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 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141
use malachite_base::num::arithmetic::traits::{DivRound, DivRoundAssign, Floor, FloorAssign};
use malachite_base::num::basic::traits::One;
use malachite_base::rounding_modes::RoundingMode;
use malachite_nz::integer::Integer;
use malachite_nz::natural::Natural;
use std::mem::swap;
use Rational;
impl Floor for Rational {
type Output = Integer;
/// Finds the floor of a [`Rational`], taking the [`Rational`] by value.
///
/// $$
/// f(x) = \lfloor x \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), other.significant_bits())`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Floor;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::ZERO.floor(), 0);
/// assert_eq!(Rational::from_signeds(22, 7).floor(), 3);
/// assert_eq!(Rational::from_signeds(-22, 7).floor(), -4);
/// ```
fn floor(self) -> Integer {
if self.sign {
Integer::from(self.numerator / self.denominator)
} else {
Integer::from_sign_and_abs(
false,
self.numerator
.div_round(self.denominator, RoundingMode::Ceiling),
)
}
}
}
impl<'a> Floor for &'a Rational {
type Output = Integer;
/// Finds the floor of a [`Rational`], taking the [`Rational`] by reference.
///
/// $$
/// f(x) = \lfloor x \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), other.significant_bits())`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Floor;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// assert_eq!((&Rational::ZERO).floor(), 0);
/// assert_eq!((&Rational::from_signeds(22, 7)).floor(), 3);
/// assert_eq!((&Rational::from_signeds(-22, 7)).floor(), -4);
/// ```
fn floor(self) -> Integer {
if self.sign {
Integer::from(&self.numerator / &self.denominator)
} else {
Integer::from_sign_and_abs(
false,
(&self.numerator).div_round(&self.denominator, RoundingMode::Ceiling),
)
}
}
}
impl FloorAssign for Rational {
/// Replaces a [`Rational`] with its floor.
///
/// $$
/// x \gets \lfloor x \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is
/// `max(self.significant_bits(), other.significant_bits())`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::FloorAssign;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// let mut x = Rational::ZERO;
/// x.floor_assign();
/// assert_eq!(x, 0);
///
/// let mut x = Rational::from_signeds(22, 7);
/// x.floor_assign();
/// assert_eq!(x, 3);
///
/// let mut x = Rational::from_signeds(-22, 7);
/// x.floor_assign();
/// assert_eq!(x, -4);
/// ```
fn floor_assign(&mut self) {
let mut d = Natural::ONE;
swap(&mut self.denominator, &mut d);
if self.sign {
self.numerator /= d;
} else {
self.numerator.div_round_assign(d, RoundingMode::Ceiling);
if !self.sign && self.numerator == 0 {
self.sign = true;
}
}
}
}