Difference between revisions of "SPO600 Algorithm Selection Lab"

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=== Background ===
 
=== Background ===
 
* Digital sound is typically represented, uncompressed, as signed 16-bit integer signal samples. There is are two streams of samples, one each for the left and right stereo channels, at typical sample rates of 44.1 or 48 thousand samples per second per channel, for a total of 88.2 or 96 thousand samples per second (kHz). Since there are 16 bits (2 bytes) per sample, the data rate is 88.2 * 1000 * 2 = 176,400 bytes/second (~172 KiB/sec) or 96 * 1000 * 2 = 192,000 bytes/second (~187.5 KiB/sec).
 
* Digital sound is typically represented, uncompressed, as signed 16-bit integer signal samples. There is are two streams of samples, one each for the left and right stereo channels, at typical sample rates of 44.1 or 48 thousand samples per second per channel, for a total of 88.2 or 96 thousand samples per second (kHz). Since there are 16 bits (2 bytes) per sample, the data rate is 88.2 * 1000 * 2 = 176,400 bytes/second (~172 KiB/sec) or 96 * 1000 * 2 = 192,000 bytes/second (~187.5 KiB/sec).
−
* To change the volume of sound, each sample can be scaled by a volume factor, in the range of 0.00 (silence) to 1.00 (full volume).
+
* To change the volume of sound, each sample can be scaled (multiplied) by a volume factor, in the range of 0.00 (silence) to 1.00 (full volume).
 
* On a mobile device, the amount of processing required to scale sound will affect battery life.
 
* On a mobile device, the amount of processing required to scale sound will affect battery life.
  
−
=== Basic Sound Scale Program ===
+
=== Three Approaches ===
  
−
Get the files for this lab on one of the [[SPO600 Servers]] -- but you can perform the lab wherever you want.
+
Three approaches to this problem are provided:
  
−
# Unpack the archive <code>/public/spo600-algorithm-selection-lab.tgz</code>
+
# The basic or Naive algorithm (<code>vol1.c</code>). This approach multiplies each sound sample by 0.75, casting from signed 16-bit integer to floating point and back again, which can be [[Expensive|expensive]] operations.
−
# Examine the <code>vol1.c</code> source code. This program:
+
# A lookup-based algorithm (<code>vol2.c</code>). This approach uses a pre-calculated table of all 65536 possible results, and looks up each sample in that table instead of multiplying.
−
## Creates 5,000,000 random "sound samples" in a data array (the number of samples is set in the <code>vol.h</code> file).
+
# A fixed-point algorithm (<code>vol3.c</code>). This approach uses fixed-point math and bit shifting to perform the multiplication without using floating-point math.
−
## Scales those samples by the volume factor 0.75 and stores them back to the data array.
+
 
−
## Sums the output array and prints the sum.
+
=== Don't Compare Across Machines ===
−
# Build and test this file.
+
 
−
#* Does it produce the same output each time?
+
In this lab, ''do not'' compare the relative performance across different machines, because the systems provided have a wide range of processor implementations, from server-class to mobile-class. However, ''do'' compare the relative performance of the various algorithms on the ''same'' machine.
−
# Test the performance of this program.
 
−
#* How long does it take to run the scaling?
 
−
#* How much time is spent scaling the sound samples? Be sure to eliminate the time taken for the non-scaling part of the program (e.g., random sample generation).
 
−
#* Do multiple runs take the same time? How much variation do you observe? What is the likely cause of this variation?
 
−
#* Is there any difference in the results produced by the various algorithms? How much does numeric accuracy matter in this application?
 
  
−
=== Alternate Approaches ===
+
=== Benchmarking ===
  
−
The sample program uses the most basic, obvious algorithm for the problem. Let's call this "Algorithm 0", or the "Naive Algorithm". Note that it uses casting between integer and floating-point formats as well as multiplication -- both of which can be [[Expensive|expensive]] operations.
+
Get the files for this lab from one of the [[SPO600 Servers]] -- but you can perform the lab wherever you want (feel free to use your laptop or home system). Test on both an x86_64 and an AArch64 system.
  
