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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<head>
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<meta content="text/html; charset=ISO-8859-1"
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http-equiv="content-type">
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<title>Bitmap Allocator</title>
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<meta content="Dhruv Matani" name="author">
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<meta content="Bitmap Allocator" name="description">
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</head>
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<body>
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<h1 style="text-align: center;">Bitmap Allocator</h1>
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<em><br>
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<small><small>The latest version of this document is always available
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at <a
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href="http://gcc.gnu.org/onlinedocs/libstdc++/ext/ballocator_doc.html">
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http://gcc.gnu.org/onlinedocs/libstdc++/ext/ballocator_doc.html</a>.</small></small></em><br>
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<br>
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<em> To the <a href="http://gcc.gnu.org/libstdc++/">libstdc++-v3
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homepage</a>.</em><br>
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<br>
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<hr style="width: 100%; height: 2px;"><br>
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As this name suggests, this allocator uses a bit-map to keep track of
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the used and unused memory locations for it's book-keeping purposes.<br>
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<br>
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This allocator will make use of 1 single bit to keep track of whether
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it has been allocated or not. A bit 1 indicates free, while 0 indicates
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allocated. This has been done so that you can easily check a collection
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of bits for a free block. This kind of Bitmapped strategy works best
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for single object allocations, and with the STL type parameterized
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allocators, we do not need to choose any size for the block which will
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be represented by a single bit. This will be the size of the parameter
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around which the allocator has been parameterized. Thus, close to
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optimal performance will result. Hence, this should be used for node
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based containers which call the allocate function with an argument of 1.<br>
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<br>
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The bitmapped allocator's internal pool is exponentially growing.
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Meaning that internally, the blocks acquired from the Free List Store
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will double every time the bitmapped allocator runs out of memory.<br>
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<br>
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<hr style="width: 100%; height: 2px;"><br>
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The macro __GTHREADS decides whether to use Mutex Protection around
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every allocation/deallocation. The state of the macro is picked up
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automatically from the gthr abstration layer.<br>
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<br>
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<hr style="width: 100%; height: 2px;">
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<h3 style="text-align: center;">What is the Free List Store?</h3>
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<br>
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The Free List Store (referred to as FLS for the remaining part of this
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document) is the Global memory pool that is shared by all instances of
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the bitmapped allocator instantiated for any type. This maintains a
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sorted order of all free memory blocks given back to it by the
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bitmapped allocator, and is also responsible for giving memory to the
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bitmapped allocator when it asks for more.<br>
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<br>
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Internally, there is a Free List threshold which indicates the Maximum
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number of free lists that the FLS can hold internally (cache).
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Currently, this value is set at 64. So, if there are more than 64 free
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lists coming in, then some of them will be given back to the OS using
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operator delete so that at any given time the Free List's size does not
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exceed 64 entries. This is done because a Binary Search is used to
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locate an entry in a free list when a request for memory comes along.
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Thus, the run-time complexity of the search would go up given an
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increasing size, for 64 entries however, lg(64) == 6 comparisons are
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enough to locate the correct free list if it exists.<br>
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<br>
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Suppose the free list size has reached it's threshold, then the largest
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block from among those in the list and the new block will be selected
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and given back to the OS. This is done because it reduces external
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fragmentation, and allows the OS to use the larger blocks later in an
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orderly fashion, possibly merging them later. Also, on some systems,
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large blocks are obtained via calls to mmap, so giving them back to
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free system resources becomes most important.<br>
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<br>
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The function _S_should_i_give decides the policy that determines
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whether the current block of memory should be given to the allocator
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for the request that it has made. That's because we may not always have
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exact fits for the memory size that the allocator requests. We do this
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mainly to prevent external fragmentation at the cost of a little
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internal fragmentation. Now, the value of this internal fragmentation
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has to be decided by this function. I can see 3 possibilities right
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now. Please add more as and when you find better strategies.<br>
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<br>
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<ol>
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<li>Equal size check. Return true only when the 2 blocks are of equal
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size.</li>
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<li>Difference Threshold: Return true only when the _block_size is
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greater than or equal to the _required_size, and if the _BS is > _RS
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by a difference of less than some THRESHOLD value, then return true,
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else return false. </li>
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<li>Percentage Threshold. Return true only when the _block_size is
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greater than or equal to the _required_size, and if the _BS is > _RS
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by a percentage of less than some THRESHOLD value, then return true,
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else return false.</li>
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</ol>
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<br>
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Currently, (3) is being used with a value of 36% Maximum wastage per
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Super Block.<br>
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<br>
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<hr style="width: 100%; height: 2px;"><span style="font-weight: bold;">1)
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What is a super block? Why is it needed?</span><br>
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<br>
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A super block is the block of memory acquired from the FLS from which
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the bitmap allocator carves out memory for single objects and satisfies
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the user's requests. These super blocks come in sizes that are powers
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of 2 and multiples of 32 (_Bits_Per_Block). Yes both at the same time!
