Benchmark: Fast approx. atan2 vs Math.atan2 vs cached atan2 (v8 optimization buster)

Script Preparation code:

const abs = Math.abs, min = Math.min, max = Math.max, PI = Math.PI, PI2 = PI / 2;
const FAT2 = {
    ax: 0.1, ay: 0.1
}; //variables for gc (v8 optimizations);
let a = 0.1, s = 0.1, r = 0.1;
var fastAtan2 = (y, x) => {
     FAT2.ax = abs(x);
     FAT2.ay = abs(y);
     a = min(FAT2.ax, FAT2.ay) / max(x, y);
     s = a * a;
     r = ((-0.0464964749 * s + 0.15931422) * s - 0.327622764) * s * a + a;
     if (FAT2.ay > FAT2.ax) r = PI2 - r;
     if (x < 0) r = PI - r;
     if (y < 0) r = -r;
     return r;
}; //this is the fastest i can get it rn
var atan2 = Math.atan2;

Tests:

Math.atan2
eval(''); var k = [1, .23, 0.12, 929, 8172, 9.2, 21.2].map(e => Math.atan2(e, .5));
fast approx. atan2
eval(''); var k = [1, .23, 0.12, 929, 8172, 9.2, 21.2].map(e => fastAtan2(e, .5));
cached Math.atan2
eval(''); var k = [1, .23, 0.12, 929, 8172, 9.2, 21.2].map(e => atan2(e, .5));

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Math.atan2
fast approx. atan2
cached Math.atan2

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 27 days ago):

LLMs can make mistakes. Check important info.

**Benchmark Overview**

The provided benchmark compares the performance of three different implementations of the `atan2` function in JavaScript:

1. **Native `Math.atan2`**: The built-in implementation of `atan2` in the JavaScript engine.
2. **Fast Approximation (`fastAtan2`)**: A custom implementation written by the test author, optimized for speed using a combination of mathematical approximations and variable handling.
3. **Cached `Math.atan2`**: An implementation that caches the results of previous calls to `Math.atan2`, potentially improving performance by avoiding redundant calculations.

**Comparison Options**

The benchmark compares these three options because they represent different approaches to implementing `atan2`:

* **Native `Math.atan2`**: The built-in implementation is often a good starting point, but its performance might not be optimized for specific use cases or hardware.
* **Fast Approximation (`fastAtan2`)**: This custom implementation uses mathematical approximations and variable handling to achieve better performance. However, it may require more maintenance and tuning compared to the native implementation.
* **Cached `Math.atan2`**: Caching previous results can improve performance by reducing redundant calculations, but it may increase memory usage and lead to cache misses if not implemented carefully.

**Pros and Cons**

Here are some pros and cons of each approach:

* **Native `Math.atan2`**:
	+ Pros: Well-maintained, widely supported, and optimized for most use cases.
	+ Cons: May have performance limitations due to the engine's internal optimizations or hardware dependencies.
* **Fast Approximation (`fastAtan2`)**:
	+ Pros: Can achieve better performance in specific use cases or on certain hardware platforms.
	+ Cons: Requires more maintenance, tuning, and expertise to ensure accurate results and optimal performance.
* **Cached `Math.atan2`**:
	+ Pros: Can improve performance by reducing redundant calculations and avoiding cache misses.
	+ Cons: May increase memory usage, lead to cache invalidations, or introduce additional complexity.

**Library Usage**

In this benchmark, the library used is the JavaScript engine's implementation of `Math.atan2`. There are no external libraries mentioned.

**Special JS Features or Syntax**

There are no special JavaScript features or syntax used in these implementations. They only utilize standard JavaScript functions and variables.

**Alternatives**

Some alternatives to consider when implementing `atan2` include:

* Using a library like `mathjs` or `lodash.math` that provides optimized implementations of mathematical functions, including `atan2`.
* Implementing a custom caching mechanism using JavaScript's built-in `Map` or `WeakMap` data structures.
* Considering the use of hardware acceleration or SIMD instructions for performance-critical applications.

Keep in mind that the choice of implementation depends on the specific requirements and constraints of your project.

Latest run results:

Run details: (Test run date: 21 days ago)

User agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:131.0) Gecko/20100101 Firefox/131.0

Browser/OS: Firefox 131 on Windows

View result in a separate tab

Test name	Executions per second
Math.atan2	3143477.0 Ops/sec
fast approx. atan2	2757651.8 Ops/sec
cached Math.atan2	2816584.5 Ops/sec

Related benchmarks:

Fast approx. atan2 vs Math.atan2 vs cached atan2 (v8 optimization buster) (version: 0)

Comparing performance of: Math.atan2 vs fast approx. atan2 vs cached Math.atan2

Created: 2 years ago by: Guest

Jump to the latest result

Math.atan2

fast approx. atan2

cached Math.atan2

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 27 days ago):