Game of Life 32b
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- 1 Original version : 65 bytes
- 2 Remove key handler and RNG : 44 bytes
- 3 Switching to Textmode : 38 bytes
- 4 Using instructions as segment adress : 36 bytes
- 5 Synchronizing SI/DI, Improved cleanup : 34 bytes
- 6 Combining exchange with alignment : 33 bytes
- 7 Modbyte tuning, jumping into modbytes, code path alignment : 32 bytes
Original version : 65 bytes
We'll start with the old 65 bytes version and bring it down to 32 bytes.
It will help to understand what the core algorithm does, before optimizing it. I will not go into the details of random number generation and key handling since these parts are removed in the final version anyway. Setting up screen mode and putting pixels to the screen is described in the basic sectionn of this Wiki. The core routine computes the "normal" game of life rules, but with a twist. Instead of regarding only eight neighbour cells inside a 3x3 neighbourhood , ALL nine cells are taken into consideration, and the rules are reinterpreted as:
- If the number of cells is 3, the center cell will be alive.
- If the number of cells is 4, the center cell keeps its state.
- Otherwise, the cell dies (or stays dead).
Like in other (trivial) implementations, the 2D space is parsed cell by cell, from left to right, and from top to bottom. Since the game of life does not work "in situ" (updating the current cell instantly will lead to wrong results of following calculations), current cells are "marked", and when the calculations are advanced far enough that the cell in question does not influence any calculation of the current iteration, it will be "corrected" by
shr [byte di-65],5 to the target value of the next iteration. The summation is as usual, an inner loop, adding up 3 cells of one column, and the outer loop, shifting from right (+1) to the left (-1), thus adding up 9 cells of a 3x3 neighbourhood.
At the start of the loop, there is already the first "trick" happening. The register of summation
cl is not properly cleaned, but at this point it can either contain 0 or 32 from the instruction
and al,0x20 after
xchg cx,ax. If an arbitrary amount of cells has this on bit set, that won't hurt the calculation because of a special property of the
rcr instruction. "The processor restricts the count to a number between 0 and 31 by masking all the bits in the count operand except the 5 leastsignificant bits."
When the summation is complete, the aforementioned
rcr is executed, but not before setting the carry flag (
stc) which will be rotated in from the left, and directly right of the original cell value. By extracting the 6th bit of this rotated value (with
and al,0x20 we get exactly the value according to the rules defined above.
This value is now set in the original cell with
or [si-1],al, which as shown before, does not hurt the computation, besides the cell value has a temporary value of 32 or 33, thus being visible as brighter blue pixel in the short time span between marking and correction.
; http://read.pudn.com/downloads208/sourcecode/asm/981812/LIFE65.ASM__.htm ; Life simulator, 72 bytes - Vladislav Kaipetsky and Tenie Remmel ; 65 bytes - Mark Andreas ; If no args, regs on startup are: ; AX = BX = 0000h ; SI = IP = 0100h ; DI = SP = FFFEh IDEAL MODEL TINY P386 CODESEG ORG 100h Start: int 1ah ; ah=00: cx=hours, dx=tic counter mov al,13h ; Set mode 13h int 10h xchg dx,ax push 09000h ; DS = last 64K segment pop ds push 0A000h ; ES = video memory pop es ; BX is already zero RandLoop: rol ax,1 ; Generate random number adc [bx],al dec bx jnz RandLoop ; BX will not be equal to 3 the first time this loop is executed, but ; it will be for all other times. As SI = 0100h and DI = FFFEh on ; startup, SI - DI will be equal to 258. LifeLoop: xchg cx,ax AccLoop: add cl,[di+bx-64] ; Add in this column add cl,[si+bx-2] add cl,[si+bx+318] dec bx ; Loop back jnz AccLoop mov al,[si] ; Get center cell, set pixel stosb stc ; 3 = birth, 4 = stay (tricky): rcr al,cl ; 1.00?0000x --> 0.0x100?00 (rcr 3) and al,20h ; ^carry | ^ ; +---> 0.00x100?0 (rcr 4) or [si-1],al ; Add in new cell ^ shr [byte di-65],5 ; Shift previous value mov bl,3 ; 3 iterations in AccLoop inc si ; Loop while not zero jnz LifeLoop mov ah,1 ; Check for key int 16h jz LifeLoop ; Loop if no key xchg ax,bx ; Set text mode int 10h ret ; Return End Start
Remove key handler and RNG : 44 bytes
In order to reach 32 bytes, all the convenient stuff has to be removed. In case there is space left, parts of it could be reintegrated again. There are tiny changes to make this work as intended. The segment where all the calculation takes place has been changed to
1000h, pointing to a lower memory location. (Note: this might be working just with DosBox) The activity there (visible on the screen) helps spawning actual game of life structures.
mov al,[si] and
inc si have been replaced with
lodsb since that saves one byte.
