Matrixmultiplikation: Unterschied zwischen den Versionen
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function MatrixMultiplySSE(const M0, M1: Tmat4x4): Tmat4x4; assembler; nostackframe; register; | function MatrixMultiplySSE(const M0, M1: Tmat4x4): Tmat4x4; assembler; nostackframe; register; | ||
asm | asm | ||
| − | Movups | + | Movups Xmm4, [M0 + $00] |
| − | Movups | + | Movups Xmm5, [M0 + $10] |
| − | Movups | + | Movups Xmm6, [M0 + $20] |
| − | Movups | + | Movups Xmm7, [M0 + $30] |
| − | + | // Spalte 0 | |
| − | + | Movups Xmm2, [M1 + $00] | |
| − | |||
| − | |||
| − | |||
| − | + | Pshufd Xmm0, Xmm2, 00000000b | |
| − | + | Mulps Xmm0, Xmm4 | |
| − | Mulps | ||
| − | |||
| − | + | Pshufd Xmm1, Xmm2, 01010101b | |
| − | + | Mulps Xmm1, Xmm5 | |
| − | Mulps | + | Addps Xmm0, Xmm1 |
| − | Addps | ||
| − | + | Pshufd Xmm1, Xmm2, 10101010b | |
| − | + | Mulps Xmm1, Xmm6 | |
| − | Mulps | + | Addps Xmm0, Xmm1 |
| − | Addps | ||
| − | + | Pshufd Xmm1, Xmm2, 11111111b | |
| + | Mulps Xmm1, Xmm7 | ||
| + | Addps Xmm0, Xmm1 | ||
| − | + | Movups [Result + $00], Xmm0 | |
| − | + | ||
| − | + | // Spalte 1 | |
| − | end;</source> | + | Movups Xmm2, [M1 + $10] |
| + | |||
| + | Pshufd Xmm0, Xmm2, 00000000b | ||
| + | Mulps Xmm0, Xmm4 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 01010101b | ||
| + | Mulps Xmm1, Xmm5 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 10101010b | ||
| + | Mulps Xmm1, Xmm6 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 11111111b | ||
| + | Mulps Xmm1, Xmm7 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Movups [Result + $10], Xmm0 | ||
| + | |||
| + | // Spalte 2 | ||
| + | Movups Xmm2, [M1 + $20] | ||
| + | |||
| + | Pshufd Xmm0, Xmm2, 00000000b | ||
| + | Mulps Xmm0, Xmm4 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 01010101b | ||
| + | Mulps Xmm1, Xmm5 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 10101010b | ||
| + | Mulps Xmm1, Xmm6 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 11111111b | ||
| + | Mulps Xmm1, Xmm7 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Movups [Result + $20], Xmm0 | ||
| + | |||
| + | // Spalte 3 | ||
| + | Movups Xmm2, [M1 + $30] | ||
| + | |||
| + | Pshufd Xmm0, Xmm2, 00000000b | ||
| + | Mulps Xmm0, Xmm4 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 01010101b | ||
| + | Mulps Xmm1, Xmm5 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 10101010b | ||
| + | Mulps Xmm1, Xmm6 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Pshufd Xmm1, Xmm2, 11111111b | ||
| + | Mulps Xmm1, Xmm7 | ||
| + | Addps Xmm0, Xmm1 | ||
| + | |||
| + | Movups [Result + $30], Xmm0 | ||
| + | end; | ||
| + | </source> | ||
=== Beispiel === | === Beispiel === | ||
Version vom 10. Juli 2018, 17:05 Uhr
Inhaltsverzeichnis
Matrix Multiplikation
Zur Theorie der Matrixmultiplikation siehe den Matrix Artikel.
Matrix Multiplikation mit Operator
Noch einfacher geht die Matrix Multiplikation, wen man es mit dem Operator "*" machen kann.
Diese Beispiel zeigt dies anhand der der OpenGL üblichen 4x4-Matrix.
type
TVector4f = array[0..3] of GLfloat;
Tmat4x4 = array[0..3] of TVector4f;
operator * (const m1, m2: Tmat4x4) Res: Tmat4x4;
var
i, j, k: integer;
begin
for i := 0 to 3 do begin
for j := 0 to 3 do begin
Res[i, j] := 0;
for k := 0 to 3 do begin
Res[i, j] := Res[i, j] + m2[i, k] * m1[k, j];
end;
end;
end;
end;
Beispiel
var
m, m0, m1: Tmat4x4;
begin
m := m0 * m1; // Sieht sehr einfach aus.
Matrix Multiplikation SSE unterstützt
Mit folgendem SSE-beschleunigtem Code, kann man Matrizen-Multiplikationen bis zu 20x schneller berechnen.
