# Project 4: Numc

## Overview

Due Monday, April 26th

This project is designed to be both a C project as well as a performance project. In this project you will be implementing a slower version of numpy. Your version of numpy, numc (how exciting!), is most likely to be slower than numpy, but much faster than the naive implementations of matrix operations. You will first complete a naive solution for some matrix functions in C, then you will experiment with the setup file in Python to install your numc module. After that, you will gain a deeper understanding of the Python-C interface by overloading some operators and defining some instance methods for numc.Matrix objects. Finally, you will speed up your naive solution, thus making numc.Matrix operations faster.

Do not expect your final completed numc module to be as good as numpy, but you should expect a very large speedup compared to the naive solution, especially for matrix multiplication and exponentiation!

## Tips and Guidelines

• Please start early! Because there are many more 61C students than Hive machines, you will likely share resources with your classmates. This might affect the measurement of your code’s speedup. We encourage you to use Hivemind to help balance the load amongst the hive machines.
• You will have 6 tokens every 6 hours for the Gradescope assignment.
• You can complete task 1 through 3 before the performance lectures (lec 21-23) and task 4 after. So again, please start early!
• You can either allocate new matrices and throw errors in src/numc.c or src/matrix.c.
• We will not be directly testing your C code. All tests will be in Python!
• You may change the function signatures in src/matrix.h and src/matrix.c as you deem appropriate, but you may not change the function signatures in numc.h and src/numc.c.
• You may change the skeleton code in src/numc.c.
• You will get negative points up to the number of points it is worth if you fail to complete task 5, so you should do it as much as you can even if you do not complete the entire project!
• You may change the skeleton code in src/numc.c, especially if you are not using a row-major setup for your matrices.
• If you would like to run the reference solution to compare your solution to, you can import the dumbpy library on hive as we have already installed it there for you!
• For this project, we strongly suggest working on Hive machines under you cs61c account. We have set up a few environment settings that only work if you use your cs61c account.

## Getting Started

ssh into one of the hive machines under your cs61c class account. Visit visit https://galloc.cs61c.org/ and get your proj4 repository. Then, clone your repository locally and add the starter remote:

$git clone YOUR_REPO_NAME$ cd YOUR_REPO_NAME
$git remote add starter https://github.com/61c-teach/sp21-proj4-starter.git$ git pull starter master

If we publish changes to the starter code, retrieve them using git pull starter master.

To be able install the modules that you will complete in this project, you must create a virtual environment with by running

$python3.6 -m venv .venv Note that you MUST use python 3.6 as our reference module dumbpy only supports this specific version of python. Finally, run the following command to activate the virtual environment:$ source .venv/bin/activate

This will put you in a virtual environment needed for this project. Please remember that if you exit the virtual environment and want to return to work on the project, you must re-run source .venv/bin/activate. This also means every time you re-ssh into the hive, you will have to re-run source .venv/bin/activate.

Then, run

pip3 install -r requirements.txt

in the virtual environment. This will install all python packages you need for running your custom python tests.

Finally, if you have to exit out of the virtual environment, you can do so by running:

