1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
// Copyright 2013-2014 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).
//!
//! A `BigUint` is represented as a vector of `BigDigit`s.
//! A `BigInt` is a combination of `BigUint` and `Sign`.
//!
//! Common numerical operations are overloaded, so we can treat them
//! the same way we treat other numbers.
//!
//! ## Example
//!
//! ```rust
//! # fn main() {
//! use num_bigint::BigUint;
//! use num_traits::{Zero, One};
//! use std::mem::replace;
//!
//! // Calculate large fibonacci numbers.
//! fn fib(n: usize) -> BigUint {
//!     let mut f0: BigUint = Zero::zero();
//!     let mut f1: BigUint = One::one();
//!     for _ in 0..n {
//!         let f2 = f0 + &f1;
//!         // This is a low cost way of swapping f0 with f1 and f1 with f2.
//!         f0 = replace(&mut f1, f2);
//!     }
//!     f0
//! }
//!
//! // This is a very large number.
//! println!("fib(1000) = {}", fib(1000));
//! # }
//! ```
//!
//! It's easy to generate large random numbers:
//!
//! ```rust,ignore
//! use num_bigint::{ToBigInt, RandBigInt};
//!
//! let mut rng = rand::thread_rng();
//! let a = rng.gen_bigint(1000);
//!
//! let low = -10000.to_bigint().unwrap();
//! let high = 10000.to_bigint().unwrap();
//! let b = rng.gen_bigint_range(&low, &high);
//!
//! // Probably an even larger number.
//! println!("{}", a * b);
//! ```
//!
//! See the "Features" section for instructions for enabling random number generation.
//!
//! ## Features
//!
//! The `std` crate feature is enabled by default, and is mandatory before Rust
//! 1.36 and the stabilized `alloc` crate.  If you depend on `num-bigint` with
//! `default-features = false`, you must manually enable the `std` feature yourself
//! if your compiler is not new enough.
//!
//! ### Random Generation
//!
//! `num-bigint` supports the generation of random big integers when the `rand`
//! feature is enabled. To enable it include rand as
//!
//! ```toml
//! rand = "0.7"
//! num-bigint = { version = "0.3", features = ["rand"] }
//! ```
//!
//! Note that you must use the version of `rand` that `num-bigint` is compatible
//! with: `0.7`.
//!
//!
//! ## Compatibility
//!
//! The `num-bigint` crate is tested for rustc 1.31 and greater.

#![doc(html_root_url = "https://docs.rs/num-bigint/0.3")]
#![no_std]

#[cfg(feature = "std")]
#[macro_use]
extern crate std;

#[cfg(feature = "std")]
mod std_alloc {
    pub(crate) use std::borrow::Cow;
    #[cfg(any(feature = "quickcheck", feature = "arbitrary"))]
    pub(crate) use std::boxed::Box;
    pub(crate) use std::string::String;
    pub(crate) use std::vec::Vec;
}

#[cfg(not(feature = "std"))]
#[macro_use]
extern crate alloc;

#[cfg(not(feature = "std"))]
mod std_alloc {
    pub(crate) use alloc::borrow::Cow;
    #[cfg(any(feature = "quickcheck", feature = "arbitrary"))]
    pub(crate) use alloc::boxed::Box;
    pub(crate) use alloc::string::String;
    pub(crate) use alloc::vec::Vec;
}

use core::fmt;
#[cfg(feature = "std")]
use std::error::Error;

#[macro_use]
mod macros;

mod bigint;
mod biguint;

#[cfg(feature = "rand")]
mod bigrand;

#[cfg(target_pointer_width = "32")]
type UsizePromotion = u32;
#[cfg(target_pointer_width = "64")]
type UsizePromotion = u64;

#[cfg(target_pointer_width = "32")]
type IsizePromotion = i32;
#[cfg(target_pointer_width = "64")]
type IsizePromotion = i64;

#[derive(Debug, Clone, PartialEq, Eq)]
pub struct ParseBigIntError {
    kind: BigIntErrorKind,
}

