num-bigint-0.2.0/.gitignore010066400247370024737000000000361327713022700140240ustar0000000000000000Cargo.lock target *.bk *.orig num-bigint-0.2.0/.travis.yml010066400247370024737000000004151330111417000141310ustar0000000000000000language: rust rust: - 1.15.0 - 1.22.0 - 1.26.0 - stable - beta - nightly sudo: false script: - cargo build --verbose - ./ci/test_full.sh notifications: email: on_success: never branches: only: - master - next - staging - trying num-bigint-0.2.0/Cargo.toml.orig010066400247370024737000000022451330207541400147220ustar0000000000000000[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/Apache-2.0" name = "num-bigint" repository = "https://github.com/rust-num/num-bigint" version = "0.2.0" readme = "README.md" build = "build.rs" [package.metadata.docs.rs] features = ["std", "serde", "rand"] [[bench]] name = "bigint" [[bench]] name = "factorial" [[bench]] name = "gcd" [[bench]] harness = false name = "shootout-pidigits" [dependencies] [dependencies.num-integer] version = "0.1.38" default-features = false [dependencies.num-traits] version = "0.2.4" default-features = false [dependencies.rand] optional = true version = "0.5" default-features = false features = ["std"] [dependencies.serde] optional = true version = "1.0" default-features = false features = ["std"] [dev-dependencies.serde_test] version = "1.0" [features] default = ["std"] i128 = ["num-integer/i128", "num-traits/i128"] std = ["num-integer/std", "num-traits/std"] num-bigint-0.2.0/Cargo.toml0000644000000032340000000000000111430ustar00# 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 believe there's an error in this file please file an # issue against the rust-lang/cargo repository. If you're # editing this file be aware that the upstream Cargo.toml # will likely look very different (and much more reasonable) [package] name = "num-bigint" version = "0.2.0" authors = ["The Rust Project Developers"] build = "build.rs" 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/Apache-2.0" repository = "https://github.com/rust-num/num-bigint" [package.metadata.docs.rs] features = ["std", "serde", "rand"] [[bench]] name = "bigint" [[bench]] name = "factorial" [[bench]] name = "gcd" [[bench]] name = "shootout-pidigits" harness = false [dependencies.num-integer] version = "0.1.38" default-features = false [dependencies.num-traits] version = "0.2.4" default-features = false [dependencies.rand] version = "0.5" features = ["std"] optional = true default-features = false [dependencies.serde] version = "1.0" features = ["std"] optional = true default-features = false [dev-dependencies.serde_test] version = "1.0" [features] default = ["std"] i128 = ["num-integer/i128", "num-traits/i128"] std = ["num-integer/std", "num-traits/std"] num-bigint-0.2.0/LICENSE-APACHE010066400247370024737000000251371321603176200137660ustar0000000000000000 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-0.2.0/LICENSE-MIT010066400247370024737000000020571321603176200134720ustar0000000000000000Copyright (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. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. num-bigint-0.2.0/README.md010066400247370024737000000042541327713052600133230ustar0000000000000000# 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 1.15](https://img.shields.io/badge/rustc-1.15+-red.svg) [![Travis status](https://travis-ci.org/rust-num/num-bigint.svg?branch=master)](https://travis-ci.org/rust-num/num-bigint) Big integer types for Rust, `BigInt` and `BigUint`. ## Usage Add this to your `Cargo.toml`: ```toml [dependencies] num-bigint = "0.2" ``` and this to your crate root: ```rust extern crate num_bigint; ``` ## Features The `std` crate feature is mandatory and enabled by default. If you depend on `num-bigint` with `default-features = false`, you must manually enable the `std` feature yourself. In the future, we hope to support `#![no_std]` with the `alloc` crate when `std` is not enabled. Implementations for `i128` and `u128` are only available with Rust 1.26 and later. The build script automatically detects this, but you can make it mandatory by enabling the `i128` crate feature. ## Releases Release notes are available in [RELEASES.md](RELEASES.md). ## Compatibility The `num-bigint` crate is tested for rustc 1.15 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 | 1.15 | pure rust | | [`ramp`] | Apache-2.0 | nightly | rust and inline assembly | | [`rug`] | LGPL-3.0+ | 1.18 | bundles [GMP] via [`gmp-mpfr-sys`] | | [`rust-gmp`] | MIT | stable? | links to [GMP] | | [`apint`] | MIT/Apache-2.0 | nightly | 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 num-bigint-0.2.0/RELEASES.md010066400247370024737000000076631330207541400135710ustar0000000000000000# Release 0.2.0 ### 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 - [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 - [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 - [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-0.2.0/benches/bigint.rs010066400247370024737000000143671324630736000153010ustar0000000000000000#![feature(test)] extern crate test; extern crate num_bigint; extern crate num_traits; extern crate rand; use std::mem::replace; use test::Bencher; use num_bigint::{BigInt, BigUint, RandBigInt}; use num_traits::{Zero, One, FromPrimitive, Num}; use rand::{SeedableRng, StdRng}; fn get_rng() -> StdRng { let seed: &[_] = &[1, 2, 3, 4]; SeedableRng::from_seed(seed) } fn multiply_bench(b: &mut Bencher, xbits: usize, ybits: usize) { 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: usize, ybits: usize) { 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+1) { let bu: BigUint = FromPrimitive::from_usize(i).unwrap(); f = 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 = 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 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) { let mut rng = get_rng(); let x = rng.gen_bigint(1009); b.iter(|| x.to_str_radix(radix)); } #[bench] fn to_str_radix_02(b: &mut Bencher) { to_str_radix_bench(b, 2); } #[bench] fn to_str_radix_08(b: &mut Bencher) { to_str_radix_bench(b, 8); } #[bench] fn to_str_radix_10(b: &mut Bencher) { to_str_radix_bench(b, 10); } #[bench] fn to_str_radix_16(b: &mut Bencher) { to_str_radix_bench(b, 16); } #[bench] fn to_str_radix_36(b: &mut Bencher) { to_str_radix_bench(b, 36); } 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); } #[bench] fn shl(b: &mut Bencher) { let n = BigUint::one() << 1000; b.iter(|| { let mut m = n.clone(); for i in 0..50 { m = m << i; } }) } #[bench] fn shr(b: &mut Bencher) { let n = BigUint::one() << 2000; b.iter(|| { let mut m = n.clone(); for i in 0..50 { m = 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_usize; for i in 2..upper + 1 { for j in 2..upper + 1 { let i_big = BigUint::from_usize(i).unwrap(); num_traits::pow(i_big, j); } } }); } /// 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: &'static 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)); } num-bigint-0.2.0/benches/factorial.rs010066400247370024737000000016601327712777300157750ustar0000000000000000#![feature(test)] extern crate num_bigint; extern crate num_traits; 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-0.2.0/benches/gcd.rs010066400247370024737000000030251323677543500145620ustar0000000000000000#![feature(test)] extern crate test; extern crate num_bigint; extern crate num_integer; extern crate num_traits; extern crate rand; use test::Bencher; use num_bigint::{BigUint, RandBigInt}; use num_integer::Integer; use num_traits::Zero; use rand::{SeedableRng, StdRng}; fn get_rng() -> StdRng { let seed: &[_] = &[1, 2, 3, 4]; SeedableRng::from_seed(seed) } fn bench(b: &mut Bencher, bits: usize, 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; } return 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-0.2.0/benches/shootout-pidigits.rs010066400247370024737000000100621324630736000175070ustar0000000000000000// 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. extern crate num_bigint; extern crate num_integer; extern crate num_traits; use std::str::FromStr; use std::io; use num_bigint::BigInt; use num_integer::Integer; use num_traits::{FromPrimitive, ToPrimitive, One, 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 io::Write) -> io::Result<()> { let mut k = 0; let mut context = Context::new(); for i in 1..(n+1) { let mut d; loop { k += 1; context.next_term(k); d = context.extract_digit(); if d != -1 {break;} } try!(write!(out, "{}", d)); if i % 10 == 0 { try!(write!(out, "\t:{}\n", i)); } context.eliminate_digit(d); } let m = n % 10; if m != 0 { for _ in m..10 { try!(write!(out, " ")); } try!(write!(out, "\t:{}\n", 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-0.2.0/bors.toml010066400247370024737000000000701321603176200136710ustar0000000000000000status = [ "continuous-integration/travis-ci/push", ] num-bigint-0.2.0/build.rs010066400247370024737000000016411327713022700135040ustar0000000000000000use std::env; use std::io::Write; use std::process::{Command, Stdio}; fn main() { if probe("fn main() { 0i128; }") { println!("cargo:rustc-cfg=has_i128"); } else if env::var_os("CARGO_FEATURE_I128").is_some() { panic!("i128 support was not detected!"); } } /// Test if a code snippet can be compiled fn probe(code: &str) -> bool { let rustc = env::var_os("RUSTC").unwrap_or_else(|| "rustc".into()); let out_dir = env::var_os("OUT_DIR").expect("environment variable OUT_DIR"); let mut child = Command::new(rustc) .arg("--out-dir") .arg(out_dir) .arg("--emit=obj") .arg("-") .stdin(Stdio::piped()) .spawn() .expect("rustc probe"); child .stdin .as_mut() .expect("rustc stdin") .write_all(code.as_bytes()) .expect("write rustc stdin"); child.wait().expect("rustc probe").success() } num-bigint-0.2.0/ci/rustup.sh010077500247370024737000000005461330112707700143330ustar0000000000000000#!/bin/sh # Use rustup to locally run the same suite of tests as .travis.yml. # (You should first install/update all versions listed below.) set -ex export TRAVIS_RUST_VERSION for TRAVIS_RUST_VERSION in 1.15.0 1.22.0 1.26.0 stable beta nightly; do run="rustup run $TRAVIS_RUST_VERSION" $run cargo build --verbose $run $PWD/ci/test_full.sh done num-bigint-0.2.0/ci/test_full.sh010077500247370024737000000015771330111425000147640ustar0000000000000000#!/bin/bash set -ex echo Testing num-bigint on rustc ${TRAVIS_RUST_VERSION} FEATURES="serde" if [[ "$TRAVIS_RUST_VERSION" =~ ^(nightly|beta|stable|1.26.0|1.22.0)$ ]]; then FEATURES="$FEATURES rand" fi if [[ "$TRAVIS_RUST_VERSION" =~ ^(nightly|beta|stable|1.26.0)$ ]]; then FEATURES="$FEATURES i128" fi # num-bigint should build and test everywhere. cargo build --verbose cargo test --verbose # It should build with minimal features too. cargo build --no-default-features --features="std" cargo test --no-default-features --features="std" # Each isolated feature should also work everywhere. for feature in $FEATURES; do cargo build --verbose --no-default-features --features="std $feature" cargo test --verbose --no-default-features --features="std $feature" done # test all supported features together cargo build --features="std $FEATURES" cargo test --features="std $FEATURES" num-bigint-0.2.0/src/algorithms.rs010066400247370024737000000524621330110107400153360ustar0000000000000000use std::borrow::Cow; use std::cmp; use std::cmp::Ordering::{self, Less, Greater, Equal}; use std::iter::repeat; use std::mem; use traits; use traits::{Zero, One}; use biguint::BigUint; use bigint::BigInt; use bigint::Sign; use bigint::Sign::{Minus, NoSign, Plus}; use big_digit::{self, BigDigit, DoubleBigDigit, SignedDoubleBigDigit}; // Generic functions for add/subtract/multiply with carry/borrow: // Add with carry: #[inline] fn adc(a: BigDigit, b: BigDigit, acc: &mut DoubleBigDigit) -> BigDigit { *acc += a as DoubleBigDigit; *acc += b as DoubleBigDigit; let lo = *acc as BigDigit; *acc >>= big_digit::BITS; lo } // Subtract with borrow: #[inline] fn sbb(a: BigDigit, b: BigDigit, acc: &mut SignedDoubleBigDigit) -> BigDigit { *acc += a as SignedDoubleBigDigit; *acc -= b as SignedDoubleBigDigit; let lo = *acc as BigDigit; *acc >>= big_digit::BITS; lo } #[inline] pub fn mac_with_carry(a: BigDigit, b: BigDigit, c: BigDigit, acc: &mut DoubleBigDigit) -> BigDigit { *acc += a as DoubleBigDigit; *acc += (b as DoubleBigDigit) * (c as DoubleBigDigit); let lo = *acc as BigDigit; *acc >>= big_digit::BITS; lo } #[inline] pub fn mul_with_carry(a: BigDigit, b: BigDigit, acc: &mut DoubleBigDigit) -> BigDigit { *acc += (a as DoubleBigDigit) * (b as DoubleBigDigit); let lo = *acc as BigDigit; *acc >>= big_digit::BITS; lo } /// 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 = divisor as DoubleBigDigit; ((lhs / rhs) as BigDigit, (lhs % rhs) as BigDigit) } pub fn div_rem_digit(mut a: BigUint, b: BigDigit) -> (BigUint, BigDigit) { let mut rem = 0; for d in a.data.iter_mut().rev() { let (q, r) = div_wide(rem, *d, b); *d = q; rem = r; } (a.normalized(), rem) } // Only for the Add impl: #[inline] pub 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) { *a = adc(*a, *b, &mut carry); } if carry != 0 { for a in a_hi { *a = adc(*a, 0, &mut carry); 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 fn add2(a: &mut [BigDigit], b: &[BigDigit]) { let carry = __add2(a, b); debug_assert!(carry == 0); } pub fn sub2(a: &mut [BigDigit], b: &[BigDigit]) { let mut borrow = 0; let len = cmp::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) { *a = sbb(*a, *b, &mut borrow); } if borrow != 0 { for a in a_hi { *a = sbb(*a, 0, &mut borrow); 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] pub fn __sub2rev(a: &[BigDigit], b: &mut [BigDigit]) -> BigDigit { debug_assert!(b.len() == a.len()); let mut borrow = 0; for (ai, bi) in a.iter().zip(b) { *bi = sbb(*ai, *bi, &mut borrow); } borrow as BigDigit } pub fn sub2rev(a: &[BigDigit], b: &mut [BigDigit]) { debug_assert!(b.len() >= a.len()); let len = cmp::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."); } pub fn sub_sign(a: &[BigDigit], b: &[BigDigit]) -> (Sign, BigUint) { // Normalize: let a = &a[..a.