$deactivate We already have the reference library dumbpy installed for you on Hive machines. You can import it with or without the virtual environment while using python3.6, and all object and function names are the same as the numc module that you will implement (please refer to Task 3). You will only be able to access the dumbpy package on hive as we will not be directly releasing it. You can use it as a reference for both correctness and speed. Again, for this project, we strongly suggest working on Hive machines in your cs61c class account. You will not be able to import dumbpy if you are using other class accounts. We may be unable to help you with issues caused by working outside of the Hive. ## Task 1: Matrix functions in C For this task, you will need to complete all functions in src/matrix.c labelled with /* TODO: YOUR CODE HERE */. The comments above each function signature in src/matrix.c contain instructions on how to implement the functions, so read them carefully before you start coding. The matrix struct is defined in src/matrix.h. Feel free to change it, but make sure your changes are compatible with our starter code. typedef struct matrix { int rows; int cols; double* data; int ref_cnt; struct matrix *parent; } matrix; rows is the number of rows of this matrix, cols is the number of columns, and data is a 1D representation of the 2D matrix data. ref_cnt is the number of existing matrix structs (including itself) that share all or part of the data array with this particular matrix struct. parent indicates whether this matrix struct is a slice of another matrix, and should be set to its parent matrix struct if it is and NULL otherwise. src/matrix.h also imports the library Python.h, but for this part you should not need any other functions besides PyErr_SetString. Depending on your implementation of src/matrix.c and src/numc.c, you may or may not assume that result is already pre-allocated or that all inputs’ dimensions are valid. However, as mentioned in the Tips and Guidelines section, your Python number methods will need to handle the case where matrix allocation fails. The function allocate_matrix_ref is called from src/numc.c’s Matrix61c_subscript function and and is used for getting a row of the from matrix (see Info: numc.Matrix indexing for an example). Currently, Matrix61c_subscript and allocate_matrix_ref assume a row-major setup. If you choose to implement your matrices as column-major, you will have to change the implementation of Matrix61c_subscript, and you might also want to change the function signature of allocate_matrix_ref. Again, you may change any function signature in src/matrix.h and src/matrix.c. Important notes: • Remember to throw a runtime error if allocate_matrix or allocate_matrix_ref fails to allocate space, or a value error if you are trying to allocate matrices with non-positive dimensions! Otherwise you would have to make sure that a runtime/value error will be thrown in src/numc.c whenever we run out of memory. This includes throwing an error in Matrix61c_init. • The deallocate function as well as the ref_cnt field in the matrix struct have caused a lot of confusions in the past semesters. It is important to remember that this ref_cnt is NOT Python’s internal reference count. It is simply a field that will help you implement the deallocate function. It does not have to reflect the true reference count if you deem that setting it to other values will simplify your implementation of deallocate. • For the deallocate function, since there can be multiple matrices that refer to the same data array in the memory, you must not free the data until you call deallocate on the last existing matrix that refers to that data. If you are having some difficulties implementing this, here’s a hint: you can keep the matrix struct in the memory even if you have already called deallocate on that matrix. You only need to make sure to that the struct is freed once the last matrix referring to its data is deallocated. • If this explanation does not make sense now, don’t worry! It will make more sense after you implement the indexing section of task 3. ### Testing for Correctness We’ve provided some sanity in tests/mat_test.c. These tests make several assumptions: • They assume that all result matrices are already pre-allocated with the correct dimensions and that all input dimensions are valid. • They assume that you have not modified the matrix struct in src/matrix.h • All tests except the tests for get and set assume that your get and set are correct • They assume that you have not modified the function signatures. Violation of one or more of these assumptions may not cause your tests to fail, but please keep this in mind if your tests are failing and you are violating at least one of these assumptions. To run the CUnit tests, run$ make test

in the root folder of your project. This will create an executable called test in the root folder and run it.

By default, CUnit will run these tests in Normal mode. When debugging a specific issue, it may be helpful to switch to Verbose mode, which can be done by commenting and uncommenting the relevant lines in mat_test.c:

// CU_basic_set_mode(CU_BRM_NORMAL);
CU_basic_set_mode(CU_BRM_VERBOSE);

Make sure that one line is uncommented at a time.

Please keep in mind that these tests are not comprehensive, and passing all the sanity tests does not necessarily mean your implementation is correct. This is especially true with the memory functions allocate_matrix, allocate_matrix_ref, and deallocate_matrix. Also keep in mind that the autograder will be using our own set of sanity tests, and will not be running your CUnit tests.

Another thing to note is that the Makefile is written for compilation on the hive machines. If you wish to run it locally, you will have to modify the Makefile by replacing the path to your CUnit/Python libraries in your CUNIT and PYTHON variables. You will also need to make sure that your local computer supports AVX extensions and OpenMP.

Finally, you are welcomed to modify the tests/mat_test.c file in the tests directory to implement your custom test cases.

## Task 2: Writing the setup file

The setup.py file is used for installing your custom-built modules. After completing it, you should be able to install numc by simply running:

$make This will uninstall your previously installed numc module if it existed and reinstall numc. We have written src/numc.c so that numc.Matrix will be initialized and ready to import upon succesful installation of the numc module. You should rerun make every time you make changes and want them to be reflected in the numc module. You can uninstall your numc module by running$ make uninstall

We have provided you with the compiler and linker flags in setup.py, and your task is to find out how to use them to build your module.

You will likely get a lot of warnings about functions being defined but not used, and that’s ok! You should ignore these warnings for now, and they will be gone after you finish writing Task 3.

Remember that you must be in the virtual environment that you set up in order to install the modules, otherwise you will get a “Read-only file system” error.

