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[[File:ParallelUniverseViews.jpg|thumb|A diagram of Parallel Universe movement in [[Hazy Maze Cave]], after [[Mario]] has returned to the main map.]]
[[File:ParallelUniverseViews.jpg|thumb|A diagram of Parallel Universe movement in [[Hazy Maze Cave]], after [[Mario]] has returned to the main map.]]
[[File:Visible PU.png|thumb|Frame of [[Peter Fedak|Peter Fedak's]] video where he uses a hack to turn Parallel Universes visible. Mario is in a PU; note the lack of [[objects]].]]
A '''Parallel Universe''', or '''PU''', is a region of space located far outside the intended map boundaries that reflects certain aspects, especially the floors and/or ceilings, of the main map. When the game looks for floors below (or ceilings above) a given object, it first "truncates" the object's position from a floating point value to a 16-bit integer value. The range of a floating point value is much larger than the range of a 16-bit integer value (which is -2<sup>15</sup> = -32,768 to 2<sup>15</sup> - 1 = 32,767). If a coordinate of the object's position falls outside this range, it "wraps around". For example, if one of these floating point values is 40,000, then 40,000 - 65,536 = -25,536 will be used when determining if the object is aligned with a floor or ceiling. This gives the illusion that the floors and ceilings of the main level map are "copied" repeatedly in a uniform 3D grid, at a spacing of 65,536 units.
A '''Parallel Universe''', or '''PU''', is an area in a map at which the game creates phantom collision for objects "outside" of the level. This is because some of the values for collision detection are truncated into the range of the real map's coordinate system, allowing some space that is intended to be [[Out of Bounds]] to become habitable.
[[File:Visible PU.png|thumb|184x184px|Frame of Peter Fedak's video where he turns Parallel Universes visible using hacks; notice the lack of [[objects]]|right]]
 
The truncation responsible for the existence of parallel universes is only performed when determining alignment with floors and ceilings. This means that walls and objects, both of which use floating point arithmetic to determine collision, do not "exist" in PUs, unless they are brought there.
The truncation responsible for the existence of parallel universes is only performed when determining alignment with floors and ceilings. This means that walls and objects, both of which use floating point arithmetic to determine collision, do not "exist" in PUs, unless they are brought there.


==Horizontal Parallel Universes==
Due to the extremely high speed required to travel to PUs, they are not accessible from all courses. The courses where PUs can or cannot be accessed are summarized in the tables below. Work is ongoing to try to access PUs in courses such as [[Bowser in the Fire Sea]] (via [[Bully battery]]) and demo courses (via massive [[Spawning displacement]]).
 
The collision glitch that causes horizontal PUs occurs because the casted position value used to check for [[floor]] below Mario (or an [[object]]) doesn't have enough bits to go above <math>\mathrm{7FFF}_{\mathrm{h}}</math> or below <math>\mathrm{-8000}_{\mathrm{h}}</math>, unlike Mario's actual position, which is a [[float]]. This is because the programmers did not anticipate Mario to stand faraway enough from the world origin to loop the collision check in standard gameplay, as that is intended to be Out of Bounds since no map is big enough; nor to be able to travel to such a faraway place, as that would require exorbitant amounts of speed beyond Mario's positive speed cap.
 
Any multiple of <math>2^{16}</math> in Mario's actual position values will be truncated off for the floor check. Therefore, if Mario tries to reach a position faraway from the real map that causes the floor check to roll over and still detect a floor from the real map, then that space is not considered Out of Bounds and he can travel there.


Where <math>|p| < 2^{16}</math> and <math>k</math> is any integer, being at position <math>p + 2^{16}k</math> along the X or Z axis is equivalent to being at position <math>p</math> for the floor check. Alternatively, being at position <math>q</math> is equivalent to being at position <math>q \bmod 2^{16}</math> for the floor check.
Methods to access a PU are:
*Speed:
**[[Backwards Long Jump#Elevator BLJ|EBLJ]]
**[[Hyperspeed Walking|HSW]]
**[[Hyperspeed Punching|HSP]]
**[[Bully battery|BB]]
**[[Speed conservation|Speed Conservation]]
* Displacement:
**Pole Teleport
**Platform Displacement


Ergo, in practice, there exists an infinite grid of imperfect copies of the main map, spread out by <math>2^{16}</math> intervals. Due to the nature of the glitch, horizontal Parallel Universes do not have anything except floors, so there are no duplicate walls, ceilings, or objects. However, certain objects can be sent to PUs.


