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|
//------------------------------------------------------------------------------
// GB_subref_template: C = A(I,J)
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
// GB_subref_templat extracts a submatrix, C = A(I,J). The method is done in
// two phases. Phase 1 just counts the entries in C, and phase 2 constructs
// the pattern and values of C. There are 3 kinds of subref:
//
// symbolic: C(i,j) is the position of A(I(i),J(j)) in the matrix A
// iso: C = A(I,J), extracting the pattern only, not the values
// numeric: C = A(I,J), extracting the pattern and values
#if defined ( GB_SYMBOLIC )
// symbolic method must tolerate zombies
#define GB_Ai(p) GBI_UNFLIP (Ai, p, avlen)
#else
// iso and non-iso numeric methods will not see any zombies
#define GB_Ai(p) GBI (Ai, p, avlen)
#endif
// to iterate across all entries in a bucket:
#define GB_for_each_index_in_bucket(inew,i) \
for (int64_t inew = Mark [i] - 1 ; inew >= 0 ; inew = Inext [inew])
//------------------------------------------------------------------------------
{
//--------------------------------------------------------------------------
// get A and I
//--------------------------------------------------------------------------
const int64_t *restrict Ai = A->i ;
const int64_t avlen = A->vlen ;
// these values are ignored if Ikind == GB_LIST
int64_t ibegin = Icolon [GxB_BEGIN] ;
int64_t iinc = Icolon [GxB_INC ] ;
int64_t inc = (iinc < 0) ? (-iinc) : iinc ;
#ifdef GB_DEBUG
int64_t iend = Icolon [GxB_END ] ;
#endif
//--------------------------------------------------------------------------
// phase1: count entries in each C(:,kC); phase2: compute C
//--------------------------------------------------------------------------
int taskid ;
#pragma omp parallel for num_threads(nthreads) schedule(dynamic,1)
for (taskid = 0 ; taskid < ntasks ; taskid++)
{
//----------------------------------------------------------------------
// get the task descriptor
//----------------------------------------------------------------------
int64_t kfirst = TaskList [taskid].kfirst ;
int64_t klast = TaskList [taskid].klast ;
bool fine_task = (klast < 0) ;
if (fine_task)
{
// a fine task operates on a slice of a single vector
klast = kfirst ;
}
// a coarse task accesses all of I for all its vectors
int64_t pI = 0 ;
int64_t pI_end = nI ;
int64_t ilen = nI ;
ASSERT (0 <= kfirst && kfirst <= klast && klast < Cnvec) ;
//----------------------------------------------------------------------
// compute all vectors C(:,kfirst:klast) for this task
//----------------------------------------------------------------------
for (int64_t kC = kfirst ; kC <= klast ; kC++)
{
//------------------------------------------------------------------
// get C(:,kC)
//------------------------------------------------------------------
#if defined ( GB_ANALYSIS_PHASE )
// phase1 simply counts the # of entries in C(*,kC).
int64_t clen = 0 ;
#else
// This task computes all or part of C(:,kC), which are the entries
// in Ci,Cx [pC:pC_end-1].
int64_t pC, pC_end ;
if (fine_task)
{
// A fine task computes a slice of C(:,kC)
pC = TaskList [taskid ].pC ;
pC_end = TaskList [taskid+1].pC ;
ASSERT (Cp [kC] <= pC && pC <= pC_end && pC_end <= Cp [kC+1]) ;
}
else
{
// The vectors of C are never sliced for a coarse task, so this
// task computes all of C(:,kC).
pC = Cp [kC] ;
pC_end = Cp [kC+1] ;
}
int64_t clen = pC_end - pC ;
if (clen == 0) continue ;
#endif
//------------------------------------------------------------------
// get A(:,kA)
//------------------------------------------------------------------
int64_t pA, pA_end ;
if (fine_task)
{
// a fine task computes a slice of a single vector C(:,kC).
