computer science question

your input image is named "santa$-$grayscale.jpg$",$ the execution command would be $"//$convolution santa$-$grayscale.jpg$"$

No command argument for filter radius is necessary in this assignment, as we utilize the constant average filter of size $55$ where the filter radius is $2.$

Within $"$

convolution.cu$",$ implement one host function and two CUDA kernels to perform convolution, respectively. Specifically,

a$.$ A host function that performs the convolution operation using CPU$-$only.

b$.$ A CUDA kernel that performs the convolution operation using GPU but without tiling. You may refer to the example provided on Slide $40$ in Module $3,$ but please modify it to incorporate the average filter matrix. It is acceptable to load the average filter from either GPU global memory or constant memory.

c$.$ An optimized CUDA kernel that presents a "tiled" version of the convolution operation using GPU shared memory. Specifically, in this optimized kernel, please load the average filter from GPU constant memory.

Ensure that your code can handle images with varying image sizes. Please also consider boundary conditions to ensure proper handling in such cases.

For testing purposes, two input images of different sizes are provided in the zipped folder accompanying this assignment.

"santa$-$grayscale.jpg$"$: a grayscale image of size $1,0001,000$

"tree$-$grayscale.jpg$"$: a grayscale image of size $345346$

You may also choose to test your program with additional grayscale images if desired.

Utilize timing techniques such as CPU timers or CUDA events, to measure the performance of your implementation of the host function and two CUDA kernels as specified above.

We also suggest structuring the $"$

convolution.cu$"$ by implementing the following macros, host functions, and CUDA kernels. At the end of this assignment, we will provide screenshots of an example of the program's structure.

#define CHECK$($call$)$

A macro for error checking.

double myCPU'Timer$()$

A timer for measuring execution time.

void blurImage$\_$h$($cv::Mat Pout$\_$Mat$\_$h$,$ cv::Mat Pin$\_$Mat$\_$h$,$ unsigned int nRows, unsigned int nCols$)$

A host function for CPU$-$only convolution.

$\_$global$\_\_$void blurImage$\_$Kernel$($unsigned char $*$ Pout, unsigned char $*$ Pin, unsigned int width, unsigned int height$)$

A CUDA kernel performs a simple convolution without using tiling.

void void blurImage$\_$d$($cv::Mat Pout$\_$Mat$\_$h$,$ cv::Mat Pin$\_$Mat$\_$h$,$ unsigned int nRows, unsigned int nCols$)$

A host function for handling device memory allocation and free, data copy, and calling the specific CUDA kernel, blurImage$\_$Kernel$().$

$2$Given a string s$,$ find the length of the longest substring without repeating characters.