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// Copyright © 2024 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright (C) 2011 Fredrik Johansson
//
// 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::Rational;
use core::cmp::Ordering;
#[cfg(not(any(feature = "test_build", feature = "random")))]
use malachite_base::num::arithmetic::traits::Ln;
use malachite_base::num::arithmetic::traits::{
CeilingLogBase, CeilingLogBasePowerOf2, CheckedLogBase, CheckedLogBase2,
CheckedLogBasePowerOf2, FloorLogBase, FloorLogBasePowerOf2, Pow,
};
use malachite_base::num::comparison::traits::OrdAbs;
use malachite_base::num::conversion::traits::{RoundingFrom, SciMantissaAndExponent};
use malachite_base::rounding_modes::RoundingMode;
fn approx_log_helper(x: &Rational) -> f64 {
let (mantissa, exponent): (f64, i64) = x.sci_mantissa_and_exponent();
mantissa.ln() + (exponent as f64) * core::f64::consts::LN_2
}
impl Rational {
/// Calculates the approximate natural logarithm of a positive [`Rational`].
///
/// $f(x) = (1+\epsilon)(\log x)$, where $|\epsilon| < 2^{-52}.$
///
/// # 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()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::{Pow, PowerOf2};
/// use malachite_base::num::float::NiceFloat;
/// use malachite_q::Rational;
///
/// assert_eq!(NiceFloat(Rational::from(10i32).approx_log()), NiceFloat(2.3025850929940455));
/// assert_eq!(
/// NiceFloat(Rational::from(10i32).pow(100u64).approx_log()),
/// NiceFloat(230.25850929940455)
/// );
/// assert_eq!(
/// NiceFloat(Rational::power_of_2(1000000u64).approx_log()),
/// NiceFloat(693147.1805599453)
/// );
/// assert_eq!(
/// NiceFloat(Rational::power_of_2(-1000000i64).approx_log()),
/// NiceFloat(-693147.1805599453)
/// );
/// ```
///
/// This is equivalent to `fmpz_dlog` from `fmpz/dlog.c`, FLINT 2.7.1.
#[inline]
pub fn approx_log(&self) -> f64 {
assert!(*self > 0u32);
approx_log_helper(self)
}
}
// # Worst-case complexity
// $T(n, m) = O(nm \log (nm) \log\log (nm))$
//
// $M(n, m) = O(nm \log (nm))$
//
// where $T$ is time, $M$ is additional memory, $n$ is `base.significant_bits()`, and $m$ is
// $|\log_b x|$, where $b$ is `base` and $x$ is `x`.
pub(crate) fn log_base_helper(x: &Rational, base: &Rational) -> (i64, bool) {
assert!(*base > 0u32);
assert_ne!(*base, 1u32);
if *x == 1u32 {
return (0, true);
}
let mut log = i64::rounding_from(
approx_log_helper(x) / approx_log_helper(base),
RoundingMode::Floor,
)
.0;
let mut power = base.pow(log);
if *base > 1u32 {
match power.cmp_abs(x) {
Ordering::Equal => (log, true),
Ordering::Less => loop {
power *= base;
match power.cmp_abs(x) {
Ordering::Equal => {
return (log + 1, true);
}
Ordering::Less => {
log += 1;
}
Ordering::Greater => {
return (log, false);
}
}
},
Ordering::Greater => loop {
power /= base;
match power.cmp_abs(x) {
Ordering::Equal => {
return (log - 1, true);
}
Ordering::Less => {
return (log - 1, false);
}
Ordering::Greater => {
log -= 1;
}
}
},
}
} else {
match power.cmp_abs(x) {
Ordering::Equal => (log, true),
Ordering::Less => loop {
power /= base;
match power.cmp_abs(x) {
Ordering::Equal => {
return (log - 1, true);
}
Ordering::Less => {
log -= 1;
}
Ordering::Greater => {
return (log - 1, false);
}
}
},
Ordering::Greater => loop {
power *= base;
match power.cmp_abs(x) {
Ordering::Equal => {
return (log + 1, true);
}
Ordering::Less => {
return (log, false);
}
Ordering::Greater => {
log += 1;
}
}
},
}
}
}
impl<'a, 'b> FloorLogBase<&'b Rational> for &'a Rational {
type Output = i64;
/// Returns the floor of the base-$b$ logarithm of a positive [`Rational`].
///
/// Note that this function may be slow if the base is very close to 1.
///
/// $f(x, b) = \lfloor\log_b x\rfloor$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(nm \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `base.significant_bits()`, and $m$ is
/// $|\log_b x|$, where $b$ is `base` and $x$ is `x`.