−
Try these alternate algorithms for scaling the sound samples by modifying copies of <code>vol1.c</code>. Edit the <code>Makefile</code> to build your modified programs as well as the original. Test each approach to see the performance impact:
+
Review the contents of this archive:
 +
* <code>vol.h</code> controls the number of samples to be processed
 +
* <code>vol1.c</code>, <code>vol2.c</code>, and <code>vol3.c</code> implement the various algorithms
 +
* The <code>Makefile</code> can be used to build the programs
  
−
# Pre-calculate a lookup table (array) of all possible sample values multiplied by the volume factor, and look up each sample in that table to get the scaled values. (You'll have to handle the fact that the input values range from -32768 to +32767, while C arrays accept only a positive index).
+
Perform these steps:
−
# Convert the volume factor 0.75 to a fix-point integer by multiplying by a binary number representing a fixed-point value "1". For example, you could use 0b100000000 (= 256 in decimal) to represent 1.00, and therefore use 0.75 * 256 = 192 for your volume factor. Multiply this fixed-point integer volume factor by each sample, then shift the result to the right the required number of bits after the multiplication (>>8 if you're using 256 as the multiplier).
+
# Unpack the archive <code>/public/spo600-algorithm-selection-lab.tgz</code>
 +
# Study each of the source code files and make sure that you understand what the code is doing.
 +
# '''Make a prediction''' of the relative performance of each scaling algorithm.
 +
# Build and test each of the programs.
 +
#* Do all of the algorithms produce the same output?
 +
#** How can you verify this?
 +
#** If there is a difference, is it significant enough to matter?
 +
#* Change the number of samples so that each program takes a reasonable amount of time to execute (suggested minimum 20 seconds, 1 minute or more is better).
 +
# Test the performance of each program.
 +
#* Find a way to measure performance ''without'' the time taken to perform the test setup pre-processing (generating the samples) and post-processing (summing the results) so that you can measure ''only'' the time taken to scale the samples. '''This is the hard part!'''
 +
#* How much time is spent scaling the sound samples?
 +
#* Do multiple runs take the same time? How much variation do you observe? What is the likely cause of this variation?
 +
#* Is there any difference in the results produced by the various algorithms?
 +
#* Does the difference between the algorithms vary depending on the architecture and implementation on which you test?
 +
#* What is the relative memory usage of each program?
 +
# Was your prediction accurate?
  
 
=== Deliverables ===
 
=== Deliverables ===
  
−
Blog about your experiments with a detailed analysis of your results, including memory usage, time performance, accuracy, and trade-offs.
+
Blog about your experiments with a detailed analysis of your results, including memory usage, performance, accuracy, and trade-offs.
  
−
Important! -- explain what you're doing so that a reader coming across your blog post understands the context (in other words, don't just jump into a discussion of optimization results -- give your post some context).
+
Make sure you convincingly prove your results to your reader! Also be sure to explain what you're doing so that a reader coming across your blog post understands the context (in other words, don't just jump into a discussion of optimization results -- give your post some context).
  
−
'''Optional - Recommended:''' Compare results across several implementations of AArch64 and x86_64 systems. Note that on different implementations, the relative performance of different algorithms will vary; for example, table lookup may outperform other algorithms on a system with a fast memory system (cache), but not on a system with a slower memory system.
+
'''Optional - Recommended:''' Compare results across several '''implementations''' of AArch64 and x86_64 systems. Note that on different CPU implementations, the relative performance of different algorithms will vary; for example, table lookup may outperform other algorithms on a system with a fast memory system (cache), but not on a system with a slower memory system.
−
* For AArch64, you could compare the performance on AArchie against another 64-bit ARM system such as a Raspberry Pi 3 or an ARM Chromebook.
+
* For AArch64, you could compare the performance on AArchie against the various class servers, or between the class servers and a Raspberry Pi 3 (in 64-bit mode) or an ARM Chromebook.
−
* For x86_64, you could compare the performance of different processors, such as xerxes, your own laptop or desktop, and Seneca systems such as Matrix, Zenit, or lab desktops.
+
* For x86_64, you could compare the performance of different processors, such as xerxes, your own laptop or desktop, and Seneca systems such as Matrix or lab desktops.
  
