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|
//------------------------------------------------------------------------------
// GB_AxB_saxpy_generic_method: C=A*B, C<M>=A*B, or C<!M>=A*B
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
// GB_AxB_saxpy_generic_method computes C=A*B, C<M>=A*B, or C<!M>=A*B.
// with arbitrary types and operators. C can have any sparsity pattern:
// hyper, sparse, bitmap, or full. For all cases, the four matrices C, M
// (if present), A, and B have the same format (by-row or by-column), or they
// represent implicitly transposed matrices with the same effect. This method
// does not handle the dot-product methods, which compute C=A'*B if A and B
// are held by column, or equivalently A*B' if both are held by row.
// This method uses GB_AxB_saxpy_generic_template.c to implement two
// meta-methods, each of which can contain further specialized methods (such as
// the fine/coarse x Gustavson/Hash, mask/no-mask methods in saxpy3):
// saxpy3: general purpose method, where C is sparse or hypersparse,
// via GB_AxB_saxpy3_template.c. SaxpyTasks holds the (fine/coarse x
// Gustavson/Hash) tasks constructed by GB_AxB_saxpy3_slice*.
// bitmap_saxpy: general purpose method, where C is bitmap or full, via
// GB_bitmap_AxB_saxpy_template.c. The method constructs its own
// tasks in workspace defined and freed in that template.
// C is not iso.
// This template is used to construct the following methods, all of which
// are called by GB_AxB_saxpy_generic:
// GB_AxB_saxpy3_generic_firsti64
// GB_AxB_saxpy3_generic_firstj64
// GB_AxB_saxpy3_generic_secondj64
// GB_AxB_saxpy3_generic_firsti32
// GB_AxB_saxpy3_generic_firstj32
// GB_AxB_saxpy3_generic_secondj32
// GB_AxB_saxpy3_generic_first
// GB_AxB_saxpy3_generic_second
// GB_AxB_saxpy3_generic_flipped
// GB_AxB_saxpy3_generic_unflipped
// GB_bitmap_AxB_saxpy_generic_firsti64
// GB_bitmap_AxB_saxpy_generic_firstj64
// GB_bitmap_AxB_saxpy_generic_secondj64
// GB_bitmap_AxB_saxpy_generic_firsti32
// GB_bitmap_AxB_saxpy_generic_firstj32
// GB_bitmap_AxB_saxpy_generic_secondj32
// GB_bitmap_AxB_saxpy_generic_first
// GB_bitmap_AxB_saxpy_generic_second
// GB_bitmap_AxB_saxpy_generic_flipped
// GB_bitmap_AxB_saxpy_generic_unflipped
//------------------------------------------------------------------------------
#include "GB_mxm.h"
#include "GB_ek_slice.h"
#include "GB_binop.h"
#include "GB_sort.h"
#include "GB_atomics.h"
#include "GB_ek_slice_search.c"
#include "GB_bitmap_assign_methods.h"
#include "GB_AxB_saxpy_generic.h"
GrB_Info GB_AXB_SAXPY_GENERIC_METHOD
(
GrB_Matrix C, // any sparsity
const GrB_Matrix M,
bool Mask_comp,
const bool Mask_struct,
const bool M_in_place, // ignored if C is bitmap
const GrB_Matrix A,
bool A_is_pattern,
const GrB_Matrix B,
bool B_is_pattern,
const GrB_Semiring semiring, // semiring that defines C=A*B
// for saxpy3 only:
GB_saxpy3task_struct *restrict SaxpyTasks, // NULL if C is bitmap
int ntasks,
int nfine,
int nthreads,
const int do_sort, // if true, sort in saxpy3
GB_Context Context
)
{
//--------------------------------------------------------------------------
// get operators, functions, workspace, contents of A, B, and C
//--------------------------------------------------------------------------
GrB_BinaryOp mult = semiring->multiply ;
GrB_Monoid add = semiring->add ;
GB_void *identity = (GB_void *) add->identity ;
ASSERT (mult->ztype == add->op->ztype) ;
ASSERT (mult->ztype == C->type) ;
GxB_binary_function fmult = mult->binop_function ; // NULL if positional
GxB_binary_function fadd = add->op->binop_function ;
GB_Opcode opcode = mult->opcode ;
size_t csize = C->type->size ;
size_t asize = A_is_pattern ? 0 : A->type->size ;
size_t bsize = B_is_pattern ? 0 : B->type->size ;
size_t xsize = mult->xtype->size ;
size_t ysize = mult->ytype->size ;
// scalar workspace: because of typecasting, the x/y types need not
// be the same as the size of the A and B types.
