Bucket Distribution in PartitionAlloc

In PartitionAlloc, a slab-based memory allocator, a “bucket” serves to categorize different memory allocation sizes. When memory is requested, PartitionAlloc rounds the requested size up to the nearest predefined size class (referred to as slot size). Allocations that map to the same bucket are then grouped together and allocated from a size-segregated slot span.

A bucket, therefore, defines a specific size category. This bucketing strategy is key to how PartitionAlloc manages and organizes memory efficiently, offering several benefits:

• Increased cache locality for same-size allocations
• Smaller metadata
• Easy mapping of address to size
• Decreased fragmentation over time

This document describes PartitionAlloc's methodology for mapping requested allocation sizes to their corresponding buckets. See //partition_alloc/bucket_lookup.h for implementation details.

Bucket Distribution Types

PartitionAlloc provides two different distributions; Neutral and Denser. As the name tells, Denser offers a more granular set of buckets, roughly doubling the number compared to the Neutral distribution.

1. Neutral Bucket Distribution (kNeutral)

• Pro: Results in fewer partially-filled slot spans, potentially reducing fragmentation caused by unused slots in these spans.
• Con: Allocations are often rounded up to a significantly larger slot size than requested. This increases fragmentation within each allocation due to the larger difference between the requested size and the allocated slot size.

2. Denser Bucket Distribution (kDenser):

• Pro: Allocations can more closely match the requested memory size. This reduces fragmentation within each allocation, as the chosen slot size is nearer to the actual need.
• Con: May lead to more partially-filled slot spans. If these slot spans are not fully utilized, it can increase fragmentation due to more unused slots across these spans.

The Neutral distribution is implemented as a variation of the Denser one, making it straightforward to understand if one understands the Denser layout.

Denser Bucket Distribution: A Closer Look

The Denser distribution itself operates as a hybrid system. For smaller allocation sizes, bucket sizes increase in a simple, linear fashion. Conversely, for larger allocation sizes, the bucket sizes increase exponentially.

Linear Sizing (for Smaller Allocations)

When an allocation request is for a relatively small amount of memory, the system employs a linear scale. This means each subsequent bucket size is larger than the previous one by a fixed increment. This increment is determined by the system's fundamental memory alignment requirement, which might be, for instance, 16 bytes. As an example, if this fixed increment is 16 bytes, the sequence of buckets might represent sizes such as 16 bytes, 32 bytes, 48 bytes, and so on.

Exponential Sizing (for Larger Allocations)

For larger memory requests, the bucket sizes adhere to an exponential pattern. The system divides broad power-of-two ranges, termed “orders,” into a fixed number of smaller bucket steps. For instance, the range of sizes from 128 bytes up to, but not including, 256 bytes constitutes an “order,” and it would contain a specific number of distinct bucket sizes. The subsequent order, such as 256 to 511 bytes, would be similarly divided.

A fixed number of buckets, for example eight, are used to subdivide each power-of-two range, creating what is known as “Buckets per Order.” This configuration results in a logarithmic scale where bucket sizes grow proportionally rather than by a fixed additive amount. To illustrate with an example using 8 buckets per order, sizes just above 128 bytes might be 128 bytes, then approximately 1.125x128 bytes, 1.25x128 bytes, and continue in this manner up to nearly 256 bytes. This pattern then repeats for sizes above 256 bytes, then 512 bytes, and so forth.

	Order-Index 0	Order-Index 1	Order-Index 2	Order-Index 3	Order-Index 4	Order-Index 5	Order-Index 6	Order-Index 7
Order 8 (2⁷)	121-128	129-144	145-160	161-176	177-192	193-208	209-224	225-240
Order 9 (2⁸)	241-256	257-288	289-320	321-352	353-384	385-416	417-448	449-480
Order 10 (2⁹)	481-512	513-576	577-640	641-704	705-768	769-832	833-896	897-960

Neutral Bucket Distribution

The Neutral Bucket Distribution offers a sparser alternative, derived from the Denser one. In the range where the Denser distribution uses linear sizing, or for the smallest exponential sizes where alignment naturally limits bucket density, the Neutral and Denser distributions are identical. However, for larger sizes within the exponential sizing range, the Neutral distribution typically uses fewer buckets per “order” compared to the Denser one. It selects every other bucket that the Denser distribution would define, leading to fewer, more widely spaced buckets.

