Tests modified collatz conjectures (including the original).
Make sure you have gcc.
Now, clone this repo with:
git clone https://github.com/ChemicalDevelopment/CollatzL.git
change to that directory:
cd CollatzL
compile and test the code:
make
There should be no errors.
If not, please open up an issue.
This program is used to verify, or counter Collatz-like problems (include original Collatz).
The original collatz conjecture is:
define f(x):
if x is even, f(x) = x / 2
if x is odd, f(x) = 3x+1
And the question is: Does iteration of f(x) f(f(f(...(x))))) eventually reach a cycle, or keep expanding?
We don't know, but all numbers <= 4*10^18 do reach a cycle.
An example of a collatz like function would be:
define f(x):
if x is 0 mod 3, f(x) = x / 3
if x is 1 mod 3, f(x) = 2 * x + 1
if x is 2 mod 3, f(x) = 5 * x + 4
And again, the question is: Does iteration of f(x) eventually reach a cycle?
To test the original collatz conjecture, run
./collatzl_c.o $MIN $RANGE $MAX_TRIALS 2 1 0 2 3 1 1
It starts at MIN, and runs RANGE numbers each at a max of MAX_TRIALS
The 2 after that tells us we take the number mod 2 (even or odd), and the 1 0 2 tells us to multiply by 1, add 0, and divide by 2
the 3 1 1 tells us to multiply by 3, add 1, and divide by 1, if it is 1 mod 2
./collatzl_c.o 0 1000 1000 2 1 0 2 3 1 1 runs quite quickly, and verifies they all work
To test our other example, the command would be:
./collatzl_c.o 0 1000 1000 3 1 0 3 2 1 1 5 4 1
There is also a version for GMP, which you can build and test with:
make gmp
The interface is the same as the normal, but the executable is collatzl_gmp.o instead of collatzl_c.o
To run the default command, use:
./collatzl_gmp.o 0 1000 1000 2 1 0 2 3 1 1
And our example would be:
./collatzl_gmp.o 0 1000 1000 3 1 0 3 2 1 1 5 4 1