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)]; let b = &b[..b.iter().rposition(|&x| x != 0).map_or(0, |i| i + 1)]; match cmp_slice(a, b) { Greater => { let mut a = a.to_vec(); sub2(&mut a, b); (Plus, BigUint::new(a)) } Less => { let mut b = b.to_vec(); sub2(&mut b, a); (Minus, BigUint::new(b)) } _ => (NoSign, Zero::zero()), } } /// Three argument multiply accumulate: /// acc += b * c pub 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 mut a = a_hi.iter_mut(); while carry != 0 { let a = a.next().expect("carry overflow during multiplication!"); *a = adc(*a, 0, &mut carry); } } /// Three argument multiply accumulate: /// acc += b * c fn mac3(acc: &mut [BigDigit], b: &[BigDigit], c: &[BigDigit]) { 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.extend(repeat(0).take(len)); // p0 = x0 * y0 mac3(&mut p.data[..], x0, y0); p.normalize(); add2(&mut 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.extend(repeat(0).take(len)); 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 = cmp::min(x.len(), i); let x1_len = cmp::min(x.len() - x0_len, i); let y0_len = i; let y1_len = cmp::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(Plus, &x[..x0_len]); let x1 = BigInt::from_slice(Plus, &x[x0_len..x0_len + x1_len]); let x2 = BigInt::from_slice(Plus, &x[x0_len + x1_len..]); // y(t) = y2*t^2 + y1*t + y0 let y0 = BigInt::from_slice(Plus, &y[..y0_len]); let y1 = BigInt::from_slice(Plus, &y[y0_len..y0_len + y1_len]); let y2 = BigInt::from_slice(Plus, &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) / 3; let mut comp1: BigInt = (r1 - &r2) / 2; let mut comp2: BigInt = r2 - &r0; comp3 = (&comp2 - comp3)/2 + &r4*2; comp2 = comp2 + &comp1 - &r4; comp1 = 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 result = r0 + (comp1 << 32*i) + (comp2 << 2*32*i) + (comp3 << 3*32*i) + (r4 << 4*32*i); let result_pos = result.to_biguint().unwrap(); add2(&mut acc[..], &result_pos.data); } } pub 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() } pub fn scalar_mul(a: &mut [BigDigit], b: BigDigit) -> BigDigit { let mut carry = 0; for a in a.iter_mut() { *a = mul_with_carry(*a, b, &mut carry); } carry as BigDigit } pub fn div_rem(u: &BigUint, d: &BigUint) -> (BigUint, BigUint) { if d.is_zero() { panic!() } if u.is_zero() { return (Zero::zero(), Zero::zero()); } if d.data == [1] { return (u.clone(), Zero::zero()); } if d.data.len() == 1 { 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; let mut a = u << shift; let b = d << shift; // The algorithm works by incrementally calculating "guesses", q0, for part of the // remainder. Once we have any number q0 such that q0 * b <= a, we can set // // q += q0 // a -= q0 * 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 few digits of a by the last digit of b // - this should give us a guess that is "close" to the actual quotient, but is possibly // greater than the actual quotient. If q0 * b > a, we simply use iterated subtraction // until we have a guess such that q0 * b <= a. // let bn = *b.data.last().unwrap(); let q_len = a.data.len() - b.data.len() + 1; let mut q = BigUint { data: vec![0; q_len] }; // We reuse the same temporary to avoid hitting the allocator in our inner loop - this is // sized to hold a0 (in the common case; if a particular digit of the quotient is zero a0 // can be bigger). // let mut tmp = BigUint { data: Vec::with_capacity(2) }; for j in (0..q_len).rev() { /* * When calculating our next guess q0, we don't need to consider the digits below j * + b.data.len() - 1: we're guessing digit j of the quotient (i.e. q0 << j) from * digit bn of the divisor (i.e. bn << (b.data.len() - 1) - so the product of those * two numbers will be zero in all digits up to (j + b.data.len() - 1). */ let offset = j + b.data.len() - 1; if offset >= a.data.len() { continue; } /* just avoiding a heap allocation: */ let mut a0 = tmp; a0.data.truncate(0); a0.data.extend(a.data[offset..].iter().cloned()); /* * q0 << j * big_digit::BITS is our actual quotient estimate - we do the shifts * implicitly at the end, when adding and subtracting to a and q. Not only do we * save the cost of the shifts, the rest of the arithmetic gets to work with * smaller numbers. */ let (mut q0, _) = div_rem_digit(a0, bn); let mut prod = &b * &q0; while cmp_slice(&prod.data[..], &a.data[j..]) == Greater { let one: BigUint = One::one(); q0 = q0 - one; prod = prod - &b; } add2(&mut q.data[j..], &q0.data[..]); sub2(&mut a.data[j..], &prod.data[..]); a.normalize(); tmp = q0; } debug_assert!(a < b); (q.normalized(), a >> shift) } /// Find last set bit /// fls(0) == 0, fls(u32::MAX) == 32 pub fn fls(v: T) -> usize { mem::size_of::() * 8 - v.leading_zeros() as usize } pub fn ilog2(v: T) -> usize { fls(v) - 1 } #[inline] pub fn biguint_shl(n: Cow, bits: usize) -> BigUint { let n_unit = bits / big_digit::BITS; let mut data = match n_unit { 0 => n.into_owned().data, _ => { let len = n_unit + n.data.len() + 1; let mut data = Vec::with_capacity(len); data.extend(repeat(0).take(n_unit)); data.extend(n.data.iter().cloned()); data } }; let n_bits = bits % big_digit::BITS; if n_bits > 0 { let mut carry = 0; for elem in data[n_unit..].iter_mut() { let new_carry = *elem >> (big_digit::BITS - n_bits); *elem = (*elem << n_bits) | carry; carry = new_carry; } if carry != 0 { data.push(carry); } } BigUint::new(data) } #[inline] pub fn biguint_shr(n: Cow, bits: usize) -> BigUint { let n_unit = bits / big_digit::BITS; if n_unit >= n.data.len() { return Zero::zero(); } let mut data = match n { Cow::Borrowed(n) => n.data[n_unit..].to_vec(), Cow::Owned(mut n) => { n.data.drain(..n_unit); n.data } }; let n_bits = bits % big_digit::BITS; if n_bits > 0 { let mut borrow = 0; for elem in data.iter_mut().rev() { let new_borrow = *elem << (big_digit::BITS - n_bits); *elem = (*elem >> n_bits) | borrow; borrow = new_borrow; } } BigUint::new(data) } pub fn cmp_slice(a: &[BigDigit], b: &[BigDigit]) -> Ordering { debug_assert!(a.last() != Some(&0)); debug_assert!(b.last() != Some(&0)); let (a_len, b_len) = (a.len(), b.len()); if a_len < b_len { return Less; } if a_len > b_len { return Greater; } for (&ai, &bi) in a.iter().rev().zip(b.iter().rev()) { if ai < bi { return Less; } if ai > bi { return Greater; } } return Equal; } #[cfg(test)] mod algorithm_tests { use big_digit::BigDigit; use {BigUint, BigInt}; use Sign::Plus; use traits::Num; #[test] fn test_sub_sign() { use super::sub_sign; 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_biguint(Plus, a.clone()); let b_i = BigInt::from_biguint(Plus, 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-0.2.0/src/bigint.rs010066400247370024737000002134611330111114300144350ustar0000000000000000use std::default::Default; use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Not, Rem, Shl, Shr, Sub, AddAssign, BitAndAssign, BitOrAssign, BitXorAssign, DivAssign, MulAssign, RemAssign, ShlAssign, ShrAssign, SubAssign}; use std::str::{self, FromStr}; use std::fmt; use std::mem; use std::cmp::Ordering::{self, Less, Greater, Equal}; use std::{i64, u64}; #[cfg(has_i128)] use std::{i128, u128}; #[allow(deprecated, unused_imports)] use std::ascii::AsciiExt; use std::iter::{Product, Sum}; #[cfg(feature = "serde")] use serde; use integer::Integer; use traits::{ToPrimitive, FromPrimitive, Num, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, Signed, Zero, One}; use self::Sign::{Minus, NoSign, Plus}; use super::ParseBigIntError; use big_digit::{self, BigDigit, DoubleBigDigit}; use biguint; use biguint::to_str_radix_reversed; use biguint::{BigUint, IntDigits}; use UsizePromotion; use IsizePromotion; /// 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, } } } 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, } } } #[cfg(feature = "serde")] impl serde::Serialize for Sign { fn serialize(&self, serializer: S) -> Result where S: serde::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), } } } #[cfg(feature = "serde")] impl<'de> serde::Deserialize<'de> for Sign { fn deserialize(deserializer: D) -> Result where D: serde::Deserializer<'de> { use serde::de::Error; use serde::de::Unexpected; let sign: i8 = serde::Deserialize::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", )), } } } /// A big signed integer type. #[derive(Clone, Debug, Hash)] pub struct BigInt { sign: Sign, data: BigUint, } /// Return the magnitude of a `BigInt`. /// /// This is in a private module, pseudo pub(crate) #[cfg(feature = "rand")] pub fn magnitude(i: &BigInt) -> &BigUint { &i.data } /// Return the owned magnitude of a `BigInt`. /// /// This is in a private module, pseudo pub(crate) #[cfg(feature = "rand")] pub fn into_magnitude(i: BigInt) -> BigUint { i.data } impl PartialEq for BigInt { #[inline] fn eq(&self, other: &BigInt) -> bool { self.cmp(other) == Equal } } 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 { 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::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) } } // 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 += (!a) as DoubleBigDigit; let lo = *acc as BigDigit; *acc >>= big_digit::BITS; lo } // !-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 | Plus => BigInt::from_biguint(Minus, &self.data + 1u32), Minus => BigInt::from_biguint(Plus, &self.data - 1u32), } } } // + 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); if a.len() > b.len() { a.truncate(b.len()); } else if b.len() > a.len() { 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); 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_and); } debug_assert!(carry_a == 0); } else if b.len() > a.len() { 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::from_slice(NoSign, &[]), (Plus, Plus) => BigInt::from_biguint(Plus, &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.assign_from_slice(NoSign, &[]), (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); if a.len() > b.len() { a.truncate(b.len()); } else if b.len() > a.len() { 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_biguint(Plus, &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.assign_from_slice(other.sign, other.digits()), (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); if a.len() > b.len() { for ai in a[b.len()..].iter_mut() { let twos_b = !0; *ai = negate_carry(*ai ^ twos_b, &mut carry_xor); } } else if b.len() > a.len() { 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); 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_xor); } debug_assert!(carry_a == 0); } else if b.len() > a.len() { 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); if a.len() > b.len() { 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); } else if b.len() > a.len() { 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.assign_from_slice(other.sign, other.digits()), (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(); } } } } 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 = try!(BigUint::from_str_radix(s, radix)); Ok(BigInt::from_biguint(sign, bu)) } } impl Shl for BigInt { type Output = BigInt; #[inline] fn shl(mut self, rhs: usize) -> BigInt { self <<= rhs; self } } impl<'a> Shl for &'a BigInt { type Output = BigInt; #[inline] fn shl(self, rhs: usize) -> BigInt { BigInt::from_biguint(self.sign, &self.data << rhs) } } impl ShlAssign for BigInt { #[inline] fn shl_assign(&mut self, rhs: usize) { self.data <<= rhs; } } // 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, rhs: usize) -> bool { i.is_negative() && biguint::trailing_zeros(&i.data) .map(|n| n < rhs) .unwrap_or(false) } impl Shr for BigInt { type Output = BigInt; #[inline] fn shr(mut self, rhs: usize) -> BigInt { self >>= rhs; self } } impl<'a> Shr for &'a BigInt { type Output = BigInt; #[inline] fn shr(self, rhs: usize) -> BigInt { let round_down = shr_round_down(self, rhs); let data = &self.data >> rhs; BigInt::from_biguint(self.sign, if round_down { data + 1u8 } else { data }) } } impl ShrAssign for BigInt { #[inline] fn shr_assign(&mut self, rhs: usize) { 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 Zero for BigInt { #[inline] fn zero() -> BigInt { BigInt::from_biguint(NoSign, Zero::zero()) } #[inline] fn is_zero(&self) -> bool { self.sign == NoSign } } impl One for BigInt { #[inline] fn one() -> BigInt { BigInt::from_biguint(Plus, One::one()) } #[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_biguint(Plus, 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::from_biguint(Plus, One::one()), Minus => BigInt::from_biguint(Minus, One::one()), NoSign => Zero::zero(), } } #[inline] fn is_positive(&self) -> bool { self.sign == Plus } #[inline] fn is_negative(&self) -> bool { self.sign == Minus } } // A convenience method for getting the absolute value of an i32 in a u32. #[inline] fn i32_abs_as_u32(a: i32) -> u32 { if a == i32::min_value() { a as u32 } else { a.abs() as u32 } } // A convenience method for getting the absolute value of an i64 in a u64. #[inline] fn i64_abs_as_u64(a: i64) -> u64 { if a == i64::min_value() { a as u64 } else { a.abs() as u64 } } // 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); impl Add for BigInt { type Output = BigInt; #[inline] fn add(self, other: BigDigit) -> BigInt { match self.sign { NoSign => From::from(other), Plus => BigInt::from_biguint(Plus, self.data + other), Minus => match self.data.cmp(&From::from(other)) { Equal => Zero::zero(), Less => BigInt::from_biguint(Plus, other - self.data), Greater => BigInt::from_biguint(Minus, self.data - other), } } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: BigDigit) { let n = mem::replace(self, BigInt::zero()); *self = n + other; } } impl Add for BigInt { type Output = BigInt; #[inline] fn add(self, other: DoubleBigDigit) -> BigInt { match self.sign { NoSign => From::from(other), Plus => BigInt::from_biguint(Plus, self.data + other), Minus => match self.data.cmp(&From::from(other)) { Equal => Zero::zero(), Less => BigInt::from_biguint(Plus, other - self.data), Greater => BigInt::from_biguint(Minus, self.data - other), } } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: DoubleBigDigit) { 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); impl Add for BigInt { type Output = BigInt; #[inline] fn add(self, other: i32) -> BigInt { if other >= 0 { self + other as u32 } else { self - i32_abs_as_u32(other) } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: i32) { if other >= 0 { *self += other as u32; } else { *self -= i32_abs_as_u32(other); } } } impl Add for BigInt { type Output = BigInt; #[inline] fn add(self, other: i64) -> BigInt { if other >= 0 { self + other as u64 } else { self - i64_abs_as_u64(other) } } } impl AddAssign for BigInt { #[inline] fn add_assign(&mut self, other: i64) { if other >= 0 { *self += other as u64; } else { *self -= i64_abs_as_u64(other); } } } // 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); impl Sub for BigInt { type Output = BigInt; #[inline] fn sub(self, other: BigDigit) -> BigInt { match self.sign { NoSign => BigInt::from_biguint(Minus, From::from(other)), Minus => BigInt::from_biguint(Minus, self.data + other), Plus => match self.data.cmp(&From::from(other)) { Equal => Zero::zero(), Greater => BigInt::from_biguint(Plus, self.data - other), Less => BigInt::from_biguint(Minus, other - self.data), } } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: BigDigit) { let n = mem::replace(self, BigInt::zero()); *self = n - other; } } impl Sub for BigDigit { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { -(other - self) } } impl Sub for BigInt { type Output = BigInt; #[inline] fn sub(self, other: DoubleBigDigit) -> BigInt { match self.sign { NoSign => BigInt::from_biguint(Minus, From::from(other)), Minus => BigInt::from_biguint(Minus, self.data + other), Plus => match self.data.cmp(&From::from(other)) { Equal => Zero::zero(), Greater => BigInt::from_biguint(Plus, self.data - other), Less => BigInt::from_biguint(Minus, other - self.data), } } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: DoubleBigDigit) { let n = mem::replace(self, BigInt::zero()); *self = n - other; } } impl Sub for DoubleBigDigit { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { -(other - self) } } 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 { if other >= 0 { self - other as u32 } else { self + i32_abs_as_u32(other) } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: i32) { if other >= 0 { *self -= other as u32; } else { *self += i32_abs_as_u32(other); } } } impl Sub for i32 { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { if self >= 0 { self as u32 - other } else { -other - i32_abs_as_u32(self) } } } impl Sub for BigInt { type Output = BigInt; #[inline] fn sub(self, other: i64) -> BigInt { if other >= 0 { self - other as u64 } else { self + i64_abs_as_u64(other) } } } impl SubAssign for BigInt { #[inline] fn sub_assign(&mut self, other: i64) { if other >= 0 { *self -= other as u64; } else { *self += i64_abs_as_u64(other); } } } impl Sub for i64 { type Output = BigInt; #[inline] fn sub(self, other: BigInt) -> BigInt { if self >= 0 { self as u64 - other } else { -other - i64_abs_as_u64(self) } } } forward_all_binop_to_ref_ref!(impl Mul for BigInt, mul); impl<'a, 'b> Mul<&'b BigInt> for &'a BigInt { type Output = BigInt; #[inline] fn mul(self, other: &BigInt) -> BigInt { BigInt::from_biguint(self.sign * other.sign, &self.data * &other.data) } } impl<'a> MulAssign<&'a BigInt> for BigInt { #[inline] fn mul_assign(&mut self, other: &BigInt) { *self = &*self * other; } } forward_val_assign!(impl MulAssign for BigInt, mul_assign); 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); impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: BigDigit) -> BigInt { BigInt::from_biguint(self.sign, self.data * other) } } impl MulAssign for BigInt { #[inline] fn mul_assign(&mut self, other: BigDigit) { self.data *= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: DoubleBigDigit) -> BigInt { BigInt::from_biguint(self.sign, self.data * other) } } impl MulAssign for BigInt { #[inline] fn mul_assign(&mut self, other: DoubleBigDigit) { 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); impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: i32) -> BigInt { if other >= 0 { self * other as u32 } else { -(self * i32_abs_as_u32(other)) } } } impl MulAssign for BigInt { #[inline] fn mul_assign(&mut self, other: i32) { if other >= 0 { *self *= other as u32; } else { self.sign = -self.sign; *self *= i32_abs_as_u32(other); } } } impl Mul for BigInt { type Output = BigInt; #[inline] fn mul(self, other: i64) -> BigInt { if other >= 0 { self * other as u64 } else { -(self * i64_abs_as_u64(other)) } } } impl MulAssign for BigInt { #[inline] fn mul_assign(&mut self, other: i64) { if other >= 0 { *self *= other as u64; } else { self.sign = -self.sign; *self *= i64_abs_as_u64(other); } } } 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); impl Div for BigInt { type Output = BigInt; #[inline] fn div(self, other: BigDigit) -> BigInt { BigInt::from_biguint(self.sign, self.data / other) } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: BigDigit) { self.data /= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Div for BigDigit { 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: DoubleBigDigit) -> BigInt { BigInt::from_biguint(self.sign, self.data / other) } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: DoubleBigDigit) { self.data /= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Div for DoubleBigDigit { 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); impl Div for BigInt { type Output = BigInt; #[inline] fn div(self, other: i32) -> BigInt { if other >= 0 { self / other as u32 } else { -(self / i32_abs_as_u32(other)) } } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: i32) { if other >= 0 { *self /= other as u32; } else { self.sign = -self.sign; *self /= i32_abs_as_u32(other); } } } impl Div for i32 { type Output = BigInt; #[inline] fn div(self, other: BigInt) -> BigInt { if self >= 0 { self as u32 / other } else { -(i32_abs_as_u32(self) / other) } } } impl Div for BigInt { type Output = BigInt; #[inline] fn div(self, other: i64) -> BigInt { if other >= 0 { self / other as u64 } else { -(self / i64_abs_as_u64(other)) } } } impl DivAssign for BigInt { #[inline] fn div_assign(&mut self, other: i64) { if other >= 0 { *self /= other as u64; } else { self.sign = -self.sign; *self /= i64_abs_as_u64(other); } } } impl Div for i64 { type Output = BigInt; #[inline] fn div(self, other: BigInt) -> BigInt { if self >= 0 { self as u64 / other } else { -(i64_abs_as_u64(self) / 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 { 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); impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: BigDigit) -> BigInt { BigInt::from_biguint(self.sign, self.data % other) } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: BigDigit) { self.data %= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Rem for BigDigit { type Output = BigInt; #[inline] fn rem(self, other: BigInt) -> BigInt { BigInt::from_biguint(Plus, self % other.data) } } impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: DoubleBigDigit) -> BigInt { BigInt::from_biguint(self.sign, self.data % other) } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: DoubleBigDigit) { self.data %= other; if self.data.is_zero() { self.sign = NoSign; } } } impl Rem for DoubleBigDigit { type Output = BigInt; #[inline] fn rem(self, other: BigInt) -> BigInt { BigInt::from_biguint(Plus, 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); impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: i32) -> BigInt { if other >= 0 { self % other as u32 } else { self % i32_abs_as_u32(other) } } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: i32) { if other >= 0 { *self %= other as u32; } else { *self %= i32_abs_as_u32(other); } } } impl Rem for i32 { type Output = BigInt; #[inline] fn rem(self, other: BigInt) -> BigInt { if self >= 0 { self as u32 % other } else { -(i32_abs_as_u32(self) % other) } } } impl Rem for BigInt { type Output = BigInt; #[inline] fn rem(self, other: i64) -> BigInt { if other >= 0 { self % other as u64 } else { self % i64_abs_as_u64(other) } } } impl RemAssign for BigInt { #[inline] fn rem_assign(&mut self, other: i64) { if other >= 0 { *self %= other as u64; } else { *self %= i64_abs_as_u64(other); } } } impl Rem for i64 { type Output = BigInt; #[inline] fn rem(self, other: BigInt) -> BigInt { if self >= 0 { self as u64 % other } else { -(i64_abs_as_u64(self) % other) } } } 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 CheckedAdd for BigInt { #[inline] fn checked_add(&self, v: &BigInt) -> Option { return Some(self.add(v)); } } impl CheckedSub for BigInt { #[inline] fn checked_sub(&self, v: &BigInt) -> Option { return Some(self.sub(v)); } } impl CheckedMul for BigInt { #[inline] fn checked_mul(&self, v: &BigInt) -> Option { return Some(self.mul(v)); } } impl CheckedDiv for BigInt { #[inline] fn checked_div(&self, v: &BigInt) -> Option { if v.is_zero() { return None; } return Some(self.div(v)); } } 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_mod_floor(&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, _) = self.div_mod_floor(other); d } #[inline] fn mod_floor(&self, other: &BigInt) -> BigInt { let (_, m) = self.div_mod_floor(other); m } fn div_mod_floor(&self, other: &BigInt) -> (BigInt, BigInt) { // m.sign == other.sign let (d_ui, m_ui) = self.data.div_rem(&other.data); let d = BigInt::from_biguint(Plus, d_ui); let m = BigInt::from_biguint(Plus, m_ui); let one: BigInt = One::one(); match (self.sign, other.sign) { (_, NoSign) => panic!(), (Plus, Plus) | (NoSign, Plus) => (d, m), (Plus, Minus) | (NoSign, Minus) => { if m.is_zero() { (-d, Zero::zero()) } else { (-d - one, m + other) } } (Minus, Plus) => { if m.is_zero() { (-d, Zero::zero()) } else { (-d - one, other - m) } } (Minus, Minus) => (d, -m), } } /// 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_biguint(Plus, 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_biguint(Plus, self.data.lcm(&other.data)) } /// Deprecated, use `is_multiple_of` instead. #[inline] fn divides(&self, other: &BigInt) -> bool { return 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() } } impl ToPrimitive for BigInt { #[inline] fn to_i64(&self) -> Option { match self.sign { Plus => self.data.to_i64(), NoSign => Some(0), Minus => { self.data.to_u64().and_then(|n| { let m: u64 = 1 << 63; if n < m { Some(-(n as i64)) } else if n == m { Some(i64::MIN) } else { None } }) } } } #[inline] #[cfg(has_i128)] fn to_i128(&self) -> Option { match self.sign { Plus => self.data.to_i128(), NoSign => Some(0), Minus => { self.data.to_u128().and_then(|n| { let m: u128 = 1 << 127; if n < m { Some(-(n as i128)) } else if n == m { Some(i128::MIN) } else { None } }) } } } #[inline] fn to_u64(&self) -> Option { match self.sign { Plus => self.data.to_u64(), NoSign => Some(0), Minus => None, } } #[inline] #[cfg(has_i128)] fn to_u128(&self) -> Option { match self.sign { Plus => self.data.to_u128(), NoSign => Some(0), Minus => None, } } #[inline] fn to_f32(&self) -> Option { self.data.to_f32().map(|n| { if self.sign == Minus { -n } else { n } }) } #[inline] fn to_f64(&self) -> Option { self.data.to_f64().map(|n| { if self.sign == Minus { -n } else { n } }) } } impl FromPrimitive for BigInt { #[inline] fn from_i64(n: i64) -> Option { Some(BigInt::from(n)) } #[inline] #[cfg(has_i128)] fn from_i128(n: i128) -> Option { Some(BigInt::from(n)) } #[inline] fn from_u64(n: u64) -> Option { Some(BigInt::from(n)) } #[inline] #[cfg(has_i128)] 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(|x| BigInt::from_biguint(Plus, x)) } else { BigUint::from_f64(-n).map(|x| BigInt::from_biguint(Minus, x)) } } } impl From for BigInt { #[inline] fn from(n: i64) -> Self { if n >= 0 { BigInt::from(n as u64) } else { let u = u64::MAX - (n as u64) + 1; BigInt { sign: Minus, data: BigUint::from(u), } } } } #[cfg(has_i128)] impl From for BigInt { #[inline] fn from(n: i128) -> Self { if n >= 0 { BigInt::from(n as u128) } else { let u = u128::MAX - (n as u128) + 1; BigInt { sign: Minus, data: BigUint::from(u), } } } } macro_rules! impl_bigint_from_int { ($T:ty) => { impl From<$T> for BigInt { #[inline] fn from(n: $T) -> Self { BigInt::from(n as i64) } } } } impl_bigint_from_int!(i8); impl_bigint_from_int!(i16); impl_bigint_from_int!(i32); impl_bigint_from_int!(isize); impl From for BigInt { #[inline] fn from(n: u64) -> Self { if n > 0 { BigInt { sign: Plus, data: BigUint::from(n), } } else { BigInt::zero() } } } #[cfg(has_i128)] impl From for BigInt { #[inline] fn from(n: u128) -> Self { if n > 0 { BigInt { sign: Plus, data: BigUint::from(n), } } else { BigInt::zero() } } } macro_rules! impl_bigint_from_uint { ($T:ty) => { impl From<$T> for BigInt { #[inline] fn from(n: $T) -> Self { BigInt::from(n as u64) } } } } impl_bigint_from_uint!(u8); impl_bigint_from_uint!(u16); impl_bigint_from_uint!(u32); impl_bigint_from_uint!(usize); impl From for BigInt { #[inline] fn from(n: BigUint) -> Self { if n.is_zero() { BigInt::zero() } else { BigInt { sign: Plus, data: n, } } } } impl IntDigits for BigInt { #[inline] fn digits(&self) -> &[BigDigit] { self.data.digits() } #[inline] fn digits_mut(&mut self) -> &mut Vec { self.data.digits_mut() } #[inline] fn normalize(&mut self) { self.data.normalize(); if self.data.is_zero() { self.sign = NoSign; } } #[inline] fn capacity(&self) -> usize { self.data.capacity() } #[inline] fn len(&self) -> usize { self.data.len() } } #[cfg(feature = "serde")] impl serde::Serialize for BigInt { fn serialize(&self, serializer: S) -> Result where S: serde::Serializer { // Note: do not change the serialization format, or it may break // forward and backward compatibility of serialized data! (self.sign, &self.data).serialize(serializer) } } #[cfg(feature = "serde")] impl<'de> serde::Deserialize<'de> for BigInt { fn deserialize(deserializer: D) -> Result where D: serde::Deserializer<'de> { let (sign, data) = serde::Deserialize::deserialize(deserializer)?; Ok(BigInt::from_biguint(sign, data)) } } /// A generic trait for converting a value to a `BigInt`. pub trait ToBigInt { /// Converts the value of `self` to a `BigInt`. fn to_bigint(&self) -> Option; } impl ToBigInt for BigInt { #[inline] fn to_bigint(&self) -> Option { Some(self.clone()) } } impl ToBigInt for BigUint { #[inline] fn to_bigint(&self) -> Option { if self.is_zero() { Some(Zero::zero()) } else { Some(BigInt { sign: Plus, data: self.clone(), }) } } } impl biguint::ToBigUint for BigInt { #[inline] fn to_biguint(&self) -> Option { match self.sign() { Plus => Some(self.data.clone()), NoSign => Some(Zero::zero()), Minus => None, } } } macro_rules! impl_to_bigint { ($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); #[cfg(has_i128)] 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); #[cfg(has_i128)] impl_to_bigint!