Trait malachite_base::num::logic::traits::BitBlockAccess

source · [−]
pub trait BitBlockAccess: Sized {
    type Bits;

    fn get_bits(&self, start: u64, end: u64) -> Self::Bits;
    fn assign_bits(&mut self, start: u64, end: u64, bits: &Self::Bits);

    fn get_bits_owned(self, start: u64, end: u64) -> Self::Bits { ... }
}
Expand description

Defines functions that access or modify blocks of adjacent bits in a number.

Required Associated Types

Required Methods

Extracts a block of bits whose first index is start and last index is end - 1.

Assigns the least-significant end - start bits of bits to bits start through end - 1 (inclusive) of self.

Provided Methods

Extracts a block of bits whose first index is start and last index is end - 1, taking ownership of self.

Worst-case complexity

For the default implementation, same as get_bits.

Panics

For the default implementation, ee panics for get_bits.

Examples
use malachite_base::num::logic::traits::BitBlockAccess;

assert_eq!((-0x5433i16).get_bits_owned(4, 8), 0xc);
assert_eq!((-0x5433i16).get_bits_owned(5, 9), 14);
assert_eq!((-0x5433i16).get_bits_owned(5, 5), 0);
assert_eq!((-0x5433i16).get_bits_owned(100, 104), 0xf);

Implementations on Foreign Types

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The block of bits has the same type as the input. If end is greater than the type’s width, the high bits of the result are all 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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if start < end.

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The block of bits has the same type as the input. If bits has fewer bits than end - start, the high bits are interpreted as 0. If end is greater than the type’s width, the high bits of bits must be 0.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p$.

Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end, or if end > W and bits W - start through end - start of bits are nonzero.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The block of bits has the same type as the input. If end is greater than the type’s width, the high bits of the result are all 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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if start < end.

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The block of bits has the same type as the input. If bits has fewer bits than end - start, the high bits are interpreted as 0. If end is greater than the type’s width, the high bits of bits must be 0.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p$.

Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end, or if end > W and bits W - start through end - start of bits are nonzero.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The block of bits has the same type as the input. If end is greater than the type’s width, the high bits of the result are all 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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if start < end.

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The block of bits has the same type as the input. If bits has fewer bits than end - start, the high bits are interpreted as 0. If end is greater than the type’s width, the high bits of bits must be 0.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p$.

Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end, or if end > W and bits W - start through end - start of bits are nonzero.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The block of bits has the same type as the input. If end is greater than the type’s width, the high bits of the result are all 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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if start < end.

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The block of bits has the same type as the input. If bits has fewer bits than end - start, the high bits are interpreted as 0. If end is greater than the type’s width, the high bits of bits must be 0.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p$.

Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end, or if end > W and bits W - start through end - start of bits are nonzero.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The block of bits has the same type as the input. If end is greater than the type’s width, the high bits of the result are all 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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if start < end.

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The block of bits has the same type as the input. If bits has fewer bits than end - start, the high bits are interpreted as 0. If end is greater than the type’s width, the high bits of bits must be 0.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p$.

Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end, or if end > W and bits W - start through end - start of bits are nonzero.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The block of bits has the same type as the input. If end is greater than the type’s width, the high bits of the result are all 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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if start < end.

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The block of bits has the same type as the input. If bits has fewer bits than end - start, the high bits are interpreted as 0. If end is greater than the type’s width, the high bits of bits must be 0.

Let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p$.

Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end, or if end > W and bits W - start through end - start of bits are nonzero.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The type of the block of bits is the unsigned version of the input type. If end is greater than the type’s width, the high bits of the result are all 0, or all 1, depending on the input value’s sign; and if the input is negative and end - start is greater than the type’s width, the function panics.

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$
Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end or (self < 0 and end - start > W).

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The type of the block of bits is the unsigned version of the input type. If bits has fewer bits than end - start, the high bits are interpreted as 0 or 1, depending on the sign of self. If end is greater than the type’s width, the high bits of bits must be 0 or 1, depending on the sign of self.

The sign of self remains unchanged, since only a finite number of bits are changed and the sign is determined by the implied infinite prefix of bits.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p - 1$. Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

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 $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 1$ for all $i \geq W + p - 1$. Then $$ f(n, p, q, m) = \left ( \sum_{i=0}^{W-1} 2^{c_i} \right ) - 2^W, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width Panics if start < end, or if end >= W and bits W - start through end - start of bits are not equal to the original sign bit of self.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The type of the block of bits is the unsigned version of the input type. If end is greater than the type’s width, the high bits of the result are all 0, or all 1, depending on the input value’s sign; and if the input is negative and end - start is greater than the type’s width, the function panics.

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$
Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end or (self < 0 and end - start > W).

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The type of the block of bits is the unsigned version of the input type. If bits has fewer bits than end - start, the high bits are interpreted as 0 or 1, depending on the sign of self. If end is greater than the type’s width, the high bits of bits must be 0 or 1, depending on the sign of self.

