Gohei Duplication

Specifications

• Versions: 1.00a - 1.00b
• Difficulty: Easy - Normal - Hard - Lunatic - Extra
• Mode: Main game - Practice mode - Spell practice
• Shottype: ReimuA - ReimuB - MarisaA - MarisaB - SakuyaA - SakuyaB

What happens

ReimuA can have multiple goheis on screen. All goheis are able to deal damage. Because of this, it is possible to speedkill by using multiple goheis. The goheis stay active as long as you keep shooting, meaning you cannot carry them over to other stages. This also means you cannot maintain multiple goheis during dialogue, because you stop shooting.

How it happens

Note: this section is technical. If you want to learn a human set-up on how to do it, you can do so by clicking here.

There are two ways for a gohei to despawn:

• The player stops shooting (whether it's through unfocussing or not holding Z)
• The gohei goes off-screen

In order duplicate one gohei, the following procedure must be done:

1. Have your first gohei (gohei 1) on-screen
2. Stop shooting such that gohei 1 is in its despawning animation
3. While the gohei 1 is despawning, spawn your second gohei (gohei 2)
4. Before gohei 1 finishes its despawning animation, let gohei 1 despawn by going off-screen.
5. On the next frame, spawn the third gohei (gohei 3)
6. You are now left with 2 goheis (gohei 2 and gohei 3)

Note that step 5 may not work due to a complicated factor that is described in the next section. This complicated factor is not related to randomness but is deterministic.

This process can be done concurrently, meaning it is possible to spawn more than two goheis at once.

This set-up is most commonly done at the top of the screen due to step 4 being hard to execute if the gohei were to go off-screen elsewhere, even though it is possible.

Why it happens

Before we dive deeper into the cause of the gohei duplication glitch, we must first talk about the mechanics of the gohei. The topics discussed are as follows:

• Gohei dimensions
• Gohei target distances
• Gohei velocity
• Gohei despawn timer
• Gohei flag
• Shot cycle
• Player bullet slots

Each of these topics are relevant to the gohei dupe. After each of these topics have been discussed, two examples are provided along with an explanation.

Gohei dimensions

The gohei has varying dimensions depending on the player's power level.

Gohei target distance

The gohei targets enemies differently based on when it was shot and how far away it is from the nearest enemy.

During the first 10 frames of spawning, if there is an enemy within 160 units of the spawn radius, the gohei targets the enemy and instantly locks onto the enemy.
After the first 10 frames, if there is an enemy within 320 units of its radius, the gohei targets the enemy but does not instantly lock onto the enemy.

Gohei velocity

The gohei starts of with an initial upwards velocity of 14.4 units per frame. Assuming that the gohei does not target an enemy, and that the player is shooting focussed, this speed value is multiplied by 0.9 on every frame. If the player is not shooting focussed, the speed value is no longer multiplied by 0.9 thus the speed remains constant.

Gohei despawn timer

The gohei enters its despawning animation under one of two conditions:

1. The gohei does not have a target, and the player is not focussed and is not shooting.
2. The gohei does have a target, and the player is not focussed and is not shooting for more than 12 consecutive frames.

Once the gohei enters its despawning animation, the gohei has 10 frames before it is fully despawned.

The limit of 12 and 10 frames are hardcoded in the game.

Gohei flag

To understand why multiple goheis can coexist, we must understand the flag goheiExists. goheiExists is a boolean that determines if a gohei exists on-screen or not. (Note: if you look for this value in the game's memory, it is actually not a flag, but an integer representing the power level. However, in the context of this page it is more comprehensible to represent goheiExists as a boolean.)

The following actions set goheiExists to true:

1. Having an active gohei on-screen (done every frame by every gohei)

The following actions set goheiExists to false:

1. Having a gohei go off-screen (done once)
2. Putting the gohei into the despawning animation. (done once)

The following actions do not change the state of goheiExists:

1. Having no goheis on-screen
2. Having a gohei that is already in its despawning animation.

A gohei is considered to be off-screen if its full sprite is off-screen.

