Backwards Long Jump

The Backwards Long Jump hyperspeed method, or BLJ for short, is the most famous hyperspeed method in Super Mario 64. Due to their versatility, BLJs are commonly used in all kinds of speedruns and challenges.

When Mario initiates a long jump, his horizontal speed is multiplied by 3/2. A BLJ occurs when a backwards long jump is interrupted before the effects of drag can counteract the speed gain from the 3/2 multiplier. This does not occur with forwards long jumps because long jumps have a "hard cap" of +48 horizontal speed which Mario's speed cannot exceed. No such cap exists in the negative direction because normally the "soft cap" of -16 speed from drag is easily enough to stop any speed gain.

There are several different types of BLJs. The distinguishing feature of different types of BLJs is what they use to interrupt the long jump:

Slope BLJs use slopes by going up the slope.
Stair BLJs use stairs by going up the stairs.
Elevator BLJs use the upwards movement of an elevator or other object.
Side BLJs use two floors at slightly different levels by oscillating between them.
Ceiling BLJs use an exposed ceiling or low-hanging ceiling by making Mario hit his head and start travelling downwards faster.

BLJs can also be pause buffered to increase the amount of long jumps that can be performed in a given amount of time or space.

The BLJ glitch was patched in the Shindou release, and therefore also the iQue version. This also means that any emulator releases of these game versions lack the BLJ glitch, namely the Japanese Wii VC release, the Japanese Wii U VC release, and all versions of Super Mario 3D All-Stars.

Slope BLJ

A slope BLJ is performed by interrupting a backwards long jump using a rising slope. Because Mario usually lands immediately after long jumping (assuming a steep enough slope), slope BLJs are normally pause bufferable.

Stair BLJ

A stair BLJ is similar to a slope BLJ, except using stairs instead of slopes to achieve the rising floor effect. Stair BLJs often cannot be performed when there are wall hitboxes sticking out from the stairs because the walls prevent Mario from landing on the higher floor. Similarly to slope BLJs, stair BLJs are often pause bufferable.

Stair BLJs are often used for bypassing doors in the castle, such as in the Lobby Backwards Long Jump.

Elevator BLJ

Elevator BLJs are also conceptually similar to slope BLJs and stair BLJs in that they too use the floor under Mario rising to interrupt Mario's long jump. Elevator BLJs use elevators as the rising floor. Elevator BLJs are a common solution for when one wishes to quickly get a lot of speed since while slope BLJs and stair BLJs can only last until the slope or stair runs out or Mario hits out-of-bounds, elevator BLJs can last as long as the elevator is moving and don't need to stop when Mario hits out-of-bounds.

Side BLJ

Side BLJs or SBLJs are the most complex type of BLJ. A side BLJ is performed by oscillating between two floors at slightly different heights to achieve an effect similar to a stair BLJ but without needing a long, wall-less staircase. Side BLJs are performed by first having Mario face slightly to the higher floor (so that when Mario's moving backwards, he moves down to the lower floor), then straining to the higher floor during the long jump so that Mario snaps up to it. After long jumping from the lower floor, Mario ends up on the higher floor due to the straining, but because of the direction Mario is facing he snaps down to the lower floor on the next frame. This can then be repeated.

Because side BLJs require 1 extra frame per long jump for Mario to snap back down to the lower floor, they cannot be pause buffered.

Ceiling BLJ

A ceiling BLJ is performed by having Mario hit a ceiling during his long jumps so that Mario starts moving downwards earlier, meaning there's less time for drag to slow Mario down. Ceiling BLJs can be performed with low ceilings or with exposed ceilings.