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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.
*/
/*
* Portions Copyright (c) 2009 Mike Giles, Oxford University. All rights
* reserved.
* Portions Copyright (c) 2008 Frances Y. Kuo and Stephen Joe. All rights
* reserved.
*
* Sobol Quasi-random Number Generator example
*
* Based on CUDA code submitted by Mike Giles, Oxford University, United Kingdom
* http://people.maths.ox.ac.uk/~gilesm/
*
* and C code developed by Stephen Joe, University of Waikato, New Zealand
* and Frances Kuo, University of New South Wales, Australia
* http://web.maths.unsw.edu.au/~fkuo/sobol/
*
* For theoretical background see:
*
* P. Bratley and B.L. Fox.
* Implementing Sobol's quasirandom sequence generator
* http://portal.acm.org/citation.cfm?id=42288
* ACM Trans. on Math. Software, 14(1):88-100, 1988
*
* S. Joe and F. Kuo.
* Remark on algorithm 659: implementing Sobol's quasirandom sequence generator.
* http://portal.acm.org/citation.cfm?id=641879
* ACM Trans. on Math. Software, 29(1):49-57, 2003
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include "sobol.h"
#include "sobol_gold.h"
#include "sobol_primitives.h"
#define k_2powneg32 2.3283064E-10F
// Windows does not provide ffs (find first set) so here is a
// fairly simple implementation.
// WIN32 is defined on 32 and 64 bit Windows
#if defined(WIN32) || defined(_WIN32) || defined(WIN64) || defined(_WIN64)
int ffs(const unsigned int &i) {
unsigned int v = i;
unsigned int count;
if (!v) {
count = 0;
} else {
count = 2;
if ((v & 0xffff) == 0) {
v >>= 16;
count += 16;
}
if ((v & 0xff) == 0) {
v >>= 8;
count += 8;
}
if ((v & 0xf) == 0) {
v >>= 4;
count += 4;
}
if ((v & 0x3) == 0) {
v >>= 2;
count += 2;
}
count -= v & 0x1;
}
return count;
}
#endif
// Create the direction numbers, based on the primitive polynomials.
void initSobolDirectionVectors(int n_dimensions, unsigned int *directions) {
unsigned int *v = directions;
for (int dim = 0; dim < n_dimensions; dim++) {
// First dimension is a special case
if (dim == 0) {
for (int i = 0; i < n_directions; i++) {
// All m's are 1
v[i] = 1 << (31 - i);
}
} else {
int d = sobol_primitives[dim].degree;
// The first direction numbers (up to the degree of the polynomial)
// are simply v[i] = m[i] / 2^i (stored in Q0.32 format)
for (int i = 0; i < d; i++) {
v[i] = sobol_primitives[dim].m[i] << (31 - i);
}
// The remaining direction numbers are computed as described in
// the Bratley and Fox paper.
// v[i] = a[1]v[i-1] ^ a[2]v[i-2] ^ ... ^ a[v-1]v[i-d+1] ^ v[i-d] ^
// v[i-d]/2^d
for (int i = d; i < n_directions; i++) {
// First do the v[i-d] ^ v[i-d]/2^d part
v[i] = v[i - d] ^ (v[i - d] >> d);
// Now do the a[1]v[i-1] ^ a[2]v[i-2] ^ ... part
// Note that the coefficients a[] are zero or one and for compactness in
// the input tables they are stored as bits of a single integer. To
// extract the relevant bit we use right shift and mask with 1.
// For example, for a 10 degree polynomial there are ten useful bits in
// a, so to get a[2] we need to right shift 7 times (to get the 8th bit
// into the LSB) and then mask with 1.
for (int j = 1; j < d; j++) {
v[i] ^= (((sobol_primitives[dim].a >> (d - 1 - j)) & 1) * v[i - j]);
}
}
}
v += n_directions;
}
}
// Reference model for generating Sobol numbers on the host
void sobolCPU(int n_vectors, int n_dimensions, unsigned int *directions,
float *output) {
unsigned int *v = directions;
for (int d = 0; d < n_dimensions; d++) {
unsigned int X = 0;
// x[0] is zero (in all dimensions)
output[n_vectors * d] = 0.0;
for (int i = 1; i < n_vectors; i++) {
// x[i] = x[i-1] ^ v[c]
// where c is the index of the rightmost zero bit in i
// minus 1 (since C arrays count from zero)
// In the Bratley and Fox paper this is equation (**)
X ^= v[ffs(~(i - 1)) - 1];
output[i + n_vectors * d] = (float)X * k_2powneg32;
}
v += n_directions;
}
}
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