use once_cell::sync::Lazy;
use ordered_float::OrderedFloat;
use std::cmp::Ordering;
pub const MINIMUM_PRECISION: i32 = 10;
pub const MAXIMUM_PRECISION: i32 = 18;
const NUMBER_OF_NEIGHBORS_IN_KNN: usize = 6;
static MEAN_DATA: Lazy<[Vec<OrderedFloat<f64>>; 9]> = Lazy::new(|| {
[
vec![
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]
.into_iter()
.map(OrderedFloat)
.collect::<Vec<_>>(),
vec![
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]
.into_iter()
.map(OrderedFloat)
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.map(OrderedFloat)
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});
pub fn alpha(precision: i32) -> f64 {
0.7213 / (1.0 + 1.079 / ((1_i64 << precision) as f64))
}
pub fn estimate_bias(estimate: f64, precision: i32) -> f64 {
let biases = closest_bias(estimate, precision);
if biases.is_empty() {
return 0.0;
}
if biases[0].distance == 0.0 {
return biases[0].bias;
}
let mut sum = 0_f64;
let mut total_weight = 0_f64;
for bias in biases {
total_weight += 1.0 / bias.distance;
sum += bias.bias / bias.distance;
}
sum / total_weight
}
fn closest_bias(estimate: f64, precision: i32) -> Vec<WeightedBias> {
if !(MINIMUM_PRECISION..=MAXIMUM_PRECISION).contains(&precision) {
return vec![];
}
let biases = &(*BIAS_DATA)[(precision - MINIMUM_PRECISION) as usize];
let means = &(*MEAN_DATA)[(precision - MINIMUM_PRECISION) as usize];
if OrderedFloat(estimate) < means[0] || means[means.len() - 1] < OrderedFloat(estimate) {
return vec![];
}
let index = match means.binary_search(&OrderedFloat(estimate)) {
Ok(idx) => idx,
Err(idx) => idx + 1,
};
let bottom = index.saturating_sub(NUMBER_OF_NEIGHBORS_IN_KNN);
let top = if index > means.len() - NUMBER_OF_NEIGHBORS_IN_KNN {
means.len()
} else {
index + NUMBER_OF_NEIGHBORS_IN_KNN
};
let mut result = (bottom..top)
.map(|i| {
let distance = (means[i] - estimate).powi(2);
WeightedBias {
bias: biases[i],
distance,
}
})
.collect::<Vec<_>>();
result.sort_by_key(|bias| OrderedFloat(bias.distance));
result.truncate(NUMBER_OF_NEIGHBORS_IN_KNN);
result
}
#[derive(Debug, Copy, Clone)]
struct WeightedBias {
bias: f64,
distance: f64,
}
impl PartialEq for WeightedBias {
fn eq(&self, other: &Self) -> bool {
self.distance == other.distance
}
}
impl Eq for WeightedBias {}
impl PartialOrd for WeightedBias {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for WeightedBias {
fn cmp(&self, other: &Self) -> Ordering {
self.distance.total_cmp(&other.distance)
}
}
const LINEAR_COUNTING_THRESHOLD: [i32; 9] = [
900, 1800, 3100, 6500, 11500, 20000, 50000, 120000, 350000, ];
pub fn linear_counting_threshold(precision: i32) -> i32 {
if (MINIMUM_PRECISION..=MAXIMUM_PRECISION).contains(&precision) {
return LINEAR_COUNTING_THRESHOLD[(precision - MINIMUM_PRECISION) as usize];
}
5 * (1 << precision) / 2
}
#[cfg(test)]
mod tests {
use super::*;
use approx::assert_relative_eq;
const TOLERANCE: f64 = 1e-4;
#[test]
fn test_alpha() {
assert_relative_eq!(alpha(14), 0.7213, epsilon = TOLERANCE);
}
#[test]
fn test_estimate_bias_when_exactly_defined() {
assert_relative_eq!(estimate_bias(738.1256, 10), 737.1256, epsilon = TOLERANCE);
assert_relative_eq!(
estimate_bias(14573.7784, 14),
9248.7784,
epsilon = TOLERANCE
);
}
#[test]
fn test_estimate_bias_when_interpolation_needed() {
assert_relative_eq!(estimate_bias(1490.0, 11), 1456.8144, epsilon = TOLERANCE);
assert_relative_eq!(estimate_bias(16300.0, 14), 8005.2257, epsilon = TOLERANCE);
assert_relative_eq!(estimate_bias(653000.0, 17), -411.7805, epsilon = TOLERANCE);
}
#[test]
fn test_estimate_bias_returns_zero_when_mean_out_of_range() {
assert_relative_eq!(estimate_bias(738.0, 10), 0.0, epsilon = TOLERANCE);
assert_relative_eq!(estimate_bias(1310000.0, 18), 0.0, epsilon = TOLERANCE);
}
#[test]
fn test_estimate_bias_returns_zero_when_precision_out_of_range() {
assert_relative_eq!(
estimate_bias(1000.0, MINIMUM_PRECISION - 1),
0.0,
epsilon = TOLERANCE
);
assert_relative_eq!(
estimate_bias(1000.0, MAXIMUM_PRECISION + 1),
0.0,
epsilon = TOLERANCE
);
}
#[test]
fn test_linear_counting_threshold_when_precisely_defined() {
assert_eq!(linear_counting_threshold(14), 11500);
}
#[test]
fn test_linear_counting_threshold_when_computed() {
assert_eq!(linear_counting_threshold(19), 1310720);
}
}