Vendor dependencies for 0.3.0 release

vendor/typenum/.cargo-checksum.json

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vendor/typenum/CHANGELOG.md

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+# Changelog
+
+This project follows semantic versioning.
+
+The MSRV (Minimum Supported Rust Version) is 1.37.0, and typenum is tested
+against this Rust version.
+
+### Unreleased
+
+### 1.18.0 (2025-02-17)
+- [changed] Remove build scripts; instead check-in the built code (PR #219)
+- [added] Constants for 3600 (PR #220)
+- [added] Elixir-style syntax for `tarr!` macro (PR #214)
+- [added] `FoldAdd` and `FoldMul` to get the sum/product of an array (PR #209)
+
+### 1.17.0 (2023-09-15)
+- [removed] Remove `force_unix_path_separator` feature, make it the default
+- [added] docs.rs metadata and cfg options
+- [added] Playground metadata
+
+### 1.16.0 (2022-12-05)
+- [added] `const INT` field to the `ToInt` trait.
+- [added] `const-generics` field with `U<N>` mapping where `N` is a const generic.
+
+### 1.15.0 (2021-12-25)
+- [fixed] Cross-compilation issue due to doing math in build script. (PR #177)
+- [added] New feature `scale_info` for using inside
+  [Substrate](https://github.com/paritytech/substrate.git)-based runtimes (PR
+  #175)
+
+### 1.14.0 (2021-09-01)
+- [changed] Sealed all marker traits. Documentation already stated that these
+  should not be implemented outside the crate, so this is not considered a
+  breaking change.
+
+### 1.13.0 (2021-03-12)
+- [changed] MSRV from 1.22.0 to 1.37.0.
+- [fixed] `op` macro with 2018 edition import.
+- [changed] Allowed calling `assert_type_eq` and `assert_type` at top level.
+- [added] Marker trait `Zero` for `Z0`, `U0`, and `B0`.
+- [added] Implementation of `Pow` trait for f32 and f64 with negative exponent.
+- [added] Trait `ToInt`.
+
+### 1.12.0 (2020-04-13)
+- [added] Feature `force_unix_path_separator` to support building without Cargo.
+- [added] Greatest common divisor operator `Gcd` with alias `Gcf`.
+- [added] `gcd` to the `op!` macro.
+- [changed] Added `Copy` bound to `Rhs` of `Mul<Rhs>` impl for `<TArr<V, A>`.
+- [changed] Added `Copy` bound to `Rhs` of `Div<Rhs>` impl for `<TArr<V, A>`.
+- [changed] Added `Copy` bound to `Rhs` of `PartialDiv<Rhs>` impl for `<TArr<V, A>`.
+- [changed] Added `Copy` bound to `Rhs` of `Rem<Rhs>` impl for `<TArr<V, A>`.
+- [fixed] Make all functions #[inline].
+
+### 1.11.2 (2019-08-26)
+- [fixed] Cross compilation from Linux to Windows.
+
+### 1.11.1 (2019-08-25)
+- [fixed] Builds on earlier Rust builds again and added Rust 1.22.0 to Travis to
+  prevent future breakage.
+
+### 1.11.0 (2019-08-25)
+- [added] Integer `log2` to the `op!` macro.
+- [added] Integer binary logarithm operator `Logarithm2` with alias `Log2`.
+- [changed] Removed `feature(i128_type)` when running with the `i128`
+  feature. Kept the feature flag.  for typenum to maintain compatibility with
+  old Rust versions.
+- [added] Integer `sqrt` to the `op!` macro.
+- [added] Integer square root operator `SquareRoot` with alias `Sqrt`.
+- [fixed] Bug with attempting to create U1024 type alias twice.
+
+### 1.10.0 (2018-03-11)
+- [added] The `PowerOfTwo` marker trait.
+- [added] Associated constants for `Bit`, `Unsigned`, and `Integer`.
+
+### 1.9.0 (2017-05-14)
+- [added] The `Abs` type operator and corresponding `AbsVal` alias.
+- [added] The feature `i128` that enables creating 128-bit integers from
+  typenums.
+- [added] The `assert_type!` and `assert_type_eq!` macros.
+- [added] Operators to the `op!` macro, including those performed by `cmp!`.
+- [fixed] Bug in `op!` macro involving functions and convoluted expressions.
+- [deprecated] The `cmp!` macro.
+
+### 1.8.0 (2017-04-12)
+- [added] The `op!` macro for conveniently performing type-level operations.
+- [added] The `cmp!` macro for conveniently performing type-level comparisons.
+- [added] Some comparison type-operators that are used by the `cmp!` macro.
+
+### 1.7.0 (2017-03-24)
+- [added] Type operators `Min` and `Max` with accompanying aliases `Minimum` and
+  `Maximum`
+
+### 1.6.0 (2017-02-24)
+- [fixed] Bug in `Array` division.
+- [fixed] Bug where `Rem` would sometimes exit early with the wrong answer.
+- [added] `PartialDiv` operator that performs division as a partial function --
+  it's defined only when there is no remainder.
+
+### 1.5.2 (2017-02-04)
+- [fixed] Bug between `Div` implementation and type system.
+
+### 1.5.1 (2016-11-08)
+- [fixed] Expanded implementation of `Pow` for primitives.
+
+### 1.5.0 (2016-11-03)
+- [added] Functions to the `Pow` and `Len` traits. This is *technically* a
+  breaking change, but it would only break someone's code if they have a custom
+  impl for `Pow`. I would be very surprised if that is anyone other than me.
+
+### 1.4.0 (2016-10-29)
+- [added] Type-level arrays of type-level integers. (PR #66)
+- [added] The types in this crate are now instantiable. (Issue #67, PR #68)
+
+### 1.3.1 (2016-03-31)
+- [fixed] Bug with recent nightlies.
+
+### 1.3.0 (2016-02-07)
+- [changed] Removed dependency on libstd. (Issue #53, PR #55)
+- [changed] Reorganized module structure. (PR #57)
+
+### 1.2.0 (2016-01-03)
+- [added] This change log!
+- [added] Convenience type aliases for operators. (Issue #48, PR #50)
+- [added] Types in this crate now derive all possible traits. (Issue #42, PR
+  #51)

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vendor/typenum/Cargo.toml

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+# THIS FILE IS AUTOMATICALLY GENERATED BY CARGO
+#
+# When uploading crates to the registry Cargo will automatically
+# "normalize" Cargo.toml files for maximal compatibility
+# with all versions of Cargo and also rewrite `path` dependencies
+# to registry (e.g., crates.io) dependencies.
+#
+# If you are reading this file be aware that the original Cargo.toml
+# will likely look very different (and much more reasonable).
+# See Cargo.toml.orig for the original contents.
+
+[package]
+edition = "2018"
+rust-version = "1.37.0"
+name = "typenum"
+version = "1.18.0"
+authors = [
+    "Paho Lurie-Gregg <paho@paholg.com>",
+    "Andre Bogus <bogusandre@gmail.com>",
+]
+build = "build.rs"
+autolib = false
+autobins = false
+autoexamples = false
+autotests = false
+autobenches = false
+description = """
+Typenum is a Rust library for type-level numbers evaluated at
+    compile time. It currently supports bits, unsigned integers, and signed
+    integers. It also provides a type-level array of type-level numbers, but its
+    implementation is incomplete."""
+documentation = "https://docs.rs/typenum"
+readme = "README.md"
+categories = ["no-std"]
+license = "MIT OR Apache-2.0"
+repository = "https://github.com/paholg/typenum"
+
+[package.metadata.docs.rs]
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+    "const-generics",
+]
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+    "docsrs",
+]
+
+[package.metadata.playground]
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+    "const-generics",
+]
+
+[lib]
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+
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+strict = []

vendor/typenum/LICENSE

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+MIT OR Apache-2.0

vendor/typenum/LICENSE-APACHE

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+                              Apache License
+                        Version 2.0, January 2004
+                     http://www.apache.org/licenses/
+
+TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
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+   as of the date such litigation is filed.
+
+4. Redistribution. You may reproduce and distribute copies of the
+   Work or Derivative Works thereof in any medium, with or without
+   modifications, and in Source or Object form, provided that You
+   meet the following conditions:
+
+   (a) You must give any other recipients of the Work or
+       Derivative Works a copy of this License; and
+
+   (b) You must cause any modified files to carry prominent notices
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+   (d) If the Work includes a "NOTICE" text file as part of its
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+       of the NOTICE file are for informational purposes only and
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+       notices within Derivative Works that You distribute, alongside
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+       that such additional attribution notices cannot be construed
+       as modifying the License.
+
+   You may add Your own copyright statement to Your modifications and
+   may provide additional or different license terms and conditions
+   for use, reproduction, or distribution of Your modifications, or
+   for any such Derivative Works as a whole, provided Your use,
+   reproduction, and distribution of the Work otherwise complies with
+   the conditions stated in this License.
+
+5. Submission of Contributions. Unless You explicitly state otherwise,
+   any Contribution intentionally submitted for inclusion in the Work
+   by You to the Licensor shall be under the terms and conditions of
+   this License, without any additional terms or conditions.
+   Notwithstanding the above, nothing herein shall supersede or modify
+   the terms of any separate license agreement you may have executed
+   with Licensor regarding such Contributions.
+
+6. Trademarks. This License does not grant permission to use the trade
+   names, trademarks, service marks, or product names of the Licensor,
+   except as required for reasonable and customary use in describing the
+   origin of the Work and reproducing the content of the NOTICE file.
+
+7. Disclaimer of Warranty. Unless required by applicable law or
+   agreed to in writing, Licensor provides the Work (and each
+   Contributor provides its Contributions) on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+   implied, including, without limitation, any warranties or conditions
+   of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+   PARTICULAR PURPOSE. You are solely responsible for determining the
+   appropriateness of using or redistributing the Work and assume any
+   risks associated with Your exercise of permissions under this License.
+
+8. Limitation of Liability. In no event and under no legal theory,
+   whether in tort (including negligence), contract, or otherwise,
+   unless required by applicable law (such as deliberate and grossly
+   negligent acts) or agreed to in writing, shall any Contributor be
+   liable to You for damages, including any direct, indirect, special,
+   incidental, or consequential damages of any character arising as a
+   result of this License or out of the use or inability to use the
+   Work (including but not limited to damages for loss of goodwill,
+   work stoppage, computer failure or malfunction, or any and all
+   other commercial damages or losses), even if such Contributor
+   has been advised of the possibility of such damages.
+
+9. Accepting Warranty or Additional Liability. While redistributing
+   the Work or Derivative Works thereof, You may choose to offer,
+   and charge a fee for, acceptance of support, warranty, indemnity,
+   or other liability obligations and/or rights consistent with this
+   License. However, in accepting such obligations, You may act only
+   on Your own behalf and on Your sole responsibility, not on behalf
+   of any other Contributor, and only if You agree to indemnify,
+   defend, and hold each Contributor harmless for any liability
+   incurred by, or claims asserted against, such Contributor by reason
+   of your accepting any such warranty or additional liability.
+
+END OF TERMS AND CONDITIONS
+
+APPENDIX: How to apply the Apache License to your work.
+
+   To apply the Apache License to your work, attach the following
+   boilerplate notice, with the fields enclosed by brackets "[]"
+   replaced with your own identifying information. (Don't include
+   the brackets!)  The text should be enclosed in the appropriate
+   comment syntax for the file format. We also recommend that a
+   file or class name and description of purpose be included on the
+   same "printed page" as the copyright notice for easier
+   identification within third-party archives.
+
+Copyright 2014 Paho Lurie-Gregg
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+	http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.

vendor/typenum/LICENSE-MIT

@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright (c) 2014 Paho Lurie-Gregg
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

vendor/typenum/README.md

@@ -0,0 +1,67 @@
+[![crates.io](https://img.shields.io/crates/v/typenum.svg)](https://crates.io/crates/typenum)
+[![Build Status](https://github.com/paholg/typenum/actions/workflows/check.yml/badge.svg)](https://github.com/paholg/typenum/actions/workflows/check.yml)
+
+Typenum
+=====
+
+Typenum is a Rust library for type-level numbers evaluated at compile time. It
+currently supports bits, unsigned integers, and signed integers.
+
+Typenum depends only on libcore, and so is suitable for use on any platform!
+
+For the full documentation, go [here](https://docs.rs/typenum).
+
+### Importing
+
+While `typenum` is divided into several modules, they are all re-exported
+through the crate root, so you can import anything contained herein with `use
+typenum::whatever;`, ignoring the crate structure.
+
+You may also find it useful to treat the `consts` module as a prelude,
+performing a glob import.
+
+### Example
+
+Here is a trivial example of `typenum`'s use:
+
+```rust
+use typenum::{Sum, Exp, Integer, N2, P3, P4};
+
+type X = Sum<P3, P4>;
+assert_eq!(<X as Integer>::to_i32(), 7);
+
+type Y = Exp<N2, P3>;
+assert_eq!(<Y as Integer>::to_i32(), -8);
+```
+
+For a non-trivial example of its use, see one of the crates that depends on
+it. The full list is
+[here](https://crates.io/crates/typenum/reverse_dependencies). Of note are
+[dimensioned](https://crates.io/crates/dimensioned/) which does compile-time
+type checking for arbitrary unit systems and
+[generic-array](https://crates.io/crates/generic-array/) which provides arrays
+whose length you can generically refer to.
+
+### Error messages
+
+
+Typenum's error messages aren't great, and can be difficult to parse. The good
+news is that the fine folks at Auxon have written a tool to help with it. Please
+take a look at [tnfilt](https://github.com/auxoncorp/tnfilt).
+
+### License
+
+Licensed under either of
+
+ * Apache License, Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or
+   http://www.apache.org/licenses/LICENSE-2.0)
+ * MIT license
+   ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
+
+at your option.
+
+### Contribution
+
+Unless you explicitly state otherwise, any contribution intentionally submitted
+for inclusion in the work by you, as defined in the Apache-2.0 license, shall be
+dual licensed as above, without any additional terms or conditions.

