# Switching to Wasm for 10x Speedup

We switched our optimizer from JS to Wasm, and everything is 10x faster!

When you write `encourage`

and `ensure`

statements in your Style program, Penrose uses numerical optimization to find a layout of shapes that minimizes your objectives while satisfying your constraints. The faster this is, the more complicated diagrams you can make, and the more easily you can iterate on any given diagram by tweaking it or trying out different random variations.

Because performance affects the user experience so much, we've recently been putting a good amount of work into making Penrose faster. One really big win has been rewriting the optimizer in Rust and compiling it to WebAssembly, which gave us an **order of magnitude performance improvement!**

## Overview

The locations, sizes, and even colors of shapes in a Penrose diagram are all made up of numbers that the optimizer can play with to find a good diagram; we call these "degrees of freedom". All the objectives and constraints get combined together into a single numerical function meant to roughly encode how "good" or "bad" the diagram is. We use automatic differentiation on that function to let us compute a "tweak" for each degree of freedom to make that number bigger or smaller in a way that makes the overall diagram "better"; this is called the gradient. Then we use the L-BFGS algorithm to find a good solution by running this gradient function over and over in a loop.

Up until this year, we had written the optimizer in TypeScript and did the gradient computation by concatenating together a long string of JavaScript code which we feed to the browser's JavaScript engine. At the end of last year, we rewrote the optimizer in Rust and rewrote our code generation to produce WebAssembly instead of JavaScript. This made optimization about ten times faster. The rest of this post describes how exactly we did that, and some of the challenges we hit along the way.

## Impetus

In September I did an experiment to see what would happen if I just went through the whole optimizer line by line (nothing clever) and rewrote it from TypeScript to Rust. Then since the optimizer takes as input a function to compute our objective and gradient values, I modified our compiler backend to produce C instead of JavaScript, so that I could compile and link that together with the Rust code for the optimizer itself.

It turns out that native is way faster. For example, consider this Penrose diagram (in the style of a couple papers from SIGGRAPH 2020 and SIGGRAPH 2022):

Here's the difference in performance I got from running the JavaScript vs native versions on my M1 MacBook Pro:

As you can see, even if you include the 2.66 seconds it takes to compile both the C *and* Rust code together, this is still over five times faster than running the JavaScript code. If you use the more fair comparison where everything is already compiled before we start measuring, the native version is over twenty times faster.

Of course, for most of our diagrams, the time to compile the Rust and C code dominates, but again, if you compare just the time to actually optimize the diagram, the difference is still huge. Take a look at this Euclidean geometry diagram, for instance:

Given how good the speed of this native optimizer was, I next wanted to compile the Rust code to WebAssembly to run it in the browser and see if we could bring some of that speedup to the web.

## Attempt 1

Luckily for me, Ben Titzer, one of the creators of WebAssembly, works in our department at CMU! So I went and asked him how I would configure a fixed WebAssembly module for our optimizer to allow me to plug in a custom WebAssembly module for the gradient computation. He told me to use a WebAssembly *table*, into which I could put a pointer to the function that computes the gradient, even if that function lives in a separate module.

It wasn't too hard to figure out how to do this in raw WebAssembly, but I was struggling to get it working in Rust. Again luckily, my advisor happened to have a connection to Will Crichton, who put us in touch with his brother Alex, who is one of the core Rust/Wasm people. Alex told me that I could pass the Rust compiler `-Clink-arg=--export-table`

to get it to export an `__indirect_function_table`

, which was what I wanted. But the table wasn't showing up. Turns out, `wasm-bindgen`

was postprocessing the WebAssembly produced by the Rust compiler, stripping out the table. So I decided to just use the Rust compiler directly, without `wasm-bindgen`

.

