546 - bombShield(int a, int script)

Sets the bomb invulnerability flag (a=0 false, a=1 true), the caller's ANM script will change to script when a bomb is active.

611 - etEx(int etId, int async, int type, float a, float b)

Adds bullet transformation to bullet manager etId, Transformation of flag type determines the specific behaviour of the bullet. Documentation can be found here.

BulletEffectType-67108864 - etExDelay(string et, string isAsync, string time)

Hide the bullet for time frames. During this time, it will not move, will be invisible and won't have a hitbox. If used as a first transformation, can be used to delay when the bullet actually appears.

6 - isDelayedSpawn

While this flag is set, the bullet will be invisible and not have a hitbox. This flag is cleared once the delay timer ends.

4 - short_timer

Integer value between -1 and 15 inclusive (by default -1). If non-negative, shooters using short_timer shoot their bullets and timer increments by 1 per frame until 15 is reached. Once 15, timer reset to -1 or 0 depending on Z key state.

5 - long_timer

Integer value between -1 and 120 inclusive (by default -1). If non-negative, shooters using long_timer shoot their bullets and timer increments by 1 per frame until 120 is reached. Once 120, timer reset to -1 or 0 depending on Z key state.

503 - flagClear(int n)

Clears flag(s) according to n. Refer to the flag table here for exact values.

91 - floatTime(int slot, float var, int time, int mode, float start, float final)

In time frames using mode mode, variable var changes from start to final. slot is used to set the slot to be used by this ins, every enemy has 8 slots.

-9980 - F1

Local float variable, inherited by spawned enemies.

-9984 - I1

Local integer variable, inherited by spawned enemies.

-9989 - ANGLE_PLAYER

Angle from the enemy to the player.

-9962 - BOSS_Y

Final Y position of the boss.

-9990 - PLAYER_Y

Player's Y position.

-9963 - BOSS_X

Final X position of the boss.

-9991 - PLAYER_X

Player's X position.

81 - circlePos(float varX, float varY, float angle, float radius)

Performs following operation: varX = cos(angle) * radius and varY = cos(angle) * radius

-9981 - F0

Local float variable, inherited by spawned enemies.

300 - enmCreate(string sub, float x, float y, int hp, int score, int item)

Creates an enemy using subroutine sub at coordinates (x, y) (relative to position of the parent), health of created enemy is hp, score bonus is score and item drop is item.

601 - etOn(int etId)

Shoots bullet(s) using properties from bullet manager etId.

23 - wait(int time)

Stops sub execution for time frames.

1 - delete()

Returns to the top of current call stack.

2 - GAME_SPEED

The value controls by how much faster the game speed is run. This variable is often set to a number between 0 and 1. This value is often changed when a (final) boss dies or when a photo is taken. Its default value is 1.

-9985 - I0

Local integer variable, inherited by spawned enemies.

-9983 - I2

Local integer variable, inherited by spawned enemies.

-9982 - I3

Local integer variable, inherited by spawned enemies.

-9954 - ENEMY_HP

Enemy's current HP.

3 - goheiExists

A flag that determines if a gohei exists on-screen or not. Flag is set to true by active gohei. Flag is set to false if gohei goes off-screen or is despawning.

-9926 - GI0

Global integer value. Value is initialised to 0 on stage load but not on stage reset.

-9925 - GI1

Global integer value. Value is initialised to 0 on stage load but not on stage reset.

-9924 - GI2

Global integer value. Value is initialised to 0 on stage load but not on stage reset.

-9923 - GI3

Global integer value. Value is initialised to 0 on stage load but not on stage reset.

17 - distortion(int a)

Triggers distortion effects on the edge of the screen. The meaning of the argument is not entirely clear. SA uses a value of 1 to create distortion at the bottom of the screen, while UFO uses this same value to create distortion at the top.

539 - spell3(int id, int timeRate, int unused, string name)

Declares a spell-card with id id and name unused. The ID passed to the spell-creating function is id + difficulty - 2 (with easy=0, normal=1, ..., overdrive=5). timeRate determines how much time the spell circle takes to shrink (in frames), as well as how fast the spell bonus decreases.

514 - setInterrupt(int slot, int hp, int duration, string subroutine)

Sets an interrupt on slot slot. Once caller's HP reaches hp or duration frames have passed since this instruction was called, the caller will terminate all subroutines it's currently running and execute subroutine subroutine.

270 - enmCreate270(string sub, float x, float y, int hp, int score, int item)

Creates an enemy using subroutine sub at coordinates (x, y) (relative to position of the stage background camera), health of created enemy is hp, score bonus is score and item drop is item.

CPU-dependent Desync

Specifications

  • Versions: 1.00 - 1.00a - 1.00b - 1.00c - 1.00d
  • Difficulty: Easy - Normal - Hard - Lunatic - Extra - Last Word
  • Mode: Main game - Practice mode - Spell Practice
  • Shottype: Border Team - Magic Team - Ghost Team - Scarlet Team - Reimu - Yukari - Marisa - Alice - Youmu - Yuyuko - Sakuya - Remilia

What happens

Replays in Imperishable Night are able to experience a desync that are dependent on the user's CPU.

How it happens

Due to the nature of this bug, the bug can occur anywhere in this game.

Why it happens

In Imperishable Night, some instructions use the RSQRTSS (Reciprocal Square Root Scalar Single-Precision) instruction. In practice, the RSQRTSS instruction estimates the following:

1.0f / sqrtf(x)

RSQRTSS calculates this in a fast way, i.e. it does not exactly perform 1.0f / sqrtf(x) but instead it uses an approximation method for calculating 1.0f / sqrtf(x). The reason RSQRTSS is used for is because RSQRTSS is faster and less performance-heavy to run. As such, the result from RSQRTSS is an approximation. From the intel specification, they state the following:

Computes an approximate reciprocal of the square root of the low single precision floating-point value in the source operand (second operand) stores the single precision floating-point result in the destination operand.

A small script run by Robert O'Callahan demonstrates the diverging behavior of the RSQRTSS between Intel and AMD CPUs:

Intel Skylake:
out = 3d7ff000, float = 0.062485

On AMD Rome:
out = 3d7ff800, float = 0.062492

Consequence of diverging RSQRTSS behaviour

How does this tie back to replays desyncing? The different outputs of RSQRTSS would mean that graphics are rendered slightly differently depending on your CPU. While this usually does not pose a problem, especially for modern Touhou games, it does not apply for Imperishable Night.

In modern Touhou games, pseudo-random events are determined by RNG values. RNG values are numbers that the game uses to determine random events such as random boss movement and graze particle effects. In particular, there are two main RNG values: ANM_RNG_SEED and ECL_RNG_SEED. They are differentiated as follows

  • ANM_RNG_SEED: provides the randomness factor of how sprites and particles look. These effects have no effect on the gameplay.
  • ECL_RNG_SEED: provides the randomness factor of how bullets and enemies behave.

However, in Imperishable Night the distinction between ANM_RNG_SEED and ECL_RNG_SEED is not made. Instead, any instruction that requires randomness uses the same single RNG_SEED. Some of the instructions that update particle effects use RSQRTSS, and some of those particle effects would call for RNG_SEED. This eventually leads to a desync in RNG_SEED which quickly evolves into a desync.

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