Consider an illustrative conceptual difference: if the Denser distribution has buckets for sizes like ..., 384, 416, 448, 480, 512, ..., the Neutral distribution, in the same range, might only have buckets for ..., 384, then skip 416 to use 448, then skip 480 to use 512, and so on.

Example Distribution

8 Bytes Alignment (Typically 32-bit Systems)

Index	Size	Bucket Distribution	Originating Formula
0	8	kNeutral and kDenser	linear [8 x 1]
1	16	kNeutral and kDenser	linear [8 x 2]
2	24	kNeutral and kDenser	linear [8 x 3]
3	32	kNeutral and kDenser	linear [8 x 4]
4	40	kNeutral and kDenser	linear [8 x 5]
5	48	kNeutral and kDenser	linear [8 x 6]
6	56	kNeutral and kDenser	linear [8 x 7]
7	64	kNeutral and kDenser	linear [8 x 8] yet exponential [2⁶ x (1 + 0)]
8	72	kNeutral and kDenser	linear [8 x 9] yet exponential [2⁶ x (1 + ⅛)]
9	80	kNeutral and kDenser	linear [8 x 10] yet exponential [2⁶ x (1 + ¼)]
10	88	kNeutral and kDenser	linear [8 x 11] yet exponential [2⁶ x (1 + ⅜)]
11	96	kNeutral and kDenser	linear [8 x 12] yet exponential [2⁶ x (1 + ½)]
12	104	kNeutral and kDenser	linear [8 x 13] yet exponential [2⁶ x (1 + ⅝)]
13	112	kNeutral and kDenser	linear [8 x 14] yet exponential [2⁶ x (1 + ¾)]
14	120	kNeutral and kDenser	linear [8 x 15] yet exponential [2⁶ x (1 + ⅞)]
15	128	kNeutral and kDenser	linear [8 x 16] yet exponential [2⁷ x (1 + 0)]
16	144	kDenser only	exponential [2⁷ x (1 + ⅛)]
17	160	kNeutral and kDenser	exponential [2⁷ x (1 + ¼)]
18	176	kDenser only	exponential [2⁷ x (1 + ⅜)]
19	192	kNeutral and kDenser	exponential [2⁷ x (1 + ½)]
20	208	kDenser only	exponential [2⁷ x (1 + ⅝)]
21	224	kNeutral and kDenser	exponential [2⁷ x (1 + ¾)]
22	240	kDenser only	exponential [2⁷ x (1 + ⅞)]
23	256	kNeutral and kDenser	exponential [2⁸ x (1 + 0)]
24	288	kDenser only	exponential [2⁸ x (1 + ⅛)]
25	320	kNeutral and kDenser	exponential [2⁸ x (1 + ¼)]
26	352	kDenser only	exponential [2⁸ x (1 + ⅜)]
27	384	kNeutral and kDenser	exponential [2⁸ x (1 + ½)]
28	416	kDenser only	exponential [2⁸ x (1 + ⅝)]
29	448	kNeutral and kDenser	exponential [2⁸ x (1 + ¾)]
30	480	kDenser only	exponential [2⁸ x (1 + ⅞)]
31	512	kNeutral and kDenser	exponential [2⁹ x (1 + 0)]
32	576	kDenser only	exponential [2⁹ x (1 + ⅛)]
33	640	kNeutral and kDenser	exponential [2⁹ x (1 + ¼)]
