Question

Please comment the MIPS code to help me understand.

Here is what the code accomplishes.

Background A square matrix A is symmetric if where AT is the transpose of the matrix A. That is, a for all values of indices i and j (where aij represents entries in A). For example, matrix A below is symmetric but B is not. 1 17 23 B-5 2 7 A- 5 2 7 Project Objective Our objective in this project is to check if a given Matrix is symmetric or not. We perform this with the following two steps. . Given a square Matrix, we first compare if aj aji for all entries. If they are equal we write "O" for those entries. If not we write "1". So if all the elements of a Matrix are "O" then it is a symmetric matrix. Note that the diagonal would always end up as "O". We write back to the same matrix location. E.g.: For the above Matrices A and B the final result would be A- 0 0 0 B- 1 0 0 We also aim at measuring the asymmetry. So we will be counting the number of entries in a matrix which are not equal to its mirror entry. Basically define a counter and increment the counter by 1 if aj # aji. For the above Matrix B, the value of counter would 2 as two elements are different. .

Here is the code, partially commented.

.data

Matrix: .word 41,45,5, 34,8, 15,16,23,44,48,12,32,18,47,22,8,22

.word 46,40,42,33,13,38,27,6, 29,25,18,40,47,22,26,14,3

.word 7, 48,35,9, 43,38,9, 49,28,25,42,5, 44,10,5, 38,14

.word 46,33,16,6, 13,20,31,1, 8, 17,1, 47,28,46,14,28,7

.word 32,2, 48,25,41,29,14,39,43,46,3, 39,32,49,41,28,46

.word 5, 43,2, 48,13,4, 33,41,32,19,9, 25,30,22,2, 9, 40

.word 14,47,22,18,47,3, 35,44,18,6, 33,22,11,6, 47,50,4

.word 28,34,20,30,18,27,38,5, 26,40,37,23,16,13,37,8,7

.word 48,38,39,12,10,39,23,20,21,20,33,16,24,21,25,3,46

.word 49,38,40,38,13,47,5, 13,4, 13,23,26,12,30,29,29, 3

.word 8, 20,10,13,31,7, 12,41,12,21,28,26,43,14,35,10,19

.word 49,33,25,26,24,29,46,22,7, 5, 15,41,10,31,19,41,27

.word 48,9, 23,35,18,24,8, 46,10,7, 38,40,12,36,12,22,16

.word 25,36,33,45,42,1, 42,10,12,48,10,33,9, 12,6,15, 16

.word 41,2, 36,48,30,17,27,14,21,48,35,19,12,6, 27,12,25

.word 8, 14,38,28,28,9, 50,8, 3, 29,10,41,22,15,12,6, 33

.word 22,3, 14,7, 46,40,4, 7, 46,3, 19,27,16,16,25,33,41

.text

.globl __start # main program starts in the next line

__start: addi $s0,$zero,0 # outer loop counter

addi $s1,$zero,0 # inner loop counter

la $t0,Matrix #load the matrix address

addi $t6,$zero,17 # number of columns

addi $t7,$zero,17 # number of rows

addi $s6,$zero,0

sll $t1,$t6,2

ext_loop: addi $s1,$s0,0 # reset the inner loop counter

inn_loop: mult $s0,$t1

mflo $t2 # calculate the low byte offset

sll $t3,$s1,2

add $t4,$t0,$t2 # add row offset

add $s2,$t4,$t3 # add column offset

lw $s3,0($s2) # load this element

mult $s1,$t1 # Repeat the offset calcluation for mirror element

mflo $t2

sll $t3,$s0,2

add $t4,$t0,$t2

add $s4,$t4,$t3

lw $s5,0($s4)

beq $s3,$s5,jump_equal

addi $s7,$zero,1 # write ones if different

sw $s7,0($s2)

sw $s7,0($s4)

add $s6,$s6,1 # increment the counter

j jump_unequal

jump_equal: addi $s7,$zero,0

sw $s7,0($s2)

sw $s7,0($s4)

jump_unequal:

