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|
//------------------------------------------------------------------------------
// GB_emult_template: C=A.*B, C<M or !M>=A.*B when C is sparse/hyper
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
// Computes C=A.*B, C<M>=A.*B, or C<!M>=A.*B when C is sparse or hypersparse:
// phase1: does not compute C itself, but just counts the # of entries in each
// vector of C. Fine tasks compute the # of entries in their slice of a
// single vector of C, and the results are cumsum'd.
// phase2: computes C, using the counts computed by phase1.
// No input matrix can be jumbled, and C is constructed as unjumbled.
// The following cases are handled:
// ------------------------------------------
// C = A .* B
// ------------------------------------------
// sparse . sparse sparse (method: 8)
// ------------------------------------------
// C <M>= A .* B
// ------------------------------------------
// sparse sparse sparse sparse (method: 8)
// sparse bitmap sparse sparse (method: 8)
// sparse full sparse sparse (method: 8)
// sparse sparse sparse bitmap (9 or 2)
// sparse sparse sparse full (9 or 2)
// sparse sparse bitmap sparse (10 or 3)
// sparse sparse full sparse (10 or 3)
// ------------------------------------------
// C <!M>= A .* B
// ------------------------------------------
// sparse sparse sparse sparse (8: M later)
// sparse bitmap sparse sparse (method: 8)
// sparse full sparse sparse (method: 8)
// Methods 9 and 10 are not yet implemented, and are currently handled by this
// Method 8 instead. those cases. Methods 2 and 3 can be used as well, but
// only if M is applied later. See GB_emult_sparsity for this decision.
{
int taskid ;
#pragma omp parallel for num_threads(C_nthreads) schedule(dynamic,1)
for (taskid = 0 ; taskid < C_ntasks ; taskid++)
{
//----------------------------------------------------------------------
// get the task descriptor
//----------------------------------------------------------------------
int64_t kfirst = TaskList [taskid].kfirst ;
int64_t klast = TaskList [taskid].klast ;
bool fine_task = (klast == -1) ;
int64_t len ;
if (fine_task)
{
// a fine task operates on a slice of a single vector
klast = kfirst ;
len = TaskList [taskid].len ;
}
else
{
// a coarse task operates on one or more whole vectors
len = vlen ;
}
//----------------------------------------------------------------------
// compute all vectors in this task
//----------------------------------------------------------------------
for (int64_t k = kfirst ; k <= klast ; k++)
{
//------------------------------------------------------------------
// get j, the kth vector of C
//------------------------------------------------------------------
int64_t j = GBH (Ch, k) ;
#if defined ( GB_PHASE_1_OF_2 )
int64_t cjnz = 0 ;
#else
int64_t pC, pC_end ;
if (fine_task)
{
// A fine task computes a slice of C(:,j)
pC = TaskList [taskid ].pC ;
pC_end = TaskList [taskid+1].pC ;
ASSERT (Cp [k] <= pC && pC <= pC_end && pC_end <= Cp [k+1]) ;
}
else
{
// The vectors of C are never sliced for a coarse task.
