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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 = "2021"
rust-version = "1.60"
name = "num-bigint"
version = "0.4.6"
authors = ["The Rust Project Developers"]
exclude = [
"/ci/*",
"/.github/*",
]
description = "Big integer implementation for Rust"
homepage = "https://github.com/rust-num/num-bigint"
documentation = "https://docs.rs/num-bigint"
readme = "README.md"
keywords = [
"mathematics",
"numerics",
"bignum",
]
categories = [
"algorithms",
"data-structures",
"science",
]
license = "MIT OR Apache-2.0"
repository = "https://github.com/rust-num/num-bigint"
[package.metadata.docs.rs]
features = [
"std",
"serde",
"rand",
"quickcheck",
"arbitrary",
]
rustdoc-args = [
"--cfg",
"docsrs",
]
[[bench]]
name = "bigint"
[[bench]]
name = "factorial"
[[bench]]
name = "gcd"
[[bench]]
name = "roots"
[[bench]]
name = "shootout-pidigits"
harness = false
[dependencies.arbitrary]
version = "1"
optional = true
default-features = false
[dependencies.num-integer]
version = "0.1.46"
features = ["i128"]
default-features = false
[dependencies.num-traits]
version = "0.2.18"
features = ["i128"]
default-features = false
[dependencies.quickcheck]
version = "1"
optional = true
default-features = false
[dependencies.rand]
version = "0.8"
optional = true
default-features = false
[dependencies.serde]
version = "1.0"
optional = true
default-features = false
[features]
arbitrary = ["dep:arbitrary"]
default = ["std"]
quickcheck = ["dep:quickcheck"]
rand = ["dep:rand"]
serde = ["dep:serde"]
std = [
"num-integer/std",
"num-traits/std",
]

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Copyright (c) 2014 The Rust Project Developers
Permission is hereby granted, free of charge, to any
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# num-bigint
[![crate](https://img.shields.io/crates/v/num-bigint.svg)](https://crates.io/crates/num-bigint)
[![documentation](https://docs.rs/num-bigint/badge.svg)](https://docs.rs/num-bigint)
[![minimum rustc 1.60](https://img.shields.io/badge/rustc-1.60+-red.svg)](https://rust-lang.github.io/rfcs/2495-min-rust-version.html)
[![build status](https://github.com/rust-num/num-bigint/workflows/master/badge.svg)](https://github.com/rust-num/num-bigint/actions)
Big integer types for Rust, `BigInt` and `BigUint`.
## Usage
Add this to your `Cargo.toml`:
```toml
[dependencies]
num-bigint = "0.4"
```
## Features
The `std` crate feature is enabled by default, and is mandatory before Rust
1.36 and the stabilized `alloc` crate. If you depend on `num-bigint` with
`default-features = false`, you must manually enable the `std` feature yourself
if your compiler is not new enough.
### Random Generation
`num-bigint` supports the generation of random big integers when the `rand`
feature is enabled. To enable it include rand as
```toml
rand = "0.8"
num-bigint = { version = "0.4", features = ["rand"] }
```
Note that you must use the version of `rand` that `num-bigint` is compatible
with: `0.8`.
## Releases
Release notes are available in [RELEASES.md](RELEASES.md).
## Compatibility
The `num-bigint` crate is tested for rustc 1.60 and greater.
## Alternatives
While `num-bigint` strives for good performance in pure Rust code, other
crates may offer better performance with different trade-offs. The following
table offers a brief comparison to a few alternatives.
| Crate | License | Min rustc | Implementation | Features |
| :--------------- | :------------- | :-------- | :------------- | :------- |
| **`num-bigint`** | MIT/Apache-2.0 | 1.60 | pure rust | dynamic width, number theoretical functions |
| [`awint`] | MIT/Apache-2.0 | 1.66 | pure rust | fixed width, heap or stack, concatenation macros |
| [`bnum`] | MIT/Apache-2.0 | 1.65 | pure rust | fixed width, parity with Rust primitives including floats |
| [`crypto-bigint`] | MIT/Apache-2.0 | 1.73 | pure rust | fixed width, stack only |
| [`ibig`] | MIT/Apache-2.0 | 1.49 | pure rust | dynamic width, number theoretical functions |
| [`rug`] | LGPL-3.0+ | 1.65 | bundles [GMP] via [`gmp-mpfr-sys`] | all the features of GMP, MPFR, and MPC |
[`awint`]: https://crates.io/crates/awint
[`bnum`]: https://crates.io/crates/bnum
[`crypto-bigint`]: https://crates.io/crates/crypto-bigint
[`ibig`]: https://crates.io/crates/ibig
[`rug`]: https://crates.io/crates/rug
[GMP]: https://gmplib.org/
[`gmp-mpfr-sys`]: https://crates.io/crates/gmp-mpfr-sys
## License
Licensed under either of
* [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
* [MIT license](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.

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# Release 0.4.6 (2024-06-27)
- [Fixed compilation on `x86_64-unknown-linux-gnux32`.][312]
**Contributors**: @cuviper, @ralphtandetzky, @yhx-12243
[312]: https://github.com/rust-num/num-bigint/pull/312
# Release 0.4.5 (2024-05-06)
- [Upgrade to 2021 edition, **MSRV 1.60**][292]
- [Add `const ZERO` and implement `num_traits::ConstZero`][298]
- [Add `modinv` methods for the modular inverse][288]
- [Optimize multiplication with imbalanced operands][295]
- [Optimize scalar division on x86 and x86-64][236]
**Contributors**: @cuviper, @joelonsql, @waywardmonkeys
[236]: https://github.com/rust-num/num-bigint/pull/236
[288]: https://github.com/rust-num/num-bigint/pull/288
[292]: https://github.com/rust-num/num-bigint/pull/292
[295]: https://github.com/rust-num/num-bigint/pull/295
[298]: https://github.com/rust-num/num-bigint/pull/298
# Release 0.4.4 (2023-08-22)
- [Implemented `From<bool>` for `BigInt` and `BigUint`.][239]
- [Implemented `num_traits::Euclid` and `CheckedEuclid` for `BigInt` and `BigUint`.][245]
- [Implemented ties-to-even for `BigInt` and `BigUint::to_f32` and `to_f64`.][271]
- [Implemented `num_traits::FromBytes` and `ToBytes` for `BigInt` and `BigUint`.][276]
- Limited pre-allocation from serde size hints against potential OOM.
- Miscellaneous other code cleanups and maintenance tasks.
**Contributors**: @AaronKutch, @archseer, @cuviper, @dramforever, @icecream17,
@icedrocket, @janmarthedal, @jaybosamiya, @OliveIsAWord, @PatrickNorton,
@smoelius, @waywardmonkeys
[239]: https://github.com/rust-num/num-bigint/pull/239
[245]: https://github.com/rust-num/num-bigint/pull/245
[271]: https://github.com/rust-num/num-bigint/pull/271
[276]: https://github.com/rust-num/num-bigint/pull/276
# Release 0.4.3 (2021-11-02)
- [GHSA-v935-pqmr-g8v9]: [Fix unexpected panics in multiplication.][228]
**Contributors**: @arvidn, @cuviper, @guidovranken
[228]: https://github.com/rust-num/num-bigint/pull/228
[GHSA-v935-pqmr-g8v9]: https://github.com/rust-num/num-bigint/security/advisories/GHSA-v935-pqmr-g8v9
# Release 0.4.2 (2021-09-03)
- [Use explicit `Integer::div_ceil` to avoid the new unstable method.][219]
**Contributors**: @catenacyber, @cuviper
[219]: https://github.com/rust-num/num-bigint/pull/219
# Release 0.4.1 (2021-08-27)
- [Fixed scalar divide-by-zero panics.][200]
- [Implemented `DoubleEndedIterator` for `U32Digits` and `U64Digits`.][208]
- [Optimized multiplication to avoid unnecessary allocations.][199]
- [Optimized string formatting for very large values.][216]
**Contributors**: @cuviper, @PatrickNorton
[199]: https://github.com/rust-num/num-bigint/pull/199
[200]: https://github.com/rust-num/num-bigint/pull/200
[208]: https://github.com/rust-num/num-bigint/pull/208
[216]: https://github.com/rust-num/num-bigint/pull/216
# Release 0.4.0 (2021-03-05)
### Breaking Changes
- Updated public dependences on [arbitrary, quickcheck][194], and [rand][185]:
- `arbitrary` support has been updated to 1.0, requiring Rust 1.40.
- `quickcheck` support has been updated to 1.0, requiring Rust 1.46.
- `rand` support has been updated to 0.8, requiring Rust 1.36.
- [`Debug` now shows plain numeric values for `BigInt` and `BigUint`][195],
rather than the raw list of internal digits.
**Contributors**: @cuviper, @Gelbpunkt
[185]: https://github.com/rust-num/num-bigint/pull/185
[194]: https://github.com/rust-num/num-bigint/pull/194
[195]: https://github.com/rust-num/num-bigint/pull/195
# Release 0.3.3 (2021-09-03)
- [Use explicit `Integer::div_ceil` to avoid the new unstable method.][219]
**Contributors**: @catenacyber, @cuviper
# Release 0.3.2 (2021-03-04)
- [The new `BigUint` methods `count_ones` and `trailing_ones`][175] return the
number of `1` bits in the entire value or just its least-significant tail,
respectively.
- [The new `BigInt` and `BigUint` methods `bit` and `set_bit`][183] will read
and write individual bits of the value. For negative `BigInt`, bits are
determined as if they were in the two's complement representation.
- [The `from_radix_le` and `from_radix_be` methods][187] now accept empty
buffers to represent zero.
- [`BigInt` and `BigUint` can now iterate digits as `u32` or `u64`][192],
regardless of the actual internal digit size.
**Contributors**: @BartMassey, @cuviper, @janmarthedal, @sebastianv89, @Speedy37
[175]: https://github.com/rust-num/num-bigint/pull/175
[183]: https://github.com/rust-num/num-bigint/pull/183
[187]: https://github.com/rust-num/num-bigint/pull/187
[192]: https://github.com/rust-num/num-bigint/pull/192
# Release 0.3.1 (2020-11-03)
- [Addition and subtraction now uses intrinsics][141] for performance on `x86`
and `x86_64` when built with Rust 1.33 or later.
- [Conversions `to_f32` and `to_f64` now return infinity][163] for very large
numbers, rather than `None`. This does preserve the sign too, so a large
negative `BigInt` will convert to negative infinity.
- [The optional `arbitrary` feature implements `arbitrary::Arbitrary`][166],
distinct from `quickcheck::Arbitrary`.
- [The division algorithm has been optimized][170] to reduce the number of
temporary allocations and improve the internal guesses at each step.
- [`BigInt` and `BigUint` will opportunistically shrink capacity][171] if the
internal vector is much larger than needed.
**Contributors**: @cuviper, @e00E, @ejmahler, @notoria, @tczajka
[141]: https://github.com/rust-num/num-bigint/pull/141
[163]: https://github.com/rust-num/num-bigint/pull/163
[166]: https://github.com/rust-num/num-bigint/pull/166
[170]: https://github.com/rust-num/num-bigint/pull/170
[171]: https://github.com/rust-num/num-bigint/pull/171
# Release 0.3.0 (2020-06-12)
### Enhancements
- [The internal `BigDigit` may now be either `u32` or `u64`][62], although that
implementation detail is not exposed in the API. For now, this is chosen to
match the target pointer size, but may change in the future.
- [No-`std` is now supported with the `alloc` crate on Rust 1.36][101].
- [`Pow` is now implemented for bigint values][137], not just references.
- [`TryFrom` is now implemented on Rust 1.34 and later][123], converting signed
integers to unsigned, and narrowing big integers to primitives.
- [`Shl` and `Shr` are now implemented for a variety of shift types][142].
- A new `trailing_zeros()` returns the number of consecutive zeros from the
least significant bit.
- The new `BigInt::magnitude` and `into_parts` methods give access to its
`BigUint` part as the magnitude.
### Breaking Changes
- `num-bigint` now requires Rust 1.31 or greater.
- The "i128" opt-in feature was removed, now always available.
- [Updated public dependences][110]:
- `rand` support has been updated to 0.7, requiring Rust 1.32.
- `quickcheck` support has been updated to 0.9, requiring Rust 1.34.
- [Removed `impl Neg for BigUint`][145], which only ever panicked.
- [Bit counts are now `u64` instead of `usize`][143].
**Contributors**: @cuviper, @dignifiedquire, @hansihe,
@kpcyrd, @milesand, @tech6hutch
[62]: https://github.com/rust-num/num-bigint/pull/62
[101]: https://github.com/rust-num/num-bigint/pull/101
[110]: https://github.com/rust-num/num-bigint/pull/110
[123]: https://github.com/rust-num/num-bigint/pull/123
[137]: https://github.com/rust-num/num-bigint/pull/137
[142]: https://github.com/rust-num/num-bigint/pull/142
[143]: https://github.com/rust-num/num-bigint/pull/143
[145]: https://github.com/rust-num/num-bigint/pull/145
# Release 0.2.6 (2020-01-27)
- [Fix the promotion of negative `isize` in `BigInt` assign-ops][133].
**Contributors**: @cuviper, @HactarCE
[133]: https://github.com/rust-num/num-bigint/pull/133
# Release 0.2.5 (2020-01-09)
- [Updated the `autocfg` build dependency to 1.0][126].
**Contributors**: @cuviper, @tspiteri
[126]: https://github.com/rust-num/num-bigint/pull/126
# Release 0.2.4 (2020-01-01)
- [The new `BigUint::to_u32_digits` method][104] returns the number as a
little-endian vector of base-2<sup>32</sup> digits. The same method on
`BigInt` also returns the sign.
- [`BigUint::modpow` now applies a modulus even for exponent 1][113], which
also affects `BigInt::modpow`.
- [`BigInt::modpow` now returns the correct sign for negative bases with even
exponents][114].
[104]: https://github.com/rust-num/num-bigint/pull/104
[113]: https://github.com/rust-num/num-bigint/pull/113
[114]: https://github.com/rust-num/num-bigint/pull/114
**Contributors**: @alex-ozdemir, @cuviper, @dingelish, @Speedy37, @youknowone
# Release 0.2.3 (2019-09-03)
- [`Pow` is now implemented for `BigUint` exponents][77].
- [The optional `quickcheck` feature enables implementations of `Arbitrary`][99].
- See the [full comparison][compare-0.2.3] for performance enhancements and more!
[77]: https://github.com/rust-num/num-bigint/pull/77
[99]: https://github.com/rust-num/num-bigint/pull/99
[compare-0.2.3]: https://github.com/rust-num/num-bigint/compare/num-bigint-0.2.2...num-bigint-0.2.3
**Contributors**: @cuviper, @lcnr, @maxbla, @mikelodder7, @mikong,
@TheLetterTheta, @tspiteri, @XAMPPRocky, @youknowone
# Release 0.2.2 (2018-12-14)
- [The `Roots` implementations now use better initial guesses][71].
- [Fixed `to_signed_bytes_*` for some positive numbers][72], where the
most-significant byte is `0x80` and the rest are `0`.
[71]: https://github.com/rust-num/num-bigint/pull/71
[72]: https://github.com/rust-num/num-bigint/pull/72
**Contributors**: @cuviper, @leodasvacas
# Release 0.2.1 (2018-11-02)
- [`RandBigInt` now uses `Rng::fill_bytes`][53] to improve performance, instead
of repeated `gen::<u32>` calls. The also affects the implementations of the
other `rand` traits. This may potentially change the values produced by some
seeded RNGs on previous versions, but the values were tested to be stable
with `ChaChaRng`, `IsaacRng`, and `XorShiftRng`.
- [`BigInt` and `BigUint` now implement `num_integer::Roots`][56].
- [`BigInt` and `BigUint` now implement `num_traits::Pow`][54].
- [`BigInt` and `BigUint` now implement operators with 128-bit integers][64].
**Contributors**: @cuviper, @dignifiedquire, @mancabizjak, @Robbepop,
@TheIronBorn, @thomwiggers
[53]: https://github.com/rust-num/num-bigint/pull/53
[54]: https://github.com/rust-num/num-bigint/pull/54
[56]: https://github.com/rust-num/num-bigint/pull/56
[64]: https://github.com/rust-num/num-bigint/pull/64
# Release 0.2.0 (2018-05-25)
### Enhancements
- [`BigInt` and `BigUint` now implement `Product` and `Sum`][22] for iterators
of any item that we can `Mul` and `Add`, respectively. For example, a
factorial can now be simply: `let f: BigUint = (1u32..1000).product();`
- [`BigInt` now supports two's-complement logic operations][26], namely
`BitAnd`, `BitOr`, `BitXor`, and `Not`. These act conceptually as if each
number had an infinite prefix of `0` or `1` bits for positive or negative.
- [`BigInt` now supports assignment operators][41] like `AddAssign`.
- [`BigInt` and `BigUint` now support conversions with `i128` and `u128`][44],
if sufficient compiler support is detected.
- [`BigInt` and `BigUint` now implement rand's `SampleUniform` trait][48], and
[a custom `RandomBits` distribution samples by bit size][49].
- The release also includes other miscellaneous improvements to performance.
### Breaking Changes
- [`num-bigint` now requires rustc 1.15 or greater][23].
- [The crate now has a `std` feature, and won't build without it][46]. This is
in preparation for someday supporting `#![no_std]` with `alloc`.
- [The `serde` dependency has been updated to 1.0][24], still disabled by
default. The `rustc-serialize` crate is no longer supported by `num-bigint`.
- [The `rand` dependency has been updated to 0.5][48], now disabled by default.
This requires rustc 1.22 or greater for `rand`'s own requirement.
- [`Shr for BigInt` now rounds down][8] rather than toward zero, matching the
behavior of the primitive integers for negative values.
- [`ParseBigIntError` is now an opaque type][37].
- [The `big_digit` module is no longer public][38], nor are the `BigDigit` and
`DoubleBigDigit` types and `ZERO_BIG_DIGIT` constant that were re-exported in
the crate root. Public APIs which deal in digits, like `BigUint::from_slice`,
will now always be base-`u32`.
**Contributors**: @clarcharr, @cuviper, @dodomorandi, @tiehuis, @tspiteri
[8]: https://github.com/rust-num/num-bigint/pull/8
[22]: https://github.com/rust-num/num-bigint/pull/22
[23]: https://github.com/rust-num/num-bigint/pull/23
[24]: https://github.com/rust-num/num-bigint/pull/24
[26]: https://github.com/rust-num/num-bigint/pull/26
[37]: https://github.com/rust-num/num-bigint/pull/37
[38]: https://github.com/rust-num/num-bigint/pull/38
[41]: https://github.com/rust-num/num-bigint/pull/41
[44]: https://github.com/rust-num/num-bigint/pull/44
[46]: https://github.com/rust-num/num-bigint/pull/46
[48]: https://github.com/rust-num/num-bigint/pull/48
[49]: https://github.com/rust-num/num-bigint/pull/49
# Release 0.1.44 (2018-05-14)
- [Division with single-digit divisors is now much faster.][42]
- The README now compares [`ramp`, `rug`, `rust-gmp`][20], and [`apint`][21].
**Contributors**: @cuviper, @Robbepop
[20]: https://github.com/rust-num/num-bigint/pull/20
[21]: https://github.com/rust-num/num-bigint/pull/21
[42]: https://github.com/rust-num/num-bigint/pull/42
# Release 0.1.43 (2018-02-08)
- [The new `BigInt::modpow`][18] performs signed modular exponentiation, using
the existing `BigUint::modpow` and rounding negatives similar to `mod_floor`.
**Contributors**: @cuviper
[18]: https://github.com/rust-num/num-bigint/pull/18
# Release 0.1.42 (2018-02-07)
- [num-bigint now has its own source repository][num-356] at [rust-num/num-bigint][home].
- [`lcm` now avoids creating a large intermediate product][num-350].
- [`gcd` now uses Stein's algorithm][15] with faster shifts instead of division.
- [`rand` support is now extended to 0.4][11] (while still allowing 0.3).
**Contributors**: @cuviper, @Emerentius, @ignatenkobrain, @mhogrefe
[home]: https://github.com/rust-num/num-bigint
[num-350]: https://github.com/rust-num/num/pull/350
[num-356]: https://github.com/rust-num/num/pull/356
[11]: https://github.com/rust-num/num-bigint/pull/11
[15]: https://github.com/rust-num/num-bigint/pull/15
# Prior releases
No prior release notes were kept. Thanks all the same to the many
contributors that have made this crate what it is!

450
vendor/num-bigint/benches/bigint.rs vendored Normal file
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@@ -0,0 +1,450 @@
#![feature(test)]
#![cfg(feature = "rand")]
extern crate test;
use num_bigint::{BigInt, BigUint, RandBigInt};
use num_traits::{FromPrimitive, Num, One, Zero};
use std::mem::replace;
use test::Bencher;
mod rng;
use rng::get_rng;
fn multiply_bench(b: &mut Bencher, xbits: u64, ybits: u64) {
let mut rng = get_rng();
let x = rng.gen_bigint(xbits);
let y = rng.gen_bigint(ybits);
b.iter(|| &x * &y);
}
fn divide_bench(b: &mut Bencher, xbits: u64, ybits: u64) {
let mut rng = get_rng();
let x = rng.gen_bigint(xbits);
let y = rng.gen_bigint(ybits);
b.iter(|| &x / &y);
}
fn remainder_bench(b: &mut Bencher, xbits: u64, ybits: u64) {
let mut rng = get_rng();
let x = rng.gen_bigint(xbits);
let y = rng.gen_bigint(ybits);
b.iter(|| &x % &y);
}
fn factorial(n: usize) -> BigUint {
let mut f: BigUint = One::one();
for i in 1..=n {
let bu: BigUint = FromPrimitive::from_usize(i).unwrap();
f *= bu;
}
f
}
/// Compute Fibonacci numbers
fn fib(n: usize) -> BigUint {
let mut f0: BigUint = Zero::zero();
let mut f1: BigUint = One::one();
for _ in 0..n {
let f2 = f0 + &f1;
f0 = replace(&mut f1, f2);
}
f0
}
/// Compute Fibonacci numbers with two ops per iteration
/// (add and subtract, like issue #200)
fn fib2(n: usize) -> BigUint {
let mut f0: BigUint = Zero::zero();
let mut f1: BigUint = One::one();
for _ in 0..n {
f1 += &f0;
f0 = &f1 - f0;
}
f0
}
#[bench]
fn multiply_0(b: &mut Bencher) {
multiply_bench(b, 1 << 8, 1 << 8);
}
#[bench]
fn multiply_1(b: &mut Bencher) {
multiply_bench(b, 1 << 8, 1 << 16);
}
#[bench]
fn multiply_2(b: &mut Bencher) {
multiply_bench(b, 1 << 16, 1 << 16);
}
#[bench]
fn multiply_3(b: &mut Bencher) {
multiply_bench(b, 1 << 16, 1 << 17);
}
#[bench]
fn multiply_4(b: &mut Bencher) {
multiply_bench(b, 1 << 12, 1 << 13);
}
#[bench]
fn multiply_5(b: &mut Bencher) {
multiply_bench(b, 1 << 12, 1 << 14);
}
#[bench]
fn divide_0(b: &mut Bencher) {
divide_bench(b, 1 << 8, 1 << 6);
}
#[bench]
fn divide_1(b: &mut Bencher) {
divide_bench(b, 1 << 12, 1 << 8);
}
#[bench]
fn divide_2(b: &mut Bencher) {
divide_bench(b, 1 << 16, 1 << 12);
}
#[bench]
fn divide_big_little(b: &mut Bencher) {
divide_bench(b, 1 << 16, 1 << 4);
}
#[bench]
fn remainder_0(b: &mut Bencher) {
remainder_bench(b, 1 << 8, 1 << 6);
}
#[bench]
fn remainder_1(b: &mut Bencher) {
remainder_bench(b, 1 << 12, 1 << 8);
}
#[bench]
fn remainder_2(b: &mut Bencher) {
remainder_bench(b, 1 << 16, 1 << 12);
}
#[bench]
fn remainder_big_little(b: &mut Bencher) {
remainder_bench(b, 1 << 16, 1 << 4);
}
#[bench]
fn factorial_100(b: &mut Bencher) {
b.iter(|| factorial(100));
}
#[bench]
fn fib_100(b: &mut Bencher) {
b.iter(|| fib(100));
}
#[bench]
fn fib_1000(b: &mut Bencher) {
b.iter(|| fib(1000));
}
#[bench]
fn fib_10000(b: &mut Bencher) {
b.iter(|| fib(10000));
}
#[bench]
fn fib2_100(b: &mut Bencher) {
b.iter(|| fib2(100));
}
#[bench]
fn fib2_1000(b: &mut Bencher) {
b.iter(|| fib2(1000));
}
#[bench]
fn fib2_10000(b: &mut Bencher) {
b.iter(|| fib2(10000));
}
#[bench]
fn fac_to_string(b: &mut Bencher) {
let fac = factorial(100);
b.iter(|| fac.to_string());
}
#[bench]
fn fib_to_string(b: &mut Bencher) {
let fib = fib(100);
b.iter(|| fib.to_string());
}
fn to_str_radix_bench(b: &mut Bencher, radix: u32, bits: u64) {
let mut rng = get_rng();
let x = rng.gen_bigint(bits);
b.iter(|| x.to_str_radix(radix));
}
#[bench]
fn to_str_radix_02(b: &mut Bencher) {
to_str_radix_bench(b, 2, 1009);
}
#[bench]
fn to_str_radix_08(b: &mut Bencher) {
to_str_radix_bench(b, 8, 1009);
}
#[bench]
fn to_str_radix_10(b: &mut Bencher) {
to_str_radix_bench(b, 10, 1009);
}
#[bench]
fn to_str_radix_10_2(b: &mut Bencher) {
to_str_radix_bench(b, 10, 10009);
}
#[bench]
fn to_str_radix_16(b: &mut Bencher) {
to_str_radix_bench(b, 16, 1009);
}
#[bench]
fn to_str_radix_36(b: &mut Bencher) {
to_str_radix_bench(b, 36, 1009);
}
fn from_str_radix_bench(b: &mut Bencher, radix: u32) {
let mut rng = get_rng();
let x = rng.gen_bigint(1009);
let s = x.to_str_radix(radix);
assert_eq!(x, BigInt::from_str_radix(&s, radix).unwrap());
b.iter(|| BigInt::from_str_radix(&s, radix));
}
#[bench]
fn from_str_radix_02(b: &mut Bencher) {
from_str_radix_bench(b, 2);
}
#[bench]
fn from_str_radix_08(b: &mut Bencher) {
from_str_radix_bench(b, 8);
}
#[bench]
fn from_str_radix_10(b: &mut Bencher) {
from_str_radix_bench(b, 10);
}
#[bench]
fn from_str_radix_16(b: &mut Bencher) {
from_str_radix_bench(b, 16);
}
#[bench]
fn from_str_radix_36(b: &mut Bencher) {
from_str_radix_bench(b, 36);
}
fn rand_bench(b: &mut Bencher, bits: u64) {
let mut rng = get_rng();
b.iter(|| rng.gen_bigint(bits));
}
#[bench]
fn rand_64(b: &mut Bencher) {
rand_bench(b, 1 << 6);
}
#[bench]
fn rand_256(b: &mut Bencher) {
rand_bench(b, 1 << 8);
}
#[bench]
fn rand_1009(b: &mut Bencher) {
rand_bench(b, 1009);
}
#[bench]
fn rand_2048(b: &mut Bencher) {
rand_bench(b, 1 << 11);
}
#[bench]
fn rand_4096(b: &mut Bencher) {
rand_bench(b, 1 << 12);
}
#[bench]
fn rand_8192(b: &mut Bencher) {
rand_bench(b, 1 << 13);
}
#[bench]
fn rand_65536(b: &mut Bencher) {
rand_bench(b, 1 << 16);
}
#[bench]
fn rand_131072(b: &mut Bencher) {
rand_bench(b, 1 << 17);
}
#[bench]
fn shl(b: &mut Bencher) {
let n = BigUint::one() << 1000u32;
let mut m = n.clone();
b.iter(|| {
m.clone_from(&n);
for i in 0..50 {
m <<= i;
}
})
}
#[bench]
fn shr(b: &mut Bencher) {
let n = BigUint::one() << 2000u32;
let mut m = n.clone();
b.iter(|| {
m.clone_from(&n);
for i in 0..50 {
m >>= i;
}
})
}
#[bench]
fn hash(b: &mut Bencher) {
use std::collections::HashSet;
let mut rng = get_rng();
let v: Vec<BigInt> = (1000..2000).map(|bits| rng.gen_bigint(bits)).collect();
b.iter(|| {
let h: HashSet<&BigInt> = v.iter().collect();
assert_eq!(h.len(), v.len());
});
}
#[bench]
fn pow_bench(b: &mut Bencher) {
b.iter(|| {
let upper = 100_u32;
let mut i_big = BigUint::from(1u32);
for _i in 2..=upper {
i_big += 1u32;
for j in 2..=upper {
i_big.pow(j);
}
}
});
}
#[bench]
fn pow_bench_bigexp(b: &mut Bencher) {
use num_traits::Pow;
b.iter(|| {
let upper = 100_u32;
let mut i_big = BigUint::from(1u32);
for _i in 2..=upper {
i_big += 1u32;
let mut j_big = BigUint::from(1u32);
for _j in 2..=upper {
j_big += 1u32;
Pow::pow(&i_big, &j_big);
}
}
});
}
#[bench]
fn pow_bench_1e1000(b: &mut Bencher) {
b.iter(|| BigUint::from(10u32).pow(1_000));
}
#[bench]
fn pow_bench_1e10000(b: &mut Bencher) {
b.iter(|| BigUint::from(10u32).pow(10_000));
}
#[bench]
fn pow_bench_1e100000(b: &mut Bencher) {
b.iter(|| BigUint::from(10u32).pow(100_000));
}
/// This modulus is the prime from the 2048-bit MODP DH group:
/// https://tools.ietf.org/html/rfc3526#section-3
const RFC3526_2048BIT_MODP_GROUP: &str = "\
FFFFFFFF_FFFFFFFF_C90FDAA2_2168C234_C4C6628B_80DC1CD1\
29024E08_8A67CC74_020BBEA6_3B139B22_514A0879_8E3404DD\
EF9519B3_CD3A431B_302B0A6D_F25F1437_4FE1356D_6D51C245\
E485B576_625E7EC6_F44C42E9_A637ED6B_0BFF5CB6_F406B7ED\
EE386BFB_5A899FA5_AE9F2411_7C4B1FE6_49286651_ECE45B3D\
C2007CB8_A163BF05_98DA4836_1C55D39A_69163FA8_FD24CF5F\
83655D23_DCA3AD96_1C62F356_208552BB_9ED52907_7096966D\
670C354E_4ABC9804_F1746C08_CA18217C_32905E46_2E36CE3B\
E39E772C_180E8603_9B2783A2_EC07A28F_B5C55DF0_6F4C52C9\
DE2BCBF6_95581718_3995497C_EA956AE5_15D22618_98FA0510\
15728E5A_8AACAA68_FFFFFFFF_FFFFFFFF";
#[bench]
fn modpow(b: &mut Bencher) {
let mut rng = get_rng();
let base = rng.gen_biguint(2048);
let e = rng.gen_biguint(2048);
let m = BigUint::from_str_radix(RFC3526_2048BIT_MODP_GROUP, 16).unwrap();
b.iter(|| base.modpow(&e, &m));
}
#[bench]
fn modpow_even(b: &mut Bencher) {
let mut rng = get_rng();
let base = rng.gen_biguint(2048);
let e = rng.gen_biguint(2048);
// Make the modulus even, so monty (base-2^32) doesn't apply.
let m = BigUint::from_str_radix(RFC3526_2048BIT_MODP_GROUP, 16).unwrap() - 1u32;
b.iter(|| base.modpow(&e, &m));
}
#[bench]
fn to_u32_digits(b: &mut Bencher) {
let mut rng = get_rng();
let n = rng.gen_biguint(2048);
b.iter(|| n.to_u32_digits());
}
#[bench]
fn iter_u32_digits(b: &mut Bencher) {
let mut rng = get_rng();
let n = rng.gen_biguint(2048);
b.iter(|| n.iter_u32_digits().max());
}
#[bench]
fn to_u64_digits(b: &mut Bencher) {
let mut rng = get_rng();
let n = rng.gen_biguint(2048);
b.iter(|| n.to_u64_digits());
}
#[bench]
fn iter_u64_digits(b: &mut Bencher) {
let mut rng = get_rng();
let n = rng.gen_biguint(2048);
b.iter(|| n.iter_u64_digits().max());
}

42
vendor/num-bigint/benches/factorial.rs vendored Normal file
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#![feature(test)]
extern crate test;
use num_bigint::BigUint;
use num_traits::One;
use std::ops::{Div, Mul};
use test::Bencher;
#[bench]
fn factorial_mul_biguint(b: &mut Bencher) {
b.iter(|| {
(1u32..1000)
.map(BigUint::from)
.fold(BigUint::one(), Mul::mul)
});
}
#[bench]
fn factorial_mul_u32(b: &mut Bencher) {
b.iter(|| (1u32..1000).fold(BigUint::one(), Mul::mul));
}
// The division test is inspired by this blog comparison:
// <https://tiehuis.github.io/big-integers-in-zig#division-test-single-limb>
#[bench]
fn factorial_div_biguint(b: &mut Bencher) {
let n: BigUint = (1u32..1000).fold(BigUint::one(), Mul::mul);
b.iter(|| {
(1u32..1000)
.rev()
.map(BigUint::from)
.fold(n.clone(), Div::div)
});
}
#[bench]
fn factorial_div_u32(b: &mut Bencher) {
let n: BigUint = (1u32..1000).fold(BigUint::one(), Mul::mul);
b.iter(|| (1u32..1000).rev().fold(n.clone(), Div::div));
}

76
vendor/num-bigint/benches/gcd.rs vendored Normal file
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#![feature(test)]
#![cfg(feature = "rand")]
extern crate test;
use num_bigint::{BigUint, RandBigInt};
use num_integer::Integer;
use num_traits::Zero;
use test::Bencher;
mod rng;
use rng::get_rng;
fn bench(b: &mut Bencher, bits: u64, gcd: fn(&BigUint, &BigUint) -> BigUint) {
let mut rng = get_rng();
let x = rng.gen_biguint(bits);
let y = rng.gen_biguint(bits);
assert_eq!(euclid(&x, &y), x.gcd(&y));
b.iter(|| gcd(&x, &y));
}
fn euclid(x: &BigUint, y: &BigUint) -> BigUint {
// Use Euclid's algorithm
let mut m = x.clone();
let mut n = y.clone();
while !m.is_zero() {
let temp = m;
m = n % &temp;
n = temp;
}
n
}
#[bench]
fn gcd_euclid_0064(b: &mut Bencher) {
bench(b, 64, euclid);
}
#[bench]
fn gcd_euclid_0256(b: &mut Bencher) {
bench(b, 256, euclid);
}
#[bench]
fn gcd_euclid_1024(b: &mut Bencher) {
bench(b, 1024, euclid);
}
#[bench]
fn gcd_euclid_4096(b: &mut Bencher) {
bench(b, 4096, euclid);
}
// Integer for BigUint now uses Stein for gcd
#[bench]
fn gcd_stein_0064(b: &mut Bencher) {
bench(b, 64, BigUint::gcd);
}
#[bench]
fn gcd_stein_0256(b: &mut Bencher) {
bench(b, 256, BigUint::gcd);
}
#[bench]
fn gcd_stein_1024(b: &mut Bencher) {
bench(b, 1024, BigUint::gcd);
}
#[bench]
fn gcd_stein_4096(b: &mut Bencher) {
bench(b, 4096, BigUint::gcd);
}

38
vendor/num-bigint/benches/rng/mod.rs vendored Normal file
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use rand::RngCore;
pub(crate) fn get_rng() -> impl RngCore {
XorShiftStar {
a: 0x0123_4567_89AB_CDEF,
}
}
/// Simple `Rng` for benchmarking without additional dependencies
struct XorShiftStar {
a: u64,
}
impl RngCore for XorShiftStar {
fn next_u32(&mut self) -> u32 {
self.next_u64() as u32
}
fn next_u64(&mut self) -> u64 {
// https://en.wikipedia.org/wiki/Xorshift#xorshift*
self.a ^= self.a >> 12;
self.a ^= self.a << 25;
self.a ^= self.a >> 27;
self.a.wrapping_mul(0x2545_F491_4F6C_DD1D)
}
fn fill_bytes(&mut self, dest: &mut [u8]) {
for chunk in dest.chunks_mut(8) {
let bytes = self.next_u64().to_le_bytes();
let slice = &bytes[..chunk.len()];
chunk.copy_from_slice(slice)
}
}
fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), rand::Error> {
Ok(self.fill_bytes(dest))
}
}