(u128, FromPrimitive::from_u128); impl_to_bigint!(f32, FromPrimitive::from_f32); impl_to_bigint!(f64, FromPrimitive::from_f64); impl BigInt { /// Creates and initializes a BigInt. /// /// The digits are in little-endian base 232. #[inline] pub fn new(sign: Sign, digits: Vec) -> BigInt { BigInt::from_biguint(sign, BigUint::new(digits)) } /// Creates and initializes a `BigInt`. /// /// The digits are in little-endian base 232. #[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: sign, data: data, } } /// Creates and initializes a `BigInt`. #[inline] pub fn from_slice(sign: Sign, slice: &[u32]) -> BigInt { BigInt::from_biguint(sign, BigUint::from_slice(slice)) } /// Reinitializes a `BigInt`. #[inline] pub fn assign_from_slice(&mut self, sign: Sign, slice: &[u32]) { if sign == NoSign { self.data.assign_from_slice(&[]); self.sign = NoSign; } else { self.data.assign_from_slice(slice); self.sign = match self.data.is_zero() { true => NoSign, false => 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 { 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)) } } /// 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 { 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)) } } /// 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 { str::from_utf8(buf).ok().and_then(|s| 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 { BigUint::from_radix_be(buf, radix).map(|u| 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 { BigUint::from_radix_le(buf, radix).map(|u| 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 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 { let mut bytes = self.data.to_bytes_be(); let first_byte = bytes.first().map(|v| *v).unwrap_or(0); if first_byte > 0x7f && !(first_byte == 0x80 && bytes.iter().skip(1).all(Zero::is_zero)) { // msb used by magnitude, extend by 1 byte bytes.insert(0, 0); } if self.sign == Sign::Minus { twos_complement_be(&mut bytes); } bytes } /// 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 { let mut bytes = self.data.to_bytes_le(); let last_byte = bytes.last().map(|v| *v).unwrap_or(0); if last_byte > 0x7f && !(last_byte == 0x80 && bytes.iter().rev().skip(1).all(Zero::is_zero)) { // msb used by magnitude, extend by 1 byte bytes.push(0); } if self.sign == Sign::Minus { twos_complement_le(&mut bytes); } bytes } /// 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::{ToBigInt, Sign}; /// /// assert_eq!(ToBigInt::to_bigint(&1234).unwrap().sign(), Sign::Plus); /// assert_eq!(ToBigInt::to_bigint(&-4321).unwrap().sign(), Sign::Minus); /// assert_eq!(ToBigInt::to_bigint(&0).unwrap().sign(), Sign::NoSign); /// ``` #[inline] pub fn sign(&self) -> Sign { self.sign } /// Determines the fewest bits necessary to express the `BigInt`, /// not including the sign. #[inline] pub fn bits(&self) -> usize { 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 { return Some(self.add(v)); } #[inline] pub fn checked_sub(&self, v: &BigInt) -> Option { return Some(self.sub(v)); } #[inline] pub fn checked_mul(&self, v: &BigInt) -> Option { return Some(self.mul(v)); } #[inline] pub fn checked_div(&self, v: &BigInt) -> Option { if v.is_zero() { return None; } return Some(self.div(v)); } /// 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 { assert!(!exponent.is_negative(), "negative exponentiation is not supported!"); assert!(!modulus.is_zero(), "divide by zero!"); let result = self.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 (self.is_negative(), 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) } } impl_sum_iter_type!(BigInt); impl_product_iter_type!(BigInt); /// 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.not(); if carry { *d = d.wrapping_add(1); carry = d.is_zero(); } } } #[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, FromPrimitive::from_usize(inp_n).unwrap()); let ans = BigInt { sign: ans_s, data: FromPrimitive::from_usize(ans_n).unwrap(), }; 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: FromPrimitive::from_u32(ans_n).unwrap(), }; 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: FromPrimitive::from_u32(ans_n).unwrap(), }; 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-0.2.0/src/bigrand.rs010066400247370024737000000140061330143405100145670ustar0000000000000000//! Randomization of big integers use rand::prelude::*; use rand::distributions::uniform::{SampleUniform, UniformSampler}; use BigInt; use BigUint; use Sign::*; use big_digit::BigDigit; use bigint::{magnitude, into_magnitude}; use traits::Zero; use integer::Integer; pub trait RandBigInt { /// Generate a random `BigUint` of the given bit size. fn gen_biguint(&mut self, bit_size: usize) -> BigUint; /// Generate a random BigInt of the given bit size. fn gen_bigint(&mut self, bit_size: usize) -> 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; } impl RandBigInt for R { fn gen_biguint(&mut self, bit_size: usize) -> BigUint { use super::big_digit::BITS; let (digits, rem) = bit_size.div_rem(&BITS); let mut data = Vec::with_capacity(digits + 1); for _ in 0..digits { data.push(self.gen()); } if rem > 0 { let final_digit: BigDigit = self.gen(); data.push(final_digit >> (BITS - rem)); } BigUint::new(data) } fn gen_bigint(&mut self, bit_size: usize) -> 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(magnitude(&ubound))) } else if ubound.is_zero() { lbound + BigInt::from(self.gen_biguint_below(magnitude(&lbound))) } else { let delta = ubound - lbound; lbound + BigInt::from(self.gen_biguint_below(magnitude(&delta))) } } } /// 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: Self::X, high: Self::X) -> Self { assert!(low < high); UniformBigUint { len: high - &low, base: low, } } #[inline] fn new_inclusive(low: Self::X, high: Self::X) -> Self { 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: Self::X, high: Self::X, rng: &mut R) -> Self::X { rng.gen_biguint_range(&low, &high) } } 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: Self::X, high: Self::X) -> Self { assert!(low < high); UniformBigInt { len: into_magnitude(high - &low), base: low, } } #[inline] fn new_inclusive(low: Self::X, high: Self::X) -> Self { 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: Self::X, high: Self::X, rng: &mut R) -> Self::X { rng.gen_bigint_range(&low, &high) } } impl SampleUniform for BigInt { type Sampler = UniformBigInt; } /// A random distribution for `BigUint` and `BigInt` values of a particular bit size. #[derive(Clone, Copy, Debug)] pub struct RandomBits { bits: usize, } impl RandomBits { #[inline] pub fn new(bits: usize) -> 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-0.2.0/src/biguint.rs010066400247370024737000002213771330110107400146310ustar0000000000000000use std::borrow::Cow; use std::default::Default; use std::iter::{Product, Sum}; use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub, AddAssign, BitAndAssign, BitOrAssign, BitXorAssign, DivAssign, MulAssign, RemAssign, ShlAssign, ShrAssign, SubAssign}; use std::str::{self, FromStr}; use std::fmt; use std::cmp; use std::mem; use std::cmp::Ordering::{self, Less, Greater, Equal}; use std::{f32, f64}; use std::{u8, u64}; #[allow(deprecated, unused_imports)] use std::ascii::AsciiExt; #[cfg(feature = "serde")] use serde; use integer::Integer; use traits::{ToPrimitive, FromPrimitive, Float, Num, Unsigned, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, Zero, One}; use big_digit::{self, BigDigit, DoubleBigDigit}; #[path = "algorithms.rs"] mod algorithms; #[path = "monty.rs"] mod monty; use self::algorithms::{mac_with_carry, mul3, scalar_mul, div_rem, div_rem_digit}; use self::algorithms::{__add2, __sub2rev, add2, sub2, sub2rev}; use self::algorithms::{biguint_shl, biguint_shr}; use self::algorithms::{cmp_slice, fls, ilog2}; use self::monty::monty_modpow; use UsizePromotion; use ParseBigIntError; /// A big unsigned integer type. #[derive(Clone, Debug, Hash)] pub struct BigUint { data: Vec, } impl PartialEq for BigUint { #[inline] fn eq(&self, other: &BigUint) -> bool { match self.cmp(other) { Equal => true, _ => false, } } } 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[..]) } } impl Default for BigUint { #[inline] fn default() -> BigUint { Zero::zero() } } 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 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 fn from_bitwise_digits_le(v: &[u8], bits: usize) -> BigUint { debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits == 0); debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits))); let digits_per_big_digit = big_digit::BITS / bits; let data = v.chunks(digits_per_big_digit) .map(|chunk| { chunk.iter().rev().fold(0, |acc, &c| (acc << bits) | c as BigDigit) }) .collect(); BigUint::new(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: usize) -> BigUint { debug_assert!(!v.is_empty() && bits <= 8 && big_digit::BITS % bits != 0); debug_assert!(v.iter().all(|&c| (c as BigDigit) < (1 << bits))); let big_digits = (v.len() * bits + big_digit::BITS - 1) / big_digit::BITS; 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 |= (c as BigDigit) << 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 = (c as BigDigit) >> (bits - dbits); } } if dbits > 0 { debug_assert!(dbits < big_digit::BITS); data.push(d as BigDigit); } BigUint::new(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| (c as u32) < radix)); // Estimate how big the result will be, so we can pre-allocate it. let bits = (radix as f64).log2() * v.len() as f64; let big_digits = (bits / big_digit::BITS as f64).ceil(); let mut data = Vec::with_capacity(big_digits as usize); let (base, power) = get_radix_base(radix); let radix = radix as BigDigit; let r = v.len() % power; let i = if r == 0 { power } else { r }; let (head, tail) = v.split_at(i); let first = head.iter().fold(0, |acc, &d| acc * radix + d as BigDigit); 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 + d as BigDigit); add2(&mut data, &[n]); } BigUint::new(data) } 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, _ => 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) } } 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(); } } impl Shl for BigUint { type Output = BigUint; #[inline] fn shl(self, rhs: usize) -> BigUint { biguint_shl(Cow::Owned(self), rhs) } } impl<'a> Shl for &'a BigUint { type Output = BigUint; #[inline] fn shl(self, rhs: usize) -> BigUint { biguint_shl(Cow::Borrowed(self), rhs) } } impl ShlAssign for BigUint { #[inline] fn shl_assign(&mut self, rhs: usize) { let n = mem::replace(self, BigUint::zero()); *self = n << rhs; } } impl Shr for BigUint { type Output = BigUint; #[inline] fn shr(self, rhs: usize) -> BigUint { biguint_shr(Cow::Owned(self), rhs) } } impl<'a> Shr for &'a BigUint { type Output = BigUint; #[inline] fn shr(self, rhs: usize) -> BigUint { biguint_shr(Cow::Borrowed(self), rhs) } } impl ShrAssign for BigUint { #[inline] fn shr_assign(&mut self, rhs: usize) { let n = mem::replace(self, BigUint::zero()); *self = n >> rhs; } } impl Zero for BigUint { #[inline] fn zero() -> BigUint { BigUint::new(Vec::new()) } #[inline] fn is_zero(&self) -> bool { self.data.is_empty() } } impl One for BigUint { #[inline] fn one() -> BigUint { BigUint::new(vec![1]) } #[inline] fn is_one(&self) -> bool { self.data[..] == [1] } } impl Unsigned for BigUint {} 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); impl Add for BigUint { type Output = BigUint; #[inline] fn add(mut self, other: BigDigit) -> BigUint { self += other; self } } impl AddAssign for BigUint { #[inline] fn add_assign(&mut self, other: BigDigit) { if other != 0 { if self.data.len() == 0 { self.data.push(0); } let carry = __add2(&mut self.data, &[other]); if carry != 0 { self.data.push(carry); } } } } impl Add for BigUint { type Output = BigUint; #[inline] fn add(mut self, other: DoubleBigDigit) -> BigUint { self += other; self } } impl AddAssign for BigUint { #[inline] fn add_assign(&mut self, other: DoubleBigDigit) { 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); } } } } 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); impl Sub for BigUint { type Output = BigUint; #[inline] fn sub(mut self, other: BigDigit) -> BigUint { self -= other; self } } impl SubAssign for BigUint { fn sub_assign(&mut self, other: BigDigit) { sub2(&mut self.data[..], &[other]); self.normalize(); } } impl Sub for BigDigit { type Output = BigUint; #[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() } } impl Sub for BigUint { type Output = BigUint; #[inline] fn sub(mut self, other: DoubleBigDigit) -> BigUint { self -= other; self } } impl SubAssign for BigUint { fn sub_assign(&mut self, other: DoubleBigDigit) { let (hi, lo) = big_digit::from_doublebigdigit(other); sub2(&mut self.data[..], &[lo, hi]); self.normalize(); } } impl Sub for DoubleBigDigit { type Output = BigUint; #[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() } } forward_all_binop_to_ref_ref!(impl Mul for BigUint, mul); forward_val_assign!(impl MulAssign for BigUint, mul_assign); impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint { type Output = BigUint; #[inline] fn mul(self, other: &BigUint) -> BigUint { mul3(&self.data[..], &other.data[..]) } } impl<'a> MulAssign<&'a BigUint> for BigUint { #[inline] fn mul_assign(&mut self, other: &'a BigUint) { *self = &*self * other } } 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); impl Mul for BigUint { type Output = BigUint; #[inline] fn mul(mut self, other: BigDigit) -> BigUint { self *= other; self } } impl MulAssign for BigUint { #[inline] fn mul_assign(&mut self, other: BigDigit) { if other == 0 { self.data.clear(); } else { let carry = scalar_mul(&mut self.data[..], other); if carry != 0 { self.data.push(carry); } } } } impl Mul for BigUint { type Output = BigUint; #[inline] fn mul(mut self, other: DoubleBigDigit) -> BigUint { self *= other; self } } impl MulAssign for BigUint { #[inline] fn mul_assign(&mut self, other: DoubleBigDigit) { if other == 0 { self.data.clear(); } else if other <= BigDigit::max_value() as DoubleBigDigit { *self *= other as BigDigit } else { let (hi, lo) = big_digit::from_doublebigdigit(other); *self = mul3(&self.data[..], &[lo, hi]) } } } forward_all_binop_to_ref_ref!