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/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of NVIDIA CORPORATION nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef QUASIRANDOMGENERATOR_KERNEL_CUH
#define QUASIRANDOMGENERATOR_KERNEL_CUH
#include <stdio.h>
#include <stdlib.h>
#include <helper_cuda.h>
#include "quasirandomGenerator_common.h"
// Fast integer multiplication
#define MUL(a, b) __umul24(a, b)
////////////////////////////////////////////////////////////////////////////////
// Niederreiter quasirandom number generation kernel
////////////////////////////////////////////////////////////////////////////////
static __constant__ unsigned int c_Table[QRNG_DIMENSIONS][QRNG_RESOLUTION];
static __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;
}
}
// Table initialization routine
extern "C" void initTableGPU(
unsigned int tableCPU[QRNG_DIMENSIONS][QRNG_RESOLUTION]) {
checkCudaErrors(cudaMemcpyToSymbol(
c_Table, tableCPU,
QRNG_DIMENSIONS * QRNG_RESOLUTION * sizeof(unsigned int)));
}
// Host-side interface
extern "C" void quasirandomGeneratorGPU(float *d_Output, unsigned int seed,
unsigned int N) {
dim3 threads(128, QRNG_DIMENSIONS);
quasirandomGeneratorKernel<<<128, threads>>>(d_Output, seed, N);
getLastCudaError("quasirandomGeneratorKernel() execution failed.\n");
}
////////////////////////////////////////////////////////////////////////////////
// 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
////////////////////////////////////////////////////////////////////////////////
static __global__ void inverseCNDKernel(float *d_Output, unsigned int *d_Input,
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 (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);
}
}
}
extern "C" void inverseCNDgpu(float *d_Output, unsigned int *d_Input,
unsigned int N) {
inverseCNDKernel<<<128, 128>>>(d_Output, d_Input, N);
getLastCudaError("inverseCNDKernel() execution failed.\n");
}
#endif
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