34	704	kDenser only	exponential [2⁹ x (1 + ⅜)]
35	768	kNeutral and kDenser	exponential [2⁹ x (1 + ½)]
36	832	kDenser only	exponential [2⁹ x (1 + ⅝)]
37	896	kNeutral and kDenser	exponential [2⁹ x (1 + ¾)]
38	960	kDenser only	exponential [2⁹ x (1 + ⅞)]
39	1024	kNeutral and kDenser	exponential [2¹⁰ x (1 + 0)]
40	1152	kDenser only	exponential [2¹⁰ x (1 + ⅛)]
41	1280	kNeutral and kDenser	exponential [2¹⁰ x (1 + ¼)]
42	1408	kDenser only	exponential [2¹⁰ x (1 + ⅜)]
43	1536	kNeutral and kDenser	exponential [2¹⁰ x (1 + ½)]
44	1664	kDenser only	exponential [2¹⁰ x (1 + ⅝)]
45	1792	kNeutral and kDenser	exponential [2¹⁰ x (1 + ¾)]
46	1920	kDenser only	exponential [2¹⁰ x (1 + ⅞)]
47	2048	kNeutral and kDenser	exponential [2¹¹ x (1 + 0)]
48	2304	kDenser only	exponential [2¹¹ x (1 + ⅛)]
49	2560	kNeutral and kDenser	exponential [2¹¹ x (1 + ¼)]
50	2816	kDenser only	exponential [2¹¹ x (1 + ⅜)]
51	3072	kNeutral and kDenser	exponential [2¹¹ x (1 + ½)]
52	3328	kDenser only	exponential [2¹¹ x (1 + ⅝)]
53	3584	kNeutral and kDenser	exponential [2¹¹ x (1 + ¾)]
54	3840	kDenser only	exponential [2¹¹ x (1 + ⅞)]
55	4096	kNeutral and kDenser	exponential [2¹² x (1 + 0)]
56	4608	kDenser only	exponential [2¹² x (1 + ⅛)]
57	5120	kNeutral and kDenser	exponential [2¹² x (1 + ¼)]
58	5632	kDenser only	exponential [2¹² x (1 + ⅜)]
59	6144	kNeutral and kDenser	exponential [2¹² x (1 + ½)]
60	6656	kDenser only	exponential [2¹² x (1 + ⅝)]
61	7168	kNeutral and kDenser	exponential [2¹² x (1 + ¾)]
62	7680	kDenser only	exponential [2¹² x (1 + ⅞)]
63	8192	kNeutral and kDenser	exponential [2¹³ x (1 + 0)]
64	9216	kDenser only	exponential [2¹³ x (1 + ⅛)]
65	10240	kNeutral and kDenser	exponential [2¹³ x (1 + ¼)]
66	11264	kDenser only	exponential [2¹³ x (1 + ⅜)]
67	12288	kNeutral and kDenser	exponential [2¹³ x (1 + ½)]
68	13312	kDenser only	exponential [2¹³ x (1 + ⅝)]
69	14336	kNeutral and kDenser	exponential [2¹³ x (1 + ¾)]
70	15360	kDenser only	exponential [2¹³ x (1 + ⅞)]
71	16384	kNeutral and kDenser	exponential [2¹⁴ x (1 + 0)]
72	18432	kDenser only	exponential [2¹⁴ x (1 + ⅛)]
73	20480	kNeutral and kDenser	exponential [2¹⁴ x (1 + ¼)]
74	22528	kDenser only	exponential [2¹⁴ x (1 + ⅜)]
75	24576	kNeutral and kDenser	exponential [2¹⁴ x (1 + ½)]
76	26624	kDenser only	exponential [2¹⁴ x (1 + ⅝)]
77	28672	kNeutral and kDenser	exponential [2¹⁴ x (1 + ¾)]