This turned out to be very... fun 🙃 and I found myself writing code like the following:

```
const rust = (await WebAssembly.instantiate(src)).instance.exports;
const withVec = (T, len, f) => {
const align = T.BYTES_PER_ELEMENT;
const size = len * align;
const ptr = rust.__wbindgen_malloc(size, align);
try {
return f(new T(rust.memory.buffer, ptr, len));
} finally {
rust.__wbindgen_free(ptr, size, align);
}
};
// ...
return withVec(Uint8Array, n, (vInputs) => {
for (let i = 0; i < n; i++) {
vInputs[i] = inputMetaToByte(inputs[i]);
}
return withVec(Float64Array, n, (vXs) => {
vXs.set(varyingValues);
rust.converge(
index,
vInputs.byteOffset,
n,
numObjEngs,
numConstrEngs,
vXs.byteOffset,
n,
);
return Array.from(vXs);
});
});
```

Exactly what you wanna see in JavaScript! And the best part is, there's a nasty bug lurking. Can you spot it?

That's right: Wasm memory can grow. So if you wrap its `buffer`

in a `TypedArray`

and the memory grows later, that array becomes invalid. A more correct version of `withVec`

would look like this:

```
const withVec = (T, len, f) => {
const align = T.BYTES_PER_ELEMENT;
const size = len * align;
const ptr = rust.__wbindgen_malloc(size, align);
try {
return f(() => new T(rust.memory.buffer, ptr, len));
} finally {
rust.__wbindgen_free(ptr, size, align);
}
};
```

But this only gets you so far. The Penrose optimizer uses a big `Params`

type to keep track of data across iterations of the numerical optimization algorithm, and these `Params`

contain some numbers, some vectors, and a couple rectangular matrices (some of which aren't always present). Dealing with all these data individually via `withVec`

would be a huge pain, and this issue is pretty much exactly what `wasm-bindgen`

is designed to solve! So I wanted to go back and try to use it after all.

## Attempt 2

Following Ben's advice, I was still trying to use the `__indirect_function_table`

. I took a look at the `wasm-bindgen`

source code, and I found a function called `unexported_unused_lld_things`

. So I opened a pull request adding a flag called `--keep-lld-exports`

which causes that function to not be called. Alex merged it a few hours later (!), so I could just use the latest `wasm-bindgen`

from GitHub `main`

to access the table while still using `wasm-bindgen`

. (I quickly realized that using `cargo install`

to build `wasm-bindgen-cli`

from source in every CI run is too slow, so instead I stashed a Linux binary in a GitHub Gist to use until the next release.)

By default, `wasm-bindgen`

exports Rust types as JavaScript classes which point to data living in the Wasm memory. This is great for efficiency because it means data doesn't get unnecessarily copied back and forth, but the downside is that the user on the JS side needs to remember to manually call `.free()`

or some other thing that consumes the object, or a memory leak springs up. For our purposes I wanted our optimizer interface to just return plain old JavaScript data, so I made use of the very nice `serde-wasm-bindgen`

and ts-rs crates. These work great together as long as you use the `Serializer::json_compatible()`

preset.

To bundle this all up into an actual `@penrose/optimizer`

package, I had to write a several-step build process, running ts-rs via `cargo test`

, and using esbuild's `binary`

loader to embed the Wasm binary directly into the JavaScript:

```
cargo test
cargo build --target=wasm32-unknown-unknown --release
wasm-bindgen --target=web --keep-lld-exports --out-dir=build target/wasm32-unknown-unknown/release/penrose_optimizer.wasm
esbuild ./source.ts --outfile=index.js --platform=neutral --bundle --loader:.wasm=binary --define:i
```mport.meta.url=null --sourcemap

`wasm-bindgen`

has several available targets. Here you can see I'm using `web`

instead of `bundler`

, despite the fact that esbuild is a bundler. What gives? Well, the `bundler`

target is designed to work well with Webpack, which is very slow; we've worked hard to get rid of all Webpack usage in Penrose, with the effect of cutting two-thirds off our build times. The `web`

target emits this function:

```
async function init(input) {
if (typeof input === "undefined") {
input = new URL("penrose_optimizer_bg.wasm", import.meta.url);
}
const imports = getImports();
if (
typeof input === "string" ||
(typeof Request === "function" && input instanceof Request) ||
(typeof URL === "function" && input instanceof URL)
) {
input = fetch(input);
}
initMemory(imports);
const { instance, module } = await load(await input, imports);
return finalizeInit(instance, module);
}
export default init;
```

