Two years after
📝 the first look at TH04's and TH05's bullets,
we finally get to finish their logic code by looking at the special motion
types. Bullets as a whole still aren't completely finished as the
rendering code is still waiting to be RE'd, but now we've got everything
about them that's required for decompiling the midboss and boss fights of
these games.
Just like the motion types of TH01's pellets, the ones we've got here really
are special enough to warrant an enum, despite all the
overlap in the "slow down and turn" and "bounce at certain edges of the
playfield" types. Sure, including them in the bitfield I proposed two years
ago would have allowed greater variety, but it wouldn't have saved any
memory. On the contrary: These types use a single global state variable for
the maximum turn count and delta speed, which a proper customizable
architecture would have to integrate into the bullet structure. Maybe it is
possible to stuff everything into the same amount of bytes, but not without
first completely rearchitecting the bullet structure and removing every
single piece of redundancy in there. Simply extending the system by adding a
new enum value for a new motion type would be way more
straightforward for modders.
Speaking about memory, TH05 already extends the bullet structure by 6 bytes
for the "exact linear movement" type exclusive to that game. This type is
particularly interesting for all the prospective PC-98 game developers out
there, as it nicely points out the precision limits of Q12.4 subpixels.
Regular bullet movement works by adding a Q12.4 velocity to a Q12.4 position
every frame, with the velocity typically being calculated only once on spawn
time from an 8-bit angle and a Q12.4 speed. Quantization errors from this
initial calculation can quickly compound over all the frames a bullet spends
moving across the playfield. If a bullet is only supposed to move on a
straight line though, there is a more precise way of calculating its
position: By storing the origin point, movement angle, and total distance
traveled, you can perform a full polar→Cartesian transformation every frame.
Out of the 10 danmaku patterns in TH05 that use this motion type, the
difference to regular bullet movement can be best seen in Louise's final
pattern:
Louise's final pattern in its original form, demonstrating
exact linear bullet movement. Note how each bullet spawns slightly
behind the delay cloud: ZUN simply forgot to shift the fixed origin
point along with it.The same pattern with standard bullet movement, corrupting
its intended appearance. No delay cloud-related oversights here though,
at least.
Not far away from the regular bullet code, we've also got the movement
function for the infamous curve / "cheeto" bullets. I would have almost
called them "cheetos" in the code as well, which surely fits more nicely
into 8.3 filenames than "curve bullets" does, but eh, trademarks…
As for hitboxes, we got a 16×16 one on the head node, and a 12×12 one on the
16 trail nodes. The latter simply store the position of the head node during
the last 16 frames, Snake style. But what you're all here for is probably
the turning and homing algorithm, right? Boiled down to its essence, it
works like this:
// [head] points to the controlled "head" part of a curve bullet entity.
// Angles are stored with 8 bits representing a full circle, providing free
// normalization on arithmetic overflow.
// The directions are ordered as you would expect:
// • 0x00: right (sin(0x00) = 0, cos(0x00) = +1)
// • 0x40: down (sin(0x40) = +1, cos(0x40) = 0)
// • 0x80: left (sin(0x80) = 0, cos(0x80) = -1)
// • 0xC0: up (sin(0xC0) = -1, cos(0xC0) = 0)
uint8_t angle_delta = (head->angle - player_angle_from(
head->pos.cur.x, head->pos.cur.y
));
// Stop turning if the player is 1/128ths of a circle away from this bullet
const uint8_t SNAP = 0x02;
// Else, turn either clockwise or counterclockwise by 1/256th of a circle,
// depending on what would reach the player the fastest.
if((angle_delta > SNAP) && (angle_delta < static_cast<uint8_t>(-SNAP))) {
angle_delta = (angle_delta >= 0x80) ? -0x01 : +0x01;
}
head_p->angle -= angle_delta;
5 lines of code, and not all too difficult to follow once you are familiar
with 8-bit angles… unlike what ZUN actually wrote. Which is 26 lines,
and includes an unused "friction" variable that is never set to any value
that makes a difference in the formula. uth05win
correctly saw through that all and simplified this code to something
equivalent to my explanation. Redoing that work certainly wasted a bit of my
time, and means that I now definitely need to spend another push on RE'ing
all the shared boss functions before I can start with Shinki.