addi $s1,$s1,1 # increment the inner loop

blt $s1,$t7,inn_loop # next inner loop

addi $s0,$s0,1 # increment the outer loop

blt $s0,$t6,ext_loop # next outer loop

.end

Answer 1

.data
Matrix: .word 41,45,5, 34,8, 15,16,23,44,48,12,32,18,47,22,8,22 #row1 element
.word 46,40,42,33,13,38,27,6, 29,25,18,40,47,22,26,14,3#row2 element
.word 7, 48,35,9, 43,38,9, 49,28,25,42,5, 44,10,5, 38,14# so on
.word 46,33,16,6, 13,20,31,1, 8, 17,1, 47,28,46,14,28,7
.word 32,2, 48,25,41,29,14,39,43,46,3, 39,32,49,41,28,46
.word 5, 43,2, 48,13,4, 33,41,32,19,9, 25,30,22,2, 9, 40
.word 14,47,22,18,47,3, 35,44,18,6, 33,22,11,6, 47,50,4
.word 28,34,20,30,18,27,38,5, 26,40,37,23,16,13,37,8,7
.word 48,38,39,12,10,39,23,20,21,20,33,16,24,21,25,3,46
.word 49,38,40,38,13,47,5, 13,4, 13,23,26,12,30,29,29, 3
.word 8, 20,10,13,31,7, 12,41,12,21,28,26,43,14,35,10,19
.word 49,33,25,26,24,29,46,22,7, 5, 15,41,10,31,19,41,27
.word 48,9, 23,35,18,24,8, 46,10,7, 38,40,12,36,12,22,16
.word 25,36,33,45,42,1, 42,10,12,48,10,33,9, 12,6,15, 16
.word 41,2, 36,48,30,17,27,14,21,48,35,19,12,6, 27,12,25
.word 8, 14,38,28,28,9, 50,8, 3, 29,10,41,22,15,12,6, 33
.word 22,3, 14,7, 46,40,4, 7, 46,3, 19,27,16,16,25,33,41
.text
.globl __start # main program starts in the next line
__start: addi $s0,$zero,0 # outer loop counter
addi $s1,$zero,0 # inner loop counter
la $t0,Matrix #load the matrix address
addi $t6,$zero,17 # number of columns (i)
addi $t7,$zero,17 # number of rows (j)
addi $s6,$zero,0 #initializing the counter to count A(ij) != A(ji)
sll $t1,$t6,2 # to address the word we multiply by 4 or shift it by 2 to get actual size of row
ext_loop: addi $s1,$s0,0 # reset the inner loop counter (j = 0)
inn_loop: mult $s0,$t1 # to calculate the row offset we mult by $s0(counter of row number)
mflo $t2 # calculate the low byte offset
sll $t3,$s1,2 # to address the word we mult by 4 or shift it by 2 to get actual col offset
add $t4,$t0,$t2 # add row offset
add $s2,$t4,$t3 # add column offset
lw $s3,0($s2) # load this element A(ij)
mult $s1,$t1 # Repeat the offset calcluation for mirror element
mflo $t2 # get the row offset from multiply of $s1(col number counter)
sll $t3,$s0,2 # to get the actual col offset
add $t4,$t0,$t2 # adding row offset
add $s4,$t4,$t3 # adding col offset
lw $s5,0($s4) # load this element A(ji)
beq $s3,$s5,jump_equal # if A(ij) == A(ji) jumps to jump_equal label
addi $s7,$zero,1 # write ones if different
sw $s7,0($s2) # store the 1 to A(ij)
sw $s7,0($s4) # store the 1 to A(ji)
add $s6,$s6,1 # increment the counter of A(ij) != A(ji)
j jump_unequal # jump to jump_unequal
jump_equal: addi $s7,$zero,0 # write 0 if equal
sw $s7,0($s2) # writes 0 to A(ij)
sw $s7,0($s4) # writes 0 to A(ji)
jump_unequal:
addi $s1,$s1,1 # increment the inner loop
blt $s1,$t7,inn_loop # next inner loop
addi $s0,$s0,1 # increment the outer loop
blt $s0,$t6,ext_loop # next outer loop
.end

# calculating the row offset and column offset is bit tricky
# first you have to multiply the row num couter to 17(num rows)*4 and then add the (4*col num counter)(col offset)
# which is done in above code two times first by $s1 * 17 * 4 for A[j][i] and $s0 * 17 * 4 for A[i][j]