 
=== Things to consider ===
 
=== Things to consider ===
  
 
==== Design of Your Tests ====
 
==== Design of Your Tests ====
−
* Most solutions for a problem of this type involve generating a large amount of data in an array, processing that array using the function being evaluated, and then storing that data back into an array. Make sure that you measure the time taken in the test function only -- you need to be able to remove the rest of the processing time from your evaluation.
+
* Most solutions for a problem of this type involve generating a large amount of data in an array, processing that array using the function being evaluated, and then storing that data back into an array. The test setup can take more time than the actual test! Make sure that you measure the time taken in the code under test only -- you need to be able to remove the rest of the processing time from your evaluation.
−
* You may need to run a very large amount of sample data through the function to be able to detect its performance. Feel free to edit the sample count in <code>vol.h</code> as necessary.
+
* You may need to run a very large amount of sample data through the function to be able to detect its performance.
 
* If you do not use the output from your calculation (e.g., do something with the output array), the compiler may recognize that, and remove the code you're trying to test. Be sure to process the results in some way so that the optimizer preserves the code you want to test. It is a good idea to calculate some sort of verification value to ensure that both approaches generate the same results.
 
* If you do not use the output from your calculation (e.g., do something with the output array), the compiler may recognize that, and remove the code you're trying to test. Be sure to process the results in some way so that the optimizer preserves the code you want to test. It is a good idea to calculate some sort of verification value to ensure that both approaches generate the same results.
 
* Be aware of what other tasks the system is handling during your test run, including software running on behalf of other users.
 
* Be aware of what other tasks the system is handling during your test run, including software running on behalf of other users.
  
−
==== Analyzing Results ====
+
=== Tips ===
−
* What is the impact of various optimization levels on the software performance? (For example, compiling with -O0 / -O1 / -O2 / -O3)
+
{{Admon/tip|Analysis|Do a thorough analysis of the results. Be certain (and prove!) that your performance measurement ''does not'' include the generation or summarization of the test data. Do multiple runs and discard the outliers. Decide whether to use mean, minimum, or maximum time values from the multiple runs, and explain why you made that decision. Control your variables well. Show relative performance as percentage change, e.g., "this approach was NN% faster than that approach".}}
−
* Does the distribution of data matter? (e.g., is there any difference if there are no absolute large numbers, or no negative numbers?)
 
−
* If samples are fed at CD rate (44100 samples per second x 2 channels x 2 bytes per sample), can each of the algorithms keep up?
 
−
* What is the memory footprint of each approach?
 
−
* What is the performance of each approach?
 
−
* What is the energy consumption of each approach? (What information do you need to calculate this?)
 
−
* Various machines within an architecture have very different performance profiles, energy consumption, and hardware costs -- so it's not reasonable to compare performance between machines, but it is reasonable to compare the relative performance of the algorithms in each context. Does the ratio of performance of the various approaches remain constant across the machines? Why or why not?
 
−
* What other optimizations can be applied to this problem?
 
  
−
=== Tips ===
 
 
{{Admon/tip|Non-Decimal Notation|In this lab, the number prefix 0x indicates a hexadecimal number, and 0b indicates a binary number, in harmony with the C language.}}
 
{{Admon/tip|Non-Decimal Notation|In this lab, the number prefix 0x indicates a hexadecimal number, and 0b indicates a binary number, in harmony with the C language.}}
 +
 
{{Admon/tip|Time and Memory Usage of a Program|You can get basic timing information for a program by running <code>time ''programName''</code> -- the output will show the total time taken (real), the amount of CPU time used to run the application (user), and the amount of CPU time used by the operating system on behalf of the application (system).
 
{{Admon/tip|Time and Memory Usage of a Program|You can get basic timing information for a program by running <code>time ''programName''</code> -- the output will show the total time taken (real), the amount of CPU time used to run the application (user), and the amount of CPU time used by the operating system on behalf of the application (system).
  