pC = Cp [k] ;
pC_end = Cp [k+1] ;
}
int64_t cjnz = pC_end - pC ;
if (cjnz == 0) continue ;
#endif
//------------------------------------------------------------------
// get A(:,j)
//------------------------------------------------------------------
int64_t pA = -1, pA_end = -1 ;
if (fine_task)
{
// A fine task operates on Ai,Ax [pA...pA_end-1], which is
// a subset of the vector A(:,j)
pA = TaskList [taskid].pA ;
pA_end = TaskList [taskid].pA_end ;
}
else
{
// A coarse task operates on the entire vector A (:,j)
int64_t kA = (Ch == Ah) ? k :
((C_to_A == NULL) ? j : C_to_A [k]) ;
if (kA >= 0)
{
pA = GBP (Ap, kA, vlen) ;
pA_end = GBP (Ap, kA+1, vlen) ;
}
}
int64_t ajnz = pA_end - pA ; // nnz in A(:,j) for this slice
int64_t pA_start = pA ;
bool adense = (ajnz == len) ;
// get the first and last indices in A(:,j) for this vector
int64_t iA_first = -1 ;
if (ajnz > 0)
{
iA_first = GBI (Ai, pA, vlen) ;
}
#if defined ( GB_PHASE_1_OF_2 ) || defined ( GB_DEBUG )
int64_t iA_last = -1 ;
if (ajnz > 0)
{
iA_last = GBI (Ai, pA_end-1, vlen) ;
}
#endif
//------------------------------------------------------------------
// get B(:,j)
//------------------------------------------------------------------
int64_t pB = -1, pB_end = -1 ;
if (fine_task)
{
// A fine task operates on Bi,Bx [pB...pB_end-1], which is
// a subset of the vector B(:,j)
pB = TaskList [taskid].pB ;
pB_end = TaskList [taskid].pB_end ;
}
else
{
// A coarse task operates on the entire vector B (:,j)
int64_t kB = (Ch == Bh) ? k :
((C_to_B == NULL) ? j : C_to_B [k]) ;
if (kB >= 0)
{
pB = GBP (Bp, kB, vlen) ;
pB_end = GBP (Bp, kB+1, vlen) ;
}
}
int64_t bjnz = pB_end - pB ; // nnz in B(:,j) for this slice
int64_t pB_start = pB ;
bool bdense = (bjnz == len) ;
// get the first and last indices in B(:,j) for this vector
int64_t iB_first = -1 ;
if (bjnz > 0)
{
iB_first = GBI (Bi, pB, vlen) ;
}
#if defined ( GB_PHASE_1_OF_2 ) || defined ( GB_DEBUG )
int64_t iB_last = -1 ;
if (bjnz > 0)
{
iB_last = GBI (Bi, pB_end-1, vlen) ;
}
#endif
//------------------------------------------------------------------
// get M(:,j) if M is sparse or hypersparse
//------------------------------------------------------------------
int64_t pM = -1 ;
int64_t pM_end = -1 ;
if (M_is_sparse_or_hyper)
{
if (fine_task)
{
// A fine task operates on Mi,Mx [pM...pM_end-1], which is
// a subset of the vector M(:,j)
pM = TaskList [taskid].pM ;
pM_end = TaskList [taskid].pM_end ;
}
else
{
int64_t kM = -1 ;
if (Ch == Mh)
{
// Ch is the same as Mh (a shallow copy), or both NULL
kM = k ;
}
else
{
kM = (C_to_M == NULL) ? j : C_to_M [k] ;
}
if (kM >= 0)
{
pM = GBP (Mp, kM, vlen) ;
pM_end = GBP (Mp, kM+1, vlen) ;
}
}
}
//------------------------------------------------------------------
// C(:,j)<optional mask> = A (:,j) .* B (:,j) or subvector
//------------------------------------------------------------------
#if defined ( GB_PHASE_1_OF_2 )
if (ajnz == 0 || bjnz == 0)
{
//--------------------------------------------------------------
// Method8(a): A(:,j) and/or B(:,j) are empty
//--------------------------------------------------------------
;
}
else if (iA_last < iB_first || iB_last < iA_first)
{
//--------------------------------------------------------------
// Method8(a): intersection of A(:,j) and B(:,j) is empty
//--------------------------------------------------------------
// the last entry of A(:,j) comes before the first entry
// of B(:,j), or visa versa
;
}
else
#endif
if (M == NULL)
{
//--------------------------------------------------------------
// Method8(b,c,d): C = A.*B, no mask
//--------------------------------------------------------------
// ------------------------------------------
// C = A .* B
// ------------------------------------------
// sparse . sparse sparse (method: 8)
