Bitwise Parallel Computation with Block Fill and Copy

Primitives

Data can be copied without modification with /clone using the most simple options.

Negation can be achieved in-place using a sequence of three /fill commands. In this example, 0 and 1 are represented by air and stone, and granite is used as the "temporary":

/fill x1 y1 z1 x2 y2 z2 granite 0 replace air

/fill x1 y1 z1 x2 y2 z2 air 0 replace stone

/fill x1 y1 z1 x2 y2 z2 stone 0 replace granite

Disjunction (logical "or") is done with a /clone using the masked option, which treats all air blocks as 0's and all non-air blocks as 1's:

/clone x1 y1 z1 x2 y2 z2 dx dy dz masked normal

All of the other 2-argument boolean functions can be built up using combinations of or and not, making it possible to implement any combinatorial function in bitwise parallel form. For example:

A and B = not(not(A) or not(B))

A xor B = not(A or not(B)) or not(B or not(A))

My practice examples

Restore starting configuration: /fill 230 68 323 238 68 326 air 0 /fill 231 68 323 231 68 326 stone 0 /fill 235 68 324 238 68 324 sand 0

In range A:

change air to cobblestone:

/fill 235 68 323 238 68 326 cobblestone 0 replace air

change sand to air:

/fill 235 68 323 238 68 326 air 0 replace sand

Then clone A onto B with options masked normal

/clone 235 68 323 238 68 326 230 68 323 masked normal

In range B:

Negate the result: /fill 231 68 323 234 68 326 granite 0 replace air /fill 231 68 323 234 68 326 air 0 replace stone /fill 231 68 323 234 68 326 air 0 replace cobblestone

The Sixteen Two-Argument Boolean Functions

A	0	0	1	1
B	0	1	0	1	Description
	0	0	0	0	0 (always false)	(contradiction)
	0	0	0	1	A & B	A and B
	0	0	1	0	A & ~B	not (A implies B)
	0	0	1	1	A	(projection)
	0	1	0	0	~A & B	not (B implies A)
	0	1	0	1	B	(projection)
	0	1	1	0	A ^ B	A xor B (non-equivalence)
	0	1	1	1	A v B	A or B
	1	0	0	0	~(A v B)	A nor B
	1	0	0	1	~(A ^ B)	A xnor B (equivalence)
	1	0	1	0	~B	not B (negation)
	1	0	1	1	~A v B	B implies A
	1	1	0	0	~A	not A (negation)
	1	1	0	1	A v ~B	A implies B
	1	1	1	0	~(A & B)	A nand B
	1	1	1	1	1 (always true)	(tautology)

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2024 Apr 23.

s.30