78	30720	kDenser only	exponential [2¹⁴ x (1 + ⅞)]
79	32768	kNeutral and kDenser	exponential [2¹⁵ x (1 + 0)]
80	36864	kDenser only	exponential [2¹⁵ x (1 + ⅛)]
81	40960	kNeutral and kDenser	exponential [2¹⁵ x (1 + ¼)]
82	45056	kDenser only	exponential [2¹⁵ x (1 + ⅜)]
83	49152	kNeutral and kDenser	exponential [2¹⁵ x (1 + ½)]
84	53248	kDenser only	exponential [2¹⁵ x (1 + ⅝)]
85	57344	kNeutral and kDenser	exponential [2¹⁵ x (1 + ¾)]
86	61440	kDenser only	exponential [2¹⁵ x (1 + ⅞)]
87	65536	kNeutral and kDenser	exponential [2¹⁶ x (1 + 0)]
88	73728	kDenser only	exponential [2¹⁶ x (1 + ⅛)]
89	81920	kNeutral and kDenser	exponential [2¹⁶ x (1 + ¼)]
90	90112	kDenser only	exponential [2¹⁶ x (1 + ⅜)]
91	98304	kNeutral and kDenser	exponential [2¹⁶ x (1 + ½)]
92	106496	kDenser only	exponential [2¹⁶ x (1 + ⅝)]
93	114688	kNeutral and kDenser	exponential [2¹⁶ x (1 + ¾)]
94	122880	kDenser only	exponential [2¹⁶ x (1 + ⅞)]
95	131072	kNeutral and kDenser	exponential [2¹⁷ x (1 + 0)]
96	147456	kDenser only	exponential [2¹⁷ x (1 + ⅛)]
97	163840	kNeutral and kDenser	exponential [2¹⁷ x (1 + ¼)]
98	180224	kDenser only	exponential [2¹⁷ x (1 + ⅜)]
99	196608	kNeutral and kDenser	exponential [2¹⁷ x (1 + ½)]
100	212992	kDenser only	exponential [2¹⁷ x (1 + ⅝)]
101	229376	kNeutral and kDenser	exponential [2¹⁷ x (1 + ¾)]
102	245760	kDenser only	exponential [2¹⁷ x (1 + ⅞)]
103	262144	kNeutral and kDenser	exponential [2¹⁸ x (1 + 0)]
104	294912	kDenser only	exponential [2¹⁸ x (1 + ⅛)]
105	327680	kNeutral and kDenser	exponential [2¹⁸ x (1 + ¼)]
106	360448	kDenser only	exponential [2¹⁸ x (1 + ⅜)]
107	393216	kNeutral and kDenser	exponential [2¹⁸ x (1 + ½)]
108	425984	kDenser only	exponential [2¹⁸ x (1 + ⅝)]
109	458752	kNeutral and kDenser	exponential [2¹⁸ x (1 + ¾)]
110	491520	kDenser only	exponential [2¹⁸ x (1 + ⅞)]
111	524288	kNeutral and kDenser	exponential [2¹⁹ x (1 + 0)]
112	589824	kDenser only	exponential [2¹⁹ x (1 + ⅛)]
113	655360	kNeutral and kDenser	exponential [2¹⁹ x (1 + ¼)]
114	720896	kDenser only	exponential [2¹⁹ x (1 + ⅜)]
115	786432	kNeutral and kDenser	exponential [2¹⁹ x (1 + ½)]
116	851968	kDenser only	exponential [2¹⁹ x (1 + ⅝)]
117	917504	kNeutral and kDenser	exponential [2¹⁹ x (1 + ¾)]
118	983040	kNeutral and kDenser	exponential [2¹⁹ x (1 + ⅞)]

