Trait malachite_base::num::logic::traits::BitAccess

source · [−]
pub trait BitAccess {
    fn get_bit(&self, index: u64) -> bool;
    fn set_bit(&mut self, index: u64);
    fn clear_bit(&mut self, index: u64);

    fn assign_bit(&mut self, index: u64, bit: bool) { ... }
    fn flip_bit(&mut self, index: u64) { ... }
}
Expand description

Defines functions that access or modify individual bits in a number.

Required Methods

Determines whether a number has a true or false bit at index.

Sets the bit at index to true.

Sets the bit at index to false.

Provided Methods

Sets the bit at index to whichever value bit is.

Worst-case complexity

$T(n) = O(\max(T_S(n), T_C(n)))$,

$M(n) = O(\max(M_S(n), M_C(n)))$

where $T$ is time, $M$ is additional memory, $T_S$ and $M_S$ are the complexities of set_bit, and $T_C$ and $M_C$ are the complexities of clear_bit.

Panics

See panics for set_bit and clear_bit.

Sets the bit at index to the opposite of its original value.

Worst-case complexity

$T(n) = O(T_G(n) + \max(T_S(n), T_C(n)))$,

$M(n) = O(M_G(n) + \max(M_S(n), M_C(n)))$

where $T$ is time, $M$ is additional memory, $T_G$ and $M_G$ are the complexities of get_bit, $T_S$ and $M_S$ are the complexities of set_bit, and $T_C$ and $M_C$ are the complexities of clear_bit.

Panics

See panics for get_bit, set_bit and clear_bit.

Implementations on Foreign Types

Determines whether the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are false.

Let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 1.

Setting bits beyond the type’s width is disallowed.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $i \geq W$, where $i$ is index and $W$ is $t::WIDTH.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 0.

Clearing bits beyond the type’s width is allowed; since those bits are already false, clearing them does nothing.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Determines whether the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are false.

Let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 1.

Setting bits beyond the type’s width is disallowed.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $i \geq W$, where $i$ is index and $W$ is $t::WIDTH.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 0.

Clearing bits beyond the type’s width is allowed; since those bits are already false, clearing them does nothing.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Determines whether the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are false.

Let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 1.

Setting bits beyond the type’s width is disallowed.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $i \geq W$, where $i$ is index and $W$ is $t::WIDTH.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 0.

Clearing bits beyond the type’s width is allowed; since those bits are already false, clearing them does nothing.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Determines whether the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are false.

Let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 1.

Setting bits beyond the type’s width is disallowed.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $i \geq W$, where $i$ is index and $W$ is $t::WIDTH.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 0.

Clearing bits beyond the type’s width is allowed; since those bits are already false, clearing them does nothing.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Determines whether the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are false.

Let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 1.

Setting bits beyond the type’s width is disallowed.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $i \geq W$, where $i$ is index and $W$ is $t::WIDTH.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 0.

Clearing bits beyond the type’s width is allowed; since those bits are already false, clearing them does nothing.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Determines whether the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are false.

Let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 1.

Setting bits beyond the type’s width is disallowed.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $i \geq W$, where $i$ is index and $W$ is $t::WIDTH.

Examples

See here.

Sets the $i$th bit of an unsigned primitive integer, or the coefficient of $2^i$ in its binary expansion, to 0.

Clearing bits beyond the type’s width is allowed; since those bits are already false, clearing them does nothing.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Determines whether the $i$th bit of a signed primitive integer is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are true if the value is negative, and false otherwise.

If $n \geq 0$, let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, i) = (b_i = 1)$.

If $n < 0$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where

  • $W$ is the type’s width
  • for all $i$, $b_i\in \{0, 1\}$, and $b_i = 1$ for $i \geq W$.

Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 1.

Setting bits beyond the type’s width is disallowed if the number is non-negative.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $n < 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n \geq 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 0.

Clearing bits beyond the type’s width is disallowed if the number is negative.

If $n \geq 0$ or $j = W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}, \end{cases} $$ where $n \geq 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n < 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Determines whether the $i$th bit of a signed primitive integer is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are true if the value is negative, and false otherwise.

