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ECE 15B Computer Organization Spring 2011 Dmitri Strukov Partially adapted from Computer Organization and Design, 4 th edition, Patterson and Hennessy,
ECE 15B Computer OrganizationSpring 2011
Dmitri Strukov
Partially adapted from Computer Organization and Design, 4th edition, Patterson and Hennessy,
ECE 15B Spring 2011
Fibonacci numbersF(n) = F(n-1)+F(n-2)F(1) = 1F(2) = 1n = 1 2 3 4 5 6 …F(n) = 1 1 2 3 5 8 …
/* Recursive function in c */int fib(int n) {
If (n==1) return 1;If (n==2) return 1;return fib(n-1)+fib(n-2);
}
ECE 15B Spring 2011
ProceduresProlog - spill all register to stack used by procedure expect for $t0-$t9 and the one used for returning values
- advance stack pointer ($sp) first then write to stackBody
code of the procedure Epilog
- restore all used registers - adjust stack pointer at the end ($sp)
ECE 15B Spring 2011
/* Recursive function in c */int fib(int n) {
If (n==1) return 1;If (n==2) return 1;return fib(n-1)+fib(n-2);
}
# Recursive function in MIPS assembler #prolog
FIB: addi $sp, $sp, -12sw $a0, 0($sp)sw $s0, 4($sp)sw $ra, 8($ra)# bodyaddi $v0, $zero, 1addi $t0, $zero, 1beq $a0, $t0, EPILOG #check for n==1addi $t0, $zero, 2beq $a0, $t0, EPILOG #check for n==2addi $a0, $a0, -1jal FIB #calculate fib(n-1)addi $s0, $zero, $v0 # save fib(n-1) to $s0addi $a0, $a0, -1 #calculate fib(n-2) jal FIBaddi $v0, $v0, $s0#epilog
EPILOG: lw $a0, 0($sp)lw $s0, 4,($sp)lw $ra, 8,($sp)addi $sp, $sp, 12 jr $ra
/* Recursive function in c */int fib(int n) { v0 = 1;
If (n==1) goto EXIT;If (n==2) goto EXIT;
n = n – 1;s0 = fib(n);
n = n – 1;v0 = fib(n);
v0 = v0 +s0; EXIT: return v0; }
ECE 15B Spring 2011
/* Recursive function in c */int fib(int n) {
If (n==1) return 1;If (n==2) return 1;return fib(n-1)+fib(n-2);
}
# Recursive function in MIPS assembler #prolog
FIB: addi $sp, $sp, -12sw $a0, 0($sp)sw $s0, 4($sp)sw $ra, 8($ra)# bodyaddi $v0, $zero, 1addi $t0, $zero, 1beq $a0, $t0, EPILOG #check for n==1addi $t0, $zero, 2beq $a0, $t0, EPILOG #check for n==2addi $a0, $a0, -1jal FIB #calculate fib(n-1)addi $s0, $zero, $v0 # save fib(n-1) to $s0addi $a0, $a0, -1 #calculate fib(n-2) jal FIBaddi $v0, $v0, $s0#epilog
EPILOG: lw $a0, 0($sp)lw $s0, 4,($sp)lw $ra, 8,($sp)addi $sp, $sp, 12 jr $ra
/* Recursive function in c */int fib(int n) { v0 = 1;
If (n==1) goto EXIT;If (n==2) goto EXIT;
n = n – 1;s0 = fib(n);
n = n – 1;v0 = fib(n);
v0 = v0 +s0; EXIT: return v0; }
ECE 15B Spring 2011
• Now let’s see changes in the memory (stack) and register file as we execute recursive function with n = 3
• First let’s review datapath and where code is stored
Simple datapath review
ECE 15B Spring 2011
Simple datapath review
ECE 15B Spring 2011
stack
instructions
Where is the code stored?
