This function computes the inverted 3x3 matrix formed by a Double FPU (Real8) data.
InvertMatrix_3x3_Double
;;
InvertMatrix_3x3_Double
This function generates the inversion of a 3x3 squared matrix
Parameters:
InputMatrix: A pointer to a 3x3 matrix used as input. The size of the element on each member
of the matrix must be a douuble (Real8) FPU data.
OutputMatrix: A pointer to a buffer that wil receive the generated 3x3 matrix.
The size of the buffer must be 72 bytes (equivalent to 9 Real8 FPU variables), representing a 3x3 matrix formed by
double FPU. So, 8*3*3 = 72.
Return Value:
If the function suceeds it returns TRUE and the OutputMatrix parameter will hold the converted data.
If it fails it returns FALSE meaning that the matrix can not be inverted. It happens when the computed determinant is 0.
Remarks:
A square matrix that is not invertible is called singular or degenerate.
A square matrix is singular if and only if its determinant is 0.
References: https://en.wikipedia.org/wiki/Invertible_matrix
Example of usage:
[TestMatrix1:
Test_M1: R$ 0.8951 Test_M2: R$ 0.2664 Test_M3: R$ -0.1614
Test_M4: R$ -0.7502 Test_M5: R$ 1.7135 Test_M6: R$ 0.0367
Test_M7: R$ 0.0389 Test_M8: R$ -0.0685 Test_M9: R$ 1.0296]
[TestMatrix2: R$ 0 #9]
call InvertMatrix_3x3_Double TestMatrix1, TestMatrix2
;;
Proc InvertMatrix_3x3_Double:
Arguments @InputMatrix, @OutputMatrix
Structure @TempStruct 264, @TmpDeterminantDis 0, @TmpOutMatrix1Dis 8, @TmpOutMatrix2Dis 136
Uses edi, esi, ecx, ebx
finit
mov esi D@InputMatrix
lea edi D@TmpOutMatrix1Dis
;;
[FloatMatrices.M1Dis (a) FloatMatrices.M2Dis (b) FloatMatrices.M3Dis (c)
FloatMatrices.M4Dis (d) FloatMatrices.M5Dis (e) FloatMatrices.M6Dis (f)
FloatMatrices.M7Dis (g) FloatMatrices.M8Dis (h) FloatMatrices.M9Dis] (i)
;;
; A = ei-fh
fld R$esi+FloatMatrices.M5Dis | fmul R$esi+FloatMatrices.M9Dis
fld R$esi+FloatMatrices.M6Dis | fmul R$esi+FloatMatrices.M8Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M1Dis
; B = -(di-fg) = fg-di
fld R$esi+FloatMatrices.M6Dis | fmul R$esi+FloatMatrices.M7Dis
fld R$esi+FloatMatrices.M4Dis | fmul R$esi+FloatMatrices.M9Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M2Dis
; C = dh-eg
fld R$esi+FloatMatrices.M4Dis | fmul R$esi+FloatMatrices.M8Dis
fld R$esi+FloatMatrices.M5Dis | fmul R$esi+FloatMatrices.M7Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M3Dis
; D = -(bi-ch) = ch-bi
fld R$esi+FloatMatrices.M3Dis | fmul R$esi+FloatMatrices.M8Dis
fld R$esi+FloatMatrices.M2Dis | fmul R$esi+FloatMatrices.M9Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M4Dis
; E = ai-cg
fld R$esi+FloatMatrices.M1Dis | fmul R$esi+FloatMatrices.M9Dis
fld R$esi+FloatMatrices.M3Dis | fmul R$esi+FloatMatrices.M7Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M5Dis
; F = -(ah-bg) = bg-ah
fld R$esi+FloatMatrices.M2Dis | fmul R$esi+FloatMatrices.M7Dis
fld R$esi+FloatMatrices.M1Dis | fmul R$esi+FloatMatrices.M8Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M6Dis
; G = bf-ce
fld R$esi+FloatMatrices.M2Dis | fmul R$esi+FloatMatrices.M6Dis
fld R$esi+FloatMatrices.M3Dis | fmul R$esi+FloatMatrices.M5Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M7Dis
; H = -(af-cd) = cd-af
fld R$esi+FloatMatrices.M3Dis | fmul R$esi+FloatMatrices.M4Dis
fld R$esi+FloatMatrices.M1Dis | fmul R$esi+FloatMatrices.M6Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M8Dis
; I = ae-bd
fld R$esi+FloatMatrices.M1Dis | fmul R$esi+FloatMatrices.M5Dis
fld R$esi+FloatMatrices.M2Dis | fmul R$esi+FloatMatrices.M4Dis | fchs | faddp ST1 ST0
fstp R$edi+FloatMatrices.M9Dis
; get determinant
lea eax D@TmpDeterminantDis
call GetDeterminantOfMatrix3x3_Double D@InputMatrix, eax
On eax = 0, ExitP ; Matrix not invertible
fld1 | fdiv R@TmpDeterminantDis | fstp R@TmpDeterminantDis
lea ebx D@TmpOutMatrix2Dis
call Fast_MatrixTranspose_Double edi, ebx, 3, 3
mov edi D@OutputMatrix
xor ecx ecx
Do
fld R$ebx+ecx*8 | fmul R@TmpDeterminantDis | fstp R$edi+ecx*8
inc ecx
Loop_Until ecx => 9
mov eax &TRUE
EndP
Aditional functions:
GetDeterminantOfMatrix3x3_Double
__________________________________________________________________________________________________
;;
GetDeterminantOfMatrix3x3_Double
This function retrieves the determinant of a 3x3 matrix
Parameters:
pMatrix - The pointer to a 3x3 squared matrix used as input from where we want to find it´s determinant
The size of each element of the matrix must be a Double FPU data (Real8)
pDeterminant - A pointer to a buffer to store the calculated determinant in Real8 data. The size of the buffer must be in
double FPU (Real8).