Shot cycle

The shoot timer is a number between -1 and 14. This number is set to -1 by default.

• If the number is -1 and the player presses Z on the next frame, the number increments by 1 every frame until the number is 14.
• If the number is 14 and the player presses Z on the next frame, the number is set back to 0 and increases by 1 every frame until the number is 14.
• If the number is 14 and the player does not press Z on the next frame, the shoot timer is set to -1 and the player stops shooting.
• If the number is between 0 and 13, the shoot timer continues to increment regardless if the player presses Z or not. This means that the player keeps shooting bullets.

In the context of this webpage, if the number is between 0 and 14 it means that the player is shooting. If the number is -1 the player is not shooting.

If the flag goheiExists is false, and the number is a multiple of 3 (0, 3, 6, 9, 12), then the game spawns a gohei on the subsequent frame. This behaviour is coded in the file pl00a.sht, which is where most of the shottype data of ReimuA is stored.

Player bullet slots

The free player bullet list is a stack of size 256 whose elements are slots (IDs) for your player shots. The list starts from 255 and ends with 0 (so [255, 254, …, 0]). The order in which the bullets occupy a slot is manually decided in the pl00a.sht file.

For example, if you are shooting focussed for a frame, the following takes place in your sht:

1. Left amulet takes up the first slot (slot 255)
2. Right amulet takes up the second slot (slot 254)
3. Gohei takes up the third slot (slot 253)

The free player bullet list would look as follows: [252, 251, …, 0].

The taken slots are freed up when the object is destroyed (e.g. by going off-screen, by hitting an enemy). Once a slot is freed up, the slot is pushed back in the order of despawning. This follows the Last In First Out (LIFO) principle, meaning the most recently added slot is the first to be accessed.

To continue the previous example, suppose the left amulet, the gohei, and the right amulet despawn in that order. The free player bullet list would be as follows: [254, 253, 255, 252, 251, …, 0].

Note that the gohei takes up a slot until it has fully despawned: if the gohei is in its despawning animation, its respective slot is still taken.

To understand why the player bullet list is relevant to the gohei dupe, we must understand how the flag goheiExists is set when there are multiple goheis on-screen.

In one frame, the following events are executed in order:

1. If on the correct shot cycle, game spawns left amulet, right amulet
2. If on the correct shot cycle, game spawns a gohei if the value of flag goheiExists is false
3. Game runs through every gohei in active player bullet list in ascending order of bullet slot
4. For every gohei, the flag goheiExists changes depending on the current gohei's action

Step 3 tells that the order in which the goheis are processed depends on their position in the player bullet list. To have goheiExists be set to false for a frame, the gohei taking up the highest bullet slot must set goheiExists to false.

Explanation

Below two explanations of gohei duplications are provided: The first explanation explains what happens during a double gohei, and the second explanation explains what happens during a quintuple gohei.

2-gohei explanation

The following steps are performed sequentially:

1. Spawn Gohei 1 (GH1)
2. Put GH1 in its despawning animation
3. Spawn Gohei 2 (GH2)
4. Let GH1 despawn by going off-screen
5. Spawn Gohei 3 (GH3)

The player is left with two goheis: GH2 and GH3.

The full explanation goes as follows:

1. We spawn GH1, preferably at the top of the screen. goheiExists is set to true. We want to make sure that GH1 despawns by going off-screen on a frame that aligns with the shot cycle. Since in this case we spawn GH1 at the top of the screen, there are three concepts to take into account: the player's y-coordinate, the speed of the gohei (which depends on when Shift is released), and the size of the gohei.
2. We put GH1 in its despawning animation, which we can only do if the gohei does not have a target. In this case, we can easily achieve this by unholding Shift for one frame. goheiExists is set to false.
3. Because goheiExists is false, GH2 can be spawned. goheiExists is set to true.
4. GH1 must despawn on a frame on which the shot cycle is divisible by 3. Additionally, GH1 must occupy a bullet slot higher than what GH2 has. goheiExists is set to false.
5. Because goheiExists is false, GH2 can be spawned. goheiExists is set to true.

