Memory copy and memory compare array of array of Single - delphi

Question

In Delphi, I declared a 3x3 matrix table as an array of array of Single, like this:
m_Table: array [0..2] of array [0..2] of Single;
Now I want to memory compare the content with another table, or memory copy the table content from another table. I know that I can create a nested loop to do that, but I want to do the job without any loop, if possible.
My question is, it is correct to copy or compare the memory like this:
CompareMem(m_Table, other.m_Table, 9 * SizeOf(Single));
CopyMemory(m_Table, other.m_Table, 9 * SizeOf(Single));
If not, what is the correct way to do that?
And as a subsidiary question, is there a better way to get the length to copy instead of 9 * SizeOf(Single), like e.g. SizeOf(m_Table^)?
Regards

Answer 1

The code in the question works fine. Personally I would say that Move is the idiomatic way to copy memory. Further I would use SizeOf(m_Table) to obtain the size of the type.
I would point out that your comparison differs from the floating point equality operator. Perhaps that's what you want, but you should be aware of this. For instance zero and minus zero compare equal using floating point comparison but not with memory compare. And NaNs always compare not equal, even with identical bit patterns.
Let me also comment that it would make your code more extendible if you declared a type for these matrices. Without that you won't be able to write functions that accept such objects.

Answer 2

The correct and easiest way may be to define a type:
type
TMatrix3x3 = array [0..2,0..2] of Single;
Then you can directly write:
var
v1, v2: TMatrix3x3;
begin
fillchar(v1,sizeof(v1),0);
move(v1,v2,sizeof(v1));
if comparemem(#v1,#v2,sizeof(v1)) then
writeln('equals');
end;
Using sizeof() make your code safe and readable.
You may define a wrapper type with methods:
{ TMatrix3x3 }
type
TMatrix3x3 = record
v: array [0..2,0..2] of Single;
procedure Zero;
procedure Copy(var dest: TMatrix3x3);
procedure Fill(const source: TMatrix3x3);
function Equals(const other: TMatrix3x3): boolean;
end;
procedure TMatrix3x3.Copy(var dest: TMatrix3x3);
begin
move(v,dest,sizeof(v));
end;
function TMatrix3x3.Equals(const other: TMatrix3x3): boolean;
begin
result := CompareMem(#v,#other.v,sizeof(v));
end;
procedure TMatrix3x3.Fill(const source: TMatrix3x3);
begin
move(source,v,sizeof(v));
end;
procedure TMatrix3x3.Zero;
begin
fillchar(v,sizeof(v),0);
end;
Including then advanced features like implicit assignment, and operators, if needed.
But don't reinvent the wheel, if you really to work with matrix arithmetic. Use an already existing and fully tested library, which will save you a lot of trouble and debugging time.

Answer 3

You should use standard TMatrix type from System.Math.Vectors unit, then you can just compare it directly as if Matrix1 = Matrix2 then and assign as Matrix1 := Matrix2