== Vertical parallel universes ==
Note that EBLJ (and other types of BLJs), and BB (Bully battery) cannot be achieved on Shindou versions. Also, if a method requires to set [[HOLP]] in a PU, then it is only possible to do it on VC (because other versions crash if a camera is in the PU, and by locking camera on the main map, the HOLP wont update, because camera being too far is one of the cases where HOLP doesn't update).
{|
|+
!
{| class="wikitable"
|+
Main Course PU Access
!Course
!PU Access
!Access by versions
!0x A Access
!Method
|-
|[[Bob-omb Battlefield]]
|Yes
|Non-Shindou
| No
|EBLJ
|-
|[[Whomp's Fortress]]
|Yes<ref>[https://www.youtube.com/watch?v=y_gELy37HHc "Going to a vertical PU in WF" by Maria Nicolae]</ref>
|VC
|No
|Platform Displacement
|-
|[[Jolly Roger Bay]]
|Yes
|All Versions
|No
|HSW
|-
|[[Cool, Cool Mountain]]
|No
|
|No
|
|-
|[[Big Boo's Haunt]]
| Yes
|Non-Shindou
|No
|EBLJ
|-
|[[Hazy Maze Cave]]
|Yes
|All Versions
|Yes
|EBLJ, HSW
|-
|[[Lethal Lava Land]]
|Yes
|Non-Shindou
|Yes
|BB
|-
|[[Shifting Sand Land]]
|Yes
|All Versions
|Yes
|EBLJ, HSP
|-
|[[Dire, Dire Docks]]
|Yes
|Unsure if All Versions or only VC
|No
|Pole Teleport
|-
|[[Snowman's Land]]
|Yes
|All Versions
|No
|HSW
|-
|[[Wet-Dry World]]
| Yes
|All Versions
|Yes
|EBLJ, HSW
|-
|[[Tall, Tall Mountain]]
|No
|
|No
|
|-
|[[Tiny-Huge Island]]
|No
|
|No
|
|-
|[[Tick Tock Clock]]
|No
|
|No
|
|-
|[[Rainbow Ride]]
|Yes
|Non-Shindou
|No
|EBLJ
|}
!
{| class="wikitable"
|+
Special Course PU Access
!Course
!PU Access
!Access by versions
!0x A Access
!Method
|-
|[[Bowser in the Dark World]]
|No
|
|No
|
|-
|[[Bowser in the Fire Sea]]
|Yes
|Non-Shindou
|No
| EBLJ
|-
|[[Bowser in the Sky]]
|No
|
|No
|
|-
|[[The Princess's Secret Slide]]
|No
|
|No
|
|-
|[[Secret Aquarium]]
|No
|
|No
|
|-
|[[Tower of the Wing Cap]]
|No
|
|No
|
|-
|[[Cavern of the Metal Cap]]
|No
|
|No
|
|-
|[[Vanish Cap under the Moat]]
|Yes
|Non-Shindou
|No
|EBLJ
|-
|[[Wing Mario over the Rainbow]]
|No
|
|No
|
|-
|[[The Castle#Castle Grounds|Castle Grounds]]
|Yes
|All Versions
|Yes
|HSW, Speed Conservation
|-
|[[The Castle#First Floor|Castle Foyer]]
|Yes
|All Versions (for simply accessing), VC (to avoid crash)
|Yes
|Speed Conservation
|-
|[[The Castle#Basement|Castle Basement]]
|No
|
|No
|
|-
|[[The Castle#Second Floor|Castle Upstairs]]
|No
|
|No
|
|-
|[[The Castle#Courtyard|Castle Courtyard]]
| No
|
|No
|
|-
|}
|}
==Vertical Parallel Universes ==
Although usually the term "PU" refers to a horizontal PU (i.e. one caused by truncation of the ''x'' and/or ''z'' coordinates of an object's position), vertical PUs (where the ''y'' coordinate is truncated) also exist. However, these behave completely differently to horizontal PUs. While truncated coordinates are used to ''find'' the floor below the object and the ceiling above the object, the original floating point values are used to determine what ''effect'' these surfaces have on the object.


