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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::{CeilingLogBase, CheckedLogBase, FloorLogBase};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
fn floor_log_base_naive<T: PrimitiveUnsigned>(x: T, base: T) -> u64 {
assert_ne!(x, T::ZERO);
assert!(base > T::ONE);
let mut result = 0;
let mut p = T::ONE;
// loop always executes at least once
while p <= x {
result += 1;
if let Some(next_p) = p.checked_mul(base) {
p = next_p;
} else {
break;
}
}
result - 1
}
pub_test! {ceiling_log_base_naive<T: PrimitiveUnsigned>(x: T, base: T) -> u64 {
assert_ne!(x, T::ZERO);
assert!(base > T::ONE);
let mut result = 0;
let mut p = T::ONE;
while p < x {
result += 1;
if let Some(next_p) = p.checked_mul(base) {
p = next_p;
} else {
break;
}
}
result
}}
pub_test! {checked_log_base_naive<T: PrimitiveUnsigned>(x: T, base: T) -> Option<u64> {
assert_ne!(x, T::ZERO);
assert!(base > T::ONE);
let mut result = 0;
let mut p = T::ONE;
while p < x {
result += 1;
if let Some(next_p) = p.checked_mul(base) {
p = next_p;
} else {
return None;
}
}
if p == x {
Some(result)
} else {
None
}
}}
fn floor_log_base<T: PrimitiveUnsigned>(x: T, base: T) -> u64 {
if let Some(log_base) = base.checked_log_base_2() {
x.floor_log_base_power_of_2(log_base)
} else {
floor_log_base_naive(x, base)
}
}
fn ceiling_log_base<T: PrimitiveUnsigned>(x: T, base: T) -> u64 {
if let Some(log_base) = base.checked_log_base_2() {
x.ceiling_log_base_power_of_2(log_base)
} else {
ceiling_log_base_naive(x, base)
}
}
fn checked_log_base<T: PrimitiveUnsigned>(x: T, base: T) -> Option<u64> {
if let Some(log_base) = base.checked_log_base_2() {
x.checked_log_base_power_of_2(log_base)
} else {
checked_log_base_naive(x, base)
}
}
macro_rules! impl_log_base_unsigned {
($t:ident) => {
impl FloorLogBase for $t {
type Output = u64;
/// Returns the floor of the base-$b$ logarithm of a positive integer.
///
/// $f(x, b) = \lfloor\log_b x\rfloor$.
///
/// # 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() /
/// base.significant_bits()`.
///
/// # Panics
/// Panics if `self` is 0 or `base` is less than 2.
///
/// # Examples
/// See [here](super::log_base#floor_log_base).
#[inline]
fn floor_log_base(self, base: $t) -> u64 {
// TODO use ilog once stabilized
floor_log_base(self, base)
}
}
impl CeilingLogBase for $t {
type Output = u64;
/// Returns the ceiling of the base-$b$ logarithm of a positive integer.
///
/// $f(x, b) = \lceil\log_b x\rceil$.
///
/// # 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() /
/// base.significant_bits()`.
///
/// # Panics
/// Panics if `self` is 0 or `base` is less than 2.
///
/// # Examples
/// See [here](super::log_base#ceiling_log_base).
#[inline]
fn ceiling_log_base(self, base: $t) -> u64 {
ceiling_log_base(self, base)
}
}
impl CheckedLogBase for $t {
type Output = u64;
/// Returns the base-$b$ logarithm of a positive integer. If the integer is not a power
/// of $b$, `None` is returned.
///
/// $$
/// f(x, b) = \\begin{cases}
/// \operatorname{Some}(\log_b x) & \text{if} \\quad \log_b x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # 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() /
/// base.significant_bits()`.
///
/// # Panics
/// Panics if `self` is 0 or `base` is less than 2.
///
/// # Examples
/// See [here](super::log_base#checked_log_base).
#[inline]
fn checked_log_base(self, base: $t) -> Option<u64> {
checked_log_base(self, base)
}
}
};
}
apply_to_unsigneds!(impl_log_base_unsigned);