Introduction to 8086 Assembly

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1 Introduction to 886 Assembly Lecture 7 D and N-D Arrays

2 D Arrays 4 5 tabular data rows and columns

3 D Arrays

4 D Arrays

5 D Arrays

6 D Arrays

7 D Arrays int a[][4] = {{,, 5, 7}, {, 4, 6, 8}, {4,,-,7}}; printf("%d\n", a[][]);

8 D Arrays int a[][4] = {{,, 5, 7}, {, 4, 6, 8}, {4,,-,7}}; printf("%d\n", a[i][j]); a[][] a[][] a[][] a[][] a[][] a[][] a[][] a[][] a[][] a[][] a[][] a[][]

9 How to implement D arrays?

10 Memory Memory row by row column by column

11 Memory Memory Row Major Column Major

12 Memory Memory Row Major (C,C++,Pascal, Python-numpy) Column Major (Fortran, Matlab, R, )

13 Memory Memory Assembly? Row Major (C,C++,Pascal, Python-numpy) Column Major (Fortran, Matlab, R, )

14 Memory Row Major (C,C++,Pascal, numpy)

15 Memory a[i][] :? Row Major (C,C++,Pascal, numpy)

16 Memory a[i][] : 4*i Row Major (C,C++,Pascal, numpy)

17 Memory a[i][] : 4*i a[i][] :? Row Major (C,C++,Pascal, numpy)

18 Memory a[i][] : 4*i a[i][] : 4*i+ Row Major (C,C++,Pascal, numpy)

19 Memory a[i][] : 4*i a[i][j] :? Row Major (C,C++,Pascal, numpy)

20 Memory a[i][] : 4*i a[i][j] : 4*i+j Row Major (C,C++,Pascal, numpy)

21 Memory int a[m][n]; n a[i][j] : n*i + j... 9 : : : : : : m Row Major (C,C++,Pascal, numpy)

22 Memory int a[m][n]; n a[i][j] offset = (n*i+j)*sizeof(int) : : : : : : m Row Major (C,C++,Pascal, numpy)

23 Memory int a[m][n]; m- n : : : : : : a[i][j] : n*i + j to find a[i][j] we need to know element size? m (no. of rows of a)? n (no. of columns of a)? Row Major (C,C++,Pascal, numpy)

24 Other standards? Column major? a[i][j] :? 4

25 Other standards? Column major? a[i][j] : 4*i+j 4

26 Other standards? Column major? a[i][j] : 4*i+j Index starting at a[i][j] :? 4

27 Other standards? Column major? a[i][j] : 4*i+j Index starting at a[i][j] : 4*i+j+ 4

28 Example: Print a D Array

29 Example: Print a D Array

30 Example: Print a D Array

31 Example: Print a D Array segment.data printdarray.asm array : dd,,, 4, 5, 6 dd,,, 4, 5, 6 dd,,, 4, 5, 6 dd 4, 4, 4, 44, 54, 64 segment.text ; printdarray (array, m, n) push 6 ; no of columns push 4 ; no of rows push array ; address of array call printdarray add esp,

32 Example: Print a D Array segment.data printdarray.asm array : dd,,, 4, 5, 6 dd,,, 4, 5, 6 dd,,, 4, 5, 6 dd 4, 4, 4, 44, 54, 64 segment.text ; printdarray (array, m, n) push 6 ; no of columns push 4 ; no of rows push array ; address of array call printdarray add esp,

33 Example: Print a D Array int printdarray(int a[][6], int m, int n) { for (int i = ; i < m; i++) { for (int j = ; j < n; j++) printf("%d,", a[i][j]); } putchar('\n'); } delim: db ", ", %define ARRAY [ebp+8] %define M [ebp+] %define N [ebp+6] ; printdarray(array, M, N) printdarray: push ebp mov ebp, esp mov ebx, ARRAY mov esi, loop: cmp esi, M jge endloop mov edi, loop: cmp edi, N jge endloop ; index = esi*n+edi mov eax, N mul esi add eax, edi mov eax, [ebx+4*eax] call print_int mov eax, delim call print_string inc edi jmp loop endloop: mov al, call print_char inc esi jmp loop endloop: mov esp, ebp pop ebp ret printdarray.asm

