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//------------------------------------------------------------------------------
// GB_AxB_dot_cij: compute C(i,j) = A(:,i)'*B(:,j)
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
// Computes C(i,j) = A (:,i)'*B(:,j) via sparse dot product. This template is
// used for all three cases: C=A'*B, C<M>=A'*B, and C<!M>=A'*B in dot2 when C
// is bitmap, and for C<M>=A'*B when C and M are sparse or hyper in dot3.
// if A_NOT_TRANSPOSED is #defined, then dot2 is computing A(i,:)*B(:,j)
// for C<#M>=A*B. In this case A is either bitmap or full, and B is always
// sparse.
// When used as the multiplicative operator, the PAIR operator provides some
// useful special cases. Its output is always one, for any matching pair of
// entries A(k,i)'*B(k,j) for some k. If the monoid is ANY, then C(i,j)=1 if
// the intersection for the dot product is non-empty. This intersection has to
// be found, in general. However, suppose B(:,j) is dense. Then every entry
// in the pattern of A(:,i)' will produce a 1 from the PAIR operator. If the
// monoid is ANY, then C(i,j)=1 if A(:,i)' is nonempty. If the monoid is PLUS,
// then C(i,j) is simply nnz(A(:,i)), assuming no overflow. The XOR monoid
// acts like a 1-bit summation, so the result of the XOR_PAIR_BOOL semiring
// will be C(i,j) = mod (nnz(A(:,i)'*B(:,j)),2).
// If both A(:,i) and B(:,j) are sparse, then the intersection must still be
// found, so these optimizations can be used only if A(:,i) and/or B(:,j) are
// entirely populated.
#undef GB_A_INDEX
#ifdef GB_A_NOT_TRANSPOSED
#define GB_A_INDEX(k) (pA+(k)*vlen)
#else
#define GB_A_INDEX(k) (pA+(k))
#endif
// MIN_FIRSTJ or MIN_FIRSTJ1 semirings:
#define GB_IS_MIN_FIRSTJ_SEMIRING (GB_IS_IMIN_MONOID && GB_IS_FIRSTJ_MULTIPLIER)
// MAX_FIRSTJ or MAX_FIRSTJ1 semirings:
#define GB_IS_MAX_FIRSTJ_SEMIRING (GB_IS_IMAX_MONOID && GB_IS_FIRSTJ_MULTIPLIER)
// GB_OFFSET is 1 for the MIN/MAX_FIRSTJ1 semirings, and 0 otherwise.
//------------------------------------------------------------------------------
// C(i,j) = A(:,i)'*B(:,j): a single dot product
//------------------------------------------------------------------------------
{
int64_t pB = pB_start ;
ASSERT (vlen > 0) ;
#if ( GB_B_IS_SPARSE || GB_B_IS_HYPER )
ASSERT (bjnz > 0) ;
#endif
#if ( GB_A_IS_SPARSE || GB_A_IS_HYPER )
ASSERT (ainz > 0) ;
#endif
#if ( GB_A_IS_FULL && GB_B_IS_FULL )
{
//----------------------------------------------------------------------
// both A and B are full
//----------------------------------------------------------------------
#if GB_IS_PAIR_MULTIPLIER
{
#if ( GB_IS_ANY_PAIR_SEMIRING )
// nothing to do; C is iso
#elif (GB_CTYPE_BITS > 0)
// PLUS, XOR monoids: A(:,i)'*B(:,j) is nnz(A(:,i)),
// for bool, 8-bit, 16-bit, or 32-bit integer
cij = (GB_CTYPE) (((uint64_t) vlen) & GB_CTYPE_BITS) ;
#else
// PLUS monoid for float, double, or 64-bit integers
cij = GB_CTYPE_CAST (vlen, 0) ;
#endif
}
#elif GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry
cij = GB_OFFSET ;
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry
cij = vlen-1 + GB_OFFSET ;
}
#else
{
// cij = A(0,i) * B(0,j)
GB_GETA (aki, Ax, pA, A_iso) ; // aki = A(0,i)
GB_GETB (bkj, Bx, pB, B_iso) ; // bkj = B(0,j)
GB_MULT (cij, aki, bkj, i, 0, j) ; // cij = aki * bkj
GB_PRAGMA_SIMD_DOT (cij)
for (int64_t k = 1 ; k < vlen ; k++)
{
GB_DOT_TERMINAL (cij) ; // break if cij terminal
// cij += A(k,i) * B(k,j)
GB_GETA (aki, Ax, pA+k, A_iso) ; // aki = A(k,i)