166
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#![feature(test)]
#![cfg(feature = "rand")]
extern crate test;
use num_bigint::{BigUint, RandBigInt};
use test::Bencher;
mod rng;
use rng::get_rng;
// The `big64` cases demonstrate the speed of cases where the value
// can be converted to a `u64` primitive for faster calculation.
//
// The `big1k` cases demonstrate those that can convert to `f64` for
// a better initial guess of the actual value.
//
// The `big2k` and `big4k` cases are too big for `f64`, and use a simpler guess.
fn check(x: &BigUint, n: u32) {
let root = x.nth_root(n);
if n == 2 {
assert_eq!(root, x.sqrt())
} else if n == 3 {
assert_eq!(root, x.cbrt())
}
let lo = root.pow(n);
assert!(lo <= *x);
assert_eq!(lo.nth_root(n), root);
assert_eq!((&lo - 1u32).nth_root(n), &root - 1u32);
let hi = (&root + 1u32).pow(n);
assert!(hi > *x);
assert_eq!(hi.nth_root(n), &root + 1u32);
assert_eq!((&hi - 1u32).nth_root(n), root);
}
fn bench_sqrt(b: &mut Bencher, bits: u64) {
let x = get_rng().gen_biguint(bits);
eprintln!("bench_sqrt({})", x);
check(&x, 2);
b.iter(|| x.sqrt());
}
#[bench]
fn big64_sqrt(b: &mut Bencher) {
bench_sqrt(b, 64);
}
#[bench]
fn big1k_sqrt(b: &mut Bencher) {
bench_sqrt(b, 1024);
}
#[bench]
fn big2k_sqrt(b: &mut Bencher) {
bench_sqrt(b, 2048);
}
#[bench]
fn big4k_sqrt(b: &mut Bencher) {
bench_sqrt(b, 4096);
}
fn bench_cbrt(b: &mut Bencher, bits: u64) {
let x = get_rng().gen_biguint(bits);
eprintln!("bench_cbrt({})", x);
check(&x, 3);
b.iter(|| x.cbrt());
}
#[bench]
fn big64_cbrt(b: &mut Bencher) {
bench_cbrt(b, 64);
}
#[bench]
fn big1k_cbrt(b: &mut Bencher) {
bench_cbrt(b, 1024);
}
#[bench]
fn big2k_cbrt(b: &mut Bencher) {
bench_cbrt(b, 2048);
}
#[bench]
fn big4k_cbrt(b: &mut Bencher) {
bench_cbrt(b, 4096);
}
fn bench_nth_root(b: &mut Bencher, bits: u64, n: u32) {
let x = get_rng().gen_biguint(bits);
eprintln!("bench_{}th_root({})", n, x);
check(&x, n);
b.iter(|| x.nth_root(n));
}
#[bench]
fn big64_nth_10(b: &mut Bencher) {
bench_nth_root(b, 64, 10);
}
#[bench]
fn big1k_nth_10(b: &mut Bencher) {
bench_nth_root(b, 1024, 10);
}
#[bench]
fn big1k_nth_100(b: &mut Bencher) {
bench_nth_root(b, 1024, 100);
}
#[bench]
fn big1k_nth_1000(b: &mut Bencher) {
bench_nth_root(b, 1024, 1000);
}
#[bench]
fn big1k_nth_10000(b: &mut Bencher) {
bench_nth_root(b, 1024, 10000);
}
#[bench]
fn big2k_nth_10(b: &mut Bencher) {
bench_nth_root(b, 2048, 10);
}
#[bench]
fn big2k_nth_100(b: &mut Bencher) {
bench_nth_root(b, 2048, 100);
}
#[bench]
fn big2k_nth_1000(b: &mut Bencher) {
bench_nth_root(b, 2048, 1000);
}
#[bench]
fn big2k_nth_10000(b: &mut Bencher) {
bench_nth_root(b, 2048, 10000);
}
#[bench]
fn big4k_nth_10(b: &mut Bencher) {
bench_nth_root(b, 4096, 10);
}
#[bench]
fn big4k_nth_100(b: &mut Bencher) {
bench_nth_root(b, 4096, 100);
}
#[bench]
fn big4k_nth_1000(b: &mut Bencher) {
bench_nth_root(b, 4096, 1000);
}
#[bench]
fn big4k_nth_10000(b: &mut Bencher) {
bench_nth_root(b, 4096, 10000);
}

138
vendor/num-bigint/benches/shootout-pidigits.rs vendored Normal file
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// The Computer Language Benchmarks Game
// http://benchmarksgame.alioth.debian.org/
//
// contributed by the Rust Project Developers
// Copyright (c) 2013-2014 The Rust Project Developers
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
// - Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// - Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in
// the documentation and/or other materials provided with the
// distribution.
//
// - Neither the name of "The Computer Language Benchmarks Game" nor
// the name of "The Computer Language Shootout Benchmarks" nor the
// names of its contributors may be used to endorse or promote
// products derived from this software without specific prior
// written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
// COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
// OF THE POSSIBILITY OF SUCH DAMAGE.
use std::io;
use std::str::FromStr;
use num_bigint::BigInt;
use num_integer::Integer;
use num_traits::{FromPrimitive, One, ToPrimitive, Zero};
struct Context {
numer: BigInt,
accum: BigInt,
denom: BigInt,
}
impl Context {
fn new() -> Context {
Context {
numer: One::one(),
accum: Zero::zero(),
denom: One::one(),
}
}
fn from_i32(i: i32) -> BigInt {
FromPrimitive::from_i32(i).unwrap()
}
fn extract_digit(&self) -> i32 {
if self.numer > self.accum {
return -1;
}
let (q, r) = (&self.numer * Context::from_i32(3) + &self.accum).div_rem(&self.denom);
if r + &self.numer >= self.denom {
return -1;
}
q.to_i32().unwrap()
}
fn next_term(&mut self, k: i32) {
let y2 = Context::from_i32(k * 2 + 1);
self.accum = (&self.accum + (&self.numer << 1)) * &y2;
self.numer = &self.numer * Context::from_i32(k);
self.denom = &self.denom * y2;
}
fn eliminate_digit(&mut self, d: i32) {
let d = Context::from_i32(d);
let ten = Context::from_i32(10);
self.accum = (&self.accum - &self.denom * d) * &ten;
self.numer = &self.numer * ten;
}
}
fn pidigits(n: isize, out: &mut dyn io::Write) -> io::Result<()> {
let mut k = 0;
let mut context = Context::new();
for i in 1..=n {
let mut d;
loop {
k += 1;
context.next_term(k);
d = context.extract_digit();
if d != -1 {
break;
}
}
write!(out, "{}", d)?;
if i % 10 == 0 {
writeln!(out, "\t:{}", i)?;
}
context.eliminate_digit(d);
}
let m = n % 10;
if m != 0 {
for _ in m..10 {
write!(out, " ")?;
}
writeln!(out, "\t:{}", n)?;
}
Ok(())
}
const DEFAULT_DIGITS: isize = 512;
fn main() {
let args = std::env::args().collect::<Vec<_>>();
let n = if args.len() < 2 {
DEFAULT_DIGITS
} else if args[1] == "--bench" {
return pidigits(DEFAULT_DIGITS, &mut std::io::sink()).unwrap();
} else {
FromStr::from_str(&args[1]).unwrap()
};
pidigits(n, &mut std::io::stdout()).unwrap();
}

1229
vendor/num-bigint/src/bigint.rs vendored Normal file
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239
vendor/num-bigint/src/bigint/addition.rs vendored Normal file
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@@ -0,0 +1,239 @@
use super::CheckedUnsignedAbs::{Negative, Positive};
use super::Sign::{Minus, NoSign, Plus};
use super::{BigInt, UnsignedAbs};
use crate::{IsizePromotion, UsizePromotion};
use core::cmp::Ordering::{Equal, Greater, Less};
use core::iter::Sum;
use core::mem;
use core::ops::{Add, AddAssign};
use num_traits::CheckedAdd;
// We want to forward to BigUint::add, but it's not clear how that will go until
// we compare both sign and magnitude. So we duplicate this body for every
// val/ref combination, deferring that decision to BigUint's own forwarding.
macro_rules! bigint_add {
($a:expr, $a_owned:expr, $a_data:expr, $b:expr, $b_owned:expr, $b_data:expr) => {
match ($a.sign, $b.sign) {
(_, NoSign) => $a_owned,
(NoSign, _) => $b_owned,
// same sign => keep the sign with the sum of magnitudes
(Plus, Plus) | (Minus, Minus) => BigInt::from_biguint($a.sign, $a_data + $b_data),
// opposite signs => keep the sign of the larger with the difference of magnitudes
(Plus, Minus) | (Minus, Plus) => match $a.data.cmp(&$b.data) {
Less => BigInt::from_biguint($b.sign, $b_data - $a_data),
Greater => BigInt::from_biguint($a.sign, $a_data - $b_data),
Equal => BigInt::ZERO,
},
}
};
}
impl Add<&BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: &BigInt) -> BigInt {
bigint_add!(
self,
self.clone(),
&self.data,
other,
other.clone(),
&other.data
)
}
}
impl Add<BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: BigInt) -> BigInt {
bigint_add!(self, self.clone(), &self.data, other, other, other.data)
}
}
impl Add<&BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: &BigInt) -> BigInt {
bigint_add!(self, self, self.data, other, other.clone(), &other.data)
}
}
impl Add<BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: BigInt) -> BigInt {
bigint_add!(self, self, self.data, other, other, other.data)
}
}
impl AddAssign<&BigInt> for BigInt {
#[inline]
fn add_assign(&mut self, other: &BigInt) {
let n = mem::replace(self, Self::ZERO);
*self = n + other;
}
}
forward_val_assign!(impl AddAssign for BigInt, add_assign);
promote_all_scalars!(impl Add for BigInt, add);
promote_all_scalars_assign!(impl AddAssign for BigInt, add_assign);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u32> for BigInt, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u64> for BigInt, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u128> for BigInt, add);
impl Add<u32> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: u32) -> BigInt {
match self.sign {
NoSign => From::from(other),
Plus => BigInt::from(self.data + other),
Minus => match self.data.cmp(&From::from(other)) {
Equal => Self::ZERO,
Less => BigInt::from(other - self.data),
Greater => -BigInt::from(self.data - other),
},
}
}
}
impl AddAssign<u32> for BigInt {
#[inline]
fn add_assign(&mut self, other: u32) {
let n = mem::replace(self, Self::ZERO);
*self = n + other;
}
}
impl Add<u64> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: u64) -> BigInt {
match self.sign {
NoSign => From::from(other),
Plus => BigInt::from(self.data + other),
Minus => match self.data.cmp(&From::from(other)) {
Equal => Self::ZERO,
Less => BigInt::from(other - self.data),
Greater => -BigInt::from(self.data - other),
},
}
}
}
impl AddAssign<u64> for BigInt {
#[inline]
fn add_assign(&mut self, other: u64) {
let n = mem::replace(self, Self::ZERO);
*self = n + other;
}
}
impl Add<u128> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: u128) -> BigInt {
match self.sign {
NoSign => BigInt::from(other),
Plus => BigInt::from(self.data + other),
Minus => match self.data.cmp(&From::from(other)) {
Equal => Self::ZERO,
Less => BigInt::from(other - self.data),
Greater => -BigInt::from(self.data - other),
},
}
}
}
impl AddAssign<u128> for BigInt {
#[inline]
fn add_assign(&mut self, other: u128) {
let n = mem::replace(self, Self::ZERO);
*self = n + other;
}
}
forward_all_scalar_binop_to_val_val_commutative!(impl Add<i32> for BigInt, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<i64> for BigInt, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<i128> for BigInt, add);
impl Add<i32> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: i32) -> BigInt {
match other.checked_uabs() {
Positive(u) => self + u,
Negative(u) => self - u,
}
}
}
impl AddAssign<i32> for BigInt {
#[inline]
fn add_assign(&mut self, other: i32) {
match other.checked_uabs() {
Positive(u) => *self += u,
Negative(u) => *self -= u,
}
}
}
impl Add<i64> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: i64) -> BigInt {
match other.checked_uabs() {
Positive(u) => self + u,
Negative(u) => self - u,
}
}
}
impl AddAssign<i64> for BigInt {
#[inline]
fn add_assign(&mut self, other: i64) {
match other.checked_uabs() {
Positive(u) => *self += u,
Negative(u) => *self -= u,
}
}
}
impl Add<i128> for BigInt {
type Output = BigInt;
#[inline]
fn add(self, other: i128) -> BigInt {
match other.checked_uabs() {
Positive(u) => self + u,
Negative(u) => self - u,
}
}
}
impl AddAssign<i128> for BigInt {
#[inline]
fn add_assign(&mut self, other: i128) {
match other.checked_uabs() {
Positive(u) => *self += u,
Negative(u) => *self -= u,
}
}
}
impl CheckedAdd for BigInt {
#[inline]
fn checked_add(&self, v: &BigInt) -> Option<BigInt> {
Some(self.add(v))
}
}
impl_sum_iter_type!(BigInt);

43
vendor/num-bigint/src/bigint/arbitrary.rs vendored Normal file
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#![cfg(any(feature = "quickcheck", feature = "arbitrary"))]
use super::{BigInt, Sign};
use crate::BigUint;
#[cfg(feature = "quickcheck")]
use alloc::boxed::Box;
#[cfg(feature = "quickcheck")]
#[cfg_attr(docsrs, doc(cfg(feature = "quickcheck")))]
impl quickcheck::Arbitrary for BigInt {
fn arbitrary(g: &mut quickcheck::Gen) -> Self {
let positive = bool::arbitrary(g);
let sign = if positive { Sign::Plus } else { Sign::Minus };
Self::from_biguint(sign, BigUint::arbitrary(g))
}
fn shrink(&self) -> Box<dyn Iterator<Item = Self>> {
let sign = self.sign();
let unsigned_shrink = self.data.shrink();
Box::new(unsigned_shrink.map(move |x| BigInt::from_biguint(sign, x)))
}
}
#[cfg(feature = "arbitrary")]
#[cfg_attr(docsrs, doc(cfg(feature = "arbitrary")))]
impl arbitrary::Arbitrary<'_> for BigInt {
fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
let positive = bool::arbitrary(u)?;
let sign = if positive { Sign::Plus } else { Sign::Minus };
Ok(Self::from_biguint(sign, BigUint::arbitrary(u)?))
}
fn arbitrary_take_rest(mut u: arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
let positive = bool::arbitrary(&mut u)?;
let sign = if positive { Sign::Plus } else { Sign::Minus };
Ok(Self::from_biguint(sign, BigUint::arbitrary_take_rest(u)?))
}
fn size_hint(depth: usize) -> (usize, Option<usize>) {
arbitrary::size_hint::and(bool::size_hint(depth), BigUint::size_hint(depth))
}
}

531
vendor/num-bigint/src/bigint/bits.rs vendored Normal file
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@@ -0,0 +1,531 @@
use super::BigInt;
use super::Sign::{Minus, NoSign, Plus};
use crate::big_digit::{self, BigDigit, DoubleBigDigit};
use crate::biguint::IntDigits;
use alloc::vec::Vec;
use core::cmp::Ordering::{Equal, Greater, Less};
use core::ops::{BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign};
use num_traits::{ToPrimitive, Zero};
// Negation in two's complement.
// acc must be initialized as 1 for least-significant digit.
//
// When negating, a carry (acc == 1) means that all the digits
// considered to this point were zero. This means that if all the
// digits of a negative BigInt have been considered, carry must be
// zero as we cannot have negative zero.
//
// 01 -> ...f ff
// ff -> ...f 01
// 01 00 -> ...f ff 00
// 01 01 -> ...f fe ff
// 01 ff -> ...f fe 01
// ff 00 -> ...f 01 00
// ff 01 -> ...f 00 ff
// ff ff -> ...f 00 01
#[inline]
fn negate_carry(a: BigDigit, acc: &mut DoubleBigDigit) -> BigDigit {
*acc += DoubleBigDigit::from(!a);
let lo = *acc as BigDigit;
*acc >>= big_digit::BITS;
lo
}
// + 1 & -ff = ...0 01 & ...f 01 = ...0 01 = + 1
// +ff & - 1 = ...0 ff & ...f ff = ...0 ff = +ff
// answer is pos, has length of a
fn bitand_pos_neg(a: &mut [BigDigit], b: &[BigDigit]) {
let mut carry_b = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_b = negate_carry(bi, &mut carry_b);
*ai &= twos_b;
}
debug_assert!(b.len() > a.len() || carry_b == 0);
}
// - 1 & +ff = ...f ff & ...0 ff = ...0 ff = +ff
// -ff & + 1 = ...f 01 & ...0 01 = ...0 01 = + 1
// answer is pos, has length of b
fn bitand_neg_pos(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_a = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_a = negate_carry(*ai, &mut carry_a);
*ai = twos_a & bi;
}
debug_assert!(a.len() > b.len() || carry_a == 0);
match Ord::cmp(&a.len(), &b.len()) {
Greater => a.truncate(b.len()),
Equal => {}
Less => {
let extra = &b[a.len()..];
a.extend(extra.iter().cloned());
}
}
}
// - 1 & -ff = ...f ff & ...f 01 = ...f 01 = - ff
// -ff & - 1 = ...f 01 & ...f ff = ...f 01 = - ff
// -ff & -fe = ...f 01 & ...f 02 = ...f 00 = -100
// answer is neg, has length of longest with a possible carry
fn bitand_neg_neg(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_a = 1;
let mut carry_b = 1;
let mut carry_and = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_a = negate_carry(*ai, &mut carry_a);
let twos_b = negate_carry(bi, &mut carry_b);
*ai = negate_carry(twos_a & twos_b, &mut carry_and);
}
debug_assert!(a.len() > b.len() || carry_a == 0);
debug_assert!(b.len() > a.len() || carry_b == 0);
match Ord::cmp(&a.len(), &b.len()) {
Greater => {
for ai in a[b.len()..].iter_mut() {
let twos_a = negate_carry(*ai, &mut carry_a);
*ai = negate_carry(twos_a, &mut carry_and);
}
debug_assert!(carry_a == 0);
}
Equal => {}
Less => {
let extra = &b[a.len()..];
a.extend(extra.iter().map(|&bi| {
let twos_b = negate_carry(bi, &mut carry_b);
negate_carry(twos_b, &mut carry_and)
}));
debug_assert!(carry_b == 0);
}
}
if carry_and != 0 {
a.push(1);
}
}
forward_val_val_binop!(impl BitAnd for BigInt, bitand);
forward_ref_val_binop!(impl BitAnd for BigInt, bitand);
// do not use forward_ref_ref_binop_commutative! for bitand so that we can
// clone as needed, avoiding over-allocation
impl BitAnd<&BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn bitand(self, other: &BigInt) -> BigInt {
match (self.sign, other.sign) {
(NoSign, _) | (_, NoSign) => BigInt::ZERO,
(Plus, Plus) => BigInt::from(&self.data & &other.data),
(Plus, Minus) => self.clone() & other,
(Minus, Plus) => other.clone() & self,
(Minus, Minus) => {
// forward to val-ref, choosing the larger to clone
if self.len() >= other.len() {
self.clone() & other
} else {
other.clone() & self
}
}
}
}
}
impl BitAnd<&BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn bitand(mut self, other: &BigInt) -> BigInt {
self &= other;
self
}
}
forward_val_assign!(impl BitAndAssign for BigInt, bitand_assign);
impl BitAndAssign<&BigInt> for BigInt {
fn bitand_assign(&mut self, other: &BigInt) {
match (self.sign, other.sign) {
(NoSign, _) => {}
(_, NoSign) => self.set_zero(),
(Plus, Plus) => {
self.data &= &other.data;
if self.data.is_zero() {
self.sign = NoSign;
}
}
(Plus, Minus) => {
bitand_pos_neg(self.digits_mut(), other.digits());
self.normalize();
}
(Minus, Plus) => {
bitand_neg_pos(self.digits_mut(), other.digits());
self.sign = Plus;
self.normalize();
}
(Minus, Minus) => {
bitand_neg_neg(self.digits_mut(), other.digits());
self.normalize();
}
}
}
}
// + 1 | -ff = ...0 01 | ...f 01 = ...f 01 = -ff
// +ff | - 1 = ...0 ff | ...f ff = ...f ff = - 1
// answer is neg, has length of b
fn bitor_pos_neg(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_b = 1;
let mut carry_or = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_b = negate_carry(bi, &mut carry_b);
*ai = negate_carry(*ai | twos_b, &mut carry_or);
}
debug_assert!(b.len() > a.len() || carry_b == 0);
match Ord::cmp(&a.len(), &b.len()) {
Greater => {
a.truncate(b.len());
}
Equal => {}
Less => {
let extra = &b[a.len()..];
a.extend(extra.iter().map(|&bi| {
let twos_b = negate_carry(bi, &mut carry_b);
negate_carry(twos_b, &mut carry_or)
}));
debug_assert!(carry_b == 0);
}
}
// for carry_or to be non-zero, we would need twos_b == 0
debug_assert!(carry_or == 0);
}
// - 1 | +ff = ...f ff | ...0 ff = ...f ff = - 1
// -ff | + 1 = ...f 01 | ...0 01 = ...f 01 = -ff
// answer is neg, has length of a
fn bitor_neg_pos(a: &mut [BigDigit], b: &[BigDigit]) {
let mut carry_a = 1;
let mut carry_or = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_a = negate_carry(*ai, &mut carry_a);
*ai = negate_carry(twos_a | bi, &mut carry_or);
}
debug_assert!(a.len() > b.len() || carry_a == 0);
if a.len() > b.len() {
for ai in a[b.len()..].iter_mut() {
let twos_a = negate_carry(*ai, &mut carry_a);
*ai = negate_carry(twos_a, &mut carry_or);
}
debug_assert!(carry_a == 0);
}
// for carry_or to be non-zero, we would need twos_a == 0
debug_assert!(carry_or == 0);
}
// - 1 | -ff = ...f ff | ...f 01 = ...f ff = -1
// -ff | - 1 = ...f 01 | ...f ff = ...f ff = -1
// answer is neg, has length of shortest
fn bitor_neg_neg(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_a = 1;
let mut carry_b = 1;
let mut carry_or = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_a = negate_carry(*ai, &mut carry_a);
let twos_b = negate_carry(bi, &mut carry_b);
*ai = negate_carry(twos_a | twos_b, &mut carry_or);
}
debug_assert!(a.len() > b.len() || carry_a == 0);
debug_assert!(b.len() > a.len() || carry_b == 0);
if a.len() > b.len() {
a.truncate(b.len());
}
// for carry_or to be non-zero, we would need twos_a == 0 or twos_b == 0
debug_assert!(carry_or == 0);
}
forward_val_val_binop!(impl BitOr for BigInt, bitor);
forward_ref_val_binop!(impl BitOr for BigInt, bitor);
// do not use forward_ref_ref_binop_commutative! for bitor so that we can
// clone as needed, avoiding over-allocation
impl BitOr<&BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn bitor(self, other: &BigInt) -> BigInt {
match (self.sign, other.sign) {
(NoSign, _) => other.clone(),
(_, NoSign) => self.clone(),
(Plus, Plus) => BigInt::from(&self.data | &other.data),
(Plus, Minus) => other.clone() | self,
(Minus, Plus) => self.clone() | other,
(Minus, Minus) => {
// forward to val-ref, choosing the smaller to clone
if self.len() <= other.len() {
self.clone() | other
} else {
other.clone() | self
}
}
}
}
}
impl BitOr<&BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn bitor(mut self, other: &BigInt) -> BigInt {
self |= other;
self
}
}
forward_val_assign!(impl BitOrAssign for BigInt, bitor_assign);
impl BitOrAssign<&BigInt> for BigInt {
fn bitor_assign(&mut self, other: &BigInt) {
match (self.sign, other.sign) {
(_, NoSign) => {}
(NoSign, _) => self.clone_from(other),
(Plus, Plus) => self.data |= &other.data,
(Plus, Minus) => {
bitor_pos_neg(self.digits_mut(), other.digits());
self.sign = Minus;
self.normalize();
}
(Minus, Plus) => {
bitor_neg_pos(self.digits_mut(), other.digits());
self.normalize();
}
(Minus, Minus) => {
bitor_neg_neg(self.digits_mut(), other.digits());
self.normalize();
}
}
}
}
// + 1 ^ -ff = ...0 01 ^ ...f 01 = ...f 00 = -100
// +ff ^ - 1 = ...0 ff ^ ...f ff = ...f 00 = -100
// answer is neg, has length of longest with a possible carry
fn bitxor_pos_neg(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_b = 1;
let mut carry_xor = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_b = negate_carry(bi, &mut carry_b);
*ai = negate_carry(*ai ^ twos_b, &mut carry_xor);
}
debug_assert!(b.len() > a.len() || carry_b == 0);
match Ord::cmp(&a.len(), &b.len()) {
Greater => {
for ai in a[b.len()..].iter_mut() {
let twos_b = !0;
*ai = negate_carry(*ai ^ twos_b, &mut carry_xor);
}
}
Equal => {}
Less => {
let extra = &b[a.len()..];
a.extend(extra.iter().map(|&bi| {
let twos_b = negate_carry(bi, &mut carry_b);
negate_carry(twos_b, &mut carry_xor)
}));
debug_assert!(carry_b == 0);
}
}
if carry_xor != 0 {
a.push(1);
}
}
// - 1 ^ +ff = ...f ff ^ ...0 ff = ...f 00 = -100
// -ff ^ + 1 = ...f 01 ^ ...0 01 = ...f 00 = -100
// answer is neg, has length of longest with a possible carry
fn bitxor_neg_pos(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_a = 1;
let mut carry_xor = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_a = negate_carry(*ai, &mut carry_a);
*ai = negate_carry(twos_a ^ bi, &mut carry_xor);
}
debug_assert!(a.len() > b.len() || carry_a == 0);
match Ord::cmp(&a.len(), &b.len()) {
Greater => {
for ai in a[b.len()..].iter_mut() {
let twos_a = negate_carry(*ai, &mut carry_a);
*ai = negate_carry(twos_a, &mut carry_xor);
}
debug_assert!(carry_a == 0);
}
Equal => {}
Less => {
let extra = &b[a.len()..];
a.extend(extra.iter().map(|&bi| {
let twos_a = !0;
negate_carry(twos_a ^ bi, &mut carry_xor)
}));
}
}
if carry_xor != 0 {
a.push(1);
}
}
// - 1 ^ -ff = ...f ff ^ ...f 01 = ...0 fe = +fe
// -ff & - 1 = ...f 01 ^ ...f ff = ...0 fe = +fe
// answer is pos, has length of longest
fn bitxor_neg_neg(a: &mut Vec<BigDigit>, b: &[BigDigit]) {
let mut carry_a = 1;
let mut carry_b = 1;
for (ai, &bi) in a.iter_mut().zip(b.iter()) {
let twos_a = negate_carry(*ai, &mut carry_a);
let twos_b = negate_carry(bi, &mut carry_b);
*ai = twos_a ^ twos_b;
}
debug_assert!(a.len() > b.len() || carry_a == 0);
debug_assert!(b.len() > a.len() || carry_b == 0);
match Ord::cmp(&a.len(), &b.len()) {
Greater => {
for ai in a[b.len()..].iter_mut() {
let twos_a = negate_carry(*ai, &mut carry_a);
let twos_b = !0;
*ai = twos_a ^ twos_b;
}
debug_assert!(carry_a == 0);
}
Equal => {}
Less => {
let extra = &b[a.len()..];
a.extend(extra.iter().map(|&bi| {
let twos_a = !0;
let twos_b = negate_carry(bi, &mut carry_b);
twos_a ^ twos_b
}));
debug_assert!(carry_b == 0);
}
}
}
forward_all_binop_to_val_ref_commutative!(impl BitXor for BigInt, bitxor);
impl BitXor<&BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn bitxor(mut self, other: &BigInt) -> BigInt {
self ^= other;
self
}
}
forward_val_assign!(impl BitXorAssign for BigInt, bitxor_assign);
impl BitXorAssign<&BigInt> for BigInt {
fn bitxor_assign(&mut self, other: &BigInt) {
match (self.sign, other.sign) {
(_, NoSign) => {}
(NoSign, _) => self.clone_from(other),
(Plus, Plus) => {
self.data ^= &other.data;
if self.data.is_zero() {
self.sign = NoSign;
}
}
(Plus, Minus) => {
bitxor_pos_neg(self.digits_mut(), other.digits());
self.sign = Minus;
self.normalize();
}
(Minus, Plus) => {
bitxor_neg_pos(self.digits_mut(), other.digits());
self.normalize();
}
(Minus, Minus) => {
bitxor_neg_neg(self.digits_mut(), other.digits());
self.sign = Plus;
self.normalize();
}
}
}
}
pub(super) fn set_negative_bit(x: &mut BigInt, bit: u64, value: bool) {
debug_assert_eq!(x.sign, Minus);
let data = &mut x.data;
let bits_per_digit = u64::from(big_digit::BITS);
if bit >= bits_per_digit * data.len() as u64 {
if !value {
data.set_bit(bit, true);
}
} else {
// If the Uint number is
// ... 0 x 1 0 ... 0
// then the two's complement is
// ... 1 !x 1 0 ... 0
// |-- bit at position 'trailing_zeros'
// where !x is obtained from x by flipping each bit
let trailing_zeros = data.trailing_zeros().unwrap();
if bit > trailing_zeros {
data.set_bit(bit, !value);
} else if bit == trailing_zeros && !value {
// Clearing the bit at position `trailing_zeros` is dealt with by doing
// similarly to what `bitand_neg_pos` does, except we start at digit
// `bit_index`. All digits below `bit_index` are guaranteed to be zero,
// so initially we have `carry_in` = `carry_out` = 1. Furthermore, we
// stop traversing the digits when there are no more carries.
let bit_index = (bit / bits_per_digit).to_usize().unwrap();
let bit_mask = (1 as BigDigit) << (bit % bits_per_digit);
let mut digit_iter = data.digits_mut().iter_mut().skip(bit_index);
let mut carry_in = 1;
let mut carry_out = 1;
let digit = digit_iter.next().unwrap();
let twos_in = negate_carry(*digit, &mut carry_in);
let twos_out = twos_in & !bit_mask;
*digit = negate_carry(twos_out, &mut carry_out);
for digit in digit_iter {
if carry_in == 0 && carry_out == 0 {
// Exit the loop since no more digits can change
break;
}
let twos = negate_carry(*digit, &mut carry_in);
*digit = negate_carry(twos, &mut carry_out);
}
if carry_out != 0 {
// All digits have been traversed and there is a carry
debug_assert_eq!(carry_in, 0);
data.digits_mut().push(1);
}
} else if bit < trailing_zeros && value {
// Flip each bit from position 'bit' to 'trailing_zeros', both inclusive
// ... 1 !x 1 0 ... 0 ... 0
// |-- bit at position 'bit'
// |-- bit at position 'trailing_zeros'
// bit_mask: 1 1 ... 1 0 .. 0
// This is done by xor'ing with the bit_mask
let index_lo = (bit / bits_per_digit).to_usize().unwrap();
let index_hi = (trailing_zeros / bits_per_digit).to_usize().unwrap();
let bit_mask_lo = big_digit::MAX << (bit % bits_per_digit);
let bit_mask_hi =
big_digit::MAX >> (bits_per_digit - 1 - (trailing_zeros % bits_per_digit));
let digits = data.digits_mut();
if index_lo == index_hi {
digits[index_lo] ^= bit_mask_lo & bit_mask_hi;
} else {
digits[index_lo] = bit_mask_lo;
for digit in &mut digits[index_lo + 1..index_hi] {
*digit = big_digit::MAX;
}
digits[index_hi] ^= bit_mask_hi;
}
} else {
// We end up here in two cases:
// bit == trailing_zeros && value: Bit is already set
// bit < trailing_zeros && !value: Bit is already cleared
}
}
}

