LC-3 Data StructuresTextbook chapter 10

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LC-3 data structures Abstract data structures are…

Defined by the rules for inserting and extracting data

In this section, we will talk about… The array The stack Arithmetic using a stack

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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[1] = 6; number[2] = 7; number[3] = 8;

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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

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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?

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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 arrays Consider two rows Array 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?

A 0 1 2 3

0 A00 A01 A02 A03

1 A10 A11 A12 A13

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Array memory mappings Row major

Read down the row first Column major

Read down the column first

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Array representation: Row major

A 0 1 2 3

0 1 2 3 4

1 5 6 7 8

x3100

x3101

x3102

x3103

x3104

x3105

x3106

x3107

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Array representation: Column major

A 0 1 2 3

0 1 2 3 4

1 5 6 7 8

x3100

x3101

x3102

x3103

x3104

x3105

x3106

x3107

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

Standard queue (waiting in line)

4 3 2 1 SHOESFR

ON

T

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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 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

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Stack overflow and underflow Trying to pop from empty stack

Underflow Trying 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 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

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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

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Stack in LC-3 In 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-3 Write 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 R0 PUSH STR R0, R6, #0

ADD R6, R6, #-1

R6[R0]

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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 ADD R6, R6, #1

LDR R0, R6, #0

R6

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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

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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 =

x3FFA

x3FFB

x3FFC

x3FFD

x3FFE

x3FFF

x4000

BASE

MAX

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Stack protocol on LC-3: An example Conventions

PUSH 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 emptyADD R6, R6, #1 ; adjust stack pointerLDR R0, R6, #0 ; the actual ‘pop’BRnzp 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 fullSTR R0, R6, #0 ; the actual ‘push’ADD R6, R6, #-1 ; adjust stack pointer

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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_exitLD 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, R2

Some 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 stack

Some 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 10.5 Ex 10.3, 10.4, 10.5 ok but tedious Ex 10.6 (and 10.7), 10.8, 10.9