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20110405

Course: CSE 220, Spring 2012
School: Stony Brook University
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Assembler Related Directives .data .byte A, B, C .half 1, 2, 3 .word 1, 2, 3 .float 6.02E23 .double 6.02E23 # # # # # initialize initialize initialize initialize initialize byte data half-word data word data float data double data Example: Saving $ra to Memory Suppose we now want functions putstr and putchar, where putstr calls putchar. Then putstr needs to save $ra before it calls putchar. # # hello5:...

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Assembler Related Directives .data .byte A, B, C .half 1, 2, 3 .word 1, 2, 3 .float 6.02E23 .double 6.02E23 # # # # # initialize initialize initialize initialize initialize byte data half-word data word data float data double data Example: Saving $ra to Memory Suppose we now want functions putstr and putchar, where putstr calls putchar. Then putstr needs to save $ra before it calls putchar. # # hello5: "Hello world" program with putstr and putchr subroutines. # la $t0, mesg1 # Load address of first string in $t0 jal putstr # Call putstr la $t0, mesg2 # Load address of second string in $t0 jal putstr # Call putstr done: ori $v0, $0, 10 # Exit system call syscall # # putstr: Subroutine to print a string. # Assumes $t0 contains address of string to be printed. # The value in $t0 is *not* preserved. # putstr: sw $ra, oldra # Save return address in oldra variable nextch: lb $a0, 0($t0) # Load next character in $a0 beq $a0, $0, return # If character is 0, then return to caller jal putchr # Call putchr addi $t0, $t0, 1 # Advance to next character bgez $0, nextch return: lw $ra, oldra # Restore saved return address jr $ra # Return to caller .data oldra: .space 4 # Space for saved return address .text # # putchr: Subroutine to print a character. # Assumes $a0 contains the character to be printed. # putchr: ori $v0, $0, 11 # Print character system call syscall jr $ra # Return to caller. .data mesg1: .asciiz "Hello world\n" mesg2: .asciiz "Wasnt that fun?\n" Its Getting Confusing! Note that putstr in the previous example modies $a0, so the caller must save this register if it needs the contents after the call. What if we want to create a recursive subroutine? Each recursive call is going to clobber the same set of registers being used by its caller. If each subroutine modies a dierent set of registers, it becomes very confusing to keep track of what is going on. We need a more systematic approach. . . Register Usage Conventions Things are made more manageable by introducing (and adhering to) conventions on the use of registers. $zero $at $v0-$v1 $a0-$a3 $t0-$t7 $s0-$s7 $t8-$t9 $k0-$k1 $gp $sp $fp $ra Hard-wired to zero Reserved for assembler for pseudo-instructions Return values from subroutines Arguments to subroutines Temporaries (not preserved across calls) Temporaries (callee-saved, preserved across calls) Temporaries (not preserved across calls) Reserved for OS kernel Global pointer Stack pointer Frame pointer Return address (used by Jump and Link) Except for $zero and $ra, these conventions are not forced on us by the hardware. Our Responsibilities Registers $s0-$s7, $fp, and $gp must be saved before modication, and restored before the current subroutine returns. Register $ra must be saved before another subroutine is called using jal. We must put arguments to a subroutine in $a0-$a3, and return results in $v0-$v1. We cannot assume these registers are preserved across a subroutine call. We must avoid entirely the use of $at and $k0-$k1. We can do whatever we want with $t0-$t9, but we cannot assume they are preserved across subroutine calls. Where to Save Registers? Q: Where do we get the space to save the registers we need to save? We could use static variables (i.e. memory in the data segment), but that wont work with recursion (why not?). A: We can allocate space on the stack. When a program starts, the OS sets up the stack pointer ($sp) to point to the high-address end of a