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

Script Preparation code:

const abs = Math.abs, min = Math.min, max = Math.max, PI = Math.PI, PI2 = PI / 2;
var fastAtan2 = (y, x) => {
     let ax = abs(x);
     let ay = abs(y);
     let a = min(ax, ay) / max(x, y);
     let s = a * a;
     let r = ((-0.0464964749 * s + 0.15931422) * s - 0.327622764) * s * a + a;
     if (ay > 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));

Historical Performance Data aggregated from 44 community runs

Desktop Results:

Chrome 25 runs

fast approx. atan2

1.7M/s

cached Math.atan2

1.5M/s

Math.atan2

1.1M/s

Fastest: fast approx. atan2 (1.5x faster)

View exact numbers

✓ fast approx. atan2: 1,669,946 ops/sec
• cached Math.atan2: 1,504,007 ops/sec
• Math.atan2: 1,137,601 ops/sec

Firefox 13 runs

fast approx. atan2

2.8M/s

cached Math.atan2

2.6M/s

Math.atan2

2.3M/s

Fastest: fast approx. atan2 (1.2x faster)

View exact numbers

✓ fast approx. atan2: 2,837,684 ops/sec
• cached Math.atan2: 2,560,304 ops/sec
• Math.atan2: 2,305,402 ops/sec

Mobile Results:

Chrome 6 runs

fast approx. atan2

847K/s

cached Math.atan2

761K/s

Math.atan2

582K/s

Fastest: fast approx. atan2 (1.5x faster)

View exact numbers

✓ fast approx. atan2: 846,816 ops/sec
• cached Math.atan2: 761,138 ops/sec
• Math.atan2: 582,132 ops/sec

Results show median performance across all community submissions. Run this benchmark yourself to verify on your device.

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: 4 months ago)

User agent: Mozilla/5.0 (Linux; Android 10; K) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/148.0.0.0 Mobile Safari/537.36

Browser/OS: Chrome Mobile 148 on Android

View result in a separate tab

fast approx. atan2

4.3M/s

cached Math.atan2

3.2M/s

Math.atan2

3.1M/s

View exact numbers

Test name	Executions per second
✓ fast approx. atan2	4,349,316 Ops/sec
cached Math.atan2	3,189,924 Ops/sec
Math.atan2	3,092,531 Ops/sec

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

LLMs can make mistakes. Check important info.

Let's dive into the world of JavaScript benchmarks.

**Benchmark Overview**

The provided benchmark measures the performance of three different implementations of the `atan2` function:

1.  `fast approx. atan2`: A custom implementation that uses an optimized formula to calculate `atan2`.
2.  `cached Math.atan2`: The built-in `Math.atan2` function with caching enabled.
3.  `Math.atan2`: The standard built-in `Math.atan2` function without any optimizations or caching.

**Options Compared**

The benchmark compares the performance of these three implementations:

*   **Custom optimization**: `fast approx. atan2` uses an optimized formula to calculate `atan2`. This implementation is likely to be faster than the standard `Math.atan2` function.
*   **Caching**: `cached Math.atan2` enables caching, which can improve performance by storing the results of previous calculations and reusing them for subsequent calls with the same arguments. However, this approach also introduces additional overhead due to cache management.
*   **Standard implementation**: The standard `Math.atan2` function without any optimizations or caching.

**Pros and Cons**

Here's a brief overview of the pros and cons of each approach:

*   **Custom optimization (fast approx. atan2)**:
    *   Pros: Optimized formula can lead to significant performance improvements.
    *   Cons: The implementation may not be as straightforward or maintainable as other approaches.
*   **Caching (cached Math.atan2)**:
    *   Pros: Can provide good performance benefits, especially for frequent calls with the same arguments.
    *   Cons: Introduces additional overhead due to cache management and may not perform well for infrequent calls.
*   **Standard implementation (Math.atan2)**:
    *   Pros: Widely supported, well-maintained, and easy to understand.
    *   Cons: May have slower performance compared to optimized implementations.

**Library Usage**

None of the benchmarked functions use any external libraries. However, `fast approx. atan2` is a custom implementation that uses some mathematical tricks to optimize the calculation.

**Special JS Feature or Syntax**

The benchmark does not use any special JavaScript features or syntax. The code is relatively straightforward and uses standard JavaScript constructs.

**Alternatives**

Some alternative approaches for implementing `atan2` could include:

*   Using a library like [Fast Atan2](https://github.com/greggman/fast-atan2), which provides an optimized implementation of the function.
*   Implementing `atan2` using a more advanced mathematical approach, such as [Taylor series expansion](https://en.wikipedia.org/wiki/Taylor_series).
*   Using JIT compilers or other optimization techniques to improve performance.

Fast approx. atan2 vs Math.atan2 vs cached atan2 (v8 optimization buster + local scope) (version: 0) Benchmark.js

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

Historical Performance Data aggregated from 44 community runs

Desktop Results:

Chrome 25 runs

Firefox 13 runs

Mobile Results:

Chrome 6 runs

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 + local scope) (version: 0) Benchmark.js

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

Historical Performance Data aggregated from 44 community runs

Desktop Results:

Chrome 25 runs

Firefox 13 runs

Mobile Results:

Chrome 6 runs

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`