ECE 15B Spring 2011
stackstack
Code (????)
static data
dynamic data (heap)
RF[$sp]
0
ANS: In main memory
Instruction memory
ECE 15B Spring 2011
stack
code
static data
dynamic data (heap)
IM: Physically different memory Logically mapped to main memory
ECE 15B Spring 2011
Direct mapped cache implementation of instruction memory
Main
Main memory
Instruction memory
At any point in time IM has a copy of a portion of main memory
Separate memory (tag) to store which location is currently mapped
0
16
24
Tag (28 bit)
If upper portion of PC (28 bit) matches tag then IM has right values (hit), otherwise stop execution and load right portion
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 0
$a0 3
$t0 0
$s0 0
$sp 0xFFFF0000
$ra 0x0108
index value
0xFFFF0000 0x00000000
0xFFFF00FC
0xFFFF00F8
0xFFFF00F4
RF (right after execution of initial jal FIB at 0x0104)
MM (initial values in stack)
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 1
$a0 2
$t0 2
$s0 0
$sp 0xFFFF00F4
$ra 0x102C
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
RF (after execution jal FIB at 0x1028) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 1
$a0 2
$t0 2
$s0 0
$sp 0xFFFF00E8
$ra 0x102C
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x102C
0xFFFF00EC 0
0xFFFF00E8 2
RF (after execution beq at 0x1020) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 1
$a0 2
$t0 2
$s0 0
$sp 0xFFFF00F4
$ra 0x102C
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x102C
0xFFFF00EC 0
0xFFFF00E8 2
RF (after execution jr at 0x104C) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 1
$a0 1
$t0 2
$s0 1
$sp 0xFFFF00F4
$ra 0x1038
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x102C
0xFFFF00EC 0
0xFFFF00E8 2
RF (after execution jal at 0x1034) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 1
$a0 1
$t0 1
$s0 1
$sp 0xFFFF00E8
$ra 0x1038
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x1038
0xFFFF00EC 1
0xFFFF00E8 1
RF (after execution beq at 0x1018) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 1
$a0 1
$t0 1
$s0 1
$sp 0xFFFF00F4
$ra 0x1038
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x1038
0xFFFF00EC 1
0xFFFF00E8 1
RF (after execution jr at 0x104C) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 2
$a0 3
$t0 1
$s0 0
$sp 0xFFFF00F4
$ra 0x0108
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x1038
0xFFFF00EC 1
0xFFFF00E8 1
RF (after execution jr at 0x104C) MM - stack
ECE 15B Spring 2011
Recursive function execution: step by step
0x0100 addi $a0, $zero, 30x0104 jal FIB0x0108 next instruction
XXXXXXXXXXXXXXXXXXXXXX
FIB: 0x1000 addi $sp, $sp, -120x1004 sw $a0, 0($sp)0x1008 sw $s0, 4($sp)0x100C sw $ra, 8($ra)0x1010 addi $v0, $zero, 10x1014 addi $t0, $zero, 10x1018 beq $a0, $t0, EPILOG0x101C addi $t0, $zero, 20x1020 beq $a0, $t0, EPILOG0x1024 addi $a0, $a0, -10x1028 jal FIB0x102C addi $s0, $zero, $v00x1030 addi $a0, $a0, -1 0x1034 jal FIB0x1038 addi $v0, $v0, $s0
EPILOG: 0x103C lw $a0, 0($sp)0x1040 lw $s0, 4,($sp)0x1044 lw $ra, 8,($sp)0x1048 addi $sp, $sp, 12 0x104C jr $ra
index value
$v0 2$a0 3
$t0 1
$s0 0
$sp 0xFFFF00F4
$ra 0x0108
index value
0xFFFF0100 0x00000000
0xFFFF00FC 0x0108
0xFFFF00F8 0
0xFFFF00F4 3
0xFFFF00F0 0x1038
0xFFFF00EC 1
0xFFFF00E8 1
RF (at the end of program)MM - stack
ECE 15B Spring 2011
Is code optimal?* No need to spill registers when n = 1 and n = 2
* F(n-2) is calculated independently of F(n-1).
Better version could be (which is linear in time with n):int fib(int a, int b, int n) {if (n==2) return a; else return fib(a+b, a, n 1);‐}
…. and use fib(1,1,n)
* Even better to use for-loop or do-while ?