Start: mov al,13h ; Set mode 13h int 10h push 01000h ; DS = low memory segment pop ds push 0A000h ; ES = video memory pop es ; BX is already zero LifeLoop: xchg cx,ax AccLoop: add cl,[di+bx-64] ; Add in this column add cl,[si+bx-2] add cl,[si+bx+318] dec bx ; Loop back jnz AccLoop ;mov al,[si] ; Get center cell, set pixel lodsb stosb stc ; 3 = birth, 4 = stay (tricky): rcr al,cl ; 1.00?0000x --> 0.0x100?00 (rcr 3) and al,20h ; ^carry | ^ ; +---> 0.00x100?0 (rcr 4) or [si-1],al ; Add in new cell ^ shr [byte di-65],5 ; Shift previous value mov bl,3 ; 3 iterations in AccLoop ; inc si ; Loop while not zero jmp short LifeLoop
Switching to Textmode : 38 bytes
Setting up screen mode and pixel access is requiring quite a bit of space, so in this version, it is removed. That is directly punished with an additional byte, because
DI is no longer involved in the process, thus, an optimization had to be removed. The assumption is that the computer this runs on, is already in text mode (40x25 chars, colors). This also helps with the calculation, since now it takes place directly on the screen (only one segment has to be set up) and no content has to be generated initially, since there is always at least something on the screen that works as seed value. A small downside is the alignment of cells, because in textmode, one cell occupies TWO bytes (one for color information). Luckily, the color information is by default set to "gray on black". An additional
dec bx, replacing
lodsw and changing
mov bl,3 to
mov bl,6 helps fixing the alignment issue. Additionally, the screen address changed (
pop ds) Another lucky coincident is, that instead of blue pixels, we now have a "smiley char" with orthogonal borders, which is a decent representation of a living cell. Inbetween marking and correction it shortly changes to an exclamation mark (!), which is barely visible.
push 0xb800 pop ds LifeLoop: stc ; 3 = birth, 4 = stay (tricky): rcr al,cl ; 1.00?0000x --> 0.0x100?00 (rcr 3) and al,20h ; ^carry | ^ or [si-2],al ; Add in new cell ^ shr byte [si-160-6],5 ; Shift previous value mov bl,6 xchg cx,ax AccLoop: add cl,[si+bx-160-4] ; Add in this column add cl,[si+bx-4] add cl,[si+bx+160-4] dec bx ; Loop back dec bx ; Loop back jnz AccLoop lodsw jmp short LifeLoop
Using instructions as segment adress : 36 bytes
Instead of using
pop to get the screen adress, there is also the instruction
lds available, which reads the segment value from memory. A value "close" to
0xb800 would be sufficient, because the visible screen in textmode is just a tiny part of the 64 kilobytes addressable by one segment. The idea is now to reuse parts of the code as segment address, which is possible when the instructions is one of the above. If there is such an instruction, it can start at the 4th byte (
[si] points to the start of the code and
lds bx,[si] puts the first two bytes into BX and the 3rd and 4th into DS, reversed). In this case
lodsw can be reused as the first (higher) byte of the segment. The 3rd byte would be only relevant for alignment, so instead of putting "0x00" there, a one-byte-instruction can be used there. The whole process saves two bytes.
lds bx,[si] LifeLoop: stc ; 3 = birth, 4 = stay (tricky): lodsw rcr al,cl ; 1.00?0000x --> 0.0x100?00 (rcr 3) and al,20h ; ^carry | ^ or [si-2],al ; Add in new cell ^ shr byte [si-160-6],5 ; Shift previous value mov bl,6 xchg cx,ax AccLoop: add cl,[si+bx-160-4] ; Add in this column add cl,[si+bx-4] add cl,[si+bx+160-4] dec bx ; Loop back dec bx ; Loop back jnz AccLoop jmp short LifeLoop
Synchronizing SI/DI, Improved cleanup : 34 bytes
A lot of tiny changes were the result of just one idea: How to optimize the clean up step? After all it is not really neccessary to correct a marked cell as soon as possible, instead, it can be waited for a certain amount of time/steps. But any nontrivial version of
shr byte [si-160-6],5 still uses four bytes, unless it is brought into one of the "pure" forms that only take up THREE bytes:
shr byte[(bp/bx)+si/di],x. Since SI and BX were already in use, and the usage of BP would implicate that the register SS is used instead of DS, the only remaining register possible is DI.
