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 sqrt(x) and 1/sqrt(x)  (Read 5542 times) 0 Members and 1 Guest are viewing this topic.
Roquen

JGO Kernel

Medals: 517

 « Posted 2009-08-08 14:37:36 »

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

 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22 `  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
 « Reply #1 - Posted 2009-08-08 17:45:26 »

Here's some background on how this technique works: http://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/
DzzD
 « Reply #2 - Posted 2009-08-08 17:57:32 »

very nice

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

Riven

« JGO Overlord »

Medals: 1339
Projects: 4
Exp: 16 years

 « Reply #3 - Posted 2009-08-08 18:37:39 »

replace
Float.floatToIntBits()

by
Float.floatToRawIntBits()

maybe it speeds up the 'conversion'

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Roquen

JGO Kernel

Medals: 517

 « Reply #4 - Posted 2009-08-08 18:46:54 »

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)
Roquen

JGO Kernel

Medals: 517

 « Reply #5 - Posted 2009-08-08 19:07:20 »

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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