1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93

// Copyright 2018 Johannes Köster.
// Licensed under the MIT license (http://opensource.org/licenses/MIT)
// This file may not be copied, modified, or distributed
// except according to those terms.

#[inline]
pub fn interpolate(a: f64, b: f64, fraction: f64) -> f64 {
    a * (1.0 - fraction) + b * fraction
}

/// Fast lookup table for arbitrary floating point functions.
/// This can be used to e.g., provide fast lookups of distribution values.
/// Input values are sampled with a given precision and results are stored in a vector.
/// During lookup, infimum and supremum of a given value are calculated and the result is
/// interpolated.
pub struct InterpolationTable<F: Fn(f64) -> f64> {
    inner: Vec<f64>,
    func: F,
    offset: usize,
    min_x: f64,
    max_x: f64,
    shift: f64,
}

impl<F: Fn(f64) -> f64> InterpolationTable<F> {
    /// Create a new `InterpolationTable`.
    ///
    /// # Arguments
    ///
    /// * `min_x` - minimum sample value
    /// * `max_x` - maximum sample value
    /// * `frac_digits` - number of fraction digits to store in sample
    /// * `func` - Function to emulate.
    ///
    /// If given value is outside of min_x and max_x, the lookup falls back to applying the
    /// function itself.
    /// The table size grows with the number of fraction digits.
    pub fn new(min_x: f64, max_x: f64, frac_digits: i32, func: F) -> Self {
        let shift = 10.0_f64.powi(frac_digits);
        let offset = (min_x * shift) as usize;
        let mut table = InterpolationTable {
            inner: Vec::new(),
            func,
            min_x,
            max_x,
            shift,
            offset,
        };

        let mut i = table.index(min_x);
        while i < table.index(max_x) {
            let x = i as f64 / shift;
            table.inner.push((table.func)(x));
            i += 1;
        }

        table
    }

    /// Return lower bound index for given f64.
    #[inline]
    fn index(&self, x: f64) -> usize {
        (x * self.shift) as usize - self.offset
    }

    /// Lookup given value in table, and interpolate the result between the sampled values if
    /// necessary. This provides an approximation that is better the more fraction digits are
    /// used to generate this table.
    pub fn get(&self, x: f64) -> f64 {
        if x < self.min_x || x >= self.max_x {
            (self.func)(x)
        } else {
            let i = self.index(x);
            // interpolate
            let fraction = (x * self.shift - i as f64) / self.shift;
            interpolate(self.inner[i], self.inner[i + 1], fraction)
        }
    }
}

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

    #[test]
    fn test_interpolation_table() {
        let table = InterpolationTable::new(0.0, 10.0, 5, |x| x.ln_1p());

        for &x in &[0.02, 0.04, 0.45678686, 0.23875, 1.45345e-6] {
            assert_relative_eq!(table.get(x), x.ln_1p(), epsilon = 0.00001);
        }
    }
}