num-bigint-0.4.3/.cargo_vcs_info.json0000644000000001120000000000100131030ustar { "git": { "sha1": "e77ffacafef7e8fa2c2b990489b7aa30dceaed64" } } num-bigint-0.4.3/.gitignore000064400000000000000000000000360072674642500137200ustar 00000000000000Cargo.lock target *.bk *.orig num-bigint-0.4.3/Cargo.toml0000644000000035200000000000100111070ustar # THIS FILE IS AUTOMATICALLY GENERATED BY CARGO # # When uploading crates to the registry Cargo will automatically # "normalize" Cargo.toml files for maximal compatibility # with all versions of Cargo and also rewrite `path` dependencies # to registry (e.g., crates.io) dependencies. # # If you are reading this file be aware that the original Cargo.toml # will likely look very different (and much more reasonable). # See Cargo.toml.orig for the original contents. [package] edition = "2018" name = "num-bigint" version = "0.4.3" authors = ["The Rust Project Developers"] build = "build.rs" exclude = ["/bors.toml", "/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"] [[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 = "0.1.42" features = ["i128"] default-features = false [dependencies.num-traits] version = "0.2.11" 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 [build-dependencies.autocfg] version = "1" [features] default = ["std"] std = ["num-integer/std", "num-traits/std"] num-bigint-0.4.3/Cargo.toml.orig000064400000000000000000000026120072674642500146210ustar 00000000000000[package] authors = ["The Rust Project Developers"] description = "Big integer implementation for Rust" documentation = "https://docs.rs/num-bigint" homepage = "https://github.com/rust-num/num-bigint" keywords = ["mathematics", "numerics", "bignum"] categories = [ "algorithms", "data-structures", "science" ] license = "MIT OR Apache-2.0" name = "num-bigint" repository = "https://github.com/rust-num/num-bigint" version = "0.4.3" readme = "README.md" build = "build.rs" exclude = ["/bors.toml", "/ci/*", "/.github/*"] edition = "2018" [features] default = ["std"] std = ["num-integer/std", "num-traits/std"] [package.metadata.docs.rs] features = ["std", "serde", "rand", "quickcheck", "arbitrary"] [[bench]] name = "bigint" [[bench]] name = "factorial" [[bench]] name = "gcd" [[bench]] name = "roots" [[bench]] harness = false name = "shootout-pidigits" [dependencies] [dependencies.num-integer] version = "0.1.42" default-features = false features = ["i128"] [dependencies.num-traits] version = "0.2.11" default-features = false features = ["i128"] [dependencies.rand] optional = true version = "0.8" default-features = false [dependencies.serde] optional = true version = "1.0" default-features = false [dependencies.quickcheck] optional = true version = "1" default-features = false [dependencies.arbitrary] optional = true version = "1" default-features = false [build-dependencies] autocfg = "1" num-bigint-0.4.3/LICENSE-APACHE000064400000000000000000000251370072674642500136650ustar 00000000000000 Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. 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See the License for the specific language governing permissions and limitations under the License. num-bigint-0.4.3/LICENSE-MIT000064400000000000000000000020570072674642500133710ustar 00000000000000Copyright (c) 2014 The Rust Project Developers Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 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IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. num-bigint-0.4.3/README.md000064400000000000000000000053240072674642500132140ustar 00000000000000# 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 1.31](https://img.shields.io/badge/rustc-1.31+-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 1.31 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 | | :--------------- | :------------- | :-------- | :------------- | | **`num-bigint`** | MIT/Apache-2.0 | 1.31 | pure rust | | [`ramp`] | Apache-2.0 | nightly | rust and inline assembly | | [`rug`] | LGPL-3.0+ | 1.37 | bundles [GMP] via [`gmp-mpfr-sys`] | | [`rust-gmp`] | MIT | stable? | links to [GMP] | | [`apint`] | MIT/Apache-2.0 | 1.26 | pure rust (unfinished) | [GMP]: https://gmplib.org/ [`gmp-mpfr-sys`]: https://crates.io/crates/gmp-mpfr-sys [`rug`]: https://crates.io/crates/rug [`rust-gmp`]: https://crates.io/crates/rust-gmp [`ramp`]: https://crates.io/crates/ramp [`apint`]: https://crates.io/crates/apint ## 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. num-bigint-0.4.3/RELEASES.md000064400000000000000000000306620072674642500134650ustar 00000000000000# 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-232 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::` 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! num-bigint-0.4.3/benches/bigint.rs000064400000000000000000000223470072674642500151720ustar 00000000000000#![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 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 = (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()); } num-bigint-0.4.3/benches/factorial.rs000064400000000000000000000017370072674642500156620ustar 00000000000000#![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: // #[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)); } num-bigint-0.4.3/benches/gcd.rs000064400000000000000000000025360072674642500144510ustar 00000000000000#![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); } num-bigint-0.4.3/benches/rng/mod.rs000064400000000000000000000016720072674642500152610ustar 00000000000000use 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)) } } num-bigint-0.4.3/benches/roots.rs000064400000000000000000000060640072674642500150620ustar 00000000000000#![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); } num-bigint-0.4.3/benches/shootout-pidigits.rs000064400000000000000000000100540072674642500174040ustar 00000000000000// 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::>(); 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(); } num-bigint-0.4.3/build.rs000064400000000000000000000052620072674642500134030ustar 00000000000000use std::env; use std::error::Error; use std::fs::File; use std::io::Write; use std::path::Path; fn main() { let pointer_width = env::var("CARGO_CFG_TARGET_POINTER_WIDTH"); let u64_digit = pointer_width.as_ref().map(String::as_str) == Ok("64"); if u64_digit { autocfg::emit("u64_digit"); } let ac = autocfg::new(); let std = if ac.probe_sysroot_crate("std") { "std" } else { "core" }; if ac.probe_path(&format!("{}::convert::TryFrom", std)) { autocfg::emit("has_try_from"); } if let Ok(target_arch) = env::var("CARGO_CFG_TARGET_ARCH") { if target_arch == "x86_64" || target_arch == "x86" { let digit = if u64_digit { "u64" } else { "u32" }; let addcarry = format!("{}::arch::{}::_addcarry_{}", std, target_arch, digit); if ac.probe_path(&addcarry) { autocfg::emit("use_addcarry"); } } } autocfg::rerun_path("build.rs"); write_radix_bases().unwrap(); } /// Write tables of the greatest power of each radix for the given bit size. These are returned /// from `biguint::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. fn write_radix_bases() -> Result<(), Box> { let out_dir = env::var("OUT_DIR")?; let dest_path = Path::new(&out_dir).join("radix_bases.rs"); let mut f = File::create(&dest_path)?; for &bits in &[16, 32, 64] { let max = if bits < 64 { (1 << bits) - 1 } else { std::u64::MAX }; writeln!(f, "#[deny(overflowing_literals)]")?; writeln!( f, "pub(crate) static BASES_{bits}: [(u{bits}, usize); 257] = [", bits = bits )?; for radix in 0u64..257 { let (base, power) = if radix == 0 || radix.is_power_of_two() { (0, 0) } else { let mut power = 1; let mut base = radix; while let Some(b) = base.checked_mul(radix) { if b > max { break; } base = b; power += 1; } (base, power) }; writeln!(f, " ({}, {}), // {}", base, power, radix)?; } writeln!(f, "];")?; } Ok(()) } num-bigint-0.4.3/src/bigint/addition.rs000064400000000000000000000150170072674642500161410ustar 00000000000000use 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, Zero}; // 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 => Zero::zero(), }, } }; } impl<'a, 'b> Add<&'b BigInt> for &'a BigInt { type Output = BigInt; #[inline] fn add(self, other: &BigInt) -> BigInt { bigint_add!( self, self.clone(), &self.data, other, other.clone(), &other.data ) } } impl<'a> Add for &'a BigInt { type Output = BigInt; #[inline] fn add(self, other: BigInt) -> BigInt { bigint_add!(self, self.clone(), &self.data, other, other, other.data) } } impl<'a> Add<&'a 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 for BigInt { type Output = BigInt; #[inline] fn add(self, other: BigInt) -> BigInt { bigint_add!(self, self, self.data, other, other, other.data) } } impl<'a> AddAssign<&'a BigInt> for BigInt { #[inline] fn add_assign(&mut self, other: &BigInt) { let n = mem::replace(self, BigInt::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 for BigInt, add); forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigInt, add); forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigInt, add); impl Add 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 => Zero::zero(), Less => BigInt::from(other - self.data), Greater => -BigInt::from(self.data - other), }, } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: u32) { let n = mem::replace(self, BigInt::zero()); *self = n + other; } } impl Add 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 => Zero::zero(), Less => BigInt::from(other - self.data), Greater => -BigInt::from(self.data - other), }, } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: u64) { let n = mem::replace(self, BigInt::zero()); *self = n + other; } } impl Add 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 => BigInt::zero(), Less => BigInt::from(other - self.data), Greater => -BigInt::from(self.data - other), }, } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: u128) { let n = mem::replace(self, BigInt::zero()); *self = n + other; } } forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigInt, add); forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigInt, add); forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigInt, add); impl Add 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 for BigInt { #[inline] fn add_assign(&mut self, other: i32) { match other.checked_uabs() { Positive(u) => *self += u, Negative(u) => *self -= u, } } } impl Add 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 for BigInt { #[inline] fn add_assign(&mut self, other: i64) { match other.checked_uabs() { Positive(u) => *self += u, Negative(u) => *self -= u, } } } impl Add 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 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 { Some(self.add(v)) } } impl_sum_iter_type!(BigInt); num-bigint-0.4.3/src/bigint/arbitrary.rs000064400000000000000000000025750072674642500163520ustar 00000000000000use super::{BigInt, Sign}; #[cfg(feature = "quickcheck")] use crate::std_alloc::Box; use crate::BigUint; #[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> { 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")] impl arbitrary::Arbitrary<'_> for BigInt { fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result { 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 { 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) { arbitrary::size_hint::and(bool::size_hint(depth), BigUint::size_hint(depth)) } } num-bigint-0.4.3/src/bigint/bits.rs000064400000000000000000000435250072674642500153140ustar 00000000000000use super::BigInt; use super::Sign::{Minus, NoSign, Plus}; use crate::big_digit::{self, BigDigit, DoubleBigDigit}; use crate::biguint::IntDigits; use crate::std_alloc::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 Vec, 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, 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, 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<'a, 'b> BitAnd<&'b BigInt> for &'a 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<'a> BitAnd<&'a 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<'a> BitAndAssign<&'a 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, 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 Vec, 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, 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<'a, 'b> BitOr<&'b BigInt> for &'a 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<'a> BitOr<&'a 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<'a> BitOrAssign<&'a 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, 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, 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, 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<'a> BitXor<&'a 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<'a> BitXorAssign<&'a 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 } } } num-bigint-0.4.3/src/bigint/convert.rs000064400000000000000000000272470072674642500160360ustar 00000000000000use super::Sign::{self, Minus, NoSign, Plus}; use super::{BigInt, ToBigInt}; use crate::std_alloc::Vec; #[cfg(has_try_from)] use crate::TryFromBigIntError; use crate::{BigUint, ParseBigIntError, ToBigUint}; use core::cmp::Ordering::{Equal, Greater, Less}; #[cfg(has_try_from)] use core::convert::TryFrom; use core::str::{self, FromStr}; use num_traits::{FromPrimitive, Num, ToPrimitive, Zero}; impl FromStr for BigInt { type Err = ParseBigIntError; #[inline] fn from_str(s: &str) -> Result { 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 { let sign = if s.starts_with('-') { let tail = &s[1..]; 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 { 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(core::i64::MIN), Greater => None, } } } } #[inline] fn to_i128(&self) -> Option { 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(core::i128::MIN), Greater => None, } } } } #[inline] fn to_u64(&self) -> Option { match self.sign { Plus => self.data.to_u64(), NoSign => Some(0), Minus => None, } } #[inline] fn to_u128(&self) -> Option { match self.sign { Plus => self.data.to_u128(), NoSign => Some(0), Minus => None, } } #[inline] fn to_f32(&self) -> Option { let n = self.data.to_f32()?; Some(if self.sign == Minus { -n } else { n }) } #[inline] fn to_f64(&self) -> Option { 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) => { #[cfg(has_try_from)] impl TryFrom<&BigInt> for $T { type Error = TryFromBigIntError<()>; #[inline] fn try_from(value: &BigInt) -> Result<$T, TryFromBigIntError<()>> { $to_ty(value).ok_or(TryFromBigIntError::new(())) } } #[cfg(has_try_from)] impl TryFrom for $T { type Error = TryFromBigIntError; #[inline] fn try_from(value: BigInt) -> Result<$T, TryFromBigIntError> { <$T>::try_from(&value).map_err(|_| TryFromBigIntError::new(value)) } } }; } impl_try_from_bigint!(u8, ToPrimitive::to_u8); impl_try_from_bigint!(u16, ToPrimitive::to_u16); impl_try_from_bigint!(u32, ToPrimitive::to_u32); impl_try_from_bigint!(u64, ToPrimitive::to_u64); impl_try_from_bigint!(usize, ToPrimitive::to_usize); impl_try_from_bigint!(u128, ToPrimitive::to_u128); impl_try_from_bigint!(i8, ToPrimitive::to_i8); impl_try_from_bigint!(i16, ToPrimitive::to_i16); impl_try_from_bigint!(i32, ToPrimitive::to_i32); impl_try_from_bigint!(i64, ToPrimitive::to_i64); impl_try_from_bigint!(isize, ToPrimitive::to_isize); impl_try_from_bigint!(i128, ToPrimitive::to_i128); impl FromPrimitive for BigInt { #[inline] fn from_i64(n: i64) -> Option { Some(BigInt::from(n)) } #[inline] fn from_i128(n: i128) -> Option { Some(BigInt::from(n)) } #[inline] fn from_u64(n: u64) -> Option { Some(BigInt::from(n)) } #[inline] fn from_u128(n: u128) -> Option { Some(BigInt::from(n)) } #[inline] fn from_f64(n: f64) -> Option { if n >= 0.0 { BigUint::from_f64(n).map(BigInt::from) } else { let x = BigUint::from_f64(-n)?; Some(-BigInt::from(x)) } } } impl From for BigInt { #[inline] fn from(n: i64) -> Self { if n >= 0 { BigInt::from(n as u64) } else { let u = core::u64::MAX - (n as u64) + 1; BigInt { sign: Minus, data: BigUint::from(u), } } } } impl From for BigInt { #[inline] fn from(n: i128) -> Self { if n >= 0 { BigInt::from(n as u128) } else { let u = core::u128::MAX - (n as u128) + 1; BigInt { sign: Minus, data: BigUint::from(u), } } } } macro_rules! impl_bigint_from_int { ($T:ty) => { impl From<$T> for BigInt { #[inline] fn from(n: $T) -> Self { BigInt::from(n as i64) } } }; } impl_bigint_from_int!(i8); impl_bigint_from_int!(i16); impl_bigint_from_int!(i32); impl_bigint_from_int!(isize); impl From for BigInt { #[inline] fn from(n: u64) -> Self { if n > 0 { BigInt { sign: Plus, data: BigUint::from(n), } } else { BigInt::zero() } } } impl From for BigInt { #[inline] fn from(n: u128) -> Self { if n > 0 { BigInt { sign: Plus, data: BigUint::from(n), } } else { BigInt::zero() } } } macro_rules! impl_bigint_from_uint { ($T:ty) => { impl From<$T> for BigInt { #[inline] fn from(n: $T) -> Self { BigInt::from(n as u64) } } }; } impl_bigint_from_uint!(u8); impl_bigint_from_uint!(u16); impl_bigint_from_uint!(u32); impl_bigint_from_uint!(usize); impl From for BigInt { #[inline] fn from(n: BigUint) -> Self { if n.is_zero() { BigInt::zero() } else { BigInt { sign: Plus, data: n, } } } } impl ToBigInt for BigInt { #[inline] fn to_bigint(&self) -> Option { Some(self.clone()) } } impl ToBigInt for BigUint { #[inline] fn to_bigint(&self) -> Option { if self.is_zero() { Some(Zero::zero()) } else { Some(BigInt { sign: Plus, data: self.clone(), }) } } } impl ToBigUint for BigInt { #[inline] fn to_biguint(&self) -> Option { match self.sign() { Plus => Some(self.data.clone()), NoSign => Some(Zero::zero()), Minus => None, } } } #[cfg(has_try_from)] impl TryFrom<&BigInt> for BigUint { type Error = TryFromBigIntError<()>; #[inline] fn try_from(value: &BigInt) -> Result> { value .to_biguint() .ok_or_else(|| TryFromBigIntError::new(())) } } #[cfg(has_try_from)] impl TryFrom for BigUint { type Error = TryFromBigIntError; #[inline] fn try_from(value: BigInt) -> Result> { if value.sign() == Sign::Minus { Err(TryFromBigIntError::new(value)) } else { Ok(value.data) } } } macro_rules! impl_to_bigint { ($T:ty, $from_ty:path) => { impl ToBigInt for $T { #[inline] fn to_bigint(&self) -> Option { $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); #[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 { 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 { 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, { let mut carry = true; for d in digits { *d = !*d; if carry { *d = d.wrapping_add(1); carry = d.is_zero(); } } } num-bigint-0.4.3/src/bigint/division.rs000064400000000000000000000232170072674642500161730ustar 00000000000000use 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, ToPrimitive, Zero}; forward_all_binop_to_ref_ref!(impl Div for BigInt, div); impl<'a, 'b> Div<&'b BigInt> for &'a BigInt { type Output = BigInt; #[inline] fn div(self, other: &BigInt) -> BigInt { let (q, _) = self.div_rem(other); q } } impl<'a> DivAssign<&'a 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 for BigInt, div); forward_all_scalar_binop_to_val_val!(impl Div for BigInt, div); forward_all_scalar_binop_to_val_val!(impl Div for BigInt, div); impl Div for BigInt { type Output = BigInt; #[inline] fn div(self, other: u32) -> BigInt { BigInt::from_biguint(self.sign, self.data / other) } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: u32) { self.data /= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Div for u32 { type Output = BigInt; #[inline] fn div(self, other: BigInt) -> BigInt { BigInt::from_biguint(other.sign, self / other.data) } } impl Div for BigInt { type Output = BigInt; #[inline] fn div(self, other: u64) -> BigInt { BigInt::from_biguint(self.sign, self.data / other) } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: u64) { self.data /= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Div for u64 { type Output = BigInt; #[inline] fn div(self, other: BigInt) -> BigInt { BigInt::from_biguint(other.sign, self / other.data) } } impl Div for BigInt { type Output = BigInt; #[inline] fn div(self, other: u128) -> BigInt { BigInt::from_biguint(self.sign, self.data / other) } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: u128) { self.data /= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Div 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 for BigInt, div); forward_all_scalar_binop_to_val_val!(impl Div for BigInt, div); forward_all_scalar_binop_to_val_val!(impl Div for BigInt, div); impl Div 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 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 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 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 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 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 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 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 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<'a, 'b> Rem<&'b BigInt> for &'a 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<'a> RemAssign<&'a 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 for BigInt, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigInt, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigInt, rem); impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: u32) -> BigInt { BigInt::from_biguint(self.sign, self.data % other) } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: u32) { self.data %= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Rem for u32 { type Output = BigInt; #[inline] fn rem(self, other: BigInt) -> BigInt { BigInt::from(self % other.data) } } impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: u64) -> BigInt { BigInt::from_biguint(self.sign, self.data % other) } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: u64) { self.data %= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Rem for u64 { type Output = BigInt; #[inline] fn rem(self, other: BigInt) -> BigInt { BigInt::from(self % other.data) } } impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: u128) -> BigInt { BigInt::from_biguint(self.sign, self.data % other) } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: u128) { self.data %= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Rem 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 for BigInt, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigInt, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigInt, rem); impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: i32) -> BigInt { self % other.uabs() } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: i32) { *self %= other.uabs(); } } impl Rem 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 for BigInt { type Output = BigInt; #[inline] fn rem(self, other: i64) -> BigInt { self % other.uabs() } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: i64) { *self %= other.uabs(); } } impl Rem 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 for BigInt { type Output = BigInt; #[inline] fn rem(self, other: i128) -> BigInt { self % other.uabs() } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: i128) { *self %= other.uabs(); } } impl Rem 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 { if v.is_zero() { return None; } Some(self.div(v)) } } num-bigint-0.4.3/src/bigint/multiplication.rs000064400000000000000000000125730072674642500174070ustar 00000000000000use 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 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<$($a:lifetime),*> Mul<$Other:ty> for $Self:ty;)*) => {$( impl<$($a),*> Mul<$Other> for $Self { type Output = BigInt; #[inline] fn mul(self, other: $Other) -> BigInt { // automatically match value/ref let BigInt { data: x, .. } = self; let BigInt { data: y, .. } = other; BigInt::from_biguint(self.sign * other.sign, x * y) } } )*} } impl_mul! { impl<> Mul for BigInt; impl<'b> Mul<&'b BigInt> for BigInt; impl<'a> Mul for &'a BigInt; impl<'a, 'b> Mul<&'b BigInt> for &'a BigInt; } macro_rules! impl_mul_assign { ($(impl<$($a:lifetime),*> MulAssign<$Other:ty> for BigInt;)*) => {$( impl<$($a),*> 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 for BigInt; impl<'a> MulAssign<&'a 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 for BigInt, mul); forward_all_scalar_binop_to_val_val_commutative!(impl Mul for BigInt, mul); forward_all_scalar_binop_to_val_val_commutative!(impl Mul for BigInt, mul); impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: u32) -> BigInt { BigInt::from_biguint(self.sign, self.data * other) } } impl MulAssign for BigInt { #[inline] fn mul_assign(&mut self, other: u32) { self.data *= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: u64) -> BigInt { BigInt::from_biguint(self.sign, self.data * other) } } impl MulAssign for BigInt { #[inline] fn mul_assign(&mut self, other: u64) { self.data *= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: u128) -> BigInt { BigInt::from_biguint(self.sign, self.data * other) } } impl MulAssign 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 for BigInt, mul); forward_all_scalar_binop_to_val_val_commutative!(impl Mul for BigInt, mul); forward_all_scalar_binop_to_val_val_commutative!(impl Mul for BigInt, mul); impl Mul 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 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 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 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 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 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 { Some(self.mul(v)) } } impl_product_iter_type!