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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::InnerFloat::Finite;
use crate::{Float, significand_bits};
use malachite_base::num::arithmetic::traits::{DivisibleByPowerOf2, NegAssign, PowerOf2};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::{Infinity, Zero};
use malachite_base::num::conversion::traits::WrappingFrom;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_nz::natural::bit_to_limb_count_floor;
use malachite_nz::platform::Limb;
impl Float {
/// Gets a [`Float`]'s ulp (unit in last place, or unit of least precision).
///
/// If the [`Float`] is positive, its ulp is the distance to the next-largest [`Float`] with the
/// same precision; if it is negative, the next-smallest. (This definition works even if the
/// [`Float`] is the largest in its binade. If the [`Float`] is the largest in its binade and
/// has the maximum exponent, we can define its ulp to be the distance to the next-smallest
/// [`Float`] with the same precision if positive, and to the next-largest [`Float`] with the
/// same precision if negative.)
///
/// If the [`Float`] is NaN, infinite, or zero, then `None` is returned.
///
/// This function does not overflow or underflow, technically. But it is possible that a
/// [`Float`]'s ulp is too small to represent, for example if the [`Float`] has the minimum
/// exponent and its precision is greater than 1, or if the precision is extremely large in
/// general. In such cases, `None` is returned.
///
/// $$
/// f(\text{NaN}) = f(\pm\infty) = f(\pm 0.0) = \text{None},
/// $$
///
/// and, if $x$ is finite and nonzero,
///
/// $$
/// f(x) = \operatorname{Some}(2^{\lfloor \log_2 x \rfloor-p+1}),
/// $$
/// where $p$ is the precision of $x$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::PowerOf2;
/// use malachite_base::num::basic::traits::{Infinity, NaN, NegativeOne, One, Zero};
/// use malachite_float::Float;
///
/// assert_eq!(Float::NAN.ulp(), None);
/// assert_eq!(Float::INFINITY.ulp(), None);
/// assert_eq!(Float::ZERO.ulp(), None);
///
/// let s = Float::ONE.ulp().map(|x| x.to_string());
/// assert_eq!(s.as_ref().map(|s| s.as_str()), Some("1.0"));
///
/// let s = Float::one_prec(100).ulp().map(|x| x.to_string());
/// assert_eq!(s.as_ref().map(|s| s.as_str()), Some("2.0e-30"));
///
/// let s = Float::from(std::f64::consts::PI)
/// .ulp()
/// .map(|x| x.to_string());
/// assert_eq!(s.as_ref().map(|s| s.as_str()), Some("4.0e-15"));
///
/// let s = Float::power_of_2(100u64).ulp().map(|x| x.to_string());
/// assert_eq!(s.as_ref().map(|s| s.as_str()), Some("1.0e30"));
///
/// let s = Float::power_of_2(-100i64).ulp().map(|x| x.to_string());
/// assert_eq!(s.as_ref().map(|s| s.as_str()), Some("8.0e-31"));
///
/// let s = Float::NEGATIVE_ONE.ulp().map(|x| x.to_string());
/// assert_eq!(s.as_ref().map(|s| s.as_str()), Some("1.0"));
/// ```
pub fn ulp(&self) -> Option<Self> {
match self {
Self(Finite {
exponent,
precision,
..
}) => {
let ulp_exponent =
i64::from(*exponent).checked_sub(i64::try_from(*precision).ok()?)?;
if i32::try_from(ulp_exponent).ok()? >= Self::MIN_EXPONENT - 1 {
Some(Self::power_of_2(ulp_exponent))
} else {
None
}
}
_ => None,
}
}
/// Increments a [`Float`] by its ulp. See [`Float::ulp`] for details.
///
/// If the [`Float`] is positive and is the largest [`Float`] in its binade with its precision,
/// then
/// - If its exponent is not the maximum exponent, it will become the smallest [`Float`] in the
/// next-higher binade, and its precision will increase by 1 (so that its ulp remains the
/// same);
/// - If its exponent is the maximum exponent, it will become $\infty$.
///
/// If the [`Float`] is negative and is closer to zero than any other [`Float`] in its binade
/// with its precision, then
/// - If its precision is 1, it will become negative zero.
/// - If its precision is greater than 1 and its exponent is not the minimum exponent, it will
/// become the farthest-from-zero [`Float`] in the next-lower binade, and its precision will
/// decrease by 1 (so that its ulp remains the same).
