Add fast inverse square root algorithm

[yan-aint-nickname]

Almost identical to C implementation but with golang specific unsafe package
https://en.wikipedia.org/wiki/Fast_inverse_square_root

[siriak]

Looks good, thanks!

[raklaptudirm]

Please make the changes to the comments as I suggested in the discussion.

[tjgurwara99]

I think this already exists in a different form - https://github.com/TheAlgorithms/Go/blob/6429dfdb87ad0b2ae462f42f5307b6c0bcaca5c4/math/binary/sqrt.go

[yan-aint-nickname]

@tjgurwara99 there is some problem with the algorithm what you send. 1/y division is very expensive operation that's why right-shift >> is used in floating point bit level hacking line. It's better to multiply by passed value. This algorithm was made to reduce divisions. And I return 1/y value not a y, because it's reverse square root. I'm going to clear comments @raklaptudirm , I just wanted to pay homage to the original algorithm. May I change what the f*** to what the hell? If you have any questions, please ask

[tjgurwara99]

I was in a hurry so I didn't write a descriptive comment but I pointed out the other implementation not because I want you to remove your implementation but rather do it without unsafe. As you can see from that function it can be done!!

Furthermore, if you look closely, it is almost identical to your function so if you move it (and name it appropriately, eg InverseSqrt or something) and change the other function to be something like func Sqrt(n float32) float32 { return 1 / InverseSqrt(x) } you solved two problems:

1. Simple is better than complex by removing the unsafe package, and
2. Keeping similar logical blocks together in the same package.

[yan-aint-nickname]

I was in a hurry so I didn't write a descriptive comment but I pointed out the other implementation not because I want you to remove your implementation but rather do it without unsafe. As you can see from that function it can be done!!

Furthermore, if you look closely, it is almost identical to your function so if you move it (and name it appropriately, eg InverseSqrt or something) and change the other function to be something like func Sqrt(n float32) float32 { return 1 / InverseSqrt(x) } you solved two problems:

1. Simple is better than complex by removing the unsafe package, and
2. Keeping similar logical blocks together in the same package.

Float32bits it's just an alias for *(*int32)(unsafe.Pointer(&y)) what I did wrong that I used int32 instead of uint32
https://github.com/golang/go/blob/master/src/math/unsafe.go#L12

So, I need to:

1. Rename Q_rsqrt to FastInverseSqrt
2. Move FastInverseSqrt to math/binary package
3. Replace unsafe with simple Float32bits and Float32frombits
4. Replace Sqrt in math/binary/sqrt.go with func Sqrt(n float32) float32 { return 1 / FastInverseSqrt(x) }
5. Improve comments for better godoc generation

Am I right?

[tjgurwara99]

So, I need to:

Rename Q_rsqrt to FastInverseSqrt
Move FastInverseSqrt to math/binary package
Replace unsafe with simple Float32bits and Float32frombits
Replace Sqrt in math/binary/sqrt.go with func Sqrt(n float32) float32 { return 1 / FastInverseSqrt(x) }
Improve comments for better godoc generation
Am I right?

Yes 😄

Float32bits it's just an alias for *(*int32)(unsafe.Pointer(&y)) what I did wrong that I used int32 instead of uint32
https://github.com/golang/go/blob/master/src/math/unsafe.go#L12

To be honest, even I didn't notice that you'd used int32 instead - one more reason why I avoid unsafe package (as much as I can)

[siriak]

Looks good, thanks!

[tjgurwara99]

LGMT