Meta-Computer (Verbose)

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{ Σπ }

In order to initialize all of the 3D lattices of wires and logic gates, a meta-computer is required. The program code of this meta-computer (concise form) fits into 64 bits. The input of the meta-computer is the set of all integers up to 2 ^ 65,536 bits long. The output of the meta-computer is the set of all possible configurations of 3D lattices. The dimensions of each lattice are (2 ^ 16) x (2 ^ 16) x (2 ^ 65,501).

The following is the program code of this meta-computer, in the form of high-level language code. First some programming notes: X := Y is an assignment statement, in which the value of Y is stored in the variable X; IF X <> 0 means IF X is not equal to zero.

Let M = an integer with 2 ^ 65,536 bits

Let X, Y = integers with 16 bits each

Let Z = an integer with 65,501 bits

Let I = an integer with 65,533 bits

Let V = an integer with 8 bits

Let L(X, Y, Z) = a grid intersection in lattice L, consisting of 6 bits

Let M(I) = I-th byte of M (a byte has 8 bits)

Let L(I) = I-th grid intersection of lattice L (3D array)

   M := 0
20 I := 0
   Z := 0
40 Y := 0
60 X := 0
80 V := M(I)
   L(X, Y, Z) := V
   I := I + 1
   X := X + 1
   IF X <> 0 GOTO 80
   Y := Y + 1
   IF Y <> 0 GOTO 60
   Z := Z + 1
   IF I <> 0 GOTO 40
   ACTIVATE L
   M := M + 1
   IF M <> 0 GOTO 20
   HALT

Here is the program code of the meta-computer, in the form of an assembly language program, beginning with its instruction set (the Siz column is the instruction length, in multiples of 4 bits):

Instruction Set:

Siz Op  Args        Function
=== === ====        ========
4   LD  V, M, I     Load V := M(I) = I-th byte of M
5   STO X, Y, Z, V  Store L(X, Y, Z) := V
4   ACC X, Val      Reserve up to 255 bits for register X
2   EXP X           Reserve 2 ^ Y bits for register X,
                    where Y is the current length of X
2   SHR X           Shrink length of register X by 1 bit
2   CLR X           Zero out X
2   INC X           Increment X
4   BNZ X, Val      Branch if X non-zero
1   RUN             Activate current lattice, start new lattice
1   HLT             Halt

Assembly Language Program (Hexadecimal):

00 ACC M, 10        30 LD  V, M, I
04 EXP M            34 STO X, Y, Z, V
06 EXP M            39 INC I
08 ACC X, 10        3B INC X
0C ACC Y, 10        3D BNZ X, 30
10 ACC I, 10        41 INC Y
14 EXP I            43 BNZ Y, 2E
16 SHR I            47 INC Z
18 SHR I            49 BNZ I, 2C
1A SHR I            4D RUN
1C ACC Z, 10        4E INC M
20 EXP Z            50 BNZ M, 28 
22 ACC V, 8         54 HLT 
26 CLR M            
28 CLR I            
2A CLR Z            
2C CLR Y            
2E CLR X
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