What I wanted was to provide a single bundle that could be used both in the browser and in Node, so this actually works great since I can write an `instance.js`

file to pass in the bytes directly, bypassing `fetch`

:

```
import init from "./build/penrose_optimizer";
import bytes from "./build/penrose_optimizer_bg.wasm";
export let maybeOptimizer = undefined;
export const optimizerReady = init(bytes).then((output) => {
maybeOptimizer = output;
});
```

The problem is that esbuild doesn't identify and eliminate the dead code in `init`

, so smarter tools like Vite (which we use for our website) see the `new URL`

and try to turn `penrose_optimizer_bg.wasm`

into a resource. Our bundle is in a different directory from the Wasm binary file itself, so Vite throws a build error. The hacky solution to this problem is to pass `--define:i`

to esbuild so that the `new URL`

no longer fits Vite's smart resource pattern-recognition.

The reason the above was `instance.js`

instead of `instance.ts`

is that TypeScript still doesn't understand the `*.wasm`

extension even if esbuild does, so we also need a separate `instance.d.ts`

file:

```
import { InitOutput } from "./build/penrose_optimizer";
export declare let maybeOptimizer: InitOutput | undefined;
export declare const optimizerReady: Promise<void>;
```

Then at the top-level of `@penrose/optimizer`

, we export a promise that can be `await`

ed to ensure the optimizer is `ready`

:

```
import { maybeOptimizer, optimizerReady } from "./instance";
let maybeIndex: number | undefined = undefined;
export const ready = optimizerReady.then(() => {
penrose_init();
maybeIndex = maybeOptimizer!.__indirect_function_table.length;
maybeOptimizer!.__indirect_function_table.grow(1);
});
```

The annoying thing is that now we need to do this before every single place where the optimizer is used:

```
import { ready } from "@penrose/optimizer";
await ready;
```

We went back and forth on this architecture for a bit, and eventually ended up deciding to solve this annoyance by using top-level `await`

. Not all of our downstream code supported top-level await because we were previously using Docusaurus for our website, so we had to migrate to VitePress first.

And the performance difference is striking!

### Before

```
| 0s 1s 2s 3s 4s 5s 6s 7s 8s 9s 10s 11s 12s 13s 14s 15s 16s 17s 18s 19s 20s 21s 22s 23s 24s 25s 26s 27s 28s 29s 30s 31s 32s 33s 34s 35s 36s 37s 38s 39s 40s 41s 42s 43s 44s 45s 46s 47s 48s 49s 50s 51s 52s 53s 54s 55s 56s 57s 58s 59s 60s 61s 62s 63s 64s 65s 66s 67s 68s 69s 70s 71s 72s 73s
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 3d-projection-fake-3d-linear-algebra ▝▀▞▖
| allShapes-allShapes ▝▀▚▚▄▄
| arrowheads-arrowheads ▝▀▞▖
| circle-example-euclidean ▝▀▀▀▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▖
| collinear-euclidean ▝▀▀▚▀▀▀▖
| congruent-triangles-euclidean ▝▀▀▀▀▀▀▀▀▞▚
| continuousmap-continuousmap ▝▀▚▚
| hypergraph-hypergraph ▝▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▖
| incenter-triangle-euclidean ▝▀▀▀▚▀▀▀▀▀▀▀▀▀▀▚
| lagrange-bases-lagrange-bases ▝▀▚▚
| midsegment-triangles-euclidean ▝▀▀▀▚▚
| non-convex-non-convex ▝▀▀▀▀▞▀▀▀▀▚
| one-water-molecule-atoms-and-bonds ▝▀▞▖
| parallel-lines-euclidean ▝▀▀▚▀▀▀▀▀▀▀▀▀▚
| persistent-homology-persistent-homology ▝▀▀▀▀▀▀▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▄
| points-around-line-shape-distance ▝▀▀▀▀▀▀▞▚
| points-around-polyline-shape-distance ▝▀▀▀▀▀▀▀▀▀▀▀▀▞▀▚
| points-around-star-shape-distance ▝▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚▀▖
| siggraph-teaser-euclidean-teaser ▝▀▀▀▀▀▞▀▀▚
| small-graph-disjoint-rect-line-horiz ▝▀▀▀▀▀▀▀▀▞▚
| small-graph-disjoint-rects ▝▀▞▖
| small-graph-disjoint-rects-large-canvas ▝▀▞▖
| small-graph-disjoint-rects-small-canvas ▝▀▚▚
| tree-tree ▝▀▀▞▖
| tree-venn ▝▀▀▀▚▞▀▖
| tree-venn-3d ▝▀▀▀▚▀▀▚▄▖
| two-vectors-perp-vectors-dashed ▝▀▀▞▖
| vector-wedge-exterior-algebra ▝▀▀▚▚
| wet-floor-atoms-and-bonds ▝▀▀▚▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▖
| wos-laplace-estimator-walk-on-spheres ▝▀▀▀▀▞▀▀▀▖
| wos-nested-estimator-walk-on-spheres ▝▀▀▀▀▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚
| wos-offcenter-estimator-walk-on-spheres ▝▀▀▀▚▀▀▀▀▖
| wos-poisson-estimator-walk-on-spheres ▝▀▀▀▚▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▖
```