vendor/typenum/build.rs

@@ -0,0 +1,417 @@
+use std::{cmp, env, fmt, fs::File, io::Write, path::PathBuf};
+
+enum UIntCode {
+    Term,
+    Zero(Box<UIntCode>),
+    One(Box<UIntCode>),
+}
+
+enum IntCode {
+    Zero,
+    Pos(Box<UIntCode>),
+    Neg(Box<UIntCode>),
+}
+
+impl fmt::Display for UIntCode {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match *self {
+            UIntCode::Term => write!(f, "UTerm"),
+            UIntCode::Zero(ref inner) => write!(f, "UInt<{}, B0>", inner),
+            UIntCode::One(ref inner) => write!(f, "UInt<{}, B1>", inner),
+        }
+    }
+}
+
+impl fmt::Display for IntCode {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match *self {
+            IntCode::Zero => write!(f, "Z0"),
+            IntCode::Pos(ref inner) => write!(f, "PInt<{}>", inner),
+            IntCode::Neg(ref inner) => write!(f, "NInt<{}>", inner),
+        }
+    }
+}
+
+fn gen_uint(u: u64) -> UIntCode {
+    let mut result = UIntCode::Term;
+    let mut x = 1u64 << 63;
+    while x > u {
+        x >>= 1
+    }
+    while x > 0 {
+        result = if x & u > 0 {
+            UIntCode::One(Box::new(result))
+        } else {
+            UIntCode::Zero(Box::new(result))
+        };
+        x >>= 1;
+    }
+    result
+}
+
+fn gen_int(i: i64) -> IntCode {
+    use std::cmp::Ordering::{Equal, Greater, Less};
+
+    match i.cmp(&0) {
+        Greater => IntCode::Pos(Box::new(gen_uint(i as u64))),
+        Less => IntCode::Neg(Box::new(gen_uint(i.abs() as u64))),
+        Equal => IntCode::Zero,
+    }
+}
+
+/// Computes the greatest common divisor of two integers.
+fn gcdi(mut a: i64, mut b: i64) -> i64 {
+    a = a.abs();
+    b = b.abs();
+
+    while a != 0 {
+        let tmp = b % a;
+        b = a;
+        a = tmp;
+    }
+
+    b
+}
+
+fn gcdu(mut a: u64, mut b: u64) -> u64 {
+    while a != 0 {
+        let tmp = b % a;
+        b = a;
+        a = tmp;
+    }
+
+    b
+}
+
+fn sign(i: i64) -> char {
+    use std::cmp::Ordering::*;
+    match i.cmp(&0) {
+        Greater => 'P',
+        Less => 'N',
+        Equal => '_',
+    }
+}
+
+struct UIntTest {
+    a: u64,
+    op: &'static str,
+    b: Option<u64>,
+    r: u64,
+}
+
+impl fmt::Display for UIntTest {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match self.b {
+            Some(b) => write!(
+                f,
+                "
+#[test]
+#[allow(non_snake_case)]
+fn test_{a}_{op}_{b}() {{
+    type A = {gen_a};
+    type B = {gen_b};
+    type U{r} = {result};
+
+    #[allow(non_camel_case_types)]
+    type U{a}{op}U{b} = <<A as {op}<B>>::Output as Same<U{r}>>::Output;
+
+    assert_eq!(<U{a}{op}U{b} as Unsigned>::to_u64(), <U{r} as Unsigned>::to_u64());
+}}",
+                gen_a = gen_uint(self.a),
+                gen_b = gen_uint(b),
+                r = self.r,
+                result = gen_uint(self.r),
+                a = self.a,
+                b = b,
+                op = self.op
+            ),
+            None => write!(
+                f,
+                "
+#[test]
+#[allow(non_snake_case)]
+fn test_{a}_{op}() {{
+    type A = {gen_a};
+    type U{r} = {result};
+
+    #[allow(non_camel_case_types)]
+    type {op}U{a} = <<A as {op}>::Output as Same<U{r}>>::Output;
+    assert_eq!(<{op}U{a} as Unsigned>::to_u64(), <U{r} as Unsigned>::to_u64());
+}}",
+                gen_a = gen_uint(self.a),
+                r = self.r,
+                result = gen_uint(self.r),
+                a = self.a,
+                op = self.op
+            ),
+        }
+    }
+}
+
+fn uint_binary_test(left: u64, operator: &'static str, right: u64, result: u64) -> UIntTest {
+    UIntTest {
+        a: left,
+        op: operator,
+        b: Option::Some(right),
+        r: result,
+    }
+}
+
+struct IntBinaryTest {
+    a: i64,
+    op: &'static str,
+    b: i64,
+    r: i64,
+}
+
+impl fmt::Display for IntBinaryTest {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(
+            f,
+            "
+#[test]
+#[allow(non_snake_case)]
+fn test_{sa}{a}_{op}_{sb}{b}() {{
+    type A = {gen_a};
+    type B = {gen_b};
+    type {sr}{r} = {result};
+
+    #[allow(non_camel_case_types)]
+    type {sa}{a}{op}{sb}{b} = <<A as {op}<B>>::Output as Same<{sr}{r}>>::Output;
+
+    assert_eq!(<{sa}{a}{op}{sb}{b} as Integer>::to_i64(), <{sr}{r} as Integer>::to_i64());
+}}",
+            gen_a = gen_int(self.a),
+            gen_b = gen_int(self.b),
+            r = self.r.abs(),
+            sr = sign(self.r),
+            result = gen_int(self.r),
+            a = self.a.abs(),
+            b = self.b.abs(),
+            sa = sign(self.a),
+            sb = sign(self.b),
+            op = self.op
+        )
+    }
+}
+
+fn int_binary_test(left: i64, operator: &'static str, right: i64, result: i64) -> IntBinaryTest {
+    IntBinaryTest {
+        a: left,
+        op: operator,
+        b: right,
+        r: result,
+    }
+}
+
+struct IntUnaryTest {
+    op: &'static str,
+    a: i64,
+    r: i64,
+}
+
+impl fmt::Display for IntUnaryTest {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(
+            f,
+            "
+#[test]
+#[allow(non_snake_case)]
+fn test_{sa}{a}_{op}() {{
+    type A = {gen_a};
+    type {sr}{r} = {result};
+
+    #[allow(non_camel_case_types)]
+    type {op}{sa}{a} = <<A as {op}>::Output as Same<{sr}{r}>>::Output;
+    assert_eq!(<{op}{sa}{a} as Integer>::to_i64(), <{sr}{r} as Integer>::to_i64());
+}}",
+            gen_a = gen_int(self.a),
+            r = self.r.abs(),
+            sr = sign(self.r),
+            result = gen_int(self.r),
+            a = self.a.abs(),
+            sa = sign(self.a),
+            op = self.op
+        )
+    }
+}
+
+fn int_unary_test(operator: &'static str, num: i64, result: i64) -> IntUnaryTest {
+    IntUnaryTest {
+        op: operator,
+        a: num,
+        r: result,
+    }
+}
+
+fn uint_cmp_test(a: u64, b: u64) -> String {
+    format!(
+        "
+#[test]
+#[allow(non_snake_case)]
+fn test_{a}_Cmp_{b}() {{
+    type A = {gen_a};
+    type B = {gen_b};
+
+    #[allow(non_camel_case_types)]
+    type U{a}CmpU{b} = <A as Cmp<B>>::Output;
+    assert_eq!(<U{a}CmpU{b} as Ord>::to_ordering(), Ordering::{result:?});
+}}",
+        a = a,
+        b = b,
+        gen_a = gen_uint(a),
+        gen_b = gen_uint(b),
+        result = a.cmp(&b)
+    )
+}
+
+fn int_cmp_test(a: i64, b: i64) -> String {
+    format!(
+        "
+#[test]
+#[allow(non_snake_case)]
+fn test_{sa}{a}_Cmp_{sb}{b}() {{
+    type A = {gen_a};
+    type B = {gen_b};
+
+    #[allow(non_camel_case_types)]
+    type {sa}{a}Cmp{sb}{b} = <A as Cmp<B>>::Output;
+    assert_eq!(<{sa}{a}Cmp{sb}{b} as Ord>::to_ordering(), Ordering::{result:?});
+}}",
+        a = a.abs(),
+        b = b.abs(),
+        sa = sign(a),
+        sb = sign(b),
+        gen_a = gen_int(a),
+        gen_b = gen_int(b),
+        result = a.cmp(&b)
+    )
+}
+pub fn gen_tests() -> String {
+    // will test all permutations of number pairs up to this (and down to its opposite for ints)
+    let high: i64 = 5;
+
+    let uints = (0u64..high as u64 + 1).flat_map(|a| (a..a + 1).cycle().zip(0..high as u64 + 1));
+    let ints = (-high..high + 1).flat_map(|a| (a..a + 1).cycle().zip(-high..high + 1));
+
+    let mut result = String::new();
+
+    result.push_str(
+        "
+use typenum::*;
+use core::ops::*;
+use core::cmp::Ordering;
+",
+    );
+    // uint operators:
+    for (a, b) in uints {
+        let mut tests = vec![
+            uint_binary_test(a, "BitAnd", b, a & b),
+            uint_binary_test(a, "BitOr", b, a | b),
+            uint_binary_test(a, "BitXor", b, a ^ b),
+            uint_binary_test(a, "Shl", b, a << b),
+            uint_binary_test(a, "Shr", b, a >> b),
+            uint_binary_test(a, "Add", b, a + b),
+            uint_binary_test(a, "Mul", b, a * b),
+            uint_binary_test(a, "Pow", b, a.pow(b as u32)),
+            uint_binary_test(a, "Min", b, cmp::min(a, b)),
+            uint_binary_test(a, "Max", b, cmp::max(a, b)),
+            uint_binary_test(a, "Gcd", b, gcdu(a, b)),
+        ];
+        if a >= b {
+            tests.push(uint_binary_test(a, "Sub", b, a - b));
+        }
+        if b != 0 {
+            tests.push(uint_binary_test(a, "Div", b, a / b));
+            tests.push(uint_binary_test(a, "Rem", b, a % b));
+            if a % b == 0 {
+                tests.push(uint_binary_test(a, "PartialDiv", b, a / b));
+            }
+        }
+
+        for test in tests {
+            result.push_str(&test.to_string());
+        }
+        result.push_str(&uint_cmp_test(a, b));
+    }
+
+    // int operators:
+    for (a, b) in ints {
+        let mut tests = vec![
+            int_binary_test(a, "Add", b, a + b),
+            int_binary_test(a, "Sub", b, a - b),
+            int_binary_test(a, "Mul", b, a * b),
+            int_binary_test(a, "Min", b, cmp::min(a, b)),
+            int_binary_test(a, "Max", b, cmp::max(a, b)),
+            int_binary_test(a, "Gcd", b, gcdi(a, b)),
+        ];
+        if b != 0 {
+            tests.push(int_binary_test(a, "Div", b, a / b));
+            tests.push(int_binary_test(a, "Rem", b, a % b));
+            if a % b == 0 {
+                tests.push(int_binary_test(a, "PartialDiv", b, a / b));
+            }
+        }
+        if b >= 0 || a.abs() == 1 {
+            let result = if b < 0 {
+                if a == 1 {
+                    a
+                } else if a == -1 {
+                    a.pow((-b) as u32)
+                } else {
+                    unreachable!()
+                }
+            } else {
+                a.pow(b as u32)
+            };
+            tests.push(int_binary_test(a, "Pow", b, result));
+        }
+        for test in tests {
+            result.push_str(&test.to_string());
+        }
+        result.push_str(&int_cmp_test(a, b));
+    }
+
+    // int unary operators:
+    for n in -high..high + 1 {
+        let tests = vec![
+            int_unary_test("Neg", n, -n),
+            int_unary_test("Abs", n, n.abs()),
+        ];
+        for test in tests {
+            result.push_str(&test.to_string());
+        }
+    }
+
+    result
+}
+
+#[cfg_attr(
+    feature = "no_std",
+    deprecated(
+        since = "1.3.0",
+        note = "the `no_std` flag is no longer necessary and will be removed in the future"
+    )
+)]
+pub fn no_std() {}
+
+#[cfg_attr(
+    feature = "force_unix_path_separator",
+    deprecated(
+        since = "1.17.0",
+        note = "the `force_unix_path_separator` flag is no longer necessary and will be removed in the future"
+    )
+)]
+pub fn force_unix_path_separator() {}
+
+fn main() {
+    no_std();
+    force_unix_path_separator();
+    println!("cargo:rerun-if-changed=tests");
+
+    let tests = gen_tests();
+    let out_dir = env::var("OUT_DIR").unwrap();
+    let dest = PathBuf::from(out_dir).join("tests.rs");
+    let mut f = File::create(&dest).unwrap();
+    f.write_all(tests.as_bytes()).unwrap();
+}

