knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
After following the "Getting Started" instructions (which can also be seen in the README) to download and or install the package, it can be imported with;
library(collatz) # Optionally library(gmp)
You can jump right into using the functions in this package with integer inputs, or you can use bigz
from the gmp
library.
Each function, amongst possible other parameters, comes with the default parameters (P=2,a=3,b=1)
as optional inputs.
In each case, P[=2]
is the modulus to check for divisibility of the input by, a[=3]
is the factor to multiply the input by,
and b[=1]
is the value to add to the product of a[=3]
and the input.
There are two basic commands to start with; the collatz_function
and the reverse_function
.
Returns the output of a single application of a Collatz-esque function.
Without gmp
or parameterisation, we can try something simple like
collatz_function(5) collatz_function(16)
If we want change the default parameterisation we can;
collatz_function(4, 5, 2, 3)
Or if we only want to change one of them
collatz_function(3, a=-2)
All the above work fine, but the function doesn't offer protection against overflowing integers by default.
To venture into the world of arbitrary integer inputs we can use an as.bigz
from gmp
. Compare the two;
collatz_function(99999999999999999999) collatz_function(as.bigz("99999999999999999999"))
Calculates the values that would return the input under the Collatz function.
Without gmp
or parameterisation, we can try something simple like
reverse_function(1) reverse_function(2) reverse_function(4)
If we want change the default parameterisation we can;
reverse_function(3, -3, -2, -5)
Or if we only want to change one of them
reverse_function(16, a=5)
All the above work fine, but the function doesn't offer protection against overflowing integers by default.
To venture into the world of arbitrary integer inputs we can use an as.bigz
from gmp
. Compare the two;
reverse_function(99999999999999999999) reverse_function(as.bigz("99999999999999999999"))
Calculates the "stopping time", or optionally the "total" stopping time.
Without gmp
or parameterisation, we can try something simple like
stopping_time(27) stopping_time(27, total_stopping_time=TRUE)
If we want change the default parameterisation we can;
stopping_time(3, 5, 2, 1)
Or if we only want to change one of them
stopping_time(17, a=5)
All the above work fine, but the function doesn't offer protection against overflowing integers by default.
To venture into the world of arbitrary integer inputs we can use an as.bigz
from gmp
. Compare the two;
stopping_time(99999999999999999999) stopping_time(as.bigz("99999999999999999999"))
As an extra note, the original motivation for creating a range of Collatz themed packages came from some earlier
scripts for calculating the stopping distances under certain parameterisations. An inconsequential result of which
was observing that all of the following, for however high k
goes, should equal 96
!
stopping_time(27) stopping_time(27+as.bigz("576460752303423488")) stopping_time(27+(2*as.bigz("576460752303423488"))) stopping_time(27+(3*as.bigz("576460752303423488"))) stopping_time(27+(4*as.bigz("576460752303423488")))
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