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6 <title>Bitmap Allocator</title>
7 <meta content="Dhruv Matani" name="author">
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11 <h1 style="text-align: center;">Bitmap Allocator</h1>
13 <small><small>The latest version of this document is always available
15 href="http://gcc.gnu.org/onlinedocs/libstdc++/ext/ballocator_doc.html">
16 http://gcc.gnu.org/onlinedocs/libstdc++/ext/ballocator_doc.html</a>.</small></small></em><br>
18 <em> To the <a href="http://gcc.gnu.org/libstdc++/">libstdc++-v3
19 homepage</a>.</em><br>
21 <hr style="width: 100%; height: 2px;"><br>
22 As this name suggests, this allocator uses a bit-map to keep track of
23 the used and unused memory locations for it's book-keeping purposes.<br>
25 This allocator will make use of 1 single bit to keep track of whether
26 it has been allocated or not. A bit 1 indicates free, while 0 indicates
27 allocated. This has been done so that you can easily check a collection
28 of bits for a free block. This kind of Bitmapped strategy works best
29 for single object allocations, and with the STL type parameterized
30 allocators, we do not need to choose any size for the block which will
31 be represented by a single bit. This will be the size of the parameter
32 around which the allocator has been parameterized. Thus, close to
33 optimal performance will result. Hence, this should be used for node
34 based containers which call the allocate function with an argument of 1.<br>
36 The bitmapped allocator's internal pool is exponentially growing.
37 Meaning that internally, the blocks acquired from the Free List Store
38 will double every time the bitmapped allocator runs out of memory.<br>
40 <hr style="width: 100%; height: 2px;"><br>
41 The macro __GTHREADS decides whether to use Mutex Protection around
42 every allocation/deallocation. The state of the macro is picked up
43 automatically from the gthr abstration layer.<br>
45 <hr style="width: 100%; height: 2px;">
46 <h3 style="text-align: center;">What is the Free List Store?</h3>
48 The Free List Store (referred to as FLS for the remaining part of this
49 document) is the Global memory pool that is shared by all instances of
50 the bitmapped allocator instantiated for any type. This maintains a
51 sorted order of all free memory blocks given back to it by the
52 bitmapped allocator, and is also responsible for giving memory to the
53 bitmapped allocator when it asks for more.<br>
55 Internally, there is a Free List threshold which indicates the Maximum
56 number of free lists that the FLS can hold internally (cache).
57 Currently, this value is set at 64. So, if there are more than 64 free
58 lists coming in, then some of them will be given back to the OS using
59 operator delete so that at any given time the Free List's size does not
60 exceed 64 entries. This is done because a Binary Search is used to
61 locate an entry in a free list when a request for memory comes along.
62 Thus, the run-time complexity of the search would go up given an
63 increasing size, for 64 entries however, lg(64) == 6 comparisons are
64 enough to locate the correct free list if it exists.<br>
66 Suppose the free list size has reached it's threshold, then the largest
67 block from among those in the list and the new block will be selected
68 and given back to the OS. This is done because it reduces external
69 fragmentation, and allows the OS to use the larger blocks later in an
70 orderly fashion, possibly merging them later. Also, on some systems,
71 large blocks are obtained via calls to mmap, so giving them back to
72 free system resources becomes most important.<br>
74 The function _S_should_i_give decides the policy that determines
75 whether the current block of memory should be given to the allocator
76 for the request that it has made. That's because we may not always have
77 exact fits for the memory size that the allocator requests. We do this
78 mainly to prevent external fragmentation at the cost of a little
79 internal fragmentation. Now, the value of this internal fragmentation
80 has to be decided by this function. I can see 3 possibilities right
81 now. Please add more as and when you find better strategies.<br>
84 <li>Equal size check. Return true only when the 2 blocks are of equal
86 <li>Difference Threshold: Return true only when the _block_size is
87 greater than or equal to the _required_size, and if the _BS is > _RS
88 by a difference of less than some THRESHOLD value, then return true,
89 else return false. </li>
90 <li>Percentage Threshold. Return true only when the _block_size is
91 greater than or equal to the _required_size, and if the _BS is > _RS
92 by a percentage of less than some THRESHOLD value, then return true,
93 else return false.</li>
96 Currently, (3) is being used with a value of 36% Maximum wastage per
99 <hr style="width: 100%; height: 2px;"><span style="font-weight: bold;">1)
100 What is a super block? Why is it needed?</span><br>
102 A super block is the block of memory acquired from the FLS from which
103 the bitmap allocator carves out memory for single objects and satisfies
104 the user's requests. These super blocks come in sizes that are powers
105 of 2 and multiples of 32 (_Bits_Per_Block). Yes both at the same time!
