Two real features of actualising Singularity

I think that it is important to note that the developments in computing mainly and in their effect on society and the world and the human worldview as it expands at exponential speed bringing new qualities to exist every 3 years as it is now is likely to go through a major breakthrough as machines that intelligently develop systems are created.
I was hopeful that Japan would develop an AI with the 5th gen Computer system, but the project had collapsed into a plethora of results that did not work together - because they did not have free open source systems thinking at the time.
The common notion is that this breakthrough would create a singularity - a straight line of growth for humans to go up. However there are other curves between the asymptotic curve and the exponential - multiple exponentials, x to x-th power,x to x to x, x to x-factorial that might fit the curve of growth without ever needing or being justified to go asymptotic.

Rather than turn into an asymptotic curve from exponential it would go through transformations or leaps from one Ackerman sequence member function to the next getting ever faster but not quite asymptotic and since it will tend to a limit there will be a limit to the rate of growth.

How reasonable quantifications for that event are formed?
Scenario A
as the machine that develops itself and new technologies that it requires takes over from human inventors it will have an exponential curve of growth that is separate from human developments and steeper.

Scenario B
Machine that autodevelops it will develop in addition to human developments so that over all growth is faster provided that there is tight cross-influence, there could be phenomenal development.

Scenario C
Machine would develop itself and enhance the methods of development, growing exponentially and also producing ever more copies of these , so having another exponential. Because this would be a product of two exponentials it appears now why it gets difficult to improve on that.

Scenario D
The development increase is significant enough to create change above linear in the acceleration of increase itself along with the development of the Machine.

The mostly likely actual outcome would be that each scenario actually comes to life at some point and carries on having its own beneficiaries and cultures.

Just so you don't have to do mental detective work unnecessarily: one is the nature of singularity not appearing as an asymptote (there is just no way for that to happen), the other is the stratification of different cultures using these different tech curves. The corollary to todays results is the nature of business determined development harnessing a minimal approach to a maximum profit gain.