vendor/typenum/clippy.toml

@@ -0,0 +1 @@
+cognitive-complexity-threshold=35

vendor/typenum/flake.lock

@@ -0,0 +1,95 @@
+{
+  "nodes": {
+    "flake-utils": {
+      "inputs": {
+        "systems": "systems"
+      },
+      "locked": {
+        "lastModified": 1731533236,
+        "narHash": "sha256-l0KFg5HjrsfsO/JpG+r7fRrqm12kzFHyUHqHCVpMMbI=",
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "rev": "11707dc2f618dd54ca8739b309ec4fc024de578b",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1739736696,
+        "narHash": "sha256-zON2GNBkzsIyALlOCFiEBcIjI4w38GYOb+P+R4S8Jsw=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "d74a2335ac9c133d6bbec9fc98d91a77f1604c1f",
+        "type": "github"
+      },
+      "original": {
+        "id": "nixpkgs",
+        "ref": "nixos-unstable",
+        "type": "indirect"
+      }
+    },
+    "nixpkgs_2": {
+      "locked": {
+        "lastModified": 1736320768,
+        "narHash": "sha256-nIYdTAiKIGnFNugbomgBJR+Xv5F1ZQU+HfaBqJKroC0=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "4bc9c909d9ac828a039f288cf872d16d38185db8",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixpkgs-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "flake-utils": "flake-utils",
+        "nixpkgs": "nixpkgs",
+        "rust-overlay": "rust-overlay"
+      }
+    },
+    "rust-overlay": {
+      "inputs": {
+        "nixpkgs": "nixpkgs_2"
+      },
+      "locked": {
+        "lastModified": 1739759407,
+        "narHash": "sha256-YIrVxD2SaUyaEdMry2nAd2qG1E0V38QIV6t6rpguFwk=",
+        "owner": "oxalica",
+        "repo": "rust-overlay",
+        "rev": "6e6ae2acf4221380140c22d65b6c41f4726f5932",
+        "type": "github"
+      },
+      "original": {
+        "owner": "oxalica",
+        "repo": "rust-overlay",
+        "type": "github"
+      }
+    },
+    "systems": {
+      "locked": {
+        "lastModified": 1681028828,
+        "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
+        "owner": "nix-systems",
+        "repo": "default",
+        "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nix-systems",
+        "repo": "default",
+        "type": "github"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

vendor/typenum/flake.nix

@@ -0,0 +1,42 @@
+{
+  inputs = {
+    nixpkgs.url = "nixpkgs/nixos-unstable";
+    flake-utils.url = "github:numtide/flake-utils";
+    rust-overlay.url = "github:oxalica/rust-overlay";
+  };
+
+  outputs =
+    {
+      nixpkgs,
+      flake-utils,
+      rust-overlay,
+      ...
+    }:
+    flake-utils.lib.eachDefaultSystem (
+      system:
+      let
+        overlays = [
+          (import rust-overlay)
+        ];
+        pkgs = import nixpkgs {
+          inherit system overlays;
+        };
+
+        rust = pkgs.rust-bin.stable.latest.default.override {
+          extensions = [
+            "rust-analyzer"
+            "rust-src"
+          ];
+        };
+      in
+      {
+        devShells.default = pkgs.mkShell {
+          packages = [
+            pkgs.just
+            rust
+          ];
+        };
+
+      }
+    );
+}

vendor/typenum/justfile

@@ -0,0 +1,34 @@
+# Generate code and run lints and tests
+test-local: gen lint test
+    @just test --features const-generics
+
+# Produce generated code
+gen:
+    cargo run --package generate
+    cargo fmt
+
+# Update lockfiles
+up:
+    nix flake update
+    cargo update
+
+# Run all lints
+lint: fmt-check clippy clippy-all
+
+# Check formatting
+fmt-check:
+    cargo fmt --all -- --check
+
+# Clippy
+clippy:
+    cargo clippy -- -D warnings
+
+# Clippy with all features
+clippy-all:
+    # Allow deprecated because we test the no_std feature.
+    cargo clippy --all-features -- -D warnings -A deprecated
+
+# Run test
+test *args:
+    cargo test --verbose --features "strict" {{args}}
+    cargo doc --features "strict" {{args}}

vendor/typenum/src/array.rs

@@ -0,0 +1,396 @@
+//! A type-level array of type-level numbers.
+//!
+//! It is not very featureful right now, and should be considered a work in progress.
+
+use core::ops::{Add, Div, Mul, Sub};
+
+use super::*;
+
+/// The terminating type for type arrays.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct ATerm;
+
+impl TypeArray for ATerm {}
+
+/// `TArr` is a type that acts as an array of types. It is defined similarly to `UInt`, only its
+/// values can be more than bits, and it is designed to act as an array. So you can only add two if
+/// they have the same number of elements, for example.
+///
+/// This array is only really designed to contain `Integer` types. If you use it with others, you
+/// may find it lacking functionality.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct TArr<V, A> {
+    first: V,
+    rest: A,
+}
+
+impl<V, A> TypeArray for TArr<V, A> {}
+
+/// Create a new type-level array. Only usable on Rust 1.13.0 or newer.
+///
+/// There's not a whole lot you can do with it right now.
+///
+/// # Example
+/// ```rust
+/// #[macro_use]
+/// extern crate typenum;
+/// use typenum::consts::*;
+///
+/// type Array = tarr![P3, N4, Z0, P38];
+/// # fn main() { let _: Array; }
+#[macro_export]
+macro_rules! tarr {
+    () => ( $crate::ATerm );
+    ($n:ty) => ( $crate::TArr<$n, $crate::ATerm> );
+    ($n:ty,) => ( $crate::TArr<$n, $crate::ATerm> );
+    ($n:ty, $($tail:ty),+) => ( $crate::TArr<$n, tarr![$($tail),+]> );
+    ($n:ty, $($tail:ty),+,) => ( $crate::TArr<$n, tarr![$($tail),+]> );
+    ($n:ty | $rest:ty) => ( $crate::TArr<$n, $rest> );
+    ($n:ty, $($tail:ty),+ | $rest:ty) => ( $crate::TArr<$n, ta![$($tail),+ | $rest]> );
+}
+
+// ---------------------------------------------------------------------------------------
+// Length
+
+/// Length of `ATerm` by itself is 0
+impl Len for ATerm {
+    type Output = U0;
+    #[inline]
+    fn len(&self) -> Self::Output {
+        UTerm
+    }
+}
+
+/// Size of a `TypeArray`
+impl<V, A> Len for TArr<V, A>
+where
+    A: Len,
+    Length<A>: Add<B1>,
+    Sum<Length<A>, B1>: Unsigned,
+{
+    type Output = Add1<Length<A>>;
+    #[inline]
+    fn len(&self) -> Self::Output {
+        self.rest.len() + B1
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// FoldAdd
+
+/// Hide our `Null` type
+const _: () = {
+    /// A type which contributes nothing when adding (i.e. a zero)
+    pub struct Null;
+    impl<T> Add<T> for Null {
+        type Output = T;
+        fn add(self, rhs: T) -> Self::Output {
+            rhs
+        }
+    }
+
+    impl FoldAdd for ATerm {
+        type Output = Null;
+    }
+};
+
+impl<V, A> FoldAdd for TArr<V, A>
+where
+    A: FoldAdd,
+    FoldSum<A>: Add<V>,
+{
+    type Output = Sum<FoldSum<A>, V>;
+}
+
+// ---------------------------------------------------------------------------------------
+// FoldMul
+
+/// Hide our `Null` type
+const _: () = {
+    /// A type which contributes nothing when multiplying (i.e. a one)
+    pub struct Null;
+    impl<T> Mul<T> for Null {
+        type Output = T;
+        fn mul(self, rhs: T) -> Self::Output {
+            rhs
+        }
+    }
+
+    impl FoldMul for ATerm {
+        type Output = Null;
+    }
+};
+
+impl<V, A> FoldMul for TArr<V, A>
+where
+    A: FoldMul,
+    FoldProd<A>: Mul<V>,
+{
+    type Output = Prod<FoldProd<A>, V>;
+}
+
+// ---------------------------------------------------------------------------------------
+// Add arrays
+// Note that two arrays are only addable if they are the same length.
+
+impl Add<ATerm> for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn add(self, _: ATerm) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<Al, Vl, Ar, Vr> Add<TArr<Vr, Ar>> for TArr<Vl, Al>
+where
+    Al: Add<Ar>,
+    Vl: Add<Vr>,
+{
+    type Output = TArr<Sum<Vl, Vr>, Sum<Al, Ar>>;
+    #[inline]
+    fn add(self, rhs: TArr<Vr, Ar>) -> Self::Output {
+        TArr {
+            first: self.first + rhs.first,
+            rest: self.rest + rhs.rest,
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// Subtract arrays
+// Note that two arrays are only subtractable if they are the same length.
+
+impl Sub<ATerm> for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn sub(self, _: ATerm) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<Vl, Al, Vr, Ar> Sub<TArr<Vr, Ar>> for TArr<Vl, Al>
+where
+    Vl: Sub<Vr>,
+    Al: Sub<Ar>,
+{
+    type Output = TArr<Diff<Vl, Vr>, Diff<Al, Ar>>;
+    #[inline]
+    fn sub(self, rhs: TArr<Vr, Ar>) -> Self::Output {
+        TArr {
+            first: self.first - rhs.first,
+            rest: self.rest - rhs.rest,
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// Multiply an array by a scalar
+
+impl<Rhs> Mul<Rhs> for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn mul(self, _: Rhs) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<V, A, Rhs> Mul<Rhs> for TArr<V, A>
+where
+    V: Mul<Rhs>,
+    A: Mul<Rhs>,
+    Rhs: Copy,
+{
+    type Output = TArr<Prod<V, Rhs>, Prod<A, Rhs>>;
+    #[inline]
+    fn mul(self, rhs: Rhs) -> Self::Output {
+        TArr {
+            first: self.first * rhs,
+            rest: self.rest * rhs,
+        }
+    }
+}
+
+impl Mul<ATerm> for Z0 {
+    type Output = ATerm;
+    #[inline]
+    fn mul(self, _: ATerm) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<U> Mul<ATerm> for PInt<U>
+where
+    U: Unsigned + NonZero,
+{
+    type Output = ATerm;
+    #[inline]
+    fn mul(self, _: ATerm) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<U> Mul<ATerm> for NInt<U>
+where
+    U: Unsigned + NonZero,
+{
+    type Output = ATerm;
+    #[inline]
+    fn mul(self, _: ATerm) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<V, A> Mul<TArr<V, A>> for Z0
+where
+    Z0: Mul<A>,
+{
+    type Output = TArr<Z0, Prod<Z0, A>>;
+    #[inline]
+    fn mul(self, rhs: TArr<V, A>) -> Self::Output {
+        TArr {
+            first: Z0,
+            rest: self * rhs.rest,
+        }
+    }
+}
+
+impl<V, A, U> Mul<TArr<V, A>> for PInt<U>
+where
+    U: Unsigned + NonZero,
+    PInt<U>: Mul<A> + Mul<V>,
+{
+    type Output = TArr<Prod<PInt<U>, V>, Prod<PInt<U>, A>>;
+    #[inline]
+    fn mul(self, rhs: TArr<V, A>) -> Self::Output {
+        TArr {
+            first: self * rhs.first,
+            rest: self * rhs.rest,
+        }
+    }
+}
+
+impl<V, A, U> Mul<TArr<V, A>> for NInt<U>
+where
+    U: Unsigned + NonZero,
+    NInt<U>: Mul<A> + Mul<V>,
+{
+    type Output = TArr<Prod<NInt<U>, V>, Prod<NInt<U>, A>>;
+    #[inline]
+    fn mul(self, rhs: TArr<V, A>) -> Self::Output {
+        TArr {
+            first: self * rhs.first,
+            rest: self * rhs.rest,
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// Divide an array by a scalar
+
+impl<Rhs> Div<Rhs> for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn div(self, _: Rhs) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<V, A, Rhs> Div<Rhs> for TArr<V, A>
+where
+    V: Div<Rhs>,
+    A: Div<Rhs>,
+    Rhs: Copy,
+{
+    type Output = TArr<Quot<V, Rhs>, Quot<A, Rhs>>;
+    #[inline]
+    fn div(self, rhs: Rhs) -> Self::Output {
+        TArr {
+            first: self.first / rhs,
+            rest: self.rest / rhs,
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// Partial Divide an array by a scalar
+
+impl<Rhs> PartialDiv<Rhs> for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn partial_div(self, _: Rhs) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<V, A, Rhs> PartialDiv<Rhs> for TArr<V, A>
+where
+    V: PartialDiv<Rhs>,
+    A: PartialDiv<Rhs>,
+    Rhs: Copy,
+{
+    type Output = TArr<PartialQuot<V, Rhs>, PartialQuot<A, Rhs>>;
+    #[inline]
+    fn partial_div(self, rhs: Rhs) -> Self::Output {
+        TArr {
+            first: self.first.partial_div(rhs),
+            rest: self.rest.partial_div(rhs),
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// Modulo an array by a scalar
+use core::ops::Rem;
+
+impl<Rhs> Rem<Rhs> for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn rem(self, _: Rhs) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<V, A, Rhs> Rem<Rhs> for TArr<V, A>
+where
+    V: Rem<Rhs>,
+    A: Rem<Rhs>,
+    Rhs: Copy,
+{
+    type Output = TArr<Mod<V, Rhs>, Mod<A, Rhs>>;
+    #[inline]
+    fn rem(self, rhs: Rhs) -> Self::Output {
+        TArr {
+            first: self.first % rhs,
+            rest: self.rest % rhs,
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------------------
+// Negate an array
+use core::ops::Neg;
+
+impl Neg for ATerm {
+    type Output = ATerm;
+    #[inline]
+    fn neg(self) -> Self::Output {
+        ATerm
+    }
+}
+
+impl<V, A> Neg for TArr<V, A>
+where
+    V: Neg,
+    A: Neg,
+{
+    type Output = TArr<Negate<V>, Negate<A>>;
+    #[inline]
+    fn neg(self) -> Self::Output {
+        TArr {
+            first: -self.first,
+            rest: -self.rest,
+        }
+    }
+}

