Complete the Code Using the Following Synchronization Mechanisms:

$1.$ pthread$\_$mutex$\_$t $($Mutex$)$:

o Implement the atomic counter using a mutex to ensure mutual exclusion when updating the shared counter.

o Use pthread$\_$mutex$\_$lock$()$ and pthread$\_$mutex$\_$unlock$()$ around the critical section.

$2.$ Semaphore:

o Use a binary semaphore $($sem$\_$t$)$ to control access to the shared counter.

o Initialize the semaphore to $1($binary semaphore$).$

o Use sem$\_$wait$()$ before entering and sem$\_$post$()$ after leaving the critical section.

$3.$ Test$-$and$-$Set $($TAS$)$:

o Implement a spinlock using the test$-$and$-$set atomic operation.

o Use GCC$\text{'}$s built$-$in function $\_\_$sync$\_$lock$\_$test$\_$and$\_$set$()$ for atomic test$-$and$-$set.

o Implement lock acquisition and release functions using TAS.

$4.$ Compare$-$and$-$Swap $($CAS$)$:

o Use the compare$-$and$-$swap atomic operation to implement a lock$-$free increment.

o Utilize GCC$\text{'}$s built$-$in function $\_\_$atomic$\_$compare$\_$exchange$\_$n$().$

o Implement an atomic increment function that retries on CAS failure.

b$.$ Measure the Total Execution Time for Each Implementation:

$$ Execution Time Measurement:

o Use gettimeofday$()$ or a similar function to measure the total execution time of each implementation.

o Record the start time before thread creation and the end time after all threads have joined.

$$ Testing with Different Parameters:

o Vary the number of threads $($NumThread$)$ and the maximum count per thread $($MaxCount$).$

$$ NumThread: $1,2,8$

$$ MaxCount: $1,000,000$; $10,000,000$

o For each combination, record the execution time and the final counter value. Analyze your observations.

$$ What are the final counter values with Dum Counter $($No Synchronization$)?$ Explain what happened.

$$ How NumThread affects the execution time of different implementations?