472
vendor/num-bigint/src/bigint/convert.rs vendored Normal file
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@@ -0,0 +1,472 @@
use super::Sign::{self, Minus, NoSign, Plus};
use super::{BigInt, ToBigInt};
use crate::TryFromBigIntError;
use crate::{BigUint, ParseBigIntError, ToBigUint};
use alloc::vec::Vec;
use core::cmp::Ordering::{Equal, Greater, Less};
use core::convert::TryFrom;
use core::str::{self, FromStr};
use num_traits::{FromPrimitive, Num, One, ToPrimitive, Zero};
impl FromStr for BigInt {
type Err = ParseBigIntError;
#[inline]
fn from_str(s: &str) -> Result<BigInt, ParseBigIntError> {
BigInt::from_str_radix(s, 10)
}
}
impl Num for BigInt {
type FromStrRadixErr = ParseBigIntError;
/// Creates and initializes a [`BigInt`].
#[inline]
fn from_str_radix(mut s: &str, radix: u32) -> Result<BigInt, ParseBigIntError> {
let sign = if let Some(tail) = s.strip_prefix('-') {
if !tail.starts_with('+') {
s = tail
}
Minus
} else {
Plus
};
let bu = BigUint::from_str_radix(s, radix)?;
Ok(BigInt::from_biguint(sign, bu))
}
}
impl ToPrimitive for BigInt {
#[inline]
fn to_i64(&self) -> Option<i64> {
match self.sign {
Plus => self.data.to_i64(),
NoSign => Some(0),
Minus => {
let n = self.data.to_u64()?;
let m: u64 = 1 << 63;
match n.cmp(&m) {
Less => Some(-(n as i64)),
Equal => Some(i64::MIN),
Greater => None,
}
}
}
}
#[inline]
fn to_i128(&self) -> Option<i128> {
match self.sign {
Plus => self.data.to_i128(),
NoSign => Some(0),
Minus => {
let n = self.data.to_u128()?;
let m: u128 = 1 << 127;
match n.cmp(&m) {
Less => Some(-(n as i128)),
Equal => Some(i128::MIN),
Greater => None,
}
}
}
}
#[inline]
fn to_u64(&self) -> Option<u64> {
match self.sign {
Plus => self.data.to_u64(),
NoSign => Some(0),
Minus => None,
}
}
#[inline]
fn to_u128(&self) -> Option<u128> {
match self.sign {
Plus => self.data.to_u128(),
NoSign => Some(0),
Minus => None,
}
}
#[inline]
fn to_f32(&self) -> Option<f32> {
let n = self.data.to_f32()?;
Some(if self.sign == Minus { -n } else { n })
}
#[inline]
fn to_f64(&self) -> Option<f64> {
let n = self.data.to_f64()?;
Some(if self.sign == Minus { -n } else { n })
}
}
macro_rules! impl_try_from_bigint {
($T:ty, $to_ty:path) => {
impl TryFrom<&BigInt> for $T {
type Error = TryFromBigIntError<()>;
#[inline]
fn try_from(value: &BigInt) -> Result<$T, TryFromBigIntError<()>> {
$to_ty(value).ok_or(TryFromBigIntError::new(()))
}
}
impl TryFrom<BigInt> for $T {
type Error = TryFromBigIntError<BigInt>;
#[inline]
fn try_from(value: BigInt) -> Result<$T, TryFromBigIntError<BigInt>> {
<$T>::try_from(&value).map_err(|_| TryFromBigIntError::new(value))
}
}
};
}
impl_try_from_bigint!(u8, ToPrimitive::to_u8);
impl_try_from_bigint!(u16, ToPrimitive::to_u16);
impl_try_from_bigint!(u32, ToPrimitive::to_u32);
impl_try_from_bigint!(u64, ToPrimitive::to_u64);
impl_try_from_bigint!(usize, ToPrimitive::to_usize);
impl_try_from_bigint!(u128, ToPrimitive::to_u128);
impl_try_from_bigint!(i8, ToPrimitive::to_i8);
impl_try_from_bigint!(i16, ToPrimitive::to_i16);
impl_try_from_bigint!(i32, ToPrimitive::to_i32);
impl_try_from_bigint!(i64, ToPrimitive::to_i64);
impl_try_from_bigint!(isize, ToPrimitive::to_isize);
impl_try_from_bigint!(i128, ToPrimitive::to_i128);
impl FromPrimitive for BigInt {
#[inline]
fn from_i64(n: i64) -> Option<BigInt> {
Some(BigInt::from(n))
}
#[inline]
fn from_i128(n: i128) -> Option<BigInt> {
Some(BigInt::from(n))
}
#[inline]
fn from_u64(n: u64) -> Option<BigInt> {
Some(BigInt::from(n))
}
#[inline]
fn from_u128(n: u128) -> Option<BigInt> {
Some(BigInt::from(n))
}
#[inline]
fn from_f64(n: f64) -> Option<BigInt> {
if n >= 0.0 {
BigUint::from_f64(n).map(BigInt::from)
} else {
let x = BigUint::from_f64(-n)?;
Some(-BigInt::from(x))
}
}
}
impl From<i64> for BigInt {
#[inline]
fn from(n: i64) -> Self {
if n >= 0 {
BigInt::from(n as u64)
} else {
let u = u64::MAX - (n as u64) + 1;
BigInt {
sign: Minus,
data: BigUint::from(u),
}
}
}
}
impl From<i128> for BigInt {
#[inline]
fn from(n: i128) -> Self {
if n >= 0 {
BigInt::from(n as u128)
} else {
let u = u128::MAX - (n as u128) + 1;
BigInt {
sign: Minus,
data: BigUint::from(u),
}
}
}
}
macro_rules! impl_bigint_from_int {
($T:ty) => {
impl From<$T> for BigInt {
#[inline]
fn from(n: $T) -> Self {
BigInt::from(n as i64)
}
}
};
}
impl_bigint_from_int!(i8);
impl_bigint_from_int!(i16);
impl_bigint_from_int!(i32);
impl_bigint_from_int!(isize);
impl From<u64> for BigInt {
#[inline]
fn from(n: u64) -> Self {
if n > 0 {
BigInt {
sign: Plus,
data: BigUint::from(n),
}
} else {
Self::ZERO
}
}
}
impl From<u128> for BigInt {
#[inline]
fn from(n: u128) -> Self {
if n > 0 {
BigInt {
sign: Plus,
data: BigUint::from(n),
}
} else {
Self::ZERO
}
}
}
macro_rules! impl_bigint_from_uint {
($T:ty) => {
impl From<$T> for BigInt {
#[inline]
fn from(n: $T) -> Self {
BigInt::from(n as u64)
}
}
};
}
impl_bigint_from_uint!(u8);
impl_bigint_from_uint!(u16);
impl_bigint_from_uint!(u32);
impl_bigint_from_uint!(usize);
impl From<BigUint> for BigInt {
#[inline]
fn from(n: BigUint) -> Self {
if n.is_zero() {
Self::ZERO
} else {
BigInt {
sign: Plus,
data: n,
}
}
}
}
impl ToBigInt for BigInt {
#[inline]
fn to_bigint(&self) -> Option<BigInt> {
Some(self.clone())
}
}
impl ToBigInt for BigUint {
#[inline]
fn to_bigint(&self) -> Option<BigInt> {
if self.is_zero() {
Some(BigInt::ZERO)
} else {
Some(BigInt {
sign: Plus,
data: self.clone(),
})
}
}
}
impl ToBigUint for BigInt {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
match self.sign() {
Plus => Some(self.data.clone()),
NoSign => Some(BigUint::ZERO),
Minus => None,
}
}
}
impl TryFrom<&BigInt> for BigUint {
type Error = TryFromBigIntError<()>;
#[inline]
fn try_from(value: &BigInt) -> Result<BigUint, TryFromBigIntError<()>> {
value
.to_biguint()
.ok_or_else(|| TryFromBigIntError::new(()))
}
}
impl TryFrom<BigInt> for BigUint {
type Error = TryFromBigIntError<BigInt>;
#[inline]
fn try_from(value: BigInt) -> Result<BigUint, TryFromBigIntError<BigInt>> {
if value.sign() == Sign::Minus {
Err(TryFromBigIntError::new(value))
} else {
Ok(value.data)
}
}
}
macro_rules! impl_to_bigint {
($T:ty, $from_ty:path) => {
impl ToBigInt for $T {
#[inline]
fn to_bigint(&self) -> Option<BigInt> {
$from_ty(*self)
}
}
};
}
impl_to_bigint!(isize, FromPrimitive::from_isize);
impl_to_bigint!(i8, FromPrimitive::from_i8);
impl_to_bigint!(i16, FromPrimitive::from_i16);
impl_to_bigint!(i32, FromPrimitive::from_i32);
impl_to_bigint!(i64, FromPrimitive::from_i64);
impl_to_bigint!(i128, FromPrimitive::from_i128);
impl_to_bigint!(usize, FromPrimitive::from_usize);
impl_to_bigint!(u8, FromPrimitive::from_u8);
impl_to_bigint!(u16, FromPrimitive::from_u16);
impl_to_bigint!(u32, FromPrimitive::from_u32);
impl_to_bigint!(u64, FromPrimitive::from_u64);
impl_to_bigint!(u128, FromPrimitive::from_u128);
impl_to_bigint!(f32, FromPrimitive::from_f32);
impl_to_bigint!(f64, FromPrimitive::from_f64);
impl From<bool> for BigInt {
fn from(x: bool) -> Self {
if x {
One::one()
} else {
Self::ZERO
}
}
}
#[inline]
pub(super) fn from_signed_bytes_be(digits: &[u8]) -> BigInt {
let sign = match digits.first() {
Some(v) if *v > 0x7f => Sign::Minus,
Some(_) => Sign::Plus,
None => return BigInt::ZERO,
};
if sign == Sign::Minus {
// two's-complement the content to retrieve the magnitude
let mut digits = Vec::from(digits);
twos_complement_be(&mut digits);
BigInt::from_biguint(sign, BigUint::from_bytes_be(&digits))
} else {
BigInt::from_biguint(sign, BigUint::from_bytes_be(digits))
}
}
#[inline]
pub(super) fn from_signed_bytes_le(digits: &[u8]) -> BigInt {
let sign = match digits.last() {
Some(v) if *v > 0x7f => Sign::Minus,
Some(_) => Sign::Plus,
None => return BigInt::ZERO,
};
if sign == Sign::Minus {
// two's-complement the content to retrieve the magnitude
let mut digits = Vec::from(digits);
twos_complement_le(&mut digits);
BigInt::from_biguint(sign, BigUint::from_bytes_le(&digits))
} else {
BigInt::from_biguint(sign, BigUint::from_bytes_le(digits))
}
}
#[inline]
pub(super) fn to_signed_bytes_be(x: &BigInt) -> Vec<u8> {
let mut bytes = x.data.to_bytes_be();
let first_byte = bytes.first().cloned().unwrap_or(0);
if first_byte > 0x7f
&& !(first_byte == 0x80 && bytes.iter().skip(1).all(Zero::is_zero) && x.sign == Sign::Minus)
{
// msb used by magnitude, extend by 1 byte
bytes.insert(0, 0);
}
if x.sign == Sign::Minus {
twos_complement_be(&mut bytes);
}
bytes
}
#[inline]
pub(super) fn to_signed_bytes_le(x: &BigInt) -> Vec<u8> {
let mut bytes = x.data.to_bytes_le();
let last_byte = bytes.last().cloned().unwrap_or(0);
if last_byte > 0x7f
&& !(last_byte == 0x80
&& bytes.iter().rev().skip(1).all(Zero::is_zero)
&& x.sign == Sign::Minus)
{
// msb used by magnitude, extend by 1 byte
bytes.push(0);
}
if x.sign == Sign::Minus {
twos_complement_le(&mut bytes);
}
bytes
}
/// Perform in-place two's complement of the given binary representation,
/// in little-endian byte order.
#[inline]
fn twos_complement_le(digits: &mut [u8]) {
twos_complement(digits)
}
/// Perform in-place two's complement of the given binary representation
/// in big-endian byte order.
#[inline]
fn twos_complement_be(digits: &mut [u8]) {
twos_complement(digits.iter_mut().rev())
}
/// Perform in-place two's complement of the given digit iterator
/// starting from the least significant byte.
#[inline]
fn twos_complement<'a, I>(digits: I)
where
I: IntoIterator<Item = &'a mut u8>,
{
let mut carry = true;
for d in digits {
*d = !*d;
if carry {
*d = d.wrapping_add(1);
carry = d.is_zero();
}
}
}

513
vendor/num-bigint/src/bigint/division.rs vendored Normal file
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@@ -0,0 +1,513 @@
use super::CheckedUnsignedAbs::{Negative, Positive};
use super::Sign::NoSign;
use super::{BigInt, UnsignedAbs};
use crate::{IsizePromotion, UsizePromotion};
use core::ops::{Div, DivAssign, Rem, RemAssign};
use num_integer::Integer;
use num_traits::{CheckedDiv, CheckedEuclid, Euclid, Signed, ToPrimitive, Zero};
forward_all_binop_to_ref_ref!(impl Div for BigInt, div);
impl Div<&BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: &BigInt) -> BigInt {
let (q, _) = self.div_rem(other);
q
}
}
impl DivAssign<&BigInt> for BigInt {
#[inline]
fn div_assign(&mut self, other: &BigInt) {
*self = &*self / other;
}
}
forward_val_assign!(impl DivAssign for BigInt, div_assign);
promote_all_scalars!(impl Div for BigInt, div);
promote_all_scalars_assign!(impl DivAssign for BigInt, div_assign);
forward_all_scalar_binop_to_val_val!(impl Div<u32> for BigInt, div);
forward_all_scalar_binop_to_val_val!(impl Div<u64> for BigInt, div);
forward_all_scalar_binop_to_val_val!(impl Div<u128> for BigInt, div);
impl Div<u32> for BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: u32) -> BigInt {
BigInt::from_biguint(self.sign, self.data / other)
}
}
impl DivAssign<u32> for BigInt {
#[inline]
fn div_assign(&mut self, other: u32) {
self.data /= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Div<BigInt> for u32 {
type Output = BigInt;
#[inline]
fn div(self, other: BigInt) -> BigInt {
BigInt::from_biguint(other.sign, self / other.data)
}
}
impl Div<u64> for BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: u64) -> BigInt {
BigInt::from_biguint(self.sign, self.data / other)
}
}
impl DivAssign<u64> for BigInt {
#[inline]
fn div_assign(&mut self, other: u64) {
self.data /= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Div<BigInt> for u64 {
type Output = BigInt;
#[inline]
fn div(self, other: BigInt) -> BigInt {
BigInt::from_biguint(other.sign, self / other.data)
}
}
impl Div<u128> for BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: u128) -> BigInt {
BigInt::from_biguint(self.sign, self.data / other)
}
}
impl DivAssign<u128> for BigInt {
#[inline]
fn div_assign(&mut self, other: u128) {
self.data /= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Div<BigInt> for u128 {
type Output = BigInt;
#[inline]
fn div(self, other: BigInt) -> BigInt {
BigInt::from_biguint(other.sign, self / other.data)
}
}
forward_all_scalar_binop_to_val_val!(impl Div<i32> for BigInt, div);
forward_all_scalar_binop_to_val_val!(impl Div<i64> for BigInt, div);
forward_all_scalar_binop_to_val_val!(impl Div<i128> for BigInt, div);
impl Div<i32> for BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: i32) -> BigInt {
match other.checked_uabs() {
Positive(u) => self / u,
Negative(u) => -self / u,
}
}
}
impl DivAssign<i32> for BigInt {
#[inline]
fn div_assign(&mut self, other: i32) {
match other.checked_uabs() {
Positive(u) => *self /= u,
Negative(u) => {
self.sign = -self.sign;
*self /= u;
}
}
}
}
impl Div<BigInt> for i32 {
type Output = BigInt;
#[inline]
fn div(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u / other,
Negative(u) => u / -other,
}
}
}
impl Div<i64> for BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: i64) -> BigInt {
match other.checked_uabs() {
Positive(u) => self / u,
Negative(u) => -self / u,
}
}
}
impl DivAssign<i64> for BigInt {
#[inline]
fn div_assign(&mut self, other: i64) {
match other.checked_uabs() {
Positive(u) => *self /= u,
Negative(u) => {
self.sign = -self.sign;
*self /= u;
}
}
}
}
impl Div<BigInt> for i64 {
type Output = BigInt;
#[inline]
fn div(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u / other,
Negative(u) => u / -other,
}
}
}
impl Div<i128> for BigInt {
type Output = BigInt;
#[inline]
fn div(self, other: i128) -> BigInt {
match other.checked_uabs() {
Positive(u) => self / u,
Negative(u) => -self / u,
}
}
}
impl DivAssign<i128> for BigInt {
#[inline]
fn div_assign(&mut self, other: i128) {
match other.checked_uabs() {
Positive(u) => *self /= u,
Negative(u) => {
self.sign = -self.sign;
*self /= u;
}
}
}
}
impl Div<BigInt> for i128 {
type Output = BigInt;
#[inline]
fn div(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u / other,
Negative(u) => u / -other,
}
}
}
forward_all_binop_to_ref_ref!(impl Rem for BigInt, rem);
impl Rem<&BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: &BigInt) -> BigInt {
if let Some(other) = other.to_u32() {
self % other
} else if let Some(other) = other.to_i32() {
self % other
} else {
let (_, r) = self.div_rem(other);
r
}
}
}
impl RemAssign<&BigInt> for BigInt {
#[inline]
fn rem_assign(&mut self, other: &BigInt) {
*self = &*self % other;
}
}
forward_val_assign!(impl RemAssign for BigInt, rem_assign);
promote_all_scalars!(impl Rem for BigInt, rem);
promote_all_scalars_assign!(impl RemAssign for BigInt, rem_assign);
forward_all_scalar_binop_to_val_val!(impl Rem<u32> for BigInt, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<u64> for BigInt, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<u128> for BigInt, rem);
impl Rem<u32> for BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: u32) -> BigInt {
BigInt::from_biguint(self.sign, self.data % other)
}
}
impl RemAssign<u32> for BigInt {
#[inline]
fn rem_assign(&mut self, other: u32) {
self.data %= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Rem<BigInt> for u32 {
type Output = BigInt;
#[inline]
fn rem(self, other: BigInt) -> BigInt {
BigInt::from(self % other.data)
}
}
impl Rem<u64> for BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: u64) -> BigInt {
BigInt::from_biguint(self.sign, self.data % other)
}
}
impl RemAssign<u64> for BigInt {
#[inline]
fn rem_assign(&mut self, other: u64) {
self.data %= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Rem<BigInt> for u64 {
type Output = BigInt;
#[inline]
fn rem(self, other: BigInt) -> BigInt {
BigInt::from(self % other.data)
}
}
impl Rem<u128> for BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: u128) -> BigInt {
BigInt::from_biguint(self.sign, self.data % other)
}
}
impl RemAssign<u128> for BigInt {
#[inline]
fn rem_assign(&mut self, other: u128) {
self.data %= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Rem<BigInt> for u128 {
type Output = BigInt;
#[inline]
fn rem(self, other: BigInt) -> BigInt {
BigInt::from(self % other.data)
}
}
forward_all_scalar_binop_to_val_val!(impl Rem<i32> for BigInt, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<i64> for BigInt, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<i128> for BigInt, rem);
impl Rem<i32> for BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: i32) -> BigInt {
self % other.unsigned_abs()
}
}
impl RemAssign<i32> for BigInt {
#[inline]
fn rem_assign(&mut self, other: i32) {
*self %= other.unsigned_abs();
}
}
impl Rem<BigInt> for i32 {
type Output = BigInt;
#[inline]
fn rem(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u % other,
Negative(u) => -(u % other),
}
}
}
impl Rem<i64> for BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: i64) -> BigInt {
self % other.unsigned_abs()
}
}
impl RemAssign<i64> for BigInt {
#[inline]
fn rem_assign(&mut self, other: i64) {
*self %= other.unsigned_abs();
}
}
impl Rem<BigInt> for i64 {
type Output = BigInt;
#[inline]
fn rem(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u % other,
Negative(u) => -(u % other),
}
}
}
impl Rem<i128> for BigInt {
type Output = BigInt;
#[inline]
fn rem(self, other: i128) -> BigInt {
self % other.unsigned_abs()
}
}
impl RemAssign<i128> for BigInt {
#[inline]
fn rem_assign(&mut self, other: i128) {
*self %= other.unsigned_abs();
}
}
impl Rem<BigInt> for i128 {
type Output = BigInt;
#[inline]
fn rem(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u % other,
Negative(u) => -(u % other),
}
}
}
impl CheckedDiv for BigInt {
#[inline]
fn checked_div(&self, v: &BigInt) -> Option<BigInt> {
if v.is_zero() {
return None;
}
Some(self.div(v))
}
}
impl CheckedEuclid for BigInt {
#[inline]
fn checked_div_euclid(&self, v: &BigInt) -> Option<BigInt> {
if v.is_zero() {
return None;
}
Some(self.div_euclid(v))
}
#[inline]
fn checked_rem_euclid(&self, v: &BigInt) -> Option<BigInt> {
if v.is_zero() {
return None;
}
Some(self.rem_euclid(v))
}
fn checked_div_rem_euclid(&self, v: &Self) -> Option<(Self, Self)> {
Some(self.div_rem_euclid(v))
}
}
impl Euclid for BigInt {
#[inline]
fn div_euclid(&self, v: &BigInt) -> BigInt {
let (q, r) = self.div_rem(v);
if r.is_negative() {
if v.is_positive() {
q - 1
} else {
q + 1
}
} else {
q
}
}
#[inline]
fn rem_euclid(&self, v: &BigInt) -> BigInt {
let r = self % v;
if r.is_negative() {
if v.is_positive() {
r + v
} else {
r - v
}
} else {
r
}
}
fn div_rem_euclid(&self, v: &Self) -> (Self, Self) {
let (q, r) = self.div_rem(v);
if r.is_negative() {
if v.is_positive() {
(q - 1, r + v)
} else {
(q + 1, r - v)
}
} else {
(q, r)
}
}
}

217
vendor/num-bigint/src/bigint/multiplication.rs vendored Normal file
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@@ -0,0 +1,217 @@
use super::CheckedUnsignedAbs::{Negative, Positive};
use super::Sign::{self, Minus, NoSign, Plus};
use super::{BigInt, UnsignedAbs};
use crate::{IsizePromotion, UsizePromotion};
use core::iter::Product;
use core::ops::{Mul, MulAssign};
use num_traits::{CheckedMul, One, Zero};
impl Mul<Sign> for Sign {
type Output = Sign;
#[inline]
fn mul(self, other: Sign) -> Sign {
match (self, other) {
(NoSign, _) | (_, NoSign) => NoSign,
(Plus, Plus) | (Minus, Minus) => Plus,
(Plus, Minus) | (Minus, Plus) => Minus,
}
}
}
macro_rules! impl_mul {
($(impl Mul<$Other:ty> for $Self:ty;)*) => {$(
impl Mul<$Other> for $Self {
type Output = BigInt;
#[inline]
fn mul(self, other: $Other) -> BigInt {
// automatically match value/ref
let BigInt { data: x, .. } = self;
let BigInt { data: y, .. } = other;
BigInt::from_biguint(self.sign * other.sign, x * y)
}
}
)*}
}
impl_mul! {
impl Mul<BigInt> for BigInt;
impl Mul<BigInt> for &BigInt;
impl Mul<&BigInt> for BigInt;
impl Mul<&BigInt> for &BigInt;
}
macro_rules! impl_mul_assign {
($(impl MulAssign<$Other:ty> for BigInt;)*) => {$(
impl MulAssign<$Other> for BigInt {
#[inline]
fn mul_assign(&mut self, other: $Other) {
// automatically match value/ref
let BigInt { data: y, .. } = other;
self.data *= y;
if self.data.is_zero() {
self.sign = NoSign;
} else {
self.sign = self.sign * other.sign;
}
}
}
)*}
}
impl_mul_assign! {
impl MulAssign<BigInt> for BigInt;
impl MulAssign<&BigInt> for BigInt;
}
promote_all_scalars!(impl Mul for BigInt, mul);
promote_all_scalars_assign!(impl MulAssign for BigInt, mul_assign);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u32> for BigInt, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u64> for BigInt, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u128> for BigInt, mul);
impl Mul<u32> for BigInt {
type Output = BigInt;
#[inline]
fn mul(self, other: u32) -> BigInt {
BigInt::from_biguint(self.sign, self.data * other)
}
}
impl MulAssign<u32> for BigInt {
#[inline]
fn mul_assign(&mut self, other: u32) {
self.data *= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Mul<u64> for BigInt {
type Output = BigInt;
#[inline]
fn mul(self, other: u64) -> BigInt {
BigInt::from_biguint(self.sign, self.data * other)
}
}
impl MulAssign<u64> for BigInt {
#[inline]
fn mul_assign(&mut self, other: u64) {
self.data *= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl Mul<u128> for BigInt {
type Output = BigInt;
#[inline]
fn mul(self, other: u128) -> BigInt {
BigInt::from_biguint(self.sign, self.data * other)
}
}
impl MulAssign<u128> for BigInt {
#[inline]
fn mul_assign(&mut self, other: u128) {
self.data *= other;
if self.data.is_zero() {
self.sign = NoSign;
}
}
}
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<i32> for BigInt, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<i64> for BigInt, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<i128> for BigInt, mul);
impl Mul<i32> for BigInt {
type Output = BigInt;
#[inline]
fn mul(self, other: i32) -> BigInt {
match other.checked_uabs() {
Positive(u) => self * u,
Negative(u) => -self * u,
}
}
}
impl MulAssign<i32> for BigInt {
#[inline]
fn mul_assign(&mut self, other: i32) {
match other.checked_uabs() {
Positive(u) => *self *= u,
Negative(u) => {
self.sign = -self.sign;
self.data *= u;
}
}
}
}
impl Mul<i64> for BigInt {
type Output = BigInt;
#[inline]
fn mul(self, other: i64) -> BigInt {
match other.checked_uabs() {
Positive(u) => self * u,
Negative(u) => -self * u,
}
}
}
impl MulAssign<i64> for BigInt {
#[inline]
fn mul_assign(&mut self, other: i64) {
match other.checked_uabs() {
Positive(u) => *self *= u,
Negative(u) => {
self.sign = -self.sign;
self.data *= u;
}
}
}
}
impl Mul<i128> for BigInt {
type Output = BigInt;
#[inline]
fn mul(self, other: i128) -> BigInt {
match other.checked_uabs() {
Positive(u) => self * u,
Negative(u) => -self * u,
}
}
}
impl MulAssign<i128> for BigInt {
#[inline]
fn mul_assign(&mut self, other: i128) {
match other.checked_uabs() {
Positive(u) => *self *= u,
Negative(u) => {
self.sign = -self.sign;
self.data *= u;
}
}
}
}
impl CheckedMul for BigInt {
#[inline]
fn checked_mul(&self, v: &BigInt) -> Option<BigInt> {
Some(self.mul(v))
}
}
impl_product_iter_type!(BigInt);

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use super::BigInt;
use super::Sign::{self, Minus, Plus};
use crate::BigUint;
use num_integer::Integer;
use num_traits::{Pow, Signed, Zero};
/// Help function for pow
///
/// Computes the effect of the exponent on the sign.
#[inline]
fn powsign<T: Integer>(sign: Sign, other: &T) -> Sign {
if other.is_zero() {
Plus
} else if sign != Minus || other.is_odd() {
sign
} else {
-sign
}
}
macro_rules! pow_impl {
($T:ty) => {
impl Pow<$T> for BigInt {
type Output = BigInt;
#[inline]
fn pow(self, rhs: $T) -> BigInt {
BigInt::from_biguint(powsign(self.sign, &rhs), self.data.pow(rhs))
}
}
impl Pow<&$T> for BigInt {
type Output = BigInt;
#[inline]
fn pow(self, rhs: &$T) -> BigInt {
BigInt::from_biguint(powsign(self.sign, rhs), self.data.pow(rhs))
}
}
impl Pow<$T> for &BigInt {
type Output = BigInt;
#[inline]
fn pow(self, rhs: $T) -> BigInt {
BigInt::from_biguint(powsign(self.sign, &rhs), Pow::pow(&self.data, rhs))
}
}
impl Pow<&$T> for &BigInt {
type Output = BigInt;
#[inline]
fn pow(self, rhs: &$T) -> BigInt {
BigInt::from_biguint(powsign(self.sign, rhs), Pow::pow(&self.data, rhs))
}
}
};
}
pow_impl!(u8);
pow_impl!(u16);
pow_impl!(u32);
pow_impl!(u64);
pow_impl!(usize);
pow_impl!(u128);
pow_impl!(BigUint);
pub(super) fn modpow(x: &BigInt, exponent: &BigInt, modulus: &BigInt) -> BigInt {
assert!(
!exponent.is_negative(),
"negative exponentiation is not supported!"
);
assert!(
!modulus.is_zero(),
"attempt to calculate with zero modulus!"
);
let result = x.data.modpow(&exponent.data, &modulus.data);
if result.is_zero() {
return BigInt::ZERO;
}
// The sign of the result follows the modulus, like `mod_floor`.
let (sign, mag) = match (x.is_negative() && exponent.is_odd(), modulus.is_negative()) {
(false, false) => (Plus, result),
(true, false) => (Plus, &modulus.data - result),
(false, true) => (Minus, &modulus.data - result),
(true, true) => (Minus, result),
};
BigInt::from_biguint(sign, mag)
}

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#![cfg(feature = "serde")]
#![cfg_attr(docsrs, doc(cfg(feature = "serde")))]
use super::{BigInt, Sign};
use serde::de::{Error, Unexpected};
use serde::{Deserialize, Deserializer, Serialize, Serializer};
impl Serialize for Sign {
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
{
// Note: do not change the serialization format, or it may break
// forward and backward compatibility of serialized data!
match *self {
Sign::Minus => (-1i8).serialize(serializer),
Sign::NoSign => 0i8.serialize(serializer),
Sign::Plus => 1i8.serialize(serializer),
}
}
}
impl<'de> Deserialize<'de> for Sign {
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: Deserializer<'de>,
{
let sign = i8::deserialize(deserializer)?;
match sign {
-1 => Ok(Sign::Minus),
0 => Ok(Sign::NoSign),
1 => Ok(Sign::Plus),
_ => Err(D::Error::invalid_value(
Unexpected::Signed(sign.into()),
&"a sign of -1, 0, or 1",
)),
}
}
}
impl Serialize for BigInt {
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
{
// Note: do not change the serialization format, or it may break
// forward and backward compatibility of serialized data!
(self.sign, &self.data).serialize(serializer)
}
}
impl<'de> Deserialize<'de> for BigInt {
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: Deserializer<'de>,
{
let (sign, data) = Deserialize::deserialize(deserializer)?;
Ok(BigInt::from_biguint(sign, data))
}
}

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use super::BigInt;
use super::Sign::NoSign;
use core::ops::{Shl, ShlAssign, Shr, ShrAssign};
use num_traits::{PrimInt, Signed, Zero};
macro_rules! impl_shift {
(@ref $Shx:ident :: $shx:ident, $ShxAssign:ident :: $shx_assign:ident, $rhs:ty) => {
impl $Shx<&$rhs> for BigInt {
type Output = BigInt;
#[inline]
fn $shx(self, rhs: &$rhs) -> BigInt {
$Shx::$shx(self, *rhs)
}
}
impl $Shx<&$rhs> for &BigInt {
type Output = BigInt;
#[inline]
fn $shx(self, rhs: &$rhs) -> BigInt {
$Shx::$shx(self, *rhs)
}
}
impl $ShxAssign<&$rhs> for BigInt {
#[inline]
fn $shx_assign(&mut self, rhs: &$rhs) {
$ShxAssign::$shx_assign(self, *rhs);
}
}
};
($($rhs:ty),+) => {$(
impl Shl<$rhs> for BigInt {
type Output = BigInt;
#[inline]
fn shl(self, rhs: $rhs) -> BigInt {
BigInt::from_biguint(self.sign, self.data << rhs)
}
}
impl Shl<$rhs> for &BigInt {
type Output = BigInt;
#[inline]
fn shl(self, rhs: $rhs) -> BigInt {
BigInt::from_biguint(self.sign, &self.data << rhs)
}
}
impl ShlAssign<$rhs> for BigInt {
#[inline]
fn shl_assign(&mut self, rhs: $rhs) {
self.data <<= rhs
}
}
impl_shift! { @ref Shl::shl, ShlAssign::shl_assign, $rhs }
impl Shr<$rhs> for BigInt {
type Output = BigInt;
#[inline]
fn shr(self, rhs: $rhs) -> BigInt {
let round_down = shr_round_down(&self, rhs);
let data = self.data >> rhs;
let data = if round_down { data + 1u8 } else { data };
BigInt::from_biguint(self.sign, data)
}
}
impl Shr<$rhs> for &BigInt {
type Output = BigInt;
#[inline]
fn shr(self, rhs: $rhs) -> BigInt {
let round_down = shr_round_down(self, rhs);
let data = &self.data >> rhs;
let data = if round_down { data + 1u8 } else { data };
BigInt::from_biguint(self.sign, data)
}
}
impl ShrAssign<$rhs> for BigInt {
#[inline]
fn shr_assign(&mut self, rhs: $rhs) {
let round_down = shr_round_down(self, rhs);
self.data >>= rhs;
if round_down {
self.data += 1u8;
} else if self.data.is_zero() {
self.sign = NoSign;
}
}
}
impl_shift! { @ref Shr::shr, ShrAssign::shr_assign, $rhs }
)*};
}
impl_shift! { u8, u16, u32, u64, u128, usize }
impl_shift! { i8, i16, i32, i64, i128, isize }
// Negative values need a rounding adjustment if there are any ones in the
// bits that are getting shifted out.
fn shr_round_down<T: PrimInt>(i: &BigInt, shift: T) -> bool {
if i.is_negative() {
let zeros = i.trailing_zeros().expect("negative values are non-zero");
shift > T::zero() && shift.to_u64().map(|shift| zeros < shift).unwrap_or(true)
} else {
false
}
}

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use super::CheckedUnsignedAbs::{Negative, Positive};
use super::Sign::{Minus, NoSign, Plus};
use super::{BigInt, UnsignedAbs};
use crate::{IsizePromotion, UsizePromotion};
use core::cmp::Ordering::{Equal, Greater, Less};
use core::mem;
use core::ops::{Sub, SubAssign};
use num_traits::CheckedSub;
// We want to forward to BigUint::sub, but it's not clear how that will go until
// we compare both sign and magnitude. So we duplicate this body for every
// val/ref combination, deferring that decision to BigUint's own forwarding.
macro_rules! bigint_sub {
($a:expr, $a_owned:expr, $a_data:expr, $b:expr, $b_owned:expr, $b_data:expr) => {
match ($a.sign, $b.sign) {
(_, NoSign) => $a_owned,
(NoSign, _) => -$b_owned,
// opposite signs => keep the sign of the left with the sum of magnitudes
(Plus, Minus) | (Minus, Plus) => BigInt::from_biguint($a.sign, $a_data + $b_data),
// same sign => keep or toggle the sign of the left with the difference of magnitudes
(Plus, Plus) | (Minus, Minus) => match $a.data.cmp(&$b.data) {
Less => BigInt::from_biguint(-$a.sign, $b_data - $a_data),
Greater => BigInt::from_biguint($a.sign, $a_data - $b_data),
Equal => BigInt::ZERO,
},
}
};
}
impl Sub<&BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: &BigInt) -> BigInt {
bigint_sub!(
self,
self.clone(),
&self.data,
other,
other.clone(),
&other.data
)
}
}
impl Sub<BigInt> for &BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
bigint_sub!(self, self.clone(), &self.data, other, other, other.data)
}
}
impl Sub<&BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: &BigInt) -> BigInt {
bigint_sub!(self, self, self.data, other, other.clone(), &other.data)
}
}
impl Sub<BigInt> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
bigint_sub!(self, self, self.data, other, other, other.data)
}
}
impl SubAssign<&BigInt> for BigInt {
#[inline]
fn sub_assign(&mut self, other: &BigInt) {
let n = mem::replace(self, Self::ZERO);
*self = n - other;
}
}
forward_val_assign!(impl SubAssign for BigInt, sub_assign);
promote_all_scalars!(impl Sub for BigInt, sub);
promote_all_scalars_assign!(impl SubAssign for BigInt, sub_assign);
forward_all_scalar_binop_to_val_val!(impl Sub<u32> for BigInt, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<u64> for BigInt, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<u128> for BigInt, sub);
impl Sub<u32> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: u32) -> BigInt {
match self.sign {
NoSign => -BigInt::from(other),
Minus => -BigInt::from(self.data + other),
Plus => match self.data.cmp(&From::from(other)) {
Equal => Self::ZERO,
Greater => BigInt::from(self.data - other),
Less => -BigInt::from(other - self.data),
},
}
}
}
impl SubAssign<u32> for BigInt {
#[inline]
fn sub_assign(&mut self, other: u32) {
let n = mem::replace(self, Self::ZERO);
*self = n - other;
}
}
impl Sub<BigInt> for u32 {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
-(other - self)
}
}
impl Sub<BigInt> for u64 {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
-(other - self)
}
}
impl Sub<BigInt> for u128 {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
-(other - self)
}
}
impl Sub<u64> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: u64) -> BigInt {
match self.sign {
NoSign => -BigInt::from(other),
Minus => -BigInt::from(self.data + other),
Plus => match self.data.cmp(&From::from(other)) {
Equal => Self::ZERO,
Greater => BigInt::from(self.data - other),
Less => -BigInt::from(other - self.data),
},
}
}
}
impl SubAssign<u64> for BigInt {
#[inline]
fn sub_assign(&mut self, other: u64) {
let n = mem::replace(self, Self::ZERO);
*self = n - other;
}
}
impl Sub<u128> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: u128) -> BigInt {
match self.sign {
NoSign => -BigInt::from(other),
Minus => -BigInt::from(self.data + other),
Plus => match self.data.cmp(&From::from(other)) {
Equal => Self::ZERO,
Greater => BigInt::from(self.data - other),
Less => -BigInt::from(other - self.data),
},
}
}
}
impl SubAssign<u128> for BigInt {
#[inline]
fn sub_assign(&mut self, other: u128) {
let n = mem::replace(self, Self::ZERO);
*self = n - other;
}
}
forward_all_scalar_binop_to_val_val!(impl Sub<i32> for BigInt, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<i64> for BigInt, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<i128> for BigInt, sub);
impl Sub<i32> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: i32) -> BigInt {
match other.checked_uabs() {
Positive(u) => self - u,
Negative(u) => self + u,
}
}
}
impl SubAssign<i32> for BigInt {
#[inline]
fn sub_assign(&mut self, other: i32) {
match other.checked_uabs() {
Positive(u) => *self -= u,
Negative(u) => *self += u,
}
}
}
impl Sub<BigInt> for i32 {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u - other,
Negative(u) => -other - u,
}
}
}
impl Sub<i64> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: i64) -> BigInt {
match other.checked_uabs() {
Positive(u) => self - u,
Negative(u) => self + u,
}
}
}
impl SubAssign<i64> for BigInt {
#[inline]
fn sub_assign(&mut self, other: i64) {
match other.checked_uabs() {
Positive(u) => *self -= u,
Negative(u) => *self += u,
}
}
}
impl Sub<BigInt> for i64 {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u - other,
Negative(u) => -other - u,
}
}
}
impl Sub<i128> for BigInt {
type Output = BigInt;
#[inline]
fn sub(self, other: i128) -> BigInt {
match other.checked_uabs() {
Positive(u) => self - u,
Negative(u) => self + u,
}
}
}
impl SubAssign<i128> for BigInt {
#[inline]
fn sub_assign(&mut self, other: i128) {
match other.checked_uabs() {
Positive(u) => *self -= u,
Negative(u) => *self += u,
}
}
}
impl Sub<BigInt> for i128 {
type Output = BigInt;
#[inline]
fn sub(self, other: BigInt) -> BigInt {
match self.checked_uabs() {
Positive(u) => u - other,
Negative(u) => -other - u,
}
}
}
impl CheckedSub for BigInt {
#[inline]
fn checked_sub(&self, v: &BigInt) -> Option<BigInt> {
Some(self.sub(v))
}
}

