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//------------------------------------------------------------------------------
// GB_ops.c: built-in types, functions, operators, and other externs
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0
//------------------------------------------------------------------------------
// This file defines the predefined built-in types, descriptors, unary
// operators, index_unary operators, binary operators, monoids, and semirings.
#include "GB.h"
//------------------------------------------------------------------------------
// compiler flags
//------------------------------------------------------------------------------
#if GB_COMPILER_ICC || GB_COMPILER_ICX
// disable icc warnings
// 144: initialize with incompatible pointer
#pragma warning (disable: 144 )
#elif GB_COMPILER_GCC
// disable gcc warnings
#if !defined ( __cplusplus )
#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#endif
#elif GB_COMPILER_MSC
// disable MS Visual Studio warnings
GB_PRAGMA (warning (disable : 4146 ))
#endif
//------------------------------------------------------------------------------
// built-in types
//------------------------------------------------------------------------------
#define GB_TYPEDEF(prefix,type,ctype,name) \
struct GB_Type_opaque GB_OPAQUE (type) = \
{ \
GB_MAGIC, 0, \
sizeof (ctype), \
GB_ ## type ## _code, \
name, \
NULL \
} ; \
GrB_Type prefix ## _ ## type = & GB_OPAQUE (type)
GB_TYPEDEF (GrB, BOOL , bool , "bool" ) ;
GB_TYPEDEF (GrB, INT8 , int8_t , "int8_t" ) ;
GB_TYPEDEF (GrB, INT16 , int16_t , "int16_t" ) ;
GB_TYPEDEF (GrB, INT32 , int32_t , "int32_t" ) ;
GB_TYPEDEF (GrB, INT64 , int64_t , "int64_t" ) ;
GB_TYPEDEF (GrB, UINT8 , uint8_t , "uint8_t" ) ;
GB_TYPEDEF (GrB, UINT16, uint16_t , "uint16_t" ) ;
GB_TYPEDEF (GrB, UINT32, uint32_t , "uint32_t" ) ;
GB_TYPEDEF (GrB, UINT64, uint64_t , "uint64_t" ) ;
GB_TYPEDEF (GrB, FP32 , float , "float" ) ;
GB_TYPEDEF (GrB, FP64 , double , "double" ) ;
GB_TYPEDEF (GxB, FC32 , GxB_FC32_t, "GxB_FC32_t" ) ;
GB_TYPEDEF (GxB, FC64 , GxB_FC64_t, "GxB_FC64_t" ) ;
//------------------------------------------------------------------------------
// built-in descriptors
//------------------------------------------------------------------------------
#define o ((GrB_Desc_Value) GxB_DEFAULT)
#define GB_DESC(name,out,mask,in0,in1) \
struct GB_Descriptor_opaque GB_OPAQUE (desc_ ## name) = \
{ \
GB_MAGIC, 0, /* initialized */ \
"", 0, /* logger */ \
(double) GxB_DEFAULT, /* chunk */ \
(GrB_Desc_Value) (out), \
(GrB_Desc_Value) (mask), \
(GrB_Desc_Value) (in0), \
(GrB_Desc_Value) (in1), \
o, o, /* default: axb, #threads */ \
0, /* default compression */ \
0, /* no sort */ \
0 /* import */ \
} ; \
GrB_Descriptor GRB (DESC_ ## name) = & GB_OPAQUE (desc_ ## name) ;
// name outp structure complement in0 in1
// GrB_NULL , o , o + o , o , o
GB_DESC (T1 , o , o + o , o , GrB_TRAN )
GB_DESC (T0 , o , o + o , GrB_TRAN, o )
GB_DESC (T0T1 , o , o + o , GrB_TRAN, GrB_TRAN )
GB_DESC (C , o , o + GrB_COMP, o , o )
GB_DESC (CT1 , o , o + GrB_COMP, o , GrB_TRAN )
GB_DESC (CT0 , o , o + GrB_COMP, GrB_TRAN, o )
GB_DESC (CT0T1 , o , o + GrB_COMP, GrB_TRAN, GrB_TRAN )