34 Example: Print a D Array int printdarray(int a[][6], int m, int n) { for (int i = ; i < m; i++) { for (int j = ; j < n; j++) printf("%d,", a[i][j]); } putchar('\n'); } delim: db ", ", %define ARRAY [ebp+8] %define M [ebp+] %define N [ebp+6] ; printdarray(array, M, N) printdarray: push ebp mov ebp, esp mov ebx, ARRAY mov esi, loop: cmp esi, M jge endloop mov edi, loop: cmp edi, N jge endloop ; index = esi*n+edi mov eax, N mul esi add eax, edi mov eax, [ebx+4*eax] call print_int mov eax, delim call print_string inc edi jmp loop endloop: mov al, call print_char inc esi jmp loop endloop: mov esp, ebp pop ebp ret printdarray.asm

35 Example: Print a D Array int printdarray(int a[][6], int m, int n) { for (int i = ; i < m; i++) { for (int j = ; j < n; j++) printf("%d,", a[i][j]); } putchar('\n'); } delim: db ", ", %define ARRAY [ebp+8] %define M [ebp+] %define N [ebp+6] ; printdarray(array, M, N) printdarray: push ebp mov ebp, esp mov ebx, ARRAY mov esi, loop: cmp esi, M jge endloop mov edi, loop: cmp edi, N jge endloop ; index = esi*n+edi mov eax, N mul esi add eax, edi mov eax, [ebx+4*eax] call print_int mov eax, delim call print_string inc edi jmp loop endloop: mov al, call print_char inc esi jmp loop endloop: mov esp, ebp pop ebp ret printdarray.asm

36 Example: Print a D Array int printdarray(int a[][6], int m, int n) { for (int i = ; i < m; i++) { for (int j = ; j < n; j++) printf("%d,", a[i][j]); } putchar('\n'); } delim: db ", ", %define ARRAY [ebp+8] %define M [ebp+] %define N [ebp+6] ; printdarray(array, M, N) printdarray: push ebp mov ebp, esp Make it faster? mov ebx, ARRAY mov esi, loop: cmp esi, M jge endloop mov edi, loop: cmp edi, N jge endloop ; index = esi*n+edi mov eax, N mul esi add eax, edi mov eax, [ebx+4*eax] call print_int mov eax, delim call print_string inc edi jmp loop endloop: mov al, call print_char inc esi jmp loop endloop: mov esp, ebp pop ebp ret printdarray.asm

37 Example: Print a D Array printdarray.asm mov ebx, ARRAY mov esi, loop: cmp esi, M jge endloop mov edi, loop: cmp edi, N jge endloop ; index = esi*n+edi mov eax, N mul esi add eax, edi mov eax, [ebx+4*eax] call print_int mov eax, delim call print_string printdarray4.asm mov ebx, ARRAY mov esi, loop: cmp esi, M jge endloop mov edi, loop: cmp edi, N jge endloop mov eax, [ebx] call print_int mov eax, delim call print_string add ebx, 4

38 D Arrays N D array M N M D arrays (rows) of size N Array[i, j] = Array[N*i + j] D array M N P M D arrays of dimension N P Array[i, j, k] = Array[ i, j*p + k] = Array[ i *N*P + j * P + k ] M P M N

39 D Arrays N D array M N M D arrays (rows) of size N Array[i, j] = Array[N*i + j] D array M N P M D arrays of dimension N P Array[i, j, k] = Array[ i, j*p + k] = Array[ i *N*P + j * P + k ] An M N D array of D arrays of size P Array[i, j, k] = Array[ i*n + j, k] = Array[ (i * N + j) P + k ] M M P N

40 D Arrays N D array M N M D arrays (rows) of size N Array[i, j] = Array[N*i + j] D array M N P M D arrays of dimension N P Array[i, j, k] = Array[ i, j*p + k] = Array[ i *N*P + j * P + k ] An M N D array of D arrays of size P Array[i, j, k] = Array[ i*n + j, k] = Array[ (i * N + j) P + k ] M M P number of + and * operations? N

41 ND Arrays D array M N M D arrays (rows) of size N Array[i, j] = Array[N*i + j] D array ND array M N P M D arrays of dimension N P Array[i, j, k] = Array[ i, j*p + k] = Array[ i *N*P + j * P + k ] An M N D array of D arrays of size P Array[i, j, k] = Array[ i*n + j, k] = Array[ (i * N + j) P + k ] M M M n Array[ i, i,, i n ] = Array[ M * * M n * i + M * * M n * i + + M n * i n- + i n ]

42 ND Arrays ND array M M M n Array[i, i,, i n ] = Array[ M * * M n * i + M * * M n * i + + M n * i n- + i n ] j = i j = M * j + i j = M * j + i : number of + and * operations? j n = M n * j n- + i n Array[i, i,, i n ] = Array[j n ]

43 ND Arrays: Row-major vs. Column-major What does row-major and column-major mean? Matlab vs Numpy ND-arrays

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