmm1, Xmm0 // 3, 3, 3, 3
Shufps Xmm1, Xmm1, $AA // AA -> 10 10 10 10
Mulps Xmm1, Xmm5 // xmm5: 2, 6, 10, 14
Addps Xmm2, Xmm1 // 2+6, 10+18, 18+30, 26+42
Movups Xmm1, Xmm0 // 4, 4, 4, 4
Shufps Xmm1, Xmm1, $55 // 55 -> 01 01 01 01
Mulps Xmm1, Xmm6 // xmm6: 3, 7, 11, 15
Addps Xmm2, Xmm1 // 8+12, 28+28, 48+44, 68+60
Movups Xmm1, Xmm0 // 5, 5, 5, 5
Shufps Xmm1, Xmm1, $00 // 00 -> 00 00 00 00
Mulps Xmm1, Xmm7 // xmm7: 4, 8, 12, 16
Addps Xmm2, Xmm1 // 20+20, 56+40, 92+60, 128+80
// 40 , 96 , 152 , 208
// write the results to vectorOut
Movups [result], Xmm2
end;
function MatrixMultiplySSE(const M1, M2: TMatrix): TMatrix; assembler;
asm
// load M1 into xxm entirely as we will need it more than once
Movups Xmm4, [M1+$00] // movaps
Movups Xmm5, [M1+$10]
Movups Xmm6, [M1+$20]
Movups Xmm7, [M1+$30]
// compute Result[0]
Movss Xmm0, [M2]
Shufps Xmm0, Xmm0, $00 //xmm0 = 4x M2[0,0]
Mulps Xmm0, Xmm4
Movss Xmm1, [M2+$04]
Shufps Xmm1, Xmm1, $00 //xmm1 = 4x M2[0,1]
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$08]
Shufps Xmm1, Xmm1, $00 //xmm1 = 4x M2[0,2]
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$0c]
Shufps Xmm1, Xmm1, $00 //xmm1 = 4x M2[0,3]
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result+$00], Xmm0 // movntps
// compute Result[1]
Movss Xmm0, [M2+$10]
Shufps Xmm0, Xmm0, $00
Mulps Xmm0, Xmm4
Movss Xmm1, [M2+$14]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$18]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$1c]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result+$10], Xmm0
// compute Result[2]
Movss Xmm0, [M2+$20]
Shufps Xmm0, Xmm0, $00
Mulps Xmm0, Xmm4
Movss Xmm1, [M2+$24]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$28]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$2c]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result+$20], Xmm0
// compute Result[3]
Movss Xmm0, [M2+$30]
Shufps Xmm0, Xmm0, $00
Mulps Xmm0, Xmm4
Movss Xmm1, [M2+$34]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$38]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Movss Xmm1, [M2+$3c]
Shufps Xmm1, Xmm1, $00
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result+$30], Xmm0
end; Code: Alles auswählen
procedure TForm1.Button1Click(Sender: TObject);
var
i: integer;
m, m0, m1: Tmat4x4;
t: TTime;
const
site = 20000001;
procedure Ausgabe;
var
i: integer;
begin
for i := 0 to 3 do begin
WriteLn(m0[i, 0]: 4: 2, ' ', m0[i, 1]: 4: 2, ' ', m0[i, 2]: 4: 2, ' ', m0[i, 3]: 4: 2);
end;
WriteLn();
end;
function GetZeit(z: TTime): string;
begin
str(z * 24 * 60 * 60: 10: 4, Result);
end;
begin
m0.Identity;
m1.Identity;
m1.RotateC(3.5);
t := now;
for i := 0 to site do begin
m0 := m0 * m1;
end;
WriteLn('FPU: ', GetZeit(now - t));
Ausgabe;
m0.Identity;
m1.Identity;
m1.RotateC(3.5);
t := now;
for i := 0 to site do begin
m0 := MatrixMultiplySSE(m0, m1);
end;
WriteLn('SSE: ', GetZeit(now - t));
Ausgabe;
WriteLn();
WriteLn();
WriteLn();
end; Code: Alles auswählen
FPU: 2.6060
0.55 0.69 0.00 0.00
-0.69 0.55 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00
SSE: 0.2920
0.55 0.69 0.00 0.00
-0.69 0.55 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00
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