READ FIRST: take a look at the function distutils.core.setup (https://docs.python.org/3.6/distutils/apiref.html), and here is an example usage. You only need two function calls to complete this section, if you’re doing more than that, please reread the docs included as you’re likely doing something wrong

## Task 3: Writing the Python-C interface

Now that you have successfully installed your numc module, you can import your numc.Matrix objects in Python programs! Here are some ready-to-use features already implemented for numc.Matrix objects. You might find them helpful when debugging Task 3.

### Info: Importing numc.Matrix

Here are several ways of importing numc.Matrix

from numc import Matrix

import numc
numc.Matrix

import numc as nc
nc.Matrix

### Info: numc.Matrix initialization

The code block below lists all the different ways of creating a numc.Matrix object.

>>> import numc as nc
CS61C Spring 2021 Project 4: numc imported!
>>> nc.Matrix(3, 3) # This creates a 3 * 3 matrix with entries all zeros
[[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
>>> nc.Matrix(3, 3, 1) # This creates a 3 * 3 matrix with entries all ones
[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
>>> nc.Matrix([[1, 2, 3], [4, 5, 6]]) # This creates a 2 * 3 matrix with first row 1, 2, 3, second row 4, 5, 6
[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
>>> nc.Matrix(1, 2, [4, 5]) # This creates a 1 * 2 matrix with entries 4, 5
[[4.0, 5.0]]

More specifically:

• nc.Matrix(rows: int, cols: int) will create a matrix with rows rows and cols cols. All entries in this matrix are defaulted to 0.
• nc.Matrix(rows: int, cols: int, val: int/float) will create a matrix with rows rows and cols cols. All entries in this matrix will be initialized to val.
• nc.Matrix(rows: int, cols: int, lst: List[int/float]) will create a matrix with rows rows and cols cols. lst must have length rows * cols, and entries of the matrix will be initialized to values of lst in a row-major order.
• nc.Matrix(lst: List[List[int/float]]) will create a matrix with the same shape as the 2D lst (i.e. each list in lst is a row for this matrix).

### Info: numc.Matrix indexing

You can index into a matrix and change either the value of one single entry or an entire row. More specifically, mat[i] should give you the ith row of matrix. If mat has more than 1 column, mat[i] should also be of type numc.Matrix with (mat’s number of columns, 1) as its shape. In other words, mat[i] returns a column vector. This is to support 2D indexing of numc matrices.

If mat only has one column, then mat[i] will return a double. mat[i][j] should give you the entry at the ith row and jth column. If you are setting one single entry by indexing, the data type must be float or int. If you are setting an entire row of a matrix that has more than one column, you must provide a 1D list that has the same length as the number of columns of that matrix. Every element of this list must be either of type float or int.

Please note that if mat[i] has more than 1 entry, it will share data with mat, and changing mat[i] will result in a change in mat.

The example given below assumes the matrices are initialized from the code block above.

>>> import numc as nc
CS61C Spring 2021 Project 4: numc imported!
>>> mat = nc.Matrix([[1, 2, 3], [4, 5, 6]]) # This creates a 2 * 3 matrix with first row 1, 2, 3, second row 4, 5, 6
>>> mat
[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
>>> slice = mat[0]
>>> slice
[[1.0], [2.0], [3.0]]
>>> slice[0]
1.0
>>> slice[1] = 10.0 # Change a value in slice
>>> slice
[[1.0], [10.0], [3.0]]
>>> mat # Mat is changed as well
[[1.0, 10.0, 3.0], [4.0, 5.0, 6.0]]

Partial slices, however, are not supported. For example,

mat[1:3] # not allowed
mat[0][1:3] # not allowed

### Info: instance attributes

The matrices and vectors have an attribute shape, which is a tuple of (rows, cols). Example is given below.

>>> mat.shape
(3, 3)

### Info: Python/C API Reference

Here is the link to the full reference manual: https://docs.python.org/3.6/c-api/index.html. If you ever find anything confusing in the skeleton code or are at a lost on how to implement src/numc.c, this is a great resource.

### Quick Overview of numc skeleton code

We define the Matrix61c struct in numc.h. It is of type PyObject (this means you can always cast Matrix61c to PyObject, but not vice versa), which according to the official documentation, “contains the information Python needs to treat a pointer to an object as an object”. Our Matrix61c has the matrix struct we defined in src/matrix.h.