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That's because the next super block acquired will be 2 times the
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previous one, and also all super blocks have to be multiples of the
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_Bits_Per_Block value. <br>
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<br>
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<span style="font-weight: bold;">2) How does it interact with the free
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list store?</span><br>
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<br>
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The super block is contained in the FLS, and the FLS is responsible for
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getting / returning Super Bocks to and from the OS using operator new
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as defined by the C++ standard.<br>
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<br>
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<hr style="width: 100%; height: 2px;">
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<h3 style="text-align: center;">How does the allocate function Work?</h3>
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<br>
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The allocate function is specialized for single object allocation ONLY.
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Thus, ONLY if n == 1, will the bitmap_allocator's specialized algorithm
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be used. Otherwise, the request is satisfied directly by calling
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operator new.<br>
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<br>
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Suppose n == 1, then the allocator does the following:<br>
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<br>
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<ol>
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<li>Checks to see whether the a free block exists somewhere in a
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region of memory close to the last satisfied request. If so, then that
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block is marked as allocated in the bit map and given to the user. If
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not, then (2) is executed.</li>
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<li>Is there a free block anywhere after the current block right upto
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the end of the memory that we have? If so, that block is found, and the
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same procedure is applied as above, and returned to the user. If not,
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then (3) is executed.</li>
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<li>Is there any block in whatever region of memory that we own free?
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This is done by checking <br>
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<div style="margin-left: 40px;">
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<ul>
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<li>The use count for each super block, and if that fails then </li>
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<li>The individual bit-maps for each super block. </li>
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</ul>
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</div>
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Note: Here we are never touching any of the memory that the user will
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be given, and we are confining all memory accesses to a small region of
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memory! This helps reduce cache misses. If this succeeds then we apply
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the same procedure on that bit-map as (1), and return that block of
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memory to the user. However, if this process fails, then we resort to
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(4).</li>
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<li>This process involves Refilling the internal exponentially
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growing memory pool. The said effect is achieved by calling
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_S_refill_pool which does the following: <br>
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<div style="margin-left: 40px;">
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<ul>
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<li>Gets more memory from the Global Free List of the Required
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size. </li>
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<li>Adjusts the size for the next call to itself. </li>
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<li>Writes the appropriate headers in the bit-maps.</li>
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<li>Sets the use count for that super-block just allocated to 0
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(zero). </li>
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<li>All of the above accounts to maintaining the basic invariant
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for the allocator. If the invariant is maintained, we are sure that all
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is well. Now, the same process is applied on the newly acquired free
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blocks, which are dispatched accordingly.</li>
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</ul>
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</div>
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</li>
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</ol>
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<br>
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Thus, you can clearly see that the allocate function is nothing but a
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combination of the next-fit and first-fit algorithm optimized ONLY for
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single object allocations.<br>
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<br>
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<br>
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<hr style="width: 100%; height: 2px;">
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<h3 style="text-align: center;">How does the deallocate function work?</h3>
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<br>
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The deallocate function again is specialized for single objects ONLY.
