Difference between revisions of "Different implementations of a simple Collatz iterator and their performance"

Revision as of 23:00, 2 January 2009

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.

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

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.

Vista 64, 2.4 GHz core 2 Q6600

• 55.4s - .net exe, one thread

Vista 32, 2.66 GHz core 2 E6750

• 66.4 - .net exe, one thread
• -- .net exe, two threads

x86 assembly language

CUDA

GeForce 1.625 GHz GTS 512

• 2.3s - 128 blocks x 256 threads

BSGP

Conclusion

External links

• http://mathworld.wolfram.com/CollatzProblem.html
• http://en.wikipedia.org/wiki/Collatz_conjecture
• http://members.chello.nl/k.ijntema/