GB_DESC (S , o , GrB_STRUCTURE + o , o , o )
GB_DESC (ST1 , o , GrB_STRUCTURE + o , o , GrB_TRAN )
GB_DESC (ST0 , o , GrB_STRUCTURE + o , GrB_TRAN, o )
GB_DESC (ST0T1 , o , GrB_STRUCTURE + o , GrB_TRAN, GrB_TRAN )
GB_DESC (SC , o , GrB_STRUCTURE + GrB_COMP, o , o )
GB_DESC (SCT1 , o , GrB_STRUCTURE + GrB_COMP, o , GrB_TRAN )
GB_DESC (SCT0 , o , GrB_STRUCTURE + GrB_COMP, GrB_TRAN, o )
GB_DESC (SCT0T1 , o , GrB_STRUCTURE + GrB_COMP, GrB_TRAN, GrB_TRAN )
GB_DESC (R , GrB_REPLACE, o + o , o , o )
GB_DESC (RT1 , GrB_REPLACE, o + o , o , GrB_TRAN )
GB_DESC (RT0 , GrB_REPLACE, o + o , GrB_TRAN, o )
GB_DESC (RT0T1 , GrB_REPLACE, o + o , GrB_TRAN, GrB_TRAN )
GB_DESC (RC , GrB_REPLACE, o + GrB_COMP, o , o )
GB_DESC (RCT1 , GrB_REPLACE, o + GrB_COMP, o , GrB_TRAN )
GB_DESC (RCT0 , GrB_REPLACE, o + GrB_COMP, GrB_TRAN, o )
GB_DESC (RCT0T1 , GrB_REPLACE, o + GrB_COMP, GrB_TRAN, GrB_TRAN )
GB_DESC (RS , GrB_REPLACE, GrB_STRUCTURE + o , o , o )
GB_DESC (RST1 , GrB_REPLACE, GrB_STRUCTURE + o , o , GrB_TRAN )
GB_DESC (RST0 , GrB_REPLACE, GrB_STRUCTURE + o , GrB_TRAN, o )
GB_DESC (RST0T1 , GrB_REPLACE, GrB_STRUCTURE + o , GrB_TRAN, GrB_TRAN )
GB_DESC (RSC , GrB_REPLACE, GrB_STRUCTURE + GrB_COMP, o , o )
GB_DESC (RSCT1 , GrB_REPLACE, GrB_STRUCTURE + GrB_COMP, o , GrB_TRAN )
GB_DESC (RSCT0 , GrB_REPLACE, GrB_STRUCTURE + GrB_COMP, GrB_TRAN, o )
GB_DESC (RSCT0T1, GrB_REPLACE, GrB_STRUCTURE + GrB_COMP, GrB_TRAN, GrB_TRAN )
#undef o
//------------------------------------------------------------------------------
// GB_OP: construct the name of an operator
//------------------------------------------------------------------------------
#define GB_OP(op) GB_EVAL3 (op, _, GB_XTYPE)
//------------------------------------------------------------------------------
// helper macros to define unary operators
//------------------------------------------------------------------------------
#define GB_OP1zx(op,str,z_t,ztype,x_t,xtype) \
extern void GB_FUNC_T (op, xtype) (z_t *z, const x_t *x) ; \
struct GB_UnaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (ztype), \
& GB_OPAQUE (xtype), \
NULL, \
(GxB_unary_function) (& GB_FUNC_T (op, xtype)), NULL, NULL, NULL, \
str, \
GB_ ## op ## _unop_code, \
NULL, 0 \
}
#define GRB_OP1z(op,str,z_t,ztype) \
GB_OP1zx (op, str, z_t, ztype, GB_TYPE, GB_XTYPE) ; \
GrB_UnaryOp GRB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
#define GRB_OP1(op,str) GRB_OP1z (op, str, GB_TYPE, GB_XTYPE)
#define GXB_OP1z(op,str,z_t,ztype) \
GB_OP1zx (op, str, z_t, ztype, GB_TYPE, GB_XTYPE) ; \
GrB_UnaryOp GXB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
#define GXB_OP1(op,str) GXB_OP1z (op, str, GB_TYPE, GB_XTYPE)
#define GXB_OP1_RENAME(op) \
GrB_UnaryOp GXB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
//------------------------------------------------------------------------------
// helper macros to define binary operators
//------------------------------------------------------------------------------
#define GB_OP2zxy(op,str,z_t,ztype,x_t,xtype,y_t,ytype) \
extern void GB_FUNC_T(op,xtype) (z_t *z, const x_t *x, const y_t *y) ; \
struct GB_BinaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (ztype), \
& GB_OPAQUE (xtype), \