Return Value: If the function suceeds, it returns TRUE and also store the determinant value on the output buffer (pDeterminant).
If the function fails, it returns FALSE meaning that the square matrix is singular and also if you are using the function
to determine the inverse of a matrix, a FALSE result can also be used to confirm that the matrix can not be inverted.
;;
Proc GetDeterminantOfMatrix3x3_Double:
Arguments @pMatrix, @pDeterminant
Structure @DeterminantData 8, @DeterminantDataDis 0
Uses esi, edi
mov esi D@pMatrix
fld R$esi+FloatMatrices.M1Dis
fld R$esi+FloatMatrices.M5Dis | fld R$esi+FloatMatrices.M9Dis | fmulp ST1 ST0
fld R$esi+FloatMatrices.M6Dis | fld R$esi+FloatMatrices.M8Dis | fmulp ST1 ST0
fchs
faddp ST1 ST0
fmulp ST1 ST0
fld R$esi+FloatMatrices.M2Dis
fchs
fld R$esi+FloatMatrices.M4Dis | fld R$esi+FloatMatrices.M9Dis | fmulp ST1 ST0
fld R$esi+FloatMatrices.M6Dis | fld R$esi+FloatMatrices.M7Dis | fmulp ST1 ST0
fchs
faddp ST1 ST0
fmulp ST1 ST0
fld R$esi+FloatMatrices.M3Dis
fld R$esi+FloatMatrices.M4Dis | fld R$esi+FloatMatrices.M8Dis | fmulp ST1 ST0
fld R$esi+FloatMatrices.M5Dis | fld R$esi+FloatMatrices.M7Dis | fmulp ST1 ST0
fchs
faddp ST1 ST0
fmulp ST1 ST0
faddp ST1 ST0
faddp ST1 ST0
fstp R@DeterminantDataDis
mov edi D@pDeterminant
Fpu_If R@DeterminantDataDis = R$Float_Zero
fldz | fstp R$edi ; make sure it is zero with any other rounding down value
xor eax eax
Fpu_Else
fld R@DeterminantDataDis | fstp R$edi
mov eax &TRUE
Fpu_End_If
EndP
Fast_MatrixTranspose_Double
;;
Fast_MatrixTranspose_Double
This function transposes a marix with any size n*n
Parameters:
Input - A pointer to a matrix of any size (width and height) to be transposed.
The elements opf the matrix must be a Real8 (Double) each.
Output - A pointer to a buffer to receive the transposed data.
The size of the buffer must be at least 128 bytes (4*4*8 = Width(4)*Height(4)*8(size of Real8FPU)).
Also, the buffer must be aligned to 32 bytes (4 Real8) so it can compute the resultant transpose
properly without affecting the data that are located after the end of the matrix.
In other words, If your matrix have a size of 5*5, it means that you will need a buffer of
200 Bytes (5*5*8) plus 24 extra bytes (3 Real8 Fpu data), since the internal computation of the transposition matrix
work from 4*4 data each. So, if the matrix size is not a multiple of you will need more Real8 Fpu on the buffer to complete.
Width - The width of the matrix (an integer)
Height - The height of the matrix (an integer)
Return Values: On exit the function will return the pointer to the start of the transposed matrix.
