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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434
// Copyright © 2024 Mikhail Hogrefe
//
// Uses code adopted from the GNU MP Library.
//
// Copyright © 1991, 1993-1995, 1997, 1999, 2000, 2001, 2002, 2012 Free Software Foundation,
// Inc.
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::integer::Integer;
use crate::natural::arithmetic::add::limbs_slice_add_limb_in_place;
use crate::natural::arithmetic::sub::limbs_sub_limb_in_place;
use crate::natural::InnerNatural::{Large, Small};
use crate::natural::Natural;
use crate::platform::Limb;
use alloc::vec::Vec;
use core::cmp::Ordering;
use malachite_base::num::arithmetic::traits::{PowerOf2, WrappingAddAssign, WrappingNegAssign};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::BitAccess;
use malachite_base::slices::{slice_leading_zeros, slice_test_zero};
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, performs an
// action equivalent to taking the two's complement of the limbs and getting the bit at the
// specified index. Sufficiently high indices will return `true`. The slice cannot be empty or
// contain only zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// This is equivalent to `mpz_tstbit` from `mpz/tstbit.c`, GMP 6.2.1, where `d` is negative.
pub_test! {limbs_get_bit_neg(xs: &[Limb], index: u64) -> bool {
let x_i = usize::exact_from(index >> Limb::LOG_WIDTH);
if x_i >= xs.len() {
// We're indexing into the infinite suffix of 1s
true
} else {
let x = if slice_test_zero(&xs[..x_i]) {
xs[x_i].wrapping_neg()
} else {
!xs[x_i]
};
x.get_bit(index & Limb::WIDTH_MASK)
}
}}
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, performs an
// action equivalent to taking the two's complement of the limbs, setting a bit at the specified
// index to `true`, and taking the two's complement again. Indices that are outside the bounds of
// the slice will result in no action being taken, since negative numbers in two's complement have
// infinitely many leading 1s. The slice cannot be empty or contain only zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `index`.
//
// # Panics
// If the slice contains only zeros a panic may occur.
//
// This is equivalent to `mpz_setbit` from `mpz/setbit.c`, GMP 6.2.1, where `d` is negative.
pub_test! {limbs_set_bit_neg(xs: &mut [Limb], index: u64) {
let x_i = usize::exact_from(index >> Limb::LOG_WIDTH);
if x_i >= xs.len() {
return;
}
let reduced_index = index & Limb::WIDTH_MASK;
let zero_bound = slice_leading_zeros(xs);
match x_i.cmp(&zero_bound) {
Ordering::Equal => {
let boundary = &mut xs[x_i];
// boundary != 0 here
*boundary -= 1;
boundary.clear_bit(reduced_index);
// boundary != Limb::MAX here
*boundary += 1;
}
Ordering::Less => {
assert!(!limbs_sub_limb_in_place(
&mut xs[x_i..],
Limb::power_of_2(reduced_index),
));
}
Ordering::Greater => {
xs[x_i].clear_bit(reduced_index);
}
}
}}
fn limbs_clear_bit_neg_helper(xs: &mut [Limb], x_i: usize, reduced_index: u64) -> bool {
let zero_bound = slice_leading_zeros(xs);
match x_i.cmp(&zero_bound) {
Ordering::Equal => {
// xs[x_i] != 0 here
let mut boundary = xs[x_i] - 1;
boundary.set_bit(reduced_index);
boundary.wrapping_add_assign(1);
xs[x_i] = boundary;
boundary == 0 && limbs_slice_add_limb_in_place(&mut xs[x_i + 1..], 1)
}
Ordering::Greater => {
xs[x_i].set_bit(reduced_index);
false
}
_ => false,
}
}
// Interpreting a slice of `Limb`s as the limbs (in ascending order) of a `Natural`, performs an
// action equivalent to taking the two's complement of the limbs, setting a bit at the specified
// index to `false`, and taking the two's complement again. Inputs that would result in new `true`
// bits outside of the slice will cause a panic. The slice cannot be empty or contain only zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `index`.
//
// # Panics
// Panics if evaluation would require new `true` bits outside of the slice. If the slice contains
// only zeros a panic may occur.