/// - If its precision is greater than 1 and its exponent is the minimum exponent, it will
/// become negative zero.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` is NaN, infinite, or zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::PowerOf2;
/// use malachite_base::num::basic::traits::{NegativeOne, One};
/// use malachite_float::Float;
///
/// let mut x = Float::ONE;
/// assert_eq!(x.to_string(), "1.0");
/// x.increment();
/// assert_eq!(x.to_string(), "2.0");
///
/// let mut x = Float::one_prec(100);
/// assert_eq!(x.to_string(), "1.0");
/// x.increment();
/// assert_eq!(x.to_string(), "1.000000000000000000000000000002");
///
/// let mut x = Float::from(std::f64::consts::PI);
/// assert_eq!(x.to_string(), "3.141592653589793");
/// x.increment();
/// assert_eq!(x.to_string(), "3.141592653589797");
///
/// let mut x = Float::power_of_2(100u64);
/// assert_eq!(x.to_string(), "1.0e30");
/// x.increment();
/// assert_eq!(x.to_string(), "3.0e30");
///
/// let mut x = Float::power_of_2(-100i64);
/// assert_eq!(x.to_string(), "8.0e-31");
/// x.increment();
/// assert_eq!(x.to_string(), "1.6e-30");
///
/// let mut x = Float::NEGATIVE_ONE;
/// assert_eq!(x.to_string(), "-1.0");
/// x.increment();
/// assert_eq!(x.to_string(), "-0.0");
/// ```
pub fn increment(&mut self) {
if self.is_sign_negative() {
self.neg_assign();
self.decrement();
self.neg_assign();
} else if let Self(Finite {
exponent,
precision,
significand,
..
}) = self
{
let ulp = Limb::power_of_2(significand_bits(significand) - *precision);
let limb_count = significand.limb_count();
significand.add_assign_at_limb(
usize::wrapping_from(limb_count) - 1 - bit_to_limb_count_floor(*precision - 1),
ulp,
);
if significand.limb_count() > limb_count {
if *exponent == Self::MAX_EXPONENT {
*self = Self::INFINITY;
return;
}
*significand >>= 1;
*exponent += 1;
if precision.divisible_by_power_of_2(Limb::LOG_WIDTH) {
*significand <<= Limb::WIDTH;
}
*precision = precision.checked_add(1).unwrap();
}
} else {
panic!("Cannot increment float is non-finite or zero");
}
}
/// Decrements a [`Float`] by its ulp. See [`Float::ulp`] for details.
///
/// If the [`Float`] is negative and is the largest [`Float`] in its binade with its precision,
/// then
/// - If its exponent is not the maximum exponent, it will become the closest-to-zero [`Float`]
/// in the next-higher binade, and its precision will increase by 1 (so that its ulp remains
/// the same);
/// - If its exponent is the maximum exponent, it will become $-\infty$.
///
/// If the [`Float`] is positive and is smaller than any other [`Float`] in its binade with its
/// precision, then
/// - If its precision is 1, it will become positive zero.
/// - If its precision is greater than 1 and its exponent is not the minimum exponent, it will
/// become the largest [`Float`] in the next-lower binade, and its precision will decrease by
/// 1 (so that its ulp remains the same).
/// - If its precision is greater than 1 and its exponent is the minimum exponent, it will
/// become positive zero.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` is NaN, infinite, or zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::PowerOf2;
/// use malachite_base::num::basic::traits::{NegativeOne, One};
/// use malachite_float::Float;
///
/// let mut x = Float::ONE;
/// assert_eq!(x.to_string(), "1.0");
/// x.decrement();
/// assert_eq!(x.to_string(), "0.0");
///
/// let mut x = Float::one_prec(100);
/// assert_eq!(x.to_string(), "1.0");
/// x.decrement();
/// assert_eq!(x.to_string(), "0.999999999999999999999999999998");
///
/// let mut x = Float::from(std::f64::consts::PI);
/// assert_eq!(x.to_string(), "3.141592653589793");
/// x.decrement();
/// assert_eq!(x.to_string(), "3.14159265358979");
///
/// let mut x = Float::power_of_2(100u64);
/// assert_eq!(x.to_string(), "1.0e30");
/// x.decrement();
/// assert_eq!(x.to_string(), "0.0");
///
/// let mut x = Float::power_of_2(-100i64);
/// assert_eq!(x.to_string(), "8.0e-31");
/// x.decrement();
/// assert_eq!(x.to_string(), "0.0");
///
/// let mut x = Float::NEGATIVE_ONE;
/// assert_eq!(x.to_string(), "-1.0");
/// x.decrement();
/// assert_eq!(x.to_string(), "-2.0");
/// ```
pub fn decrement(&mut self) {
if self.is_sign_negative() {
self.neg_assign();
self.increment();
self.neg_assign();
} else if let Self(Finite {
exponent,
precision,
significand,
..
}) = self
{
let bits = significand_bits(significand);
let ulp = Limb::power_of_2(bits - *precision);
significand.sub_assign_at_limb(
usize::wrapping_from(significand.limb_count())
- 1
- bit_to_limb_count_floor(*precision - 1),
ulp,
);
if *significand == 0u32 {
*self = Self::ZERO;
} else if significand.significant_bits() < bits {
if *exponent == Self::MIN_EXPONENT {
*self = Self::ZERO;
return;
}
*significand <<= 1;
*exponent -= 1;
*precision = precision.checked_sub(1).unwrap();
if bits - *precision == Limb::WIDTH {
*significand >>= Limb::WIDTH;
}
}
} else {
panic!("Cannot decrement float that is non-finite or zero");
}
}
}