An algorithm for locating adjacent storage blocks in the buddy system

Abstract

A simple scheme for the determination of the location of a block of storage relative to other blocks is described. This scheme is applieahle to the buddy type storage allocation systems.Two storage allocation schemes that have been presented by Knowlton [1] and Hirschberg [2] are similar in many basic features, and both are referred to as buddy systems. The purpose of both these methods is to keep track of a large memory pool used to satisfy storage requests.These two systems have the following basic actions in common:Step A. To satisfy a storage request:1. The smallest block of storage that is at least as big as the request is selected as the candidate block. 2. The candidate is checked for size and, if large enough, is split into two smaller blocks (buddies); otherwise the candidate block is returned as the block satisfying the request and the algorithm terminates. 3. One of the buddies (the smaller of the two, if possible) is selected as the new candidate and the other is inserted into the free storage pool. The algorithm then proceeds from Step A. 2.Step B. To return a block to the storage pool:1. The buddy of the newly returned block is located. 2. The buddy is inspected to see that it is whole (not split into subbuddies) and free (not allocated). If both conditions are met, then the buddy is removed from free storage and merged with the newly returned block to create a larger block. This larger block is then taken as the newly returned block and execution proceeds with Step B.1.3. If it is impossible to merge, then the newly returned block is returned to the free storage area and the algorithm terminates.In both of these schemes it is important to notice that the merges exactly correspond to the splits. For example, if a block at storage location 30 of length 10 is split into buddies starting at 30 and 36 with lengths 6 and 4 respectively, the corresponding merge must be done using exactly these two blocks. In this case it is impossible to merge the block at 30 with length 6 with any other block except that block starting at location 36 and only when that block has a length of 4. This means that sufficient information must be carried in each block to indicate the relative location of the proper buddy.In Knowlton's original buddy system the blocks had lengths of powers of two, and so the addresses of the blocks were an encoding of the relative locations of the blocks. Hirschberg's system used blocks whose length were elements of the familiar Fibonacci series. To locate the buddy of a block, an auxiliary list was consulted that gave the possible starting locations of blocks. Both of the techniques used are special purpose and break down for other sequences of block sizes.Knowlton allowed block sizes SIZEa = SIZEa-1 -}-SlZEn-1 ; SIZE0 = 1. Hirschberg allowed blocks of sizes SIZEa = SIZEr~_I -q-SIZEa_2 ; SIZE0 = 3, SIZEx = 5. This paper describes a very simple and efficient technique for locating buddies that allows sizes to be elements of an arbitrary (but fixed) generalized Fibonacci sequence. These are sequ...

No-break dynamic defragmentation of reconfigurable devices

“…Differing only in the choice of the standard size different, buddy systems are proposed in [8,9,10,11,12,6]. Newer approaches that use cacheoblivious structures for allocating space in memory hierarchies include [13,14].…”

A note on weighted buddy systems for dynamic storage allocation

“…The buddy system [4,5,6] is a nice algorithm for dynamic storage atlocation, but it suffers from a serious degree of infernal fragmentation. The Shen and Peterson system [1] presents a modified form of the buddy system.…”

“…The present paper assumes that the reader is familiar with the buddy system [4,5,6] and the Shen and Peterson system [1]. We have tried to keep all the symbols which are used in this paper as close as possible to those of Shen and Peterson.…”

Dynamic memory allocation in computer simulation

“…Knowlton [13] describes a binary block splitting technique for use in a hst processing language, Purdom [20] looks at the statistical properties of the external space fragmentation of this technique under the assumptions of Poisson requests and exponential holding times. Hinds [7] presents a coding scheme for locating the buddy of a block of storage. Isoda, Goto, and Kimura [11] provide a modified buddy system for greater efficiency of memory usage.…”