Assignment 1: Performance Analysis on a Quad-Core CPU

Due Fri Oct 1, 11:59pm

100 points total + 6 points extra credit

Overview

This assignment is intended to help you develop an understanding of the two primary forms of parallel execution present in a modern multi-core CPU:

1. SIMD execution within a single processing core
2. Parallel execution using multiple cores (You'll see effects of Intel Hyper-threading as well.)

You will also gain experience measuring and reasoning about the performance of parallel programs (a challenging, but important, skill you will use throughout this class). This assignment involves only a small amount of programming, but a lot of analysis!

Environment Setup

You will need to run code on the new myth machines for this assignment. (Hostnames for these machines are myth[51-66].stanford.edu) These machines contain four-core 4.2 GHz Intel Core i7 processors (although dynamic frequency scaling can take them to 4.5 GHz when the chip decides it is useful and possible to do so). Each core in the processor supports two hardware threads (Intel calls this "Hyper-Threading") and the cores can execute AVX2 vector instructions which describe simultaneous execution of the same eight-wide operation on multiple single-precision data values. For the curious, a complete specification for this CPU can be found at https://ark.intel.com/products/97129/Intel-Core-i7-7700K-Processor-8M-Cache-up-to-4-50-GHz-. Students that want to dig deeper might enjoy this writeup.

Note: For grading purposes, we expect you to report on the performance of code run on the Stanford myth machines, however for kicks, you may also want to run the programs in this assignment on your own machine. (You will first need to install the Intel SPMD Program Compiler (ISPC) available here: http://ispc.github.io/). Feel free to include your findings from running code on other machines in your report as well, just be very clear what machine you were running on.

To get started:

1. ISPC is needed to compile many of the programs used in this assignment. ISPC can be easily installed on the myth machines through the following steps:

From a myth machine, download the linux binary into a local directory of your choice. You can get ISPC compiler binaries for Linux from the ISPC downloads page. From myth, we recommend you use wget to directly download the binary from the downloads page. As of Fall 2021 Week 1, the wget line below works:

wget https://github.com/ispc/ispc/releases/download/v1.16.1/ispc-v1.16.1-linux.tar.gz

Untar the downloaded file: tar -xvf ispc-v1.16.1-linux.tar.gz

Add the ISPC bin directory to your system path. For example, if untarring the downloaded file produces the directory ~/Downloads/ispc-v1.14.1-linux, in bash you'd update your path variable with:

export PATH=$PATH:${HOME}/Downloads/ispc-v1.16.1-linux/bin

The above line can be added to your .bashrc file for permanence.

If you are using csh, you'll update your PATH using setenv. A quick Google search will teach you how.

2. The assignment starter code is available on https://github.com/stanford-cs149/asst1. Please clone the Assignment 1 starter code using:

   git clone https://github.com/stanford-cs149/asst1.git

Program 1: Parallel Fractal Generation Using Threads (25 points)

Build and run the code in the prog1_mandelbrot_threads/ directory of the code base. (Type make to build, and ./mandelbrot to run it.) This program produces the image file mandelbrot-serial.ppm, which is a visualization of a famous set of complex numbers called the Mandelbrot set. (Most platforms have a .ppm view. For example, to view the resulting images remotely, use ssh -Y and the display command.) As you can see in the images below, the result is a familiar and beautiful fractal. Each pixel in the image corresponds to a value in the complex plane, and the brightness of each pixel is proportional to the computational cost of determining whether the value is contained in the Mandelbrot set. To get image 2, use the command option --view 2. (See function mandelbrotSerial() defined in mandelbrotSerial.cpp). You can learn more about the definition of the Mandelbrot set at http://en.wikipedia.org/wiki/Mandelbrot_set.

Your job is to parallelize the computation of the images using std::thread. Starter code that spawns one additional thread is provided in the function mandelbrotThread() located in mandelbrotThread.cpp. In this function, the main application thread creates another additional thread using the constructor std::thread(function, args...) It waits for this thread to complete by calling join on the thread object. Currently the launched thread does not do any computation and returns immediately. You should add code to workerThreadStart function to accomplish this task. You will not need to make use of any other std::thread API calls in this assignment.

