Description
This assignment is all about caching. It consists of two theoretical questions, along with a
question that will ask you to complete the implementation of a cache in C. The assignment is
to be done alone. The late penalty is 33% per day. No late assignments accepted after 3 days.
[16] 1. Suppose we have a system with the following properties:
• The memory is byte addressable,
• Memory accesses are to 1-byte words (not to 4-byte words).
• Addresses are 15-bits.
• The cache is four-way set associative (E = 4) with a 8-byte block size (B = 8) and
eight sets (S = 8).
The contents of the cache are as follows, with all addresses, tags and values given in
hexadecimal.
1
Set Valid Tag Byte0 Byte1 Byte2 Byte3 Byte4 Byte5 Byte6 Byte7
0 0 032 43 F6 A8 88 5A 30 8D 31
1 131 98 A2 E0 37 07 34 4A 40
1 193 82 22 99 F3 1D 00 82 EF
1 1A9 8E C4 E6 C8 94 52 82 1E
1 0 193 82 22 99 F3 1D 00 82 EF
0 04E 90 C6 CC 0A C2 9B 7C 97
1 063 8D 01 37 7B E5 46 6C F3
0 191 79 21 6D 5D 98 97 9F B1
2 1 1C5 0D D3 F8 4D 5B 5B 54 70
1 0FF D7 2D BD 01 AD FB 7B 8E
1 1BD 13 10 BA 69 8D FB 5A C2
0 004 5F 12 C7 F9 92 4A 19 94
3 1 01A FE D6 A2 67 E9 6B A7 C9
1 058 EF C1 66 36 92 0D 87 15
1 17B 39 16 CF 70 80 1F 2E 28
1 0D7 E0 D9 57 48 F7 28 EB 65
4 1 087 18 BC D5 88 21 54 AE E7
1 1B5 4A 41 DC 25 A5 9B 59 C3
0 00D 53 92 AF 26 01 3C 5D 1B
1 002 32 86 08 5F 0C A4 17 91
5 1 18B 8D B3 8E F8 E7 9D CB 06
1 103 A1 80 E6 C9 E0 E8 BB 01
1 1E8 A3 ED 71 57 7C 1B D3 14
1 1B2 77 8A F2 FD A5 56 05 C6
6 1 10E 65 52 5F 3A A5 5A B9 45
0 074 89 86 26 3E 81 44 05 5C
0 0A3 96 A2 AA B1 0B 6B 4C C5
1 1C3 41 14 1E 8C EA 15 48 6A
7 0 1F7 C7 2E 99 3B 3E E1 41 16
1 036 FB C2 A2 BA 9C 55 D7 41
1 083 1F 6C E5 C3 E1 69 B8 79
1 031 EA FD 6B A3 36 C2 4C F5
[2] (a) The following diagram shows the format of an address (one bit per box). Indicate
the fields that would be used to determine the following:
• CO: the cache block offset.
• CI: the cache set index.
• CT: the cache tag.
14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
[14] (b) For each of the following memory accesses, indicate the cache set that will be
searched, if it will be a cache hit or miss when carried out in sequence as
listed, and the value of a read if it can be inferred from the information in the
cache. Justify your answers.
2
Operation Address Cache Set Tag Hit? Value (or unknown)
Read 0x0362
Read 0x7BFE
Read 0x3FC9
Read 0x0361
[16] 2. One way to determine what a cache’s miss rate will be in practice is to run through a
number of programs using a simulated cache, and take note of the number of cache hits
and misses as a function of the total number of memory accesses. In this question, you
will complete a C implementation of a simulated cache. Five files are provided in the
a4.zip file:
• cache.h: a header file with some declarations.
• cache.c: the incomplete implementation of the cache.
• cache-test.c: a test program to help you debug your implementation.
• cache-ref.o: The object code from a reference implementation of the cache.c file.
To use this file copy (don’t rename it) it to cache.c and type make. The resulting
cache-test program will be built and will run with the reference cache. Be warned
that if you make changes to cache.c or cache.h when you type make it will overwrite
cache.o, hence the reason for copying as opposed to renaming.
• Makefile: typing make at the command prompt will recompile any of the .c files
that have changed.
File cache.c contains the comment /* TO BE COMPLETED BY THE STUDENT */ whenever you need to supply code. The first two functions where this occur can be completed
using a single line of code. The next three will need between 10 and 20 lines of code
each (the exact number may of course vary depending on whether or not you place curly
braces on separate lines, how you write the code, etc).
Complete the implementation of the cache in cache.c, and then run program cache-test
to verify that it works correctly. Here is the expected output:
Sum = 4326400
Miss rate = 0.2500
Sum = 4326400
Miss rate = 1.0000
Sum = 4326400
Miss rate = 0.5000
[18] 3. This problem tests your ability to predict the cache behaviour of C code. For each of
the following caches, array sizes and functions, first determine the miss rate using your
cache implementation from the previous question (or the reference solution contained
in the file cache.o), and then explain how you would have derived the miss rate given
only the program code and the characteristics of the cache (that is, using pencil and
paper only). You may need to make modifications to cache-test.c to get the information
needed. Assume that we execute the code under the following conditions:
• sizeof(int) = 4
• The cache contains 128, sixteen-byte blocks.
3
• The arrays are stored in row-major order.
• The only memory accesses are to the entries of the array a.
In order to simplify your explanations, you can write them assuming that a[0][0] ends
up in cache set 0, even if this isn’t actually the case when you run the program. Note
that specific cache set numbers may in fact vary depending on things like the compiler
or machine used. However the miss rate will remain the same.
Note: if you set the cache policies to CACHE TRACEPOLICY, then the reference solution
will output additional information about cache hits, misses, and which set was used in
each case. You may find such information helpful. The scenarios you are to predict the
cache behaviour for are:
[3] a. An array with 64 rows and 64 columns, a direct-mapped cache, and the function
sumA from the program cache-test provided with question 2.
[3] b. An array with 64 rows and 64 columns, a direct-mapped cache, and the function
sumB from the program cache-test provided with question 2.
[3] c. An array with 64 rows and 64 columns, a direct-mapped cache, and the function
sumC from the program cache-test provided with question 2.
[3] d. An array with 68 rows and 68 columns, a direct-mapped cache, and the function
sumB from the program cache-test provided with question 2.
[3] e. An array with 48 rows and 48 columns, a direct-mapped cache, and the function
sumB from the program cache-test provided with question 2.
[3] f. An array with 48 rows and 48 columns, a two-way set-associative cache, and the
function sumB from the program cache-test provided with question 2.
Deliverables
You should use the handin program to submit your assignment. The assignment name is a4,
and the files to submit are:
1. A text file containing the following information:
• Your name and student number.
• Your answers questions 1 and 3
• How long it took you to complete the assignment (not including any time you may have
spent revising before starting to work on it).
2. The completed cache.c file.
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