Then we define a struct PyTypeObject named Matrix61cType to specify the intended behaviors of our Python object Matrix61c. This struct will then be initialized to be our numc.Matrix objects.

static PyTypeObject Matrix61cType = {
.tp_name = "numc.Matrix",
.tp_basicsize = sizeof(Matrix61c),
.tp_dealloc = (destructor)Matrix61c_dealloc,
.tp_repr = (reprfunc)Matrix61c_repr,
.tp_as_number = &Matrix61c_as_number,
.tp_flags = Py_TPFLAGS_DEFAULT |
Py_TPFLAGS_BASETYPE,
.tp_doc = "numc.Matrix objects",
.tp_methods = Matrix61c_methods,
.tp_members = Matrix61c_members,
.tp_as_mapping = &Matrix61c_mapping,
.tp_init = (initproc)Matrix61c_init,
.tp_new = Matrix61c_new
};

For example, .tp_dealloc tells Python which function to call to destroy a numc.Matrix object when its reference count becomes 0, and .tp_members tells Python what instance attributes numc.Matrix objects have. You can take a look at the official documentation if you are curious.

### Useful functions:

Here is a list of some functions and Python objects from <Python.h> that you may find useful. You can also choose any other functions at this link.

Now you are ready to complete src/numc.c, the Python-C interface! As before, you will need to fill out all functions and variables labeled /* TODO: YOUR CODE HERE */. The code for initializing the module numc and the object type numc.Matrix is already done for you. Although not required, we encourage you to take a look at the existing code to better understand the interface.

Below are the two main parts for this task.

### Number Methods

For this part, we ask you to overload operators for numc.Matrix objects. Here are the expected behaviors of overloaded operators:

• a + b: Element-wise sum of a and b. Returns a numc.Matrix object.
• Throwing errors:
• TypeError if not both a and b are of type numc.Matrix.
• ValueError if a and b do not have the same dimensions.
• a - b: Element-wise subtraction of a and b. Returns a numc.Matrix object.
• Throwing errors:
• TypeError if not both a and b are of type numc.Matrix.
• ValueError if a and b do not have the same dimensions.
• a * b: Matrix multiplication of a and b. Returns a numc.Matrix object. Remember that this is a matrix multiplication, not an element-wise multiplication.
• Throwing errors:
• TypeError if not both a and b are of type numc.Matrix
• ValueError if a’s number of columns is not equal to b’s number of rows.
• -a: Element-wise negation of a. Returns a numc.Matrix object.
• abs(a): Element-wise absolute value of a. Returns a numc.Matrix object.
• a ** pow: Raise a to the powth power. a to the 0th power is the identity matrix (1 on the top left to bottom right diagonal and 0 everywhere else). Returns a numc.Matrix object. This operator is defined in terms of matrix multiplication, not element-wise multiplication.
• Throwing errors:
• TypeError if a is not of type numc.Matrix or pow is not an integer.
• ValueError if a is not a square matrix or if pow is negative.

Please note that for all these operations above, you never directly modify the matrix that you pass in. You always make a new numc.Matrix object to hold your result, so make sure you set the shape attribute of the new numc.Matrix. You can use Matrix61c_new to create new numc.Matrix objects. Take a look at the implementation of Matrix61c_subscript for an example.

For all the functions above, throw a runtime error if any error occurs (such as matrix allocation failure) and causes the operation to fail. Moreover, for any operations that involve two instances of numc.Matrix, you will have to make sure that both a and b are indeed of type numc.Matrix as we do not support operations between numc.Matrix and other data/object types. Please read the comments in src/numc.c carefully.

Here is a table that tells you which function in src/numc.c in which you will implement each of the above operators

Operator Function
- (subtraction) Matrix61c_sub
* Matrix61c_multiply
- (negation) Matrix61c_neg
abs() Matrix61c_abs
** Matrix61c_pow

All these functions will be called through a Python-C interface after you complete the numc module. In other words, these are the functions that will be called when you do matrix operations with numc.Matrix objects, and these interface methods will call src/matrix.c methods that you just implemented. You will have to check for the validity of the dimensions before actually carrying out the arithmetic, and throw an error if needed. Specifically, throw an type error if the arguments’ dimensions are invalid, and a runtime error if any memory allocation fails during execution. Again, depending on your implementation, these error checks could either be in src/matrix.c or src/numc.c

After you implement all the functions above, you will need to fill out the struct Matrix61c_as_number, which is used to define the object type numc.Matrix. Remember to cast your functions to the correct types when assigning them to Matrix61c_as_number’s fields!

