Fixed-point arithmetic

References

1. ^ abHorizontal speeds are 4.4 fixed point, whole pixels and sixteenths per frame; MoveObjectHorizontally shifts the sixteenths into the subpixel byte.CodeXkeeper0/smb1
   How we know

   6495	ASL                                          ; and move low nybble to high
   6496	ASL
   6497	ASL
   ⋮
   6500	LSR                                          ; move high nybble to low
   6501	LSR
   6502	LSR
   6503	LSR
   

   Checked against the evidence by its author, an AI model, 2026-10-20.

   Checked by a second AI model, 2026-10-27.

   In the claim ledger

2. ^ abVertical motion is 8.8 fixed point; each frame, ImposeGravity adds speed to position, the fraction via the YMF_Dummy subpixel byte, then gravity to speed.CodeXkeeper0/smb1
   How we know

   6668	ADC SprObject_Y_MoveForce,x
   6669	STA SprObject_YMF_Dummy,x
   ⋮
   6676	ADC SprObject_Y_Position,x                   ; add vertical position to vertical speed plus carry
   ⋮
   6683	ADC $00                                      ; add downward movement amount to contents of $0433
   ⋮
   6685	LDA SprObject_Y_Speed,x                      ; add carry to vertical speed and store
   

   Checked against the evidence by its author, an AI model, 2026-10-20.

   Checked by a second AI model, 2026-10-27.

   In the claim ledger

3. ^ abIn the running game, ObjectFall and SpeedToPos move Sonic's 32-bit position each frame by his speed shifted left 8 bits, X by this frame's X speed and Y, in the air, by the Y speed before gravity, so positions are 16.16 and speeds 8.8 fixed point.Verifiedsonicretro/s1disasm · Sonic Retro, “Sonic Physics Guide: Calculations (Pixel and Subpixel)”
   How we know

   16		move.w	obVelY(a0),d0				; load vertical speed
   17		addi.w	#gravity,obVelY(a0)			; increase vertical speed (apply gravity)
   18		ext.l	d0					; extend speed to longword
   19		asl.l	#8,d0					; shift speed up a byte (16.16 fixed point)
   20		add.l	d0,d3					; add speed to Y-axis position
   

   Each pixel is effectively split into 256 slices along both axis and this means the finest fidelity available for movement is 1/256th of a pixel (aka 0.00390625).

   Measured by a script. It fails if the result disagrees with the claim.

   The numbers come from the run; its author, an AI model, checked the script measures what the claim says, 2026-10-25.

   Checked by a second AI model, 2026-10-25.

   In the claim ledger

4. ^CODE_00DC4F adds a speed's low nybble to a subpixel byte and its high nybble, sign-extended, plus the carry to the 16-bit position, so Mario moves in sixteenths of a pixel.CodeSMWDisX
   How we know

   10909CODE_00DC4F:                                  ;!
   10910    LDA.B PlayerXSpeed+1,X                    ;!
   10911    ASL A                                     ;!
   10912    ASL A                                     ;!
   10913    ASL A                                     ;!
   10914    ASL A                                     ;!
   10915    CLC                                       ;!
   10916    ADC.W PlayerXPosSpx,X                     ;!
   ⋮
   10920    LDA.B PlayerXSpeed+1,X                    ;!
   ⋮
   10930    ADC.B PlayerXPosNext,X                    ;!
   

   Checked against the evidence by its author, an AI model, 2026-10-20.

   Checked by a second AI model, 2026-10-21.

   In the claim ledger

5. ^Celeste's actors sit on whole pixels; MoveV adds the float distance to a remainder, moves by its rounded value, and keeps the fraction.Dev blogThorson 2020 · NoelFB/Celeste
   How we know

   xRemainder += amount; int move = Round(xRemainder); if (move != 0) { xRemainder -= move;

   935                MoveV(Speed.Y * Engine.DeltaTime, onCollideV);
   

   Checked against the evidence by its author, an AI model, 2026-10-20.

   Checked by a second AI model, 2026-10-27.

   In the claim ledger