Binghamton University. CS-120 Summer Stacking Up. Text: Introduction to Computer Systems : Chapter 10

Transcription

1 Stacking Up Text: Introduction to Computer Systems : Chapter 10

2 Data Structures Conceptual Models Organize how we think about data Imply extra rules on how we can interact with data Reduce freedom of interaction with data Enables clearer (implied) understanding, more power Challenge apply the right data structure to the right problem

3 Vector Data Structure List of data n items Each data item contains a single word We can read or write any data item using an index Index starts at zero, and ends at n-1 Hard to insert or delete individual data elements at arbitrary indexes

4 Vectors in LC3 lea r1,vec ld r2,i add r3,r1,r2 ; r1->vec ; r2=i ; r3->vec[i] ldr r4,r3,#0 ; r4=vec[i] Read VEC[I] str r5,r3,#0 ; VEC[I]=r5 Write VEC[I] VEC.blkw 23 ; VEC vector with n=23

5 Data Structure Type Data structures: Organized collection of lower level data Vector: List of numbers Vector: List of LC3 instructions Vector: List of LC3 words Vector: List of LC3 pairs of words

6 Example: Vector of (x,y) coordinates ; Subroutines getx ; put r6[r0].x in r1 add r2,r0,r0 add r2,r2,r6 ldr r1,r2,#0 ret gety ; put r6[r0].y in r1 add r2,r0,r0 add r2,r2,r6 ldr r1,r2,#1 ret negr3 ; negate the value in r3 not r3,r3 add r3,r3,#1 ret ; find lowest x coord ld r3,nmax ld r0,count lea r6,vec minl add r0,r0,#-1 brn done jsr getx add r4,r3,r1 brzp minl add r3,r1,#0 jsr negr3 br minl done jsr negr3 st r3,minx HALT ; data NMAX.fill x8001 COUNT.fill #23 MINX.fill #0 VEC.blkw 46

7 The Stack

8 Stack Terminology (Stack of Books) Empty Stack : space on the floor for a stack of books Push : put a new book on the top of the stack of books Pop : take a book from the top of the stack of books Full Stack : the top of the stack of books hits the ceiling Stack Size : the number of books that can fit between the floor and the ceiling Stack Underflow : Trying to take a book from an empty stack Stack Overflow : Trying to add a book to a full stack

9 Other Pipe-Like Data Structures Stack Last-in / First-out List (LIFO) Supports PUSH and POP Que - First-in / First out List (FIFO) Supports QUE and POP DeQue (pronounced deck ) Combo Stack/Que Supports PUSH/QUE to add Supports POP/DEQUE to remove

10 Pipe Data Structures QUE PUSH DEQUE POP

11 Stack Direction Push/Pop from the top of the stack Stack grows up Push on top of stack, Pop from top of stack Obvious and Intuitive (like a stack of books) Push/Pop from the bottom of the stack Stack grows down Push on bottom of stack, Pop from bottom of stack Counter intuitive!!!! Useful when two stacks grow towards the middle Implemented this way in text

12 Implementing a Stack in LC3 Each element in the stack is a 16 bit word Need a pointer to the base of the stack (BASE) Negate for quick compare (STKMIN) Need a pointer to the current top of the stack (R6) Need a pointer to the maximum stack entry (STKMAX) Negated for quick compare

13 Creating an Empty Stack INITSTK ; Initialize a stack st r5,inr5 ld r6,base ; not r5,r6 add r5,r5,#1 st r5,stkmin ld r5,stksize add r5,r5,r6 not r5,r5 add r5,r5,#1 st r5,stkmax ld r5,inr5 ret BASE.fill 0x6000 STKSIZE.fill 0x1000 STKMIN.fill #0 STKMAX.fill #0 INR5.fill #0 OVERFLOW.fill #0 UNDERFLOW.fill #0

14 Pushing on the stack PUSH ; push the value in r0 on the stack st r5,psr5 ld r5,stkmax add r5,r5,r6 brnz PUSHOK ld r7,overflow br PUSHEX PUSHOK str r0,r6,#0 add r6,r6,#1 PUSHEX ld r5,psr5 ret PSR5.fill #0

15 Popping from this stack POP ; Pop value from the stack into r0 st r5,por5 add r6,r6,#-1 ld r5,stkmin add r5,r5,r6 brzp POPOK add r6,r6,#1 ld r7,underflow br POPEX POPOK ldr r0,r6,#0 POPEX ld r5,por5 ret POR5.fill #0