(BigInt); num-bigint-0.4.3/src/bigint/power.rs000064400000000000000000000046070072674642500155050ustar 00000000000000use 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(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<'b> Pow<&'b $T> for BigInt { type Output = BigInt; #[inline] fn pow(self, rhs: &$T) -> BigInt { BigInt::from_biguint(powsign(self.sign, rhs), self.data.pow(rhs)) } } impl<'a> Pow<$T> for &'a BigInt { type Output = BigInt; #[inline] fn pow(self, rhs: $T) -> BigInt { BigInt::from_biguint(powsign(self.sign, &rhs), Pow::pow(&self.data, rhs)) } } impl<'a, 'b> Pow<&'b $T> for &'a BigInt { type Output = BigInt; #[inline] fn pow(self, rhs: &$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) } num-bigint-0.4.3/src/bigint/serde.rs000064400000000000000000000032610072674642500154460ustar 00000000000000use super::{BigInt, Sign}; use serde::de::{Error, Unexpected}; use serde::{Deserialize, Deserializer, Serialize, Serializer}; impl Serialize for Sign { fn serialize(&self, serializer: S) -> Result 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(deserializer: D) -> Result 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(&self, serializer: S) -> Result 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(deserializer: D) -> Result where D: Deserializer<'de>, { let (sign, data) = Deserialize::deserialize(deserializer)?; Ok(BigInt::from_biguint(sign, data)) } } num-bigint-0.4.3/src/bigint/shift.rs000064400000000000000000000065440072674642500154700ustar 00000000000000use 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<'b> $Shx<&'b $rhs> for BigInt { type Output = BigInt; #[inline] fn $shx(self, rhs: &'b $rhs) -> BigInt { $Shx::$shx(self, *rhs) } } impl<'a, 'b> $Shx<&'b $rhs> for &'a BigInt { type Output = BigInt; #[inline] fn $shx(self, rhs: &'b $rhs) -> BigInt { $Shx::$shx(self, *rhs) } } impl<'b> $ShxAssign<&'b $rhs> for BigInt { #[inline] fn $shx_assign(&mut self, rhs: &'b $rhs) { $ShxAssign::$shx_assign(self, *rhs); } } }; ($($rhs:ty),+) => {$( impl Shl<$rhs> for BigInt { type Output = BigInt; #[inline] fn shl(self, rhs: $rhs) -> BigInt { BigInt::from_biguint(self.sign, self.data << rhs) } } impl<'a> Shl<$rhs> for &'a 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: $rhs) -> BigInt { let round_down = shr_round_down(&self, rhs); let data = self.data >> rhs; let data = if round_down { data + 1u8 } else { data }; BigInt::from_biguint(self.sign, data) } } impl<'a> Shr<$rhs> for &'a 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, $rhs } )*}; } impl_shift! { u8, u16, u32, u64, u128, usize } impl_shift! { i8, i16, i32, i64, i128, isize } // Negative values need a rounding adjustment if there are any ones in the // bits that are getting shifted out. fn shr_round_down(i: &BigInt, shift: T) -> bool { if i.is_negative() { let zeros = i.trailing_zeros().expect("negative values are non-zero"); shift > T::zero() && shift.to_u64().map(|shift| zeros < shift).unwrap_or(true) } else { false } } num-bigint-0.4.3/src/bigint/subtraction.rs000064400000000000000000000171040072674642500167020ustar 00000000000000use super::CheckedUnsignedAbs::{Negative, Positive}; use super::Sign::{Minus, NoSign, Plus}; use super::{BigInt, UnsignedAbs}; use crate::{IsizePromotion, UsizePromotion}; use core::cmp::Ordering::{Equal, Greater, Less}; use core::mem; use core::ops::{Sub, SubAssign}; use num_traits::{CheckedSub, Zero}; // We want to forward to BigUint::sub, but it's not clear how that will go until // we compare both sign and magnitude. So we duplicate this body for every // val/ref combination, deferring that decision to BigUint's own forwarding. macro_rules! bigint_sub { ($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 => Zero::zero(), }, } }; } impl<'a, 'b> Sub<&'b BigInt> for &'a BigInt { type Output = BigInt; #[inline] fn sub(self, other: &BigInt) -> BigInt { bigint_sub!( self, self.clone(), &self.data, other, other.clone(), &other.data ) } } impl<'a> Sub for &'a BigInt { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { bigint_sub!(self, self.clone(), &self.data, other, other, other.data) } } impl<'a> Sub<&'a 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 for BigInt { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { bigint_sub!(self, self, self.data, other, other, other.data) } } impl<'a> SubAssign<&'a BigInt> for BigInt { #[inline] fn sub_assign(&mut self, other: &BigInt) { let n = mem::replace(self, BigInt::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 for BigInt, sub); forward_all_scalar_binop_to_val_val!(impl Sub for BigInt, sub); forward_all_scalar_binop_to_val_val!(impl Sub for BigInt, sub); impl Sub 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 => Zero::zero(), Greater => BigInt::from(self.data - other), Less => -BigInt::from(other - self.data), }, } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: u32) { let n = mem::replace(self, BigInt::zero()); *self = n - other; } } impl Sub for u32 { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { -(other - self) } } impl Sub for u64 { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { -(other - self) } } impl Sub for u128 { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { -(other - self) } } impl Sub 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 => Zero::zero(), Greater => BigInt::from(self.data - other), Less => -BigInt::from(other - self.data), }, } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: u64) { let n = mem::replace(self, BigInt::zero()); *self = n - other; } } impl Sub 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 => Zero::zero(), Greater => BigInt::from(self.data - other), Less => -BigInt::from(other - self.data), }, } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: u128) { let n = mem::replace(self, BigInt::zero()); *self = n - other; } } forward_all_scalar_binop_to_val_val!(impl Sub for BigInt, sub); forward_all_scalar_binop_to_val_val!(impl Sub for BigInt, sub); forward_all_scalar_binop_to_val_val!(impl Sub for BigInt, sub); impl Sub 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 for BigInt { #[inline] fn sub_assign(&mut self, other: i32) { match other.checked_uabs() { Positive(u) => *self -= u, Negative(u) => *self += u, } } } impl Sub 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 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 for BigInt { #[inline] fn sub_assign(&mut self, other: i64) { match other.checked_uabs() { Positive(u) => *self -= u, Negative(u) => *self += u, } } } impl Sub 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 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 for BigInt { #[inline] fn sub_assign(&mut self, other: i128) { match other.checked_uabs() { Positive(u) => *self -= u, Negative(u) => *self += u, } } } impl Sub 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 { Some(self.sub(v)) } } num-bigint-0.4.3/src/bigint.rs000064400000000000000000001022030072674642500143400ustar 00000000000000// `Add`/`Sub` ops may flip from `BigInt` to its `BigUint` magnitude #![allow(clippy::suspicious_arithmetic_impl)] use crate::std_alloc::{String, Vec}; use core::cmp::Ordering::{self, Equal}; use core::default::Default; use core::fmt; use core::hash; use core::ops::{Neg, Not}; use core::str; use core::{i128, u128}; use core::{i64, u64}; use num_integer::{Integer, Roots}; use num_traits::{Num, One, Pow, Signed, Zero}; use self::Sign::{Minus, NoSign, Plus}; use crate::big_digit::BigDigit; use crate::biguint::to_str_radix_reversed; use crate::biguint::{BigUint, IntDigits, U32Digits, U64Digits}; mod addition; mod division; mod multiplication; mod subtraction; mod bits; mod convert; mod power; mod shift; #[cfg(any(feature = "quickcheck", feature = "arbitrary"))] mod arbitrary; #[cfg(feature = "serde")] mod serde; /// A Sign is a `BigInt`'s composing element. #[derive(PartialEq, PartialOrd, Eq, Ord, Copy, Clone, Debug, Hash)] pub enum Sign { Minus, NoSign, Plus, } impl Neg for Sign { type Output = Sign; /// Negate Sign value. #[inline] fn neg(self) -> Sign { match self { Minus => Plus, NoSign => NoSign, Plus => Minus, } } } /// A big signed integer type. pub struct BigInt { sign: Sign, data: BigUint, } // Note: derived `Clone` doesn't specialize `clone_from`, // but we want to keep the allocation in `data`. impl Clone for BigInt { #[inline] fn clone(&self) -> Self { BigInt { sign: self.sign, data: self.data.clone(), } } #[inline] fn clone_from(&mut self, other: &Self) { self.sign = other.sign; self.data.clone_from(&other.data); } } impl hash::Hash for BigInt { #[inline] fn hash(&self, state: &mut H) { debug_assert!((self.sign != NoSign) ^ self.data.is_zero()); self.sign.hash(state); if self.sign != NoSign { self.data.hash(state); } } } impl PartialEq for BigInt { #[inline] fn eq(&self, other: &BigInt) -> bool { debug_assert!((self.sign != NoSign) ^ self.data.is_zero()); debug_assert!((other.sign != NoSign) ^ other.data.is_zero()); self.sign == other.sign && (self.sign == NoSign || self.data == other.data) } } impl Eq for BigInt {} impl PartialOrd for BigInt { #[inline] fn partial_cmp(&self, other: &BigInt) -> Option { Some(self.cmp(other)) } } impl Ord for BigInt { #[inline] fn cmp(&self, other: &BigInt) -> Ordering { debug_assert!((self.sign != NoSign) ^ self.data.is_zero()); debug_assert!((other.sign != NoSign) ^ other.data.is_zero()); let scmp = self.sign.cmp(&other.sign); if scmp != Equal { return scmp; } match self.sign { NoSign => Equal, Plus => self.data.cmp(&other.data), Minus => other.data.cmp(&self.data), } } } impl Default for BigInt { #[inline] fn default() -> BigInt { Zero::zero() } } impl fmt::Debug for BigInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { fmt::Display::fmt(self, f) } } impl fmt::Display for BigInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(!self.is_negative(), "", &self.data.to_str_radix(10)) } } impl fmt::Binary for BigInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(!self.is_negative(), "0b", &self.data.to_str_radix(2)) } } impl fmt::Octal for BigInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(!self.is_negative(), "0o", &self.data.to_str_radix(8)) } } impl fmt::LowerHex for BigInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(!self.is_negative(), "0x", &self.data.to_str_radix(16)) } } impl fmt::UpperHex for BigInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { let mut s = self.data.to_str_radix(16); s.make_ascii_uppercase(); f.pad_integral(!self.is_negative(), "0x", &s) } } // !-2 = !...f fe = ...0 01 = +1 // !-1 = !...f ff = ...0 00 = 0 // ! 0 = !...0 00 = ...f ff = -1 // !+1 = !...0 01 = ...f fe = -2 impl Not for BigInt { type Output = BigInt; fn not(mut self) -> BigInt { match self.sign { NoSign | Plus => { self.data += 1u32; self.sign = Minus; } Minus => { self.data -= 1u32; self.sign = if self.data.is_zero() { NoSign } else { Plus }; } } self } } impl<'a> Not for &'a BigInt { type Output = BigInt; fn not(self) -> BigInt { match self.sign { NoSign => -BigInt::one(), Plus => -BigInt::from(&self.data + 1u32), Minus => BigInt::from(&self.data - 1u32), } } } impl Zero for BigInt { #[inline] fn zero() -> BigInt { BigInt { sign: NoSign, data: BigUint::zero(), } } #[inline] fn set_zero(&mut self) { self.data.set_zero(); self.sign = NoSign; } #[inline] fn is_zero(&self) -> bool { self.sign == NoSign } } impl One for BigInt { #[inline] fn one() -> BigInt { BigInt { sign: Plus, data: BigUint::one(), } } #[inline] fn set_one(&mut self) { self.data.set_one(); self.sign = Plus; } #[inline] fn is_one(&self) -> bool { self.sign == Plus && self.data.is_one() } } impl Signed for BigInt { #[inline] fn abs(&self) -> BigInt { match self.sign { Plus | NoSign => self.clone(), Minus => BigInt::from(self.data.clone()), } } #[inline] fn abs_sub(&self, other: &BigInt) -> BigInt { if *self <= *other { Zero::zero() } else { self - other } } #[inline] fn signum(&self) -> BigInt { match self.sign { Plus => BigInt::one(), Minus => -BigInt::one(), NoSign => BigInt::zero(), } } #[inline] fn is_positive(&self) -> bool { self.sign == Plus } #[inline] fn is_negative(&self) -> bool { self.sign == Minus } } trait UnsignedAbs { type Unsigned; /// A convenience method for getting the absolute value of a signed primitive as unsigned /// See also `unsigned_abs`: https://github.com/rust-lang/rust/issues/74913 fn uabs(self) -> Self::Unsigned; fn checked_uabs(self) -> CheckedUnsignedAbs; } enum CheckedUnsignedAbs { Positive(T), Negative(T), } use self::CheckedUnsignedAbs::{Negative, Positive}; macro_rules! impl_unsigned_abs { ($Signed:ty, $Unsigned:ty) => { impl UnsignedAbs for $Signed { type Unsigned = $Unsigned; #[inline] fn uabs(self) -> $Unsigned { self.wrapping_abs() as $Unsigned } #[inline] fn checked_uabs(self) -> CheckedUnsignedAbs { if self >= 0 { Positive(self as $Unsigned) } else { Negative(self.wrapping_neg() as $Unsigned) } } } }; } impl_unsigned_abs!(i8, u8); impl_unsigned_abs!(i16, u16); impl_unsigned_abs!(i32, u32); impl_unsigned_abs!(i64, u64); impl_unsigned_abs!(i128, u128); impl_unsigned_abs!(isize, usize); impl Neg for BigInt { type Output = BigInt; #[inline] fn neg(mut self) -> BigInt { self.sign = -self.sign; self } } impl<'a> Neg for &'a BigInt { type Output = BigInt; #[inline] fn neg(self) -> BigInt { -self.clone() } } impl Integer for BigInt { #[inline] fn div_rem(&self, other: &BigInt) -> (BigInt, BigInt) { // r.sign == self.sign let (d_ui, r_ui) = self.data.div_rem(&other.data); let d = BigInt::from_biguint(self.sign, d_ui); let r = BigInt::from_biguint(self.sign, r_ui); if other.is_negative() { (-d, r) } else { (d, r) } } #[inline] fn div_floor(&self, other: &BigInt) -> BigInt { let (d_ui, m) = self.data.div_mod_floor(&other.data); let d = BigInt::from(d_ui); match (self.sign, other.sign) { (Plus, Plus) | (NoSign, Plus) | (Minus, Minus) => d, (Plus, Minus) | (NoSign, Minus) | (Minus, Plus) => { if m.is_zero() { -d } else { -d - 1u32 } } (_, NoSign) => unreachable!(), } } #[inline] fn mod_floor(&self, other: &BigInt) -> BigInt { // m.sign == other.sign let m_ui = self.data.mod_floor(&other.data); let m = BigInt::from_biguint(other.sign, m_ui); match (self.sign, other.sign) { (Plus, Plus) | (NoSign, Plus) | (Minus, Minus) => m, (Plus, Minus) | (NoSign, Minus) | (Minus, Plus) => { if m.is_zero() { m } else { other - m } } (_, NoSign) => unreachable!(), } } fn div_mod_floor(&self, other: &BigInt) -> (BigInt, BigInt) { // m.sign == other.sign let (d_ui, m_ui) = self.data.div_mod_floor(&other.data); let d = BigInt::from(d_ui); let m = BigInt::from_biguint(other.sign, m_ui); match (self.sign, other.sign) { (Plus, Plus) | (NoSign, Plus) | (Minus, Minus) => (d, m), (Plus, Minus) | (NoSign, Minus) | (Minus, Plus) => { if m.is_zero() { (-d, m) } else { (-d - 1u32, other - m) } } (_, NoSign) => unreachable!(), } } #[inline] fn div_ceil(&self, other: &Self) -> Self { let (d_ui, m) = self.data.div_mod_floor(&other.data); let d = BigInt::from(d_ui); match (self.sign, other.sign) { (Plus, Minus) | (NoSign, Minus) | (Minus, Plus) => -d, (Plus, Plus) | (NoSign, Plus) | (Minus, Minus) => { if m.is_zero() { d } else { d + 1u32 } } (_, NoSign) => unreachable!(), } } /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. /// /// The result is always positive. #[inline] fn gcd(&self, other: &BigInt) -> BigInt { BigInt::from(self.data.gcd(&other.data)) } /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. #[inline] fn lcm(&self, other: &BigInt) -> BigInt { BigInt::from(self.data.lcm(&other.data)) } /// Calculates the Greatest Common Divisor (GCD) and /// Lowest Common Multiple (LCM) together. #[inline] fn gcd_lcm(&self, other: &BigInt) -> (BigInt, BigInt) { let (gcd, lcm) = self.data.gcd_lcm(&other.data); (BigInt::from(gcd), BigInt::from(lcm)) } /// Greatest common divisor, least common multiple, and Bézout coefficients. #[inline] fn extended_gcd_lcm(&self, other: &BigInt) -> (num_integer::ExtendedGcd, BigInt) { let egcd = self.extended_gcd(other); let lcm = if egcd.gcd.is_zero() { BigInt::zero() } else { BigInt::from(&self.data / &egcd.gcd.data * &other.data) }; (egcd, lcm) } /// Deprecated, use `is_multiple_of` instead. #[inline] fn divides(&self, other: &BigInt) -> bool { self.is_multiple_of(other) } /// Returns `true` if the number is a multiple of `other`. #[inline] fn is_multiple_of(&self, other: &BigInt) -> bool { self.data.is_multiple_of(&other.data) } /// Returns `true` if the number is divisible by `2`. #[inline] fn is_even(&self) -> bool { self.data.is_even() } /// Returns `true` if the number is not divisible by `2`. #[inline] fn is_odd(&self) -> bool { self.data.is_odd() } /// Rounds up to nearest multiple of argument. #[inline] fn next_multiple_of(&self, other: &Self) -> Self { let m = self.mod_floor(other); if m.is_zero() { self.clone() } else { self + (other - m) } } /// Rounds down to nearest multiple of argument. #[inline] fn prev_multiple_of(&self, other: &Self) -> Self { self - self.mod_floor(other) } } impl Roots for BigInt { fn nth_root(&self, n: u32) -> Self { assert!( !(self.is_negative() && n.is_even()), "root of degree {} is imaginary", n ); BigInt::from_biguint(self.sign, self.data.nth_root(n)) } fn sqrt(&self) -> Self { assert!(!self.is_negative(), "square root is imaginary"); BigInt::from_biguint(self.sign, self.data.sqrt()) } fn cbrt(&self) -> Self { BigInt::from_biguint(self.sign, self.data.cbrt()) } } impl IntDigits for BigInt { #[inline] fn digits(&self) -> &[BigDigit] { self.data.digits() } #[inline] fn digits_mut(&mut self) -> &mut Vec { self.data.digits_mut() } #[inline] fn normalize(&mut self) { self.data.normalize(); if self.data.is_zero() { self.sign = NoSign; } } #[inline] fn capacity(&self) -> usize { self.data.capacity() } #[inline] fn len(&self) -> usize { self.data.len() } } /// A generic trait for converting a value to a `BigInt`. This may return /// `None` when converting from `f32` or `f64`, and will always succeed /// when converting from any integer or unsigned primitive, or `BigUint`. pub trait ToBigInt { /// Converts the value of `self` to a `BigInt`. fn to_bigint(&self) -> Option; } impl BigInt { /// Creates and initializes a BigInt. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn new(sign: Sign, digits: Vec) -> BigInt { BigInt::from_biguint(sign, BigUint::new(digits)) } /// Creates and initializes a `BigInt`. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn from_biguint(mut sign: Sign, mut data: BigUint) -> BigInt { if sign == NoSign { data.assign_from_slice(&[]); } else if data.is_zero() { sign = NoSign; } BigInt { sign, data } } /// Creates and initializes a `BigInt`. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn from_slice(sign: Sign, slice: &[u32]) -> BigInt { BigInt::from_biguint(sign, BigUint::from_slice(slice)) } /// Reinitializes a `BigInt`. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn assign_from_slice(&mut self, sign: Sign, slice: &[u32]) { if sign == NoSign { self.set_zero(); } else { self.data.assign_from_slice(slice); self.sign = if self.data.is_zero() { NoSign } else { sign }; } } /// Creates and initializes a `BigInt`. /// /// The bytes are in big-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"A"), /// BigInt::parse_bytes(b"65", 10).unwrap()); /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"AA"), /// BigInt::parse_bytes(b"16705", 10).unwrap()); /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"AB"), /// BigInt::parse_bytes(b"16706", 10).unwrap()); /// assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"Hello world!"), /// BigInt::parse_bytes(b"22405534230753963835153736737", 10).unwrap()); /// ``` #[inline] pub fn from_bytes_be(sign: Sign, bytes: &[u8]) -> BigInt { BigInt::from_biguint(sign, BigUint::from_bytes_be(bytes)) } /// Creates and initializes a `BigInt`. /// /// The bytes are in little-endian byte order. #[inline] pub fn from_bytes_le(sign: Sign, bytes: &[u8]) -> BigInt { BigInt::from_biguint(sign, BigUint::from_bytes_le(bytes)) } /// Creates and initializes a `BigInt` from an array of bytes in /// two's complement binary representation. /// /// The digits are in big-endian base 28. #[inline] pub fn from_signed_bytes_be(digits: &[u8]) -> BigInt { convert::from_signed_bytes_be(digits) } /// Creates and initializes a `BigInt` from an array of bytes in two's complement. /// /// The digits are in little-endian base 28. #[inline] pub fn from_signed_bytes_le(digits: &[u8]) -> BigInt { convert::from_signed_bytes_le(digits) } /// Creates and initializes a `BigInt`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, ToBigInt}; /// /// assert_eq!(BigInt::parse_bytes(b"1234", 10), ToBigInt::to_bigint(&1234)); /// assert_eq!(BigInt::parse_bytes(b"ABCD", 16), ToBigInt::to_bigint(&0xABCD)); /// assert_eq!(BigInt::parse_bytes(b"G", 16), None); /// ``` #[inline] pub fn parse_bytes(buf: &[u8], radix: u32) -> Option { let s = str::from_utf8(buf).ok()?; BigInt::from_str_radix(s, radix).ok() } /// Creates and initializes a `BigInt`. Each u8 of the input slice is /// interpreted as one digit of the number /// and must therefore be less than `radix`. /// /// The bytes are in big-endian byte order. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// let inbase190 = vec![15, 33, 125, 12, 14]; /// let a = BigInt::from_radix_be(Sign::Minus, &inbase190, 190).unwrap(); /// assert_eq!(a.to_radix_be(190), (Sign:: Minus, inbase190)); /// ``` pub fn from_radix_be(sign: Sign, buf: &[u8], radix: u32) -> Option { let u = BigUint::from_radix_be(buf, radix)?; Some(BigInt::from_biguint(sign, u)) } /// Creates and initializes a `BigInt`. Each u8 of the input slice is /// interpreted as one digit of the number /// and must therefore be less than `radix`. /// /// The bytes are in little-endian byte order. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// let inbase190 = vec![14, 12, 125, 33, 15]; /// let a = BigInt::from_radix_be(Sign::Minus, &inbase190, 190).unwrap(); /// assert_eq!(a.to_radix_be(190), (Sign::Minus, inbase190)); /// ``` pub fn from_radix_le(sign: Sign, buf: &[u8], radix: u32) -> Option { let u = BigUint::from_radix_le(buf, radix)?; Some(BigInt::from_biguint(sign, u)) } /// Returns the sign and the byte representation of the `BigInt` in big-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::{ToBigInt, Sign}; /// /// let i = -1125.to_bigint().unwrap(); /// assert_eq!(i.to_bytes_be(), (Sign::Minus, vec![4, 101])); /// ``` #[inline] pub fn to_bytes_be(&self) -> (Sign, Vec) { (self.sign, self.data.to_bytes_be()) } /// Returns the sign and the byte representation of the `BigInt` in little-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::{ToBigInt, Sign}; /// /// let i = -1125.to_bigint().unwrap(); /// assert_eq!(i.to_bytes_le(), (Sign::Minus, vec![101, 4])); /// ``` #[inline] pub fn to_bytes_le(&self) -> (Sign, Vec) { (self.sign, self.data.to_bytes_le()) } /// Returns the sign and the `u32` digits representation of the `BigInt` ordered least /// significant digit first. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// assert_eq!(BigInt::from(-1125).to_u32_digits(), (Sign::Minus, vec![1125])); /// assert_eq!(BigInt::from(4294967295u32).to_u32_digits(), (Sign::Plus, vec![4294967295])); /// assert_eq!(BigInt::from(4294967296u64).to_u32_digits(), (Sign::Plus, vec![0, 1])); /// assert_eq!(BigInt::from(-112500000000i64).to_u32_digits(), (Sign::Minus, vec![830850304, 26])); /// assert_eq!(BigInt::from(112500000000i64).to_u32_digits(), (Sign::Plus, vec![830850304, 26])); /// ``` #[inline] pub fn to_u32_digits(&self) -> (Sign, Vec) { (self.sign, self.data.to_u32_digits()) } /// Returns the sign and the `u64` digits representation of the `BigInt` ordered least /// significant digit first. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// assert_eq!(BigInt::from(-1125).to_u64_digits(), (Sign::Minus, vec![1125])); /// assert_eq!(BigInt::from(4294967295u32).to_u64_digits(), (Sign::Plus, vec![4294967295])); /// assert_eq!(BigInt::from(4294967296u64).to_u64_digits(), (Sign::Plus, vec![4294967296])); /// assert_eq!(BigInt::from(-112500000000i64).to_u64_digits(), (Sign::Minus, vec![112500000000])); /// assert_eq!(BigInt::from(112500000000i64).to_u64_digits(), (Sign::Plus, vec![112500000000])); /// assert_eq!(BigInt::from(1u128 << 64).to_u64_digits(), (Sign::Plus, vec![0, 1])); /// ``` #[inline] pub fn to_u64_digits(&self) -> (Sign, Vec) { (self.sign, self.data.to_u64_digits()) } /// Returns an iterator of `u32` digits representation of the `BigInt` ordered least /// significant digit first. /// /// # Examples /// /// ``` /// use num_bigint::BigInt; /// /// assert_eq!(BigInt::from(-1125).iter_u32_digits().collect::>(), vec![1125]); /// assert_eq!(BigInt::from(4294967295u32).iter_u32_digits().collect::>(), vec![4294967295]); /// assert_eq!(BigInt::from(4294967296u64).iter_u32_digits().collect::>(), vec![0, 1]); /// assert_eq!(BigInt::from(-112500000000i64).iter_u32_digits().collect::>(), vec![830850304, 26]); /// assert_eq!(BigInt::from(112500000000i64).iter_u32_digits().collect::>(), vec![830850304, 26]); /// ``` #[inline] pub fn iter_u32_digits(&self) -> U32Digits<'_> { self.data.iter_u32_digits() } /// Returns an iterator of `u64` digits representation of the `BigInt` ordered least /// significant digit first. /// /// # Examples /// /// ``` /// use num_bigint::BigInt; /// /// assert_eq!(BigInt::from(-1125).iter_u64_digits().collect::>(), vec![1125u64]); /// assert_eq!(BigInt::from(4294967295u32).iter_u64_digits().collect::>(), vec![4294967295u64]); /// assert_eq!(BigInt::from(4294967296u64).iter_u64_digits().collect::>(), vec![4294967296u64]); /// assert_eq!(BigInt::from(-112500000000i64).iter_u64_digits().collect::>(), vec![112500000000u64]); /// assert_eq!(BigInt::from(112500000000i64).iter_u64_digits().collect::>(), vec![112500000000u64]); /// assert_eq!(BigInt::from(1u128 << 64).iter_u64_digits().collect::>(), vec![0, 1]); /// ``` #[inline] pub fn iter_u64_digits(&self) -> U64Digits<'_> { self.data.iter_u64_digits() } /// Returns the two's-complement byte representation of the `BigInt` in big-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::ToBigInt; /// /// let i = -1125.to_bigint().unwrap(); /// assert_eq!