vendor/typenum/src/bit.rs

@@ -0,0 +1,347 @@
+//! Type-level bits.
+//!
+//! These are rather simple and are used as the building blocks of the
+//! other number types in this crate.
+//!
+//!
+//! **Type operators** implemented:
+//!
+//! - From `core::ops`: `BitAnd`, `BitOr`, `BitXor`, and `Not`.
+//! - From `typenum`: `Same` and `Cmp`.
+
+use crate::{private::InternalMarker, Cmp, Equal, Greater, Less, NonZero, PowerOfTwo, Zero};
+use core::ops::{BitAnd, BitOr, BitXor, Not};
+
+pub use crate::marker_traits::Bit;
+
+/// The type-level bit 0.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct B0;
+
+impl B0 {
+    /// Instantiates a singleton representing this bit.
+    #[inline]
+    pub fn new() -> B0 {
+        B0
+    }
+}
+
+/// The type-level bit 1.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct B1;
+
+impl B1 {
+    /// Instantiates a singleton representing this bit.
+    #[inline]
+    pub fn new() -> B1 {
+        B1
+    }
+}
+
+impl Bit for B0 {
+    const U8: u8 = 0;
+    const BOOL: bool = false;
+
+    #[inline]
+    fn new() -> Self {
+        Self
+    }
+    #[inline]
+    fn to_u8() -> u8 {
+        0
+    }
+    #[inline]
+    fn to_bool() -> bool {
+        false
+    }
+}
+
+impl Bit for B1 {
+    const U8: u8 = 1;
+    const BOOL: bool = true;
+
+    #[inline]
+    fn new() -> Self {
+        Self
+    }
+    #[inline]
+    fn to_u8() -> u8 {
+        1
+    }
+    #[inline]
+    fn to_bool() -> bool {
+        true
+    }
+}
+
+impl Zero for B0 {}
+impl NonZero for B1 {}
+impl PowerOfTwo for B1 {}
+
+/// Not of 0 (!0 = 1)
+impl Not for B0 {
+    type Output = B1;
+    #[inline]
+    fn not(self) -> Self::Output {
+        B1
+    }
+}
+/// Not of 1 (!1 = 0)
+impl Not for B1 {
+    type Output = B0;
+    #[inline]
+    fn not(self) -> Self::Output {
+        B0
+    }
+}
+
+/// And with 0 ( 0 & B = 0)
+impl<Rhs: Bit> BitAnd<Rhs> for B0 {
+    type Output = B0;
+    #[inline]
+    fn bitand(self, _: Rhs) -> Self::Output {
+        B0
+    }
+}
+
+/// And with 1 ( 1 & 0 = 0)
+impl BitAnd<B0> for B1 {
+    type Output = B0;
+    #[inline]
+    fn bitand(self, _: B0) -> Self::Output {
+        B0
+    }
+}
+
+/// And with 1 ( 1 & 1 = 1)
+impl BitAnd<B1> for B1 {
+    type Output = B1;
+    #[inline]
+    fn bitand(self, _: B1) -> Self::Output {
+        B1
+    }
+}
+
+/// Or with 0 ( 0 | 0 = 0)
+impl BitOr<B0> for B0 {
+    type Output = B0;
+    #[inline]
+    fn bitor(self, _: B0) -> Self::Output {
+        B0
+    }
+}
+
+/// Or with 0 ( 0 | 1 = 1)
+impl BitOr<B1> for B0 {
+    type Output = B1;
+    #[inline]
+    fn bitor(self, _: B1) -> Self::Output {
+        B1
+    }
+}
+
+/// Or with 1 ( 1 | B = 1)
+impl<Rhs: Bit> BitOr<Rhs> for B1 {
+    type Output = B1;
+    #[inline]
+    fn bitor(self, _: Rhs) -> Self::Output {
+        B1
+    }
+}
+
+/// Xor between 0 and 0 ( 0 ^ 0 = 0)
+impl BitXor<B0> for B0 {
+    type Output = B0;
+    #[inline]
+    fn bitxor(self, _: B0) -> Self::Output {
+        B0
+    }
+}
+/// Xor between 1 and 0 ( 1 ^ 0 = 1)
+impl BitXor<B0> for B1 {
+    type Output = B1;
+    #[inline]
+    fn bitxor(self, _: B0) -> Self::Output {
+        B1
+    }
+}
+/// Xor between 0 and 1 ( 0 ^ 1 = 1)
+impl BitXor<B1> for B0 {
+    type Output = B1;
+    #[inline]
+    fn bitxor(self, _: B1) -> Self::Output {
+        B1
+    }
+}
+/// Xor between 1 and 1 ( 1 ^ 1 = 0)
+impl BitXor<B1> for B1 {
+    type Output = B0;
+    #[inline]
+    fn bitxor(self, _: B1) -> Self::Output {
+        B0
+    }
+}
+
+#[cfg(test)]
+mod bit_op_tests {
+    use core::ops::{BitAnd, BitOr, BitXor, Not};
+
+    use crate::{B0, B1};
+
+    // macro for testing operation results. Uses `Same` to ensure the types are equal and
+    // not just the values they evaluate to.
+    macro_rules! test_bit_op {
+        ($op:ident $Lhs:ident = $Answer:ident) => {{
+            type Test = <<$Lhs as $op>::Output as $crate::Same<$Answer>>::Output;
+            assert_eq!(
+                <$Answer as $crate::Bit>::to_u8(),
+                <Test as $crate::Bit>::to_u8()
+            );
+        }};
+        ($Lhs:ident $op:ident $Rhs:ident = $Answer:ident) => {{
+            type Test = <<$Lhs as $op<$Rhs>>::Output as $crate::Same<$Answer>>::Output;
+            assert_eq!(
+                <$Answer as $crate::Bit>::to_u8(),
+                <Test as $crate::Bit>::to_u8()
+            );
+        }};
+    }
+
+    #[test]
+    fn bit_operations() {
+        test_bit_op!(Not B0 = B1);
+        test_bit_op!(Not B1 = B0);
+
+        test_bit_op!(B0 BitAnd B0 = B0);
+        test_bit_op!(B0 BitAnd B1 = B0);
+        test_bit_op!(B1 BitAnd B0 = B0);
+        test_bit_op!(B1 BitAnd B1 = B1);
+
+        test_bit_op!(B0 BitOr B0 = B0);
+        test_bit_op!(B0 BitOr B1 = B1);
+        test_bit_op!(B1 BitOr B0 = B1);
+        test_bit_op!(B1 BitOr B1 = B1);
+
+        test_bit_op!(B0 BitXor B0 = B0);
+        test_bit_op!(B0 BitXor B1 = B1);
+        test_bit_op!(B1 BitXor B0 = B1);
+        test_bit_op!(B1 BitXor B1 = B0);
+    }
+}
+
+impl Cmp<B0> for B0 {
+    type Output = Equal;
+
+    #[inline]
+    fn compare<P: InternalMarker>(&self, _: &B0) -> Self::Output {
+        Equal
+    }
+}
+
+impl Cmp<B1> for B0 {
+    type Output = Less;
+
+    #[inline]
+    fn compare<P: InternalMarker>(&self, _: &B1) -> Self::Output {
+        Less
+    }
+}
+
+impl Cmp<B0> for B1 {
+    type Output = Greater;
+
+    #[inline]
+    fn compare<P: InternalMarker>(&self, _: &B0) -> Self::Output {
+        Greater
+    }
+}
+
+impl Cmp<B1> for B1 {
+    type Output = Equal;
+
+    #[inline]
+    fn compare<P: InternalMarker>(&self, _: &B1) -> Self::Output {
+        Equal
+    }
+}
+
+use crate::Min;
+impl Min<B0> for B0 {
+    type Output = B0;
+    #[inline]
+    fn min(self, _: B0) -> B0 {
+        self
+    }
+}
+impl Min<B1> for B0 {
+    type Output = B0;
+    #[inline]
+    fn min(self, _: B1) -> B0 {
+        self
+    }
+}
+impl Min<B0> for B1 {
+    type Output = B0;
+    #[inline]
+    fn min(self, rhs: B0) -> B0 {
+        rhs
+    }
+}
+impl Min<B1> for B1 {
+    type Output = B1;
+    #[inline]
+    fn min(self, _: B1) -> B1 {
+        self
+    }
+}
+
+use crate::Max;
+impl Max<B0> for B0 {
+    type Output = B0;
+    #[inline]
+    fn max(self, _: B0) -> B0 {
+        self
+    }
+}
+impl Max<B1> for B0 {
+    type Output = B1;
+    #[inline]
+    fn max(self, rhs: B1) -> B1 {
+        rhs
+    }
+}
+impl Max<B0> for B1 {
+    type Output = B1;
+    #[inline]
+    fn max(self, _: B0) -> B1 {
+        self
+    }
+}
+impl Max<B1> for B1 {
+    type Output = B1;
+    #[inline]
+    fn max(self, _: B1) -> B1 {
+        self
+    }
+}
+
+#[cfg(test)]
+mod bit_creation_tests {
+    #[test]
+    fn bit_creation() {
+        {
+            use crate::{B0, B1};
+            let _: B0 = B0::new();
+            let _: B1 = B1::new();
+        }
+
+        {
+            use crate::{Bit, B0, B1};
+
+            let _: B0 = <B0 as Bit>::new();
+            let _: B1 = <B1 as Bit>::new();
+        }
+    }
+}

vendor/typenum/src/gen.rs

@@ -0,0 +1,4 @@
+pub mod consts;
+#[cfg(feature = "const-generics")]
+pub mod generic_const_mappings;
+pub mod op;

vendor/typenum/src/lib.rs

@@ -0,0 +1,175 @@
+//! This crate provides type-level numbers evaluated at compile time. It depends only on libcore.
+//!
+//! The traits defined or used in this crate are used in a typical manner. They can be divided into
+//! two categories: **marker traits** and **type operators**.
+//!
+//! Many of the marker traits have functions defined, but they all do essentially the same thing:
+//! convert a type into its runtime counterpart, and are really just there for debugging. For
+//! example,
+//!
+//! ```rust
+//! use typenum::{Integer, N4};
+//!
+//! assert_eq!(N4::to_i32(), -4);
+//! ```
+//!
+//! **Type operators** are traits that behave as functions at the type level. These are the meat of
+//! this library. Where possible, traits defined in libcore have been used, but their attached
+//! functions have not been implemented.
+//!
+//! For example, the `Add` trait is implemented for both unsigned and signed integers, but the
+//! `add` function is not. As there are never any objects of the types defined here, it wouldn't
+//! make sense to implement it. What is important is its associated type `Output`, which is where
+//! the addition happens.
+//!
+//! ```rust
+//! use std::ops::Add;
+//! use typenum::{Integer, P3, P4};
+//!
+//! type X = <P3 as Add<P4>>::Output;
+//! assert_eq!(<X as Integer>::to_i32(), 7);
+//! ```
+//!
+//! In addition, helper aliases are defined for type operators. For example, the above snippet
+//! could be replaced with
+//!
+//! ```rust
+//! use typenum::{Integer, Sum, P3, P4};
+//!
+//! type X = Sum<P3, P4>;
+//! assert_eq!(<X as Integer>::to_i32(), 7);
+//! ```
+//!
+//! Documented in each module is the full list of type operators implemented.
+
+#![no_std]
+#![forbid(unsafe_code)]
+#![warn(missing_docs)]
+#![cfg_attr(feature = "strict", deny(missing_docs))]
+#![cfg_attr(feature = "strict", deny(warnings))]
+#![doc(html_root_url = "https://docs.rs/typenum/1.18.0")]
+#![cfg_attr(docsrs, feature(doc_auto_cfg, doc_cfg))]
+
+// For debugging macros:
+// #![feature(trace_macros)]
+// trace_macros!(true);
+
+use core::cmp::Ordering;
+
+pub mod bit;
+mod gen;
+pub mod int;
+pub mod marker_traits;
+pub mod operator_aliases;
+pub mod private;
+pub mod type_operators;
+pub mod uint;
+
+pub mod array;
+
+pub use crate::{
+    array::{ATerm, TArr},
+    gen::consts,
+    int::{NInt, PInt},
+    marker_traits::*,
+    operator_aliases::*,
+    type_operators::*,
+    uint::{UInt, UTerm},
+};
+
+#[doc(no_inline)]
+#[rustfmt::skip]
+pub use consts::*;
+
+#[cfg(feature = "const-generics")]
+pub use crate::gen::generic_const_mappings;
+
+#[cfg(feature = "const-generics")]
+#[doc(no_inline)]
+pub use generic_const_mappings::{Const, ToUInt, U};
+
+/// A potential output from `Cmp`, this is the type equivalent to the enum variant
+/// `core::cmp::Ordering::Greater`.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct Greater;
+
+/// A potential output from `Cmp`, this is the type equivalent to the enum variant
+/// `core::cmp::Ordering::Less`.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct Less;
+
+/// A potential output from `Cmp`, this is the type equivalent to the enum variant
+/// `core::cmp::Ordering::Equal`.
+#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
+#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
+pub struct Equal;
+
+/// Returns `core::cmp::Ordering::Greater`
+impl Ord for Greater {
+    #[inline]
+    fn to_ordering() -> Ordering {
+        Ordering::Greater
+    }
+}
+
+/// Returns `core::cmp::Ordering::Less`
+impl Ord for Less {
+    #[inline]
+    fn to_ordering() -> Ordering {
+        Ordering::Less
+    }
+}
+
+/// Returns `core::cmp::Ordering::Equal`
+impl Ord for Equal {
+    #[inline]
+    fn to_ordering() -> Ordering {
+        Ordering::Equal
+    }
+}
+
+/// Asserts that two types are the same.
+#[macro_export]
+macro_rules! assert_type_eq {
+    ($a:ty, $b:ty) => {
+        const _: core::marker::PhantomData<<$a as $crate::Same<$b>>::Output> =
+            core::marker::PhantomData;
+    };
+}
+
+/// Asserts that a type is `True`, aka `B1`.
+#[macro_export]
+macro_rules! assert_type {
+    ($a:ty) => {
+        const _: core::marker::PhantomData<<$a as $crate::Same<True>>::Output> =
+            core::marker::PhantomData;
+    };
+}
+
+mod sealed {
+    use crate::{
+        ATerm, Bit, Equal, Greater, Less, NInt, NonZero, PInt, TArr, UInt, UTerm, Unsigned, B0, B1,
+        Z0,
+    };
+
+    pub trait Sealed {}
+
+    impl Sealed for B0 {}
+    impl Sealed for B1 {}
+
+    impl Sealed for UTerm {}
+    impl<U: Unsigned, B: Bit> Sealed for UInt<U, B> {}
+
+    impl Sealed for Z0 {}
+    impl<U: Unsigned + NonZero> Sealed for PInt<U> {}
+    impl<U: Unsigned + NonZero> Sealed for NInt<U> {}
+
+    impl Sealed for Less {}
+    impl Sealed for Equal {}
+    impl Sealed for Greater {}
+
+    impl Sealed for ATerm {}
+    impl<V, A> Sealed for TArr<V, A> {}
+}

