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cuda-samples/Samples/2_Concepts_and_Techniques/interval/cuda_interval_lib.h
Rutwik Choughule 2e41896e1b add and update samples for CUDA 11.6
2022-01-13 11:35:24 +05:30

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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 CUDA_INTERVAL_LIB_H
#define CUDA_INTERVAL_LIB_H
#include "cuda_interval_rounded_arith.h"
// Interval template class and basic operations
// Interface inspired from the Boost Interval library (www.boost.org)
template <class T>
class interval_gpu {
public:
__device__ __host__ interval_gpu();
__device__ __host__ interval_gpu(T const &v);
__device__ __host__ interval_gpu(T const &l, T const &u);
__device__ __host__ T const &lower() const;
__device__ __host__ T const &upper() const;
static __device__ __host__ interval_gpu empty();
private:
T low;
T up;
};
// Constructors
template <class T>
inline __device__ __host__ interval_gpu<T>::interval_gpu() {}
template <class T>
inline __device__ __host__ interval_gpu<T>::interval_gpu(T const &l, T const &u)
: low(l), up(u) {}
template <class T>
inline __device__ __host__ interval_gpu<T>::interval_gpu(T const &v)
: low(v), up(v) {}
template <class T>
inline __device__ __host__ T const &interval_gpu<T>::lower() const {
return low;
}
template <class T>
inline __device__ __host__ T const &interval_gpu<T>::upper() const {
return up;
}
template <class T>
inline __device__ __host__ interval_gpu<T> interval_gpu<T>::empty() {
rounded_arith<T> rnd;
return interval_gpu<T>(rnd.nan(), rnd.nan());
}
template <class T>
inline __device__ __host__ bool empty(interval_gpu<T> x) {
T hash = x.lower() + x.upper();
return (hash != hash);
}
template <class T>
inline __device__ T width(interval_gpu<T> x) {
if (empty(x)) return 0;
rounded_arith<T> rnd;
return rnd.sub_up(x.upper(), x.lower());
}
// Arithmetic operations
// Unary operators
template <class T>
inline __device__ interval_gpu<T> const &operator+(interval_gpu<T> const &x) {
return x;
}
template <class T>
inline __device__ interval_gpu<T> operator-(interval_gpu<T> const &x) {
return interval_gpu<T>(-x.upper(), -x.lower());
}
// Binary operators
template <class T>
inline __device__ interval_gpu<T> operator+(interval_gpu<T> const &x,
interval_gpu<T> const &y) {
rounded_arith<T> rnd;
return interval_gpu<T>(rnd.add_down(x.lower(), y.lower()),
rnd.add_up(x.upper(), y.upper()));
}
template <class T>
inline __device__ interval_gpu<T> operator-(interval_gpu<T> const &x,
interval_gpu<T> const &y) {
rounded_arith<T> rnd;
return interval_gpu<T>(rnd.sub_down(x.lower(), y.upper()),
rnd.sub_up(x.upper(), y.lower()));
}
inline __device__ float min4(float a, float b, float c, float d) {
return fminf(fminf(a, b), fminf(c, d));
}
inline __device__ float max4(float a, float b, float c, float d) {
return fmaxf(fmaxf(a, b), fmaxf(c, d));
}
inline __device__ double min4(double a, double b, double c, double d) {
return fmin(fmin(a, b), fmin(c, d));
}
inline __device__ double max4(double a, double b, double c, double d) {
return fmax(fmax(a, b), fmax(c, d));
}
template <class T>
inline __device__ interval_gpu<T> operator*(interval_gpu<T> const &x,
interval_gpu<T> const &y) {
// Textbook implementation: 14 flops, but no branch.
rounded_arith<T> rnd;
return interval_gpu<T>(
min4(rnd.mul_down(x.lower(), y.lower()),
rnd.mul_down(x.lower(), y.upper()),
rnd.mul_down(x.upper(), y.lower()),
rnd.mul_down(x.upper(), y.upper())),
max4(rnd.mul_up(x.lower(), y.lower()), rnd.mul_up(x.lower(), y.upper()),
rnd.mul_up(x.upper(), y.lower()), rnd.mul_up(x.upper(), y.upper())));
}
// Center of an interval
// Typically used for bisection
template <class T>
inline __device__ T median(interval_gpu<T> const &x) {
rounded_arith<T> rnd;
return rnd.median(x.lower(), x.upper());
}
// Intersection between two intervals (can be empty)
template <class T>
inline __device__ interval_gpu<T> intersect(interval_gpu<T> const &x,
interval_gpu<T> const &y) {
rounded_arith<T> rnd;
T const &l = rnd.max(x.lower(), y.lower());
T const &u = rnd.min(x.upper(), y.upper());
if (l <= u)
return interval_gpu<T>(l, u);
else
return interval_gpu<T>::empty();
}
// Division by an interval which does not contain 0.
