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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.
*/
/* Determine eigenvalues for large matrices for intervals that contained after
* the first step one eigenvalue
*/
#ifndef _BISECT_KERNEL_LARGE_ONEI_H_
#define _BISECT_KERNEL_LARGE_ONEI_H_
#include <cooperative_groups.h>
namespace cg = cooperative_groups;
// includes, project
#include "config.h"
#include "util.h"
// additional kernel
#include "bisect_util.cu"
////////////////////////////////////////////////////////////////////////////////
//! Determine eigenvalues for large matrices for intervals that after
//! the first step contained one eigenvalue
//! @param g_d diagonal elements of symmetric, tridiagonal matrix
//! @param g_s superdiagonal elements of symmetric, tridiagonal matrix
//! @param n matrix size
//! @param num_intervals total number of intervals containing one eigenvalue
//! after the first step
//! @param g_left left interval limits
//! @param g_right right interval limits
//! @param g_pos index of interval / number of intervals that are smaller than
//! right interval limit
//! @param precision desired precision of eigenvalues
////////////////////////////////////////////////////////////////////////////////
__global__ void bisectKernelLarge_OneIntervals(
float *g_d, float *g_s, const unsigned int n, unsigned int num_intervals,
float *g_left, float *g_right, unsigned int *g_pos, float precision) {
// Handle to thread block group
cg::thread_block cta = cg::this_thread_block();
const unsigned int gtid = (blockDim.x * blockIdx.x) + threadIdx.x;
__shared__ float s_left_scratch[MAX_THREADS_BLOCK];
__shared__ float s_right_scratch[MAX_THREADS_BLOCK];
// active interval of thread
// left and right limit of current interval
float left, right;
// number of threads smaller than the right limit (also corresponds to the
// global index of the eigenvalues contained in the active interval)
unsigned int right_count;
// flag if current thread converged
unsigned int converged = 0;
// midpoint when current interval is subdivided
float mid = 0.0f;
// number of eigenvalues less than mid
unsigned int mid_count = 0;
// read data from global memory
if (gtid < num_intervals) {
left = g_left[gtid];
right = g_right[gtid];
right_count = g_pos[gtid];
}
// flag to determine if all threads converged to eigenvalue
__shared__ unsigned int converged_all_threads;
// initialized shared flag
if (0 == threadIdx.x) {
converged_all_threads = 0;
}
cg::sync(cta);
// process until all threads converged to an eigenvalue
// while( 0 == converged_all_threads) {
while (true) {
atomicExch(&converged_all_threads, 1);
// update midpoint for all active threads
if ((gtid < num_intervals) && (0 == converged)) {
mid = computeMidpoint(left, right);
}
// find number of eigenvalues that are smaller than midpoint
mid_count = computeNumSmallerEigenvalsLarge(
g_d, g_s, n, mid, gtid, num_intervals, s_left_scratch, s_right_scratch,
converged, cta);
cg::sync(cta);
// for all active threads
if ((gtid < num_intervals) && (0 == converged)) {
// udpate intervals -- always one child interval survives
if (right_count == mid_count) {
right = mid;
} else {
left = mid;
}
// check for convergence
float t0 = right - left;
float t1 = max(abs(right), abs(left)) * precision;
if (t0 < min(precision, t1)) {
float lambda = computeMidpoint(left, right);
left = lambda;
right = lambda;
converged = 1;
} else {
atomicExch(&converged_all_threads, 0);
}
}
cg::sync(cta);
if (1 == converged_all_threads) {
break;
}
cg::sync(cta);
}
// write data back to global memory
cg::sync(cta);
if (gtid < num_intervals) {
// intervals converged so left and right interval limit are both identical
// and identical to the eigenvalue
g_left[gtid] = left;
}
}
#endif // #ifndef _BISECT_KERNEL_LARGE_ONEI_H_
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