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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::Rational;
use crate::arithmetic::traits::SimplestRationalInInterval;
use crate::conversion::from_primitive_float::RationalFromPrimitiveFloatError;
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::conversion::traits::ExactFrom;
impl Rational {
/// Converts a primitive float to the simplest [`Rational`] that rounds to that value.
///
/// To be more specific: Suppose the floating-point input is $x$. If $x$ is an integer, its
/// [`Rational`] equivalent is returned. Otherwise, this function finds $a$ and $b$, which are
/// the floating point predecessor and successor of $x$, and finds the simplest [`Rational`] in
/// the open interval $(\frac{x + a}{2}, \frac{x + b}{2})$. "Simplicity" refers to low
/// complexity. See [`Rational::cmp_complexity`] for a definition of complexity.
///
/// For example, `0.1f32` is converted to $1/10$ rather than to the exact value of the float,
/// which is $13421773/134217728$. If you want the exact value, use `Rational::from` instead.
///
/// If the floating point value is `NaN` or infinite, an error is returned.
///
/// # Worst-case complexity
/// $T(n) = O(n^2 \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `x.sci_exponent()`.
///
/// # Examples
/// ```
/// use malachite_base::strings::ToDebugString;
/// use malachite_q::conversion::from_primitive_float::RationalFromPrimitiveFloatError;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// Rational::try_from_float_simplest(0.0).to_debug_string(),
/// "Ok(0)"
/// );
/// assert_eq!(
/// Rational::try_from_float_simplest(1.5).to_debug_string(),
/// "Ok(3/2)"
/// );
/// assert_eq!(
/// Rational::try_from_float_simplest(-1.5).to_debug_string(),
/// "Ok(-3/2)"
/// );
/// assert_eq!(
/// Rational::try_from_float_simplest(0.1f32).to_debug_string(),
/// "Ok(1/10)"
/// );
/// assert_eq!(
/// Rational::try_from_float_simplest(0.33333334f32).to_debug_string(),
/// "Ok(1/3)"
/// );
/// assert_eq!(
/// Rational::try_from_float_simplest(f32::NAN),
/// Err(RationalFromPrimitiveFloatError)
/// );
/// ```
pub fn try_from_float_simplest<T: PrimitiveFloat>(
x: T,
) -> Result<Self, RationalFromPrimitiveFloatError>
where
Self: TryFrom<T, Error = RationalFromPrimitiveFloatError>,
{
let q = Self::try_from(x)?;
Ok(if *q.denominator_ref() <= 2u32 {
q
} else {
let succ_q = Self::exact_from(x.next_higher());
let pred_q = Self::exact_from(x.next_lower());
let x = (pred_q + &q) >> 1;
let y = (succ_q + q) >> 1;
Self::simplest_rational_in_open_interval(&x, &y)
})
}
}