For (fixed width) add1 & reverse, most of the graph should consist of long strings. Imagine the number split into left & right halves. The left half propagates carries backwards, to the right; and the add1 is done on the leftmost bit. The add1 step counts in the two halves independently, until a carry propagates across the middle. Then it gets interesting. Odd & even lengths may have different behaviors, since the odd lengths have a center bit shared between the two halves. [hidden corollary: L=1 :-)] Rich ------ Quoting Warren D Smith <warren.wds@gmail.com>:
On 9/29/15, Warren D Smith <warren.wds@gmail.com> wrote:
Actually, I'd suggest tabulating C so that the "Add C and reverse" operation yields large period mod 2^m (C likely will depend upon m)
That way you'd get useful random number generator components, at least on future machines featuring a fast reverse operation.
--especially useful: large PRIME periods.
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