region of memory that can be used as temporary storage. We can allocate space in this region by subtracting from the stack pointer. We can free space by adding to the stack pointer. This works, as long as a last-allocated, rst-freed discipline is followed. Each subroutine can allocate as much stack space as it needs, as long as it frees it before it returns. Stack Space Management Stack space can be allocated by subtracting from the stack pointer: addiu $sp, $sp, -SPACE # SPACE is how many bytes we need Stack space can be freed by adding to the stack pointer: addiu $sp, $sp, SPACE We can load and store to locations in the stack: sw $ra, 0($sp) # save $ra in the stack area lw $ra, 0($sp) # restore $ra from the stack area Example Lets re-visit the previous example, adhering to register conventions and using the stack as the place to save registers. # # hello5a: "Hello world" program with putstr and putchr subroutines, # following register conventions and using the stack to save registers. # la $a0, mesg1 # Load address of first string in $a0 jal putstr # Call putstr la $a0, mesg2 # Load address of second string in $a0 jal putstr # Call putstr done: ori $v0, $0, 10 # Exit system call syscall # # putstr: Subroutine to print a string. # Assumes $a0 contains address of string to be printed. # putstr: addiu $sp, $sp, -8 # Get stack space (to save $ra, $s0) sw $ra, 0($sp) # Save $ra on stack sw $s0, 4($sp) # Save $s0 on stack or $s0, $0, $a0 # Move argument to $s0 nextch: lb $a0, 0($s0) # Load next character in $a0 beq $a0, $0, return # If character is 0, then return jal putchr # Call putchr addi $s0, $s0, 1 # Advance to next character bgez $0, nextch return: lw $s0, 4($sp) # Restore saved $s0 lw $ra, 0($sp) # Restore saved $ra addiu $sp, $sp, 8 # Free stack space jr $ra # Return to caller # # putchr: Subroutine to print a character. # Assumes $a0 contains the character to be printed. # No stack space needed here, because we dont modify any # registers that are required to be saved. # putchr: ori $v0, $0, 11 # Print character system call syscall jr $ra # Return to caller. .data mesg1: .asciiz "Hello world\n" mesg2: .asciiz "Wasnt that fun?\n" Multiple Allocations in Stack One Subroutine In the previous example, all the data stored on the stack is accessed by an index over $sp. We have to keep track of the oset for each item stored on the stack. If just one stack region is allocated per subroutine, this is ne. If we allocate another stack region in the same subroutine, all the osets of previously saved data change. It would be less confusing if we could access stack data using xed osets, which dont change with subsequent stack allocations. Frame Pointer A frame pointer is a register that is maintained so that data allocated on the stack can be accessed at xed osets, independent of the stack pointer. The stack area allocated by a subroutine is called its activation record. When a subroutine is called, the frame pointer is set to point to the base of the activation record. The stack pointer points to the other (active) end of the activation record. Data in the activation record is accessed at xed osets from the frame pointer. Example Activation Record Format <-----------+ | -------------------| saved ra >-----------+ saved fp <-----------+ DATA | ... | -------------------| saved ra | FP-> saved fp >-----------+ DATA SP-> ... -------------------ARs form a linked list via saved frame pointers. PREVIOUS AR CURRENT AR Subroutine Linkage with Frame Pointer In Caller: Subroutine is called using jal. jal subr (call will return here) In Callee: Linkage protocol executed at beginning of subroutine: subr: addiu sw sw or $sp, $ra, $fp, $fp, $sp, -8 4($sp) 0($sp) $0, $sp # # # # allocate space to save $ra, $fp save $ra save $fp update $fp At this point, we can allocate whatever additional space we want (e.g. for local variables) on the stack, and we dont have to keep track of how much it is. In Callee: Allocating space on stack: addiu $sp, $sp, -LOCALS # allocate space for locals In Callee: Accessing data in AR: sw lw $s0, -4($fp) $s0, -4($fp) # save $s0 # restore $s0 Access to local variables will be at xed osets to the frame pointer, regardless of whatever else we do with the stack pointer. In Callee: Exit protocol executed before return: or lw lw addiu $sp, $ra, $fp, $sp, $0, $fp 4($fp) 0($fp) $sp, 8 # # # # delete junk on stack restore $ra restore $fp delete space for $ra, $fp In Callee: Returning from subroutine: jr $ra # return to caller There are many possible AR formats and many possible linkage protocols. I presented here a simple one, with some useful properties, but which is not the fastest possible. People spend time thinking about how to minimize subroutine linkage overhead. Example: Recursive Factorial # # factorial: Recursive factorial # main: ori $a0, 5 jal factorial or $a0, $0, $v0 ori $v0, $0, 1 syscall ori $v0, $0, 10 syscall demo using a frame pointer. # # # # argument = 5 call factorial move result to arg 0 print integer # exit syscall # hasta la vista, baby! # # Recursive factorial: argument in $a0, result to $v0. # Uses callee-save register $s0 to preserve argument # over recursive call. # factorial: # Subroutine linkage protocol addiu $sp, $sp, -8 # allocate space to save $ra, $fp sw $ra, 4($sp) # save $ra sw $fp, 0($sp) # save $fp or $fp, $0, $sp # update $fp ####################### # Allocate space on stack for $s0 addiu $sp, $sp, -4 # allocate space to save $s0 sw $s0, -4($fp) # save $s0 bne $a0, $0, nonz # check for base case ori $v0, $0, 1 # arg = 0, return 1 b return nonz: or $s0, $0, $a0 # addi $a0, $a0, -1 # jal factorial # mult $v0, $s0 # mflo $v0 # return: lw $s0, -4($fp) # # Subroutine exit protocol or $sp, $0, $fp # lw $ra, 4($fp) # lw $fp, 0($fp) # addiu $sp, $sp, 8 # ####################### jr $ra # copy $a0 to $s0 decrement $a0 recursive call multiply $s0 by recursive result get product in $v0 restore $s0 for caller delete junk on stack restore $ra restore $fp delete space for $ra, $fp return to caller Passing Arguments on the Stack The normal MIPS convention is to pass up to four arguments in $a0-$a3. The linkage protocol presented above can also handle arguments passed on the stack. In Caller: addiu $sp, $sp, -ARGS (store args on stack) jal subr addiu $sp, $sp, ARGS # allocate space for args # deallocate space for args In Callee: Args are accessible starting at 8($fp). Example: Factorial with Arg on Stack # # factorial1: Recursive factorial # rather than in $a0. # main: ori $t0, 5 addiu $sp, $sp, -4 sw $t0, 0($sp) jal factorial addiu $sp, $sp, 4 or $a0, $0, $v0 ori $v0, $0, 1 syscall ori $v0, $0, 10 syscall demo that passes argument on stack, # # # # # # # argument = 5 allocate space for argument store argument on stack call factorial deallocate space for argument move result to arg 0 print integer # exit syscall # hasta la vista, baby! # # Recursive factorial: argument on stack, result to $v0. # factorial: # Subroutine linkage protocol addiu $sp, $sp, -8 # allocate space to save $ra, $fp sw $ra, 4($sp) # save $ra sw $fp, 0($sp) # save $fp or $fp, $0, $sp # update $fp ####################### lw $t0, 8($fp) # get argument in $t0 bne $t0, $0, nonz # check for base case ori $v0, $0, 1 # arg = 0, return 1 b return nonz: addi $t0, $t0, -1 addiu $sp, $sp, -4 sw $t0, 0($sp) jal factorial addiu $sp, $sp, 4 lw $t0, 8($fp) mult $v0, $t0 mflo $v0 return: # Subroutine exit protocol or $sp, $0, $fp lw $ra, 4($fp) lw $fp, 0($fp) addiu $sp, $sp, 8 ####################### jr $ra # # # # # # # # decrement $t0 allocate space for arg store arg on stack recursive call deallocate space for arg recover arg to this call multiply $t0 by recursive result get product in $v0 # # # # delete junk on stack restore $ra restore $fp delete space for $ra, $fp # return to caller
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Stony Brook University - CSE - 220
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Stony Brook University - CSE - 220
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Stony Brook University - CSE - 312
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Munich Business - BUSINESS - MG301
