mirror of
https://github.com/NVIDIA/cuda-samples.git
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308 lines
9.2 KiB
C++
308 lines
9.2 KiB
C++
/* Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* * Neither the name of NVIDIA CORPORATION nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
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* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/* Simple CPU implementation
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* Depends on Boost.Interval
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*/
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#ifndef CPU_INTERVAL_H
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#define CPU_INTERVAL_H
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#ifndef __USE_ISOC99
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#define __USE_ISOC99
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#endif
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#include <iostream>
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#include <vector>
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#include <boost/numeric/interval.hpp>
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//#include <iomanip>
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#define UNPROTECTED 0
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#define USE_RECURSION_CPU 1
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using boost::numeric::interval;
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using namespace boost::numeric;
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template <class T, int N, int THREADS>
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class global_stack_cpu {
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private:
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T *buf;
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int free_index;
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public:
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// buf should point to an allocated global buffer of size N * THREADS *
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// sizeof(T)
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global_stack_cpu(T *buf, int thread_id) : buf(buf), free_index(thread_id) {}
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void push(T const &v) {
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buf[free_index] = v;
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free_index += THREADS;
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}
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T pop() {
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free_index -= THREADS;
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return buf[free_index];
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}
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bool full() { return free_index >= N * THREADS; }
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bool empty() { return free_index < THREADS; }
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int size() { return free_index / THREADS; }
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};
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// The function F of which we want to find roots, defined on intervals
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// Should typically depend on thread_id (indexing an array of coefficients...)
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template <class I>
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I f_cpu(I const &x, int thread_id) {
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typedef typename I::base_type T;
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T alpha = -T(thread_id) / T(THREADS);
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return square(x - I(1)) + I(alpha) * x;
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}
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// First derivative of F, also defined on intervals
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template <class I>
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I fd_cpu(I const &x, int thread_id) {
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typedef typename I::base_type T;
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T alpha = -T(thread_id) / T(THREADS);
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return I(2) * x + I(alpha - 2);
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}
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// Is this interval small enough to stop iterating?
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template <class I>
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bool is_minimal_cpu(I const &x, int thread_id) {
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typedef typename I::base_type T;
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T const epsilon_x = 1e-6f;
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T const epsilon_y = 1e-6f;
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return !empty(x) && (width(x) <= epsilon_x * abs(median(x)) ||
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width(f_cpu(x, thread_id)) <= epsilon_y);
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}
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// In some cases, Newton iterations converge slowly.
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// Bisecting the interval accelerates convergence.
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template <class I>
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bool should_bisect_cpu(I const &x, I const &x1, I const &x2,
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typename I::base_type alpha) {
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typedef typename I::base_type T;
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T wmax = alpha * width(x);
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return width(x1) > wmax || width(x2) > wmax;
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}
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int const DEPTH_WORK = 128;
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// Main interval Newton loop.
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// Keep refining a list of intervals stored in a stack.
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// Always keep the next interval to work on in registers (avoids excessive
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// spilling to local mem)
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template <class I, int THREADS, int DEPTH_RESULT>
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void newton_interval_cpu(global_stack_cpu<I, DEPTH_RESULT, THREADS> &result,
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I const &ix0, int thread_id) {
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typedef typename I::base_type T;
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T const alpha = .99f; // Threshold before switching to bisection
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// Intervals to be processed
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I local_buffer[DEPTH_WORK];
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global_stack_cpu<I, DEPTH_WORK, 1> work(local_buffer, 0);
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// We start with the whole domain
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I ix = ix0;
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while (true) {
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// Compute (x - F({x})/F'(ix)) inter ix
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// -> may yield 0, 1 or 2 intervals
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T x = median(ix);
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I iq = f_cpu(I(x), thread_id);
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I id = fd_cpu(ix, thread_id);
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bool has_part2;
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I part1, part2;
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part1 = division_part1(iq, id, has_part2);
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part1 = intersect(I(x) - part1, ix);
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if (has_part2) {
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part2 = division_part2(iq, id);
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part2 = intersect(I(x) - part2, ix);
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}
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// Do we have small-enough intervals?
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if (is_minimal_cpu(part1, thread_id)) {
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result.push(part1);
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part1 = I::empty();
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}
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if (has_part2 && is_minimal_cpu(part2, thread_id)) {
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result.push(part2);
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part2 = I::empty();
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}
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if (should_bisect_cpu(ix, part1, part2, alpha)) {
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// Not so good improvement
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// Switch to bisection method for this step
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part1 = I(ix.lower(), x);
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part2 = I(x, ix.upper());
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has_part2 = true;
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}
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if ((part1.lower() <= part1.upper()) && !empty(part1)) {
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// At least 1 solution
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// We will compute part1 next
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ix = part1;
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if (has_part2 && !empty(part2)) {
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// 2 solutions
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// Save the second solution for later
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work.push(part2);
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}
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} else if (has_part2 && !empty(part2)) {
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// 1 solution
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// Work on that next
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ix = part2;
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} else {
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// No solution
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// Do we still have work to do in the stack?
