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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"/><meta name="viewport" content="width=device-width, initial-scale=1"/><title> &#60loganGatlin/&#62 </title><link href="resources/favicon.svg" rel="icon" type="image/x-icon"/><style>
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color: #586e75;
}
</style></head><body><div class="pure-g"><div class="pure-u-1-1"><header class="header"><h1> nd-range <a target="_blank" href="https://github.com/Xterminate1818/nd-range"><svg viewBox="0 0 128 128" style="padding-bottom: 0.2em;"><title> View source on GitHub </title><g fill="#181616"><path d="M64 5.103c-33.347 0-60.388 27.035-60.388 60.388 0 26.682 17.303 49.317 41.297 57.303 3.017.56 4.125-1.31 4.125-2.905 0-1.44-.056-6.197-.082-11.243-16.8 3.653-20.345-7.125-20.345-7.125-2.747-6.98-6.705-8.836-6.705-8.836-5.48-3.748.413-3.67.413-3.67 6.063.425 9.257 6.223 9.257 6.223 5.386 9.23 14.127 6.562 17.573 5.02.542-3.903 2.107-6.568 3.834-8.076-13.413-1.525-27.514-6.704-27.514-29.843 0-6.593 2.36-11.98 6.223-16.21-.628-1.52-2.695-7.662.584-15.98 0 0 5.07-1.623 16.61 6.19C53.7 35 58.867 34.327 64 34.304c5.13.023 10.3.694 15.127 2.033 11.526-7.813 16.59-6.19 16.59-6.19 3.287 8.317 1.22 14.46.593 15.98 3.872 4.23 6.215 9.617 6.215 16.21 0 23.194-14.127 28.3-27.574 29.796 2.167 1.874 4.097 5.55 4.097 11.183 0 8.08-.07 14.583-.07 16.572 0 1.607 1.088 3.49 4.148 2.897 23.98-7.994 41.263-30.622 41.263-57.294C124.388 32.14 97.35 5.104 64 5.104z" clip-rule="evenodd" fill-rule="evenodd"></path><path d="M26.484 91.806c-.133.3-.605.39-1.035.185-.44-.196-.685-.605-.543-.906.13-.31.603-.395 1.04-.188.44.197.69.61.537.91zm2.446 2.729c-.287.267-.85.143-1.232-.28-.396-.42-.47-.983-.177-1.254.298-.266.844-.14 1.24.28.394.426.472.984.17 1.255zM31.312 98.012c-.37.258-.976.017-1.35-.52-.37-.538-.37-1.183.01-1.44.373-.258.97-.025 1.35.507.368.545.368 1.19-.01 1.452zm3.261 3.361c-.33.365-1.036.267-1.552-.23-.527-.487-.674-1.18-.343-1.544.336-.366 1.045-.264 1.564.23.527.486.686 1.18.333 1.543zm4.5 1.951c-.147.473-.825.688-1.51.486-.683-.207-1.13-.76-.99-1.238.14-.477.823-.7 1.512-.485.683.206 1.13.756.988 1.237zm4.943.361c.017.498-.563.91-1.28.92-.723.017-1.308-.387-1.315-.877 0-.503.568-.91 1.29-.924.717-.013 1.306.387 1.306.88zm4.598-.782c.086.485-.413.984-1.126 1.117-.7.13-1.35-.172-1.44-.653-.086-.498.422-.997 1.122-1.126.714-.123 1.354.17 1.444.663zm0 0"></path></g></svg></a></h1><h2> Vector Math - Standard Library </h2></header><div class="content"><h2 class="distinct"> Motivation </h2>
The Rust standard library provides several 'Range' types which
represent integers inside a given bounds (i.e. 1 &#8804; n &#8804; 100).
Ranges can be iterated over, and used for bounds testing of numbers.
In designing video games, it is often necessary to express 2 or 3
dimensional quantities or bounds. Problems like iterating over
voxels in a 3D world, or testing for an intersection between rectangles
lend themselves to the idea of Ranges.
<div class="code-block">
<pre><code>
<span class="comment">&#x2f;&#x2f; A 3D array representing a 128x128x128 voxel world</span>
<span class="keyword storage">let</span> <span class="variable">world_data</span> <span class="operator">=</span> <span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="constant numeric integer">0</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
<span class="comment">&#x2f;&#x2f; The &#x27;0..128&#x27; here is a range from 0 to 127 inclusive</span>
<span class="keyword control repeat">for</span> <span class="variable">x</span> <span class="keyword control">in</span> <span class="constant numeric integer">0</span><span class="operator">..</span><span class="constant numeric integer">128</span> <span class="punctuation bracket">{</span>
<span class="keyword control repeat">for</span> <span class="variable">y</span> <span class="keyword control">in</span> <span class="constant numeric integer">0</span><span class="operator">..</span><span class="constant numeric integer">128</span> <span class="punctuation bracket">{</span>
<span class="keyword control repeat">for</span> <span class="variable">z</span> <span class="keyword control">in</span> <span class="constant numeric integer">0</span><span class="operator">..</span><span class="constant numeric integer">128</span> <span class="punctuation bracket">{</span>
<span class="keyword storage">let</span> <span class="variable">voxel</span> <span class="operator">=</span> <span class="operator">&amp;</span><span class="variable">world</span><span class="punctuation bracket">[</span><span class="variable">x</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">y</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">z</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
<span class="comment">&#x2f;&#x2f; Do something with voxel</span>
<span class="punctuation bracket">}</span>
<span class="punctuation bracket">}</span>
<span class="punctuation bracket">}</span>
</code></pre>
</div>
However, in these contexts the Range type is not particularly helpful.
