A 2D array
Three rows of four words, one element reached by row and column, and a whole column added up by stepping a row at a time.
Twelve words laid out as three rows of four. The program reads one element by its row and column, and then adds up a whole column, which means stepping through memory a row at a time instead of an element at a time.
Every array up to here was one line of memory. A 2D array is the same line read in rows, and the two
numbers you write in C as grid[row][col] have to be turned into one offset before anything can be
read.
You need to know: the "Arrays and strings" lecture and the "Loads, stores and immediates" lecture. What is new here is the stride, the distance in bytes between one row and the next, which is what walking a column adds every pass.
The three .word lines are one array of twelve words at 0x10010000, and the rows exist only in
how they are written down. row * COLS + col is the element's number in that one line, and the
sll by two turns a number of elements into a number of bytes, which is what the address arithmetic
actually needs. $t5 comes out at 000000C8, which is 200, the second element of the last row.
mul $t4, $t1, $t3 is a real instruction and it is what a row of any width needs. Here COLS is 4,
a power of two, so sll $t4, $t1, 2 would do the same job in one cheaper instruction, and the two
shifts could be one: sll $t4, $t1, 4 scales the row all the way to bytes, with the column shifted
by 2 and added on.
Walking a column is the same arithmetic done once. $t6 starts at the top of the column and then
adds 16 at every pass: one row further down is one whole row of elements further along in memory.
$t7 comes out at 000000DE, which is 222, from 2, 20 and 200.
That 16 is written as a number because the assembler does no arithmetic. The M68K writes the same
stride as #COLS*2 and lets the assembler multiply; here COLS*4 in an instruction is a build
error, so either the number goes in with a comment saying where it came from, or the program
computes it.
Walking a row would be the same loop with addi $t6, $t6, 4, since the elements of a row sit
next to each other. A column is the direction the array is not laid out in, and it costs the same
one instruction per pass to say so, with a bigger number in it.
Try changing li $t2, 1 to li $t2, 3. $t5 comes out at 00000190, which is 400, and the column
total in $t7 at 000001BC, which is 444.