// The task accesses Ai,Ax [pA:pA_end-1], which holds either
// the entire vector A(imin:imax,kA) for method 6, the entire
// dense A(:,kA) for methods 1 and 2, or a slice of the
// A(imin:max,kA) vector for all other methods.
pA = TaskList [taskid].pA ;
pA_end = TaskList [taskid].pA_end ;
}
else
{
// a coarse task computes the entire vector C(:,kC). The task
// accesses all of A(imin:imax,kA), for most methods, or all of
// A(:,kA) for methods 1 and 2. The vector A(*,kA) appears in
// Ai,Ax [pA:pA_end-1].
pA = Ap_start [kC] ;
pA_end = Ap_end [kC] ;
}
int64_t alen = pA_end - pA ;
if (alen == 0) continue ;
//------------------------------------------------------------------
// get I
//------------------------------------------------------------------
if (fine_task)
{
// A fine task accesses I [pI:pI_end-1]. For methods 2 and 6,
// pI:pI_end is a subset of the entire 0:nI-1 list. For all
// other methods, pI = 0 and pI_end = nI, and the task can
// access all of I.
pI = TaskList [taskid].pB ;
pI_end = TaskList [taskid].pB_end ;
ilen = pI_end - pI ;
}
//------------------------------------------------------------------
// determine the method to use
//------------------------------------------------------------------
int method ;
if (fine_task)
{
// The method that the fine task uses for its slice of A(*,kA)
// and C(*,kC) has already been determined by GB_subref_slice.
method = (int) (-TaskList [taskid].klast) ;
}
else
{
// determine the method based on A(*,kA) and I
method = GB_subref_method (NULL, NULL, alen, avlen, Ikind, nI,
(Mark != NULL), need_qsort, iinc, nduplicates) ;
}
//------------------------------------------------------------------
// extract C (:,kC) = A (I,kA): consider all cases
//------------------------------------------------------------------
switch (method)
{
//--------------------------------------------------------------
case 1 : // C(:,kC) = A(:,kA) where A(:,kA) is dense
//--------------------------------------------------------------
// A (:,kA) has not been sliced
ASSERT (Ikind == GB_ALL) ;
ASSERT (pA == Ap_start [kC]) ;
ASSERT (pA_end == Ap_end [kC]) ;
// copy the entire vector and construct indices
#if defined ( GB_ANALYSIS_PHASE )
clen = ilen ;
#else
for (int64_t k = 0 ; k < ilen ; k++)
{
int64_t inew = k + pI ;
ASSERT (inew == GB_ijlist (I, inew, Ikind, Icolon)) ;
ASSERT (inew == GB_Ai (pA + inew)) ;
Ci [pC + k] = inew ;
}
GB_COPY_RANGE (pC, pA + pI, ilen) ;
#endif
break ;
//--------------------------------------------------------------
case 2 : // C(:,kC) = A(I,kA) where A(I,kA) is dense
//--------------------------------------------------------------
// This method handles any kind of list I, but A(:,kA)
// must be dense. A(:,kA) has not been sliced.
ASSERT (pA == Ap_start [kC]) ;
ASSERT (pA_end == Ap_end [kC]) ;
// scan I and get the entry in A(:,kA) via direct lookup
#if defined ( GB_ANALYSIS_PHASE )
clen = ilen ;
#else
for (int64_t k = 0 ; k < ilen ; k++)
{
// C(inew,kC) = A(i,kA), and it always exists.
int64_t inew = k + pI ;
int64_t i = GB_ijlist (I, inew, Ikind, Icolon) ;
ASSERT (i == GB_Ai (pA + i)) ;
Ci [pC + k] = inew ;
GB_COPY_ENTRY (pC + k, pA + i) ;
}
#endif
break ;
//--------------------------------------------------------------
case 3 : // the list I has a single index, ibegin
//--------------------------------------------------------------
// binary search in GB_subref_phase0 has already found it.
// This can be any Ikind with nI=1: GB_ALL with A->vlen=1,
// GB_RANGE with ibegin==iend, GB_STRIDE such as 0:-1:0
// (with length 1), or a GB_LIST with ni=1.