(impl Div for BigUint, div); forward_val_assign!(impl DivAssign for BigUint, div_assign); 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); impl Div for BigUint { type Output = BigUint; #[inline] fn div(self, other: BigDigit) -> BigUint { let (q, _) = div_rem_digit(self, other); q } } impl DivAssign for BigUint { #[inline] fn div_assign(&mut self, other: BigDigit) { *self = &*self / other; } } impl Div for BigDigit { type Output = BigUint; #[inline] fn div(self, other: BigUint) -> BigUint { match other.data.len() { 0 => panic!(), 1 => From::from(self / other.data[0]), _ => Zero::zero(), } } } impl Div for BigUint { type Output = BigUint; #[inline] fn div(self, other: DoubleBigDigit) -> BigUint { let (q, _) = self.div_rem(&From::from(other)); q } } impl DivAssign for BigUint { #[inline] fn div_assign(&mut self, other: DoubleBigDigit) { *self = &*self / other; } } impl Div for DoubleBigDigit { type Output = BigUint; #[inline] fn div(self, other: BigUint) -> BigUint { match other.data.len() { 0 => panic!(), 1 => From::from(self / other.data[0] as u64), 2 => From::from(self / big_digit::to_doublebigdigit(other.data[1], other.data[0])), _ => Zero::zero(), } } } forward_all_binop_to_ref_ref!(impl Rem for BigUint, rem); forward_val_assign!(impl RemAssign for BigUint, rem_assign); impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint { type Output = BigUint; #[inline] fn rem(self, other: &BigUint) -> BigUint { 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_val_val!(impl Rem for BigUint, rem); forward_all_scalar_binop_to_val_val!(impl Rem for BigUint, rem); impl Rem for BigUint { type Output = BigUint; #[inline] fn rem(self, other: BigDigit) -> BigUint { let (_, r) = div_rem_digit(self, other); From::from(r) } } impl RemAssign for BigUint { #[inline] fn rem_assign(&mut self, other: BigDigit) { *self = &*self % other; } } impl Rem for BigDigit { type Output = BigUint; #[inline] fn rem(mut self, other: BigUint) -> BigUint { self %= other; From::from(self) } } macro_rules! impl_rem_assign_scalar { ($scalar:ty, $to_scalar:ident) => { forward_val_assign_scalar!(impl RemAssign for BigUint, $scalar, rem_assign); impl<'a> RemAssign<&'a BigUint> for $scalar { #[inline] fn rem_assign(&mut self, other: &BigUint) { *self = match other.$to_scalar() { None => *self, Some(0) => panic!(), Some(v) => *self % v }; } } } } // we can scalar %= BigUint for any scalar, including signed types 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!(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: DoubleBigDigit) -> BigUint { let (_, r) = self.div_rem(&From::from(other)); r } } impl RemAssign for BigUint { #[inline] fn rem_assign(&mut self, other: DoubleBigDigit) { *self = &*self % other; } } impl Rem for DoubleBigDigit { type Output = BigUint; #[inline] fn rem(mut self, other: BigUint) -> BigUint { self %= other; From::from(self) } } impl Neg for BigUint { type Output = BigUint; #[inline] fn neg(self) -> BigUint { panic!() } } impl<'a> Neg for &'a BigUint { type Output = BigUint; #[inline] fn neg(self) -> BigUint { panic!() } } impl CheckedAdd for BigUint { #[inline] fn checked_add(&self, v: &BigUint) -> Option { return Some(self.add(v)); } } 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)), } } } impl CheckedMul for BigUint { #[inline] fn checked_mul(&self, v: &BigUint) -> Option { return Some(self.mul(v)); } } impl CheckedDiv for BigUint { #[inline] fn checked_div(&self, v: &BigUint) -> Option { if v.is_zero() { return None; } return Some(self.div(v)); } } impl Integer for BigUint { #[inline] fn div_rem(&self, other: &BigUint) -> (BigUint, BigUint) { div_rem(self, other) } #[inline] fn div_floor(&self, other: &BigUint) -> BigUint { let (d, _) = div_rem(self, other); d } #[inline] fn mod_floor(&self, other: &BigUint) -> BigUint { let (_, m) = div_rem(self, other); m } #[inline] fn div_mod_floor(&self, other: &BigUint) -> (BigUint, BigUint) { div_rem(self, other) } /// 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) -> usize { trailing_zeros(x).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 { self / self.gcd(other) * other } /// 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() } } fn high_bits_to_u64(v: &BigUint) -> u64 { match v.data.len() { 0 => 0, 1 => v.data[0] as u64, _ => { 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) % big_digit::BITS + 1; let bits_want = cmp::min(64 - ret_bits, digit_bits); if bits_want != 64 { ret <<= bits_want; } ret |= *d as u64 >> (digit_bits - bits_want); 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] #[cfg(has_i128)] fn to_i128(&self) -> Option { self.to_u128().as_ref().and_then(u128::to_i128) } #[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; } ret += (*i as u64) << bits; bits += big_digit::BITS; } Some(ret) } #[inline] #[cfg(has_i128)] 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 += (*i as u128) << bits; bits += big_digit::BITS; } Some(ret) } #[inline] fn to_f32(&self) -> Option { let mantissa = high_bits_to_u64(self); let exponent = self.bits() - fls(mantissa); if exponent > f32::MAX_EXP as usize { None } else { let ret = (mantissa as f32) * 2.0f32.powi(exponent as i32); if ret.is_infinite() { None } else { Some(ret) } } } #[inline] fn to_f64(&self) -> Option { let mantissa = high_bits_to_u64(self); let exponent = self.bits() - fls(mantissa); if exponent > f64::MAX_EXP as usize { None } else { let ret = (mantissa as f64) * 2.0f64.powi(exponent as i32); if ret.is_infinite() { None } else { Some(ret) } } } } impl FromPrimitive for BigUint { #[inline] fn from_i64(n: i64) -> Option { if n >= 0 { Some(BigUint::from(n as u64)) } else { None } } #[inline] #[cfg(has_i128)] 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] #[cfg(has_i128)] 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) = Float::integer_decode(n); if sign == -1 { return None; } let mut ret = BigUint::from(mantissa); if exponent > 0 { ret = ret << exponent as usize; } else if exponent < 0 { ret = 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 } } #[cfg(has_i128)] 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: $T) -> Self { BigUint::from(n as u64) } } } } impl_biguint_from_uint!(u8); impl_biguint_from_uint!(u16); impl_biguint_from_uint!(u32); impl_biguint_from_uint!(usize); /// A generic trait for converting a value to a `BigUint`. pub trait ToBigUint { /// Converts the value of `self` to a `BigUint`. fn to_biguint(&self) -> Option; } impl ToBigUint for BigUint { #[inline] fn to_biguint(&self) -> Option { Some(self.clone()) } } macro_rules! impl_to_biguint { ($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); #[cfg(has_i128)] 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); #[cfg(has_i128)] 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 fn to_bitwise_digits_le(u: &BigUint, bits: usize) -> 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 = (u.bits() + bits - 1) / bits; 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: usize) -> Vec { debug_assert!(!u.is_zero() && bits <= 8 && big_digit::BITS % bits != 0); let mask: BigDigit = (1 << bits) - 1; let digits = (u.bits() + bits - 1) / bits; 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 fn to_radix_digits_le(u: &BigUint, radix: u32) -> Vec { debug_assert!(!u.is_zero() && !radix.is_power_of_two()); // Estimate how big the result will be, so we can pre-allocate it. let radix_digits = ((u.bits() as f64) / (radix as f64).log2()).ceil(); let mut res = Vec::with_capacity(radix_digits as usize); let mut digits = u.clone(); let (base, power) = get_radix_base(radix); let radix = radix as BigDigit; 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 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 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!((*r as u32) < radix); if *r < 10 { *r += b'0'; } else { *r += b'a' - 10; } } res } impl BigUint { /// Creates and initializes a `BigUint`. /// /// The digits are in little-endian base 232. #[inline] pub fn new(digits: Vec) -> BigUint { BigUint { data: digits }.normalized() } /// Creates and initializes a `BigUint`. /// /// The digits are in little-endian base 232. #[inline] pub fn from_slice(slice: &[u32]) -> BigUint { BigUint::new(slice.to_vec()) } /// Assign a value to a `BigUint`. /// /// The digits are in little-endian base 232. #[inline] pub fn assign_from_slice(&mut self, slice: &[u32]) { self.data.resize(slice.len(), 0); self.data.clone_from_slice(slice); 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 { 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 { str::from_utf8(buf).ok().and_then(|s| 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 { assert!(2 <= radix && radix <= 256, "The radix must be within 2...256"); 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) } /// 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 { assert!(2 <= radix && radix <= 256, "The radix must be within 2...256"); 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) } /// 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 { to_bitwise_digits_le(self, 8) } } /// 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 = 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 { to_radix_le(self, radix) } /// Determines the fewest bits necessary to express the `BigUint`. #[inline] pub fn bits(&self) -> usize { if self.is_zero() { return 0; } let zeros = self.data.last().unwrap().leading_zeros(); return self.data.len() * big_digit::BITS - zeros as usize; } /// Strips off trailing zero bigdigits - comparisons require the last element in the vector to /// be nonzero. #[inline] fn normalize(&mut self) { while let Some(&0) = self.data.last() { self.data.pop(); } } /// Returns a normalized `BigUint`. #[inline] fn normalized(mut self) -> BigUint { self.normalize(); self } /// Returns `(self ^ exponent) % modulus`. /// /// Panics if the modulus is zero. pub fn modpow(&self, exponent: &Self, modulus: &Self) -> Self { assert!(!modulus.is_zero(), "divide by zero!"); // For an odd modulus, we can use Montgomery multiplication in base 2^32. if modulus.is_odd() { return monty_modpow(self, exponent, modulus); } // Otherwise do basically the same as `num::pow`, but with a modulus. let one = BigUint::one(); if exponent.is_zero() { return one; } let mut base = self % modulus; let mut exp = exponent.clone(); while exp.is_even() { base = &base * &base % modulus; exp >>= 1; } if exp == one { return base } let mut acc = base.clone(); while exp > one { exp >>= 1; base = &base * &base % modulus; if exp.is_odd() { acc = acc * &base % modulus; } } acc } } /// Returns the number of least-significant bits that are zero, /// or `None` if the entire number is zero. pub fn trailing_zeros(u: &BigUint) -> Option { u.data .iter() .enumerate() .find(|&(_, &digit)| digit != 0) .map(|(i, digit)| i * big_digit::BITS + digit.trailing_zeros() as usize) } impl_sum_iter_type!(BigUint); impl_product_iter_type!(BigUint); pub 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() } } #[cfg(feature = "serde")] impl serde::Serialize for BigUint { fn serialize(&self, serializer: S) -> Result where S: serde::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: &Vec = &self.data; data.serialize(serializer) } } #[cfg(feature = "serde")] impl<'de> serde::Deserialize<'de> for BigUint { fn deserialize(deserializer: D) -> Result where D: serde::Deserializer<'de> { let data: Vec = try!(Vec::deserialize(deserializer)); Ok(BigUint::new(data)) } } /// Returns the greatest power of the radix <= big_digit::BASE #[inline] fn get_radix_base(radix: u32) -> (BigDigit, usize) { debug_assert!(2 <= radix && radix <= 256, "The radix must be within 2...256"); debug_assert!(!radix.is_power_of_two()); // To generate this table: // for radix in 2u64..257 { // let mut power = big_digit::BITS / fls(radix as u64); // let mut base = radix.pow(power as u32); // // while let Some(b) = base.checked_mul(radix) { // if b > big_digit::MAX { // break; // } // base = b; // power += 1; // } // // println!("({:10}, {:2}), // {:2}", base, power, radix); // } // and // for radix in 2u64..257 { // let mut power = 64 / fls(radix as u64); // let mut base = radix.pow(power as u32); // // while let Some(b) = base.checked_mul(radix) { // base = b; // power += 1; // } // // println!