Note that we do not necessarily have to do the gohei duplication at the top of the screen: GH1 is able to go off-screen through the side or the bottom of the screen, though it is easier to manipulate the gohei going off-screen through the top. Additionally, to put the gohei into the despawning animation the player could stop shooting by either releasing the Shift or the Z key, although the latter is much harder to perform.

5-gohei explanation

This section explains a gohei dupe that generates 5 goheis. This dupe is a TAS (Tool Assisted Speedrun) performed by Nylilsa using a custom stage. This custom stage does not modify the shottype ReimuA.

The following steps are performed sequentially:

1. Spawn Gohei 1 (GH1)
2. Put GH1 in its despawning animation

Steps 1-13 of this section are similar to the steps taken of the previous section, but in this case we repeat the steps multiple times. We do this to get multiple despawning goheis that are going off-screen.

3. Spawn Gohei 2 (GH2)
4. Put GH2 in its despawning animation
5. Spawn Gohei 3 (GH3)
6. Put GH3 in its despawning animation
7. Spawn Gohei 4 (GH4)
8. Let GH1 despawn by going off-screen
9. Spawn Gohei 5 (GH5)
10. Let GH2 despawn by going off-screen
11. Spawn Gohei 6 (GH6)
12. Let GH3 despawn by going off-screen
13. Spawn Gohei 7 (GH7)
14. Put GH6 despawn in its despawning animation (gohei GH6 was chosen arbitrarily)
15. Spawn Gohei 8 (GH8)
16. Let GH6 despawn by going off-screen
17. Spawn Gohei 9 (GH9)

The player is left with five goheis: GH4, GH5, GH7, GH8, and GH9.

Recall the steps taken in the How section: we repeat steps 1 and 2 at the start to spawn multiple goheis, put them in their despawning animation, and let them go off screen. This allows for more goheis to be generated because there are more instances of a gohei going off-screen.

The full explanation goes as follows:

1. We spawn GH1, preferably at the top of the screen. goheiExists is set to true. We want to make sure that GH1 despawns by going off-screen on a frame that aligns with the shot cycle. Since in this case we spawn GH1 at the top of the screen, there are three concepts to take into account: the player's y-coordinate, the speed of the gohei (which depends on when Shift is released), and the size of the gohei.
2. We put GH1 in its despawning animation, which we can only do if the gohei does not have a target. In this case, we can easily achieve this by unholding Shift for one frame. goheiExists is set to false.
3. Similar to step 1, we spawn GH2 at the top of the screen. goheiExists is set to true.
4. Similar to step 2, we put GH2 in its despawning animation. goheiExists is set to false.
5. Again, similar to step 1, we spawn GH3 at the top of the screen. goheiExists is set to true.
6. Again, similar to step 2, we put GH3 in its despawning animation. goheiExists is set to false.
7. Once again, similar to step 1, we spawn GH4 at the top of the screen. goheiExists is set to true.
8. GH1 must despawn on a frame on which the shot cycle is divisible by 3. Additionally, GH1 must occupy a bullet slot higher than what GH4 has. goheiExists is set to false.
9. One frame later GH5 can be spawned. goheiExists is set to true.
10. GH2 must despawn on a frame on which the shot cycle is divisible by 3. Additionally, GH2 must occupy a bullet slot higher than what GH4 and GH5 has. goheiExists is set to false.
11. One frame later GH6 can be spawned. goheiExists is set to true.
12. GH3 must despawn on a frame on which the shot cycle is divisible by 3. Additionally, GH3 must occupy a bullet slot higher than what GH4, GH5, and GH6 has. goheiExists is set to false.
13. One frame later GH7 can be spawned. goheiExists is set to true.

