233 lines
6.7 KiB
Rust
233 lines
6.7 KiB
Rust
#![no_std]
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#![feature(test)]
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extern crate conv;
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#[cfg(test)] extern crate rand;
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#[cfg(test)] #[macro_use] extern crate std;
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#[cfg(test)] extern crate stats;
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#[cfg(test)] extern crate test;
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use conv::ApproxFrom;
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/// Represent an average value of a sequence of numbers.
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///
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/// The average is calculated iteratively, so the sequence of numbers can be an
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/// iterator.
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///
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/// ```
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/// use average::Average;
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///
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/// let a: Average = (1..6).map(Into::into).collect();
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/// assert_eq!(a.mean(), 3.0);
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/// assert_eq!(a.sample_variance(), 2.5);
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/// ```
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#[derive(Debug, Clone)]
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pub struct Average {
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/// Average value.
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avg: f64,
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/// Number of samples.
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n: u64,
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/// Intermediate sum of squares for calculating the variance.
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v: f64,
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}
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impl Average {
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/// Create a new average.
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pub fn new() -> Average {
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Average { avg: 0., n: 0, v: 0. }
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}
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/// Add a number to the sequence of which the average is calculated.
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pub fn add(&mut self, x: f64) {
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// This algorithm introduced by Welford in 1962 trades numerical
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// stability for a division inside the loop.
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//
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// See https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
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self.n += 1;
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let delta = x - self.avg;
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self.avg += delta / f64::approx_from(self.n).unwrap();
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self.v += delta * (x - self.avg);
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}
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/// Return the mean of the sequence.
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pub fn mean(&self) -> f64 {
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self.avg
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}
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/// Return the number of elements in the sequence.
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pub fn len(&self) -> u64 {
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self.n
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}
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/// Calculate the unbiased sample variance of the sequence.
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///
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/// This assumes that sequence consists of samples of a larger population.
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pub fn sample_variance(&self) -> f64 {
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if self.n < 2 {
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return 0.;
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}
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self.v / f64::approx_from(self.n - 1).unwrap()
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}
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/// Calculate the population variance of the sequence.
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///
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/// This assumes that sequence consists of the entire population.
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pub fn population_variance(&self) -> f64 {
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if self.n < 2 {
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return 0.;
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}
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self.v / f64::approx_from(self.n).unwrap()
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}
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/// Calculate the standard error of the mean of the sequence.
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pub fn err(&self) -> f64 {
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if self.n == 0 {
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return 0.;
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}
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(self.sample_variance() / f64::approx_from(self.n).unwrap()).sqrt()
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}
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/// Merge the average of another sequence into this one.
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pub fn merge(&mut self, other: &Average) {
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// This algorithm was proposed by Chan et al. in 1979.
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//
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// See https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
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let delta = other.avg - self.avg;
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let len_self = f64::approx_from(self.n).unwrap();
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let len_other = f64::approx_from(other.n).unwrap();
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let len_total = len_self + len_other;
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self.n += other.n;
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self.avg = (len_self * self.avg + len_other * other.avg) / len_total;
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// Chan et al. use
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//
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// self.avg += delta * len_other / len_total;
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//
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// instead but this results in cancelation if the number of samples are similar.
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self.v += other.v + delta*delta * len_self * len_other / len_total;
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}
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}
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impl core::default::Default for Average {
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fn default() -> Average {
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Average::new()
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}
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}
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impl core::iter::FromIterator<f64> for Average {
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fn from_iter<T>(iter: T) -> Average
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where T: IntoIterator<Item=f64>
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{
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let mut a = Average::new();
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for i in iter {
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a.add(i);
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}
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a
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}
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}
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macro_rules! assert_almost_eq {
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($a:expr, $b:expr, $prec:expr) => (
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if ($a - $b).abs() > $prec {
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panic!(format!(
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"assertion failed: `abs(left - right) < {:e}`, \
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(left: `{}`, right: `{}`)",
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$prec, $a, $b));
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}
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);
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use core::iter::Iterator;
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use std::vec::Vec;
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#[test]
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fn average_trivial() {
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let mut a = Average::new();
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assert_eq!(a.len(), 0);
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a.add(1.0);
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assert_eq!(a.mean(), 1.0);
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assert_eq!(a.len(), 1);
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assert_eq!(a.sample_variance(), 0.0);
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assert_eq!(a.err(), 0.0);
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}
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#[test]
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fn average_simple() {
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let a: Average = (1..6).map(f64::from).collect();
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assert_eq!(a.mean(), 3.0);
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assert_eq!(a.len(), 5);
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assert_eq!(a.sample_variance(), 2.5);
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assert_almost_eq!(a.err(), f64::sqrt(0.5), 1e-16);
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}
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#[test]
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fn average_numerically_unstable() {
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// The naive algorithm fails for this example due to cancelation.
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let big = 1e9;
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let sample = &[big + 4., big + 7., big + 13., big + 16.];
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let a: Average = sample.iter().map(|x| *x).collect();
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assert_eq!(a.sample_variance(), 30.);
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}
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#[test]
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fn average_normal_distribution() {
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use rand::distributions::{Normal, IndependentSample};
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let normal = Normal::new(2.0, 3.0);
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let mut a = Average::new();
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for _ in 0..1_000_000 {
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a.add(normal.ind_sample(&mut ::rand::thread_rng()));
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}
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assert_almost_eq!(a.mean(), 2.0, 1e-2);
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assert_almost_eq!(a.sample_variance().sqrt(), 3.0, 1e-2);
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}
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#[test]
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fn merge() {
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let sequence: &[f64] = &[1., 2., 3., 4., 5., 6., 7., 8., 9.];
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for mid in 0..sequence.len() {
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let (left, right) = sequence.split_at(mid);
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let avg_total: Average = sequence.iter().map(|x| *x).collect();
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let mut avg_left: Average = left.iter().map(|x| *x).collect();
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let avg_right: Average = right.iter().map(|x| *x).collect();
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avg_left.merge(&avg_right);
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assert_eq!(avg_total.n, avg_left.n);
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assert_eq!(avg_total.avg, avg_left.avg);
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assert_eq!(avg_total.v, avg_left.v);
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}
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}
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fn initialize_vec() -> Vec<f64> {
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use rand::distributions::{Normal, IndependentSample};
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use rand::{XorShiftRng, SeedableRng};
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let normal = Normal::new(2.0, 3.0);
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let n = 1_000_000;
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let mut values = Vec::with_capacity(n);
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let mut rng = XorShiftRng::from_seed([1, 2, 3, 4]);
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for _ in 0..n {
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values.push(normal.ind_sample(&mut rng));
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}
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values
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}
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#[bench]
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fn bench_average(b: &mut test::Bencher) {
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let values = initialize_vec();
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b.iter(|| {
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let a: Average = values.iter().map(|x| *x).collect();
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a
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});
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}
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#[bench]
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fn bench_stats(b: &mut test::Bencher) {
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let values = initialize_vec();
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b.iter(|| {
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let a: stats::OnlineStats = values.iter().map(|x| *x).collect();
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a
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});
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}
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}
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