Here is the link to the official documentation of a PyNumberMethods struct: https://docs.python.org/3/c-api/typeobj.html#c.PyNumberMethods

### Instance Methods

You will implement two instance methods for numc.Matrix:

• set(self, i, j, val): Set self’s entry at the ith row and jth column to val.
• Throwing errors:
• TypeError if the number of arguments parsed from args is not 3, if i and j are not integers, or if val is not a float or int.
• IndexError if i or j or both are out of range.
• get(self, i, j): Returns the entry at the ith row and jth column. Throw a type error if the number of arguments parsed from args is not 2 or if the arguments are of the wrong types. Throw an index error if either i, j, or both are out of range. Return value is a Python float.
• Throwing errors:
• TypeError if the number of arguments parsed from args is not 2 or if either i or j is not an integer.
• IndexError if i or j or both are out of range. These functions will call get and set in src/matrix.c to actually get or set the value. Again, you can throw errors either in src/numc.c or src/matrix.c.

Here is a table that tells you which functions in src/numc.c in which you will implement each of the above instance methods

Python method C Function
set Matrix61c_set_value
get Matrix61c_get_value

After you implement all the functions above, you will need to fill out the array of PyMethodDef structs Matrix61c_methods, which is used to define the object type numc.Matrix.

This link tells you what goes into a PyMethodDef struct: https://docs.python.org/3/c-api/structures.html

### Indexing

As mentioned in task 1, if you are storing your matrix data in a non-row-major order, you might want to change your Matrix61c_subscript.

Regardless of how you are storing you matrices, now is a good time to check if your allocate_matrix_ref in src/matrix.c is working as intended. A correct implementation of allocate_matrix_ref and Matrix61c_subscript should result in behaviors specified in the indexing info section above. More importantly, please take some time to make sure that you don’t have memory leaks! In other words, you need to make sure that when all references to a matrix is gone, that matrix’s data need to be free’d immediately. However, when the parent itself is gone but there are still existing slices of this matrix, you can delay the freeing of the parent’s data until all those slices are also gone. Here’s an example to what is meant by the above.

import numc as nc
a = nc.Matrix(2, 2)
b = a[0] # b is referencing a's data
del a # a is gone, but you don't have to free a's data right now
del b # b is gone, now you need to free a's data

### How to Debug

To debug the Python-C interface, we suggest that you write your test files in Python, and use gdb or both gdb and pdb to debug.

#### Using only gdb

You don’t have to use pdb if you do not wish to set breakpoints in your Python test file. Open your terminal and run

$gdb python3 Then you can set breakpoints in your C files using the normal gdb commands. gdb will warn you with No source file named {your c file} Make breakpoint pending on future shared library load? (y or [n]) Press ‘y’ (without the quotes) to proceed. After that, you can run run {your python test file name}.py in gdb, and gdb will break at the breakpoints that you just set. #### Using both gdb and pdb You will have to use pdb if you wish to set breakpoints in your Python file. Here’s how it works. Start gdb by running$ gdb python3

and set your breakpoints in C (see previous section). Then you will need to run in gdb

run -m pdb {your python file}.py

After this step, you can set breakpoints in your Python file using gdb syntax (for example, b test.py:5). With this approach, your debugger will switch between pdb and gdb depending on whether you are stepping through a Python file or a C file. If you are seeing values being optimized out on gdb, try changing O3 to O0 in setup.py, then reinstalling your module.

## Task 4: Speeding up matrix operations

Now that you have completed the three steps above and successfully installed your naive version of numc, it’s time to speed up your matrix functions in src/matrix.c! Below we outline some steps for boosting performance.

### Step 1: Unrolling and Other Optimizations

You should first try to speed up the computation by trying to apply conventional code optimizations (i.e. without using SSE or OpenMP). While we won’t tell you the exact steps, here are some hints that should help you get started:

1. Function calls are expensive since they involve setting up a stack frame and jumping to a different part of code. See if there are any functions that are frequently called that don’t necessarily need to be.
2. Are there any places where you could do manual loop unrolling?
3. Is there any unnecessary computation being done?

Note that the above hints relate to general optimization practices. You do not necessarily need to do all of these to achieve a good speedup.

Once you have improved performance using these optimizations, you can start applying vectorization and parallelization to make the program even faster. Note that you have considerable freedom to apply any of these optimizations, and there is more than one correct solution. Try to experiment with different approaches and see which one gives you the best performance.

### Step 2: SIMD Instructions

From lectures, you learned how to apply SIMD instructions to improve performance. The processors in the hive machines support the Intel AVX extensions, which allow you to do SIMD operations on 256 bit values (not just 128 bit, as we have seen in the lab). You should use these extensions to perform four operations in parallel (since all floating point numbers are doubles, which are 64 bit in size). If you are unfamiliar with SIMD instructions, lab 9 can be a good warmup.

