The stack (Textbook chapter 10)
Summary 1. The array data structure 2. The stack data structure 3. Arithmetic using a stack
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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Arrays Definition: A list of values arranged sequentially in memory and grouped under a single name Example: a list of telephone numbers 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)
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Properties of Arrays 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 – Ex:
myArray .BLKW
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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Pointer Address of a variable in memory Allows us to indirectly access variables Base of an array = pointer to the first element
LEA LDR STR myArray
R2, myArray R0, R2, #0 R0, R2, #2
.BLKW 5
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Multi-dimensional arrays 4 columns
2 rows
A 0 1 2 3 0 A00 A01 A02 A03 1 A10 A11 A12 A13
x3100 x3101 x3102 x3103 x3104 x3105
2 “major” memory mappings:
x3106 x3107
Row-major CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Column-major 6
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LIFO and FIFO • Abstract Data Structures – defined by the rules for inserting and extracting data
• LIFO (Last In-First Out) A, B, C
FIFO (First In-First Out) A, B, C
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Stack Data Structure • A stack is a LIFO structure • Operations: • PUSH (enter item at top of stack) • POP (remove item from top of stack)
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
TOS = Top Of Stack
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Stack overflow and underflow Error conditions: • Underflow (trying to pop from empty stack) • Overflow (trying to push onto full stack)
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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A “physical” stack • A coin holder as a stack
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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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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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
A software stack • Implemented in memory
NOTE that the stack grows “downward”!
– The Top Of Stack moves as new data is entered – Here R6 is the TOS register, a pointer to the Top Of Stack
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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Stack in LC-3 1. Declare an array to be your stack 2. Use a register to point to the TOS (R6 is the convention) 3. Implement PUSH and POP
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Push in LC-3 • Assume data to push is in a specific register (R0) • Decrement TOS pointer (our stack is moving down) • Then write data in R0 to new TOS PUSH
ADD STR
R6, R6, #-1 R0, R6, #0
NOTE: the TOS points to the last element pushed CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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Pop in LC-3 • Assume data to pop will go to a specific register (R0) • Read data at current TOS into R0 • Then increment TOS pointer
POP
LDR ADD
R0, R6, #0 R6, R6, #1
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Checking for over/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
POP
Same for PUSH and overflow CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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When is the stack empty or full? First way: TOS always points to top valid element
x3FFA x3FFB
Stack Overflow:
x3FFC
TOS =
x3FFD
Stack Underflow:
x3FFF
TOS =
x4000
MAX
x3FFE
BASE
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
When is the stack empty or full? Second way: TOS always points to next available location to push
x3FFA
Stack Overflow:
x3FFD
TOS =
x3FFE
Stack Underflow:
x4000
x3FFB
MAX
x3FFC
x3FFF
BASE
TOS = CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
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Stack protocol on LC-3 - Example • Use standard conventions: – – – – –
PUSH pushes R0, returns success in R5 POP pops into R0, returns success in R5 Stack pointer is R6 All other used registers need to be callee-saved The TOS points to the top valid element
• The stack goes from x3FFF to x3FFB
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Stack protocol in LC-3: POP POP
ST ST LD ADD ADD BRz LDR ADD BRnzp
R2, Save2 R1, Save1 R1, BASE R1, R1, #-1 R2, R6, R1 fail_exit R0, R6, #0 R6, R6, #1 success_exit
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
; ; ; ; ; ; ; ;
(1/3)
save, needed by POP save, needed by POP BASE contains x-3FFF R1 now has x-4000 compare SP to x-4000 branch if stack is empty the actual ‘pop’ adjust stack pointer
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Stack protocol in LC-3: PUSH PUSH
ST ST LD ADD BRz ADD STR
R2, Save2 R1, Save1 R1, MAX R2, R6, R1 fail_exit R6, R6, #-1 R0, R6, #0
; ; ; ; ; ; ;
(2/3)
needed by PUSH needed by PUSH MAX has x-3FFB compare SP to x-3FFB branch is stack is full adjust Stack Pointer the actual ‘push’
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CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
Stack prot. in LC-3: Return values (3/3)
success_exit
fail_exit
BASE MAX Save1 Save2
LD R1, Save1 LD R2, Save2 AND R5, R5, #0 RET LD R1, Save1 LD R2, Save2 AND R5, R5, #0 ADD R5, R5, #1 RET .FILL xC001 .FILL xC005 .FILL x0000 .FILL x0000
CMPE12 – Fall 2006 – A. Di Blas (Orig. by C. Barzeghi)
; restore registers ; R5