// Time: 50x faster
ASSERT (!fine_task) ;
ASSERT (alen == 1) ;
ASSERT (nI == 1) ;
ASSERT (GB_Ai (pA) == GB_ijlist (I, 0, Ikind, Icolon)) ;
#if defined ( GB_ANALYSIS_PHASE )
clen = 1 ;
#else
Ci [pC] = 0 ;
GB_COPY_ENTRY (pC, pA) ;
#endif
break ;
//--------------------------------------------------------------
case 4 : // Ikind is ":", thus C(:,kC) = A (:,kA)
//--------------------------------------------------------------
// Time: 1x faster but low speedup on the Mac. Why?
// Probably memory bound since it is just memcpy's.
ASSERT (Ikind == GB_ALL && ibegin == 0) ;
#if defined ( GB_ANALYSIS_PHASE )
clen = alen ;
#else
#if defined ( GB_SYMBOLIC )
if (nzombies == 0)
{
memcpy (Ci + pC, Ai + pA, alen * sizeof (int64_t)) ;
}
else
{
// with zombies
for (int64_t k = 0 ; k < alen ; k++)
{
// symbolic C(:,kC) = A(:,kA) where A has zombies
int64_t i = GB_Ai (pA + k) ;
ASSERT (i == GB_ijlist (I, i, Ikind, Icolon)) ;
Ci [pC + k] = i ;
}
}
#else
memcpy (Ci + pC, Ai + pA, alen * sizeof (int64_t)) ;
#endif
GB_COPY_RANGE (pC, pA, alen) ;
#endif
break ;
//--------------------------------------------------------------
case 5 : // Ikind is GB_RANGE = ibegin:iend
//--------------------------------------------------------------
// Time: much faster. Good speedup too.
ASSERT (Ikind == GB_RANGE) ;
#if defined ( GB_ANALYSIS_PHASE )
clen = alen ;
#else
for (int64_t k = 0 ; k < alen ; k++)
{
int64_t i = GB_Ai (pA + k) ;
int64_t inew = i - ibegin ;
ASSERT (i == GB_ijlist (I, inew, Ikind, Icolon)) ;
Ci [pC + k] = inew ;
}
GB_COPY_RANGE (pC, pA, alen) ;
#endif
break ;
//--------------------------------------------------------------
case 6 : // I is short vs nnz (A (:,kA)), use binary search
//--------------------------------------------------------------
// Time: very slow unless I is very short and A(:,kA) is
// very long.
// This case can handle any kind of I, and A(:,kA) of any
// properties. For a fine task, A(:,kA) has not been
// sliced; I has been sliced instead.
// If the I bucket inverse has not been created, this
// method is the only option. Alternatively, if nI =
// length (I) is << nnz (A (:,kA)), then scanning I and
// doing a binary search of A (:,kA) is faster than doing a
// linear-time search of A(:,kA) and a lookup into the I
// bucket inverse.
// The vector of C is constructed in sorted order, so no
// sort is needed.
// A(:,kA) has not been sliced.
ASSERT (pA == Ap_start [kC]) ;
ASSERT (pA_end == Ap_end [kC]) ;
// scan I, in order, and search for the entry in A(:,kA)
for (int64_t k = 0 ; k < ilen ; k++)
{
// C(inew,kC) = A (i,kA), if it exists.
// i = I [inew] ; or from a colon expression
int64_t inew = k + pI ;
int64_t i = GB_ijlist (I, inew, Ikind, Icolon) ;
bool found ;
int64_t pleft = pA ;
int64_t pright = pA_end - 1 ;
#if defined ( GB_SYMBOLIC )
bool is_zombie ;
GB_BINARY_SEARCH_ZOMBIE (i, Ai, pleft, pright, found,
nzombies, is_zombie) ;
#else
GB_BINARY_SEARCH (i, Ai, pleft, pright, found) ;
#endif
if (found)
{
ASSERT (i == GB_Ai (pleft)) ;
#if defined ( GB_ANALYSIS_PHASE )
clen++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pleft) ;
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
break ;
//--------------------------------------------------------------
case 7 : // I is ibegin:iinc:iend with iinc > 1
//--------------------------------------------------------------
// Time: 1 thread: C=A(1:2:n,:) is 3x slower
// but has good speedup. About as fast with
// enough threads.
