Lab Assignment 5: Tuning Performance

Introduction

This assignment deals with optimizing memory intensive code. Image processing offers many examples of functions that can benefit from optimization. In this lab, we will consider two image processing operations: rotate, which rotates an image counter-clockwise by 90° and smooth, which “smooths” or “blurs” an image.

For this lab, we will consider an image to be represented as a two-dimensional matrix M, where M_i,j denotes the value of the (i,j)th pixel of M. Pixel values are triples of red, green, and blue (RGB) values. We will only consider square images. Let N denote the number of rows (or columns) of an image. Rows and columns are numbered, in C-style, from 0 to N-1.

The rotate operation turns an image 90° counter-clockwise, by moving each element M1[i][j] into M2[N-j-1][i]. Pictorially,

The smooth operation is implemented by replacing every pixel value with the average of all the pixels around it (in a maximum of 3 X 3 window centered at that pixel). Consider the following figure:

The values of pixels M2[1][1] and M2[N-1][N-1] are given below:

Logistics

You may work in a group of up to two people in solving the problems for this assignment. The only “hand-in” will be electronic. Any clarifications and revisions to the assignment will be posted to Blackboard.

Hand Out Instructions

Start by copying /u/cs252/labs14/lab4/perflab-handout.tar to a protected directory in which you plan to do your work. (You can also download a copy HERE.) Then give the command: tar xvf perflab-handout.tar. This will cause a number of files to be unpacked into the directory. The only file you will be modifying and handing in is kernels.c. The driver.c program is a driver program that allows you to evaluate the performance of your solutions. Use the command make driver to generate the driver code and run it with the command ./driver.

Looking at the file kernels.c you’ll notice a C structure team into which you should insert the requested identifying information about the one or two individuals comprising your programming team. Do this right away so you don’t forget. Use your login ids and email adresses for your CS accounts.

Team name in the struct is of the form “ID”, where “ID” is your CS account login name, if you are working alone, or “ID1+ID2”, where “ID1” is the CS login name of the first team member and “ID2” is the CS login name of the second team member.

Implementation Overview

Data Structures

The core data structure deals with image representation. A pixel is a struct as shown below:

typedef struct {
    unsigned short red;   /* R value */
    unsigned short green; /* G value */
    unsigned short blue;  /* B value */
} pixel;

As can be seen, RGB values have 16-bit representations. An image I is represented as a one dimensional array of pixels, where the (i,j)th pixel is I[RIDX(i,j,N)]. Here N is the width (height) of the image matrix, and RIDX is a macro defined as follows:

#define RIDX(i,j,N) ((i)*(N)+(j))

See the file defs.h for this code.

Rotate

The following C function computes the result of rotating the source image src by 90° and stores the result in destination image dst. N is the width (height) of the image.

void naive_rotate(int N, pixel *src, pixel *dst) {
    int i, j;
    for(i=0; i < N; i++)
        for(j=0; j < N; j++)
            dst[RIDX(N-1-j,i,N)] = src[RIDX(i,j,N)];
    return;
}

The above code scans the rows of the source image matrix, copying to the columns of the destination image matrix. Your task is to rewrite this code to make it run as fast as possible using techniques like code motion, loop unrolling and blocking.

See the file kernels.c for this code.

Smooth

The smoothing function takes as input a source image src and returns the smoothed result in the destination image dst. Here is part of an implementation:

void naive_smooth(int N, pixel *src, pixel *dst) {
    int i, j;
    for(i=0; i < N; i++)
        for(j=0; j < N; j++)
            dst[RIDX(i,j,N)] = avg(N, i, j, src); /* Smooth the (i,j)th pixel */
    return;
}

The function avg returns the average of all the pixels around the (i,j)th pixel. Your task is to optimize smooth (and avg) to run as fast as possible. (Note: The function avg is a local function and you can get rid of it altogether to implement smooth in some other way.)

This code (and an implementation of avg) is in the file kernels.c.

Performance measures

Our main performance measure is CPE or Cycles per Element. If a function takes C cycles to run for an image of size N X N, the CPE value is C/N². Table 1 summarizes the performance of the naive implementations shown above and compares it against an optimized implementation. Performance is shown for for 5 different values of N. All measurements were made on cycle2.csug.rochester.edu. As you know from the last project, these results may be very different on different machines. Your code will be tested and graded on cycle2 so you should keep this in mind as you program. Note in particular that the reference baseline CPEs listed are specific to cycle2.