Though usually the term "PU" refers to a horizontal PU (i.e. one caused by truncation of the ''x'' and/or ''z'' coordinates of an object's position), vertical PUs (where the ''y'' coordinate is truncated) also exist. However, these behave completely differently to horizontal PUs. While truncated coordinates are used to ''find'' the floor below the object and the ceiling above the object, the original floating point values are used to determine what ''effect'' these surfaces have on the object.
For example, when Mario is less than 160 units below the nearest ceiling, he is considered to be "above" the ceiling, his vertical speed is killed, and he bonks. If Mario moves to a positive (upward) vertical PU, the "nearest" ceiling will be determined based on truncated coordinates, and will therefore be in the main map. But when checking whether he is above this ceiling, floating point coordinates are used instead, and so Mario behaves as though he is stuck in a ceiling. This behavior results in positive vertical PUs appearing to be filled entirely with ceilings.<ref>[https://www.youtube.com/watch?v=av42uJ-04A4 "Walls, Floors, and Ceilings in PUs" by Maria Nicolae]</ref>


For example, when Mario is less than 160 units below the nearest ceiling, he is considered to be "above" the ceiling, his vertical speed is killed, and he bonks. If Mario moves to a positive (upward) vertical PU, the "nearest" ceiling will be determined based on truncated coordinates, and will therefore be in the main map. But when checking whether he is above this ceiling, floating point coordinates are used instead, and so Mario behaves as though he is stuck in a ceiling. This behavior results in positive vertical PUs appearing to be filled entirely with ceilings.
On the other hand, when Mario is below his "nearest" floor, he will snap up to it. This means that if Mario moves to a negative vertical PU, he will usually upwarp back to the main PU grid. This is called an '''overflow jump''', or '''OJ''' for short.
 
On the other hand, when Mario is below his "nearest" floor, he will snap up to it. This means that if Mario moves to a negative vertical PU, he will, in certain circumstances, upwarp back to the main map. This is called an '''overflow jump'''.


It is typically difficult to get to a vertical PU. In the positive direction, there is a ceiling at ''y'' = 20,000 that prevents upward movement. We can bypass this ceiling by pressing against OoB, for example by using [[Hyperspeed Flying|hyperspeed flying]]. We can also use [[Platform Displacement|platform displacement]] or [[Indefinite Owl Flight|indefinite owl flight]] to reach a positive vertical PU.
It is typically difficult to get to a vertical PU. In the positive direction, there is a ceiling at ''y'' = 20,000 that prevents upward movement. We can bypass this ceiling by pressing against OoB, for example by using [[Hyperspeed Flying|hyperspeed flying]]. We can also use [[Platform Displacement|platform displacement]] or [[Indefinite Owl Flight|indefinite owl flight]] to reach a positive vertical PU.


In the negative direction, we can use a [[Negative Jump|negative jump]] to jump downward with large amounts of negative speed, or platform displacement.
In the negative direction, we can use a [[Negative Jump|negative jump]] to jump downward with large amounts of negative speed, or platform displacement.
==Travel and movement==
==Travel and movement==
[[File:Mario looking from a PU.png|thumb|251x251px|Mario looking to the original map from a PU]]
[[File:Mario looking from a PU.png|thumb|251x251px|Mario looking to the original map from a PU]]
[[File:PUBLJ.gif|thumb|Mario [[BLJ]]ing to a PU]]
Parallel universes have found uses in both speed TASes and the [[A Button Challenge]] since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modeled as traveling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. These PU axis integers are Mario's coordinates on the PU grid. Mario can adjust his [[speed]] and [[angle]] to move relatively around the stage regardless of how many PUs he moves in the ''x'' or ''z'' dimensions.


Parallel universes have found uses in both speed TASes and the [[A Button Challenge]] since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modelled as travelling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. Mario can adjust his [[speed]] and [[angle]] to move relatively around the stage regardless of how many PUs he moves in the ''x'' or ''z'' dimensions.
{{Anchor|QPU}}
 
Mario's movement is split up into four [[Movement Steps|quarter steps]], and if any of these quarter steps attempts to place Mario out of bounds, his movement is canceled. Therefore in order to move to a PU, Mario's speed must be a multiple of four times the distance between PUs. If Mario takes all four quarter steps, then he will move four PUs in a single frame. This distance is called the '''Quadruple Parallel Universe''', or '''QPU''', distance.
Since Mario's movement is split up into 4 quarter steps, and Mario cannot move [[Out of Bounds]], Mario must travel at least a '''Quadruple Parallel Universe''' distance in 1 frame, '''QPU''' for short. The QPU distance is <math>2^{16} \times 4 = 2^{18}</math> [[unit]]s. However, if one of Mario's quarter steps (other than the first one) ends Out of Bounds, the game will cut his movement short. In this case, Mario does not travel a full 4 PU, instead ending up at some quarter-step between the QPUs, depending on where the movement is cut off. This is referred to as a '''QPU misalignment'''.
 