vendor/typenum/src/marker_traits.rs

@@ -0,0 +1,189 @@
+//! All of the **marker traits** used in typenum.
+//!
+//! Note that the definition here for marker traits is slightly different than
+//! the conventional one -- we include traits with functions that convert a type
+//! to the corresponding value, as well as associated constants that do the
+//! same.
+//!
+//! For example, the `Integer` trait includes the function (among others) `fn
+//! to_i32() -> i32` and the associated constant `I32` so that one can do this:
+//!
+//! ```
+//! use typenum::{Integer, N42};
+//!
+//! assert_eq!(-42, N42::to_i32());
+//! assert_eq!(-42, N42::I32);
+//! ```
+
+use crate::sealed::Sealed;
+
+/// A **marker trait** to designate that a type is not zero. All number types in this
+/// crate implement `NonZero` except `B0`, `U0`, and `Z0`.
+pub trait NonZero: Sealed {}
+
+/// A **marker trait** to designate that a type is zero. Only `B0`, `U0`, and `Z0`
+/// implement this trait.
+pub trait Zero: Sealed {}
+
+/// A **Marker trait** for the types `Greater`, `Equal`, and `Less`.
+pub trait Ord: Sealed {
+    #[allow(missing_docs)]
+    fn to_ordering() -> ::core::cmp::Ordering;
+}
+
+/// The **marker trait** for compile time bits.
+pub trait Bit: Sealed + Copy + Default + 'static {
+    #[allow(missing_docs)]
+    const U8: u8;
+    #[allow(missing_docs)]
+    const BOOL: bool;
+
+    /// Instantiates a singleton representing this bit.
+    fn new() -> Self;
+
+    #[allow(missing_docs)]
+    fn to_u8() -> u8;
+    #[allow(missing_docs)]
+    fn to_bool() -> bool;
+}
+
+/// The **marker trait** for compile time unsigned integers.
+///
+/// # Example
+/// ```rust
+/// use typenum::{Unsigned, U3};
+///
+/// assert_eq!(U3::to_u32(), 3);
+/// assert_eq!(U3::I32, 3);
+/// ```
+pub trait Unsigned: Sealed + Copy + Default + 'static {
+    #[allow(missing_docs)]
+    const U8: u8;
+    #[allow(missing_docs)]
+    const U16: u16;
+    #[allow(missing_docs)]
+    const U32: u32;
+    #[allow(missing_docs)]
+    const U64: u64;
+    #[cfg(feature = "i128")]
+    #[allow(missing_docs)]
+    const U128: u128;
+    #[allow(missing_docs)]
+    const USIZE: usize;
+
+    #[allow(missing_docs)]
+    const I8: i8;
+    #[allow(missing_docs)]
+    const I16: i16;
+    #[allow(missing_docs)]
+    const I32: i32;
+    #[allow(missing_docs)]
+    const I64: i64;
+    #[cfg(feature = "i128")]
+    #[allow(missing_docs)]
+    const I128: i128;
+    #[allow(missing_docs)]
+    const ISIZE: isize;
+
+    #[allow(missing_docs)]
+    fn to_u8() -> u8;
+    #[allow(missing_docs)]
+    fn to_u16() -> u16;
+    #[allow(missing_docs)]
+    fn to_u32() -> u32;
+    #[allow(missing_docs)]
+    fn to_u64() -> u64;
+    #[cfg(feature = "i128")]
+    #[allow(missing_docs)]
+    fn to_u128() -> u128;
+    #[allow(missing_docs)]
+    fn to_usize() -> usize;
+
+    #[allow(missing_docs)]
+    fn to_i8() -> i8;
+    #[allow(missing_docs)]
+    fn to_i16() -> i16;
+    #[allow(missing_docs)]
+    fn to_i32() -> i32;
+    #[allow(missing_docs)]
+    fn to_i64() -> i64;
+    #[cfg(feature = "i128")]
+    #[allow(missing_docs)]
+    fn to_i128() -> i128;
+    #[allow(missing_docs)]
+    fn to_isize() -> isize;
+}
+
+/// The **marker trait** for compile time signed integers.
+///
+/// # Example
+/// ```rust
+/// use typenum::{Integer, P3};
+///
+/// assert_eq!(P3::to_i32(), 3);
+/// assert_eq!(P3::I32, 3);
+/// ```
+pub trait Integer: Sealed + Copy + Default + 'static {
+    #[allow(missing_docs)]
+    const I8: i8;
+    #[allow(missing_docs)]
+    const I16: i16;
+    #[allow(missing_docs)]
+    const I32: i32;
+    #[allow(missing_docs)]
+    const I64: i64;
+    #[cfg(feature = "i128")]
+    #[allow(missing_docs)]
+    const I128: i128;
+    #[allow(missing_docs)]
+    const ISIZE: isize;
+
+    #[allow(missing_docs)]
+    fn to_i8() -> i8;
+    #[allow(missing_docs)]
+    fn to_i16() -> i16;
+    #[allow(missing_docs)]
+    fn to_i32() -> i32;
+    #[allow(missing_docs)]
+    fn to_i64() -> i64;
+    #[cfg(feature = "i128")]
+    #[allow(missing_docs)]
+    fn to_i128() -> i128;
+    #[allow(missing_docs)]
+    fn to_isize() -> isize;
+}
+
+/// The **marker trait** for type-level arrays of type-level numbers.
+///
+/// Someday, it may contain an associated constant to produce a runtime array,
+/// like the other marker traits here. However, that is blocked by [this
+/// issue](https://github.com/rust-lang/rust/issues/44168).
+pub trait TypeArray: Sealed {}
+
+/// The **marker trait** for type-level numbers which are a power of two.
+///
+/// # Examples
+///
+/// Here's a working example:
+///
+/// ```rust
+/// use typenum::{PowerOfTwo, P4, P8};
+///
+/// fn only_p2<P: PowerOfTwo>() {}
+///
+/// only_p2::<P4>();
+/// only_p2::<P8>();
+/// ```
+///
+/// Numbers which are not a power of two will fail to compile in this example:
+///
+/// ```rust,compile_fail
+/// use typenum::{P9, P511, P1023, PowerOfTwo};
+///
+/// fn only_p2<P: PowerOfTwo>() { }
+///
+/// only_p2::<P9>();
+/// only_p2::<P511>();
+/// only_p2::<P1023>();
+/// ```
+pub trait PowerOfTwo: Sealed {}

vendor/typenum/src/operator_aliases.rs

@@ -0,0 +1,115 @@
+//! Aliases for the type operators used in this crate.
+
+//! Their purpose is to increase the ergonomics of performing operations on the types defined
+//! here. For even more ergonomics, consider using the `op!` macro instead.
+//!
+//! For example, type `X` and type `Y` are the same here:
+//!
+//! ```rust
+//! # #[macro_use] extern crate typenum;
+//! use std::ops::Mul;
+//! use typenum::{Prod, P5, P7};
+//!
+//! type X = <P7 as Mul<P5>>::Output;
+//! type Y = Prod<P7, P5>;
+//!
+//! assert_type_eq!(X, Y);
+//! ```
+
+// Aliases!!!
+use crate::type_operators::{
+    Abs, Cmp, FoldAdd, FoldMul, Gcd, Len, Logarithm2, Max, Min, PartialDiv, Pow, SquareRoot,
+};
+use core::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub};
+
+/// Alias for the associated type of `BitAnd`: `And<A, B> = <A as BitAnd<B>>::Output`
+pub type And<A, B> = <A as BitAnd<B>>::Output;
+/// Alias for the associated type of `BitOr`: `Or<A, B> = <A as BitOr<B>>::Output`
+pub type Or<A, B> = <A as BitOr<B>>::Output;
+/// Alias for the associated type of `BitXor`: `Xor<A, B> = <A as BitXor<B>>::Output`
+pub type Xor<A, B> = <A as BitXor<B>>::Output;
+
+/// Alias for the associated type of `Shl`: `Shleft<A, B> = <A as Shl<B>>::Output`
+pub type Shleft<A, B> = <A as Shl<B>>::Output;
+/// Alias for the associated type of `Shr`: `Shright<A, B> = <A as Shr<B>>::Output`
+pub type Shright<A, B> = <A as Shr<B>>::Output;
+
+/// Alias for the associated type of `Add`: `Sum<A, B> = <A as Add<B>>::Output`
+pub type Sum<A, B> = <A as Add<B>>::Output;
+/// Alias for the associated type of `Sub`: `Diff<A, B> = <A as Sub<B>>::Output`
+pub type Diff<A, B> = <A as Sub<B>>::Output;
+/// Alias for the associated type of `Mul`: `Prod<A, B> = <A as Mul<B>>::Output`
+pub type Prod<A, B> = <A as Mul<B>>::Output;
+/// Alias for the associated type of `Div`: `Quot<A, B> = <A as Div<B>>::Output`
+pub type Quot<A, B> = <A as Div<B>>::Output;
+/// Alias for the associated type of `Rem`: `Mod<A, B> = <A as Rem<B>>::Output`
+pub type Mod<A, B> = <A as Rem<B>>::Output;
+
+/// Alias for the associated type of
+/// `PartialDiv`: `PartialQuot<A, B> = <A as PartialDiv<B>>::Output`
+pub type PartialQuot<A, B> = <A as PartialDiv<B>>::Output;
+
+/// Alias for the associated type of `Neg`: `Negate<A> = <A as Neg>::Output`
+pub type Negate<A> = <A as Neg>::Output;
+
+/// Alias for the associated type of `Abs`: `AbsVal<A> = <A as Abs>::Output`
+pub type AbsVal<A> = <A as Abs>::Output;
+
+/// Alias for the associated type of `Pow`: `Exp<A, B> = <A as Pow<B>>::Output`
+pub type Exp<A, B> = <A as Pow<B>>::Output;
+
+/// Alias for the associated type of `Gcd`: `Gcf<A, B> = <A as Gcd<B>>::Output>`
+pub type Gcf<A, B> = <A as Gcd<B>>::Output;
+
+/// Alias to make it easy to add 1: `Add1<A> = <A as Add<B1>>::Output`
+pub type Add1<A> = <A as Add<crate::bit::B1>>::Output;
+/// Alias to make it easy to subtract 1: `Sub1<A> = <A as Sub<B1>>::Output`
+pub type Sub1<A> = <A as Sub<crate::bit::B1>>::Output;
+
+/// Alias to make it easy to multiply by 2. `Double<A> = Shleft<A, B1>`
+pub type Double<A> = Shleft<A, crate::bit::B1>;
+
+/// Alias to make it easy to square. `Square<A> = <A as Mul<A>>::Output`
+pub type Square<A> = <A as Mul>::Output;
+/// Alias to make it easy to cube. `Cube<A> = <Square<A> as Mul<A>>::Output`
+pub type Cube<A> = <Square<A> as Mul<A>>::Output;
+
+/// Alias for the associated type of `SquareRoot`: `Sqrt<A> = <A as SquareRoot>::Output`
+pub type Sqrt<A> = <A as SquareRoot>::Output;
+
+/// Alias for the associated type of `Cmp`: `Compare<A, B> = <A as Cmp<B>>::Output`
+pub type Compare<A, B> = <A as Cmp<B>>::Output;
+
+/// Alias for the associated type of `Len`: `Length<A> = <A as Len>::Output`
+pub type Length<T> = <T as Len>::Output;
+
+/// Alias for the associated type of `FoldAdd`: `FoldSum<A> = <A as FoldAdd>::Output`
+pub type FoldSum<A> = <A as FoldAdd>::Output;
+
+/// Alias for the associated type of `FoldMul`: `FoldProd<A> = <A as FoldMul>::Output`
+pub type FoldProd<A> = <A as FoldMul>::Output;
+
+/// Alias for the associated type of `Min`: `Minimum<A, B> = <A as Min<B>>::Output`
+pub type Minimum<A, B> = <A as Min<B>>::Output;
+
+/// Alias for the associated type of `Max`: `Maximum<A, B> = <A as Max<B>>::Output`
+pub type Maximum<A, B> = <A as Max<B>>::Output;
+
+use crate::type_operators::{
+    IsEqual, IsGreater, IsGreaterOrEqual, IsLess, IsLessOrEqual, IsNotEqual,
+};
+/// Alias for the associated type of `IsLess`: `Le<A, B> = <A as IsLess<B>>::Output`
+pub type Le<A, B> = <A as IsLess<B>>::Output;
+/// Alias for the associated type of `IsEqual`: `Eq<A, B> = <A as IsEqual<B>>::Output`
+pub type Eq<A, B> = <A as IsEqual<B>>::Output;
+/// Alias for the associated type of `IsGreater`: `Gr<A, B> = <A as IsGreater<B>>::Output`
+pub type Gr<A, B> = <A as IsGreater<B>>::Output;
+/// Alias for the associated type of `IsGreaterOrEqual`:
+/// `GrEq<A, B> = <A as IsGreaterOrEqual<B>>::Output`
+pub type GrEq<A, B> = <A as IsGreaterOrEqual<B>>::Output;
+/// Alias for the associated type of `IsLessOrEqual`: `LeEq<A, B> = <A as IsLessOrEqual<B>>::Output`
+pub type LeEq<A, B> = <A as IsLessOrEqual<B>>::Output;
+/// Alias for the associated type of `IsNotEqual`: `NotEq<A, B> = <A as IsNotEqual<B>>::Output`
+pub type NotEq<A, B> = <A as IsNotEqual<B>>::Output;
+/// Alias for the associated type of `Logarithm2`: `Log2<A> = <A as Logarithm2>::Output`
+pub type Log2<A> = <A as Logarithm2>::Output;