The ratios (speedups) of the optimized implementation over the naive one will constitute a score of your implementation. To summarize the overall effect over different values of N, we will compute the geometric mean of the results for these 5 values. That is, if the measured speedups for N = {32,64,128,256,512} are R₃₂, R₆₄, R₁₂₈, R₂₅₆ and R₅₁₂ then we compute the overall performance as

$\begin{eqnarray*} R & = & \sqrt[5]{R_{32} \times R_{64} \times R_{128} \times R_{256} \times R_{512}}\end{eqnarray*}$

Test case		1	2	3	4	5
Method	N	64	128	256	512	1024	Geom. Mean
Naive `rotate` (CPE)		3.3	4.8	7.0	11.8	14.4
Optimized `rotate` (CPE)		3.0	3.1	3.2	4.0	4.7
Speedup (naive/opt)		1.1	1.5	2.2	2.9	3.1	2.0
Method	N	32	64	128	256	512	Geom. Mean
Naive `smooth` (CPE)		76.2	77.2	77.4	77.6	77.7
Optimized `smooth` (CPE)		25.1	27.0	27.3	27.5	27.6
Speedup (naive/opt)		3.0	2.9	2.8	2.8	2.8	2.9

Assumptions

To make life easier, you may assume that N is a multiple of 32. Your code must run correctly for all such values of N, but we will measure its performance only for the 5 values shown in Table 1.

Infrastructure

We have provided support code to help you test the correctness of your implementations and measure their performance. This section describes how to use this infrastructure. The exact details of each part of the assignment are described in the following section.

Note: The only source file you will be modifying is kernels.c.

Versioning

You will be writing many versions of the rotate and smooth routines. To help you compare the performance of all the different versions you’ve written, we provide a way of “registering” functions.

For example, the file kernels.c that we have provided you contains the following function:

void register_rotate_functions() {
    add_rotate_function(&rotate, rotate_descr);
}

This function contains one or more calls to add_rotate_function. In the above example, add_rotate_function registers the function rotate along with a string rotate_descr which is an ASCII description of what the function does. See the file kernels.c to see how to create the string descriptions. This string can be at most 256 characters long.

A similar function for your smooth kernels is provided in the file kernels.c.

Driver

The source code you will write will be linked with object code that we supply into a “driver” binary. To create this binary, you will need to execute the command

unix> make driver

You will need to re-make driver each time you change the code in kernels.c. To test your implementations, you can then run the command:

unix> ./driver

The driver can be run in four different modes:

Default mode, in which all versions of your implementation are run.
Autograder mode, in which only the rotate() and smooth() functions are run. This is the mode we will run in when we use the driver to grade your hand-in.
File mode, in which only versions that are mentioned in an input file are run.
Dump mode, in which a one-line description of each version is dumped to a text file. You can then edit this text file to keep only those versions that you’d like to test using the file mode. You can specify whether to quit after dumping the file or to run your implementations.

If run without any arguments, driver will run all of your versions (default mode). Other modes and options can be specified by command-line arguments to driver, as listed below:

-g : Run only rotate() and smooth() functions (autograder mode).

-f <funcfile> : Execute only those versions specified in <funcfile> (file mode).

-d <dumpfile> : Dump the names of all versions to a dump file called <dumpfile>, one line to a version (dump mode).

-q : Quit after dumping version names to a dump file. To be used in tandem with -d. For example, to quit immediately after printing the dump file, type ./driver -qd dumpfile.

-h : Print the command line usage.

Team Information

Important: Before you start, you should fill in the struct in kernels.c with information about your team (group name, team member names and email addresses). This struct is just like the one for the Data Lab (assignment 1).

