2018-11-17 05:05:19 +05:30
|
|
|
This is a security-focused general purpose memory allocator providing the
|
|
|
|
malloc API along with various extensions. It provides substantial hardening
|
|
|
|
against heap corruption vulnerabilities. The security-focused design also leads
|
|
|
|
to much less metadata overhead and memory waste from fragmentation than a more
|
|
|
|
traditional allocator design. It aims to provide decent overall performance
|
|
|
|
with a focus on long-term performance and memory usage rather than allocator
|
2018-11-17 21:23:04 +05:30
|
|
|
micro-benchmarks. It has relatively fine-grained locking and will offer good
|
|
|
|
scalability once arenas are implemented.
|
2018-11-17 05:05:19 +05:30
|
|
|
|
2018-09-02 15:35:37 +05:30
|
|
|
This project currently aims to support Android, musl and glibc. It may support
|
|
|
|
other non-Linux operating systems in the future. For Android and musl, there
|
|
|
|
will be custom integration and other hardening features. The glibc support will
|
|
|
|
be limited to replacing the malloc implementation because musl is a much more
|
|
|
|
robust and cleaner base to build on and can cover the same use cases.
|
|
|
|
|
2018-11-17 05:11:27 +05:30
|
|
|
# Dependencies
|
|
|
|
|
2018-08-25 04:28:55 +05:30
|
|
|
Debian stable determines the most ancient set of supported dependencies:
|
|
|
|
|
|
|
|
* glibc 2.24
|
|
|
|
* Linux 4.9
|
|
|
|
* Clang 3.8 or GCC 6.3
|
|
|
|
|
|
|
|
However, using more recent releases is highly recommended. Older versions of
|
|
|
|
the dependencies may be compatible at the moment but are not tested and will
|
|
|
|
explicitly not be supported.
|
2018-08-26 15:53:24 +05:30
|
|
|
|
2018-09-07 05:22:09 +05:30
|
|
|
For external malloc replacement with musl, musl 1.1.20 is required. However,
|
|
|
|
there will be custom integration offering better performance in the future
|
|
|
|
along with other hardening for the C standard library implementation.
|
|
|
|
|
2018-09-02 15:35:37 +05:30
|
|
|
Major releases of Android will be supported until tags stop being pushed to
|
|
|
|
the Android Open Source Project (AOSP). Google supports each major release
|
|
|
|
with security patches for 3 years, but tagged releases of the Android Open
|
|
|
|
Source Project are more than just security patches and are no longer pushed
|
|
|
|
once no officially supported devices are using them anymore. For example, at
|
|
|
|
the time of writing (September 2018), AOSP only has tagged releases for 8.1
|
|
|
|
(Nexus 5X, Nexus 5X, Pixel C) and 9.0 (Pixel, Pixel XL, Pixel 2, Pixel 2 XL).
|
|
|
|
There are ongoing security patches for 6.0, 6.0.1, 7.0, 7.1.1, 7.1.2, 8.0, 8.1
|
|
|
|
and 9.0 but only the active AOSP branches (8.1 and 9.0) are supported by this
|
|
|
|
project and it doesn't make much sense to use much older releases with far
|
|
|
|
less privacy and security hardening.
|
2018-08-30 20:37:20 +05:30
|
|
|
|
2018-10-04 12:57:30 +05:30
|
|
|
# Testing
|
|
|
|
|
|
|
|
The `preload.sh` script can be used for testing with dynamically linked
|
|
|
|
executables using glibc or musl:
|
|
|
|
|
|
|
|
./preload.sh krita --new-image RGBA,U8,500,500
|
|
|
|
|
2018-10-04 13:14:19 +05:30
|
|
|
It can be necessary to substantially increase the `vm.max_map_count` sysctl to
|
|
|
|
accomodate the large number of mappings caused by guard slabs and large
|
2018-11-17 04:34:46 +05:30
|
|
|
allocation guard regions. The number of mappings can also be drastically
|
|
|
|
reduced via a significant increase to `CONFIG_GUARD_SLABS_INTERVAL` but the
|
|
|
|
feature has a low performance and memory usage cost so that isn't recommended.