//
// This is equivalent to `mpz_clrbit` from `mpz/clrbit.c`, GMP 6.2.1, where `d` is negative and
// `bit_idx` small enough that no additional memory needs to be given to `d`.
pub fn limbs_slice_clear_bit_neg(xs: &mut [Limb], index: u64) {
let x_i = usize::exact_from(index >> Limb::LOG_WIDTH);
let reduced_index = index & Limb::WIDTH_MASK;
if x_i >= xs.len() || limbs_clear_bit_neg_helper(xs, x_i, reduced_index) {
panic!("Setting bit cannot be done within existing slice");
}
}
// Interpreting a `Vec` of `Limb`s as the limbs (in ascending order) of a `Natural`, performs an
// action equivalent to taking the two's complement of the limbs, setting a bit at the specified
// index to `false`, and taking the two's complement again. Sufficiently high indices will increase
// the length of the limbs vector. The slice cannot be empty or contain only zeros.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(n)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `index`.
//
// # Panics
// If the slice contains only zeros a panic may occur.
//
// This is equivalent to `mpz_clrbit` from `mpz/clrbit.c`, GMP 6.2.1, where `d` is negative.
pub_test! {limbs_vec_clear_bit_neg(xs: &mut Vec<Limb>, index: u64) {
let x_i = usize::exact_from(index >> Limb::LOG_WIDTH);
let reduced_index = index & Limb::WIDTH_MASK;
if x_i < xs.len() {
if limbs_clear_bit_neg_helper(xs, x_i, reduced_index) {
xs.push(1);
}
} else {
xs.resize(x_i, 0);
xs.push(Limb::power_of_2(reduced_index));
}
}}
impl Natural {
// self cannot be zero
pub(crate) fn get_bit_neg(&self, index: u64) -> bool {
match *self {
Natural(Small(small)) => index >= Limb::WIDTH || small.wrapping_neg().get_bit(index),
Natural(Large(ref limbs)) => limbs_get_bit_neg(limbs, index),
}
}
// self cannot be zero
fn set_bit_neg(&mut self, index: u64) {
match *self {
Natural(Small(ref mut small)) => {
if index < Limb::WIDTH {
small.wrapping_neg_assign();
small.set_bit(index);
small.wrapping_neg_assign();
}
}
Natural(Large(ref mut limbs)) => {
limbs_set_bit_neg(limbs, index);
self.trim()
}
}
}
// self cannot be zero
fn clear_bit_neg(&mut self, index: u64) {
match *self {
Natural(Small(ref mut small)) if index < Limb::WIDTH => {
let mut cleared_small = small.wrapping_neg();
cleared_small.clear_bit(index);
if cleared_small == 0 {
*self = Natural(Large(vec![0, 1]));
} else {
*small = cleared_small.wrapping_neg();
}
}
Natural(Small(_)) => {
let limbs = self.promote_in_place();
limbs_vec_clear_bit_neg(limbs, index);
}
Natural(Large(ref mut limbs)) => {
limbs_vec_clear_bit_neg(limbs, index);
}
}
}
}
/// Provides functions for accessing and modifying the $i$th bit of a [`Integer`], or the
/// coefficient of $2^i$ in its two's complement binary expansion.
///
/// # Examples
/// ```
/// use malachite_base::num::logic::traits::BitAccess;
/// use malachite_base::num::basic::traits::{NegativeOne, Zero};
/// use malachite_nz::integer::Integer;
///
/// let mut x = Integer::ZERO;
/// x.assign_bit(2, true);
/// x.assign_bit(5, true);
/// x.assign_bit(6, true);
/// assert_eq!(x, 100);
/// x.assign_bit(2, false);
/// x.assign_bit(5, false);
/// x.assign_bit(6, false);
/// assert_eq!(x, 0);
///
/// let mut x = Integer::from(-0x100);
/// x.assign_bit(2, true);
/// x.assign_bit(5, true);
/// x.assign_bit(6, true);
/// assert_eq!(x, -156);
/// x.assign_bit(2, false);
/// x.assign_bit(5, false);
/// x.assign_bit(6, false);
/// assert_eq!(x, -256);
///
/// let mut x = Integer::ZERO;
/// x.flip_bit(10);
/// assert_eq!(x, 1024);
/// x.flip_bit(10);
/// assert_eq!(x, 0);
///
/// let mut x = Integer::NEGATIVE_ONE;
/// x.flip_bit(10);
/// assert_eq!(x, -1025);
/// x.flip_bit(10);
/// assert_eq!(x, -1);
/// ```
impl BitAccess for Integer {
/// Determines whether the $i$th bit of an [`Integer`], or the coefficient of $2^i$ in its two's
/// complement binary expansion, is 0 or 1.