// GPU-optimized implementation assuming division is expensive
template <class T>
inline __device__ interval_gpu<T> div_non_zero(interval_gpu<T> const &x,
interval_gpu<T> const &y) {
rounded_arith<T> rnd;
typedef interval_gpu<T> I;
T xl, yl, xu, yu;
if (y.upper() < 0) {
xl = x.upper();
xu = x.lower();
} else {
xl = x.lower();
xu = x.upper();
}
if (x.upper() < 0) {
yl = y.lower();
yu = y.upper();
} else if (x.lower() < 0) {
if (y.upper() < 0) {
yl = y.upper();
yu = y.upper();
} else {
yl = y.lower();
yu = y.lower();
}
} else {
yl = y.upper();
yu = y.lower();
}
return I(rnd.div_down(xl, yl), rnd.div_up(xu, yu));
}
template <class T>
inline __device__ interval_gpu<T> div_positive(interval_gpu<T> const &x,
T const &yu) {
// assert(yu > 0);
if (x.lower() == 0 && x.upper() == 0) return x;
rounded_arith<T> rnd;
typedef interval_gpu<T> I;
const T &xl = x.lower();
const T &xu = x.upper();
if (xu < 0)
return I(rnd.neg_inf(), rnd.div_up(xu, yu));
else if (xl < 0)
return I(rnd.neg_inf(), rnd.pos_inf());
else
return I(rnd.div_down(xl, yu), rnd.pos_inf());
}
template <class T>
inline __device__ interval_gpu<T> div_negative(interval_gpu<T> const &x,
T const &yl) {
// assert(yu > 0);
if (x.lower() == 0 && x.upper() == 0) return x;
rounded_arith<T> rnd;
typedef interval_gpu<T> I;
const T &xl = x.lower();
const T &xu = x.upper();
if (xu < 0)
return I(rnd.div_down(xu, yl), rnd.pos_inf());
else if (xl < 0)
return I(rnd.neg_inf(), rnd.pos_inf());
else
return I(rnd.neg_inf(), rnd.div_up(xl, yl));
}
template <class T>
inline __device__ interval_gpu<T> div_zero_part1(interval_gpu<T> const &x,
interval_gpu<T> const &y,
bool &b) {
if (x.lower() == 0 && x.upper() == 0) {
b = false;
return x;
}
rounded_arith<T> rnd;
typedef interval_gpu<T> I;
const T &xl = x.lower();
const T &xu = x.upper();
const T &yl = y.lower();
const T &yu = y.upper();
if (xu < 0) {
b = true;
return I(rnd.neg_inf(), rnd.div_up(xu, yu));
} else if (xl < 0) {
b = false;
return I(rnd.neg_inf(), rnd.pos_inf());
} else {
b = true;
return I(rnd.neg_inf(), rnd.div_up(xl, yl));
}
}
template <class T>
inline __device__ interval_gpu<T> div_zero_part2(interval_gpu<T> const &x,
interval_gpu<T> const &y) {
rounded_arith<T> rnd;
typedef interval_gpu<T> I;
const T &xl = x.lower();
const T &xu = x.upper();
const T &yl = y.lower();
const T &yu = y.upper();
if (xu < 0)
return I(rnd.div_down(xu, yl), rnd.pos_inf());
else
return I(rnd.div_down(xl, yu), rnd.pos_inf());
}
template <class T>
inline __device__ interval_gpu<T> division_part1(interval_gpu<T> const &x,
interval_gpu<T> const &y,
bool &b) {
b = false;
if (y.lower() <= 0 && y.upper() >= 0)
if (y.lower() != 0)
if (y.upper() != 0)
return div_zero_part1(x, y, b);
else
return div_negative(x, y.lower());
else if (y.upper() != 0)
return div_positive(x, y.upper());
else
return interval_gpu<T>::empty();
else
return div_non_zero(x, y);
}
template <class T>
inline __device__ interval_gpu<T> division_part2(interval_gpu<T> const &x,
interval_gpu<T> const &y,
bool b = true) {
if (!b) return interval_gpu<T>::empty();
return div_zero_part2(x, y);
}
template <class T>
inline __device__ interval_gpu<T> square(interval_gpu<T> const &x) {
typedef interval_gpu<T> I;
rounded_arith<T> rnd;
const T &xl = x.lower();
const T &xu = x.upper();
if (xl >= 0)
return I(rnd.mul_down(xl, xl), rnd.mul_up(xu, xu));
else if (xu <= 0)
return I(rnd.mul_down(xu, xu), rnd.mul_up(xl, xl));
else
return I(static_cast<T>(0),
rnd.max(rnd.mul_up(xl, xl), rnd.mul_up(xu, xu)));
}
#endif
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