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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
use malachite_base::num::arithmetic::traits::{
CeilingLogBase2, CeilingLogBasePowerOf2, CheckedLogBase2, CheckedLogBasePowerOf2, DivMod,
DivRound, FloorLogBase2, FloorLogBasePowerOf2, Sign,
};
use malachite_base::rounding_modes::RoundingMode;
use std::cmp::Ordering;
use Rational;
impl<'a> FloorLogBasePowerOf2<i64> for &'a Rational {
type Output = i64;
/// Returns the floor of the base-$2^k$ logarithm of a positive [`Rational`].
///
/// $k$ may be negative.
///
/// $f(x, k) = \lfloor\log_{2^k} x\rfloor$.
///
/// # 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()`.
///
/// # Panics
/// Panics if `self` is less than or equal to 0 or `pow` is 0.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::FloorLogBasePowerOf2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(100).floor_log_base_power_of_2(2), 3);
/// assert_eq!(Rational::from(4294967296u64).floor_log_base_power_of_2(8), 4);
///
/// // 4^(-2) < 1/10 < 4^(-1)
/// assert_eq!(Rational::from_signeds(1, 10).floor_log_base_power_of_2(2), -2);
/// // (1/4)^2 < 1/10 < (1/4)^1
/// assert_eq!(Rational::from_signeds(1, 10).floor_log_base_power_of_2(-2), 1);
/// ```
fn floor_log_base_power_of_2(self, pow: i64) -> i64 {
assert!(*self > 0u32);
match pow.sign() {
Ordering::Equal => panic!("Cannot take base-1 logarithm"),
Ordering::Greater => self.floor_log_base_2().div_round(pow, RoundingMode::Floor),
Ordering::Less => {
-(self
.ceiling_log_base_2()
.div_round(-pow, RoundingMode::Ceiling))
}
}
}
}
impl<'a> CeilingLogBasePowerOf2<i64> for &'a Rational {
type Output = i64;
/// Returns the ceiling of the base-$2^k$ logarithm of a positive [`Rational`].
///
/// $k$ may be negative.
///
/// $f(x, p) = \lceil\log_{2^p} x\rceil$.
///
/// # 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()`.
///
/// # Panics
/// Panics if `self` is less than or equal to 0 or `pow` is 0.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::CeilingLogBasePowerOf2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(100).ceiling_log_base_power_of_2(2), 4);
/// assert_eq!(Rational::from(4294967296u64).ceiling_log_base_power_of_2(8), 4);
///
/// // 4^(-2) < 1/10 < 4^(-1)
/// assert_eq!(Rational::from_signeds(1, 10).ceiling_log_base_power_of_2(2), -1);
/// // (1/4)^2 < 1/10 < (1/4)^1
/// assert_eq!(Rational::from_signeds(1, 10).ceiling_log_base_power_of_2(-2), 2);
/// ```
fn ceiling_log_base_power_of_2(self, pow: i64) -> i64 {
assert!(*self > 0u32);
match pow.sign() {
Ordering::Equal => panic!("Cannot take base-1 logarithm"),
Ordering::Greater => self
.ceiling_log_base_2()
.div_round(pow, RoundingMode::Ceiling),
Ordering::Less => -self.floor_log_base_2().div_round(-pow, RoundingMode::Floor),
}
}
}
impl<'a> CheckedLogBasePowerOf2<i64> for &'a Rational {
type Output = i64;
/// Returns the base-$2^k$ logarithm of a positive [`Rational`]. If the [`Rational`] is not a
/// power of $2^k$, then `None` is returned.
///
/// $k$ may be negative.
///
/// $$
/// f(x, p) = \\begin{cases}
/// \operatorname{Some}(\log_{2^p} x) & \text{if} \\quad \log_{2^p} x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # 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()`.
///
/// # Panics
/// Panics if `self` is 0 or `pow` is 0.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::CheckedLogBasePowerOf2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(100).checked_log_base_power_of_2(2), None);
/// assert_eq!(Rational::from(4294967296u64).checked_log_base_power_of_2(8), Some(4));
///
/// // 4^(-2) < 1/10 < 4^(-1)
/// assert_eq!(Rational::from_signeds(1, 10).checked_log_base_power_of_2(2), None);
/// assert_eq!(Rational::from_signeds(1, 16).checked_log_base_power_of_2(2), Some(-2));
/// // (1/4)^2 < 1/10 < (1/4)^1
/// assert_eq!(Rational::from_signeds(1, 10).checked_log_base_power_of_2(-2), None);
/// assert_eq!(Rational::from_signeds(1, 16).checked_log_base_power_of_2(-2), Some(2));
/// ```
fn checked_log_base_power_of_2(self, pow: i64) -> Option<i64> {
assert!(*self > 0u32);
let log_base_2 = self.checked_log_base_2()?;
let (pow, neg) = match pow.sign() {
Ordering::Equal => panic!("Cannot take base-1 logarithm"),
Ordering::Greater => (pow, false),
Ordering::Less => (-pow, true),
};
let (log, rem) = log_base_2.div_mod(pow);
if rem != 0 {
None
} else if neg {
Some(-log)
} else {
Some(log)
}
}
}