Implementation

Implementation
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Free List Store

- The Free List Store (referred to as FLS for the remaining part of this - document) is the Global memory pool that is shared by all instances of - the bitmapped allocator instantiated for any type. This maintains a - sorted order of all free memory blocks given back to it by the - bitmapped allocator, and is also responsible for giving memory to the - bitmapped allocator when it asks for more. -

- Internally, there is a Free List threshold which indicates the - Maximum number of free lists that the FLS can hold internally - (cache). Currently, this value is set at 64. So, if there are - more than 64 free lists coming in, then some of them will be given - back to the OS using operator delete so that at any given time the - Free List's size does not exceed 64 entries. This is done because - a Binary Search is used to locate an entry in a free list when a - request for memory comes along. Thus, the run-time complexity of - the search would go up given an increasing size, for 64 entries - however, lg(64) == 6 comparisons are enough to locate the correct - free list if it exists. -

- Suppose the free list size has reached its threshold, then the - largest block from among those in the list and the new block will - be selected and given back to the OS. This is done because it - reduces external fragmentation, and allows the OS to use the - larger blocks later in an orderly fashion, possibly merging them - later. Also, on some systems, large blocks are obtained via calls - to mmap, so giving them back to free system resources becomes most - important. -

- The function _S_should_i_give decides the policy that determines - whether the current block of memory should be given to the - allocator for the request that it has made. That's because we may - not always have exact fits for the memory size that the allocator - requests. We do this mainly to prevent external fragmentation at - the cost of a little internal fragmentation. Now, the value of - this internal fragmentation has to be decided by this function. I - can see 3 possibilities right now. Please add more as and when you - find better strategies. -

Equal size check. Return true only when the 2 blocks are of equal -size.
Difference Threshold: Return true only when the _block_size is -greater than or equal to the _required_size, and if the _BS is > _RS -by a difference of less than some THRESHOLD value, then return true, -else return false.
Percentage Threshold. Return true only when the _block_size is -greater than or equal to the _required_size, and if the _BS is > _RS -by a percentage of less than some THRESHOLD value, then return true, -else return false.

- Currently, (3) is being used with a value of 36% Maximum wastage per - Super Block. -

Super Block

- A super block is the block of memory acquired from the FLS from - which the bitmap allocator carves out memory for single objects - and satisfies the user's requests. These super blocks come in - sizes that are powers of 2 and multiples of 32 - (_Bits_Per_Block). Yes both at the same time! That's because the - next super block acquired will be 2 times the previous one, and - also all super blocks have to be multiples of the _Bits_Per_Block - value. -

- How does it interact with the free list store? -

- The super block is contained in the FLS, and the FLS is responsible for - getting / returning Super Bocks to and from the OS using operator new - as defined by the C++ standard. -

Super Block Data Layout

- Each Super Block will be of some size that is a multiple of the - number of Bits Per Block. Typically, this value is chosen as - Bits_Per_Byte x sizeof(size_t). On an x86 system, this gives the - figure 8 x 4 = 32. Thus, each Super Block will be of size 32 - x Some_Value. This Some_Value is sizeof(value_type). For now, let - it be called 'K'. Thus, finally, Super Block size is 32 x K bytes. -

- This value of 32 has been chosen because each size_t has 32-bits - and Maximum use of these can be made with such a figure. -

- Consider a block of size 64 ints. In memory, it would look like this: - (assume a 32-bit system where, size_t is a 32-bit entity). -

Table 21.1. Bitmap Allocator Memory Map

268

4294967295

Data -> Space for 64 ints

- The first Column(268) represents the size of the Block in bytes as - seen by the Bitmap Allocator. Internally, a global free list is - used to keep track of the free blocks used and given back by the - bitmap allocator. It is this Free List Store that is responsible - for writing and managing this information. Actually the number of - bytes allocated in this case would be: 4 + 4 + (4x2) + (64x4) = - 272 bytes, but the first 4 bytes are an addition by the Free List - Store, so the Bitmap Allocator sees only 268 bytes. These first 4 - bytes about which the bitmapped allocator is not aware hold the - value 268. -

- What do the remaining values represent?

