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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::{
CeilingLogBasePowerOf2, CheckedLogBasePowerOf2, DivMod, DivRound, FloorLogBasePowerOf2,
};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::{ExactFrom, SciMantissaAndExponent};
use crate::rounding_modes::RoundingMode::*;
#[cfg(feature = "test_build")]
pub fn ceiling_log_base_power_of_2_naive<T: PrimitiveUnsigned>(x: T, pow: u64) -> u64 {
assert_ne!(x, T::ZERO);
assert_ne!(pow, 0);
if pow >= T::WIDTH {
return u64::from(x != T::ONE);
}
let mut result = 0;
let mut p = T::ONE;
while p < x {
let highest_possible = p.leading_zeros() < pow;
result += 1;
if highest_possible {
break;
}
p <<= pow;
}
result
}
fn floor_log_base_power_of_2<T: PrimitiveUnsigned>(x: T, pow: u64) -> u64 {
assert!(x != T::ZERO, "Cannot take the base-2 logarithm of 0.");
assert_ne!(pow, 0);
(x.significant_bits() - 1) / pow
}
fn ceiling_log_base_power_of_2<T: PrimitiveUnsigned>(x: T, pow: u64) -> u64 {
assert!(x != T::ZERO, "Cannot take the base-2 logarithm of 0.");
assert_ne!(pow, 0);
let (floor_log, rem) = (x.significant_bits() - 1).div_mod(pow);
if rem == 0 && T::is_power_of_2(&x) {
floor_log
} else {
floor_log + 1
}
}
fn checked_log_base_power_of_2<T: PrimitiveUnsigned>(x: T, pow: u64) -> Option<u64> {
assert!(x != T::ZERO, "Cannot take the base-2 logarithm of 0.");
assert_ne!(pow, 0);
let (floor_log, rem) = (x.significant_bits() - 1).div_mod(pow);
if rem == 0 && T::is_power_of_2(&x) {
Some(floor_log)
} else {
None
}
}
macro_rules! impl_log_base_power_of_2_unsigned {
($t:ident) => {
impl FloorLogBasePowerOf2<u64> for $t {
type Output = u64;
/// Returns the floor of the base-$2^k$ logarithm of a positive integer.
///
/// $f(x, k) = \lfloor\log_{2^k} x\rfloor$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is infinite, `NaN`, or less than or equal to zero, or if `pow` is
/// zero.
///
/// # Examples
/// See [here](super::log_base_power_of_2#floor_log_base_power_of_2).
#[inline]
fn floor_log_base_power_of_2(self, pow: u64) -> u64 {
floor_log_base_power_of_2(self, pow)
}
}
impl CeilingLogBasePowerOf2<u64> for $t {
type Output = u64;
/// Returns the ceiling of the base-$2^k$ logarithm of a positive integer.
///
/// $f(x, k) = \lceil\log_{2^k} x\rceil$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is infinite, `NaN`, or less than or equal to zero, or if `pow` is
/// zero.
///
/// # Examples
/// See [here](super::log_base_power_of_2#ceiling_log_base_power_of_2).
#[inline]
fn ceiling_log_base_power_of_2(self, pow: u64) -> u64 {
ceiling_log_base_power_of_2(self, pow)
}
}
impl CheckedLogBasePowerOf2<u64> for $t {
type Output = u64;
/// Returns the base-$2^k$ logarithm of a positive integer. If the integer is not a
/// power of $2^k$, `None` is returned.
///
/// $$
/// f(x, k) = \\begin{cases}
/// \operatorname{Some}(\log_{2^k} x) & \text{if} \\quad \log_{2^k} x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` is infinite, `NaN`, or less than or equal to zero, or if `pow` is
/// zero.
///
/// # Examples
/// See [here](super::log_base_power_of_2#ceiling_log_base_power_of_2).
#[inline]
fn checked_log_base_power_of_2(self, pow: u64) -> Option<u64> {
checked_log_base_power_of_2(self, pow)
}
}
};
}
apply_to_unsigneds!(impl_log_base_power_of_2_unsigned);
macro_rules! impl_log_base_power_of_2_primitive_float {
($t:ident) => {
impl FloorLogBasePowerOf2<u64> for $t {
type Output = i64;
/// Returns the floor of the base-$2^k$ logarithm of a positive float.
///
/// $f(x, k) = \lfloor\log_{2^k} x\rfloor$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` or `pow` are 0.
///
/// # Examples
/// See [here](super::log_base_power_of_2#floor_log_base_power_of_2).
#[inline]
fn floor_log_base_power_of_2(self, pow: u64) -> i64 {
assert!(self > 0.0);
self.sci_exponent().div_round(i64::exact_from(pow), Floor).0
}
}
impl CeilingLogBasePowerOf2<u64> for $t {
type Output = i64;
/// Returns the ceiling of the base-$2^k$ logarithm of a positive float.
///
/// $f(x, k) = \lceil\log_{2^k} x\rceil$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` or `pow` are 0.
///
/// # Examples
/// See [here](super::log_base_power_of_2#ceiling_log_base_power_of_2).
#[inline]
fn ceiling_log_base_power_of_2(self, pow: u64) -> i64 {
assert!(self > 0.0);
let (mantissa, exponent) = self.sci_mantissa_and_exponent();
let exact = mantissa == 1.0;
let (q, r) = exponent.div_mod(i64::exact_from(pow));
if exact && r == 0 { q } else { q + 1 }
}
}
impl CheckedLogBasePowerOf2<u64> for $t {
type Output = i64;
/// Returns the base-$2^k$ logarithm of a positive float. If the float is not a power of
/// $2^k$, `None` is returned.
///
/// $$
/// f(x, k) = \\begin{cases}
/// \operatorname{Some}(\log_{2^k} x) & \text{if} \\quad \log_{2^k} x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Panics
/// Panics if `self` or `pow` are 0.
///
/// # Examples
/// See [here](super::log_base_power_of_2#checked_log_base_power_of_2).
#[inline]
fn checked_log_base_power_of_2(self, pow: u64) -> Option<i64> {
assert!(self > 0.0);
let (mantissa, exponent) = self.sci_mantissa_and_exponent();
if mantissa != 1.0 {
return None;
}
let (q, r) = exponent.div_mod(i64::exact_from(pow));
if r == 0 { Some(q) } else { None }
}
}
};
}
apply_to_primitive_floats!(impl_log_base_power_of_2_primitive_float);