// FLIPXY false: aik = (xtype) A(i,k) and bkj = (ytype) B(k,j)
// FLIPXY true: aik = (ytype) A(i,k) and bkj = (xtype) B(k,j)
size_t aik_size = FLIPXY ? ysize : xsize ;
size_t bkj_size = FLIPXY ? xsize : ysize ;
GB_cast_function cast_A, cast_B ;
#if FLIPXY
{
// A is typecasted to y, and B is typecasted to x
cast_A = A_is_pattern ? NULL :
GB_cast_factory (mult->ytype->code, A->type->code) ;
cast_B = B_is_pattern ? NULL :
GB_cast_factory (mult->xtype->code, B->type->code) ;
}
#else
{
// A is typecasted to x, and B is typecasted to y
cast_A = A_is_pattern ? NULL :
GB_cast_factory (mult->xtype->code, A->type->code) ;
cast_B = B_is_pattern ? NULL :
GB_cast_factory (mult->ytype->code, B->type->code) ;
}
#endif
//--------------------------------------------------------------------------
// C = A*B via saxpy3 or bitmap method, function pointers, and typecasting
//--------------------------------------------------------------------------
// memcpy (&(Cx [pC]), &(Hx [i]), len*csize)
#define GB_CIJ_MEMCPY(pC,i,len) memcpy (GB_CX (pC), GB_HX (i), (len)*csize)
// atomic update not available for function pointers
#define GB_HAS_ATOMIC 0
// user-defined monoid update cannot be done with an OpenMP atomic
#define GB_HAS_OMP_ATOMIC 0
// no special cases (C is not iso)
#define GB_IS_ANY_MONOID 0
#define GB_IS_ANY_FC32_MONOID 0
#define GB_IS_ANY_FC64_MONOID 0
#define GB_IS_PLUS_FC32_MONOID 0
#define GB_IS_PLUS_FC64_MONOID 0
#define GB_IS_ANY_PAIR_SEMIRING 0
#define GB_IS_PAIR_MULTIPLIER 0
#define GB_ATYPE GB_void
#define GB_BTYPE GB_void
#define GB_ASIZE asize
#define GB_BSIZE bsize
// no vectorization
#define GB_PRAGMA_SIMD_VECTORIZE ;
// The monoid identity byte value is not used in saxpy3
#define GB_GENERIC
#define GB_HAS_IDENTITY_BYTE 0
#define GB_IDENTITY_BYTE (none)
// definitions for GB_AxB_saxpy_generic_template.c
#include "GB_AxB_saxpy3_template.h"
#if OP_IS_POSITIONAL
{
//----------------------------------------------------------------------
// generic semirings with positional mulitiply operators
//----------------------------------------------------------------------
GB_BURBLE_MATRIX (C, "(generic positional C=A*B) ") ;
// C always has type int64_t or int32_t. The monoid must be used via
// its function pointer. The positional multiply operator must be
// hard-coded since it has no function pointer. The numerical values
// and types of A and B are not accessed.