As travelling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant affect on Mario's position, angle, and collision.
 
===Object behavior===
Spawning a [[100 Coin Star]] in a PU will softlock the game.
 
[[Koopa the Quick]] can be sent to a PU by strategically using bowling ball [[clone]]s to force him to accelerate backwards into OoB until his speed syncs with a PU. However, going to a PU moves him away from the bowling ball clones, so he will slowly lose speed with every jump. Koopa the Quick's behavior with normal positive speed in a PU is not currently known.
 
[[Bob-omb]]s and Crazy Boxes can be brought to PUs, and appear to function normally. Naturally, they also update the [[HOLP]] to the PU location.
 
==Vertical Parallel Universes==
A '''Vertical Parallel Universe''', or '''VPU''', is a vertical extension of the PU phenomenon. Objects behave differently depending on what checks they use for collision. While it could be assumed that VPUs are a wall collision glitch, Mario's real position is used for the wall check, so he cannot experience duplicate walls at all in PUs. In addition, floor and ceiling collision may extend vertically into VPUs, causing some objects to experience their hitboxes.
 
Since Mario's Y position cannot exceed 20,000 (the default ceiling detection value) in most circumstances, there are only two ways to reach a positive vertical PU: Hyper Speed Flying, and Platform Release Displacement. Negative vertical PUs can be reached with those methods or the Overflow Jump.
 
In positive VPUs (above the real map), Mario is (correctly) detected as being too high above real map floors to stand on PU duplicates, so he falls through. He is also detected as being high above [[ceiling]]s, thereby putting him in their hitboxes and constricting his movement. The game also uses Mario's real position to check for walls, so he can't experience any duplicate walls in VPUs. Therefore, positive VPUs are entirely ceiling.
 
In negative VPUs (below the real map), Mario is detected as being below real map floors, so he is snapped up onto the horizontal PU grid upon a floor collision. He is also detected as being far below ceilings, so ceilings have no effect. Again, the game also uses Mario's real position to check for walls, so he can't experience duplicate walls in VPUs. Therefore, negative VPUs are entirely floor.


===Object behavior===
If one of Mario's quarter steps (other than the first one) ends out of bounds, the game will cut his movement short. In this case, Mario does not travel the full QPU distance, and instead ends at whichever PU he made it to before his intended quarter step became out of bounds. He is then "QPU misaligned."
[[Scuttlebug]]s can be raised through VPUs. In a VPU, they are considered Out of Bounds, so they can't move laterally. Much like Mario with negative VPU floors, a Scuttlebug will snap to a main map wall if it interacts with a VPU duplicate.


== Floating point truncation crash ==
As traveling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant effect on Mario's position, angle, and collision. When Mario's position becomes large enough, this imprecision will result in the coordinates in PUs becoming so coarse that Mario cannot cross from one coordinate to the next and, eventually, will result in certain PUs being completely unaccessible.


While in theory the grid of PUs extends indefinitely, the behavior of the truncation operation becomes "undefined" when the floating point value is outside the range -2<sup>31</sup> to 2<sup>31</sup> - 1. The Nintendo 64 versions of the game crash when such a truncation is attempted. The Wii and Wii U virtual console versions of the game do not crash, though it is not currently known whether they wrap around the 32-bit integer range, or cap to the endpoints of the range. Nothing is currently known about iQue version's behavior in this case, since the usual RTA-viable methods of triggering this crash ([[BLJ]] and getting a bully stuck out of bounds) were patched in this version. Most emulators do not properly emulate the crash, except for a specific version of Mupen64, modded to crash correctly.
==Floating point truncation crash==
While in theory the grid of PUs extends indefinitely, the behavior of the truncation operation becomes "undefined" when the floating point value is outside the range -2<sup>31</sup> to 2<sup>31</sup> - 1. The Nintendo 64 and [[iQue]] Player<ref>[https://youtu.be/_dAGdYd9KUY "Do Parallel Universes Crash on iQue?" by CadBrad]</ref> versions of the game crash when such a truncation is attempted. The Wii and Wii U virtual console versions of the game do not crash, though it is not currently known whether they wrap around the 32-bit integer range, or cap to the endpoints of the range. Most emulators do not properly emulate the crash, except for a specific version of Mupen64, modded to crash correctly.


