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//------------------------------------------------------------------------------
// GB_add_sparsity: determine the sparsity structure for C<M or !M>=A+B
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2025, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
// Determines the sparsity structure for C, for computing C=A+B, C<M>=A+B,
// or C<!M>=A+B, based on the sparsity structures of M, A, and B, and whether
// or not M is complemented. It also decides if the mask M should be applied
// by GB_add, or if C=A+B should be computed without the mask, and the mask
// applied later.
// If C should be hypersparse or sparse, on output, this function simply
// returns GxB_SPARSE. The final determination is made by GB_add_phase0.
#include "add/GB_add.h"
#include "mask/GB_mask_very_sparse.h"
int GB_add_sparsity // return the sparsity structure for C
(
// output:
bool *apply_mask, // if true then mask will be applied by GB_add
// input:
const GrB_Matrix M, // optional mask for C, unused if NULL
const bool Mask_struct, // if true, use only the structure of M
const bool Mask_comp, // if true, use !M
const GrB_Matrix A, // input A matrix
const GrB_Matrix B // input B matrix
)
{
//--------------------------------------------------------------------------
// determine the sparsity of C
//--------------------------------------------------------------------------
// Unless deciding otherwise, use the mask if it appears
(*apply_mask) = (M != NULL) ;
int C_sparsity ;
// In the table below, sparse/hypersparse are listed as "sparse". If C is
// listed as sparse: it is hypersparse if M is hypersparse (and not
// complemented), or if both A and B are hypersparse, and sparse otherwise.
// This is determined by GB_add_phase0. If M is complemented and all 4
// matrices are sparse, then C=A+B is always computed. So C is hypersparse
// if both A and B are hypersparse, in this case.
bool M_is_sparse_or_hyper = GB_IS_SPARSE (M) || GB_IS_HYPERSPARSE (M) ;
bool A_is_sparse_or_hyper = GB_IS_SPARSE (A) || GB_IS_HYPERSPARSE (A) ;
bool B_is_sparse_or_hyper = GB_IS_SPARSE (B) || GB_IS_HYPERSPARSE (B) ;
bool A_is_full = GB_IS_FULL (A) ;
bool B_is_full = GB_IS_FULL (B) ;
if (M == NULL)
{
// ------------------------------------------
// C = A + B
// ------------------------------------------
// sparse . sparse sparse
// bitmap . sparse bitmap
// full . sparse full
// bitmap . bitmap sparse
// bitmap . bitmap bitmap
// full . bitmap full
// full . full sparse
// full . full bitmap
// full . full full
if (A_is_sparse_or_hyper && B_is_sparse_or_hyper)
{
C_sparsity = GxB_SPARSE ;
}
else if (A_is_full || B_is_full)
{
C_sparsity = GxB_FULL ;
}
else
{
C_sparsity = GxB_BITMAP ;
}
}
else if (!Mask_comp)
{
if (M_is_sparse_or_hyper)
{
// ------------------------------------------
// C <M> = A + B
// ------------------------------------------
// sparse sparse sparse sparse
// sparse sparse sparse bitmap
// sparse sparse sparse full
// sparse sparse bitmap sparse
// sparse sparse bitmap bitmap
// sparse sparse bitmap full
// sparse sparse full sparse
// sparse sparse full bitmap
// sparse sparse full full
// if A and B are both bitmap or full, then always use the mask.
// if M and A and/or B are all sparse, use the mask only if
// M is very easy to use, or if:
// 8*nnz(M) <= ( (A sparse or hyper) ? nnz(A) : 0 ) +
// ( (B sparse or hyper) ? nnz(B) : 0 )
if (A_is_sparse_or_hyper || B_is_sparse_or_hyper)
{
// see ewise/template/GB_add_sparse_M_sparse.c for a
// vector-by-vector test of the "easy mask" condition. This
// test is global for all vectors of the matrices:
bool M_is_A = GB_all_aliased (M, A) ;
bool M_is_B = GB_all_aliased (M, B) ;
bool all_easy_mask = Mask_struct &&
((A_is_full && M_is_B) ||
(B_is_full && M_is_A) ||
(M_is_A && M_is_B)) ;
// GB_add_sparse_template handles this case, but exploiting the
// mask can be asympotically slow, when C and M are sparse, and
// A and/or B are sparse, and M has many entries. So in that
// case, apply the mask later.