In other words, it will return the same start address of the buffer you settled on Output parameter
but will then contain the transposed matrix
Example of usage:
[Teste6x4: R$ 1, 2, 3, 4, 5, 6,
R$ 26, 7, 8, 9, 10,27
R$ 11, 12, 13, 14, 15,28
R$ 16, 17, 18, 19, 20,29]
[MyMatrixBuffer: R$ 0 #(6*4)]; No need for padding buffers, since it is a multiple of 4
call Fast_MatrixTranspose_Double Teste6x4, ebx, 6, 4
[Teste5x5: R$ 1, 2, 3, 4, 5,
R$ 26, 7, 8, 9, 10,
R$ 11, 12, 13, 14, 15,
R$ 16, 17, 18, 19, 20,
R$ 46, 117, 4, 129, 23,]
[MyMatrixBuffer: R$ 0 #(5*5)
PaddingBuffer: R$ 0 #3] ; Extra 3 Real8 FPU to complete the buffer size
call Fast_MatrixTranspose_Double Teste6x4, ebx, 6, 4
Reference:
http://masm32.com/board/index.php?topic=6105.15
;;
Proc Fast_MatrixTranspose_Double:
Arguments @Input, @Output, @Width, @Height
Local @CurXPos, @RemainderY, @MaxYPos
Uses esi, edi, ebx, ecx, edx
mov esi D@Input
mov edi D@Output
; get remainders for edi
mov D@RemainderY 0
mov edx D@Height | mov ecx edx | shr edx 2 | mov D@MaxYPos edx | and ecx 3; Check if value (Height) is a multiple of 4
jz L1>
; found not multiple of 4
inc D@MaxYPos ; if height have a remainder (i mean, not multiple of 4, increment it)
mov eax 4 | sub eax ecx | shl eax 3
mov D@RemainderY eax
L1:
mov eax D@Width | mov D@CurXPos eax | shl eax 3 | lea ebx D$eax+eax*2 ; muylby 3; ebx = Width*4*3 . Width*8*3
L2:
mov ecx D@MaxYPos
mov edx esi
Align 16 ; <---- Must be aligned to 16 to gain more speed and stability
L8:
; copy the 1st 4 Qwords from esi to register XMM
movq XMM1 Q$edx+eax
movq XMM0 Q$edx
pslldq xmm1 8
xorps XMM0 XMM1
movupd X$edi xmm0
movq XMM1 Q$edx+ebx
pslldq xmm1 8
movq XMM0 Q$edx+eax*2
xorps XMM0 XMM1
movupd X$edi+16 xmm0
lea edx D$edx+eax*4
add edi (8*4) ; advance one xmm reg
dec ecx | jg L8<
sub edi D@RemainderY; adjust edi from the remainder in YPos only
add esi 8
dec D@CurXPos | jnz L2<<
mov eax D@RemainderY
; clear remainder bytes if any
test eax eax | jz L1>
shr eax 3 | jz L1> | mov D$edi 0 | mov D$edi+4 0
dec eax | jz L1> | mov D$edi+8 0 | mov D$edi+12 0
dec eax | jz L1> | mov D$edi+16 0 | mov D$edi+20 0
L1:
mov eax D@Output
EndP
Extra Macros to compute the FPU comparitions
[Fpu_Do | C0:]
[Fpu_Loop_Until | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 C0<<]
[.Fpu_Do | C1:]
[.Fpu_Loop_Until | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 C1<<]
[Fpu_While | B0: | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 B1>>]
[Fpu_End_While | jmp B0<< | B1:]
[.Fpu_While | B2: | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 B3>>]
[.Fpu_End_While | jmp B2<< | B3:]
[Fpu_If | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R0>>]
[Fpu_Else_If | jmp R5>> | R0: | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R0>>]
[Fpu_Else | jmp R5>> | R0:]
[Fpu_End_If | R0: | R5:]
[.Fpu_If | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R1>>]
[.Fpu_Else_If | jmp R6>> | R1: | fld #3 | fld #1| fcompp | fstsw ax | fwait | sahf | jn#2 R1>>]
[.Fpu_Else | jmp R6>> | R1:]
[.Fpu_End_If | R1: | R6:]
[..Fpu_If | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R2>>]
[..Fpu_Else_If | jmp R7>> | R2: | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R2>>]
[..Fpu_Else | jmp R7>> | R2:]
[..Fpu_End_If | R2: | R7:]
[...Fpu_If | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R3>>]
[...Fpu_Else_If | jmp R8>> | R3: | fld #3 | fld #1 | fcompp | fstsw ax | fwait | sahf | jn#2 R3>>]
[...Fpu_Else | jmp R8>> | R3:]
[...Fpu_End_If | R3: | R8:]
[Fpu_If_And | Fpu_If #1 #2 #3 | #+3]
[.Fpu_If_And | .Fpu_If #1 #2 #3 | #+3]
[..Fpu_If_And | ..Fpu_If #1 #2 #3 | #+3]
[...Fpu_If_And | ...Fpu_If #1 #2 #3 | #+3]
[Fpu_Else_If_And | Fpu_Else | Fpu_If_And #F>L]
[.Fpu_Else_If_And | .Fpu_Else | .Fpu_If_And #F>L]
[..Fpu_Else_If_And | ..Fpu_Else | ..Fpu_If_And #F>L]
[...Fpu_Else_If_And | ...Fpu_Else | ...Fpu_If_And #F>L]
Many tks to Rui, JJ and Siekmanski :t :t :t :t :t
Btw....If someone have a faster code that also can invert a squared matrix on any size, please post :) (And if you guys have, please post both versions, one using Real8 and other using Real4 Fpu ;) )