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.