Author:

• Name: Sean Barrett
  Location: US - United States of America (United States)

To build:

    make all

To use:

    ./buzzard.1 num num

Try:

    ./try.sh

Judges’ remarks:

To see good C Preprocessor buzzard.1, try:

    make babble.cppcb
    cat babble.cppcb

Notice how many statements it takes to do anything useful?

Author’s remarks:

What you shouldn’t think about buzzard.1:

buzzard.1 doesn’t just do a mass of #defines as its obfuscation.

What you should be glad about:

I didn’t just submit the post-C-preprocessed output as an entry.

Cute trick warning

buzzard.1 contains only a numeric printf(3), yet sometimes it prints out short strings.

What it does

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.

What it is

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.

How to try to understand it

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.

What it doesn’t do quite right as an emulator

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.

Theoretical observations

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.

Definition of the input language to buzzard.1 (OR What Exactly Do All The Macros Do?)

[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    Divide
              constant

    U(c,a,b)  let c = a / b,
              where b is      Unknown
              anything

    M(c,a,b)  let c = a * b   Multiply

    O(c,a,b)  let c = a       Or
              boolean-or
              b (a,b are
              0 or 1)

    B(b, a)   let             Boolean
              b = boolean
              value of a

    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    Zero
              0 or 1)

    E(a,d)    if a is 1
              goto d          Else
              (a is 0 or 1)

    H         halt            Halt

    K(x)      let x = number
              of cmdline      Kount
              arguments

    G(x,y)    let x = the
              value
              of the yth      Get arg
              argument

    T         end of code;
              begin output    Terminate
              section

    X(y)      print hex
              value of y      heX

    T         end of output   Terminate
              section
              and program

You 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.

How it works, i.e., how to get useful programs from a op= b

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.

Primary files

• buzzard.1.c - entry source code
• Makefile - entry Makefile
• buzzard.1.orig.c - original source code
• try.sh - script to try entry

Secondary files

• 1992_buzzard.1.tar.bz2 - download entry tarball
• README.md - markdown source for this web page
• .entry.json - entry summary and manifest in JSON
• .gitignore - list of files that should not be committed under git
• .path - directory path from top level directory
• index.html - this web page

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