vendor/typenum/src/private.rs

@@ -0,0 +1,592 @@
+//! **Ignore me!** This module is for things that are conceptually private but that must
+//! be made public for typenum to work correctly.
+//!
+//! Unless you are working on typenum itself, **there is no need to view anything here**.
+//!
+//! Certainly don't implement any of the traits here for anything.
+//!
+//!
+//! Just look away.
+//!
+//!
+//! Loooooooooooooooooooooooooooooooooook awaaaaaaaaaaaayyyyyyyyyyyyyyyyyyyyyyyyyyyyy...
+//!
+//!
+//! If you do manage to find something of use in here, please let me know. If you can make a
+//! compelling case, it may be moved out of __private.
+//!
+//! Note: Aliases for private type operators will all be named simply that operator followed
+//! by an abbreviated name of its associated type.
+
+#![doc(hidden)]
+
+use crate::{
+    bit::{Bit, B0, B1},
+    uint::{UInt, UTerm, Unsigned},
+};
+
+/// A marker for restricting a method on a public trait to internal use only.
+pub(crate) enum Internal {}
+
+pub trait InternalMarker {}
+
+impl InternalMarker for Internal {}
+
+/// Convenience trait. Calls `Invert` -> `TrimTrailingZeros` -> `Invert`
+pub trait Trim {
+    type Output;
+
+    fn trim(self) -> Self::Output;
+}
+pub type TrimOut<A> = <A as Trim>::Output;
+
+/// Gets rid of all zeros until it hits a one.
+// ONLY IMPLEMENT FOR INVERTED NUMBERS!
+pub trait TrimTrailingZeros {
+    type Output;
+
+    fn trim_trailing_zeros(self) -> Self::Output;
+}
+pub type TrimTrailingZerosOut<A> = <A as TrimTrailingZeros>::Output;
+
+/// Converts between standard numbers and inverted ones that have the most significant
+/// digit on the outside.
+pub trait Invert {
+    type Output;
+
+    fn invert(self) -> Self::Output;
+}
+pub type InvertOut<A> = <A as Invert>::Output;
+
+/// Doubly private! Called by invert to make the magic happen once its done the first step.
+/// The Rhs is what we've got so far.
+pub trait PrivateInvert<Rhs> {
+    type Output;
+
+    fn private_invert(self, rhs: Rhs) -> Self::Output;
+}
+pub type PrivateInvertOut<A, Rhs> = <A as PrivateInvert<Rhs>>::Output;
+
+/// Terminating character for `InvertedUInt`s
+pub struct InvertedUTerm;
+
+/// Inverted `UInt` (has most significant digit on the outside)
+pub struct InvertedUInt<IU: InvertedUnsigned, B: Bit> {
+    msb: IU,
+    lsb: B,
+}
+
+/// Does the real anding for `UInt`s; `And` just calls this and then `Trim`.
+pub trait PrivateAnd<Rhs = Self> {
+    type Output;
+
+    fn private_and(self, rhs: Rhs) -> Self::Output;
+}
+pub type PrivateAndOut<A, Rhs> = <A as PrivateAnd<Rhs>>::Output;
+
+/// Does the real xoring for `UInt`s; `Xor` just calls this and then `Trim`.
+pub trait PrivateXor<Rhs = Self> {
+    type Output;
+
+    fn private_xor(self, rhs: Rhs) -> Self::Output;
+}
+pub type PrivateXorOut<A, Rhs> = <A as PrivateXor<Rhs>>::Output;
+
+/// Does the real subtraction for `UInt`s; `Sub` just calls this and then `Trim`.
+pub trait PrivateSub<Rhs = Self> {
+    type Output;
+
+    fn private_sub(self, rhs: Rhs) -> Self::Output;
+}
+pub type PrivateSubOut<A, Rhs> = <A as PrivateSub<Rhs>>::Output;
+
+/// Used for addition of signed integers; `C = P.cmp(N)`
+/// Assumes `P = Self` is positive and `N` is negative
+/// where `P` and `N` are both passed as unsigned integers
+pub trait PrivateIntegerAdd<C, N> {
+    type Output;
+
+    fn private_integer_add(self, _: C, _: N) -> Self::Output;
+}
+pub type PrivateIntegerAddOut<P, C, N> = <P as PrivateIntegerAdd<C, N>>::Output;
+
+pub trait PrivatePow<Y, N> {
+    type Output;
+
+    fn private_pow(self, _: Y, _: N) -> Self::Output;
+}
+pub type PrivatePowOut<A, Y, N> = <A as PrivatePow<Y, N>>::Output;
+
+/// Performs `Shl` on `Lhs` so that `SizeOf(Lhs) = SizeOf(Rhs)`
+/// Fails if `SizeOf(Lhs) > SizeOf(Rhs)`
+pub trait ShiftDiff<Rhs> {
+    type Output;
+}
+pub type ShiftDiffOut<A, Rhs> = <A as ShiftDiff<Rhs>>::Output;
+
+/// Gives `SizeOf(Lhs) - SizeOf(Rhs)`
+pub trait BitDiff<Rhs> {
+    type Output;
+}
+pub type BitDiffOut<A, Rhs> = <A as BitDiff<Rhs>>::Output;
+
+/// Inverted unsigned numbers
+pub trait InvertedUnsigned {
+    fn to_u64() -> u64;
+}
+
+impl InvertedUnsigned for InvertedUTerm {
+    #[inline]
+    fn to_u64() -> u64 {
+        0
+    }
+}
+
+impl<IU: InvertedUnsigned, B: Bit> InvertedUnsigned for InvertedUInt<IU, B> {
+    #[inline]
+    fn to_u64() -> u64 {
+        u64::from(B::to_u8()) | IU::to_u64() << 1
+    }
+}
+
+impl Invert for UTerm {
+    type Output = InvertedUTerm;
+
+    #[inline]
+    fn invert(self) -> Self::Output {
+        InvertedUTerm
+    }
+}
+
+impl<U: Unsigned, B: Bit> Invert for UInt<U, B>
+where
+    U: PrivateInvert<InvertedUInt<InvertedUTerm, B>>,
+{
+    type Output = PrivateInvertOut<U, InvertedUInt<InvertedUTerm, B>>;
+
+    #[inline]
+    fn invert(self) -> Self::Output {
+        self.msb.private_invert(InvertedUInt {
+            msb: InvertedUTerm,
+            lsb: self.lsb,
+        })
+    }
+}
+
+impl<IU: InvertedUnsigned> PrivateInvert<IU> for UTerm {
+    type Output = IU;
+
+    #[inline]
+    fn private_invert(self, rhs: IU) -> Self::Output {
+        rhs
+    }
+}
+
+impl<IU: InvertedUnsigned, U: Unsigned, B: Bit> PrivateInvert<IU> for UInt<U, B>
+where
+    U: PrivateInvert<InvertedUInt<IU, B>>,
+{
+    type Output = PrivateInvertOut<U, InvertedUInt<IU, B>>;
+
+    #[inline]
+    fn private_invert(self, rhs: IU) -> Self::Output {
+        self.msb.private_invert(InvertedUInt {
+            msb: rhs,
+            lsb: self.lsb,
+        })
+    }
+}
+
+#[test]
+fn test_inversion() {
+    type Test4 = <crate::consts::U4 as Invert>::Output;
+    type Test5 = <crate::consts::U5 as Invert>::Output;
+    type Test12 = <crate::consts::U12 as Invert>::Output;
+    type Test16 = <crate::consts::U16 as Invert>::Output;
+
+    assert_eq!(1, <Test4 as InvertedUnsigned>::to_u64());
+    assert_eq!(5, <Test5 as InvertedUnsigned>::to_u64());
+    assert_eq!(3, <Test12 as InvertedUnsigned>::to_u64());
+    assert_eq!(1, <Test16 as InvertedUnsigned>::to_u64());
+}
+
+impl Invert for InvertedUTerm {
+    type Output = UTerm;
+
+    #[inline]
+    fn invert(self) -> Self::Output {
+        UTerm
+    }
+}
+
+impl<IU: InvertedUnsigned, B: Bit> Invert for InvertedUInt<IU, B>
+where
+    IU: PrivateInvert<UInt<UTerm, B>>,
+{
+    type Output = <IU as PrivateInvert<UInt<UTerm, B>>>::Output;
+
+    #[inline]
+    fn invert(self) -> Self::Output {
+        self.msb.private_invert(UInt {
+            msb: UTerm,
+            lsb: self.lsb,
+        })
+    }
+}
+
+impl<U: Unsigned> PrivateInvert<U> for InvertedUTerm {
+    type Output = U;
+
+    #[inline]
+    fn private_invert(self, rhs: U) -> Self::Output {
+        rhs
+    }
+}
+
+impl<U: Unsigned, IU: InvertedUnsigned, B: Bit> PrivateInvert<U> for InvertedUInt<IU, B>
+where
+    IU: PrivateInvert<UInt<U, B>>,
+{
+    type Output = <IU as PrivateInvert<UInt<U, B>>>::Output;
+
+    #[inline]
+    fn private_invert(self, rhs: U) -> Self::Output {
+        self.msb.private_invert(UInt {
+            msb: rhs,
+            lsb: self.lsb,
+        })
+    }
+}
+
+#[test]
+fn test_double_inversion() {
+    type Test4 = <<crate::consts::U4 as Invert>::Output as Invert>::Output;
+    type Test5 = <<crate::consts::U5 as Invert>::Output as Invert>::Output;
+    type Test12 = <<crate::consts::U12 as Invert>::Output as Invert>::Output;
+    type Test16 = <<crate::consts::U16 as Invert>::Output as Invert>::Output;
+
+    assert_eq!(4, <Test4 as Unsigned>::to_u64());
+    assert_eq!(5, <Test5 as Unsigned>::to_u64());
+    assert_eq!(12, <Test12 as Unsigned>::to_u64());
+    assert_eq!(16, <Test16 as Unsigned>::to_u64());
+}
+
+impl TrimTrailingZeros for InvertedUTerm {
+    type Output = InvertedUTerm;
+
+    #[inline]
+    fn trim_trailing_zeros(self) -> Self::Output {
+        InvertedUTerm
+    }
+}
+
+impl<IU: InvertedUnsigned> TrimTrailingZeros for InvertedUInt<IU, B1> {
+    type Output = Self;
+
+    #[inline]
+    fn trim_trailing_zeros(self) -> Self::Output {
+        self
+    }
+}
+
+impl<IU: InvertedUnsigned> TrimTrailingZeros for InvertedUInt<IU, B0>
+where
+    IU: TrimTrailingZeros,
+{
+    type Output = <IU as TrimTrailingZeros>::Output;
+
+    #[inline]
+    fn trim_trailing_zeros(self) -> Self::Output {
+        self.msb.trim_trailing_zeros()
+    }
+}
+
+impl<U: Unsigned> Trim for U
+where
+    U: Invert,
+    <U as Invert>::Output: TrimTrailingZeros,
+    <<U as Invert>::Output as TrimTrailingZeros>::Output: Invert,
+{
+    type Output = <<<U as Invert>::Output as TrimTrailingZeros>::Output as Invert>::Output;
+
+    #[inline]
+    fn trim(self) -> Self::Output {
+        self.invert().trim_trailing_zeros().invert()
+    }
+}
+
+// Note: Trimming is tested when we do subtraction.
+
+pub trait PrivateCmp<Rhs, SoFar> {
+    type Output;
+
+    fn private_cmp(&self, _: &Rhs, _: SoFar) -> Self::Output;
+}
+pub type PrivateCmpOut<A, Rhs, SoFar> = <A as PrivateCmp<Rhs, SoFar>>::Output;
+
+// Set Bit
+pub trait PrivateSetBit<I, B> {
+    type Output;
+
+    fn private_set_bit(self, _: I, _: B) -> Self::Output;
+}
+pub type PrivateSetBitOut<N, I, B> = <N as PrivateSetBit<I, B>>::Output;
+
+// Div
+pub trait PrivateDiv<N, D, Q, R, I> {
+    type Quotient;
+    type Remainder;
+
+    fn private_div_quotient(self, _: N, _: D, _: Q, _: R, _: I) -> Self::Quotient;
+
+    fn private_div_remainder(self, _: N, _: D, _: Q, _: R, _: I) -> Self::Remainder;
+}
+
+pub type PrivateDivQuot<N, D, Q, R, I> = <() as PrivateDiv<N, D, Q, R, I>>::Quotient;
+pub type PrivateDivRem<N, D, Q, R, I> = <() as PrivateDiv<N, D, Q, R, I>>::Remainder;
+
+pub trait PrivateDivIf<N, D, Q, R, I, RcmpD> {
+    type Quotient;
+    type Remainder;
+
+    fn private_div_if_quotient(self, _: N, _: D, _: Q, _: R, _: I, _: RcmpD) -> Self::Quotient;
+
+    fn private_div_if_remainder(self, _: N, _: D, _: Q, _: R, _: I, _: RcmpD) -> Self::Remainder;
+}
+
+pub type PrivateDivIfQuot<N, D, Q, R, I, RcmpD> =
+    <() as PrivateDivIf<N, D, Q, R, I, RcmpD>>::Quotient;
+pub type PrivateDivIfRem<N, D, Q, R, I, RcmpD> =
+    <() as PrivateDivIf<N, D, Q, R, I, RcmpD>>::Remainder;
+
+// Div for signed ints
+pub trait PrivateDivInt<C, Divisor> {
+    type Output;
+
+    fn private_div_int(self, _: C, _: Divisor) -> Self::Output;
+}
+pub type PrivateDivIntOut<A, C, Divisor> = <A as PrivateDivInt<C, Divisor>>::Output;
+
+pub trait PrivateRem<URem, Divisor> {
+    type Output;
+
+    fn private_rem(self, _: URem, _: Divisor) -> Self::Output;
+}
+pub type PrivateRemOut<A, URem, Divisor> = <A as PrivateRem<URem, Divisor>>::Output;
+
+// min max
+pub trait PrivateMin<Rhs, CmpResult> {
+    type Output;
+    fn private_min(self, rhs: Rhs) -> Self::Output;
+}
+pub type PrivateMinOut<A, B, CmpResult> = <A as PrivateMin<B, CmpResult>>::Output;
+
+pub trait PrivateMax<Rhs, CmpResult> {
+    type Output;
+    fn private_max(self, rhs: Rhs) -> Self::Output;
+}
+pub type PrivateMaxOut<A, B, CmpResult> = <A as PrivateMax<B, CmpResult>>::Output;
+
+// Comparisons
+
+use crate::{Equal, False, Greater, Less, True};
+
+pub trait IsLessPrivate<Rhs, Cmp> {
+    type Output: Bit;
+
+    #[allow(clippy::wrong_self_convention)]
+    fn is_less_private(self, _: Rhs, _: Cmp) -> Self::Output;
+}
+
+impl<A, B> IsLessPrivate<B, Less> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_less_private(self, _: B, _: Less) -> Self::Output {
+        B1
+    }
+}
+impl<A, B> IsLessPrivate<B, Equal> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_less_private(self, _: B, _: Equal) -> Self::Output {
+        B0
+    }
+}
+impl<A, B> IsLessPrivate<B, Greater> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_less_private(self, _: B, _: Greater) -> Self::Output {
+        B0
+    }
+}
+
+pub trait IsEqualPrivate<Rhs, Cmp> {
+    type Output: Bit;
+
+    #[allow(clippy::wrong_self_convention)]
+    fn is_equal_private(self, _: Rhs, _: Cmp) -> Self::Output;
+}
+
+impl<A, B> IsEqualPrivate<B, Less> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_equal_private(self, _: B, _: Less) -> Self::Output {
+        B0
+    }
+}
+impl<A, B> IsEqualPrivate<B, Equal> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_equal_private(self, _: B, _: Equal) -> Self::Output {
+        B1
+    }
+}
+impl<A, B> IsEqualPrivate<B, Greater> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_equal_private(self, _: B, _: Greater) -> Self::Output {
+        B0
+    }
+}
+
+pub trait IsGreaterPrivate<Rhs, Cmp> {
+    type Output: Bit;
+
+    #[allow(clippy::wrong_self_convention)]
+    fn is_greater_private(self, _: Rhs, _: Cmp) -> Self::Output;
+}
+
+impl<A, B> IsGreaterPrivate<B, Less> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_greater_private(self, _: B, _: Less) -> Self::Output {
+        B0
+    }
+}
+impl<A, B> IsGreaterPrivate<B, Equal> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_greater_private(self, _: B, _: Equal) -> Self::Output {
+        B0
+    }
+}
+impl<A, B> IsGreaterPrivate<B, Greater> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_greater_private(self, _: B, _: Greater) -> Self::Output {
+        B1
+    }
+}
+
+pub trait IsLessOrEqualPrivate<Rhs, Cmp> {
+    type Output: Bit;
+
+    #[allow(clippy::wrong_self_convention)]
+    fn is_less_or_equal_private(self, _: Rhs, _: Cmp) -> Self::Output;
+}
+
+impl<A, B> IsLessOrEqualPrivate<B, Less> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_less_or_equal_private(self, _: B, _: Less) -> Self::Output {
+        B1
+    }
+}
+impl<A, B> IsLessOrEqualPrivate<B, Equal> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_less_or_equal_private(self, _: B, _: Equal) -> Self::Output {
+        B1
+    }
+}
+impl<A, B> IsLessOrEqualPrivate<B, Greater> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_less_or_equal_private(self, _: B, _: Greater) -> Self::Output {
+        B0
+    }
+}
+
+pub trait IsNotEqualPrivate<Rhs, Cmp> {
+    type Output: Bit;
+
+    #[allow(clippy::wrong_self_convention)]
+    fn is_not_equal_private(self, _: Rhs, _: Cmp) -> Self::Output;
+}
+
+impl<A, B> IsNotEqualPrivate<B, Less> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_not_equal_private(self, _: B, _: Less) -> Self::Output {
+        B1
+    }
+}
+impl<A, B> IsNotEqualPrivate<B, Equal> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_not_equal_private(self, _: B, _: Equal) -> Self::Output {
+        B0
+    }
+}
+impl<A, B> IsNotEqualPrivate<B, Greater> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_not_equal_private(self, _: B, _: Greater) -> Self::Output {
+        B1
+    }
+}
+
+pub trait IsGreaterOrEqualPrivate<Rhs, Cmp> {
+    type Output: Bit;
+
+    #[allow(clippy::wrong_self_convention)]
+    fn is_greater_or_equal_private(self, _: Rhs, _: Cmp) -> Self::Output;
+}
+
+impl<A, B> IsGreaterOrEqualPrivate<B, Less> for A {
+    type Output = False;
+
+    #[inline]
+    fn is_greater_or_equal_private(self, _: B, _: Less) -> Self::Output {
+        B0
+    }
+}
+impl<A, B> IsGreaterOrEqualPrivate<B, Equal> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_greater_or_equal_private(self, _: B, _: Equal) -> Self::Output {
+        B1
+    }
+}
+impl<A, B> IsGreaterOrEqualPrivate<B, Greater> for A {
+    type Output = True;
+
+    #[inline]
+    fn is_greater_or_equal_private(self, _: B, _: Greater) -> Self::Output {
+        B1
+    }
+}
+
+pub trait PrivateSquareRoot {
+    type Output;
+}
+
+pub trait PrivateLogarithm2 {
+    type Output;
+}

