Thursday, November 24, 2005

C++ templates are turing complete

Here you will find a short C++ program that takes more than 24 hrs to compile on a dedicated dual processor, 1GB memory machine!! Here we go...

template<int Depth, int A, typename B>
struct K17 {
static const int x =
K17 <Depth+1, 0, K17<Depth,A,B> >::x
+ K17 <Depth+1, 1, K17<Depth,A,B> >::x
+ K17 <Depth+1, 2, K17<Depth,A,B> >::x
+ K17 <Depth+1, 3, K17<Depth,A,B> >::x
+ K17 <Depth+1, 4, K17<Depth,A,B> >::x;
};
template <int A, typename B>
struct K17 <16,A,B> { static const int x = 1;
};
static const int z = K17 <0,0,int>::x;
int main(void) { }

Source: C++ Templates are Turing Complete by Todd L. Veldhuizen

This program is taken from the above paper which takes unreasonably long to compile. I belive, a simple dynamic programming solution will reduce the exponential time required by this program to compile to polynomial time. I also believe, it might be quite difficult to apply dynamic programming solution, in general, to all C++ programs of this nature. You need to have a good understanding of template meta-programming to make sense of this program. One good article by the same author is here:

This post is motivated by a anonymous comment I received on an earlier post. I am quoting him here:

"It is ___provably___ impossible to write a correct C++ parser which will complete compilation with either success or failure because the C++ template system is Turing complete. This means that code generation is based on a turing complete program. Code generation in C++ isn't based on a program description, but an actual turing complete program. As such, it is subject to the halting problem. Therefore, it is unknowable whether a compilation will complete, and unknowable if you are looking at a valid C++ program."

4 comments:

Crunch said...

there is an error in the code :

K17 >:x

should be :

K17 >::x

otherwise, it won't compile

Sumant said...

Fixed. Thanks!

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David Stone said...

The only reason it takes so long to compile is because it adds in unused template arguments A and B. Once those are deleted, you give addition of the same thing 5 times, so you just replace that with multiplication.

There is also a compile-time error caused by integer overflow in a constant expression. The type of x and z need to be able to hold a 38-bit integer. Something like std::int64_t should be good enough.

Once you make the changes to get rid of useless code and allow it to compile, it finishes in about .2 seconds on my machine.