& GB_OPAQUE (ytype), \
NULL, NULL, (GxB_binary_function) (& GB_FUNC_T (op, xtype)), NULL, \
str, \
GB_ ## op ## _binop_code, \
NULL, 0 \
}
#define GRB_OP2z(op,str,z_t,ztype) \
GB_OP2zxy (op, str, z_t, ztype, GB_TYPE, GB_XTYPE, GB_TYPE, GB_XTYPE) ; \
GrB_BinaryOp GRB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
#define GRB_OP2(op,str) GRB_OP2z (op, str, GB_TYPE, GB_XTYPE)
#define GXB_OP2z(op,str,z_t,ztype) \
GB_OP2zxy (op, str, z_t, ztype, GB_TYPE, GB_XTYPE, GB_TYPE, GB_XTYPE) ; \
GrB_BinaryOp GXB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
#define GXB_OP2(op,str) GXB_OP2z (op, str, GB_TYPE, GB_XTYPE)
#define GXB_OP2shift(op,str) \
GB_OP2zxy (op, str, GB_TYPE, GB_XTYPE, GB_TYPE, GB_XTYPE, int8_t, INT8) ; \
GrB_BinaryOp GXB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
//------------------------------------------------------------------------------
// positional unary and binary operators
//------------------------------------------------------------------------------
// The function pointer inside a positional operator cannot be called directly,
// since it does not depend on the values of its two arguments. The operator
// can only be implemented via its opcode.
// helper macros to define positional unary operators
#define GXB_OP1_POS(op,str,type) \
struct GB_UnaryOp_opaque GB_OPAQUE (op ## _ ## type) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (type), /* ztype */ \
& GB_OPAQUE (type), /* xtype */ \
NULL, /* ytype */ \
NULL, NULL, NULL, NULL, \
str, \
GB_ ## op ## _unop_code, \
NULL, 0 \
} ; \
GrB_UnaryOp GXB (op ## _ ## type) = & GB_OPAQUE (op ## _ ## type)
// helper macros to define positional binary operators
#define GXB_OP2_POS(op,str,type) \
struct GB_BinaryOp_opaque GB_OPAQUE (op ## _ ## type) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (type), /* ztype */ \
& GB_OPAQUE (type), /* xtype */ \
& GB_OPAQUE (type), /* ytype */ \
NULL, NULL, NULL, NULL, \
str, \
GB_ ## op ## _binop_code, \
NULL, 0 \
} ; \
GrB_BinaryOp GXB (op ## _ ## type) = & GB_OPAQUE (op ## _ ## type)
GXB_OP1_POS (POSITIONI , "positioni" , INT32) ;
GXB_OP1_POS (POSITIONI , "positioni" , INT64) ;
GXB_OP1_POS (POSITIONI1, "positioni1", INT32) ;
GXB_OP1_POS (POSITIONI1, "positioni1", INT64) ;
GXB_OP1_POS (POSITIONJ , "positionj" , INT32) ;
GXB_OP1_POS (POSITIONJ , "positionj" , INT64) ;
GXB_OP1_POS (POSITIONJ1, "positionj1", INT32) ;
GXB_OP1_POS (POSITIONJ1, "positionj1", INT64) ;
GXB_OP2_POS (FIRSTI , "firsti" , INT32) ;
GXB_OP2_POS (FIRSTI , "firsti" , INT64) ;
GXB_OP2_POS (FIRSTI1 , "firsti1" , INT32) ;
GXB_OP2_POS (FIRSTI1 , "firsti1" , INT64) ;
GXB_OP2_POS (FIRSTJ , "firstj" , INT32) ;
GXB_OP2_POS (FIRSTJ , "firstj" , INT64) ;
GXB_OP2_POS (FIRSTJ1 , "firstj1" , INT32) ;
GXB_OP2_POS (FIRSTJ1 , "firstj1" , INT64) ;
GXB_OP2_POS (SECONDI , "secondi" , INT32) ;
GXB_OP2_POS (SECONDI , "secondi" , INT64) ;
GXB_OP2_POS (SECONDI1 , "secondi1" , INT32) ;
GXB_OP2_POS (SECONDI1 , "secondi1" , INT64) ;
GXB_OP2_POS (SECONDJ , "secondj" , INT32) ;
GXB_OP2_POS (SECONDJ , "secondj" , INT64) ;
GXB_OP2_POS (SECONDJ1 , "secondj1" , INT32) ;
GXB_OP2_POS (SECONDJ1 , "secondj1" , INT64) ;
//------------------------------------------------------------------------------