vendor/typenum/src/type_operators.rs

@@ -0,0 +1,626 @@
+//! Useful **type operators** that are not defined in `core::ops`.
+
+use crate::{
+    private::{Internal, InternalMarker},
+    Bit, NInt, NonZero, PInt, UInt, UTerm, Unsigned, Z0,
+};
+
+/// A **type operator** that ensures that `Rhs` is the same as `Self`, it is mainly useful
+/// for writing macros that can take arbitrary binary or unary operators.
+///
+/// `Same` is implemented generically for all types; it should never need to be implemented
+/// for anything else.
+///
+/// Note that Rust lazily evaluates types, so this will only fail for two different types if
+/// the `Output` is used.
+///
+/// # Example
+/// ```rust
+/// use typenum::{Same, Unsigned, U4, U5};
+///
+/// assert_eq!(<U5 as Same<U5>>::Output::to_u32(), 5);
+///
+/// // Only an error if we use it:
+/// # #[allow(dead_code)]
+/// type Undefined = <U5 as Same<U4>>::Output;
+/// // Compiler error:
+/// // Undefined::to_u32();
+/// ```
+pub trait Same<Rhs = Self> {
+    /// Should always be `Self`
+    type Output;
+}
+
+impl<T> Same<T> for T {
+    type Output = T;
+}
+
+/// A **type operator** that returns the absolute value.
+///
+/// # Example
+/// ```rust
+/// use typenum::{Abs, Integer, N5};
+///
+/// assert_eq!(<N5 as Abs>::Output::to_i32(), 5);
+/// ```
+pub trait Abs {
+    /// The absolute value.
+    type Output;
+}
+
+impl Abs for Z0 {
+    type Output = Z0;
+}
+
+impl<U: Unsigned + NonZero> Abs for PInt<U> {
+    type Output = Self;
+}
+
+impl<U: Unsigned + NonZero> Abs for NInt<U> {
+    type Output = PInt<U>;
+}
+
+/// A **type operator** that provides exponentiation by repeated squaring.
+///
+/// # Example
+/// ```rust
+/// use typenum::{Integer, Pow, N3, P3};
+///
+/// assert_eq!(<N3 as Pow<P3>>::Output::to_i32(), -27);
+/// ```
+pub trait Pow<Exp> {
+    /// The result of the exponentiation.
+    type Output;
+    /// This function isn't used in this crate, but may be useful for others.
+    /// It is implemented for primitives.
+    ///
+    /// # Example
+    /// ```rust
+    /// use typenum::{Pow, U3};
+    ///
+    /// let a = 7u32.powi(U3::new());
+    /// let b = 7u32.pow(3);
+    /// assert_eq!(a, b);
+    ///
+    /// let x = 3.0.powi(U3::new());
+    /// let y = 27.0;
+    /// assert_eq!(x, y);
+    /// ```
+    fn powi(self, exp: Exp) -> Self::Output;
+}
+
+macro_rules! impl_pow_f {
+    ($t:ty) => {
+        impl Pow<UTerm> for $t {
+            type Output = $t;
+            #[inline]
+            fn powi(self, _: UTerm) -> Self::Output {
+                1.0
+            }
+        }
+
+        impl<U: Unsigned, B: Bit> Pow<UInt<U, B>> for $t {
+            type Output = $t;
+            // powi is unstable in core, so we have to write this function ourselves.
+            // copied from num::pow::pow
+            #[inline]
+            fn powi(self, _: UInt<U, B>) -> Self::Output {
+                let mut exp = <UInt<U, B> as Unsigned>::to_u32();
+                let mut base = self;
+
+                if exp == 0 {
+                    return 1.0;
+                }
+
+                while exp & 1 == 0 {
+                    base *= base;
+                    exp >>= 1;
+                }
+                if exp == 1 {
+                    return base;
+                }
+
+                let mut acc = base.clone();
+                while exp > 1 {
+                    exp >>= 1;
+                    base *= base;
+                    if exp & 1 == 1 {
+                        acc *= base.clone();
+                    }
+                }
+                acc
+            }
+        }
+
+        impl Pow<Z0> for $t {
+            type Output = $t;
+            #[inline]
+            fn powi(self, _: Z0) -> Self::Output {
+                1.0
+            }
+        }
+
+        impl<U: Unsigned + NonZero> Pow<PInt<U>> for $t {
+            type Output = $t;
+            // powi is unstable in core, so we have to write this function ourselves.
+            // copied from num::pow::pow
+            #[inline]
+            fn powi(self, _: PInt<U>) -> Self::Output {
+                let mut exp = U::to_u32();
+                let mut base = self;
+
+                if exp == 0 {
+                    return 1.0;
+                }
+
+                while exp & 1 == 0 {
+                    base *= base;
+                    exp >>= 1;
+                }
+                if exp == 1 {
+                    return base;
+                }
+
+                let mut acc = base.clone();
+                while exp > 1 {
+                    exp >>= 1;
+                    base *= base;
+                    if exp & 1 == 1 {
+                        acc *= base.clone();
+                    }
+                }
+                acc
+            }
+        }
+
+        impl<U: Unsigned + NonZero> Pow<NInt<U>> for $t {
+            type Output = $t;
+
+            #[inline]
+            fn powi(self, _: NInt<U>) -> Self::Output {
+                <$t as Pow<PInt<U>>>::powi(self, PInt::new()).recip()
+            }
+        }
+    };
+}
+
+impl_pow_f!(f32);
+impl_pow_f!(f64);
+
+macro_rules! impl_pow_i {
+    () => ();
+    ($(#[$meta:meta])*  $t: ty $(, $tail:tt)*) => (
+        $(#[$meta])*
+        impl Pow<UTerm> for $t {
+            type Output = $t;
+            #[inline]
+            fn powi(self, _: UTerm) -> Self::Output {
+                1
+            }
+        }
+
+        $(#[$meta])*
+        impl<U: Unsigned, B: Bit> Pow<UInt<U, B>> for $t {
+            type Output = $t;
+            #[inline]
+            fn powi(self, _: UInt<U, B>) -> Self::Output {
+                self.pow(<UInt<U, B> as Unsigned>::to_u32())
+            }
+        }
+
+        $(#[$meta])*
+        impl Pow<Z0> for $t {
+            type Output = $t;
+            #[inline]
+            fn powi(self, _: Z0) -> Self::Output {
+                1
+            }
+        }
+
+        $(#[$meta])*
+        impl<U: Unsigned + NonZero> Pow<PInt<U>> for $t {
+            type Output = $t;
+            #[inline]
+            fn powi(self, _: PInt<U>) -> Self::Output {
+                self.pow(U::to_u32())
+            }
+        }
+
+        impl_pow_i!($($tail),*);
+    );
+}
+
+impl_pow_i!(u8, u16, u32, u64, usize, i8, i16, i32, i64, isize);
+#[cfg(feature = "i128")]
+impl_pow_i!(
+    #[cfg_attr(docsrs, doc(cfg(feature = "i128")))]
+    u128,
+    i128
+);
+
+#[test]
+fn pow_test() {
+    use crate::consts::*;
+    let z0 = Z0::new();
+    let p3 = P3::new();
+
+    let u0 = U0::new();
+    let u3 = U3::new();
+    let n3 = N3::new();
+
+    macro_rules! check {
+        ($x:ident) => {
+            assert_eq!($x.powi(z0), 1);
+            assert_eq!($x.powi(u0), 1);
+
+            assert_eq!($x.powi(p3), $x * $x * $x);
+            assert_eq!($x.powi(u3), $x * $x * $x);
+        };
+        ($x:ident, $f:ident) => {
+            assert!((<$f as Pow<Z0>>::powi(*$x, z0) - 1.0).abs() < ::core::$f::EPSILON);
+            assert!((<$f as Pow<U0>>::powi(*$x, u0) - 1.0).abs() < ::core::$f::EPSILON);
+
+            assert!((<$f as Pow<P3>>::powi(*$x, p3) - $x * $x * $x).abs() < ::core::$f::EPSILON);
+            assert!((<$f as Pow<U3>>::powi(*$x, u3) - $x * $x * $x).abs() < ::core::$f::EPSILON);
+
+            if *$x == 0.0 {
+                assert!(<$f as Pow<N3>>::powi(*$x, n3).is_infinite());
+            } else {
+                assert!(
+                    (<$f as Pow<N3>>::powi(*$x, n3) - 1. / $x / $x / $x).abs()
+                        < ::core::$f::EPSILON
+                );
+            }
+        };
+    }
+
+    for x in &[0i8, -3, 2] {
+        check!(x);
+    }
+    for x in &[0u8, 1, 5] {
+        check!(x);
+    }
+    for x in &[0usize, 1, 5, 40] {
+        check!(x);
+    }
+    for x in &[0isize, 1, 2, -30, -22, 48] {
+        check!(x);
+    }
+    for x in &[0.0f32, 2.2, -3.5, 378.223] {
+        check!(x, f32);
+    }
+    for x in &[0.0f64, 2.2, -3.5, -2387.2, 234.22] {
+        check!(x, f64);
+    }
+}
+
+/// A **type operator** for comparing `Self` and `Rhs`. It provides a similar functionality to
+/// the function
+/// [`core::cmp::Ord::cmp`](https://doc.rust-lang.org/nightly/core/cmp/trait.Ord.html#tymethod.cmp)
+/// but for types.
+///
+/// # Example
+/// ```rust
+/// use typenum::{Cmp, Ord, N3, P2, P5};
+/// use std::cmp::Ordering;
+///
+/// assert_eq!(<P2 as Cmp<N3>>::Output::to_ordering(), Ordering::Greater);
+/// assert_eq!(<P2 as Cmp<P2>>::Output::to_ordering(), Ordering::Equal);
+/// assert_eq!(<P2 as Cmp<P5>>::Output::to_ordering(), Ordering::Less);
+pub trait Cmp<Rhs = Self> {
+    /// The result of the comparison. It should only ever be one of `Greater`, `Less`, or `Equal`.
+    type Output;
+
+    #[doc(hidden)]
+    fn compare<IM: InternalMarker>(&self, _: &Rhs) -> Self::Output;
+}
+
+/// A **type operator** that gives the length of an `Array` or the number of bits in a `UInt`.
+#[allow(clippy::len_without_is_empty)]
+pub trait Len {
+    /// The length as a type-level unsigned integer.
+    type Output: crate::Unsigned;
+    /// This function isn't used in this crate, but may be useful for others.
+    fn len(&self) -> Self::Output;
+}
+
+/// A **type operator** that gives the sum of all elements of an `Array`.
+pub trait FoldAdd {
+    /// The type of the result of the sum
+    type Output;
+}
+