ASSERT (A_is_pattern) ;
ASSERT (B_is_pattern) ;
// aik = A(i,k), located in Ax [A_iso ? 0:pA], value not used
#define GB_A_IS_PATTERN 1
#define GB_GETA(aik,Ax,pA,A_iso) ;
// bkj = B(k,j), located in Bx [B_iso ? 0:pB], value not used
#define GB_B_IS_PATTERN 1
#define GB_GETB(bkj,Bx,pB,B_iso) ;
// Gx [pG] = A(i,k), located in Ax [A_iso ? 0:pA], value not used
#define GB_LOADA(Gx,pG,Ax,pA,A_iso) ;
// Gx [pG] = B(k,j), located in Bx [B_iso ? 0:pB], value not used
#define GB_LOADB(Gx,pG,Bx,pB,B_iso) ;
// define t for each task
#define GB_CIJ_DECLARE(t) GB_CTYPE t
// address of Cx [p]
#define GB_CX(p) (&Cx [p])
// Cx [p] = t
#define GB_CIJ_WRITE(p,t) Cx [p] = t
// address of Hx [i]
#define GB_HX(i) (&Hx [i])
// Hx [i] = t
#define GB_HX_WRITE(i,t) Hx [i] = t
// Cx [p] = Hx [i]
#define GB_CIJ_GATHER(p,i) Cx [p] = Hx [i]
// Cx [p] += Hx [i]
#define GB_CIJ_GATHER_UPDATE(p,i) fadd (GB_CX (p), GB_CX (p), GB_HX (i))
// Cx [p] += t
#define GB_CIJ_UPDATE(p,t) fadd (GB_CX (p), GB_CX (p), &t)
// Hx [i] += t
#define GB_HX_UPDATE(i,t) fadd (GB_HX (i), GB_HX (i), &t)
// the original multiplier op may have been flipped, but the offset
// is unchanged
int64_t offset = GB_positional_offset (mult->opcode, NULL) ;
#if OP_IS_INT64
{
#undef GB_CTYPE
#define GB_CTYPE int64_t
#undef GB_CSIZE
#define GB_CSIZE (sizeof (int64_t))
ASSERT (C->type == GrB_INT64) ;
ASSERT (csize == sizeof (int64_t)) ;
#if OP_IS_FIRSTI
{
// GB_FIRSTI_binop_code : // z = first_i(A(i,k),y) == i
// GB_FIRSTI1_binop_code : // z = first_i1(A(i,k),y) == i+1
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) t = i + offset
#include "GB_AxB_saxpy_generic_template.c"
}
#elif OP_IS_FIRSTJ
{
// GB_FIRSTJ_binop_code : // z = first_j(A(i,k),y) == k
// GB_FIRSTJ1_binop_code : // z = first_j1(A(i,k),y) == k+1
// GB_SECONDI_binop_code : // z = second_i(x,B(k,j)) == k
// GB_SECONDI1_binop_code : // z = second_i1(x,B(k,j))== k+1
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) t = k + offset
#include "GB_AxB_saxpy_generic_template.c"
}
#else
{
// GB_SECONDJ_binop_code : // z = second_j(x,B(k,j)) == j
// GB_SECONDJ1_binop_code : // z = second_j1(x,B(k,j))== j+1
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) t = j + offset
#include "GB_AxB_saxpy_generic_template.c"
}
#endif
}
#else
{
#undef GB_CTYPE
#define GB_CTYPE int32_t
#undef GB_CSIZE
#define GB_CSIZE (sizeof (int32_t))
ASSERT (C->type == GrB_INT32) ;
ASSERT (csize == sizeof (int32_t)) ;
#if OP_IS_FIRSTI
{
// GB_FIRSTI_binop_code : // z = first_i(A(i,k),y) == i
// GB_FIRSTI1_binop_code : // z = first_i1(A(i,k),y) == i+1
#undef GB_MULT
#define GB_MULT(t,aik,bkj,i,k,j) t = (int32_t) (i + offset)
#include "GB_AxB_saxpy_generic_template.c"
}
#elif OP_IS_FIRSTJ
{
// GB_FIRSTJ_binop_code : // z = first_j(A(i,k),y) == k
// GB_FIRSTJ1_binop_code : // z = first_j1(A(i,k),y) == k+1
// GB_SECONDI_binop_code : // z = second_i(x,B(k,j)) == k
// GB_SECONDI1_binop_code : // z = second_i1(x,B(k,j))== k+1
#undef GB_MULT
#define GB_MULT(t,aik,bkj,i,k,j) t = (int32_t) (k + offset)
#include "GB_AxB_saxpy_generic_template.c"
}
#else
{
