SPO600 Algorithm Selection Lab

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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


  • 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.


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?


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.


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".
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.
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
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.
The stdint.h header provides definitions for many specialized integer size types. Use int16_t for 16-bit signed integers.