GB_GETB (bkj, Bx, pB+k, B_iso) ; // bkj = B(k,j)
GB_MULTADD (cij, aki, bkj, i, k, j) ; // cij += aki * bkj
}
}
#endif
GB_DOT_ALWAYS_SAVE_CIJ ;
}
#elif ( GB_A_IS_FULL && GB_B_IS_BITMAP )
{
//----------------------------------------------------------------------
// A is full and B is bitmap
//----------------------------------------------------------------------
#if GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry in B(:,j)
for (int64_t k = 0 ; k < vlen ; k++)
{
if (Bb [pB+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry in B(:,j)
for (int64_t k = vlen-1 ; k >= 0 ; k--)
{
if (Bb [pB+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#else
{
for (int64_t k = 0 ; k < vlen ; k++)
{
if (Bb [pB+k])
{
GB_DOT (k, pA+k, pB+k) ;
}
}
}
#endif
GB_DOT_SAVE_CIJ ;
}
#elif ( GB_A_IS_FULL && ( GB_B_IS_SPARSE || GB_B_IS_HYPER ) )
{
//----------------------------------------------------------------------
// A is full and B is sparse/hyper (C = A'*B or A*B)
//----------------------------------------------------------------------
#if GB_IS_PAIR_MULTIPLIER
{
#if ( GB_IS_ANY_PAIR_SEMIRING )
// nothing to do; C is iso
#elif (GB_CTYPE_BITS > 0)
// PLUS, XOR monoids: A(:,i)'*B(:,j) is nnz(A(:,i)),
// for bool, 8-bit, 16-bit, or 32-bit integer
cij = (GB_CTYPE) (((uint64_t) bjnz) & GB_CTYPE_BITS) ;
#else
// PLUS monoid for float, double, or 64-bit integers
cij = GB_CTYPE_CAST (bjnz, 0) ;
#endif
}
#elif GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry in B(:,j)
cij = Bi [pB] + GB_OFFSET ;
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry in B(:,j)
cij = Bi [pB_end-1] + GB_OFFSET ;
}
#else
{
int64_t k = Bi [pB] ; // first row index of B(:,j)
// cij = (A(k,i) or A(i,k)) * B(k,j)
GB_GETA (aki, Ax, GB_A_INDEX(k), A_iso) ; // aki = A(k,i) or A(i,k)
GB_GETB (bkj, Bx, pB , B_iso) ; // bkj = B(k,j)
GB_MULT (cij, aki, bkj, i, k, j) ; // cij = aki * bkj
GB_PRAGMA_SIMD_DOT (cij)
for (int64_t p = pB+1 ; p < pB_end ; p++)
{
GB_DOT_TERMINAL (cij) ; // break if cij terminal
int64_t k = Bi [p] ;
// cij += (A(k,i) or A(i,k)) * B(k,j)
GB_GETA (aki, Ax, GB_A_INDEX(k), A_iso) ; //aki=A(k,i) or A(i,k)
GB_GETB (bkj, Bx, p, B_iso) ; // bkj = B(k,j)
GB_MULTADD (cij, aki, bkj, i, k, j) ; // cij += aki * bkj
}
}
#endif
GB_DOT_ALWAYS_SAVE_CIJ ;
}
#elif ( GB_A_IS_BITMAP && GB_B_IS_FULL )
{
//----------------------------------------------------------------------
// A is bitmap and B is full
//----------------------------------------------------------------------
#if GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry in A(:,i)
for (int64_t k = 0 ; k < vlen ; k++)
{
if (Ab [pA+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry in A(:,i)
for (int64_t k = vlen-1 ; k >= 0 ; k--)
{
if (Ab [pA+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#else
{
for (int64_t k = 0 ; k < vlen ; k++)
{
if (Ab [pA+k])
{
GB_DOT (k, pA+k, pB+k) ;
}
}
}
#endif
GB_DOT_SAVE_CIJ ;
}
#elif ( GB_A_IS_BITMAP && GB_B_IS_BITMAP )
{
//----------------------------------------------------------------------
// both A and B are bitmap
//----------------------------------------------------------------------
#if GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry
for (int64_t k = 0 ; k < vlen ; k++)
{
if (Ab [pA+k] && Bb [pB+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry
for (int64_t k = vlen-1 ; k >= 0 ; k--)
{
if (Ab [pA+k] && Bb [pB+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#else
{
for (int64_t k = 0 ; k < vlen ; k++)
{
if (Ab [pA+k] && Bb [pB+k])