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//! Randomization of big integers
#![cfg(feature = "rand")]
#![cfg_attr(docsrs, doc(cfg(feature = "rand")))]
use rand::distributions::uniform::{SampleBorrow, SampleUniform, UniformSampler};
use rand::prelude::*;
use crate::BigInt;
use crate::BigUint;
use crate::Sign::*;
use crate::biguint::biguint_from_vec;
use num_integer::Integer;
use num_traits::{ToPrimitive, Zero};
/// A trait for sampling random big integers.
///
/// The `rand` feature must be enabled to use this. See crate-level documentation for details.
pub trait RandBigInt {
/// Generate a random [`BigUint`] of the given bit size.
fn gen_biguint(&mut self, bit_size: u64) -> BigUint;
/// Generate a random [ BigInt`] of the given bit size.
fn gen_bigint(&mut self, bit_size: u64) -> BigInt;
/// Generate a random [`BigUint`] less than the given bound. Fails
/// when the bound is zero.
fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint;
/// Generate a random [`BigUint`] within the given range. The lower
/// bound is inclusive; the upper bound is exclusive. Fails when
/// the upper bound is not greater than the lower bound.
fn gen_biguint_range(&mut self, lbound: &BigUint, ubound: &BigUint) -> BigUint;
/// Generate a random [`BigInt`] within the given range. The lower
/// bound is inclusive; the upper bound is exclusive. Fails when
/// the upper bound is not greater than the lower bound.
fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt;
}
fn gen_bits<R: Rng + ?Sized>(rng: &mut R, data: &mut [u32], rem: u64) {
// `fill` is faster than many `gen::<u32>` calls
rng.fill(data);
if rem > 0 {
let last = data.len() - 1;
data[last] >>= 32 - rem;
}
}
impl<R: Rng + ?Sized> RandBigInt for R {
cfg_digit!(
fn gen_biguint(&mut self, bit_size: u64) -> BigUint {
let (digits, rem) = bit_size.div_rem(&32);
let len = (digits + (rem > 0) as u64)
.to_usize()
.expect("capacity overflow");
let mut data = vec![0u32; len];
gen_bits(self, &mut data, rem);
biguint_from_vec(data)
}
fn gen_biguint(&mut self, bit_size: u64) -> BigUint {
use core::slice;
let (digits, rem) = bit_size.div_rem(&32);
let len = (digits + (rem > 0) as u64)
.to_usize()
.expect("capacity overflow");
let native_digits = Integer::div_ceil(&bit_size, &64);
let native_len = native_digits.to_usize().expect("capacity overflow");
let mut data = vec![0u64; native_len];
unsafe {
// Generate bits in a `&mut [u32]` slice for value stability
let ptr = data.as_mut_ptr() as *mut u32;
debug_assert!(native_len * 2 >= len);
let data = slice::from_raw_parts_mut(ptr, len);
gen_bits(self, data, rem);
}
#[cfg(target_endian = "big")]
for digit in &mut data {
// swap u32 digits into u64 endianness
*digit = (*digit << 32) | (*digit >> 32);
}
biguint_from_vec(data)
}
);
fn gen_bigint(&mut self, bit_size: u64) -> BigInt {
loop {
// Generate a random BigUint...
let biguint = self.gen_biguint(bit_size);
// ...and then randomly assign it a Sign...
let sign = if biguint.is_zero() {
// ...except that if the BigUint is zero, we need to try
// again with probability 0.5. This is because otherwise,
// the probability of generating a zero BigInt would be
// double that of any other number.
if self.gen() {
continue;
} else {
NoSign
}
} else if self.gen() {
Plus
} else {
Minus
};
return BigInt::from_biguint(sign, biguint);
}
}
fn gen_biguint_below(&mut self, bound: &BigUint) -> BigUint {
assert!(!bound.is_zero());
let bits = bound.bits();
loop {
let n = self.gen_biguint(bits);
if n < *bound {
return n;
}
}
}
fn gen_biguint_range(&mut self, lbound: &BigUint, ubound: &BigUint) -> BigUint {
assert!(*lbound < *ubound);
if lbound.is_zero() {
self.gen_biguint_below(ubound)
} else {
lbound + self.gen_biguint_below(&(ubound - lbound))
}
}
fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt {
assert!(*lbound < *ubound);
if lbound.is_zero() {
BigInt::from(self.gen_biguint_below(ubound.magnitude()))
} else if ubound.is_zero() {
lbound + BigInt::from(self.gen_biguint_below(lbound.magnitude()))
} else {
let delta = ubound - lbound;
lbound + BigInt::from(self.gen_biguint_below(delta.magnitude()))
}
}
}
/// The back-end implementing rand's [`UniformSampler`] for [`BigUint`].
#[derive(Clone, Debug)]
pub struct UniformBigUint {
base: BigUint,
len: BigUint,
}
impl UniformSampler for UniformBigUint {
type X = BigUint;
#[inline]
fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = low_b.borrow();
let high = high_b.borrow();
assert!(low < high);
UniformBigUint {
len: high - low,
base: low.clone(),
}
}
#[inline]
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = low_b.borrow();
let high = high_b.borrow();
assert!(low <= high);
Self::new(low, high + 1u32)
}
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
&self.base + rng.gen_biguint_below(&self.len)
}
#[inline]
fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R) -> Self::X
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
rng.gen_biguint_range(low.borrow(), high.borrow())
}
}
impl SampleUniform for BigUint {
type Sampler = UniformBigUint;
}
/// The back-end implementing rand's [`UniformSampler`] for [`BigInt`].
#[derive(Clone, Debug)]
pub struct UniformBigInt {
base: BigInt,
len: BigUint,
}
impl UniformSampler for UniformBigInt {
type X = BigInt;
#[inline]
fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = low_b.borrow();
let high = high_b.borrow();
assert!(low < high);
UniformBigInt {
len: (high - low).into_parts().1,
base: low.clone(),
}
}
#[inline]
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = low_b.borrow();
let high = high_b.borrow();
assert!(low <= high);
Self::new(low, high + 1u32)
}
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
&self.base + BigInt::from(rng.gen_biguint_below(&self.len))
}
#[inline]
fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R) -> Self::X
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
rng.gen_bigint_range(low.borrow(), high.borrow())
}
}
impl SampleUniform for BigInt {
type Sampler = UniformBigInt;
}
/// A random distribution for [`BigUint`] and [`BigInt`] values of a particular bit size.
///
/// The `rand` feature must be enabled to use this. See crate-level documentation for details.
#[derive(Clone, Copy, Debug)]
pub struct RandomBits {
bits: u64,
}
impl RandomBits {
#[inline]
pub fn new(bits: u64) -> RandomBits {
RandomBits { bits }
}
}
impl Distribution<BigUint> for RandomBits {
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> BigUint {
rng.gen_biguint(self.bits)
}
}
impl Distribution<BigInt> for RandomBits {
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> BigInt {
rng.gen_bigint(self.bits)
}
}

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use super::{BigUint, IntDigits};
use crate::big_digit::{self, BigDigit};
use crate::UsizePromotion;
use core::iter::Sum;
use core::ops::{Add, AddAssign};
use num_traits::CheckedAdd;
#[cfg(target_arch = "x86_64")]
use core::arch::x86_64 as arch;
#[cfg(target_arch = "x86")]
use core::arch::x86 as arch;
// Add with carry:
#[cfg(target_arch = "x86_64")]
cfg_64!(
#[inline]
fn adc(carry: u8, a: u64, b: u64, out: &mut u64) -> u8 {
// Safety: There are absolutely no safety concerns with calling `_addcarry_u64`.
// It's just unsafe for API consistency with other intrinsics.
unsafe { arch::_addcarry_u64(carry, a, b, out) }
}
);
#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
cfg_32!(
#[inline]
fn adc(carry: u8, a: u32, b: u32, out: &mut u32) -> u8 {
// Safety: There are absolutely no safety concerns with calling `_addcarry_u32`.
// It's just unsafe for API consistency with other intrinsics.
unsafe { arch::_addcarry_u32(carry, a, b, out) }
}
);
// fallback for environments where we don't have an addcarry intrinsic
// (copied from the standard library's `carrying_add`)
#[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
#[inline]
fn adc(carry: u8, lhs: BigDigit, rhs: BigDigit, out: &mut BigDigit) -> u8 {
let (a, b) = lhs.overflowing_add(rhs);
let (c, d) = a.overflowing_add(carry as BigDigit);
*out = c;
u8::from(b || d)
}
/// Two argument addition of raw slices, `a += b`, returning the carry.
///
/// This is used when the data `Vec` might need to resize to push a non-zero carry, so we perform
/// the addition first hoping that it will fit.
///
/// The caller _must_ ensure that `a` is at least as long as `b`.
#[inline]
pub(super) fn __add2(a: &mut [BigDigit], b: &[BigDigit]) -> BigDigit {
debug_assert!(a.len() >= b.len());
let mut carry = 0;
let (a_lo, a_hi) = a.split_at_mut(b.len());
for (a, b) in a_lo.iter_mut().zip(b) {
carry = adc(carry, *a, *b, a);
}
if carry != 0 {
for a in a_hi {
carry = adc(carry, *a, 0, a);
if carry == 0 {
break;
}
}
}
carry as BigDigit
}
/// Two argument addition of raw slices:
/// a += b
///
/// The caller _must_ ensure that a is big enough to store the result - typically this means
/// resizing a to max(a.len(), b.len()) + 1, to fit a possible carry.
pub(super) fn add2(a: &mut [BigDigit], b: &[BigDigit]) {
let carry = __add2(a, b);
debug_assert!(carry == 0);
}
forward_all_binop_to_val_ref_commutative!(impl Add for BigUint, add);
forward_val_assign!(impl AddAssign for BigUint, add_assign);
impl Add<&BigUint> for BigUint {
type Output = BigUint;
fn add(mut self, other: &BigUint) -> BigUint {
self += other;
self
}
}
impl AddAssign<&BigUint> for BigUint {
#[inline]
fn add_assign(&mut self, other: &BigUint) {
let self_len = self.data.len();
let carry = if self_len < other.data.len() {
let lo_carry = __add2(&mut self.data[..], &other.data[..self_len]);
self.data.extend_from_slice(&other.data[self_len..]);
__add2(&mut self.data[self_len..], &[lo_carry])
} else {
__add2(&mut self.data[..], &other.data[..])
};
if carry != 0 {
self.data.push(carry);
}
}
}
promote_unsigned_scalars!(impl Add for BigUint, add);
promote_unsigned_scalars_assign!(impl AddAssign for BigUint, add_assign);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u32> for BigUint, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u64> for BigUint, add);
forward_all_scalar_binop_to_val_val_commutative!(impl Add<u128> for BigUint, add);
impl Add<u32> for BigUint {
type Output = BigUint;
#[inline]
fn add(mut self, other: u32) -> BigUint {
self += other;
self
}
}
impl AddAssign<u32> for BigUint {
#[inline]
fn add_assign(&mut self, other: u32) {
if other != 0 {
if self.data.is_empty() {
self.data.push(0);
}
let carry = __add2(&mut self.data, &[other as BigDigit]);
if carry != 0 {
self.data.push(carry);
}
}
}
}
impl Add<u64> for BigUint {
type Output = BigUint;
#[inline]
fn add(mut self, other: u64) -> BigUint {
self += other;
self
}
}
impl AddAssign<u64> for BigUint {
cfg_digit!(
#[inline]
fn add_assign(&mut self, other: u64) {
let (hi, lo) = big_digit::from_doublebigdigit(other);
if hi == 0 {
*self += lo;
} else {
while self.data.len() < 2 {
self.data.push(0);
}
let carry = __add2(&mut self.data, &[lo, hi]);
if carry != 0 {
self.data.push(carry);
}
}
}
#[inline]
fn add_assign(&mut self, other: u64) {
if other != 0 {
if self.data.is_empty() {
self.data.push(0);
}
let carry = __add2(&mut self.data, &[other as BigDigit]);
if carry != 0 {
self.data.push(carry);
}
}
}
);
}
impl Add<u128> for BigUint {
type Output = BigUint;
#[inline]
fn add(mut self, other: u128) -> BigUint {
self += other;
self
}
}
impl AddAssign<u128> for BigUint {
cfg_digit!(
#[inline]
fn add_assign(&mut self, other: u128) {
if other <= u128::from(u64::MAX) {
*self += other as u64
} else {
let (a, b, c, d) = super::u32_from_u128(other);
let carry = if a > 0 {
while self.data.len() < 4 {
self.data.push(0);
}
__add2(&mut self.data, &[d, c, b, a])
} else {
debug_assert!(b > 0);
while self.data.len() < 3 {
self.data.push(0);
}
__add2(&mut self.data, &[d, c, b])
};
if carry != 0 {
self.data.push(carry);
}
}
}
#[inline]
fn add_assign(&mut self, other: u128) {
let (hi, lo) = big_digit::from_doublebigdigit(other);
if hi == 0 {
*self += lo;
} else {
while self.data.len() < 2 {
self.data.push(0);
}
let carry = __add2(&mut self.data, &[lo, hi]);
if carry != 0 {
self.data.push(carry);
}
}
}
);
}
impl CheckedAdd for BigUint {
#[inline]
fn checked_add(&self, v: &BigUint) -> Option<BigUint> {
Some(self.add(v))
}
}
impl_sum_iter_type!(BigUint);

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#![cfg(any(feature = "quickcheck", feature = "arbitrary"))]
use super::{biguint_from_vec, BigUint};
use crate::big_digit::BigDigit;
#[cfg(feature = "quickcheck")]
use alloc::boxed::Box;
use alloc::vec::Vec;
#[cfg(feature = "quickcheck")]
#[cfg_attr(docsrs, doc(cfg(feature = "quickcheck")))]
impl quickcheck::Arbitrary for BigUint {
fn arbitrary(g: &mut quickcheck::Gen) -> Self {
// Use arbitrary from Vec
biguint_from_vec(Vec::<BigDigit>::arbitrary(g))
}
fn shrink(&self) -> Box<dyn Iterator<Item = Self>> {
// Use shrinker from Vec
Box::new(self.data.shrink().map(biguint_from_vec))
}
}
#[cfg(feature = "arbitrary")]
#[cfg_attr(docsrs, doc(cfg(feature = "arbitrary")))]
impl arbitrary::Arbitrary<'_> for BigUint {
fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
Ok(biguint_from_vec(Vec::<BigDigit>::arbitrary(u)?))
}
fn arbitrary_take_rest(u: arbitrary::Unstructured<'_>) -> arbitrary::Result<Self> {
Ok(biguint_from_vec(Vec::<BigDigit>::arbitrary_take_rest(u)?))
}
fn size_hint(depth: usize) -> (usize, Option<usize>) {
Vec::<BigDigit>::size_hint(depth)
}
}

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use super::{BigUint, IntDigits};
use core::ops::{BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign};
forward_val_val_binop!(impl BitAnd for BigUint, bitand);
forward_ref_val_binop!(impl BitAnd for BigUint, bitand);
// do not use forward_ref_ref_binop_commutative! for bitand so that we can
// clone the smaller value rather than the larger, avoiding over-allocation
impl BitAnd<&BigUint> for &BigUint {
type Output = BigUint;
#[inline]
fn bitand(self, other: &BigUint) -> BigUint {
// forward to val-ref, choosing the smaller to clone
if self.data.len() <= other.data.len() {
self.clone() & other
} else {
other.clone() & self
}
}
}
forward_val_assign!(impl BitAndAssign for BigUint, bitand_assign);
impl BitAnd<&BigUint> for BigUint {
type Output = BigUint;
#[inline]
fn bitand(mut self, other: &BigUint) -> BigUint {
self &= other;
self
}
}
impl BitAndAssign<&BigUint> for BigUint {
#[inline]
fn bitand_assign(&mut self, other: &BigUint) {
for (ai, &bi) in self.data.iter_mut().zip(other.data.iter()) {
*ai &= bi;
}
self.data.truncate(other.data.len());
self.normalize();
}
}
forward_all_binop_to_val_ref_commutative!(impl BitOr for BigUint, bitor);
forward_val_assign!(impl BitOrAssign for BigUint, bitor_assign);
impl BitOr<&BigUint> for BigUint {
type Output = BigUint;
fn bitor(mut self, other: &BigUint) -> BigUint {
self |= other;
self
}
}
impl BitOrAssign<&BigUint> for BigUint {
#[inline]
fn bitor_assign(&mut self, other: &BigUint) {
for (ai, &bi) in self.data.iter_mut().zip(other.data.iter()) {
*ai |= bi;
}
if other.data.len() > self.data.len() {
let extra = &other.data[self.data.len()..];
self.data.extend(extra.iter().cloned());
}
}
}
forward_all_binop_to_val_ref_commutative!(impl BitXor for BigUint, bitxor);
forward_val_assign!(impl BitXorAssign for BigUint, bitxor_assign);
impl BitXor<&BigUint> for BigUint {
type Output = BigUint;
fn bitxor(mut self, other: &BigUint) -> BigUint {
self ^= other;
self
}
}
impl BitXorAssign<&BigUint> for BigUint {
#[inline]
fn bitxor_assign(&mut self, other: &BigUint) {
for (ai, &bi) in self.data.iter_mut().zip(other.data.iter()) {
*ai ^= bi;
}
if other.data.len() > self.data.len() {
let extra = &other.data[self.data.len()..];
self.data.extend(extra.iter().cloned());
}
self.normalize();
}
}

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// This uses stdlib features higher than the MSRV
#![allow(clippy::manual_range_contains)] // 1.35
use super::{biguint_from_vec, BigUint, ToBigUint};
use super::addition::add2;
use super::division::{div_rem_digit, FAST_DIV_WIDE};
use super::multiplication::mac_with_carry;
use crate::big_digit::{self, BigDigit};
use crate::ParseBigIntError;
use crate::TryFromBigIntError;
use alloc::vec::Vec;
use core::cmp::Ordering::{Equal, Greater, Less};
use core::convert::TryFrom;
use core::mem;
use core::str::FromStr;
use num_integer::{Integer, Roots};
use num_traits::float::FloatCore;
use num_traits::{FromPrimitive, Num, One, PrimInt, ToPrimitive, Zero};
/// Find last set bit
/// fls(0) == 0, fls(u32::MAX) == 32
fn fls<T: PrimInt>(v: T) -> u8 {
mem::size_of::<T>() as u8 * 8 - v.leading_zeros() as u8
}
fn ilog2<T: PrimInt>(v: T) -> u8 {
fls(v) - 1
}
impl FromStr for BigUint {
type Err = ParseBigIntError;
#[inline]
fn from_str(s: &str) -> Result<BigUint, ParseBigIntError> {
BigUint::from_str_radix(s, 10)
}
}
// Convert from a power of two radix (bits == ilog2(radix)) where bits evenly divides
// BigDigit::BITS
pub(super) fn from_bitwise_digits_le(v: &[u8], bits: u8) -> BigUint {
debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits == 0);
debug_assert!(v.iter().all(|&c| BigDigit::from(c) < (1 << bits)));
let digits_per_big_digit = big_digit::BITS / bits;
let data = v
.chunks(digits_per_big_digit.into())
.map(|chunk| {
chunk
.iter()
.rev()
.fold(0, |acc, &c| (acc << bits) | BigDigit::from(c))
})
.collect();
biguint_from_vec(data)
}
// Convert from a power of two radix (bits == ilog2(radix)) where bits doesn't evenly divide
// BigDigit::BITS
fn from_inexact_bitwise_digits_le(v: &[u8], bits: u8) -> BigUint {
debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits != 0);
debug_assert!(v.iter().all(|&c| BigDigit::from(c) < (1 << bits)));
let total_bits = (v.len() as u64).saturating_mul(bits.into());
let big_digits = Integer::div_ceil(&total_bits, &big_digit::BITS.into())
.to_usize()
.unwrap_or(usize::MAX);
let mut data = Vec::with_capacity(big_digits);
let mut d = 0;
let mut dbits = 0; // number of bits we currently have in d
// walk v accumululating bits in d; whenever we accumulate big_digit::BITS in d, spit out a
// big_digit:
for &c in v {
d |= BigDigit::from(c) << dbits;
dbits += bits;
if dbits >= big_digit::BITS {
data.push(d);
dbits -= big_digit::BITS;
// if dbits was > big_digit::BITS, we dropped some of the bits in c (they couldn't fit
// in d) - grab the bits we lost here:
d = BigDigit::from(c) >> (bits - dbits);
}
}
if dbits > 0 {
debug_assert!(dbits < big_digit::BITS);
data.push(d as BigDigit);
}
biguint_from_vec(data)
}
// Read little-endian radix digits
fn from_radix_digits_be(v: &[u8], radix: u32) -> BigUint {
debug_assert!(!v.is_empty() && !radix.is_power_of_two());
debug_assert!(v.iter().all(|&c| u32::from(c) < radix));
// Estimate how big the result will be, so we can pre-allocate it.
#[cfg(feature = "std")]
let big_digits = {
let radix_log2 = f64::from(radix).log2();
let bits = radix_log2 * v.len() as f64;
(bits / big_digit::BITS as f64).ceil()
};
#[cfg(not(feature = "std"))]
let big_digits = {
let radix_log2 = ilog2(radix.next_power_of_two()) as usize;
let bits = radix_log2 * v.len();
(bits / big_digit::BITS as usize) + 1
};
let mut data = Vec::with_capacity(big_digits.to_usize().unwrap_or(0));
let (base, power) = get_radix_base(radix);
let radix = radix as BigDigit;
let r = v.len() % power;
let i = if r == 0 { power } else { r };
let (head, tail) = v.split_at(i);
let first = head
.iter()
.fold(0, |acc, &d| acc * radix + BigDigit::from(d));
data.push(first);
debug_assert!(tail.len() % power == 0);
for chunk in tail.chunks(power) {
if data.last() != Some(&0) {
data.push(0);
}
let mut carry = 0;
for d in data.iter_mut() {
*d = mac_with_carry(0, *d, base, &mut carry);
}
debug_assert!(carry == 0);
let n = chunk
.iter()
.fold(0, |acc, &d| acc * radix + BigDigit::from(d));
add2(&mut data, &[n]);
}
biguint_from_vec(data)
}
pub(super) fn from_radix_be(buf: &[u8], radix: u32) -> Option<BigUint> {
assert!(
2 <= radix && radix <= 256,
"The radix must be within 2...256"
);
if buf.is_empty() {
return Some(BigUint::ZERO);
}
if radix != 256 && buf.iter().any(|&b| b >= radix as u8) {
return None;
}
let res = if radix.is_power_of_two() {
// Powers of two can use bitwise masks and shifting instead of multiplication
let bits = ilog2(radix);
let mut v = Vec::from(buf);
v.reverse();
if big_digit::BITS % bits == 0 {
from_bitwise_digits_le(&v, bits)
} else {
from_inexact_bitwise_digits_le(&v, bits)
}
} else {
from_radix_digits_be(buf, radix)
};
Some(res)
}
pub(super) fn from_radix_le(buf: &[u8], radix: u32) -> Option<BigUint> {
assert!(
2 <= radix && radix <= 256,
"The radix must be within 2...256"
);
if buf.is_empty() {
return Some(BigUint::ZERO);
}
if radix != 256 && buf.iter().any(|&b| b >= radix as u8) {
return None;
}
let res = if radix.is_power_of_two() {
// Powers of two can use bitwise masks and shifting instead of multiplication
let bits = ilog2(radix);
if big_digit::BITS % bits == 0 {
from_bitwise_digits_le(buf, bits)
} else {
from_inexact_bitwise_digits_le(buf, bits)
}
} else {
let mut v = Vec::from(buf);
v.reverse();
from_radix_digits_be(&v, radix)
};
Some(res)
}
impl Num for BigUint {
type FromStrRadixErr = ParseBigIntError;
/// Creates and initializes a `BigUint`.
fn from_str_radix(s: &str, radix: u32) -> Result<BigUint, ParseBigIntError> {
assert!(2 <= radix && radix <= 36, "The radix must be within 2...36");
let mut s = s;
if let Some(tail) = s.strip_prefix('+') {
if !tail.starts_with('+') {
s = tail
}
}
if s.is_empty() {
return Err(ParseBigIntError::empty());
}
if s.starts_with('_') {
// Must lead with a real digit!
return Err(ParseBigIntError::invalid());
}
// First normalize all characters to plain digit values
let mut v = Vec::with_capacity(s.len());
for b in s.bytes() {
let d = match b {
b'0'..=b'9' => b - b'0',
b'a'..=b'z' => b - b'a' + 10,
b'A'..=b'Z' => b - b'A' + 10,
b'_' => continue,
_ => u8::MAX,
};
if d < radix as u8 {
v.push(d);
} else {
return Err(ParseBigIntError::invalid());
}
}
let res = if radix.is_power_of_two() {
// Powers of two can use bitwise masks and shifting instead of multiplication
let bits = ilog2(radix);
v.reverse();
if big_digit::BITS % bits == 0 {
from_bitwise_digits_le(&v, bits)
} else {
from_inexact_bitwise_digits_le(&v, bits)
}
} else {
from_radix_digits_be(&v, radix)
};
Ok(res)
}
}
fn high_bits_to_u64(v: &BigUint) -> u64 {
match v.data.len() {
0 => 0,
1 => {
// XXX Conversion is useless if already 64-bit.
#[allow(clippy::useless_conversion)]
let v0 = u64::from(v.data[0]);
v0
}
_ => {
let mut bits = v.bits();
let mut ret = 0u64;
let mut ret_bits = 0;
for d in v.data.iter().rev() {
let digit_bits = (bits - 1) % u64::from(big_digit::BITS) + 1;
let bits_want = Ord::min(64 - ret_bits, digit_bits);
if bits_want != 0 {
if bits_want != 64 {
ret <<= bits_want;
}
// XXX Conversion is useless if already 64-bit.
#[allow(clippy::useless_conversion)]
let d0 = u64::from(*d) >> (digit_bits - bits_want);
ret |= d0;
}
// Implement round-to-odd: If any lower bits are 1, set LSB to 1
// so that rounding again to floating point value using
// nearest-ties-to-even is correct.
//
// See: https://en.wikipedia.org/wiki/Rounding#Rounding_to_prepare_for_shorter_precision
if digit_bits - bits_want != 0 {
// XXX Conversion is useless if already 64-bit.
#[allow(clippy::useless_conversion)]
let masked = u64::from(*d) << (64 - (digit_bits - bits_want) as u32);
ret |= (masked != 0) as u64;
}
ret_bits += bits_want;
bits -= bits_want;
}
ret
}
}
}
impl ToPrimitive for BigUint {
#[inline]
fn to_i64(&self) -> Option<i64> {
self.to_u64().as_ref().and_then(u64::to_i64)
}
#[inline]
fn to_i128(&self) -> Option<i128> {
self.to_u128().as_ref().and_then(u128::to_i128)
}
#[allow(clippy::useless_conversion)]
#[inline]
fn to_u64(&self) -> Option<u64> {
let mut ret: u64 = 0;
let mut bits = 0;
for i in self.data.iter() {
if bits >= 64 {
return None;
}
// XXX Conversion is useless if already 64-bit.
ret += u64::from(*i) << bits;
bits += big_digit::BITS;
}
Some(ret)
}
#[inline]
fn to_u128(&self) -> Option<u128> {
let mut ret: u128 = 0;
let mut bits = 0;
for i in self.data.iter() {
if bits >= 128 {
return None;
}
ret |= u128::from(*i) << bits;
bits += big_digit::BITS;
}
Some(ret)
}
#[inline]
fn to_f32(&self) -> Option<f32> {
let mantissa = high_bits_to_u64(self);
let exponent = self.bits() - u64::from(fls(mantissa));
if exponent > f32::MAX_EXP as u64 {
Some(f32::INFINITY)
} else {
Some((mantissa as f32) * 2.0f32.powi(exponent as i32))
}
}
#[inline]
fn to_f64(&self) -> Option<f64> {
let mantissa = high_bits_to_u64(self);
let exponent = self.bits() - u64::from(fls(mantissa));
if exponent > f64::MAX_EXP as u64 {
Some(f64::INFINITY)
} else {
Some((mantissa as f64) * 2.0f64.powi(exponent as i32))
}
}
}
macro_rules! impl_try_from_biguint {
($T:ty, $to_ty:path) => {
impl TryFrom<&BigUint> for $T {
type Error = TryFromBigIntError<()>;
#[inline]
fn try_from(value: &BigUint) -> Result<$T, TryFromBigIntError<()>> {
$to_ty(value).ok_or(TryFromBigIntError::new(()))
}
}
impl TryFrom<BigUint> for $T {
type Error = TryFromBigIntError<BigUint>;
#[inline]
fn try_from(value: BigUint) -> Result<$T, TryFromBigIntError<BigUint>> {
<$T>::try_from(&value).map_err(|_| TryFromBigIntError::new(value))
}
}
};
}
impl_try_from_biguint!(u8, ToPrimitive::to_u8);
impl_try_from_biguint!(u16, ToPrimitive::to_u16);
impl_try_from_biguint!(u32, ToPrimitive::to_u32);
impl_try_from_biguint!(u64, ToPrimitive::to_u64);
impl_try_from_biguint!(usize, ToPrimitive::to_usize);
impl_try_from_biguint!(u128, ToPrimitive::to_u128);
impl_try_from_biguint!(i8, ToPrimitive::to_i8);
impl_try_from_biguint!(i16, ToPrimitive::to_i16);
impl_try_from_biguint!(i32, ToPrimitive::to_i32);
impl_try_from_biguint!(i64, ToPrimitive::to_i64);
impl_try_from_biguint!(isize, ToPrimitive::to_isize);
impl_try_from_biguint!(i128, ToPrimitive::to_i128);
impl FromPrimitive for BigUint {
#[inline]
fn from_i64(n: i64) -> Option<BigUint> {
if n >= 0 {
Some(BigUint::from(n as u64))
} else {
None
}
}
#[inline]
fn from_i128(n: i128) -> Option<BigUint> {
if n >= 0 {
Some(BigUint::from(n as u128))
} else {
None
}
}
#[inline]
fn from_u64(n: u64) -> Option<BigUint> {
Some(BigUint::from(n))
}
#[inline]
fn from_u128(n: u128) -> Option<BigUint> {
Some(BigUint::from(n))
}
#[inline]
fn from_f64(mut n: f64) -> Option<BigUint> {
// handle NAN, INFINITY, NEG_INFINITY
if !n.is_finite() {
return None;
}
// match the rounding of casting from float to int
n = n.trunc();
// handle 0.x, -0.x
if n.is_zero() {
return Some(Self::ZERO);
}
let (mantissa, exponent, sign) = FloatCore::integer_decode(n);
if sign == -1 {
return None;
}
let mut ret = BigUint::from(mantissa);
match exponent.cmp(&0) {
Greater => ret <<= exponent as usize,
Equal => {}
Less => ret >>= (-exponent) as usize,
}
Some(ret)
}
}
impl From<u64> for BigUint {
#[inline]
fn from(mut n: u64) -> Self {
let mut ret: BigUint = Self::ZERO;
while n != 0 {
ret.data.push(n as BigDigit);
// don't overflow if BITS is 64:
n = (n >> 1) >> (big_digit::BITS - 1);
}
ret
}
}
impl From<u128> for BigUint {
#[inline]
fn from(mut n: u128) -> Self {
let mut ret: BigUint = Self::ZERO;
while n != 0 {
ret.data.push(n as BigDigit);
n >>= big_digit::BITS;
}
ret
}
}
macro_rules! impl_biguint_from_uint {
($T:ty) => {
impl From<$T> for BigUint {
#[inline]
fn from(n: $T) -> Self {
BigUint::from(n as u64)
}
}
};
}
impl_biguint_from_uint!(u8);
impl_biguint_from_uint!(u16);
impl_biguint_from_uint!(u32);
impl_biguint_from_uint!(usize);
macro_rules! impl_biguint_try_from_int {
($T:ty, $from_ty:path) => {
impl TryFrom<$T> for BigUint {
type Error = TryFromBigIntError<()>;
#[inline]
fn try_from(value: $T) -> Result<BigUint, TryFromBigIntError<()>> {
$from_ty(value).ok_or(TryFromBigIntError::new(()))
}
}
};
}
impl_biguint_try_from_int!(i8, FromPrimitive::from_i8);
impl_biguint_try_from_int!(i16, FromPrimitive::from_i16);
impl_biguint_try_from_int!(i32, FromPrimitive::from_i32);
impl_biguint_try_from_int!(i64, FromPrimitive::from_i64);
impl_biguint_try_from_int!(isize, FromPrimitive::from_isize);
impl_biguint_try_from_int!(i128, FromPrimitive::from_i128);
impl ToBigUint for BigUint {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
Some(self.clone())
}
}
macro_rules! impl_to_biguint {
($T:ty, $from_ty:path) => {
impl ToBigUint for $T {
#[inline]
fn to_biguint(&self) -> Option<BigUint> {
$from_ty(*self)
}
}
};
}
impl_to_biguint!(isize, FromPrimitive::from_isize);
impl_to_biguint!(i8, FromPrimitive::from_i8);
impl_to_biguint!(i16, FromPrimitive::from_i16);
impl_to_biguint!(i32, FromPrimitive::from_i32);
impl_to_biguint!(i64, FromPrimitive::from_i64);
impl_to_biguint!(i128, FromPrimitive::from_i128);
impl_to_biguint!(usize, FromPrimitive::from_usize);
impl_to_biguint!(u8, FromPrimitive::from_u8);
impl_to_biguint!(u16, FromPrimitive::from_u16);
impl_to_biguint!(u32, FromPrimitive::from_u32);
impl_to_biguint!(u64, FromPrimitive::from_u64);
impl_to_biguint!(u128, FromPrimitive::from_u128);
impl_to_biguint!(f32, FromPrimitive::from_f32);
impl_to_biguint!(f64, FromPrimitive::from_f64);
impl From<bool> for BigUint {
fn from(x: bool) -> Self {
if x {
One::one()
} else {
Self::ZERO
}
}
}
// Extract bitwise digits that evenly divide BigDigit
pub(super) fn to_bitwise_digits_le(u: &BigUint, bits: u8) -> Vec<u8> {
debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits == 0);
let last_i = u.data.len() - 1;
let mask: BigDigit = (1 << bits) - 1;
let digits_per_big_digit = big_digit::BITS / bits;
let digits = Integer::div_ceil(&u.bits(), &u64::from(bits))
.to_usize()
.unwrap_or(usize::MAX);
let mut res = Vec::with_capacity(digits);
for mut r in u.data[..last_i].iter().cloned() {
for _ in 0..digits_per_big_digit {
res.push((r & mask) as u8);
r >>= bits;
}
}
let mut r = u.data[last_i];
while r != 0 {
res.push((r & mask) as u8);
r >>= bits;
}
res
}
// Extract bitwise digits that don't evenly divide BigDigit
fn to_inexact_bitwise_digits_le(u: &BigUint, bits: u8) -> Vec<u8> {
debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits != 0);
let mask: BigDigit = (1 << bits) - 1;
let digits = Integer::div_ceil(&u.bits(), &u64::from(bits))
.to_usize()
.unwrap_or(usize::MAX);
let mut res = Vec::with_capacity(digits);
let mut r = 0;
let mut rbits = 0;
for c in &u.data {
r |= *c << rbits;
rbits += big_digit::BITS;
while rbits >= bits {
res.push((r & mask) as u8);
r >>= bits;
// r had more bits than it could fit - grab the bits we lost
if rbits > big_digit::BITS {
r = *c >> (big_digit::BITS - (rbits - bits));
}
rbits -= bits;
}
}
if rbits != 0 {
res.push(r as u8);
}
while let Some(&0) = res.last() {
res.pop();
}
res
}
// Extract little-endian radix digits
#[inline(always)] // forced inline to get const-prop for radix=10
pub(super) fn to_radix_digits_le(u: &BigUint, radix: u32) -> Vec<u8> {
debug_assert!(!u.is_zero() && !radix.is_power_of_two());
#[cfg(feature = "std")]
let radix_digits = {
let radix_log2 = f64::from(radix).log2();
((u.bits() as f64) / radix_log2).ceil()
};
#[cfg(not(feature = "std"))]
let radix_digits = {
let radix_log2 = ilog2(radix) as usize;
((u.bits() as usize) / radix_log2) + 1
};
// Estimate how big the result will be, so we can pre-allocate it.
let mut res = Vec::with_capacity(radix_digits.to_usize().unwrap_or(0));
let mut digits = u.clone();
// X86 DIV can quickly divide by a full digit, otherwise we choose a divisor
// that's suitable for `div_half` to avoid slow `DoubleBigDigit` division.
let (base, power) = if FAST_DIV_WIDE {
get_radix_base(radix)
} else {
get_half_radix_base(radix)
};
let radix = radix as BigDigit;
// For very large numbers, the O(n²) loop of repeated `div_rem_digit` dominates the
// performance. We can mitigate this by dividing into chunks of a larger base first.
// The threshold for this was chosen by anecdotal performance measurements to
// approximate where this starts to make a noticeable difference.
if digits.data.len() >= 64 {
let mut big_base = BigUint::from(base);
let mut big_power = 1usize;
// Choose a target base length near √n.
let target_len = digits.data.len().sqrt();
while big_base.data.len() < target_len {
big_base = &big_base * &big_base;
big_power *= 2;
}
// This outer loop will run approximately √n times.
while digits > big_base {
// This is still the dominating factor, with n digits divided by √n digits.
let (q, mut big_r) = digits.div_rem(&big_base);
digits = q;
// This inner loop now has O(√n²)=O(n) behavior altogether.
for _ in 0..big_power {
let (q, mut r) = div_rem_digit(big_r, base);
big_r = q;
for _ in 0..power {
res.push((r % radix) as u8);
r /= radix;
}
}
}
}
while digits.data.len() > 1 {
let (q, mut r) = div_rem_digit(digits, base);
for _ in 0..power {
res.push((r % radix) as u8);
r /= radix;
}
digits = q;
}
let mut r = digits.data[0];
while r != 0 {
res.push((r % radix) as u8);
r /= radix;
}
res
}
pub(super) fn to_radix_le(u: &BigUint, radix: u32) -> Vec<u8> {
if u.is_zero() {
vec![0]
} else if radix.is_power_of_two() {
// Powers of two can use bitwise masks and shifting instead of division
let bits = ilog2(radix);
if big_digit::BITS % bits == 0 {
to_bitwise_digits_le(u, bits)
} else {
to_inexact_bitwise_digits_le(u, bits)
}
} else if radix == 10 {
// 10 is so common that it's worth separating out for const-propagation.
// Optimizers can often turn constant division into a faster multiplication.
to_radix_digits_le(u, 10)
} else {
to_radix_digits_le(u, radix)
}
}
pub(crate) fn to_str_radix_reversed(u: &BigUint, radix: u32) -> Vec<u8> {
assert!(2 <= radix && radix <= 36, "The radix must be within 2...36");
if u.is_zero() {
return vec![b'0'];
}
let mut res = to_radix_le(u, radix);
// Now convert everything to ASCII digits.
for r in &mut res {
debug_assert!(u32::from(*r) < radix);
if *r < 10 {
*r += b'0';
} else {
*r += b'a' - 10;
}
}
res
}
/// Returns the greatest power of the radix for the `BigDigit` bit size
#[inline]
fn get_radix_base(radix: u32) -> (BigDigit, usize) {
static BASES: [(BigDigit, usize); 257] = generate_radix_bases(big_digit::MAX);
debug_assert!(!radix.is_power_of_two());
debug_assert!((3..256).contains(&radix));
BASES[radix as usize]
}
/// Returns the greatest power of the radix for half the `BigDigit` bit size
#[inline]
fn get_half_radix_base(radix: u32) -> (BigDigit, usize) {
static BASES: [(BigDigit, usize); 257] = generate_radix_bases(big_digit::HALF);
debug_assert!(!radix.is_power_of_two());
debug_assert!((3..256).contains(&radix));
BASES[radix as usize]
}
/// Generate tables of the greatest power of each radix that is less that the given maximum. These
/// are returned from `get_radix_base` to batch the multiplication/division of radix conversions on
/// full `BigUint` values, operating on primitive integers as much as possible.
///
/// e.g. BASES_16[3] = (59049, 10) // 3¹⁰ fits in u16, but 3¹¹ is too big
/// BASES_32[3] = (3486784401, 20)
/// BASES_64[3] = (12157665459056928801, 40)
///
/// Powers of two are not included, just zeroed, as they're implemented with shifts.
const fn generate_radix_bases(max: BigDigit) -> [(BigDigit, usize); 257] {
let mut bases = [(0, 0); 257];
let mut radix: BigDigit = 3;
while radix < 256 {
if !radix.is_power_of_two() {
let mut power = 1;
let mut base = radix;
while let Some(b) = base.checked_mul(radix) {
if b > max {
break;
}
base = b;
power += 1;
}
bases[radix as usize] = (base, power)
}
radix += 1;
}
bases
}
#[test]
fn test_radix_bases() {
for radix in 3u32..256 {
if !radix.is_power_of_two() {
let (base, power) = get_radix_base(radix);
let radix = BigDigit::from(radix);
let power = u32::try_from(power).unwrap();
assert_eq!(base, radix.pow(power));
assert!(radix.checked_pow(power + 1).is_none());
}
}
}
#[test]
fn test_half_radix_bases() {
for radix in 3u32..256 {
if !radix.is_power_of_two() {
let (base, power) = get_half_radix_base(radix);
let radix = BigDigit::from(radix);
let power = u32::try_from(power).unwrap();
assert_eq!(base, radix.pow(power));
assert!(radix.pow(power + 1) > big_digit::HALF);
}
}
}