Assignment Details

Optimizing Rotate (50 points)

In this part, you will optimize rotate to achieve as low a CPE as possible. You should compile driver and then run it with the appropriate arguments to test your implementations. For example, running driver with the supplied naive version (for rotate) generates the output shown below:

unix> ./driver
Teamname: ta
Member 1: ta
Email 1: ta's email address

Rotate: Version = naive_rotate: Naive baseline implementation:
Dim             64      128     256     512     1024    Mean
Your CPEs       3.3     4.8     7.3     11.9    14.3
Baseline CPEs   3.3     4.8     7.0     11.8    14.4
Speedup         1.0     1.0     1.0     1.0     1.0     1.0

Optimizing Smooth (50 points)

In this part, you will optimize smooth to achieve as low a CPE as possible.

For example, running driver with the supplied naive version (for smooth) generates the output shown below:

unix> ./driver
Teamname: ta
Member 1: ta
Email 1: ta's email address

Smooth: Version = naive_smooth: Naive baseline implementation:
Dim             32      64      128     256     512     Mean
Your CPEs       76.4    77.2    77.4    77.5    77.7
Baseline CPEs   76.2    77.2    77.4    77.6    77.7
Speedup         1.0     1.0     1.0     1.0     1.0     1.0

Some advice: Look at the assembly code generated for rotate and smooth. Focus on optimizing the inner loop (the code that gets repeatedly executed in a loop) using the optimization tricks covered in class and in chapters 5 and 6 of the text. (Note: if you didn’t read chapter 5 carefully before the midterm, you’ll want to read it now. You won’t do well on this assignment without it.) The smooth function is more compute-intensive and less memory-sensitive than the rotate function, so the optimizations are of somewhat different flavors. You may want to consult the authors’ “Web Aside” on using blocking to increase temporal locality.

Coding Rules

You may write any code you want, as long as it satisfies the following requirements:

It must be in ANSI C. You may not use any embedded assembly language statements.
It must not interfere with the time measurement mechanism. You will also be penalized if your code prints any extraneous information.

You can only modify code in kernels.c. You are allowed to define macros, additional global variables, and other procedures in this file.

Evaluation

Your solutions for rotate and smooth will each count for 50% of your grade. The score for each will be based on the following:

Correctness: You will get NO CREDIT for buggy code that causes the driver to complain! This includes code that correctly operates on the test sizes, but incorrectly on image matrices of other sizes. As mentioned earlier, you may assume that the image width (height) is a multiple of 32.
CPE: You will get full credit for your implementations of rotate and smooth if they are correct and achieve mean CPE speedups above thresholds 1.5 and 2.0 respectively. We will award up to 10 points extra credit for each function if you match or beat the performance of the optimized version described above. You will get partial credit for a correct implementation that does better than the supplied naive one.

“Trivia” Assignment

Before noon, Thursday, March 20, send email to containing answers to the following questions (a single email per team is acceptable). Please use the subject

    [cs252] Assignment 5 Trivia - uname1, uname2

for your email.

List your team name and the full name and email address of each team member.
Fill your team name and member information into the team structure, and make and run the driver. What output do you get?

Review section 5.8 in the text, then analyze foo() and bar() below. Do they do the same thing? If not, why not? If so, which would you expect to be faster and why? (Assume that arrays a[100] and b[100] are initialized globals.)

void foo() {
    int i;
    for (i = 0; i < 100; i++){
        a[i] = a[i] + b[i];
    }
}

void bar() {
    int i = 0;
    while (i < 100){
        a[i] += b[i++];
        a[i] += b[i++];
        a[i] += b[i++];
        a[i] += b[i++];
    }
}

How might the topic in section 5.5 of the text be used to improve the functionality of naive_smooth?

Turn In Instructions

When you have completed the lab, you will hand in one file, kernels.c, that contains your solution. Here is how to hand in your solution:

Make sure you have included your identifying information in the team struct in kernels.c.
Make sure that the rotate() and smooth() functions correspond to your fastest implementations, as these are the only functions that will be tested when we use the driver to grade your assignement.
Remove any extraneous print statements.
Place your kernels.c file in a directory by itself, go into that directory, and type:
```
/u/cs252/bin/TURN_IN .
```
Note that there’s a dot in that command!
After the hand-in, if you discover a mistake and want to submit a revised copy, follow the instructions above. We’ll grade the latest version (up to the due date).

DUE DATES:

For the “trivia” assignment: 11am, Thursday, March 20.

For the main assignment: 11:59pm, Monday, March 31.

Last Change: 21 December 2017 / Michael Scott's email address