Run results for: Fast approx. atan2 vs Math.atan2 vs fast accurate atan2

Run details:

User agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/26.0.1 Safari/605.1.15

Browser: Safari 26

Operating system: Mac OS X 10.15.7

Device Platform: Desktop

Date tested: 9 months ago

fast approx. atan2

33.6M/s

accurate approx atan2

20.3M/s

Math.atan2

13.6M/s

View exact numbers

Test name	Executions per second
✓ fast approx. atan2	33,551,266 Ops/sec
accurate approx atan2	20,342,814 Ops/sec
Math.atan2	13,583,317 Ops/sec

Script Preparation code:

const ONEQTR_PI = Math.PI / 4;
const THRQTR_PI = (3 * Math.PI) / 4;

const HALF_PI = Math.PI / 2;

// https://gist.github.com/volkansalma/2972237#file-atan2_approximation-c-L29
const fastAtan2 = (y, x) => {
	const abs_y = Math.abs(y) + 1e-10; // kludge to prevent 0/0 condition
	let angle, r;
	if (x < 0) {
		r = (x + abs_y) / (abs_y - x);
		angle = THRQTR_PI;
	} else {
		r = (x - abs_y) / (x + abs_y);
		angle = ONEQTR_PI;
	}
	angle += (0.1963 * r * r - 0.9817) * r;
	return y < 0 ? -angle : angle;
};

// https://mazzo.li/posts/vectorized-atan2.html
const accurateFastAtan2 = (y, x) => {
	const swap = Math.abs(x) < Math.abs(y);
	const denominator = (swap ? y : x) === 0 ? 0.00000001 : swap ? y : x;
	const atan_input = (swap ? x : y) / denominator;

	const a1 = 0.99997726;
	const a3 = -0.33262347;
	const a5 = 0.19354346;
	const a7 = -0.11643287;
	const a9 = 0.05265332;
	const a11 = -0.0117212;

	const z_sq = atan_input * atan_input;
	let res = atan_input * (a1 + z_sq * (a3 + z_sq * (a5 + z_sq * (a7 + z_sq * (a9 + z_sq * a11)))));

	if (swap) res = Math.sign(atan_input) * HALF_PI - res;
	if (x < 0.0) res = Math.sign(y) * MATH.PI + res;

	return res;
};

Tests:

Math.atan2
eval(''); var k = [1, .23, 0.12, 929, 8172, 9.2, 21.2].map(e => Math.atan2(e, .5));
fast approx. atan2
eval(''); var k = [1, .23, 0.12, 929, 8172, 9.2, 21.2].map(e => fastAtan2(e, .5));
accurate approx atan2
eval(''); var k = [1, .23, 0.12, 929, 8172, 9.2, 21.2].map(e => accurateFastAtan2(e, .5));