16 Bytes Alignment (Typically 64-bit Systems)

Index	Size	Bucket Distribution	Originating Formula
0	16	kNeutral and kDenser	linear [16 x 1]
1	32	kNeutral and kDenser	linear [16 x 2]
2	48	kNeutral and kDenser	linear [16 x 3]
3	64	kNeutral and kDenser	linear [16 x 4]
4	80	kNeutral and kDenser	linear [16 x 5]
5	96	kNeutral and kDenser	linear [16 x 6]
6	112	kNeutral and kDenser	linear [16 x 7]
7	128	kNeutral and kDenser	linear [16 x 8] yet exponential [2⁷ x (1 + 0)]
8	144	kNeutral and kDenser	linear [16 x 9] yet exponential [2⁷ x (1 + ⅛)]
9	160	kNeutral and kDenser	linear [16 x 10] yet exponential [2⁷ x (1 + ¼)]
10	176	kNeutral and kDenser	linear [16 x 11] yet exponential [2⁷ x (1 + ⅜)]
11	192	kNeutral and kDenser	linear [16 x 12] yet exponential [2⁷ x (1 + ½)]
12	208	kNeutral and kDenser	linear [16 x 13] yet exponential [2⁷ x (1 + ⅝)]
13	224	kNeutral and kDenser	linear [16 x 14] yet exponential [2⁷ x (1 + ¾)]
14	240	kNeutral and kDenser	linear [16 x 15] yet exponential [2⁷ x (1 + ⅞)]
15	256	kNeutral and kDenser	linear [16 x 16] yet exponential [2⁸ x (1 + 0)]
16	288	kDenser only	exponential [2⁸ x (1 + ⅛)]
17	320	kNeutral and kDenser	exponential [2⁸ x (1 + ¼)]
18	352	kDenser only	exponential [2⁸ x (1 + ⅜)]
19	384	kNeutral and kDenser	exponential [2⁸ x (1 + ½)]
20	416	kDenser only	exponential [2⁸ x (1 + ⅝)]
21	448	kNeutral and kDenser	exponential [2⁸ x (1 + ¾)]
22	480	kDenser only	exponential [2⁸ x (1 + ⅞)]
23	512	kNeutral and kDenser	exponential [2⁹ x (1 + 0)]
24	576	kDenser only	exponential [2⁹ x (1 + ⅛)]
25	640	kNeutral and kDenser	exponential [2⁹ x (1 + ¼)]
26	704	kDenser only	exponential [2⁹ x (1 + ⅜)]
27	768	kNeutral and kDenser	exponential [2⁹ x (1 + ½)]
28	832	kDenser only	exponential [2⁹ x (1 + ⅝)]
29	896	kNeutral and kDenser	exponential [2⁹ x (1 + ¾)]
30	960	kDenser only	exponential [2⁹ x (1 + ⅞)]
31	1024	kNeutral and kDenser	exponential [2¹⁰ x (1 + 0)]
32	1152	kDenser only	exponential [2¹⁰ x (1 + ⅛)]
33	1280	kNeutral and kDenser	exponential [2¹⁰ x (1 + ¼)]
34	1408	kDenser only	exponential [2¹⁰ x (1 + ⅜)]
35	1536	kNeutral and kDenser	exponential [2¹⁰ x (1 + ½)]
36	1664	kDenser only	exponential [2¹⁰ x (1 + ⅝)]
37	1792	kNeutral and kDenser	exponential [2¹⁰ x (1 + ¾)]
38	1920	kDenser only	exponential [2¹⁰ x (1 + ⅞)]
39	2048	kNeutral and kDenser	exponential [2¹¹ x (1 + 0)]
40	2304	kDenser only	exponential [2¹¹ x (1 + ⅛)]
41	2560	kNeutral and kDenser	exponential [2¹¹ x (1 + ¼)]
42	2816	kDenser only	exponential [2¹¹ x (1 + ⅜)]
43	3072	kNeutral and kDenser	exponential [2¹¹ x (1 + ½)]
44	3328	kDenser only	exponential [2¹¹ x (1 + ⅝)]
45	3584	kNeutral and kDenser	exponential [2¹¹ x (1 + ¾)]
46	3840	kDenser only	exponential [2¹¹ x (1 + ⅞)]
47	4096	kNeutral and kDenser	exponential [2¹² x (1 + 0)]
48	4608	kDenser only	exponential [2¹² x (1 + ⅛)]
49	5120	kNeutral and kDenser	exponential [2¹² x (1 + ¼)]
50	5632	kDenser only	exponential [2¹² x (1 + ⅜)]
51	6144	kNeutral and kDenser	exponential [2¹² x (1 + ½)]
52	6656	kDenser only	exponential [2¹² x (1 + ⅝)]
53	7168	kNeutral and kDenser	exponential [2¹² x (1 + ¾)]
54	7680	kDenser only	exponential [2¹² x (1 + ⅞)]
