Benchmark: Fast approx. atan2 vs Math.atan2 vs cached atan2

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

User agent: Mozilla/5.0 (X11; Linux x86_64; rv:133.0) Gecko/20100101 Firefox/133.0

Browser/OS: Firefox 133 on Linux

View result in a separate tab

fast approx. atan2

7.2M/s

Math.atan2

5.9M/s

cached Math.atan2

5.2M/s

View exact numbers

Test name	Executions per second
✓ fast approx. atan2	7,164,206 Ops/sec
Math.atan2	5,875,750 Ops/sec
cached Math.atan2	5,210,516 Ops/sec

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

LLMs can make mistakes. Check important info.

Let's break down the provided benchmark definitions and compare the options.

**Benchmark Definitions:**

The test cases measure three different implementations of the `atan2` function:

1. **Original Math.atan2**: This is the standard implementation provided by JavaScript, which uses a more complex algorithm to calculate the inverse tangent of two arguments.
2. **Fast Approximation (fastAtan2)**: This implementation is a simplified approximation of the original `atan2` function, optimized for performance. It uses some V8-specific optimizations and caching techniques to reduce the number of calculations required.
3. **Cached Math.atan2**: This implementation is similar to the original `atan2` function but has been modified to cache its results for repeated calls with the same arguments.

**Options Compared:**

The three implementations differ in their approach:

* Original `Math.atan2`: uses a complex algorithm, which provides high accuracy but lower performance.
* Fast Approximation (`fastAtan2`): uses simplifications and optimizations to reduce performance overhead, but may sacrifice some accuracy.
* Cached `Math.atan2`: caches results for repeated calls with the same arguments, reducing the number of calculations required.

**Pros and Cons:**

* **Original Math.atan2**: Pros:
	+ High accuracy
	+ Well-tested and maintained implementation
	+ Suitable for most use cases where performance is not critical.
* Cons:
	+ Lower performance due to complex algorithm
	+ May be slower than optimized implementations
* **Fast Approximation (fastAtan2)**: Pros:
	+ Improved performance due to simplifications and optimizations
	+ Still provides good accuracy for most use cases
* Cons:
	+ Simplifications may lead to reduced accuracy in certain edge cases
	+ Not suitable for all scenarios where high accuracy is required.
* **Cached Math.atan2**: Pros:
	+ Reduces performance overhead by caching results
	+ Suitable for scenarios where repeated calls with the same arguments are common.
* Cons:
	+ May require additional memory allocation to store cached results
	+ Cache may become outdated if implementation changes

**Library and Syntax:**

The test case uses a custom `fastAtan2` function that is defined in the "Script Preparation Code" section of the benchmark definition. This function is similar to the original `Math.atan2` function but with some optimizations applied.

**Special JS Feature or Syntax:**

There are no special JavaScript features or syntax used in this benchmark. The implementations focus on optimizing the performance and accuracy of the `atan2` function.

**Other Alternatives:**

If you need to measure other mathematical functions, consider using:

* **BenchMarking frameworks**: like Benchmark.js or Microbenchmark
* **JavaScript engines**: like V8 (used by Chrome) or SpiderMonkey (used by Firefox)
* **Math libraries**: like Mathjs or NumJS

These alternatives can provide more comprehensive benchmarking and insights into the performance of different JavaScript implementations.

Fast approx. atan2 vs Math.atan2 vs cached atan2 (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 (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):

Related benchmarks

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