Miri is an Undefined Behavior detection tool for Rust. It can run binaries and test suites of cargo projects and detect unsafe code that fails to uphold its safety requirements. For instance:
- Out-of-bounds memory accesses and use-after-free
- Invalid use of uninitialized data
- Violation of intrinsic preconditions (an
unreachable_unchecked
being reached, callingcopy_nonoverlapping
with overlapping ranges, ...) - Not sufficiently aligned memory accesses and references
- Violation of basic type invariants (a
bool
that is not 0 or 1, for example, or an invalid enum discriminant) - Experimental: Violations of the Stacked Borrows rules governing aliasing for reference types
- Experimental: Violations of the Tree Borrows aliasing rules, as an optional alternative to Stacked Borrows
- Experimental: Data races and emulation of weak memory effects, i.e., atomic reads can return outdated values.
On top of that, Miri will also tell you about memory leaks: when there is memory
still allocated at the end of the execution, and that memory is not reachable
from a global static
, Miri will raise an error.
You can use Miri to emulate programs on other targets, e.g. to ensure that byte-level data manipulation works correctly both on little-endian and big-endian systems. See cross-interpretation below.
Miri has already discovered many real-world bugs. If you found a bug with Miri, we'd appreciate if you tell us and we'll add it to the list!
By default, Miri ensures a fully deterministic execution and isolates the
program from the host system. Some APIs that would usually access the host, such
as gathering entropy for random number generators, environment variables, and
clocks, are replaced by deterministic "fake" implementations. Set
MIRIFLAGS="-Zmiri-disable-isolation"
to access the real system APIs instead.
(In particular, the "fake" system RNG APIs make Miri not suited for
cryptographic use! Do not generate keys using Miri.)
All that said, be aware that Miri does not catch every violation of the Rust specification in your program, not least because there is no such specification. Miri uses its own approximation of what is and is not Undefined Behavior in Rust. To the best of our knowledge, all Undefined Behavior that has the potential to affect a program's correctness is being detected by Miri (modulo bugs), but you should consult the Reference for the official definition of Undefined Behavior. Miri will be updated with the Rust compiler to protect against UB as it is understood by the current compiler, but it makes no promises about future versions of rustc.
Further caveats that Miri users should be aware of:
- If the program relies on unspecified details of how data is laid out, it will
still run fine in Miri -- but might break (including causing UB) on different
compiler versions or different platforms. (You can use
-Zrandomize-layout
to detect some of these cases.) - Program execution is non-deterministic when it depends, for example, on where
exactly in memory allocations end up, or on the exact interleaving of
concurrent threads. Miri tests one of many possible executions of your
program, but it will miss bugs that only occur in a different possible execution.
You can alleviate this to some extent by running Miri with different
values for
-Zmiri-seed
, but that will still by far not explore all possible executions. - Miri runs the program as a platform-independent interpreter, so the program
has no access to most platform-specific APIs or FFI. A few APIs have been
implemented (such as printing to stdout, accessing environment variables, and
basic file system access) but most have not: for example, Miri currently does
not support networking. System API support varies between targets; if you run
on Windows it is a good idea to use
--target x86_64-unknown-linux-gnu
to get better support. - Weak memory emulation may produce weak behaviors
when
SeqCst
fences are used that are not actually permitted by the Rust memory model, and it cannot produce all behaviors possibly observable on real hardware.
Moreover, Miri fundamentally cannot ensure that your code is sound. Soundness is the property of never causing undefined behavior when invoked from arbitrary safe code, even in combination with other sound code. In contrast, Miri can just tell you if a particular way of interacting with your code (e.g., a test suite) causes any undefined behavior in a particular execution (of which there may be many, e.g. when concurrency or other forms of non-determinism are involved). When Miri finds UB, your code is definitely unsound, but when Miri does not find UB, then you may just have to test more inputs or more possible non-deterministic choices.
Install Miri on Rust nightly via rustup
:
rustup +nightly component add miri
All the following commands assume the nightly toolchain is pinned via rustup override set nightly
.
Alternatively, use cargo +nightly
for each of the following commands.
Now you can run your project in Miri:
- To run all tests in your project through Miri, use
cargo miri test
. - If you have a binary project, you can run it through Miri using
cargo miri run
.