// sparse sparse sparse sparse (8, M later)
// both A and B are sparse/hyper
ASSERT (A_is_sparse || A_is_hyper) ;
ASSERT (B_is_sparse || B_is_hyper) ;
if (ajnz > 32 * bjnz)
{
//----------------------------------------------------------
// Method8(b): A(:,j) is much denser than B(:,j)
//----------------------------------------------------------
for ( ; pB < pB_end ; pB++)
{
int64_t i = Bi [pB] ;
// find i in A(:,j)
int64_t pright = pA_end - 1 ;
bool found ;
GB_BINARY_SEARCH (i, Ai, pA, pright, found) ;
if (found)
{
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = i ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, i, j) ;
#endif
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
else if (bjnz > 32 * ajnz)
{
//----------------------------------------------------------
// Method8(c): B(:,j) is much denser than A(:,j)
//----------------------------------------------------------
for ( ; pA < pA_end ; pA++)
{
int64_t i = Ai [pA] ;
// find i in B(:,j)
int64_t pright = pB_end - 1 ;
bool found ;
GB_BINARY_SEARCH (i, Bi, pB, pright, found) ;
if (found)
{
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = i ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, i, j) ;
#endif
pC++ ;
#endif
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
else
{
//----------------------------------------------------------
// Method8(d): A(:,j) and B(:,j) about the sparsity
//----------------------------------------------------------
// linear-time scan of A(:,j) and B(:,j)
while (pA < pA_end && pB < pB_end)
{
int64_t iA = Ai [pA] ;
int64_t iB = Bi [pB] ;
if (iA < iB)
{
// A(i,j) exists but not B(i,j)
pA++ ;
}
else if (iB < iA)
{
// B(i,j) exists but not A(i,j)
pB++ ;
}
else
{
// both A(i,j) and B(i,j) exist
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = iB ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, iB, j) ;
#endif
pC++ ;
#endif
pA++ ;
pB++ ;
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
}
else if (M_is_sparse_or_hyper)
{
//--------------------------------------------------------------
// Method8(e): C and M are sparse or hypersparse
//--------------------------------------------------------------
// ------------------------------------------
// C <M>= A .* B
// ------------------------------------------
// sparse sparse sparse sparse (method: 8)
// sparse sparse sparse bitmap (9 or 2)
// sparse sparse sparse full (9 or 2)
// sparse sparse bitmap sparse (10 or 3)
// sparse sparse full sparse (10 or 3)
// Methods 9 and 10 are not yet implemented; using Method 8
// (GB_emult_phase[123]) instead.
// ether A or B are sparse/hyper
ASSERT (A_is_sparse || A_is_hyper || B_is_sparse || B_is_hyper);
for ( ; pM < pM_end ; pM++)
{
//----------------------------------------------------------
// get M(i,j) for A(i,j) .* B (i,j)
//----------------------------------------------------------
int64_t i = GBI (Mi, pM, vlen) ;
bool mij = GB_mcast (Mx, pM, msize) ;
if (!mij) continue ;
//----------------------------------------------------------
// get A(i,j)
//----------------------------------------------------------
bool afound ;
if (adense)
{
// A(:,j) is dense, bitmap, or full; use quick lookup
pA = pA_start + i - iA_first ;
afound = GBB (Ab, pA) ;
}
else
{
// A(:,j) is sparse; use binary search for A(i,j)
int64_t apright = pA_end - 1 ;
GB_BINARY_SEARCH (i, Ai, pA, apright, afound) ;
}
if (!afound) continue ;
ASSERT (GBI (Ai, pA, vlen) == i) ;
//----------------------------------------------------------
// get B(i,j)
//----------------------------------------------------------
bool bfound ;
if (bdense)
{
// B(:,j) is dense; use direct lookup for B(i,j)
pB = pB_start + i - iB_first ;
bfound = GBB (Bb, pB) ;
}
else
{
// B(:,j) is sparse; use binary search for B(i,j)
int64_t bpright = pB_end - 1 ;
GB_BINARY_SEARCH (i, Bi, pB, bpright, bfound) ;