The sign of self remains unchanged, since only a finite number of bits are changed and the sign is determined by the implied infinite prefix of bits.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p - 1$. Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

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 $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 1$ for all $i \geq W + p - 1$. Then $$ f(n, p, q, m) = \left ( \sum_{i=0}^{W-1} 2^{c_i} \right ) - 2^W, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width Panics if start < end, or if end >= W and bits W - start through end - start of bits are not equal to the original sign bit of self.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The type of the block of bits is the unsigned version of the input type. If end is greater than the type’s width, the high bits of the result are all 0, or all 1, depending on the input value’s sign; and if the input is negative and end - start is greater than the type’s width, the function panics.

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$
Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end or (self < 0 and end - start > W).

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The type of the block of bits is the unsigned version of the input type. If bits has fewer bits than end - start, the high bits are interpreted as 0 or 1, depending on the sign of self. If end is greater than the type’s width, the high bits of bits must be 0 or 1, depending on the sign of self.

The sign of self remains unchanged, since only a finite number of bits are changed and the sign is determined by the implied infinite prefix of bits.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p - 1$. Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

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 $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 1$ for all $i \geq W + p - 1$. Then $$ f(n, p, q, m) = \left ( \sum_{i=0}^{W-1} 2^{c_i} \right ) - 2^W, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width Panics if start < end, or if end >= W and bits W - start through end - start of bits are not equal to the original sign bit of self.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The type of the block of bits is the unsigned version of the input type. If end is greater than the type’s width, the high bits of the result are all 0, or all 1, depending on the input value’s sign; and if the input is negative and end - start is greater than the type’s width, the function panics.

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$
Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end or (self < 0 and end - start > W).

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The type of the block of bits is the unsigned version of the input type. If bits has fewer bits than end - start, the high bits are interpreted as 0 or 1, depending on the sign of self. If end is greater than the type’s width, the high bits of bits must be 0 or 1, depending on the sign of self.

The sign of self remains unchanged, since only a finite number of bits are changed and the sign is determined by the implied infinite prefix of bits.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p - 1$. Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

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 $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 1$ for all $i \geq W + p - 1$. Then $$ f(n, p, q, m) = \left ( \sum_{i=0}^{W-1} 2^{c_i} \right ) - 2^W, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width Panics if start < end, or if end >= W and bits W - start through end - start of bits are not equal to the original sign bit of self.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The type of the block of bits is the unsigned version of the input type. If end is greater than the type’s width, the high bits of the result are all 0, or all 1, depending on the input value’s sign; and if the input is negative and end - start is greater than the type’s width, the function panics.

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$
Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end or (self < 0 and end - start > W).

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The type of the block of bits is the unsigned version of the input type. If bits has fewer bits than end - start, the high bits are interpreted as 0 or 1, depending on the sign of self. If end is greater than the type’s width, the high bits of bits must be 0 or 1, depending on the sign of self.

The sign of self remains unchanged, since only a finite number of bits are changed and the sign is determined by the implied infinite prefix of bits.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p - 1$. Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

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 $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 1$ for all $i \geq W + p - 1$. Then $$ f(n, p, q, m) = \left ( \sum_{i=0}^{W-1} 2^{c_i} \right ) - 2^W, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width Panics if start < end, or if end >= W and bits W - start through end - start of bits are not equal to the original sign bit of self.

Examples

See here.

Extracts a block of adjacent bits from a number.

The first index is start and last index is end - 1.

The type of the block of bits is the unsigned version of the input type. If end is greater than the type’s width, the high bits of the result are all 0, or all 1, depending on the input value’s sign; and if the input is negative and end - start is greater than the type’s width, the function panics.

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$

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 $$ f(n, p, q) = \sum_{i=p}^{q-1} 2^{b_{i-p}}. $$
Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width. Panics if start < end or (self < 0 and end - start > W).

Examples

See here.

Replaces a block of adjacent bits in a number with other bits.

The least-significant end - start bits of bits are assigned to bits start through end - 1, inclusive, of self.

The type of the block of bits is the unsigned version of the input type. If bits has fewer bits than end - start, the high bits are interpreted as 0 or 1, depending on the sign of self. If end is greater than the type’s width, the high bits of bits must be 0 or 1, depending on the sign of self.

The sign of self remains unchanged, since only a finite number of bits are changed and the sign is determined by the implied infinite prefix of bits.

If $n \geq 0$ and $j \neq W - 1$, let $$ n = \sum_{i=0}^{W-1} 2^{b_i}, $$ where for all $i$, $b_i\in \{0, 1\}$ and $W$ is $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 0$ for all $i \geq W + p - 1$. Then $$ n \gets \sum_{i=0}^{W-1} 2^{c_i}, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

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 $t::WIDTH. Let $$ m = \sum_{i=0}^k 2^{d_i}, $$ where for all $i$, $d_i\in \{0, 1\}$. Also, let $p, q \in \mathbb{N}$, where $d_i = 1$ for all $i \geq W + p - 1$. Then $$ f(n, p, q, m) = \left ( \sum_{i=0}^{W-1} 2^{c_i} \right ) - 2^W, $$ where $$ \{c_0, c_1, c_2, \ldots, c_ {W-1}\} = \{b_0, b_1, b_2, \ldots, b_{p-1}, d_0, d_1, \ldots, d_{p-q-1}, b_q, \ldots, b_ {W-1}\}. $$

Worst-case complexity

Constant time and additional memory.

Panics

Let W be the type’s width Panics if start < end, or if end >= W and bits W - start through end - start of bits are not equal to the original sign bit of self.

Examples

See here.

Implementors