Can I add numbers with the C/C++ preprocessor?

Question

For some base. Base 1 even. Some sort of complex substitution -ing.

Also, and of course, doing this is not a good idea in real life production code. I just asked out of curiosity.

Solution 1

You can relatively easy write macro which adds two integers in binary. For example - macro which sums two 4-bit integers in binary :

#include "stdio.h"

// XOR truth table
#define XOR_0_0 0
#define XOR_0_1 1
#define XOR_1_0 1
#define XOR_1_1 0

// OR truth table
#define OR_0_0 0
#define OR_0_1 1
#define OR_1_0 1
#define OR_1_1 1

// AND truth table
#define AND_0_0 0
#define AND_0_1 0
#define AND_1_0 0
#define AND_1_1 1

// concatenation macros
#define XOR_X(x,y) XOR_##x##_##y
#define   OR_X(x,y) OR_##x##_##y
#define  AND_X(x,y) AND_##x##_##y
#define OVERFLOW_X(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) OVERFLOW_##rc1 (rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)

// stringification macros
#define STR_X(x) #x
#define STR(x) STR_X(x)

// boolean operators
#define XOR(x,y) XOR_X(x,y)
#define   OR(x,y) OR_X(x,y)
#define  AND(x,y) AND_X(x,y)

// carry_bit + bit1 + bit2
#define BIT_SUM(carry,bit1,bit2) XOR(carry, XOR(bit1,bit2))
// carry_bit + carry_bit_of(bit1 + bit2)
#define CARRY_SUM(carry,bit1,bit2) OR(carry, AND(bit1,bit2))

// do we have overflow or maybe result perfectly fits into 4 bits ?
#define OVERFLOW_0(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) SHOW_RESULT(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)
#define OVERFLOW_1(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) SHOW_OVERFLOW(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)

// draft-horse macros which performs addition of two 4-bit integers
#define ADD_BIN_NUM(a1,a2,a3,a4, b1,b2,b3,b4) ADD_BIN_NUM_4(0,0,0,0, 0,0,0,0, a1,a2,a3,a4, b1,b2,b3,b4)
#define ADD_BIN_NUM_4(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) ADD_BIN_NUM_3(rc1,rc2,rc3,AND(CARRY_SUM(0,a4,b4),OR(a4,b4)), rb1,rb2,rb3,BIT_SUM(0,a4,b4), a1,a2,a3,a4, b1,b2,b3,b4)
#define ADD_BIN_NUM_3(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) ADD_BIN_NUM_2(rc1,rc2,AND(CARRY_SUM(rc4,a3,b3),OR(a3,b3)),rc4, rb1,rb2,BIT_SUM(rc4,a3,b3),rb4, a1,a2,a3,a4, b1,b2,b3,b4)
#define ADD_BIN_NUM_2(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) ADD_BIN_NUM_1(rc1,AND(CARRY_SUM(rc3,a2,b2),OR(a2,b2)),rc3,rc4, rb1,BIT_SUM(rc3,a2,b2),rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)
#define ADD_BIN_NUM_1(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)      OVERFLOW(AND(CARRY_SUM(rc2,a1,b1),OR(a1,b1)),rc2,rc3,rc4, BIT_SUM(rc2,a1,b1),rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)
#define OVERFLOW(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) OVERFLOW_X(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4)
#define   SHOW_RESULT(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) STR(a1) STR(a2) STR(a3) STR(a4) " + " STR(b1) STR(b2) STR(b3) STR(b4) " = " STR(rb1) STR(rb2) STR(rb3) STR(rb4)
#define   SHOW_OVERFLOW(rc1,rc2,rc3,rc4, rb1,rb2,rb3,rb4, a1,a2,a3,a4, b1,b2,b3,b4) STR(a1) STR(a2) STR(a3) STR(a4) " + " STR(b1) STR(b2) STR(b3) STR(b4) " = overflow"

void main()
{
    printf("%s\n", 
        ADD_BIN_NUM(
                    0,0,0,1, // first  4-bit int
                    1,0,1,1) // second 4-bit int
                    );

    printf("%s\n", 
        ADD_BIN_NUM(
                    0,1,0,0, // first  4-bit int
                    0,1,0,1) // second 4-bit int
                );

    printf("%s\n", 
        ADD_BIN_NUM(
                    1,0,1,1, // first  4-bit int
                    0,1,1,0) // second 4-bit int
                );
}