### After

```
| 0s 1s 2s 3s 4s 5s 6s 7s 8s
| | | | | | | | | |
| 3d-projection-fake-3d-linear-algebra ▝▀▞▖
| allShapes-allShapes ▝▀▚▞▄▄
| arrowheads-arrowheads ▝▀▞▖
| circle-example-euclidean ▝▀▀▀▀▀▞▀▀▚
| collinear-euclidean ▝▀▀▚▚
| congruent-triangles-euclidean ▝▀▀▀▀▀▀▀▀▞▖
| continuousmap-continuousmap ▝▀▚▚
| hypergraph-hypergraph ▝▀▀▀▀▀▀▀▀▀▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▖
| incenter-triangle-euclidean ▝▀▀▀▚▚
| lagrange-bases-lagrange-bases ▝▀▀▞▖
| midsegment-triangles-euclidean ▝▀▀▀▀▞▖
| non-convex-non-convex ▝▀▀▀▚▚
| one-water-molecule-atoms-and-bonds ▝▚▚
| parallel-lines-euclidean ▝▀▀▚▚
| persistent-homology-persistent-homology ▝▀▀▀▀▀▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚
| points-around-line-shape-distance ▝▀▀▀▞▖
| points-around-polyline-shape-distance ▝▀▀▀▀▀▀▀▀▀▀▚▚
| points-around-star-shape-distance ▝▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚▚
| siggraph-teaser-euclidean-teaser ▝▀▀▀▀▀▚▚
| small-graph-disjoint-rect-line-horiz ▝▀▀▀▀▀▀▀▀▚▚
| small-graph-disjoint-rects ▝▀▞▖
| small-graph-disjoint-rects-large-canvas ▝▀▞▖
| small-graph-disjoint-rects-small-canvas ▝▀▚▚
| tree-tree ▝▀▚▞▖
| tree-venn ▝▀▀▀▚▞▖
| tree-venn-3d ▝▀▀▀▞▄▖
| two-vectors-perp-vectors-dashed ▝▀▚▚
| vector-wedge-exterior-algebra ▝▀▚▚
| wet-floor-atoms-and-bonds ▝▀▀▞▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚
| wos-laplace-estimator-walk-on-spheres ▝▀▀▀▀▀▀▀▞▖
| wos-nested-estimator-walk-on-spheres ▝▀▀▀▀▀▀▀▀▀▀▀▀▀▚▀▀▀▀▀▀▀▚
| wos-offcenter-estimator-walk-on-spheres ▝▀▀▀▀▀▀▀▀▚▚
| wos-poisson-estimator-walk-on-spheres ▝▀▀▀▀▀▀▀▀▚▀▀▖
```