106 That's because the next super block acquired will be 2 times the
107 previous one, and also all super blocks have to be multiples of the
108 _Bits_Per_Block value. <br>
110 <span style="font-weight: bold;">2) How does it interact with the free
111 list store?</span><br>
113 The super block is contained in the FLS, and the FLS is responsible for
114 getting / returning Super Bocks to and from the OS using operator new
115 as defined by the C++ standard.<br>
117 <hr style="width: 100%; height: 2px;">
118 <h3 style="text-align: center;">How does the allocate function Work?</h3>
120 The allocate function is specialized for single object allocation ONLY.
121 Thus, ONLY if n == 1, will the bitmap_allocator's specialized algorithm
122 be used. Otherwise, the request is satisfied directly by calling
125 Suppose n == 1, then the allocator does the following:<br>
128 <li>Checks to see whether the a free block exists somewhere in a
129 region of memory close to the last satisfied request. If so, then that
130 block is marked as allocated in the bit map and given to the user. If
131 not, then (2) is executed.</li>
132 <li>Is there a free block anywhere after the current block right upto
133 the end of the memory that we have? If so, that block is found, and the
134 same procedure is applied as above, and returned to the user. If not,
135 then (3) is executed.</li>
136 <li>Is there any block in whatever region of memory that we own free?
137 This is done by checking <br>
138 <div style="margin-left: 40px;">
140 <li>The use count for each super block, and if that fails then </li>
141 <li>The individual bit-maps for each super block. </li>
144 Note: Here we are never touching any of the memory that the user will
145 be given, and we are confining all memory accesses to a small region of
146 memory! This helps reduce cache misses. If this succeeds then we apply
147 the same procedure on that bit-map as (1), and return that block of
148 memory to the user. However, if this process fails, then we resort to
150 <li>This process involves Refilling the internal exponentially
151 growing memory pool. The said effect is achieved by calling
152 _S_refill_pool which does the following: <br>
153 <div style="margin-left: 40px;">
155 <li>Gets more memory from the Global Free List of the Required
157 <li>Adjusts the size for the next call to itself. </li>
158 <li>Writes the appropriate headers in the bit-maps.</li>
159 <li>Sets the use count for that super-block just allocated to 0
161 <li>All of the above accounts to maintaining the basic invariant
162 for the allocator. If the invariant is maintained, we are sure that all
163 is well. Now, the same process is applied on the newly acquired free
164 blocks, which are dispatched accordingly.</li>
170 Thus, you can clearly see that the allocate function is nothing but a
171 combination of the next-fit and first-fit algorithm optimized ONLY for
172 single object allocations.<br>
175 <hr style="width: 100%; height: 2px;">
176 <h3 style="text-align: center;">How does the deallocate function work?</h3>
178 The deallocate function again is specialized for single objects ONLY.
179 For all n belonging to > 1, the operator delete is called without
180 further ado, and the deallocate function returns.<br>
182 However for n == 1, a series of steps are performed:<br>
185 <li>We first need to locate that super-block which holds the memory
186 location given to us by the user. For that purpose, we maintain a
187 static variable _S_last_dealloc_index, which holds the index into the
188 vector of block pairs which indicates the index of the last super-block
189 from which memory was freed. We use this strategy in the hope that the
190 user will deallocate memory in a region close to what he/she
191 deallocated the last time around. If the check for belongs_to succeeds,
192 then we determine the bit-map for the given pointer, and locate the
193 index into that bit-map, and mark that bit as free by setting it.</li>
194 <li>If the _S_last_dealloc_index does not point to the memory block
195 that we're looking for, then we do a linear search on the block stored
196 in the vector of Block Pairs. This vector in code is called
197 _S_mem_blocks. When the corresponding super-block is found, we apply
198 the same procedure as we did for (1) to mark the block as free in the
202 Now, whenever a block is freed, the use count of that particular super
203 block goes down by 1. When this use count hits 0, we remove that super
204 block from the list of all valid super blocks stored in the vector.