+/// A **type operator** that gives the product of all elements of an `Array`.
+pub trait FoldMul {
+    /// The type of the result of the product
+    type Output;
+}
+
+#[test]
+fn fold_test() {
+    use crate::*;
+    assert_eq!(10, <FoldSum::<tarr![U2, U3, U5]>>::to_u32());
+    assert_eq!(30, <FoldProd::<tarr![U2, U3, U5]>>::to_u32());
+}
+
+/// Division as a partial function. This **type operator** performs division just as `Div`, but is
+/// only defined when the result is an integer (i.e. there is no remainder).
+pub trait PartialDiv<Rhs = Self> {
+    /// The type of the result of the division
+    type Output;
+    /// Method for performing the division
+    fn partial_div(self, _: Rhs) -> Self::Output;
+}
+
+/// A **type operator** that returns the minimum of `Self` and `Rhs`.
+pub trait Min<Rhs = Self> {
+    /// The type of the minimum of `Self` and `Rhs`
+    type Output;
+    /// Method returning the minimum
+    fn min(self, rhs: Rhs) -> Self::Output;
+}
+
+/// A **type operator** that returns the maximum of `Self` and `Rhs`.
+pub trait Max<Rhs = Self> {
+    /// The type of the maximum of `Self` and `Rhs`
+    type Output;
+    /// Method returning the maximum
+    fn max(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::Compare;
+
+/// A **type operator** that returns `True` if `Self < Rhs`, otherwise returns `False`.
+pub trait IsLess<Rhs = Self> {
+    /// The type representing either `True` or `False`
+    type Output: Bit;
+    /// Method returning `True` or `False`.
+    #[allow(clippy::wrong_self_convention)]
+    fn is_less(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::private::IsLessPrivate;
+impl<A, B> IsLess<B> for A
+where
+    A: Cmp<B> + IsLessPrivate<B, Compare<A, B>>,
+{
+    type Output = <A as IsLessPrivate<B, Compare<A, B>>>::Output;
+
+    #[inline]
+    fn is_less(self, rhs: B) -> Self::Output {
+        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
+        self.is_less_private(rhs, lhs_cmp_rhs)
+    }
+}
+
+/// A **type operator** that returns `True` if `Self == Rhs`, otherwise returns `False`.
+pub trait IsEqual<Rhs = Self> {
+    /// The type representing either `True` or `False`
+    type Output: Bit;
+    /// Method returning `True` or `False`.
+    #[allow(clippy::wrong_self_convention)]
+    fn is_equal(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::private::IsEqualPrivate;
+impl<A, B> IsEqual<B> for A
+where
+    A: Cmp<B> + IsEqualPrivate<B, Compare<A, B>>,
+{
+    type Output = <A as IsEqualPrivate<B, Compare<A, B>>>::Output;
+
+    #[inline]
+    fn is_equal(self, rhs: B) -> Self::Output {
+        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
+        self.is_equal_private(rhs, lhs_cmp_rhs)
+    }
+}
+
+/// A **type operator** that returns `True` if `Self > Rhs`, otherwise returns `False`.
+pub trait IsGreater<Rhs = Self> {
+    /// The type representing either `True` or `False`
+    type Output: Bit;
+    /// Method returning `True` or `False`.
+    #[allow(clippy::wrong_self_convention)]
+    fn is_greater(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::private::IsGreaterPrivate;
+impl<A, B> IsGreater<B> for A
+where
+    A: Cmp<B> + IsGreaterPrivate<B, Compare<A, B>>,
+{
+    type Output = <A as IsGreaterPrivate<B, Compare<A, B>>>::Output;
+
+    #[inline]
+    fn is_greater(self, rhs: B) -> Self::Output {
+        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
+        self.is_greater_private(rhs, lhs_cmp_rhs)
+    }
+}
+
+/// A **type operator** that returns `True` if `Self <= Rhs`, otherwise returns `False`.
+pub trait IsLessOrEqual<Rhs = Self> {
+    /// The type representing either `True` or `False`
+    type Output: Bit;
+    /// Method returning `True` or `False`.
+    #[allow(clippy::wrong_self_convention)]
+    fn is_less_or_equal(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::private::IsLessOrEqualPrivate;
+impl<A, B> IsLessOrEqual<B> for A
+where
+    A: Cmp<B> + IsLessOrEqualPrivate<B, Compare<A, B>>,
+{
+    type Output = <A as IsLessOrEqualPrivate<B, Compare<A, B>>>::Output;
+
+    #[inline]
+    fn is_less_or_equal(self, rhs: B) -> Self::Output {
+        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
+        self.is_less_or_equal_private(rhs, lhs_cmp_rhs)
+    }
+}
+
+/// A **type operator** that returns `True` if `Self != Rhs`, otherwise returns `False`.
+pub trait IsNotEqual<Rhs = Self> {
+    /// The type representing either `True` or `False`
+    type Output: Bit;
+    /// Method returning `True` or `False`.
+    #[allow(clippy::wrong_self_convention)]
+    fn is_not_equal(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::private::IsNotEqualPrivate;
+impl<A, B> IsNotEqual<B> for A
+where
+    A: Cmp<B> + IsNotEqualPrivate<B, Compare<A, B>>,
+{
+    type Output = <A as IsNotEqualPrivate<B, Compare<A, B>>>::Output;
+
+    #[inline]
+    fn is_not_equal(self, rhs: B) -> Self::Output {
+        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
+        self.is_not_equal_private(rhs, lhs_cmp_rhs)
+    }
+}
+
+/// A **type operator** that returns `True` if `Self >= Rhs`, otherwise returns `False`.
+pub trait IsGreaterOrEqual<Rhs = Self> {
+    /// The type representing either `True` or `False`
+    type Output: Bit;
+    /// Method returning `True` or `False`.
+    #[allow(clippy::wrong_self_convention)]
+    fn is_greater_or_equal(self, rhs: Rhs) -> Self::Output;
+}
+
+use crate::private::IsGreaterOrEqualPrivate;
+impl<A, B> IsGreaterOrEqual<B> for A
+where
+    A: Cmp<B> + IsGreaterOrEqualPrivate<B, Compare<A, B>>,
+{
+    type Output = <A as IsGreaterOrEqualPrivate<B, Compare<A, B>>>::Output;
+
+    #[inline]
+    fn is_greater_or_equal(self, rhs: B) -> Self::Output {
+        let lhs_cmp_rhs = self.compare::<Internal>(&rhs);
+        self.is_greater_or_equal_private(rhs, lhs_cmp_rhs)
+    }
+}
+
+/**
+A convenience macro for comparing type numbers. Use `op!` instead.
+
+Due to the intricacies of the macro system, if the left-hand operand is more complex than a simple
+`ident`, you must place a comma between it and the comparison sign.
+
+For example, you can do `cmp!(P5 > P3)` or `cmp!(typenum::P5, > typenum::P3)` but not
+`cmp!(typenum::P5 > typenum::P3)`.
+
+The result of this comparison will always be one of `True` (aka `B1`) or `False` (aka `B0`).
+
+# Example
+```rust
+#[macro_use] extern crate typenum;
+use typenum::consts::*;
+use typenum::Bit;
+
+fn main() {
+type Result = cmp!(P9 == op!(P1 + P2 * (P2 - N2)));
+assert_eq!(Result::to_bool(), true);
+}
+```
+ */
+#[deprecated(since = "1.9.0", note = "use the `op!` macro instead")]
+#[macro_export]
+macro_rules! cmp {
+    ($a:ident < $b:ty) => {
+        <$a as $crate::IsLess<$b>>::Output
+    };
+    ($a:ty, < $b:ty) => {
+        <$a as $crate::IsLess<$b>>::Output
+    };
+
+    ($a:ident == $b:ty) => {
+        <$a as $crate::IsEqual<$b>>::Output
+    };
+    ($a:ty, == $b:ty) => {
+        <$a as $crate::IsEqual<$b>>::Output
+    };
+
+    ($a:ident > $b:ty) => {
+        <$a as $crate::IsGreater<$b>>::Output
+    };
+    ($a:ty, > $b:ty) => {
+        <$a as $crate::IsGreater<$b>>::Output
+    };
+
+    ($a:ident <= $b:ty) => {
+        <$a as $crate::IsLessOrEqual<$b>>::Output
+    };
+    ($a:ty, <= $b:ty) => {
+        <$a as $crate::IsLessOrEqual<$b>>::Output
+    };
+
+    ($a:ident != $b:ty) => {
+        <$a as $crate::IsNotEqual<$b>>::Output
+    };
+    ($a:ty, != $b:ty) => {
+        <$a as $crate::IsNotEqual<$b>>::Output
+    };
+
+    ($a:ident >= $b:ty) => {
+        <$a as $crate::IsGreaterOrEqual<$b>>::Output
+    };
+    ($a:ty, >= $b:ty) => {
+        <$a as $crate::IsGreaterOrEqual<$b>>::Output
+    };
+}
+
+/// A **type operator** for taking the integer square root of `Self`.
+///
+/// The integer square root of `n` is the largest integer `m` such
+/// that `n >= m*m`. This definition is equivalent to truncating the
+/// real-valued square root: `floor(real_sqrt(n))`.
+pub trait SquareRoot {
+    /// The result of the integer square root.
+    type Output;
+}
+
+/// A **type operator** for taking the integer binary logarithm of `Self`.
+///
+/// The integer binary logarighm of `n` is the largest integer `m` such
+/// that `n >= 2^m`. This definition is equivalent to truncating the
+/// real-valued binary logarithm: `floor(log2(n))`.
+pub trait Logarithm2 {
+    /// The result of the integer binary logarithm.
+    type Output;
+}
+
+/// A **type operator** that computes the [greatest common divisor][gcd] of `Self` and `Rhs`.
+///
+/// [gcd]: https://en.wikipedia.org/wiki/Greatest_common_divisor
+///
+/// # Example
+///
+/// ```rust
+/// use typenum::{Gcd, Unsigned, U12, U8};
+///
+/// assert_eq!(<U12 as Gcd<U8>>::Output::to_i32(), 4);
+/// ```
+pub trait Gcd<Rhs> {
+    /// The greatest common divisor.
+    type Output;
+}
+
+/// A **type operator** for taking a concrete integer value from a type.
+///
+/// It returns arbitrary integer value without explicitly specifying the
+/// type. It is useful when you pass the values to methods that accept
+/// distinct types without runtime casting.
+pub trait ToInt<T> {
+    /// Method returning the concrete value for the type.
+    fn to_int() -> T;
+    /// The concrete value for the type. Can be used in `const` contexts.
+    const INT: T;
+}

vendor/typenum/tests/test.rs

@@ -0,0 +1,2 @@
+#[cfg(test)]
+include!(concat!(env!("OUT_DIR"), "/tests.rs"));