quasirandomGenerator_kernel.cu

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#ifndef QUASIRANDOMGENERATOR_KERNEL_CUH
#define QUASIRANDOMGENERATOR_KERNEL_CUH

#include "quasirandomGenerator_common.h"

// Fast integer multiplication
#define MUL(a, b) __umul24(a, b)

////////////////////////////////////////////////////////////////////////////////
// Niederreiter quasirandom number generation kernel
////////////////////////////////////////////////////////////////////////////////
__constant__ unsigned int c_Table[QRNG_DIMENSIONS][QRNG_RESOLUTION];

extern "C" __global__ void quasirandomGeneratorKernel(float *d_Output,
                                                      unsigned int seed,
                                                      unsigned int N) {
  unsigned int *dimBase = &c_Table[threadIdx.y][0];
  unsigned int tid = MUL(blockDim.x, blockIdx.x) + threadIdx.x;
  unsigned int threadN = MUL(blockDim.x, gridDim.x);

  for (unsigned int pos = tid; pos < N; pos += threadN) {
    unsigned int result = 0;
    unsigned int data = seed + pos;

    for (int bit = 0; bit < QRNG_RESOLUTION; bit++, data >>= 1)
      if (data & 1) {
        result ^= dimBase[bit];
      }

    d_Output[MUL(threadIdx.y, N) + pos] = (float)(result + 1) * INT_SCALE;
  }
}

////////////////////////////////////////////////////////////////////////////////
// Moro's Inverse Cumulative Normal Distribution function approximation
////////////////////////////////////////////////////////////////////////////////
__device__ inline float MoroInvCNDgpu(unsigned int x) {
  const float a1 = 2.50662823884f;
  const float a2 = -18.61500062529f;
  const float a3 = 41.39119773534f;
  const float a4 = -25.44106049637f;
  const float b1 = -8.4735109309f;
  const float b2 = 23.08336743743f;
  const float b3 = -21.06224101826f;
  const float b4 = 3.13082909833f;
  const float c1 = 0.337475482272615f;
  const float c2 = 0.976169019091719f;
  const float c3 = 0.160797971491821f;
  const float c4 = 2.76438810333863E-02f;
  const float c5 = 3.8405729373609E-03f;
  const float c6 = 3.951896511919E-04f;
  const float c7 = 3.21767881768E-05f;
  const float c8 = 2.888167364E-07f;
  const float c9 = 3.960315187E-07f;

  float z;

  bool negate = false;

  // Ensure the conversion to floating point will give a value in the
  // range (0,0.5] by restricting the input to the bottom half of the
  // input domain. We will later reflect the result if the input was
  // originally in the top half of the input domain
  if (x >= 0x80000000UL) {
    x = 0xffffffffUL - x;
    negate = true;
  }

  // x is now in the range [0,0x80000000) (i.e. [0,0x7fffffff])
  // Convert to floating point in (0,0.5]
  const float x1 = 1.0f / static_cast<float>(0xffffffffUL);
  const float x2 = x1 / 2.0f;
  float p1 = x * x1 + x2;
  // Convert to floating point in (-0.5,0]
  float p2 = p1 - 0.5f;

  // The input to the Moro inversion is p2 which is in the range
  // (-0.5,0]. This means that our output will be the negative side
  // of the bell curve (which we will reflect if "negate" is true).

  // Main body of the bell curve for |p| < 0.42
  if (p2 > -0.42f) {
    z = p2 * p2;
    z = p2 * (((a4 * z + a3) * z + a2) * z + a1) /
        ((((b4 * z + b3) * z + b2) * z + b1) * z + 1.0f);
  }
  // Special case (Chebychev) for tail
  else {
    z = __logf(-__logf(p1));
    z = -(c1 + z * (c2 + z * (c3 + z * (c4 + z * (c5 + z * (c6 + z * 
        (c7 + z * (c8 + z * c9))))))));
  }

  // If the original input (x) was in the top half of the range, reflect
  // to get the positive side of the bell curve

  return negate ? -z : z;
}

////////////////////////////////////////////////////////////////////////////////
// Main kernel. Choose between transforming
// input sequence and uniform ascending (0, 1) sequence
////////////////////////////////////////////////////////////////////////////////

extern "C" __global__ void inverseCNDKernel(float *d_Output,
                                            unsigned int pathN) {
  unsigned int distance = ((unsigned int)-1) / (pathN + 1);
  unsigned int tid = MUL(blockDim.x, blockIdx.x) + threadIdx.x;
  unsigned int threadN = MUL(blockDim.x, gridDim.x);

  // Transform input number sequence if it's supplied
  if (0)  // d_Input)
  {
    /*
      for (unsigned int pos = tid; pos < pathN; pos += threadN)
      {
          unsigned int d = d_Input[pos];
          d_Output[pos] = (float)MoroInvCNDgpu(d);
      }
      */
  }
  // Else generate input uniformly placed samples on the fly
  // and write to destination
  else {
    for (unsigned int pos = tid; pos < pathN; pos += threadN) {
      unsigned int d = (pos + 1) * distance;
      d_Output[pos] = (float)MoroInvCNDgpu(d);
    }
  }
}

#endif