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use crate::num::arithmetic::traits::{ModPowerOf2, UnsignedAbs};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::WrappingFrom;
use crate::num::logic::traits::{BitBlockAccess, LeadingZeros};
use std::cmp::min;
const ERROR_MESSAGE: &str = "Result exceeds width of output type";
fn get_bits_unsigned<T: PrimitiveUnsigned>(x: &T, start: u64, end: u64) -> T {
assert!(start <= end);
if start >= T::WIDTH {
T::ZERO
} else {
(*x >> start).mod_power_of_2(end - start)
}
}
fn assign_bits_unsigned<T: PrimitiveUnsigned>(x: &mut T, start: u64, end: u64, bits: &T) {
assert!(start <= end);
let width = T::WIDTH;
let bits_width = end - start;
let bits = bits.mod_power_of_2(bits_width);
if bits != T::ZERO && LeadingZeros::leading_zeros(bits) < start {
panic!("{}", ERROR_MESSAGE);
} else if start < width {
*x &= !(T::MAX.mod_power_of_2(min(bits_width, width - start)) << start);
*x |= bits << start;
}
}
macro_rules! impl_bit_block_access_unsigned {
($t:ident) => {
impl BitBlockAccess for $t {
type Bits = $t;
/// 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](super::bit_block_access#get_bits).
#[inline]
fn get_bits(&self, start: u64, end: u64) -> Self {
get_bits_unsigned(self, start, end)
}
/// 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](super::bit_block_access#assign_bits).
#[inline]
fn assign_bits(&mut self, start: u64, end: u64, bits: &Self::Bits) {
assign_bits_unsigned(self, start, end, bits)
}
}
};
}
apply_to_unsigneds!(impl_bit_block_access_unsigned);
fn get_bits_signed<T: ModPowerOf2<Output = U> + PrimitiveSigned, U>(
x: &T,
start: u64,
end: u64,
) -> U {
assert!(start <= end);
(if start >= T::WIDTH {
-T::iverson(*x < T::ZERO)
} else {
*x >> start
})
.mod_power_of_2(end - start)
}
fn assign_bits_signed<
T: PrimitiveSigned + UnsignedAbs<Output = U> + WrappingFrom<U>,
U: PrimitiveUnsigned,
>(
x: &mut T,
start: u64,
end: u64,
bits: &U,
) {
assert!(start <= end);
if *x >= T::ZERO {
let mut abs_x = x.unsigned_abs();
abs_x.assign_bits(start, end, bits);
if abs_x.get_highest_bit() {
panic!("{}", ERROR_MESSAGE);
}
*x = T::wrapping_from(abs_x);
} else {
let width = T::WIDTH - 1;
let bits_width = end - start;
let bits = bits.mod_power_of_2(bits_width);
let max = U::MAX;
if bits_width > width + 1 {
panic!("{}", ERROR_MESSAGE);
} else if start >= width {
if bits != max.mod_power_of_2(bits_width) {
panic!("{}", ERROR_MESSAGE);
}
} else {
let lower_width = width - start;
if end > width && bits >> lower_width != max.mod_power_of_2(end - width) {
panic!("{}", ERROR_MESSAGE);
} else {
*x &=
T::wrapping_from(!(max.mod_power_of_2(min(bits_width, lower_width)) << start));
*x |= T::wrapping_from(bits << start);
}
}
}
}
macro_rules! impl_bit_block_access_signed {
($u:ident, $s:ident) => {
impl BitBlockAccess for $s {
type Bits = $u;
/// 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](super::bit_block_access#get_bits).
#[inline]
fn get_bits(&self, start: u64, end: u64) -> Self::Bits {
get_bits_signed(self, start, end)
}
/// 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](super::bit_block_access#assign_bits).
#[inline]
fn assign_bits(&mut self, start: u64, end: u64, bits: &Self::Bits) {
assign_bits_signed(self, start, end, bits)
}
}
};
}
apply_to_unsigned_signed_pairs!(impl_bit_block_access_signed);