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
// Copyright © 2024 Mikhail Hogrefe
//
// 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::natural::InnerNatural::{Large, Small};
use crate::natural::Natural;
use crate::platform::Limb;
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::WrappingFrom;
use malachite_base::num::logic::traits::TrailingZeros;
use malachite_base::slices::slice_leading_zeros;
// Interpreting a slice of `Limb`s as the limbs of a `Natural` in ascending order, returns the
// number of trailing zeros in the binary expansion of a `Natural` (equivalently, the multiplicity
// of 2 in its prime factorization). The limbs cannot be empty or all zero.
//
// # Worst-case complexity
// $T(n) = O(n)$
//
// $M(n) = O(1)$
//
// where $T$ is time, $M$ is additional memory, and $n$ is `xs.len()`.
//
// # Panics
// Panics if `xs` only contains zeros.
pub_crate_test! {limbs_trailing_zeros(xs: &[Limb]) -> u64 {
let zeros = slice_leading_zeros(xs);
let remaining_zeros = TrailingZeros::trailing_zeros(xs[zeros]);
(u64::wrapping_from(zeros) << Limb::LOG_WIDTH) + remaining_zeros
}}
impl Natural {
/// Returns the number of trailing zeros in the binary expansion of a [`Natural`] (equivalently,
/// the multiplicity of 2 in its prime factorization), or `None` is the [`Natural`] is 0.
///
/// # 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::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::ZERO.trailing_zeros(), None);
/// assert_eq!(Natural::from(3u32).trailing_zeros(), Some(0));
/// assert_eq!(Natural::from(72u32).trailing_zeros(), Some(3));
/// assert_eq!(Natural::from(100u32).trailing_zeros(), Some(2));
/// assert_eq!(Natural::from(10u32).pow(12).trailing_zeros(), Some(12));
/// ```
pub fn trailing_zeros(&self) -> Option<u64> {
match *self {
Natural::ZERO => None,
Natural(Small(small)) => Some(TrailingZeros::trailing_zeros(small)),
Natural(Large(ref limbs)) => Some(limbs_trailing_zeros(limbs)),
}
}
}