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// Copyright © 2026 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::num::arithmetic::traits::{CeilingLogBase2, CheckedLogBase2, FloorLogBase2};
use crate::num::basic::integers::PrimitiveInt;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::SciMantissaAndExponent;
use crate::num::logic::traits::{LeadingZeros, TrailingZeros};
fn floor_log_base_2<T: PrimitiveUnsigned>(x: T) -> u64 {
assert!(x != T::ZERO, "Cannot take the base-2 logarithm of 0.");
x.significant_bits() - 1
}
fn ceiling_log_base_2<T: PrimitiveUnsigned>(x: T) -> u64 {
let floor_log_base_2 = x.floor_log_base_2();
if x.is_power_of_2() {
floor_log_base_2
} else {
floor_log_base_2 + 1
}
}
fn checked_log_base_2<T: PrimitiveInt>(x: T) -> Option<u64> {
assert!(x != T::ZERO, "Cannot take the base-2 logarithm of 0.");
let leading_zeros = LeadingZeros::leading_zeros(x);
let trailing_zeros = TrailingZeros::trailing_zeros(x);
if leading_zeros + trailing_zeros == T::WIDTH - 1 {
Some(trailing_zeros)
} else {
None
}
}
macro_rules! impl_log_base_2_unsigned {
($t:ident) => {
impl FloorLogBase2 for $t {
type Output = u64;
/// Returns the floor of the base-2 logarithm of a positive integer.
///
/// $f(x) = \lfloor\log_2 x\rfloor$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is 0.
///
/// # Examples
/// See [here](super::log_base_2#floor_log_base_2).
#[inline]
fn floor_log_base_2(self) -> u64 {
// TODO use ilog2 once stabilized
floor_log_base_2(self)
}
}
impl CeilingLogBase2 for $t {
type Output = u64;
/// Returns the ceiling of the base-2 logarithm of a positive integer.
///
/// $f(x) = \lceil\log_2 x\rceil$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is 0.
///
/// # Examples
/// See [here](super::log_base_2#ceiling_log_base_2).
#[inline]
fn ceiling_log_base_2(self) -> u64 {
ceiling_log_base_2(self)
}
}
impl CheckedLogBase2 for $t {
type Output = u64;
/// Returns the base-2 logarithm of a positive integer. If the integer is not a power of
/// 2, `None` is returned.
///
/// $$
/// f(x) = \\begin{cases}
/// \operatorname{Some}(\log_2 x) & \text{if} \\quad \log_2 x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is 0.
///
/// # Examples
/// See [here](super::log_base_2#checked_log_base_2).
#[inline]
fn checked_log_base_2(self) -> Option<u64> {
checked_log_base_2(self)
}
}
};
}
apply_to_unsigneds!(impl_log_base_2_unsigned);
macro_rules! impl_log_base_2_primitive_float {
($t:ident) => {
impl FloorLogBase2 for $t {
type Output = i64;
/// Returns the floor of the base-2 logarithm of a positive float.
///
/// $f(x) = \lfloor\log_2 x\rfloor$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is infinite, `NaN`, or less than or equal to zero.
///
/// # Examples
/// See [here](super::log_base_2#floor_log_base_2).
#[inline]
fn floor_log_base_2(self) -> i64 {
assert!(self > 0.0);
self.sci_exponent()
}
}
impl CeilingLogBase2 for $t {
type Output = i64;
/// Returns the ceiling of the base-2 logarithm of a positive float.
///
/// $f(x) = \lceil\log_2 x\rceil$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is infinite, `NaN`, or less than or equal to zero.
///
/// # Examples
/// See [here](super::log_base_2#ceiling_log_base_2).
#[inline]
fn ceiling_log_base_2(self) -> i64 {
assert!(self > 0.0);
let (mantissa, exponent) = self.sci_mantissa_and_exponent();
if mantissa == 1.0 {
exponent
} else {
exponent + 1
}
}
}
impl CheckedLogBase2 for $t {
type Output = i64;
/// Returns the base-2 logarithm of a positive float If the float is not a power of 2,
/// `None` is returned.
///
/// $$
/// f(x) = \\begin{cases}
/// \operatorname{Some}(\log_2 x) & \text{if} \\quad \log_2 x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is infinite, `NaN`, or less than or equal to zero.
///
/// # Examples
/// See [here](super::log_base_2#checked_log_base_2).
#[inline]
fn checked_log_base_2(self) -> Option<i64> {
assert!(self > 0.0);
let (mantissa, exponent) = self.sci_mantissa_and_exponent();
if mantissa == 1.0 {
Some(exponent)
} else {
None
}
}
}
};
}
apply_to_primitive_floats!(impl_log_base_2_primitive_float);