FUZxxl - 6 months ago 27

C Question

I am writing a tablebase for a Japanese chess variant. To index the table base, I encode each chess position as an integer. In one of the encoding steps, I encode where the pieces are on the board. Since the actual method is a bit complicated, let me explain the problem in a simplified manner.

In the endgame tablebase, I have (let's say) six distinct chess pieces that I want to distribute over a board with 9 squares. I can naïvely represent their positions by a six-tuple (

However, this representation is not optimal: no two chess pieces can occupy the same square but the aforementioned encoding happily allows this. We can encode the same position by a six-tuple [

`1st piece: 0 1 2 3 4 5 6 7 8`

2nd piece: 0 1 2 - 3 4 5 6 7

the other pieces are encoded similarly,

`1st: 0 1 2 3 4 5 6 7 8 --> 5`

2nd: 0 1 2 3 4 - 5 6 7 --> 2

3rd: 0 1 - 2 3 - 4 5 6 --> 2

4th: 0 1 - - 2 - 3 4 5 --> 0

5th: - 0 - - 1 - 2 3 4 --> 3

6th: - 0 - - 1 - 2 - 3 --> 1

In my actual encoding, the number of pieces I want to encode is not fixed. The number of squares on the board however is.

How can I efficiently convert the naïve representation to the compact representation and vice versa? I use standard C99 for the program. In the context of this question, I am not interested in answers that use non-standard constructs, inline assembly or intrinsics.

As there seems to be some confusion about the question:

- The question is to find a practically efficient way to implement the conversion between the
*naïve*and the*compact*position representations - Both representations are
*n*-tuples of integers in certain ranges. The question is not about how to encode these representations into anything else. - In one of the cases I have, the number of squares is 25 and the number of pieces is up to 12. I am however interested in an implementation that works for a reasonable parameter space (e.g. up to 64 squares and up to 32 pieces).
- I am not interested in alternative representations or encodings, especially representations or encodings that are not optimal.
- Nor am I interested in remarks that the
*compact*representation isn't worth the effort. - Nor am I interested in answers that use intrinsics, inline assembly or any other non-standard constructs (except perhaps those described by POSIX).

Answer

I have found a more elegant solution for up to 16 positions using 64-bit integers with a single loop for both encoding and decoding:

```
#include <stdio.h>
#include <stdlib.h>
void encode16(int dest[], int src[], int n) {
unsigned long long state = 0xfedcba9876543210;
for (int i = 0; i < n; i++) {
int p4 = src[i] * 4;
dest[i] = (state >> p4) & 15;
state -= 0x1111111111111110 << p4;
}
}
void decode16(int dest[], int src[], int n) {
unsigned long long state = 0xfedcba9876543210;
for (int i = 0; i < n; i++) {
int p4 = src[i] * 4;
dest[i] = (state >> p4) & 15;
unsigned long long mask = ((unsigned long long)1 << p4) - 1;
state = (state & mask) | ((state >> 4) & ~mask);
}
}
int main(int argc, char *argv[]) {
int naive[argc], compact[argc];
int n = argc - 1;
for (int i = 0; i < n; i++) {
naive[i] = atoi(argv[i + 1]);
}
encode16(compact, naive, n);
for (int i = 0; i < n; i++) {
printf("%d ", compact[i]);
}
printf("\n");
decode16(naive, compact, n);
for (int i = 0; i < n; i++) {
printf("%d ", naive[i]);
}
printf("\n");
return 0;
}
```

The code uses 64-bit unsigned integers to hold arrays of 16 values in the range `0..15`

. Such an array can be updated in parallel in a single step, extracting a value is straightforward and deleting a value is a bit more cumbersome but still only a few steps.

You could extend this method to 25 positions using non-portable 128-bit integers (type `__int128`

is supported by both gcc and clang), encoding each position on 5 bits, taking advantage of the fact that `5 * 25 < 128`

, but the magical constants are more cumbersome to write.