|
2018-10-04 13:14:19 +05:30
|
|
|
|
2018-10-04 12:57:30 +05:30
|
|
|
It can offer slightly better performance when integrated into the C standard
|
|
|
|
library and there are other opportunities for similar hardening within C
|
|
|
|
standard library and dynamic linker implementations. For example, a library
|
|
|
|
region can be implemented to offer similar isolation for dynamic libraries as
|
|
|
|
this allocator offers across different size classes. The intention is that this
|
|
|
|
will be offered as part of hardened variants of the Bionic and musl C standard
|
|
|
|
libraries.
|
|
|
|
|
2018-10-04 12:45:55 +05:30
|
|
|
# Configuration
|
|
|
|
|
2018-09-19 23:27:35 +05:30
|
|
|
You can set some configuration options at compile-time via arguments to the
|
|
|
|
make command as follows:
|
|
|
|
|
|
|
|
make CONFIG_EXAMPLE=false
|
|
|
|
|
2018-11-03 07:05:09 +05:30
|
|
|
Configuration options are provided when there are significant compromises
|
2018-11-17 05:05:19 +05:30
|
|
|
between portability, performance, memory usage or security. The core design
|
|
|
|
choices are not configurable and the allocator remains very security-focused
|
|
|
|
even with all the optional features disabled.
|
2018-11-17 02:06:34 +05:30
|
|
|
|
|
|
|
The following boolean configuration options are available:
|
2018-09-19 23:27:35 +05:30
|
|
|
|
2018-10-29 08:01:46 +05:30
|
|
|
* `CONFIG_NATIVE`: `true` (default) or `false` to control whether the code is
|
|
|
|
optimized for the detected CPU on the host. If this is disabled, setting up a
|
|
|
|
custom `-march` higher than the baseline architecture is highly recommended
|
|
|
|
due to substantial performance benefits for this code.
|
2018-09-19 23:27:35 +05:30
|
|
|
* `CONFIG_CXX_ALLOCATOR`: `true` (default) or `false` to control whether the
|
2018-10-19 00:27:05 +05:30
|
|
|
C++ allocator is replaced for slightly improved performance and detection of
|
|
|
|
mismatched sizes for sized deallocation (often type confusion bugs). This
|
|
|
|
will result in linking against the C++ standard library.
|
2018-11-03 07:05:09 +05:30
|
|
|
* `CONFIG_ZERO_ON_FREE`: `true` (default) or `false` to control whether small
|
|
|
|
allocations are zeroed on free, to mitigate use-after-free and uninitialized
|
|
|
|
use vulnerabilities along with purging lots of potentially sensitive data
|
|
|
|
from the process as soon as possible. This has a performance cost scaling to
|
|
|
|
the size of the allocation, which is usually acceptable.
|
|
|
|
* `CONFIG_WRITE_AFTER_FREE_CHECK`: `true` (default) or `false` to control
|
|
|
|
sanity checking that new allocations contain zeroed memory. This can detect
|
|
|
|
writes caused by a write-after-free vulnerability and mixes well with the
|
|
|
|
features for making memory reuse randomized / delayed. This has a performance
|
|
|
|
cost scaling to the size of the allocation, which is usually acceptable.
|
|
|
|
* `CONFIG_SLOT_RANDOMIZE`: `true` (default) or `false` to randomize selection
|
|
|
|
of free slots within slabs. This has a measurable performance cost and isn't
|
|
|
|
one of the important security features, but the cost has been deemed more
|
|
|
|
than acceptable to be enabled by default.
|
|
|
|
* `CONFIG_SLAB_CANARY`: `true` (default) or `false` to enable support for
|
|
|
|
adding 8 byte canaries to the end of memory allocations. The primary purpose
|
|
|
|
of the canaries is to render small fixed size buffer overflows harmless by
|
|
|
|
absorbing them. The first byte of the canary is always zero, containing
|
|
|
|
overflows caused by a missing C string NUL terminator. The other 7 bytes are
|
|
|
|
a per-slab random value. On free, integrity of the canary is checked to
|
|
|
|
detect attacks like linear overflows or other forms of heap corruption caused
|
|
|
|
by imprecise exploit primitives. However, checking on free will often be too
|
|
|
|
late to prevent exploitation so it's not the main purpose of the canaries.