704
vendor/num-bigint/src/biguint/division.rs vendored Normal file
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@@ -0,0 +1,704 @@
use super::addition::__add2;
use super::{cmp_slice, BigUint};
use crate::big_digit::{self, BigDigit, DoubleBigDigit};
use crate::UsizePromotion;
use core::cmp::Ordering::{Equal, Greater, Less};
use core::mem;
use core::ops::{Div, DivAssign, Rem, RemAssign};
use num_integer::Integer;
use num_traits::{CheckedDiv, CheckedEuclid, Euclid, One, ToPrimitive, Zero};
pub(super) const FAST_DIV_WIDE: bool = cfg!(any(target_arch = "x86", target_arch = "x86_64"));
/// Divide a two digit numerator by a one digit divisor, returns quotient and remainder:
///
/// Note: the caller must ensure that both the quotient and remainder will fit into a single digit.
/// This is _not_ true for an arbitrary numerator/denominator.
///
/// (This function also matches what the x86 divide instruction does).
#[cfg(any(miri, not(any(target_arch = "x86", target_arch = "x86_64"))))]
#[inline]
fn div_wide(hi: BigDigit, lo: BigDigit, divisor: BigDigit) -> (BigDigit, BigDigit) {
debug_assert!(hi < divisor);
let lhs = big_digit::to_doublebigdigit(hi, lo);
let rhs = DoubleBigDigit::from(divisor);
((lhs / rhs) as BigDigit, (lhs % rhs) as BigDigit)
}
/// x86 and x86_64 can use a real `div` instruction.
#[cfg(all(not(miri), any(target_arch = "x86", target_arch = "x86_64")))]
#[inline]
fn div_wide(hi: BigDigit, lo: BigDigit, divisor: BigDigit) -> (BigDigit, BigDigit) {
// This debug assertion covers the potential #DE for divisor==0 or a quotient too large for one
// register, otherwise in release mode it will become a target-specific fault like SIGFPE.
// This should never occur with the inputs from our few `div_wide` callers.
debug_assert!(hi < divisor);
// SAFETY: The `div` instruction only affects registers, reading the explicit operand as the
// divisor, and implicitly reading RDX:RAX or EDX:EAX as the dividend. The result is implicitly
// written back to RAX or EAX for the quotient and RDX or EDX for the remainder. No memory is
// used, and flags are not preserved.
unsafe {
let (div, rem);
cfg_digit!(
macro_rules! div {
() => {
"div {0:e}"
};
}
macro_rules! div {
() => {
"div {0:r}"
};
}
);
core::arch::asm!(
div!(),
in(reg) divisor,
inout("dx") hi => rem,
inout("ax") lo => div,
options(pure, nomem, nostack),
);
(div, rem)
}
}
/// For small divisors, we can divide without promoting to `DoubleBigDigit` by
/// using half-size pieces of digit, like long-division.
#[inline]
fn div_half(rem: BigDigit, digit: BigDigit, divisor: BigDigit) -> (BigDigit, BigDigit) {
use crate::big_digit::{HALF, HALF_BITS};
debug_assert!(rem < divisor && divisor <= HALF);
let (hi, rem) = ((rem << HALF_BITS) | (digit >> HALF_BITS)).div_rem(&divisor);
let (lo, rem) = ((rem << HALF_BITS) | (digit & HALF)).div_rem(&divisor);
((hi << HALF_BITS) | lo, rem)
}
#[inline]
pub(super) fn div_rem_digit(mut a: BigUint, b: BigDigit) -> (BigUint, BigDigit) {
if b == 0 {
panic!("attempt to divide by zero")
}
let mut rem = 0;
if !FAST_DIV_WIDE && b <= big_digit::HALF {
for d in a.data.iter_mut().rev() {
let (q, r) = div_half(rem, *d, b);
*d = q;
rem = r;
}
} else {
for d in a.data.iter_mut().rev() {
let (q, r) = div_wide(rem, *d, b);
*d = q;
rem = r;
}
}
(a.normalized(), rem)
}
#[inline]
fn rem_digit(a: &BigUint, b: BigDigit) -> BigDigit {
if b == 0 {
panic!("attempt to divide by zero")
}
let mut rem = 0;
if !FAST_DIV_WIDE && b <= big_digit::HALF {
for &digit in a.data.iter().rev() {
let (_, r) = div_half(rem, digit, b);
rem = r;
}
} else {
for &digit in a.data.iter().rev() {
let (_, r) = div_wide(rem, digit, b);
rem = r;
}
}
rem
}
/// Subtract a multiple.
/// a -= b * c
/// Returns a borrow (if a < b then borrow > 0).
fn sub_mul_digit_same_len(a: &mut [BigDigit], b: &[BigDigit], c: BigDigit) -> BigDigit {
debug_assert!(a.len() == b.len());
// carry is between -big_digit::MAX and 0, so to avoid overflow we store
// offset_carry = carry + big_digit::MAX
let mut offset_carry = big_digit::MAX;
for (x, y) in a.iter_mut().zip(b) {
// We want to calculate sum = x - y * c + carry.
// sum >= -(big_digit::MAX * big_digit::MAX) - big_digit::MAX
// sum <= big_digit::MAX
// Offsetting sum by (big_digit::MAX << big_digit::BITS) puts it in DoubleBigDigit range.
let offset_sum = big_digit::to_doublebigdigit(big_digit::MAX, *x)
- big_digit::MAX as DoubleBigDigit
+ offset_carry as DoubleBigDigit
- *y as DoubleBigDigit * c as DoubleBigDigit;
let (new_offset_carry, new_x) = big_digit::from_doublebigdigit(offset_sum);
offset_carry = new_offset_carry;
*x = new_x;
}
// Return the borrow.
big_digit::MAX - offset_carry
}
fn div_rem(mut u: BigUint, mut d: BigUint) -> (BigUint, BigUint) {
if d.is_zero() {
panic!("attempt to divide by zero")
}
if u.is_zero() {
return (BigUint::ZERO, BigUint::ZERO);
}
if d.data.len() == 1 {
if d.data == [1] {
return (u, BigUint::ZERO);
}
let (div, rem) = div_rem_digit(u, d.data[0]);
// reuse d
d.data.clear();
d += rem;
return (div, d);
}
// Required or the q_len calculation below can underflow:
match u.cmp(&d) {
Less => return (BigUint::ZERO, u),
Equal => {
u.set_one();
return (u, BigUint::ZERO);
}
Greater => {} // Do nothing
}
// This algorithm is from Knuth, TAOCP vol 2 section 4.3, algorithm D:
//
// First, normalize the arguments so the highest bit in the highest digit of the divisor is
// set: the main loop uses the highest digit of the divisor for generating guesses, so we
// want it to be the largest number we can efficiently divide by.
//
let shift = d.data.last().unwrap().leading_zeros() as usize;
if shift == 0 {
// no need to clone d
div_rem_core(u, &d.data)
} else {
let (q, r) = div_rem_core(u << shift, &(d << shift).data);
// renormalize the remainder
(q, r >> shift)
}
}
pub(super) fn div_rem_ref(u: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
if d.is_zero() {
panic!("attempt to divide by zero")
}
if u.is_zero() {
return (BigUint::ZERO, BigUint::ZERO);
}
if d.data.len() == 1 {
if d.data == [1] {
return (u.clone(), BigUint::ZERO);
}
let (div, rem) = div_rem_digit(u.clone(), d.data[0]);
return (div, rem.into());
}
// Required or the q_len calculation below can underflow:
match u.cmp(d) {
Less => return (BigUint::ZERO, u.clone()),
Equal => return (One::one(), BigUint::ZERO),
Greater => {} // Do nothing
}
// This algorithm is from Knuth, TAOCP vol 2 section 4.3, algorithm D:
//
// First, normalize the arguments so the highest bit in the highest digit of the divisor is
// set: the main loop uses the highest digit of the divisor for generating guesses, so we
// want it to be the largest number we can efficiently divide by.
//
let shift = d.data.last().unwrap().leading_zeros() as usize;
if shift == 0 {
// no need to clone d
div_rem_core(u.clone(), &d.data)
} else {
let (q, r) = div_rem_core(u << shift, &(d << shift).data);
// renormalize the remainder
(q, r >> shift)
}
}
/// An implementation of the base division algorithm.
/// Knuth, TAOCP vol 2 section 4.3.1, algorithm D, with an improvement from exercises 19-21.
fn div_rem_core(mut a: BigUint, b: &[BigDigit]) -> (BigUint, BigUint) {
debug_assert!(a.data.len() >= b.len() && b.len() > 1);
debug_assert!(b.last().unwrap().leading_zeros() == 0);
// The algorithm works by incrementally calculating "guesses", q0, for the next digit of the
// quotient. Once we have any number q0 such that (q0 << j) * b <= a, we can set
//
// q += q0 << j
// a -= (q0 << j) * b
//
// and then iterate until a < b. Then, (q, a) will be our desired quotient and remainder.
//
// q0, our guess, is calculated by dividing the last three digits of a by the last two digits of
// b - this will give us a guess that is close to the actual quotient, but is possibly greater.
// It can only be greater by 1 and only in rare cases, with probability at most
// 2^-(big_digit::BITS-1) for random a, see TAOCP 4.3.1 exercise 21.
//
// If the quotient turns out to be too large, we adjust it by 1:
// q -= 1 << j
// a += b << j
// a0 stores an additional extra most significant digit of the dividend, not stored in a.
let mut a0 = 0;
// [b1, b0] are the two most significant digits of the divisor. They never change.
let b0 = b[b.len() - 1];
let b1 = b[b.len() - 2];
let q_len = a.data.len() - b.len() + 1;
let mut q = BigUint {
data: vec![0; q_len],
};
for j in (0..q_len).rev() {
debug_assert!(a.data.len() == b.len() + j);
let a1 = *a.data.last().unwrap();
let a2 = a.data[a.data.len() - 2];
// The first q0 estimate is [a1,a0] / b0. It will never be too small, it may be too large
// by at most 2.
let (mut q0, mut r) = if a0 < b0 {
let (q0, r) = div_wide(a0, a1, b0);
(q0, r as DoubleBigDigit)
} else {
debug_assert!(a0 == b0);
// Avoid overflowing q0, we know the quotient fits in BigDigit.
// [a1,a0] = b0 * (1<<BITS - 1) + (a0 + a1)
(big_digit::MAX, a0 as DoubleBigDigit + a1 as DoubleBigDigit)
};
// r = [a1,a0] - q0 * b0
//
// Now we want to compute a more precise estimate [a2,a1,a0] / [b1,b0] which can only be
// less or equal to the current q0.
//
// q0 is too large if:
// [a2,a1,a0] < q0 * [b1,b0]
// (r << BITS) + a2 < q0 * b1
while r <= big_digit::MAX as DoubleBigDigit
&& big_digit::to_doublebigdigit(r as BigDigit, a2)
< q0 as DoubleBigDigit * b1 as DoubleBigDigit
{
q0 -= 1;
r += b0 as DoubleBigDigit;
}
// q0 is now either the correct quotient digit, or in rare cases 1 too large.
// Subtract (q0 << j) from a. This may overflow, in which case we will have to correct.
let mut borrow = sub_mul_digit_same_len(&mut a.data[j..], b, q0);
if borrow > a0 {
// q0 is too large. We need to add back one multiple of b.
q0 -= 1;
borrow -= __add2(&mut a.data[j..], b);
}
// The top digit of a, stored in a0, has now been zeroed.
debug_assert!(borrow == a0);
q.data[j] = q0;
// Pop off the next top digit of a.
a0 = a.data.pop().unwrap();
}
a.data.push(a0);
a.normalize();
debug_assert_eq!(cmp_slice(&a.data, b), Less);
(q.normalized(), a)
}
forward_val_ref_binop!(impl Div for BigUint, div);
forward_ref_val_binop!(impl Div for BigUint, div);
forward_val_assign!(impl DivAssign for BigUint, div_assign);
impl Div<BigUint> for BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: BigUint) -> BigUint {
let (q, _) = div_rem(self, other);
q
}
}
impl Div<&BigUint> for &BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: &BigUint) -> BigUint {
let (q, _) = self.div_rem(other);
q
}
}
impl DivAssign<&BigUint> for BigUint {
#[inline]
fn div_assign(&mut self, other: &BigUint) {
*self = &*self / other;
}
}
promote_unsigned_scalars!(impl Div for BigUint, div);
promote_unsigned_scalars_assign!(impl DivAssign for BigUint, div_assign);
forward_all_scalar_binop_to_val_val!(impl Div<u32> for BigUint, div);
forward_all_scalar_binop_to_val_val!(impl Div<u64> for BigUint, div);
forward_all_scalar_binop_to_val_val!(impl Div<u128> for BigUint, div);
impl Div<u32> for BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: u32) -> BigUint {
let (q, _) = div_rem_digit(self, other as BigDigit);
q
}
}
impl DivAssign<u32> for BigUint {
#[inline]
fn div_assign(&mut self, other: u32) {
*self = &*self / other;
}
}
impl Div<BigUint> for u32 {
type Output = BigUint;
#[inline]
fn div(self, other: BigUint) -> BigUint {
match other.data.len() {
0 => panic!("attempt to divide by zero"),
1 => From::from(self as BigDigit / other.data[0]),
_ => BigUint::ZERO,
}
}
}
impl Div<u64> for BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: u64) -> BigUint {
let (q, _) = div_rem(self, From::from(other));
q
}
}
impl DivAssign<u64> for BigUint {
#[inline]
fn div_assign(&mut self, other: u64) {
// a vec of size 0 does not allocate, so this is fairly cheap
let temp = mem::replace(self, Self::ZERO);
*self = temp / other;
}
}
impl Div<BigUint> for u64 {
type Output = BigUint;
cfg_digit!(
#[inline]
fn div(self, other: BigUint) -> BigUint {
match other.data.len() {
0 => panic!("attempt to divide by zero"),
1 => From::from(self / u64::from(other.data[0])),
2 => From::from(self / big_digit::to_doublebigdigit(other.data[1], other.data[0])),
_ => BigUint::ZERO,
}
}
#[inline]
fn div(self, other: BigUint) -> BigUint {
match other.data.len() {
0 => panic!("attempt to divide by zero"),
1 => From::from(self / other.data[0]),
_ => BigUint::ZERO,
}
}
);
}
impl Div<u128> for BigUint {
type Output = BigUint;
#[inline]
fn div(self, other: u128) -> BigUint {
let (q, _) = div_rem(self, From::from(other));
q
}
}
impl DivAssign<u128> for BigUint {
#[inline]
fn div_assign(&mut self, other: u128) {
*self = &*self / other;
}
}
impl Div<BigUint> for u128 {
type Output = BigUint;
cfg_digit!(
#[inline]
fn div(self, other: BigUint) -> BigUint {
use super::u32_to_u128;
match other.data.len() {
0 => panic!("attempt to divide by zero"),
1 => From::from(self / u128::from(other.data[0])),
2 => From::from(
self / u128::from(big_digit::to_doublebigdigit(other.data[1], other.data[0])),
),
3 => From::from(self / u32_to_u128(0, other.data[2], other.data[1], other.data[0])),
4 => From::from(
self / u32_to_u128(other.data[3], other.data[2], other.data[1], other.data[0]),
),
_ => BigUint::ZERO,
}
}
#[inline]
fn div(self, other: BigUint) -> BigUint {
match other.data.len() {
0 => panic!("attempt to divide by zero"),
1 => From::from(self / other.data[0] as u128),
2 => From::from(self / big_digit::to_doublebigdigit(other.data[1], other.data[0])),
_ => BigUint::ZERO,
}
}
);
}
forward_val_ref_binop!(impl Rem for BigUint, rem);
forward_ref_val_binop!(impl Rem for BigUint, rem);
forward_val_assign!(impl RemAssign for BigUint, rem_assign);
impl Rem<BigUint> for BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: BigUint) -> BigUint {
if let Some(other) = other.to_u32() {
&self % other
} else {
let (_, r) = div_rem(self, other);
r
}
}
}
impl Rem<&BigUint> for &BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: &BigUint) -> BigUint {
if let Some(other) = other.to_u32() {
self % other
} else {
let (_, r) = self.div_rem(other);
r
}
}
}
impl RemAssign<&BigUint> for BigUint {
#[inline]
fn rem_assign(&mut self, other: &BigUint) {
*self = &*self % other;
}
}
promote_unsigned_scalars!(impl Rem for BigUint, rem);
promote_unsigned_scalars_assign!(impl RemAssign for BigUint, rem_assign);
forward_all_scalar_binop_to_ref_val!(impl Rem<u32> for BigUint, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<u64> for BigUint, rem);
forward_all_scalar_binop_to_val_val!(impl Rem<u128> for BigUint, rem);
impl Rem<u32> for &BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: u32) -> BigUint {
rem_digit(self, other as BigDigit).into()
}
}
impl RemAssign<u32> for BigUint {
#[inline]
fn rem_assign(&mut self, other: u32) {
*self = &*self % other;
}
}
impl Rem<&BigUint> for u32 {
type Output = BigUint;
#[inline]
fn rem(mut self, other: &BigUint) -> BigUint {
self %= other;
From::from(self)
}
}
macro_rules! impl_rem_assign_scalar {
($scalar:ty, $to_scalar:ident) => {
forward_val_assign_scalar!(impl RemAssign for BigUint, $scalar, rem_assign);
impl RemAssign<&BigUint> for $scalar {
#[inline]
fn rem_assign(&mut self, other: &BigUint) {
*self = match other.$to_scalar() {
None => *self,
Some(0) => panic!("attempt to divide by zero"),
Some(v) => *self % v
};
}
}
}
}
// we can scalar %= BigUint for any scalar, including signed types
impl_rem_assign_scalar!(u128, to_u128);
impl_rem_assign_scalar!(usize, to_usize);
impl_rem_assign_scalar!(u64, to_u64);
impl_rem_assign_scalar!(u32, to_u32);
impl_rem_assign_scalar!(u16, to_u16);
impl_rem_assign_scalar!(u8, to_u8);
impl_rem_assign_scalar!(i128, to_i128);
impl_rem_assign_scalar!(isize, to_isize);
impl_rem_assign_scalar!(i64, to_i64);
impl_rem_assign_scalar!(i32, to_i32);
impl_rem_assign_scalar!(i16, to_i16);
impl_rem_assign_scalar!(i8, to_i8);
impl Rem<u64> for BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: u64) -> BigUint {
let (_, r) = div_rem(self, From::from(other));
r
}
}
impl RemAssign<u64> for BigUint {
#[inline]
fn rem_assign(&mut self, other: u64) {
*self = &*self % other;
}
}
impl Rem<BigUint> for u64 {
type Output = BigUint;
#[inline]
fn rem(mut self, other: BigUint) -> BigUint {
self %= other;
From::from(self)
}
}
impl Rem<u128> for BigUint {
type Output = BigUint;
#[inline]
fn rem(self, other: u128) -> BigUint {
let (_, r) = div_rem(self, From::from(other));
r
}
}
impl RemAssign<u128> for BigUint {
#[inline]
fn rem_assign(&mut self, other: u128) {
*self = &*self % other;
}
}
impl Rem<BigUint> for u128 {
type Output = BigUint;
#[inline]
fn rem(mut self, other: BigUint) -> BigUint {
self %= other;
From::from(self)
}
}
impl CheckedDiv for BigUint {
#[inline]
fn checked_div(&self, v: &BigUint) -> Option<BigUint> {
if v.is_zero() {
return None;
}
Some(self.div(v))
}
}
impl CheckedEuclid for BigUint {
#[inline]
fn checked_div_euclid(&self, v: &BigUint) -> Option<BigUint> {
if v.is_zero() {
return None;
}
Some(self.div_euclid(v))
}
#[inline]
fn checked_rem_euclid(&self, v: &BigUint) -> Option<BigUint> {
if v.is_zero() {
return None;
}
Some(self.rem_euclid(v))
}
fn checked_div_rem_euclid(&self, v: &Self) -> Option<(Self, Self)> {
Some(self.div_rem_euclid(v))
}
}
impl Euclid for BigUint {
#[inline]
fn div_euclid(&self, v: &BigUint) -> BigUint {
// trivially same as regular division
self / v
}
#[inline]
fn rem_euclid(&self, v: &BigUint) -> BigUint {
// trivially same as regular remainder
self % v
}
fn div_rem_euclid(&self, v: &Self) -> (Self, Self) {
// trivially same as regular division and remainder
self.div_rem(v)
}
}

361
vendor/num-bigint/src/biguint/iter.rs vendored Normal file
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@@ -0,0 +1,361 @@
use core::iter::FusedIterator;
cfg_digit!(
/// An iterator of `u32` digits representation of a `BigUint` or `BigInt`,
/// ordered least significant digit first.
pub struct U32Digits<'a> {
it: core::slice::Iter<'a, u32>,
}
/// An iterator of `u32` digits representation of a `BigUint` or `BigInt`,
/// ordered least significant digit first.
pub struct U32Digits<'a> {
data: &'a [u64],
next_is_lo: bool,
last_hi_is_zero: bool,
}
);
cfg_digit!(
const _: () = {
impl<'a> U32Digits<'a> {
#[inline]
pub(super) fn new(data: &'a [u32]) -> Self {
Self { it: data.iter() }
}
}
impl Iterator for U32Digits<'_> {
type Item = u32;
#[inline]
fn next(&mut self) -> Option<u32> {
self.it.next().cloned()
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
self.it.size_hint()
}
#[inline]
fn nth(&mut self, n: usize) -> Option<u32> {
self.it.nth(n).cloned()
}
#[inline]
fn last(self) -> Option<u32> {
self.it.last().cloned()
}
#[inline]
fn count(self) -> usize {
self.it.count()
}
}
impl DoubleEndedIterator for U32Digits<'_> {
fn next_back(&mut self) -> Option<Self::Item> {
self.it.next_back().cloned()
}
}
impl ExactSizeIterator for U32Digits<'_> {
#[inline]
fn len(&self) -> usize {
self.it.len()
}
}
};
const _: () = {
impl<'a> U32Digits<'a> {
#[inline]
pub(super) fn new(data: &'a [u64]) -> Self {
let last_hi_is_zero = data
.last()
.map(|&last| {
let last_hi = (last >> 32) as u32;
last_hi == 0
})
.unwrap_or(false);
U32Digits {
data,
next_is_lo: true,
last_hi_is_zero,
}
}
}
impl Iterator for U32Digits<'_> {
type Item = u32;
#[inline]
fn next(&mut self) -> Option<u32> {
match self.data.split_first() {
Some((&first, data)) => {
let next_is_lo = self.next_is_lo;
self.next_is_lo = !next_is_lo;
if next_is_lo {
Some(first as u32)
} else {
self.data = data;
if data.is_empty() && self.last_hi_is_zero {
self.last_hi_is_zero = false;
None
} else {
Some((first >> 32) as u32)
}
}
}
None => None,
}
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
let len = self.len();
(len, Some(len))
}
#[inline]
fn last(self) -> Option<u32> {
self.data.last().map(|&last| {
if self.last_hi_is_zero {
last as u32
} else {
(last >> 32) as u32
}
})
}
#[inline]
fn count(self) -> usize {
self.len()
}
}
impl DoubleEndedIterator for U32Digits<'_> {
fn next_back(&mut self) -> Option<Self::Item> {
match self.data.split_last() {
Some((&last, data)) => {
let last_is_lo = self.last_hi_is_zero;
self.last_hi_is_zero = !last_is_lo;
if last_is_lo {
self.data = data;
if data.is_empty() && !self.next_is_lo {
self.next_is_lo = true;
None
} else {
Some(last as u32)
}
} else {
Some((last >> 32) as u32)
}
}
None => None,
}
}
}
impl ExactSizeIterator for U32Digits<'_> {
#[inline]
fn len(&self) -> usize {
self.data.len() * 2
- usize::from(self.last_hi_is_zero)
- usize::from(!self.next_is_lo)
}
}
};
);
impl FusedIterator for U32Digits<'_> {}
cfg_digit!(
/// An iterator of `u64` digits representation of a `BigUint` or `BigInt`,
/// ordered least significant digit first.
pub struct U64Digits<'a> {
it: core::slice::Chunks<'a, u32>,
}
/// An iterator of `u64` digits representation of a `BigUint` or `BigInt`,
/// ordered least significant digit first.
pub struct U64Digits<'a> {
it: core::slice::Iter<'a, u64>,
}
);
cfg_digit!(
const _: () = {
impl<'a> U64Digits<'a> {
#[inline]
pub(super) fn new(data: &'a [u32]) -> Self {
U64Digits { it: data.chunks(2) }
}
}
impl Iterator for U64Digits<'_> {
type Item = u64;
#[inline]
fn next(&mut self) -> Option<u64> {
self.it.next().map(super::u32_chunk_to_u64)
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
let len = self.len();
(len, Some(len))
}
#[inline]
fn last(self) -> Option<u64> {
self.it.last().map(super::u32_chunk_to_u64)
}
#[inline]
fn count(self) -> usize {
self.len()
}
}
impl DoubleEndedIterator for U64Digits<'_> {
fn next_back(&mut self) -> Option<Self::Item> {
self.it.next_back().map(super::u32_chunk_to_u64)
}
}
};
const _: () = {
impl<'a> U64Digits<'a> {
#[inline]
pub(super) fn new(data: &'a [u64]) -> Self {
Self { it: data.iter() }
}
}
impl Iterator for U64Digits<'_> {
type Item = u64;
#[inline]
fn next(&mut self) -> Option<u64> {
self.it.next().cloned()
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
self.it.size_hint()
}
#[inline]
fn nth(&mut self, n: usize) -> Option<u64> {
self.it.nth(n).cloned()
}
#[inline]
fn last(self) -> Option<u64> {
self.it.last().cloned()
}
#[inline]
fn count(self) -> usize {
self.it.count()
}
}
impl DoubleEndedIterator for U64Digits<'_> {
fn next_back(&mut self) -> Option<Self::Item> {
self.it.next_back().cloned()
}
}
};
);
impl ExactSizeIterator for U64Digits<'_> {
#[inline]
fn len(&self) -> usize {
self.it.len()
}
}
impl FusedIterator for U64Digits<'_> {}
#[test]
fn test_iter_u32_digits() {
let n = super::BigUint::from(5u8);
let mut it = n.iter_u32_digits();
assert_eq!(it.len(), 1);
assert_eq!(it.next(), Some(5));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
let n = super::BigUint::from(112500000000u64);
let mut it = n.iter_u32_digits();
assert_eq!(it.len(), 2);
assert_eq!(it.next(), Some(830850304));
assert_eq!(it.len(), 1);
assert_eq!(it.next(), Some(26));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
}
#[test]
fn test_iter_u64_digits() {
let n = super::BigUint::from(5u8);
let mut it = n.iter_u64_digits();
assert_eq!(it.len(), 1);
assert_eq!(it.next(), Some(5));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
let n = super::BigUint::from(18_446_744_073_709_551_616u128);
let mut it = n.iter_u64_digits();
assert_eq!(it.len(), 2);
assert_eq!(it.next(), Some(0));
assert_eq!(it.len(), 1);
assert_eq!(it.next(), Some(1));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
}
#[test]
fn test_iter_u32_digits_be() {
let n = super::BigUint::from(5u8);
let mut it = n.iter_u32_digits();
assert_eq!(it.len(), 1);
assert_eq!(it.next(), Some(5));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
let n = super::BigUint::from(112500000000u64);
let mut it = n.iter_u32_digits();
assert_eq!(it.len(), 2);
assert_eq!(it.next(), Some(830850304));
assert_eq!(it.len(), 1);
assert_eq!(it.next(), Some(26));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
}
#[test]
fn test_iter_u64_digits_be() {
let n = super::BigUint::from(5u8);
let mut it = n.iter_u64_digits();
assert_eq!(it.len(), 1);
assert_eq!(it.next_back(), Some(5));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
let n = super::BigUint::from(18_446_744_073_709_551_616u128);
let mut it = n.iter_u64_digits();
assert_eq!(it.len(), 2);
assert_eq!(it.next_back(), Some(1));
assert_eq!(it.len(), 1);
assert_eq!(it.next_back(), Some(0));
assert_eq!(it.len(), 0);
assert_eq!(it.next(), None);
}

226
vendor/num-bigint/src/biguint/monty.rs vendored Normal file
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@@ -0,0 +1,226 @@
use alloc::vec::Vec;
use core::mem;
use core::ops::Shl;
use num_traits::One;
use crate::big_digit::{self, BigDigit, DoubleBigDigit};
use crate::biguint::BigUint;
struct MontyReducer {
n0inv: BigDigit,
}
// k0 = -m**-1 mod 2**BITS. Algorithm from: Dumas, J.G. "On Newton–Raphson
// Iteration for Multiplicative Inverses Modulo Prime Powers".
fn inv_mod_alt(b: BigDigit) -> BigDigit {
assert_ne!(b & 1, 0);
let mut k0 = BigDigit::wrapping_sub(2, b);
let mut t = b - 1;
let mut i = 1;
while i < big_digit::BITS {
t = t.wrapping_mul(t);
k0 = k0.wrapping_mul(t + 1);
i <<= 1;
}
debug_assert_eq!(k0.wrapping_mul(b), 1);
k0.wrapping_neg()
}
impl MontyReducer {
fn new(n: &BigUint) -> Self {
let n0inv = inv_mod_alt(n.data[0]);
MontyReducer { n0inv }
}
}
/// Computes z mod m = x * y * 2 ** (-n*_W) mod m
/// assuming k = -1/m mod 2**_W
/// See Gueron, "Efficient Software Implementations of Modular Exponentiation".
/// <https://eprint.iacr.org/2011/239.pdf>
/// In the terminology of that paper, this is an "Almost Montgomery Multiplication":
/// x and y are required to satisfy 0 <= z < 2**(n*_W) and then the result
/// z is guaranteed to satisfy 0 <= z < 2**(n*_W), but it may not be < m.
#[allow(clippy::many_single_char_names)]
fn montgomery(x: &BigUint, y: &BigUint, m: &BigUint, k: BigDigit, n: usize) -> BigUint {
// This code assumes x, y, m are all the same length, n.
// (required by addMulVVW and the for loop).
// It also assumes that x, y are already reduced mod m,
// or else the result will not be properly reduced.
assert!(
x.data.len() == n && y.data.len() == n && m.data.len() == n,
"{:?} {:?} {:?} {}",
x,
y,
m,
n
);
let mut z = BigUint::ZERO;
z.data.resize(n * 2, 0);
let mut c: BigDigit = 0;
for i in 0..n {
let c2 = add_mul_vvw(&mut z.data[i..n + i], &x.data, y.data[i]);
let t = z.data[i].wrapping_mul(k);
let c3 = add_mul_vvw(&mut z.data[i..n + i], &m.data, t);
let cx = c.wrapping_add(c2);
let cy = cx.wrapping_add(c3);
z.data[n + i] = cy;
if cx < c2 || cy < c3 {
c = 1;
} else {
c = 0;
}
}
if c == 0 {
z.data = z.data[n..].to_vec();
} else {
{
let (first, second) = z.data.split_at_mut(n);
sub_vv(first, second, &m.data);
}
z.data = z.data[..n].to_vec();
}
z
}
#[inline(always)]
fn add_mul_vvw(z: &mut [BigDigit], x: &[BigDigit], y: BigDigit) -> BigDigit {
let mut c = 0;
for (zi, xi) in z.iter_mut().zip(x.iter()) {
let (z1, z0) = mul_add_www(*xi, y, *zi);
let (c_, zi_) = add_ww(z0, c, 0);
*zi = zi_;
c = c_ + z1;
}
c
}
/// The resulting carry c is either 0 or 1.
#[inline(always)]
fn sub_vv(z: &mut [BigDigit], x: &[BigDigit], y: &[BigDigit]) -> BigDigit {
let mut c = 0;
for (i, (xi, yi)) in x.iter().zip(y.iter()).enumerate().take(z.len()) {
let zi = xi.wrapping_sub(*yi).wrapping_sub(c);
z[i] = zi;
// see "Hacker's Delight", section 2-12 (overflow detection)
c = ((yi & !xi) | ((yi | !xi) & zi)) >> (big_digit::BITS - 1)
}
c
}
/// z1<<_W + z0 = x+y+c, with c == 0 or 1
#[inline(always)]
fn add_ww(x: BigDigit, y: BigDigit, c: BigDigit) -> (BigDigit, BigDigit) {
let yc = y.wrapping_add(c);
let z0 = x.wrapping_add(yc);
let z1 = if z0 < x || yc < y { 1 } else { 0 };
(z1, z0)
}
/// z1 << _W + z0 = x * y + c
#[inline(always)]
fn mul_add_www(x: BigDigit, y: BigDigit, c: BigDigit) -> (BigDigit, BigDigit) {
let z = x as DoubleBigDigit * y as DoubleBigDigit + c as DoubleBigDigit;
((z >> big_digit::BITS) as BigDigit, z as BigDigit)
}
/// Calculates x ** y mod m using a fixed, 4-bit window.
#[allow(clippy::many_single_char_names)]
pub(super) fn monty_modpow(x: &BigUint, y: &BigUint, m: &BigUint) -> BigUint {
assert!(m.data[0] & 1 == 1);
let mr = MontyReducer::new(m);
let num_words = m.data.len();
let mut x = x.clone();
// We want the lengths of x and m to be equal.
// It is OK if x >= m as long as len(x) == len(m).
if x.data.len() > num_words {
x %= m;
// Note: now len(x) <= numWords, not guaranteed ==.
}
if x.data.len() < num_words {
x.data.resize(num_words, 0);
}
// rr = 2**(2*_W*len(m)) mod m
let mut rr = BigUint::one();
rr = (rr.shl(2 * num_words as u64 * u64::from(big_digit::BITS))) % m;
if rr.data.len() < num_words {
rr.data.resize(num_words, 0);
}
// one = 1, with equal length to that of m
let mut one = BigUint::one();
one.data.resize(num_words, 0);
let n = 4;
// powers[i] contains x^i
let mut powers = Vec::with_capacity(1 << n);
powers.push(montgomery(&one, &rr, m, mr.n0inv, num_words));
powers.push(montgomery(&x, &rr, m, mr.n0inv, num_words));
for i in 2..1 << n {
let r = montgomery(&powers[i - 1], &powers[1], m, mr.n0inv, num_words);
powers.push(r);
}
// initialize z = 1 (Montgomery 1)
let mut z = powers[0].clone();
z.data.resize(num_words, 0);
let mut zz = BigUint::ZERO;
zz.data.resize(num_words, 0);
// same windowed exponent, but with Montgomery multiplications
for i in (0..y.data.len()).rev() {
let mut yi = y.data[i];
let mut j = 0;
while j < big_digit::BITS {
if i != y.data.len() - 1 || j != 0 {
zz = montgomery(&z, &z, m, mr.n0inv, num_words);
z = montgomery(&zz, &zz, m, mr.n0inv, num_words);
zz = montgomery(&z, &z, m, mr.n0inv, num_words);
z = montgomery(&zz, &zz, m, mr.n0inv, num_words);
}
zz = montgomery(
&z,
&powers[(yi >> (big_digit::BITS - n)) as usize],
m,
mr.n0inv,
num_words,
);
mem::swap(&mut z, &mut zz);
yi <<= n;
j += n;
}
}
// convert to regular number
zz = montgomery(&z, &one, m, mr.n0inv, num_words);
zz.normalize();
// One last reduction, just in case.
// See golang.org/issue/13907.
if zz >= *m {
// Common case is m has high bit set; in that case,
// since zz is the same length as m, there can be just
// one multiple of m to remove. Just subtract.
// We think that the subtract should be sufficient in general,
// so do that unconditionally, but double-check,
// in case our beliefs are wrong.
// The div is not expected to be reached.
zz -= m;
if zz >= *m {
zz %= m;
}
}
zz.normalize();
zz
}

