Geometric Memory Management

In this report we discuss the concepts of geometric memory alignment and geometric memory allocation. We introduce ledging as a process to deal with chunk sizes that are not a power of two. We introduce range trees as an efficient datastructure for representing geometric memory range allocation states. We introduce niche maps as an efficient means to find the right place to allocate a chunk of a given size whilst maintaining good packing and avoiding fragmentation. And, finally, we discuss geometric virtual memory management. 1 Geometric Memory Allocation Traditional memory allocation schemes typically align slots upto eight, sometimes sixteen bytes. This basic design choice leads to what we will refer to as the misaligned slots problem, which in turn leads to a myriad of fragmentation problems down the road. The misaligned slot problem occurs when two consecutive slots of size 2n are being coalesced into a bigger slot of size 2 on an address that is not a multiple of 2. A simple way to avoid these problems altogether is to: align slots to their own size. If we follow the latter alignment principle we end up with a geometric allocation scheme. To see why the misaligned slot problem leads to fragmentation, and to see how a geometric allocation scheme remedies this, consider the following example. Say for sake of simplicity we have a memory of 16 bytes, and we are aligning to words of 2 bytes each. We initially consider the case of just two size classes. We have large slots of 2 words (4 bytes) in size, and small slots of 1 word (2 bytes) in size. Now say we have two allocated large slots at the start and at the end of the memory, and four allocated small slots inbetween: Step 1: |xxxxxxxxxxxxxxx|xxxxxxx|xxxxxxx|xxxxxxx|xxxxxxx|xxxxxxxxxxxxxxx| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | Next we consider what happens when two of the smaller slots in the center get freed: Step 2: |xxxxxxxxxxxxxxx|xxxxxxx|-------|-------|xxxxxxx|xxxxxxxxxxxxxxx| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |