make all./buzzard.1 num num./try.shTo see good C Preprocessor buzzard.1, try:
make babble.cppcb
cat babble.cppcbNotice how many statements it takes to do anything useful?
What you shouldn’t think about buzzard.1:
buzzard.1 doesn’t just do a mass of #defines as its obfuscation.
I didn’t just submit the post-C-preprocessed output as an entry.
buzzard.1 contains only a numeric printf(3), yet sometimes it prints out
short strings.
buzzard.1 is a simple mathematical program. It expects two numeric
arguments.
./buzzard.1 0 <num>will print out the factorial of <num>.
./buzzard.1 <num1> <num2>will print out the largest common factor of num1 and num2.
./buzzard.1 1 <num2>will print out a factor of num2 if it’s composite, or else
it will print a string informing you that num2 is prime.
If the first argument is less than 0, it prints out an error message.
buzzard.1 is a translator from a pseudo-assembly language into a subset of C
suitable for execution on Charles Babbage’s Analytical Engine. Or rather, the
#defines in buzzard.1 are that translator. The rest of buzzard.1 is a
buzzard.1 program. If you run the whole mess through CPP and a beautifier, you
will see that all you have is a loop that runs until a variable is not 0, and a
sequence of assignment statements. The assignment statements are all of the
form a op= b or a = b. The Engine actually allowed ‘a = b op c’. Only +,
-, /, and * are used–no boolean or bitwise operators. The infinite loop
could have been simulated on the AE by connecting the already-processed card
stack to the input card stack.
Don’t expand the #defines! Rather, decipher what they do.
Some of them are mere obfuscation fodder, put in to encourage
you to run it through CPP.
Because of the definitional constraints, calls to atoi(argv[#]) also appear
inside the loop. These could be put outside–the initial values of the
“registers” on the AE–but the macro conventions being used didn’t lend
themselves to it.
The simulated comparison operations only work with a certain range of numbers;
numbers that are too large will cause the output code to fail to simulate the
input code. This means that this implementation of buzzard.1 would not be
Turing-complete, even if the AE could process indefinitely-sized numbers.
However, this is actually a constraint that no actual computer can meet, either,
so we can conclude that if an AE, with card bins connected as suggested above,
were hooked up to a memory unit of sufficient size, it would be as Turing
complete as any existing machine (or, for those who interpret that excessively
critically, i.e. “not at all” for both, we can simply say that the AE could
simulate any existing machine–although not quickly). This would be a good
place to site some references on the AE, but I don’t have any.
[Don’t read this unless you’re stumped!]
MACRO FUNCTION MNEMONIC
V begin variable declarations Variable
C begin program Code
Q(b,a) let b = a eQuals
A(c,a,b) let c = a + b Add
S(c,a,b) let c = a - b Subtract
D(c,a,b) let c = a / b, where b is a *constant* Divide
U(c,a,b) let c = a / b, where b is anything Unknown
M(c,a,b) let c = a * b Multiply
O(c,a,b) let c = a boolean-or b (a,b are 0 or 1) Or
B(b, a) let b = boolean value of a Boolean
P(b, a) let b = 1 if a>0, else 0. Positive
l emit next sequential label Label
J(x) goto label #x Jump
Z(a,d) if a is 0 goto d (a is 0 or 1) Zero
E(a,d) if a is 1 goto d (a is 0 or 1) Else
H halt Haly
K(x) let x = number of cmd line arguments Kount
G(x,y) let x = the value if the yth argument Get argument
T end of code; begin output section Terminate
X(y) print out hexadecimal value of y heXadecimal
T end of output section and program TerminateYou can figure out the other macros yourself. In the sample program, I’ve actually implemented subroutines by saving a return address in a variable and then jumping to a routine– specifically, a routine that converts a number into BCD, so it can be output by the hexadecimal output statement.
The essential statement to be able to make interesting programs is the conditional (given that we have loops). Since all you can do in the given operation output set is assignment, we implement “conditional assignment”:
if (x) y = z;To implement this, we constrain x to be either 0 or 1, and
simply compute:
y = (z * x) + (y * (1-x));This is more obscured by factoring out common terms and restricting ourselves to two operand operations:
temp = z; (temp == z)
temp -= y; (temp == z-y)
temp *= x; (temp == (z-y)*x)
y += temp; (y == (z-y)*x + y)
( == z*x - y*x + y)
( == z*x + y*(1-x))Next we imagine we have a pc. “I’m supposed to execute statement pc next”, says our emulator. But suppose we’re not currently coming up on statement pc. To handle this, we simply make every operation conditional on the pc having the correct value:
if (pc == some_constant) y = z;To combine this with other operations, we simply multiply by our
(pc == some_constant) flag right after the above temp *= x.
To evaluate pc == some_constant requires one more trick. We assume that
numbers can only be in some limited range. Then we use successive additions and
divisions to reduce that number down to -1, 0, or 1. You could, for
instance, do this by using mod by 2 and div by 2 to count bits, stopping
after, say, 32 iterations. The number you get is between 0..32, so another
6 iterations on it reduces it to 0..6. Three iterations on this produces
0..2 (3 would be 7), and then two iterations on this produces 0 or 1.
Instead I use a shorter two-divide approach that assumes I’m allowed to use
numbers slightly larger than the numbers I’m operating on.
A similar approach is used to detect positive numbers.
Note that the obvious code to compute y/x will not work correctly,
because every value is computed, even if the pc is not set correctly;
if x is ever 0 when the real C code reaches this computation the
program will die. (This was discovered the hard way.) The solution
is to stick x in a temporary, and if the current code is not about
to be executed, set the temporary to 1.
Thanks to Bill Pugh for bringing the loop-ability of the AE to my attention.
buzzard.1 was originally named ‘cb’, for obvious reasons, and is
dedicated to the memory of Charles Barrett.