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if (work.empty()) // If not, we are done
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break;
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else
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ix = work.pop(); // Otherwise, pick an interval to work on
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}
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}
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}
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template <class I, int THREADS, int DEPTH_RESULT>
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void newton_interval_rec_cpu(global_stack_cpu<I, DEPTH_RESULT, THREADS> &result,
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I const &ix, int thread_id) {
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typedef typename I::base_type T;
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T const alpha = .99f; // Threshold before switching to bisection
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if (is_minimal_cpu(ix, thread_id)) {
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result.push(ix);
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return;
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}
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// Compute (x - F({x})/F'(ix)) inter ix
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// -> may yield 0, 1 or 2 intervals
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T x = median(ix);
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I iq = f_cpu(I(x), thread_id);
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I id = fd_cpu(ix, thread_id);
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bool has_part2;
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I part1, part2;
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part1 = division_part1(iq, id, has_part2);
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part1 = intersect(I(x) - part1, ix);
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if (has_part2) {
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part2 = division_part2(iq, id);
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part2 = intersect(I(x) - part2, ix);
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}
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if (should_bisect_cpu(ix, part1, part2, alpha)) {
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// Not so good improvement
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// Switch to bisection method for this step
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part1 = I(ix.lower(), x);
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part2 = I(x, ix.upper());
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has_part2 = true;
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}
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if ((part1.lower() <= part1.upper()) && (!empty(part1))) {
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newton_interval_rec_cpu<I, THREADS, DEPTH_RESULT>(result, part1, thread_id);
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}
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if (has_part2 && !empty(part2)) {
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newton_interval_rec_cpu<I, THREADS, DEPTH_RESULT>(result, part2, thread_id);
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}
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}
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template <class I>
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void test_interval_newton_cpu(I *buffer, int *nresults, I i) {
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typedef typename I::base_type T;
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// Intervals to return
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// std::vector<I> local_buffer(BLOCK_SIZE * GRID_SIZE * DEPTH_WORK);
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for (int thread_id = 0; thread_id != BLOCK_SIZE * GRID_SIZE; ++thread_id) {
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global_stack_cpu<I, DEPTH_RESULT, THREADS> result(buffer, thread_id);
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#if USE_RECURSION_CPU
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newton_interval_rec_cpu<I, THREADS>(result, i, thread_id);
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#else
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newton_interval_cpu<I, THREADS>(result, i, thread_id);
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#endif
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nresults[thread_id] = result.size();
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}
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}
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typedef interval<T, interval_lib::policies<interval_lib::rounded_math<T>,
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interval_lib::checking_base<T> > >
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Ibase;
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#if UNPROTECTED
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typedef interval_lib::unprotect<Ibase>::type I_CPU;
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Ibase::traits_type::rounding rnd;
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#else
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typedef Ibase I_CPU;
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#endif
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bool checkAgainstHost(int *h_nresults, int *h_nresults_cpu, I_CPU *h_result,
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I_CPU *h_result_cpu) {
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std::cout << "\nCheck against Host computation...\n\n";
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int success = 1;
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int success1 = 1;
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int success2 = 1;
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if (h_nresults_cpu[0] == h_nresults[0]) {
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for (int i = 0; i != h_nresults[0]; ++i) {
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TYPE diff1 = abs(h_result[THREADS * i + 0].lower() -
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h_result_cpu[THREADS * i + 0].lower());
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TYPE diff2 = abs(h_result[THREADS * i + 0].upper() -
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h_result_cpu[THREADS * i + 0].upper());
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if ((diff1 > 1.0e-6f) || (diff2 > 1.0e-6f)) {
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success1 = 0;
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break;
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}
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}
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// in case the two intervals are reversed
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for (int i = 0; i != h_nresults[0]; ++i) {
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TYPE diff1 =
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abs(h_result[THREADS * i + 0].lower() -
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h_result_cpu[THREADS * (h_nresults[0] - i - 1) + 0].lower());
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TYPE diff2 =
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abs(h_result[THREADS * i + 0].upper() -
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h_result_cpu[THREADS * (h_nresults[0] - i - 1) + 0].upper());
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if ((diff1 > 1.0e-6f) || (diff2 > 1.0e-6f)) {
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success2 = 0;
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break;
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}
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}
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success = success1 || success2;
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} else
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success = 0;
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return (bool)success;
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}
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#endif
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