Advanced Mathematics and Data Analysis With JavaScript

Hi, I'm Gun Joshi, an open source developer and this year's Google Summer of Code contributor for Standard Lib. In this talk, we will be discussing advanced mathematics and data analysis with JavaScript. Let's get started.

We start by discussing why JavaScript is a good choice for numeric and scientific computing in the web browser. Then we'll compare its speed with Python and R, and touch upon WebAssembly's role and explore cases where plain JavaScript falls short. Finally, we'll introduce Standard Lib, which is a fundamental library for numerical computation on the web, similar to what we have NumPy or SciPy in Python.

Let's start by discussing why should you use JavaScript for mathematical and data visualization. It's way beyond just web development these days. Take Bilibili for example. It's an entertainment content platform in China and Southeast Asia. Bilibili used on-device in-browser image segmentation to display real-time viewer feedback across video streams. This led to a 30% increase in session duration and a 19% improvement in click-through rate. Or let us take Adobe Photoshop Web Beta for example. It is an online version of Adobe Photoshop. They used in-browser machine learning for on-device inference to enhance ML features like the object selection tool. They achieved up to 200% performance improvement in model execution, which provided near real-time editing capabilities in the web browser itself.

Alright, so we discussed JavaScript can get your job done. But what about speed? Isn't Python or R supposed to be faster? Well, not necessarily. This graph compares execution speed for different array sizes on the x-axis where we are computing the sum of elements of a vector using a simple for loop. No surprise C is the fastest, but JavaScript closely follows with near-native speed because of the just-in-time compilers optimizing code at runtime. Meanwhile, Python and R struggle to keep up, especially when the array sizes grow.

We talked about speed, but what about WebAssembly? How does it compare? This chart shows performance for specific functions like the error function, exponential and logarithmic function. C is the fastest across the board, but notice that WebAssembly often underperforms plain JavaScript, especially for complex functions like exponential and logarithmic. For these kinds of one-off tasks, plain JavaScript performs well. But the whole story changes while applying the same operation to many elements in an array. Here we compare JavaScript against C, Wasm and WasmCopy for blast routines. In the first graph, Wasm performs much better as WasmCopy isn't worth it for routines such as DAXP because copying over the data adds a significant overhead when compared to the actual operation, which DAXP does. But for cases when operations are heavier, such as matrix multiplication in DGEMM, as we have in the second graph, the overhead for copying array data is less significant when compared with the actual operation. So there's a very small difference in the performance of Wasm and WasmCopy. So plain JS may not be the most efficient for these kind of operations, but we have instances where we can get accelerated performance in JavaScript run times.

In the first chart, we're evaluating the error function for multiple elements in a vector. With increasing vector sizes, calling a native add-on introduces significant overhead. So when we have small vector sizes, there's a significant overhead for adding a native add-on. But when the array sizes becomes large, that overhead becomes negligible and native add-ons show clear performance gains about three times faster for larger vectors. Now in the second chart, the second chart looks at the hardware accelerated blast using the Apple accelerate framework on macOS. Once again, there's a noticeable overhead for small vectors, but beyond 1000 elements, it drops significantly. Here native add-ons are around five times faster and the performance gap grows even more complex as we go towards more complex operations, such as matrix multiplication in case of DGEMM. So while JavaScript's just-in-time compilers are fast, they can deliver up to 25 or 50% of native code speed. In order to go even faster, we can leverage complementary technologies like Node.js native add-ons and hardware acceleration for a significant boost. So what is the solution that we can infer from all this? The solution is standard lib. Standard lib is a fundamental library for numerical computation on the web, similar to what we have numpy or scipy in Python. Some of its features include fancy indexing and by fancy indexing, we mean what we have in Python, the indexing where you can create and set arbitrary slices of array data and apply things like Boolean and integer array mask for filtering and data extraction. It also has blast, which is a collection of fundamental operations used for linear algebra, statistical analysis, image transformation, machine learning, and includes operations for matrix multiplication, manipulation, scaling, and transformation, some of which consist of examples such as DASM, which is used to compute the sum of absolute values or D.

Standard lib is a fundamental library for numerical computation on the web, similar to what we have numpy or scipy in Python. Some of its features include fancy indexing and by fancy indexing, we mean what we have in Python, the indexing where you can create and set arbitrary slices of array data and apply things like Boolean and integer array mask for filtering and data extraction. It also has blast, which is a collection of fundamental operations used for linear algebra, statistical analysis, image transformation, machine learning, and includes operations for matrix multiplication, manipulation, scaling, and transformation, some of which consist of examples such as DASM, which is used to compute the sum of absolute values or D. to calculate the dot product of two double-precision floating point vectors or even Gswap, which is used to interchange two vectors. Moreover, it has various pseudo-random number generators, such as uniform, gamma, discrete uniform and much more. They take arguments such as min and max in case of uniform or shape and rate parameters alpha and beta in case of gamma and they generate a pseudo-random number from that particular distribution.

Standard lib also comes with a REPL, which is an interactive interpreter environment for executing JavaScript. It comes with customizable themes, syntax highlighting, and much more features. Now some folks might ask about whether is it possible to just compile and load libraries such as NumPy and Scipy to run directly inside web browsers. While this is possible, doing so comes with a significant disadvantage compared to using standard lib. For some context, Pyodide, WebR and standard lib enable running Python or JavaScript functions directly into the web browser. And based on these charts, we can conclude that standard lib is better or equal to other alternatives based on loading speed as we can see in the first chart, whereas there is a huge difference between what there is in the case of Pyodide and there's standard lib. There's a huge difference in case of speed as well, as we can observe from the second chart. Standard lib also provides orders of magnitude more APIs than other libraries within the numerical web ecosystem such as TensorFlow, JSTAT, MathJS, SciJS, and there is a very much significant difference if you have a look over the number of APIs with standard lib as and the rest of them. There's one particular example which demonstrates how one can implement the famous PageRank algorithm which powers Google Search using only standard lib functionality. At a high level, I want to draw your attention to the import statements. These may seem like a lot but this is actually a benefit as the entire project decomposes into individual packages allowing users to import and use only that functions that they require thus reducing bundle sizes. Every function called in this implementation is a standard lib function so no need to import other libraries. Standard lib can be a one-stop shop for numerical and scientific computation and in this implementation such functions include those for scaling vectors, performing matrix vector multiplication, computing the norm, array creation and element-wise arithmetic.

But that is not all we have even prototype integration of standard lib directly into Google Sheets. Here we are using standard lib pseudo random number generators in Google Sheets. The function names follow the same conventions as that are used in Google Sheets. So there is no new syntax for you to learn. Also all highlighted functions are powered by standard lib routines which run pure JavaScript under the hood. Again standard lib functions use familiar syntax but with blast routines it gets even better. Spreadsheet integration helps to visualize complex operations like strides or offsets making debugging and understanding a lot more easier. So are you thinking to be a part of all this cool stuff. Yes you can go ahead and access the GitHub repository of standard lib. You can start by starting the repository going through the contributing guidelines and diving through the code base. There is a helpful and engaging community out there. If you have any doubts or you want to add new features as well you can throw all your questions at them. They also have a blog where regular posts are updated related to standard lib and like this year as well standard lib also plans to apply for Google summer of code in 2025 again. So that was all from my side. Thank you. Have a nice day.