(i.to_signed_bytes_be(), vec![251, 155]); /// ``` #[inline] pub fn to_signed_bytes_be(&self) -> Vec { convert::to_signed_bytes_be(self) } /// Returns the two's-complement byte representation of the `BigInt` in little-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::ToBigInt; /// /// let i = -1125.to_bigint().unwrap(); /// assert_eq!(i.to_signed_bytes_le(), vec![155, 251]); /// ``` #[inline] pub fn to_signed_bytes_le(&self) -> Vec { convert::to_signed_bytes_le(self) } /// Returns the integer formatted as a string in the given radix. /// `radix` must be in the range `2...36`. /// /// # Examples /// /// ``` /// use num_bigint::BigInt; /// /// let i = BigInt::parse_bytes(b"ff", 16).unwrap(); /// assert_eq!(i.to_str_radix(16), "ff"); /// ``` #[inline] pub fn to_str_radix(&self, radix: u32) -> String { let mut v = to_str_radix_reversed(&self.data, radix); if self.is_negative() { v.push(b'-'); } v.reverse(); unsafe { String::from_utf8_unchecked(v) } } /// Returns the integer in the requested base in big-endian digit order. /// The output is not given in a human readable alphabet but as a zero /// based u8 number. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// assert_eq!(BigInt::from(-0xFFFFi64).to_radix_be(159), /// (Sign::Minus, vec![2, 94, 27])); /// // 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27 /// ``` #[inline] pub fn to_radix_be(&self, radix: u32) -> (Sign, Vec) { (self.sign, self.data.to_radix_be(radix)) } /// Returns the integer in the requested base in little-endian digit order. /// The output is not given in a human readable alphabet but as a zero /// based u8 number. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// /// assert_eq!(BigInt::from(-0xFFFFi64).to_radix_le(159), /// (Sign::Minus, vec![27, 94, 2])); /// // 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2) /// ``` #[inline] pub fn to_radix_le(&self, radix: u32) -> (Sign, Vec) { (self.sign, self.data.to_radix_le(radix)) } /// Returns the sign of the `BigInt` as a `Sign`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, Sign}; /// use num_traits::Zero; /// /// assert_eq!(BigInt::from(1234).sign(), Sign::Plus); /// assert_eq!(BigInt::from(-4321).sign(), Sign::Minus); /// assert_eq!(BigInt::zero().sign(), Sign::NoSign); /// ``` #[inline] pub fn sign(&self) -> Sign { self.sign } /// Returns the magnitude of the `BigInt` as a `BigUint`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, BigUint}; /// use num_traits::Zero; /// /// assert_eq!(BigInt::from(1234).magnitude(), &BigUint::from(1234u32)); /// assert_eq!(BigInt::from(-4321).magnitude(), &BigUint::from(4321u32)); /// assert!(BigInt::zero().magnitude().is_zero()); /// ``` #[inline] pub fn magnitude(&self) -> &BigUint { &self.data } /// Convert this `BigInt` into its `Sign` and `BigUint` magnitude, /// the reverse of `BigInt::from_biguint`. /// /// # Examples /// /// ``` /// use num_bigint::{BigInt, BigUint, Sign}; /// use num_traits::Zero; /// /// assert_eq!(BigInt::from(1234).into_parts(), (Sign::Plus, BigUint::from(1234u32))); /// assert_eq!(BigInt::from(-4321).into_parts(), (Sign::Minus, BigUint::from(4321u32))); /// assert_eq!(BigInt::zero().into_parts(), (Sign::NoSign, BigUint::zero())); /// ``` #[inline] pub fn into_parts(self) -> (Sign, BigUint) { (self.sign, self.data) } /// Determines the fewest bits necessary to express the `BigInt`, /// not including the sign. #[inline] pub fn bits(&self) -> u64 { self.data.bits() } /// Converts this `BigInt` into a `BigUint`, if it's not negative. #[inline] pub fn to_biguint(&self) -> Option { match self.sign { Plus => Some(self.data.clone()), NoSign => Some(Zero::zero()), Minus => None, } } #[inline] pub fn checked_add(&self, v: &BigInt) -> Option { Some(self + v) } #[inline] pub fn checked_sub(&self, v: &BigInt) -> Option { Some(self - v) } #[inline] pub fn checked_mul(&self, v: &BigInt) -> Option { Some(self * v) } #[inline] pub fn checked_div(&self, v: &BigInt) -> Option { if v.is_zero() { return None; } Some(self / v) } /// Returns `self ^ exponent`. pub fn pow(&self, exponent: u32) -> Self { Pow::pow(self, exponent) } /// Returns `(self ^ exponent) mod modulus` /// /// Note that this rounds like `mod_floor`, not like the `%` operator, /// which makes a difference when given a negative `self` or `modulus`. /// The result will be in the interval `[0, modulus)` for `modulus > 0`, /// or in the interval `(modulus, 0]` for `modulus < 0` /// /// Panics if the exponent is negative or the modulus is zero. pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self { power::modpow(self, exponent, modulus) } /// Returns the truncated principal square root of `self` -- /// see [Roots::sqrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.sqrt). pub fn sqrt(&self) -> Self { Roots::sqrt(self) } /// Returns the truncated principal cube root of `self` -- /// see [Roots::cbrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.cbrt). pub fn cbrt(&self) -> Self { Roots::cbrt(self) } /// Returns the truncated principal `n`th root of `self` -- /// See [Roots::nth_root](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#tymethod.nth_root). pub fn nth_root(&self, n: u32) -> Self { Roots::nth_root(self, n) } /// Returns the number of least-significant bits that are zero, /// or `None` if the entire number is zero. pub fn trailing_zeros(&self) -> Option { self.data.trailing_zeros() } /// Returns whether the bit in position `bit` is set, /// using the two's complement for negative numbers pub fn bit(&self, bit: u64) -> bool { if self.is_negative() { // Let the binary representation of a number be // ... 0 x 1 0 ... 0 // Then the two's complement is // ... 1 !x 1 0 ... 0 // where !x is obtained from x by flipping each bit if bit >= u64::from(crate::big_digit::BITS) * self.len() as u64 { true } else { let trailing_zeros = self.data.trailing_zeros().unwrap(); match Ord::cmp(&bit, &trailing_zeros) { Ordering::Less => false, Ordering::Equal => true, Ordering::Greater => !self.data.bit(bit), } } } else { self.data.bit(bit) } } /// Sets or clears the bit in the given position, /// using the two's complement for negative numbers /// /// Note that setting/clearing a bit (for positive/negative numbers, /// respectively) greater than the current bit length, a reallocation /// may be needed to store the new digits pub fn set_bit(&mut self, bit: u64, value: bool) { match self.sign { Sign::Plus => self.data.set_bit(bit, value), Sign::Minus => bits::set_negative_bit(self, bit, value), Sign::NoSign => { if value { self.data.set_bit(bit, true); self.sign = Sign::Plus; } else { // Clearing a bit for zero is a no-op } } } // The top bit may have been cleared, so normalize self.normalize(); } } #[test] fn test_from_biguint() { fn check(inp_s: Sign, inp_n: usize, ans_s: Sign, ans_n: usize) { let inp = BigInt::from_biguint(inp_s, BigUint::from(inp_n)); let ans = BigInt { sign: ans_s, data: BigUint::from(ans_n), }; assert_eq!(inp, ans); } check(Plus, 1, Plus, 1); check(Plus, 0, NoSign, 0); check(Minus, 1, Minus, 1); check(NoSign, 1, NoSign, 0); } #[test] fn test_from_slice() { fn check(inp_s: Sign, inp_n: u32, ans_s: Sign, ans_n: u32) { let inp = BigInt::from_slice(inp_s, &[inp_n]); let ans = BigInt { sign: ans_s, data: BigUint::from(ans_n), }; assert_eq!(inp, ans); } check(Plus, 1, Plus, 1); check(Plus, 0, NoSign, 0); check(Minus, 1, Minus, 1); check(NoSign, 1, NoSign, 0); } #[test] fn test_assign_from_slice() { fn check(inp_s: Sign, inp_n: u32, ans_s: Sign, ans_n: u32) { let mut inp = BigInt::from_slice(Minus, &[2627_u32, 0_u32, 9182_u32, 42_u32]); inp.assign_from_slice(inp_s, &[inp_n]); let ans = BigInt { sign: ans_s, data: BigUint::from(ans_n), }; assert_eq!(inp, ans); } check(Plus, 1, Plus, 1); check(Plus, 0, NoSign, 0); check(Minus, 1, Minus, 1); check(NoSign, 1, NoSign, 0); } num-bigint-0.4.3/src/bigrand.rs000064400000000000000000000204450072674642500145010ustar 00000000000000//! Randomization of big integers 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(rng: &mut R, data: &mut [u32], rem: u64) { // `fill` is faster than many `gen::` calls rng.fill(data); if rem > 0 { let last = data.len() - 1; data[last] >>= 32 - rem; } } impl RandBigInt for R { #[cfg(not(u64_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) } #[cfg(u64_digit)] 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(low_b: B1, high_b: B2) -> Self where B1: SampleBorrow + Sized, B2: SampleBorrow + 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(low_b: B1, high_b: B2) -> Self where B1: SampleBorrow + Sized, B2: SampleBorrow + Sized, { let low = low_b.borrow(); let high = high_b.borrow(); assert!(low <= high); Self::new(low, high + 1u32) } #[inline] fn sample(&self, rng: &mut R) -> Self::X { &self.base + rng.gen_biguint_below(&self.len) } #[inline] fn sample_single(low: B1, high: B2, rng: &mut R) -> Self::X where B1: SampleBorrow + Sized, B2: SampleBorrow + 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(low_b: B1, high_b: B2) -> Self where B1: SampleBorrow + Sized, B2: SampleBorrow + 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(low_b: B1, high_b: B2) -> Self where B1: SampleBorrow + Sized, B2: SampleBorrow + Sized, { let low = low_b.borrow(); let high = high_b.borrow(); assert!(low <= high); Self::new(low, high + 1u32) } #[inline] fn sample(&self, rng: &mut R) -> Self::X { &self.base + BigInt::from(rng.gen_biguint_below(&self.len)) } #[inline] fn sample_single(low: B1, high: B2, rng: &mut R) -> Self::X where B1: SampleBorrow + Sized, B2: SampleBorrow + 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 for RandomBits { #[inline] fn sample(&self, rng: &mut R) -> BigUint { rng.gen_biguint(self.bits) } } impl Distribution for RandomBits { #[inline] fn sample(&self, rng: &mut R) -> BigInt { rng.gen_bigint(self.bits) } } num-bigint-0.4.3/src/biguint/addition.rs000064400000000000000000000153670072674642500163360ustar 00000000000000#[cfg(not(u64_digit))] use super::u32_from_u128; 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, Zero}; #[cfg(all(use_addcarry, target_arch = "x86_64"))] use core::arch::x86_64 as arch; #[cfg(all(use_addcarry, target_arch = "x86"))] use core::arch::x86 as arch; // Add with carry: #[cfg(all(use_addcarry, u64_digit))] #[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(all(use_addcarry, not(u64_digit)))] #[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 #[cfg(not(use_addcarry))] #[inline] fn adc(carry: u8, a: BigDigit, b: BigDigit, out: &mut BigDigit) -> u8 { use crate::big_digit::DoubleBigDigit; let sum = DoubleBigDigit::from(a) + DoubleBigDigit::from(b) + DoubleBigDigit::from(carry); *out = sum as BigDigit; (sum >> big_digit::BITS) as u8 } /// 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<'a> Add<&'a BigUint> for BigUint { type Output = BigUint; fn add(mut self, other: &BigUint) -> BigUint { self += other; self } } impl<'a> AddAssign<&'a 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 for BigUint, add); forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigUint, add); forward_all_scalar_binop_to_val_val_commutative!(impl Add for BigUint, add); impl Add for BigUint { type Output = BigUint; #[inline] fn add(mut self, other: u32) -> BigUint { self += other; self } } impl AddAssign 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 for BigUint { type Output = BigUint; #[inline] fn add(mut self, other: u64) -> BigUint { self += other; self } } impl AddAssign for BigUint { #[cfg(not(u64_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); } } } #[cfg(u64_digit)] #[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 for BigUint { type Output = BigUint; #[inline] fn add(mut self, other: u128) -> BigUint { self += other; self } } impl AddAssign for BigUint { #[cfg(not(u64_digit))] #[inline] fn add_assign(&mut self, other: u128) { if other <= u128::from(u64::max_value()) { *self += other as u64 } else { let (a, b, c, d) = 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); } } } #[cfg(u64_digit)] #[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 { Some(self.add(v)) } } impl_sum_iter_type!(BigUint); num-bigint-0.4.3/src/biguint/arbitrary.rs000064400000000000000000000020160072674642500165250ustar 00000000000000use super::{biguint_from_vec, BigUint}; use crate::big_digit::BigDigit; #[cfg(feature = "quickcheck")] use crate::std_alloc::Box; use crate::std_alloc::Vec; #[cfg(feature = "quickcheck")] impl quickcheck::Arbitrary for BigUint { fn arbitrary(g: &mut quickcheck::Gen) -> Self { // Use arbitrary from Vec biguint_from_vec(Vec::::arbitrary(g)) } fn shrink(&self) -> Box> { // Use shrinker from Vec Box::new(self.data.shrink().map(biguint_from_vec)) } } #[cfg(feature = "arbitrary")] impl arbitrary::Arbitrary<'_> for BigUint { fn arbitrary(u: &mut arbitrary::Unstructured<'_>) -> arbitrary::Result { Ok(biguint_from_vec(Vec::::arbitrary(u)?)) } fn arbitrary_take_rest(u: arbitrary::Unstructured<'_>) -> arbitrary::Result { Ok(biguint_from_vec(Vec::::arbitrary_take_rest(u)?)) } fn size_hint(depth: usize) -> (usize, Option) { Vec::::size_hint(depth) } } num-bigint-0.4.3/src/biguint/bits.rs000064400000000000000000000052360072674642500154760ustar 00000000000000use 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<'a, 'b> BitAnd<&'b BigUint> for &'a 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<'a> BitAnd<&'a BigUint> for BigUint { type Output = BigUint; #[inline] fn bitand(mut self, other: &BigUint) -> BigUint { self &= other; self } } impl<'a> BitAndAssign<&'a 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<'a> BitOr<&'a BigUint> for BigUint { type Output = BigUint; fn bitor(mut self, other: &BigUint) -> BigUint { self |= other; self } } impl<'a> BitOrAssign<&'a 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<'a> BitXor<&'a BigUint> for BigUint { type Output = BigUint; fn bitxor(mut self, other: &BigUint) -> BigUint { self ^= other; self } } impl<'a> BitXorAssign<&'a 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(); } } num-bigint-0.4.3/src/biguint/convert.rs000064400000000000000000000532640072674642500162210ustar 00000000000000use super::{biguint_from_vec, BigUint, ToBigUint}; use super::addition::add2; use super::division::div_rem_digit; use super::multiplication::mac_with_carry; use crate::big_digit::{self, BigDigit}; use crate::std_alloc::Vec; use crate::ParseBigIntError; #[cfg(has_try_from)] use crate::TryFromBigIntError; use core::cmp::Ordering::{Equal, Greater, Less}; #[cfg(has_try_from)] 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, PrimInt, ToPrimitive, Zero}; /// Find last set bit /// fls(0) == 0, fls(u32::MAX) == 32 fn fls(v: T) -> u8 { mem::size_of::() as u8 * 8 - v.leading_zeros() as u8 } fn ilog2(v: T) -> u8 { fls(v) - 1 } impl FromStr for BigUint { type Err = ParseBigIntError; #[inline] fn from_str(s: &str) -> Result { 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(core::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)); #[cfg(feature = "std")] let radix_log2 = f64::from(radix).log2(); #[cfg(not(feature = "std"))] let radix_log2 = ilog2(radix.next_power_of_two()) as f64; // Estimate how big the result will be, so we can pre-allocate it. let bits = radix_log2 * v.len() as f64; let big_digits = (bits / big_digit::BITS as f64).ceil(); let mut data = Vec::with_capacity(big_digits.to_usize().unwrap_or(0)); let (base, power) = get_radix_base(radix, big_digit::BITS); 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 { assert!( 2 <= radix && radix <= 256, "The radix must be within 2...256" ); if buf.is_empty() { return Some(Zero::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 { assert!( 2 <= radix && radix <= 256, "The radix must be within 2...256" ); if buf.is_empty() { return Some(Zero::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 { assert!(2 <= radix && radix <= 36, "The radix must be within 2...36"); let mut s = s; if s.starts_with('+') { let tail = &s[1..]; 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, _ => core::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 != 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; ret_bits += bits_want; bits -= bits_want; if ret_bits == 64 { break; } } ret } } } impl ToPrimitive for BigUint { #[inline] fn to_i64(&self) -> Option { self.to_u64().as_ref().and_then(u64::to_i64) } #[inline] fn to_i128(&self) -> Option { self.to_u128().as_ref().and_then(u128::to_i128) } #[allow(clippy::useless_conversion)] #[inline] fn to_u64(&self) -> Option { 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 { 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 { let mantissa = high_bits_to_u64(self); let exponent = self.bits() - u64::from(fls(mantissa)); if exponent > core::f32::MAX_EXP as u64 { Some(core::f32::INFINITY) } else { Some((mantissa as f32) * 2.0f32.powi(exponent as i32)) } } #[inline] fn to_f64(&self) -> Option { let mantissa = high_bits_to_u64(self); let exponent = self.bits() - u64::from(fls(mantissa)); if exponent > core::f64::MAX_EXP as u64 { Some(core::f64::INFINITY) } else { Some((mantissa as f64) * 2.0f64.powi(exponent as i32)) } } } macro_rules! impl_try_from_biguint { ($T:ty, $to_ty:path) => { #[cfg(has_try_from)] impl TryFrom<&BigUint> for $T { type Error = TryFromBigIntError<()>; #[inline] fn try_from(value: &BigUint) -> Result<$T, TryFromBigIntError<()>> { $to_ty(value).ok_or(TryFromBigIntError::new(())) } } #[cfg(has_try_from)] impl TryFrom for $T { type Error = TryFromBigIntError; #[inline] fn try_from(value: BigUint) -> Result<$T, TryFromBigIntError> { <$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 { if n >= 0 { Some(BigUint::from(n as u64)) } else { None } } #[inline] fn from_i128(n: i128) -> Option { if n >= 0 { Some(BigUint::from(n as u128)) } else { None } } #[inline] fn from_u64(n: u64) -> Option { Some(BigUint::from(n)) } #[inline] fn from_u128(n: u128) -> Option { Some(BigUint::from(n)) } #[inline] fn from_f64(mut n: f64) -> Option { // 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(BigUint::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 for BigUint { #[inline] fn from(mut n: u64) -> Self { let mut ret: BigUint = Zero::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 for BigUint { #[inline] fn from(mut n: u128) -> Self { let mut ret: BigUint = Zero::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, $from_ty:path) => { #[cfg(has_try_from)] impl TryFrom<$T> for BigUint { type Error = TryFromBigIntError<()>; #[inline] fn try_from(value: $T) -> Result> { $from_ty(value).ok_or(TryFromBigIntError::new(())) } } }; } impl_biguint_try_from_int!(i8, FromPrimitive::from_i8); impl_biguint_try_from_int!(i16, FromPrimitive::from_i16); impl_biguint_try_from_int!(i32, FromPrimitive::from_i32); impl_biguint_try_from_int!(i64, FromPrimitive::from_i64); impl_biguint_try_from_int!(isize, FromPrimitive::from_isize); impl_biguint_try_from_int!(i128, FromPrimitive::from_i128); impl ToBigUint for BigUint { #[inline] fn to_biguint(&self) -> Option { Some(self.clone()) } } macro_rules! impl_to_biguint { ($T:ty, $from_ty:path) => { impl ToBigUint for $T { #[inline] fn to_biguint(&self) -> Option { $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); // Extract bitwise digits that evenly divide BigDigit pub(super) fn to_bitwise_digits_le(u: &BigUint, bits: u8) -> Vec { 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(core::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 { 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(core::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 { debug_assert!(!u.is_zero() && !radix.is_power_of_two()); #[cfg(feature = "std")] let radix_log2 = f64::from(radix).log2(); #[cfg(not(feature = "std"))] let radix_log2 = ilog2(radix) as f64; // Estimate how big the result will be, so we can pre-allocate it. let radix_digits = ((u.bits() as f64) / radix_log2).ceil(); let mut res = Vec::with_capacity(radix_digits.to_usize().unwrap_or(0)); let mut digits = u.clone(); let (base, power) = get_radix_base(radix, big_digit::HALF_BITS); 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 * base); let mut big_power = 2usize; // 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 { 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 { 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 given bit size #[inline] fn get_radix_base(radix: u32, bits: u8) -> (BigDigit, usize) { mod gen { include! { concat!(env!("OUT_DIR"), "/radix_bases.rs") } } debug_assert!( 2 <= radix && radix <= 256, "The radix must be within 2...256" ); debug_assert!(!radix.is_power_of_two()); debug_assert!(bits <= big_digit::BITS); match bits { 16 => { let (base, power) = gen::BASES_16[radix as usize]; (base as BigDigit, power) } 32 => { let (base, power) = gen::BASES_32[radix as usize]; (base as BigDigit, power) } 64 => { let (base, power) = gen::BASES_64[radix as usize]; (base as BigDigit, power) } _ => panic!("Invalid bigdigit size"), } } num-bigint-0.4.3/src/biguint/division.rs000064400000000000000000000433470072674642500163660ustar 00000000000000use super::addition::__add2; #[cfg(not(u64_digit))] use super::u32_to_u128; 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, One, ToPrimitive, Zero}; /// 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). #[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) } /// 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 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 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 (Zero::zero(), Zero::zero()); } if d.data.len() == 1 { if d.data == [1] { return (u, Zero::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 (Zero::zero(), u), Equal => { u.set_one(); return (u, Zero::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 (Zero::zero(), Zero::zero()); } if d.data.len() == 1 { if d.data == [1] { return (u.clone(), Zero::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 (Zero::zero(), u.clone()), Equal => return (One::one(), Zero::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.last().unwrap(); 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< 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 for BigUint { type Output = BigUint; #[inline] fn div(self, other: BigUint) -> BigUint { let (q, _) = div_rem(self, other); q } } impl<'a, 'b> Div<&'b BigUint> for &'a BigUint { type Output = BigUint; #[inline] fn div(self, other: &BigUint) -> BigUint { let (q, _) = self.div_rem(other); q } } impl<'a> DivAssign<&'a BigUint> for BigUint { #[inline] fn div_assign(&mut self, other: &'a 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 for BigUint, div); forward_all_scalar_binop_to_val_val!(impl Div for BigUint, div); forward_all_scalar_binop_to_val_val!