Variadic recursive preprocessor macros - is it possible?

I've run into a little theoretical problem. In a piece of code I'm maintaining there's a set of macros like

#define MAX_OF_2(a, b)       (a) > (b) ? (a) : (b)
#define MAX_OF_3(a, b, c)    MAX_OF_2(MAX_OF_2(a, b), c)
#define MAX_OF_4(a, b, c, d) MAX_OF_2(MAX_OF_3(a, b, c), d)
...etc up to MAX_OF_8

What I'd like to do is replace them with something like this:

/* Base case #1, single input */
#define MAX_OF_N(x)      (x)

/* Base case #2, two inputs */
#define MAX_OF_N(x, y)   (x) > (y) ? (x) : (y)

/* Recursive definition, arbitrary number of inputs */
#define MAX_OF_N(x, ...) MAX_OF_N(x, MAX_OF_N(__VA_ARGS__))

...which, of course, is not valid preprocessor code.

Ignoring that this particular case should probably be solved using a function rather than a preprocessor macro, is it possible to define a variadic MAX_OF_N() macro?

Just for clarity, the end result should be a single macro that takes an arbitrary number of parameters and evaluates to the largest of them. I've got an odd feeling that this should be possible, but I'm not seeing how.

Solution 1:

It's possible to write a macro that evaluates to the number of arguments it's called with. (I couldn't find a link to the place where I first saw it.) So you could write MAX_OF_N() that would work as you'd like, but you'd still need all the numbered macros up until some limit:

#define MAX_OF_1(a)         (a)         
#define MAX_OF_2(a,b)       max(a, b)

#define MAX_OF_3(a,...)    MAX_OF_2(a,MAX_OF_2(__VA_ARGS__))
#define MAX_OF_4(a,...)    MAX_OF_2(a,MAX_OF_3(__VA_ARGS__))
#define MAX_OF_5(a,...)    MAX_OF_2(a,MAX_OF_4(__VA_ARGS__))
...
#define MAX_OF_64(a,...)   MAX_OF_2(a,MAX_OF_63(__VA_ARGS__))

// NUM_ARGS(...) evaluates to the literal number of the passed-in arguments.
#define _NUM_ARGS2(X,X64,X63,X62,X61,X60,X59,X58,X57,X56,X55,X54,X53,X52,X51,X50,X49,X48,X47,X46,X45,X44,X43,X42,X41,X40,X39,X38,X37,X36,X35,X34,X33,X32,X31,X30,X29,X28,X27,X26,X25,X24,X23,X22,X21,X20,X19,X18,X17,X16,X15,X14,X13,X12,X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1,N,...) N
#define NUM_ARGS(...) _NUM_ARGS2(0, __VA_ARGS__ ,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0)

#define _MAX_OF_N3(N, ...) MAX_OF_ ## N(__VA_ARGS__)
#define _MAX_OF_N2(N, ...) _MAX_OF_N3(N, __VA_ARGS__)
#define MAX_OF_N(...)      _MAX_OF_N2(NUM_ARGS(__VA_ARGS__), __VA_ARGS__)

Now MAX_OF_N(a,b,c,d,e) will evaluate to max(a, max(b, max(c, max(d, e)))). (I've tested on gcc 4.2.1.)

Note that it's critical that the base case (MAX_OF_2) doesn't repeat its arguments more than once in the expansion (which is why I put max in this example). Otherwise, you'd be doubling the length of the expansion for every level, so you can imagine what will happen with 64 arguments :)

Solution 2:

You might consider this cheating, since it is not recursive and it doesn't do the work in the preprocessor. And it uses a GCC extension. And it only works for one type. It is, however, a variadic MAX_OF_N macro:

#include <iostream>
#include <algorithm>

#define MAX_OF_N(...) ({\
        int ra[] = { __VA_ARGS__ }; \
        *std::max_element(&ra[0], &ra[sizeof(ra)/sizeof(int)]); \
    })

int main() {
    int i = 12;
    std::cout << MAX_OF_N(1,3,i,6);
}

Oh yes, and because of the potential variable expression in the initializer list, I don't think that an equivalent of this (using its own function to avoid std::max_element) would work in C89. But I'm not sure variadic macros are in C89 either.