As a reminder, you can use the Intel Intrinsics Guide as a reference to look up the relevant instructions. You will have to use the __m256d type to hold 4 doubles in a YMM register, and then use the _mm256_* intrinsics to operate on them.

Here is a list of AVX instructions that you may find helpful, although you are also allowed to use other AVX instructions not on the list.

void _mm256_storeu_pd (double * mem_addr, __m256d a)
__m256d _mm256_set1_pd (double a)
__m256d _mm256_set_pd (double e3, double e2, double e1, double e0)
__m256d _mm256_add_pd (__m256d a, __m256d b)
__m256d _mm256_sub_pd (__m256d a, __m256d b)
__m256d _mm256_fmadd_pd (__m256d a, __m256d b, __m256d c)
__m256d _mm256_mul_pd (__m256d a, __m256d b)
__m256d _mm256_cmp_pd (__m256d a, __m256d b, const int imm8)
__m256d _mm256_and_pd (__m256d a, __m256d b)
__m256d _mm256_max_pd (__m256d a, __m256d b)

### Step 3: OpenMP

Finally you should use OpenMP to parallelize computation. Note that you will need to make sure that none of the different threads overwrites each others’ data. Just adding a #pragma omp parallel for may cause errors.

Note that the Hive machines have 4 cores with two hyperthreads each. This means that you should expect a speed-up of 4-8x (note that hyperthreads mean that two different threads execute on the same physical core at the same time; they will therefore compete for processor resources, and as a result, you will not get the same performance as if you were running on two completely separate cores).

## Task 5: Tell us what you did!

Write up what you did in your README.md! While we do not have a specific format we are looking for, you should discuss what you did as a whole, the different python functions you implemented, what performance improvements you had, what were you surprised about, etc. More specifically, we want you to document your numc module and provide example usages. We expect a minimum of 3000 characters. This may seem like a lot, but documenting you’ve done actually takes quite a number of words, so just sufficiently covering all the things you did in the project should get you to the word count requirement. Again, failure to complete this task may result in negative points, so make sure you do it or you will lose points!

## Testing

We will not be grading your tests but we will NOT help you debug unless you have written a test which shows how your code is failing. This means just using the autograder to figure out your issues will not be acceptable for office hours.

We use tests/unittests as the framework for testing and have provided a tests/unittests folder that contains this framework for testing your python module. You should be familiar with unittest by now as you have had experience with it in project 2. Here is the official documentation for the standard Python unittest library. tests/unittests/unittests.py contains all the skeleton code for both correctness and performance tests, and tests/unittests/utils.py has all the functions that you might need in order to write tests. We have provided some sample tests for you, but it is up to you to design and code up the tests. We will not be grading your tests.

As mentioned in Tips and Guidelines and Getting Started, we have installed the naive solution which we will be comparing against on hive! The python package is called dumbpy and you can import it like any other python library (so long as you are on hive)! Please note we will not be distributing this binary which means you must work on hive if you want to test with it. You should use this and the time package to determine how much you sped up your code.

### Functions in tests/unittests/utils.py

• dp_nc_matrix(*args, **kwargs)
• This function will return a dumbpy matrix and a numc matrix that are identical. *args and **kwargs will be used as the arguments to instantiate both matrices in the exact same format as you would instantiate a numc.Matrix. We provide some examples below.
>>> dp_mat, nc_mat = dp_nc_matrix(2, 2, 0)
>>> dp_mat
[[0.0, 0.0], [0.0, 0.0]]
>>> nc_mat
[[0.0, 0.0], [0.0, 0.0]]
>>> dp_mat, nc_mat = dp_nc_matrix([[1, 2, 3]])
>>> dp_mat
[[1.0, 2.0, 3.0]]
>>> nc_mat
[[1.0, 2.0, 3.0]]

• rand_dp_nc_matrix(rows, cols, low=0, high=1, seed=0)
• This function will instantiate a random dumbpy matrix and a random numc matrix with seed where each element is in the range [low, high). The two matrices are identical with rows rows and cols. seed is defaulted to 0.
>>>> dp_mat, nc_mat = rand_dp_nc_matrix(2, 2, seed=5)
>>> dp_mat
[[0.27474559623503386, 0.046467764790387715], [0.9927552244592249, 0.08003044504673706]]
>>> nc_mat
[[0.27474559623503386, 0.046467764790387715], [0.9927552244592249, 0.08003044504673706]]