What you need to do:

1. Modify the starter code to parallelize the Mandelbrot generation using two processors. Specifically, compute the top half of the image in thread 0, and the bottom half of the image in thread 1. This type of problem decomposition is referred to as spatial decomposition since different spatial regions of the image are computed by different processors.
2. Extend your code to use 2, 3, 4, 5, 6, 7, and 8 threads, partitioning the image generation work accordingly (threads should get blocks of the image). Note that the processor only has four cores but each core supports two hyper-threads, so it can execute a total of eight threads interleaved on its execution contents. In your write-up, produce a graph of speedup compared to the reference sequential implementation as a function of the number of threads used FOR VIEW 1. Is speedup linear in the number of threads used? In your writeup hypothesize why this is (or is not) the case? (you may also wish to produce a graph for VIEW 2 to help you come up with a good answer. Hint: take a careful look at the three-thread datapoint.)
3. To confirm (or disprove) your hypothesis, measure the amount of time each thread requires to complete its work by inserting timing code at the beginning and end of workerThreadStart(). How do your measurements explain the speedup graph you previously created?
4. Modify the mapping of work to threads to achieve to improve speedup to at about 7-8x on both views of the Mandelbrot set (if you're above 7x that's fine, don't sweat it). You may not use any synchronization between threads in your solution. We are expecting you to come up with a single work decomposition policy that will work well for all thread counts---hard coding a solution specific to each configuration is not allowed! (Hint: There is a very simple static assignment that will achieve this goal, and no communication/synchronization among threads is necessary.). In your writeup, describe your approach to parallelization and report the final 8-thread speedup obtained.
5. Now run your improved code with 16 threads. Is performance noticably greater than when running with eight threads? Why or why not?

Program 2: Vectorizing Code Using SIMD Intrinsics (25 points)

Take a look at the function clampedExpSerial in prog2_vecintrin/main.cpp of the Assignment 1 code base. The clampedExp() function raises values[i] to the power given by exponents[i] for all elements of the input array and clamps the resulting values at 9.999999. In program 2, your job is to vectorize this piece of code so it can be run on a machine with SIMD vector instructions.

However, rather than craft an implementation using SSE or AVX2 vector intrinsics that map to real SIMD vector instructions on modern CPUs, to make things a little easier, we're asking you to implement your version using CS149's "fake vector intrinsics" defined in CS149intrin.h. The CS149intrin.h library provides you with a set of vector instructions that operate on vector values and/or vector masks. (These functions don't translate to real CPU vector instructions, instead we simulate these operations for you in our library, and provide feedback that makes for easier debugging.) As an example of using the CS149 intrinsics, a vectorized version of the abs() function is given in main.cpp. This example contains some basic vector loads and stores and manipulates mask registers. Note that the abs() example is only a simple example, and in fact the code does not correctly handle all inputs! (We will let you figure out why!) You may wish to read through all the comments and function definitions in CS149intrin.h to know what operations are available to you.

Here are few hints to help you in your implementation:

• Every vector instruction is subject to an optional mask parameter. The mask parameter defines which lanes whose output is "masked" for this operation. A 0 in the mask indicates a lane is masked, and so its value will not be overwritten by the results of the vector operation. If no mask is specified in the operation, no lanes are masked. (Note this equivalent to providing a mask of all ones.) Hint: Your solution will need to use multiple mask registers and various mask operations provided in the library.
• Hint: Use _cs149_cntbits function helpful in this problem.
• Consider what might happen if the total number of loop iterations is not a multiple of SIMD vector width. We suggest you test your code with ./myexp -s 3. Hint: You might find _cs149_init_ones helpful.
• Hint: Use ./myexp -l to print a log of executed vector instruction at the end. Use function addUserLog() to add customized debug information in log. Feel free to add additional CS149Logger.printLog() to help you debug.

The output of the program will tell you if your implementation generates correct output. If there are incorrect results, the program will print the first one it finds and print out a table of function inputs and outputs. Your function's output is after "output = ", which should match with the results after "gold = ". The program also prints out a list of statistics describing utilization of the CS149 fake vector units. You should consider the performance of your implementation to be the value "Total Vector Instructions". (You can assume every CS149 fake vector instruction takes one cycle on the CS149 fake SIMD CPU.) "Vector Utilization" shows the percentage of vector lanes that are enabled.

