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use crate::InnerFloat::Finite;
use crate::{significand_bits, Float};
use malachite_base::num::arithmetic::traits::{DivisibleByPowerOf2, NegAssign, PowerOf2};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::conversion::traits::{ExactFrom, WrappingFrom};
use malachite_base::num::logic::traits::SignificantBits;
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 NaN, infinite, or zero, then `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_nz::natural::Natural;
/// 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-16"));
///
/// 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<Float> {
match self {
Float(Finite {
exponent,
precision,
..
}) => Some(Float::power_of_2(exponent - i64::exact_from(*precision))),
_ => None,
}
}
/// Increments a [`Float`] by its ulp.
///
/// See [`Float::ulp`] for details. If the [`Float`] is equal to the negative of its ulp, it
/// becomes 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::{Infinity, NaN, NegativeOne, One, Zero};
/// use malachite_nz::natural::Natural;
/// 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(), "3.1415926535897931");
/// x.increment();
/// assert_eq!(x.to_string(), "3.1415926535897936");
///
/// 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 Float(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
- usize::exact_from((*precision - 1) >> Limb::LOG_WIDTH),
ulp,
);
if significand.limb_count() > limb_count {
*significand >>= 1;
*exponent = exponent.checked_add(1).unwrap();
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 equal to its ulp, it becomes 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::{Infinity, NaN, NegativeOne, One, Zero};
/// use malachite_nz::natural::Natural;
/// 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(), "3.1415926535897931");
/// x.decrement();
/// assert_eq!(x.to_string(), "3.1415926535897927");
///
/// 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 Float(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
- usize::exact_from((*precision - 1) >> Limb::LOG_WIDTH),
ulp,
);
if *significand == 0u32 {
*self = Float::ZERO;
} else if significand.significant_bits() < bits {
*significand <<= 1;
*exponent = exponent.checked_sub(1).unwrap();
*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");
}
}
}