The first time you run Miri, it will perform some extra setup and install some dependencies. It will ask you for confirmation before installing anything.
cargo miri run/test
supports the exact same flags as cargo run/test
. For
example, cargo miri test filter
only runs the tests containing filter
in
their name.
You can pass flags to Miri via MIRIFLAGS
. For example,
MIRIFLAGS="-Zmiri-disable-stacked-borrows" cargo miri run
runs the program
without checking the aliasing of references.
When compiling code via cargo miri
, the cfg(miri)
config flag is set for code
that will be interpreted under Miri. You can use this to ignore test cases that fail
under Miri because they do things Miri does not support:
#[test]
#[cfg_attr(miri, ignore)]
fn does_not_work_on_miri() {
tokio::run(futures::future::ok::<_, ()>(()));
}
There is no way to list all the infinite things Miri cannot do, but the interpreter will explicitly tell you when it finds something unsupported:
error: unsupported operation: can't call foreign function: bind
...
= help: this is likely not a bug in the program; it indicates that the program \
performed an operation that Miri does not support
Miri can not only run a binary or test suite for your host target, it can also
perform cross-interpretation for arbitrary foreign targets: cargo miri run --target x86_64-unknown-linux-gnu
will run your program as if it was a Linux
program, no matter your host OS. This is particularly useful if you are using
Windows, as the Linux target is much better supported than Windows targets.
You can also use this to test platforms with different properties than your host
platform. For example cargo miri test --target s390x-unknown-linux-gnu
will run your test suite on a big-endian target, which is useful for testing
endian-sensitive code.
Certain parts of the execution are picked randomly by Miri, such as the exact base address
allocations are stored at and the interleaving of concurrently executing threads. Sometimes, it can
be useful to explore multiple different execution, e.g. to make sure that your code does not depend
on incidental "super-alignment" of new allocations and to test different thread interleavings.
This can be done with the --many-seeds
flag:
cargo miri test --many-seeds # tries the seeds in 0..64
cargo miri test --many-seeds=0..16
The default of 64 different seeds is quite slow, so you probably want to specify a smaller range.
When running Miri on CI, use the following snippet to install a nightly toolchain with the Miri component:
rustup toolchain install nightly --component miri
rustup override set nightly
cargo miri test
Here is an example job for GitHub Actions:
miri:
name: "Miri"
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v3
- name: Install Miri
run: |
rustup toolchain install nightly --component miri
rustup override set nightly
cargo miri setup
- name: Test with Miri
run: cargo miri test
The explicit cargo miri setup
helps to keep the output of the actual test step
clean.
Miri does not support all targets supported by Rust. The good news, however, is
that no matter your host OS/platform, it is easy to run code for any target
using --target
!
The following targets are tested on CI and thus should always work (to the degree documented below):
- All Rust Tier 1 targets are supported by Miri. They are all checked on Miri's CI, and some (at least one per OS) are even checked on every Rust PR, so the shipped Miri should always work on these targets.
aarch64-apple-darwin
is supported.s390x-unknown-linux-gnu
is supported as our "big-endian target of choice".- For every other target with OS
linux
,macos
, orwindows
, Miri should generally work, but we make no promises and we don't run tests for such targets. - We have unofficial support (not maintained by the Miri team itself) for some further operating systems.
freebsd
: maintainer wanted. Supportsstd::env
and parts ofstd::{thread, fs}
, but notstd::sync
.android
: maintainer wanted. Support very incomplete, but a basic "hello world" works.solaris
/illumos
: maintained by @devnexen. Support very incomplete, but a basic "hello world" works.wasm
: maintainer wanted. Support very incomplete, not even standard output works, but an emptymain
function works.
- For targets on other operating systems, Miri might fail before even reaching the
main
function.
However, even for targets that we do support, the degree of support for accessing platform APIs (such as the file system) differs between targets: generally, Linux targets have the best support, and macOS targets are usually on par. Windows is supported less well.
Though it implements Rust threading, Miri itself is a single-threaded interpreter.
This means that when running cargo miri test
, you will probably see a dramatic
increase in the amount of time it takes to run your whole test suite due to the
inherent interpreter slowdown and a loss of parallelism.
You can get your test suite's parallelism back by running cargo miri nextest run -jN
(note that you will need cargo-nextest
installed).