−
Another version of the <code>time</code> command, located in <code>/bin/time</code>, gives slightly different information, including maximum resident memory usage: <code>/bin/time ''programName''</code>}}
+
The version of the <code>time</code> command located in <code>/bin/time</code> gives slightly different information than the version built in to bash -- including maximum resident memory usage: <code>/bin/time ''./programName''</code>}}
  
 
{{Admon/tip|SOX|If you want to try this with actual sound samples, you can convert a sound file of your choice to raw 16-bit signed integer PCM data using the [http://sox.sourceforge.net/ sox] utility present on most Linux systems and available for a wide range of platforms.}}
 
{{Admon/tip|SOX|If you want to try this with actual sound samples, you can convert a sound file of your choice to raw 16-bit signed integer PCM data using the [http://sox.sourceforge.net/ sox] utility present on most Linux systems and available for a wide range of platforms.}}
−
 
−
{{Admon/tip|Stack Limit|Fixed-size, non-static arrays will be placed in the stack space. The size of the stack space is controlled by per-process limits, inherited from the shell, and adjustable with the <code>ulimit</code> command. Allocating an array larger than the stack size limit will cause a segmentation fault, usually on the first write. To see the current stack limit, use <code>ulimit -s</code> (displayed value is in KB; default is usually 8192 KB or 8 MB). To set the current stack limit, place a new size in KB or the keyword <code>unlimited</code>after the <code>-s</code> argument.<br /><br />Alternate (and preferred) approach, as used in the provided sample code: allocate the array space with <code>malloc()</code> or <code>calloc()</code>.}}
 
  
 
{{Admon/tip|stdint.h|The <code>stdint.h</code> header provides definitions for many specialized integer size types. Use <code>int16_t</code> for 16-bit signed integers.}}
 
{{Admon/tip|stdint.h|The <code>stdint.h</code> header provides definitions for many specialized integer size types. Use <code>int16_t</code> for 16-bit signed integers.}}

Revision as of 10:05, 9 March 2020

Lab icon.png
Purpose of this Lab
In this lab, you will investigate the impact of different algorithms which produce the same effect. You will test and select one of three algorithms for adjusting the volume of PCM audio samples based on benchmarking.

Lab 4

Background

  • Digital sound is typically represented, uncompressed, as signed 16-bit integer signal samples. There is are two streams of samples, one each for the left and right stereo channels, at typical sample rates of 44.1 or 48 thousand samples per second per channel, for a total of 88.2 or 96 thousand samples per second (kHz). Since there are 16 bits (2 bytes) per sample, the data rate is 88.2 * 1000 * 2 = 176,400 bytes/second (~172 KiB/sec) or 96 * 1000 * 2 = 192,000 bytes/second (~187.5 KiB/sec).
  • To change the volume of sound, each sample can be scaled (multiplied) by a volume factor, in the range of 0.00 (silence) to 1.00 (full volume).
  • On a mobile device, the amount of processing required to scale sound will affect battery life.

Three Approaches

Three approaches to this problem are provided:

  1. The basic or Naive algorithm (vol1.c). This approach multiplies each sound sample by 0.75, casting from signed 16-bit integer to floating point and back again, which can be expensive operations.
  2. A lookup-based algorithm (vol2.c). This approach uses a pre-calculated table of all 65536 possible results, and looks up each sample in that table instead of multiplying.
  3. A fixed-point algorithm (vol3.c). This approach uses fixed-point math and bit shifting to perform the multiplication without using floating-point math.

Don't Compare Across Machines

In this lab, do not compare the relative performance across different machines, because the systems provided have a wide range of processor implementations, from server-class to mobile-class. However, do compare the relative performance of the various algorithms on the same machine.

Benchmarking

Get the files for this lab from one of the SPO600 Servers -- but you can perform the lab wherever you want (feel free to use your laptop or home system). Test on both an x86_64 and an AArch64 system.