While movement to PUs at coordinates this large is rarely useful, this crash can occur due to other instances of truncation in the game, even in PUs close to the main map. For example, when determining Mario's tilt while walking, the game multiples Mario's speed by 16,384 and then truncates this value. This means that the game can crash in certain conditions when Mario has a speed of about 131,000, which is below QPU speed.
While movement to PUs at coordinates this large is rarely useful, this crash can occur due to other instances of truncation in the game, even in PUs close to the main map. For example, when determining Mario's tilt while walking, the game multiples Mario's speed by 16,384 and then truncates this value. This means that the game can crash in certain conditions when Mario has a speed of about 131,000, which is below QPU speed.


While not all conditions for these types of crashes are known, there are some that come up frequently. These are when:
While not all conditions for these types of crashes are known, there are some that come up frequently. These are when:
* The camera enters a PU
*The camera enters a PU
* Mario bonks while in a PU
*Mario bonks while in a PU
* Mario's quarter step gets cancelled while on the ground
*Mario's quarter step gets canceled while on the ground
* Mario collides with a wall head-on with PU speed
*Mario collides with a wall head-on with PU speed
==Miscellaneous behavior==
Certain objects and graphics behave interestingly while in parallel universes. For example:
*Shadows and coin twinkle effects are glitchy
*TODO: Add more
==References==
<references />
[[Category:Glitches]]
{{Glitches}}

Latest revision as of 07:21, 18 June 2024

A diagram of Parallel Universe movement in Hazy Maze Cave, after Mario has returned to the main map.

A Parallel Universe, or PU, is a region of space located far outside the intended map boundaries that reflects certain aspects, especially the floors and/or ceilings, of the main map. When the game looks for floors below (or ceilings above) a given object, it first "truncates" the object's position from a floating point value to a 16-bit integer value. The range of a floating point value is much larger than the range of a 16-bit integer value (which is -215 = -32,768 to 215 - 1 = 32,767). If a coordinate of the object's position falls outside this range, it "wraps around". For example, if one of these floating point values is 40,000, then 40,000 - 65,536 = -25,536 will be used when determining if the object is aligned with a floor or ceiling. This gives the illusion that the floors and ceilings of the main level map are "copied" repeatedly in a uniform 3D grid, at a spacing of 65,536 units.

Frame of Peter Fedak's video where he turns Parallel Universes visible using hacks; notice the lack of objects

The truncation responsible for the existence of parallel universes is only performed when determining alignment with floors and ceilings. This means that walls and objects, both of which use floating point arithmetic to determine collision, do not "exist" in PUs, unless they are brought there.

Due to the extremely high speed required to travel to PUs, they are not accessible from all courses. The courses where PUs can or cannot be accessed are summarized in the tables below. Work is ongoing to try to access PUs in courses such as Bowser in the Fire Sea (via Bully battery) and demo courses (via massive Spawning displacement).

Methods to access a PU are:


Note that EBLJ (and other types of BLJs), and BB (Bully battery) cannot be achieved on Shindou versions. Also, if a method requires to set HOLP in a PU, then it is only possible to do it on VC (because other versions crash if a camera is in the PU, and by locking camera on the main map, the HOLP wont update, because camera being too far is one of the cases where HOLP doesn't update).

Main Course PU Access
Course PU Access Access by versions 0x A Access Method
Bob-omb Battlefield Yes Non-Shindou No EBLJ
Whomp's Fortress Yes[1] VC No Platform Displacement
Jolly Roger Bay Yes All Versions No HSW
Cool, Cool Mountain No No
Big Boo's Haunt Yes Non-Shindou No EBLJ
Hazy Maze Cave Yes All Versions Yes EBLJ, HSW
Lethal Lava Land Yes Non-Shindou Yes BB
Shifting Sand Land Yes All Versions Yes EBLJ, HSP
Dire, Dire Docks Yes Unsure if All Versions or only VC No Pole Teleport
Snowman's Land Yes All Versions No HSW
Wet-Dry World Yes All Versions Yes EBLJ, HSW
Tall, Tall Mountain No No
Tiny-Huge Island No No
Tick Tock Clock No No
Rainbow Ride Yes Non-Shindou No EBLJ
Special Course PU Access
Course PU Access Access by versions 0x A Access Method
Bowser in the Dark World No No
Bowser in the Fire Sea Yes Non-Shindou No EBLJ
Bowser in the Sky No No
The Princess's Secret Slide No No
Secret Aquarium No No
Tower of the Wing Cap No No
Cavern of the Metal Cap No No
Vanish Cap under the Moat Yes Non-Shindou No EBLJ
Wing Mario over the Rainbow No No
Castle Grounds Yes All Versions Yes HSW, Speed Conservation
Castle Foyer Yes All Versions (for simply accessing), VC (to avoid crash) Yes Speed Conservation
Castle Basement No No
Castle Upstairs No No
Castle Courtyard No No

