/*!

A module for managing axes

*/

#[derive(Debug)]
pub struct Axis {
    lower: f64,
    upper: f64,
    ticks: Vec<f64>,
}

impl Axis {
    /// Constructs a new Axis
    pub fn new(lower: f64, upper: f64) -> Axis {
        assert!(lower < upper);
        let default_max_ticks = 6;
        Axis {
            lower: lower,
            upper: upper,
            ticks: calculate_ticks(lower, upper, default_max_ticks),
        }
    }

    pub fn max(&self) -> f64 {
        self.upper
    }

    pub fn min(&self) -> f64 {
        self.lower
    }

    /// Get the positions of the ticks on the axis
    pub fn ticks(&self) -> &Vec<f64> {
        &self.ticks
    }
}

/// The base units for the step sizes
/// They should be within one order of magnitude, e.g. [1,10)
const BASE_STEPS: [u32; 4] = [1, 2, 4, 5];

#[derive(Debug,Clone)]
struct TickSteps {
    next: f64,
}

impl TickSteps {
    fn start_at(start: f64) -> TickSteps {
        let start_options = TickSteps::scaled_steps(start);
        let overflow = start_options[0] * 10.0;
        let curr = start_options.iter().skip_while(|&step| step < &start).next();

        TickSteps { next: *curr.unwrap_or(&overflow) }
    }

    fn scaled_steps(curr: f64) -> Vec<f64> {
        let power = curr.log10().floor();
        let base_step_scale = 10f64.powf(power);
        BASE_STEPS.iter().map(|&s| (s as f64 * base_step_scale)).collect()
    }
}

impl Iterator for TickSteps {
    type Item = f64;

    fn next(&mut self) -> Option<f64> {
        let curr = self.next; // cache the value we're currently on
        let curr_steps = TickSteps::scaled_steps(self.next);
        let overflow = curr_steps[0] * 10.0;
        self.next = *curr_steps.iter().skip_while(|&s| s <= &curr).next().unwrap_or(&overflow);
        Some(curr)
    }
}

fn generate_ticks(min: f64, max: f64, step_size: f64) -> Vec<f64> {
    let mut ticks: Vec<f64> = vec![];
    if min <= 0.0 {
        if max >= 0.0 {
            // standard spanning axis
            ticks.extend((1..)
                .map(|n| -1.0 * n as f64 * step_size)
                .take_while(|&v| v >= min)
                .collect::<Vec<f64>>()
                .iter()
                .rev());
            ticks.push(0.0);
            ticks.extend((1..).map(|n| n as f64 * step_size).take_while(|&v| v <= max));
        } else {
            // entirely negative axis
            ticks.extend((1..)
                .map(|n| -1.0 * n as f64 * step_size)
                .skip_while(|&v| v > max)
                .take_while(|&v| v >= min)
                .collect::<Vec<f64>>()
                .iter()
                .rev());
        }
    } else {
        // entirely positive axis
        ticks.extend((1..)
            .map(|n| n as f64 * step_size)
            .skip_while(|&v| v < min)
            .take_while(|&v| v <= max));
    }
    ticks
}

/// Given a range and a step size, work out how many ticks will be displayed
fn number_of_ticks(min: f64, max: f64, step_size: f64) -> usize {
    generate_ticks(min, max, step_size).len()
}

/// Given a range of values, and a maximum number of ticks, calulate the step between the ticks
fn calculate_tick_step_for_range(min: f64, max: f64, max_ticks: usize) -> f64 {
    let range = max - min;
    let min_tick_step = range / max_ticks as f64;
    // Get the first entry which is our smallest possible tick step size
    let smallest_valid_step = TickSteps::start_at(min_tick_step)
        .skip_while(|&s| number_of_ticks(min, max, s) > max_ticks)
        .next()
        .expect("ERROR: We've somehow run out of tick step options!");
    // Count how many ticks that relates to
    let actual_num_ticks = number_of_ticks(min, max, smallest_valid_step);

    // Create a new TickStep iterator, starting at the correct lower bound
    let tick_steps = TickSteps::start_at(smallest_valid_step);
    // Get all the possible tick step sizes that give just as many ticks
    let step_options = tick_steps.take_while(|&s| number_of_ticks(min, max, s) == actual_num_ticks);
    // Get the largest tick step size from the list
    step_options.fold(-1. / 0., f64::max)
}