16 Using the Stack Example Specification Given VEC, a numeric vector with N entries, sort the vector from lowest to highest

17 Stack Sort init stack; ordered=0 do { push vec[0] on stack j=0; ordered=1 for (i=1, i<n; i++) { if (vec[i]>=stack) { while(x=pop()) { vec[j]=x, j=j+1 } } else ordered=0 push vec[i] on stack; } while(x=pop()) { vec[j]=x, j=j+1 } } until (ordered=1)

18 New Routine: SCOMP SCOMP ; Compare value in R0 with head of stack. set CC ; CC=N R0<Stk ; CC=Z R0=Stk ; CC=P R0>Stk ; WARNING: Assumes stack is not empty! ; WARNING: Modifies R5 ldr r5,r6,#-1 not r5,r5 add r5,r5,#1 add r5,r0,r5 ret

19 StackSort Register Usage REG R0 R1 R2 R3 R4 R5 R6 R7 Usage Current Value (usually VEC[i] or VEC[j]) ORDERED flag (0=not ordered, 1=ordered) VEC[i] VEC[j] Negative N Temp Values (Used in SCOMP) Current Stack Pointer Subroutine Return Address

20 StackSort LC3 jsr INITSTK and r1,r1,#0 ld r4,n lea r5,vec add r4,r4,r5 not r4,r4 add r4,r4,#1 oloop: lea r2,vec add r3,r2,#0 ldr r0,r2,#0 jsr PUSH add r1,r1,#1 lea r7,iempty st r7,underflow iloop add r2,r2,#1 add r5,r4,r2 brp eiloop ldr r0,r2,#0 jsr SCOMP brnz norder ipl jsr POP str r0,r3,#0 add r3,r3,#1 br ipl norder and r1,r1,#0 iempty ldr r0,r2,#0 jsr PUSH br iloop eiloop lea r7,oempty st r7,underflow opl jsr POP str r0,r3,#0 add r3,r3,#1 br opl oempty add r1,r1,#0 brz oloop HALT

21 Stack Application 2 - Calculator Reverse Polish Notation If you get a number, push it If you get an operator: pop arguments Calculate push the result For example, instead of 3 + 4, we write For example, instead of (3 + 4) x 5 we write x For example, instead of x 5 we write x +

22 Example Calculator ADD function ADD ; pop 2 values, add, and push the result jsr pop add r1,r0,#0 jsr pop add r0,r1,r0 jsr push ret

23 Subroutine Calling Itself (Recursion) For example: Factorial fact(n)=fact(n-1) x n for n>1 fact(1)=1 Q: How where do I save/restore R7? Q: Can I assume FACT does not change R1????? FACT ; arg in r1 result in r2 (uses r3) ; Save R7 add r2,r1,#0 ; add r1r1,#-1 brnz fend jsr FACT add r3,r2,#0 fml add r2,r2,r3 add r1,r1,#-1 brp fml fend ; Restore R7 ret

24 Subroutine Calling Itself (Recursion) For example: Factorial fact(n)=fact(n-1) x n for n>1 fact(1)=1 Need to save R7 before calling save Need to restore R7 after calling restore FACT ; arg in r1 result in r2 (uses r3) st r7,factr7 jsr FACTSAVE add r2,r1,#0 add r1,r1,#-1 brnz fend jsr FACT add r3,r2,#0 fml add r2,r2,r3 add r1,r1,#-1 brp fml fend jsr FACTREST ld r7,factr7 ret FACTR7.fill #0

25 Stack Usage Manage Recursion FACTSAVE ; Save FACTR7 and R1 in stack st r7,fsr7 st r0,fsr0 ld r0,factr7 jsr PUSH add r0,r1,#0 jsr PUSH ld r0,fsr0 ld r7,fsr7 ret FSR0.fill #0 FSR7.fill #0 FACTREST ; Restore FACTR7 and R1 from stack st r7,frr7 st r0,frr0 jsr POP add r1,r0,#0 jsr POP st r0,factr7 ld r0,frr0 ld r7,frr7 ret FRR0.fill #0 FRR7.fill #0

26 Invoking FACT jsr INITSTK ld r1,qfact jsr FACT st r2,ans HALT QFACT.fill #5 ANS.fill #0