///
/// # Panics
/// Panics if `self` less than or equal to zero or `base` is 1.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::FloorLogBase;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(80u32).floor_log_base(&Rational::from(3u32)), 3);
/// assert_eq!(Rational::from(81u32).floor_log_base(&Rational::from(3u32)), 4);
/// assert_eq!(Rational::from(82u32).floor_log_base(&Rational::from(3u32)), 4);
/// assert_eq!(Rational::from(4294967296u64).floor_log_base(&Rational::from(10u32)), 9);
/// assert_eq!(
/// Rational::from_signeds(936851431250i64, 1397).floor_log_base(&Rational::from(10u32)),
/// 8
/// );
/// assert_eq!(
/// Rational::from_signeds(5153632, 16807).floor_log_base(&Rational::from_signeds(22, 7)),
/// 5
/// );
/// ```
fn floor_log_base(self, base: &Rational) -> i64 {
assert!(*self > 0u32);
if let Some(log_base) = base.checked_log_base_2() {
return self.floor_log_base_power_of_2(log_base);
}
log_base_helper(self, base).0
}
}
impl<'a, 'b> CeilingLogBase<&'b Rational> for &'a Rational {
type Output = i64;
/// Returns the ceiling of the base-$b$ logarithm of a positive [`Rational`].
///
/// Note that this function may be slow if the base is very close to 1.
///
/// $f(x, b) = \lceil\log_b x\rceil$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(nm \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `base.significant_bits()`, and $m$ is
/// $|\log_b x|$, where $b$ is `base` and $x$ is `x`.
///
/// # Panics
/// Panics if `self` less than or equal to zero or `base` is 1.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CeilingLogBase;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(80u32).ceiling_log_base(&Rational::from(3u32)), 4);
/// assert_eq!(Rational::from(81u32).ceiling_log_base(&Rational::from(3u32)), 4);
/// assert_eq!(Rational::from(82u32).ceiling_log_base(&Rational::from(3u32)), 5);
/// assert_eq!(Rational::from(4294967296u64).ceiling_log_base(&Rational::from(10u32)), 10);
/// assert_eq!(
/// Rational::from_signeds(936851431250i64, 1397).ceiling_log_base(&Rational::from(10u32)),
/// 9
/// );
/// assert_eq!(
/// Rational::from_signeds(5153632, 16807)
/// .ceiling_log_base(&Rational::from_signeds(22, 7)),
/// 5
/// );
/// ```
fn ceiling_log_base(self, base: &Rational) -> i64 {
assert!(*self > 0u32);
if let Some(log_base) = base.checked_log_base_2() {
return self.ceiling_log_base_power_of_2(log_base);
}
let (log, exact) = log_base_helper(self, base);
if exact {
log
} else {
log + 1
}
}
}
impl<'a, 'b> CheckedLogBase<&'b Rational> for &'a Rational {
type Output = i64;
/// Returns the base-$b$ logarithm of a positive [`Rational`]. If the [`Rational`] is not a
/// power of $b$, then `None` is returned.
///
/// Note that this function may be slow if the base is very close to 1.
///
/// $$
/// f(x, b) = \\begin{cases}
/// \operatorname{Some}(\log_b x) & \text{if} \\quad \log_b x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(nm \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is `base.significant_bits()`, and $m$ is
/// $|\log_b x|$, where $b$ is `base` and $x$ is `x`.
///
/// # Panics
/// Panics if `self` less than or equal to zero or `base` is 1.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CheckedLogBase;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(80u32).checked_log_base(&Rational::from(3u32)), None);
/// assert_eq!(Rational::from(81u32).checked_log_base(&Rational::from(3u32)), Some(4));
/// assert_eq!(Rational::from(82u32).checked_log_base(&Rational::from(3u32)), None);
/// assert_eq!(Rational::from(4294967296u64).checked_log_base(&Rational::from(10u32)), None);
/// assert_eq!(
/// Rational::from_signeds(936851431250i64, 1397).checked_log_base(&Rational::from(10u32)),
/// None
/// );
/// assert_eq!(
/// Rational::from_signeds(5153632, 16807)
/// .checked_log_base(&Rational::from_signeds(22, 7)),
/// Some(5)
/// );
/// ```
fn checked_log_base(self, base: &Rational) -> Option<i64> {
assert!(*self > 0u32);
if let Some(log_base) = base.checked_log_base_2() {
return self.checked_log_base_power_of_2(log_base);
}
let (log, exact) = log_base_helper(self, base);
if exact {
Some(log)
} else {
None
}
}
}