## Attempt 3

At this point we've achieved our performance goal, but the `@penrose/optimizer`

module is basically impossible to use since it's so tightly coupled to our autodiff codegen; for instance, it exports a `class Gradient`

with this docstring:

```
/**
* An instantiated WebAssembly function that can be used either to directly
* compute outputs and gradients or to step a state via the optimizer.
*
* Each WebAssembly module used to construct an instance of this class must
* follow some conventions using other things exported from this package:
*
* - The module name of every import must match `importModule`.
*
* - One import must be a memory whose name matches `importMemoryName`.
*
* - The rest of the imports must be functions in the same order as the the
* insertion order of `builtins`. The name of each of these imports must be a
* base-36 integer (`"0"`-`"9"`, `"a"`-`"z"`) corresponding to the index of
* the name in `builtins`. The type of the import is determined by its value
* in `builtins`, which is an element of `BuiltinType`:
*
* - `"addToStackPointer"` takes one `i32` and returns one `i32`.
* - `"unary"` takes one `f64` and returns one `f64`.
* - `"binary"` takes two `f64`s and returns one `f64`.
* - `"polyRoots"` takes two `i32`s and returns nothing.
*
* - The module must export a function whose name matches `exportFunctionName`,
* which takes four `i32`s and returns one `f64`.
*/
```

Yikes. The reason for this is that I took Ben's original advice a bit too literally, thinking that I needed to directly put the WebAssembly function produced by our autodiff compiler directly into our Rust optimizer module's indirect function table (for #performance of course). Premature optimization! What I should have done instead is take advantage of `wasm-bindgen`

's various features for calling JavaScript functions from Rust/Wasm. So last month I wrote pull requests #1338 and #1368 which expose a much more reasonable `@penrose/optimizer`

interface: it now just takes in an arbitrary JavaScript function to compute the objective and gradient:

```
/**
* Given an objective function `f` and some constraint functions `g_j`, where we
* want to minimize `f` subject to `g_j(x) \leq 0` for all `j`, this function
* computes the following, where `\lambda` is `weight`:
*
* `\phi(x, \lambda) = f(x) + \lambda * \sum_j \max(g_j(x), 0)^2`
*
* The gradient with respect to `x` is stored in `grad`.
*
* @param x input vector
* @param weight `\lambda`, the weight of the constraint term
* @param grad mutable array to store gradient in
* @returns the augmented objective value `\phi(x, \lambda)`
*/
export type Fn = (
x: Float64Array,
weight: number,
grad: Float64Array,
) => number;
/**
* Steps the optimizer until either convergence or `stop` returns `true`.
* @param f to compute objective, constraints, and gradient
* @param x mutable array to update at each step
* @param state initial optimizer state
* @param stop early stopping criterion
* @returns optimizer state after stepping
*/
export const stepUntil = (
f: Fn,
x: Float64Array,
state: Params,
stop: () => boolean,
): Params => penrose_step_until(f, x, state, stop);
```

And our autodiff compiler just wraps its raw WebAssembly function to conform to that interface. I think there might be a small performance drop (hard to notice since the performance data we currently collect are fairly noisy), but the tradeoff is worth it.

The other consequence of this is that we now no longer use the `--keep-lld-exports`

flag at all! So I guess I should have thought more about the design and the tools available before going to submit upstream patches.

## Takeaways

While there is some debate about how fast Wasm actually is in practice (and indeed, our Wasm optimizer is a few times slower than the native one), we found a *significant* performance gain compared to JavaScript. Definitely worth the effort.

This project took a lot of trial and error, though! I also leaned heavily on experts like Ben and Alex to get me through some of the trickier parts. I'm super excited about all the work going on in the Rust/Wasm space; there are a lot of great tools and resources already, and I'm hoping that going forward we can continue making all of this more accessible to newcomers.