|
2018-10-20 06:59:40 +05:30
|
|
|
* `CONFIG_SEAL_METADATA`: `true` or `false` (default) to control whether Memory
|
|
|
|
Protection Keys are used to disable access to all writable allocator state
|
|
|
|
outside of the memory allocator code. It's currently disabled by default due
|
2018-10-24 05:08:00 +05:30
|
|
|
to being extremely experimental and a significant performance cost for this
|
|
|
|
use case on current generation hardware, which may become drastically lower
|
2018-10-29 05:58:10 +05:30
|
|
|
in the future. Whether or not this feature is enabled, the metadata is all
|
|
|
|
contained within an isolated memory region with high entropy random guard
|
|
|
|
regions around it.
|
|
|
|
|
2018-11-17 02:06:34 +05:30
|
|
|
The following integer configuration options are available. Proper sanity checks
|
|
|
|
for the chosen values are not written yet, so use them at your own peril:
|
|
|
|
|
|
|
|
* `CONFIG_SLAB_QUARANTINE_RANDOM_SIZE`: `0` (default) to control the number of
|
|
|
|
slots in the random array used to randomize reuse for small memory
|
|
|
|
allocations
|
|
|
|
* `CONFIG_SLAB_QUARANTINE_QUEUE_SIZE`: `0` (default) to control the number of
|
|
|
|
slots in the queue used to delay reuse for small memory allocations
|
|
|
|
* `CONFIG_GUARD_SLABS_INTERVAL`: `1` (default) to control the number of slabs
|
|
|
|
before a slab is skipped and left as an unused memory protected guard slab
|
|
|
|
* `CONFIG_GUARD_SIZE_DIVISOR`: `2` (default) to control the maximum size of the
|
|
|
|
guard regions placed on both sides of large memory allocations, relative to
|
|
|
|
the usable size of the memory allocation
|
|
|
|
* `CONFIG_REGION_QUARANTINE_RANDOM_SIZE`: `128` (default) to control the number
|
|
|
|
of slots in the random array used to randomize region reuse for large memory
|
|
|
|
allocations
|
|
|
|
* `CONFIG_REGION_QUARANTINE_QUEUE_SIZE`: `1024` (default) to control the number
|
|
|
|
of slots in the queue used to delay region reuse for large memory allocations
|
|
|
|
* `CONFIG_REGION_QUARANTINE_SKIP_THRESHOLD`: `33554432` (default) to control
|
|
|
|
the size threshold where large allocations will not be quarantined
|
|
|
|
* `CONFIG_FREE_SLABS_QUARANTINE_RANDOM_SIZE`: `32` (default) to control the
|
|
|
|
number of slots in the random array used to randomize free slab reuse
|
2018-10-04 12:45:55 +05:30
|
|
|
|
|
|
|
There will be more control over enabled features in the future along with
|
|
|
|
control over fairly arbitrarily chosen values like the size of empty slab
|
2018-11-03 14:17:45 +05:30
|
|
|
caches (making them smaller improves security and reduces memory usage while
|
|
|
|
larger caches can substantially improves performance).
|
2018-10-04 12:45:55 +05:30
|
|
|
|
2018-08-26 15:53:24 +05:30
|
|
|
# Basic design
|
|
|
|
|
|
|
|
The current design is very simple and will become a bit more sophisticated as
|
|
|
|
the basic features are completed and the implementation is hardened and
|
|
|
|
optimized. The allocator is exclusive to 64-bit platforms in order to take full
|
|
|
|
advantage of the abundant address space without being constrained by needing to
|
|
|
|
keep the design compatible with 32-bit.
