Determinant Calculation of a NxN Matrix Using AT

1
Determinant Calculation of a NxN Matrix Using
ATT Assembly Syntax

• Algorithm
• High-level language implementation
• ATT assembly language implementation
• Image of the stack before and after a function is
  called

2
Algorithm

• Suppose we have a 3x3 matrix

• Use the recursive expansion by minors method

• Or in general, for a matrix M of NxN dimensions

where Msub(N-1)x(N-1) is a sub-matrix of the
matrix M whose dimension is (N-1)x(N-1) and does
not contain the first row and i column
3
Algorithm (cont.)

• Observations
• If N2, compute determinant directly (base case)
• If Ngt2, recursive calls must be done successively
  until N2
• For each matrix element M(1,i), need to determine
  the sub-matrix that does not contain the first
  row and ith column of the currently computing
  matrix.

4
High-level Language Implementation C
int det(int M, int N) if (N2)
return (M0M3 - M1M2)
else int
new_dimension (N-1) int
tdet0 int temp new
int(N-1)(N-1)
for (int ref_ele0 ref_eleltNref_ele)
int counter0
for (int i0iltNi)
for (int j0jltNj)
if ( (j!
ref_ele) (i!0))
tempcounter M(Ni
j)
counter
int t det(temp,
new_dimension) if
((ref_ele 2) ! 0)
t (-1)t tdet
Mref_elet
return tdet
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ATT Assembly Language Implementation

• Specification of the determinant function det
  in the assembly language implementation. The
  following steps must be done successively
• All elements of the matrix M must be PUSHED
  onto the stack, in the major-row ordered, before
  the det function is called
• The dimension N of the matrix M must also be
  PUSHED onto the stack
• A variable that will hold the result of the
  determinant of the currently computing matrix
  must also be PUSHED onto the stack (make space
  for the return result)
• A variable that will hold an error flag, if ever
  occurs, must also be PUSHED onto the stack
  (make space for the return error)
• See attachment sheets for the program.

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The Image of the Stack Just Before the det
Function Is Called
Stack pointer esp
7
The Image of the Stack Just AFTER the det
Function Is Called
Stack pointer esp