(impl Div for BigUint, div); impl Div for BigUint { type Output = BigUint; #[inline] fn div(self, other: u32) -> BigUint { let (q, _) = div_rem_digit(self, other as BigDigit); q } } impl DivAssign for BigUint { #[inline] fn div_assign(&mut self, other: u32) { *self = &*self / other; } } impl Div 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]), _ => Zero::zero(), } } } impl Div for BigUint { type Output = BigUint; #[inline] fn div(self, other: u64) -> BigUint { let (q, _) = div_rem(self, From::from(other)); q } } impl DivAssign 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, Zero::zero()); *self = temp / other; } } impl Div for u64 { type Output = BigUint; #[cfg(not(u64_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])), _ => Zero::zero(), } } #[cfg(u64_digit)] #[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]), _ => Zero::zero(), } } } impl Div for BigUint { type Output = BigUint; #[inline] fn div(self, other: u128) -> BigUint { let (q, _) = div_rem(self, From::from(other)); q } } impl DivAssign for BigUint { #[inline] fn div_assign(&mut self, other: u128) { *self = &*self / other; } } impl Div for u128 { type Output = BigUint; #[cfg(not(u64_digit))] #[inline] fn div(self, other: BigUint) -> BigUint { 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]), ), _ => Zero::zero(), } } #[cfg(u64_digit)] #[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])), _ => Zero::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 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<'a, 'b> Rem<&'b BigUint> for &'a 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<'a> RemAssign<&'a 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 for BigUint, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigUint, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigUint, rem); impl<'a> Rem for &'a BigUint { type Output = BigUint; #[inline] fn rem(self, other: u32) -> BigUint { rem_digit(self, other as BigDigit).into() } } impl RemAssign for BigUint { #[inline] fn rem_assign(&mut self, other: u32) { *self = &*self % other; } } impl<'a> Rem<&'a BigUint> for u32 { type Output = BigUint; #[inline] fn rem(mut self, other: &'a 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<'a> RemAssign<&'a 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 for BigUint { type Output = BigUint; #[inline] fn rem(self, other: u64) -> BigUint { let (_, r) = div_rem(self, From::from(other)); r } } impl RemAssign for BigUint { #[inline] fn rem_assign(&mut self, other: u64) { *self = &*self % other; } } impl Rem for u64 { type Output = BigUint; #[inline] fn rem(mut self, other: BigUint) -> BigUint { self %= other; From::from(self) } } impl Rem for BigUint { type Output = BigUint; #[inline] fn rem(self, other: u128) -> BigUint { let (_, r) = div_rem(self, From::from(other)); r } } impl RemAssign for BigUint { #[inline] fn rem_assign(&mut self, other: u128) { *self = &*self % other; } } impl Rem 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 { if v.is_zero() { return None; } Some(self.div(v)) } } num-bigint-0.4.3/src/biguint/iter.rs000064400000000000000000000206000072674642500154700ustar 00000000000000use core::iter::FusedIterator; #[cfg(not(u64_digit))] use super::u32_chunk_to_u64; /// An iterator of `u32` digits representation of a `BigUint` or `BigInt`, /// ordered least significant digit first. pub struct U32Digits<'a> { #[cfg(u64_digit)] data: &'a [u64], #[cfg(u64_digit)] next_is_lo: bool, #[cfg(u64_digit)] last_hi_is_zero: bool, #[cfg(not(u64_digit))] it: core::slice::Iter<'a, u32>, } #[cfg(u64_digit)] 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, } } } #[cfg(u64_digit)] impl Iterator for U32Digits<'_> { type Item = u32; #[inline] fn next(&mut self) -> Option { 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) { let len = self.len(); (len, Some(len)) } #[inline] fn last(self) -> Option { 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() } } #[cfg(u64_digit)] impl DoubleEndedIterator for U32Digits<'_> { fn next_back(&mut self) -> Option { 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, } } } #[cfg(u64_digit)] 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) } } #[cfg(not(u64_digit))] impl<'a> U32Digits<'a> { #[inline] pub(super) fn new(data: &'a [u32]) -> Self { Self { it: data.iter() } } } #[cfg(not(u64_digit))] impl Iterator for U32Digits<'_> { type Item = u32; #[inline] fn next(&mut self) -> Option { self.it.next().cloned() } #[inline] fn size_hint(&self) -> (usize, Option) { self.it.size_hint() } #[inline] fn nth(&mut self, n: usize) -> Option { self.it.nth(n).cloned() } #[inline] fn last(self) -> Option { self.it.last().cloned() } #[inline] fn count(self) -> usize { self.it.count() } } #[cfg(not(u64_digit))] impl DoubleEndedIterator for U32Digits<'_> { fn next_back(&mut self) -> Option { self.it.next_back().copied() } } #[cfg(not(u64_digit))] impl ExactSizeIterator for U32Digits<'_> { #[inline] fn len(&self) -> usize { self.it.len() } } impl FusedIterator for U32Digits<'_> {} /// An iterator of `u64` digits representation of a `BigUint` or `BigInt`, /// ordered least significant digit first. pub struct U64Digits<'a> { #[cfg(not(u64_digit))] it: core::slice::Chunks<'a, u32>, #[cfg(u64_digit)] it: core::slice::Iter<'a, u64>, } #[cfg(not(u64_digit))] impl<'a> U64Digits<'a> { #[inline] pub(super) fn new(data: &'a [u32]) -> Self { U64Digits { it: data.chunks(2) } } } #[cfg(not(u64_digit))] impl Iterator for U64Digits<'_> { type Item = u64; #[inline] fn next(&mut self) -> Option { self.it.next().map(u32_chunk_to_u64) } #[inline] fn size_hint(&self) -> (usize, Option) { let len = self.len(); (len, Some(len)) } #[inline] fn last(self) -> Option { self.it.last().map(u32_chunk_to_u64) } #[inline] fn count(self) -> usize { self.len() } } #[cfg(not(u64_digit))] impl DoubleEndedIterator for U64Digits<'_> { fn next_back(&mut self) -> Option { self.it.next_back().map(u32_chunk_to_u64) } } #[cfg(u64_digit)] impl<'a> U64Digits<'a> { #[inline] pub(super) fn new(data: &'a [u64]) -> Self { Self { it: data.iter() } } } #[cfg(u64_digit)] impl Iterator for U64Digits<'_> { type Item = u64; #[inline] fn next(&mut self) -> Option { self.it.next().cloned() } #[inline] fn size_hint(&self) -> (usize, Option) { self.it.size_hint() } #[inline] fn nth(&mut self, n: usize) -> Option { self.it.nth(n).cloned() } #[inline] fn last(self) -> Option { self.it.last().cloned() } #[inline] fn count(self) -> usize { self.it.count() } } #[cfg(u64_digit)] impl DoubleEndedIterator for U64Digits<'_> { fn next_back(&mut self) -> Option { 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); } num-bigint-0.4.3/src/biguint/monty.rs000064400000000000000000000153360072674642500157050ustar 00000000000000use crate::std_alloc::Vec; use core::mem; use core::ops::Shl; use num_traits::{One, Zero}; use crate::big_digit::{self, BigDigit, DoubleBigDigit, SignedDoubleBigDigit}; 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 = 2 - b as SignedDoubleBigDigit; let mut t = (b - 1) as SignedDoubleBigDigit; let mut i = 1; while i < big_digit::BITS { t = t.wrapping_mul(t); k0 = k0.wrapping_mul(t + 1); i <<= 1; } -k0 as BigDigit } 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 (mut first, second) = z.data.split_at_mut(n); sub_vv(&mut 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 } num-bigint-0.4.3/src/biguint/multiplication.rs000064400000000000000000000430400072674642500175650ustar 00000000000000use super::addition::{__add2, add2}; use super::subtraction::sub2; #[cfg(not(u64_digit))] use super::u32_from_u128; 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 three algorithms for different input sizes. // // - For small inputs, long multiplication is fastest. // - 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() <= 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(1)/6 // 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, Zero::zero()), } } macro_rules! impl_mul { ($(impl<$($a:lifetime),*> Mul<$Other:ty> for $Self:ty;)*) => {$( impl<$($a),*> Mul<$Other> for $Self { type Output = BigUint; #[inline] fn mul(self, other: $Other) -> BigUint { match (&*self.data, &*other.data) { // multiply by zero (&[], _) | (_, &[]) => BigUint::zero(), // multiply by a scalar (_, &[digit]) => self * digit, (&[digit], _) => other * digit, // full multiplication (x, y) => mul3(x, y), } } } )*} } impl_mul! { impl<> Mul for BigUint; impl<'b> Mul<&'b BigUint> for BigUint; impl<'a> Mul for &'a BigUint; impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint; } macro_rules! impl_mul_assign { ($(impl<$($a:lifetime),*> MulAssign<$Other:ty> for BigUint;)*) => {$( impl<$($a),*> 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 for BigUint; impl<'a> MulAssign<&'a 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 for BigUint, mul); forward_all_scalar_binop_to_val_val_commutative!(impl Mul for BigUint, mul); forward_all_scalar_binop_to_val_val_commutative!(impl Mul for BigUint, mul); impl Mul for BigUint { type Output = BigUint; #[inline] fn mul(mut self, other: u32) -> BigUint { self *= other; self } } impl MulAssign for BigUint { #[inline] fn mul_assign(&mut self, other: u32) { scalar_mul(self, other as BigDigit); } } impl Mul for BigUint { type Output = BigUint; #[inline] fn mul(mut self, other: u64) -> BigUint { self *= other; self } } impl MulAssign for BigUint { #[cfg(not(u64_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]); } } #[cfg(u64_digit)] #[inline] fn mul_assign(&mut self, other: u64) { scalar_mul(self, other); } } impl Mul for BigUint { type Output = BigUint; #[inline] fn mul(mut self, other: u128) -> BigUint { self *= other; self } } impl MulAssign for BigUint { #[cfg(not(u64_digit))] #[inline] fn mul_assign(&mut self, other: u128) { if let Some(other) = BigDigit::from_u128(other) { scalar_mul(self, other); } else { *self = match 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]), }; } } #[cfg(u64_digit)] #[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 { 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); } num-bigint-0.4.3/src/biguint/power.rs000064400000000000000000000142470072674642500156730ustar 00000000000000use 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<'b> Pow<&'b 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 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 for BigUint { type Output = BigUint; #[inline] fn pow(self, exp: BigUint) -> BigUint { Pow::pow(self, &exp) } } impl<'a, 'b> Pow<&'b BigUint> for &'a 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<'a> Pow for &'a 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<'b> Pow<&'b $T> for BigUint { type Output = BigUint; #[inline] fn pow(self, exp: &$T) -> BigUint { Pow::pow(self, *exp) } } impl<'a> Pow<$T> for &'a BigUint { type Output = BigUint; #[inline] fn pow(self, exp: $T) -> BigUint { if exp == 0 { return BigUint::one(); } Pow::pow(self.clone(), exp) } } impl<'a, 'b> Pow<&'b $T> for &'a BigUint { type Output = BigUint; #[inline] fn pow(self, exp: &$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)); } num-bigint-0.4.3/src/biguint/serde.rs000064400000000000000000000061130072674642500156320ustar 00000000000000use super::{biguint_from_vec, BigUint}; use crate::std_alloc::Vec; use core::fmt; use serde::de::{SeqAccess, Visitor}; use serde::{Deserialize, Deserializer, Serialize, Serializer}; impl Serialize for BigUint { #[cfg(not(u64_digit))] fn serialize(&self, serializer: S) -> Result 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) } #[cfg(u64_digit)] fn serialize(&self, serializer: S) -> Result 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(deserializer: D) -> Result 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(not(u64_digit))] fn visit_seq(self, mut seq: S) -> Result where S: SeqAccess<'de>, { let len = seq.size_hint().unwrap_or(0); let mut data = Vec::with_capacity(len); while let Some(value) = seq.next_element::()? { data.push(value); } Ok(biguint_from_vec(data)) } #[cfg(u64_digit)] fn visit_seq(self, mut seq: S) -> Result where S: SeqAccess<'de>, { use crate::big_digit::BigDigit; use num_integer::Integer; let u32_len = seq.size_hint().unwrap_or(0); let len = Integer::div_ceil(&u32_len, &2); let mut data = Vec::with_capacity(len); while let Some(lo) = seq.next_element::()? { let mut value = BigDigit::from(lo); if let Some(hi) = seq.next_element::()? { value |= BigDigit::from(hi) << 32; data.push(value); } else { data.push(value); break; } } Ok(biguint_from_vec(data)) } } num-bigint-0.4.3/src/biguint/shift.rs000064400000000000000000000115400072674642500156450ustar 00000000000000use super::{biguint_from_vec, BigUint}; use crate::big_digit; use crate::std_alloc::{Cow, Vec}; use core::mem; use core::ops::{Shl, ShlAssign, Shr, ShrAssign}; use num_traits::{PrimInt, Zero}; #[inline] fn biguint_shl(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 as u8 - 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(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(core::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 as u8 - 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<'b> $Shx<&'b $rhs> for BigUint { type Output = BigUint; #[inline] fn $shx(self, rhs: &'b $rhs) -> BigUint { $Shx::$shx(self, *rhs) } } impl<'a, 'b> $Shx<&'b $rhs> for &'a BigUint { type Output = BigUint; #[inline] fn $shx(self, rhs: &'b $rhs) -> BigUint { $Shx::$shx(self, *rhs) } } impl<'b> $ShxAssign<&'b $rhs> for BigUint { #[inline] fn $shx_assign(&mut self, rhs: &'b $rhs) { $ShxAssign::$shx_assign(self, *rhs); } } }; ($($rhs:ty),+) => {$( impl Shl<$rhs> for BigUint { type Output = BigUint; #[inline] fn shl(self, rhs: $rhs) -> BigUint { biguint_shl(Cow::Owned(self), rhs) } } impl<'a> Shl<$rhs> for &'a 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, BigUint::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: $rhs) -> BigUint { biguint_shr(Cow::Owned(self), rhs) } } impl<'a> Shr<$rhs> for &'a 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, BigUint::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 } num-bigint-0.4.3/src/biguint/subtraction.rs000064400000000000000000000176760072674642500171050ustar 00000000000000#[cfg(not(u64_digit))] use super::u32_from_u128; 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, Zero}; #[cfg(all(use_addcarry, target_arch = "x86_64"))] use core::arch::x86_64 as arch; #[cfg(all(use_addcarry, target_arch = "x86"))] use core::arch::x86 as arch; // Subtract with borrow: #[cfg(all(use_addcarry, u64_digit))] #[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(all(use_addcarry, not(u64_digit)))] #[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 #[cfg(not(use_addcarry))] #[inline] fn sbb(borrow: u8, a: BigDigit, b: BigDigit, out: &mut BigDigit) -> u8 { use crate::big_digit::SignedDoubleBigDigit; let difference = SignedDoubleBigDigit::from(a) - SignedDoubleBigDigit::from(b) - SignedDoubleBigDigit::from(borrow); *out = difference as BigDigit; u8::from(difference < 0) } 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<'a> Sub<&'a BigUint> for BigUint { type Output = BigUint; fn sub(mut self, other: &BigUint) -> BigUint { self -= other; self } } impl<'a> SubAssign<&'a BigUint> for BigUint { fn sub_assign(&mut self, other: &'a BigUint) { sub2(&mut self.data[..], &other.data[..]); self.normalize(); } } impl<'a> Sub for &'a 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 for BigUint, sub); forward_all_scalar_binop_to_val_val!(impl Sub for BigUint, sub); forward_all_scalar_binop_to_val_val!(impl Sub for BigUint, sub); impl Sub for BigUint { type Output = BigUint; #[inline] fn sub(mut self, other: u32) -> BigUint { self -= other; self } } impl SubAssign for BigUint { fn sub_assign(&mut self, other: u32) { sub2(&mut self.data[..], &[other as BigDigit]); self.normalize(); } } impl Sub for u32 { type Output = BigUint; #[cfg(not(u64_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() } #[cfg(u64_digit)] #[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 for BigUint { type Output = BigUint; #[inline] fn sub(mut self, other: u64) -> BigUint { self -= other; self } } impl SubAssign for BigUint { #[cfg(not(u64_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(); } #[cfg(u64_digit)] #[inline] fn sub_assign(&mut self, other: u64) { sub2(&mut self.data[..], &[other as BigDigit]); self.normalize(); } } impl Sub for u64 { type Output = BigUint; #[cfg(not(u64_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() } #[cfg(u64_digit)] #[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 for BigUint { type Output = BigUint; #[inline] fn sub(mut self, other: u128) -> BigUint { self -= other; self } } impl SubAssign for BigUint { #[cfg(not(u64_digit))] #[inline] fn sub_assign(&mut self, other: u128) { let (a, b, c, d) = u32_from_u128(other); sub2(&mut self.data[..], &[d, c, b, a]); self.normalize(); } #[cfg(u64_digit)] #[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 for u128 { type Output = BigUint; #[cfg(not(u64_digit))] #[inline] fn sub(self, mut other: BigUint) -> BigUint { while other.data.len() < 4 { other.data.push(0); } let (a, b, c, d) = u32_from_u128(self); sub2rev(&[d, c, b, a], &mut other.data[..]); other.normalized() } #[cfg(u64_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() } } impl CheckedSub for BigUint { #[inline] fn checked_sub(&self, v: &BigUint) -> Option { match self.cmp(v) { Less => None, Equal => Some(Zero::zero()), Greater => Some(self.sub(v)), } } } num-bigint-0.4.3/src/biguint.rs000064400000000000000000000763010072674642500145360ustar 00000000000000use crate::big_digit::{self, BigDigit}; use crate::std_alloc::{String, Vec}; use core::cmp; use core::cmp::Ordering; use core::default::Default; use core::fmt; use core::hash; use core::mem; use core::str; use core::{u32, u64, u8}; use num_integer::{Integer, Roots}; use num_traits::{Num, One, Pow, ToPrimitive, Unsigned, Zero}; mod addition; mod division; mod multiplication; mod subtraction; mod bits; mod convert; mod iter; mod monty; mod power; mod shift; #[cfg(any(feature = "quickcheck", feature = "arbitrary"))] mod arbitrary; #[cfg(feature = "serde")] mod serde; pub(crate) use self::convert::to_str_radix_reversed; pub use self::iter::{U32Digits, U64Digits}; /// A big unsigned integer type. pub struct BigUint { data: Vec, } // Note: derived `Clone` doesn't specialize `clone_from`, // but we want to keep the allocation in `data`. impl Clone for BigUint { #[inline] fn clone(&self) -> Self { BigUint { data: self.data.clone(), } } #[inline] fn clone_from(&mut self, other: &Self) { self.data.clone_from(&other.data); } } impl hash::Hash for BigUint { #[inline] fn hash(&self, state: &mut H) { debug_assert!(self.data.last() != Some(&0)); self.data.hash(state); } } impl PartialEq for BigUint { #[inline] fn eq(&self, other: &BigUint) -> bool { debug_assert!(self.data.last() != Some(&0)); debug_assert!(other.data.last() != Some(&0)); self.data == other.data } } impl Eq for BigUint {} impl PartialOrd for BigUint { #[inline] fn partial_cmp(&self, other: &BigUint) -> Option { Some(self.cmp(other)) } } impl Ord for BigUint { #[inline] fn cmp(&self, other: &BigUint) -> Ordering { cmp_slice(&self.data[..], &other.data[..]) } } #[inline] fn cmp_slice(a: &[BigDigit], b: &[BigDigit]) -> Ordering { debug_assert!(a.last() != Some(&0)); debug_assert!(b.last() != Some(&0)); match Ord::cmp(&a.len(), &b.len()) { Ordering::Equal => Iterator::cmp(a.iter().rev(), b.iter().rev()), other => other, } } impl Default for BigUint { #[inline] fn default() -> BigUint { Zero::zero() } } impl fmt::Debug for BigUint { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { fmt::Display::fmt(self, f) } } impl fmt::Display for BigUint { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(true, "", &self.to_str_radix(10)) } } impl fmt::LowerHex for BigUint { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(true, "0x", &self.to_str_radix(16)) } } impl fmt::UpperHex for BigUint { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { let mut s = self.to_str_radix(16); s.make_ascii_uppercase(); f.pad_integral(true, "0x", &s) } } impl fmt::Binary for BigUint { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(true, "0b", &self.to_str_radix(2)) } } impl fmt::Octal for BigUint { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { f.pad_integral(true, "0o", &self.to_str_radix(8)) } } impl Zero for BigUint { #[inline] fn zero() -> BigUint { BigUint { data: Vec::new() } } #[inline] fn set_zero(&mut self) { self.data.clear(); } #[inline] fn is_zero(&self) -> bool { self.data.is_empty() } } impl One for BigUint { #[inline] fn one() -> BigUint { BigUint { data: vec![1] } } #[inline] fn set_one(&mut self) { self.data.clear(); self.data.push(1); } #[inline] fn is_one(&self) -> bool { self.data[..] == [1] } } impl Unsigned for BigUint {} impl Integer for BigUint { #[inline] fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) { division::div_rem_ref(self, other) } #[inline] fn div_floor(&self, other: &BigUint) -> BigUint { let (d, _) = division::div_rem_ref(self, other); d } #[inline] fn mod_floor(&self, other: &BigUint) -> BigUint { let (_, m) = division::div_rem_ref(self, other); m } #[inline] fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) { division::div_rem_ref(self, other) } #[inline] fn div_ceil(&self, other: &BigUint) -> BigUint { let (d, m) = division::div_rem_ref(self, other); if m.is_zero() { d } else { d + 1u32 } } /// Calculates the Greatest Common Divisor (GCD) of the number and `other`. /// /// The result is always positive. #[inline] fn gcd(&self, other: &Self) -> Self { #[inline] fn twos(x: &BigUint) -> u64 { x.trailing_zeros().unwrap_or(0) } // Stein's algorithm if self.is_zero() { return other.clone(); } if other.is_zero() { return self.clone(); } let mut m = self.clone(); let mut n = other.clone(); // find common factors of 2 let shift = cmp::min(twos(&n), twos(&m)); // divide m and n by 2 until odd // m inside loop n >>= twos(&n); while !m.is_zero() { m >>= twos(&m); if n > m { mem::swap(&mut n, &mut m) } m -= &n; } n << shift } /// Calculates the Lowest Common Multiple (LCM) of the number and `other`. #[inline] fn lcm(&self, other: &BigUint) -> BigUint { if self.is_zero() && other.is_zero() { Self::zero() } else { self / self.gcd(other) * other } } /// Calculates the Greatest Common Divisor (GCD) and /// Lowest Common Multiple (LCM) together. #[inline] fn gcd_lcm(&self, other: &Self) -> (Self, Self) { let gcd = self.gcd(other); let lcm = if gcd.is_zero() { Self::zero() } else { self / &gcd * other }; (gcd, lcm) } /// Deprecated, use `is_multiple_of` instead. #[inline] fn divides(&self, other: &BigUint) -> bool { self.is_multiple_of(other) } /// Returns `true` if the number is a multiple of `other`. #[inline] fn is_multiple_of(&self, other: &BigUint) -> bool { (self % other).is_zero() } /// Returns `true` if the number is divisible by `2`. #[inline] fn is_even(&self) -> bool { // Considering only the last digit. match self.data.first() { Some(x) => x.is_even(), None => true, } } /// Returns `true` if the number is not divisible by `2`. #[inline] fn is_odd(&self) -> bool { !self.is_even() } /// Rounds up to nearest multiple of argument. #[inline] fn next_multiple_of(&self, other: &Self) -> Self { let m = self.mod_floor(other); if m.is_zero() { self.clone() } else { self + (other - m) } } /// Rounds down to nearest multiple of argument. #[inline] fn prev_multiple_of(&self, other: &Self) -> Self { self - self.mod_floor(other) } } #[inline] fn fixpoint(mut x: BigUint, max_bits: u64, f: F) -> BigUint where F: Fn(&BigUint) -> BigUint, { let mut xn = f(&x); // If the value increased, then the initial guess must have been low. // Repeat until we reverse course. while x < xn { // Sometimes an increase will go way too far, especially with large // powers, and then take a long time to walk back. We know an upper // bound based on bit size, so saturate on that. x = if xn.bits() > max_bits { BigUint::one() << max_bits } else { xn }; xn = f(&x); } // Now keep repeating while the estimate is decreasing. while x > xn { x = xn; xn = f(&x); } x } impl Roots for BigUint { // nth_root, sqrt and cbrt use Newton's method to compute // principal root of a given degree for a given integer. // Reference: // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.14 fn nth_root(&self, n: u32) -> Self { assert!(n > 0, "root degree n must be at least 1"); if self.is_zero() || self.is_one() { return self.clone(); } match n { // Optimize for small n 1 => return self.clone(), 2 => return self.sqrt(), 3 => return self.cbrt(), _ => (), } // The root of non-zero values less than 2ⁿ can only be 1. let bits = self.bits(); let n64 = u64::from(n); if bits <= n64 { return BigUint::one(); } // If we fit in `u64`, compute the root that way. if let Some(x) = self.to_u64() { return x.nth_root(n).into(); } let max_bits = bits / n64 + 1; #[cfg(feature = "std")] let guess = match self.to_f64() { Some(f) if f.is_finite() => { use num_traits::FromPrimitive; // We fit in `f64` (lossy), so get a better initial guess from that. BigUint::from_f64((f.ln() / f64::from(n)).exp()).unwrap() } _ => { // Try to guess by scaling down such that it does fit in `f64`. // With some (x * 2ⁿᵏ), its nth root ≈ (ⁿ√x * 2ᵏ) let extra_bits = bits - (core::f64::MAX_EXP as u64 - 1); let root_scale = Integer::div_ceil(&extra_bits, &n64); let scale = root_scale * n64; if scale < bits && bits - scale > n64 { (self >> scale).nth_root(n) << root_scale } else { BigUint::one() << max_bits } } }; #[cfg(not(feature = "std"))] let guess = BigUint::one() << max_bits; let n_min_1 = n - 1; fixpoint(guess, max_bits, move |s| { let q = self / s.pow(n_min_1); let t = n_min_1 * s + q; t / n }) } // Reference: // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.13 fn sqrt(&self) -> Self { if self.is_zero() || self.is_one() { return self.clone(); } // If we fit in `u64`, compute the root that way. if let Some(x) = self.to_u64() { return x.sqrt().into(); } let bits = self.bits(); let max_bits = bits / 2 + 1; #[cfg(feature = "std")] let guess = match self.to_f64() { Some(f) if f.is_finite() => { use num_traits::FromPrimitive; // We fit in `f64` (lossy), so get a better initial guess from that. BigUint::from_f64(f.sqrt()).unwrap() } _ => { // Try to guess by scaling down such that it does fit in `f64`. // With some (x * 2²ᵏ), its sqrt ≈ (√x * 2ᵏ) let extra_bits = bits - (core::f64::MAX_EXP as u64 - 1); let root_scale = (extra_bits + 1) / 2; let scale = root_scale * 2; (self >> scale).sqrt() << root_scale } }; #[cfg(not(feature = "std"))] let guess = BigUint::one() << max_bits; fixpoint(guess, max_bits, move |s| { let q = self / s; let t = s + q; t >> 1 }) } fn cbrt(&self) -> Self { if self.is_zero() || self.is_one() { return self.clone(); } // If we fit in `u64`, compute the root that way. if let Some(x) = self.to_u64() { return x.cbrt().into(); } let bits = self.bits(); let max_bits = bits / 3 + 1; #[cfg(feature = "std")] let guess = match self.to_f64() { Some(f) if f.is_finite() => { use num_traits::FromPrimitive; // We fit in `f64` (lossy), so get a better initial guess from that. BigUint::from_f64(f.cbrt()).unwrap() } _ => { // Try to guess by scaling down such that it does fit in `f64`. // With some (x * 2³ᵏ), its cbrt ≈ (∛x * 2ᵏ) let extra_bits = bits - (core::f64::MAX_EXP as u64 - 1); let root_scale = (extra_bits + 2) / 3; let scale = root_scale * 3; (self >> scale).cbrt() << root_scale } }; #[cfg(not(feature = "std"))] let guess = BigUint::one() << max_bits; fixpoint(guess, max_bits, move |s| { let q = self / (s * s); let t = (s << 1) + q; t / 3u32 }) } } /// A generic trait for converting a value to a `BigUint`. pub trait ToBigUint { /// Converts the value of `self` to a `BigUint`. fn to_biguint(&self) -> Option; } /// Creates and initializes a `BigUint`. /// /// The digits are in little-endian base matching `BigDigit`. #[inline] pub(crate) fn biguint_from_vec(digits: Vec) -> BigUint { BigUint { data: digits }.normalized() } impl BigUint { /// Creates and initializes a `BigUint`. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn new(digits: Vec) -> BigUint { let mut big = BigUint::zero(); #[cfg(not(u64_digit))] { big.data = digits; big.normalize(); } #[cfg(u64_digit)] big.assign_from_slice(&digits); big } /// Creates and initializes a `BigUint`. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn from_slice(slice: &[u32]) -> BigUint { let mut big = BigUint::zero(); big.assign_from_slice(slice); big } /// Assign a value to a `BigUint`. /// /// The base 232 digits are ordered least significant digit first. #[inline] pub fn assign_from_slice(&mut self, slice: &[u32]) { self.data.clear(); #[cfg(not(u64_digit))] self.data.extend_from_slice(slice); #[cfg(u64_digit)] self.data.extend(slice.chunks(2).map(u32_chunk_to_u64)); self.normalize(); } /// Creates and initializes a `BigUint`. /// /// The bytes are in big-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from_bytes_be(b"A"), /// BigUint::parse_bytes(b"65", 10).unwrap()); /// assert_eq!