205 While doing this, we also make sure that the basic invariant is
206 maintained by making sure that _S_last_request and
207 _S_last_dealloc_index point to valid locations within the vector.<br>
209 <hr style="width: 100%; height: 2px;"><br>
210 <h3 style="text-align: center;">Data Layout for a Super Block:</h3>
212 Each Super Block will be of some size that is a multiple of the number
213 of Bits Per Block. Typically, this value is chosen as Bits_Per_Byte x
214 sizeof(size_t). On an x86 system, this gives the figure 8 x
215 4 = 32. Thus, each Super Block will be of size 32 x Some_Value. This
216 Some_Value is sizeof(value_type). For now, let it be called 'K'. Thus,
217 finally, Super Block size is 32 x K bytes.<br>
219 This value of 32 has been chosen because each size_t has 32-bits
220 and Maximum use of these can be made with such a figure.<br>
222 Consider a block of size 64 ints. In memory, it would look like this:
223 (assume a 32-bit system where, size_t is a 32-bit entity).<br>
225 <table cellpadding="0" cellspacing="0" border="1"
226 style="text-align: left; width: 763px; height: 21px;">
229 <td style="vertical-align: top; text-align: center;">268<br>
231 <td style="vertical-align: top; text-align: center;">0<br>
233 <td style="vertical-align: top; text-align: center;">4294967295<br>
235 <td style="vertical-align: top; text-align: center;">4294967295<br>
237 <td style="vertical-align: top; text-align: center;">Data ->
238 Space for 64 ints<br>
245 The first Column(268) represents the size of the Block in bytes as seen
247 the Bitmap Allocator. Internally, a global free list is used to keep
248 track of the free blocks used and given back by the bitmap allocator.
249 It is this Free List Store that is responsible for writing and managing
250 this information. Actually the number of bytes allocated in this case
251 would be: 4 + 4 + (4x2) + (64x4) = 272 bytes, but the first 4 bytes are
253 addition by the Free List Store, so the Bitmap Allocator sees only 268
254 bytes. These first 4 bytes about which the bitmapped allocator is not
255 aware hold the value 268.<br>
257 <span style="font-weight: bold;">What do the remaining values represent?</span><br>
259 The 2nd 4 in the expression is the sizeof(size_t) because the
260 Bitmapped Allocator maintains a used count for each Super Block, which
261 is initially set to 0 (as indicated in the diagram). This is
262 incremented every time a block is removed from this super block
263 (allocated), and decremented whenever it is given back. So, when the
264 used count falls to 0, the whole super block will be given back to the
267 The value 4294967295 represents the integer corresponding to the bit
268 representation of all bits set: 11111111111111111111111111111111.<br>
270 The 3rd 4x2 is size of the bitmap itself, which is the size of 32-bits
272 which is 8-bytes, or 2 x sizeof(size_t).<br>
274 <hr style="width: 100%; height: 2px;"><br>
275 Another issue would be whether to keep the all bitmaps in a separate
276 area in memory, or to keep them near the actual blocks that will be
277 given out or allocated for the client. After some testing, I've decided
278 to keep these bitmaps close to the actual blocks. this will help in 2
282 <li>Constant time access for the bitmap themselves, since no kind of
283 look up will be needed to find the correct bitmap list or it's
285 <li>And also this would preserve the cache as far as possible.</li>
288 So in effect, this kind of an allocator might prove beneficial from a
289 purely cache point of view. But this allocator has been made to try and
290 roll out the defects of the node_allocator, wherein the nodes get
291 skewed about in memory, if they are not returned in the exact reverse
292 order or in the same order in which they were allocated. Also, the
293 new_allocator's book keeping overhead is too much for small objects and
294 single object allocations, though it preserves the locality of blocks
295 very well when they are returned back to the allocator.<br>
297 <hr style="width: 100%; height: 2px;"><br>
298 Expected overhead per block would be 1 bit in memory. Also, once the
299 address of the free list has been found, the cost for
300 allocation/deallocation would be negligible, and is supposed to be
301 constant time. For these very reasons, it is very important to minimize
302 the linear time costs, which include finding a free list with a free
303 block while allocating, and finding the corresponding free list for a
304 block while deallocating. Therefore, I have decided that the growth of
305 the internal pool for this allocator will be exponential as compared to
306 linear for node_allocator. There, linear time works well, because we
307 are mainly concerned with speed of allocation/deallocation and memory
308 consumption, whereas here, the allocation/deallocation part does have
309 some linear/logarithmic complexity components in it. Thus, to try and
310 minimize them would be a good thing to do at the cost of a little bit
313 Another thing to be noted is the the pool size will double every time
314 the internal pool gets exhausted, and all the free blocks have been
315 given away. The initial size of the pool would be sizeof(size_t) x 8
316 which is the number of bits in an integer, which can fit exactly
317 in a CPU register. Hence, the term given is exponential growth of the
320 <hr style="width: 100%; height: 2px;">After reading all this, you may
321 still have a few questions about the internal working of this
322 allocator, like my friend had!<br>
324 Well here are the exact questions that he posed:<br>
326 <span style="font-weight: bold;">Q1) The "Data Layout" section is
327 cryptic. I have no idea of what you are trying to say. Layout of what?
