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LC-3 Data StructuresTextbook chapter 10

CMPE12 – Summer 2008

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LC-3 data structuresAbstract data structures are…

Defined by the rules for inserting and extracting data

In this section, we will talk about…The arrayThe stackArithmetic using a stack

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The array data structureArray: A list of values arranged sequentially in memory and grouped under a single nameIn C, the expression a[4] refers to the 5th element of the array aMost 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[1] = 6;number[2] = 7;number[3] = 8;

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Properties of arraysEach element is the same size (i.e. same type)Elements are stored contiguouslyFirst element is located at the lowest memory address

In assembly language we mustAllocate correct amount of space for an arrayMap array addresses to memory addresses

E.g.,myArray .BLKW 5

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What is a pointer?A pointer is an address of a variable in memory

It’s just an addressLets the programmer use indirect addressing

Indirectly address variablesBase of an array is the pointer to the first element

Wait, what?myArray .BLKW 5

What happens when LEA R2, myARRAY?

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Array exampleLEA R2, myArrayLDR R0, R2, #0STR R0, R2, #2

myArray .BLKW 5

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Multi-dimensional arrays?How do you represent a checkerboard?The problem: memory is linear

One-dimensional

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Multi-dimensional arraysConsider two rowsArray elements are sub-labeled with their row and column

A: 2 rows (numbered 0 and 1)A: 4 columns (numbered 0 to 3)

In array A: A02 is the 0th row and 2nd column

How do you map this onto a linear structure?

A13A12A11A101

A03A02A01A000

3210A

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Array memory mappingsRow major

Read down the row firstColumn major

Read down the column first

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Array representation: Row major

87651

43210

3210A

x3107

x3106

x3105

x3104

x3103

x3102

x3101

x3100

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Array representation: Column major

87651

43210

3210A

x3107

x3106

x3105

x3104

x3103

x3102

x3101

x3100

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FIFO (Standard queue)FIFO is “first in, first out”

Standard queue (waiting in line)

4 3 2 1 SHOES

FRO

NT

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LIFO (Standard stack)LIFO is “last in, first out”

Sometimes called FILO, “first in, last out”Standard stack

1234

TOP

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Example: LIFO and FIFO(LIFO) Stack: (FIFO) Queue:

A, B, C D, E, F

A

B

C

D

E

F

C, B, A D, E, F

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The stack data structureStack structure is LIFO (last in, first out)Basic pieces of stack

Stack itselfTop of stack

Two basic stack operationsPush: Put data on top of stackPop: Remove top element from stack

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Stack overflow and underflowTrying to pop from empty stack

UnderflowTrying to push onto full stack

Overflow

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Stack overflow

TOPR0R1 .

.

push R0

push R1

.

.

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Stack underflow

TOP

.

.

pop R0

pop R1

.

.

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A coin holder as a stack

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A hardware stackImplemented in hardware (i.e., with registers)Previous data entries move up to accommodate each new data entryNote that the Top Of Stack is always in the same place

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Stacks in hardware and softwareImplemented in hardware with registers

Previous data entries move up to accommodate each new data entry

Implemented in software with code, in memoryStack pointer points to the top (empty) elementStack grows from high (0xffff) to low (0x0000) memory

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Stack in LC-3In LC-3

The stack pointer moves as new data is enteredR6 acts as the stack pointer (the TOS register)

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PUSH in LC-3Write data to top empty location of stack

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 R0PUSH ADD R6, R6, #-1

STR R0, R6, #1

R6[R0]

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POP in LC-3Increment stack pointer (stack is moving down in memory)

Now points to full locationRead data from top of stack

E.g., Assume data to pop goes into R0POP LDR R0, R6, #1

ADD R6, R6, #1

R6

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Checking for overflow and underflowBefore pushing, we have to test for overflowBefore popping, we have to test for underflowIn both cases, use R5 to report success or failureFlow chart is similar for push and overflow

POP

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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 =

x4000

x3FFF

x3FFE

x3FFD

x3FFC

x3FFB

x3FFA

BASE

MAX

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Stack protocol on LC-3: An exampleConventionsPUSH pushes R0, returns success in R5POP pops into R0, returns success in R5Stack pointer is R6 and points to the top empty elementAll other used registers need to be callee-savedPUSH and POP should not overwrite any other registers

The stack goes from x3FFF to x3FFB

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Stack protocol in LC-3: POP

POP ST R2, Save2 ; save, needed by POPST R1, Save1 ; save, needed by POPLD R1, nBASE ; nBASE contains -x3FFFADD R1, R1, #-1 ; R1 now has -x4000ADD R2, R6, R1 ; compare SP to BASEBRz fail_exit ; branch if stack is emptyLDR R0, R6, #1 ; the actual popADD R6, R6, #1 ; adjust stack pointerBRnzp success_exit

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Stack protocol in LC-3: PUSH

PUSH ST R2, Save2 ; needed by PUSHST R1, Save1 ; needed by PUSHLD R1, nMAX ; nMAX has -x3FFBADD R2, R6, R1 ; compare SP to x3FFBBRz fail_exit ; branch is stack is fullADD R6, R6, #-1 ; adjust stack pointerSTR R0, R6, #1 ; the actual push

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Stack protocol in LC-3: Return valuessuccess_exit:

LD R1, Save1 ; restore registers LD R2, Save2AND R5, R5, #0 ; R5 <-- successRET

fail_exit:LD R1, Save1 ; restore registers LD R2, Save2AND R5, R5, #0ADD R5, R5, #1 ; R5 <-- failRET

nBASE: .FILL xC001 ; nBASE has -x3FFFnMAX: .FILL xC005 ; nMAX has –x3FFBSave1: .FILL x0000Save2: .FILL x0000

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Stack as an alternative to registersThree-address vs zero-address

The LC-3 explicitly specifies the location of each operand: it is a three-address machine

e.g. ADD R0, R1, R2Some machines use a stack data structure for all temporary data storage: these are zero-address machines

The instruction ADD would simply pop the top two values from the stack, add them, and push the result back on the stackSome calculators use a stack to do arithmetic; most general purpose microprocessors use a register bank

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Recommended exercises

Read and implement the examples in textbook sections 10.3, 10.4, and 10.5Ex 10.3, 10.4, 10.5 ok but tediousEx 10.6 (and 10.7), 10.8, 10.9