lecture 09 recursion

More MIPS: Recursion

Computer Science 104 Lecture 9

2 © Andrew D. Hilton / Alvin R. Lebeck CPS 104

Homework • Homework 1: graded. 50% As, 27% Bs • Homework 2: Due Wed

Midterm 1 • This Wed • 1 page of notes

Admin

3 © Andrew D. Hilton / Alvin R. Lebeck

Last time…

What did we do last time?

CPS 104


Last time…

What did we do last time? • More MIPS! • Functions:

− jal − jr − Calling conventions − Stack Frames, saving registers

• Worked “bubble sort” example

CPS 104


0 zero constant 0

1 at reserved for assembler

2 v0 expression evaluation &

3 v1 function results

4 a0 arguments

5 a1

6 a2

7 a3

8 t0 temporary: caller saves

. . .

15 t7

16 s0 callee saves

. . .

23 s7

24 t8 temporary (cont’d)

25 t9

26 k0 reserved for OS kernel

27 k1

28 gp Pointer to global area

29 sp Stack pointer

30 fp frame pointer

31 ra Return Address (HW)

Review: MIPS Registers


Review: Calling a function

Calling Procedure Step-1: Setup the arguments:

• The first four arguments (arg0-arg3) are passed in registers $a0-$a3 • Remaining arguments are pushed onto the stack (in reverse order arg5 is at the top of the stack).

Step-2: Save caller-saved registers • Save registers $t0-$t9 if they contain live values at the call site.

Step-3: Execute a jal instruction.


Review: Callee setup

Called Routine Step-1: Establish stack frame.

• Subtract the frame size from the stack pointer. addiu $sp, $sp, - <frame-size>

• Typically, minimum frame size is 32 bytes (8 words).

Step-2: Save callee saved registers in the frame.

• Register $fp is always saved. • Register $ra is saved if routine makes a call. • Registers $s0-$s7 are saved if they are used.

Step-3: Establish Frame pointer • Add the stack <frame size> - 4 to the address in $sp

addiu $fp, $sp, <frame-size> - 4


Review: Returning

On return from a call Step-1: Put returned values in registers $v0.

(if a value is returned) Step-2: Restore callee-saved registers.

• Restore $fp and other saved registers. [$ra, $s0 - $s7]

Step-3: Pop the stack • Add the frame size to $sp.

addiu $sp, $sp, <frame-size>

Step-4: Return • Jump to the address in $ra.

jr $ra


Today

More MIPS! • Recursion

Won’t be required on the exam… • But you could use recursion if you want… • And good MIPSing practice anyways

Extra time? • I’ll work example problems, answer review

questions, etc…

CPS 104


Recursion

Why do we want recursion? • Because recursion is a wonderful thing!

Canonical recursion example? • Factorial

CPS 104


Factorial in C

int fact (int n) { if (n <= 0) {

return 1;

}

return n * fact (n – 1);

}

…

int x = fact(3);

CPS 104


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0

C1

factorial

n 2 return C1


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0

C1

factorial

n 2 return C1

factorial

n 1 return C1


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0

C1

factorial

n 2 return C1

factorial

n 1 return C1

factorial

n 0 return C1


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0

C1

factorial

n 2 return C1

factorial

n 1 return C1

fact returned 1


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0

C1

factorial

n 2 return C1

fact returned 1


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x ???

C0

factorial

n 3 return C0

fact returned 2


Factorial in C


return 1;

}


}

…

int main (void) {

int x = fact(3);

…

CPS 104

main

x 6


Factorial in Assembly


return 1;

}

return n * fact (n – 1); }

…

int main (void) {

int x = fact(3);

…

CPS 104

Observe: Parameter n in $a0 Need to put n-1 in $a0 to call Need n after call




return 1;

}


…

int main (void) {

int x = fact(3);

…

CPS 104


Conclusion: Need to move n to other reg Which one: $t0 or $s0?




return 1;

}


…

int main (void) {

int x = fact(3);

…

CPS 104


Conclusion: Need to move n to other reg Which one: $t0 or $s0? Would need save/restore => May as well use $s0


Convert C to Assembly


return 1;

}


…

int main (void) {

int x = fact(3);

…

CPS 104

(We’ll switch to emacs For this part)



fact:

<<frame setup>>

move $s0, $a0

blez $s0, factEndZero

addi $a0, $a0, -1

jal fact

mul $v0, $v0, $s0

factRet:

<<frame cleanup>>

jr $ra

factEndZero:

li $v0, 1

b factRet

CPS 104

Reg Value $a0 0003 $s0 1234 $v0 ABCD $sp FF80 $fp FFCC $ra 4000

Addr Value FF7C FF78 FF74 FF70 FF6C FF68 FF64 FF60 FF5C FF58 FF54 FF50 FF4C FF48 FF44 FF40



<<Frame Setup>>

addiu $sp, $sp, -16

sw $fp, 0($sp)

sw $ra, 4($sp)

sw $s0, 8($sp)

addiu $fp, $sp, 12

CPS 104





<<Frame Setup>>

addiu $sp, $sp, -16

sw $fp, 0($sp)

sw $ra, 4($sp)

sw $s0, 8($sp)

addiu $fp, $sp, 12

CPS 104


Addr Value FF7C FF78 FF74 FF70 FFCC FF6C FF68 FF64 FF60 FF5C FF58 FF54 FF50 FF4C FF48 FF44 FF40



<<Frame Setup>>

addiu $sp, $sp, -16

sw $fp, 0($sp)

sw $ra, 4($sp)

sw $s0, 8($sp)

addiu $fp, $sp, 12

CPS 104


Addr Value FF7C FF78 FF74 4000 FF70 FFCC FF6C FF68 FF64 FF60 FF5C FF58 FF54 FF50 FF4C FF48 FF44 FF40



<<Frame Setup>>

addiu $sp, $sp, -16

sw $fp, 0($sp)

sw $ra, 4($sp)

sw $s0, 8($sp)

addiu $fp, $sp, 12

CPS 104


Addr Value FF7C FF78 1234 FF74 4000 FF70 FFCC FF6C FF68 FF64 FF60 FF5C FF58 FF54 FF50 FF4C FF48 FF44 FF40



<<Frame Setup>>

addiu $sp, $sp, -16

sw $fp, 0($sp)

sw $ra, 4($sp)

sw $s0, 8($sp)

addiu $fp, $sp, 12

CPS 104

Reg Value $a0 0003 $s0 1234 $v0 ABCD $sp FF70 $fp FF7C $ra 4000




fact:

<<frame setup>>

move $s0, $a0


addi $a0, $a0, -1

jal fact

mul $v0, $v0, $s0

factRet:

<<frame cleanup>>

jr $ra

factEndZero:

li $v0, 1

b factRet

CPS 104





fact:

<<frame setup>>

move $s0, $a0


addi $a0, $a0, -1

jal fact # Addr 1040 mul $v0, $v0, $s0

factRet:

<<frame cleanup>>

jr $ra

factEndZero:

li $v0, 1

b factRet

CPS 104