Now there are very short instructions available to advance the registers SI and DI, some of them at the same time, and one of them is
cmpsw. Not only does it not "hurt" the intended computation (the "compare" part of the instruction can be ignored), it also advances both SI and DI by TWO, so that the alignment of the screen in text mode is perfectly matched.
The usage of
cmpsw requires to remove
lodsw since there is no simple command to advance SI in the opposite direction (without involving direction flags), so it had been changed again to
lodsb to be one of the commands that also works as high byte of a segment adress, and an additional
dec si to align DI and SI, so that the clean up step is always in the same distance "behind" the current calculation. The assumption DI = SI - 258 is true on almost every DOS system. As a byproduct, one of the memory access instruction can now be rewritten to use DI instead of SI (like in the original), to save one byte.
lds bx,[si] LifeLoop: stc ; 3 = birth, 4 = stay (tricky): lodsb dec si rcr al,cl ; 1.00?0000x --> 0.0x100?00 (rcr 3) and al,20h ; ^carry | ^ or [si],al ; Add in new cell ^ cmpsw shr byte [di],5 ; Shift previous value mov bl,6 xchg cx,ax AccLoop: add cl,[di+bx+94] ; Add in this column add cl,[si+bx-4] add cl,[si+bx+160-4] dec bx ; Loop back dec bx ; Loop back jnz AccLoop jmp short LifeLoop
Combining exchange with alignment : 33 bytes
When thinking about
xchg cx,ax and how to skip one row to get rid of one of the double
dec bx, my own production "M8trix" (2015) came to mind, where i did pretty much the same as here, pulling the
xchginto the loop and doing alternating counting, so that
cl counts the acual cells, while
al is never actually used (it "counts" the colors). To make that little dance work,
bl has to start at 7.
lds bx,[si] LifeLoop: stc ; 3 = birth, 4 = stay (tricky): lodsb dec si rcr al,cl ; 1.00?0000x --> 0.0x100?00 (rcr 3) and al,20h ; ^carry | ^ or [si],al ; Add in new cell ^ cmpsw shr byte [di],5 ; Shift previous value mov bl,7 AccLoop: xchg cx,ax add al,[di+bx+94] ; Add in this column add al,[si+bx-4] add al,[si+bx+160-4] dec bx ; Loop back jnz AccLoop jmp short LifeLoop
Modbyte tuning, jumping into modbytes, code path alignment : 32 bytes
Sometimes, an instruction has several degrees of "freedom". That means, that the effect of that instruction can also be achieved by an alternative version of that instruction. In this case, the
lds instruction, which puts two bytes of the code into the segment DS, also loads two bytes into a register we (almost) don't care about. The only requirement is that
lds points to the start of the code, which can either be done by [SI] or [BX+SI]. The right image shows which modbyte numbers would be satisfying (highlighted green). Now, this selection can be applied to the instruction table below (highlighted red). It becomes clear that the used instruction
and al,0x20 would, interpreted as modbyte, be
SP,[SI] and thus it would be possible to jump into this modbyte to execute.
To be more clear:
lds sp,[si] is
and al, 0x20 is
0x24 0x20, so TWO
0x24are merged into ONE.
To make this work, the "host" instruction has to be only executed once (it would not work in a loop). Also, the parameter of the injected instruction has to be put "behind" the "host" instruction (a single
db 32 in the code). Finally, it has to be made sure that this second code path aligns with the rest of the code, and does no damage to the intended effect (for example, critical registers could be modified, or worse, illegal instructions could be created that way). In this case the new codepath consists of
and [bp+di+0807h],dh and
add al,0a7h, after which it aligns normally. These instructions are executed only once and do not modify critical registers.
Sometimes, a bit of code shuffling has to be performed to make such a trick work. Here, the
dec si have been replaced with
mov al,[si]. The critical function of being also a good segment value has been overtaken by
mov bl (see table above).
lds sp,[si] X: db 32 mov bl,7 ; O: 3 iterations or [si],al ; O: Add in new cell cmpsw shr byte [di],5 ; O: Shift previous value C: xchg cx,ax add al,[di+bx+94] ; O: Add in this column add al,[si+bx-4] add al,[si+bx+156] dec bx ; O: Loop back jnz C mov al,[si] ; O: 3 = birth, 4 = stay (tricky): stc ; O: 1.00?0000x --> 0.0x100?00 (rcr 3) rcr al,cl ; O: +---> 0.00x100?0 (rcr 4) jmp short X-1