Btw what that mathematician was saying about integers I think is this.
Each loop you calculate a new value for i. This is an integer. For any floating point number and list size, this will produce a specific list of integral values for i. If you recorded this list, you could use it instead of calculating i with a floating point value.
Given though that with this method, the list of integers used for i changes with the list size, the mathematician was probably wrong when he said you could do the same thing with a list of integers, because there is no one set of integers that would fit any list for any particular divisor.
Now, I dunno if that affects the outcome or not... but if given a specific list of a specific size then you should be able to use a list of integers to get the same result.
Anyhow I don't understand why this is going faster than dividing by 2. But I suspect you are mistaken about this:
"Most people seem to use 2 or some sequence based on powers of 2 where 1.6 occurs below."
It says here:
http://linux.wku.edu/~lamonml/algor/sort/shell.html
That two guys came up with a list of integers to use that would be faster than the basic algorithm. So maybe 2 is actually an exceptionally poor value to use?
Each loop you calculate a new value for i. This is an integer. For any floating point number and list size, this will produce a specific list of integral values for i. If you recorded this list, you could use it instead of calculating i with a floating point value.
Given though that with this method, the list of integers used for i changes with the list size, the mathematician was probably wrong when he said you could do the same thing with a list of integers, because there is no one set of integers that would fit any list for any particular divisor.
Now, I dunno if that affects the outcome or not... but if given a specific list of a specific size then you should be able to use a list of integers to get the same result.
Anyhow I don't understand why this is going faster than dividing by 2. But I suspect you are mistaken about this:
"Most people seem to use 2 or some sequence based on powers of 2 where 1.6 occurs below."
It says here:
http://linux.wku.edu/~lamonml/algor/sort/shell.html
That two guys came up with a list of integers to use that would be faster than the basic algorithm. So maybe 2 is actually an exceptionally poor value to use?