Subpixels

This game uses subpixels for its movement. This is how Link gets the movement speed of 2-1-2-1 on normal ground etc.

How the coordinate and subpixel is updated during movement

Speed

See the table below for what speed Link has in different situations. The speed values only apply to one axis, so for diagonal movement or movement into a slope, the total speed will be higher.

Movement	Where	Speed (hex)	Speed (pixels/frame)
Walking	Ground	$18	1.5
Dashing	Ground	$40	4.0
Diagonal	Ground	$10	1.0
Walking	Stairs	$0B	0.6875
Dashing	Stairs	$0A	0.625
Diagonal	Stairs	$0B	0.6875
Walking	Shallow water	$14	1.25
Dashing	Shallow water	$30	3.0
Diagonal	Shallow water	$0D	0.8125
Walking	Holding object, Ground	$14	1.25
Diagonal	Holding object, Ground	$0D	0.8125
Walking	Shallow water, Holding object	$10	1.0
Diagonal	Shallow water, Holding object	$08	0.5
Walking	Slope	$10	1.0
Dashing	Slope	$2A	2.625
Walking	Old man follower	$14	1.25
Dashing	Old man follower	$14	1.25
Diagonal	Old man follower	$0D	0.8125

• When walking leftwards or upwards, the speed is reversed ($18 becomes $E8)
• The most significant digit (1 in the case of walking on normal ground) is added to the coordinate directly, no matter what.
• The least significant digit (8 in the case of walking on normal ground) is shifted left four times, and added first to the subpixel. If this causes the subpixel to overflow/wrap, we add an additional pixel to the coordinate.

Subpixel

• The game will reset Link's subpixel whenever you change direction of movement. A movement after a standstill counts as changing the direction of movement.
  • The game only looks at your dpad to find out if the direction changed. So if you walk upwards alongside a wall, and then press up and rightwards into the wall, it will treat this as a change of direction, even though Link is still moving upwards.

This means that pumping into a wall will function as two pumps, both when you press (from ^ to ^>) and when you release (from ^> to ^).

• Starting/executing a dash will not reset the subpixel accumulator. But if you cancel the dash with a movement, it will be reset.
  • If you however start a dash that ends up transitioning to another screen, the subpixel accumulator is not reset unless you start moving in a different direction on the next screen.

Example: Walking on ground (movement speed is $18)

• Downwards
  • frame 1: Subpixel = 0x00 + 0x80 = 0x80. Coordinate = 0 + 1 + 0 = 1
  • frame 2: Subpixel = 0x80 + 0x80 = 0x00. Coordinate = 1 + 1 + 1 = 3 (subpixel overflow)
  • frame 3: Subpixel = 0x00 + 0x80 = 0x80. Coordinate = 3 + 1 + 0 = 4
  • frame 4: Subpixel = 0x80 + 0x80 = 0x00. Coordinate = 4 + 1 + 1 = 6 (subpixel overflow)
  • Etc

• Upwards
  • frame 1: Subpixel = 0x00 - 0x80 = 0x80. Coordinate = 0 + 1 + 1 = 2 (subpixel overflow)
  • frame 2: Subpixel = 0x80 - 0x80 = 0x00. Coordinate = 2 + 1 + 0 = 3
  • Etc

Example: Walking on stairs (movement speed is $0B)

• Downwards
  • frame 1: Subpixel = 0x00 + 0xB0 = 0xB0. Coordinate = 0 + 0 + 0 = 0
  • frame 2: Subpixel = 0xB0 + 0xB0 = 0x60. Coordinate = 0 + 0 + 1 = 1 (subpixel overflow)
  • frame 3: Subpixel = 0x60 + 0xB0 = 0x10. Coordinate = 1 + 0 + 1 = 2 (subpixel overflow)
  • frame 4: Subpixel = 0x10 + 0xB0 = 0xC0. Coordinate = 2 + 0 + 0 = 2
  • Etc

• Upwards
  • frame 1: Subpixel = 0x00 - 0xB0 = 0x50. Coordinate = 0 + 0 + 1 = 1 (subpixel overflow)
  • frame 2: Subpixel = 0x50 - 0xB0 = 0xA0. Coordinate = 1 + 0 + 1 = 2 (subpixel overflow)
  • frame 3: Subpixel = 0xA0 - 0xB0 = 0xF0. Coordinate = 2 + 0 + 1 = 3 (subpixel overflow)
  • frame 4: Subpixel = 0xF0 - 0xB0 = 0x40. Coordinate = 3 + 0 + 0 = 3
  • Etc

How it affects slope dashes

Dashing on a slope is a fairly volatile thing when you frame advance through it. Link will move anything from 0 to 3 pixels in both the horizontal or vertical direction, seemingly at random. This is now understood better. The base speed is 2, and when the subpixel overflows you will get a 3 movement.

We're not completely sure why we get the 0 movements, but it looks like the game is trying to align Link with the slope. For example if you start your dash at the very first pixel you can start a slope dash, Link will move 1px/f until he's properly aligned and can start the slope dash. This also happens sporadically mid-slopedash and is the cause for slowing down the dash.

In any event, the subpixel you have when a dash is started, will affect how the slopedash will end up working out. If it's close to overflowing, you might get an extra pixel boost immediately, which will completely change the coordinates Link travels through during the slope dash. Basically, even if you start your dash from the exact same coordinate, the slopedash can go fast or slow depending what the subpixel value is before the dash.

One way to make sure you get the same subpixel every time is to hit diagonal before starting the dash.

Bomb Clips

Since a criteria for performing a Bomb Clip is that you are positioned exactly below the explosion, your subpixel value will matter just as much as your coordinate when you start the slopedash, since different paths through the slope might or might not include the coordinate you need to visit.

Some setups works the same for all subpixels, in which case only the coordinate matters.