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229 lines
8.9 KiB
Plaintext
229 lines
8.9 KiB
Plaintext
/* Copyright (c) 2022, 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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/* Determine eigenvalues for small symmetric, tridiagonal matrix */
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#ifndef _BISECT_KERNEL_SMALL_H_
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#define _BISECT_KERNEL_SMALL_H_
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#include <cooperative_groups.h>
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namespace cg = cooperative_groups;
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// includes, project
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#include "config.h"
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#include "util.h"
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// additional kernel
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#include "bisect_util.cu"
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////////////////////////////////////////////////////////////////////////////////
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//! Bisection to find eigenvalues of a real, symmetric, and tridiagonal matrix
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//! @param g_d diagonal elements in global memory
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//! @param g_s superdiagonal elements in global elements (stored so that the
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//! element *(g_s - 1) can be accessed an equals 0
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//! @param n size of matrix
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//! @param lg lower bound of input interval (e.g. Gerschgorin interval)
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//! @param ug upper bound of input interval (e.g. Gerschgorin interval)
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//! @param lg_eig_count number of eigenvalues that are smaller than \a lg
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//! @param lu_eig_count number of eigenvalues that are smaller than \a lu
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//! @param epsilon desired accuracy of eigenvalues to compute
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////////////////////////////////////////////////////////////////////////////////
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__global__ void bisectKernel(float *g_d, float *g_s, const unsigned int n,
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float *g_left, float *g_right,
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unsigned int *g_left_count,
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unsigned int *g_right_count, const float lg,
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const float ug, const unsigned int lg_eig_count,
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const unsigned int ug_eig_count, float epsilon) {
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// Handle to thread block group
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cg::thread_block cta = cg::this_thread_block();
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// intervals (store left and right because the subdivision tree is in general
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// not dense
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__shared__ float s_left[MAX_THREADS_BLOCK_SMALL_MATRIX];
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__shared__ float s_right[MAX_THREADS_BLOCK_SMALL_MATRIX];
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// number of eigenvalues that are smaller than s_left / s_right
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// (correspondence is realized via indices)
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__shared__ unsigned int s_left_count[MAX_THREADS_BLOCK_SMALL_MATRIX];
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__shared__ unsigned int s_right_count[MAX_THREADS_BLOCK_SMALL_MATRIX];
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// helper for stream compaction
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__shared__ unsigned int s_compaction_list[MAX_THREADS_BLOCK_SMALL_MATRIX + 1];
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// state variables for whole block
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// if 0 then compaction of second chunk of child intervals is not necessary
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// (because all intervals had exactly one non-dead child)
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__shared__ unsigned int compact_second_chunk;
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__shared__ unsigned int all_threads_converged;
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// number of currently active threads
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__shared__ unsigned int num_threads_active;
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// number of threads to use for stream compaction
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__shared__ unsigned int num_threads_compaction;
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// helper for exclusive scan
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unsigned int *s_compaction_list_exc = s_compaction_list + 1;
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// variables for currently processed interval
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// left and right limit of active interval
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float left = 0.0f;
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float right = 0.0f;
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unsigned int left_count = 0;
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unsigned int right_count = 0;
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// midpoint of active interval
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float mid = 0.0f;
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// number of eigenvalues smaller then mid
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unsigned int mid_count = 0;
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// affected from compaction
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unsigned int is_active_second = 0;
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s_compaction_list[threadIdx.x] = 0;
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s_left[threadIdx.x] = 0;
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s_right[threadIdx.x] = 0;
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s_left_count[threadIdx.x] = 0;
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s_right_count[threadIdx.x] = 0;
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cg::sync(cta);
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// set up initial configuration
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if (0 == threadIdx.x) {
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s_left[0] = lg;
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s_right[0] = ug;
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s_left_count[0] = lg_eig_count;
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s_right_count[0] = ug_eig_count;
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compact_second_chunk = 0;
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num_threads_active = 1;
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num_threads_compaction = 1;
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}
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// for all active threads read intervals from the last level
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// the number of (worst case) active threads per level l is 2^l
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while (true) {
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all_threads_converged = 1;
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cg::sync(cta);
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is_active_second = 0;
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subdivideActiveInterval(threadIdx.x, s_left, s_right, s_left_count,
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s_right_count, num_threads_active, left, right,
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left_count, right_count, mid,
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all_threads_converged);
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cg::sync(cta);
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// check if done
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if (1 == all_threads_converged) {
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break;
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}
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cg::sync(cta);
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// compute number of eigenvalues smaller than mid
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// use all threads for reading the necessary matrix data from global
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// memory
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// use s_left and s_right as scratch space for diagonal and
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// superdiagonal of matrix
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mid_count = computeNumSmallerEigenvals(g_d, g_s, n, mid, threadIdx.x,
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num_threads_active, s_left, s_right,
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(left == right), cta);
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cg::sync(cta);
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// store intervals
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// for all threads store the first child interval in a continuous chunk of
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// memory, and the second child interval -- if it exists -- in a second
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// chunk; it is likely that all threads reach convergence up to
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// \a epsilon at the same level; furthermore, for higher level most / all
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// threads will have only one child, storing the first child compactly will
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// (first) avoid to perform a compaction step on the first chunk, (second)
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// make it for higher levels (when all threads / intervals have
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// exactly one child) unnecessary to perform a compaction of the second
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// chunk
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if (threadIdx.x < num_threads_active) {
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if (left != right) {
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// store intervals
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storeNonEmptyIntervals(threadIdx.x, num_threads_active, s_left, s_right,
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s_left_count, s_right_count, left, mid, right,
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left_count, mid_count, right_count, epsilon,
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compact_second_chunk, s_compaction_list_exc,
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is_active_second);
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} else {
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storeIntervalConverged(
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s_left, s_right, s_left_count, s_right_count, left, mid, right,
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left_count, mid_count, right_count, s_compaction_list_exc,
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compact_second_chunk, num_threads_active, is_active_second);
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}
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}
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// necessary so that compact_second_chunk is up-to-date
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cg::sync(cta);
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// perform compaction of chunk where second children are stored
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// scan of (num_threads_active / 2) elements, thus at most
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// (num_threads_active / 4) threads are needed
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if (compact_second_chunk > 0) {
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createIndicesCompaction(s_compaction_list_exc, num_threads_compaction,
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cta);
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compactIntervals(s_left, s_right, s_left_count, s_right_count, mid, right,
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mid_count, right_count, s_compaction_list,
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num_threads_active, is_active_second);
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}
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cg::sync(cta);
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if (0 == threadIdx.x) {
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// update number of active threads with result of reduction
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num_threads_active += s_compaction_list[num_threads_active];
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num_threads_compaction = ceilPow2(num_threads_active);
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compact_second_chunk = 0;
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}
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cg::sync(cta);
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}
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cg::sync(cta);
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// write resulting intervals to global mem
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// for all threads write if they have been converged to an eigenvalue to
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// a separate array
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// at most n valid intervals
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if (threadIdx.x < n) {
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// intervals converged so left and right limit are identical
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g_left[threadIdx.x] = s_left[threadIdx.x];
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// left count is sufficient to have global order
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g_left_count[threadIdx.x] = s_left_count[threadIdx.x];
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}
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}
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#endif // #ifndef _BISECT_KERNEL_SMALL_H_
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