// GB_SECONDJ_binop_code : // z = second_j(x,B(k,j)) == j
// GB_SECONDJ1_binop_code : // z = second_j1(x,B(k,j))== j+1
#undef GB_MULT
#define GB_MULT(t,aik,bkj,i,k,j) t = (int32_t) (j + offset)
#include "GB_AxB_saxpy_generic_template.c"
}
#endif
}
#endif
}
#else
{
//----------------------------------------------------------------------
// generic semirings with standard multiply operators
//----------------------------------------------------------------------
GB_BURBLE_MATRIX (C, "(generic C=A*B) ") ;
// aik = A(i,k), located in Ax [A_iso ? 0:pA]
#undef GB_A_IS_PATTERN
#define GB_A_IS_PATTERN 0
#undef GB_GETA
#define GB_GETA(aik,Ax,pA,A_iso) \
GB_void aik [GB_VLA(aik_size)] ; \
if (!A_is_pattern) \
{ \
cast_A (aik, Ax +((A_iso) ? 0:((pA)*asize)), asize) ; \
}
// bkj = B(k,j), located in Bx [B_iso ? 0:pB]
#undef GB_B_IS_PATTERN
#define GB_B_IS_PATTERN 0
#undef GB_GETB
#define GB_GETB(bkj,Bx,pB,B_iso) \
GB_void bkj [GB_VLA(bkj_size)] ; \
if (!B_is_pattern) \
{ \
cast_B (bkj, Bx +((B_iso) ? 0:((pB)*bsize)), bsize) ; \
}
// Gx [pG] = A(i,k), located in Ax [A_iso ? 0:pA], no typecasting
#undef GB_LOADA
#define GB_LOADA(Gx,pG,Ax,pA,A_iso) \
memcpy (Gx + ((pG)*asize), Ax +((A_iso) ? 0:((pA)*asize)), asize)
// Gx [pG] = B(k,j), located in Bx [B_iso ? 0:pB], no typecasting
#undef GB_LOADB
#define GB_LOADB(Gx,pG,Bx,pB,B_iso) \
memcpy (Gx + ((pG)*bsize), Bx +((B_iso) ? 0:((pB)*bsize)), bsize)
// define t for each task
#undef GB_CIJ_DECLARE
#define GB_CIJ_DECLARE(t) GB_void t [GB_VLA(csize)]
// address of Cx [p]
#undef GB_CX
#define GB_CX(p) (Cx +((p)*csize))
// Cx [p] = t
#undef GB_CIJ_WRITE
#define GB_CIJ_WRITE(p,t) memcpy (GB_CX (p), t, csize)
// address of Hx [i]
#undef GB_HX
#define GB_HX(i) (Hx +((i)*csize))
// Hx [i] = t
#undef GB_HX_WRITE
#define GB_HX_WRITE(i,t) memcpy (GB_HX (i), t, csize)
// Cx [p] = Hx [i]
#undef GB_CIJ_GATHER
#define GB_CIJ_GATHER(p,i) memcpy (GB_CX (p), GB_HX(i), csize)
// Cx [p] += Hx [i]
#undef GB_CIJ_GATHER_UPDATE
#define GB_CIJ_GATHER_UPDATE(p,i) fadd (GB_CX (p), GB_CX (p), GB_HX (i))
// Cx [p] += t
#undef GB_CIJ_UPDATE
#define GB_CIJ_UPDATE(p,t) fadd (GB_CX (p), GB_CX (p), t)
// Hx [i] += t
#undef GB_HX_UPDATE
#define GB_HX_UPDATE(i,t) fadd (GB_HX (i), GB_HX (i), t)
#undef GB_CTYPE
#define GB_CTYPE GB_void
#undef GB_CSIZE
#define GB_CSIZE csize
#if OP_IS_FIRST
{
// t = A(i,k)
ASSERT (B_is_pattern) ;
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) memcpy (t, aik, csize)
#include "GB_AxB_saxpy_generic_template.c"
}
#elif OP_IS_SECOND
{
// t = B(i,k)
ASSERT (A_is_pattern) ;
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) memcpy (t, bkj, csize)
#include "GB_AxB_saxpy_generic_template.c"
}
#elif FLIPXY
{
// t = B(k,j) * A(i,k)
ASSERT (fmult != NULL) ;
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) fmult (t, bkj, aik)
#include "GB_AxB_saxpy_generic_template.c"
}
#else
{
// t = A(i,k) * B(k,j)
ASSERT (fmult != NULL) ;
#undef GB_MULT
#define GB_MULT(t, aik, bkj, i, k, j) fmult (t, aik, bkj)
#include "GB_AxB_saxpy_generic_template.c"
}
#endif
}
#endif
return (GrB_SUCCESS) ;
}
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