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Purdue - STAT - 479
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Purdue - STAT - 479
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Purdue - STAT - 479
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Purdue - STAT - 479
STAT 490C Quiz1. You are given: j 1 2 3 4 5 yj 10 17 22 29 35 sj 1 2 3 4 5 rj 15 14 12 9 5fu(x) is the kernel density estimator of the density function using the uniform kernel. ft(x) is the kernel density estimator of the density function using the tri
Purdue - STAT - 479
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Purdue - STAT - 479
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Purdue - STAT - 479
Quiz 7 STAT 479 Spring 2012April 12, 20121. You are given the following claim amounts: 8 12 24 30 You Hypothesis is that these claims come from an exponential distribution with a variance of 400. Calculate the Kolmogorov-Smirnov test Statistic to test t
Purdue - STAT - 479
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Purdue - STAT - 532
2Homework 2 - Additional Problems2.1. Let cfw_Xn n0 be a Markov chain on a finite state space I. Define Tcov to be the cover time of the Markov chain to be the first time that the Markov chain has visited every site in I. That is, Tcov = mincfw_n 0 : i
Purdue - STAT - 532
2Homework 2 - Additional Problems2.1. Let cfw_Xn n0 be a Markov chain on a finite state space I. Define Tcov to be the cover time of the Markov chain to be the first time that the Markov chain has visited every site in I. That is, Tcov = mincfw_n 0 : i
Purdue - STAT - 532
3Homework 3 - Additional Problems3.1. There is a typo on page 20 of the book, just after the bold heading Using the TI83 calculator is easier. The book says .we write (1.10) in matrix form as -.2 .1 1 (1 , 2 , 3 ) .2 -.5 1 = (0, 0, 1) .3 .3 1 If we let
Purdue - STAT - 532
5Homework 5 - Additional Problems5.1. (This is exercise 1.8 in Introduction to Stochastic Processes by Lawler). Consider a simple random walk on the graph below. (Recall that simple random walk on a graph is the markov chain which at each time moves to
Purdue - STAT - 532
5Homework 5 - Additional Problems5.1. (This is exercise 1.8 in Introduction to Stochastic Processes by Lawler). Consider a simple random walk on the graph below. (Recall that simple random walk on a graph is the markov chain which at each time moves to
Purdue - STAT - 532
10Homework 10 - Additional Problems10.1. Consider the following modification to the Poisson janitor example (example 3.5 in the book). Suppose that the average lifetime of the lightbulbs is F = 60 and that the janitor comes to check on the bulb accordin
Purdue - STAT - 532
13Homework 13 - Additional Problems13.1. In the standard branching process model individuals reproduce offspring at rate and die at rate (see Example 4.4 in the book). Consider the following modification where there the population can also grow by immig
Purdue - STAT - 532
Stationary distributions of continuous time Markov chainsJonathon Peterson April 13, 2012The following are some notes containing the statement and proof of some theorems I covered in class regarding explicit formulas for the stationary distribution and
Purdue - STAT - 532
1Stopping TimesIn class we defined a stopping time in the following way. T is a stopping time for the Markov chain cfw_Xn n0 if for any n the event cfw_T = n can be expressed in terms of X0 , X1 , . . . , Xn . Lemma 1. There are two other equivalent def
Purdue - MA - 232
Purdue - MA - 232
71. Perform Gauss-Jordan elimination on the following matrix. I am grading yourwork not just your answer so be clear what you are doing and write legibly.(20 pts)12A:L;A--F3+sr4 lZl-e+rz-rl ZOoL,+-f-tI4ilIN0'l- (r+C1at*tt )lzloooLa
Purdue - MA - 232
MA 232Calculus II Group Work Solutions (L4-L5)Fall '101. Find the general form of the integral using integration by parts twice. x2 cos(x) dx Solution: x cos(x) dx = x sin(x) -2 22x sin(x) dx - cos(x) 2 dx]u = x2 dv = cos(x) dx du = 2x dx v = sin(x)
Purdue - MA - 232
Purdue - MA - 232