Fast inverse square root in Javascript

fisr.js

//Based on the fast inverse square root function
// https://en.wikipedia.org/wiki/Fast_inverse_square_root
// Some original comments preserved for humor value
// Designed to try to mimic the original as closely as possible
function Q_rsqrt(number)
{ 
    var i;
    var x2, y;
    const threehalfs = 1.5;
  
    x2 = number * 0.5;
    y = number;
    //evil floating bit level hacking
    var buf = new ArrayBuffer(4);
    (new Float32Array(buf))[0] = number;
    i =  (new Uint32Array(buf))[0];
    i = (0x5f3759df - (i >> 1)); //What the fuck?
    (new Uint32Array(buf))[0] = i;
    y = (new Float32Array(buf))[0];
    y  = y * ( threehalfs - ( x2 * y * y ) );   // 1st iteration
//  y  = y * ( threehalfs - ( x2 * y * y ) );   // 2nd iteration, this can be removed

    return y;
}

If you don't call new Float32Array and new Uint32Array so much, it's about twice the speed of 1/Math.sqrt(x):

• isqrt: 1.237ms

• Q_rsqrt: 11.280ms

• q2: 0.647ms

  var buf = new ArrayBuffer(4),
      f32=new Float32Array(buf),
      u32=new Uint32Array(buf);
  function q2(x) {
    var x2 = 0.5 * (f32[0] = x);
    u32[0] = (0x5f3759df - (u32[0] >> 1));
    var y = f32[0];
    y  = y * ( 1.5 - ( x2 * y * y ) );   // 1st iteration
    return y;
  }
  

@geocar Q_rsqrt is now allot slower than the default implementation (at-least in chrome).
https://repl.it/MA07/8

const buf = new ArrayBuffer(4)
const f32 = new Float32Array(buf)
const u32 = new Uint32Array(buf)

function fisr(x) {
	const x2 = 0.5 * (f32[0] = x)
	u32[0] = (0x5f3759df - (u32[0] >> 1))
	let y = f32[0]
	y = y * (1.5 - (x2 * y * y))
	return y
}

const itterations = 999999999

function benchFisr(){
	for(let i = 0; i < itterations; i++){
		(fisr(i + 1))
	}
}

function benchSqrt() {
	for (let i = 0; i < itterations; i++) {
		(1/Math.sqrt(i + 1))
	}
}

function benchmark(){
	let startTS = Date.now()
	benchFisr()
	console.log('fisr: ',Date.now() - startTS, 'ms')
	
	startTS = Date.now()
	benchSqrt()
	console.log('1/sqrt: ',Date.now() - startTS, 'ms')
}

benchmark()

nodejs 14:

fisr:  982 ms
1/sqrt:  496 ms

chrome 92

fisr:  1573 ms
1/sqrt:  747 ms

am i missing something, or that the sqrt implementation on x86 is just that much better?
(hint: it is)

no your using to many iterations

no your using to many iterations

Please, take a minute to try to understand the code before you post your reply, thank you.

moving computation impl to native is better most of the time, that's why they introduced WASM.

@ingvardm Here's my take on it, fisr seems to become faster in higher orders of magnitude of iterations.

const buffer = new ArrayBuffer(4);
const ui32 = new Uint32Array(buffer);
const f32 = new Float32Array(buffer);

function Q_rsqrt (number)
{
    f32[0] = number;
    ui32[0] = 0x5F3759DF - (ui32[0] >> 1);
    const x = f32[0];
    return x * (1.5 - 0.5 * x * x * number);
}

let qTotal = 0, sTotal = 0;
const iters = 999999999;

for (let i = 0; i < iters; ++i)
{
    const s = Date.now();
    Q_rsqrt(i + 1);
    qTotal += Date.now() - s; 
}

for (let i = 0; i < iters; ++i)
{
    const s = Date.now();
    (1 / Math.sqrt(i + 1));
    sTotal += Date.now() - s; 
}

console.log("Q_rsqrt:", qTotal);       // Q_rsqrt: 34027
console.log("1 / Math.sqrt:", sTotal); // 1 / Math.sqrt: 34372

So, at least in terms of javascript, this seems to be a problem of theoretical vs practical time complexity. Q_rsqrt is probably faster per iteration, but the additional overhead of the buffers and such causes native implementations to be faster for most use cases. But if you do happen to be running a billion calls to inverse square root, you probably shouldn't be using naked javascript. As valen214 said, WASM is probably a better investment if you're chasing performance.