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use crate::num::arithmetic::traits::UnsignedAbs;
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::logic::traits::{LeadingZeros, SignificantBits};
fn significant_bits_unsigned<T: PrimitiveUnsigned>(x: T) -> u64 {
T::WIDTH - LeadingZeros::leading_zeros(x)
}
macro_rules! impl_significant_bits_unsigned {
($t:ident) => {
impl SignificantBits for $t {
/// Returns the number of significant bits of an unsigned primitive integer.
///
/// This is the integer's width minus the number of leading zeros.
///
/// $$
/// f(n) = \\begin{cases}
/// 0 & \text{if} \\quad n = 0, \\\\
/// \lfloor \log_2 n \rfloor + 1 & \text{if} \\quad n > 0.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::significant_bits#significant_bits).
#[inline]
fn significant_bits(self) -> u64 {
significant_bits_unsigned(self)
}
}
};
}
apply_to_unsigneds!(impl_significant_bits_unsigned);
fn significant_bits_signed<U: PrimitiveUnsigned, S: PrimitiveSigned + UnsignedAbs<Output = U>>(
x: S,
) -> u64 {
x.unsigned_abs().significant_bits()
}
macro_rules! impl_significant_bits_signed {
($u:ident, $s:ident) => {
/// Returns the number of significant bits of a signed primitive integer.
///
/// This is the integer's width minus the number of leading zeros of its absolute value.
///
/// $$
/// f(n) = \\begin{cases}
/// 0 & \text{if} \\quad n = 0, \\\\
/// \lfloor \log_2 |n| \rfloor + 1 & \text{if} \\quad n \neq 0.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::significant_bits#significant_bits).
impl SignificantBits for $s {
#[inline]
fn significant_bits(self) -> u64 {
significant_bits_signed(self)
}
}
};
}
apply_to_unsigned_signed_pairs!(impl_significant_bits_signed);