This can save 1 frame, sometimes 2 frames over accelerating normally on the ground.
This is the same theory as standard fast accel, but in the opposite direction.
This is done in the turnaround room of 8-4 to save 5 frames over standard turnaround movement. If you stop within the first few pixels that'll work for the turnaround, the inputs will be different in order to avoid bonking on the pipe.
Falling Fast Accel refers to a a very quick wiggle that allows Mario to accelerate to top speed faster by falling in the opposite direction off of a pipe.
This is typically done to save an extra frame over perfect fast accel in the wall jump and final room of 8-4.
There are various inputs that will allow a runner to save those 2 frames with FFA, please refer to the GIFs with input display to see all humanly viable inputs.
0/8 FFA is the fastest in regards to how quickly you accelerate to top speed, however in a lot of scenarios it is undesirable because of the subpixels string it puts you on.
The fastest method of accelerating to top speed. After reaching running you want to instantly turn around to the left for one frame and then back to right the next frame, while starting to jump.
This can save 2 frames, sometimes 3 frames over accelerating normally on the ground.
In most circumstances, D/5 TAS accel is the most desirable, however in rare cicumstances where you are required to be in a different subpixel string than D/5 TAS accel's, E/6 may be better suited.