• cmp_dp_nc_matrix(dp_mat: dp.Matrix, nc_mat: nc.Matrix)
• This function will return True if dp_mat has the same size of nc_mat and all corresponding elements are equal (within a margin of error).
• compute(dp_mat_lst: List[Union[dp.Matrix, int]], nc_mat_lst: List[Union[nc.Matrix, int]], op: str)
• This function takes in a list of dumbpy matrices and a list of numc matrices, then applies the specified operation op on these matrices. Note that op is a string. "add", "sub", "mul", "neg", "abs", and "pow" correspond to the operations +, -(subtraction), *, -(negation), and abs, respectively. This function will return whether the computed dumbpy matrix is equal to the computed numc matrix, as well as the speedup for this specific computation.
• For unary operations like "neg" and "abs", each matrix list must only contain 1 matrix. For the binary operations, they must contain more than 1 matrix.
• Note that to compute "pow", dp_mat_lst and nc_mat_lst should look like something like [Matrix(2, 2), 1].
• You can also do chained operations like compute([a, b, c], [d, e, f], "add") where a, b, c, d, e, f are matrices, and the function will compute a + b + c and d + e + f.

• Running
$python -m unittest unittests.py -v will run all tests in unittests.py. • If you only want to run tests of one particular class, run$ python -m unittest unittests.{classname} -v

For example, running

$python -m unittest unittests.TestAdd -v will only run the tests under the TestAdd class. • If you want to run a specific test under a specific class, run$ python -m unittest unittests.{classname}.{testname} -v

For example, running

will only run the test_small_add test.

• Q 1.1: Will we be graded on what types of errors we threw? Or do we just have to throw some error?
A 1.1: Yes we expect you to throw the correct error types. We do not care about the error strings tho.

• Q 1.2: I’m getting this when I run make test, what is happening?
rm -f test
gcc -g -Wall -std=c99 -fopenmp -mavx -mfma -pthread -O3 mat_test.c src/matrix.c -o test -fopenmp -L/home/ff/cs61c/cunit/install/lib -I/home/ff/cs61c/cunit/install/include -lcunit -I/usr/include/python3.6 -lpython3.6m
./test
CUnit - A unit testing framework for C - Version 2.1-2
http://cunit.sourceforge.net/
Makefile:25: recipe for target 'test' failed
make: *** [test] Illegal instruction (core dumped)

A 1.2: This means your code segfaulted before any assert statements was reached and none of the tests passed. Use gdb to locate your bug.

• Q 1.3: Do we assume rows and cols start at 1 or 0?
A 1.3: They are both zero-indexed.

• Q 1.4: Do our functions need to support self-referential operations? For example, mul_matrix(mat, mat, mat).
A 1.4: No.

• Q 1.5: Is it reasonable to run valgrind on ./test?
A 1.5: You can try, but would not recommend. Setting up valgrind for C-Python interface can be difficult.

• Q 1.6: When we throw an error, is it just a fprintf call to stderr?
A 1.6: Nope, you should throw errors in a python context. i.e., when your python code calls this underlying C function, it should error. Take a look at the Python/C API’s reference manual for exception handling.

• Q 1.7: Can we make a slice on slice? for example, mat1 = [[1,2,3],[4,5,6]], mat2 = mat1[0]. Can we do mat3 = mat2[0]?
A 1.7: No a “slice” on slice is just a number and is pass by value. In this case, mat3 will just be a number and changing its value will not change mat2.

• Q 1.8: Does our solution need to exactly match the reference?
A 1.8: No, we allow an error margin of 1e-6.

• Q 2.1: I’m getting undefined symbols upon import (for example, undefined symbol: allocate_matrix_ref). What is happening?
A 2.1: Think about what files your module needs, especially where the undefined symbol is located.

• Q 2.2: The values in my matrices change after I print their slices.
A 2.2: This is likely a memory leak. Double check your deallocate_matrix implementation. What happens when you call print(mat[0]) is that it will create a slice, then immediately deallocate it after this line.

• Q 3.1: Getting <class 'AttributeError'> -- shape.
A 3.1: Make sure the relevant method in src/numc.c is setting mat->shape

• Q 3.2: Getting <class 'SystemError'> -- <built-in method set of numc.Matrix object at 0x7f175faffef0> returned NULL without setting an error!
A 3.2: You need to throw an error before returning NULL in any interface function.