/// Given an axis range, calculate the sensible places to place the ticks
fn calculate_ticks(min: f64, max: f64, max_ticks: usize) -> Vec<f64> {
    let tick_step = calculate_tick_step_for_range(min, max, max_ticks);
    generate_ticks(min, max, tick_step)
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_tick_step_generator() {
        let t = TickSteps::start_at(1.0);
        let ts: Vec<_> = t.take(7).collect();
        assert_eq!(ts, [1.0, 2.0, 4.0, 5.0, 10.0, 20.0, 40.0]);

        let t = TickSteps::start_at(100.0);
        let ts: Vec<_> = t.take(5).collect();
        assert_eq!(ts, [100.0, 200.0, 400.0, 500.0, 1000.0]);

        let t = TickSteps::start_at(3.0);
        let ts: Vec<_> = t.take(5).collect();
        assert_eq!(ts, [4.0, 5.0, 10.0, 20.0, 40.0]);

        let t = TickSteps::start_at(8.0);
        let ts: Vec<_> = t.take(3).collect();
        assert_eq!(ts, [10.0, 20.0, 40.0]);
    }

    #[test]
    fn test_number_of_ticks() {
        assert_eq!(number_of_ticks(-7.93, 15.58, 4.0), 5);
        assert_eq!(number_of_ticks(-7.93, 15.58, 5.0), 5);
        assert_eq!(number_of_ticks(0.0, 15.0, 4.0), 4);
        assert_eq!(number_of_ticks(0.0, 15.0, 5.0), 4);
        assert_eq!(number_of_ticks(5.0, 21.0, 4.0), 4);
        assert_eq!(number_of_ticks(5.0, 21.0, 5.0), 4);
        assert_eq!(number_of_ticks(-8.0, 15.58, 4.0), 6);
        assert_eq!(number_of_ticks(-8.0, 15.58, 5.0), 5);
    }

    #[test]
    fn test_calculate_tick_step_for_range() {
        assert_eq!(calculate_tick_step_for_range(0.0, 3.0, 6), 1.0);
        assert_eq!(calculate_tick_step_for_range(0.0, 6.0, 6), 2.0);
        assert_eq!(calculate_tick_step_for_range(0.0, 11.0, 6), 2.0);
        assert_eq!(calculate_tick_step_for_range(0.0, 14.0, 6), 4.0);
        assert_eq!(calculate_tick_step_for_range(0.0, 15.0, 6), 5.0);
        assert_eq!(calculate_tick_step_for_range(-1.0, 5.0, 6), 2.0);
        assert_eq!(calculate_tick_step_for_range(-7.93, 15.58, 6), 5.0);
        assert_eq!(calculate_tick_step_for_range(0.0, 0.06, 6), 0.02);
    }

    #[test]
    fn test_calculate_ticks() {

        macro_rules! assert_approx_eq {
            ($a:expr, $b:expr) => ({
                let (a, b) = (&$a, &$b);
                assert!((*a - *b).abs() < 1.0e-6,
                        "{} is not approximately equal to {}", *a, *b);
            })
        }