What you need to do:

1. Implement a vectorized version of clampedExpSerial in clampedExpVector . Your implementation should work with any combination of input array size (N) and vector width (VECTOR_WIDTH).
2. Run ./myexp -s 10000 and sweep the vector width from 2, 4, 8, to 16. Record the resulting vector utilization. You can do this by changing the #define VECTOR_WIDTH value in CS149intrin.h. Does the vector utilization increase, decrease or stay the same as VECTOR_WIDTH changes? Why?
3. Extra credit: (1 point) Implement a vectorized version of arraySumSerial in arraySumVector. Your implementation may assume that VECTOR_WIDTH is a factor of the input array size N. Whereas the serial implementation has O(N) span, your implementation should have at most O(N / VECTOR_WIDTH + log2(VECTOR_WIDTH)) span. You may find the hadd and interleave operations useful.

Program 3: Parallel Fractal Generation Using ISPC (20 points)

Now that you're comfortable with SIMD execution, we'll return to parallel Mandelbrot fractal generation (like in program 1). Like Program 1, Program 3 computes a mandelbrot fractal image, but it achieves even greater speedups by utilizing both the CPU's four cores and the SIMD execution units within each core.

In Program 1, you parallelized image generation by creating one thread for each processing core in the system. Then, you assigned parts of the computation to each of these concurrently executing threads. (Since threads were one-to-one with processing cores in Program 1, you effectively assigned work explicitly to cores.) Instead of specifying a specific mapping of computations to concurrently executing threads, Program 3 uses ISPC language constructs to describe independent computations. These computations may be executed in parallel without violating program correctness (and indeed they will!). In the case of the Mandelbrot image, computing the value of each pixel is an independent computation. With this information, the ISPC compiler and runtime system take on the responsibility of generating a program that utilizes the CPU's collection of parallel execution resources as efficiently as possible.

You will make a simple fix to Program 3 which is written in a combination of C++ and ISPC (the error causes a performance problem, not a correctness one). With the correct fix, you should observe performance that is over forty times greater than that of the original sequential Mandelbrot implementation from mandelbrotSerial().

Program 3, Part 1. A Few ISPC Basics (10 of 20 points)

When reading ISPC code, you must keep in mind that although the code appears much like C/C++ code, the ISPC execution model differs from that of standard C/C++. In contrast to C, multiple program instances of an ISPC program are always executed in parallel on the CPU's SIMD execution units. The number of program instances executed simultaneously is determined by the compiler (and chosen specifically for the underlying machine). This number of concurrent instances is available to the ISPC programmer via the built-in variable programCount. ISPC code can reference its own program instance identifier via the built-in programIndex. Thus, a call from C code to an ISPC function can be thought of as spawning a group of concurrent ISPC program instances (referred to in the ISPC documentation as a gang). The gang of instances runs to completion, then control returns back to the calling C code.

Stop. This is your friendly instructor. Please read the preceding paragraph again. Trust me.

As an example, the following program uses a combination of regular C code and ISPC code to add two 1024-element vectors. As we discussed in class, since each instance in a gang is independent and performing the exact same program logic, execution can be accelerated via implementation using SIMD instructions.

A simple ISPC program is given below. The following C code will call the following ISPC code:

------------------------------------------------------------------------
C program code: myprogram.cpp
------------------------------------------------------------------------
const int TOTAL_VALUES = 1024;
float a[TOTAL_VALUES];
float b[TOTAL_VALUES];
float c[TOTAL_VALUES]

// Initialize arrays a and b here.
 
sum(TOTAL_VALUES, a, b, c);

// Upon return from sumArrays, result of a + b is stored in c.

The corresponding ISPC code:

------------------------------------------------------------------------
ISPC code: myprogram.ispc
------------------------------------------------------------------------
export sum(uniform int N, uniform float* a, uniform float* b, uniform float* c)
{
  // Assumption programCount divides N evenly.
  for (int i=0; i<N; i+=programCount)
  {
    c[programIndex + i] = a[programIndex + i] + b[programIndex + i];
  }
}

The ISPC program code above interleaves the processing of array elements among program instances. Note the similarity to Program 1, where you statically assigned parts of the image to threads.