Review the contents of this archive:

  • vol.h controls the number of samples to be processed
  • vol1.c, vol2.c, and vol3.c implement the various algorithms
  • The Makefile can be used to build the programs

Perform these steps:

  1. Unpack the archive /public/spo600-algorithm-selection-lab.tgz
  2. Study each of the source code files and make sure that you understand what the code is doing.
  3. Make a prediction of the relative performance of each scaling algorithm.
  4. Build and test each of the programs.
    • Do all of the algorithms produce the same output?
      • How can you verify this?
      • If there is a difference, is it significant enough to matter?
    • Change the number of samples so that each program takes a reasonable amount of time to execute (suggested minimum 20 seconds, 1 minute or more is better).
  5. Test the performance of each program.
    • Find a way to measure performance without the time taken to perform the test setup pre-processing (generating the samples) and post-processing (summing the results) so that you can measure only the time taken to scale the samples. This is the hard part!
    • How much time is spent scaling the sound samples?
    • Do multiple runs take the same time? How much variation do you observe? What is the likely cause of this variation?
    • Is there any difference in the results produced by the various algorithms?
    • Does the difference between the algorithms vary depending on the architecture and implementation on which you test?
    • What is the relative memory usage of each program?
  6. Was your prediction accurate?

Deliverables

Blog about your experiments with a detailed analysis of your results, including memory usage, performance, accuracy, and trade-offs.

Make sure you convincingly prove your results to your reader! Also be sure to explain what you're doing so that a reader coming across your blog post understands the context (in other words, don't just jump into a discussion of optimization results -- give your post some context).

Optional - Recommended: Compare results across several implementations of AArch64 and x86_64 systems. Note that on different CPU implementations, the relative performance of different algorithms will vary; for example, table lookup may outperform other algorithms on a system with a fast memory system (cache), but not on a system with a slower memory system.

  • For AArch64, you could compare the performance on AArchie against the various class servers, or between the class servers and a Raspberry Pi 3 (in 64-bit mode) or an ARM Chromebook.
  • For x86_64, you could compare the performance of different processors, such as xerxes, your own laptop or desktop, and Seneca systems such as Matrix or lab desktops.

Things to consider

Design of Your Tests

  • Most solutions for a problem of this type involve generating a large amount of data in an array, processing that array using the function being evaluated, and then storing that data back into an array. The test setup can take more time than the actual test! Make sure that you measure the time taken in the code under test only -- you need to be able to remove the rest of the processing time from your evaluation.
  • You may need to run a very large amount of sample data through the function to be able to detect its performance.
  • If you do not use the output from your calculation (e.g., do something with the output array), the compiler may recognize that, and remove the code you're trying to test. Be sure to process the results in some way so that the optimizer preserves the code you want to test. It is a good idea to calculate some sort of verification value to ensure that both approaches generate the same results.
  • Be aware of what other tasks the system is handling during your test run, including software running on behalf of other users.

Tips

Idea.png
Analysis
Do a thorough analysis of the results. Be certain (and prove!) that your performance measurement does not include the generation or summarization of the test data. Do multiple runs and discard the outliers. Decide whether to use mean, minimum, or maximum time values from the multiple runs, and explain why you made that decision. Control your variables well. Show relative performance as percentage change, e.g., "this approach was NN% faster than that approach".
Idea.png
Non-Decimal Notation
In this lab, the number prefix 0x indicates a hexadecimal number, and 0b indicates a binary number, in harmony with the C language.
Idea.png
Time and Memory Usage of a Program
You can get basic timing information for a program by running time programName -- the output will show the total time taken (real), the amount of CPU time used to run the application (user), and the amount of CPU time used by the operating system on behalf of the application (system). The version of the time command located in /bin/time gives slightly different information than the version built in to bash -- including maximum resident memory usage: /bin/time ./programName
Idea.png
SOX
If you want to try this with actual sound samples, you can convert a sound file of your choice to raw 16-bit signed integer PCM data using the sox utility present on most Linux systems and available for a wide range of platforms.
Idea.png
stdint.h
The stdint.h header provides definitions for many specialized integer size types. Use int16_t for 16-bit signed integers.
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