        for (prod, want) in calculate_ticks(0.0, 1.0, 6)
            .iter()
            .zip([0.0, 0.2, 0.4, 0.6, 0.8, 1.0].iter()) {
            assert_approx_eq!(prod, want);
        }
        for (prod, want) in calculate_ticks(0.0, 2.0, 6)
            .iter()
            .zip([0.0, 0.4, 0.8, 1.2, 1.6, 2.0].iter()) {
            assert_approx_eq!(prod, want);
        }
        assert_eq!(calculate_ticks(0.0, 3.0, 6), [0.0, 1.0, 2.0, 3.0]);
        assert_eq!(calculate_ticks(0.0, 4.0, 6), [0.0, 1.0, 2.0, 3.0, 4.0]);
        assert_eq!(calculate_ticks(0.0, 5.0, 6), [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]);
        assert_eq!(calculate_ticks(0.0, 6.0, 6), [0.0, 2.0, 4.0, 6.0]);
        assert_eq!(calculate_ticks(0.0, 7.0, 6), [0.0, 2.0, 4.0, 6.0]);
        assert_eq!(calculate_ticks(0.0, 8.0, 6), [0.0, 2.0, 4.0, 6.0, 8.0]);
        assert_eq!(calculate_ticks(0.0, 9.0, 6), [0.0, 2.0, 4.0, 6.0, 8.0]);
        assert_eq!(calculate_ticks(0.0, 10.0, 6),
                   [0.0, 2.0, 4.0, 6.0, 8.0, 10.0]);
        assert_eq!(calculate_ticks(0.0, 11.0, 6),
                   [0.0, 2.0, 4.0, 6.0, 8.0, 10.0]);
        assert_eq!(calculate_ticks(0.0, 12.0, 6), [0.0, 4.0, 8.0, 12.0]);
        assert_eq!(calculate_ticks(0.0, 13.0, 6), [0.0, 4.0, 8.0, 12.0]);
        assert_eq!(calculate_ticks(0.0, 14.0, 6), [0.0, 4.0, 8.0, 12.0]);
        assert_eq!(calculate_ticks(0.0, 15.0, 6), [0.0, 5.0, 10.0, 15.0]);
        assert_eq!(calculate_ticks(0.0, 16.0, 6), [0.0, 4.0, 8.0, 12.0, 16.0]);
        assert_eq!(calculate_ticks(0.0, 17.0, 6), [0.0, 4.0, 8.0, 12.0, 16.0]);
        assert_eq!(calculate_ticks(0.0, 18.0, 6), [0.0, 4.0, 8.0, 12.0, 16.0]);
        assert_eq!(calculate_ticks(0.0, 19.0, 6), [0.0, 4.0, 8.0, 12.0, 16.0]);
        assert_eq!(calculate_ticks(0.0, 20.0, 6),
                   [0.0, 4.0, 8.0, 12.0, 16.0, 20.0]);
        assert_eq!(calculate_ticks(0.0, 21.0, 6),
                   [0.0, 4.0, 8.0, 12.0, 16.0, 20.0]);
        assert_eq!(calculate_ticks(0.0, 22.0, 6),
                   [0.0, 4.0, 8.0, 12.0, 16.0, 20.0]);
        assert_eq!(calculate_ticks(0.0, 23.0, 6),
                   [0.0, 4.0, 8.0, 12.0, 16.0, 20.0]);
        assert_eq!(calculate_ticks(0.0, 24.0, 6), [0.0, 5.0, 10.0, 15.0, 20.0]);
        assert_eq!(calculate_ticks(0.0, 25.0, 6),
                   [0.0, 5.0, 10.0, 15.0, 20.0, 25.0]);
        assert_eq!(calculate_ticks(0.0, 26.0, 6),
                   [0.0, 5.0, 10.0, 15.0, 20.0, 25.0]);
        assert_eq!(calculate_ticks(0.0, 27.0, 6),
                   [0.0, 5.0, 10.0, 15.0, 20.0, 25.0]);
        assert_eq!(calculate_ticks(0.0, 28.0, 6),
                   [0.0, 5.0, 10.0, 15.0, 20.0, 25.0]);
        assert_eq!(calculate_ticks(0.0, 29.0, 6),
                   [0.0, 5.0, 10.0, 15.0, 20.0, 25.0]);
        assert_eq!(calculate_ticks(0.0, 30.0, 6), [0.0, 10.0, 20.0, 30.0]);
        assert_eq!(calculate_ticks(0.0, 31.0, 6), [0.0, 10.0, 20.0, 30.0]);
        //...
        assert_eq!(calculate_ticks(0.0, 40.0, 6), [0.0, 10.0, 20.0, 30.0, 40.0]);
        assert_eq!(calculate_ticks(0.0, 50.0, 6),
                   [0.0, 10.0, 20.0, 30.0, 40.0, 50.0]);
        assert_eq!(calculate_ticks(0.0, 60.0, 6), [0.0, 20.0, 40.0, 60.0]);
        assert_eq!(calculate_ticks(0.0, 70.0, 6), [0.0, 20.0, 40.0, 60.0]);
        assert_eq!(calculate_ticks(0.0, 80.0, 6), [0.0, 20.0, 40.0, 60.0, 80.0]);
        assert_eq!(calculate_ticks(0.0, 90.0, 6), [0.0, 20.0, 40.0, 60.0, 80.0]);
        assert_eq!(calculate_ticks(0.0, 100.0, 6),
                   [0.0, 20.0, 40.0, 60.0, 80.0, 100.0]);
        assert_eq!(calculate_ticks(0.0, 110.0, 6),
                   [0.0, 20.0, 40.0, 60.0, 80.0, 100.0]);
        assert_eq!(calculate_ticks(0.0, 120.0, 6), [0.0, 40.0, 80.0, 120.0]);
        assert_eq!(calculate_ticks(0.0, 130.0, 6), [0.0, 40.0, 80.0, 120.0]);
        assert_eq!(calculate_ticks(0.0, 140.0, 6), [0.0, 40.0, 80.0, 120.0]);
        assert_eq!(calculate_ticks(0.0, 150.0, 6), [0.0, 50.0, 100.0, 150.0]);
        //...
        assert_eq!(calculate_ticks(0.0, 3475.0, 6),
                   [0.0, 1000.0, 2000.0, 3000.0]);

        assert_eq!(calculate_ticks(-10.0, -3.0, 6), [-10.0, -8.0, -6.0, -4.0]);
    }
}