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ECE 15B Computer Organization Spring 2011 Dmitri Strukov

ECE 15B Computer Organization Spring 2011 Dmitri Strukov. Partially adapted from Computer Organization and Design, 4 th edition, Patterson and Hennessy,. Fibonacci numbers. F(n) = F(n-1)+F(n-2) F(1) = 1 F(2) = 1 n = 1 2 3 4 5 6 …

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ECE 15B Computer Organization Spring 2011 Dmitri Strukov

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  1. ECE 15B Computer OrganizationSpring 2011Dmitri Strukov Partially adapted from Computer Organization and Design, 4th edition, Patterson and Hennessy,

  2. Fibonacci numbers F(n) = F(n-1)+F(n-2) F(1) = 1 F(2) = 1 n = 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

  3. Procedures Prolog - spill all register to stack used by procedure expect for $t0-$t9 and the one used for returning values - advance stack pointer ($sp) first then write to stack Body code of the procedure Epilog - restore all used registers - adjust stack pointer at the end ($sp) ECE 15B Spring 2011

  4. # Recursive function in MIPS assembler • #prolog • FIB: addi $sp, $sp, -12 • sw $a0, 0($sp) • sw $s0, 4($sp) • sw $ra, 8($ra) • # body • addi $v0, $zero, 1 • addi $t0, $zero, 1 • beq $a0, $t0, EPILOG #check for n==1 • addi $t0, $zero, 2 • beq $a0, $t0, EPILOG #check for n==2 • addi $a0, $a0, -1 • jal FIB #calculate fib(n-1) • addi $s0, $zero, $v0 # save fib(n-1) to $s0 • addi $a0, $a0, -1 #calculate fib(n-2) • jal FIB • addi $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) { If (n==1) return 1; If (n==2) return 1; return fib(n-1)+fib(n-2); } /* 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

  5. # Recursive function in MIPS assembler • #prolog • FIB: addi $sp, $sp, -12 • sw $a0, 0($sp) • sw $s0, 4($sp) • sw $ra, 8($ra) • # body • addi $v0, $zero, 1 • addi $t0, $zero, 1 • beq $a0, $t0, EPILOG #check for n==1 • addi $t0, $zero, 2 • beq $a0, $t0, EPILOG #check for n==2 • addi $a0, $a0, -1 • jal FIB #calculate fib(n-1) • addi $s0, $zero, $v0 # save fib(n-1) to $s0 • addi $a0, $a0, -1 #calculate fib(n-2) • jal FIB • addi $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) { If (n==1) return 1; If (n==2) return 1; return fib(n-1)+fib(n-2); } /* 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

  6. 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 ECE 15B Spring 2011

  7. Simple datapath review ECE 15B Spring 2011

  8. Simple datapath review stack instructions ECE 15B Spring 2011

  9. Where is the code stored? stack stack RF[$sp] dynamic data (heap) static data Code (????) 0 ANS: In main memory ECE 15B Spring 2011

  10. Instruction memory stack IM: Physically different memory Logically mapped to main memory dynamic data (heap) static data code ECE 15B Spring 2011

  11. Direct mapped cache implementation of instruction memory At any point in time IM has a copy of a portion of main memory Main memory Main Separate memory (tag) to store which location is currently mapped If upper portion of PC (28 bit) matches tag then IM has right values (hit), otherwise stop execution and load right portion 24 Instruction memory Tag (28 bit) 16 0 ECE 15B Spring 2011

  12. Recursive function execution: step by step RF (right after execution of initial jal FIB at 0x0104) MM (initial values in stack) • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  13. Recursive function execution: step by step RF (after execution jal FIB at 0x1028) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  14. Recursive function execution: step by step RF (after execution beq at 0x1020) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  15. Recursive function execution: step by step RF (after execution jr at 0x104C) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  16. Recursive function execution: step by step RF (after execution jal at 0x1034) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  17. Recursive function execution: step by step RF (after execution beq at 0x1018) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  18. Recursive function execution: step by step RF (after execution jr at 0x104C) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  19. Recursive function execution: step by step RF (after execution jr at 0x104C) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  20. Recursive function execution: step by step RF (at the end of program) MM - stack • 0x0100addi $a0, $zero, 3 • 0x0104 jal FIB • 0x0108 next instruction • XXXXXXXXXXXXXXXXXXXXXX • FIB: 0x1000addi $sp, $sp, -12 • 0x1004 sw $a0, 0($sp) • 0x1008 sw $s0, 4($sp) • 0x100C sw $ra, 8($ra) • 0x1010 addi $v0, $zero, 1 • 0x1014 addi $t0, $zero, 1 • 0x1018 beq $a0, $t0, EPILOG • 0x101C addi $t0, $zero, 2 • 0x1020 beq $a0, $t0, EPILOG • 0x1024 addi $a0, $a0, -1 • 0x1028 jal FIB • 0x102C addi $s0, $zero, $v0 • 0x1030 addi $a0, $a0, -1 • 0x1034 jal FIB • 0x1038 addi $v0, $v0, $s0 • EPILOG: 0x103Clw $a0, 0($sp) • 0x1040 lw $s0, 4,($sp) • 0x1044 lw $ra, 8,($sp) • 0x1048 addi $sp, $sp, 12 • 0x104C jr $ra ECE 15B Spring 2011

  21. 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 ? ECE 15B Spring 2011

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