626
vendor/num-bigint/src/biguint/multiplication.rs vendored Normal file
View File

@@ -0,0 +1,626 @@
use super::addition::{__add2, add2};
use super::subtraction::sub2;
use super::{biguint_from_vec, cmp_slice, BigUint, IntDigits};
use crate::big_digit::{self, BigDigit, DoubleBigDigit};
use crate::Sign::{self, Minus, NoSign, Plus};
use crate::{BigInt, UsizePromotion};
use core::cmp::Ordering;
use core::iter::Product;
use core::ops::{Mul, MulAssign};
use num_traits::{CheckedMul, FromPrimitive, One, Zero};
#[inline]
pub(super) fn mac_with_carry(
a: BigDigit,
b: BigDigit,
c: BigDigit,
acc: &mut DoubleBigDigit,
) -> BigDigit {
*acc += DoubleBigDigit::from(a);
*acc += DoubleBigDigit::from(b) * DoubleBigDigit::from(c);
let lo = *acc as BigDigit;
*acc >>= big_digit::BITS;
lo
}
#[inline]
fn mul_with_carry(a: BigDigit, b: BigDigit, acc: &mut DoubleBigDigit) -> BigDigit {
*acc += DoubleBigDigit::from(a) * DoubleBigDigit::from(b);
let lo = *acc as BigDigit;
*acc >>= big_digit::BITS;
lo
}
/// Three argument multiply accumulate:
/// acc += b * c
fn mac_digit(acc: &mut [BigDigit], b: &[BigDigit], c: BigDigit) {
if c == 0 {
return;
}
let mut carry = 0;
let (a_lo, a_hi) = acc.split_at_mut(b.len());
for (a, &b) in a_lo.iter_mut().zip(b) {
*a = mac_with_carry(*a, b, c, &mut carry);
}
let (carry_hi, carry_lo) = big_digit::from_doublebigdigit(carry);
let final_carry = if carry_hi == 0 {
__add2(a_hi, &[carry_lo])
} else {
__add2(a_hi, &[carry_hi, carry_lo])
};
assert_eq!(final_carry, 0, "carry overflow during multiplication!");
}
fn bigint_from_slice(slice: &[BigDigit]) -> BigInt {
BigInt::from(biguint_from_vec(slice.to_vec()))
}
/// Three argument multiply accumulate:
/// acc += b * c
#[allow(clippy::many_single_char_names)]
fn mac3(mut acc: &mut [BigDigit], mut b: &[BigDigit], mut c: &[BigDigit]) {
// Least-significant zeros have no effect on the output.
if let Some(&0) = b.first() {
if let Some(nz) = b.iter().position(|&d| d != 0) {
b = &b[nz..];
acc = &mut acc[nz..];
} else {
return;
}
}
if let Some(&0) = c.first() {
if let Some(nz) = c.iter().position(|&d| d != 0) {
c = &c[nz..];
acc = &mut acc[nz..];
} else {
return;
}
}
let acc = acc;
let (x, y) = if b.len() < c.len() { (b, c) } else { (c, b) };
// We use four algorithms for different input sizes.
//
// - For small inputs, long multiplication is fastest.
// - If y is at least least twice as long as x, split using Half-Karatsuba.
// - Next we use Karatsuba multiplication (Toom-2), which we have optimized
// to avoid unnecessary allocations for intermediate values.
// - For the largest inputs we use Toom-3, which better optimizes the
// number of operations, but uses more temporary allocations.
//
// The thresholds are somewhat arbitrary, chosen by evaluating the results
// of `cargo bench --bench bigint multiply`.
if x.len() <= 32 {
// Long multiplication:
for (i, xi) in x.iter().enumerate() {
mac_digit(&mut acc[i..], y, *xi);
}
} else if x.len() * 2 <= y.len() {
// Karatsuba Multiplication for factors with significant length disparity.
//
// The Half-Karatsuba Multiplication Algorithm is a specialized case of
// the normal Karatsuba multiplication algorithm, designed for the scenario
// where y has at least twice as many base digits as x.
//
// In this case y (the longer input) is split into high2 and low2,
// at m2 (half the length of y) and x (the shorter input),
// is used directly without splitting.
//
// The algorithm then proceeds as follows:
//
// 1. Compute the product z0 = x * low2.
// 2. Compute the product temp = x * high2.
// 3. Adjust the weight of temp by adding m2 (* NBASE ^ m2)
// 4. Add temp and z0 to obtain the final result.
//
// Proof:
//
// The algorithm can be derived from the original Karatsuba algorithm by
// simplifying the formula when the shorter factor x is not split into
// high and low parts, as shown below.
//
// Original Karatsuba formula:
//
// result = (z2 * NBASE ^ (m2 × 2)) + ((z1 - z2 - z0) * NBASE ^ m2) + z0
//
// Substitutions:
//
// low1 = x
// high1 = 0
//
// Applying substitutions:
//
// z0 = (low1 * low2)
// = (x * low2)
//
// z1 = ((low1 + high1) * (low2 + high2))
// = ((x + 0) * (low2 + high2))
// = (x * low2) + (x * high2)
//
// z2 = (high1 * high2)
// = (0 * high2)
// = 0
//
// Simplified using the above substitutions:
//
// result = (z2 * NBASE ^ (m2 × 2)) + ((z1 - z2 - z0) * NBASE ^ m2) + z0
// = (0 * NBASE ^ (m2 × 2)) + ((z1 - 0 - z0) * NBASE ^ m2) + z0
// = ((z1 - z0) * NBASE ^ m2) + z0
// = ((z1 - z0) * NBASE ^ m2) + z0
// = (x * high2) * NBASE ^ m2 + z0
let m2 = y.len() / 2;
let (low2, high2) = y.split_at(m2);
// (x * high2) * NBASE ^ m2 + z0
mac3(acc, x, low2);
mac3(&mut acc[m2..], x, high2);
} else if x.len() <= 256 {
// Karatsuba multiplication:
//
// The idea is that we break x and y up into two smaller numbers that each have about half
// as many digits, like so (note that multiplying by b is just a shift):
//
// x = x0 + x1 * b
// y = y0 + y1 * b
//
// With some algebra, we can compute x * y with three smaller products, where the inputs to
// each of the smaller products have only about half as many digits as x and y:
//
// x * y = (x0 + x1 * b) * (y0 + y1 * b)
//
// x * y = x0 * y0
// + x0 * y1 * b
// + x1 * y0 * b
// + x1 * y1 * b^2
//
// Let p0 = x0 * y0 and p2 = x1 * y1:
//
// x * y = p0
// + (x0 * y1 + x1 * y0) * b
// + p2 * b^2
//
// The real trick is that middle term:
//
// x0 * y1 + x1 * y0
//
// = x0 * y1 + x1 * y0 - p0 + p0 - p2 + p2
//
// = x0 * y1 + x1 * y0 - x0 * y0 - x1 * y1 + p0 + p2
//
// Now we complete the square:
//
// = -(x0 * y0 - x0 * y1 - x1 * y0 + x1 * y1) + p0 + p2
//
// = -((x1 - x0) * (y1 - y0)) + p0 + p2
//
// Let p1 = (x1 - x0) * (y1 - y0), and substitute back into our original formula:
//
// x * y = p0
// + (p0 + p2 - p1) * b
// + p2 * b^2
//
// Where the three intermediate products are:
//
// p0 = x0 * y0
// p1 = (x1 - x0) * (y1 - y0)
// p2 = x1 * y1
//
// In doing the computation, we take great care to avoid unnecessary temporary variables
// (since creating a BigUint requires a heap allocation): thus, we rearrange the formula a
// bit so we can use the same temporary variable for all the intermediate products:
//
// x * y = p2 * b^2 + p2 * b
// + p0 * b + p0
// - p1 * b
//
// The other trick we use is instead of doing explicit shifts, we slice acc at the
// appropriate offset when doing the add.
// When x is smaller than y, it's significantly faster to pick b such that x is split in
// half, not y:
let b = x.len() / 2;
let (x0, x1) = x.split_at(b);
let (y0, y1) = y.split_at(b);
// We reuse the same BigUint for all the intermediate multiplies and have to size p
// appropriately here: x1.len() >= x0.len and y1.len() >= y0.len():
let len = x1.len() + y1.len() + 1;
let mut p = BigUint { data: vec![0; len] };
// p2 = x1 * y1
mac3(&mut p.data, x1, y1);
// Not required, but the adds go faster if we drop any unneeded 0s from the end:
p.normalize();
add2(&mut acc[b..], &p.data);
add2(&mut acc[b * 2..], &p.data);
// Zero out p before the next multiply:
p.data.truncate(0);
p.data.resize(len, 0);
// p0 = x0 * y0
mac3(&mut p.data, x0, y0);
p.normalize();
add2(acc, &p.data);
add2(&mut acc[b..], &p.data);
// p1 = (x1 - x0) * (y1 - y0)
// We do this one last, since it may be negative and acc can't ever be negative:
let (j0_sign, j0) = sub_sign(x1, x0);
let (j1_sign, j1) = sub_sign(y1, y0);
match j0_sign * j1_sign {
Plus => {
p.data.truncate(0);
p.data.resize(len, 0);
mac3(&mut p.data, &j0.data, &j1.data);
p.normalize();
sub2(&mut acc[b..], &p.data);
}
Minus => {
mac3(&mut acc[b..], &j0.data, &j1.data);
}
NoSign => (),
}
} else {
// Toom-3 multiplication:
//
// Toom-3 is like Karatsuba above, but dividing the inputs into three parts.
// Both are instances of Toom-Cook, using `k=3` and `k=2` respectively.
//
// The general idea is to treat the large integers digits as
// polynomials of a certain degree and determine the coefficients/digits
// of the product of the two via interpolation of the polynomial product.
let i = y.len() / 3 + 1;
let x0_len = Ord::min(x.len(), i);
let x1_len = Ord::min(x.len() - x0_len, i);
let y0_len = i;
let y1_len = Ord::min(y.len() - y0_len, i);
// Break x and y into three parts, representating an order two polynomial.
// t is chosen to be the size of a digit so we can use faster shifts
// in place of multiplications.
//
// x(t) = x2*t^2 + x1*t + x0
let x0 = bigint_from_slice(&x[..x0_len]);
let x1 = bigint_from_slice(&x[x0_len..x0_len + x1_len]);
let x2 = bigint_from_slice(&x[x0_len + x1_len..]);
// y(t) = y2*t^2 + y1*t + y0
let y0 = bigint_from_slice(&y[..y0_len]);
let y1 = bigint_from_slice(&y[y0_len..y0_len + y1_len]);
let y2 = bigint_from_slice(&y[y0_len + y1_len..]);
// Let w(t) = x(t) * y(t)
//
// This gives us the following order-4 polynomial.
//
// w(t) = w4*t^4 + w3*t^3 + w2*t^2 + w1*t + w0
//
// We need to find the coefficients w4, w3, w2, w1 and w0. Instead
// of simply multiplying the x and y in total, we can evaluate w
// at 5 points. An n-degree polynomial is uniquely identified by (n + 1)
// points.
//
// It is arbitrary as to what points we evaluate w at but we use the
// following.
//
// w(t) at t = 0, 1, -1, -2 and inf
//
// The values for w(t) in terms of x(t)*y(t) at these points are:
//
// let a = w(0) = x0 * y0
// let b = w(1) = (x2 + x1 + x0) * (y2 + y1 + y0)
// let c = w(-1) = (x2 - x1 + x0) * (y2 - y1 + y0)
// let d = w(-2) = (4*x2 - 2*x1 + x0) * (4*y2 - 2*y1 + y0)
// let e = w(inf) = x2 * y2 as t -> inf
// x0 + x2, avoiding temporaries
let p = &x0 + &x2;
// y0 + y2, avoiding temporaries
let q = &y0 + &y2;
// x2 - x1 + x0, avoiding temporaries
let p2 = &p - &x1;
// y2 - y1 + y0, avoiding temporaries
let q2 = &q - &y1;
// w(0)
let r0 = &x0 * &y0;
// w(inf)
let r4 = &x2 * &y2;
// w(1)
let r1 = (p + x1) * (q + y1);
// w(-1)
let r2 = &p2 * &q2;
// w(-2)
let r3 = ((p2 + x2) * 2 - x0) * ((q2 + y2) * 2 - y0);
// Evaluating these points gives us the following system of linear equations.
//
// 0 0 0 0 1 | a
// 1 1 1 1 1 | b
// 1 -1 1 -1 1 | c
// 16 -8 4 -2 1 | d
// 1 0 0 0 0 | e
//
// The solved equation (after gaussian elimination or similar)
// in terms of its coefficients:
//
// w0 = w(0)
// w1 = w(0)/2 + w(1)/3 - w(-1) + w(-2)/6 - 2*w(inf)
// w2 = -w(0) + w(1)/2 + w(-1)/2 - w(inf)
// w3 = -w(0)/2 + w(1)/6 + w(-1)/2 - w(-2)/6 + 2*w(inf)
// w4 = w(inf)
//
// This particular sequence is given by Bodrato and is an interpolation
// of the above equations.
let mut comp3: BigInt = (r3 - &r1) / 3u32;
let mut comp1: BigInt = (r1 - &r2) >> 1;
let mut comp2: BigInt = r2 - &r0;
comp3 = ((&comp2 - comp3) >> 1) + (&r4 << 1);
comp2 += &comp1 - &r4;
comp1 -= &comp3;
// Recomposition. The coefficients of the polynomial are now known.
//
// Evaluate at w(t) where t is our given base to get the result.
//
// let bits = u64::from(big_digit::BITS) * i as u64;
// let result = r0
// + (comp1 << bits)
// + (comp2 << (2 * bits))
// + (comp3 << (3 * bits))
// + (r4 << (4 * bits));
// let result_pos = result.to_biguint().unwrap();
// add2(&mut acc[..], &result_pos.data);
//
// But with less intermediate copying:
for (j, result) in [&r0, &comp1, &comp2, &comp3, &r4].iter().enumerate().rev() {
match result.sign() {
Plus => add2(&mut acc[i * j..], result.digits()),
Minus => sub2(&mut acc[i * j..], result.digits()),
NoSign => {}
}
}
}
}
fn mul3(x: &[BigDigit], y: &[BigDigit]) -> BigUint {
let len = x.len() + y.len() + 1;
let mut prod = BigUint { data: vec![0; len] };
mac3(&mut prod.data, x, y);
prod.normalized()
}
fn scalar_mul(a: &mut BigUint, b: BigDigit) {
match b {
0 => a.set_zero(),
1 => {}
_ => {
if b.is_power_of_two() {
*a <<= b.trailing_zeros();
} else {
let mut carry = 0;
for a in a.data.iter_mut() {
*a = mul_with_carry(*a, b, &mut carry);
}
if carry != 0 {
a.data.push(carry as BigDigit);
}
}
}
}
}
fn sub_sign(mut a: &[BigDigit], mut b: &[BigDigit]) -> (Sign, BigUint) {
// Normalize:
if let Some(&0) = a.last() {
a = &a[..a.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)];
}
if let Some(&0) = b.last() {
b = &b[..b.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)];
}
match cmp_slice(a, b) {
Ordering::Greater => {
let mut a = a.to_vec();
sub2(&mut a, b);
(Plus, biguint_from_vec(a))
}
Ordering::Less => {
let mut b = b.to_vec();
sub2(&mut b, a);
(Minus, biguint_from_vec(b))
}
Ordering::Equal => (NoSign, BigUint::ZERO),
}
}
macro_rules! impl_mul {
($(impl Mul<$Other:ty> for $Self:ty;)*) => {$(
impl Mul<$Other> for $Self {
type Output = BigUint;
#[inline]
fn mul(self, other: $Other) -> BigUint {
match (&*self.data, &*other.data) {
// multiply by zero
(&[], _) | (_, &[]) => BigUint::ZERO,
// multiply by a scalar
(_, &[digit]) => self * digit,
(&[digit], _) => other * digit,
// full multiplication
(x, y) => mul3(x, y),
}
}
}
)*}
}
impl_mul! {
impl Mul<BigUint> for BigUint;
impl Mul<BigUint> for &BigUint;
impl Mul<&BigUint> for BigUint;
impl Mul<&BigUint> for &BigUint;
}
macro_rules! impl_mul_assign {
($(impl MulAssign<$Other:ty> for BigUint;)*) => {$(
impl MulAssign<$Other> for BigUint {
#[inline]
fn mul_assign(&mut self, other: $Other) {
match (&*self.data, &*other.data) {
// multiply by zero
(&[], _) => {},
(_, &[]) => self.set_zero(),
// multiply by a scalar
(_, &[digit]) => *self *= digit,
(&[digit], _) => *self = other * digit,
// full multiplication
(x, y) => *self = mul3(x, y),
}
}
}
)*}
}
impl_mul_assign! {
impl MulAssign<BigUint> for BigUint;
impl MulAssign<&BigUint> for BigUint;
}
promote_unsigned_scalars!(impl Mul for BigUint, mul);
promote_unsigned_scalars_assign!(impl MulAssign for BigUint, mul_assign);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u32> for BigUint, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u64> for BigUint, mul);
forward_all_scalar_binop_to_val_val_commutative!(impl Mul<u128> for BigUint, mul);
impl Mul<u32> for BigUint {
type Output = BigUint;
#[inline]
fn mul(mut self, other: u32) -> BigUint {
self *= other;
self
}
}
impl MulAssign<u32> for BigUint {
#[inline]
fn mul_assign(&mut self, other: u32) {
scalar_mul(self, other as BigDigit);
}
}
impl Mul<u64> for BigUint {
type Output = BigUint;
#[inline]
fn mul(mut self, other: u64) -> BigUint {
self *= other;
self
}
}
impl MulAssign<u64> for BigUint {
cfg_digit!(
#[inline]
fn mul_assign(&mut self, other: u64) {
if let Some(other) = BigDigit::from_u64(other) {
scalar_mul(self, other);
} else {
let (hi, lo) = big_digit::from_doublebigdigit(other);
*self = mul3(&self.data, &[lo, hi]);
}
}
#[inline]
fn mul_assign(&mut self, other: u64) {
scalar_mul(self, other);
}
);
}
impl Mul<u128> for BigUint {
type Output = BigUint;
#[inline]
fn mul(mut self, other: u128) -> BigUint {
self *= other;
self
}
}
impl MulAssign<u128> for BigUint {
cfg_digit!(
#[inline]
fn mul_assign(&mut self, other: u128) {
if let Some(other) = BigDigit::from_u128(other) {
scalar_mul(self, other);
} else {
*self = match super::u32_from_u128(other) {
(0, 0, c, d) => mul3(&self.data, &[d, c]),
(0, b, c, d) => mul3(&self.data, &[d, c, b]),
(a, b, c, d) => mul3(&self.data, &[d, c, b, a]),
};
}
}
#[inline]
fn mul_assign(&mut self, other: u128) {
if let Some(other) = BigDigit::from_u128(other) {
scalar_mul(self, other);
} else {
let (hi, lo) = big_digit::from_doublebigdigit(other);
*self = mul3(&self.data, &[lo, hi]);
}
}
);
}
impl CheckedMul for BigUint {
#[inline]
fn checked_mul(&self, v: &BigUint) -> Option<BigUint> {
Some(self.mul(v))
}
}
impl_product_iter_type!(BigUint);
#[test]
fn test_sub_sign() {
use crate::BigInt;
use num_traits::Num;
fn sub_sign_i(a: &[BigDigit], b: &[BigDigit]) -> BigInt {
let (sign, val) = sub_sign(a, b);
BigInt::from_biguint(sign, val)
}
let a = BigUint::from_str_radix("265252859812191058636308480000000", 10).unwrap();
let b = BigUint::from_str_radix("26525285981219105863630848000000", 10).unwrap();
let a_i = BigInt::from(a.clone());
let b_i = BigInt::from(b.clone());
assert_eq!(sub_sign_i(&a.data, &b.data), &a_i - &b_i);
assert_eq!(sub_sign_i(&b.data, &a.data), &b_i - &a_i);
}

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use super::monty::monty_modpow;
use super::BigUint;
use crate::big_digit::{self, BigDigit};
use num_integer::Integer;
use num_traits::{One, Pow, ToPrimitive, Zero};
impl Pow<&BigUint> for BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: &BigUint) -> BigUint {
if self.is_one() || exp.is_zero() {
BigUint::one()
} else if self.is_zero() {
Self::ZERO
} else if let Some(exp) = exp.to_u64() {
self.pow(exp)
} else if let Some(exp) = exp.to_u128() {
self.pow(exp)
} else {
// At this point, `self >= 2` and `exp >= 2¹²⁸`. The smallest possible result given
// `2.pow(2¹²⁸)` would require far more memory than 64-bit targets can address!
panic!("memory overflow")
}
}
}
impl Pow<BigUint> for BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: BigUint) -> BigUint {
Pow::pow(self, &exp)
}
}
impl Pow<&BigUint> for &BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: &BigUint) -> BigUint {
if self.is_one() || exp.is_zero() {
BigUint::one()
} else if self.is_zero() {
BigUint::ZERO
} else {
self.clone().pow(exp)
}
}
}
impl Pow<BigUint> for &BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: BigUint) -> BigUint {
Pow::pow(self, &exp)
}
}
macro_rules! pow_impl {
($T:ty) => {
impl Pow<$T> for BigUint {
type Output = BigUint;
fn pow(self, mut exp: $T) -> BigUint {
if exp == 0 {
return BigUint::one();
}
let mut base = self;
while exp & 1 == 0 {
base = &base * &base;
exp >>= 1;
}
if exp == 1 {
return base;
}
let mut acc = base.clone();
while exp > 1 {
exp >>= 1;
base = &base * &base;
if exp & 1 == 1 {
acc *= &base;
}
}
acc
}
}
impl Pow<&$T> for BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: &$T) -> BigUint {
Pow::pow(self, *exp)
}
}
impl Pow<$T> for &BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: $T) -> BigUint {
if exp == 0 {
return BigUint::one();
}
Pow::pow(self.clone(), exp)
}
}
impl Pow<&$T> for &BigUint {
type Output = BigUint;
#[inline]
fn pow(self, exp: &$T) -> BigUint {
Pow::pow(self, *exp)
}
}
};
}
pow_impl!(u8);
pow_impl!(u16);
pow_impl!(u32);
pow_impl!(u64);
pow_impl!(usize);
pow_impl!(u128);
pub(super) fn modpow(x: &BigUint, exponent: &BigUint, modulus: &BigUint) -> BigUint {
assert!(
!modulus.is_zero(),
"attempt to calculate with zero modulus!"
);
if modulus.is_odd() {
// For an odd modulus, we can use Montgomery multiplication in base 2^32.
monty_modpow(x, exponent, modulus)
} else {
// Otherwise do basically the same as `num::pow`, but with a modulus.
plain_modpow(x, &exponent.data, modulus)
}
}
fn plain_modpow(base: &BigUint, exp_data: &[BigDigit], modulus: &BigUint) -> BigUint {
assert!(
!modulus.is_zero(),
"attempt to calculate with zero modulus!"
);
let i = match exp_data.iter().position(|&r| r != 0) {
None => return BigUint::one(),
Some(i) => i,
};
let mut base = base % modulus;
for _ in 0..i {
for _ in 0..big_digit::BITS {
base = &base * &base % modulus;
}
}
let mut r = exp_data[i];
let mut b = 0u8;
while r.is_even() {
base = &base * &base % modulus;
r >>= 1;
b += 1;
}
let mut exp_iter = exp_data[i + 1..].iter();
if exp_iter.len() == 0 && r.is_one() {
return base;
}
let mut acc = base.clone();
r >>= 1;
b += 1;
{
let mut unit = |exp_is_odd| {
base = &base * &base % modulus;
if exp_is_odd {
acc *= &base;
acc %= modulus;
}
};
if let Some(&last) = exp_iter.next_back() {
// consume exp_data[i]
for _ in b..big_digit::BITS {
unit(r.is_odd());
r >>= 1;
}
// consume all other digits before the last
for &r in exp_iter {
let mut r = r;
for _ in 0..big_digit::BITS {
unit(r.is_odd());
r >>= 1;
}
}
r = last;
}
debug_assert_ne!(r, 0);
while !r.is_zero() {
unit(r.is_odd());
r >>= 1;
}
}
acc
}
#[test]
fn test_plain_modpow() {
let two = &BigUint::from(2u32);
let modulus = BigUint::from(0x1100u32);
let exp = vec![0, 0b1];
assert_eq!(
two.pow(0b1_00000000_u32) % &modulus,
plain_modpow(two, &exp, &modulus)
);
let exp = vec![0, 0b10];
assert_eq!(
two.pow(0b10_00000000_u32) % &modulus,
plain_modpow(two, &exp, &modulus)
);
let exp = vec![0, 0b110010];
assert_eq!(
two.pow(0b110010_00000000_u32) % &modulus,
plain_modpow(two, &exp, &modulus)
);
let exp = vec![0b1, 0b1];
assert_eq!(
two.pow(0b1_00000001_u32) % &modulus,
plain_modpow(two, &exp, &modulus)
);
let exp = vec![0b1100, 0, 0b1];
assert_eq!(
two.pow(0b1_00000000_00001100_u32) % &modulus,
plain_modpow(two, &exp, &modulus)
);
}
#[test]
fn test_pow_biguint() {
let base = BigUint::from(5u8);
let exponent = BigUint::from(3u8);
assert_eq!(BigUint::from(125u8), base.pow(exponent));
}

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#![cfg(feature = "serde")]
#![cfg_attr(docsrs, doc(cfg(feature = "serde")))]
use super::{biguint_from_vec, BigUint};
use alloc::vec::Vec;
use core::{cmp, fmt, mem};
use serde::de::{SeqAccess, Visitor};
use serde::{Deserialize, Deserializer, Serialize, Serializer};
// `cautious` is based on the function of the same name in `serde`, but specialized to `u32`:
// https://github.com/dtolnay/serde/blob/399ef081ecc36d2f165ff1f6debdcbf6a1dc7efb/serde/src/private/size_hint.rs#L11-L22
fn cautious(hint: Option<usize>) -> usize {
const MAX_PREALLOC_BYTES: usize = 1024 * 1024;
cmp::min(
hint.unwrap_or(0),
MAX_PREALLOC_BYTES / mem::size_of::<u32>(),
)
}
impl Serialize for BigUint {
cfg_digit!(
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
{
// Note: do not change the serialization format, or it may break forward
// and backward compatibility of serialized data! If we ever change the
// internal representation, we should still serialize in base-`u32`.
let data: &[u32] = &self.data;
data.serialize(serializer)
}
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
{
use serde::ser::SerializeSeq;
if let Some((&last, data)) = self.data.split_last() {
let last_lo = last as u32;
let last_hi = (last >> 32) as u32;
let u32_len = data.len() * 2 + 1 + (last_hi != 0) as usize;
let mut seq = serializer.serialize_seq(Some(u32_len))?;
for &x in data {
seq.serialize_element(&(x as u32))?;
seq.serialize_element(&((x >> 32) as u32))?;
}
seq.serialize_element(&last_lo)?;
if last_hi != 0 {
seq.serialize_element(&last_hi)?;
}
seq.end()
} else {
let data: &[u32] = &[];
data.serialize(serializer)
}
}
);
}
impl<'de> Deserialize<'de> for BigUint {
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: Deserializer<'de>,
{
deserializer.deserialize_seq(U32Visitor)
}
}
struct U32Visitor;
impl<'de> Visitor<'de> for U32Visitor {
type Value = BigUint;
fn expecting(&self, formatter: &mut fmt::Formatter<'_>) -> fmt::Result {
formatter.write_str("a sequence of unsigned 32-bit numbers")
}
cfg_digit!(
fn visit_seq<S>(self, mut seq: S) -> Result<Self::Value, S::Error>
where
S: SeqAccess<'de>,
{
let len = cautious(seq.size_hint());
let mut data = Vec::with_capacity(len);
while let Some(value) = seq.next_element::<u32>()? {
data.push(value);
}
Ok(biguint_from_vec(data))
}
fn visit_seq<S>(self, mut seq: S) -> Result<Self::Value, S::Error>
where
S: SeqAccess<'de>,
{
use crate::big_digit::BigDigit;
use num_integer::Integer;
let u32_len = cautious(seq.size_hint());
let len = Integer::div_ceil(&u32_len, &2);
let mut data = Vec::with_capacity(len);
while let Some(lo) = seq.next_element::<u32>()? {
let mut value = BigDigit::from(lo);
if let Some(hi) = seq.next_element::<u32>()? {
value |= BigDigit::from(hi) << 32;
data.push(value);
} else {
data.push(value);
break;
}
}
Ok(biguint_from_vec(data))
}
);
}

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use super::{biguint_from_vec, BigUint};
use crate::big_digit;
use alloc::borrow::Cow;
use alloc::vec::Vec;
use core::mem;
use core::ops::{Shl, ShlAssign, Shr, ShrAssign};
use num_traits::{PrimInt, Zero};
#[inline]
fn biguint_shl<T: PrimInt>(n: Cow<'_, BigUint>, shift: T) -> BigUint {
if shift < T::zero() {
panic!("attempt to shift left with negative");
}
if n.is_zero() {
return n.into_owned();
}
let bits = T::from(big_digit::BITS).unwrap();
let digits = (shift / bits).to_usize().expect("capacity overflow");
let shift = (shift % bits).to_u8().unwrap();
biguint_shl2(n, digits, shift)
}
fn biguint_shl2(n: Cow<'_, BigUint>, digits: usize, shift: u8) -> BigUint {
let mut data = match digits {
0 => n.into_owned().data,
_ => {
let len = digits.saturating_add(n.data.len() + 1);
let mut data = Vec::with_capacity(len);
data.resize(digits, 0);
data.extend(n.data.iter());
data
}
};
if shift > 0 {
let mut carry = 0;
let carry_shift = big_digit::BITS - shift;
for elem in data[digits..].iter_mut() {
let new_carry = *elem >> carry_shift;
*elem = (*elem << shift) | carry;
carry = new_carry;
}
if carry != 0 {
data.push(carry);
}
}
biguint_from_vec(data)
}
#[inline]
fn biguint_shr<T: PrimInt>(n: Cow<'_, BigUint>, shift: T) -> BigUint {
if shift < T::zero() {
panic!("attempt to shift right with negative");
}
if n.is_zero() {
return n.into_owned();
}
let bits = T::from(big_digit::BITS).unwrap();
let digits = (shift / bits).to_usize().unwrap_or(usize::MAX);
let shift = (shift % bits).to_u8().unwrap();
biguint_shr2(n, digits, shift)
}
fn biguint_shr2(n: Cow<'_, BigUint>, digits: usize, shift: u8) -> BigUint {
if digits >= n.data.len() {
let mut n = n.into_owned();
n.set_zero();
return n;
}
let mut data = match n {
Cow::Borrowed(n) => n.data[digits..].to_vec(),
Cow::Owned(mut n) => {
n.data.drain(..digits);
n.data
}
};
if shift > 0 {
let mut borrow = 0;
let borrow_shift = big_digit::BITS - shift;
for elem in data.iter_mut().rev() {
let new_borrow = *elem << borrow_shift;
*elem = (*elem >> shift) | borrow;
borrow = new_borrow;
}
}
biguint_from_vec(data)
}
macro_rules! impl_shift {
(@ref $Shx:ident :: $shx:ident, $ShxAssign:ident :: $shx_assign:ident, $rhs:ty) => {
impl $Shx<&$rhs> for BigUint {
type Output = BigUint;
#[inline]
fn $shx(self, rhs: &$rhs) -> BigUint {
$Shx::$shx(self, *rhs)
}
}
impl $Shx<&$rhs> for &BigUint {
type Output = BigUint;
#[inline]
fn $shx(self, rhs: &$rhs) -> BigUint {
$Shx::$shx(self, *rhs)
}
}
impl $ShxAssign<&$rhs> for BigUint {
#[inline]
fn $shx_assign(&mut self, rhs: &$rhs) {
$ShxAssign::$shx_assign(self, *rhs);
}
}
};
($($rhs:ty),+) => {$(
impl Shl<$rhs> for BigUint {
type Output = BigUint;
#[inline]
fn shl(self, rhs: $rhs) -> BigUint {
biguint_shl(Cow::Owned(self), rhs)
}
}
impl Shl<$rhs> for &BigUint {
type Output = BigUint;
#[inline]
fn shl(self, rhs: $rhs) -> BigUint {
biguint_shl(Cow::Borrowed(self), rhs)
}
}
impl ShlAssign<$rhs> for BigUint {
#[inline]
fn shl_assign(&mut self, rhs: $rhs) {
let n = mem::replace(self, Self::ZERO);
*self = n << rhs;
}
}
impl_shift! { @ref Shl::shl, ShlAssign::shl_assign, $rhs }
impl Shr<$rhs> for BigUint {
type Output = BigUint;
#[inline]
fn shr(self, rhs: $rhs) -> BigUint {
biguint_shr(Cow::Owned(self), rhs)
}
}
impl Shr<$rhs> for &BigUint {
type Output = BigUint;
#[inline]
fn shr(self, rhs: $rhs) -> BigUint {
biguint_shr(Cow::Borrowed(self), rhs)
}
}
impl ShrAssign<$rhs> for BigUint {
#[inline]
fn shr_assign(&mut self, rhs: $rhs) {
let n = mem::replace(self, Self::ZERO);
*self = n >> rhs;
}
}
impl_shift! { @ref Shr::shr, ShrAssign::shr_assign, $rhs }
)*};
}
impl_shift! { u8, u16, u32, u64, u128, usize }
impl_shift! { i8, i16, i32, i64, i128, isize }

