代写159.735语言、C++编程代做、c++程序设计调试

日期：2020-11-02 11:30

159.735 Assignment 5

You have been commissioned to help design a new quantum warp drive

engine. Since this engine is designed to drive spaceships through hyperspace,

you will need to deal with spatial dimensions greater than 3.

Given an N-dimensional sphere of radius, r, centred at the origin of an

N-dimensional coordinate system, first complete a sequential function to

count the number of integer coordinate points inside the sphere. Here are

some examples to allow you to check your work:

1. A 1-dimensional sphere of radius 25.5 has 51 integer coordinate points:

{(±25, ±24, ±23, · · · , ±1, 0)}

2. A 2-dimensional sphere of radius 2.05 has 13 integer coordinate points

within the sphere:

{(0, 0),(−1, 0),(−2, 0),(1, 0),(2, 0),(−1, −1),(−1, 1),(1, −1),(1, 1),(0, −2),

(0, −1),(0, 1),(0, 2)}

3. A 3-dimensional sphere of radius 1.5 has 19 integer coordinate points

inside the sphere:

{(−1, 0, 0),(−1, 0, 1),(−1, 0, −1),(−1, −1, 0),(−1, 1, 0),(1, 0, 0),(1, 0, 1),

(1, 0, −1),(1, −1, 0),(1, 1, 0),(0, 0, 0),(0, 1, 0),(0, 1, 1),(0, 1, −1),(0, −1, 0),

(0, −1, 1),(0, −1, −1),(0, 0, −1),(0, 0, 1)}

A small start up program will be provided, where you are asked to complete

the sequential function count_inside. This function will be invoked

for a number of different values of r and N. The pseudo-code for the sequential

implementation goes like:

for (n=0; n < ntrials; ++n) {

radius = selected_at_random()

ndim = select_at_random()

// Invoke function to count inside integer coordinates

count = count_inside(radius, ndim)

}

Having completed the sequential program, then develop an implementation

to run on your GPU.

You will need to decide what your kernel function will do and how to

organize your threads. It is also likely you will encounter some limitations

on your graphics card that will affect performance and the values for r and

N that will actually work.

Submission

Please submit your C or C++ source code together with a brief report.

In your report you should address at least the following. Marks will be

awarded for discussions that demonstrate clear understanding on GPU

architectures.

• State the graphics card you used together with any relevant specs.

• Briefly describe your algorithm for counting the number of integer

coordinates within an N-sphere

• Provide a description on how you parallelized the above problem.

• Present appropriate performance data, and comment on your result.

Due date: TBD

This assignment is worth 20% of your final grade

Appendix: Coding Hints

To convert a decimal integer number, num, into a number in base B, you

can use a number of possible algorithms, for example:

idx = 0;

while (num != 0) {

rem = num % B;

num = num / B;

digit[idx] = rem;

++idx;

}

Examples: 120810 = 101110002, 120810 = 11222023, 120810 = 22708, · · · .

You can use cudaMalloc() to create a single data word, not just arrays,

on the GPU device. Also, you can use cudaMemset() to initialize a device

value and you can use cudaMemcpy() to copy single data words from the

device to the host.

You will probably encounter a situation where a number of threads can

modify a single value. Clearly, this would have to be done atomically. The

CUDA library provides a (overloaded) function atomicAdd() that makes

this easy.