If $n \geq 0$, let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, i) = (b_i = 1)$.

If $n < 0$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where

  • $W$ is the type’s width
  • for all $i$, $b_i\in \{0, 1\}$, and $b_i = 1$ for $i \geq W$.

Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 1.

Setting bits beyond the type’s width is disallowed if the number is non-negative.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $n < 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n \geq 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 0.

Clearing bits beyond the type’s width is disallowed if the number is negative.

If $n \geq 0$ or $j = W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}, \end{cases} $$ where $n \geq 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n < 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Determines whether the $i$th bit of a signed primitive integer is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are true if the value is negative, and false otherwise.

If $n \geq 0$, let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, i) = (b_i = 1)$.

If $n < 0$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where

  • $W$ is the type’s width
  • for all $i$, $b_i\in \{0, 1\}$, and $b_i = 1$ for $i \geq W$.

Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 1.

Setting bits beyond the type’s width is disallowed if the number is non-negative.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $n < 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n \geq 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 0.

Clearing bits beyond the type’s width is disallowed if the number is negative.

If $n \geq 0$ or $j = W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}, \end{cases} $$ where $n \geq 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n < 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Determines whether the $i$th bit of a signed primitive integer is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are true if the value is negative, and false otherwise.

If $n \geq 0$, let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, i) = (b_i = 1)$.

If $n < 0$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where

  • $W$ is the type’s width
  • for all $i$, $b_i\in \{0, 1\}$, and $b_i = 1$ for $i \geq W$.

Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 1.

Setting bits beyond the type’s width is disallowed if the number is non-negative.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $n < 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n \geq 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 0.

Clearing bits beyond the type’s width is disallowed if the number is negative.

If $n \geq 0$ or $j = W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}, \end{cases} $$ where $n \geq 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n < 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Determines whether the $i$th bit of a signed primitive integer is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are true if the value is negative, and false otherwise.

If $n \geq 0$, let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, i) = (b_i = 1)$.

If $n < 0$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where

  • $W$ is the type’s width
  • for all $i$, $b_i\in \{0, 1\}$, and $b_i = 1$ for $i \geq W$.

Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 1.

Setting bits beyond the type’s width is disallowed if the number is non-negative.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $n < 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n \geq 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 0.

Clearing bits beyond the type’s width is disallowed if the number is negative.

If $n \geq 0$ or $j = W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}, \end{cases} $$ where $n \geq 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n < 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Determines whether the $i$th bit of a signed primitive integer is 0 or 1.

false means 0 and true means 1. Getting bits beyond the type’s width is allowed; those bits are true if the value is negative, and false otherwise.

If $n \geq 0$, let $$ n = \sum_{i=0}^\infty 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$; so finitely many of the bits are 1, and the rest are 0. Then $f(n, i) = (b_i = 1)$.

If $n < 0$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where

  • $W$ is the type’s width
  • for all $i$, $b_i\in \{0, 1\}$, and $b_i = 1$ for $i \geq W$.

Then $f(n, j) = (b_j = 1)$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 1.

Setting bits beyond the type’s width is disallowed if the number is non-negative.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$, and $W$ is the width of the type. Then $$ n \gets \begin{cases} n + 2^j & \text{if} \quad b_j = 0, \\ n & \text{otherwise}, \end{cases} $$ where $n < 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n \geq 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Sets the $i$th bit of a signed primitive integer to 0.

Clearing bits beyond the type’s width is disallowed if the number is negative.

If $n \geq 0$ or $j = W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}; $$ but if $n < 0$ or $j = W - 1$, let $$ 2^W + n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is the width of the type. Then $$ n \gets \begin{cases} n - 2^j & \text{if} \quad b_j = 1, \\ n & \text{otherwise}, \end{cases} $$ where $n \geq 0$ or $j < W$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if $n < 0$ and $i \geq W$, where $n$ is self, $i$ is index and $W$ is the width of the type.

Examples

See here.

Implementors