- The 2nd 4 in the expression is the sizeof(size_t) because the - Bitmapped Allocator maintains a used count for each Super Block, - which is initially set to 0 (as indicated in the diagram). This is - incremented every time a block is removed from this super block - (allocated), and decremented whenever it is given back. So, when - the used count falls to 0, the whole super block will be given - back to the Free List Store. -

- The value 4294967295 represents the integer corresponding to the bit - representation of all bits set: 11111111111111111111111111111111. -

- The 3rd 4x2 is size of the bitmap itself, which is the size of 32-bits - x 2, - which is 8-bytes, or 2 x sizeof(size_t). -

Maximum Wasted Percentage

- This has nothing to do with the algorithm per-se, - only with some vales that must be chosen correctly to ensure that the - allocator performs well in a real word scenario, and maintains a good - balance between the memory consumption and the allocation/deallocation - speed. -

- The formula for calculating the maximum wastage as a percentage: -

-(32 x k + 1) / (2 x (32 x k + 1 + 32 x c)) x 100. -

- where k is the constant overhead per node (e.g., for list, it is - 8 bytes, and for map it is 12 bytes) and c is the size of the - base type on which the map/list is instantiated. Thus, suppose the - type1 is int and type2 is double, they are related by the relation - sizeof(double) == 2*sizeof(int). Thus, all types must have this - double size relation for this formula to work properly. -

- Plugging-in: For List: k = 8 and c = 4 (int and double), we get: - 33.376% -

-For map/multimap: k = 12, and c = 4 (int and double), we get: 37.524% -

- Thus, knowing these values, and based on the sizeof(value_type), we may - create a function that returns the Max_Wastage_Percentage for us to use. -

`allocate`

- The allocate function is specialized for single object allocation - ONLY. Thus, ONLY if n == 1, will the bitmap_allocator's - specialized algorithm be used. Otherwise, the request is satisfied - directly by calling operator new. -

- Suppose n == 1, then the allocator does the following: -

- Checks to see whether a free block exists somewhere in a region - of memory close to the last satisfied request. If so, then that - block is marked as allocated in the bit map and given to the - user. If not, then (2) is executed. -
- Is there a free block anywhere after the current block right - up to the end of the memory that we have? If so, that block is - found, and the same procedure is applied as above, and - returned to the user. If not, then (3) is executed. -
- Is there any block in whatever region of memory that we own - free? This is done by checking -
- - The use count for each super block, and if that fails then -
- - The individual bit-maps for each super block. -
- Note: Here we are never touching any of the memory that the - user will be given, and we are confining all memory accesses - to a small region of memory! This helps reduce cache - misses. If this succeeds then we apply the same procedure on - that bit-map as (1), and return that block of memory to the - user. However, if this process fails, then we resort to (4). -
- This process involves Refilling the internal exponentially - growing memory pool. The said effect is achieved by calling - _S_refill_pool which does the following: -
- - Gets more memory from the Global Free List of the Required - size. -
- - Adjusts the size for the next call to itself. -
- - Writes the appropriate headers in the bit-maps. -
- - Sets the use count for that super-block just allocated to 0 - (zero). -
- - All of the above accounts to maintaining the basic invariant - for the allocator. If the invariant is maintained, we are - sure that all is well. Now, the same process is applied on - the newly acquired free blocks, which are dispatched - accordingly. -

-Thus, you can clearly see that the allocate function is nothing but a -combination of the next-fit and first-fit algorithm optimized ONLY for -single object allocations. -

`deallocate`

- The deallocate function again is specialized for single objects ONLY. - For all n belonging to > 1, the operator delete is called without - further ado, and the deallocate function returns. -

- However for n == 1, a series of steps are performed: -

- We first need to locate that super-block which holds the memory - location given to us by the user. For that purpose, we maintain - a static variable _S_last_dealloc_index, which holds the index - into the vector of block pairs which indicates the index of the - last super-block from which memory was freed. We use this - strategy in the hope that the user will deallocate memory in a - region close to what he/she deallocated the last time around. If - the check for belongs_to succeeds, then we determine the bit-map - for the given pointer, and locate the index into that bit-map, - and mark that bit as free by setting it. -
- If the _S_last_dealloc_index does not point to the memory block - that we're looking for, then we do a linear search on the block - stored in the vector of Block Pairs. This vector in code is - called _S_mem_blocks. When the corresponding super-block is - found, we apply the same procedure as we did for (1) to mark the - block as free in the bit-map. -

- Now, whenever a block is freed, the use count of that particular - super block goes down by 1. When this use count hits 0, we remove - that super block from the list of all valid super blocks stored in - the vector. While doing this, we also make sure that the basic - invariant is maintained by making sure that _S_last_request and - _S_last_dealloc_index point to valid locations within the vector. -