|
|
|
|
|
|
|
|
Small allocations are always located in a large memory region reserved for slab
|
|
|
|
allocations. It can be determined that an allocation is one of the small size
|
|
|
|
classes from the address range. Each small size class has a separate reserved
|
|
|
|
region within the larger region, and the size of a small allocation can simply
|
|
|
|
be determined from the range. Each small size class has a separate out-of-line
|
|
|
|
metadata array outside of the overall allocation region, with the index of the
|
|
|
|
metadata struct within the array mapping to the index of the slab within the
|
|
|
|
dedicated size class region. Slabs are a multiple of the page size and are
|
2018-10-04 13:42:21 +05:30
|
|
|
page aligned. The entire small size class region starts out memory protected
|
2018-08-26 15:53:24 +05:30
|
|
|
and becomes readable / writable as it gets allocated, with idle slabs beyond
|
|
|
|
the cache limit having their pages dropped and the memory protected again.
|
|
|
|
|
|
|
|
Large allocations are tracked via a global hash table mapping their address to
|
|
|
|
their size and guard size. They're simply memory mappings and get mapped on
|
|
|
|
allocation and then unmapped on free.
|
|
|
|
|
2018-10-15 13:34:51 +05:30
|
|
|
This allocator is aimed at production usage, not aiding with finding and fixing
|
|
|
|
memory corruption bugs for software development. It does find many latent bugs
|
|
|
|
but won't include features like the option of generating and storing stack
|
|
|
|
traces for each allocation to include the allocation site in related error
|
|
|
|
messages. The design choices are based around minimizing overhead and
|
|
|
|
maximizing security which often leads to different decisions than a tool
|
|
|
|
attempting to find bugs. For example, it uses zero-based sanitization on free
|
|
|
|
and doesn't minimize slack space from size class rounding between the end of an
|
|
|
|
allocation and the canary / guard region. Zero-based filling has the least
|
|
|
|
chance of uncovering latent bugs, but also the best chance of mitigating
|
|
|
|
vulnerabilities. The canary feature is primarily meant to act as padding
|
|
|
|
absorbing small overflows to render them harmless, so slack space is helpful
|
|
|
|
rather than harmful despite not detecting the corruption on free. The canary
|
|
|
|
needs detection on free in order to have any hope of stopping other kinds of
|
|
|
|
issues like a sequential overflow, which is why it's included. It's assumed
|
|
|
|
that an attacker can figure out the allocator is in use so the focus is
|
|
|
|
explicitly not on detecting bugs that are impossible to exploit with it in use
|
|
|
|
like an 8 byte overflow. The design choices would be different if performance
|
|
|
|
was a bit less important and if a core goal was finding latent bugs.
|
|
|
|
|
2018-08-26 15:53:24 +05:30
|
|
|
# Security properties
|
|
|
|
|
|
|
|
* Fully out-of-line metadata
|
|
|
|
* Deterministic detection of any invalid free (unallocated, unaligned, etc.)
|
2018-10-11 04:18:45 +05:30
|
|
|
* Validation of the size passed for C++14 sized deallocation by `delete`
|
2018-11-05 05:22:01 +05:30
|
|
|
even for code compiled with earlier standards (detects type confusion if
|
|
|
|
the size is different) and by various containers using the allocator API
|
|
|
|
directly
|
2018-08-26 15:53:24 +05:30
|
|
|
* Isolated memory region for slab allocations
|
2018-08-30 20:37:20 +05:30
|
|
|
* Divided up into isolated inner regions for each size class
|
|
|
|
* High entropy random base for each size class region
|
|
|
|
* No deterministic / low entropy offsets between allocations with
|
|
|
|
different size classes
|
2018-08-26 16:41:22 +05:30
|
|
|
* Metadata is completely outside the slab allocation region
|
2018-08-30 20:37:20 +05:30
|
|
|
* No references to metadata within the slab allocation region
|
|
|
|
* No deterministic / low entropy offsets to metadata
|
|
|
|
* Entire slab region starts out non-readable and non-writable
|
|
|
|
* Slabs beyond the cache limit are purged and become non-readable and
|
|
|
|