///
/// `false` means 0 and `true` means 1. Getting bits beyond the [`Integer`]'s width is allowed;
/// those bits are `false` if the [`Integer`] is non-negative and `true` if it is negative.
///
/// If $n \geq 0$, let
/// $$
/// n = \sum_{i=0}^\infty 2^{b_i};
/// $$
/// but if $n < 0$, let
/// $$
/// -n - 1 = \sum_{i=0}^\infty 2^{1 - b_i},
/// $$
/// where for all $i$, $b_i\in \\{0, 1\\}$.
///
/// $f(n, i) = (b_i = 1)$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::logic::traits::BitAccess;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(Integer::from(123).get_bit(2), false);
/// assert_eq!(Integer::from(123).get_bit(3), true);
/// assert_eq!(Integer::from(123).get_bit(100), false);
/// assert_eq!(Integer::from(-123).get_bit(0), true);
/// assert_eq!(Integer::from(-123).get_bit(1), false);
/// assert_eq!(Integer::from(-123).get_bit(100), true);
/// assert_eq!(Integer::from(10u32).pow(12).get_bit(12), true);
/// assert_eq!(Integer::from(10u32).pow(12).get_bit(100), false);
/// assert_eq!((-Integer::from(10u32).pow(12)).get_bit(12), true);
/// assert_eq!((-Integer::from(10u32).pow(12)).get_bit(100), true);
/// ```
fn get_bit(&self, index: u64) -> bool {
match *self {
Integer {
sign: true,
ref abs,
} => abs.get_bit(index),
Integer {
sign: false,
ref abs,
} => abs.get_bit_neg(index),
}
}
/// Sets the $i$th bit of an [`Integer`], or the coefficient of $2^i$ in its two's complement
/// binary expansion, to 1.
///
/// If $n \geq 0$, let
/// $$
/// n = \sum_{i=0}^\infty 2^{b_i};
/// $$
/// but if $n < 0$, let
/// $$
/// -n - 1 = \sum_{i=0}^\infty 2^{1 - b_i},
/// $$
/// where for all $i$, $b_i\in \\{0, 1\\}$.
/// $$
/// n \gets \\begin{cases}
/// n + 2^j & \text{if} \\quad b_j = 0, \\\\
/// n & \text{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `index`.
///
/// # Examples
/// ```
/// use malachite_base::num::logic::traits::BitAccess;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
///
/// let mut x = Integer::ZERO;
/// x.set_bit(2);
/// x.set_bit(5);
/// x.set_bit(6);
/// assert_eq!(x, 100);
///
/// let mut x = Integer::from(-0x100);
/// x.set_bit(2);
/// x.set_bit(5);
/// x.set_bit(6);
/// assert_eq!(x, -156);
/// ```
fn set_bit(&mut self, index: u64) {
match *self {
Integer {
sign: true,
ref mut abs,
} => abs.set_bit(index),
Integer {
sign: false,
ref mut abs,
} => abs.set_bit_neg(index),
}
}
/// Sets the $i$th bit of an [`Integer`], or the coefficient of $2^i$ in its binary expansion,
/// to 0.
///
/// If $n \geq 0$, let
/// $$
/// n = \sum_{i=0}^\infty 2^{b_i};
/// $$
/// but if $n < 0$, let
/// $$
/// -n - 1 = \sum_{i=0}^\infty 2^{1 - b_i},
/// $$
/// where for all $i$, $b_i\in \\{0, 1\\}$.
/// $$
/// n \gets \\begin{cases}
/// n - 2^j & \text{if} \\quad b_j = 1, \\\\
/// n & \text{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `index`.
///
/// # Examples
/// ```
/// use malachite_base::num::logic::traits::BitAccess;
/// use malachite_nz::integer::Integer;
///
/// let mut x = Integer::from(0x7f);
/// x.clear_bit(0);
/// x.clear_bit(1);
/// x.clear_bit(3);
/// x.clear_bit(4);
/// assert_eq!(x, 100);
///
/// let mut x = Integer::from(-156);
/// x.clear_bit(2);
/// x.clear_bit(5);
/// x.clear_bit(6);
/// assert_eq!(x, -256);
/// ```
fn clear_bit(&mut self, index: u64) {
match *self {
Integer {
sign: true,
ref mut abs,
} => abs.clear_bit(index),
Integer {
sign: false,
ref mut abs,
} => abs.clear_bit_neg(index),
}
}
}