However, rather than thinking about how to divide work among program instances (that is, how work is mapped to execution units), it is often more convenient, and more powerful, to instead focus only on the partitioning of a problem into independent parts. ISPCs foreach construct provides a mechanism to express problem decomposition. Below, the foreach loop in the ISPC function sum2 defines an iteration space where all iterations are independent and therefore can be carried out in any order. ISPC handles the assignment of loop iterations to concurrent program instances. The difference between sum and sum2 below is subtle, but very important. sum is imperative: it describes how to map work to concurrent instances. The example below is declarative: it specifies only the set of work to be performed.

-------------------------------------------------------------------------
ISPC code:
-------------------------------------------------------------------------
export sum2(uniform int N, uniform float* a, uniform float* b, uniform float* c)
{
  foreach (i = 0 ... N)
  {
    c[i] = a[i] + b[i];
  }
}

Before proceeding, you are encouraged to familiarize yourself with ISPC language constructs by reading through the ISPC walkthrough available at http://ispc.github.io/example.html. The example program in the walkthrough is almost exactly the same as Program 3's implementation of mandelbrot_ispc() in mandelbrot.ispc. In the assignment code, we have changed the bounds of the foreach loop to yield a more straightforward implementation.

What you need to do:

1. Compile and run the program mandelbrot ispc. The ISPC compiler is currently configured to emit 8-wide AVX2 vector instructions. What is the maximum speedup you expect given what you know about these CPUs? Why might the number you observe be less than this ideal? (Hint: Consider the characteristics of the computation you are performing? Describe the parts of the image that present challenges for SIMD execution? Comparing the performance of rendering the different views of the Mandelbrot set may help confirm your hypothesis.).

We remind you that for the code described in this subsection, the ISPC compiler maps gangs of program instances to SIMD instructions executed on a single core. This parallelization scheme differs from that of Program 1, where speedup was achieved by running threads on multiple cores.

If you look into detailed technical material about the CPUs in the myth machines, you will find there are a complicated set of rules about how many scalar and vector instructions can be run per clock. For the purposes of this assignment, you can assume that there are about as many 8-wide vector execution units as there are scalar execution units for floating point math.

Program 3, Part 2: ISPC Tasks (10 of 20 points)

ISPCs SPMD execution model and mechanisms like foreach facilitate the creation of programs that utilize SIMD processing. The language also provides an additional mechanism utilizing multiple cores in an ISPC computation. This mechanism is launching ISPC tasks.

See the launch[2] command in the function mandelbrot_ispc_withtasks. This command launches two tasks. Each task defines a computation that will be executed by a gang of ISPC program instances. As given by the function mandelbrot_ispc_task, each task computes a region of the final image. Similar to how the foreach construct defines loop iterations that can be carried out in any order (and in parallel by ISPC program instances, the tasks created by this launch operation can be processed in any order (and in parallel on different CPU cores).

What you need to do:

1. Run mandelbrot_ispc with the parameter --tasks. What speedup do you observe on view 1? What is the speedup over the version of mandelbrot_ispc that does not partition that computation into tasks?
2. There is a simple way to improve the performance of mandelbrot_ispc --tasks by changing the number of tasks the code creates. By only changing code in the function mandelbrot_ispc_withtasks(), you should be able to achieve performance that exceeds the sequential version of the code by over 32 times! How did you determine how many tasks to create? Why does the number you chose work best?
3. Extra Credit: (2 points) What are differences between the thread abstraction (used in Program 1) and the ISPC task abstraction? There are some obvious differences in semantics between the (create/join and (launch/sync) mechanisms, but the implications of these differences are more subtle. Here's a thought experiment to guide your answer: what happens when you launch 10,000 ISPC tasks? What happens when you launch 10,000 threads? (For this thought experiment, please discuss in the general case

• i.e. don't tie your discussion to this given mandelbrot program.)

The smart-thinking student's question: Hey wait! Why are there two different mechanisms (foreach and launch) for expressing independent, parallelizable work to the ISPC system? Couldn't the system just partition the many iterations of foreach across all cores and also emit the appropriate SIMD code for the cores?

Answer: Great question! And there are a lot of possible answers. Come to office hours.

Program 4: Iterative sqrt (15 points)

Program 4 is an ISPC program that computes the square root of 20 million random numbers between 0 and 3. It uses a fast, iterative implementation of square root that uses Newton's method to solve the equation ${\frac{1}{x^2}} - S = 0$. The value 1.0 is used as the initial guess in this implementation. The graph below shows the number of iterations required for sqrt to converge to an accurate solution for values in the (0-3) range. (The implementation does not converge for inputs outside this range). Notice that the speed of convergence depends on the accuracy of the initial guess.