Vertical Parallel Universes

Although usually the term "PU" refers to a horizontal PU (i.e. one caused by truncation of the x and/or z coordinates of an object's position), vertical PUs (where the y coordinate is truncated) also exist. However, these behave completely differently to horizontal PUs. While truncated coordinates are used to find the floor below the object and the ceiling above the object, the original floating point values are used to determine what effect these surfaces have on the object.

For example, when Mario is less than 160 units below the nearest ceiling, he is considered to be "above" the ceiling, his vertical speed is killed, and he bonks. If Mario moves to a positive (upward) vertical PU, the "nearest" ceiling will be determined based on truncated coordinates, and will therefore be in the main map. But when checking whether he is above this ceiling, floating point coordinates are used instead, and so Mario behaves as though he is stuck in a ceiling. This behavior results in positive vertical PUs appearing to be filled entirely with ceilings.[2]

On the other hand, when Mario is below his "nearest" floor, he will snap up to it. This means that if Mario moves to a negative vertical PU, he will usually upwarp back to the main PU grid. This is called an overflow jump, or OJ for short.

It is typically difficult to get to a vertical PU. In the positive direction, there is a ceiling at y = 20,000 that prevents upward movement. We can bypass this ceiling by pressing against OoB, for example by using hyperspeed flying. We can also use platform displacement or indefinite owl flight to reach a positive vertical PU.

In the negative direction, we can use a negative jump to jump downward with large amounts of negative speed, or platform displacement.

Travel and movement

Mario looking to the original map from a PU
Mario BLJing to a PU

Parallel universes have found uses in both speed TASes and the A Button Challenge since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modeled as traveling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. These PU axis integers are Mario's coordinates on the PU grid. Mario can adjust his speed and angle to move relatively around the stage regardless of how many PUs he moves in the x or z dimensions.

Mario's movement is split up into four quarter steps, and if any of these quarter steps attempts to place Mario out of bounds, his movement is canceled. Therefore in order to move to a PU, Mario's speed must be a multiple of four times the distance between PUs. If Mario takes all four quarter steps, then he will move four PUs in a single frame. This distance is called the Quadruple Parallel Universe, or QPU, distance.

If one of Mario's quarter steps (other than the first one) ends out of bounds, the game will cut his movement short. In this case, Mario does not travel the full QPU distance, and instead ends at whichever PU he made it to before his intended quarter step became out of bounds. He is then "QPU misaligned."

As traveling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant effect on Mario's position, angle, and collision. When Mario's position becomes large enough, this imprecision will result in the coordinates in PUs becoming so coarse that Mario cannot cross from one coordinate to the next and, eventually, will result in certain PUs being completely unaccessible.

Floating point truncation crash

While in theory the grid of PUs extends indefinitely, the behavior of the truncation operation becomes "undefined" when the floating point value is outside the range -231 to 231 - 1. The Nintendo 64 and iQue Player[3] versions of the game crash when such a truncation is attempted. The Wii and Wii U virtual console versions of the game do not crash, though it is not currently known whether they wrap around the 32-bit integer range, or cap to the endpoints of the range. Most emulators do not properly emulate the crash, except for a specific version of Mupen64, modded to crash correctly.

While movement to PUs at coordinates this large is rarely useful, this crash can occur due to other instances of truncation in the game, even in PUs close to the main map. For example, when determining Mario's tilt while walking, the game multiples Mario's speed by 16,384 and then truncates this value. This means that the game can crash in certain conditions when Mario has a speed of about 131,000, which is below QPU speed.

While not all conditions for these types of crashes are known, there are some that come up frequently. These are when:

  • The camera enters a PU
  • Mario bonks while in a PU
  • Mario's quarter step gets canceled while on the ground
  • Mario collides with a wall head-on with PU speed

Miscellaneous behavior

Certain objects and graphics behave interestingly while in parallel universes. For example:

  • Shadows and coin twinkle effects are glitchy
  • TODO: Add more

References