(*apply_mask) = all_easy_mask ||
GB_MASK_VERY_SPARSE (8, M,
A_is_sparse_or_hyper ? A : NULL,
B_is_sparse_or_hyper ? B : NULL) ;
}
if (!(*apply_mask))
{
// redo the analysis as if there is no mask
if (A_is_sparse_or_hyper && B_is_sparse_or_hyper)
{
C_sparsity = GxB_SPARSE ;
}
else if (A_is_full || B_is_full)
{
C_sparsity = GxB_FULL ;
}
else
{
C_sparsity = GxB_BITMAP ;
}
}
else
{
// the mask is applied and C is sparse
C_sparsity = GxB_SPARSE ;
}
}
else
{
// ------------------------------------------
// C <M> = A + B
// ------------------------------------------
// sparse bitmap sparse sparse
// bitmap bitmap sparse bitmap
// bitmap bitmap sparse full
// bitmap bitmap bitmap sparse
// bitmap bitmap bitmap bitmap
// bitmap bitmap bitmap full
// bitmap bitmap full sparse
// bitmap bitmap full bitmap
// bitmap bitmap full full
// ------------------------------------------
// C <M> = A + B
// ------------------------------------------
// sparse full sparse sparse
// bitmap full sparse bitmap
// bitmap full sparse full
// bitmap full bitmap sparse
// bitmap full bitmap bitmap
// bitmap full bitmap full
// bitmap full full sparse
// bitmap full full bitmap
// bitmap full full full
// The mask is very efficient to use in the case, when C is sparse.
if (A_is_sparse_or_hyper && B_is_sparse_or_hyper)
{
C_sparsity = GxB_SPARSE ;
}
else
{
C_sparsity = GxB_BITMAP ;
}
}
}
else // Mask_comp
{
// ------------------------------------------
// C <!M> = A + B
// ------------------------------------------
// sparse sparse sparse sparse (mask later)
// bitmap sparse sparse bitmap
// bitmap sparse sparse full
// bitmap sparse bitmap sparse
// bitmap sparse bitmap bitmap
// bitmap sparse bitmap full
// bitmap sparse full sparse
// bitmap sparse full bitmap
// bitmap sparse full full
// ------------------------------------------
// C <!M> = A + B
// ------------------------------------------
// sparse bitmap sparse sparse
// bitmap bitmap sparse bitmap
// bitmap bitmap sparse full
// bitmap bitmap bitmap sparse
// bitmap bitmap bitmap bitmap
// bitmap bitmap bitmap full
// bitmap bitmap full sparse
// bitmap bitmap full bitmap
// bitmap bitmap full full
// ------------------------------------------
// C <!M> = A + B
// ------------------------------------------
// sparse full sparse sparse
// bitmap full sparse bitmap
// bitmap full sparse full
// bitmap full bitmap sparse
// bitmap full bitmap bitmap
// bitmap full bitmap full
// bitmap full full sparse
// bitmap full full bitmap
// bitmap full full full
if (A_is_sparse_or_hyper && B_is_sparse_or_hyper)
{
// !M must be applied later if all 4 matrices are sparse or
// hypersparse, since the GB_add_sparse_template method does not
// handle this case. See the "(mask later)" above. The method can
// construct a sparse/hyper C with !M as bitmap or full.
(*apply_mask) = !M_is_sparse_or_hyper ;
C_sparsity = GxB_SPARSE ;
}
else
{
// !M can be applied now, or later. TODO: If M is sparse and
// either A or B are sparse/hyper, then there might be cases where
// !M should be applied later, for better performance.
C_sparsity = GxB_BITMAP ;
}
}
return (C_sparsity) ;
}
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