Given the index of a point in an Ulam Spiral, return the cartesian Coordinates in O(1)

ulam_spiral.rs

#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct Coords {
    pub x: i64,
    pub y: i64,
}

/// Given an Ulam spiral index, returns the Cartesian coordiantes
/// for it.
///
/// # Examples
/// ```
/// assert_eq!(idx_to_coords(22), Ok(Coords { x: -1, y: -2 }));
/// ```
pub fn idx_to_coords(idx: u64) -> Result<Coords, &'static str> {
    if idx > 0 {
        let r = {
            let idx_to_check = idx as i64;
            let layer = (((idx as f64).sqrt() - 1f64) / 2f64).ceil() as i64;
            let points_in_layer = 2 * layer + 1;
            // this is the greatest index in the layer
            let lower_right_idx = points_in_layer.pow(2);
            let side_width = points_in_layer - 1;
            if idx_to_check >= (lower_right_idx - side_width) {
                // we are on the south-side of the layer
                Coords {
                    x: layer - (lower_right_idx - idx_to_check),
                    y: -layer,
                }
            } else {
                let lower_left_idx = lower_right_idx - side_width;
                if idx_to_check >= (lower_left_idx - side_width) {
                    Coords {
                        x: -layer,
                        y: -layer + (lower_left_idx - idx_to_check),
                    }
                } else {
                    let upper_left_idx = lower_left_idx - side_width;
                    if idx_to_check >= upper_left_idx - side_width {
                        Coords {
                            x: -layer + (upper_left_idx - idx_to_check),
                            y: layer,
                        }
                    } else {
                        let upper_right_idx = upper_left_idx - side_width;
                        Coords {
                            x: layer,
                            y: layer - (upper_right_idx - idx_to_check),
                        }
                    }
                }
            }
        };
        Ok(r)
    } else {
        Err("Idx must be greater than 0")
    }
}