Note: This problem is a review to double-check your understanding, as it covers similar concepts as programs 2 and 3.

What you need to do:

1. Build and run sqrt. Report the ISPC implementation speedup for single CPU core (no tasks) and when using all cores (with tasks). What is the speedup due to SIMD parallelization? What is the speedup due to multi-core parallelization?
2. Modify the contents of the array values to improve the relative speedup of the ISPC implementations. Construct a specifc input that maximizes speedup over the sequential version of the code and report the resulting speedup achieved (for both the with- and without-tasks ISPC implementations). Does your modification improve SIMD speedup? Does it improve multi-core speedup (i.e., the benefit of moving from ISPC without-tasks to ISPC with tasks)? Please explain why.
3. Construct a specific input for sqrt that minimizes speedup for ISPC (without-tasks) over the sequential version of the code. Describe this input, describe why you chose it, and report the resulting relative performance of the ISPC implementations. What is the reason for the loss in efficiency? (keep in mind we are using the --target=avx2 option for ISPC, which generates 8-wide SIMD instructions).
4. Extra Credit: (up to 2 points) Write your own version of the sqrt function manually using AVX2 intrinsics. To get credit your implementation should be nearly as fast (or faster) than the binary produced using ISPC. You may find the Intel Intrinsics Guide very helpful.

Program 5: BLAS saxpy (15 points)

Program 5 is an implementation of the saxpy routine in the BLAS (Basic Linear Algebra Subproblems) library that is widely used (and heavily optimized) on many systems. saxpy computes the simple operation result = scale*X+Y, where X, Y, and result are vectors of N elements (in Program 5, N = 20 million) and scale is a scalar. Note that saxpy performs two math operations (one multiply, one add) for every three elements used. saxpy is a trivially parallelizable computation and features predictable, regular data access and predictable execution cost.

What you need to do:

1. Compile and run saxpy. The program will report the performance of ISPC (without tasks) and ISPC (with tasks) implementations of saxpy. What speedup from using ISPC with tasks do you observe? Explain the performance of this program. Do you think it can be substantially improved? (For example, could you rewrite the code to achieve near linear speedup? Yes or No? Please justify your answer.)
2. Extra Credit: (1 point) Note that the total memory bandwidth consumed computation in main.cpp is TOTAL_BYTES = 4 * N * sizeof(float);. Even though saxpy loads one element from X, one element from Y, and writes one element to result the multiplier by 4 is correct. Why is this the case? (Hint, think about how CPU caches work.)
3. Extra Credit: (points handled on a case-by-case basis) Improve the performance of saxpy. We're looking for a significant speedup here, not just a few percentage points. If successful, describe how you did it and what a best-possible implementation on these systems might achieve.

Notes: Some students have gotten hung up on this question (thinking too hard) in the past. We expect a simple answer, but the results from running this problem might trigger more questions in your head. Feel free to come talk to the staff.

For the curious

For those interested and with access, try changing the compilation target to ARM, and produce a report of performance of the various programs on a new Apple M1 laptop. The staff is curious about what you will find. What speedups are you observing from SIMD execution? Those without access to a fancy M1 Macbook could use the ARM-based servers that are available on AWS.

Hand-in Instructions

Handin will be performed via Canvas. Only one handin per group is required. Please place the following files in your handin:

• Your writeup, in a file called writeup.pdf
  • In your writeup, please make sure both group members' names and SUNet id's are in the document. (if you are a group of two)
• Your implementation of main.cpp in Program 2, in a file called prob2.cpp

If you would like to hand in additional code, for example, because you attempted an extra credit, you are free to include that as well. Please tell the CAs to look for your extra credit. When handed in, all code must be compilable and runnable out of the box on the myth machines!

Resources and Notes

• Extensive ISPC documentation and examples can be found at http://ispc.github.io/
• Zooming into different locations of the mandelbrot image can be quite fascinating
• Intel provides a lot of supporting material about AVX2 vector instructions at http://software.intel.com/en-us/avx/.
• The Intel Intrinsics Guide is very useful.