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use super::BigUint;
use crate::big_digit::{self, BigDigit};
use crate::UsizePromotion;
use core::cmp::Ordering::{Equal, Greater, Less};
use core::ops::{Sub, SubAssign};
use num_traits::CheckedSub;
#[cfg(target_arch = "x86_64")]
use core::arch::x86_64 as arch;
#[cfg(target_arch = "x86")]
use core::arch::x86 as arch;
// Subtract with borrow:
#[cfg(target_arch = "x86_64")]
cfg_64!(
#[inline]
fn sbb(borrow: u8, a: u64, b: u64, out: &mut u64) -> u8 {
// Safety: There are absolutely no safety concerns with calling `_subborrow_u64`.
// It's just unsafe for API consistency with other intrinsics.
unsafe { arch::_subborrow_u64(borrow, a, b, out) }
}
);
#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
cfg_32!(
#[inline]
fn sbb(borrow: u8, a: u32, b: u32, out: &mut u32) -> u8 {
// Safety: There are absolutely no safety concerns with calling `_subborrow_u32`.
// It's just unsafe for API consistency with other intrinsics.
unsafe { arch::_subborrow_u32(borrow, a, b, out) }
}
);
// fallback for environments where we don't have a subborrow intrinsic
// (copied from the standard library's `borrowing_sub`)
#[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
#[inline]
fn sbb(borrow: u8, lhs: BigDigit, rhs: BigDigit, out: &mut BigDigit) -> u8 {
let (a, b) = lhs.overflowing_sub(rhs);
let (c, d) = a.overflowing_sub(borrow as BigDigit);
*out = c;
u8::from(b || d)
}
pub(super) fn sub2(a: &mut [BigDigit], b: &[BigDigit]) {
let mut borrow = 0;
let len = Ord::min(a.len(), b.len());
let (a_lo, a_hi) = a.split_at_mut(len);
let (b_lo, b_hi) = b.split_at(len);
for (a, b) in a_lo.iter_mut().zip(b_lo) {
borrow = sbb(borrow, *a, *b, a);
}
if borrow != 0 {
for a in a_hi {
borrow = sbb(borrow, *a, 0, a);
if borrow == 0 {
break;
}
}
}
// note: we're _required_ to fail on underflow
assert!(
borrow == 0 && b_hi.iter().all(|x| *x == 0),
"Cannot subtract b from a because b is larger than a."
);
}
// Only for the Sub impl. `a` and `b` must have same length.
#[inline]
fn __sub2rev(a: &[BigDigit], b: &mut [BigDigit]) -> u8 {
debug_assert!(b.len() == a.len());
let mut borrow = 0;
for (ai, bi) in a.iter().zip(b) {
borrow = sbb(borrow, *ai, *bi, bi);
}
borrow
}
fn sub2rev(a: &[BigDigit], b: &mut [BigDigit]) {
debug_assert!(b.len() >= a.len());
let len = Ord::min(a.len(), b.len());
let (a_lo, a_hi) = a.split_at(len);
let (b_lo, b_hi) = b.split_at_mut(len);
let borrow = __sub2rev(a_lo, b_lo);
assert!(a_hi.is_empty());
// note: we're _required_ to fail on underflow
assert!(
borrow == 0 && b_hi.iter().all(|x| *x == 0),
"Cannot subtract b from a because b is larger than a."
);
}
forward_val_val_binop!(impl Sub for BigUint, sub);
forward_ref_ref_binop!(impl Sub for BigUint, sub);
forward_val_assign!(impl SubAssign for BigUint, sub_assign);
impl Sub<&BigUint> for BigUint {
type Output = BigUint;
fn sub(mut self, other: &BigUint) -> BigUint {
self -= other;
self
}
}
impl SubAssign<&BigUint> for BigUint {
fn sub_assign(&mut self, other: &BigUint) {
sub2(&mut self.data[..], &other.data[..]);
self.normalize();
}
}
impl Sub<BigUint> for &BigUint {
type Output = BigUint;
fn sub(self, mut other: BigUint) -> BigUint {
let other_len = other.data.len();
if other_len < self.data.len() {
let lo_borrow = __sub2rev(&self.data[..other_len], &mut other.data);
other.data.extend_from_slice(&self.data[other_len..]);
if lo_borrow != 0 {
sub2(&mut other.data[other_len..], &[1])
}
} else {
sub2rev(&self.data[..], &mut other.data[..]);
}
other.normalized()
}
}
promote_unsigned_scalars!(impl Sub for BigUint, sub);
promote_unsigned_scalars_assign!(impl SubAssign for BigUint, sub_assign);
forward_all_scalar_binop_to_val_val!(impl Sub<u32> for BigUint, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<u64> for BigUint, sub);
forward_all_scalar_binop_to_val_val!(impl Sub<u128> for BigUint, sub);
impl Sub<u32> for BigUint {
type Output = BigUint;
#[inline]
fn sub(mut self, other: u32) -> BigUint {
self -= other;
self
}
}
impl SubAssign<u32> for BigUint {
fn sub_assign(&mut self, other: u32) {
sub2(&mut self.data[..], &[other as BigDigit]);
self.normalize();
}
}
impl Sub<BigUint> for u32 {
type Output = BigUint;
cfg_digit!(
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
if other.data.len() == 0 {
other.data.push(self);
} else {
sub2rev(&[self], &mut other.data[..]);
}
other.normalized()
}
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
if other.data.is_empty() {
other.data.push(self as BigDigit);
} else {
sub2rev(&[self as BigDigit], &mut other.data[..]);
}
other.normalized()
}
);
}
impl Sub<u64> for BigUint {
type Output = BigUint;
#[inline]
fn sub(mut self, other: u64) -> BigUint {
self -= other;
self
}
}
impl SubAssign<u64> for BigUint {
cfg_digit!(
#[inline]
fn sub_assign(&mut self, other: u64) {
let (hi, lo) = big_digit::from_doublebigdigit(other);
sub2(&mut self.data[..], &[lo, hi]);
self.normalize();
}
#[inline]
fn sub_assign(&mut self, other: u64) {
sub2(&mut self.data[..], &[other as BigDigit]);
self.normalize();
}
);
}
impl Sub<BigUint> for u64 {
type Output = BigUint;
cfg_digit!(
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
while other.data.len() < 2 {
other.data.push(0);
}
let (hi, lo) = big_digit::from_doublebigdigit(self);
sub2rev(&[lo, hi], &mut other.data[..]);
other.normalized()
}
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
if other.data.is_empty() {
other.data.push(self);
} else {
sub2rev(&[self], &mut other.data[..]);
}
other.normalized()
}
);
}
impl Sub<u128> for BigUint {
type Output = BigUint;
#[inline]
fn sub(mut self, other: u128) -> BigUint {
self -= other;
self
}
}
impl SubAssign<u128> for BigUint {
cfg_digit!(
#[inline]
fn sub_assign(&mut self, other: u128) {
let (a, b, c, d) = super::u32_from_u128(other);
sub2(&mut self.data[..], &[d, c, b, a]);
self.normalize();
}
#[inline]
fn sub_assign(&mut self, other: u128) {
let (hi, lo) = big_digit::from_doublebigdigit(other);
sub2(&mut self.data[..], &[lo, hi]);
self.normalize();
}
);
}
impl Sub<BigUint> for u128 {
type Output = BigUint;
cfg_digit!(
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
while other.data.len() < 4 {
other.data.push(0);
}
let (a, b, c, d) = super::u32_from_u128(self);
sub2rev(&[d, c, b, a], &mut other.data[..]);
other.normalized()
}
#[inline]
fn sub(self, mut other: BigUint) -> BigUint {
while other.data.len() < 2 {
other.data.push(0);
}
let (hi, lo) = big_digit::from_doublebigdigit(self);
sub2rev(&[lo, hi], &mut other.data[..]);
other.normalized()
}
);
}
impl CheckedSub for BigUint {
#[inline]
fn checked_sub(&self, v: &BigUint) -> Option<BigUint> {
match self.cmp(v) {
Less => None,
Equal => Some(Self::ZERO),
Greater => Some(self.sub(v)),
}
}
}

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// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! Big Integer Types for Rust
//!
//! * A [`BigUint`] is unsigned and represented as a vector of digits.
//! * A [`BigInt`] is signed and is a combination of [`BigUint`] and [`Sign`].
//!
//! Common numerical operations are overloaded, so we can treat them
//! the same way we treat other numbers.
//!
//! ## Example
//!
//! ```rust
//! # fn main() {
//! use num_bigint::BigUint;
//! use num_traits::One;
//!
//! // Calculate large fibonacci numbers.
//! fn fib(n: usize) -> BigUint {
//! let mut f0 = BigUint::ZERO;
//! let mut f1 = BigUint::one();
//! for _ in 0..n {
//! let f2 = f0 + &f1;
//! f0 = f1;
//! f1 = f2;
//! }
//! f0
//! }
//!
//! // This is a very large number.
//! println!("fib(1000) = {}", fib(1000));
//! # }
//! ```
//!
//! It's easy to generate large random numbers:
//!
//! ```rust,ignore
//! use num_bigint::{ToBigInt, RandBigInt};
//!
//! let mut rng = rand::thread_rng();
//! let a = rng.gen_bigint(1000);
//!
//! let low = -10000.to_bigint().unwrap();
//! let high = 10000.to_bigint().unwrap();
//! let b = rng.gen_bigint_range(&low, &high);
//!
//! // Probably an even larger number.
//! println!("{}", a * b);
//! ```
//!
//! See the "Features" section for instructions for enabling random number generation.
//!
//! ## Features
//!
//! The `std` crate feature is enabled by default, which enables [`std::error::Error`]
//! implementations and some internal use of floating point approximations. This can be disabled by
//! depending on `num-bigint` with `default-features = false`. Either way, the `alloc` crate is
//! always required for heap allocation of the `BigInt`/`BigUint` digits.
//!
//! ### Random Generation
//!
//! `num-bigint` supports the generation of random big integers when the `rand`
//! feature is enabled. To enable it include rand as
//!
//! ```toml
//! rand = "0.8"
//! num-bigint = { version = "0.4", features = ["rand"] }
//! ```
//!
//! Note that you must use the version of `rand` that `num-bigint` is compatible
//! with: `0.8`.
//!
//! ### Arbitrary Big Integers
//!
//! `num-bigint` supports `arbitrary` and `quickcheck` features to implement
//! [`arbitrary::Arbitrary`] and [`quickcheck::Arbitrary`], respectively, for both `BigInt` and
//! `BigUint`. These are useful for fuzzing and other forms of randomized testing.
//!
//! ### Serialization
//!
//! The `serde` feature adds implementations of [`Serialize`][serde::Serialize] and
//! [`Deserialize`][serde::Deserialize] for both `BigInt` and `BigUint`. Their serialized data is
//! generated portably, regardless of platform differences like the internal digit size.
//!
//!
//! ## Compatibility
//!
//! The `num-bigint` crate is tested for rustc 1.60 and greater.
#![cfg_attr(docsrs, feature(doc_cfg))]
#![doc(html_root_url = "https://docs.rs/num-bigint/0.4")]
#![warn(rust_2018_idioms)]
#![no_std]
#[macro_use]
extern crate alloc;
#[cfg(feature = "std")]
extern crate std;
use core::fmt;
#[macro_use]
mod macros;
mod bigint;
mod bigrand;
mod biguint;
#[cfg(target_pointer_width = "32")]
type UsizePromotion = u32;
#[cfg(target_pointer_width = "64")]
type UsizePromotion = u64;
#[cfg(target_pointer_width = "32")]
type IsizePromotion = i32;
#[cfg(target_pointer_width = "64")]
type IsizePromotion = i64;
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct ParseBigIntError {
kind: BigIntErrorKind,
}
#[derive(Debug, Clone, PartialEq, Eq)]
enum BigIntErrorKind {
Empty,
InvalidDigit,
}
impl ParseBigIntError {
fn __description(&self) -> &str {
use crate::BigIntErrorKind::*;
match self.kind {
Empty => "cannot parse integer from empty string",
InvalidDigit => "invalid digit found in string",
}
}
fn empty() -> Self {
ParseBigIntError {
kind: BigIntErrorKind::Empty,
}
}
fn invalid() -> Self {
ParseBigIntError {
kind: BigIntErrorKind::InvalidDigit,
}
}
}
impl fmt::Display for ParseBigIntError {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
self.__description().fmt(f)
}
}
#[cfg(feature = "std")]
#[cfg_attr(docsrs, doc(cfg(feature = "std")))]
impl std::error::Error for ParseBigIntError {
fn description(&self) -> &str {
self.__description()
}
}
/// The error type returned when a checked conversion regarding big integer fails.
#[derive(Debug, Copy, Clone, PartialEq, Eq)]
pub struct TryFromBigIntError<T> {
original: T,
}
impl<T> TryFromBigIntError<T> {
fn new(original: T) -> Self {
TryFromBigIntError { original }
}
fn __description(&self) -> &str {
"out of range conversion regarding big integer attempted"
}
/// Extract the original value, if available. The value will be available
/// if the type before conversion was either [`BigInt`] or [`BigUint`].
pub fn into_original(self) -> T {
self.original
}
}
#[cfg(feature = "std")]
#[cfg_attr(docsrs, doc(cfg(feature = "std")))]
impl<T> std::error::Error for TryFromBigIntError<T>
where
T: fmt::Debug,
{
fn description(&self) -> &str {
self.__description()
}
}
impl<T> fmt::Display for TryFromBigIntError<T> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
self.__description().fmt(f)
}
}
pub use crate::biguint::BigUint;
pub use crate::biguint::ToBigUint;
pub use crate::biguint::U32Digits;
pub use crate::biguint::U64Digits;
pub use crate::bigint::BigInt;
pub use crate::bigint::Sign;
pub use crate::bigint::ToBigInt;
#[cfg(feature = "rand")]
#[cfg_attr(docsrs, doc(cfg(feature = "rand")))]
pub use crate::bigrand::{RandBigInt, RandomBits, UniformBigInt, UniformBigUint};
mod big_digit {
// A [`BigDigit`] is a [`BigUint`]'s composing element.
cfg_digit!(
pub(crate) type BigDigit = u32;
pub(crate) type BigDigit = u64;
);
// A [`DoubleBigDigit`] is the internal type used to do the computations. Its
// size is the double of the size of [`BigDigit`].
cfg_digit!(
pub(crate) type DoubleBigDigit = u64;
pub(crate) type DoubleBigDigit = u128;
);
pub(crate) const BITS: u8 = BigDigit::BITS as u8;
pub(crate) const HALF_BITS: u8 = BITS / 2;
pub(crate) const HALF: BigDigit = (1 << HALF_BITS) - 1;
pub(crate) const MAX: BigDigit = BigDigit::MAX;
const LO_MASK: DoubleBigDigit = MAX as DoubleBigDigit;
#[inline]
fn get_hi(n: DoubleBigDigit) -> BigDigit {
(n >> BITS) as BigDigit
}
#[inline]
fn get_lo(n: DoubleBigDigit) -> BigDigit {
(n & LO_MASK) as BigDigit
}
/// Split one [`DoubleBigDigit`] into two [`BigDigit`]s.
#[inline]
pub(crate) fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) {
(get_hi(n), get_lo(n))
}
/// Join two [`BigDigit`]s into one [`DoubleBigDigit`].
#[inline]
pub(crate) fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit {
DoubleBigDigit::from(lo) | (DoubleBigDigit::from(hi) << BITS)
}
}

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#![allow(unused_macros)]
macro_rules! cfg_32 {
($($any:tt)+) => {
#[cfg(not(target_pointer_width = "64"))] $($any)+
}
}
macro_rules! cfg_32_or_test {
($($any:tt)+) => {
#[cfg(any(not(target_pointer_width = "64"), test))] $($any)+
}
}
macro_rules! cfg_64 {
($($any:tt)+) => {
#[cfg(target_pointer_width = "64")] $($any)+
}
}
macro_rules! cfg_digit {
($item32:item $item64:item) => {
cfg_32!($item32);
cfg_64!($item64);
};
}
macro_rules! cfg_digit_expr {
($expr32:expr, $expr64:expr) => {
cfg_32!($expr32);
cfg_64!($expr64);
};
}
macro_rules! forward_val_val_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for $res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// forward to val-ref
$imp::$method(self, &other)
}
}
};
}
macro_rules! forward_val_val_binop_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for $res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// forward to val-ref, with the larger capacity as val
if self.capacity() >= other.capacity() {
$imp::$method(self, &other)
} else {
$imp::$method(other, &self)
}
}
}
};
}
macro_rules! forward_ref_val_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// forward to ref-ref
$imp::$method(self, &other)
}
}
};
}
macro_rules! forward_ref_val_binop_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
// reverse, forward to val-ref
$imp::$method(other, self)
}
}
};
}
macro_rules! forward_val_ref_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<&$res> for $res {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
// forward to ref-ref
$imp::$method(&self, other)
}
}
};
}
macro_rules! forward_ref_ref_binop {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<&$res> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
// forward to val-ref
$imp::$method(self.clone(), other)
}
}
};
}
macro_rules! forward_ref_ref_binop_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<&$res> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
// forward to val-ref, choosing the larger to clone
if self.len() >= other.len() {
$imp::$method(self.clone(), other)
} else {
$imp::$method(other.clone(), self)
}
}
}
};
}
macro_rules! forward_val_assign {
(impl $imp:ident for $res:ty, $method:ident) => {
impl $imp<$res> for $res {
#[inline]
fn $method(&mut self, other: $res) {
self.$method(&other);
}
}
};
}
macro_rules! forward_val_assign_scalar {
(impl $imp:ident for $res:ty, $scalar:ty, $method:ident) => {
impl $imp<$res> for $scalar {
#[inline]
fn $method(&mut self, other: $res) {
self.$method(&other);
}
}
};
}
/// use this if val_val_binop is already implemented and the reversed order is required
macro_rules! forward_scalar_val_val_binop_commutative {
(impl $imp:ident < $scalar:ty > for $res:ty, $method:ident) => {
impl $imp<$res> for $scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(other, self)
}
}
};
}
// Forward scalar to ref-val, when reusing storage is not helpful
macro_rules! forward_scalar_val_val_binop_to_ref_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl $imp<$scalar> for $res {
type Output = $res;
#[inline]
fn $method(self, other: $scalar) -> $res {
$imp::$method(&self, other)
}
}
impl $imp<$res> for $scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(self, &other)
}
}
};
}
macro_rules! forward_scalar_ref_ref_binop_to_ref_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl $imp<&$scalar> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: &$scalar) -> $res {
$imp::$method(self, *other)
}
}
impl $imp<&$res> for &$scalar {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
$imp::$method(*self, other)
}
}
};
}
macro_rules! forward_scalar_val_ref_binop_to_ref_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl $imp<&$scalar> for $res {
type Output = $res;
#[inline]
fn $method(self, other: &$scalar) -> $res {
$imp::$method(&self, *other)
}
}
impl $imp<$res> for &$scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(*self, &other)
}
}
};
}
macro_rules! forward_scalar_val_ref_binop_to_val_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl $imp<&$scalar> for $res {
type Output = $res;
#[inline]
fn $method(self, other: &$scalar) -> $res {
$imp::$method(self, *other)
}
}
impl $imp<$res> for &$scalar {
type Output = $res;
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(*self, other)
}
}
};
}
macro_rules! forward_scalar_ref_val_binop_to_val_val {
(impl $imp:ident < $scalar:ty > for $res:ty, $method:ident) => {
impl $imp<$scalar> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: $scalar) -> $res {
$imp::$method(self.clone(), other)
}
}
impl $imp<&$res> for $scalar {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
$imp::$method(self, other.clone())
}
}
};
}
macro_rules! forward_scalar_ref_ref_binop_to_val_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
impl $imp<&$scalar> for &$res {
type Output = $res;
#[inline]
fn $method(self, other: &$scalar) -> $res {
$imp::$method(self.clone(), *other)
}
}
impl $imp<&$res> for &$scalar {
type Output = $res;
#[inline]
fn $method(self, other: &$res) -> $res {
$imp::$method(*self, other.clone())
}
}
};
}
macro_rules! promote_scalars {
(impl $imp:ident<$promo:ty> for $res:ty, $method:ident, $( $scalar:ty ),*) => {
$(
forward_all_scalar_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
impl $imp<$scalar> for $res {
type Output = $res;
#[allow(clippy::cast_lossless)]
#[inline]
fn $method(self, other: $scalar) -> $res {
$imp::$method(self, other as $promo)
}
}
impl $imp<$res> for $scalar {
type Output = $res;
#[allow(clippy::cast_lossless)]
#[inline]
fn $method(self, other: $res) -> $res {
$imp::$method(self as $promo, other)
}
}
)*
}
}
macro_rules! promote_scalars_assign {
(impl $imp:ident<$promo:ty> for $res:ty, $method:ident, $( $scalar:ty ),*) => {
$(
impl $imp<$scalar> for $res {
#[allow(clippy::cast_lossless)]
#[inline]
fn $method(&mut self, other: $scalar) {
self.$method(other as $promo);
}
}
)*
}
}
macro_rules! promote_unsigned_scalars {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars!(impl $imp<u32> for $res, $method, u8, u16);
promote_scalars!(impl $imp<UsizePromotion> for $res, $method, usize);
}
}
macro_rules! promote_unsigned_scalars_assign {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars_assign!(impl $imp<u32> for $res, $method, u8, u16);
promote_scalars_assign!(impl $imp<UsizePromotion> for $res, $method, usize);
}
}
macro_rules! promote_signed_scalars {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars!(impl $imp<i32> for $res, $method, i8, i16);
promote_scalars!(impl $imp<IsizePromotion> for $res, $method, isize);
}
}
macro_rules! promote_signed_scalars_assign {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_scalars_assign!(impl $imp<i32> for $res, $method, i8, i16);
promote_scalars_assign!(impl $imp<IsizePromotion> for $res, $method, isize);
}
}
// Forward everything to ref-ref, when reusing storage is not helpful
macro_rules! forward_all_binop_to_ref_ref {
(impl $imp:ident for $res:ty, $method:ident) => {
forward_val_val_binop!(impl $imp for $res, $method);
forward_val_ref_binop!(impl $imp for $res, $method);
forward_ref_val_binop!(impl $imp for $res, $method);
};
}
// Forward everything to val-ref, so LHS storage can be reused
macro_rules! forward_all_binop_to_val_ref {
(impl $imp:ident for $res:ty, $method:ident) => {
forward_val_val_binop!(impl $imp for $res, $method);
forward_ref_val_binop!(impl $imp for $res, $method);
forward_ref_ref_binop!(impl $imp for $res, $method);
};
}
// Forward everything to val-ref, commutatively, so either LHS or RHS storage can be reused
macro_rules! forward_all_binop_to_val_ref_commutative {
(impl $imp:ident for $res:ty, $method:ident) => {
forward_val_val_binop_commutative!(impl $imp for $res, $method);
forward_ref_val_binop_commutative!(impl $imp for $res, $method);
forward_ref_ref_binop_commutative!(impl $imp for $res, $method);
};
}
macro_rules! forward_all_scalar_binop_to_ref_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
forward_scalar_val_val_binop_to_ref_val!(impl $imp<$scalar> for $res, $method);
forward_scalar_val_ref_binop_to_ref_val!(impl $imp<$scalar> for $res, $method);
forward_scalar_ref_ref_binop_to_ref_val!(impl $imp<$scalar> for $res, $method);
}
}
macro_rules! forward_all_scalar_binop_to_val_val {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
forward_scalar_val_ref_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
forward_scalar_ref_val_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
forward_scalar_ref_ref_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
}
}
macro_rules! forward_all_scalar_binop_to_val_val_commutative {
(impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => {
forward_scalar_val_val_binop_commutative!(impl $imp<$scalar> for $res, $method);
forward_all_scalar_binop_to_val_val!(impl $imp<$scalar> for $res, $method);
}
}
macro_rules! promote_all_scalars {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_unsigned_scalars!(impl $imp for $res, $method);
promote_signed_scalars!(impl $imp for $res, $method);
}
}
macro_rules! promote_all_scalars_assign {
(impl $imp:ident for $res:ty, $method:ident) => {
promote_unsigned_scalars_assign!(impl $imp for $res, $method);
promote_signed_scalars_assign!(impl $imp for $res, $method);
}
}
macro_rules! impl_sum_iter_type {
($res:ty) => {
impl<T> Sum<T> for $res
where
$res: Add<T, Output = $res>,
{
fn sum<I>(iter: I) -> Self
where
I: Iterator<Item = T>,
{
iter.fold(Self::ZERO, <$res>::add)
}
}
};
}
macro_rules! impl_product_iter_type {
($res:ty) => {
impl<T> Product<T> for $res
where
$res: Mul<T, Output = $res>,
{
fn product<I>(iter: I) -> Self
where
I: Iterator<Item = T>,
{
iter.fold(One::one(), <$res>::mul)
}
}
};
}

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{"name":"num-bigint","vers":"0.4.6","deps":[{"name":"arbitrary","req":"^1","features":[],"optional":true,"default_features":false,"target":null,"kind":"normal","registry":"https://github.com/rust-lang/crates.io-index","package":null,"public":null,"artifact":null,"bindep_target":null,"lib":false},{"name":"num-integer","req":"^0.1.46","features":["i128"],"optional":false,"default_features":false,"target":null,"kind":"normal","registry":"https://github.com/rust-lang/crates.io-index","package":null,"public":null,"artifact":null,"bindep_target":null,"lib":false},{"name":"num-traits","req":"^0.2.18","features":["i128"],"optional":false,"default_features":false,"target":null,"kind":"normal","registry":"https://github.com/rust-lang/crates.io-index","package":null,"public":null,"artifact":null,"bindep_target":null,"lib":false},{"name":"quickcheck","req":"^1","features":[],"optional":true,"default_features":false,"target":null,"kind":"normal","registry":"https://github.com/rust-lang/crates.io-index","package":null,"public":null,"artifact":null,"bindep_target":null,"lib":false},{"name":"rand","req":"^0.8","features":[],"optional":true,"default_features":false,"target":null,"kind":"normal","registry":"https://github.com/rust-lang/crates.io-index","package":null,"public":null,"artifact":null,"bindep_target":null,"lib":false},{"name":"serde","req":"^1.0","features":[],"optional":true,"default_features":false,"target":null,"kind":"normal","registry":"https://github.com/rust-lang/crates.io-index","package":null,"public":null,"artifact":null,"bindep_target":null,"lib":false}],"features":{"arbitrary":["dep:arbitrary"],"default":["std"],"quickcheck":["dep:quickcheck"],"rand":["dep:rand"],"serde":["dep:serde"],"std":["num-integer/std","num-traits/std"]},"features2":null,"cksum":"f125d0b0359be772552dd92d1af463cca7c3283451842a808b97f8aaaa3808ad","yanked":null,"links":null,"rust_version":null,"v":2}

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use num_bigint::{BigInt, Sign, ToBigInt};
use num_traits::ToPrimitive;
enum ValueVec {
N,
P(&'static [u32]),
M(&'static [u32]),
}
use crate::ValueVec::*;
impl ToBigInt for ValueVec {
fn to_bigint(&self) -> Option<BigInt> {
match self {
&N => Some(BigInt::from_slice(Sign::NoSign, &[])),
&P(s) => Some(BigInt::from_slice(Sign::Plus, s)),
&M(s) => Some(BigInt::from_slice(Sign::Minus, s)),
}
}
}
// a, !a
const NOT_VALUES: &[(ValueVec, ValueVec)] = &[
(N, M(&[1])),
(P(&[1]), M(&[2])),
(P(&[2]), M(&[3])),
(P(&[!0 - 2]), M(&[!0 - 1])),
(P(&[!0 - 1]), M(&[!0])),
(P(&[!0]), M(&[0, 1])),
(P(&[0, 1]), M(&[1, 1])),
(P(&[1, 1]), M(&[2, 1])),
];
// a, b, a & b, a | b, a ^ b
const BITWISE_VALUES: &[(ValueVec, ValueVec, ValueVec, ValueVec, ValueVec)] = &[
(N, N, N, N, N),
(N, P(&[1]), N, P(&[1]), P(&[1])),
(N, P(&[!0]), N, P(&[!0]), P(&[!0])),
(N, P(&[0, 1]), N, P(&[0, 1]), P(&[0, 1])),
(N, M(&[1]), N, M(&[1]), M(&[1])),
(N, M(&[!0]), N, M(&[!0]), M(&[!0])),
(N, M(&[0, 1]), N, M(&[0, 1]), M(&[0, 1])),
(P(&[1]), P(&[!0]), P(&[1]), P(&[!0]), P(&[!0 - 1])),
(P(&[!0]), P(&[!0]), P(&[!0]), P(&[!0]), N),
(P(&[!0]), P(&[1, 1]), P(&[1]), P(&[!0, 1]), P(&[!0 - 1, 1])),
(P(&[1]), M(&[!0]), P(&[1]), M(&[!0]), M(&[0, 1])),
(P(&[!0]), M(&[1]), P(&[!0]), M(&[1]), M(&[0, 1])),
(P(&[!0]), M(&[!0]), P(&[1]), M(&[1]), M(&[2])),
(P(&[!0]), M(&[1, 1]), P(&[!0]), M(&[1, 1]), M(&[0, 2])),
(P(&[1, 1]), M(&[!0]), P(&[1, 1]), M(&[!0]), M(&[0, 2])),
(M(&[1]), M(&[!0]), M(&[!0]), M(&[1]), P(&[!0 - 1])),
(M(&[!0]), M(&[!0]), M(&[!0]), M(&[!0]), N),
(M(&[!0]), M(&[1, 1]), M(&[!0, 1]), M(&[1]), P(&[!0 - 1, 1])),
];
const I32_MIN: i64 = i32::MIN as i64;
const I32_MAX: i64 = i32::MAX as i64;
const U32_MAX: i64 = u32::MAX as i64;
// some corner cases
const I64_VALUES: &[i64] = &[
i64::MIN,
i64::MIN + 1,
i64::MIN + 2,
i64::MIN + 3,
-U32_MAX - 3,
-U32_MAX - 2,
-U32_MAX - 1,
-U32_MAX,
-U32_MAX + 1,
-U32_MAX + 2,
-U32_MAX + 3,
I32_MIN - 3,
I32_MIN - 2,
I32_MIN - 1,
I32_MIN,
I32_MIN + 1,
I32_MIN + 2,
I32_MIN + 3,
-3,
-2,
-1,
0,
1,
2,
3,
I32_MAX - 3,
I32_MAX - 2,
I32_MAX - 1,
I32_MAX,
I32_MAX + 1,
I32_MAX + 2,
I32_MAX + 3,
U32_MAX - 3,
U32_MAX - 2,
U32_MAX - 1,
U32_MAX,
U32_MAX + 1,
U32_MAX + 2,
U32_MAX + 3,
i64::MAX - 3,
i64::MAX - 2,
i64::MAX - 1,
i64::MAX,
];
#[test]
fn test_not() {
for &(ref a, ref not) in NOT_VALUES.iter() {
let a = a.to_bigint().unwrap();
let not = not.to_bigint().unwrap();
// sanity check for tests that fit in i64
if let (Some(prim_a), Some(prim_not)) = (a.to_i64(), not.to_i64()) {
assert_eq!(!prim_a, prim_not);
}
assert_eq!(!a.clone(), not, "!{:x}", a);
assert_eq!(!not.clone(), a, "!{:x}", not);
}
}
#[test]
fn test_not_i64() {
for &prim_a in I64_VALUES.iter() {
let a = prim_a.to_bigint().unwrap();
let not = (!prim_a).to_bigint().unwrap();
assert_eq!(!a.clone(), not, "!{:x}", a);
}
}
#[test]
fn test_bitwise() {
for &(ref a, ref b, ref and, ref or, ref xor) in BITWISE_VALUES.iter() {
let a = a.to_bigint().unwrap();
let b = b.to_bigint().unwrap();
let and = and.to_bigint().unwrap();
let or = or.to_bigint().unwrap();
let xor = xor.to_bigint().unwrap();
// sanity check for tests that fit in i64
if let (Some(prim_a), Some(prim_b)) = (a.to_i64(), b.to_i64()) {
if let Some(prim_and) = and.to_i64() {
assert_eq!(prim_a & prim_b, prim_and);
}
if let Some(prim_or) = or.to_i64() {
assert_eq!(prim_a | prim_b, prim_or);
}
if let Some(prim_xor) = xor.to_i64() {
assert_eq!(prim_a ^ prim_b, prim_xor);
}
}
assert_eq!(a.clone() & &b, and, "{:x} & {:x}", a, b);
assert_eq!(b.clone() & &a, and, "{:x} & {:x}", b, a);
assert_eq!(a.clone() | &b, or, "{:x} | {:x}", a, b);
assert_eq!(b.clone() | &a, or, "{:x} | {:x}", b, a);
assert_eq!(a.clone() ^ &b, xor, "{:x} ^ {:x}", a, b);
assert_eq!(b.clone() ^ &a, xor, "{:x} ^ {:x}", b, a);
}
}
#[test]
fn test_bitwise_i64() {
for &prim_a in I64_VALUES.iter() {
let a = prim_a.to_bigint().unwrap();
for &prim_b in I64_VALUES.iter() {
let b = prim_b.to_bigint().unwrap();
let and = (prim_a & prim_b).to_bigint().unwrap();
let or = (prim_a | prim_b).to_bigint().unwrap();
let xor = (prim_a ^ prim_b).to_bigint().unwrap();
assert_eq!(a.clone() & &b, and, "{:x} & {:x}", a, b);
assert_eq!(a.clone() | &b, or, "{:x} | {:x}", a, b);
assert_eq!(a.clone() ^ &b, xor, "{:x} ^ {:x}", a, b);
}
}
}

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use num_bigint::BigInt;
use num_bigint::Sign::Plus;
use num_traits::{One, Signed, ToPrimitive, Zero};
use std::ops::Neg;
use std::panic::catch_unwind;
mod consts;
use crate::consts::*;
#[macro_use]
mod macros;
#[test]
fn test_scalar_add() {
fn check(x: &BigInt, y: &BigInt, z: &BigInt) {
let (x, y, z) = (x.clone(), y.clone(), z.clone());
assert_signed_scalar_op!(x + y == z);
assert_signed_scalar_assign_op!(x += y == z);
}
for elm in SUM_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let (na, nb, nc) = (-&a, -&b, -&c);
check(&a, &b, &c);
check(&b, &a, &c);
check(&c, &na, &b);
check(&c, &nb, &a);
check(&a, &nc, &nb);
check(&b, &nc, &na);
check(&na, &nb, &nc);
check(&a, &na, &Zero::zero());
}
}
#[test]
fn test_scalar_sub() {
fn check(x: &BigInt, y: &BigInt, z: &BigInt) {
let (x, y, z) = (x.clone(), y.clone(), z.clone());
assert_signed_scalar_op!(x - y == z);
assert_signed_scalar_assign_op!(x -= y == z);
}
for elm in SUM_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let (na, nb, nc) = (-&a, -&b, -&c);
check(&c, &a, &b);
check(&c, &b, &a);
check(&nb, &a, &nc);
check(&na, &b, &nc);
check(&b, &na, &c);
check(&a, &nb, &c);
check(&nc, &na, &nb);
check(&a, &a, &Zero::zero());
}
}
#[test]
fn test_scalar_mul() {
fn check(x: &BigInt, y: &BigInt, z: &BigInt) {
let (x, y, z) = (x.clone(), y.clone(), z.clone());
assert_signed_scalar_op!(x * y == z);
assert_signed_scalar_assign_op!(x *= y == z);
}
for elm in MUL_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
let (na, nb, nc) = (-&a, -&b, -&c);
check(&a, &b, &c);
check(&b, &a, &c);
check(&na, &nb, &c);
check(&na, &b, &nc);
check(&nb, &a, &nc);
}
}
#[test]
fn test_scalar_div_rem() {
fn check_sub(a: &BigInt, b: u32, ans_q: &BigInt, ans_r: &BigInt) {
let (q, r) = (a / b, a % b);
if !r.is_zero() {
assert_eq!(r.sign(), a.sign());
}
assert!(r.abs() <= BigInt::from(b));
assert!(*a == b * &q + &r);
assert!(q == *ans_q);
assert!(r == *ans_r);
let b = BigInt::from(b);
let (a, ans_q, ans_r) = (a.clone(), ans_q.clone(), ans_r.clone());
assert_signed_scalar_op!(a / b == ans_q);
assert_signed_scalar_op!(a % b == ans_r);
assert_signed_scalar_assign_op!(a /= b == ans_q);
assert_signed_scalar_assign_op!(a %= b == ans_r);
let nb = -b;
assert_signed_scalar_op!(a / nb == -ans_q.clone());
assert_signed_scalar_op!(a % nb == ans_r);
assert_signed_scalar_assign_op!(a /= nb == -ans_q.clone());
assert_signed_scalar_assign_op!(a %= nb == ans_r);
}
fn check(a: &BigInt, b: u32, q: &BigInt, r: &BigInt) {
check_sub(a, b, q, r);
check_sub(&a.neg(), b, &q.neg(), &r.neg());
}
for elm in MUL_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let b = BigInt::from_slice(Plus, b_vec);
let c = BigInt::from_slice(Plus, c_vec);
if a_vec.len() == 1 && a_vec[0] != 0 {
let a = a_vec[0];
check(&c, a, &b, &Zero::zero());
}
if b_vec.len() == 1 && b_vec[0] != 0 {
let b = b_vec[0];
check(&c, b, &a, &Zero::zero());
}
}
for elm in DIV_REM_QUADRUPLES.iter() {
let (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigInt::from_slice(Plus, a_vec);
let c = BigInt::from_slice(Plus, c_vec);
let d = BigInt::from_slice(Plus, d_vec);
if b_vec.len() == 1 && b_vec[0] != 0 {
let b = b_vec[0];
check(&a, b, &c, &d);
}
}
}
#[test]
fn test_scalar_div_rem_zero() {
catch_unwind(|| BigInt::zero() / 0u32).unwrap_err();
catch_unwind(|| BigInt::zero() % 0u32).unwrap_err();
catch_unwind(|| BigInt::one() / 0u32).unwrap_err();
catch_unwind(|| BigInt::one() % 0u32).unwrap_err();
}

