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Computer Architecture and Engineering – Assignment 1

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Assignment 1 02155 – Computer Architecture and Engineering
02155 – Assignment 1
Practical information
This is a deliverable assignment, meaning that you have to write a small report in English
with the requirements listed below. The grade you will obtain for the report will be part
of the final grade. There should be one report per group. Groups may contain at most
two students. At this point, you do not need to communicate your group members, after
we receive your reports we will register the groups and assign you a group number to be
used for the final project (the second deliverable assignment is individual).
The report should have a front page similar to the one appended at the end of this document. There are no other requirements on the template to be used for the report.
The report should include the following:
• Detailed problem solutions for the exercises in the section Problems.
• Detailed answers to questions specified in each exercise in the section Lab Exercises.
• Assembly code of the designed procedures properly formatted and commented.
The report should be handed-in only in electronic format (PDF and assembly code as
appendix in the PDF) using the Assignment utility in DUT Inside. Hand-in the report as
a group.
Feel free to ask or send an e-mail or use Slack if you have questions regarding the practical
information and the assignment in general.
Problems
Exercise A1.1 – Textbook problems
Solve the following four problems from the lecture textbook1
.
• Problem 2.34 (page 169).
• Problems 2.39.1 and 2.39.2 (page 170).
• Problem 3.32 (page 230).
1David A. Patterson, John L. Hennessy, Computer Organization and Design – The Hardware/Software
Interface, Risc-V Edition, Morgan Kaufmann, 2017.
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Assignment 1 02155 – Computer Architecture and Engineering
Exercise A1.2 – Exam problem (fall 2009)
Consider a benchmark program containing 106
instructions with the following mix of
operations.
Floating-point
multiplication
Floating-point
addition
Floating-point
division
Other
instructions
20% 30% 10% 40%
A processor P1 requires the following number of cycles to execute these instructions.
Floating-point
multiplication
Floating-point
addition
Floating-point
division
Other
instructions
8 5 30 4
a) Determine the CPI for the benchmark program.
b) For a clock rate of 200 MHz, what is the CPU execution time?
c) A new divide unit is introduced in the processor. This new divider requires 10 cycles
to compute a floating-point division, but the clock cycle is 20% longer. The latency,
in terms of cycles, in the other instructions is not changed. What is the speed-up of
the new processor over processor P1?
Lab Exercises
In this section of the assignment your task is to write an assembly program capable of
calculating the product of two complex numbers. Remember that the product of the two
complex numbers z = a + i b and w = c + id can be expanded as follows
(a + i b)(c + id) = (ac − bd) + i(ad + bc)
The program should be able to handle 32-bit signed and unsigned integers where the result
fits in a 32-bit register. You do not have to handle overflow. All the procedures you write
in this exercise should follow the caller/callee conventions outlined in Section 2.8 and the
green sheet of the lecture textbook1
. You should avoid using the frame pointer by only
changing the stack pointer on entry and exit of a routine.
You can use the following template for your solution.
# Course 02155 , Assignment 1 , A1 template
. data
aa : . word a # Re part of z
bb : . word b # Im part of z
cc : . word c # Re part of w
dd : . word d # Im part of w
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Assignment 1 02155 – Computer Architecture and Engineering
. text
. globl main
main :
lw a0 , aa
lw a1 , bb
lw a2 , cc
lw a3 , dd
jal complexMul # Multiply z and w
nop
j end # Jump to end of program
nop
# #################################
# #
# YOUR CODE HERE #
# #
# #################################
end :
nop
Exercise A1.3 – Integers product
Write an assembly routine myMult that takes 2 arguments, a and b in registers a0 and a1
respectively, and returns their product in register a0 without using the dedicated RISCV multiplication instruction. Figure 3.4 (page 185) of the lecture textbook1
contains an
algorithm for integer multiplication, but you must extend it to handle signed numbers.
When you have written myMult answer the following questions.
a) Is myMult a leaf or non-leaf procedure?
b) Did you need to use the stack? Explain why.
c) What are the overflow conditions for your procedure?
Exercise A1.4 – Complex numbers product
Write an assembly routine complexMul that takes two complex numbers z and w and returns their product. This routine should make use of the subroutine you wrote in Exercise
A1.3. The routine should expect the real parts of z and w to be placed in a0 and a2, and
the imaginary parts in a1 and a3. Likewise, the real part of the result should be returned
in a0 and the imaginary part in a1.
When you have written complexMul answer the following questions.
a) Is complexMul a leaf or non-leaf procedure?
b) Did you need to use the stack? Explain why.
c) What are the overflow conditions for your procedure?
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Assignment 1 02155 – Computer Architecture and Engineering
Exercise A1.5 – RISC-V instruction for multiplication
Modify your program to use the RISC-V instruction mul instead of your myMult procedure.
When you have modified your program answer the following question.
a) How many clock cycles did you save?
Exercise A1.6 – Extra questions
Answer the following questions.
a) How would your program have differed if RISC-V only had 2 argument passing
registers, a0 and a1, and one result register a0?
b) Which registers are saved and not saved across a procedure call? What does this
mean?
c) How would you extend your program to handle 64-bit results of multiplication?
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Assignment 1 02155 – Computer Architecture and Engineering
Report front page
The report should have a front page similar the one shown below.
02155 – Computer Architecture and Engineering
Fall <year>
Assignment 1
Group members:
<student number> – <student name>
<student number> – <student name>
This report contains <n> pages
<month> <year>
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Computer Architecture and Engineering – Assignment 1
$30.00
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