### Defining n-ary trees using the C preprocessor

In this article I introduce a compile time C technique used to define inheritance. Instead of giving a lengthy motivation I’ll jump directly to the algorithm and discuss it later. I hope lovers of C and its preprocessor find it useful. #defines first!

#define TOP 0 #define SET_CHILD(n,parent) ( parent==TOP ? n: \ ( parent<(1<<4) ? (n<<4) + parent : \ ( parent<(1<<8) ? (n<<8) + parent : (n<<12)+parent))) #define IS_SUBNODE(child, parent) ((child & parent) == parent) #define SELECT(X, a, best) ( a > best && IS_SUBNODE(X, a)? a : best) #define SELECT_FROM_5(X, a, b, c, d, e) SELECT(X, a, \ SELECT(X, b, \ SELECT(X, c, \ SELECT(X, d, \ SELECT(X, e, 0))))) #define SELECT_FROM_4(X, a, b, c, d) SELECT_FROM_5(X, a, b, c, d, 0) #define SELECT_FROM_3(X, a, b, c) SELECT_FROM_5(X, a, b, c, 0, 0) #define SELECT_FROM_2(X, a, b) SELECT_FROM_5(X, a, b, 0, 0, 0) |

The `SET_CHILD` macro is used to define up to 15 child nodes of a given root for a n-ary tree of depth 5 with a single root node, named `TOP`. This is encoded within a single number of type `word` which is adequate for most embedded compilers. For 32 or 64 bit processors one can either support more child nodes or a deeper tree.

`SET_CHILD` is assigning a name to n-th child of a given `parent`. One starts with `TOP` as the parent of all nodes and recurses down:

#define A SET_CHILD(1, TOP) #define B SET_CHILD(2, TOP) ... #define A1 SET_CHILD(1, A) #define A2 SET_CHILD(2, A) ... #define B1 SET_CHILD(1, B) #define B2 SET_CHILD(2, B) ... #define A11 SET_CHILD(1, A1) #define A12 SET_CHILD(2, A1) ... #define A21 SET_CHILD(1, A2) #define A22 SET_CHILD(2, A2) ... |

By construction no more than 15 child nodes for a given parent are permitted. If more are used, macros like `IS_CHILD` will fail to work correctly.

Once a tree is created with the appropriate nodes, one can use `IS_CHILD` to check for child/parent relationships. The tree is constructed s.t. `IS_CHILD(A, B)` returns 1 iff `A` is a direct child of `B` or a grandchild of `B` etc. otherwise 0. So `IS_CHILD(A22, A)` evaluates to 1 just like `IS_CHILD(A22, A2) ` or `IS_CHILD(A22, TOP)` but `IS_CHILD(A22, A1)` is 0.

The C preprocessor doesn’t support overloading and the flavors I checked didn’t support varargs wich wouldn’t probably be much helpful in this case either. So I defined a group of 5 `SELECT_FROM_xx` macros being distinguished only be the number of arguments. The number 5 isn’t magic and one can extend the range of `SELECT_FROM_xx` macros by need.

How is `SELECT_FROM_xx` used? The first argument `X` is an arbitary node of the tree. If one of the susequent nodes `a`, `b`, … `c` is identical with `X`, `X` will be the value of `SELECT_FROM_xx(X, a, b, …, c)`. Otherwise the *most-direct-parent* of `X` among the nodes `a`, …`c` will be returned. If none of them is a parent of `X` the return value is `TOP`.

**Example:**

If we set

#define X A22 |

then we get

SELECT_FROM_2(X, A, B) // = A SELECT_FROM_3(X, A, B, A1) // = A SELECT_FROM_3(X, A, B, A2) // = A2 SELECT_FROM_3(X, A2, B, A) // = A2 SELECT_FROM_3(X, A2, A, A22) // = A2 SELECT_FROM_2(X, A1, B) // = TOP |

### Inheritance

With the definitions above we can influence conditional compilation:

#if SELECT_FROM_3(X,A2,A,B) == A2 const int a = 0; #else if SELECT_FROM_3(X,A2,A,B) == A const int a = 1; #else if SELECT_FROM_3(X,A2,A,B) == B const int a = 2; #else const int a = -1; #endif |

The virtue of the construction lies in its robustness. Suppose X is `A22` then the first branch is selected but this remains true also if we build a “subclass” `A22k , k = 1, …, 9, A, …, F` of `A22` and assign e.g.

#define X A225 |

So if we use conditional compilation for a given System `S` and create a subsystem `T` of `S` e.g. a new version of `S`, we have to adapt our C code only in places where `T` differs explicitely from `S`. This robustness is also the major virtue of using inheritance / polymorphism in OOP. It has led to disrespect of using case-statements in OOP since those do not exploit polymorphism and cause in turn less robust code. We see that case- or if-else statements can be confined with the very same idea and robustness even on the level of the C preprocessor. The additional charme of using the C preprocessor is that child/parent relationships are computed at compile time and do not cause any runtime performance penalty.

a ,0 is missing in the SELECT_FROM_5 call in the definition of SELECT_FROM_3.

Nice post. Maybe you could

define A SET_CHILD(1, TOP)

define B SET_CHILD(2, TOP)

for better readability.

Francesco, Pistahh,

thanks for your responses. I changed the article according to your suggestions.