This works because cargo-nextest
collects a list of all tests then launches a
separate cargo miri run
for each test. You will need to specify a -j
or --test-threads
;
by default cargo miri nextest run
runs one test at a time. For more details, see the
cargo-nextest
Miri documentation.
Note: This one-test-per-process model means that cargo miri test
is able to detect data
races where two tests race on a shared resource, but cargo miri nextest run
will not detect
such races.
Note: cargo-nextest
does not support doctests, see nextest-rs/nextest#16
When using the above instructions, you may encounter a number of confusing compiler errors.
You may see this when trying to get Miri to display a backtrace. By default, Miri
doesn't expose any environment to the program, so running
RUST_BACKTRACE=1 cargo miri test
will not do what you expect.
To get a backtrace, you need to disable isolation
using -Zmiri-disable-isolation
:
RUST_BACKTRACE=1 MIRIFLAGS="-Zmiri-disable-isolation" cargo miri test
You may be running cargo miri
with a different compiler version than the one
used to build the custom libstd that Miri uses, and Miri failed to detect that.
Try running cargo miri clean
.
Miri adds its own set of -Z
flags, which are usually set via the MIRIFLAGS
environment variable. We first document the most relevant and most commonly used flags:
-Zmiri-address-reuse-rate=<rate>
changes the probability that a freed non-stack allocation will be added to the pool for address reuse, and the probability that a new non-stack allocation will be taken from the pool. Stack allocations never get added to or taken from the pool. The default is0.5
.-Zmiri-address-reuse-cross-thread-rate=<rate>
changes the probability that an allocation which attempts to reuse a previously freed block of memory will also consider blocks freed by other threads. The default is0.1
, which means by default, in 90% of the cases where an address reuse attempt is made, only addresses from the same thread will be considered. Reusing an address from another thread induces synchronization between those threads, which can mask data races and weak memory bugs.-Zmiri-compare-exchange-weak-failure-rate=<rate>
changes the failure rate ofcompare_exchange_weak
operations. The default is0.8
(so 4 out of 5 weak ops will fail). You can change it to any value between0.0
and1.0
, where1.0
means it will always fail and0.0
means it will never fail. Note than setting it to1.0
will likely cause hangs, since it means programs usingcompare_exchange_weak
cannot make progress.-Zmiri-disable-isolation
disables host isolation. As a consequence, the program has access to host resources such as environment variables, file systems, and randomness.-Zmiri-disable-leak-backtraces
disables backtraces reports for memory leaks. By default, a backtrace is captured for every allocation when it is created, just in case it leaks. This incurs some memory overhead to store data that is almost never used. This flag is implied by-Zmiri-ignore-leaks
.-Zmiri-env-forward=<var>
forwards thevar
environment variable to the interpreted program. Can be used multiple times to forward several variables. Execution will still be deterministic if the value of forwarded variables stays the same. Has no effect if-Zmiri-disable-isolation
is set.-Zmiri-env-set=<var>=<value>
sets thevar
environment variable tovalue
in the interpreted program. It can be used to pass environment variables without needing to alter the host environment. It can be used multiple times to set several variables. If-Zmiri-disable-isolation
or-Zmiri-env-forward
is set, values set with this option will have priority over values from the host environment.-Zmiri-ignore-leaks
disables the memory leak checker, and also allows some remaining threads to exist when the main thread exits.-Zmiri-isolation-error=<action>
configures Miri's response to operations requiring host access while isolation is enabled.abort
,hide
,warn
, andwarn-nobacktrace
are the supported actions. The default is toabort
, which halts the machine. Some (but not all) operations also support continuing execution with a "permission denied" error being returned to the program.warn
prints a full backtrace each time that happens;warn-nobacktrace
is less verbose and shown at most once per operation.hide
hides the warning entirely.-Zmiri-num-cpus
states the number of available CPUs to be reported by miri. By default, the number of available CPUs is1
. Note that this flag does not affect how miri handles threads in any way.-Zmiri-permissive-provenance
disables the warning for integer-to-pointer casts andptr::with_exposed_provenance
. This will necessarily miss some bugs as those operations are not efficiently and accurately implementable in a sanitizer, but it will only miss bugs that concern memory/pointers which is subject to these operations.-Zmiri-preemption-rate
configures the probability that at the end of a basic block, the active thread will be preempted. The default is0.01
(i.e., 1%). Setting this to0
disables preemption.-Zmiri-report-progress
makes Miri print the current stacktrace every now and then, so you can tell what it is doing when a program just keeps running. You can customize how frequently the report is printed via-Zmiri-report-progress=<blocks>
, which prints the report every N basic blocks.-Zmiri-seed=<num>
configures the seed of the RNG that Miri uses to resolve non-determinism. This RNG is used to pick base addresses for allocations, to determine preemption and failure ofcompare_exchange_weak