{
GB_DOT (k, pA+k, pB+k) ;
}
}
}
#endif
GB_DOT_SAVE_CIJ ;
}
#elif ( GB_A_IS_BITMAP && ( GB_B_IS_SPARSE || GB_B_IS_HYPER ) )
{
//----------------------------------------------------------------------
// A is bitmap and B is sparse/hyper (C = A'*B or A*B)
//----------------------------------------------------------------------
#if GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry
for (int64_t p = pB ; p < pB_end ; p++)
{
int64_t k = Bi [p] ;
if (Ab [GB_A_INDEX (k)])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry
for (int64_t p = pB_end-1 ; p >= pB ; p--)
{
int64_t k = Bi [p] ;
if (Ab [GB_A_INDEX (k)])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#else
{
for (int64_t p = pB ; p < pB_end ; p++)
{
int64_t k = Bi [p] ;
if (Ab [GB_A_INDEX (k)])
{
GB_DOT (k, GB_A_INDEX (k), p) ;
}
}
}
#endif
GB_DOT_SAVE_CIJ ;
}
#elif ( (GB_A_IS_SPARSE || GB_A_IS_HYPER) && GB_B_IS_FULL )
{
//----------------------------------------------------------------------
// A is sparse/hyper and B is full
//----------------------------------------------------------------------
#if GB_IS_PAIR_MULTIPLIER
{
#if ( GB_IS_ANY_PAIR_SEMIRING )
// nothing to do; C is iso
#elif (GB_CTYPE_BITS > 0)
// PLUS, XOR monoids: A(:,i)'*B(:,j) is nnz(A(:,i)),
// for bool, 8-bit, 16-bit, or 32-bit integer
cij = (GB_CTYPE) (((uint64_t) ainz) & GB_CTYPE_BITS) ;
#else
// PLUS monoid for float, double, or 64-bit integers
cij = GB_CTYPE_CAST (ainz, 0) ;
#endif
}
#elif GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry in A(:,i)
cij = Ai [pA] + GB_OFFSET ;
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry in A(:,i)
cij = Ai [pA_end-1] + GB_OFFSET ;
}
#else
{
int64_t k = Ai [pA] ; // first row index of A(:,i)
// cij = A(k,i) * B(k,j)
GB_GETA (aki, Ax, pA , A_iso) ; // aki = A(k,i)
GB_GETB (bkj, Bx, pB+k, B_iso) ; // bkj = B(k,j)
GB_MULT (cij, aki, bkj, i, k, j) ; // cij = aki * bkj
GB_PRAGMA_SIMD_DOT (cij)
for (int64_t p = pA+1 ; p < pA_end ; p++)
{
GB_DOT_TERMINAL (cij) ; // break if cij terminal
int64_t k = Ai [p] ;
// cij += A(k,i) * B(k,j)
GB_GETA (aki, Ax, p , A_iso) ; // aki = A(k,i)
GB_GETB (bkj, Bx, pB+k, B_iso) ; // bkj = B(k,j)
GB_MULTADD (cij, aki, bkj, i, k, j) ; // cij += aki * bkj
}
}
#endif
GB_DOT_ALWAYS_SAVE_CIJ ;
}
#elif ( (GB_A_IS_SPARSE || GB_A_IS_HYPER) && GB_B_IS_BITMAP )
{
//----------------------------------------------------------------------
// A is sparse/hyper and B is bitmap
//----------------------------------------------------------------------
#if GB_IS_MIN_FIRSTJ_SEMIRING
{
// MIN_FIRSTJ semiring: take the first entry
for (int64_t p = pA ; p < pA_end ; p++)
{
int64_t k = Ai [p] ;
if (Bb [pB+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#elif GB_IS_MAX_FIRSTJ_SEMIRING
{
// MAX_FIRSTJ semiring: take the last entry
for (int64_t p = pA_end-1 ; p >= pA ; p--)
{
int64_t k = Ai [p] ;
if (Bb [pB+k])
{
cij_exists = true ;
cij = k + GB_OFFSET ;
break ;
}
}
}
#else
{
for (int64_t p = pA ; p < pA_end ; p++)
{
int64_t k = Ai [p] ;
if (Bb [pB+k])
{
GB_DOT (k, p, pB+k) ;
}
}
}
#endif
GB_DOT_SAVE_CIJ ;
}
#else
{
//----------------------------------------------------------------------
// both A and B are sparse/hyper
//----------------------------------------------------------------------
// The MIN_FIRSTJ semirings are exploited, by terminating as soon as
// any entry is found. The MAX_FIRSTJ semirings are not treated
// specially here. They could be done with a backwards traversal of
// the sparse vectors A(:,i) and B(:,j).
