sqrt(x) and 1/sqrt(x)

[Roquen]

Popular way to approximate sqrt(x) and 1/sqrt(x):

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public static float isqrt(float x)   {     float hx = x * 0.5f;     int   ix;     float r;     // make initial guess     ix = Float.floatToRawIntBits(x);     ix = 0x5f3759df - (ix>>1);     r  = Float.intBitsToFloat(ix);     // do some number of newton-ralphson steps,     // each doubles the number of accurate     // binary digits.     r  = r*(1.5f-hx*r*r);   //r  = r*(1.5f-hx*r*r);   //r  = r*(1.5f-hx*r*r);   //r  = r*(1.5f-hx*r*r);     return r;    // 1/sqrt(x)   //return r*x;  // sqrt(x)   }

[woogley]

Here's some background on how this technique works: http://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/

[DzzD]

very nice


EDIT : tested.... and unfortunatly due to the slowness of Float.floatToIntBits(x) it seems to doesn't give any performance gain

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[Riven]

replace
Float.floatToIntBits()

by
Float.floatToRawIntBits()

maybe it speeds up the 'conversion'

[Roquen]

Yeah, I just logged in to note using 'raw' instead comment (bad me).  The 'guess' part can be changed to something else (such as a small table for limited ranges).

Another thing to note is for renormalizing vectors, quaternions, etc. ... the guessed value is '1' and normally a single N-R step will commonly give you the renormalization multiplier.

(edit: many typos)

[Roquen]

Yeah, I just logged in to note using 'raw' instead comment (bad me).  The 'guess' part can be changed to something else (such as a small table for limited ranges).

Another thing to note is for renormalizing vectors, quaternions, etc. ... the guessed value is '1' and normally a single N-R step will commonly give you the renormalization multiplier. (edit: I'm pretty sure I have a better method for refining than N-R, post here if you'd like me to try to dig it up:  Kahan-Ng refinement).

(edit: many typos)