(BigUint::from_bytes_be(b"AA"), /// BigUint::parse_bytes(b"16705", 10).unwrap()); /// assert_eq!(BigUint::from_bytes_be(b"AB"), /// BigUint::parse_bytes(b"16706", 10).unwrap()); /// assert_eq!(BigUint::from_bytes_be(b"Hello world!"), /// BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap()); /// ``` #[inline] pub fn from_bytes_be(bytes: &[u8]) -> BigUint { if bytes.is_empty() { Zero::zero() } else { let mut v = bytes.to_vec(); v.reverse(); BigUint::from_bytes_le(&*v) } } /// Creates and initializes a `BigUint`. /// /// The bytes are in little-endian byte order. #[inline] pub fn from_bytes_le(bytes: &[u8]) -> BigUint { if bytes.is_empty() { Zero::zero() } else { convert::from_bitwise_digits_le(bytes, 8) } } /// Creates and initializes a `BigUint`. The input slice must contain /// ascii/utf8 characters in [0-9a-zA-Z]. /// `radix` must be in the range `2...36`. /// /// The function `from_str_radix` from the `Num` trait provides the same logic /// for `&str` buffers. /// /// # Examples /// /// ``` /// use num_bigint::{BigUint, ToBigUint}; /// /// assert_eq!(BigUint::parse_bytes(b"1234", 10), ToBigUint::to_biguint(&1234)); /// assert_eq!(BigUint::parse_bytes(b"ABCD", 16), ToBigUint::to_biguint(&0xABCD)); /// assert_eq!(BigUint::parse_bytes(b"G", 16), None); /// ``` #[inline] pub fn parse_bytes(buf: &[u8], radix: u32) -> Option { let s = str::from_utf8(buf).ok()?; BigUint::from_str_radix(s, radix).ok() } /// Creates and initializes a `BigUint`. Each u8 of the input slice is /// interpreted as one digit of the number /// and must therefore be less than `radix`. /// /// The bytes are in big-endian byte order. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::{BigUint}; /// /// let inbase190 = &[15, 33, 125, 12, 14]; /// let a = BigUint::from_radix_be(inbase190, 190).unwrap(); /// assert_eq!(a.to_radix_be(190), inbase190); /// ``` pub fn from_radix_be(buf: &[u8], radix: u32) -> Option { convert::from_radix_be(buf, radix) } /// Creates and initializes a `BigUint`. Each u8 of the input slice is /// interpreted as one digit of the number /// and must therefore be less than `radix`. /// /// The bytes are in little-endian byte order. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::{BigUint}; /// /// let inbase190 = &[14, 12, 125, 33, 15]; /// let a = BigUint::from_radix_be(inbase190, 190).unwrap(); /// assert_eq!(a.to_radix_be(190), inbase190); /// ``` pub fn from_radix_le(buf: &[u8], radix: u32) -> Option { convert::from_radix_le(buf, radix) } /// Returns the byte representation of the `BigUint` in big-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); /// assert_eq!(i.to_bytes_be(), vec![4, 101]); /// ``` #[inline] pub fn to_bytes_be(&self) -> Vec { let mut v = self.to_bytes_le(); v.reverse(); v } /// Returns the byte representation of the `BigUint` in little-endian byte order. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// let i = BigUint::parse_bytes(b"1125", 10).unwrap(); /// assert_eq!(i.to_bytes_le(), vec![101, 4]); /// ``` #[inline] pub fn to_bytes_le(&self) -> Vec { if self.is_zero() { vec![0] } else { convert::to_bitwise_digits_le(self, 8) } } /// Returns the `u32` digits representation of the `BigUint` ordered least significant digit /// first. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from(1125u32).to_u32_digits(), vec![1125]); /// assert_eq!(BigUint::from(4294967295u32).to_u32_digits(), vec![4294967295]); /// assert_eq!(BigUint::from(4294967296u64).to_u32_digits(), vec![0, 1]); /// assert_eq!(BigUint::from(112500000000u64).to_u32_digits(), vec![830850304, 26]); /// ``` #[inline] pub fn to_u32_digits(&self) -> Vec { self.iter_u32_digits().collect() } /// Returns the `u64` digits representation of the `BigUint` ordered least significant digit /// first. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from(1125u32).to_u64_digits(), vec![1125]); /// assert_eq!(BigUint::from(4294967295u32).to_u64_digits(), vec![4294967295]); /// assert_eq!(BigUint::from(4294967296u64).to_u64_digits(), vec![4294967296]); /// assert_eq!(BigUint::from(112500000000u64).to_u64_digits(), vec![112500000000]); /// assert_eq!(BigUint::from(1u128 << 64).to_u64_digits(), vec![0, 1]); /// ``` #[inline] pub fn to_u64_digits(&self) -> Vec { self.iter_u64_digits().collect() } /// Returns an iterator of `u32` digits representation of the `BigUint` ordered least /// significant digit first. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from(1125u32).iter_u32_digits().collect::>(), vec![1125]); /// assert_eq!(BigUint::from(4294967295u32).iter_u32_digits().collect::>(), vec![4294967295]); /// assert_eq!(BigUint::from(4294967296u64).iter_u32_digits().collect::>(), vec![0, 1]); /// assert_eq!(BigUint::from(112500000000u64).iter_u32_digits().collect::>(), vec![830850304, 26]); /// ``` #[inline] pub fn iter_u32_digits(&self) -> U32Digits<'_> { U32Digits::new(self.data.as_slice()) } /// Returns an iterator of `u64` digits representation of the `BigUint` ordered least /// significant digit first. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from(1125u32).iter_u64_digits().collect::>(), vec![1125]); /// assert_eq!(BigUint::from(4294967295u32).iter_u64_digits().collect::>(), vec![4294967295]); /// assert_eq!(BigUint::from(4294967296u64).iter_u64_digits().collect::>(), vec![4294967296]); /// assert_eq!(BigUint::from(112500000000u64).iter_u64_digits().collect::>(), vec![112500000000]); /// assert_eq!(BigUint::from(1u128 << 64).iter_u64_digits().collect::>(), vec![0, 1]); /// ``` #[inline] pub fn iter_u64_digits(&self) -> U64Digits<'_> { U64Digits::new(self.data.as_slice()) } /// Returns the integer formatted as a string in the given radix. /// `radix` must be in the range `2...36`. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// let i = BigUint::parse_bytes(b"ff", 16).unwrap(); /// assert_eq!(i.to_str_radix(16), "ff"); /// ``` #[inline] pub fn to_str_radix(&self, radix: u32) -> String { let mut v = to_str_radix_reversed(self, radix); v.reverse(); unsafe { String::from_utf8_unchecked(v) } } /// Returns the integer in the requested base in big-endian digit order. /// The output is not given in a human readable alphabet but as a zero /// based u8 number. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_be(159), /// vec![2, 94, 27]); /// // 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27 /// ``` #[inline] pub fn to_radix_be(&self, radix: u32) -> Vec { let mut v = convert::to_radix_le(self, radix); v.reverse(); v } /// Returns the integer in the requested base in little-endian digit order. /// The output is not given in a human readable alphabet but as a zero /// based u8 number. /// `radix` must be in the range `2...256`. /// /// # Examples /// /// ``` /// use num_bigint::BigUint; /// /// assert_eq!(BigUint::from(0xFFFFu64).to_radix_le(159), /// vec![27, 94, 2]); /// // 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2) /// ``` #[inline] pub fn to_radix_le(&self, radix: u32) -> Vec { convert::to_radix_le(self, radix) } /// Determines the fewest bits necessary to express the `BigUint`. #[inline] pub fn bits(&self) -> u64 { if self.is_zero() { return 0; } let zeros: u64 = self.data.last().unwrap().leading_zeros().into(); self.data.len() as u64 * u64::from(big_digit::BITS) - zeros } /// Strips off trailing zero bigdigits - comparisons require the last element in the vector to /// be nonzero. #[inline] fn normalize(&mut self) { if let Some(&0) = self.data.last() { let len = self.data.iter().rposition(|&d| d != 0).map_or(0, |i| i + 1); self.data.truncate(len); } if self.data.len() < self.data.capacity() / 4 { self.data.shrink_to_fit(); } } /// Returns a normalized `BigUint`. #[inline] fn normalized(mut self) -> BigUint { self.normalize(); self } /// Returns `self ^ exponent`. pub fn pow(&self, exponent: u32) -> Self { Pow::pow(self, exponent) } /// Returns `(self ^ exponent) % modulus`. /// /// Panics if the modulus is zero. pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self { power::modpow(self, exponent, modulus) } /// Returns the truncated principal square root of `self` -- /// see [Roots::sqrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.sqrt) pub fn sqrt(&self) -> Self { Roots::sqrt(self) } /// Returns the truncated principal cube root of `self` -- /// see [Roots::cbrt](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#method.cbrt). pub fn cbrt(&self) -> Self { Roots::cbrt(self) } /// Returns the truncated principal `n`th root of `self` -- /// see [Roots::nth_root](https://docs.rs/num-integer/0.1/num_integer/trait.Roots.html#tymethod.nth_root). pub fn nth_root(&self, n: u32) -> Self { Roots::nth_root(self, n) } /// Returns the number of least-significant bits that are zero, /// or `None` if the entire number is zero. pub fn trailing_zeros(&self) -> Option { let i = self.data.iter().position(|&digit| digit != 0)?; let zeros: u64 = self.data[i].trailing_zeros().into(); Some(i as u64 * u64::from(big_digit::BITS) + zeros) } /// Returns the number of least-significant bits that are ones. pub fn trailing_ones(&self) -> u64 { if let Some(i) = self.data.iter().position(|&digit| !digit != 0) { // XXX u64::trailing_ones() introduced in Rust 1.46, // but we need to be compatible further back. // Thanks to cuviper for this workaround. let ones: u64 = (!self.data[i]).trailing_zeros().into(); i as u64 * u64::from(big_digit::BITS) + ones } else { self.data.len() as u64 * u64::from(big_digit::BITS) } } /// Returns the number of one bits. pub fn count_ones(&self) -> u64 { self.data.iter().map(|&d| u64::from(d.count_ones())).sum() } /// Returns whether the bit in the given position is set pub fn bit(&self, bit: u64) -> bool { let bits_per_digit = u64::from(big_digit::BITS); if let Some(digit_index) = (bit / bits_per_digit).to_usize() { if let Some(digit) = self.data.get(digit_index) { let bit_mask = (1 as BigDigit) << (bit % bits_per_digit); return (digit & bit_mask) != 0; } } false } /// Sets or clears the bit in the given position /// /// Note that setting a bit greater than the current bit length, a reallocation may be needed /// to store the new digits pub fn set_bit(&mut self, bit: u64, value: bool) { // Note: we're saturating `digit_index` and `new_len` -- any such case is guaranteed to // fail allocation, and that's more consistent than adding our own overflow panics. let bits_per_digit = u64::from(big_digit::BITS); let digit_index = (bit / bits_per_digit) .to_usize() .unwrap_or(core::usize::MAX); let bit_mask = (1 as BigDigit) << (bit % bits_per_digit); if value { if digit_index >= self.data.len() { let new_len = digit_index.saturating_add(1); self.data.resize(new_len, 0); } self.data[digit_index] |= bit_mask; } else if digit_index < self.data.len() { self.data[digit_index] &= !bit_mask; // the top bit may have been cleared, so normalize self.normalize(); } } } pub(crate) trait IntDigits { fn digits(&self) -> &[BigDigit]; fn digits_mut(&mut self) -> &mut Vec; fn normalize(&mut self); fn capacity(&self) -> usize; fn len(&self) -> usize; } impl IntDigits for BigUint { #[inline] fn digits(&self) -> &[BigDigit] { &self.data } #[inline] fn digits_mut(&mut self) -> &mut Vec { &mut self.data } #[inline] fn normalize(&mut self) { self.normalize(); } #[inline] fn capacity(&self) -> usize { self.data.capacity() } #[inline] fn len(&self) -> usize { self.data.len() } } /// Convert a u32 chunk (len is either 1 or 2) to a single u64 digit #[inline] fn u32_chunk_to_u64(chunk: &[u32]) -> u64 { // raw could have odd length let mut digit = chunk[0] as u64; if let Some(&hi) = chunk.get(1) { digit |= (hi as u64) << 32; } digit } /// Combine four `u32`s into a single `u128`. #[cfg(any(test, not(u64_digit)))] #[inline] fn u32_to_u128(a: u32, b: u32, c: u32, d: u32) -> u128 { u128::from(d) | (u128::from(c) << 32) | (u128::from(b) << 64) | (u128::from(a) << 96) } /// Split a single `u128` into four `u32`. #[cfg(any(test, not(u64_digit)))] #[inline] fn u32_from_u128(n: u128) -> (u32, u32, u32, u32) { ( (n >> 96) as u32, (n >> 64) as u32, (n >> 32) as u32, n as u32, ) } #[cfg(not(u64_digit))] #[test] fn test_from_slice() { fn check(slice: &[u32], data: &[BigDigit]) { assert_eq!(BigUint::from_slice(slice).data, data); } check(&[1], &[1]); check(&[0, 0, 0], &[]); check(&[1, 2, 0, 0], &[1, 2]); check(&[0, 0, 1, 2], &[0, 0, 1, 2]); check(&[0, 0, 1, 2, 0, 0], &[0, 0, 1, 2]); check(&[-1i32 as u32], &[-1i32 as BigDigit]); } #[cfg(u64_digit)] #[test] fn test_from_slice() { fn check(slice: &[u32], data: &[BigDigit]) { assert_eq!( BigUint::from_slice(slice).data, data, "from {:?}, to {:?}", slice, data ); } check(&[1], &[1]); check(&[0, 0, 0], &[]); check(&[1, 2], &[8_589_934_593]); check(&[1, 2, 0, 0], &[8_589_934_593]); check(&[0, 0, 1, 2], &[0, 8_589_934_593]); check(&[0, 0, 1, 2, 0, 0], &[0, 8_589_934_593]); check(&[-1i32 as u32], &[(-1i32 as u32) as BigDigit]); } #[test] fn test_u32_u128() { assert_eq!(u32_from_u128(0u128), (0, 0, 0, 0)); assert_eq!( u32_from_u128(u128::max_value()), ( u32::max_value(), u32::max_value(), u32::max_value(), u32::max_value() ) ); assert_eq!( u32_from_u128(u32::max_value() as u128), (0, 0, 0, u32::max_value()) ); assert_eq!( u32_from_u128(u64::max_value() as u128), (0, 0, u32::max_value(), u32::max_value()) ); assert_eq!( u32_from_u128((u64::max_value() as u128) + u32::max_value() as u128), (0, 1, 0, u32::max_value() - 1) ); assert_eq!(u32_from_u128(36_893_488_151_714_070_528), (0, 2, 1, 0)); } #[test] fn test_u128_u32_roundtrip() { // roundtrips let values = vec![ 0u128, 1u128, u64::max_value() as u128 * 3, u32::max_value() as u128, u64::max_value() as u128, (u64::max_value() as u128) + u32::max_value() as u128, u128::max_value(), ]; for val in &values { let (a, b, c, d) = u32_from_u128(*val); assert_eq!(u32_to_u128(a, b, c, d), *val); } } num-bigint-0.4.3/src/lib.rs000064400000000000000000000173350072674642500136450ustar 00000000000000// 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 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`). //! //! A `BigUint` is represented as a vector of `BigDigit`s. //! A `BigInt` 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::{Zero, One}; //! use std::mem::replace; //! //! // Calculate large 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; //! // This is a low cost way of swapping f0 with f1 and f1 with f2. //! f0 = replace(&mut 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, 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`. //! //! //! ## Compatibility //! //! The `num-bigint` crate is tested for rustc 1.31 and greater. #![doc(html_root_url = "https://docs.rs/num-bigint/0.4")] #![warn(rust_2018_idioms)] #![no_std] #[cfg(feature = "std")] #[macro_use] extern crate std; #[cfg(feature = "std")] mod std_alloc { pub(crate) use std::borrow::Cow; #[cfg(any(feature = "quickcheck"))] pub(crate) use std::boxed::Box; pub(crate) use std::string::String; pub(crate) use std::vec::Vec; } #[cfg(not(feature = "std"))] #[macro_use] extern crate alloc; #[cfg(not(feature = "std"))] mod std_alloc { pub(crate) use alloc::borrow::Cow; #[cfg(any(feature = "quickcheck"))] pub(crate) use alloc::boxed::Box; pub(crate) use alloc::string::String; pub(crate) use alloc::vec::Vec; } use core::fmt; #[cfg(feature = "std")] use std::error::Error; #[macro_use] mod macros; mod bigint; mod biguint; #[cfg(feature = "rand")] mod bigrand; #[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")] impl Error for ParseBigIntError { fn description(&self) -> &str { self.__description() } } /// The error type returned when a checked conversion regarding big integer fails. #[cfg(has_try_from)] #[derive(Debug, Copy, Clone, PartialEq, Eq)] pub struct TryFromBigIntError { original: T, } #[cfg(has_try_from)] impl TryFromBigIntError { 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`]. /// /// [`BigInt`]: struct.BigInt.html /// [`BigUint`]: struct.BigUint.html pub fn into_original(self) -> T { self.original } } #[cfg(all(feature = "std", has_try_from))] impl std::error::Error for TryFromBigIntError where T: fmt::Debug, { fn description(&self) -> &str { self.__description() } } #[cfg(has_try_from)] impl fmt::Display for TryFromBigIntError { 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")] pub use crate::bigrand::{RandBigInt, RandomBits, UniformBigInt, UniformBigUint}; mod big_digit { /// A `BigDigit` is a `BigUint`'s composing element. #[cfg(not(u64_digit))] pub(crate) type BigDigit = u32; #[cfg(u64_digit)] 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(not(u64_digit))] pub(crate) type DoubleBigDigit = u64; #[cfg(u64_digit)] pub(crate) type DoubleBigDigit = u128; /// A `SignedDoubleBigDigit` is the signed version of `DoubleBigDigit`. #[cfg(not(u64_digit))] pub(crate) type SignedDoubleBigDigit = i64; #[cfg(u64_digit)] pub(crate) type SignedDoubleBigDigit = i128; // `DoubleBigDigit` size dependent #[cfg(not(u64_digit))] pub(crate) const BITS: u8 = 32; #[cfg(u64_digit)] pub(crate) const BITS: u8 = 64; pub(crate) const HALF_BITS: u8 = BITS / 2; pub(crate) const HALF: BigDigit = (1 << HALF_BITS) - 1; const LO_MASK: DoubleBigDigit = (1 << BITS) - 1; pub(crate) const MAX: BigDigit = LO_MASK as BigDigit; #[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) } } num-bigint-0.4.3/src/macros.rs000064400000000000000000000316360072674642500143630ustar 00000000000000#![allow(unused_macros)] 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<'a> $imp<$res> for &'a $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<'a> $imp<$res> for &'a $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<'a> $imp<&'a $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<'a, 'b> $imp<&'b $res> for &'a $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<'a, 'b> $imp<&'b $res> for &'a $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<'a, 'b> $imp<&'b $scalar> for &'a $res { type Output = $res; #[inline] fn $method(self, other: &$scalar) -> $res { $imp::$method(self, *other) } } impl<'a, 'b> $imp<&'a $res> for &'b $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<'a> $imp<&'a $scalar> for $res { type Output = $res; #[inline] fn $method(self, other: &$scalar) -> $res { $imp::$method(&self, *other) } } impl<'a> $imp<$res> for &'a $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<'a> $imp<&'a $scalar> for $res { type Output = $res; #[inline] fn $method(self, other: &$scalar) -> $res { $imp::$method(self, *other) } } impl<'a> $imp<$res> for &'a $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<'a> $imp<$scalar> for &'a $res { type Output = $res; #[inline] fn $method(self, other: $scalar) -> $res { $imp::$method(self.clone(), other) } } impl<'a> $imp<&'a $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<'a, 'b> $imp<&'b $scalar> for &'a $res { type Output = $res; #[inline] fn $method(self, other: &$scalar) -> $res { $imp::$method(self.clone(), *other) } } impl<'a, 'b> $imp<&'a $res> for &'b $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 for $res, $method, u8, u16); promote_scalars!(impl $imp for $res, $method, usize); } } macro_rules! promote_unsigned_scalars_assign { (impl $imp:ident for $res:ty, $method:ident) => { promote_scalars_assign!(impl $imp for $res, $method, u8, u16); promote_scalars_assign!(impl $imp for $res, $method, usize); } } macro_rules! promote_signed_scalars { (impl $imp:ident for $res:ty, $method:ident) => { promote_scalars!(impl $imp for $res, $method, i8, i16); promote_scalars!(impl $imp for $res, $method, isize); } } macro_rules! promote_signed_scalars_assign { (impl $imp:ident for $res:ty, $method:ident) => { promote_scalars_assign!(impl $imp for $res, $method, i8, i16); promote_scalars_assign!(impl $imp 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 Sum for $res where $res: Add, { fn sum(iter: I) -> Self where I: Iterator, { iter.fold(Zero::zero(), <$res>::add) } } }; } macro_rules! impl_product_iter_type { ($res:ty) => { impl Product for $res where $res: Mul, { fn product(iter: I) -> Self where I: Iterator, { iter.fold(One::one(), <$res>::mul) } } }; } num-bigint-0.4.3/tests/bigint.rs000064400000000000000000001255240072674642500147260ustar 00000000000000use num_bigint::BigUint; use num_bigint::Sign::{Minus, NoSign, Plus}; use num_bigint::{BigInt, ToBigInt}; use std::cmp::Ordering::{Equal, Greater, Less}; use std::collections::hash_map::RandomState; use std::hash::{BuildHasher, Hash, Hasher}; use std::iter::repeat; use std::ops::Neg; use std::{f32, f64}; use std::{i128, u128}; use std::{i16, i32, i64, i8, isize}; use std::{u16, u32, u64, u8, usize}; use num_integer::Integer; use num_traits::{pow, FromPrimitive, Num, One, Pow, Signed, ToPrimitive, Zero}; mod consts; use crate::consts::*; #[macro_use] mod macros; #[test] fn test_from_bytes_be() { fn check(s: &str, result: &str) { assert_eq!( BigInt::from_bytes_be(Plus, s.as_bytes()), BigInt::parse_bytes(result.as_bytes(), 10).unwrap() ); } check("A", "65"); check("AA", "16705"); check("AB", "16706"); check("Hello world!", "22405534230753963835153736737"); assert_eq!(BigInt::from_bytes_be(Plus, &[]), BigInt::zero()); assert_eq!(BigInt::from_bytes_be(Minus, &[]), BigInt::zero()); } #[test] fn test_to_bytes_be() { fn check(s: &str, result: &str) { let b = BigInt::parse_bytes(result.as_bytes(), 10).unwrap(); let (sign, v) = b.to_bytes_be(); assert_eq!((Plus, s.as_bytes()), (sign, &*v)); } check("A", "65"); check("AA", "16705"); check("AB", "16706"); check("Hello world!", "22405534230753963835153736737"); let b: BigInt = Zero::zero(); assert_eq!(b.to_bytes_be(), (NoSign, vec![0])); // Test with leading/trailing zero bytes and a full BigDigit of value 0 let b = BigInt::from_str_radix("00010000000000000200", 16).unwrap(); assert_eq!(b.to_bytes_be(), (Plus, vec![1, 0, 0, 0, 0, 0, 0, 2, 0])); } #[test] fn test_from_bytes_le() { fn check(s: &str, result: &str) { assert_eq!( BigInt::from_bytes_le(Plus, s.as_bytes()), BigInt::parse_bytes(result.as_bytes(), 10).unwrap() ); } check("A", "65"); check("AA", "16705"); check("BA", "16706"); check("!dlrow olleH", "22405534230753963835153736737"); assert_eq!(BigInt::from_bytes_le(Plus, &[]), BigInt::zero()); assert_eq!(BigInt::from_bytes_le(Minus, &[]), BigInt::zero()); } #[test] fn test_to_bytes_le() { fn check(s: &str, result: &str) { let b = BigInt::parse_bytes(result.as_bytes(), 10).unwrap(); let (sign, v) = b.to_bytes_le(); assert_eq!((Plus, s.as_bytes()), (sign, &*v)); } check("A", "65"); check("AA", "16705"); check("BA", "16706"); check("!dlrow olleH", "22405534230753963835153736737"); let b: BigInt = Zero::zero(); assert_eq!(b.to_bytes_le(), (NoSign, vec![0])); // Test with leading/trailing zero bytes and a full BigDigit of value 0 let b = BigInt::from_str_radix("00010000000000000200", 16).unwrap(); assert_eq!(b.to_bytes_le(), (Plus, vec![0, 2, 0, 0, 0, 0, 0, 0, 1])); } #[test] fn test_to_signed_bytes_le() { fn check(s: &str, result: Vec) { assert_eq!( BigInt::parse_bytes(s.as_bytes(), 10) .unwrap() .to_signed_bytes_le(), result ); } check("0", vec![0]); check("32767", vec![0xff, 0x7f]); check("-1", vec![0xff]); check("16777216", vec![0, 0, 0, 1]); check("-100", vec![156]); check("-8388608", vec![0, 0, 0x80]); check("-192", vec![0x40, 0xff]); check("128", vec![0x80, 0]) } #[test] fn test_from_signed_bytes_le() { fn check(s: &[u8], result: &str) { assert_eq!( BigInt::from_signed_bytes_le(s), BigInt::parse_bytes(result.as_bytes(), 10).unwrap() ); } check(&[], "0"); check(&[0], "0"); check(&[0; 10], "0"); check(&[0xff, 0x7f], "32767"); check(&[0xff], "-1"); check(&[0, 0, 0, 1], "16777216"); check(&[156], "-100"); check(&[0, 0, 0x80], "-8388608"); check(&[0xff; 10], "-1"); check(&[0x40, 0xff], "-192"); } #[test] fn test_to_signed_bytes_be() { fn check(s: &str, result: Vec) { assert_eq!( BigInt::parse_bytes(s.as_bytes(), 10) .unwrap() .to_signed_bytes_be(), result ); } check("0", vec![0]); check("32767", vec![0x7f, 0xff]); check("-1", vec![255]); check("16777216", vec![1, 0, 0, 0]); check("-100", vec![156]); check("-8388608", vec![128, 0, 0]); check("-192", vec![0xff, 0x40]); check("128", vec![0, 0x80]); } #[test] fn test_from_signed_bytes_be() { fn check(s: &[u8], result: &str) { assert_eq!( BigInt::from_signed_bytes_be(s), BigInt::parse_bytes(result.as_bytes(), 10).unwrap() ); } check(&[], "0"); check(&[0], "0"); check(&[0; 10], "0"); check(&[127, 255], "32767"); check(&[255], "-1"); check(&[1, 0, 0, 0], "16777216"); check(&[156], "-100"); check(&[128, 0, 0], "-8388608"); check(&[255; 10], "-1"); check(&[0xff, 0x40], "-192"); } #[test] fn test_signed_bytes_be_round_trip() { for i in -0x1FFFF..0x20000 { let n = BigInt::from(i); assert_eq!(n, BigInt::from_signed_bytes_be(&n.to_signed_bytes_be())); } } #[test] fn test_signed_bytes_le_round_trip() { for i in -0x1FFFF..0x20000 { let n = BigInt::from(i); assert_eq!(n, BigInt::from_signed_bytes_le(&n.to_signed_bytes_le())); } } #[test] fn test_cmp() { let vs: [&[u32]; 4] = [&[2 as u32], &[1, 1], &[2, 1], &[1, 1, 1]]; let mut nums = Vec::new(); for s in vs.iter().rev() { nums.push(BigInt::from_slice(Minus, *s)); } nums.push(Zero::zero()); nums.extend(vs.iter().map(|s| BigInt::from_slice(Plus, *s))); for (i, ni) in nums.iter().enumerate() { for (j0, nj) in nums[i..].iter().enumerate() { let j = i + j0; if i == j { assert_eq!(ni.cmp(nj), Equal); assert_eq!(nj.cmp(ni), Equal); assert_eq!(ni, nj); assert!(!(ni != nj)); assert!(ni <= nj); assert!(ni >= nj); assert!(!(ni < nj)); assert!(!(ni > nj)); } else { assert_eq!(ni.cmp(nj), Less); assert_eq!(nj.cmp(ni), Greater); assert!(!(ni == nj)); assert!(ni != nj); assert!(ni <= nj); assert!(!(ni >= nj)); assert!(ni < nj); assert!(!(ni > nj)); assert!(!(nj <= ni)); assert!(nj >= ni); assert!(!(nj < ni)); assert!