I am forced to use three different ranges and a triple nested 'for' loop.
The idea for nd-range is to expand the native Range type so that it
can be used over arbitrary dimensions. This allows us to iterate over
X, Y, and Z coordinates in a single loop.
<div class="code-block">
<pre><code>
<span class="keyword storage">let</span> <span class="variable">world_data</span> <span class="operator">=</span> <span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="punctuation bracket">[</span><span class="constant numeric integer">0</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span> <span class="constant numeric integer">128</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
<span class="keyword control repeat">for</span> <span class="punctuation bracket">[</span><span class="variable">x</span><span class="punctuation delimiter">,</span> <span class="variable">y</span><span class="punctuation delimiter">,</span> <span class="variable">z</span><span class="punctuation bracket">]</span> <span class="keyword control">in</span> <span class="function macro">nrange</span><span class="function macro">!</span><span class="punctuation bracket">(</span><span class="constant numeric integer">0</span><span class="operator"><span class="punctuation delimiter">.</span><span class="punctuation delimiter">.</span></span><span class="constant numeric integer">128</span><span class="punctuation delimiter">,</span> <span class="constant numeric integer">0</span><span class="operator"><span class="punctuation delimiter">.</span><span class="punctuation delimiter">.</span></span><span class="constant numeric integer">128</span><span class="punctuation delimiter">,</span> <span class="constant numeric integer">0</span><span class="operator"><span class="punctuation delimiter">.</span><span class="punctuation delimiter">.</span></span><span class="constant numeric integer">128</span><span class="punctuation bracket">)</span><span class="punctuation delimiter"></span> <span class="punctuation bracket">{</span>
<span class="keyword storage">let</span> <span class="variable">voxel</span> <span class="operator">=</span> <span class="operator">&amp;</span><span class="variable">world</span><span class="punctuation bracket">[</span><span class="variable">x</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">y</span><span class="punctuation bracket">]</span><span class="punctuation bracket">[</span><span class="variable">z</span><span class="punctuation bracket">]</span><span class="punctuation delimiter">;</span>
<span class="comment">&#x2f;&#x2f; Do something with voxel</span>
<span class="punctuation bracket">}</span>
</code></pre>
</div><h2 class="distinct"> Approach </h2>
An nd-range is similar in concept to an axis-aligned bounding box,
or AABB. These are common abstractions used in game development,
and there are well established algorithms that test for overlap.
Iterating over is slightly more complex, requiring some vector
algebra. If we interpret the range of values over each axis as a
vector, we can apply the cartesian product algorithm to find every
position within the bounded space. Below is a diagram from Wikipedia
(CC BY-SA 3.0).
<img src="https://upload.wikimedia.org/wikipedia/commons/4/4e/Cartesian_Product_qtl1.svg" class="centered"/>
Because a range is contiguous by definition, generating a cartesian
product is simple and performant. The iterator object has a space
complexity of O(N), where n is the number of dimensions. Rust's const generics
allow the entire struct to exist on the stack, which is a boon to performance.
<h2 class="distinct"> Performance </h2>
My points of comparison are the itertools and cartesian crates, which provide
comparable algorithms. Despite its popularity, I was shocked to discover how
slow the itertools implementation of the cartesian product is. The cartesian-rs
crate is lesser known, and uses a creative macro-based solution. I benchmarked
all three approaches, as well as the nested for-loop base case, over a 100x100x100
range.
<table class="striped"><thead><th scope="col"> Implementation </th><th scope="col"> Average Time (ns) </th><th scope="col"> Error (+/- ns) </th></thead><tbody><tr><th scope="row"><a href="https://docs.rs/itertools/latest/itertools/trait.Itertools.html#method.cartesian_product">
itertools
</a></th><td> 1,821,573 </td><td> 31,501 </td></tr><tr><th scope="row"><a href="https://crates.io/crates/cartesian">
cartesian-rs
</a></th><td> 989,242 </td><td> 50,835 </td></tr><tr><th scope="row"> nd-range </th><td> 968,853 </td><td> 15,792 </td></tr><tr><th scope="row"> nested loops </th><td> 911,853 </td><td> 46,066 </td></tr></tbody></table><h2 class="distinct"> Pros and Cons</h2>
My implementation is competitive with, and possibly faster than
its competitors for my use case. While nd-range only works for
ranges of contiguous integers, itertools and cartesian-rs work
for any iterators. However, by restricting my use case I can
extract more performance gains and integrate better with the Rust
standard library.
</div></div></div></body></html>
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