• Q 3.3: UnicodeDecodeError: ‘utf-8’ codec can't decode byte 0x89 in position 5: invalid start byte upon import. What’s wrong?
A 3.3: {NULL, NULL, 0, NULL} from starter code must be last element of Matrix61c_methods, so make sure you don’t accidentally remove that!

• Q 3.4: Are we allowed to call methods we wrote in src/matrix.c?

• Q 3.5: How do we know what gets passed into PyObject* args?
A 3.5: Read the official documentation! (You can also take a look at the starter code for examples.)

• Q 3.6: Is it safe to cast PyLong_AsLong as int?
A 3.6: Yes! You can assume that all integer values in this project will never overflow.

• Q 3.7: Does the sign of 0.0 matter when negating matrices?
A 3.7: No.

• Q 3.8: Should Matrix61c_multiply cover both nb_matrix_multiply and nb_multiply, or just nb_multiply?
A 3.8: Just nb_multiply. nb_matrix_multiply corresponds to the operator @.

• Q 3.9: My dumbpy and numc matrices are exactly the same, however, comparing them using == returns False.
A 3.9: You cannot compare them like that as they are of different object types. Please use cmp_dp_nc_matrix, which is provided in unittests/utils.py.

• Q 4.1: #pragma omp parallel for above a simple for loop slows down my add_matrix drastically?
A 4.1: You need big matrices to actually see the effect of speedup (something around 1000 * 1000).

• Q 4.2: I’m getting warning: ignoring #pragma omp parallel [-Wunknown-pragmas] but I have not changed the Makefile?
A 4.2: It might be your task 2. Take a look at the compiler and linker flags we provided you.

• Q 5.1: I’m passing my local correctness tests but failing autograder. What might be the case?
A 5.1: Here are some common sources of bugs:
• Make sure you test your matrix operations on non-integer floating point values (such as 1.2, 1.3). In the past semester, some students’ code was only able to generate correct results when every floating point value in their matrices were integer-valued floating points (such as 1.0, 2.0).
• Make sure you are setting the shape attribute of every returned matrix!
• Please do NOT modify anything related to generating random matrices! Do NOT try to speed them up! We use those to generate matrices to test on the autograder. We don’t include the time for generating matrices when testing for performance.
• Please make sure that you have removed all your debug print statements.

• Q 5.2: Performance tests are failing but correctness tests all pass.
A 5.2: Our performance tests test on much larger matrices than the correctness tests, so make sure you handle those cases correctly!

• Q 5.3: Failing tests that are related to throwing errors.
A 5.3: Make sure you are throwing the correct type of error, not just any error.

• Q 5.4: Failing abs correctness test, even though my abs_matrix logic is very simple.
A 5.4: Check if you are using C’s built-in abs function. If so, you probably want to manually write another one since the built-in abs function will round off all decimal places.

### Testing Questions

• Q6.1: Why are there TODO: YOUR CODE HERE comments in the test functions in unittests.py even though these functions have already been implemented for us?
A6.1: The tests we have provided are VERY simple and they are purely examples to help you write more tests. Please modify these tests or add more tests for more comprehensive testing.

• Q6.2: My tests are failing inside rand_md5, is this a bug from the starter code?
A6.2: No. Make sure your implementations Matrix61c_get_value and Matrix61c_get_value are correct! Otherwise rand_md5 might error.

The grading breakdown for Project 4 is as follows:

• Correctness: 55%
• Speedup: 40%
• Multiplication: 20%
• Power: 25%
• Simple: 12.5%
• Comprehensive: 42.5%

**Updated on April 20th: ** Here are the graphs for the speedup tests. The x-axis is your speedup times and the y-axis indicates what percentage of that test’s total score you will receive.

Multiplication Power
Simple Comprehensive

Minimum speedup for 100% on each test:

• Multiplication: 90x
• Power: 900x
• Simple: 4x
• Comprehensive: 92x

Since we are running your submissions on hive, albeit reserved, speedup times may fluctuate a bit. You should try to go above the speedup value as we will rerun the ag after the deadline and your speedup may go up or down. We will not rerun submissions if they went down unless we made another change to the autograder.

We will only be using your src/matrix.h, src/matrix.c, src/numc.c, setup.py, and README.md for grading. Gradescope only shows you all the core correctness tests that are needed to run performance tests. Other tests will stay hidden until the late due date. Keep in mind that your Matrix61c_get method in src/numc.c as well as the shapes you set for your matrices need to be correct in order for you to pass any of those correctness tests.