Benchmark: Math.pow(2,n) vs Table lookup?

Script Preparation code:

var POWERS = [
		1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,
		65536,131072,262144,524288,1048576,2097152
		
];

Tests:

Table lookup
let p = 15; let x; if (p > 20) { x = Math.pow(2,p); } else { x = POWERS[20]; }
Math.pow
let p = 15; let x; x = Math.pow(2,p);

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
Table lookup
Math.pow

Fastest: N/A

Slowest: N/A

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

LLMs can make mistakes. Check important info.

I'll break down the explanation into sections for better understanding.

**Benchmark Definition JSON**

The provided JSON represents a JavaScript microbenchmark test case on MeasureThat.net. The test case compares two approaches to compute `Math.pow(2, n)`: using a table lookup (`Table lookup`) and directly applying `Math.pow` with a literal exponent (`Math.pow`).

**Table Lookup Approach**

In the table lookup approach, an array `POWERS` is defined in the script preparation code. This array contains powers of 2 from 1 to 16384. In the benchmark definition, a variable `x` is declared and assigned a value using this table lookup. If the input `p` is greater than 20, it uses the corresponding power of 2 from the `POWERS` array. Otherwise, it uses the value at index 20 (which corresponds to `Math.pow(2, 20)`).

**Pros of Table Lookup Approach:**

1. **Cache-friendliness**: Since the powers of 2 are precomputed and stored in an array, the lookup is likely to be cache-friendly, reducing memory access overhead.
2. **Better performance for large exponents**: As `n` increases, the table lookup approach may perform better since it can directly access the precomputed values.

**Cons of Table Lookup Approach:**

1. **More memory usage**: The array `POWERS` requires additional memory to store the precomputed powers of 2.
2. **Increased script size**: The script preparation code needs to include the definition of the `POWERS` array, which may increase the overall script size.

**Math.pow Approach**

The Math.pow approach directly applies the `Math.pow` function with a literal exponent `n`. In the benchmark definition, a variable `x` is declared and assigned a value using this approach.

**Pros of Math.pow Approach:**

1. **Less memory usage**: The script preparation code only needs to include the necessary imports and declarations.
2. **Smaller script size**: The overall script size is reduced compared to the table lookup approach.

**Cons of Math.pow Approach:**

1. **More memory access overhead**: Since `Math.pow` computes the value on-the-fly, it may incur more memory access overhead due to the intermediate calculations.
2. **Potential performance degradation for large exponents**: As `n` increases, the performance of the `Math.pow` approach may degrade due to increased computation time.

**Library Used: None**

There is no library explicitly used in this benchmark definition.

**Special JavaScript Features or Syntax: None**

There are no special JavaScript features or syntax used in this benchmark definition.

**Alternatives**

Other alternatives for computing powers of 2 include:

1. **Bitwise operations**: Using bitwise shifts (`<<`) to compute powers of 2.
```javascript
let x = 1 << n;
```
This approach is more efficient than using `Math.pow` but may not be as cache-friendly.

2. **Exponential functions from other libraries**: Depending on the use case, alternative exponential functions like `exponentiationBySquaring` or `fastExp` from libraries like MathJS or Exponent might be used.
```javascript
import { fastExp } from 'mathjs';

let x = fastExp(2, n);
```
However, these alternatives may not be available by default in all JavaScript environments.

3. **Custom implementation**: Depending on the specific requirements and performance constraints, a custom implementation using loops or recursive functions might be used.
```javascript
function powerOfTwo(n) {
  let result = 1;
  for (let i = 0; i < n; i++) {
    result *= 2;
  }
  return result;
}

let x = powerOfTwo(n);
```
Keep in mind that this approach may not be as efficient or cache-friendly as the table lookup approach.

Latest run results:

Run details: (Test run date: 5 months ago)

User agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/125.0.0.0 Safari/537.36

Browser/OS: Chrome 125 on Windows

View result in a separate tab

Test name	Executions per second
Table lookup	11681200.0 Ops/sec
Math.pow	6886847.5 Ops/sec

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Created: 7 years ago by: Registered User

Jump to the latest result

Table lookup

Math.pow

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

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