## D   A   T   A   W   O   K

Creation: January 01 1970
Modified: October 12 2019

# Buddy Memory Allocator

At any point in time, the memory consists of a collection of blocks of consecutive memory, each of which is a power of two in size. Each block is marked either busy or free, depending of whether it is allocated to the user.

For each block we also know its order, that is equal to the logarithm, base 2, of the "block-size" divided by the "block unit size". The block unit size is the power of two value representing the minimum block size that is allocable.

The system provides two operations for supporting dynamic memory allocation:

• Allocate : finds a free block that satisfies the requested size eventually splitting a bigger block in smaller power of two blocks, marks is as busy, and returns a pointer to it.
• Deallocate : marks a previously allocated block as free and may merge it with others to form a larger free block.

### Allocation

The buddy system maintains a list of the free blocks of each order, so that it is easy to find a block of the desired order, if one is available. If no block of the requested order is available, allocate searches for the first non-empty list for blocks of at least the size requested. In either case, a block is removed from the free list.

If the found block is larger that the requested size, say b^k instead of the desired b^i, with k > i, then the block is split in half, making two blocks of size b^(k-1). If this is still too large, k-1 > i, then one of the blocks of size b^(k-1) is split in half. This process is repeated until we have blocks of size b^(k-1), b^(k-2),..., b^(i+1), b^i. Then one of the blocks of size b^i is marked as busy and returned to the user. The others are added to the appropriate free list.

``````    +---------------------------------------------------------------+
512 |                               S                               |
+-------------------------------+-------------------------------+
256 |               S               |               F               |
+---------------+---------------+-------------------------------+
128 |       S       |       F       |
+-------+-------+---------------+
64 |   S   |   F   |                        S - split
+-------+-------+                        F - free
32 | B | F |                                B - busy
+-------+``````

The allocator user usually asks for a chunk of memory of certain size. It doesn't know about memory blocks and internal things. Thus there will be a wrapper function that takes as parameter a generic size. This size will be rounded to the next power of two and the buddy allocator is then invoked.

Pseudocode to allocate a block of order n:

``````block allocate(order n)
if the list of free blocks of order n is not empty
return the first block in that list
else
B = allocate(n+1)
<B1,B2> = split(B);
append B2 to the free-list of order n
return B1;``````

The only data structure we need at this point is an array a list of free blocks. One array element for each possible order

``struct list_link free_list[MAX_ORDER];``

With The prev and next pointers for the lists are stored directly in the free blocks themselves.

### Deallocation

When a block is deallocated, the buddy system checks whether the block can be merged with any other, or more precisely whether we can undo any splits that were performed to make this block. Each block B (except the initial block) was created by splitting another into two halves, B1 and B2. Note that each one is the unique buddy of the other.

The merging process checks whether the buddy of a deallocated block is also free, in which case the two are merged; then it checks whether the buddy of the resulting block is also free, in which case they are merged; and so on.

Because the buddy systems is often used in contexts where the address returned to the user must be aligned to the unit block (e.g. as a physical page frames allocator) we cannot store block information within the block itself but we'll store the meta-information in a dedicated memory chunk.

Because of the way we split any merge blocks, blocks stay aligned relatively to the first block address. More precisely, the relative address of a block of size 2^k ends with k zeros. As a result, to find the address of the buddy of a block of size 2^k we simply flip the (k+1)-st bit from the right. Once that we have the address of the block buddy we must check whether it's free or not. We could look through the free list of order n but there could be thousands of blocks and walking the list is hard on the cache. Instead we'll use some extra meta-information.

For each order n we maintain a couple of structures:

• a list of free blocks;
• a bitset representing each possible block (of a given order)

To access to the correct bit in a particular order bitset we infer the `block_index` using the block address and the block order. Given a unit block size equal to `1 << unit_bit` then

``index = (block_address - base_address) >> (unit_bit + order);``

That is, we just need to divide the relative block address by `2^(unit_bits+order)`.

Note that by working on the relative address we are independent from the pool alignment. Otherwise it is mandatory to have a base address that is aligned to the size of the unit block.

The overhead of storing these extra bits is one byte for every 8 blocks of a given order. But in fact we can do better, we can get by with just half a bit per block.

For each pair of buddies B1 and B2 we store a sigle bit representing `is_free(B1) XOR is_free(B2)`. We can easily maintain the state of that bit by flipping it each time one of the buddies is freed or allocated.

When we consider making a merge we know that one of buddies is free, because it is only when a block has just been freed that we consider a merge. This means we can find out the state of the other block from the XORed bit. If it is 0, then both blocks are free, if it is 1 then it is just our block that is free. Thus we've reduced the bitset overhead by a factor of two.