, and to control store buffering for weak memory emulation. When isolation is enabled (the default), this is also used to emulate system entropy. The default seed is 0. You can increase test coverage by running Miri multiple times with different seeds.-Zmiri-strict-provenance
enables strict provenance checking in Miri. This means that casting an integer to a pointer yields a result with 'invalid' provenance, i.e., with provenance that cannot be used for any memory access.-Zmiri-symbolic-alignment-check
makes the alignment check more strict. By default, alignment is checked by casting the pointer to an integer, and making sure that is a multiple of the alignment. This can lead to cases where a program passes the alignment check by pure chance, because things "happened to be" sufficiently aligned -- there is no UB in this execution but there would be UB in others. To avoid such cases, the symbolic alignment check only takes into account the requested alignment of the relevant allocation, and the offset into that allocation. This avoids missing such bugs, but it also incurs some false positives when the code does manual integer arithmetic to ensure alignment. (The standard libraryalign_to
method works fine in both modes; under symbolic alignment it only fills the middle slice when the allocation guarantees sufficient alignment.)
The remaining flags are for advanced use only, and more likely to change or be removed. Some of these are unsound, which means they can lead to Miri failing to detect cases of undefined behavior in a program.
-Zmiri-disable-alignment-check
disables checking pointer alignment, so you can focus on other failures, but it means Miri can miss bugs in your program. Using this flag is unsound.-Zmiri-disable-data-race-detector
disables checking for data races. Using this flag is unsound. This implies-Zmiri-disable-weak-memory-emulation
.-Zmiri-disable-stacked-borrows
disables checking the experimental aliasing rules to track borrows (Stacked Borrows and Tree Borrows). This can make Miri run faster, but it also means no aliasing violations will be detected. Using this flag is unsound (but the affected soundness rules are experimental). Later flags take precedence: borrow tracking can be reactivated by-Zmiri-tree-borrows
.-Zmiri-disable-validation
disables enforcing validity invariants, which are enforced by default. This is mostly useful to focus on other failures (such as out-of-bounds accesses) first. Setting this flag means Miri can miss bugs in your program. However, this can also help to make Miri run faster. Using this flag is unsound.-Zmiri-disable-weak-memory-emulation
disables the emulation of some C++11 weak memory effects.-Zmiri-native-lib=<path to a shared object file>
is an experimental flag for providing support for calling native functions from inside the interpreter via FFI. Functions not provided by that file are still executed via the usual Miri shims. WARNING: If an invalid/incorrect.so
file is specified, this can cause Undefined Behavior in Miri itself! And of course, Miri cannot do any checks on the actions taken by the native code. Note that Miri has its own handling of file descriptors, so if you want to replace some functions working on file descriptors, you will have to replace all of them, or the two kinds of file descriptors will be mixed up. This is work in progress; currently, only integer arguments and return values are supported (and no, pointer/integer casts to work around this limitation will not work; they will fail horribly). It also only works on Linux hosts for now.-Zmiri-measureme=<name>
enablesmeasureme
profiling for the interpreted program. This can be used to find which parts of your program are executing slowly under Miri. The profile is written out to a file inside a directory called<name>
, and can be processed using the tools in the repository https://github.com/rust-lang/measureme.-Zmiri-mute-stdout-stderr
silently ignores all writes to stdout and stderr, but reports to the program that it did actually write. This is useful when you are not interested in the actual program's output, but only want to see Miri's errors and warnings.-Zmiri-panic-on-unsupported
will makes some forms of unsupported functionality, such as FFI and unsupported syscalls, panic within the context of the emulated application instead of raising an error within the context of Miri (and halting execution). Note that code might not expect these operations to ever panic, so this flag can lead to strange (mis)behavior.-Zmiri-retag-fields[=<all|none|scalar>]
controls when Stacked Borrows retagging recurses into fields.all
means it always recurses (the default, and equivalent to-Zmiri-retag-fields
without an explicit value),none
means it never recurses,scalar
means it only recurses for types where we would also emitnoalias
annotations in the generated LLVM IR (types passed as individual scalars or pairs of scalars). Setting this tonone
is unsound.-Zmiri-provenance-gc=<blocks>
configures how often the pointer provenance garbage collector runs. The default is to search for and remove unreachable provenance once every10000
basic blocks. Setting this to0
disables the garbage collector, which causes some programs to have explosive memory usage and/or super-linear runtime.-Zmiri-track-alloc-accesses
show not only allocation and free events for tracked allocations, but also reads and writes.-Zmiri-track-alloc-id=<id1>,<id2>,...