("({:20}, {:2}), // {:2}", base, power, radix); // } match big_digit::BITS { 32 => { const BASES: [(u32, usize); 257] = [ ( 0, 0), ( 0, 0), ( 0, 0), // 2 (3486784401, 20), // 3 ( 0, 0), // 4 (1220703125, 13), // 5 (2176782336, 12), // 6 (1977326743, 11), // 7 ( 0, 0), // 8 (3486784401, 10), // 9 (1000000000, 9), // 10 (2357947691, 9), // 11 ( 429981696, 8), // 12 ( 815730721, 8), // 13 (1475789056, 8), // 14 (2562890625, 8), // 15 ( 0, 0), // 16 ( 410338673, 7), // 17 ( 612220032, 7), // 18 ( 893871739, 7), // 19 (1280000000, 7), // 20 (1801088541, 7), // 21 (2494357888, 7), // 22 (3404825447, 7), // 23 ( 191102976, 6), // 24 ( 244140625, 6), // 25 ( 308915776, 6), // 26 ( 387420489, 6), // 27 ( 481890304, 6), // 28 ( 594823321, 6), // 29 ( 729000000, 6), // 30 ( 887503681, 6), // 31 ( 0, 0), // 32 (1291467969, 6), // 33 (1544804416, 6), // 34 (1838265625, 6), // 35 (2176782336, 6), // 36 (2565726409, 6), // 37 (3010936384, 6), // 38 (3518743761, 6), // 39 (4096000000, 6), // 40 ( 115856201, 5), // 41 ( 130691232, 5), // 42 ( 147008443, 5), // 43 ( 164916224, 5), // 44 ( 184528125, 5), // 45 ( 205962976, 5), // 46 ( 229345007, 5), // 47 ( 254803968, 5), // 48 ( 282475249, 5), // 49 ( 312500000, 5), // 50 ( 345025251, 5), // 51 ( 380204032, 5), // 52 ( 418195493, 5), // 53 ( 459165024, 5), // 54 ( 503284375, 5), // 55 ( 550731776, 5), // 56 ( 601692057, 5), // 57 ( 656356768, 5), // 58 ( 714924299, 5), // 59 ( 777600000, 5), // 60 ( 844596301, 5), // 61 ( 916132832, 5), // 62 ( 992436543, 5), // 63 ( 0, 0), // 64 (1160290625, 5), // 65 (1252332576, 5), // 66 (1350125107, 5), // 67 (1453933568, 5), // 68 (1564031349, 5), // 69 (1680700000, 5), // 70 (1804229351, 5), // 71 (1934917632, 5), // 72 (2073071593, 5), // 73 (2219006624, 5), // 74 (2373046875, 5), // 75 (2535525376, 5), // 76 (2706784157, 5), // 77 (2887174368, 5), // 78 (3077056399, 5), // 79 (3276800000, 5), // 80 (3486784401, 5), // 81 (3707398432, 5), // 82 (3939040643, 5), // 83 (4182119424, 5), // 84 ( 52200625, 4), // 85 ( 54700816, 4), // 86 ( 57289761, 4), // 87 ( 59969536, 4), // 88 ( 62742241, 4), // 89 ( 65610000, 4), // 90 ( 68574961, 4), // 91 ( 71639296, 4), // 92 ( 74805201, 4), // 93 ( 78074896, 4), // 94 ( 81450625, 4), // 95 ( 84934656, 4), // 96 ( 88529281, 4), // 97 ( 92236816, 4), // 98 ( 96059601, 4), // 99 ( 100000000, 4), // 100 ( 104060401, 4), // 101 ( 108243216, 4), // 102 ( 112550881, 4), // 103 ( 116985856, 4), // 104 ( 121550625, 4), // 105 ( 126247696, 4), // 106 ( 131079601, 4), // 107 ( 136048896, 4), // 108 ( 141158161, 4), // 109 ( 146410000, 4), // 110 ( 151807041, 4), // 111 ( 157351936, 4), // 112 ( 163047361, 4), // 113 ( 168896016, 4), // 114 ( 174900625, 4), // 115 ( 181063936, 4), // 116 ( 187388721, 4), // 117 ( 193877776, 4), // 118 ( 200533921, 4), // 119 ( 207360000, 4), // 120 ( 214358881, 4), // 121 ( 221533456, 4), // 122 ( 228886641, 4), // 123 ( 236421376, 4), // 124 ( 244140625, 4), // 125 ( 252047376, 4), // 126 ( 260144641, 4), // 127 ( 0, 0), // 128 ( 276922881, 4), // 129 ( 285610000, 4), // 130 ( 294499921, 4), // 131 ( 303595776, 4), // 132 ( 312900721, 4), // 133 ( 322417936, 4), // 134 ( 332150625, 4), // 135 ( 342102016, 4), // 136 ( 352275361, 4), // 137 ( 362673936, 4), // 138 ( 373301041, 4), // 139 ( 384160000, 4), // 140 ( 395254161, 4), // 141 ( 406586896, 4), // 142 ( 418161601, 4), // 143 ( 429981696, 4), // 144 ( 442050625, 4), // 145 ( 454371856, 4), // 146 ( 466948881, 4), // 147 ( 479785216, 4), // 148 ( 492884401, 4), // 149 ( 506250000, 4), // 150 ( 519885601, 4), // 151 ( 533794816, 4), // 152 ( 547981281, 4), // 153 ( 562448656, 4), // 154 ( 577200625, 4), // 155 ( 592240896, 4), // 156 ( 607573201, 4), // 157 ( 623201296, 4), // 158 ( 639128961, 4), // 159 ( 655360000, 4), // 160 ( 671898241, 4), // 161 ( 688747536, 4), // 162 ( 705911761, 4), // 163 ( 723394816, 4), // 164 ( 741200625, 4), // 165 ( 759333136, 4), // 166 ( 777796321, 4), // 167 ( 796594176, 4), // 168 ( 815730721, 4), // 169 ( 835210000, 4), // 170 ( 855036081, 4), // 171 ( 875213056, 4), // 172 ( 895745041, 4), // 173 ( 916636176, 4), // 174 ( 937890625, 4), // 175 ( 959512576, 4), // 176 ( 981506241, 4), // 177 (1003875856, 4), // 178 (1026625681, 4), // 179 (1049760000, 4), // 180 (1073283121, 4), // 181 (1097199376, 4), // 182 (1121513121, 4), // 183 (1146228736, 4), // 184 (1171350625, 4), // 185 (1196883216, 4), // 186 (1222830961, 4), // 187 (1249198336, 4), // 188 (1275989841, 4), // 189 (1303210000, 4), // 190 (1330863361, 4), // 191 (1358954496, 4), // 192 (1387488001, 4), // 193 (1416468496, 4), // 194 (1445900625, 4), // 195 (1475789056, 4), // 196 (1506138481, 4), // 197 (1536953616, 4), // 198 (1568239201, 4), // 199 (1600000000, 4), // 200 (1632240801, 4), // 201 (1664966416, 4), // 202 (1698181681, 4), // 203 (1731891456, 4), // 204 (1766100625, 4), // 205 (1800814096, 4), // 206 (1836036801, 4), // 207 (1871773696, 4), // 208 (1908029761, 4), // 209 (1944810000, 4), // 210 (1982119441, 4), // 211 (2019963136, 4), // 212 (2058346161, 4), // 213 (2097273616, 4), // 214 (2136750625, 4), // 215 (2176782336, 4), // 216 (2217373921, 4), // 217 (2258530576, 4), // 218 (2300257521, 4), // 219 (2342560000, 4), // 220 (2385443281, 4), // 221 (2428912656, 4), // 222 (2472973441, 4), // 223 (2517630976, 4), // 224 (2562890625, 4), // 225 (2608757776, 4), // 226 (2655237841, 4), // 227 (2702336256, 4), // 228 (2750058481, 4), // 229 (2798410000, 4), // 230 (2847396321, 4), // 231 (2897022976, 4), // 232 (2947295521, 4), // 233 (2998219536, 4), // 234 (3049800625, 4), // 235 (3102044416, 4), // 236 (3154956561, 4), // 237 (3208542736, 4), // 238 (3262808641, 4), // 239 (3317760000, 4), // 240 (3373402561, 4), // 241 (3429742096, 4), // 242 (3486784401, 4), // 243 (3544535296, 4), // 244 (3603000625, 4), // 245 (3662186256, 4), // 246 (3722098081, 4), // 247 (3782742016, 4), // 248 (3844124001, 4), // 249 (3906250000, 4), // 250 (3969126001, 4), // 251 (4032758016, 4), // 252 (4097152081, 4), // 253 (4162314256, 4), // 254 (4228250625, 4), // 255 ( 0, 0), // 256 ]; let (base, power) = BASES[radix as usize]; (base as BigDigit, power) } 64 => { const BASES: [(u64, usize); 257] = [ ( 0, 0), ( 0, 0), ( 9223372036854775808, 63), // 2 (12157665459056928801, 40), // 3 ( 4611686018427387904, 31), // 4 ( 7450580596923828125, 27), // 5 ( 4738381338321616896, 24), // 6 ( 3909821048582988049, 22), // 7 ( 9223372036854775808, 21), // 8 (12157665459056928801, 20), // 9 (10000000000000000000, 19), // 10 ( 5559917313492231481, 18), // 11 ( 2218611106740436992, 17), // 12 ( 8650415919381337933, 17), // 13 ( 2177953337809371136, 16), // 14 ( 6568408355712890625, 16), // 15 ( 1152921504606846976, 15), // 16 ( 2862423051509815793, 15), // 17 ( 6746640616477458432, 15), // 18 (15181127029874798299, 15), // 19 ( 1638400000000000000, 14), // 20 ( 3243919932521508681, 14), // 21 ( 6221821273427820544, 14), // 22 (11592836324538749809, 14), // 23 ( 876488338465357824, 13), // 24 ( 1490116119384765625, 13), // 25 ( 2481152873203736576, 13), // 26 ( 4052555153018976267, 13), // 27 ( 6502111422497947648, 13), // 28 (10260628712958602189, 13), // 29 (15943230000000000000, 13), // 30 ( 787662783788549761, 12), // 31 ( 1152921504606846976, 12), // 32 ( 1667889514952984961, 12), // 33 ( 2386420683693101056, 12), // 34 ( 3379220508056640625, 12), // 35 ( 4738381338321616896, 12), // 36 ( 6582952005840035281, 12), // 37 ( 9065737908494995456, 12), // 38 (12381557655576425121, 12), // 39 (16777216000000000000, 12), // 40 ( 550329031716248441, 11), // 41 ( 717368321110468608, 11), // 42 ( 929293739471222707, 11), // 43 ( 1196683881290399744, 11), // 44 ( 1532278301220703125, 11), // 45 ( 1951354384207722496, 11), // 46 ( 2472159215084012303, 11), // 47 ( 3116402981210161152, 11), // 48 ( 3909821048582988049, 11), // 49 ( 4882812500000000000, 11), // 50 ( 6071163615208263051, 11), // 51 ( 7516865509350965248, 11), // 52 ( 9269035929372191597, 11), // 53 (11384956040305711104, 11), // 54 (13931233916552734375, 11), // 55 (16985107389382393856, 11), // 56 ( 362033331456891249, 10), // 57 ( 430804206899405824, 10), // 58 ( 511116753300641401, 10), // 59 ( 604661760000000000, 10), // 60 ( 713342911662882601, 10), // 61 ( 839299365868340224, 10), // 62 ( 984930291881790849, 10), // 63 ( 1152921504606846976, 10), // 64 ( 1346274334462890625, 10), // 65 ( 1568336880910795776, 10), // 66 ( 1822837804551761449, 10), // 67 ( 2113922820157210624, 10), // 68 ( 2446194060654759801, 10), // 69 ( 2824752490000000000, 10), // 70 ( 3255243551009881201, 10), // 71 ( 3743906242624487424, 10), // 72 ( 4297625829703557649, 10), // 73 ( 4923990397355877376, 10), // 74 ( 5631351470947265625, 10), // 75 ( 6428888932339941376, 10), // 76 ( 7326680472586200649, 10), // 77 ( 8335775831236199424, 10), // 78 ( 9468276082626847201, 10), // 79 (10737418240000000000, 10), // 80 (12157665459056928801, 10), // 81 (13744803133596058624, 10), // 82 (15516041187205853449, 10), // 83 (17490122876598091776, 10), // 84 ( 231616946283203125, 9), // 85 ( 257327417311663616, 9), // 86 ( 285544154243029527, 9), // 87 ( 316478381828866048, 9), // 88 ( 350356403707485209, 9), // 89 ( 387420489000000000, 9), // 90 ( 427929800129788411, 9), // 91 ( 472161363286556672, 9), // 92 ( 520411082988487293, 9), // 93 ( 572994802228616704, 9), // 94 ( 630249409724609375, 9), // 95 ( 692533995824480256, 9), // 96 ( 760231058654565217, 9), // 97 ( 833747762130149888, 9), // 98 ( 913517247483640899, 9), // 99 ( 1000000000000000000, 9), // 100 ( 1093685272684360901, 9), // 101 ( 1195092568622310912, 9), // 102 ( 1304773183829244583, 9), // 103 ( 1423311812421484544, 9), // 104 ( 1551328215978515625, 9), // 105 ( 1689478959002692096, 9), // 106 ( 1838459212420154507, 9), // 107 ( 1999004627104432128, 9), // 108 ( 2171893279442309389, 9), // 109 ( 2357947691000000000, 9), // 110 ( 2558036924386500591, 9), // 111 ( 2773078757450186752, 9), // 112 ( 3004041937984268273, 9), // 113 ( 3251948521156637184, 9), // 114 ( 3517876291919921875, 9), // 115 ( 3802961274698203136, 9), // 116 ( 4108400332687853397, 9), // 117 ( 4435453859151328768, 9), // 118 ( 4785448563124474679, 9), // 119 ( 5159780352000000000, 9), // 120 ( 5559917313492231481, 9), // 121 ( 5987402799531080192, 9), // 122 ( 6443858614676334363, 9), // 123 ( 6930988311686938624, 9), // 124 ( 7450580596923828125, 9), // 125 ( 8004512848309157376, 9), // 126 ( 8594754748609397887, 9), // 127 ( 9223372036854775808, 9), // 128 ( 9892530380752880769, 9), // 129 (10604499373000000000, 9), // 130 (11361656654439817571, 9), // 131 (12166492167065567232, 9), // 132 (13021612539908538853, 9), // 133 (13929745610903012864, 9), // 134 (14893745087865234375, 9), // 135 (15916595351771938816, 9), // 136 (17001416405572203977, 9), // 137 (18151468971815029248, 9), // 138 ( 139353667211683681, 8), // 139 ( 147578905600000000, 8), // 140 ( 156225851787813921, 8), // 141 ( 165312903998914816, 8), // 142 ( 174859124550883201, 8), // 143 ( 184884258895036416, 8), // 144 ( 195408755062890625, 8), // 145 ( 206453783524884736, 8), // 146 ( 218041257467152161, 8), // 147 ( 230193853492166656, 8), // 148 ( 242935032749128801, 8), // 149 ( 256289062500000000, 8), // 150 ( 270281038127131201, 8), // 151 ( 284936905588473856, 8), // 152 ( 300283484326400961, 8), // 153 ( 316348490636206336, 8), // 154 ( 333160561500390625, 8), // 155 ( 350749278894882816, 8), // 156 ( 369145194573386401, 8), // 157 ( 388379855336079616, 8), // 158 ( 408485828788939521, 8), // 159 ( 429496729600000000, 8), // 160 ( 451447246258894081, 8), // 161 ( 474373168346071296, 8), // 162 ( 498311414318121121, 8), // 163 ( 523300059815673856, 8), // 164 ( 549378366500390625, 8), // 165 ( 576586811427594496, 8), // 166 ( 604967116961135041, 8), // 167 ( 634562281237118976, 8), // 168 ( 665416609183179841, 8), // 169 ( 697575744100000000, 8), // 170 ( 731086699811838561, 8), // 171 ( 765997893392859136, 8), // 172 ( 802359178476091681, 8), // 173 ( 840221879151902976, 8), // 174 ( 879638824462890625, 8), // 175 ( 920664383502155776, 8), // 176 ( 963354501121950081, 8), // 177 ( 1007766734259732736, 8), // 178 ( 1053960288888713761, 8), // 179 ( 1101996057600000000, 8), // 180 ( 1151936657823500641, 8), // 181 ( 1203846470694789376, 8), // 182 ( 1257791680575160641, 8), // 183 ( 1313840315232157696, 8), // 184 ( 1372062286687890625, 8), // 185 ( 1432529432742502656, 8), // 186 ( 1495315559180183521, 8), // 187 ( 1560496482665168896, 8), // 188 ( 1628150074335205281, 8), // 189 ( 1698356304100000000, 8), // 190 ( 1771197285652216321, 8), // 191 ( 1846757322198614016, 8), // 192 ( 1925122952918976001, 8), // 193 ( 2006383000160502016, 8), // 194 ( 2090628617375390625, 8), // 195 ( 2177953337809371136, 8), // 196 ( 2268453123948987361, 8), // 197 ( 2362226417735475456, 8), // 198 ( 2459374191553118401, 8), // 199 ( 2560000000000000000, 8), // 200 ( 2664210032449121601, 8), // 201 ( 2772113166407885056, 8), // 202 ( 2883821021683985761, 8), // 203 ( 2999448015365799936, 8), // 204 ( 3119111417625390625, 8), // 205 ( 3242931408352297216, 8), // 206 ( 3371031134626313601, 8), // 207 ( 3503536769037500416, 8), // 208 ( 3640577568861717121, 8), // 209 ( 3782285936100000000, 8), // 210 ( 3928797478390152481, 8), // 211 ( 4080251070798954496, 8), // 212 ( 4236788918503437921, 8), // 213 ( 4398556620369715456, 8), // 214 ( 4565703233437890625, 8), // 215 ( 4738381338321616896, 8), // 216 ( 4916747105530914241, 8), // 217 ( 5100960362726891776, 8), // 218 ( 5291184662917065441, 8), // 219 ( 5487587353600000000, 8), // 220 ( 5690339646868044961, 8), // 221 ( 5899616690476974336, 8), // 222 ( 6115597639891380481, 8), // 223 ( 6338465731314712576, 8), // 224 ( 6568408355712890625, 8), // 225 ( 6805617133840466176, 8), // 226 ( 7050287992278341281, 8), // 227 ( 7302621240492097536, 8), // 228 ( 7562821648920027361, 8), // 229 ( 7831098528100000000, 8), // 230 ( 8107665808844335041, 8), // 231 ( 8392742123471896576, 8), // 232 ( 8686550888106661441, 8), // 233 ( 8989320386052055296, 8), // 234 ( 9301283852250390625, 8), // 235 ( 9622679558836781056, 8), // 236 ( 9953750901796946721, 8), // 237 (10294746488738365696, 8), // 238 (10645920227784266881, 8), // 239 (11007531417600000000, 8), // 240 (11379844838561358721, 8), // 241 (11763130845074473216, 8), // 242 (12157665459056928801, 8), // 243 (12563730464589807616, 8), // 244 (12981613503750390625, 8), // 245 (13411608173635297536, 8), // 246 (13854014124583882561, 8), // 247 (14309137159611744256, 8), // 248 (14777289335064248001, 8), // 249 (15258789062500000000, 8), // 250 (15753961211814252001, 8), // 251 (16263137215612256256, 8), // 252 (16786655174842630561, 8), // 253 (17324859965700833536, 8), // 254 (17878103347812890625, 8), // 255 ( 72057594037927936, 7), // 256 ]; let (base, power) = BASES[radix as usize]; (base as BigDigit, power) } _ => panic!("Invalid bigdigit size") } } #[test] fn test_from_slice() { fn check(slice: &[BigDigit], data: &[BigDigit]) { assert!(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 BigDigit], &[-1i32 as BigDigit]); } #[test] fn test_assign_from_slice() { fn check(slice: &[BigDigit], data: &[BigDigit]) { let mut p = BigUint::from_slice(&[2627_u32, 0_u32, 9182_u32, 42_u32]); p.assign_from_slice(slice); assert!(p.