Dies wird von allen gängigen Intel/AMD-CPUs unterstützt. Dies betrifft alle CPUs ab Intel-Core, teilweise auch ältere.
type
TVector4f = array[0..3] of GLfloat;
Tmat4x4 = array[0..3] of TVector4f;
{$asmmode intel}
function MatrixMultiplySSE(const M0, M1: Tmat4x4): Tmat4x4; assembler; nostackframe; register;
asm
Movups Xmm4, [M0 + $00]
Movups Xmm5, [M0 + $10]
Movups Xmm6, [M0 + $20]
Movups Xmm7, [M0 + $30]
// Spalte 0
Movups Xmm2, [M1 + $00]
Pshufd Xmm0, Xmm2, 00000000b
Mulps Xmm0, Xmm4
Pshufd Xmm1, Xmm2, 01010101b
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 10101010b
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 11111111b
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result + $00], Xmm0
// Spalte 1
Movups Xmm2, [M1 + $10]
Pshufd Xmm0, Xmm2, 00000000b
Mulps Xmm0, Xmm4
Pshufd Xmm1, Xmm2, 01010101b
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 10101010b
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 11111111b
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result + $10], Xmm0
// Spalte 2
Movups Xmm2, [M1 + $20]
Pshufd Xmm0, Xmm2, 00000000b
Mulps Xmm0, Xmm4
Pshufd Xmm1, Xmm2, 01010101b
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 10101010b
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 11111111b
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result + $20], Xmm0
// Spalte 3
Movups Xmm2, [M1 + $30]
Pshufd Xmm0, Xmm2, 00000000b
Mulps Xmm0, Xmm4
Pshufd Xmm1, Xmm2, 01010101b
Mulps Xmm1, Xmm5
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 10101010b
Mulps Xmm1, Xmm6
Addps Xmm0, Xmm1
Pshufd Xmm1, Xmm2, 11111111b
Mulps Xmm1, Xmm7
Addps Xmm0, Xmm1
Movups [Result + $30], Xmm0
end;
Beispiel
var
m, m0, m1: Tmat4x4;
begin
m := MatrixMultiplySSE(m0, m1);
Matrix / Vektor Multiplikation mit Operator
Dies funktioniert auch mit Vektoren.
type
TVector4f = array[0..3] of GLfloat;
Tmat4x4 = array[0..3] of TVector4f;
operator * (const m: Tmat4x4; v: TVector4f) Res: TVector4f;
var
i: integer;
begin
for i := 0 to 3 do begin
Res[i] := m[0, i] * v[0] + m[1, i] * v[1] + m[2, i] * v[2]+ m[3, i] * v[3];
end;
end;
Beispiel
var
v : TVector4f;
m, m0: Tmat4x4;
begin
m := m0 * v; // Sieht sehr einfach aus.
Matrix / Vektor Multiplikation SSE-unterstützt
Die SSE-Beschleunigung funktioniert auch mit Vektoren.
type
TVector4f = array[0..3] of GLfloat;
Tmat4x4 = array[0..3] of TVector4f;
{$asmmode intel}
function VectorMultiplySSE(const M: TMatrix; const V: TVector4f): TVector4f; assembler; nostackframe; register;
asm
Movups Xmm4, [M + $00]
Movups Xmm5, [M + $10]
Movups Xmm6, [M + $20]
Movups Xmm7, [M + $30]
// Zeile 0
Movss Xmm0, [V + $00]
Shufps Xmm0, Xmm0, 00000000b
Mulps Xmm0, Xmm4
// Zeile 1
Movss Xmm2, [V + $04]
Shufps Xmm2, Xmm2, 00000000b
Mulps Xmm2, Xmm5
Addps Xmm0, Xmm2
// Zeile 2
Movss Xmm2, [V + $08]
Shufps Xmm2, Xmm2, 00000000b
Mulps Xmm2, Xmm6
Addps Xmm0, Xmm2
// Zeile 3
Movss Xmm2, [V + $0C]
Shufps Xmm2, Xmm2, 00000000b
Mulps Xmm2, Xmm7
Addps Xmm0, Xmm2
Movups [Result], Xmm0
end;
Beispiel
var
v : TVector4f;
m, m0: Tmat4x4;
begin
m := VectorMultiplySSE(m0, v);
Matrix Multiplikation mit dynamischen Matrizen ( no OpenGL )
Dies ist weniger für OpenGL geeignet. Für OpenGL verwendet man besser statische 4x4 oder 3x3 Arrays, siehe oben.
Emre lieferte im Forum diesen kleinen Codeschnipsel für die Matrixmultiplikation ab:
Type
TSMatrix = Array of Array of Single;
// sMatrix := sMatrix * Matrix
procedure pSMatrixMatrixProduct( var sMatrix: TSMatrix; const Matrix: TSMatrix );
var
m, n, o: Integer;
Res : TSMatrix;
begin
// Matrices can only be multiplicated, if the row count of the matrix#1 is the same
// as the column of the second matrix:
if High(sMatrix[0]) <> High(Matrix) then Exit;
// if a k*l matrix is multiplicated by a m*n matrix,
// the result matrix will have a k*n dimension:
SetLength(Res, Length(sMatrix), Length(Matrix[0]));
for m := 0 to High(Res) do
for n := 0 to High(Res[m]) do
for o := 0 to High(Matrix) do
incS(Res[m, n], sMatrix[m, o] * Matrix[o, n]);
sMatrix := Res;
end;
