You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: animations.rs
    path of file: ./repos/slint/internal/core
    
    the code of the file until where you have to start completion: // Copyright Â© SixtyFPS GmbH <info@slint.dev>
// SPDX-License-Identifier: GPL-3.0-only OR LicenseRef-Slint-Royalty-free-1.1 OR LicenseRef-Slint-commercial

#![warn(missing_docs)]
//! The animation system

#[cfg(not(feature = "std"))]
use alloc::boxed::Box;
use core::cell::Cell;
#[cfg(not(feature = "std"))]
use num_traits::Float;

mod cubic_bezier {
    //! This is a copy from lyon_algorithms::geom::cubic_bezier implementation
    //! (from lyon_algorithms 0.17)
    type S = f32;
    use euclid::default::Point2D as Point;
    #[cfg
    
        pub fn solve_t_for_x(&self, x: S, t_range: core::ops::Range<S>, tolerance: S) -> S {
            debug_assert!(t_range.start <= t_range.end);
            let from = self.x(t_range.start);
            let to = self.x(t_range.end);
            if x <= from {
                return t_range.start;
            }
            if x >= to {
                return t_range.end;
            }

            // Newton's method.
            let mut t = x - from / (to - from);
            for _ in 0..8 {
                let x2 = self.x(t);

                if S::abs(x2 - x) <= tolerance {
                    return t;
                }

                let dx = self.dx(t);

                if dx <= S::EPSILON {
                    break;
                }

                t -= (x2 - x) / dx;
            }

            // Fall back to binary search.
            let mut min = t_range.start;
            let mut max = t_range.end;
            let mut t = S::HALF;

            while min < max {
                let x2 = self.x(t);

                if S::abs(x2 - x) < tolerance {
                    return t;
                }

                if x > x2 {
                    min = t;
                } else {
                    max = t;
                }

                t = (max - min) * S::HALF + min;
            }

            t
        }