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 BigDigit], &[-1i32 as BigDigit]); } num-bigint-0.2.0/src/lib.rs010066400247370024737000000122771330140126100137340ustar0000000000000000// 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 //! extern crate num_bigint; //! extern crate num_traits; //! //! # 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 //! # #[cfg(feature = "rand")] //! extern crate rand; //! extern crate num_bigint as bigint; //! //! # #[cfg(feature = "rand")] //! # fn main() { //! use 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); //! # } //! //! # #[cfg(not(feature = "rand"))] //! # fn main() { //! # } //! ``` //! //! ## Compatibility //! //! The `num-bigint` crate is tested for rustc 1.15 and greater. #![doc(html_root_url = "https://docs.rs/num-bigint/0.2")] // We don't actually support `no_std` yet, and probably won't until `alloc` is stable. We're just // reserving this ability with the "std" feature now, and compilation will fail without. #![cfg_attr(not(feature = "std"), no_std)] #[cfg(feature = "rand")] extern crate rand; #[cfg(feature = "serde")] extern crate serde; extern crate num_integer as integer; extern crate num_traits as traits; use std::error::Error; use std::fmt; #[macro_use] mod macros; mod biguint; mod bigint; #[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 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) } } impl Error for ParseBigIntError { fn description(&self) -> &str { self.__description() } } pub use biguint::BigUint; pub use biguint::ToBigUint; pub use bigint::Sign; pub use bigint::BigInt; pub use bigint::ToBigInt; #[cfg(feature = "rand")] pub use bigrand::{RandBigInt, RandomBits, UniformBigUint, UniformBigInt}; mod big_digit { /// A `BigDigit` is a `BigUint`'s composing element. pub type BigDigit = u32; /// A `DoubleBigDigit` is the internal type used to do the computations. Its /// size is the double of the size of `BigDigit`. pub type DoubleBigDigit = u64; /// A `SignedDoubleBigDigit` is the signed version of `DoubleBigDigit`. pub type SignedDoubleBigDigit = i64; // `DoubleBigDigit` size dependent pub const BITS: usize = 32; const LO_MASK: DoubleBigDigit = (-1i32 as DoubleBigDigit) >> BITS; #[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 fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) { (get_hi(n), get_lo(n)) } /// Join two `BigDigit`s into one `DoubleBigDigit` #[inline] pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit { (lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << BITS) } } num-bigint-0.2.0/src/macros.rs010066400247370024737000000250161327713022700144620ustar0000000000000000#![allow(unknown_lints)] // older rustc doesn't know `unused_macros` #![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); } } } } 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) } } } } macro_rules! forward_scalar_val_ref_binop { (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 { (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 { (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; #[inline] fn $method(self, other: $scalar) -> $res { $imp::$method(self, other as $promo) } } impl $imp<$res> for $scalar { type Output = $res; #[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 { #[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_val_val { (impl $imp:ident<$scalar:ty> for $res:ty, $method:ident) => { forward_scalar_val_ref_binop!(impl $imp<$scalar> for $res, $method); forward_scalar_ref_val_binop!(impl $imp<$scalar> for $res, $method); forward_scalar_ref_ref_binop!(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-0.2.0/src/monty.rs010066400247370024737000000062751324770400700143520ustar0000000000000000use integer::Integer; use traits::Zero; use biguint::BigUint; struct MontyReducer<'a> { n: &'a BigUint, n0inv: u32 } // Calculate the modular inverse of `num`, using Extended GCD. // // Reference: // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.20 fn inv_mod_u32(num: u32) -> u32 { // num needs to be relatively prime to 2**32 -- i.e. it must be odd. assert!(num % 2 != 0); let mut a: i64 = num as i64; let mut b: i64 = (u32::max_value() as i64) + 1; // ExtendedGcd // Input: positive integers a and b // Output: integers (g, u, v) such that g = gcd(a, b) = ua + vb // As we don't need v for modular inverse, we don't calculate it. // 1: (u, w) <- (1, 0) let mut u = 1; let mut w = 0; // 3: while b != 0 while b != 0 { // 4: (q, r) <- DivRem(a, b) let q = a / b; let r = a % b; // 5: (a, b) <- (b, r) a = b; b = r; // 6: (u, w) <- (w, u - qw) let m = u - w*q; u = w; w = m; } assert!(a == 1); // Downcasting acts like a mod 2^32 too. u as u32 } impl<'a> MontyReducer<'a> { fn new(n: &'a BigUint) -> Self { let n0inv = inv_mod_u32(n.data[0]); MontyReducer { n: n, n0inv: n0inv } } } // Montgomery Reduction // // Reference: // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 2.6 fn monty_redc(a: BigUint, mr: &MontyReducer) -> BigUint { let mut c = a.data; let n = &mr.n.data; let n_size = n.len(); // Allocate sufficient work space c.resize(2 * n_size + 2, 0); // β is the size of a word, in this case 32 bits. So "a mod β" is // equivalent to masking a to 32 bits. // mu <- -N^(-1) mod β let mu = 0u32.wrapping_sub(mr.n0inv); // 1: for i = 0 to (n-1) for i in 0..n_size { // 2: q_i <- mu*c_i mod β let q_i = c[i].wrapping_mul(mu); // 3: C <- C + q_i * N * β^i super::algorithms::mac_digit(&mut c[i..], n, q_i); } // 4: R <- C * β^(-n) // This is an n-word bitshift, equivalent to skipping n words. let ret = BigUint::new(c[n_size..].to_vec()); // 5: if R >= β^n then return R-N else return R. if &ret < mr.n { ret } else { ret - mr.n } } // Montgomery Multiplication fn monty_mult(a: BigUint, b: &BigUint, mr: &MontyReducer) -> BigUint { monty_redc(a * b, mr) } // Montgomery Squaring fn monty_sqr(a: BigUint, mr: &MontyReducer) -> BigUint { // TODO: Replace with an optimised squaring function monty_redc(&a * &a, mr) } pub fn monty_modpow(a: &BigUint, exp: &BigUint, modulus: &BigUint) -> BigUint{ let mr = MontyReducer::new(modulus); // Calculate the Montgomery parameter let mut v = vec![0; modulus.data.len()]; v.push(1); let r = BigUint::new(v); // Map the base to the Montgomery domain let mut apri = a * &r % modulus; // Binary exponentiation let mut ans = &r % modulus; let mut e = exp.clone(); while !e.is_zero() { if e.is_odd() { ans = monty_mult(ans, &apri, &mr); } apri = monty_sqr(apri, &mr); e = e >> 1; } // Map the result back to the residues domain monty_redc(ans, &mr) } num-bigint-0.2.0/tests/bigint.rs010066400247370024737000001057601330112115100150120ustar0000000000000000extern crate num_bigint; extern crate num_integer; extern crate num_traits; #[cfg(feature = "rand")] extern crate rand; use num_bigint::BigUint; use num_bigint::{BigInt, ToBigInt}; use num_bigint::Sign::{Minus, NoSign, Plus}; use std::cmp::Ordering::{Less, Equal, Greater}; use std::{f32, f64}; use std::{i8, i16, i32, i64, isize}; use std::iter::repeat; use std::{u8, u16, u32, u64, usize}; #[cfg(has_i128)] use std::{i128, u128}; use std::ops::Neg; use std::hash::{BuildHasher, Hasher, Hash}; use std::collections::hash_map::RandomState; use num_integer::Integer; use num_traits::{Zero, One, Signed, ToPrimitive, FromPrimitive, Num, Float}; mod consts; use 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, &[]), Zero::zero()); assert_eq!(BigInt::from_bytes_be(Minus, &[]), Zero::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, &[]), Zero::zero()); assert_eq!(BigInt::from_bytes_le(Minus, &[]), Zero::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]); } #[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]); } #[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_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] #[cfg(has_i128)] 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] #[cfg(has_i128)] 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] 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), 2.0.powi(16) - 1.0); check(&BigInt::from(1u64 << 32), 2.0.powi(32)); check(&BigInt::from_slice(Plus, &[0, 0, 1]), 2.0.powi(64)); check(&((BigInt::one() << 100) + (BigInt::one() << 123)), 2.0.powi(100) + 2.0.powi(123)); check(&(BigInt::one() << 127), 2.0.powi(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 = 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 = 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() << 128) - BigInt::one() - (BigInt::one() << (128 - 25)); assert_eq!(big_num.to_f32(), Some(f32::MAX)); assert_eq!((&big_num + BigInt::one()).to_f32(), None); assert_eq!((-&big_num).to_f32(), Some(f32::MIN)); assert_eq!(((-&big_num) - BigInt::one()).to_f32(), None); assert_eq!(((BigInt::one() << 128) - BigInt::one()).to_f32(), None); assert_eq!((BigInt::one() << 128).to_f32(), None); assert_eq!((-((BigInt::one() << 128) - BigInt::one())).to_f32(), None); assert_eq!((-(BigInt::one() << 128)).to_f32(), None); } #[test] 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), 2.0.powi(32) - 1.0); check(&BigInt::from(1u64 << 32), 2.0.powi(32)); check(&BigInt::from_slice(Plus, &[0, 0, 1]), 2.0.powi(64)); check(&((BigInt::one() << 100) + (BigInt::one() << 152)), 2.0.powi(100) + 2.0.powi(152)); check(&(BigInt::one() << 1023), 2.0.powi(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 = 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 = 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() << 1024) - BigInt::one() - (BigInt::one() << (1024 - 54)); assert_eq!(big_num.to_f64(), Some(f64::MAX)); assert_eq!((&big_num + BigInt::one()).to_f64(), None); assert_eq!((-&big_num).to_f64(), Some(f64::MIN)); assert_eq!(((-&big_num) - BigInt::one()).to_f64(), None); assert_eq!(((BigInt::one() << 1024) - BigInt::one()).to_f64(), None); assert_eq!((BigInt::one() << 1024).to_f64(), None); assert_eq!((-((BigInt::one() << 1024) - BigInt::one())).to_f64(), None); assert_eq!((-(BigInt::one() << 1024)).to_f64(), None); } #[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), $max); }; } check!(u8, BigInt::from_slice(Plus, &[u8::MAX as u32])); check!(u16, BigInt::from_slice(Plus, &[u16::MAX as u32])); check!(u32, BigInt::from_slice(Plus, &[u32::MAX])); check!(u64, BigInt::from_slice(Plus, &[u32::MAX, u32::MAX])); #[cfg(has_i128)] check!(u128, BigInt::from_slice(Plus, &[u32::MAX, u32::MAX, u32::MAX, u32::MAX])); check!(usize, BigInt::from(usize::MAX as u64)); } #[test] fn test_convert_from_int() { macro_rules! check { ($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])); #[cfg(has_i128)] 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 == Zero::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 == Zero::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 == Zero::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 == Zero::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); 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_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() == Zero::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() == Zero::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); } 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); } 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_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("-22405534230753963835153736737".as_bytes(), 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("-22405534230753963835153736737".as_bytes(), 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("-224055342307539".as_bytes(), 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("-22405534230753963835153736737".as_bytes(), 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("-22405534230753963835153736737".as_bytes(), 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] #[cfg(feature = "rand")] fn test_random_shr() { use rand::Rng; use rand::distributions::Standard; let mut rng = rand::thread_rng(); for p in rng.sample_iter::(&Standard).take(1000) { let big = BigInt::from(p); let bigger = &big << 1000; assert_eq!(&bigger >> 1000, big); for i in 0..64 { let answer = BigInt::from(p >> i); assert_eq!(&big >> i, answer); assert_eq!(&bigger >> (1000 + i), answer); } } } #[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()); } num-bigint-0.2.0/tests/bigint_bitwise.rs010066400247370024737000000117641327713022700165600ustar0000000000000000extern crate num_bigint; extern crate num_traits; use num_bigint::{BigInt, Sign, ToBigInt}; use num_traits::ToPrimitive; use std::{i32, i64, u32}; enum ValueVec { N, P(&'static [u32]), M(&'static [u32]), } use 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: &'static [(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: &'static [(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: &'static [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-0.2.0/tests/bigint_scalar.rs010066400247370024737000000076171327713022700163610ustar0000000000000000extern crate num_bigint; extern crate num_traits; use num_bigint::BigInt; use num_bigint::Sign::Plus; use num_traits::{Zero, Signed, ToPrimitive}; use std::ops::Neg; mod consts; use 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); } 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); } 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); } 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() <= From::from(b)); 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); if b <= i32::max_value() as u32 { let nb = -(b as i32); assert_op!(a / nb == -ans_q.clone()); assert_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); } } } num-bigint-0.2.0/tests/biguint.rs010066400247370024737000001504251330111771500152100ustar0000000000000000extern crate num_bigint; extern crate num_integer; extern crate num_traits; use num_integer::Integer; use num_bigint::{BigUint, ToBigUint}; use num_bigint::{BigInt, ToBigInt}; use num_bigint::Sign::Plus; use std::cmp::Ordering::{Less, Equal, Greater}; use std::{f32, f64}; use std::i64; use std::iter::repeat; use std::str::FromStr; use std::{u8, u16, u32, u64, usize}; #[cfg(has_i128)] use std::{i128, u128}; use std::hash::{BuildHasher, Hasher, Hash}; use std::collections::hash_map::RandomState; use num_traits::{Num, Zero, One, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, ToPrimitive, FromPrimitive, Float}; mod consts; use 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(&[]), Zero::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(&[]), Zero::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 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: &'static [( &'static [u32], &'static [u32], &'static [u32], &'static [u32], &'static [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] #[cfg(has_i128)] 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] #[cfg(has_i128)] 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] 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), 2.0.powi(16) - 1.0); check(&BigUint::from(1u64 << 32), 2.0.powi(32)); check(&BigUint::from_slice(&[0, 0, 1]), 2.0.powi(64)); check(&((BigUint::one() << 100) + (BigUint::one() << 123)), 2.0.powi(100) + 2.0.powi(123)); check(&(BigUint::one() << 127), 2.0.powi(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 = 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 = 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() << 128) - BigUint::one() - (BigUint::one() << (128 - 25)); assert_eq!