| # 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](https://source.chromium.org/chromium/chromium/src/+/main:base/allocator/partition_allocator/src/partition_alloc/partition_root.h;l=238;drc=b3b10b6e91991505faa738b47ad263534341e05d); |
| 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)] | |