(nj > ni); } } } } fn hash(x: &T) -> u64 { let mut hasher = ::Hasher::new(); x.hash(&mut hasher); hasher.finish() } #[test] fn test_hash() { let a = BigInt::new(NoSign, vec![]); let b = BigInt::new(NoSign, vec![0]); let c = BigInt::new(Plus, vec![1]); let d = BigInt::new(Plus, vec![1, 0, 0, 0, 0, 0]); let e = BigInt::new(Plus, vec![0, 0, 0, 0, 0, 1]); let f = BigInt::new(Minus, vec![1]); assert!(hash(&a) == hash(&b)); assert!(hash(&b) != hash(&c)); assert!(hash(&c) == hash(&d)); assert!(hash(&d) != hash(&e)); assert!(hash(&c) != hash(&f)); } #[test] fn test_convert_i64() { fn check(b1: BigInt, i: i64) { let b2: BigInt = FromPrimitive::from_i64(i).unwrap(); assert!(b1 == b2); assert!(b1.to_i64().unwrap() == i); } check(Zero::zero(), 0); check(One::one(), 1); check(i64::MIN.to_bigint().unwrap(), i64::MIN); check(i64::MAX.to_bigint().unwrap(), i64::MAX); assert_eq!((i64::MAX as u64 + 1).to_bigint().unwrap().to_i64(), None); assert_eq!( BigInt::from_biguint(Plus, BigUint::new(vec![1, 2, 3, 4, 5])).to_i64(), None ); assert_eq!( BigInt::from_biguint(Minus, BigUint::new(vec![1, 0, 0, 1 << 31])).to_i64(), None ); assert_eq!( BigInt::from_biguint(Minus, BigUint::new(vec![1, 2, 3, 4, 5])).to_i64(), None ); } #[test] fn test_convert_i128() { fn check(b1: BigInt, i: i128) { let b2: BigInt = FromPrimitive::from_i128(i).unwrap(); assert!(b1 == b2); assert!(b1.to_i128().unwrap() == i); } check(Zero::zero(), 0); check(One::one(), 1); check(i128::MIN.to_bigint().unwrap(), i128::MIN); check(i128::MAX.to_bigint().unwrap(), i128::MAX); assert_eq!((i128::MAX as u128 + 1).to_bigint().unwrap().to_i128(), None); assert_eq!( BigInt::from_biguint(Plus, BigUint::new(vec![1, 2, 3, 4, 5])).to_i128(), None ); assert_eq!( BigInt::from_biguint(Minus, BigUint::new(vec![1, 0, 0, 1 << 31])).to_i128(), None ); assert_eq!( BigInt::from_biguint(Minus, BigUint::new(vec![1, 2, 3, 4, 5])).to_i128(), None ); } #[test] fn test_convert_u64() { fn check(b1: BigInt, u: u64) { let b2: BigInt = FromPrimitive::from_u64(u).unwrap(); assert!(b1 == b2); assert!(b1.to_u64().unwrap() == u); } check(Zero::zero(), 0); check(One::one(), 1); check(u64::MIN.to_bigint().unwrap(), u64::MIN); check(u64::MAX.to_bigint().unwrap(), u64::MAX); assert_eq!( BigInt::from_biguint(Plus, BigUint::new(vec![1, 2, 3, 4, 5])).to_u64(), None ); let max_value: BigUint = FromPrimitive::from_u64(u64::MAX).unwrap(); assert_eq!(BigInt::from_biguint(Minus, max_value).to_u64(), None); assert_eq!( BigInt::from_biguint(Minus, BigUint::new(vec![1, 2, 3, 4, 5])).to_u64(), None ); } #[test] fn test_convert_u128() { fn check(b1: BigInt, u: u128) { let b2: BigInt = FromPrimitive::from_u128(u).unwrap(); assert!(b1 == b2); assert!(b1.to_u128().unwrap() == u); } check(Zero::zero(), 0); check(One::one(), 1); check(u128::MIN.to_bigint().unwrap(), u128::MIN); check(u128::MAX.to_bigint().unwrap(), u128::MAX); assert_eq!( BigInt::from_biguint(Plus, BigUint::new(vec![1, 2, 3, 4, 5])).to_u128(), None ); let max_value: BigUint = FromPrimitive::from_u128(u128::MAX).unwrap(); assert_eq!(BigInt::from_biguint(Minus, max_value).to_u128(), None); assert_eq!( BigInt::from_biguint(Minus, BigUint::new(vec![1, 2, 3, 4, 5])).to_u128(), None ); } #[test] #[allow(clippy::float_cmp)] fn test_convert_f32() { fn check(b1: &BigInt, f: f32) { let b2 = BigInt::from_f32(f).unwrap(); assert_eq!(b1, &b2); assert_eq!(b1.to_f32().unwrap(), f); let neg_b1 = -b1; let neg_b2 = BigInt::from_f32(-f).unwrap(); assert_eq!(neg_b1, neg_b2); assert_eq!(neg_b1.to_f32().unwrap(), -f); } check(&BigInt::zero(), 0.0); check(&BigInt::one(), 1.0); check(&BigInt::from(u16::MAX), pow(2.0_f32, 16) - 1.0); check(&BigInt::from(1u64 << 32), pow(2.0_f32, 32)); check(&BigInt::from_slice(Plus, &[0, 0, 1]), pow(2.0_f32, 64)); check( &((BigInt::one() << 100) + (BigInt::one() << 123)), pow(2.0_f32, 100) + pow(2.0_f32, 123), ); check(&(BigInt::one() << 127), pow(2.0_f32, 127)); check(&(BigInt::from((1u64 << 24) - 1) << (128 - 24)), f32::MAX); // keeping all 24 digits with the bits at different offsets to the BigDigits let x: u32 = 0b00000000101111011111011011011101; let mut f = x as f32; let mut b = BigInt::from(x); for _ in 0..64 { check(&b, f); f *= 2.0; b <<= 1; } // this number when rounded to f64 then f32 isn't the same as when rounded straight to f32 let mut n: i64 = 0b0000000000111111111111111111111111011111111111111111111111111111; assert!((n as f64) as f32 != n as f32); assert_eq!(BigInt::from(n).to_f32(), Some(n as f32)); n = -n; assert!((n as f64) as f32 != n as f32); assert_eq!(BigInt::from(n).to_f32(), Some(n as f32)); // test rounding up with the bits at different offsets to the BigDigits let mut f = ((1u64 << 25) - 1) as f32; let mut b = BigInt::from(1u64 << 25); for _ in 0..64 { assert_eq!(b.to_f32(), Some(f)); f *= 2.0; b <<= 1; } // rounding assert_eq!( BigInt::from_f32(-f32::consts::PI), Some(BigInt::from(-3i32)) ); assert_eq!(BigInt::from_f32(-f32::consts::E), Some(BigInt::from(-2i32))); assert_eq!(BigInt::from_f32(-0.99999), Some(BigInt::zero())); assert_eq!(BigInt::from_f32(-0.5), Some(BigInt::zero())); assert_eq!(BigInt::from_f32(-0.0), Some(BigInt::zero())); assert_eq!( BigInt::from_f32(f32::MIN_POSITIVE / 2.0), Some(BigInt::zero()) ); assert_eq!(BigInt::from_f32(f32::MIN_POSITIVE), Some(BigInt::zero())); assert_eq!(BigInt::from_f32(0.5), Some(BigInt::zero())); assert_eq!(BigInt::from_f32(0.99999), Some(BigInt::zero())); assert_eq!(BigInt::from_f32(f32::consts::E), Some(BigInt::from(2u32))); assert_eq!(BigInt::from_f32(f32::consts::PI), Some(BigInt::from(3u32))); // special float values assert_eq!(BigInt::from_f32(f32::NAN), None); assert_eq!(BigInt::from_f32(f32::INFINITY), None); assert_eq!(BigInt::from_f32(f32::NEG_INFINITY), None); // largest BigInt that will round to a finite f32 value let big_num = (BigInt::one() << 128u8) - 1u8 - (BigInt::one() << (128u8 - 25)); assert_eq!(big_num.to_f32(), Some(f32::MAX)); assert_eq!((&big_num + 1u8).to_f32(), Some(f32::INFINITY)); assert_eq!((-&big_num).to_f32(), Some(f32::MIN)); assert_eq!(((-&big_num) - 1u8).to_f32(), Some(f32::NEG_INFINITY)); assert_eq!( ((BigInt::one() << 128u8) - 1u8).to_f32(), Some(f32::INFINITY) ); assert_eq!((BigInt::one() << 128u8).to_f32(), Some(f32::INFINITY)); assert_eq!( (-((BigInt::one() << 128u8) - 1u8)).to_f32(), Some(f32::NEG_INFINITY) ); assert_eq!( (-(BigInt::one() << 128u8)).to_f32(), Some(f32::NEG_INFINITY) ); } #[test] #[allow(clippy::float_cmp)] fn test_convert_f64() { fn check(b1: &BigInt, f: f64) { let b2 = BigInt::from_f64(f).unwrap(); assert_eq!(b1, &b2); assert_eq!(b1.to_f64().unwrap(), f); let neg_b1 = -b1; let neg_b2 = BigInt::from_f64(-f).unwrap(); assert_eq!(neg_b1, neg_b2); assert_eq!(neg_b1.to_f64().unwrap(), -f); } check(&BigInt::zero(), 0.0); check(&BigInt::one(), 1.0); check(&BigInt::from(u32::MAX), pow(2.0_f64, 32) - 1.0); check(&BigInt::from(1u64 << 32), pow(2.0_f64, 32)); check(&BigInt::from_slice(Plus, &[0, 0, 1]), pow(2.0_f64, 64)); check( &((BigInt::one() << 100) + (BigInt::one() << 152)), pow(2.0_f64, 100) + pow(2.0_f64, 152), ); check(&(BigInt::one() << 1023), pow(2.0_f64, 1023)); check(&(BigInt::from((1u64 << 53) - 1) << (1024 - 53)), f64::MAX); // keeping all 53 digits with the bits at different offsets to the BigDigits let x: u64 = 0b0000000000011110111110110111111101110111101111011111011011011101; let mut f = x as f64; let mut b = BigInt::from(x); for _ in 0..128 { check(&b, f); f *= 2.0; b <<= 1; } // test rounding up with the bits at different offsets to the BigDigits let mut f = ((1u64 << 54) - 1) as f64; let mut b = BigInt::from(1u64 << 54); for _ in 0..128 { assert_eq!(b.to_f64(), Some(f)); f *= 2.0; b <<= 1; } // rounding assert_eq!( BigInt::from_f64(-f64::consts::PI), Some(BigInt::from(-3i32)) ); assert_eq!(BigInt::from_f64(-f64::consts::E), Some(BigInt::from(-2i32))); assert_eq!(BigInt::from_f64(-0.99999), Some(BigInt::zero())); assert_eq!(BigInt::from_f64(-0.5), Some(BigInt::zero())); assert_eq!(BigInt::from_f64(-0.0), Some(BigInt::zero())); assert_eq!( BigInt::from_f64(f64::MIN_POSITIVE / 2.0), Some(BigInt::zero()) ); assert_eq!(BigInt::from_f64(f64::MIN_POSITIVE), Some(BigInt::zero())); assert_eq!(BigInt::from_f64(0.5), Some(BigInt::zero())); assert_eq!(BigInt::from_f64(0.99999), Some(BigInt::zero())); assert_eq!(BigInt::from_f64(f64::consts::E), Some(BigInt::from(2u32))); assert_eq!(BigInt::from_f64(f64::consts::PI), Some(BigInt::from(3u32))); // special float values assert_eq!(BigInt::from_f64(f64::NAN), None); assert_eq!(BigInt::from_f64(f64::INFINITY), None); assert_eq!(BigInt::from_f64(f64::NEG_INFINITY), None); // largest BigInt that will round to a finite f64 value let big_num = (BigInt::one() << 1024u16) - 1u8 - (BigInt::one() << (1024u16 - 54)); assert_eq!(big_num.to_f64(), Some(f64::MAX)); assert_eq!((&big_num + 1u8).to_f64(), Some(f64::INFINITY)); assert_eq!((-&big_num).to_f64(), Some(f64::MIN)); assert_eq!(((-&big_num) - 1u8).to_f64(), Some(f64::NEG_INFINITY)); assert_eq!( ((BigInt::one() << 1024u16) - 1u8).to_f64(), Some(f64::INFINITY) ); assert_eq!((BigInt::one() << 1024u16).to_f64(), Some(f64::INFINITY)); assert_eq!( (-((BigInt::one() << 1024u16) - 1u8)).to_f64(), Some(f64::NEG_INFINITY) ); assert_eq!( (-(BigInt::one() << 1024u16)).to_f64(), Some(f64::NEG_INFINITY) ); } #[test] fn test_convert_to_biguint() { fn check(n: BigInt, ans_1: BigUint) { assert_eq!(n.to_biguint().unwrap(), ans_1); assert_eq!(n.to_biguint().unwrap().to_bigint().unwrap(), n); } let zero: BigInt = Zero::zero(); let unsigned_zero: BigUint = Zero::zero(); let positive = BigInt::from_biguint(Plus, BigUint::new(vec![1, 2, 3])); let negative = -&positive; check(zero, unsigned_zero); check(positive, BigUint::new(vec![1, 2, 3])); assert_eq!(negative.to_biguint(), None); } #[test] fn test_convert_from_uint() { macro_rules! check { ($ty:ident, $max:expr) => { assert_eq!(BigInt::from($ty::zero()), BigInt::zero()); assert_eq!(BigInt::from($ty::one()), BigInt::one()); assert_eq!(BigInt::from($ty::MAX - $ty::one()), $max - BigInt::one()); assert_eq!(BigInt::from($ty::MAX), $max); }; } check!(u8, BigInt::from_slice(Plus, &[u8::MAX as u32])); check!(u16, BigInt::from_slice(Plus, &[u16::MAX as u32])); check!(u32, BigInt::from_slice(Plus, &[u32::MAX])); check!(u64, BigInt::from_slice(Plus, &[u32::MAX, u32::MAX])); check!( u128, BigInt::from_slice(Plus, &[u32::MAX, u32::MAX, u32::MAX, u32::MAX]) ); check!(usize, BigInt::from(usize::MAX as u64)); } #[test] fn test_convert_from_int() { macro_rules! check { ($ty:ident, $min:expr, $max:expr) => { assert_eq!(BigInt::from($ty::MIN), $min); assert_eq!(BigInt::from($ty::MIN + $ty::one()), $min + BigInt::one()); assert_eq!(BigInt::from(-$ty::one()), -BigInt::one()); assert_eq!(BigInt::from($ty::zero()), BigInt::zero()); assert_eq!(BigInt::from($ty::one()), BigInt::one()); assert_eq!(BigInt::from($ty::MAX - $ty::one()), $max - BigInt::one()); assert_eq!(BigInt::from($ty::MAX), $max); }; } check!( i8, BigInt::from_slice(Minus, &[1 << 7]), BigInt::from_slice(Plus, &[i8::MAX as u32]) ); check!( i16, BigInt::from_slice(Minus, &[1 << 15]), BigInt::from_slice(Plus, &[i16::MAX as u32]) ); check!( i32, BigInt::from_slice(Minus, &[1 << 31]), BigInt::from_slice(Plus, &[i32::MAX as u32]) ); check!( i64, BigInt::from_slice(Minus, &[0, 1 << 31]), BigInt::from_slice(Plus, &[u32::MAX, i32::MAX as u32]) ); check!( i128, BigInt::from_slice(Minus, &[0, 0, 0, 1 << 31]), BigInt::from_slice(Plus, &[u32::MAX, u32::MAX, u32::MAX, i32::MAX as u32]) ); check!( isize, BigInt::from(isize::MIN as i64), BigInt::from(isize::MAX as i64) ); } #[test] fn test_convert_from_biguint() { assert_eq!(BigInt::from(BigUint::zero()), BigInt::zero()); assert_eq!(BigInt::from(BigUint::one()), BigInt::one()); assert_eq!( BigInt::from(BigUint::from_slice(&[1, 2, 3])), BigInt::from_slice(Plus, &[1, 2, 3]) ); } #[test] fn test_add() { 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); assert_op!(a + b == c); assert_op!(b + a == c); assert_op!(c + na == b); assert_op!(c + nb == a); assert_op!(a + nc == nb); assert_op!(b + nc == na); assert_op!(na + nb == nc); assert_op!(a + na == BigInt::zero()); assert_assign_op!(a += b == c); assert_assign_op!(b += a == c); assert_assign_op!(c += na == b); assert_assign_op!(c += nb == a); assert_assign_op!(a += nc == nb); assert_assign_op!(b += nc == na); assert_assign_op!(na += nb == nc); assert_assign_op!(a += na == BigInt::zero()); } } #[test] fn test_sub() { 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); assert_op!(c - a == b); assert_op!(c - b == a); assert_op!(nb - a == nc); assert_op!(na - b == nc); assert_op!(b - na == c); assert_op!(a - nb == c); assert_op!(nc - na == nb); assert_op!(a - a == BigInt::zero()); assert_assign_op!(c -= a == b); assert_assign_op!(c -= b == a); assert_assign_op!(nb -= a == nc); assert_assign_op!(na -= b == nc); assert_assign_op!(b -= na == c); assert_assign_op!(a -= nb == c); assert_assign_op!(nc -= na == nb); assert_assign_op!(a -= a == BigInt::zero()); } } #[test] fn test_mul() { 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); assert_op!(a * b == c); assert_op!(b * a == c); assert_op!(na * nb == c); assert_op!(na * b == nc); assert_op!(nb * a == nc); assert_assign_op!(a *= b == c); assert_assign_op!(b *= a == c); assert_assign_op!(na *= nb == c); assert_assign_op!(na *= b == nc); assert_assign_op!(nb *= a == nc); } 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 b = BigInt::from_slice(Plus, b_vec); let c = BigInt::from_slice(Plus, c_vec); let d = BigInt::from_slice(Plus, d_vec); assert!(a == &b * &c + &d); assert!(a == &c * &b + &d); } } #[test] fn test_div_mod_floor() { fn check_sub(a: &BigInt, b: &BigInt, ans_d: &BigInt, ans_m: &BigInt) { let (d, m) = a.div_mod_floor(b); assert_eq!(d, a.div_floor(b)); assert_eq!(m, a.mod_floor(b)); if !m.is_zero() { assert_eq!(m.sign(), b.sign()); } assert!(m.abs() <= b.abs()); assert!(*a == b * &d + &m); assert!(d == *ans_d); assert!(m == *ans_m); } fn check(a: &BigInt, b: &BigInt, d: &BigInt, m: &BigInt) { if m.is_zero() { check_sub(a, b, d, m); check_sub(a, &b.neg(), &d.neg(), m); check_sub(&a.neg(), b, &d.neg(), m); check_sub(&a.neg(), &b.neg(), d, m); } else { let one: BigInt = One::one(); check_sub(a, b, d, m); check_sub(a, &b.neg(), &(d.neg() - &one), &(m - b)); check_sub(&a.neg(), b, &(d.neg() - &one), &(b - m)); check_sub(&a.neg(), &b.neg(), d, &m.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.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 = BigInt::from_slice(Plus, a_vec); let b = BigInt::from_slice(Plus, b_vec); let c = BigInt::from_slice(Plus, c_vec); let d = BigInt::from_slice(Plus, d_vec); if !b.is_zero() { check(&a, &b, &c, &d); } } } #[test] fn test_div_rem() { fn check_sub(a: &BigInt, b: &BigInt, ans_q: &BigInt, ans_r: &BigInt) { let (q, r) = a.div_rem(b); if !r.is_zero() { assert_eq!(r.sign(), a.sign()); } assert!(r.abs() <= b.abs()); assert!(*a == b * &q + &r); assert!(q == *ans_q); assert!(r == *ans_r); let (a, b, ans_q, ans_r) = (a.clone(), b.clone(), ans_q.clone(), ans_r.clone()); assert_op!(a / b == ans_q); assert_op!(a % b == ans_r); assert_assign_op!(a /= b == ans_q); assert_assign_op!(a %= b == ans_r); } fn check(a: &BigInt, b: &BigInt, q: &BigInt, r: &BigInt) { check_sub(a, b, q, r); check_sub(a, &b.neg(), &q.neg(), r); check_sub(&a.neg(), b, &q.neg(), &r.neg()); check_sub(&a.neg(), &b.neg(), q, &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.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 = BigInt::from_slice(Plus, a_vec); let b = BigInt::from_slice(Plus, b_vec); let c = BigInt::from_slice(Plus, c_vec); let d = BigInt::from_slice(Plus, d_vec); if !b.is_zero() { check(&a, &b, &c, &d); } } } #[test] fn test_div_ceil() { fn check_sub(a: &BigInt, b: &BigInt, ans_d: &BigInt) { assert_eq!(a.div_ceil(b), *ans_d); } fn check(a: &BigInt, b: &BigInt, d: &BigInt, m: &BigInt) { if m.is_zero() { check_sub(a, b, d); check_sub(a, &b.neg(), &d.neg()); check_sub(&a.neg(), b, &d.neg()); check_sub(&a.neg(), &b.neg(), d); } else { check_sub(a, b, &(d + 1)); check_sub(a, &b.neg(), &d.neg()); check_sub(&a.neg(), b, &d.neg()); check_sub(&a.neg(), &b.neg(), &(d + 1)); } } 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.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 = BigInt::from_slice(Plus, a_vec); let b = BigInt::from_slice(Plus, b_vec); let c = BigInt::from_slice(Plus, c_vec); let d = BigInt::from_slice(Plus, d_vec); if !b.is_zero() { check(&a, &b, &c, &d); } } } #[test] fn test_checked_add() { 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); assert!(a.checked_add(&b).unwrap() == c); assert!(b.checked_add(&a).unwrap() == c); assert!(c.checked_add(&(-&a)).unwrap() == b); assert!(c.checked_add(&(-&b)).unwrap() == a); assert!(a.checked_add(&(-&c)).unwrap() == (-&b)); assert!(b.checked_add(&(-&c)).unwrap() == (-&a)); assert!((-&a).checked_add(&(-&b)).unwrap() == (-&c)); assert!(a.checked_add(&(-&a)).unwrap() == BigInt::zero()); } } #[test] fn test_checked_sub() { 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); assert!(c.checked_sub(&a).unwrap() == b); assert!(c.checked_sub(&b).unwrap() == a); assert!((-&b).checked_sub(&a).unwrap() == (-&c)); assert!((-&a).checked_sub(&b).unwrap() == (-&c)); assert!(b.checked_sub(&(-&a)).unwrap() == c); assert!(a.checked_sub(&(-&b)).unwrap() == c); assert!((-&c).checked_sub(&(-&a)).unwrap() == (-&b)); assert!(a.checked_sub(&a).unwrap() == BigInt::zero()); } } #[test] fn test_checked_mul() { 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); assert!(a.checked_mul(&b).unwrap() == c); assert!(b.checked_mul(&a).unwrap() == c); assert!((-&a).checked_mul(&b).unwrap() == -&c); assert!((-&b).checked_mul(&a).unwrap() == -&c); } 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 b = BigInt::from_slice(Plus, b_vec); let c = BigInt::from_slice(Plus, c_vec); let d = BigInt::from_slice(Plus, d_vec); assert!(a == b.checked_mul(&c).unwrap() + &d); assert!(a == c.checked_mul(&b).unwrap() + &d); } } #[test] fn test_checked_div() { 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.is_zero() { assert!(c.checked_div(&a).unwrap() == b); assert!((-&c).checked_div(&(-&a)).unwrap() == b); assert!((-&c).checked_div(&a).unwrap() == -&b); } if !b.is_zero() { assert!(c.checked_div(&b).unwrap() == a); assert!((-&c).checked_div(&(-&b)).unwrap() == a); assert!((-&c).checked_div(&b).unwrap() == -&a); } assert!(c.checked_div(&Zero::zero()).is_none()); assert!((-&c).checked_div(&Zero::zero()).is_none()); } } #[test] fn test_gcd() { fn check(a: isize, b: isize, c: isize) { let big_a: BigInt = FromPrimitive::from_isize(a).unwrap(); let big_b: BigInt = FromPrimitive::from_isize(b).unwrap(); let big_c: BigInt = FromPrimitive::from_isize(c).unwrap(); assert_eq!(big_a.gcd(&big_b), big_c); assert_eq!(big_a.extended_gcd(&big_b).gcd, big_c); assert_eq!(big_a.gcd_lcm(&big_b).0, big_c); assert_eq!(big_a.extended_gcd_lcm(&big_b).0.gcd, big_c); } check(10, 2, 2); check(10, 3, 1); check(0, 3, 3); check(3, 3, 3); check(56, 42, 14); check(3, -3, 3); check(-6, 3, 3); check(-4, -2, 2); } #[test] fn test_lcm() { fn check(a: isize, b: isize, c: isize) { let big_a: BigInt = FromPrimitive::from_isize(a).unwrap(); let big_b: BigInt = FromPrimitive::from_isize(b).unwrap(); let big_c: BigInt = FromPrimitive::from_isize(c).unwrap(); assert_eq!(big_a.lcm(&big_b), big_c); assert_eq!(big_a.gcd_lcm(&big_b).1, big_c); assert_eq!(big_a.extended_gcd_lcm(&big_b).1, big_c); } check(0, 0, 0); check(1, 0, 0); check(0, 1, 0); check(1, 1, 1); check(-1, 1, 1); check(1, -1, 1); check(-1, -1, 1); check(8, 9, 72); check(11, 5, 55); } #[test] fn test_next_multiple_of() { assert_eq!( BigInt::from(16).next_multiple_of(&BigInt::from(8)), BigInt::from(16) ); assert_eq!( BigInt::from(23).next_multiple_of(&BigInt::from(8)), BigInt::from(24) ); assert_eq!( BigInt::from(16).next_multiple_of(&BigInt::from(-8)), BigInt::from(16) ); assert_eq!( BigInt::from(23).next_multiple_of(&BigInt::from(-8)), BigInt::from(16) ); assert_eq!( BigInt::from(-16).next_multiple_of(&BigInt::from(8)), BigInt::from(-16) ); assert_eq!( BigInt::from(-23).next_multiple_of(&BigInt::from(8)), BigInt::from(-16) ); assert_eq!( BigInt::from(-16).next_multiple_of(&BigInt::from(-8)), BigInt::from(-16) ); assert_eq!( BigInt::from(-23).next_multiple_of(&BigInt::from(-8)), BigInt::from(-24) ); } #[test] fn test_prev_multiple_of() { assert_eq!( BigInt::from(16).prev_multiple_of(&BigInt::from(8)), BigInt::from(16) ); assert_eq!( BigInt::from(23).prev_multiple_of(&BigInt::from(8)), BigInt::from(16) ); assert_eq!( BigInt::from(16).prev_multiple_of(&BigInt::from(-8)), BigInt::from(16) ); assert_eq!( BigInt::from(23).prev_multiple_of(&BigInt::from(-8)), BigInt::from(24) ); assert_eq!( BigInt::from(-16).prev_multiple_of(&BigInt::from(8)), BigInt::from(-16) ); assert_eq!( BigInt::from(-23).prev_multiple_of(&BigInt::from(8)), BigInt::from(-24) ); assert_eq!( BigInt::from(-16).prev_multiple_of(&BigInt::from(-8)), BigInt::from(-16) ); assert_eq!( BigInt::from(-23).prev_multiple_of(&BigInt::from(-8)), BigInt::from(-16) ); } #[test] fn test_abs_sub() { let zero: BigInt = Zero::zero(); let one: BigInt = One::one(); assert_eq!((-&one).abs_sub(&one), zero); let one: BigInt = One::one(); let zero: BigInt = Zero::zero(); assert_eq!(one.abs_sub(&one), zero); let one: BigInt = One::one(); let zero: BigInt = Zero::zero(); assert_eq!(one.abs_sub(&zero), one); let one: BigInt = One::one(); let two: BigInt = FromPrimitive::from_isize(2).unwrap(); assert_eq!(one.abs_sub(&-&one), two); } #[test] fn test_from_str_radix() { fn check(s: &str, ans: Option) { let ans = ans.map(|n| { let x: BigInt = FromPrimitive::from_isize(n).unwrap(); x }); assert_eq!(BigInt::from_str_radix(s, 10).ok(), ans); } check("10", Some(10)); check("1", Some(1)); check("0", Some(0)); check("-1", Some(-1)); check("-10", Some(-10)); check("+10", Some(10)); check("--7", None); check("++5", None); check("+-9", None); check("-+3", None); check("Z", None); check("_", None); // issue 10522, this hit an edge case that caused it to // attempt to allocate a vector of size (-1u) == huge. let x: BigInt = format!("1{}", repeat("0").take(36).collect::()) .parse() .unwrap(); let _y = x.to_string(); } #[test] fn test_lower_hex() { let a = BigInt::parse_bytes(b"A", 16).unwrap(); let hello = BigInt::parse_bytes(b"-22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{:x}", a), "a"); assert_eq!(format!("{:x}", hello), "-48656c6c6f20776f726c6421"); assert_eq!(format!("{:♥>+#8x}", a), "♥♥♥♥+0xa"); } #[test] fn test_upper_hex() { let a = BigInt::parse_bytes(b"A", 16).unwrap(); let hello = BigInt::parse_bytes(b"-22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{:X}", a), "A"); assert_eq!(format!("{:X}", hello), "-48656C6C6F20776F726C6421"); assert_eq!(format!("{:♥>+#8X}", a), "♥♥♥♥+0xA"); } #[test] fn test_binary() { let a = BigInt::parse_bytes(b"A", 16).unwrap(); let hello = BigInt::parse_bytes(b"-224055342307539", 10).unwrap(); assert_eq!(format!("{:b}", a), "1010"); assert_eq!( format!("{:b}", hello), "-110010111100011011110011000101101001100011010011" ); assert_eq!(format!("{:♥>+#8b}", a), "♥+0b1010"); } #[test] fn test_octal() { let a = BigInt::parse_bytes(b"A", 16).unwrap(); let hello = BigInt::parse_bytes(b"-22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{:o}", a), "12"); assert_eq!(format!("{:o}", hello), "-22062554330674403566756233062041"); assert_eq!(format!("{:♥>+#8o}", a), "♥♥♥+0o12"); } #[test] fn test_display() { let a = BigInt::parse_bytes(b"A", 16).unwrap(); let hello = BigInt::parse_bytes(b"-22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{}", a), "10"); assert_eq!(format!("{}", hello), "-22405534230753963835153736737"); assert_eq!(format!("{:♥>+#8}", a), "♥♥♥♥♥+10"); } #[test] fn test_neg() { assert!(-BigInt::new(Plus, vec![1, 1, 1]) == BigInt::new(Minus, vec![1, 1, 1])); assert!(-BigInt::new(Minus, vec![1, 1, 1]) == BigInt::new(Plus, vec![1, 1, 1])); let zero: BigInt = Zero::zero(); assert_eq!(-&zero, zero); } #[test] fn test_negative_shr() { assert_eq!(BigInt::from(-1) >> 1, BigInt::from(-1)); assert_eq!(BigInt::from(-2) >> 1, BigInt::from(-1)); assert_eq!(BigInt::from(-3) >> 1, BigInt::from(-2)); assert_eq!(BigInt::from(-3) >> 2, BigInt::from(-1)); } #[test] fn test_iter_sum() { let result: BigInt = FromPrimitive::from_isize(-1234567).unwrap(); let data: Vec = vec![ FromPrimitive::from_i32(-1000000).unwrap(), FromPrimitive::from_i32(-200000).unwrap(), FromPrimitive::from_i32(-30000).unwrap(), FromPrimitive::from_i32(-4000).unwrap(), FromPrimitive::from_i32(-500).unwrap(), FromPrimitive::from_i32(-60).unwrap(), FromPrimitive::from_i32(-7).unwrap(), ]; assert_eq!(result, data.iter().sum::()); assert_eq!(result, data.into_iter().sum::()); } #[test] fn test_iter_product() { let data: Vec = vec![ FromPrimitive::from_i32(1001).unwrap(), FromPrimitive::from_i32(-1002).unwrap(), FromPrimitive::from_i32(1003).unwrap(), FromPrimitive::from_i32(-1004).unwrap(), FromPrimitive::from_i32(1005).unwrap(), ]; let result = data.get(0).unwrap() * data.get(1).unwrap() * data.get(2).unwrap() * data.get(3).unwrap() * data.get(4).unwrap(); assert_eq!(result, data.iter().product::()); assert_eq!(result, data.into_iter().product::()); } #[test] fn test_iter_sum_generic() { let result: BigInt = FromPrimitive::from_isize(-1234567).unwrap(); let data = vec![-1000000, -200000, -30000, -4000, -500, -60, -7]; assert_eq!(result, data.iter().sum::()); assert_eq!(result, data.into_iter().sum::()); } #[test] fn test_iter_product_generic() { let data = vec![1001, -1002, 1003, -1004, 1005]; let result = data[0].to_bigint().unwrap() * data[1].to_bigint().unwrap() * data[2].to_bigint().unwrap() * data[3].to_bigint().unwrap() * data[4].to_bigint().unwrap(); assert_eq!(result, data.iter().product::()); assert_eq!(result, data.into_iter().product::()); } #[test] fn test_pow() { let one = BigInt::from(1i32); let two = BigInt::from(2i32); let four = BigInt::from(4i32); let eight = BigInt::from(8i32); let minus_two = BigInt::from(-2i32); macro_rules! check { ($t:ty) => { assert_eq!