non-writable memory again
|
2018-10-15 07:49:10 +05:30
|
|
|
* Placed into a queue for reuse in FIFO order to maximize the time
|
|
|
|
spent memory protected
|
|
|
|
* Randomized array is used to add a random delay for reuse
|
2018-08-26 15:53:24 +05:30
|
|
|
* Fine-grained randomization within memory regions
|
|
|
|
* Randomly sized guard regions for large allocations
|
|
|
|
* Random slot selection within slabs
|
2018-11-06 02:49:50 +05:30
|
|
|
* Randomized delayed free for slab allocations
|
2018-11-06 04:36:54 +05:30
|
|
|
* [in-progress] Randomized choice of slabs
|
2018-08-26 15:53:24 +05:30
|
|
|
* [in-progress] Randomized allocation of slabs
|
2018-10-09 01:20:31 +05:30
|
|
|
* Slab allocations are zeroed on free
|
2018-11-16 13:56:07 +05:30
|
|
|
* Detection of write-after-free for slab allocations by verifying zero filling
|
|
|
|
is intact at allocation time
|
2018-10-09 01:20:31 +05:30
|
|
|
* Large allocations are purged and memory protected on free with the memory
|
|
|
|
mapping kept reserved in a quarantine to detect use-after-free
|
2018-10-13 00:40:35 +05:30
|
|
|
* The quarantine is primarily based on a FIFO ring buffer, with the oldest
|
|
|
|
mapping in the quarantine being unmapped to make room for the most
|
|
|
|
recently freed mapping
|
|
|
|
* Another layer of the quarantine swaps with a random slot in an array to
|
|
|
|
randomize the number of large deallocations required to push mappings out
|
|
|
|
of the quarantine
|
2018-08-27 10:44:15 +05:30
|
|
|
* Memory in fresh allocations is consistently zeroed due to it either being
|
|
|
|
fresh pages or zeroed on free after previous usage
|
2018-11-06 02:49:50 +05:30
|
|
|
* Delayed free via a combination of FIFO and randomization for slab allocations
|
2018-09-05 09:49:27 +05:30
|
|
|
* Random canaries placed after each slab allocation to *absorb*
|
2018-08-26 15:53:24 +05:30
|
|
|
and then later detect overflows/underflows
|
|
|
|
* High entropy per-slab random values
|
2018-10-04 02:39:57 +05:30
|
|
|
* Leading byte is zeroed to contain C string overflows
|
2018-09-07 04:23:06 +05:30
|
|
|
* Possible slab locations are skipped and remain memory protected, leaving slab
|
|
|
|
size class regions interspersed with guard pages
|
2018-11-03 14:10:13 +05:30
|
|
|
* Zero size allocations are a dedicated size class with the entire region
|
|
|
|
remaining non-readable and non-writable
|
2018-10-15 07:42:03 +05:30
|
|
|
* Protected allocator state (including all metadata)
|
|
|
|
* Address space for state is entirely reserved during initialization and
|
2018-10-11 04:25:31 +05:30
|
|
|
never reused for allocations or anything else
|
2018-10-15 07:42:03 +05:30
|
|
|
* State within global variables is entirely read-only after initialization
|
|
|
|
with pointers to the isolated allocator state so leaking the address of
|
|
|
|
the library doesn't leak the address of writable state
|
2018-10-19 01:40:49 +05:30
|
|
|
* Allocator state is located within a dedicated region with high entropy
|
|
|
|
randomly sized guard regions around it
|
2018-11-03 12:41:59 +05:30
|
|
|
* Protection via Memory Protection Keys (MPK) on x86\_64 (disabled by
|
|
|
|
default due to low benefit-cost ratio on top of baseline protections)
|
2018-10-19 06:03:48 +05:30
|
|
|
* [future] Protection via MTE on ARMv8.5+
|
2018-08-30 20:37:20 +05:30
|
|
|
* Extension for retrieving the size of allocations with fallback
|
2018-08-26 15:53:24 +05:30
|
|
|
to a sentinel for pointers not managed by the allocator
|
|
|
|
* Can also return accurate values for pointers *within* small allocations
|
|
|
|
* The same applies to pointers within the first page of large allocations,
|
|
|
|
otherwise it currently has to return a sentinel
|
2018-08-30 20:37:20 +05:30
|
|
|
* No alignment tricks interfering with ASLR like jemalloc, PartitionAlloc, etc.
|
|
|
|
* No usage of the legacy brk heap
|
|
|
|
* Aggressive sanity checks
|
|
|
|
* Errors other than ENOMEM from mmap, munmap, mprotect and mremap treated
|
2018-10-04 02:53:20 +05:30
|
|
|
as fatal, which can help to detect memory management gone wrong elsewhere
|
|
|
|
in the process.