55	8192	kNeutral and kDenser	exponential [2¹³ x (1 + 0)]
56	9216	kDenser only	exponential [2¹³ x (1 + ⅛)]
57	10240	kNeutral and kDenser	exponential [2¹³ x (1 + ¼)]
58	11264	kDenser only	exponential [2¹³ x (1 + ⅜)]
59	12288	kNeutral and kDenser	exponential [2¹³ x (1 + ½)]
60	13312	kDenser only	exponential [2¹³ x (1 + ⅝)]
61	14336	kNeutral and kDenser	exponential [2¹³ x (1 + ¾)]
62	15360	kDenser only	exponential [2¹³ x (1 + ⅞)]
63	16384	kNeutral and kDenser	exponential [2¹⁴ x (1 + 0)]
64	18432	kDenser only	exponential [2¹⁴ x (1 + ⅛)]
65	20480	kNeutral and kDenser	exponential [2¹⁴ x (1 + ¼)]
66	22528	kDenser only	exponential [2¹⁴ x (1 + ⅜)]
67	24576	kNeutral and kDenser	exponential [2¹⁴ x (1 + ½)]
68	26624	kDenser only	exponential [2¹⁴ x (1 + ⅝)]
69	28672	kNeutral and kDenser	exponential [2¹⁴ x (1 + ¾)]
70	30720	kDenser only	exponential [2¹⁴ x (1 + ⅞)]
71	32768	kNeutral and kDenser	exponential [2¹⁵ x (1 + 0)]
72	36864	kDenser only	exponential [2¹⁵ x (1 + ⅛)]
73	40960	kNeutral and kDenser	exponential [2¹⁵ x (1 + ¼)]
74	45056	kDenser only	exponential [2¹⁵ x (1 + ⅜)]
75	49152	kNeutral and kDenser	exponential [2¹⁵ x (1 + ½)]
76	53248	kDenser only	exponential [2¹⁵ x (1 + ⅝)]
77	57344	kNeutral and kDenser	exponential [2¹⁵ x (1 + ¾)]
78	61440	kDenser only	exponential [2¹⁵ x (1 + ⅞)]
79	65536	kNeutral and kDenser	exponential [2¹⁶ x (1 + 0)]
80	73728	kDenser only	exponential [2¹⁶ x (1 + ⅛)]
81	81920	kNeutral and kDenser	exponential [2¹⁶ x (1 + ¼)]
82	90112	kDenser only	exponential [2¹⁶ x (1 + ⅜)]
83	98304	kNeutral and kDenser	exponential [2¹⁶ x (1 + ½)]
84	106496	kDenser only	exponential [2¹⁶ x (1 + ⅝)]
85	114688	kNeutral and kDenser	exponential [2¹⁶ x (1 + ¾)]
86	122880	kDenser only	exponential [2¹⁶ x (1 + ⅞)]
87	131072	kNeutral and kDenser	exponential [2¹⁷ x (1 + 0)]
88	147456	kDenser only	exponential [2¹⁷ x (1 + ⅛)]
89	163840	kNeutral and kDenser	exponential [2¹⁷ x (1 + ¼)]
90	180224	kDenser only	exponential [2¹⁷ x (1 + ⅜)]
91	196608	kNeutral and kDenser	exponential [2¹⁷ x (1 + ½)]
92	212992	kDenser only	exponential [2¹⁷ x (1 + ⅝)]
93	229376	kNeutral and kDenser	exponential [2¹⁷ x (1 + ¾)]
94	245760	kDenser only	exponential [2¹⁷ x (1 + ⅞)]
95	262144	kNeutral and kDenser	exponential [2¹⁸ x (1 + 0)]
96	294912	kDenser only	exponential [2¹⁸ x (1 + ⅛)]
97	327680	kNeutral and kDenser	exponential [2¹⁸ x (1 + ¼)]
98	360448	kDenser only	exponential [2¹⁸ x (1 + ⅜)]
99	393216	kNeutral and kDenser	exponential [2¹⁸ x (1 + ½)]
100	425984	kDenser only	exponential [2¹⁸ x (1 + ⅝)]
101	458752	kNeutral and kDenser	exponential [2¹⁸ x (1 + ¾)]
102	491520	kDenser only	exponential [2¹⁸ x (1 + ⅞)]
103	524288	kNeutral and kDenser	exponential [2¹⁹ x (1 + 0)]
104	589824	kDenser only	exponential [2¹⁹ x (1 + ⅛)]
105	655360	kNeutral and kDenser	exponential [2¹⁹ x (1 + ¼)]
106	720896	kDenser only	exponential [2¹⁹ x (1 + ⅜)]
107	786432	kNeutral and kDenser	exponential [2¹⁹ x (1 + ½)]
108	851968	kDenser only	exponential [2¹⁹ x (1 + ⅝)]
109	917504	kNeutral and kDenser	exponential [2¹⁹ x (1 + ¾)]
110	983040	kNeutral and kDenser	exponential [2¹⁹ x (1 + ⅞)]