ASSERT (Ikind == GB_STRIDE && iinc > 1) ;
for (int64_t k = 0 ; k < alen ; k++)
{
// A(i,kA) present; see if it is in ibegin:iinc:iend
int64_t i = GB_Ai (pA + k) ;
ASSERT (ibegin <= i && i <= iend) ;
i = i - ibegin ;
if (i % iinc == 0)
{
// i is in the sequence ibegin:iinc:iend
#if defined ( GB_ANALYSIS_PHASE )
clen++ ;
#else
int64_t inew = i / iinc ;
ASSERT (pC < pC_end) ;
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pA + k) ;
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
break ;
//----------------------------------------------------------
case 8 : // I = ibegin:(-iinc):iend, with iinc < -1
//----------------------------------------------------------
// Time: 2x slower for iinc = -2 or -8.
// Good speedup though. Faster for
// large values (iinc = -128).
ASSERT (Ikind == GB_STRIDE && iinc < -1) ;
for (int64_t k = alen - 1 ; k >= 0 ; k--)
{
// A(i,kA) present; see if it is in ibegin:iinc:iend
int64_t i = GB_Ai (pA + k) ;
ASSERT (iend <= i && i <= ibegin) ;
i = ibegin - i ;
if (i % inc == 0)
{
// i is in the sequence ibegin:iinc:iend
#if defined ( GB_ANALYSIS_PHASE )
clen++ ;
#else
int64_t inew = i / inc ;
ASSERT (pC < pC_end) ;
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pA + k) ;
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
break ;
//----------------------------------------------------------
case 9 : // I = ibegin:(-1):iend
//----------------------------------------------------------
// Time: much faster. Good speedup.
ASSERT (Ikind == GB_STRIDE && iinc == -1) ;
#if defined ( GB_ANALYSIS_PHASE )
clen = alen ;
#else
for (int64_t k = alen - 1 ; k >= 0 ; k--)
{
// A(i,kA) is present
int64_t i = GB_Ai (pA + k) ;
int64_t inew = (ibegin - i) ;
ASSERT (i == GB_ijlist (I, inew, Ikind, Icolon)) ;
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pA + k) ;
pC++ ;
}
#endif
break ;
//--------------------------------------------------------------
case 10 : // I unsorted, and C needs qsort, duplicates OK
//--------------------------------------------------------------
// Time: with one thread: 2x slower, probably
// because of the qsort. Good speedup however. This used
// if qsort is needed but ndupl == 0. Try a method that
// needs qsort, but no duplicates?
// Case 10 works well when I has many entries and A(:,kA)
// has few entries. C(:,kC) must be sorted after this pass.
ASSERT (Ikind == GB_LIST) ;
for (int64_t k = 0 ; k < alen ; k++)
{
// A(i,kA) present, look it up in the I inverse buckets
int64_t i = GB_Ai (pA + k) ;
// traverse bucket i for all indices inew where
// i == I [inew] or where i is from a colon expression
GB_for_each_index_in_bucket (inew, i)
{
ASSERT (inew >= 0 && inew < nI) ;
ASSERT (i == GB_ijlist (I, inew, Ikind, Icolon)) ;
#if defined ( GB_ANALYSIS_PHASE )
clen++ ;
#else
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pA + k) ;
pC++ ;
#endif
}
}
// TODO: skip the sort if C is allowed to be jumbled on
// output. Flag C as jumbled instead.
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
if (!fine_task)
{
// a coarse task owns this entire C(:,kC) vector, so
// the sort can be done now. The sort for vectors
// handled by multiple fine tasks must wait until all
// task are completed, below in the post sort.
pC = Cp [kC] ;
#if defined ( GB_ISO_SUBREF )
// iso numeric subref C=A(I,J)
// just sort the pattern of C(:,kC)
GB_qsort_1 (Ci + pC, clen) ;
#else
// sort the pattern of C(:,kC), and the values
GB_qsort_1b (Ci + pC, (GB_void *) (Cx + pC*GB_CSIZE1),
GB_CSIZE2, clen) ;
#endif
}
#endif
break ;
//--------------------------------------------------------------
case 11 : // I not contiguous, with duplicates. No qsort needed
//--------------------------------------------------------------
// Case 11 works well when I has many entries and A(:,kA)
// has few entries. It requires that I be sorted on input,
// so that no sort is required for C(:,kC). It is
// otherwise identical to Case 10.