|
2018-11-03 12:39:03 +05:30
|
|
|
* [future] Memory tagging for slab allocations via MTE on ARMv8.5+
|
|
|
|
* random memory tags as the baseline, providing probabilistic protection
|
|
|
|
against various forms of memory corruption
|
|
|
|
* dedicated tag for free slots, set on free, for deterministic protection
|
|
|
|
against accessing freed memory
|
|
|
|
* store previous random tag within freed slab allocations, and increment it
|
|
|
|
to get the next tag for that slot to provide deterministic use-after-free
|
|
|
|
detection through multiple cycles of memory reuse
|
|
|
|
* guarantee distinct tags for adjacent memory allocations by incrementing
|
|
|
|
past matching values for deterministic detection of linear overflows
|
2018-08-30 20:37:20 +05:30
|
|
|
|
|
|
|
# Randomness
|
|
|
|
|
|
|
|
The current implementation of random number generation for randomization-based
|
|
|
|
mitigations is based on generating a keystream from a stream cipher (ChaCha8)
|
|
|
|
in small chunks. A separate CSPRNG is used for each small size class, large
|
|
|
|
allocations, etc. in order to fit into the existing fine-grained locking model
|
|
|
|
without needing to waste memory per thread by having the CSPRNG state in Thread
|
|
|
|
Local Storage. Similarly, it's protected via the same approach taken for the
|
|
|
|
rest of the metadata. The stream cipher is regularly reseeded from the OS to
|
|
|
|
provide backtracking and prediction resistance with a negligible cost. The
|
|
|
|
reseed interval simply needs to be adjusted to the point that it stops
|
|
|
|
registering as having any significant performance impact. The performance
|
|
|
|
impact on recent Linux kernels is primarily from the high cost of system calls
|
|
|
|
and locking since the implementation is quite efficient (ChaCha20), especially
|
|
|
|
for just generating the key and nonce for another stream cipher (ChaCha8).
|
|
|
|
|
|
|
|
ChaCha8 is a great fit because it's extremely fast across platforms without
|
|
|
|
relying on hardware support or complex platform-specific code. The security
|
|
|
|
margins of ChaCha20 would be completely overkill for the use case. Using
|
|
|
|
ChaCha8 avoids needing to resort to a non-cryptographically secure PRNG or
|
|
|
|
something without a lot of scrunity. The current implementation is simply the
|
|
|
|
reference implementation of ChaCha8 converted into a pure keystream by ripping
|
|
|
|
out the XOR of the message into the keystream.
|
|
|
|
|
|
|
|
The random range generation functions are a highly optimized implementation
|
|
|
|
too. Traditional uniform random number generation within a range is very high
|
|
|
|
overhead and can easily dwarf the cost of an efficient CSPRNG.
|
2018-08-26 15:53:24 +05:30
|
|
|
|
|
|
|
# Size classes
|
|
|
|
|
2018-11-03 14:10:13 +05:30
|
|
|
The zero byte size class is a special case of the smallest regular size class.
|
|
|
|
It's allocated in a dedicated region like other size classes but with the slabs
|
|
|
|
never being made readable and writable so the only memory usage is for the slab
|
|
|
|
metadata.
|
2018-08-26 15:53:24 +05:30
|
|
|
|
|
|
|
The slab slot count for each size class is not yet finely tuned beyond choosing values avoiding
|
|
|
|
internal fragmentation for slabs (i.e. avoiding wasted space due to page size rounding).
|
|
|
|
|
2018-11-19 10:41:15 +05:30
|
|
|
The choice of size classes for slab allocation is the same as jemalloc, which
|
|
|
|
is a careful balance between minimizing internal and external fragmentation. If
|
|
|
|
there are more size classes, more memory is wasted on free slots available only
|
|
|
|
to allocation requests of those sizes (external fragmentation). If there are
|
|
|
|
fewer size classes, the spacing between them is larger and more memory is
|
|
|
|
wasted due to rounding up to the size classes (internal fragmentation). There
|
|
|
|
are 4 special size classes for the smallest sizes (16, 32, 48, 64) that are
|
|
|
|
simply spaced out by the minimum spacing (16). Afterwards, there are four size
|
|
|
|
classes for every power of two spacing which results in bounding the internal
|
|
|
|
fragmentation below 20% for each size class. This also means there are 4 size
|
|
|
|
classes for each doubling in size.