We can only spawn a gohei once every 3 frames, and there is a limit of 10 frames before a gohei fully despawns, meaning we can have at most 4 goheis at the moment (GH4, GH5, GH6, and GH7). To continue the dupe, we need to despawn the gohei that takes up the highest bullet slot. We arbitrarily choose GH6 to be the gohei with the highest bullet slot taken. We spawn two enemies which are called Enemy 1 and Enemy 2. GH6 targets Enemy 1 while GH4, GH5, and GH7 target Enemy 2. We want to make sure that GH6 is more than 320 units away from Enemy 2 such that GH6 doesn't target Enemy 2. We want GH6 to exit the screen with a high enough velocity. We achieve this by letting Enemy 2 go off-screen and despawn.

14. We put GH6 in its despawning animation, which we can only do if the gohei does not have a target. In this case, we can easily achieve this by unholding Shift for one frame. goheiExists is set to false.
15. One frame later GH8 can be spawned. goheiExists is set to true.
16. GH6 must despawn on a frame on which the shot cycle is divisible by 3. Additionally, GH3 must occupy a bullet slot higher than what GH4, GH5, GH7, and GH8 has. goheiExists is set to false.
17. One frame later GH9 can be spawned. goheiExists is set to true.

Note that this is extremely difficult to do under normal circumstances. In order to generate 5 goheis, 3 goheis must be targeting an enemy, and 1 gohei must have enough velocity to go off-screen on its own. That one gohei must also be 320 units away from any enemy. On top of this, the unfocus and despawning must take place where the shot cycle is divisible by 3. Lastly, that one gohei must occupy a bullet slot whose ID is higher than every other gohei.

Notes

• Having to release Shift is not a requirement for the dupe to be done, but it is much harder this way.
• To perform the dupe, you do not need any enemies on-screen.
• The dupe can be performed regardless of the player's y-coordinate, but the set-up is much easier to achieve while being high on-screen.
• The dupe works if the gohei goes off-screen through the side or the bottom.
• The gohei dupe does not rely on RNG. The previously described inconsistency factor is the ordering of goheis in the player bullet list.
• Although understanding the bug makes the gohei dupe more consistent on a TAS-level, understanding the dupe may not necessarily make the bug easier to replicate in real time. This trick still requires skill to perform in real time.
• In theory, there can be up to 254 goheis (two slots must be devoted to the left and right amulet). However, the difficulty comes from letting a gohei despawn by going off-screen while maintaining your other goheis and keeping track of the player bullet list. Because of this, getting more than 4 goheis is a very difficult task to achieve, especially in an unmodified version of the game.
• If you want to perform the gohei dupe yourself, you can do so by clicking here.

Conclusion

Links

Replays

Videos

• NNN_shooter. 「July 10, 2017」. "【TAS】TH14 DDC "Extra" ReimuA NN in 06:58.96" https://www.youtube.com/watch?v=r9DZlKJkDfo
• NNN_shooter. 「April 4, 2017」. "【TAS】TH14 DDC "Lunatic" ReimuA in 17:13.63" https://www.youtube.com/watch?v=bZfXgqf210k
• Helio Knight. 「June 22, 2022」. "Baby's first DDC ReimuA Gohei dupe" https://www.youtube.com/watch?v=1qKdnwl5-OE
• Nylilsa. 「September 21, 2024」. "5 goheis" https://www.youtube.com/watch?v=s96Bvwoptqg

Other

• NNN_shooter. 「July 1, 2017」. "東方輝針城speedrunで重要なお祓い棒分裂の詳細（現状判明分 + 推測）" https://nnn-shooter.hatenablog.com/entry/ar1291350
• Wikipedia. 「n.d.」. "Stack (abstract data type)" https://en.wikipedia.org/wiki/Stack_(abstract_data_type)
• Khangaroo. 「n.d.」. "Touhou Patches" https://github.com/khang06/touhou-patches/tree/master/gohei_debug (This links to a patch that allows for debugging goheis run through thcrap. If you do not know how to install thcrap patches, ignore this link)