This macro can be easily extended for addition of two 8-bit or 16-bit or even 32-bit ints. So basically all that we need is token concatenation and substitution rules to achieve amazing results with macros.

EDIT: I have changed formating of results and more importantly - I've added overflow check.

HTH!

Solution 2

The preprocessor operates on preprocessing tokens and the only time that it evaluates numbers is during the evaluation of a #if or #elif directive. Other than that, numbers aren't really numbers during preprocessing; they are classified as preprocessing number tokens, which aren't actually numbers.

You could evaluate basic arithmetic using token concatenation:

#define ADD_0_0 0
#define ADD_0_1 1
#define ADD_1_0 1
#define ADD_1_1 2

#define ADD(x, y) ADD##_##x##_##y

ADD(1, 0) // expands to 1
ADD(1, 1) // expands to 2

Really, though, there's no reason to do this, and it would be silly to do so (you'd have to define a huge number of macros for it to be even remotely useful).

It would be more sensible to have a macro that expands to an integral constant expression that can be evaluated by the compiler:

#define ADD(x, y) ((x) + (y))

ADD(1, 1) // expands to ((1) + (1))

The compiler will be able to evaluate the 1 + 1 expression.

Solution 3

It is quite possible to do bounded integer addition in the preprocessor. And, it is actually needed more often than one would really hope, i.e., the alternative to just have ((2) + (3)) in the program doesn't work. (E.g., you can't have a variable called x((2)+(3))). The idea is simple: turn the addition to increments, which you don't mind (too much) listing them all out. E.g.,

#define INC(x) INC_ ## x
#define INC_0 1
#define INC_1 2
#define INC_2 3
#define INC_3 4
#define INC_4 5
#define INC_5 6
#define INC_6 7
#define INC_7 8
#define INC_8 9
#define INC_9 10
INC(7) // => 8

Now we know how to do addition to up to 1.

#define ADD(x, y) ADD_ ## x(y)
#define ADD_0(x) x
#define ADD_1(x) INC(x)
ADD(0, 2) // => 2
ADD(1, 2) // => 3

To add to even larger numbers, you need some sort of "recursion".

#define ADD_2(x) ADD_1(INC(x))
#define ADD_3(x) ADD_2(INC(x))
#define ADD_4(x) ADD_3(INC(x))
#define ADD_5(x) ADD_4(INC(x))
#define ADD_6(x) ADD_5(INC(x))
#define ADD_7(x) ADD_6(INC(x))
#define ADD_8(x) ADD_7(INC(x))
#define ADD_9(x) ADD_8(INC(x))
#define ADD_10(x) ADD_9(INC(x))
ADD(5, 2) // => 7

One has to be careful in this, however. E.g., the following does not work.

#define ADD_2(x) INC(ADD_1(x))
ADD(2, 2) // => INC_ADD_1(2)

For any extended use of such tricks, Boost Preprocessor is your friend.

Solution 4

I know it's not the preprocessor, but if it helps, you can do it with templates. Perhaps you could use this in conjunction with a macro to achieve what you need.

#include <iostream>
using namespace std;

template <int N, int M>
struct Add
{
    static const int Value = N + M;
};

int main()
{
    cout << Add<4, 5>::Value << endl;
    return 0;
}

Solution 5

Apparently, you can. If you take a look at the Boost Preprocessor library, you can do all sorts of stuff with the preprocessor, even integer addition.

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