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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::{Reciprocal, ReciprocalAssign};
macro_rules! impl_reciprocal {
($t:ident) => {
impl Reciprocal for $t {
type Output = $t;
/// Takes the reciprocal of a floating-point number.
///
/// $$
/// f(x) = 1/x+\varepsilon.
/// $$
/// Let $p$ be the precision of the input float (typically 24 for `f32`s and 53 for
/// `f64`s, unless the float is subnormal).
/// - If $1/x$ is infinite, zero, or `NaN`, $\varepsilon$ may be ignored or assumed to
/// be 0.
/// - If $1/x$ is finite and nonzero, and $m$ is not `Nearest`, then $|\varepsilon| <
/// 2^{\lfloor\log_2 |1/x|\rfloor-p+1}$.
/// - If $1/x$ is finite and nonzero, and $m$ is `Nearest`, then $|\varepsilon| <
/// 2^{\lfloor\log_2 |1/x|\rfloor-p}$.
///
/// If the output has a precision, it is `prec`.
///
/// Special cases:
/// - $f(\text{NaN})=\text{NaN}$
/// - $f(\infty)=0.0$
/// - $f(-\infty)=-0.0$
/// - $f(0.0)=\infty$
/// - $f(-0.0)=-\infty$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::reciprocal#reciprocal).
#[inline]
fn reciprocal(self) -> $t {
1.0 / self
}
}
impl ReciprocalAssign for $t {
/// Takes the reciprocal of a floating-point number, in place.
///
/// $x \gets 1/x+\varepsilon$. Let $p$ be the precision of the input float (typically 24
/// for `f32`s and 53 for `f64`s, unless the float is subnormal).
/// - If $1/x$ is infinite, zero, or `NaN`, $\varepsilon$ may be ignored or assumed to
/// be 0.
/// - If $1/x$ is finite and nonzero, and $m$ is not `Nearest`, then $|\varepsilon| <
/// 2^{\lfloor\log_2 |1/x|\rfloor-p+1}$.
/// - If $1/x$ is finite and nonzero, and $m$ is `Nearest`, then $|\varepsilon| <
/// 2^{\lfloor\log_2 |1/x|\rfloor-p}$.
///
/// See the `reciprocal` documentation for information on special cases.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// See [here](super::reciprocal#reciprocal_assign).
#[inline]
fn reciprocal_assign(&mut self) {
*self = 1.0 / *self;
}
}
};
}
apply_to_primitive_floats!(impl_reciprocal);