(Pow::pow(&two, 0 as $t), one); assert_eq!(Pow::pow(&two, 1 as $t), two); assert_eq!(Pow::pow(&two, 2 as $t), four); assert_eq!(Pow::pow(&two, 3 as $t), eight); assert_eq!(Pow::pow(&two, &(3 as $t)), eight); assert_eq!(Pow::pow(&minus_two, 0 as $t), one, "-2^0"); assert_eq!(Pow::pow(&minus_two, 1 as $t), minus_two, "-2^1"); assert_eq!(Pow::pow(&minus_two, 2 as $t), four, "-2^2"); assert_eq!(Pow::pow(&minus_two, 3 as $t), -&eight, "-2^3"); }; } check!(u8); check!(u16); check!(u32); check!(u64); check!(usize); let pow_1e10000 = BigInt::from(10u32).pow(10_000_u32); let manual_1e10000 = repeat(10u32).take(10_000).product::(); assert!(manual_1e10000 == pow_1e10000); } #[test] fn test_bit() { // 12 = (1100)_2 assert!(!BigInt::from(0b1100u8).bit(0)); assert!(!BigInt::from(0b1100u8).bit(1)); assert!(BigInt::from(0b1100u8).bit(2)); assert!(BigInt::from(0b1100u8).bit(3)); assert!(!BigInt::from(0b1100u8).bit(4)); assert!(!BigInt::from(0b1100u8).bit(200)); assert!(!BigInt::from(0b1100u8).bit(u64::MAX)); // -12 = (...110100)_2 assert!(!BigInt::from(-12i8).bit(0)); assert!(!BigInt::from(-12i8).bit(1)); assert!(BigInt::from(-12i8).bit(2)); assert!(!BigInt::from(-12i8).bit(3)); assert!(BigInt::from(-12i8).bit(4)); assert!(BigInt::from(-12i8).bit(200)); assert!(BigInt::from(-12i8).bit(u64::MAX)); } #[test] fn test_set_bit() { let mut x: BigInt; // zero x = BigInt::zero(); x.set_bit(200, true); assert_eq!(x, BigInt::one() << 200); x = BigInt::zero(); x.set_bit(200, false); assert_eq!(x, BigInt::zero()); // positive numbers x = BigInt::from_biguint(Plus, BigUint::one() << 200); x.set_bit(10, true); x.set_bit(200, false); assert_eq!(x, BigInt::one() << 10); x.set_bit(10, false); x.set_bit(5, false); assert_eq!(x, BigInt::zero()); // negative numbers x = BigInt::from(-12i8); x.set_bit(200, true); assert_eq!(x, BigInt::from(-12i8)); x.set_bit(200, false); assert_eq!( x, BigInt::from_biguint(Minus, BigUint::from(12u8) | (BigUint::one() << 200)) ); x.set_bit(6, false); assert_eq!( x, BigInt::from_biguint(Minus, BigUint::from(76u8) | (BigUint::one() << 200)) ); x.set_bit(6, true); assert_eq!( x, BigInt::from_biguint(Minus, BigUint::from(12u8) | (BigUint::one() << 200)) ); x.set_bit(200, true); assert_eq!(x, BigInt::from(-12i8)); x = BigInt::from_biguint(Minus, BigUint::one() << 30); x.set_bit(10, true); assert_eq!( x, BigInt::from_biguint(Minus, (BigUint::one() << 30) - (BigUint::one() << 10)) ); x = BigInt::from_biguint(Minus, BigUint::one() << 200); x.set_bit(40, true); assert_eq!( x, BigInt::from_biguint(Minus, (BigUint::one() << 200) - (BigUint::one() << 40)) ); x = BigInt::from_biguint(Minus, (BigUint::one() << 200) | (BigUint::one() << 100)); x.set_bit(100, false); assert_eq!( x, BigInt::from_biguint(Minus, (BigUint::one() << 200) | (BigUint::one() << 101)) ); x = BigInt::from_biguint(Minus, (BigUint::one() << 63) | (BigUint::one() << 62)); x.set_bit(62, false); assert_eq!(x, BigInt::from_biguint(Minus, BigUint::one() << 64)); x = BigInt::from_biguint(Minus, (BigUint::one() << 200) - BigUint::one()); x.set_bit(0, false); assert_eq!(x, BigInt::from_biguint(Minus, BigUint::one() << 200)); } num-bigint-0.4.3/tests/bigint_bitwise.rs000064400000000000000000000117430072674642500164510ustar 00000000000000use num_bigint::{BigInt, Sign, ToBigInt}; use num_traits::ToPrimitive; use std::{i32, i64, u32}; enum ValueVec { N, P(&'static [u32]), M(&'static [u32]), } use crate::ValueVec::*; impl ToBigInt for ValueVec { fn to_bigint(&self) -> Option { 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); } } } num-bigint-0.4.3/tests/bigint_scalar.rs000064400000000000000000000110530072674642500162420ustar 00000000000000use 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(); } num-bigint-0.4.3/tests/biguint.rs000064400000000000000000001661630072674642500151170ustar 00000000000000use num_bigint::Sign::Plus; use num_bigint::{BigInt, ToBigInt}; use num_bigint::{BigUint, ToBigUint}; use num_integer::Integer; use std::cmp::Ordering::{Equal, Greater, Less}; use std::collections::hash_map::RandomState; use std::hash::{BuildHasher, Hash, Hasher}; use std::i64; use std::iter::repeat; use std::str::FromStr; use std::{f32, f64}; use std::{i128, u128}; use std::{u16, u32, u64, u8, usize}; use num_traits::{ pow, CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, FromPrimitive, Num, One, Pow, ToPrimitive, Zero, }; mod consts; use crate::consts::*; #[macro_use] mod macros; #[test] fn test_from_bytes_be() { fn check(s: &str, result: &str) { assert_eq!( BigUint::from_bytes_be(s.as_bytes()), BigUint::parse_bytes(result.as_bytes(), 10).unwrap() ); } check("A", "65"); check("AA", "16705"); check("AB", "16706"); check("Hello world!", "22405534230753963835153736737"); assert_eq!(BigUint::from_bytes_be(&[]), BigUint::zero()); } #[test] fn test_to_bytes_be() { fn check(s: &str, result: &str) { let b = BigUint::parse_bytes(result.as_bytes(), 10).unwrap(); assert_eq!(b.to_bytes_be(), s.as_bytes()); } check("A", "65"); check("AA", "16705"); check("AB", "16706"); check("Hello world!", "22405534230753963835153736737"); let b: BigUint = Zero::zero(); assert_eq!(b.to_bytes_be(), [0]); // Test with leading/trailing zero bytes and a full BigDigit of value 0 let b = BigUint::from_str_radix("00010000000000000200", 16).unwrap(); assert_eq!(b.to_bytes_be(), [1, 0, 0, 0, 0, 0, 0, 2, 0]); } #[test] fn test_from_bytes_le() { fn check(s: &str, result: &str) { assert_eq!( BigUint::from_bytes_le(s.as_bytes()), BigUint::parse_bytes(result.as_bytes(), 10).unwrap() ); } check("A", "65"); check("AA", "16705"); check("BA", "16706"); check("!dlrow olleH", "22405534230753963835153736737"); assert_eq!(BigUint::from_bytes_le(&[]), BigUint::zero()); } #[test] fn test_to_bytes_le() { fn check(s: &str, result: &str) { let b = BigUint::parse_bytes(result.as_bytes(), 10).unwrap(); assert_eq!(b.to_bytes_le(), s.as_bytes()); } check("A", "65"); check("AA", "16705"); check("BA", "16706"); check("!dlrow olleH", "22405534230753963835153736737"); let b: BigUint = Zero::zero(); assert_eq!(b.to_bytes_le(), [0]); // Test with leading/trailing zero bytes and a full BigDigit of value 0 let b = BigUint::from_str_radix("00010000000000000200", 16).unwrap(); assert_eq!(b.to_bytes_le(), [0, 2, 0, 0, 0, 0, 0, 0, 1]); } #[test] fn test_cmp() { let data: [&[_]; 7] = [&[], &[1], &[2], &[!0], &[0, 1], &[2, 1], &[1, 1, 1]]; let data: Vec = data.iter().map(|v| BigUint::from_slice(*v)).collect(); for (i, ni) in data.iter().enumerate() { for (j0, nj) in data[i..].iter().enumerate() { let j = j0 + i; if i == j { assert_eq!(ni.cmp(nj), Equal); assert_eq!(nj.cmp(ni), Equal); assert_eq!(ni, nj); assert!(!(ni != nj)); assert!(ni <= nj); assert!(ni >= nj); assert!(!(ni < nj)); assert!(!(ni > nj)); } else { assert_eq!(ni.cmp(nj), Less); assert_eq!(nj.cmp(ni), Greater); assert!(!(ni == nj)); assert!(ni != nj); assert!(ni <= nj); assert!(!(ni >= nj)); assert!(ni < nj); assert!(!(ni > nj)); assert!(!(nj <= ni)); assert!(nj >= ni); assert!(!(nj < ni)); assert!(nj > ni); } } } } fn hash(x: &T) -> u64 { let mut hasher = ::Hasher::new(); x.hash(&mut hasher); hasher.finish() } #[test] fn test_hash() { use crate::hash; let a = BigUint::new(vec![]); let b = BigUint::new(vec![0]); let c = BigUint::new(vec![1]); let d = BigUint::new(vec![1, 0, 0, 0, 0, 0]); let e = BigUint::new(vec![0, 0, 0, 0, 0, 1]); assert!(hash(&a) == hash(&b)); assert!(hash(&b) != hash(&c)); assert!(hash(&c) == hash(&d)); assert!(hash(&d) != hash(&e)); } // LEFT, RIGHT, AND, OR, XOR const BIT_TESTS: &[(&[u32], &[u32], &[u32], &[u32], &[u32])] = &[ (&[], &[], &[], &[], &[]), (&[1, 0, 1], &[1, 1], &[1], &[1, 1, 1], &[0, 1, 1]), (&[1, 0, 1], &[0, 1, 1], &[0, 0, 1], &[1, 1, 1], &[1, 1]), ( &[268, 482, 17], &[964, 54], &[260, 34], &[972, 502, 17], &[712, 468, 17], ), ]; #[test] fn test_bitand() { for elm in BIT_TESTS { 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); assert_op!(a & b == c); assert_op!(b & a == c); assert_assign_op!(a &= b == c); assert_assign_op!(b &= a == c); } } #[test] fn test_bitor() { for elm in BIT_TESTS { 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); assert_op!(a | b == c); assert_op!(b | a == c); assert_assign_op!(a |= b == c); assert_assign_op!(b |= a == c); } } #[test] fn test_bitxor() { for elm in BIT_TESTS { 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); assert_op!(a ^ b == c); assert_op!(b ^ a == c); assert_op!(a ^ c == b); assert_op!(c ^ a == b); assert_op!(b ^ c == a); assert_op!(c ^ b == a); assert_assign_op!(a ^= b == c); assert_assign_op!(b ^= a == c); assert_assign_op!(a ^= c == b); assert_assign_op!(c ^= a == b); assert_assign_op!(b ^= c == a); assert_assign_op!(c ^= b == a); } } #[test] fn test_shl() { fn check(s: &str, shift: usize, ans: &str) { let opt_biguint = BigUint::from_str_radix(s, 16).ok(); let mut bu_assign = opt_biguint.unwrap(); let bu = (bu_assign.clone() << shift).to_str_radix(16); assert_eq!(bu, ans); bu_assign <<= shift; assert_eq!(bu_assign.to_str_radix(16), ans); } check("0", 3, "0"); check("1", 3, "8"); check( "1\ 0000\ 0000\ 0000\ 0001\ 0000\ 0000\ 0000\ 0001", 3, "8\ 0000\ 0000\ 0000\ 0008\ 0000\ 0000\ 0000\ 0008", ); check( "1\ 0000\ 0001\ 0000\ 0001", 2, "4\ 0000\ 0004\ 0000\ 0004", ); check( "1\ 0001\ 0001", 1, "2\ 0002\ 0002", ); check( "\ 4000\ 0000\ 0000\ 0000", 3, "2\ 0000\ 0000\ 0000\ 0000", ); check( "4000\ 0000", 2, "1\ 0000\ 0000", ); check( "4000", 2, "1\ 0000", ); check( "4000\ 0000\ 0000\ 0000", 67, "2\ 0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0000", ); check( "4000\ 0000", 35, "2\ 0000\ 0000\ 0000\ 0000", ); check( "4000", 19, "2\ 0000\ 0000", ); check( "fedc\ ba98\ 7654\ 3210\ fedc\ ba98\ 7654\ 3210", 4, "f\ edcb\ a987\ 6543\ 210f\ edcb\ a987\ 6543\ 2100", ); check( "88887777666655554444333322221111", 16, "888877776666555544443333222211110000", ); } #[test] fn test_shr() { fn check(s: &str, shift: usize, ans: &str) { let opt_biguint = BigUint::from_str_radix(s, 16).ok(); let mut bu_assign = opt_biguint.unwrap(); let bu = (bu_assign.clone() >> shift).to_str_radix(16); assert_eq!(bu, ans); bu_assign >>= shift; assert_eq!(bu_assign.to_str_radix(16), ans); } check("0", 3, "0"); check("f", 3, "1"); check( "1\ 0000\ 0000\ 0000\ 0001\ 0000\ 0000\ 0000\ 0001", 3, "2000\ 0000\ 0000\ 0000\ 2000\ 0000\ 0000\ 0000", ); check( "1\ 0000\ 0001\ 0000\ 0001", 2, "4000\ 0000\ 4000\ 0000", ); check( "1\ 0001\ 0001", 1, "8000\ 8000", ); check( "2\ 0000\ 0000\ 0000\ 0001\ 0000\ 0000\ 0000\ 0001", 67, "4000\ 0000\ 0000\ 0000", ); check( "2\ 0000\ 0001\ 0000\ 0001", 35, "4000\ 0000", ); check( "2\ 0001\ 0001", 19, "4000", ); check( "1\ 0000\ 0000\ 0000\ 0000", 1, "8000\ 0000\ 0000\ 0000", ); check( "1\ 0000\ 0000", 1, "8000\ 0000", ); check( "1\ 0000", 1, "8000", ); check( "f\ edcb\ a987\ 6543\ 210f\ edcb\ a987\ 6543\ 2100", 4, "fedc\ ba98\ 7654\ 3210\ fedc\ ba98\ 7654\ 3210", ); check( "888877776666555544443333222211110000", 16, "88887777666655554444333322221111", ); } // `DoubleBigDigit` size dependent #[test] fn test_convert_i64() { fn check(b1: BigUint, i: i64) { let b2: BigUint = FromPrimitive::from_i64(i).unwrap(); assert_eq!(b1, b2); assert_eq!(b1.to_i64().unwrap(), i); } check(Zero::zero(), 0); check(One::one(), 1); check(i64::MAX.to_biguint().unwrap(), i64::MAX); check(BigUint::new(vec![]), 0); check(BigUint::new(vec![1]), 1); check(BigUint::new(vec![N1]), (1 << 32) - 1); check(BigUint::new(vec![0, 1]), 1 << 32); check(BigUint::new(vec![N1, N1 >> 1]), i64::MAX); assert_eq!(i64::MIN.to_biguint(), None); assert_eq!(BigUint::new(vec![N1, N1]).to_i64(), None); assert_eq!(BigUint::new(vec![0, 0, 1]).to_i64(), None); assert_eq!(BigUint::new(vec![N1, N1, N1]).to_i64(), None); } #[test] fn test_convert_i128() { fn check(b1: BigUint, i: i128) { let b2: BigUint = FromPrimitive::from_i128(i).unwrap(); assert_eq!(b1, b2); assert_eq!(b1.to_i128().unwrap(), i); } check(Zero::zero(), 0); check(One::one(), 1); check(i128::MAX.to_biguint().unwrap(), i128::MAX); check(BigUint::new(vec![]), 0); check(BigUint::new(vec![1]), 1); check(BigUint::new(vec![N1]), (1 << 32) - 1); check(BigUint::new(vec![0, 1]), 1 << 32); check(BigUint::new(vec![N1, N1, N1, N1 >> 1]), i128::MAX); assert_eq!(i128::MIN.to_biguint(), None); assert_eq!(BigUint::new(vec![N1, N1, N1, N1]).to_i128(), None); assert_eq!(BigUint::new(vec![0, 0, 0, 0, 1]).to_i128(), None); assert_eq!(BigUint::new(vec![N1, N1, N1, N1, N1]).to_i128(), None); } // `DoubleBigDigit` size dependent #[test] fn test_convert_u64() { fn check(b1: BigUint, u: u64) { let b2: BigUint = FromPrimitive::from_u64(u).unwrap(); assert_eq!(b1, b2); assert_eq!(b1.to_u64().unwrap(), u); } check(Zero::zero(), 0); check(One::one(), 1); check(u64::MIN.to_biguint().unwrap(), u64::MIN); check(u64::MAX.to_biguint().unwrap(), u64::MAX); check(BigUint::new(vec![]), 0); check(BigUint::new(vec![1]), 1); check(BigUint::new(vec![N1]), (1 << 32) - 1); check(BigUint::new(vec![0, 1]), 1 << 32); check(BigUint::new(vec![N1, N1]), u64::MAX); assert_eq!(BigUint::new(vec![0, 0, 1]).to_u64(), None); assert_eq!(BigUint::new(vec![N1, N1, N1]).to_u64(), None); } #[test] fn test_convert_u128() { fn check(b1: BigUint, u: u128) { let b2: BigUint = FromPrimitive::from_u128(u).unwrap(); assert_eq!(b1, b2); assert_eq!(b1.to_u128().unwrap(), u); } check(Zero::zero(), 0); check(One::one(), 1); check(u128::MIN.to_biguint().unwrap(), u128::MIN); check(u128::MAX.to_biguint().unwrap(), u128::MAX); check(BigUint::new(vec![]), 0); check(BigUint::new(vec![1]), 1); check(BigUint::new(vec![N1]), (1 << 32) - 1); check(BigUint::new(vec![0, 1]), 1 << 32); check(BigUint::new(vec![N1, N1, N1, N1]), u128::MAX); assert_eq!(BigUint::new(vec![0, 0, 0, 0, 1]).to_u128(), None); assert_eq!(BigUint::new(vec![N1, N1, N1, N1, N1]).to_u128(), None); } #[test] #[allow(clippy::float_cmp)] fn test_convert_f32() { fn check(b1: &BigUint, f: f32) { let b2 = BigUint::from_f32(f).unwrap(); assert_eq!(b1, &b2); assert_eq!(b1.to_f32().unwrap(), f); } check(&BigUint::zero(), 0.0); check(&BigUint::one(), 1.0); check(&BigUint::from(u16::MAX), pow(2.0_f32, 16) - 1.0); check(&BigUint::from(1u64 << 32), pow(2.0_f32, 32)); check(&BigUint::from_slice(&[0, 0, 1]), pow(2.0_f32, 64)); check( &((BigUint::one() << 100) + (BigUint::one() << 123)), pow(2.0_f32, 100) + pow(2.0_f32, 123), ); check(&(BigUint::one() << 127), pow(2.0_f32, 127)); check(&(BigUint::from((1u64 << 24) - 1) << (128 - 24)), f32::MAX); // keeping all 24 digits with the bits at different offsets to the BigDigits let x: u32 = 0b00000000101111011111011011011101; let mut f = x as f32; let mut b = BigUint::from(x); for _ in 0..64 { check(&b, f); f *= 2.0; b <<= 1; } // this number when rounded to f64 then f32 isn't the same as when rounded straight to f32 let n: u64 = 0b0000000000111111111111111111111111011111111111111111111111111111; assert!((n as f64) as f32 != n as f32); assert_eq!(BigUint::from(n).to_f32(), Some(n as f32)); // test rounding up with the bits at different offsets to the BigDigits let mut f = ((1u64 << 25) - 1) as f32; let mut b = BigUint::from(1u64 << 25); for _ in 0..64 { assert_eq!(b.to_f32(), Some(f)); f *= 2.0; b <<= 1; } // rounding assert_eq!(BigUint::from_f32(-1.0), None); assert_eq!(BigUint::from_f32(-0.99999), Some(BigUint::zero())); assert_eq!(BigUint::from_f32(-0.5), Some(BigUint::zero())); assert_eq!(BigUint::from_f32(-0.0), Some(BigUint::zero())); assert_eq!( BigUint::from_f32(f32::MIN_POSITIVE / 2.0), Some(BigUint::zero()) ); assert_eq!(BigUint::from_f32(f32::MIN_POSITIVE), Some(BigUint::zero())); assert_eq!(BigUint::from_f32(0.5), Some(BigUint::zero())); assert_eq!(BigUint::from_f32(0.99999), Some(BigUint::zero())); assert_eq!(BigUint::from_f32(f32::consts::E), Some(BigUint::from(2u32))); assert_eq!( BigUint::from_f32(f32::consts::PI), Some(BigUint::from(3u32)) ); // special float values assert_eq!(BigUint::from_f32(f32::NAN), None); assert_eq!(BigUint::from_f32(f32::INFINITY), None); assert_eq!(BigUint::from_f32(f32::NEG_INFINITY), None); assert_eq!(BigUint::from_f32(f32::MIN), None); // largest BigUint that will round to a finite f32 value let big_num = (BigUint::one() << 128u8) - 1u8 - (BigUint::one() << (128u8 - 25)); assert_eq!(big_num.to_f32(), Some(f32::MAX)); assert_eq!((big_num + 1u8).to_f32(), Some(f32::INFINITY)); assert_eq!( ((BigUint::one() << 128u8) - 1u8).to_f32(), Some(f32::INFINITY) ); assert_eq!((BigUint::one() << 128u8).to_f32(), Some(f32::INFINITY)); } #[test] #[allow(clippy::float_cmp)] fn test_convert_f64() { fn check(b1: &BigUint, f: f64) { let b2 = BigUint::from_f64(f).unwrap(); assert_eq!(b1, &b2); assert_eq!(b1.to_f64().unwrap(), f); } check(&BigUint::zero(), 0.0); check(&BigUint::one(), 1.0); check(&BigUint::from(u32::MAX), pow(2.0_f64, 32) - 1.0); check(&BigUint::from(1u64 << 32), pow(2.0_f64, 32)); check(&BigUint::from_slice(&[0, 0, 1]), pow(2.0_f64, 64)); check( &((BigUint::one() << 100) + (BigUint::one() << 152)), pow(2.0_f64, 100) + pow(2.0_f64, 152), ); check(&(BigUint::one() << 1023), pow(2.0_f64, 1023)); check(&(BigUint::from((1u64 << 53) - 1) << (1024 - 53)), f64::MAX); // keeping all 53 digits with the bits at different offsets to the BigDigits let x: u64 = 0b0000000000011110111110110111111101110111101111011111011011011101; let mut f = x as f64; let mut b = BigUint::from(x); for _ in 0..128 { check(&b, f); f *= 2.0; b <<= 1; } // test rounding up with the bits at different offsets to the BigDigits let mut f = ((1u64 << 54) - 1) as f64; let mut b = BigUint::from(1u64 << 54); for _ in 0..128 { assert_eq!(b.to_f64(), Some(f)); f *= 2.0; b <<= 1; } // rounding assert_eq!(BigUint::from_f64(-1.0), None); assert_eq!(BigUint::from_f64(-0.99999), Some(BigUint::zero())); assert_eq!(BigUint::from_f64(-0.5), Some(BigUint::zero())); assert_eq!(BigUint::from_f64(-0.0), Some(BigUint::zero())); assert_eq!( BigUint::from_f64(f64::MIN_POSITIVE / 2.0), Some(BigUint::zero()) ); assert_eq!(BigUint::from_f64(f64::MIN_POSITIVE), Some(BigUint::zero())); assert_eq!(BigUint::from_f64(0.5), Some(BigUint::zero())); assert_eq!(BigUint::from_f64(0.99999), Some(BigUint::zero())); assert_eq!(BigUint::from_f64(f64::consts::E), Some(BigUint::from(2u32))); assert_eq!( BigUint::from_f64(f64::consts::PI), Some(BigUint::from(3u32)) ); // special float values assert_eq!(BigUint::from_f64(f64::NAN), None); assert_eq!(BigUint::from_f64(f64::INFINITY), None); assert_eq!(BigUint::from_f64(f64::NEG_INFINITY), None); assert_eq!(BigUint::from_f64(f64::MIN), None); // largest BigUint that will round to a finite f64 value let big_num = (BigUint::one() << 1024u16) - 1u8 - (BigUint::one() << (1024u16 - 54)); assert_eq!(big_num.to_f64(), Some(f64::MAX)); assert_eq!((big_num + 1u8).to_f64(), Some(f64::INFINITY)); assert_eq!( ((BigUint::one() << 1024u16) - 1u8).to_f64(), Some(f64::INFINITY) ); assert_eq!((BigUint::one() << 1024u16).to_f64(), Some(f64::INFINITY)); } #[test] fn test_convert_to_bigint() { fn check(n: BigUint, ans: BigInt) { assert_eq!(n.to_bigint().unwrap(), ans); assert_eq!(n.to_bigint().unwrap().to_biguint().unwrap(), n); } check(Zero::zero(), Zero::zero()); check( BigUint::new(vec![1, 2, 3]), BigInt::from_biguint(Plus, BigUint::new(vec![1, 2, 3])), ); } #[test] fn test_convert_from_uint() { macro_rules! check { ($ty:ident, $max:expr) => { assert_eq!(BigUint::from($ty::zero()), BigUint::zero()); assert_eq!(BigUint::from($ty::one()), BigUint::one()); assert_eq!(BigUint::from($ty::MAX - $ty::one()), $max - BigUint::one()); assert_eq!(BigUint::from($ty::MAX), $max); }; } check!(u8, BigUint::from_slice(&[u8::MAX as u32])); check!(u16, BigUint::from_slice(&[u16::MAX as u32])); check!(u32, BigUint::from_slice(&[u32::MAX])); check!(u64, BigUint::from_slice(&[u32::MAX, u32::MAX])); check!( u128, BigUint::from_slice(&[u32::MAX, u32::MAX, u32::MAX, u32::MAX]) ); check!(usize, BigUint::from(usize::MAX as u64)); } #[test] fn test_add() { 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); assert_op!(a + b == c); assert_op!(b + a == c); assert_assign_op!(a += b == c); assert_assign_op!(b += a == c); } } #[test] fn test_sub() { 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); assert_op!(c - a == b); assert_op!(c - b == a); assert_assign_op!(c -= a == b); assert_assign_op!(c -= b == a); } } #[test] #[should_panic] fn test_sub_fail_on_underflow() { let (a, b): (BigUint, BigUint) = (Zero::zero(), One::one()); let _ = a - b; } #[test] fn test_mul() { 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); assert_op!(a * b == c); assert_op!(b * a == c); assert_assign_op!(a *= b == c); assert_assign_op!(b *= a == c); } 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); assert!(a == &b * &c + &d); assert!(a == &c * &b + &d); } } #[test] fn test_div_rem() { 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() { assert_op!(c / a == b); assert_op!(c % a == BigUint::zero()); assert_assign_op!(c /= a == b); assert_assign_op!(c %= a == BigUint::zero()); assert_eq!(c.div_rem(&a), (b.clone(), BigUint::zero())); } if !b.is_zero() { assert_op!(c / b == a); assert_op!(c % b == BigUint::zero()); assert_assign_op!(c /= b == a); assert_assign_op!(c %= b == BigUint::zero()); assert_eq!(c.div_rem(&b), (a.clone(), BigUint::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() { assert_op!(a / b == c); assert_op!(a % b == d); assert_assign_op!(a /= b == c); assert_assign_op!(a %= b == d); assert!(a.div_rem(&b) == (c, d)); } } } #[test] fn test_div_rem_big_multiple() { let a = BigUint::from(3u32).pow(100u32); let a2 = &a * &a; let (div, rem) = a2.div_rem(&a); assert_eq!(div, a); assert!(rem.is_zero()); let (div, rem) = (&a2 - 1u32).div_rem(&a); assert_eq!(div, &a - 1u32); assert_eq!(rem, &a - 1u32); } #[test] fn test_div_ceil() { fn check(a: &BigUint, b: &BigUint, d: &BigUint, m: &BigUint) { if m.is_zero() { assert_eq!(a.div_ceil(b), *d); } else { assert_eq!(a.div_ceil(b), d + 1u32); } } 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); } } } #[test] fn test_checked_add() { 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); assert!(a.checked_add(&b).unwrap() == c); assert!(b.checked_add(&a).unwrap() == c); } } #[test] fn test_checked_sub() { 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); assert!(c.checked_sub(&a).unwrap() == b); assert!(c.checked_sub(&b).unwrap() == a); if a > c { assert!(a.checked_sub(&c).is_none()); } if b > c { assert!(b.checked_sub(&c).is_none()); } } } #[test] fn test_checked_mul() { 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); assert!(a.checked_mul(&b).unwrap() == c); assert!(b.checked_mul(&a).unwrap() == c); } 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); assert!(a == b.checked_mul(&c).unwrap() + &d); assert!(a == c.checked_mul(&b).unwrap() + &d); } } #[test] fn test_mul_overflow() { // Test for issue #187 - overflow due to mac3 incorrectly sizing temporary let s = "5311379928167670986895882065524686273295931177270319231994441382\ 0040355986085224273916250223263671004753755210595137000079652876\ 0829212940754539968588340162273730474622005920097370111"; let a: BigUint = s.parse().unwrap(); let b = a.clone(); let _ = a.checked_mul(&b); } #[test] fn test_mul_overflow_2() { // Try a bunch of sizes that are right on the edge of multiplication length // overflow, where (x * x).data.len() == 2 * x.data.len() + 1. for i in 1u8..20 { let bits = 1u32 << i; let x = (BigUint::one() << bits) - 1u32; let x2 = (BigUint::one() << (2 * bits)) - &x - &x - 1u32; assert_eq!(&x * &x, x2); } } #[test] fn test_checked_div() { 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() { assert!(c.checked_div(&a).unwrap() == b); } if !b.is_zero() { assert!(c.checked_div(&b).unwrap() == a); } assert!(c.checked_div(&Zero::zero()).is_none()); } } #[test] fn test_gcd() { fn check(a: usize, b: usize, c: usize) { let big_a: BigUint = FromPrimitive::from_usize(a).unwrap(); let big_b: BigUint = FromPrimitive::from_usize(b).unwrap(); let big_c: BigUint = FromPrimitive::from_usize(c).unwrap(); assert_eq!(big_a.gcd(&big_b), big_c); assert_eq!(big_a.gcd_lcm(&big_b).0, big_c); } check(10, 2, 2); check(10, 3, 1); check(0, 3, 3); check(3, 3, 3); check(56, 42, 14); } #[test] fn test_lcm() { fn check(a: usize, b: usize, c: usize) { let big_a: BigUint = FromPrimitive::from_usize(a).unwrap(); let big_b: BigUint = FromPrimitive::from_usize(b).unwrap(); let big_c: BigUint = FromPrimitive::from_usize(c).unwrap(); assert_eq!(big_a.lcm(&big_b), big_c); assert_eq!(big_a.gcd_lcm(&big_b).1, big_c); } check(0, 0, 0); check(1, 0, 0); check(0, 1, 0); check(1, 1, 1); check(8, 9, 72); check(11, 5, 55); check(99, 17, 1683); } #[test] fn test_next_multiple_of() { assert_eq!( BigUint::from(16u32).next_multiple_of(&BigUint::from(8u32)), BigUint::from(16u32) ); assert_eq!( BigUint::from(23u32).next_multiple_of(&BigUint::from(8u32)), BigUint::from(24u32) ); } #[test] fn test_prev_multiple_of() { assert_eq!( BigUint::from(16u32).prev_multiple_of(&BigUint::from(8u32)), BigUint::from(16u32) ); assert_eq!( BigUint::from(23u32).prev_multiple_of(&BigUint::from(8u32)), BigUint::from(16u32) ); } #[test] fn test_is_even() { let one: BigUint = FromStr::from_str("1").unwrap(); let two: BigUint = FromStr::from_str("2").unwrap(); let thousand: BigUint = FromStr::from_str("1000").unwrap(); let big: BigUint = FromStr::from_str("1000000000000000000000").unwrap(); let bigger: BigUint = FromStr::from_str("1000000000000000000001").unwrap(); assert!(one.is_odd()); assert!(two.is_even()); assert!(thousand.is_even()); assert!(big.is_even()); assert!(bigger.is_odd()); assert!((&one << 64u8).is_even()); assert!