The benchmark created on MeasureThat.net evaluates various approaches for calculating the Euclidean distance between points in a 2D space using JavaScript. This is done by comparing performance across different methods for computing distance, which fundamentally involves operations such as squaring, taking square roots, and using specific mathematical functions.

Benchmark Approaches

1. Math.hypot(i, j):

   • Test Name: hypot
   • Description: This function computes the square root of the sum of the squares of its arguments. It is a built-in JavaScript function introduced in ECMAScript 2015 (ES6) and is designed to handle complex calculations in a simple and reliable manner.
   • Performance: This method is the most straightforward and most reliable for calculating the Euclidean distance, but it may come with some overhead due to internal optimizations.

2. Math.sqrt(i * i + j * j):

   • Test Name: sqrt
   • Description: This calculates the distance using the manual formulation of the square root of the sum of the squares. This approach uses the Math.sqrt function to obtain the distance.
   • Performance: This method is generally faster than using Math.hypot, but it involves manual squaring of the variables which can impact performance slightly as well.

3. Math.sqrt(Math.pow(i, 2) + Math.pow(j, 2)):

   • Test Name: sqrt + pow
   • Description: This method explicitly uses the Math.pow function to square the two values. While semantically clear, it can lead to unnecessary performance overhead.
   • Performance: This approach is usually slower than the direct squaring method due to the function call overhead associated with Math.pow.

4. i * i + j * j:

   • Test Name: i*i
   • Description: This avoids any square root computation entirely and focuses only on the pre-squared values. This is not calculating the distance but may be part of calculations where the actual distance is unnecessary.
   • Performance: This is the fastest of all methods tested, as it performs only basic arithmetic without any function calls or square roots.

5. Math.pow(i, 2) + Math.pow(j, 2):

   • Test Name: pow
   • Description: It employs the Math.pow function to square the points, similar to the previous methods but includes function calls which add overhead.
   • Performance: This is slower than straight multiplication due to the use of Math.pow.

Performance Results

In the latest benchmark results:

• The fastest method is the simple multiplication i*i, achieving approximately 781.83 executions per second.
• The Math.sqrt(i*i + j*j) method follows next but is significantly slower at around 157.89 executions per second.
• The Math.pow approach is also quite slow when compared to direct arithmetic.

Pros and Cons of Different Approaches

• Math.hypot:

  • Pros: Clear, concise, handles more edge cases (like dealing with infinities or NaNs).
  • Cons: More overhead and potentially slower for simple calculations.

• Math.sqrt with direct multiplications:

  • Pros: Faster than Math.hypot, also provides a straightforward formula.
  • Cons: Might not be as precise for certain inputs due to the squaring operation.

• Math.sqrt with Math.pow:

  • Pros: Semantically clear and adaptable for more complex operations.
  • Cons: Slower and adds unnecessary complexity in this context.

• Direct arithmetic (i*i):

  • Pros: Extremely fast as it avoids additional complexity.
  • Cons: Does not provide actual distance and thus is contextually limited.

• Math.pow:

  • Pros: Readable and allows for easy adjustments for higher power calculations.
  • Cons: Slower than simple multiplication and over-engineered for this specific case.

Other Considerations

While the benchmark primarily tests methods intended for straightforward distance calculations, other alternatives could involve more advanced libraries or techniques:

• Using Typed Arrays and SIMD (Single Instruction Multiple Data) for performance-sensitive applications, especially in graphics or physics calculations.
• WebAssembly (Wasm) could also be employed to perform heavy mathematical operations more efficiently because it can run in tandem with JavaScript while providing better performance for computational tasks.

This benchmark provides valuable insights for software engineers, helping them choose the most suitable method for distance calculations based on their specific needs for performance and complexity.