Benchmark: math pow vs multiply (with few extra variants)

Script Preparation code:

function powNaive(x, y) {
	if (!y) return 1;
	let tmp = x;
	for (let i = 1; i < y; i++) {
		tmp *= x;
  	}
	return tmp;
}

// from https://codereview.stackexchange.com/a/217369
function pow2B(x, y) {
    if (y < 2) { return y ? x : 1 }
    if (y & 1) { return x * pow2B(x, y & 0x7FFFFFFE)}
    const p = pow2B(x, y >> 1);
    return p * p;
}

// other two functions from the same stackexchange post
function pow(x, y) {
  if (!y) { return 1 }
  let tmp = res = x;
  for (let i = 1; i < y; i++) {
    for (let j = 1; j < x; j++) { tmp += res }
    res = tmp;
  }
  return res;
}

function pow2(x, y) {
  if (!y) { return 1; }
  if (y % 2) {
    return x * pow2(x, y - 1);
  }
  const p = pow2(x, y/2);
  return p * p;
}

Tests:

pow
var x = Math.pow(54,2);
mult
var y = 54*54
pow2 bitwise
var y = pow2B(54, 2)
pow2 summ
var y = pow(54, 2)
pow2 multiplication
var y = pow2(54, 2)
pow (multiplication in for loop)
var y = powNaive(54, 2)

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
pow
mult
pow2 bitwise
pow2 summ
pow2 multiplication
pow (multiplication in for loop)

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 24 days ago):

LLMs can make mistakes. Check important info.

**Benchmark Overview**

The provided JSON represents a JavaScript benchmark test case on the MeasureThat.net website. The test compares four different approaches for calculating exponentiation: `Math.pow`, multiplication, and two optimized implementations (`pow2B` and `pow2`). Each individual test case measures the execution time of a single function call.

**Tested Options**

The options being compared are:

1. `Math.pow`: The built-in `Math.pow` function.
2. Multiplication: A simple multiplication approach using two variables.
3. `pow2B`: An optimized implementation using bitwise operations to reduce the number of multiplications required.
4. `pow2`: Another optimized implementation that uses a summation loop to calculate exponentiation.

**Pros and Cons**

* **Math.pow**: Fast, but may not be optimal due to the overhead of the built-in function.
	+ Pros: Easy to use, no implementation details required.
	+ Cons: May not be as efficient as other approaches.
* **Multiplication**: Simple, but can be slow due to repeated calculations.
	+ Pros: Easy to implement, minimal code changes required.
	+ Cons: Can lead to slower execution times due to repeated multiplications.
* **pow2B**: Optimized using bitwise operations, reducing the number of multiplications required.
	+ Pros: Efficient, optimized for performance.
	+ Cons: May require understanding of bitwise operations and exponentiation properties.
* **pow2**: Another optimized implementation that uses a summation loop.
	+ Pros: Efficient, optimized for performance.
	+ Cons: May be more complex to understand than `pow2B`.

**Libraries and Special Features**

None of the test cases use any external libraries or special JavaScript features beyond the standard language.

**Other Considerations**

* The benchmark measures the execution time of individual function calls, which may not accurately represent real-world usage patterns.
* The test cases only consider integer exponentiation; for floating-point numbers, additional considerations would be needed (e.g., handling NaNs and infinity).
* The benchmark results are based on a single browser and platform combination; results may vary across different environments.

**Alternatives**

Other alternatives to the optimized implementations (`pow2B` and `pow2`) could include:

1. **Exponentiation by squaring**: A mathematical approach that uses repeated squaring to calculate exponentiation.
2. **Karatsuba multiplication**: An algorithm for multiplying large numbers using a divide-and-conquer approach, which can be adapted for exponentiation.
3. **Fast exponentiation algorithms**: Other specialized algorithms, such as the "exponentiation by squaring and reduction" method or the "binary exponentiation" method.

These alternatives may offer improved performance or efficiency over the optimized implementations used in the benchmark.

Latest run results:

Run details: (Test run date: one year ago)

User agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/118.0.0.0 Safari/537.36

Browser/OS: Chrome 118 on Mac OS X 10.15.7

View result in a separate tab

Test name	Executions per second
pow	15817362.0 Ops/sec
mult	1023584704.0 Ops/sec
pow2 bitwise	15534520.0 Ops/sec
pow2 summ	291965.8 Ops/sec
pow2 multiplication	10302923.0 Ops/sec
pow (multiplication in for loop)	32646062.0 Ops/sec

Related benchmarks:

math pow vs multiply (with few extra variants) (version: 0)

Comparing performance of: pow vs mult vs pow2 bitwise vs pow2 summ vs pow2 multiplication vs pow (multiplication in for loop)

Created: one year ago by: Guest

Jump to the latest result

pow

mult

pow2 bitwise

pow2 summ

pow2 multiplication

pow (multiplication in for loop)

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 24 days ago):