Hello,

I correct some typos, please read gain...

I will prove it to you again, so follow with me carefully please...

Let say we have 4 threads, and 4 cores, and let say that each

thread is running the same parallel code, and let say we have also a serial code inside some critical section, and let say that the parallel part is

0.1% and the serial part is 0.9%, so let say that the serial part

takes 1 second(it means 0.1%) and the parallel part takes 9 seconds(it means 0.9%), what i have tried to explain to you is that the Amadhl's law or equation is not a correct law and it doesn't give a correct results,

here is why: so if the 4 threads are all looping and looping again

for a number of times running the same parallel code and the same serial code and let say that they are contending at the same time

for the critical section, this is why i have called an ideal contention

scenario, so if they are contending AT THE SAME TIME for the critical section(the serial part) they will run 4 serial parts in 4 seconds in one loop and they will run 4 parallel parts in 9 seconds in one loop, hence it will take 13 seconds in one loop , but if you run the parallel part and the serial part serially they will take 40 seconds, so the scalability will equal 40 seconds divide by 13 seconds = 3.07X, this is the result that gives us the Amdahl's law, it's 1 /(0.1 + 0.9/4) = 3.07X, but this is not the end of the story , so follow now carefully with me, so let divide the parallel part into 9 small parts each equal to

1 seconds, and the serial part is equal to 1 second, so if the threads

are looping and not contending at the same time for the critical section and let say that when the threads are looping the first thread will be on the first small part equal to 1 seconds of the 9 small parts of the 9 seconds of the parallel part , the second thread will be on the second small part equal to 1 seconds of the 9 parts of the 9 seconds of the parallel part, and the third threads will be on the third small part equal to 1 second of the 9 parts of the 9 seconds of the parallel part , and the fourth thread will be on the fourth small part equal to 1 second of the 9 parts of the 9 seconds of the parallel part , so imagine the 4 threads

looping again and again and not changing there places like that , so

there will be no serial part at all, cause when each thread will be on the 1 second of the serial part the other threads will not be on the the same serial part, so this is a none contention scenario , so since

there is no serial part so the scalability will be perfect and

equal to 4X , so as you have noticed the Amdahl equation gives

the scalability of the ideal contention scenario all the threads

are contending at the same time so the scalability will equal 3.07X, but if they are not contending at all the scalability will be perfect

and equal to 4X, and if you have less contention this will scale

better than 3.07X, so now i have proved to you that the Amdahl's law

doesn't give you a correct result.

Hope you have understood my arguments and my ideas against the

Amdahl's law.

And of course in my example each thread have the same number of loops and the same number of work, and each thread is running on a separate core in my example. so that you understand more my example.

Thank you,

Amine Moulay Ramdane.

## Here is my proof

Hello,

I have noticed that Robert Wessel didn't understood my ideas..

So i will prove it to you right now , so follow with me carefully please...

Let say we have 4 threads, and 4 cores, and let say that each

thread is running the same parallel code, and let say we have also a serial code inside some critical section, and let say that the parallel part is

0.1% and the serial part is 0.9%, so let say that the serial part

takes 1 second(it means 0.1%) and the parallel part takes 9 seconds(it means 0.9%), what i have tried to explain to you is that the Amadhl's law or equation is not a correct law and it doesn't give a correct results,

here is why: so if the 4 threads are all looping and looping again

for a number of times running the same parallel code and the same serial code and let say that they are contending at the same time

for the critical section, this is why i have called an ideal contention

scenario, so if they are contending AT THE SAME TIME for the critical section(the serial part) they will run 4 serial parts in 4 seconds in one loop and they will run 4 parallel parts in 9 seconds in one loop, hence it will take 13 seconds in one loop , but if you run the parallel part and the serial part serially they will take 40 seconds, so the scalability will equal 40 seconds divide by 13 seconds = 3.07X, this is the result that gives us the Amdahl's law, it's 1 /(0.1 + 0.9/4) = 3.07X, but this is not the end of the story , so follow now carefully with me, so let divide the parallel part into 9 small parts each equal to

1 seconds, and the serial part is equal to 1 second, so if the threads

are looping and not contending at the same time for the critical section and let say that when the threads are looping the first thread will be on the first small part equal to 1 seconds of the 9 small parts of the 9 seconds of the parallel part , the second thread will be on the second small part equal to 1 seconds of the 9 parts of the 9 seconds of the parallel part, and the third threads will be on the third small part equal to 1 second of the 9 parts of the 9 seconds of the parallel part , and the fourth thread will be on the third small part equal to 1 second of the 9 parts of the 9 seconds of the parallel part , so imagine the 4 threads

looping again and again and not changing there places like that , so

there will be no serial part at all, cause when each thread will be on the 1 second of the serial part the other threads will not be on the the same serial part, so this is a none contention scenario , so since

there is no serial part so the scalability will be perfect and

equal to 4X , so as you have noticed the Amdahl equation gives

the scalability of the ideal contention scenario all the threads

are contending at the same time so the scalability will equal 3.07X, but if they are not contending at all the scalability will be perfect

and equal to 4X, and if you have less contention this will scale

better than 3.07X, so now i have proved to you that the Amdahl's law

doesn't give you a correct result.

Hope you have understood my arguments and my ideas against the

Amdahl's law.

Thank you,

Amine Moulay Ramdane.