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For all n belonging to > 1, the operator delete is called without
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further ado, and the deallocate function returns.<br>
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<br>
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However for n == 1, a series of steps are performed:<br>
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<br>
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<ol>
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<li>We first need to locate that super-block which holds the memory
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location given to us by the user. For that purpose, we maintain a
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static variable _S_last_dealloc_index, which holds the index into the
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vector of block pairs which indicates the index of the last super-block
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from which memory was freed. We use this strategy in the hope that the
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user will deallocate memory in a region close to what he/she
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deallocated the last time around. If the check for belongs_to succeeds,
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then we determine the bit-map for the given pointer, and locate the
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index into that bit-map, and mark that bit as free by setting it.</li>
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<li>If the _S_last_dealloc_index does not point to the memory block
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that we're looking for, then we do a linear search on the block stored
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in the vector of Block Pairs. This vector in code is called
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_S_mem_blocks. When the corresponding super-block is found, we apply
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the same procedure as we did for (1) to mark the block as free in the
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bit-map.</li>
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</ol>
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<br>
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Now, whenever a block is freed, the use count of that particular super
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block goes down by 1. When this use count hits 0, we remove that super
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block from the list of all valid super blocks stored in the vector.
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While doing this, we also make sure that the basic invariant is
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maintained by making sure that _S_last_request and
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_S_last_dealloc_index point to valid locations within the vector.<br>
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<br>
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<hr style="width: 100%; height: 2px;"><br>
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<h3 style="text-align: center;">Data Layout for a Super Block:</h3>
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<br>
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Each Super Block will be of some size that is a multiple of the number
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of Bits Per Block. Typically, this value is chosen as Bits_Per_Byte x
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sizeof(size_t). On an x86 system, this gives the figure 8 x
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4 = 32. Thus, each Super Block will be of size 32 x Some_Value. This
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Some_Value is sizeof(value_type). For now, let it be called 'K'. Thus,
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finally, Super Block size is 32 x K bytes.<br>
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<br>
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This value of 32 has been chosen because each size_t has 32-bits
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and Maximum use of these can be made with such a figure.<br>
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<br>
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Consider a block of size 64 ints. In memory, it would look like this:
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(assume a 32-bit system where, size_t is a 32-bit entity).<br>
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<br>
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<table cellpadding="0" cellspacing="0" border="1"
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style="text-align: left; width: 763px; height: 21px;">
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<tbody>
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<tr>
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<td style="vertical-align: top; text-align: center;">268<br>
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</td>
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<td style="vertical-align: top; text-align: center;">0<br>
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</td>
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<td style="vertical-align: top; text-align: center;">4294967295<br>
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</td>
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<td style="vertical-align: top; text-align: center;">4294967295<br>
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</td>
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<td style="vertical-align: top; text-align: center;">Data ->
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Space for 64 ints<br>
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</td>
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</tr>
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</tbody>
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</table>
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<br>
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<br>
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The first Column(268) represents the size of the Block in bytes as seen
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by
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the Bitmap Allocator. Internally, a global free list is used to keep
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track of the free blocks used and given back by the bitmap allocator.
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It is this Free List Store that is responsible for writing and managing
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this information. Actually the number of bytes allocated in this case
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would be: 4 + 4 + (4x2) + (64x4) = 272 bytes, but the first 4 bytes are
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an
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addition by the Free List Store, so the Bitmap Allocator sees only 268
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bytes. These first 4 bytes about which the bitmapped allocator is not
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aware hold the value 268.<br>
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<br>