}
if (!bfound) continue ;
ASSERT (GBI (Bi, pB, vlen) == i) ;
//----------------------------------------------------------
// C(i,j) = A(i,j) .* B(i,j)
//----------------------------------------------------------
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
Ci [pC] = i ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, i, j) ;
#endif
pC++ ;
#endif
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
else
{
//--------------------------------------------------------------
// M is bitmap or full, for either C<M>=A.*B or C<!M>=A.*B
//--------------------------------------------------------------
// ------------------------------------------
// C <M>= A .* B
// ------------------------------------------
// sparse bitmap sparse sparse (method: 8)
// sparse full sparse sparse (method: 8)
// ------------------------------------------
// C <!M>= A .* B
// ------------------------------------------
// sparse bitmap sparse sparse (method: 8)
// sparse full sparse sparse (method: 8)
// GB_GET_MIJ: get M(i,j) where M is bitmap or full
#undef GB_GET_MIJ
#define GB_GET_MIJ(i) \
int64_t pM = pM_start + i ; \
bool mij = GBB (Mb, pM) && GB_mcast (Mx, pM, msize) ; \
if (Mask_comp) mij = !mij ;
// both A and B are sparse/hyper
ASSERT (A_is_sparse || A_is_hyper) ;
ASSERT (B_is_sparse || B_is_hyper) ;
int64_t pM_start = j * vlen ;
if (ajnz > 32 * bjnz)
{
//----------------------------------------------------------
// Method8(f): A(:,j) much denser than B(:,j), M bitmap/full
//----------------------------------------------------------
for ( ; pB < pB_end ; pB++)
{
int64_t i = Bi [pB] ;
GB_GET_MIJ (i) ;
if (mij)
{
// find i in A(:,j)
int64_t pright = pA_end - 1 ;
bool found ;
GB_BINARY_SEARCH (i, Ai, pA, pright, found) ;
if (found)
{
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = i ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, i, j) ;
#endif
pC++ ;
#endif
}
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
else if (bjnz > 32 * ajnz)
{
//----------------------------------------------------------
// Method8(g): B(:,j) much denser than A(:,j), M bitmap/full
//----------------------------------------------------------
for ( ; pA < pA_end ; pA++)
{
int64_t i = Ai [pA] ;
GB_GET_MIJ (i) ;
if (mij)
{
// find i in B(:,j)
int64_t pright = pB_end - 1 ;
bool found ;
GB_BINARY_SEARCH (i, Bi, pB, pright, found) ;
if (found)
{
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = i ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, i, j) ;
#endif
pC++ ;
#endif
}
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
else
{
//----------------------------------------------------------
// Method8(h): A(:,j) and B(:,j) about same, M bitmap/full
//----------------------------------------------------------
// linear-time scan of A(:,j) and B(:,j)
while (pA < pA_end && pB < pB_end)
{
int64_t iA = Ai [pA] ;
int64_t iB = Bi [pB] ;
if (iA < iB)
{
// A(i,j) exists but not B(i,j)
pA++ ;
}
else if (iB < iA)
{
// B(i,j) exists but not A(i,j)
pB++ ;
}
else
{
// both A(i,j) and B(i,j) exist
int64_t i = iA ;
GB_GET_MIJ (i) ;
if (mij)
{
// C (i,j) = A (i,j) .* B (i,j)
#if defined ( GB_PHASE_1_OF_2 )
cjnz++ ;
#else
ASSERT (pC < pC_end) ;
Ci [pC] = i ;
#ifndef GB_ISO_EMULT
GB_GETA (aij, Ax, pA, A_iso) ;
GB_GETB (bij, Bx, pB, B_iso) ;
GB_BINOP (GB_CX (pC), aij, bij, iB, j) ;
#endif
pC++ ;
#endif
}
pA++ ;
pB++ ;
}
}
#if defined ( GB_PHASE_2_OF_2 )
ASSERT (pC == pC_end) ;
#endif
}
}
//------------------------------------------------------------------
// final count of nnz (C (:,j))
//------------------------------------------------------------------
#if defined ( GB_PHASE_1_OF_2 )
if (fine_task)
{
TaskList [taskid].pC = cjnz ;
}
else
{
Cp [k] = cjnz ;
}
#endif
}
}
}
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