So while a curve bullet's speed does get faster over time, its
angular velocity is always limited to 1/256th of a
circle per frame. This reveals the optimal strategy for dodging them:
Maximize this delta angle by staying as close to 180° away from their
current direction as possible, and let their acceleration do the rest.
At least that's the theory for dodging a single one. As a danmaku
designer, you can now of course place other bullets at these technically
optimal places to prevent a curve bullet pattern from being cheesed like
that. I certainly didn't record the video above in a single take either…
After another bunch of boring entity spawn and update functions, the
playfield shaking feature turned out as the most notable (and tricky) one to
round out these two pushes. It's actually implemented quite well in how it
simply "un-shakes" the screen by just marking every stage tile to be
redrawn. In the context of all the other tile invalidation that can take
place during a frame, that's definitely more performant than
📝 doing another EGC-accelerated memmove().
Due to these two games being double-buffered via page flipping, this
invalidation only really needs to happen for the frame after the next
one though. The immediately next frame will show the regular, un-shaken
playfield on the other VRAM page first, except during the multi-frame
shake animation when defeating a midboss, where it will also appear shifted
in a different direction… 😵 Yeah, no wonder why ZUN just always invalidates
all stage tiles for the next two frames after every shaking animation, which
is guaranteed to handle both sporadic single-frame shakes and continuous
ones. So close to good-code here.
Finally, this delivery was delayed a bit because -Tom-
requested his round-up amount to be limited to the cap in the future. Since
that makes it kind of hard to explain on a static page how much money he
will exactly provide, I now properly modeled these discounts in the website
code. The exact round-up amount is now included in both the pre-purchase
breakdown, as well as the cap bar on the main page.
With that in place, the system is now also set up for round-up offers from
other patrons. If you'd also like to support certain goals in this way, with
any amount of money, now's the time for getting in touch with me about that.
Known contributors only, though! 😛
Next up: The final bunch of shared boring boss functions. Which certainly
will give me a break from all the maintenance and research work, and speed
up delivery progress again… right?
Y'know, I kinda prefer the pending crowdfunded workload to stay more near
the middle of the cap, rather than being sold out all the time. So to reach
this point more quickly, let's do the most relaxing thing that can be
easily done in TH05 right now: The boss backgrounds, starting with Shinki's,
📝 now that we've got the time to look at it in detail.
… Oh come on, more things that are borderline undecompilable, and
require new workarounds to be developed? Yup, Borland C++ always optimizes
any comparison of a register with a literal 0 to OR reg, reg,
no matter how many calculations and inlined function calls you replace the
0 with. Shinki's background particle rendering function contains a
CMP AX, 0 instruction though… so yeah,
📝 yet another piece of custom ASM that's worse
than what Turbo C++ 4.0J would have generated if ZUN had just written
readable C. This was probably motivated by ZUN insisting that his modified
master.lib function for blitting particles takes its X and Y parameters as
registers. If he had just used the __fastcall convention, he
also would have got the sprite ID passed as a register. 🤷
So, we really don't want to be forced into inline assembly just
because of the third comparison in the otherwise perfectly decompilable
four-comparison if() expression that prevents invisible
particles from being drawn. The workaround: Comparing to a pointer
instead, which only the linker gets to resolve to the actual value of 0.
This way, the compiler has to make room for
any 16-bit literal, and can't optimize anything.
And then we go straight from micro-optimization to
waste, with all the duplication in the code that
animates all those particles together with the zooming and spinning lines.
This push decompiled 1.31% of all code in TH05, and thanks to alignment,
we're still missing Shinki's high-level background rendering function that
calls all the subfunctions I decompiled here.
With all the manipulated state involved here, it's not at all trivial to
see how this code produces what you see in-game. Like:
If all lines have the same Y velocity, how do the other three lines in
background type B get pushed down into this vertical formation while the
top one stays still? (Answer: This velocity is only applied to the top
line, the other lines are only pushed based on some delta.)