Here's something that I think gets around the "only one type" restriction. It's getting a bit hairy, though:

#include <iostream>
#include <algorithm>

#define MAX_OF_N(x, ...) ({\
        typeof(x) ra[] = { (x), __VA_ARGS__ }; \
        *std::max_element(&ra[0], &ra[sizeof(ra)/sizeof(ra[0])]); \
    })

int main() {
    int i = 12;
    std::cout << MAX_OF_N(i+1,1,3,6,i);
}

Solution 3:

No, because the preprocessor only takes one "swipe" at the file. There's no way to get it to recursively define macros.

The only code that I've seen do something like this was not variadic, but used default values the user had to pass:

x = MAX_OF_8 (a, b, -1, -1, -1, -1, -1, -1)

assuming all values were non-negative.

Inline functions should give you the same for C++ at least. As you state, it's probably better left to a function with variable arguments similar to printf().

Solution 4:

I think that, even if you could expand macros recursively, there would be one little problem with your approach in terms of efficiency... when the macros are expanded, if the MAX_OF_[N-1] is greater, then you have to evaluate it again from scratch.

Here is a silly and stupid answer that probably no one will like xD

file "source.c"

#include "my_macros.h"
...

file "Makefile"

myprogram: source.c my_macros.h
 gcc source.c -o myprogram

my_macros.h: make_macros.py
 python make_macros.py > my_macros.h

file "make_macros.py"

def split(l):
    n = len(l)
    return l[:n/2], l[n/2:]

def gen_param_seq(n):
    return [chr(i + ord("A")) for i in range(n)]

def make_max(a, b):
    if len(a) == 1:
        parta = "("+a[0]+")"
    else:
        parta = make_max(*split(a))

    if len(b) == 1:
        partb = "("+b[0]+")"
    else:
        partb = make_max(*split(b))

    return "("+parta +">"+partb+"?"+parta+":"+partb+")"

for i in range(2, 9):
    p = gen_param_seq(i)
    print "#define MAX_"+str(i)+"("+", ".join(p)+") "+make_max(*split(p))

then you'll have those pretty macros defined:

#define MAX_2(A, B) ((A)>(B)?(A):(B))
#define MAX_3(A, B, C) ((A)>((B)>(C)?(B):(C))?(A):((B)>(C)?(B):(C)))
#define MAX_4(A, B, C, D) (((A)>(B)?(A):(B))>((C)>(D)?(C):(D))?((A)>(B)?(A):(B)):((C)>(D)?(C):(D)))
#define MAX_5(A, B, C, D, E) (((A)>(B)?(A):(B))>((C)>((D)>(E)?(D):(E))?(C):((D)>(E)?(D):(E)))?((A)>(B)?(A):(B)):((C)>((D)>(E)?(D):(E))?(C):((D)>(E)?(D):(E))))
#define MAX_6(A, B, C, D, E, F) (((A)>((B)>(C)?(B):(C))?(A):((B)>(C)?(B):(C)))>((D)>((E)>(F)?(E):(F))?(D):((E)>(F)?(E):(F)))?((A)>((B)>(C)?(B):(C))?(A):((B)>(C)?(B):(C))):((D)>((E)>(F)?(E):(F))?(D):((E)>(F)?(E):(F))))
#define MAX_7(A, B, C, D, E, F, G) (((A)>((B)>(C)?(B):(C))?(A):((B)>(C)?(B):(C)))>(((D)>(E)?(D):(E))>((F)>(G)?(F):(G))?((D)>(E)?(D):(E)):((F)>(G)?(F):(G)))?((A)>((B)>(C)?(B):(C))?(A):((B)>(C)?(B):(C))):(((D)>(E)?(D):(E))>((F)>(G)?(F):(G))?((D)>(E)?(D):(E)):((F)>(G)?(F):(G))))
#define MAX_8(A, B, C, D, E, F, G, H) ((((A)>(B)?(A):(B))>((C)>(D)?(C):(D))?((A)>(B)?(A):(B)):((C)>(D)?(C):(D)))>(((E)>(F)?(E):(F))>((G)>(H)?(G):(H))?((E)>(F)?(E):(F)):((G)>(H)?(G):(H)))?(((A)>(B)?(A):(B))>((C)>(D)?(C):(D))?((A)>(B)?(A):(B)):((C)>(D)?(C):(D))):(((E)>(F)?(E):(F))>((G)>(H)?(G):(H))?((E)>(F)?(E):(F)):((G)>(H)?(G):(H))))

and the best thing about it is that... it works ^_^