# Prime Time Tactics--Sieve Tweaks and Boosters
## 3 Parallel Sieving Strategies
### Generic Considerations
* **Loop Kernel Executions*
* Divide the range of numbers into segments or chunks, each corresponding to a separate interval to sieve for prime numbers. * Iterate over each segment and perform the following steps: a. _Launching the Kernel_:
* Prepare any necessary parameters or buffers to the kernel. * Launch the GPU kernel responsible for sieving prime numbers within the current segment. b. _Waiting for the Kernel to complete the sieving_:
* Wait for the GPU kernel to complete its execution. c. _Downloading Sieved Buffer_:
* Wait for the previous counting step (if any) to finish. * Transfer the results (sieved buffer) from the GPU back to the CPU. * This buffer contains information about which numbers in the current segment are primes. * Release the semaphore or whatever sync mechanism in place, in order to signal the parallel counting thread that it can start counting. d. _Generating Primes_ (this step is executed in parallel with all others):
* On the parallel CPU thread(s), wait to receive a new sieved buffer. * Process the sieved buffer to identify and generate the prime numbers within the current segment. * This step involves parsing the buffer and extracting the prime numbers based on the sieve results. * At the end of counting, release the semaphore or whatever sync mechanism to signal the main thread that it can download the new buffer from the GPU. * Go back to waiting for the new buffer or exit if finished. e. _Repeating the Process_:
* Repeat steps _a_-_c_ and \(d\) for each remaining segment until the entire interval is exhausted. * **Completion and Cleanup*
* Once all segments have been processed and the prime numbers have been generated, finalize any necessary cleanup tasks. * Release GPU resources, free memory buffers, and perform any other necessary cleanup operations. **Algorithm 1**_Cont._

To exemplify a non-trivial kernel, in Algorithm 2, we have a straightforward kernel for a basic OpenCL implementation of the Sieve of Sundaram on a GPU. ```
1 typedefunsignedintuint32_t;
2 typedefunsignedlonguint64_t;
3 fendif
```
We can also compile and use this kernel on the normal CPU, thus helping with the development process, as compile errors are signalled immediately and most of the logical errors can be debugged using the IDE debugger, which is much easier; of course, more subtle bugs that are specific to a GPU environment will still have to be investigated natively, but in any case, the development process may accelerate significantly. Here is an example for such simulation code using the kernel above as such, but also prepared to use other experimental kernels:
```
1 tpPrimeSimulate0 CL(consttpPrimeInt){
2 limit=Int/2;
3 unsignedexpected_winstate=0;
4 num_primes=1;AddPrime(2);//toaccountfor2
5 for(tpPrimeofst=0;ofst<limit;ofst+=BUFFER_SIZE){
6 cl_intclerror=CLSUCCESS;
7
8//resetbuffer
9 memeet(buffer_out.data(),true,BUFFER_SIZE);
10 memset(buffer_in.data(),true,BUFFER_SIZE);
11
12 constexpr unsignedCTOF1-2;
13 constexprunsignedCTOF2-2;
14 constexprunsignedNO_OF_SIMULATED_THREADS-2;
15//simulate
16 for(unsignedgid=0;gid<NO_OF_SIMULATED_THREADS;gid++){
17 if! 18 SoS_simple(buffer_out.data(), BUFF_SIZE,ofst,gid,NO_OF_SIMULATED_THREADS);
19_felif0
20 SoS_smlno(buffer_out.data(), BUFF_SIZE,ofst,CTOF1,gid,NO_OF_SIMULATED_THREADS);
21 SoS_big(buffer_out.data(), BUFF_SIZE,ofst,CTOF1,gid,NO_OF_SIMULATED_THREADS);
22_felse
23 SoS_bigman1(buffer_out.data(), BUFF_SIZE,ofst,CTOF1,gid,NO_OF_SIMULATED_THREADS);
24_fendif
25}
26 if(ofst==0)buffer_out[0]=false;
27 Count0 CLBuffer(ofst);
28}
29 returnnum_primes;
30}
```
The problem with such non-trivial but basic implementations of sieving algorithms is that the internal mechanics of sieving are not linear. Practically all sieves are executed in a nested loop technique; the outer loop iterates a primary parameter, while the inner will iterate a second parameter and the number of iterations varies significantly, usually non-linearly.