C pre-processor fun

Math in the C pre-processor by breaking up Numbers into arrays of 8 bits and implementing common operations on those arrays.

Stuff it can do

#include "convert.h"
#include "math.h"

//this is esentially (6 / 2) * (15 - 13)
BYTE2CONST(
	MUL(
		DIV(
			CONST2BYTE(6),
			CONST2BYTE(2)
		),
		SUB(
			CONST2BYTE(15),
			CONST2BYTE(13)
		)
	)
)

running with cpp test.h gives

6

See also

I got the idea when looking at orangeduck's cpp Brainfuck interpreter The readme gives a good overview on how one can have fun with the C pre-processor. Be sure to also check out C Preprocessor tricks, tips, and idioms by pfultz2. However they both do math by simply incrementing/decrementing numbers using macros in the form of

#define INC(x) INC_##x
#define INC_0 1
#define INC_1 2
#define INC_2 3
//...

When i saw this together with orangeduck's list functionality, i thought why not represent numbers as a list of 8 ones and zeros. Allowing us to easily implement common operations like addition/subtraction/multiplication and of course bitwise operations such as not/and/or/xor. See below for more information

How this works

Basics

First of all the very basics. When you "program" in/with/for the C pre-processor you often use variable pasting. This looks something like this:

#define NOT_1 0
#define NOT_0 1
#define NOT(X) NOT_##X

When we now enter NOT(1) it gets evaluated to NOT_1 which is again a macro for 0.

Lists

Basically cpp only pastes strings, so we need some trickery to create lists or arrays if you wish. However when we pass a list as (0,0,0,0) we can just use the list as arguments like. Let me give an example

#define _NOT_4BIT(b3, b2, b1, b0) (NOT(b3), NOT(b2), NOT(b1), NOT(b0))
#define NOT_4BIT(X) _NOT_4BIT X

Now when we run NOT_4BIT((0,1,0,1)) we get (1,0,1,0). Thats great! Now using the same scheme we can create macros for the other bitwise operations and/or/xor. Then we can implement addition, and using ADD(X, NOT(Y)) and setting the carry-in we can subtract.

In this repo all of this is done on 8 bit values

Conversion

For now conversion between between numbers and bit arrays (BYTE2CONST and CONST2BYTE) is done using 256 macros each. That code gets generated by generate_convert. You can run it using ./generate_convert.sh

License

The code is published under the EUPL

The “European Union Public Licence” (EUPL) is a copyleft free/open source software license created on the initiative of and approved by the European Commission in 22 official languages of the European Union.