## To build:

``` <!---sh-->
    make all
```


### Bugs and (Mis)features:

The current status of this entry is:

> **STATUS: INABIAF - please DO NOT fix**

For more detailed information see [1993/vanb in bugs.html](../../bugs.html#1993_vanb).


## To use:

``` <!---sh-->
    ./vanb 'exp'
```

where `exp` is an octal expression. See below for how it can also have
hexadecimal and decimal numbers.


## Try:

``` <!---sh-->
    ./try.sh
```

What happens if you use something other than valid digits?


## Judges' remarks:

The octal expression may contain:

- unary operators:     `+`, `-`
- binary operators:    `+`, `-`, `*`, `/`, `%`
- hex numbers:         `x` or `X` followed by hex digits
- decimal numbers:     `d` or `D` followed by decimal digits
- octal numbers:       octal digits
- grouping:            `()`

No spaces are allowed in the expression.  To avoid shell expansion,
one should surround the expression in single quotes.

It is a good thing that this program consists of only one
expression, otherwise it might become hard to understand.  :-)


## Author's remarks:

The program does no error checking - erroneous expressions will
produce spurious results. Note that unary `-` is an operator. Thus,
decimal `-46` would be entered as `-d46` and not `d-46`.


### What Makes This Program Special:

0. Of course, the fact that the program takes input and produces output in
octal, rather than a more useful system like decimal, makes it "special".

1. The entire program consists of a single expression, returned from `main()`.

2. There are no global or local variables other than the parameters to `main()`.

3. All of the constants in the program are expressed in octal - including the
`printf(3)` string.

4. The variables are given names which cause visual confusion with the octal
constants.

5. The program is formatted like a Roman numeral 8. The significance of 8 is
obvious. I chose Roman numerals because it is a numbering system even more
arcane than octal. It's not very 'deceptive', but it's difficult to deceptively
format a program which has no explicit control structures (other than `?:`s).

6. Many simple tasks are done many times. I tried to do these differently each
time, to make the program harder to understand.


### How It Works:

It's a recursive descent parser, calling `main()`
for all of its recursion. `O2` is a state variable, telling `main()`
what grammar non-terminal to parse. `**O7` is the next character.
`O3` is an intermediate result. Whenever you see a construct like:

```
    !(expression with O2)?
```

it's decrementing and testing `O2` to see what state it's in. Comparisons
involving `**O7` and octal constants are looking for certain characters.

Here's the grammar (`'e'` denotes the empty string) :


```
    <E>  ::=  <T><E'>
    <E'> ::=  +<T><E'> |
              -<T><E'> | e
    <T>  ::=  <F><T'>
    <T'> ::=  *<F><T'> |
              /<F><T'> |
              %<F><T'> | e
    <F>  ::=  +<F> |
              -<F> |
              (<E><C> |
              d<D> |
              D<D> |
              x<X> |
              X<X> |
              <O>
    <C>  ::=  )
    <D>  ::=  [0-9]<D> |
              e
    <X>  ::=  [0-9]<X> |
              [A-F]<X> |
              [a-f]<X> |
              e
    <O>  ::=  [0-7]<O> |
              e
```

Here's how the grammar nonterminals map to octal state numbers:

```
    <E>  is  012
    <E'> is  011
    <T>  is  010
    <T'> is   07
    <F>  is   06
    <C>  is  013
    <D>  is   04
    <X>  is   05
    <O>  is   03
```

Here's a version of the program before it got formatted into the VIII,
augmented with comments showing where each state begins. `N1` and `N2` are
notes:

``` <!---c-->
    #define O5 main
    O5(O2,O7,O3)char**O7;
    {
             return
    /* N1 */ !(O2+=~01+01) ?\
                  00:
    /* N2 */ !(O2-=02>01) ?\
                  printf("\045\157\012",O5(012,O7+01,00)):
    /* O  */ !(O2-=02>>01) ?\
                  (**O7<=067 && **O7>057 ? O5(03,O7,*(*O7)++-060+010*O3):O3):
    /* D  */ !(O2-=-O3-~O3) ?\
                  (072>**O7 && 060<=**O7 ? O5(04,O7,012*O3-060+*(*O7)++):O3):
    /* X  */ !(O2-=!O3+!!O3) ?\
                  (**O7>057 && **O7<=071 ? O5(05,O7,*(*O7)+++O3*020-060):
                  **O7<=0106 && 0101<=**O7 ? O5(05,O7,020*O3+*(*O7)++-067):
                  0140<**O7 && **O7<0147 ? O5(05,O7,-0127+*(*O7)+++020*O3):O3):
    /* F  */ !(O2-=02-01) ?\
                  (**O7==050 ? 050**++*O7,O5(013,O7,O5(012,O7,00)):
                  **O7<056 && 054<**O7 ? 055**++*O7,-O5(06,O7,00):
                  054>**O7 && 052<**O7 ? 050**(*O7)++,O5(06,O7,00):
                  !(**O7^0170)||!(0130^**O7) ? *++*O7,O5(05,O7,00):
                  **O7==0144||**O7==0104 ? ++*O7,O5(04,O7,00):O5(03,O7,00)):
    /* T' */ !--O2 ?\
                  (**O7==052 ? O5(07,O7,O3*(*++*O7,O5(06,O7,00))):
                  !(045-**O7) ? O5(07,O7,O3%(03+(*O7)++,O5(06,O7,00))):
                  !(**O7^057) ? O5(07,O7,O3/(03-*++*O7,O5(06,O7,00))):O3):
    /* T  */ !(O2+=01-02) ?\
                  O5(07,O7,O5(06,O7,00)):
    /* E' */ !(O2+=-02/02) ?\
                  (!(**O7-053)?O5(011,O7,O3+(++*O7,O5(010,O7,00))):
                  !(055^**O7) ? O5(011,O7,O3-(03+*(*O7)++,O5(010,O7,00))):O3):
    /* E  */ !(O2-=0563&0215) ?\
                  O5(011,O7,O5(010,O7,00)):
    /* C  */ (++*O7,O3);
    }
```

Note `N1`: It should never enter this state, unless the user invokes the
program with no parameters, in which case it just returns 0.

Note `N2`: Since the program is properly invoked with 1 parameter, this is
the first state it will go into. This state just invokes
printf, and sends the parser to state `012` (which is `<E>`).

The `E` and `T` states work like this:

``` <!---c-->
    int e(){ return eprime( t() ); }
```


The `E'` and `T'` states work like this:

``` <!---c-->
    int eprime( int intermediate )
    {
        if( ch == '+' )
        {
            ch = nextchar();
            return eprime( intermediate + t() );
        }
        else return intermediate;
    }
```

The `D`, `X` and `O` states work like this (they assume that they're initially
called with `0`):

``` <!---c-->
    int octal( int intermediate )
    {
        if( ch>='0' && ch<='7' )
        {
            intermediate = intermediate * 8 + ch - '0';
            ch = nextchar();
            return octal( intermediate );
        }
        else return intermediate;
    }
```

`F` and `C` work similarly.


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