Questions

1

-Q1) The "Data Layout" section is -cryptic. I have no idea of what you are trying to say. Layout of what? -The free-list? Each bitmap? The Super Block? -

- The layout of a Super Block of a given -size. In the example, a super block of size 32 x 1 is taken. The -general formula for calculating the size of a super block is -32 x sizeof(value_type) x 2^n, where n ranges from 0 to 32 for 32-bit -systems. -

2

- And since I just mentioned the -term `each bitmap', what in the world is meant by it? What does each -bitmap manage? How does it relate to the super block? Is the Super -Block a bitmap as well? -

- Each bitmap is part of a Super Block which is made up of 3 parts - as I have mentioned earlier. Re-iterating, 1. The use count, - 2. The bit-map for that Super Block. 3. The actual memory that - will be eventually given to the user. Each bitmap is a multiple - of 32 in size. If there are 32 x (2^3) blocks of single objects - to be given, there will be '32 x (2^3)' bits present. Each 32 - bits managing the allocated / free status for 32 blocks. Since - each size_t contains 32-bits, one size_t can manage up to 32 - blocks' status. Each bit-map is made up of a number of size_t, - whose exact number for a super-block of a given size I have just - mentioned. -

3

- How do the allocate and deallocate functions work in regard to - bitmaps? -

- The allocate and deallocate functions manipulate the bitmaps and - have nothing to do with the memory that is given to the user. As - I have earlier mentioned, a 1 in the bitmap's bit field - indicates free, while a 0 indicates allocated. This lets us - check 32 bits at a time to check whether there is at lease one - free block in those 32 blocks by testing for equality with - (0). Now, the allocate function will given a memory block find - the corresponding bit in the bitmap, and will reset it (i.e., - make it re-set (0)). And when the deallocate function is called, - it will again set that bit after locating it to indicate that - that particular block corresponding to this bit in the bit-map - is not being used by anyone, and may be used to satisfy future - requests. -

- e.g.: Consider a bit-map of 64-bits as represented below: - 1111111111111111111111111111111111111111111111111111111111111111 -

- Now, when the first request for allocation of a single object - comes along, the first block in address order is returned. And - since the bit-maps in the reverse order to that of the address - order, the last bit (LSB if the bit-map is considered as a - binary word of 64-bits) is re-set to 0. -

- The bit-map now looks like this: - 1111111111111111111111111111111111111111111111111111111111111110 -

Locality

- Another issue would be whether to keep the all bitmaps in a - separate area in memory, or to keep them near the actual blocks - that will be given out or allocated for the client. After some - testing, I've decided to keep these bitmaps close to the actual - blocks. This will help in 2 ways. -

Constant time access for the bitmap themselves, since no kind of -look up will be needed to find the correct bitmap list or its -equivalent.
And also this would preserve the cache as far as possible.

- So in effect, this kind of an allocator might prove beneficial from a - purely cache point of view. But this allocator has been made to try and - roll out the defects of the node_allocator, wherein the nodes get - skewed about in memory, if they are not returned in the exact reverse - order or in the same order in which they were allocated. Also, the - new_allocator's book keeping overhead is too much for small objects and - single object allocations, though it preserves the locality of blocks - very well when they are returned back to the allocator. -

Overhead and Grow Policy

- Expected overhead per block would be 1 bit in memory. Also, once - the address of the free list has been found, the cost for - allocation/deallocation would be negligible, and is supposed to be - constant time. For these very reasons, it is very important to - minimize the linear time costs, which include finding a free list - with a free block while allocating, and finding the corresponding - free list for a block while deallocating. Therefore, I have - decided that the growth of the internal pool for this allocator - will be exponential as compared to linear for - node_allocator. There, linear time works well, because we are - mainly concerned with speed of allocation/deallocation and memory - consumption, whereas here, the allocation/deallocation part does - have some linear/logarithmic complexity components in it. Thus, to - try and minimize them would be a good thing to do at the cost of a - little bit of memory. -

- Another thing to be noted is the pool size will double every time - the internal pool gets exhausted, and all the free blocks have - been given away. The initial size of the pool would be - sizeof(size_t) x 8 which is the number of bits in an integer, - which can fit exactly in a CPU register. Hence, the term given is - exponential growth of the internal pool. -