ASSERT (Ikind == GB_LIST) ;
for (int64_t k = 0 ; k < alen ; k++)
{
// A(i,kA) present, look it up in the I inverse buckets
int64_t i = GB_Ai (pA + k) ;
// traverse bucket i for all indices inew where
// i == I [inew] or where i is from a colon expression
GB_for_each_index_in_bucket (inew, i)
{
ASSERT (inew >= 0 && inew < nI) ;
ASSERT (i == GB_ijlist (I, inew, Ikind, Icolon)) ;
#if defined ( GB_ANALYSIS_PHASE )
clen++ ;
#else
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pA + k) ;
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
break ;
//--------------------------------------------------------------
case 12 : // I not contiguous, no duplicates. No qsort needed.
//--------------------------------------------------------------
// Identical to Case 11, except GB_for_each_index_in_bucket
// just needs to iterate 0 or 1 times. Works well when I
// has many entries and A(:,kA) has few entries.
ASSERT (Ikind == GB_LIST && nduplicates == 0) ;
for (int64_t k = 0 ; k < alen ; k++)
{
// A(i,kA) present, look it up in the I inverse buckets
int64_t i = GB_Ai (pA + k) ;
// bucket i has at most one index inew such that
// i == I [inew]
int64_t inew = Mark [i] - 1 ;
if (inew >= 0)
{
ASSERT (inew >= 0 && inew < nI) ;
ASSERT (i == GB_ijlist (I, inew, Ikind, Icolon)) ;
#if defined ( GB_ANALYSIS_PHASE )
clen++ ;
#else
Ci [pC] = inew ;
GB_COPY_ENTRY (pC, pA + k) ;
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
break ;
//--------------------------------------------------------------
default: ;
//--------------------------------------------------------------
}
//------------------------------------------------------------------
// final count of nnz (C (:,j))
//------------------------------------------------------------------
#if defined ( GB_ANALYSIS_PHASE )
if (fine_task)
{
TaskList [taskid].pC = clen ;
}
else
{
Cp [kC] = clen ;
}
#endif
}
}
//--------------------------------------------------------------------------
// phase2: post sort for any vectors handled by fine tasks with method 10
//--------------------------------------------------------------------------
#if defined ( GB_PHASE_2_OF_2 )
{
if (post_sort)
{
int taskid ;
#pragma omp parallel for num_threads(nthreads) schedule(dynamic,1)
for (taskid = 0 ; taskid < ntasks ; taskid++)
{
int64_t kC = TaskList [taskid].kfirst ;
bool do_post_sort = (TaskList [taskid].len != 0) ;
if (do_post_sort)
{
// This is the first fine task with method 10 for C(:,kC).
// The vector C(:,kC) must be sorted, since method 10 left
// it with unsorted indices.
int64_t pC = Cp [kC] ;
int64_t clen = Cp [kC+1] - pC ;
#if defined ( GB_ISO_SUBREF )
{
// iso numeric subref C=A(I,J)
// just sort the pattern of C(:,kC)
GB_qsort_1 (Ci + pC, clen) ;
}
#else
{
// sort the pattern of C(:,kC), and the values
GB_qsort_1b (Ci + pC, (GB_void *) (Cx + pC*GB_CSIZE1),
GB_CSIZE2, clen) ;
}
#endif
}
}
}
}
#endif
}
#undef GB_Ai
#undef GB_for_each_index_in_bucket
#undef GB_COPY_RANGE
#undef GB_COPY_ENTRY
#undef GB_CSIZE1
#undef GB_CSIZE2
#undef GB_SYMBOLIC
#undef GB_ISO_SUBREF
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