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<span style="font-weight: bold;">What do the remaining values represent?</span><br>
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<br>
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The 2nd 4 in the expression is the sizeof(size_t) because the
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Bitmapped Allocator maintains a used count for each Super Block, which
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is initially set to 0 (as indicated in the diagram). This is
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incremented every time a block is removed from this super block
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(allocated), and decremented whenever it is given back. So, when the
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used count falls to 0, the whole super block will be given back to the
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Free List Store.<br>
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<br>
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The value 4294967295 represents the integer corresponding to the bit
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representation of all bits set: 11111111111111111111111111111111.<br>
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<br>
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The 3rd 4x2 is size of the bitmap itself, which is the size of 32-bits
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x 2,
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which is 8-bytes, or 2 x sizeof(size_t).<br>
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<br>
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<hr style="width: 100%; height: 2px;"><br>
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Another issue would be whether to keep the all bitmaps in a separate
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area in memory, or to keep them near the actual blocks that will be
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given out or allocated for the client. After some testing, I've decided
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to keep these bitmaps close to the actual blocks. this will help in 2
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ways. <br>
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<br>
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<ol>
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<li>Constant time access for the bitmap themselves, since no kind of
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look up will be needed to find the correct bitmap list or it's
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equivalent.</li>
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<li>And also this would preserve the cache as far as possible.</li>
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</ol>
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<br>
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So in effect, this kind of an allocator might prove beneficial from a
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purely cache point of view. But this allocator has been made to try and
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roll out the defects of the node_allocator, wherein the nodes get
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skewed about in memory, if they are not returned in the exact reverse
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order or in the same order in which they were allocated. Also, the
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new_allocator's book keeping overhead is too much for small objects and
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|
single object allocations, though it preserves the locality of blocks
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|
very well when they are returned back to the allocator.<br>
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|
|
<br>
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|
|
<hr style="width: 100%; height: 2px;"><br>
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Expected overhead per block would be 1 bit in memory. Also, once the
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|
|
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
|
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|
|
the internal pool for this allocator will be exponential as compared to
|
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|
|
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
|
| 311 |
|
|
of memory.<br>
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|
|
<br>
|
| 313 |
|
|
Another thing to be noted is the the pool size will double every time
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| 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
|
| 318 |
|
|
internal pool.<br>
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|
|
<br>
|
| 320 |
|
|
<hr style="width: 100%; height: 2px;">After reading all this, you may
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| 321 |
|
|
still have a few questions about the internal working of this
|
| 322 |
|
|
allocator, like my friend had!<br>
|
| 323 |
|
|
<br>
|
| 324 |
|
|
Well here are the exact questions that he posed:<br>
|
| 325 |
|
|
<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>
|
| 329 |
|
|
<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
|
| 334 |
|
|
systems.<br>
|
| 335 |
|
|
</div>
|
| 336 |
|
|
<br>
|
| 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;">
|
| 341 |
|
|
<br>
|
| 342 |
|
|
<div style="margin-left: 40px;"> Good question! Each bitmap is part of
|
| 343 |
|
|
a
|
| 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.
|
| 349 |
|
|
Each
|
| 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
|
| 354 |
|
|
mentioned.<br>
|
| 355 |
|
|
</div>
|
| 356 |
|
|
<br>
|
| 357 |
|
|
<span style="font-weight: bold;">Q3) How do the allocate and deallocate
|
| 358 |
|
|
functions work in regard to bitmaps?</span><br>
|
| 359 |
|
|
<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>
|
| 372 |
|
|
<br>
|
| 373 |
|
|
eg: Consider a bit-map of 64-bits as represented below:<br>
|
| 374 |
|
|
1111111111111111111111111111111111111111111111111111111111111111<br>
|
| 375 |
|
|
<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
|
| 380 |
|
|
re-set to 0.<br>
|
| 381 |
|
|
<br>
|
| 382 |
|
|
The bit-map now looks like this:<br>
|
| 383 |
|
|
1111111111111111111111111111111111111111111111111111111111111110<br>
|
| 384 |
|
|
</div>
|
| 385 |
|
|
<br>
|
| 386 |
|
|
<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
|
| 393 |
|
|
speed).<br>
|
| 394 |
|
|
<br>
|
| 395 |
|
|
The formula for calculating the maximum wastage as a percentage:<br>
|
| 396 |
|
|
<br>
|
| 397 |
|
|
(32 x k + 1) / (2 x (32 x k + 1 + 32 x c)) x 100.<br>
|
| 398 |
|
|
<br>
|
| 399 |
|
|
Where,<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
|
| 406 |
|
|
properly.<br>
|
| 407 |
|
|
<br>
|
| 408 |
|
|
Plugging-in: For List: k = 8 and c = 4 (int and double), we get:<br>
|
| 409 |
|
|
33.376%<br>
|
| 410 |
|
|
<br>
|
| 411 |
|
|
For map/multimap: k = 12, and c = 4 (int and double), we get:<br>
|
| 412 |
|
|
37.524%<br>
|
| 413 |
|
|
<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>
|
| 416 |
|
|
<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
|
| 420 |
|
|
be
|
| 421 |
|
|
sent to <a href="mailto:libstdc++@gcc.gnu.org">the libstdc++ mailing
|
| 422 |
|
|
list</a>.</em><br>
|
| 423 |
|
|
</small></small><br>
|
| 424 |
|
|
<br>
|
| 425 |
|
|
</body>
|
| 426 |
|
|
</html>
|
