Textbook chapter 10. Abstract data structures are. In this section, we will talk about. The array The stack Arithmetic using a stack

Transcription

1 LC-3 Data Structures Textbook chapter 0 CMPE2 Summer 2008 Abstract data structures are LC-3 data structures Defined by the rules for inserting and extracting data In this section, we will talk about The array The stack Arithmetic using a stack CMPE2 Summer 2008 Slides by ADB 2

2 The array data structure Array: A list of values arranged sequentially in memory and grouped under a single name In C, the expression a[4] refers to the 5th element of the array a Most assembly languages have only basic concept of arrays (.blkw in LC-3) E.g., a list of integers starting at 5 number[0] = 5; number[] = 6; number[2] = 7; number[3] = 8; CMPE2 Summer 2008 Slides by ADB 3 Properties of arrays Each element is the same size (i.e. same type) Elements are stored contiguously First element is located at the lowest memory address In assembly language we must Allocate correct amount of space for an array Map array addresses to memory addresses E.g., myarray.blkw 5 CMPE2 Summer 2008 Slides by ADB 4 2

3 What is a pointer? A pointer is an address of a variable in memory It s just an address Lets the programmer use indirect addressing Indirectly address variables Base of an array is the pointer to the first element Wait, what? myarray.blkw 5 What happens when LEA R2, myarray? CMPE2 Summer 2008 Slides by ADB 5 myarray.blkw 5 LEA R2, myarray LDR R0, R2, #0 STR R0, R2, #2 Array example CMPE2 Summer 2008 Slides by ADB 6 3

4 How do you represent a checkerboard? The problem: memory is linear One-dimensional Multi-dimensional arrays? CMPE2 Summer 2008 Slides by ADB 7 Consider two rows Array elements are sublabeled with their row and column A: 2 rows (numbered 0 and ) A: 4 columns (numbered 0 to 3) In array A: A02 is the 0 th row and 2 nd column How do you map this onto a linear structure? Multi-dimensional arrays A 0 0 A00 A0 A0 A 2 A02 A2 3 A03 A3 CMPE2 Summer 2008 Slides by ADB 8 4

5 Row major Read down the row first Column major Read down the column first Array memory mappings CMPE2 Summer 2008 Slides by ADB 9 Array representation: Row major A x300 x30 x x303 x304 x x306 x307 CMPE2 Summer 2008 Slides by ADB 0 5

6 Array representation: Column major A x300 x30 x x303 x304 x x306 x307 CMPE2 Summer 2008 Slides by ADB FIFO is first in, first out Standard queue (waiting in line) FIFO (Standard queue) FRONT SHOES CMPE2 Summer 2008 Slides by ADB 3 6

7 LIFO (Standard stack) LIFO is last in, first out Sometimes called FILO, first in, last out Standard stack TOP CMPE2 Summer 2008 Slides by ADB 4 Example: LIFO and FIFO (LIFO) Stack: (FIFO) Queue: A, B, C C, B, A D, E, F D, E, F C F B E A D CMPE2 Summer 2008 Slides by ADB 5 7

8 The stack data structure Stack structure is LIFO (last in, first out) Basic pieces of stack Stack itself Top of stack Two basic stack operations Push: Put data on top of stack Pop: Remove top element from stack CMPE2 Summer 2008 Slides by ADB 6 Stack overflow and underflow Trying to pop from empty stack Underflow Trying to push onto full stack Overflow CMPE2 Summer 2008 Slides by ADB 8 8

9 Stack overflow R R0 TOP.. push R0 push R.. CMPE2 Summer 2008 Slides by ADB 9 Stack underflow.. pop R0 pop R. TOP. CMPE2 Summer 2008 Slides by ADB 20 9

10 A coin holder as a stack CMPE2 Summer 2008 Slides by ADB 2 A hardware stack Implemented in hardware (i.e., with registers) Previous data entries move up to accommodate each new data entry Note that the Top Of Stack is always in the same place CMPE2 Summer 2008 Slides by ADB 22 0

