LingSieve

CUDA (GPU) implementation of the sieve of Eratosthenes.

Key components used to make it really fast:

• segmented sieve of Eratosthenes
• sieve in shared memory
• bucket concept
• wheel concept
• blackkey concept - compact layout of primes to be sieved, one odd number per bit
• reuse all data structures again and again - no malloc, no free hence no memory leaks and init time can be neglected
• no bulk data transfer between CPU and GPU, only the sieve result will be transfered from GPU to CPU
• different sieving method for very small, small, medium, large and very large numbers

The program LingSieve counts primes and is designed for long duration tests (LDT), to handle large quantities of data, for the generation of large prime tables. That is what GPU computing is all about. It makes no sense to use the GPU for small sieve jobs. The granularity is 1.000.000.000 = 10^9 = 1" = 1 cycle, that is the smallest quantity to be sieved. It can be started with multiples of 1", and the sieve width is also in multiples of 1". It can sieve short of 2^64 (1,8446744x10^19).

Benchmark and HW Scaling

The GPU HW will scale the program accordingly, there is no need to configure anything.
All measurements were taken with a NVIDIA GeForce GTX 1080 (Palit Gamerock)

Range	Count	V2.1	V2.2	V2.3	Vx.y	Vx.z
0 … 10^11	4.118.054.813	0,60s	0,577s
0 … 10^12	37.607.912.018	8,31s	7,32s
0 … 10^13	346.065.536.839	103s	87,2s
0 … 10^14	3.204.941.750.802	1231s	1019s
10^12 + 10^11	3.612.791.400	0,90s	0,795s
10^13 + 10^11	3.340.141.707	1,08s	0,919s
10^14 + 10^11	3.102.063.927	1,26s	1,057s
10^15 + 10^11	2.895.317.534	1,44s	1,235s
10^16 + 10^11	2.714.336.584	1,62s	1,494s
10^17 + 10^11	2.554.712.095	1,81s	1,664s
10^18 + 10^11	2.412.731.214	2,08s	1,912s
4x10^18 + 10^11	2.334.654.194	2,34s	2,166s
10^19 + 10^11	2.285.693.139	2,64s	2,518s
1,4x10^19 + 10^11	2.268.304.926	2,81s	2,646s
1,8x10^19 + 10^11	2.255.482.326	2,91s	2,747s

This is the fastest implementation of the sieve of Eratosthenes on a GPU to the best of my knowledge.

Prerequisite

• NVIDIA graphics card with driver >= 384.81 for V2.1 and >= 398.26 for V2.2
• works best with compute capabilities 3.7, 5.2, 6.1 and 7.0 because of available quantities of registers and shared memory
• a 64-bit host application and non-embedded operating system (Linux, Windows, macOS)
• GPU memory: 1874MB .. 2304MB depending on the range to be sieved

Binary

The available binaries have been compiled for 64bit Windows and NVIDIA GPUs with compute capabilities 3.7 and higher.
It has been compiled with Microsoft Visual Studio Community 2017 and NVIDIA CUDA Toolkit V9.0 for V2.1 and V9.2 for V2.2.

Usage

Open a Command Prompt and run the program LingSieve:

1. start without parameter - it will use initial values - StartValue (0), segment size (100") and start a LDT
2. if there is a valid Result file it will use the last entry as StartValue, segment size (100") and start a LDT
3. if there is a user input it will use it instead of 1) or 2)

Examples	Comment
LingSieve -verbose -bench	to get on overview of the capabilities of your graphics card
LingSieve	Start LDT from 0 or from the last entry of file Result.txt if there is any
LingSieve 0	Count the primes from 0 .. 10^11
LingSieve 0 -s1	Count the primes from 0 .. 10^9
LingSieve 0 -s10	Count the primes from 0 .. 10^10
LingSieve 1000000	Count the primes from 10^15 .. 10^15+10^11
LingSieve 100000000 -s1000	Count the primes from 10^17 .. 10^17+10^12
LingSieve /?	Display help text

Status

I've sifted 6,8x10^16 numbers in various ranges without any errors, that is 68.000.000 cycles. Once I run it for more than 60 hours continuously without any problems, it just works as it is supposed to. The results were compared with the extensive prime sieve tables of Tomás Oliveira e Silva and Jan Büthe, randomly with the program primesieve 64bit of Kim Walisch.

Basic development is finished.