Computer architecture

1. Vector Performance (40 marks)

Consider the following code fragment:

lv      v1,rx         // load vector x
lv      v2,ry         // load vector y
mulvs.d v3,v1,f0      // z1 = a * x
addvv.d v4,v2,v3      // z2 = y + z1
mulvs.d v5,v2,f2      // z3 = b * y
sv      v4,ry         // store z2 as vector y
sv      v5,rx         // store z3 as vector x

Make the following assumptions:

– this is a four-lane vector processor—this affects the running time of
  vector instructions, according to our formula
– there are two copies of each arithmetic vector functional unit and two
  copies of the vector load-store functional unit—this affects the number
  of vector instructions that can run in parallel in a gang
– a vector store completes as soon as the last element is sent to memory
– start-up penalties of functional units are: l/s = 12, add = 6, mul = 7
– the vector length is 256

a) In the absence of vector chaining, determine the execution time of this
code fragment by drawing the timing diagram.  Indicate starting time, first
result, and last result for each gang.  Hint: draw the flow-dependence graph
first.

b) In the presence of vector chaining, determine the execution time of this
code fragment by drawing the timing diagram.  Indicate starting time, first
result, and last result for each gang.

2. Vectorizing Compiler (30 marks)

Consider this familiar loop:

loop: l.d    f4,0(r1)    l1  
      l.d    f6,0(r2)    l2  
      mul.d  f4,f4,f0    m1  
      mul.d  f6,f6,f2    m2  
      add.d  f4,f4,f6    a1  
      s.d    f4,0(r1)    s1  
      daddui r1,r1,#-8   sub1
      daddui r2,r2,#-8   sub2
      bnez   r1,loop     br  

Rewrite the code using vector instructions.  Draw the flow-dependence graph
of vector instructions.  Using vector chaining, make a rough estimate of
the running time of the program, using the data in question 1.

3. Vectorizing Loop Nests (30 marks)

Consider the following loop nest that computes the lengths of many
strings.

for( i=0; i<n; i++ ) {
  char *p = str[i];
  while( *p )
    p++;
  len[i] = p – str[i];
}

Comment, with a reasonable explanation, on the relative abilities of
parallelizing and vectorizing compilers to compile this loop nest.
A parallelizing compiler breaks a loop nest into multiple threads.
A vectorizing compiler expresses a loop-nest computation using vector
instructions.