How can this delta be calculated based on the distance of the top line
with its supposed target point around Shinki's wings? (Answer: The velocity
is never set to 0, so the top line overshoots this target point in every
frame. After calculating the delta, the top line itself is pushed down as
well, canceling out the movement. )
Why don't they get pushed down infinitely, but stop eventually?
(Answer: We only see four lines out of 20, at indices #0, #6, #12, and
#18. In each frame, lines [0..17] are copied to lines [1..18], before
anything gets moved. The invisible lines are pushed down based on the delta
as well, which defines a distance between the visible lines of (velocity *
array gap). And since the velocity is capped at -14 pixels per frame, this
also means a maximum distance of 84 pixels between the midpoints of each
line.)
And why are the lines moving back up when switching to background type
C, before moving down? (Answer: Because type C increases the
velocity rather than decreasing it. Therefore, it relies on the previous
velocity state from type B to show a gapless animation.)
So yeah, it's a nice-looking effect, just very hard to understand. 😵
With the amount of effort I'm putting into this project, I typically
gravitate towards more descriptive function names. Here, however,
uth05win's simple and seemingly tiny-brained "background type A/B/C/D" was
quite a smart choice. It clearly defines the sequence in which these
animations are intended to be shown, and as we've seen with point 4
from the list above, that does indeed matter.
Next up: At least EX-Alice's background animations, and probably also the
high-level parts of the background rendering for all the other TH05 bosses.
To finish this TH05 stretch, we've got a feature that's exclusive to TH05
for once! As the final memory management innovation in PC-98 Touhou, TH05
provides a single static (64 * 26)-byte array for storing up to 64
entities of a custom type, specific to a stage or boss portion.
(Edit (2023-05-29): This system actually debuted in
📝 TH04, where it was used for much simpler
entities.)
TH05 uses this array for
the Stage 2 star particles,
Alice's puppets,
the tip of curve ("jello") bullets,
Mai's snowballs and Yuki's fireballs,
Yumeko's swords,
and Shinki's 32×32 bullets,
which makes sense, given that only one of those will be active at any
given time.
On the surface, they all appear to share the same 26-byte structure, with
consistently sized fields, merely using its 5 generic fields for different
purposes. Looking closer though, there actually are differences in
the signedness of certain fields across the six types. uth05win chose to
declare them as entirely separate structures, and given all the semantic
differences (pixels vs. subpixels, regular vs. tiny master.lib sprites,
…), it made sense to do the same in ReC98. It quickly turned out to be the
only solution to meet my own standards of code readability.
Which blew this one up to two pushes once again… But now, modders can
trivially resize any of those structures without affecting the other types
within the original (64 * 26)-byte boundary, even without full position
independence. While you'd still have to reduce the type-specific
number of distinct entities if you made any structure larger, you
could also have more entities with fewer structure members.
As for the types themselves, they're full of redundancy once again – as
you might have already expected from seeing #4, #5, and #6 listed as
unrelated to each other. Those could have indeed been merged into a single
32×32 bullet type, supporting all the unique properties of #4
(destructible, with optional revenge bullets), #5 (optional number of
twirl animation frames before they begin to move) and #6 (delay clouds).
The *_add(), *_update(), and *_render()
functions of #5 and #6 could even already be completely
reverse-engineered from just applying the structure onto the ASM, with the
ones of #3 and #4 only needing one more RE push.
But perhaps the most interesting discovery here is in the curve bullets:
TH05 only renders every second one of the 17 nodes in a curve
bullet, yet hit-tests every single one of them. In practice, this is an
acceptable optimization though – you only start to notice jagged edges and
gaps between the fragments once their speed exceeds roughly 11 pixels per
second:
And that brings us to the last 20% of TH05 position independence! But
first, we'll have more cheap and fast TH01 progress.
uth05win
correctly saw through that all and simplified this code to something
equivalent to my explanation. Redoing that work certainly wasted a bit of my
time, and means that I now definitely need to spend another push on RE'ing
all the shared boss functions before I can start with Shinki.
