Different implementations of a simple Collatz iterator and their performance
The Collatz conjecture was proposed by Lothar Collatz in 1937. The conjecture is also known as the 3n + 1 conjecture.
The procedure is that if n is divisible by two then divide by two, else multiply by 3 and add 1, iterate until n reaches 1. The unproven conjecture is that for all values of n the procedure will always reach 1.
The benchmark times the iteration of the 226 first values of n.
Contents
Visual C++
Vista 64, 2.4 GHz core 2 Q6600
- 22.1s - 64 bit exe, one thread, unrolled 1000 times
- 30.5s - 64 bit exe, one thread, unrolled 10 times
- 45.9s - 32 bit exe, one thread, unrolled 1000 times
- 49.2s - 64 bit exe, one thread, not unrolled
- 53.3s - 32 bit exe, one thread, unrolled 10 times
- 76.1s - 32 bit exe, one thread, not unrolled
Vista 32, 2.66 GHz core 2 E6750
- 41.3 - 32 bit exe, one thread, unrolled 1000 times
- 47.7 - 32 bit exe, one thread, unrolled 10 times
- 65.6 - 32 bit exe, one thread, not unrolled
Visual Basic 2008
The code is compiled to common intermediate language that is made executable by the .net just in time compiler. The advantage is that the JIT compiler can optimize the code for the specific CPU at runtime. In this case the slower CPU with 64 bit registers is the fastest because of the optimization. The code should also run unmodified on Linux with Mono installed. The multithreaded version uses Microsoft Parallel Extensions to .NET Framework 3.5 and required almost no change to the program.
Vista 64, 2.4 GHz core 2 Q6600
- 55.4s - .net exe, one thread
- 11.3s - .net exe, four threads, unrolled 100 times
Vista 32, 2.66 GHz core 2 E6750
- 66.4s - .net exe, one thread
- 42.9s - .net exe, one thread, unrolled 100 times
- 33.6s - .net exe, two threads
- 22.9s - .net exe, two threads, unrolled 100 times
x86 assembly language
Because of the suspected low quality of 32 bit code generated by modern C++ compilers a hand crafted assembly version was made for comparison. The performance gain was made by keeping the value in a 64 bit MMX register and exploiting some statistical properties of thg ealgorithm that is not obvious to a normal compiler.
Vista 32, 2.66 GHz core 2 E6750
- 55.2s - optimized, not unrolled
- 26.4s - optimized, unrolled 10 times
CUDA
GeForce 8800 GTS 512 MB (G92) 1.625 GHz
- 2.07s - 128 blocks x 256 threads
BSGP
The Bulk-Synchronous GPU Programming compiler is advanced and is capable of impressive results but the documentation is severely lacking and the future of the compiler seems unclear.
GeForce 8800 GTS 512 MB (G92) 1.625 GHz
- 2.04s - 32768 threads