if (Ai [pA_end-1] < ib_first || ib_last < Ai [pA])
{
//------------------------------------------------------------------
// pattern of A(:,i) and B(:,j) don't overlap; C(i,j) doesn't exist
//------------------------------------------------------------------
ASSERT (!GB_CIJ_EXISTS) ;
}
else if (ainz > 8 * bjnz)
{
//------------------------------------------------------------------
// B(:,j) is very sparse compared to A(:,i)
//------------------------------------------------------------------
while (pA < pA_end && pB < pB_end)
{
int64_t ia = Ai [pA] ;
int64_t ib = Bi [pB] ;
if (ia < ib)
{
// A(ia,i) appears before B(ib,j)
// discard all entries A(ia:ib-1,i)
int64_t pleft = pA + 1 ;
int64_t pright = pA_end - 1 ;
GB_TRIM_BINARY_SEARCH (ib, Ai, pleft, pright) ;
ASSERT (pleft > pA) ;
pA = pleft ;
}
else if (ib < ia)
{
// B(ib,j) appears before A(ia,i)
pB++ ;
}
else // ia == ib == k
{
// A(k,i) and B(k,j) are the next entries to merge
GB_DOT (ia, pA, pB) ;
#if GB_IS_MIN_FIRSTJ_SEMIRING
break ;
#endif
pA++ ;
pB++ ;
}
}
GB_DOT_SAVE_CIJ ;
}
else if (bjnz > 8 * ainz)
{
//------------------------------------------------------------------
// A(:,i) is very sparse compared to B(:,j)
//------------------------------------------------------------------
while (pA < pA_end && pB < pB_end)
{
int64_t ia = Ai [pA] ;
int64_t ib = Bi [pB] ;
if (ia < ib)
{
// A(ia,i) appears before B(ib,j)
pA++ ;
}
else if (ib < ia)
{
// B(ib,j) appears before A(ia,i)
// discard all entries B(ib:ia-1,j)
int64_t pleft = pB + 1 ;
int64_t pright = pB_end - 1 ;
GB_TRIM_BINARY_SEARCH (ia, Bi, pleft, pright) ;
ASSERT (pleft > pB) ;
pB = pleft ;
}
else // ia == ib == k
{
// A(k,i) and B(k,j) are the next entries to merge
GB_DOT (ia, pA, pB) ;
#if GB_IS_MIN_FIRSTJ_SEMIRING
break ;
#endif
pA++ ;
pB++ ;
}
}
GB_DOT_SAVE_CIJ ;
}
else
{
//------------------------------------------------------------------
// A(:,i) and B(:,j) have about the same sparsity
//------------------------------------------------------------------
while (pA < pA_end && pB < pB_end)
{
int64_t ia = Ai [pA] ;
int64_t ib = Bi [pB] ;
if (ia < ib)
{
// A(ia,i) appears before B(ib,j)
pA++ ;
}
else if (ib < ia)
{
// B(ib,j) appears before A(ia,i)
pB++ ;
}
else // ia == ib == k
{
// A(k,i) and B(k,j) are the next entries to merge
GB_DOT (ia, pA, pB) ;
#if GB_IS_MIN_FIRSTJ_SEMIRING
break ;
#endif
pA++ ;
pB++ ;
}
}
GB_DOT_SAVE_CIJ ;
}
}
#endif
}
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