11 Stacks in hardware and software Implemented in hardware with registers Previous data entries move up to accommodate each new data entry Implemented in software with code, in memory Stack pointer points to the top (empty) element Stack grows from high (0xffff) to low (0x0000) memory CMPE2 Summer 2008 Slides by ADB 23 In LC-3 Stack in LC-3 The stack pointer moves as new data is entered R6 acts as the stack pointer (the TOS register) CMPE2 Summer 2008 Slides by ADB 24

12 Write data to top empty location of stack PUSH in LC-3 Top of stack is pointed to by stack pointer (SP) Decrement stack pointer (stack is moving down in memory) E.g., Assume data to push is in R0 PUSH ADD R6, R6, #- STR R0, R6, # [R0] R6 CMPE2 Summer 2008 Slides by ADB 25 POP in LC-3 Increment stack pointer (stack is moving down in memory) Now points to full location Read data from top of stack E.g., Assume data to pop goes into R0 POP LDR R0, R6, # ADD R6, R6, # R6 CMPE2 Summer 2008 Slides by ADB 26 2

13 Checking for overflow and underflow Before pushing, we have to test for overflow Before popping, we have to test for underflow In both cases, use R5 to report success or failure Flow chart is similar for push and overflow POP CMPE2 Summer 2008 Slides by ADB 27 When is the stack empty or full? If SP always points to next empty element (next available location to push) Stack overflow when SP = Stack underflow when SP = x3ffa x3ffb x3ffc x3ffd x3ffe x3fff x4000 MAX BASE CMPE2 Summer 2008 Slides by ADB 28 3

14 Stack protocol on LC-3: An example Conventions PUSH pushes R0, returns success in R5 POP pops into R0, returns success in R5 Stack pointer is R6 and points to the top empty element All other used registers need to be calleesaved PUSH and POP should not overwrite any other registers The stack goes from x3fff to x3ffb CMPE2 Summer 2008 Slides by ADB 30 Stack protocol in LC-3: POP POP ST R2, Save2 ; save, needed by POP ST R, Save ; save, needed by POP LD R, nbase ; nbase contains -x3fff ADD R, R, #- ; R now has -x4000 ADD R2, R6, R ; compare SP to BASE BRz fail_exit ; branch if stack is empty LDR R0, R6, # ; the actual pop ADD R6, R6, # ; adjust stack pointer BRnzp success_exit CMPE2 Summer 2008 Slides by ADB 3 4

15 Stack protocol in LC-3: PUSH PUSH ST R2, Save2 ; needed by PUSH ST R, Save ; needed by PUSH LD R, nmax ; nmax has -x3ffb ADD R2, R6, R ; compare SP to x3ffb BRz fail_exit ; branch is stack is full ADD R6, R6, #- ; adjust stack pointer STR R0, R6, # ; the actual push CMPE2 Summer 2008 Slides by ADB 32 Stack protocol in LC-3: Return values success_exit: LD R, Save ; restore registers LD R2, Save2 AND R5, R5, #0 ; R5 <-- success RET fail_exit: LD R, Save ; restore registers LD R2, Save2 AND R5, R5, #0 ADD R5, R5, # ; R5 <-- fail RET nbase:.fill xc00 ; nbase has -x3fff nmax:.fill xc005 ; nmax has x3ffb Save:.FILL x0000 Save2:.FILL x0000 CMPE2 Summer 2008 Slides by ADB 33 5

16 Stack as an alternative to registers Three-address vs zero-address The LC-3 explicitly specifies the location of each operand: it is a three-address machine e.g. ADD R0, R, R2 Some machines use a stack data structure for all temporary data storage: these are zeroaddress machines The instruction ADD would simply pop the top two values from the stack, add them, and push the result back on the stack Some calculators use a stack to do arithmetic; most general purpose microprocessors use a register bank CMPE2 Summer 2008 Slides by ADB 34 Recommended exercises Read and implement the examples in textbook sections 0.3, 0.4, and 0.5 Ex 0.3, 0.4, 0.5 ok but tedious Ex 0.6 (and 0.7), 0.8, 0.9 CMPE2 Summer 2008 Slides by ADB 35 6