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use num_bigint::BigUint;
use num_traits::{One, ToPrimitive, Zero};
use std::panic::catch_unwind;
mod consts;
use crate::consts::*;
#[macro_use]
mod macros;
#[test]
fn test_scalar_add() {
fn check(x: &BigUint, y: &BigUint, z: &BigUint) {
let (x, y, z) = (x.clone(), y.clone(), z.clone());
assert_unsigned_scalar_op!(x + y == z);
assert_unsigned_scalar_assign_op!(x += y == z);
}
for elm in SUM_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
check(&a, &b, &c);
check(&b, &a, &c);
}
}
#[test]
fn test_scalar_sub() {
fn check(x: &BigUint, y: &BigUint, z: &BigUint) {
let (x, y, z) = (x.clone(), y.clone(), z.clone());
assert_unsigned_scalar_op!(x - y == z);
assert_unsigned_scalar_assign_op!(x -= y == z);
}
for elm in SUM_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
check(&c, &a, &b);
check(&c, &b, &a);
}
}
#[test]
fn test_scalar_mul() {
fn check(x: &BigUint, y: &BigUint, z: &BigUint) {
let (x, y, z) = (x.clone(), y.clone(), z.clone());
assert_unsigned_scalar_op!(x * y == z);
assert_unsigned_scalar_assign_op!(x *= y == z);
}
for elm in MUL_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
check(&a, &b, &c);
check(&b, &a, &c);
}
}
#[test]
fn test_scalar_rem_noncommutative() {
assert_eq!(5u8 % BigUint::from(7u8), BigUint::from(5u8));
assert_eq!(BigUint::from(5u8) % 7u8, BigUint::from(5u8));
}
#[test]
fn test_scalar_div_rem() {
fn check(x: &BigUint, y: &BigUint, z: &BigUint, r: &BigUint) {
let (x, y, z, r) = (x.clone(), y.clone(), z.clone(), r.clone());
assert_unsigned_scalar_op!(x / y == z);
assert_unsigned_scalar_op!(x % y == r);
assert_unsigned_scalar_assign_op!(x /= y == z);
assert_unsigned_scalar_assign_op!(x %= y == r);
}
for elm in MUL_TRIPLES.iter() {
let (a_vec, b_vec, c_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
if !a.is_zero() {
check(&c, &a, &b, &Zero::zero());
}
if !b.is_zero() {
check(&c, &b, &a, &Zero::zero());
}
}
for elm in DIV_REM_QUADRUPLES.iter() {
let (a_vec, b_vec, c_vec, d_vec) = *elm;
let a = BigUint::from_slice(a_vec);
let b = BigUint::from_slice(b_vec);
let c = BigUint::from_slice(c_vec);
let d = BigUint::from_slice(d_vec);
if !b.is_zero() {
check(&a, &b, &c, &d);
assert_unsigned_scalar_op!(a / b == c);
assert_unsigned_scalar_op!(a % b == d);
assert_unsigned_scalar_assign_op!(a /= b == c);
assert_unsigned_scalar_assign_op!(a %= b == d);
}
}
}
#[test]
fn test_scalar_div_rem_zero() {
catch_unwind(|| BigUint::zero() / 0u32).unwrap_err();
catch_unwind(|| BigUint::zero() % 0u32).unwrap_err();
catch_unwind(|| BigUint::one() / 0u32).unwrap_err();
catch_unwind(|| BigUint::one() % 0u32).unwrap_err();
}

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vendor/num-bigint/tests/consts/mod.rs vendored Normal file
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#![allow(unused)]
pub const N1: u32 = -1i32 as u32;
pub const N2: u32 = -2i32 as u32;
pub const SUM_TRIPLES: &[(&[u32], &[u32], &[u32])] = &[
(&[], &[], &[]),
(&[], &[1], &[1]),
(&[1], &[1], &[2]),
(&[1], &[1, 1], &[2, 1]),
(&[1], &[N1], &[0, 1]),
(&[1], &[N1, N1], &[0, 0, 1]),
(&[N1, N1], &[N1, N1], &[N2, N1, 1]),
(&[1, 1, 1], &[N1, N1], &[0, 1, 2]),
(&[2, 2, 1], &[N1, N2], &[1, 1, 2]),
(&[1, 2, 2, 1], &[N1, N2], &[0, 1, 3, 1]),
];
pub const M: u32 = u32::MAX;
pub const MUL_TRIPLES: &[(&[u32], &[u32], &[u32])] = &[
(&[], &[], &[]),
(&[], &[1], &[]),
(&[2], &[], &[]),
(&[1], &[1], &[1]),
(&[2], &[3], &[6]),
(&[1], &[1, 1, 1], &[1, 1, 1]),
(&[1, 2, 3], &[3], &[3, 6, 9]),
(&[1, 1, 1], &[N1], &[N1, N1, N1]),
(&[1, 2, 3], &[N1], &[N1, N2, N2, 2]),
(&[1, 2, 3, 4], &[N1], &[N1, N2, N2, N2, 3]),
(&[N1], &[N1], &[1, N2]),
(&[N1, N1], &[N1], &[1, N1, N2]),
(&[N1, N1, N1], &[N1], &[1, N1, N1, N2]),
(&[N1, N1, N1, N1], &[N1], &[1, N1, N1, N1, N2]),
(&[M / 2 + 1], &[2], &[0, 1]),
(&[0, M / 2 + 1], &[2], &[0, 0, 1]),
(&[1, 2], &[1, 2, 3], &[1, 4, 7, 6]),
(&[N1, N1], &[N1, N1, N1], &[1, 0, N1, N2, N1]),
(&[N1, N1, N1], &[N1, N1, N1, N1], &[1, 0, 0, N1, N2, N1, N1]),
(&[0, 0, 1], &[1, 2, 3], &[0, 0, 1, 2, 3]),
(&[0, 0, 1], &[0, 0, 0, 1], &[0, 0, 0, 0, 0, 1]),
];
pub const DIV_REM_QUADRUPLES: &[(&[u32], &[u32], &[u32], &[u32])] = &[
(&[1], &[2], &[], &[1]),
(&[3], &[2], &[1], &[1]),
(&[1, 1], &[2], &[M / 2 + 1], &[1]),
(&[1, 1, 1], &[2], &[M / 2 + 1, M / 2 + 1], &[1]),
(&[0, 1], &[N1], &[1], &[1]),
(&[N1, N1], &[N2], &[2, 1], &[3]),
];

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//! Check buggy inputs that were found by fuzzing
use num_bigint::BigUint;
use num_traits::Num;
#[test]
fn fuzzed_mul_1() {
let hex1 = "\
cd6839ee857cf791a40494c2e522846eefbca9eca9912fdc1feed4561dbde75c75f1ddca2325ebb1\
b9cd6eae07308578e58e57f4ddd7dc239b4fd347b883e37d87232a8e5d5a8690c8dba69c97fe8ac4\
58add18be7e460e03c9d1ae8223db53d20681a4027ffc17d1e43b764791c4db5ff7add849da7e378\
ac8d9be0e8b517c490da3c0f944b6a52a0c5dc5217c71da8eec35d2c3110d8b041d2b52f3e2a8904\
abcaaca517a8f2ef6cd26ceadd39a1cf9f770bc08f55f5a230cd81961348bb18534245430699de77\
d93b805153cffd05dfd0f2cfc2332888cec9c5abf3ece9b4d7886ad94c784bf74fce12853b2a9a75\
b62a845151a703446cc20300eafe7332330e992ae88817cd6ccef8877b66a7252300a4664d7074da\
181cd9fd502ea1cd71c0b02db3c009fe970a7d226382cdba5b5576c5c0341694681c7adc4ca2d059\
d9a6b300957a2235a4eb6689b71d34dcc4037b520eabd2c8b66604bb662fe2bcf533ba8d242dbc91\
f04c1795b9f0fee800d197d8c6e998248b15855a9602b76cb3f94b148d8f71f7d6225b79d63a8e20\
8ec8f0fa56a1c381b6c09bad9886056aec17fc92b9bb0f8625fd3444e40cccc2ede768ddb23c66ad\
59a680a26a26d519d02e4d46ce93cce9e9dd86702bdd376abae0959a0e8e418aa507a63fafb8f422\
83b03dc26f371c5e261a8f90f3ac9e2a6bcc7f0a39c3f73043b5aa5a950d4e945e9f68b2c2e593e3\
b995be174714c1967b71f579043f89bfce37437af9388828a3ba0465c88954110cae6d38b638e094\
13c15c9faddd6fb63623fd50e06d00c4d5954e787158b3e4eea7e9fae8b189fa8a204b23ac2f7bbc\
b601189c0df2075977c2424336024ba3594172bea87f0f92beb20276ce8510c8ef2a4cd5ede87e7e\
38b3fa49d66fbcd322be686a349c24919f4000000000000000000000000000000000000000000000\
000000000000000000000000000000000";
let hex2 = "\
40000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000007";
// Result produced independently in Python
let hex_result = "\
335a0e7ba15f3de469012530b948a11bbbef2a7b2a644bf707fbb515876f79d71d7c777288c97aec\
6e735bab81cc215e396395fd3775f708e6d3f4d1ee20f8df61c8caa39756a1a43236e9a725ffa2b1\
162b7462f9f918380f2746ba088f6d4f481a069009fff05f4790edd91e47136d7fdeb7612769f8de\
2b2366f83a2d45f124368f03e512da94a831771485f1c76a3bb0d74b0c44362c1074ad4bcf8aa241\
2af2ab2945ea3cbbdb349b3ab74e6873e7ddc2f023d57d688c33606584d22ec614d09150c1a6779d\
f64ee01454f3ff4177f43cb3f08cca2233b2716afcfb3a6d35e21ab6531e12fdd3f384a14ecaa69d\
6d8aa1145469c0d11b3080c03abf9ccc8cc3a64aba2205f35b33be21ded9a9c948c02919935c1d36\
8607367f540ba8735c702c0b6cf0027fa5c29f4898e0b36e96d55db1700d05a51a071eb71328b416\
7669acc0255e888d693ad9a26dc74d373100ded483aaf4b22d99812ed98bf8af3d4ceea3490b6f24\
7c1305e56e7c3fba003465f631ba660922c56156a580addb2cfe52c52363dc7df58896de758ea388\
23b23c3e95a870e06db026eb6621815abb05ff24ae6ec3e1897f4d1139033330bb79da376c8f19ab\
5669a0289a89b546740b9351b3a4f33a7a77619c0af74ddaaeb8256683a39062a941e98febee3d08\
a0ec0f709bcdc7178986a3e43ceb278a9af31fc28e70fdcc10ed6a96a54353a517a7da2cb0b964f8\
ee656f85d1c530659edc7d5e410fe26ff38dd0debe4e220a28ee811972225504432b9b4e2d8e3825\
04f05727eb775bed8d88ff54381b40313565539e1c562cf93ba9fa7eba2c627ea28812c8eb0bdeef\
2d804627037c81d65df09090cd8092e8d6505cafaa1fc3e4afac809db3a144323bca93358117f935\
13d3695771180f461cf38bb995b531c9e072f84f04df87ce5ad0315387399d1086f60971dc149e06\
c23253a64e46e467b210e704f93f2ec6f60b9b386eb1f629e48d79adf57e018e4827f5cb5e6cc0ba\
d3573ea621a84bbc58efaff4abe2d8b7c117fe4a6bd3da03bf4fc61ff9fc5c0ea04f97384cb7df43\
265cf3a65ff5f7a46d0e0fe8426569063ea671cf9e87578c355775ecd1ccc2f44ab329bf20b28ab8\
83a59ea48bf9c0fa6c0c936cad5c415243eb59b76f559e8b1a86fd1daa46cfe4d52e351546f0a082\
394aafeb291eb6a3ae4f661bbda78467b3ab7a63f1e4baebf1174a13c32ea281a49e2a3937fb299e\
393b9116def94e15066cf5265f6566302c5bb8a69df9a8cbb45fce9203f5047ecc1e1331f6a8c9f5\
ed31466c9e1c44d13fea4045f621496bf0b893a0187f563f68416c9e0ed8c75c061873b274f38ee5\
041656ef77826fcdc401cc72095c185f3e66b2c37cfcca211fcb4f332ab46a19dbfd4027fd9214a5\
181596f85805bb26ed706328ffcd96a57a1a1303f8ebd10d8fdeec1dc6daf08054db99e2e3e77e96\
d85e6c588bff4441bf2baa25ec74a7e803141d6cab09ec6de23c5999548153de0fdfa6cebd738d84\
70e70fd3b4b1441cefa60a9a65650ead11330c83eb1c24173665e3caca83358bbdce0eacf199d1b0\
510a81c6930ab9ecf6a9b85328f2977947945bc251d9f7a87a135d260e965bdce354470b3a131832\
a2f1914b1d601db64f1dbcc43ea382d85cd08bb91c7a161ec87bc14c7758c4fc8cfb8e240c8a4988\
5dc10e0dfb7afbed3622fb0561d715254b196ceb42869765dc5cdac5d9c6e20df9b54c6228fa07ac\
44619e3372464fcfd67a10117770ca23369b796d0336de113fa5a3757e8a2819d9815b75738cebd8\
04dd0e29c5f334dae77044fffb5ac000000000000000000000000000000000000000000000000000\
000000000000000000000000000";
let bn1 = &BigUint::from_str_radix(hex1, 16).unwrap();
let bn2 = &BigUint::from_str_radix(hex2, 16).unwrap();
let result = BigUint::from_str_radix(hex_result, 16).unwrap();
assert_eq!(bn1 * bn2, result);
assert_eq!(bn2 * bn1, result);
}
#[test]
fn fuzzed_mul_2() {
let hex_a = "\
812cff04ff812cff04ff8180ff80ffff11ff80ff2cff04ff812cff04ff812cff04ff81232cff047d\
ff04ff812cff04ff812cff04ff812cff047f812cff04ff8180ff2cff04ff04ff8180ff2cff04ff04\
ff812cbf04ff8180ff2cff04ff812cff0401010000000000000000ffff1a80ffc006c70084ffff80\
ffc0064006000084ffff72ffc020ffffffffffff06d709000000dbffffffc799999999b999999999\
99999999000084ffff72ffc02006e1ffffffc70900ffffff00f312ff80ebffffff6f505f6c2e6712\
108970ffff5f6c6f6727020000000000007400000000000000000000a50000000000000000000000\
000000000000000000000000ff812cff04ff812cff2c04ff812cff8180ff2cff04ff04ff818b8b8b\
8b8b8b8b8b8b8b8b8b8b8b8b8b06c70084ffff80ffc006c700847fff80ffc006c700ffff12c70084\
ffff80ffc0060000000000000056ff00c789bfff80ffc006c70084ffff80ffc006c700ffff840100\
00000000001289ffc08b8b8b8b8b8b8b2c";
let hex_b = "\
7ed300fb007ed300fb007e7f00db00fb007ed3007ed300fb007edcd300fb8200fb007ed300fb007e\
d300fb007ed300fb007ed300fbfeffffffffffffa8fb007e7f00d300fb00fb007ed340fb007e7f00\
00fb007ed300fb007ed300fb007e7f00d300fb00fb007e7f00d300fb007efb007e7f00d300fb007e\
d300fb007e7f0097d300fb00bf007ed300fb007ed300fb00fb00fb00fbffffffffffffffffffff00\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
000000000000df9b3900ff908fa08d9e968c9a0000e7fffb7fff0000003fd9004c90d8f600de7f00\
3fdf9b3900ff908fa08d9e968cf9b9ff0000ed38ff7b00007f003ff9ffffffffffffffa900ff3876\
000078003ff938ff7b00007f003ff938ff00007bfeffffffffffffed76003f74747474747474d300\
fb00fb007e7f00d300fb007efb007e7f00d3003e7f007ed300fb007ed300fb007e7f00d300fb017e\
d300fb007ed300fb007edcd300fb8200fb007e0000e580";
let hex_c = "\
7b00387ffff938ff7b80007f003ff9b9ff00fdec38ff7b00007f003ff9ffffffffffffffa900ff38\
76000078003ff938ff7b00007f003ff938ff00007bfeffffffffffffed76003f74747474747474d3\
00fb00fb007e7f00d300fb007efb007e7f00d3003e7f007ed300fb007ed300fb007e7f00d300fb01\
7ed300fb007ed300fb007edcd300fb8200fb007e000000ee7f003f0000007b00387ffff938ff7b80\
007f003ff9b9ff00fdec38ff7b00007f003ff9ffffffffffffffa900ff3876000078003ff938ff7b\
00007f003ff938ff00007bfeffffffffffffed76003f74747474747474d300fb00fb007e7f00d300\
fb007efb007e7f00d3003e7f007ed300fb007ed300fb007e7f00d300fb017ed300fb007ed300fb00\
7edcd300fb8200fb007e000000ee7f003f000000000000000000000000000000002a000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000df9b3900ff908fa08d9e968c9a0000e7fffb7fff0000003fd9004c90d8\
f600de7f003fdf9b3900ff908fa08d9e968c9a0000e7fffa7fff0000004005004c90d8f600de908f\
dcd300fb8200fb007e0000e57f003ff938ff7b00007f003d7ed300fb007ed300fb007ed300fb007e\
fa00fb007ed300fbf9ffffffffffffffa900ff387600007f003ff938ff7b00007f003ff938fd0000\
7bfeffffffffffffed76003f74747474747474d300fc";
// Result produced independently in Python
let hex_result = "\
1ebf6415da7ac71a689cd450727b7a361402a1626e0b6cd057e0e2a77d4cb722c1b7d0cbd73a7c07\
d756813fe97d73d5905c4a26404c7162769ba2dbc1e2742855a1db803e2d2c2fddc77c0598cc70fe\
066fd4b81cae3e23c55b4795de63acacd1343cf5ad5e715e6919d140c01bab1af1a737ebbf8a7775\
7602acd611f555ee2d5be56cc14b97c248009cd77490a3dfd6762bae25459a544e369eb4b0cc952a\
8e6a551ff35a4a7a6e5f5b0b72495c4baadf3a26b9d5d97402ad60fa2324e93adc96ca159b62d147\
5695f26ff27da100a76e2d273420572e61b4dfbd97e826d9d946f85b87434523f6aa7ce43c443285\
33f5b5adf32574167b1e9ea3bf6254d6afacf865894907de196285169cfcc1c0fcf438873d13f7e8\
654acc27c1abb00bec2729e34c994ff2152f60406f75db3ab616541795d9db8ca0b381148de7875f\
e7a8191407abc390718003698ca28498948caf1dbc3f02593dd85fa929ebae86cfe783d7be473e98\
0060d9ec60843661cb4cb9b8ddb24bb710f93700b22530501b5ea26c5c94c7370fe0ccbafe0ce7e4\
cd4f071d0cf0ac151c85a5b132ecaa75793abfb4a6ee33fddd2aa2f5cf2a8eb19c75322792c0d8dc\
1efb2dcd8ae2b49dd57b84898f531c7f745464f637716151831db56b3e293f587dc95a5e12edfe6b\
8458033dddf3556da55bef55ba3c3769def0c0f0c86786aca8313dc0ce09118760721eb545d69b46\
cdb89d377f2c80e67b572da0f75760c2849288a8457c18c6f0b58244b7f95a7567ce23756f1fe359\
64f7e84fbe28b188157519dd99b8798b076e21984d15c37f41da1309e0fbc539e8b9b09fed36a908\
28c94f72e7b755c187e58db6bfef0c02309086626ad0fe2efd2ff1467b3de11e057687865f4f85e7\
0a39bcbc4674dcaded9b04562afe08eb92fbd96ea4a99aa4f9347a075d4421f070ce3a33225f5af1\
9c27ec5d1720e659ca7fff9686f46b01d76d7de64c738671aaec57ee5582ef7956206fb37c6a36f8\
8f226ce2124a7f9894a0e9a7aa02001746e6def35699d7adc84a7dcf513ff3da20fd849950f41a5d\
bb02c91666697156d69ebbe2ef26732b6595d1b6d014a60006d2d3c7055ff9b531779195b8dcd7d9\
426e776cbc9041735384568ba4adbf7eeea7e0e6cbb47b70335a7ed12a68904eecd334921e4ae6d9\
c983af20d73215c39573963f03bc87082450cc1c70250e1e8eaa318acaf044a072891fc60324d134\
6c0a1d02cceb4d4806e536d6017bf6bc125c41694ded38766fea51bfbf7a008ca0b3eb1168766486\
8aa8469b3e6787a5d5bad6cd67c24005a5cbaa10b63d1b4d05ac42a8b31263052a1260b5900be628\
4dcab4eb0cf5cda815412ced7bd78f87c00ac3581f41a04352a4a186805a5c9e37b14561a5fc97d2\
52ca4654fe3d82f42080c21483789cc4b4cbb568f79844f7a317aa2a6555774da26c6f027d3cb0ee\
9276c6dc4f285fc3b4b9a3cd51c8815cebf110e73c80a9b842cc3b7c80af13f702662b10e868eb61\
947000b390cd2f3a0899f6f1bab86acf767062f5526507790645ae13b9701ba96b3f873047c9d3b8\
5e8a5d904a01fbfe10e63495b6021e7cc082aa66679e4d92b3e4e2d62490b44f7e250584cedff0e7\
072a870ddaa9687a1eae11afc874d83065fb98dbc3cfd90f39517ff3015c71a8c0ab36a6483c7b87\
f41b2c832fa9428fe95ffba4e49cc553d9e2d33a540958da51588e5120fef6497bfaa96a4dcfc024\
8170c57f78e9ab9546efbbaf8e9ad6a993493577edd3d29ce8fd9a2e9eb4363b5b472a4ecb2065eb\
38f876a841af1f227a703248955c8978329dffcd8e065d8da4d42504796ff7abc62832ed86c4f8d0\
0f55cd567fb9d42524be57ebdacef730c3f94c0372f86fa1b0114f8620f553e4329b2a586fcfeedc\
af47934909090e14a1f1204e6f1681fb2df05356381e6340f4feaf0787e06218b0b0d8df51acb0bc\
f98546f33273adf260da959d6fc4a04872122af6508d124abb963c14c30e7c07fee368324921fe33\
9ae89490c5d6cdae0c356bb6921de95ea13b54e23800";
let a = &BigUint::from_str_radix(hex_a, 16).unwrap();
let b = &BigUint::from_str_radix(hex_b, 16).unwrap();
let c = &BigUint::from_str_radix(hex_c, 16).unwrap();
let result = BigUint::from_str_radix(hex_result, 16).unwrap();
assert_eq!(a * b * c, result);
assert_eq!(a * c * b, result);
assert_eq!(b * a * c, result);
assert_eq!(b * c * a, result);
assert_eq!(c * a * b, result);
assert_eq!(c * b * a, result);
}

78
vendor/num-bigint/tests/macros/mod.rs vendored Normal file
View File

@@ -0,0 +1,78 @@
#![allow(unused)]
/// Assert that an op works for all val/ref combinations
macro_rules! assert_op {
($left:ident $op:tt $right:ident == $expected:expr) => {
assert_eq!((&$left) $op (&$right), $expected);
assert_eq!((&$left) $op $right.clone(), $expected);
assert_eq!($left.clone() $op (&$right), $expected);
assert_eq!($left.clone() $op $right.clone(), $expected);
};
}
/// Assert that an assign-op works for all val/ref combinations
macro_rules! assert_assign_op {
($left:ident $op:tt $right:ident == $expected:expr) => {{
let mut left = $left.clone();
assert_eq!({ left $op &$right; left}, $expected);
let mut left = $left.clone();
assert_eq!({ left $op $right.clone(); left}, $expected);
}};
}
/// Assert that an op works for scalar left or right
macro_rules! assert_scalar_op {
(($($to:ident),*) $left:ident $op:tt $right:ident == $expected:expr) => {
$(
if let Some(left) = $left.$to() {
assert_op!(left $op $right == $expected);
}
if let Some(right) = $right.$to() {
assert_op!($left $op right == $expected);
}
)*
};
}
macro_rules! assert_unsigned_scalar_op {
($left:ident $op:tt $right:ident == $expected:expr) => {
assert_scalar_op!((to_u8, to_u16, to_u32, to_u64, to_usize, to_u128)
$left $op $right == $expected);
};
}
macro_rules! assert_signed_scalar_op {
($left:ident $op:tt $right:ident == $expected:expr) => {
assert_scalar_op!((to_u8, to_u16, to_u32, to_u64, to_usize, to_u128,
to_i8, to_i16, to_i32, to_i64, to_isize, to_i128)
$left $op $right == $expected);
};
}
/// Assert that an op works for scalar right
macro_rules! assert_scalar_assign_op {
(($($to:ident),*) $left:ident $op:tt $right:ident == $expected:expr) => {
$(
if let Some(right) = $right.$to() {
let mut left = $left.clone();
assert_eq!({ left $op right; left}, $expected);
}
)*
};
}
macro_rules! assert_unsigned_scalar_assign_op {
($left:ident $op:tt $right:ident == $expected:expr) => {
assert_scalar_assign_op!((to_u8, to_u16, to_u32, to_u64, to_usize, to_u128)
$left $op $right == $expected);
};
}
macro_rules! assert_signed_scalar_assign_op {
($left:ident $op:tt $right:ident == $expected:expr) => {
assert_scalar_assign_op!((to_u8, to_u16, to_u32, to_u64, to_usize, to_u128,
to_i8, to_i16, to_i32, to_i64, to_isize, to_i128)
$left $op $right == $expected);
};
}

181
vendor/num-bigint/tests/modpow.rs vendored Normal file
View File

@@ -0,0 +1,181 @@
static BIG_B: &str = "\
efac3c0a_0de55551_fee0bfe4_67fa017a_1a898fa1_6ca57cb1\
ca9e3248_cacc09a9_b99d6abc_38418d0f_82ae4238_d9a68832\
aadec7c1_ac5fed48_7a56a71b_67ac59d5_afb28022_20d9592d\
247c4efc_abbd9b75_586088ee_1dc00dc4_232a8e15_6e8191dd\
675b6ae0_c80f5164_752940bc_284b7cee_885c1e10_e495345b\
8fbe9cfd_e5233fe1_19459d0b_d64be53c_27de5a02_a829976b\
33096862_82dad291_bd38b6a9_be396646_ddaf8039_a2573c39\
1b14e8bc_2cb53e48_298c047e_d9879e9c_5a521076_f0e27df3\
990e1659_d3d8205b_6443ebc0_9918ebee_6764f668_9f2b2be3\
b59cbc76_d76d0dfc_d737c3ec_0ccf9c00_ad0554bf_17e776ad\
b4edf9cc_6ce540be_76229093_5c53893b";
static BIG_E: &str = "\
be0e6ea6_08746133_e0fbc1bf_82dba91e_e2b56231_a81888d2\
a833a1fc_f7ff002a_3c486a13_4f420bf3_a5435be9_1a5c8391\
774d6e6c_085d8357_b0c97d4d_2bb33f7c_34c68059_f78d2541\
eacc8832_426f1816_d3be001e_b69f9242_51c7708e_e10efe98\
449c9a4a_b55a0f23_9d797410_515da00d_3ea07970_4478a2ca\
c3d5043c_bd9be1b4_6dce479d_4302d344_84a939e6_0ab5ada7\
12ae34b2_30cc473c_9f8ee69d_2cac5970_29f5bf18_bc8203e4\
f3e895a2_13c94f1e_24c73d77_e517e801_53661fdd_a2ce9e47\
a73dd7f8_2f2adb1e_3f136bf7_8ae5f3b8_08730de1_a4eff678\
e77a06d0_19a522eb_cbefba2a_9caf7736_b157c5c6_2d192591\
17946850_2ddb1822_117b68a0_32f7db88";
// This modulus is the prime from the 2048-bit MODP DH group:
// https://tools.ietf.org/html/rfc3526#section-3
static BIG_M: &str = "\
FFFFFFFF_FFFFFFFF_C90FDAA2_2168C234_C4C6628B_80DC1CD1\
29024E08_8A67CC74_020BBEA6_3B139B22_514A0879_8E3404DD\
EF9519B3_CD3A431B_302B0A6D_F25F1437_4FE1356D_6D51C245\
E485B576_625E7EC6_F44C42E9_A637ED6B_0BFF5CB6_F406B7ED\
EE386BFB_5A899FA5_AE9F2411_7C4B1FE6_49286651_ECE45B3D\
C2007CB8_A163BF05_98DA4836_1C55D39A_69163FA8_FD24CF5F\
83655D23_DCA3AD96_1C62F356_208552BB_9ED52907_7096966D\
670C354E_4ABC9804_F1746C08_CA18217C_32905E46_2E36CE3B\
E39E772C_180E8603_9B2783A2_EC07A28F_B5C55DF0_6F4C52C9\
DE2BCBF6_95581718_3995497C_EA956AE5_15D22618_98FA0510\
15728E5A_8AACAA68_FFFFFFFF_FFFFFFFF";
static BIG_R: &str = "\
a1468311_6e56edc9_7a98228b_5e924776_0dd7836e_caabac13\
eda5373b_4752aa65_a1454850_40dc770e_30aa8675_6be7d3a8\
9d3085e4_da5155cf_b451ef62_54d0da61_cf2b2c87_f495e096\
055309f7_77802bbb_37271ba8_1313f1b5_075c75d1_024b6c77\
fdb56f17_b05bce61_e527ebfd_2ee86860_e9907066_edd526e7\
93d289bf_6726b293_41b0de24_eff82424_8dfd374b_4ec59542\
35ced2b2_6b195c90_10042ffb_8f58ce21_bc10ec42_64fda779\
d352d234_3d4eaea6_a86111ad_a37e9555_43ca78ce_2885bed7\
5a30d182_f1cf6834_dc5b6e27_1a41ac34_a2e91e11_33363ff0\
f88a7b04_900227c9_f6e6d06b_7856b4bb_4e354d61_060db6c8\
109c4735_6e7db425_7b5d74c7_0b709508";
mod biguint {
use num_bigint::BigUint;
use num_integer::Integer;
use num_traits::Num;
fn check_modpow<T: Into<BigUint>>(b: T, e: T, m: T, r: T) {
let b: BigUint = b.into();
let e: BigUint = e.into();
let m: BigUint = m.into();
let r: BigUint = r.into();
assert_eq!(b.modpow(&e, &m), r);
let even_m = &m << 1;
let even_modpow = b.modpow(&e, &even_m);
assert!(even_modpow < even_m);
assert_eq!(even_modpow.mod_floor(&m), r);
}
#[test]
fn test_modpow_single() {
check_modpow::<u32>(1, 0, 11, 1);
check_modpow::<u32>(0, 15, 11, 0);
check_modpow::<u32>(3, 7, 11, 9);
check_modpow::<u32>(5, 117, 19, 1);
check_modpow::<u32>(20, 1, 2, 0);
check_modpow::<u32>(20, 1, 3, 2);
}
#[test]
fn test_modpow_small() {
for b in 0u64..11 {
for e in 0u64..11 {
for m in 1..11 {
check_modpow::<u64>(b, e, m, b.pow(e as u32) % m);
}
}
}
}
#[test]
fn test_modpow_big() {
let b = BigUint::from_str_radix(super::BIG_B, 16).unwrap();
let e = BigUint::from_str_radix(super::BIG_E, 16).unwrap();
let m = BigUint::from_str_radix(super::BIG_M, 16).unwrap();
let r = BigUint::from_str_radix(super::BIG_R, 16).unwrap();
assert_eq!(b.modpow(&e, &m), r);
let even_m = &m << 1;
let even_modpow = b.modpow(&e, &even_m);
assert!(even_modpow < even_m);
assert_eq!(even_modpow % m, r);
}
}
mod bigint {
use num_bigint::BigInt;
use num_integer::Integer;
use num_traits::{Num, One, Signed};
fn check_modpow<T: Into<BigInt>>(b: T, e: T, m: T, r: T) {
fn check(b: &BigInt, e: &BigInt, m: &BigInt, r: &BigInt) {
assert_eq!(&b.modpow(e, m), r, "{} ** {} (mod {}) != {}", b, e, m, r);
let even_m = m << 1u8;
let even_modpow = b.modpow(e, m);
assert!(even_modpow.abs() < even_m.abs());
assert_eq!(&even_modpow.mod_floor(m), r);
// the sign of the result follows the modulus like `mod_floor`, not `rem`
assert_eq!(b.modpow(&BigInt::one(), m), b.mod_floor(m));
}
let b: BigInt = b.into();
let e: BigInt = e.into();
let m: BigInt = m.into();
let r: BigInt = r.into();
let neg_b_r = if e.is_odd() {
(-&r).mod_floor(&m)
} else {
r.clone()
};
let neg_m_r = r.mod_floor(&-&m);
let neg_bm_r = neg_b_r.mod_floor(&-&m);
check(&b, &e, &m, &r);
check(&-&b, &e, &m, &neg_b_r);
check(&b, &e, &-&m, &neg_m_r);
check(&-b, &e, &-&m, &neg_bm_r);
}
#[test]
fn test_modpow() {
check_modpow(1, 0, 11, 1);
check_modpow(0, 15, 11, 0);
check_modpow(3, 7, 11, 9);
check_modpow(5, 117, 19, 1);
check_modpow(-20, 1, 2, 0);
check_modpow(-20, 1, 3, 1);
}
#[test]
fn test_modpow_small() {
for b in -10i64..11 {
for e in 0i64..11 {
for m in -10..11 {
if m == 0 {
continue;
}
check_modpow(b, e, m, b.pow(e as u32).mod_floor(&m));
}
}
}
}
#[test]
fn test_modpow_big() {
let b = BigInt::from_str_radix(super::BIG_B, 16).unwrap();
let e = BigInt::from_str_radix(super::BIG_E, 16).unwrap();
let m = BigInt::from_str_radix(super::BIG_M, 16).unwrap();
let r = BigInt::from_str_radix(super::BIG_R, 16).unwrap();
check_modpow(b, e, m, r);
}
}

159
vendor/num-bigint/tests/roots.rs vendored Normal file
View File

@@ -0,0 +1,159 @@
mod biguint {
use num_bigint::BigUint;
use num_traits::{One, Zero};
fn check<T: Into<BigUint>>(x: T, n: u32) {
let x: BigUint = x.into();
let root = x.nth_root(n);
println!("check {}.nth_root({}) = {}", x, n, root);
if n == 2 {
assert_eq!(root, x.sqrt())
} else if n == 3 {
assert_eq!(root, x.cbrt())
}
let lo = root.pow(n);
assert!(lo <= x);
assert_eq!(lo.nth_root(n), root);
if !lo.is_zero() {
assert_eq!((&lo - 1u32).nth_root(n), &root - 1u32);
}
let hi = (&root + 1u32).pow(n);
assert!(hi > x);
assert_eq!(hi.nth_root(n), &root + 1u32);
assert_eq!((&hi - 1u32).nth_root(n), root);
}
#[test]
fn test_sqrt() {
check(99u32, 2);
check(100u32, 2);
check(120u32, 2);
}
#[test]
fn test_cbrt() {
check(8u32, 3);
check(26u32, 3);
}
#[test]
fn test_nth_root() {
check(0u32, 1);
check(10u32, 1);
check(100u32, 4);
}
#[test]
#[should_panic]
fn test_nth_root_n_is_zero() {
check(4u32, 0);
}
#[test]
fn test_nth_root_big() {
let x = BigUint::from(123_456_789_u32);
let expected = BigUint::from(6u32);
assert_eq!(x.nth_root(10), expected);
check(x, 10);
}
#[test]
fn test_nth_root_googol() {
let googol = BigUint::from(10u32).pow(100u32);
// perfect divisors of 100
for &n in &[2, 4, 5, 10, 20, 25, 50, 100] {
let expected = BigUint::from(10u32).pow(100u32 / n);
assert_eq!(googol.nth_root(n), expected);
check(googol.clone(), n);
}
}
#[test]
fn test_nth_root_twos() {
const EXP: u32 = 12;
const LOG2: usize = 1 << EXP;
let x = BigUint::one() << LOG2;
// the perfect divisors are just powers of two
for exp in 1..=EXP {
let n = 2u32.pow(exp);
let expected = BigUint::one() << (LOG2 / n as usize);
assert_eq!(x.nth_root(n), expected);
check(x.clone(), n);
}
// degenerate cases should return quickly
assert!(x.nth_root(x.bits() as u32).is_one());
assert!(x.nth_root(i32::MAX as u32).is_one());
assert!(x.nth_root(u32::MAX).is_one());
}
#[test]
fn test_roots_rand1() {
// A random input that found regressions
let s = "575981506858479247661989091587544744717244516135539456183849\
986593934723426343633698413178771587697273822147578889823552\
182702908597782734558103025298880194023243541613924361007059\
353344183590348785832467726433749431093350684849462759540710\
026019022227591412417064179299354183441181373862905039254106\
4781867";
let x: BigUint = s.parse().unwrap();
check(x.clone(), 2);
check(x.clone(), 3);
check(x.clone(), 10);
check(x, 100);
}
}
mod bigint {
use num_bigint::BigInt;
use num_traits::Signed;
fn check(x: i64, n: u32) {
let big_x = BigInt::from(x);
let res = big_x.nth_root(n);
if n == 2 {
assert_eq!(&res, &big_x.sqrt())
} else if n == 3 {
assert_eq!(&res, &big_x.cbrt())
}
if big_x.is_negative() {
assert!(res.pow(n) >= big_x);
assert!((res - 1u32).pow(n) < big_x);
} else {
assert!(res.pow(n) <= big_x);
assert!((res + 1u32).pow(n) > big_x);
}
}
#[test]
fn test_nth_root() {
check(-100, 3);
}
#[test]
#[should_panic]
fn test_nth_root_x_neg_n_even() {
check(-100, 4);
}
#[test]
#[should_panic]
fn test_sqrt_x_neg() {
check(-4, 2);
}
#[test]
fn test_cbrt() {
check(8, 3);
check(-8, 3);
}
}