328 The free-list? Each bitmap? The Super Block?</span><br>
330 <div style="margin-left: 40px;"> The layout of a Super Block of a given
331 size. In the example, a super block of size 32 x 1 is taken. The
332 general formula for calculating the size of a super block is
333 32 x sizeof(value_type) x 2^n, where n ranges from 0 to 32 for 32-bit
337 <span style="font-weight: bold;">Q2) And since I just mentioned the
338 term `each bitmap', what in the world is meant by it? What does each
339 bitmap manage? How does it relate to the super block? Is the Super
340 Block a bitmap as well?</span><br style="font-weight: bold;">
342 <div style="margin-left: 40px;"> Good question! Each bitmap is part of
344 Super Block which is made up of 3 parts as I have mentioned earlier.
345 Re-iterating, 1. The use count, 2. The bit-map for that Super Block. 3.
346 The actual memory that will be eventually given to the user. Each
347 bitmap is a multiple of 32 in size. If there are 32 x (2^3) blocks of
348 single objects to be given, there will be '32 x (2^3)' bits present.
350 32 bits managing the allocated / free status for 32 blocks. Since each
351 size_t contains 32-bits, one size_t can manage upto 32
352 blocks' status. Each bit-map is made up of a number of size_t,
353 whose exact number for a super-block of a given size I have just
357 <span style="font-weight: bold;">Q3) How do the allocate and deallocate
358 functions work in regard to bitmaps?</span><br>
360 <div style="margin-left: 40px;"> The allocate and deallocate functions
361 manipulate the bitmaps and have nothing to do with the memory that is
362 given to the user. As I have earlier mentioned, a 1 in the bitmap's bit
363 field indicates free, while a 0 indicates allocated. This lets us check
364 32 bits at a time to check whether there is at lease one free block in
365 those 32 blocks by testing for equality with (0). Now, the allocate
366 function will given a memory block find the corresponding bit in the
367 bitmap, and will reset it (ie. make it re-set (0)). And when the
368 deallocate function is called, it will again set that bit after
369 locating it to indicate that that particular block corresponding to
370 this bit in the bit-map is not being used by anyone, and may be used to
371 satisfy future requests.<br>
373 eg: Consider a bit-map of 64-bits as represented below:<br>
374 1111111111111111111111111111111111111111111111111111111111111111<br>
376 Now, when the first request for allocation of a single object comes
377 along, the first block in address order is returned. And since the
378 bit-maps in the reverse order to that of the address order, the last
379 bit(LSB if the bit-map is considered as a binary word of 64-bits) is
382 The bit-map now looks like this:<br>
383 1111111111111111111111111111111111111111111111111111111111111110<br>
387 <hr style="width: 100%; height: 2px;"><br>
388 (Tech-Stuff, Please stay out if you are not interested in the selection
389 of certain constants. This has nothing to do with the algorithm per-se,
390 only with some vales that must be chosen correctly to ensure that the
391 allocator performs well in a real word scenario, and maintains a good
392 balance between the memory consumption and the allocation/deallocation
395 The formula for calculating the maximum wastage as a percentage:<br>
397 (32 x k + 1) / (2 x (32 x k + 1 + 32 x c)) x 100.<br>
400 k => The constant overhead per node. eg. for list, it is 8 bytes,
401 and for map it is 12 bytes.<br>
402 c => The size of the base type on which the map/list is
403 instantiated. Thus, suppose the the type1 is int and type2 is double,
404 they are related by the relation sizeof(double) == 2*sizeof(int). Thus,
405 all types must have this double size relation for this formula to work
408 Plugging-in: For List: k = 8 and c = 4 (int and double), we get:<br>
411 For map/multimap: k = 12, and c = 4 (int and double), we get:<br>
414 Thus, knowing these values, and based on the sizeof(value_type), we may
415 create a function that returns the Max_Wastage_Percentage for us to use.<br>
417 <hr style="width: 100%; height: 2px;"><small><small><em> See <a
418 href="file:///home/dhruv/projects/libstdc++-v3/gcc/libstdc++-v3/docs/html/17_intro/license.html">license.html</a>
419 for copying conditions. Comments and suggestions are welcome, and may
421 sent to <a href="mailto:libstdc++@gcc.gnu.org">the libstdc++ mailing
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