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

Latest run results:

Run details: (Test run date: 10 months ago)

User agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:142.0) Gecko/20100101 Firefox/142.0

Browser/OS: Firefox 142 on Windows

View result in a separate tab

Math.atan2

1.6M/s

fast approx. atan2

1.5M/s

cached Math.atan2

1.4M/s

View exact numbers

Test name	Executions per second
✓ Math.atan2	1,558,176 Ops/sec
fast approx. atan2	1,465,685 Ops/sec
cached Math.atan2	1,445,158 Ops/sec

Autogenerated LLM Summary (model llama3.2:3b, generated one year 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.

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: 4 years ago by: Guest

Go to the latest result

Math.atan2

fast approx. atan2

cached Math.atan2

Suite status: <idle, ready to run>

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated one year ago):

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: 4 years ago by: Guest

Go to the latest result

Math.atan2

fast approx. atan2

cached Math.atan2

Suite status: <idle, ready to run>

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated one year ago):

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