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Berühmter bit-hack-Algorithmus from QUAKE III
to that Invertieren of Quadratwurzeln
... becomes with the Normierung the length of 3D-Vektoren in Single precision float-variables inserted. In Assembler over three time faster as 1/Sqrt() !, Error max. 1 %:

Youtube-Link (engl.): [...]

Computer: Gerät, daß es in Mikrosekunden erlaubt, 50.000 Fehler zu machen, zB 'daß' statt 'das'...

01/03/21 ▲

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« this Posting watts as Solution marked. »

Michael
W.

now Yes, whom should we really emulate can.

there The (Microsoft-)Floats Yes through Single() in a Longint stored go can...

Compile Mark Separation


// Inverse Square Root

// Def !threehalfs 1.5  // or as wirkliche Constant, then as prefix

Proc Q_rsqrt
   Parameters number!
   Declare i&, x2!, y!
   Var threehalfs! = 1.5  // with richtiger Constant becomes these row then removes

   x2! = number! * 0.5
   y!  = number!

   i&  = Single(y!)
   i&  = $5F3759DF - (i& >> 1)
   y!  = double(i&)

   y!  = y! * (threehalfs! - (x2! * y! * y!))  // y! * (threehalfs! - (x2! * Sqr(y!)))
// y!  = y! * (threehalfs! - (x2! * y! * y!))  // y! * (threehalfs! - (x2! * Sqr(y!)))
   Return y!
ENDPROC

I have only To to Formel geschaut.
simply test times.

Alle Sprachen
System: Windows 8/10, XProfan X4
Programmieren, das spannendste Detektivspiel der Welt.

01/06/21 ▲

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p.specht

Mutiger attempt, large THANK YOU!

sees well from:

Compile Mark Separation

// Inverse Square Root
// Def !threehalfs 1.5  // or as wirkliche Constant, then as prefix

Proc Q_rsqrt

    Parameters number!
    Declare i&, x2!, y!
    Var threehalfs! = 1.5// with richtiger Constant becomes these row then removes
    x2! = number! * 0.5
    y!  = number!
    i&  = Single(y!)
    i&  = $5F3759DF - (i& >> 1)
    y!  = double(i&)
    y!  = y! * (threehalfs! - (x2! * y! * y!))// y! * (threehalfs! - (x2! * Sqr(y!)))
    '//y!  = y! * (threehalfs! - (x2! * y! * y!))  // y! * (threehalfs! - (x2! * Sqr(y!)))
    Return y!

ENDPROC

Window Title "Testbench for Michael Wodrichs Quake-Trick"
AppendMenubar 100,"   Testwert           Quake-output          1/Sqrt()         Abs.Error         Rel.Err %"
cls:Set("decimals",7):Print
Declare w!

WhileLoop 1,999999,50:w!=&Loop/100//generiert 5000 Test steps

    Print "  ",w!,Q_rsqrt(w!),1/Sqrt(w!),(Q_rsqrt(w!)-1/Sqrt(w!)),(Abs(Q_rsqrt(w!)-1/Sqrt(w!))/(1/Sqrt(w!)))*100,"%"

    If %csrlin>27:WaitInput 8000:cls:Print:EndIf

    EndWhile

    Print:Print "---":Beep
    WaitInput
    End

Computer: Gerät, daß es in Mikrosekunden erlaubt, 50.000 Fehler zu machen, zB 'daß' statt 'das'...

01/06/21 ▲

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Sven
Bader

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whether it in XProfan objectively faster is have I not yet ausprobiert.

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