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  sqrt(x) and 1/sqrt(x)  (Read 3058 times)
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Offline Roquen
« Posted 2009-08-08 16:37:36 »

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)
 }
Offline woogley
« Reply #1 - Posted 2009-08-08 19:45:26 »

Here's some background on how this technique works: http://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/
Offline DzzD
« Reply #2 - Posted 2009-08-08 19:57:32 »

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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Offline Riven
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« Reply #3 - Posted 2009-08-08 20:37:39 »

replace
Float.floatToIntBits()

by
Float.floatToRawIntBits()

maybe it speeds up the 'conversion'

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Offline Roquen
« Reply #4 - Posted 2009-08-08 20:46:54 »

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)
Offline Roquen
« Reply #5 - Posted 2009-08-08 21:07:20 »

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)
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