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 // Copyright (c) 2012 Leonhard Gruenschloss (leonhard@gruenschloss.org)
 //
 // Permission is hereby granted, free of charge, to any person obtaining a copy
 // of this software and associated documentation files (the "Software"), to deal
 // in the Software without restriction, including without limitation the rights to
 // use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
 // of the Software, and to permit persons to whom the Software is furnished to do
 // so, subject to the following conditions:
 //
 // The above copyright notice and this permission notice shall be included in
 // all copies or substantial portions of the Software.
 //
 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 // SOFTWARE.
 
 #ifndef _OpenGl_HaltonSampler_H
 #define _OpenGl_HaltonSampler_H
 
 #include <vector>
 
 //! Compute points of the Halton sequence with digit-permutations for different bases.
 class OpenGl_HaltonSampler
 {
 public:
 
   //! Return the number of supported dimensions.
   static unsigned get_num_dimensions() { return 3u; }
 
 public:
 
   //! Init the permutation arrays using Faure-permutations.
   OpenGl_HaltonSampler()
   {
     initFaure();
   }
 
   //! Return the Halton sample for the given dimension (component) and index.
   //! The client must have called initFaure() at least once before.
   //! dimension must be smaller than the value returned by get_num_dimensions().
   float sample (unsigned theDimension, unsigned theIndex) const
   {
     switch (theDimension)
     {
       case 0: return halton2 (theIndex);
       case 1: return halton3 (theIndex);
       case 2: return halton5 (theIndex);
     }
     return 0.0f;
   }
 
 private:
 
   //! Init the permutation arrays using Faure-permutations.
   void initFaure();
 
   static unsigned short invert (unsigned short theBase, unsigned short theDigits,
                                 unsigned short theIndex, const std::vector<unsigned short>& thePerm)
   {
     unsigned short aResult = 0;
     for (unsigned short i = 0; i < theDigits; ++i)
     {
       aResult = aResult * theBase + thePerm[theIndex % theBase];
       theIndex /= theBase;
     }
     return aResult;
   }
 
   void initTables (const std::vector<std::vector<unsigned short> >& thePerm)
   {
     for (unsigned short i = 0; i < 243; ++i)
     {
       myPerm3[i] = invert (3, 5, i, thePerm[3]);
     }
     for (unsigned short i = 0; i < 125; ++i)
     {
       myPerm5[i] = invert (5, 3, i, thePerm[5]);
     }
   }
 
   //! Special case: radical inverse in base 2, with direct bit reversal.
   float halton2 (unsigned theIndex) const
   {
     theIndex = (theIndex << 16) | (theIndex >> 16);
     theIndex = ((theIndex & 0x00ff00ff) << 8) | ((theIndex & 0xff00ff00) >> 8);
     theIndex = ((theIndex & 0x0f0f0f0f) << 4) | ((theIndex & 0xf0f0f0f0) >> 4);
     theIndex = ((theIndex & 0x33333333) << 2) | ((theIndex & 0xcccccccc) >> 2);
     theIndex = ((theIndex & 0x55555555) << 1) | ((theIndex & 0xaaaaaaaa) >> 1);
     union Result { unsigned u; float f; } aResult; // Write reversed bits directly into floating-point mantissa.
     aResult.u = 0x3f800000u | (theIndex >> 9);
     return aResult.f - 1.0f;
   }
 
   float halton3 (unsigned theIndex) const
   {
     return (myPerm3[theIndex % 243u] * 14348907u
           + myPerm3[(theIndex / 243u)      % 243u] * 59049u
           + myPerm3[(theIndex / 59049u)    % 243u] * 243u
           + myPerm3[(theIndex / 14348907u) % 243u]) * float(0.999999999999999 / 3486784401u); // Results in [0,1).
   }
 
   float halton5 (unsigned theIndex) const
   {
     return (myPerm5[theIndex % 125u] * 1953125u
           + myPerm5[(theIndex / 125u)     % 125u] * 15625u
           + myPerm5[(theIndex / 15625u)   % 125u] * 125u
           + myPerm5[(theIndex / 1953125u) % 125u]) * float(0.999999999999999 / 244140625u); // Results in [0,1).
   }
 
 private:
 
   unsigned short myPerm3[243];
   unsigned short myPerm5[125];
 
 };
 
 inline void OpenGl_HaltonSampler::initFaure()
 {
   const unsigned THE_MAX_BASE = 5u;
   std::vector<std::vector<unsigned short> > aPerms(THE_MAX_BASE + 1);
   for (unsigned k = 1; k <= 3; ++k) // Keep identity permutations for base 1, 2, 3.
   {
     aPerms[k].resize(k);
     for (unsigned i = 0; i < k; ++i)
     {
       aPerms[k][i] = static_cast<unsigned short> (i);
     }
   }
 
   for (unsigned aBase = 4; aBase <= THE_MAX_BASE; ++aBase)
   {
     aPerms[aBase].resize(aBase);
     const unsigned b = aBase / 2;
     if (aBase & 1) // odd
     {
       for (unsigned i = 0; i < aBase - 1; ++i)
       {
         aPerms[aBase][i + (i >= b)] = aPerms[aBase - 1][i] + (aPerms[aBase - 1][i] >= b);
       }
       aPerms[aBase][b] = static_cast<unsigned short> (b);
     }
     else // even
     {
       for (unsigned i = 0; i < b; ++i)
       {
         aPerms[aBase][i]     = 2 * aPerms[b][i];
         aPerms[aBase][b + i] = 2 * aPerms[b][i] + 1;
       }
     }
   }
   initTables (aPerms);
 }
 
 #endif // _OpenGl_HaltonSampler_H

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