shows a backtrace when the given allocations are being allocated or freed. This helps in debugging memory leaks and use after free bugs. Specifying this argument multiple times does not overwrite the previous values, instead it appends its values to the list. Listing an id multiple times has no effect.-Zmiri-track-call-id=<id1>,<id2>,...
shows a backtrace when the given call ids are assigned to a stack frame. This helps in debugging UB related to Stacked Borrows "protectors". Specifying this argument multiple times does not overwrite the previous values, instead it appends its values to the list. Listing an id multiple times has no effect.-Zmiri-track-pointer-tag=<tag1>,<tag2>,...
shows a backtrace when a given pointer tag is created and when (if ever) it is popped from a borrow stack (which is where the tag becomes invalid and any future use of it will error). This helps you in finding out why UB is happening and where in your code would be a good place to look for it. Specifying this argument multiple times does not overwrite the previous values, instead it appends its values to the list. Listing a tag multiple times has no effect.-Zmiri-track-weak-memory-loads
shows a backtrace when weak memory emulation returns an outdated value from a load. This can help diagnose problems that disappear under-Zmiri-disable-weak-memory-emulation
.-Zmiri-tree-borrows
replaces Stacked Borrows with the Tree Borrows rules. Tree Borrows is even more experimental than Stacked Borrows. While Tree Borrows is still sound in the sense of catching all aliasing violations that current versions of the compiler might exploit, it is likely that the eventual final aliasing model of Rust will be stricter than Tree Borrows. In other words, if you use Tree Borrows, even if your code is accepted today, it might be declared UB in the future. This is much less likely with Stacked Borrows.-Zmiri-force-page-size=<num>
overrides the default page size for an architecture, in multiples of 1k.4
is default for most targets. This value should always be a power of 2 and nonzero.-Zmiri-unique-is-unique
performs additional aliasing checks forcore::ptr::Unique
to ensure that it could theoretically be considerednoalias
. This flag is experimental and has an effect only when used with-Zmiri-tree-borrows
.
Some native rustc -Z
flags are also very relevant for Miri:
-Zmir-opt-level
controls how many MIR optimizations are performed. Miri overrides the default to be0
; be advised that using any higher level can make Miri miss bugs in your program because they got optimized away.-Zalways-encode-mir
makes rustc dump MIR even for completely monomorphic functions. This is needed so that Miri can execute such functions, so Miri sets this flag per default.-Zmir-emit-retag
controls whetherRetag
statements are emitted. Miri enables this per default because it is needed for Stacked Borrows and Tree Borrows.
Moreover, Miri recognizes some environment variables:
MIRIFLAGS
defines extra flags to be passed to Miri.MIRI_LIB_SRC
defines the directory where Miri expects the sources of the standard library that it will build and use for interpretation. This directory must point to thelibrary
subdirectory of arust-lang/rust
repository checkout.MIRI_SYSROOT
indicates the sysroot to use. When usingcargo miri test
/cargo miri run
, this skips the automatic setup -- only set this if you do not want to use the automatically created sysroot. When invokingcargo miri setup
, this indicates where the sysroot will be put.MIRI_NO_STD
makes sure that the target's sysroot is built without libstd. This allows testing and running no_std programs. This should not usually be used; Miri has a heuristic to detect no-std targets based on the target name. Setting this on a target that does support libstd can lead to confusing results.
