DSP: Power of Two Approximation

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#1 (In Topic #288)
Cedron
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This is in support of my answer here:  

Fixed point exponentiation

The following program shows how to calculate an approximation of two raised to a float value.  The argument is assumed to be positive.


Code (gambas)

  1. ' Gambas module file
  2.  
  3. Private Lookup_V As New Float[]
  4. Private Lookup_L As New Float[]
  6.  
  7. '========================================================================
  8. Public Sub Main()
  9.  
  10.         Dim v, ev As Float
  11.  
  12.         v = 1 / 32
  13.        
  14.         Do
  15.             ev = Exp(v)
  16.             Lookup_V.Add(v)
  17.             Lookup_L.Add(ev)
  18.             Print v, ev
  19.             v += 1 / 16
  20.         Loop Until ev > 2.0
  21.        
  22.         Ln2 = Log(2)
  23.        
  24.         Print 2 ^ (0.5), Sqr(2.0), TwoToPower(0.5)
  25.  
  27. '========================================================================
  28. Sub TwoToPower(x As Float) As Float
  29.  
  30.         Dim n, bbbb As Integer, f, v, y, ey As Float
  31.  
  32.         n = Int(x)
  33.         f = x - n
  34.         v = Ln2 * f
  35.         bbbb = Int(16 * v)
  36.         y = v - Lookup_V[bbbb]
  37.  
  38.         ey = 1 + y * (1 + y * (1 / 2 + y / 6))
  39.        
  40.         Print y, Exp(y), ey
  41.        
  42.         Return 2 ^ n * Lookup_L[bbbb] * ey
  43.  
  45. '========================================================================
  46.  

Here is the output:

Code

0.03125 1.0317434074991
0.09375 1.09828514030783
0.15625 1.1691184461695
0.21875 1.2445201077661
0.28125 1.32478475872887
0.34375 1.41022603492571
0.40625 1.50117780000012
0.46875 1.59799544995063
0.53125 1.7010573018484
0.59375 1.81076607211939
0.65625 1.92755045016754
0.71875 2.05186677348798
0.002823590279973       1.00282758036558        1.00282758036293
1.4142135623731 1.4142135623731 1.41421356236936
.... and carry a big stick!
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