iter-num-tools

This is a collection if iterator extensions that make heavy use of number properties. Mostly extending on Range.

LinSpace

LinSpace is an iterator over a range with a fixed number of values all evenly spaced.

use iter_num_tools::lin_space;

// Count from 1.0 up to and including 5.0, with 5 numbers counted in total
let it = lin_space(1.0..=5.0, 5);
assert!(it.eq([1.0, 2.0, 3.0, 4.0, 5.0]));

// Count from 0.0 up to and excluding 5.0, with 5 numbers counted in total
let it = lin_space(0.0..5.0, 5);
assert!(it.eq([0.0, 1.0, 2.0, 3.0, 4.0]));

GridSpace

GridSpace extends on LinSpace.

use iter_num_tools::grid_space;

// count in 2 dimensions (excluding end points),
// from 0.0 up to 1.0 in the x direction with 2 even steps,
// and 0.0 up to 2.0 in the y direction with 4 even steps
let it = grid_space([0.0, 0.0]..[1.0, 2.0], [2, 4]);
assert!(it.eq([
    [0.0, 0.0], [0.5, 0.0],
    [0.0, 0.5], [0.5, 0.5],
    [0.0, 1.0], [0.5, 1.0],
    [0.0, 1.5], [0.5, 1.5],
]));

// count in 2 dimensions (including end points),
// from 0.0 up to 1.0 in the x direction,
// and 0.0 up to 2.0 in the y direction with 3 even steps in all directions
let it = grid_space([0.0, 0.0]..=[1.0, 2.0], 3);
assert!(it.eq([
    [0.0, 0.0], [0.5, 0.0], [1.0, 0.0],
    [0.0, 1.0], [0.5, 1.0], [1.0, 1.0],
    [0.0, 2.0], [0.5, 2.0], [1.0, 2.0],
]));

Arange

Arange is similar to LinSpace, but instead of a fixed amount of steps, it steps by a fixed amount.

use iter_num_tools::arange;

let it = arange(0.0..2.0, 0.5);
assert!(it.eq([0.0, 0.5, 1.0, 1.5]));

Note

There is no inclusive version of arange. Consider the following

use iter_num_tools::arange;

let it = arange(0.0..=2.1, 0.5);

We would not expect 2.1 to ever be a value that the iterator will ever meet, but the range suggests it should be included. Therefore, no RangeInclusive implementation is provided.

ArangeGrid

ArangeGrid is the same as GridSpace but for Arange instead of LinSpace.

use iter_num_tools::arange_grid;

// count in 2 dimensions,
// from 0.0 up to 1.0 in the x direction,
// and 0.0 up to 2.0 in the y direction,
// stepping by 0.5 each time
let it = arange_grid([0.0, 0.0]..[1.0, 2.0], 0.5);
assert!(it.eq([
    [0.0, 0.0], [0.5, 0.0],
    [0.0, 0.5], [0.5, 0.5],
    [0.0, 1.0], [0.5, 1.0],
    [0.0, 1.5], [0.5, 1.5],
]));

// count in 2 dimensions,
// from 0.0 up to 1.0 in the x direction stepping by 0.5 each time,
// and 0.0 up to 2.0 in the y direction stepping by 1.0 each time
let it = arange_grid([0.0, 0.0]..[1.0, 2.0], [0.5, 1.0]);
assert!(it.eq([
    [0.0, 0.0], [0.5, 0.0],
    [0.0, 1.0], [0.5, 1.0],
]));

LogSpace

LogSpace is similar to LinSpace, but instead of evenly spaced linear steps, it has evenly spaced logarithmic steps.

use iter_num_tools::log_space;
use itertools::zip_eq;

// From 1.0 up to and including 1000.0, taking 4 logarithmic steps
let it = log_space(1.0..=1000.0, 4);
let expected: [f64; 4] = [1.0, 10.0, 100.0, 1000.0];

assert!(zip_eq(it, expected).all(|(x, y)| (x-y).abs() < 1e-10));

// From 1.0 up to 1000.0, taking 3 logarithmic steps
let it = log_space(1.0..1000.0, 3);
let expected: [f64; 3] = [1.0, 10.0, 100.0];

assert!(zip_eq(it, expected).all(|(x, y)| (x-y).abs() < 1e-10));

Alternatives

There is already a project called itertools-num which has quite a few downloads but it isn't optimised for speed or flexibility.

(try this benchmark for yourself: clone the repo and run cargo bench --bench "linspace" --all-features)

LinSpace/linspace [1.0, 3.0] x100 (iter-num-tools)
                        time:   [65.311 ns 65.579 ns 65.898 ns]
LinSpace/linspace [1.0, 3.0] x100 (std)
                        time:   [67.545 ns 67.762 ns 68.047 ns]
LinSpace/linspace [1.0, 3.0] x100 (itertools-num)
                        time:   [117.05 ns 117.59 ns 118.23 ns]

fn bench(i: impl Iterator<Item=f64>) -> Vec<f64> {
    black_box(i.map(|x| x * 2.0).collect())
}

// first benchmark (fastest)
bench(iter_num_tools::lin_space(1.0..=3.0, 100));

// second benchmark
fn lin_space_std(start: f64, end: f64, steps: usize) -> impl Iterator<Item = f64> {
    let len = end - start;
    let step = len / steps as f64;
    (0..=steps).map(move |i| start + i as f64 * step)
}
bench(lin_space_std(1.0, 3.0, 100));

// third benchmark (slowest)
bench(itertools_num::linspace(1.0, 3.0, 100));

It also does not provide any other utilities. Only linspace (inclusive) and a 'Cumulative sum' iterator adaptor.