|
2018-08-26 15:53:24 +05:30
|
|
|
|
2018-11-03 15:14:49 +05:30
|
|
|
| size class | worst case internal fragmentation | slab slots | slab size | internal fragmentation for slabs |
|
2018-08-26 15:53:24 +05:30
|
|
|
| - | - | - | - | - |
|
2018-11-03 14:10:13 +05:30
|
|
|
| 16 | 93.75% | 256 | 4096 | 0.0% |
|
2018-08-26 15:53:24 +05:30
|
|
|
| 32 | 46.875% | 128 | 4096 | 0.0% |
|
|
|
|
| 48 | 31.25% | 85 | 4096 | 0.390625% |
|
|
|
|
| 64 | 23.4375% | 64 | 4096 | 0.0% |
|
|
|
|
| 80 | 18.75% | 51 | 4096 | 0.390625% |
|
|
|
|
| 96 | 15.625% | 42 | 4096 | 1.5625% |
|
|
|
|
| 112 | 13.392857142857139% | 36 | 4096 | 1.5625% |
|
|
|
|
| 128 | 11.71875% | 64 | 8192 | 0.0% |
|
|
|
|
| 160 | 19.375% | 51 | 8192 | 0.390625% |
|
|
|
|
| 192 | 16.145833333333343% | 64 | 12288 | 0.0% |
|
|
|
|
| 224 | 13.839285714285708% | 54 | 12288 | 1.5625% |
|
|
|
|
| 256 | 12.109375% | 64 | 16384 | 0.0% |
|
|
|
|
| 320 | 19.6875% | 64 | 20480 | 0.0% |
|
|
|
|
| 384 | 16.40625% | 64 | 24576 | 0.0% |
|
|
|
|
| 448 | 14.0625% | 64 | 28672 | 0.0% |
|
|
|
|
| 512 | 12.3046875% | 64 | 32768 | 0.0% |
|
|
|
|
| 640 | 19.84375% | 64 | 40960 | 0.0% |
|
|
|
|
| 768 | 16.536458333333343% | 64 | 49152 | 0.0% |
|
|
|
|
| 896 | 14.174107142857139% | 64 | 57344 | 0.0% |
|
|
|
|
| 1024 | 12.40234375% | 64 | 65536 | 0.0% |
|
|
|
|
| 1280 | 19.921875% | 16 | 20480 | 0.0% |
|
|
|
|
| 1536 | 16.6015625% | 16 | 24576 | 0.0% |
|
|
|
|
| 1792 | 14.229910714285708% | 16 | 28672 | 0.0% |
|
|
|
|
| 2048 | 12.451171875% | 16 | 32768 | 0.0% |
|
|
|
|
| 2560 | 19.9609375% | 8 | 20480 | 0.0% |
|
|
|
|
| 3072 | 16.634114583333343% | 8 | 24576 | 0.0% |
|
|
|
|
| 3584 | 14.2578125% | 8 | 28672 | 0.0% |
|
|
|
|
| 4096 | 12.4755859375% | 8 | 32768 | 0.0% |
|
|
|
|
| 5120 | 19.98046875% | 8 | 40960 | 0.0% |
|
|
|
|
| 6144 | 16.650390625% | 8 | 49152 | 0.0% |
|
|
|
|
| 7168 | 14.271763392857139% | 8 | 57344 | 0.0% |
|
|
|
|
| 8192 | 12.48779296875% | 8 | 65536 | 0.0% |
|
|
|
|
| 10240 | 19.990234375% | 6 | 61440 | 0.0% |
|
|
|
|
| 12288 | 16.658528645833343% | 5 | 61440 | 0.0% |
|
|
|
|
| 14336 | 14.278738839285708% | 4 | 57344 | 0.0% |
|
|
|
|
| 16384 | 12.493896484375% | 4 | 65536 | 0.0% |
|