Coalescing block structures

author Gavin Matthews
date 1998-05-01
index terms pair: coalescing block structures; design
revision //
status complete design


.intro: This is the design for, which implements a data structure for the management of non-intersecting memory ranges, with eager coalescence.

.readership: This document is intended for any MM developer.

.source: design.mps.poolmvt, design.mps.poolmvff.

.overview: The "coalescing block structure" is a set of addresses (or a subset of address space), with provision for efficient management of contiguous ranges, including insertion and deletion, high level communication with the client about the size of contiguous ranges, and detection of protocol violations.


In addition to the generic land requirements (see, the CBS must satisfy: Common operations must have a low amortized cost.

.req.small: Must have a small space overhead for the storage of typical subsets of address space and not have abysmal overhead for the storage of any subset of address space.


.land: CBS is an implementation of the land abstract data type, so the interface consists of the generic functions for lands. See

External types

typedef struct CBSStruct *CBS The type of coalescing block structures. A CBSStruct is typically embedded in another structure.

External classes CLASS(CBS) is the CBS class, a subclass of CLASS(Land) suitable for passing to LandInit(). CLASS(CBSFast) is subclass of CLASS(CBS) that maintains, for each subtree, the size of the largest block in that subtree. This enables the LandFindFirst(), LandFindLast(), and LandFindLargest() generic functions.

.class.zoned: CLASS(CBSZoned) is a subclass of CLASS(CBSFast) that maintains, for each subtree, the union of the zone sets of all ranges in that subtree. This enables the LandFindInZones() generic function.

Keyword arguments

When initializing a CBS, LandInit() takes the following optional keyword arguments:

  • CBSBlockPool (type Pool) is the pool from which the CBS block descriptors will be allocated. If omitted, a new MFS pool is created for this purpose.
  • MPS_KEY_CBS_EXTEND_BY (type Size; default 4096) is passed as the MPS_KEY_EXTEND_BY keyword argument to PoolCreate() if a block descriptor pool is created. It specifies the size of segment that the block descriptor pool will request from the arena.
  • MFSExtendSelf (type Bool; default TRUE) is passed to PoolCreate() if a block descriptor pool is created. If TRUE, the block descriptor pool automatically extends itself when out of space; if FALSE, the pool returns ResLIMIT in this case. (This feature is used by the arena to bootstrap its own CBS of free memory. See


.limit.find: CBSLandClass does not support the LandFindFirst(), LandFindLast(), and LandFindLargest() generic functions (the subclasses do support these operations).

.limit.zones: CBSLandClass and CBSFastLandClass do not support the LandFindInZones() generic function (the subclass CBSZonedLandClass does support this operation).

.limit.iterate: CBS does not provide an implementation for the LandIterateAndDelete() generic function. This is because TreeTraverse() does not permit modification, for speed and to avoid perturbing the splay tree balance.

.limit.flush: CBS cannot be used as the source in a call to LandFlush(). (Because of .limit.iterate.)


Splay tree

.impl.splay: The CBS is implemented using a splay tree (see design.mps.splay). Each splay tree node is embedded in a block structure with a semi-open address range (design.mps.range). The splay tree is ordered by the range base address. In the CBSFastLandClass class, cbsFindFirst() and cbsFindLast() use the update/refresh facility of splay trees to store, in each block, an accurate summary of the maximum block size in the tree rooted at the corresponding splay node. This allows rapid location of the first or last suitable block, and very rapid failure if there is no suitable block. For example, this is used in the implementation of allocation in the MVFF pool class (design.mps.poolmvff).

.impl.find-largest: cbsFindLargest() simply finds out the size of the largest block in the CBS from the root of the tree, using SplayRoot(), and does SplayFindFirst() for a block of that size. This takes time proportional to the logarithm of the size of the free list, so it's about the best you can do without maintaining a separate priority queue, just to do cbsFindLargest(). For example, this is used in the implementation of allocation buffers in the MVFF pool class (design.mps.poolmvff).

.impl.splay.zones: In the CBSZonedLandClass class, cbsFindInZones() uses the update/refresh facility of splay trees to store, in each block, the union of the zones of the ranges in the tree rooted at the corresponding splay node. This allows rapid location of a block in a set of zones. For example, this is used to allocate segments in particular zones in the arena to optimised garbage collection (see design.mps.critical-path).

Low memory behaviour

.impl.low-mem: When the CBS tries to allocate a new CBSBlock structure for a new isolated range as a result of either LandInsert() or LandDelete(), and there is insufficient memory to allocate the block structure, then the range is not added to the CBS or deleted from it, and the call to LandInsert() or LandDelete() returns ResMEMORY.

The CBS block The block contains a non-empty range and a splay tree node. The range may be empty if the block is halfway through being deleted. This conflates values and status, but is justified because block size is very important.


.test: The following testing will be performed on this module: A generic test for land implementations. See

.test.pool: The arena and two pools (MVT and MVFF) are implemented on top of a CBS. These are subject to testing in development, QA, and are heavily exercised by customers.

Notes for future development

.future.not-splay: The implementation of CBSs is based on splay trees. It could be revised to use other data structures that meet the requirements (especially

.future.hybrid: It would be possible to attenuate the problem of .risk.overhead (below) by using a single word bit set to represent the membership in a (possibly aligned) word-width of grains. This might be used for block sizes less than a word-width of grains, converting them when they reach all free in the bit set. Note that this would make coalescence slightly less eager, by up to (word-width - 1).

.future.iterate.and.delete: It would be possible to provide an implementation for the LandIterateAndDelete() generic function using TreeTraverseAndDelete(), which calls TreeToVine() first, iterates over the vine (where deletion is straightforward), and then rebalances the tree. Note that this is little better than using SplayFirst() and SplayNext().

.future.lazy-coalesce: It's long been observed that small blocks are often freed and then reallocated, so that coalescing them is a waste of time. It might be worth considering how a splay tree could implement a lazy coalescing scheme, where blocks are coalesced with their adjacent neighbours during the search only if they aren't big enough. This would break .impl.find-largest and so might be best done as a different kind of land. On the other hand, since the MPS does not use client memory to store the tree, eager coalescing avoids allocation.


.risk.overhead: Clients should note that the current implementation of CBSs has a space overhead proportional to the number of isolated contiguous ranges. [Four words per range.] If the CBS contains every other grain in an area, then the overhead will be large compared to the size of that area. [Four words per two grains.] The CBS structure is thus suitable only for managing large enough ranges.

Document History

  • 1998-05-01 Gavin Matthews. This document was derived from the outline in design.mps.poolmv2.
  • 1998-07-22 Gavin Matthews. Updated in response to approval comments in change.epcore.anchovy.160040. There is too much fragmentation in trapping memory.
  • Gavin Matthews. Updated (as part of change.epcore.brisling.160158: MVFF cannot be instantiated with 4-byte alignment) to document new alignment restrictions.
  • 2002-06-07 RB Converted from MMInfo database design document.
  • 2013-04-14 GDR Converted to reStructuredText.
  • 2013-05-19 GDR Removed the "emergency" free list allocator, the design notes on an unimplemented "future hybrid" scheme, the callbacks, block interface, and minimum size interface. Updated the arguments for CBSIterateMethod, CBSInit(), CBSInsert(), and CBSDelete().
  • 2013-05-23 RB Removed references to "contingency methods" that were talking about the deleted "emergency" free list allocator. Documented fastFind argument to CBSInit().
  • 2014-04-01 GDR Moved generic material to Documented new keyword arguments.
  • 2016-03-27 RB Adding cross references to usage. Updating future with reference to TreeTraverseAndDelete(). Adding future idea about lazy coalescing.