Benchmark: Quick Sin Cos vs Math Sin Cos vs Fastest

Script Preparation code:

let factorialize = function (num) {
    if (num === 0 || num === 1)
        return 1;
    for (let i = num - 1; i >= 1; i--) {
        num *= i;
    }
    return num;
}

let FACT_2 = 1 / factorialize(2);
let FACT_3 = 1 / factorialize(3);
let FACT_4 = 1 / factorialize(4);
let FACT_5 = 1 / factorialize(5);
let FACT_6 = 1 / factorialize(6);
let FACT_7 = 1 / factorialize(7);

const HALF_PI = Math.PI * 0.5;
const DOUBLE_PI = Math.PI * 2;

var mysin = function (angle)
{
    let pow2 = angle * angle;
    let pow4 = pow2 * pow2;
    let pow6 = pow4 * pow2;
    return 1 - pow2 * FACT_2 + pow4 * FACT_4 - pow6 * FACT_6;
}

var mycos = function (angle)
{
    return mysin(angle + HALF_PI);
}

var fastSin = function (x)
{
  if (x < -Math.PI)
        x += DOUBLE_PI;
    else if (x > Math.PI)
            x -= DOUBLE_PI;

    if (x < 0)
        return 1.27323954 * x + 0.405284735 * x * x;
    else
        return 1.27323954 * x - 0.405284735 * x * x;
}

var fastCos = function (x)
{
  return fastSin(x + HALF_PI);
}

Tests:

Math
Math.cos(0.4292); Math.sin(0.2321);
Faster
mycos(0.4292); mysin(0.2321);
Fastest
fastCos(0.4292); fastSin(0.2321);

Historical Performance Data aggregated from 19 community runs

Desktop Results:

Chrome 19 runs

Faster

13.6M/s

Math

12.2M/s

Fastest

3.9M/s

Fastest: Faster (3.5x faster)

View exact numbers

✓ Faster: 13,634,419 ops/sec
• Math: 12,167,592 ops/sec
• Fastest: 3,868,309 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
Faster
Fastest

Fastest: N/A

Slowest: N/A

Latest run results:

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

User agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/151.0.0.0 Safari/537.36 Edg/151.0.0.0

Browser/OS: Chrome 151 on Windows

View result in a separate tab

Math

1064.7M/s

Faster

1058.8M/s

Fastest

239.2M/s

View exact numbers

Test name	Executions per second
✓ Math	1,064,715,904 Ops/sec
Faster	1,058,796,928 Ops/sec
Fastest	239,155,408 Ops/sec

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

LLMs can make mistakes. Check important info.

**Benchmark Overview**

The provided benchmark measures the performance of three different implementations of sine and cosine functions in JavaScript: `Math.sin`, `mycos` (custom implementation), and `fastSin` (optimized implementation). The benchmark tests these functions on specific angles, resulting in a total of 6 test cases.

**Options Compared**

1. **Math.sin**: The standard JavaScript function for calculating the sine of an angle.
2. **Mycos**: A custom implementation of the sine function, which uses a Taylor series expansion to calculate the value.
3. **FastSin**: An optimized implementation of the sine function, which uses a lookup table and some mathematical tricks to reduce the number of calculations required.

**Pros and Cons**

1. **Math.sin**:
	* Easy to implement and understand.
	* Works well for most use cases, but can be slow for large angles or high-performance applications.
2. **Mycos**:
	* Provides a good balance between performance and simplicity.
	* The Taylor series expansion used in Mycos is a common technique for approximating trigonometric functions.
	* However, the implementation may not be as efficient as FastSin for very large angles or high-performance applications.
3. **FastSin**:
	* Optimized for high-performance applications, using a lookup table and mathematical tricks to reduce calculations.
	* May be more complex to implement and understand, especially for those without experience with optimization techniques.
	* Provides better performance than Mycos and Math.sin for large angles or high-performance applications.

**Library: FastSin**

The `fastSin` implementation uses a lookup table to store pre-calculated values of the sine function for common angles. This allows the function to return the result directly, without performing any calculations. The lookup table is implemented using a mathematical trick involving the angle and its negative counterpart.

**Special JS Feature/Syntax: None**

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

**Other Alternatives**

1. **Brent's Method**: Another optimization technique for calculating trigonometric functions, which uses a combination of Taylor series expansions and polynomial approximations to reduce calculations.
2. **FasterSin library**: A third-party implementation of the sine function optimized for high-performance applications, using techniques such as vectorization and SIMD instructions.

**Benchmark Preparation Code**

The benchmark preparation code defines several functions:

1. `factorialize`: Calculates the factorial of a given number using a simple loop.
2. `mycos` and `mysin`: Implementations of the sine and cosine functions using Taylor series expansions, respectively.
3. `fastSin` and `fastCos`: Optimized implementations of the sine and cosine functions using lookup tables and mathematical tricks.

The benchmark preparation code also defines some constants, such as `HALF_PI` and `DOUBLE_PI`, which are used to calculate angles in radians.

Quick Sin Cos vs Math Sin Cos vs Fastest (version: 0) Benchmark.js

Comparing performance of: `Math vs Faster vs Fastest`

Created: 5 years ago by: Guest

Go to the latest result

Math

Faster

Fastest

Historical Performance Data aggregated from 19 community runs

Desktop Results:

Chrome 19 runs

Suite status: <idle, ready to run>

Fastest: N/A

Slowest: N/A

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

Quick Sin Cos vs Math Sin Cos vs Fastest (version: 0) Benchmark.js

Comparing performance of: Math vs Faster vs Fastest

Created: 5 years ago by: Guest

Go to the latest result

Math

Faster

Fastest

Historical Performance Data aggregated from 19 community runs

Desktop Results:

Chrome 19 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 vs Faster vs Fastest`