(big_num.to_f32(), Some(f32::MAX)); assert_eq!((big_num + BigUint::one()).to_f32(), None); assert_eq!(((BigUint::one() << 128) - BigUint::one()).to_f32(), None); assert_eq!((BigUint::one() << 128).to_f32(), None); } #[test] 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), 2.0.powi(32) - 1.0); check(&BigUint::from(1u64 << 32), 2.0.powi(32)); check(&BigUint::from_slice(&[0, 0, 1]), 2.0.powi(64)); check(&((BigUint::one() << 100) + (BigUint::one() << 152)), 2.0.powi(100) + 2.0.powi(152)); check(&(BigUint::one() << 1023), 2.0.powi(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 = 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 = 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() << 1024) - BigUint::one() - (BigUint::one() << (1024 - 54)); assert_eq!(big_num.to_f64(), Some(f64::MAX)); assert_eq!((big_num + BigUint::one()).to_f64(), None); assert_eq!(((BigInt::one() << 1024) - BigInt::one()).to_f64(), None); assert_eq!((BigUint::one() << 1024).to_f64(), None); } #[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])); #[cfg(has_i128)] 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()); 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 == Zero::zero()); assert_assign_op!(c /= a == b); assert_assign_op!(c %= a == Zero::zero()); assert_eq!(c.div_rem(&a), (b.clone(), Zero::zero())); } if !b.is_zero() { assert_op!(c / b == a); assert_op!(c % b == Zero::zero()); assert_assign_op!(c /= b == a); assert_assign_op!(c %= b == Zero::zero()); assert_eq!(c.div_rem(&b), (a.clone(), 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() { 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_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 = "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502232636710047537552105951370000796528760829212940754539968588340162273730474622005920097370111"; let a: BigUint = s.parse().unwrap(); let b = a.clone(); let _ = a.checked_mul(&b); } #[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); } 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); } 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_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 << 64).is_even()); assert!(((&one << 64) + 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 : &'static[(&'static[u8], u32, &'static[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()); } #[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() { #[allow(deprecated, unused_imports)] use std::ascii::AsciiExt; 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_lower_hex() { let a = BigUint::parse_bytes(b"A", 16).unwrap(); let hello = BigUint::parse_bytes("22405534230753963835153736737".as_bytes(), 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("22405534230753963835153736737".as_bytes(), 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("224055342307539".as_bytes(), 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("22405534230753963835153736737".as_bytes(), 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("22405534230753963835153736737".as_bytes(), 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 + 1 { // FIXME(#5992): assignment operator overloads // f *= FromPrimitive::from_usize(i); let bu: BigUint = FromPrimitive::from_usize(i).unwrap(); f = f * bu; } return f; } fn check(n: usize, s: &str) { let n = factor(n); let ans = match BigUint::from_str_radix(s, 10) { Ok(x) => x, Err(_) => panic!(), }; 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 << 426).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()); } num-bigint-0.2.0/tests/biguint_scalar.rs010066400247370024737000000052141327713022700165350ustar0000000000000000extern crate num_bigint; extern crate num_traits; use num_bigint::BigUint; use num_traits::{Zero, ToPrimitive}; mod consts; use 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); } 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); } 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); } 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_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); } 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); } } } num-bigint-0.2.0/tests/consts/mod.rs010066400247370024737000000034231327713022700156370ustar0000000000000000#![allow(unused)] pub const N1: u32 = -1i32 as u32; pub const N2: u32 = -2i32 as u32; pub const SUM_TRIPLES: &'static [( &'static [u32], &'static [u32], &'static [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]), ]; pub const M: u32 = ::std::u32::MAX; pub const MUL_TRIPLES: &'static [( &'static [u32], &'static [u32], &'static [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: &'static [( &'static [u32], &'static [u32], &'static [u32], &'static [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-0.2.0/tests/macros/mod.rs010066400247370024737000000033751327713022700156200ustar0000000000000000#![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) $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_i8, to_i16, to_i32, to_i64, to_isize) $left $op $right == $expected); }; } num-bigint-0.2.0/tests/modpow.rs010066400247370024737000000130141324516574200150560ustar0000000000000000extern crate num_bigint; extern crate num_integer; extern crate num_traits; static BIG_B: &'static 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: &'static 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: &'static 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: &'static 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() { check_modpow::(1, 0, 11, 1); check_modpow::(0, 15, 11, 0); check_modpow::(3, 7, 11, 9); check_modpow::(5, 117, 19, 1); } #[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, Zero, 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); let even_m = m << 1; 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_r = if r.is_zero() { BigInt::zero() } else { &m - &r }; check(&b, &e, &m, &r); check(&-&b, &e, &m, &neg_r); check(&b, &e, &-&m, &-neg_r); check(&-b, &e, &-m, &-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); } #[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-0.2.0/tests/rand.rs010066400247370024737000000120441330140237300144620ustar0000000000000000#![cfg(feature = "rand")] extern crate num_bigint; extern crate num_traits; extern crate rand; mod biguint { use num_bigint::{BigUint, RandBigInt, RandomBits}; use num_traits::Zero; use rand::thread_rng; use rand::Rng; use rand::distributions::Uniform; #[test] fn test_rand() { let mut rng = thread_rng(); let n: BigUint = rng.gen_biguint(137); assert!(n.bits() <= 137); assert!(rng.gen_biguint(0).is_zero()); } #[test] fn test_rand_bits() { let mut rng = thread_rng(); let n: BigUint = rng.sample(&RandomBits::new(137)); assert!(n.bits() <= 137); let z: BigUint = rng.sample(&RandomBits::new(0)); assert!(z.is_zero()); } #[test] fn test_rand_range() { let mut rng = thread_rng(); for _ in 0..10 { assert_eq!( rng.gen_biguint_range(&BigUint::from(236u32), &BigUint::from(237u32)), BigUint::from(236u32) ); } let l = BigUint::from(403469000u32 + 2352); let u = BigUint::from(403469000u32 + 3513); for _ in 0..1000 { let n: BigUint = rng.gen_biguint_below(&u); assert!(n < u); let n: BigUint = rng.gen_biguint_range(&l, &u); assert!(n >= l); assert!(n < u); } } #[test] #[should_panic] fn test_zero_rand_range() { thread_rng().gen_biguint_range(&BigUint::from(54u32), &BigUint::from(54u32)); } #[test] #[should_panic] fn test_negative_rand_range() { let mut rng = thread_rng(); let l = BigUint::from(2352u32); let u = BigUint::from(3513u32); // Switching u and l should fail: let _n: BigUint = rng.gen_biguint_range(&u, &l); } #[test] fn test_rand_uniform() { let mut rng = thread_rng(); let tiny = Uniform::new(BigUint::from(236u32), BigUint::from(237u32)); for _ in 0..10 { assert_eq!(rng.sample(&tiny), BigUint::from(236u32)); } let l = BigUint::from(403469000u32 + 2352); let u = BigUint::from(403469000u32 + 3513); let below = Uniform::new(BigUint::zero(), u.clone()); let range = Uniform::new(l.clone(), u.clone()); for _ in 0..1000 { let n: BigUint = rng.sample(&below); assert!(n < u); let n: BigUint = rng.sample(&range); assert!(n >= l); assert!(n < u); } } } mod bigint { use num_bigint::{BigInt, RandBigInt, RandomBits}; use num_traits::Zero; use rand::thread_rng; use rand::Rng; use rand::distributions::Uniform; #[test] fn test_rand() { let mut rng = thread_rng(); let n: BigInt = rng.gen_bigint(137); assert!(n.bits() <= 137); assert!(rng.gen_bigint(0).is_zero()); } #[test] fn test_rand_bits() { let mut rng = thread_rng(); let n: BigInt = rng.sample(&RandomBits::new(137)); assert!(n.bits() <= 137); let z: BigInt = rng.sample(&RandomBits::new(0)); assert!(z.is_zero()); } #[test] fn test_rand_range() { let mut rng = thread_rng(); for _ in 0..10 { assert_eq!( rng.gen_bigint_range(&BigInt::from(236), &BigInt::from(237)), BigInt::from(236) ); } fn check(l: BigInt, u: BigInt) { let mut rng = thread_rng(); for _ in 0..1000 { let n: BigInt = rng.gen_bigint_range(&l, &u); assert!(n >= l); assert!(n < u); } } let l: BigInt = BigInt::from(403469000 + 2352); let u: BigInt = BigInt::from(403469000 + 3513); check(l.clone(), u.clone()); check(-l.clone(), u.clone()); check(-u.clone(), -l.clone()); } #[test] #[should_panic] fn test_zero_rand_range() { thread_rng().gen_bigint_range(&BigInt::from(54), &BigInt::from(54)); } #[test] #[should_panic] fn test_negative_rand_range() { let mut rng = thread_rng(); let l = BigInt::from(2352); let u = BigInt::from(3513); // Switching u and l should fail: let _n: BigInt = rng.gen_bigint_range(&u, &l); } #[test] fn test_rand_uniform() { let mut rng = thread_rng(); let tiny = Uniform::new(BigInt::from(236u32), BigInt::from(237u32)); for _ in 0..10 { assert_eq!(rng.sample(&tiny), BigInt::from(236u32)); } fn check(l: BigInt, u: BigInt) { let mut rng = thread_rng(); let range = Uniform::new(l.clone(), u.clone()); for _ in 0..1000 { let n: BigInt = rng.sample(&range); assert!(n >= l); assert!(n < u); } } let l: BigInt = BigInt::from(403469000 + 2352); let u: BigInt = BigInt::from(403469000 + 3513); check(l.clone(), u.clone()); check(-l.clone(), u.clone()); check(-u.clone(), -l.clone()); } } num-bigint-0.2.0/tests/serde.rs010066400247370024737000000050401327713022700146460ustar0000000000000000//! Test serialization and deserialization of `BigUint` and `BigInt` //! //! The serialized formats should not change, even if we change our //! internal representation, because we want to preserve forward and //! backward compatibility of serialized data! #![cfg(feature = "serde")] extern crate num_bigint; extern crate num_traits; extern crate serde_test; use num_bigint::{BigInt, BigUint}; use num_traits::{One, Zero}; use serde_test::{assert_tokens, Token}; #[test] fn biguint_zero() { let tokens = [Token::Seq { len: Some(0) }, Token::SeqEnd]; assert_tokens(&BigUint::zero(), &tokens); } #[test] fn bigint_zero() { let tokens = [ Token::Tuple { len: 2 }, Token::I8(0), Token::Seq { len: Some(0) }, Token::SeqEnd, Token::TupleEnd, ]; assert_tokens(&BigInt::zero(), &tokens); } #[test] fn biguint_one() { let tokens = [Token::Seq { len: Some(1) }, Token::U32(1), Token::SeqEnd]; assert_tokens(&BigUint::one(), &tokens); } #[test] fn bigint_one() { let tokens = [ Token::Tuple { len: 2 }, Token::I8(1), Token::Seq { len: Some(1) }, Token::U32(1), Token::SeqEnd, Token::TupleEnd, ]; assert_tokens(&BigInt::one(), &tokens); } #[test] fn bigint_negone() { let tokens = [ Token::Tuple { len: 2 }, Token::I8(-1), Token::Seq { len: Some(1) }, Token::U32(1), Token::SeqEnd, Token::TupleEnd, ]; assert_tokens(&-BigInt::one(), &tokens); } // Generated independently from python `hex(factorial(100))` const FACTORIAL_100: &'static [u32] = &[ 0x00000000, 0x00000000, 0x00000000, 0x2735c61a, 0xee8b02ea, 0xb3b72ed2, 0x9420c6ec, 0x45570cca, 0xdf103917, 0x943a321c, 0xeb21b5b2, 0x66ef9a70, 0xa40d16e9, 0x28d54bbd, 0xdc240695, 0x964ec395, 0x1b30, ]; #[test] fn biguint_factorial_100() { let n: BigUint = (1u8..101).product(); let mut tokens = vec![]; tokens.push(Token::Seq { len: Some(FACTORIAL_100.len()), }); tokens.extend(FACTORIAL_100.iter().map(|&u| Token::U32(u))); tokens.push(Token::SeqEnd); assert_tokens(&n, &tokens); } #[test] fn bigint_factorial_100() { let n: BigInt = (1i8..101).product(); let mut tokens = vec![]; tokens.push(Token::Tuple { len: 2 }); tokens.push(Token::I8(1)); tokens.push(Token::Seq { len: Some(FACTORIAL_100.len()), }); tokens.extend(FACTORIAL_100.iter().map(|&u| Token::U32(u))); tokens.push(Token::SeqEnd); tokens.push(Token::TupleEnd); assert_tokens(&n, &tokens); } num-bigint-0.2.0/tests/torture.rs010066400247370024737000000017221330112641700152450ustar0000000000000000#![cfg(feature = "rand")] extern crate num_bigint; extern crate num_traits; extern crate rand; use num_bigint::RandBigInt; use num_traits::Zero; use rand::prelude::*; fn test_mul_divide_torture_count(count: usize) { let bits_max = 1 << 12; let seed = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]; let mut rng = SmallRng::from_seed(seed); for _ in 0..count { // Test with numbers of random sizes: let xbits = rng.gen_range(0, bits_max); let ybits = rng.gen_range(0, bits_max); let x = rng.gen_biguint(xbits); let y = rng.gen_biguint(ybits); if x.is_zero() || y.is_zero() { continue; } let prod = &x * &y; assert_eq!(&prod / &x, y); assert_eq!(&prod / &y, x); } } #[test] fn test_mul_divide_torture() { test_mul_divide_torture_count(1000); } #[test] #[ignore] fn test_mul_divide_torture_long() { test_mul_divide_torture_count(1000000); }