#[derive(Debug, Clone, PartialEq, Eq)]
enum BigIntErrorKind {
    Empty,
    InvalidDigit,
}

impl ParseBigIntError {
    fn __description(&self) -> &str {
        use crate::BigIntErrorKind::*;
        match self.kind {
            Empty => "cannot parse integer from empty string",
            InvalidDigit => "invalid digit found in string",
        }
    }

    fn empty() -> Self {
        ParseBigIntError {
            kind: BigIntErrorKind::Empty,
        }
    }

    fn invalid() -> Self {
        ParseBigIntError {
            kind: BigIntErrorKind::InvalidDigit,
        }
    }
}

impl fmt::Display for ParseBigIntError {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        self.__description().fmt(f)
    }
}

#[cfg(feature = "std")]
impl Error for ParseBigIntError {
    fn description(&self) -> &str {
        self.__description()
    }
}

/// The error type returned when a checked conversion regarding big integer fails.
#[cfg(has_try_from)]
#[derive(Debug, Copy, Clone, PartialEq, Eq)]
pub struct TryFromBigIntError<T> {
    original: T,
}

#[cfg(has_try_from)]
impl<T> TryFromBigIntError<T> {
    fn new(original: T) -> Self {
        TryFromBigIntError { original }
    }

    fn __description(&self) -> &str {
        "out of range conversion regarding big integer attempted"
    }

    /// Extract the original value, if available. The value will be available
    /// if the type before conversion was either [`BigInt`] or [`BigUint`].
    ///
    /// [`BigInt`]: struct.BigInt.html
    /// [`BigUint`]: struct.BigUint.html
    pub fn into_original(self) -> T {
        self.original
    }
}

#[cfg(all(feature = "std", has_try_from))]
impl<T> std::error::Error for TryFromBigIntError<T>
where
    T: fmt::Debug,
{
    fn description(&self) -> &str {
        self.__description()
    }
}

#[cfg(has_try_from)]
impl<T> fmt::Display for TryFromBigIntError<T> {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        self.__description().fmt(f)
    }
}

pub use crate::biguint::BigUint;
pub use crate::biguint::ToBigUint;
pub use crate::biguint::U32Digits;
pub use crate::biguint::U64Digits;

pub use crate::bigint::BigInt;
pub use crate::bigint::Sign;
pub use crate::bigint::ToBigInt;

#[cfg(feature = "rand")]
pub use crate::bigrand::{RandBigInt, RandomBits, UniformBigInt, UniformBigUint};

mod big_digit {
    /// A `BigDigit` is a `BigUint`'s composing element.
    #[cfg(not(u64_digit))]
    pub(crate) type BigDigit = u32;
    #[cfg(u64_digit)]
    pub(crate) type BigDigit = u64;

    /// A `DoubleBigDigit` is the internal type used to do the computations.  Its
    /// size is the double of the size of `BigDigit`.
    #[cfg(not(u64_digit))]
    pub(crate) type DoubleBigDigit = u64;
    #[cfg(u64_digit)]
    pub(crate) type DoubleBigDigit = u128;

    /// A `SignedDoubleBigDigit` is the signed version of `DoubleBigDigit`.
    #[cfg(not(u64_digit))]
    pub(crate) type SignedDoubleBigDigit = i64;
    #[cfg(u64_digit)]
    pub(crate) type SignedDoubleBigDigit = i128;

    // `DoubleBigDigit` size dependent
    #[cfg(not(u64_digit))]
    pub(crate) const BITS: u8 = 32;
    #[cfg(u64_digit)]
    pub(crate) const BITS: u8 = 64;

    pub(crate) const HALF_BITS: u8 = BITS / 2;
    pub(crate) const HALF: BigDigit = (1 << HALF_BITS) - 1;

    const LO_MASK: DoubleBigDigit = (1 << BITS) - 1;
    pub(crate) const MAX: BigDigit = LO_MASK as BigDigit;

    #[inline]
    fn get_hi(n: DoubleBigDigit) -> BigDigit {
        (n >> BITS) as BigDigit
    }
    #[inline]
    fn get_lo(n: DoubleBigDigit) -> BigDigit {
        (n & LO_MASK) as BigDigit
    }

    /// Split one `DoubleBigDigit` into two `BigDigit`s.
    #[inline]
    pub(crate) fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) {
        (get_hi(n), get_lo(n))
    }

    /// Join two `BigDigit`s into one `DoubleBigDigit`
    #[inline]
    pub(crate) fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit {
        DoubleBigDigit::from(lo) | (DoubleBigDigit::from(hi) << BITS)
    }
}