(((&one << 64u8) + one).is_odd()); } fn to_str_pairs() -> Vec<(BigUint, Vec<(u32, String)>)> { let bits = 32; vec![ ( Zero::zero(), vec![(2, "0".to_string()), (3, "0".to_string())], ), ( BigUint::from_slice(&[0xff]), vec![ (2, "11111111".to_string()), (3, "100110".to_string()), (4, "3333".to_string()), (5, "2010".to_string()), (6, "1103".to_string()), (7, "513".to_string()), (8, "377".to_string()), (9, "313".to_string()), (10, "255".to_string()), (11, "212".to_string()), (12, "193".to_string()), (13, "168".to_string()), (14, "143".to_string()), (15, "120".to_string()), (16, "ff".to_string()), ], ), ( BigUint::from_slice(&[0xfff]), vec![ (2, "111111111111".to_string()), (4, "333333".to_string()), (16, "fff".to_string()), ], ), ( BigUint::from_slice(&[1, 2]), vec![ ( 2, format!("10{}1", repeat("0").take(bits - 1).collect::()), ), ( 4, format!("2{}1", repeat("0").take(bits / 2 - 1).collect::()), ), ( 10, match bits { 64 => "36893488147419103233".to_string(), 32 => "8589934593".to_string(), 16 => "131073".to_string(), _ => panic!(), }, ), ( 16, format!("2{}1", repeat("0").take(bits / 4 - 1).collect::()), ), ], ), ( BigUint::from_slice(&[1, 2, 3]), vec![ ( 2, format!( "11{}10{}1", repeat("0").take(bits - 2).collect::(), repeat("0").take(bits - 1).collect::() ), ), ( 4, format!( "3{}2{}1", repeat("0").take(bits / 2 - 1).collect::(), repeat("0").take(bits / 2 - 1).collect::() ), ), ( 8, match bits { 64 => "14000000000000000000004000000000000000000001".to_string(), 32 => "6000000000100000000001".to_string(), 16 => "140000400001".to_string(), _ => panic!(), }, ), ( 10, match bits { 64 => "1020847100762815390427017310442723737601".to_string(), 32 => "55340232229718589441".to_string(), 16 => "12885032961".to_string(), _ => panic!(), }, ), ( 16, format!( "3{}2{}1", repeat("0").take(bits / 4 - 1).collect::(), repeat("0").take(bits / 4 - 1).collect::() ), ), ], ), ] } #[test] fn test_to_str_radix() { let r = to_str_pairs(); for num_pair in r.iter() { let &(ref n, ref rs) = num_pair; for str_pair in rs.iter() { let &(ref radix, ref str) = str_pair; assert_eq!(n.to_str_radix(*radix), *str); } } } #[test] fn test_from_and_to_radix() { const GROUND_TRUTH: &[(&[u8], u32, &[u8])] = &[ (b"0", 42, &[0]), ( b"ffffeeffbb", 2, &[ 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ], ), ( b"ffffeeffbb", 3, &[ 2, 2, 1, 1, 2, 1, 1, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, ], ), ( b"ffffeeffbb", 4, &[3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3], ), ( b"ffffeeffbb", 5, &[0, 4, 3, 3, 1, 4, 2, 4, 1, 4, 4, 2, 3, 0, 0, 1, 2, 1], ), ( b"ffffeeffbb", 6, &[5, 5, 4, 5, 5, 0, 0, 1, 2, 5, 3, 0, 1, 0, 2, 2], ), ( b"ffffeeffbb", 7, &[4, 2, 3, 6, 0, 1, 6, 1, 6, 2, 0, 3, 2, 4, 1], ), ( b"ffffeeffbb", 8, &[3, 7, 6, 7, 7, 5, 3, 7, 7, 7, 7, 7, 7, 1], ), (b"ffffeeffbb", 9, &[8, 4, 5, 7, 0, 0, 3, 2, 0, 3, 0, 8, 3]), (b"ffffeeffbb", 10, &[5, 9, 5, 3, 1, 5, 0, 1, 5, 9, 9, 0, 1]), (b"ffffeeffbb", 11, &[10, 7, 6, 5, 2, 0, 3, 3, 3, 4, 9, 3]), (b"ffffeeffbb", 12, &[11, 8, 5, 10, 1, 10, 3, 1, 1, 9, 5, 1]), (b"ffffeeffbb", 13, &[0, 5, 7, 4, 6, 5, 6, 11, 8, 12, 7]), (b"ffffeeffbb", 14, &[11, 4, 4, 11, 8, 4, 6, 0, 3, 11, 3]), (b"ffffeeffbb", 15, &[5, 11, 13, 2, 1, 10, 2, 0, 9, 13, 1]), (b"ffffeeffbb", 16, &[11, 11, 15, 15, 14, 14, 15, 15, 15, 15]), (b"ffffeeffbb", 17, &[0, 2, 14, 12, 2, 14, 8, 10, 4, 9]), (b"ffffeeffbb", 18, &[17, 15, 5, 13, 10, 16, 16, 13, 9, 5]), (b"ffffeeffbb", 19, &[14, 13, 2, 8, 9, 0, 1, 14, 7, 3]), (b"ffffeeffbb", 20, &[15, 19, 3, 14, 0, 17, 19, 18, 2, 2]), (b"ffffeeffbb", 21, &[11, 5, 4, 13, 5, 18, 9, 1, 8, 1]), (b"ffffeeffbb", 22, &[21, 3, 7, 21, 15, 12, 17, 0, 20]), (b"ffffeeffbb", 23, &[21, 21, 6, 9, 10, 7, 21, 0, 14]), (b"ffffeeffbb", 24, &[11, 10, 19, 14, 22, 11, 17, 23, 9]), (b"ffffeeffbb", 25, &[20, 18, 21, 22, 21, 14, 3, 5, 7]), (b"ffffeeffbb", 26, &[13, 15, 24, 11, 17, 6, 23, 6, 5]), (b"ffffeeffbb", 27, &[17, 16, 7, 0, 21, 0, 3, 24, 3]), (b"ffffeeffbb", 28, &[11, 16, 11, 15, 14, 18, 13, 25, 2]), (b"ffffeeffbb", 29, &[6, 8, 7, 19, 14, 13, 21, 5, 2]), (b"ffffeeffbb", 30, &[5, 13, 18, 11, 10, 7, 8, 20, 1]), (b"ffffeeffbb", 31, &[22, 26, 15, 19, 8, 27, 29, 8, 1]), (b"ffffeeffbb", 32, &[27, 29, 31, 29, 30, 31, 31, 31]), (b"ffffeeffbb", 33, &[32, 20, 27, 12, 1, 12, 26, 25]), (b"ffffeeffbb", 34, &[17, 9, 16, 33, 13, 25, 31, 20]), (b"ffffeeffbb", 35, &[25, 32, 2, 25, 11, 4, 3, 17]), (b"ffffeeffbb", 36, &[35, 34, 5, 6, 32, 3, 1, 14]), (b"ffffeeffbb", 37, &[16, 21, 18, 4, 33, 19, 21, 11]), (b"ffffeeffbb", 38, &[33, 25, 19, 29, 20, 6, 23, 9]), (b"ffffeeffbb", 39, &[26, 27, 29, 23, 16, 18, 0, 8]), (b"ffffeeffbb", 40, &[35, 39, 30, 11, 16, 17, 28, 6]), (b"ffffeeffbb", 41, &[36, 30, 9, 18, 12, 19, 26, 5]), (b"ffffeeffbb", 42, &[11, 34, 37, 27, 1, 13, 32, 4]), (b"ffffeeffbb", 43, &[3, 24, 11, 2, 10, 40, 1, 4]), (b"ffffeeffbb", 44, &[43, 12, 40, 32, 3, 23, 19, 3]), (b"ffffeeffbb", 45, &[35, 38, 44, 18, 22, 18, 42, 2]), (b"ffffeeffbb", 46, &[21, 45, 18, 41, 17, 2, 24, 2]), (b"ffffeeffbb", 47, &[37, 37, 11, 12, 6, 0, 8, 2]), (b"ffffeeffbb", 48, &[11, 41, 40, 43, 5, 43, 41, 1]), (b"ffffeeffbb", 49, &[18, 45, 7, 13, 20, 21, 30, 1]), (b"ffffeeffbb", 50, &[45, 21, 5, 34, 21, 18, 20, 1]), (b"ffffeeffbb", 51, &[17, 6, 26, 22, 38, 24, 11, 1]), (b"ffffeeffbb", 52, &[39, 33, 38, 30, 46, 31, 3, 1]), (b"ffffeeffbb", 53, &[31, 7, 44, 23, 9, 32, 49]), (b"ffffeeffbb", 54, &[17, 35, 8, 37, 31, 18, 44]), (b"ffffeeffbb", 55, &[10, 52, 9, 48, 36, 39, 39]), (b"ffffeeffbb", 56, &[11, 50, 51, 22, 25, 36, 35]), (b"ffffeeffbb", 57, &[14, 55, 12, 43, 20, 3, 32]), (b"ffffeeffbb", 58, &[35, 18, 45, 56, 9, 51, 28]), (b"ffffeeffbb", 59, &[51, 28, 20, 26, 55, 3, 26]), (b"ffffeeffbb", 60, &[35, 6, 27, 46, 58, 33, 23]), (b"ffffeeffbb", 61, &[58, 7, 6, 54, 49, 20, 21]), (b"ffffeeffbb", 62, &[53, 59, 3, 14, 10, 22, 19]), (b"ffffeeffbb", 63, &[53, 50, 23, 4, 56, 36, 17]), (b"ffffeeffbb", 64, &[59, 62, 47, 59, 63, 63, 15]), (b"ffffeeffbb", 65, &[0, 53, 39, 4, 40, 37, 14]), (b"ffffeeffbb", 66, &[65, 59, 39, 1, 64, 19, 13]), (b"ffffeeffbb", 67, &[35, 14, 19, 16, 25, 10, 12]), (b"ffffeeffbb", 68, &[51, 38, 63, 50, 15, 8, 11]), (b"ffffeeffbb", 69, &[44, 45, 18, 58, 68, 12, 10]), (b"ffffeeffbb", 70, &[25, 51, 0, 60, 13, 24, 9]), (b"ffffeeffbb", 71, &[54, 30, 9, 65, 28, 41, 8]), (b"ffffeeffbb", 72, &[35, 35, 55, 54, 17, 64, 7]), (b"ffffeeffbb", 73, &[34, 4, 48, 40, 27, 19, 7]), (b"ffffeeffbb", 74, &[53, 47, 4, 56, 36, 51, 6]), (b"ffffeeffbb", 75, &[20, 56, 10, 72, 24, 13, 6]), (b"ffffeeffbb", 76, &[71, 31, 52, 60, 48, 53, 5]), (b"ffffeeffbb", 77, &[32, 73, 14, 63, 15, 21, 5]), (b"ffffeeffbb", 78, &[65, 13, 17, 32, 64, 68, 4]), (b"ffffeeffbb", 79, &[37, 56, 2, 56, 25, 41, 4]), (b"ffffeeffbb", 80, &[75, 59, 37, 41, 43, 15, 4]), (b"ffffeeffbb", 81, &[44, 68, 0, 21, 27, 72, 3]), (b"ffffeeffbb", 82, &[77, 35, 2, 74, 46, 50, 3]), (b"ffffeeffbb", 83, &[52, 51, 19, 76, 10, 30, 3]), (b"ffffeeffbb", 84, &[11, 80, 19, 19, 76, 10, 3]), (b"ffffeeffbb", 85, &[0, 82, 20, 14, 68, 77, 2]), (b"ffffeeffbb", 86, &[3, 12, 78, 37, 62, 61, 2]), (b"ffffeeffbb", 87, &[35, 12, 20, 8, 52, 46, 2]), (b"ffffeeffbb", 88, &[43, 6, 54, 42, 30, 32, 2]), (b"ffffeeffbb", 89, &[49, 52, 85, 21, 80, 18, 2]), (b"ffffeeffbb", 90, &[35, 64, 78, 24, 18, 6, 2]), (b"ffffeeffbb", 91, &[39, 17, 83, 63, 17, 85, 1]), (b"ffffeeffbb", 92, &[67, 22, 85, 79, 75, 74, 1]), (b"ffffeeffbb", 93, &[53, 60, 39, 29, 4, 65, 1]), (b"ffffeeffbb", 94, &[37, 89, 2, 72, 76, 55, 1]), (b"ffffeeffbb", 95, &[90, 74, 89, 9, 9, 47, 1]), (b"ffffeeffbb", 96, &[59, 20, 46, 35, 81, 38, 1]), (b"ffffeeffbb", 97, &[94, 87, 60, 71, 3, 31, 1]), (b"ffffeeffbb", 98, &[67, 22, 63, 50, 62, 23, 1]), (b"ffffeeffbb", 99, &[98, 6, 69, 12, 61, 16, 1]), (b"ffffeeffbb", 100, &[95, 35, 51, 10, 95, 9, 1]), (b"ffffeeffbb", 101, &[87, 27, 7, 8, 62, 3, 1]), (b"ffffeeffbb", 102, &[17, 3, 32, 79, 59, 99]), (b"ffffeeffbb", 103, &[30, 22, 90, 0, 87, 94]), (b"ffffeeffbb", 104, &[91, 68, 87, 68, 38, 90]), (b"ffffeeffbb", 105, &[95, 80, 54, 73, 15, 86]), (b"ffffeeffbb", 106, &[31, 30, 24, 16, 17, 82]), (b"ffffeeffbb", 107, &[51, 50, 10, 12, 42, 78]), (b"ffffeeffbb", 108, &[71, 71, 96, 78, 89, 74]), (b"ffffeeffbb", 109, &[33, 18, 93, 22, 50, 71]), (b"ffffeeffbb", 110, &[65, 53, 57, 88, 29, 68]), (b"ffffeeffbb", 111, &[53, 93, 67, 90, 27, 65]), (b"ffffeeffbb", 112, &[11, 109, 96, 65, 43, 62]), (b"ffffeeffbb", 113, &[27, 23, 106, 56, 76, 59]), (b"ffffeeffbb", 114, &[71, 84, 31, 112, 11, 57]), (b"ffffeeffbb", 115, &[90, 22, 1, 56, 76, 54]), (b"ffffeeffbb", 116, &[35, 38, 98, 57, 40, 52]), (b"ffffeeffbb", 117, &[26, 113, 115, 62, 17, 50]), (b"ffffeeffbb", 118, &[51, 14, 5, 18, 7, 48]), (b"ffffeeffbb", 119, &[102, 31, 110, 108, 8, 46]), (b"ffffeeffbb", 120, &[35, 93, 96, 50, 22, 44]), (b"ffffeeffbb", 121, &[87, 61, 2, 36, 47, 42]), (b"ffffeeffbb", 122, &[119, 64, 1, 22, 83, 40]), (b"ffffeeffbb", 123, &[77, 119, 32, 90, 6, 39]), (b"ffffeeffbb", 124, &[115, 122, 31, 79, 62, 37]), (b"ffffeeffbb", 125, &[95, 108, 47, 74, 3, 36]), (b"ffffeeffbb", 126, &[53, 25, 116, 39, 78, 34]), (b"ffffeeffbb", 127, &[22, 23, 125, 67, 35, 33]), (b"ffffeeffbb", 128, &[59, 127, 59, 127, 127, 31]), (b"ffffeeffbb", 129, &[89, 36, 1, 59, 100, 30]), (b"ffffeeffbb", 130, &[65, 91, 123, 89, 79, 29]), (b"ffffeeffbb", 131, &[58, 72, 39, 63, 65, 28]), (b"ffffeeffbb", 132, &[131, 62, 92, 82, 57, 27]), (b"ffffeeffbb", 133, &[109, 31, 51, 123, 55, 26]), (b"ffffeeffbb", 134, &[35, 74, 21, 27, 60, 25]), (b"ffffeeffbb", 135, &[125, 132, 49, 37, 70, 24]), (b"ffffeeffbb", 136, &[51, 121, 117, 133, 85, 23]), (b"ffffeeffbb", 137, &[113, 60, 135, 22, 107, 22]), (b"ffffeeffbb", 138, &[113, 91, 73, 93, 133, 21]), (b"ffffeeffbb", 139, &[114, 75, 102, 51, 26, 21]), (b"ffffeeffbb", 140, &[95, 25, 35, 16, 62, 20]), (b"ffffeeffbb", 141, &[131, 137, 16, 110, 102, 19]), (b"ffffeeffbb", 142, &[125, 121, 108, 34, 6, 19]), (b"ffffeeffbb", 143, &[65, 78, 138, 55, 55, 18]), (b"ffffeeffbb", 144, &[107, 125, 121, 15, 109, 17]), (b"ffffeeffbb", 145, &[35, 13, 122, 42, 22, 17]), (b"ffffeeffbb", 146, &[107, 38, 103, 123, 83, 16]), (b"ffffeeffbb", 147, &[116, 96, 71, 98, 2, 16]), (b"ffffeeffbb", 148, &[127, 23, 75, 99, 71, 15]), (b"ffffeeffbb", 149, &[136, 110, 53, 114, 144, 14]), (b"ffffeeffbb", 150, &[95, 140, 133, 130, 71, 14]), (b"ffffeeffbb", 151, &[15, 50, 29, 137, 0, 14]), (b"ffffeeffbb", 152, &[147, 15, 89, 121, 83, 13]), (b"ffffeeffbb", 153, &[17, 87, 93, 72, 17, 13]), (b"ffffeeffbb", 154, &[109, 113, 3, 133, 106, 12]), (b"ffffeeffbb", 155, &[115, 141, 120, 139, 44, 12]), (b"ffffeeffbb", 156, &[143, 45, 4, 82, 140, 11]), (b"ffffeeffbb", 157, &[149, 92, 15, 106, 82, 11]), (b"ffffeeffbb", 158, &[37, 107, 79, 46, 26, 11]), (b"ffffeeffbb", 159, &[137, 37, 146, 51, 130, 10]), (b"ffffeeffbb", 160, &[155, 69, 29, 115, 77, 10]), (b"ffffeeffbb", 161, &[67, 98, 46, 68, 26, 10]), (b"ffffeeffbb", 162, &[125, 155, 60, 63, 138, 9]), (b"ffffeeffbb", 163, &[96, 43, 118, 93, 90, 9]), (b"ffffeeffbb", 164, &[159, 99, 123, 152, 43, 9]), (b"ffffeeffbb", 165, &[65, 17, 1, 69, 163, 8]), (b"ffffeeffbb", 166, &[135, 108, 25, 165, 119, 8]), (b"ffffeeffbb", 167, &[165, 116, 164, 103, 77, 8]), (b"ffffeeffbb", 168, &[11, 166, 67, 44, 36, 8]), (b"ffffeeffbb", 169, &[65, 59, 71, 149, 164, 7]), (b"ffffeeffbb", 170, &[85, 83, 26, 76, 126, 7]), (b"ffffeeffbb", 171, &[71, 132, 140, 157, 88, 7]), (b"ffffeeffbb", 172, &[3, 6, 127, 47, 52, 7]), (b"ffffeeffbb", 173, &[122, 66, 53, 83, 16, 7]), (b"ffffeeffbb", 174, &[35, 6, 5, 88, 155, 6]), (b"ffffeeffbb", 175, &[95, 20, 84, 56, 122, 6]), (b"ffffeeffbb", 176, &[43, 91, 57, 159, 89, 6]), (b"ffffeeffbb", 177, &[110, 127, 54, 40, 58, 6]), (b"ffffeeffbb", 178, &[49, 115, 43, 47, 27, 6]), (b"ffffeeffbb", 179, &[130, 91, 4, 178, 175, 5]), (b"ffffeeffbb", 180, &[35, 122, 109, 70, 147, 5]), (b"ffffeeffbb", 181, &[94, 94, 4, 79, 119, 5]), (b"ffffeeffbb", 182, &[39, 54, 66, 19, 92, 5]), (b"ffffeeffbb", 183, &[119, 2, 143, 69, 65, 5]), (b"ffffeeffbb", 184, &[67, 57, 90, 44, 39, 5]), (b"ffffeeffbb", 185, &[90, 63, 141, 123, 13, 5]), (b"ffffeeffbb", 186, &[53, 123, 172, 119, 174, 4]), (b"ffffeeffbb", 187, &[153, 21, 68, 28, 151, 4]), (b"ffffeeffbb", 188, &[131, 138, 94, 32, 128, 4]), (b"ffffeeffbb", 189, &[179, 121, 156, 130, 105, 4]), (b"ffffeeffbb", 190, &[185, 179, 164, 131, 83, 4]), (b"ffffeeffbb", 191, &[118, 123, 37, 31, 62, 4]), (b"ffffeeffbb", 192, &[59, 106, 83, 16, 41, 4]), (b"ffffeeffbb", 193, &[57, 37, 47, 86, 20, 4]), (b"ffffeeffbb", 194, &[191, 140, 63, 45, 0, 4]), (b"ffffeeffbb", 195, &[65, 169, 83, 84, 175, 3]), (b"ffffeeffbb", 196, &[67, 158, 64, 6, 157, 3]), (b"ffffeeffbb", 197, &[121, 26, 167, 3, 139, 3]), (b"ffffeeffbb", 198, &[197, 151, 165, 75, 121, 3]), (b"ffffeeffbb", 199, &[55, 175, 36, 22, 104, 3]), (b"ffffeeffbb", 200, &[195, 167, 162, 38, 87, 3]), (b"ffffeeffbb", 201, &[35, 27, 136, 124, 70, 3]), (b"ffffeeffbb", 202, &[87, 64, 153, 76, 54, 3]), (b"ffffeeffbb", 203, &[151, 191, 14, 94, 38, 3]), (b"ffffeeffbb", 204, &[119, 103, 135, 175, 22, 3]), (b"ffffeeffbb", 205, &[200, 79, 123, 115, 7, 3]), (b"ffffeeffbb", 206, &[133, 165, 202, 115, 198, 2]), (b"ffffeeffbb", 207, &[44, 153, 193, 175, 184, 2]), (b"ffffeeffbb", 208, &[91, 190, 125, 86, 171, 2]), (b"ffffeeffbb", 209, &[109, 151, 34, 53, 158, 2]), (b"ffffeeffbb", 210, &[95, 40, 171, 74, 145, 2]), (b"ffffeeffbb", 211, &[84, 195, 162, 150, 132, 2]), (b"ffffeeffbb", 212, &[31, 15, 59, 68, 120, 2]), (b"ffffeeffbb", 213, &[125, 57, 127, 36, 108, 2]), (b"ffffeeffbb", 214, &[51, 132, 2, 55, 96, 2]), (b"ffffeeffbb", 215, &[175, 133, 177, 122, 84, 2]), (b"ffffeeffbb", 216, &[179, 35, 78, 23, 73, 2]), (b"ffffeeffbb", 217, &[53, 101, 208, 186, 61, 2]), (b"ffffeeffbb", 218, &[33, 9, 214, 179, 50, 2]), (b"ffffeeffbb", 219, &[107, 147, 175, 217, 39, 2]), (b"ffffeeffbb", 220, &[175, 81, 179, 79, 29, 2]), (b"ffffeeffbb", 221, &[0, 76, 95, 204, 18, 2]), (b"ffffeeffbb", 222, &[53, 213, 16, 150, 8, 2]), (b"ffffeeffbb", 223, &[158, 161, 42, 136, 221, 1]), (b"ffffeeffbb", 224, &[123, 54, 52, 162, 212, 1]), (b"ffffeeffbb", 225, &[170, 43, 151, 2, 204, 1]), (b"ffffeeffbb", 226, &[27, 68, 224, 105, 195, 1]), (b"ffffeeffbb", 227, &[45, 69, 157, 20, 187, 1]), (b"ffffeeffbb", 228, &[71, 213, 64, 199, 178, 1]), (b"ffffeeffbb", 229, &[129, 203, 66, 186, 170, 1]), (b"ffffeeffbb", 230, &[205, 183, 57, 208, 162, 1]), (b"ffffeeffbb", 231, &[32, 50, 164, 33, 155, 1]), (b"ffffeeffbb", 232, &[35, 135, 53, 123, 147, 1]), (b"ffffeeffbb", 233, &[209, 47, 89, 13, 140, 1]), (b"ffffeeffbb", 234, &[143, 56, 175, 168, 132, 1]), (b"ffffeeffbb", 235, &[225, 157, 216, 121, 125, 1]), (b"ffffeeffbb", 236, &[51, 66, 119, 105, 118, 1]), (b"ffffeeffbb", 237, &[116, 150, 26, 119, 111, 1]), (b"ffffeeffbb", 238, &[221, 15, 87, 162, 104, 1]), (b"ffffeeffbb", 239, &[234, 155, 214, 234, 97, 1]), (b"ffffeeffbb", 240, &[155, 46, 84, 96, 91, 1]), (b"ffffeeffbb", 241, &[187, 48, 90, 225, 84, 1]), (b"ffffeeffbb", 242, &[87, 212, 151, 140, 78, 1]), (b"ffffeeffbb", 243, &[206, 22, 189, 81, 72, 1]), (b"ffffeeffbb", 244, &[119, 93, 122, 48, 66, 1]), (b"ffffeeffbb", 245, &[165, 224, 117, 40, 60, 1]), (b"ffffeeffbb", 246, &[77, 121, 100, 57, 54, 1]), (b"ffffeeffbb", 247, &[52, 128, 242, 98, 48, 1]), (b"ffffeeffbb", 248, &[115, 247, 224, 164, 42, 1]), (b"ffffeeffbb", 249, &[218, 127, 223, 5, 37, 1]), (b"ffffeeffbb", 250, &[95, 54, 168, 118, 31, 1]), (b"ffffeeffbb", 251, &[121, 204, 240, 3, 26, 1]), (b"ffffeeffbb", 252, &[179, 138, 123, 162, 20, 1]), (b"ffffeeffbb", 253, &[21, 50, 1, 91, 15, 1]), (b"ffffeeffbb", 254, &[149, 11, 63, 40, 10, 1]), (b"ffffeeffbb", 255, &[170, 225, 247, 9, 5, 1]), (b"ffffeeffbb", 256, &[187, 255, 238, 255, 255]), ]; for &(bigint, radix, inbaseradix_le) in GROUND_TRUTH.iter() { let bigint = BigUint::parse_bytes(bigint, 16).unwrap(); // to_radix_le assert_eq!(bigint.to_radix_le(radix), inbaseradix_le); // to_radix_be let mut inbase_be = bigint.to_radix_be(radix); inbase_be.reverse(); // now le assert_eq!(inbase_be, inbaseradix_le); // from_radix_le assert_eq!( BigUint::from_radix_le(inbaseradix_le, radix).unwrap(), bigint ); // from_radix_be let mut inbaseradix_be = Vec::from(inbaseradix_le); inbaseradix_be.reverse(); assert_eq!( BigUint::from_radix_be(&inbaseradix_be, radix).unwrap(), bigint ); } assert!(BigUint::from_radix_le(&[10, 100, 10], 50).is_none()); assert_eq!(BigUint::from_radix_le(&[], 2), Some(BigUint::zero())); assert_eq!(BigUint::from_radix_be(&[], 2), Some(BigUint::zero())); } #[test] fn test_from_str_radix() { let r = to_str_pairs(); for num_pair in r.iter() { let &(ref n, ref rs) = num_pair; for str_pair in rs.iter() { let &(ref radix, ref str) = str_pair; assert_eq!(n, &BigUint::from_str_radix(str, *radix).unwrap()); } } let zed = BigUint::from_str_radix("Z", 10).ok(); assert_eq!(zed, None); let blank = BigUint::from_str_radix("_", 2).ok(); assert_eq!(blank, None); let blank_one = BigUint::from_str_radix("_1", 2).ok(); assert_eq!(blank_one, None); let plus_one = BigUint::from_str_radix("+1", 10).ok(); assert_eq!(plus_one, Some(BigUint::from_slice(&[1]))); let plus_plus_one = BigUint::from_str_radix("++1", 10).ok(); assert_eq!(plus_plus_one, None); let minus_one = BigUint::from_str_radix("-1", 10).ok(); assert_eq!(minus_one, None); let zero_plus_two = BigUint::from_str_radix("0+2", 10).ok(); assert_eq!(zero_plus_two, None); let three = BigUint::from_str_radix("1_1", 2).ok(); assert_eq!(three, Some(BigUint::from_slice(&[3]))); let ff = BigUint::from_str_radix("1111_1111", 2).ok(); assert_eq!(ff, Some(BigUint::from_slice(&[0xff]))); } #[test] fn test_all_str_radix() { let n = BigUint::new((0..10).collect()); for radix in 2..37 { let s = n.to_str_radix(radix); let x = BigUint::from_str_radix(&s, radix); assert_eq!(x.unwrap(), n); let s = s.to_ascii_uppercase(); let x = BigUint::from_str_radix(&s, radix); assert_eq!(x.unwrap(), n); } } #[test] fn test_big_str() { for n in 2..=20_u32 { let x: BigUint = BigUint::from(n).pow(10_000_u32); let s = x.to_string(); let y: BigUint = s.parse().unwrap(); assert_eq!(x, y); } } #[test] fn test_lower_hex() { let a = BigUint::parse_bytes(b"A", 16).unwrap(); let hello = BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{:x}", a), "a"); assert_eq!(format!("{:x}", hello), "48656c6c6f20776f726c6421"); assert_eq!(format!("{:♥>+#8x}", a), "♥♥♥♥+0xa"); } #[test] fn test_upper_hex() { let a = BigUint::parse_bytes(b"A", 16).unwrap(); let hello = BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{:X}", a), "A"); assert_eq!(format!("{:X}", hello), "48656C6C6F20776F726C6421"); assert_eq!(format!("{:♥>+#8X}", a), "♥♥♥♥+0xA"); } #[test] fn test_binary() { let a = BigUint::parse_bytes(b"A", 16).unwrap(); let hello = BigUint::parse_bytes(b"224055342307539", 10).unwrap(); assert_eq!(format!("{:b}", a), "1010"); assert_eq!( format!("{:b}", hello), "110010111100011011110011000101101001100011010011" ); assert_eq!(format!("{:♥>+#8b}", a), "♥+0b1010"); } #[test] fn test_octal() { let a = BigUint::parse_bytes(b"A", 16).unwrap(); let hello = BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{:o}", a), "12"); assert_eq!(format!("{:o}", hello), "22062554330674403566756233062041"); assert_eq!(format!("{:♥>+#8o}", a), "♥♥♥+0o12"); } #[test] fn test_display() { let a = BigUint::parse_bytes(b"A", 16).unwrap(); let hello = BigUint::parse_bytes(b"22405534230753963835153736737", 10).unwrap(); assert_eq!(format!("{}", a), "10"); assert_eq!(format!("{}", hello), "22405534230753963835153736737"); assert_eq!(format!("{:♥>+#8}", a), "♥♥♥♥♥+10"); } #[test] fn test_factor() { fn factor(n: usize) -> BigUint { let mut f: BigUint = One::one(); for i in 2..=n { // FIXME(#5992): assignment operator overloads // f *= FromPrimitive::from_usize(i); let bu: BigUint = FromPrimitive::from_usize(i).unwrap(); f *= bu; } f } fn check(n: usize, s: &str) { let n = factor(n); let ans = BigUint::from_str_radix(s, 10).unwrap(); assert_eq!(n, ans); } check(3, "6"); check(10, "3628800"); check(20, "2432902008176640000"); check(30, "265252859812191058636308480000000"); } #[test] fn test_bits() { assert_eq!(BigUint::new(vec![0, 0, 0, 0]).bits(), 0); let n: BigUint = FromPrimitive::from_usize(0).unwrap(); assert_eq!(n.bits(), 0); let n: BigUint = FromPrimitive::from_usize(1).unwrap(); assert_eq!(n.bits(), 1); let n: BigUint = FromPrimitive::from_usize(3).unwrap(); assert_eq!(n.bits(), 2); let n: BigUint = BigUint::from_str_radix("4000000000", 16).unwrap(); assert_eq!(n.bits(), 39); let one: BigUint = One::one(); assert_eq!((one << 426u16).bits(), 427); } #[test] fn test_iter_sum() { let result: BigUint = FromPrimitive::from_isize(1234567).unwrap(); let data: Vec = vec![ FromPrimitive::from_u32(1000000).unwrap(), FromPrimitive::from_u32(200000).unwrap(), FromPrimitive::from_u32(30000).unwrap(), FromPrimitive::from_u32(4000).unwrap(), FromPrimitive::from_u32(500).unwrap(), FromPrimitive::from_u32(60).unwrap(), FromPrimitive::from_u32(7).unwrap(), ]; assert_eq!(result, data.iter().sum::()); assert_eq!(result, data.into_iter().sum::()); } #[test] fn test_iter_product() { let data: Vec = vec![ FromPrimitive::from_u32(1001).unwrap(), FromPrimitive::from_u32(1002).unwrap(), FromPrimitive::from_u32(1003).unwrap(), FromPrimitive::from_u32(1004).unwrap(), FromPrimitive::from_u32(1005).unwrap(), ]; let result = data.get(0).unwrap() * data.get(1).unwrap() * data.get(2).unwrap() * data.get(3).unwrap() * data.get(4).unwrap(); assert_eq!(result, data.iter().product::()); assert_eq!(result, data.into_iter().product::()); } #[test] fn test_iter_sum_generic() { let result: BigUint = FromPrimitive::from_isize(1234567).unwrap(); let data = vec![1000000_u32, 200000, 30000, 4000, 500, 60, 7]; assert_eq!(result, data.iter().sum::()); assert_eq!(result, data.into_iter().sum::()); } #[test] fn test_iter_product_generic() { let data = vec![1001_u32, 1002, 1003, 1004, 1005]; let result = data[0].to_biguint().unwrap() * data[1].to_biguint().unwrap() * data[2].to_biguint().unwrap() * data[3].to_biguint().unwrap() * data[4].to_biguint().unwrap(); assert_eq!(result, data.iter().product::()); assert_eq!(result, data.into_iter().product::()); } #[test] fn test_pow() { let one = BigUint::from(1u32); let two = BigUint::from(2u32); let four = BigUint::from(4u32); let eight = BigUint::from(8u32); let tentwentyfour = BigUint::from(1024u32); let twentyfourtyeight = BigUint::from(2048u32); macro_rules! check { ($t:ty) => { assert_eq!(Pow::pow(&two, 0 as $t), one); assert_eq!(Pow::pow(&two, 1 as $t), two); assert_eq!(Pow::pow(&two, 2 as $t), four); assert_eq!(Pow::pow(&two, 3 as $t), eight); assert_eq!(Pow::pow(&two, 10 as $t), tentwentyfour); assert_eq!(Pow::pow(&two, 11 as $t), twentyfourtyeight); assert_eq!(Pow::pow(&two, &(11 as $t)), twentyfourtyeight); }; } check!(u8); check!(u16); check!(u32); check!(u64); check!(u128); check!(usize); let pow_1e10000 = BigUint::from(10u32).pow(10_000_u32); let manual_1e10000 = repeat(10u32).take(10_000).product::(); assert!(manual_1e10000 == pow_1e10000); } #[test] fn test_trailing_zeros() { assert!(BigUint::from(0u8).trailing_zeros().is_none()); assert_eq!(BigUint::from(1u8).trailing_zeros().unwrap(), 0); assert_eq!(BigUint::from(2u8).trailing_zeros().unwrap(), 1); let x: BigUint = BigUint::one() << 128; assert_eq!(x.trailing_zeros().unwrap(), 128); } #[test] fn test_trailing_ones() { assert_eq!(BigUint::from(0u8).trailing_ones(), 0); assert_eq!(BigUint::from(1u8).trailing_ones(), 1); assert_eq!(BigUint::from(2u8).trailing_ones(), 0); assert_eq!(BigUint::from(3u8).trailing_ones(), 2); let x: BigUint = (BigUint::from(3u8) << 128) | BigUint::from(3u8); assert_eq!(x.trailing_ones(), 2); let x: BigUint = (BigUint::one() << 128) - BigUint::one(); assert_eq!(x.trailing_ones(), 128); } #[test] fn test_count_ones() { assert_eq!(BigUint::from(0u8).count_ones(), 0); assert_eq!(BigUint::from(1u8).count_ones(), 1); assert_eq!(BigUint::from(2u8).count_ones(), 1); assert_eq!(BigUint::from(3u8).count_ones(), 2); let x: BigUint = (BigUint::from(3u8) << 128) | BigUint::from(3u8); assert_eq!(x.count_ones(), 4); } #[test] fn test_bit() { assert!(!BigUint::from(0u8).bit(0)); assert!(!BigUint::from(0u8).bit(100)); assert!(!BigUint::from(42u8).bit(4)); assert!(BigUint::from(42u8).bit(5)); let x: BigUint = (BigUint::from(3u8) << 128) | BigUint::from(3u8); assert!(x.bit(129)); assert!(!x.bit(130)); } #[test] fn test_set_bit() { let mut x = BigUint::from(3u8); x.set_bit(128, true); x.set_bit(129, true); assert_eq!(x, (BigUint::from(3u8) << 128) | BigUint::from(3u8)); x.set_bit(0, false); x.set_bit(128, false); x.set_bit(130, false); assert_eq!(x, (BigUint::from(2u8) << 128) | BigUint::from(2u8)); x.set_bit(129, false); x.set_bit(1, false); assert_eq!(x, BigUint::zero()); } num-bigint-0.4.3/tests/biguint_scalar.rs000064400000000000000000000067220072674642500164360ustar 00000000000000use 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(); } num-bigint-0.4.3/tests/consts/mod.rs000064400000000000000000000032510072674642500155320ustar 00000000000000#![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 = ::std::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]), ]; num-bigint-0.4.3/tests/fuzzed.rs000064400000000000000000000326350072674642500147610ustar 00000000000000//! 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); } num-bigint-0.4.3/tests/macros/mod.rs000064400000000000000000000053160072674642500155110ustar 00000000000000#![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); }; } num-bigint-0.4.3/tests/modpow.rs000064400000000000000000000161530072674642500147540ustar 00000000000000static 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>(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::(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, 2); } #[test] fn test_modpow_small() { for b in 0u64..11 { for e in 0u64..11 { for m in 1..11 { check_modpow::(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>(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); } } num-bigint-0.4.3/tests/roots.rs000064400000000000000000000076600072674642500146200ustar 00000000000000mod biguint { use num_bigint::BigUint; use num_traits::{One, Zero}; use std::{i32, u32}; fn check>(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); } }