Miri provides some extern
functions that programs can import to access
Miri-specific functionality. They are declared in
/tests/utils/miri_extern.rs.
If you want to contribute to Miri, great! Please check out our contribution guide.
For help with running Miri, you can open an issue here on GitHub or use the Miri stream on the Rust Zulip.
This project began as part of an undergraduate research course in 2015 by
@solson at the University of Saskatchewan. There are slides and a
report available from that project. In 2016, @oli-obk joined to prepare Miri
for eventually being used as const evaluator in the Rust compiler itself
(basically, for const
and static
stuff), replacing the old evaluator that
worked directly on the AST. In 2017, @RalfJung did an internship with Mozilla
and began developing Miri towards a tool for detecting undefined behavior, and
also using Miri as a way to explore the consequences of various possible
definitions for undefined behavior in Rust. @oli-obk's move of the Miri engine
into the compiler finally came to completion in early 2018. Meanwhile, later
that year, @RalfJung did a second internship, developing Miri further with
support for checking basic type invariants and verifying that references are
used according to their aliasing restrictions.
Miri has already found a number of bugs in the Rust standard library and beyond, some of which we collect here. If Miri helped you find a subtle UB bug in your code, we'd appreciate a PR adding it to the list!
Definite bugs found:
Debug for vec_deque::Iter
accessing uninitialized memoryVec::into_iter
doing an unaligned ZST readFrom<&[T]> for Rc
creating a not sufficiently aligned referenceBTreeMap
creating a shared reference pointing to a too small allocationVec::append
creating a dangling reference- Futures turning a shared reference into a mutable one
str
turning a shared reference into a mutable onerand
performing unaligned reads- The Unix allocator calling
posix_memalign
in an invalid way getrandom
calling thegetrandom
syscall in an invalid wayVec
andBTreeMap
leaking memory under some (panicky) conditionsbeef
leaking memoryEbrCell
using uninitialized memory incorrectly- TiKV performing an unaligned pointer access
servo_arc
creating a dangling shared reference- TiKV constructing out-of-bounds pointers (and overlapping mutable references)
encoding_rs
doing out-of-bounds pointer arithmetic- TiKV using
Vec::from_raw_parts
incorrectly - Incorrect doctests for
AtomicPtr
andBox::from_raw_in
- Insufficient alignment in
ThinVec
crossbeam-epoch
callingassume_init
on a partly-initializedMaybeUninit
integer-encoding
dereferencing a misaligned pointerrkyv
constructing aBox<[u8]>
from an overaligned allocation- Data race in
arc-swap
- Data race in
thread::scope
regex
incorrectly handling unalignedVec<u8>
buffers- Incorrect use of
compare_exchange_weak
inonce_cell
- Dropping with unaligned pointers in
vec::IntoIter
- Deallocating with the wrong layout in new specializations for in-place
Iterator::collect
- Incorrect offset computation for highly-aligned types in
portable-atomic-util
- Occasional memory leak in
std::mpsc
channels (original code in crossbeam) - Weak-memory-induced memory leak in Windows thread-local storage
Violations of Stacked Borrows found that are likely bugs (but Stacked Borrows is currently just an experiment):
VecDeque::drain
creating overlapping mutable references- Various
BTreeMap
problems LinkedList
cursor insertion creating overlapping mutable referencesVec::push
invalidating existing references into the vectoralign_to_mut
violating uniqueness of mutable referencessized-chunks
creating aliasing mutable referencesString::push_str
invalidating existing references into the stringryu
using raw pointers outside their valid memory area- ink! creating overlapping mutable references
- TiKV creating overlapping mutable reference and raw pointer
- Windows
Env
iterator using a raw pointer outside its valid memory area VecDeque::iter_mut
creating overlapping mutable references- Various standard library aliasing issues involving raw pointers
<[T]>::copy_within
using a loan after invalidating it
- Stacked Borrows: An Aliasing Model for Rust
- Using Lightweight Formal Methods to Validate a Key-Value Storage Node in Amazon S3
- SyRust: Automatic Testing of Rust Libraries with Semantic-Aware Program Synthesis
Licensed under either of
- Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
- MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)
at your option.
Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you shall be dual licensed as above, without any additional terms or conditions.