// built-in index_unary operators
//------------------------------------------------------------------------------
// IndexUnaryOps that depend on i,j,y but not A(i,j), and result has
// the same type as the scalar y: ROWINDEX, COLINDEX, DIAGINDEX
#define GRB_IDXOP_POSITIONAL(op,str) \
extern void GB_FUNC_T(op,GB_XTYPE) (GB_TYPE *z, const void *unused, \
GrB_Index i, GrB_Index j, const GB_TYPE *y) ; \
struct GB_IndexUnaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (GB_XTYPE), /* ztype */ \
NULL, /* xtype */ \
& GB_OPAQUE (GB_XTYPE), /* ytype */ \
NULL, (GxB_index_unary_function) (& GB_FUNC_T (op, GB_XTYPE)), \
NULL, NULL, \
str, \
GB_ ## op ## _idxunop_code, \
NULL, 0 \
} ; \
GrB_IndexUnaryOp GRB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
// GxB_IndexUnaryOps that depend on i,j,y but not A(i,j), and result has
// the same type as the scalar y: FLIPDIAGINDEX
#define GXB_IDXOP_POSITIONAL(op,str) \
extern void GB_FUNC_T(op,GB_XTYPE) (GB_TYPE *z, const void *unused, \
GrB_Index i, GrB_Index j, const GB_TYPE *y) ; \
struct GB_IndexUnaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (GB_XTYPE), /* ztype */ \
NULL, /* xtype */ \
& GB_OPAQUE (GB_XTYPE), /* ytype */ \
NULL, (GxB_index_unary_function) (& GB_FUNC_T (op, GB_XTYPE)), \
NULL, NULL, \
str, \
GB_ ## op ## _idxunop_code, \
NULL, 0 \
} ; \
GrB_IndexUnaryOp GXB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
// IndexUnaryOps that depend on i,j, and y but not A(i,j), and result is
// bool: TRIL, TRIU, DIAG, OFFDIAG, COLLE, COLGT, ROWLE, ROWGT
#define GRB_IDXOP_POSITIONAL_BOOL(op,str) \
extern void GB_FUNC_T(op,GB_XTYPE) (bool *z, const void *unused, \
GrB_Index i, GrB_Index j, const GB_TYPE *y) ; \
struct GB_IndexUnaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (BOOL), /* ztype */ \
NULL, /* xtype */ \
& GB_OPAQUE (GB_XTYPE), /* ytype */ \
NULL, (GxB_index_unary_function) (& GB_FUNC_T (op, GB_XTYPE)), \
NULL, NULL, \
str, \
GB_ ## op ## _idxunop_code, \
NULL, 0 \
} ; \
GrB_IndexUnaryOp GRB (op) = & GB_OPAQUE (GB_OP (op))
// GrB_IndexUnaryOps that depend on A(i,j), and result is bool: VALUE* ops
#define GRB_IDXOP_VALUE(op,str) \
extern void GB_FUNC_T(op,GB_XTYPE) (bool *z, const GB_TYPE *x, \
GrB_Index i_unused, GrB_Index j_unused, const GB_TYPE *y) ; \
struct GB_IndexUnaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (BOOL), /* ztype */ \
& GB_OPAQUE (GB_XTYPE), /* xtype */ \
& GB_OPAQUE (GB_XTYPE), /* ytype */ \
NULL, (GxB_index_unary_function) (& GB_FUNC_T (op, GB_XTYPE)), \
NULL, NULL, \
str, \
GB_ ## op ## _idxunop_code, \
NULL, 0 \
} ; \
GrB_IndexUnaryOp GRB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
// GrB_IndexUnaryOps that depend on A(i,j), result is bool: VALUE* complex ops
#define GXB_IDXOP_VALUE(op,str) \
extern void GB_FUNC_T(op,GB_XTYPE) (bool *z, const GB_TYPE *x, \
GrB_Index i_unused, GrB_Index j_unused, const GB_TYPE *y) ; \
struct GB_IndexUnaryOp_opaque GB_OPAQUE (GB_OP (op)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (BOOL), /* ztype */ \
& GB_OPAQUE (GB_XTYPE), /* xtype */ \
& GB_OPAQUE (GB_XTYPE), /* ytype */ \
NULL, (GxB_index_unary_function) (& GB_FUNC_T (op, GB_XTYPE)), \
NULL, NULL, \
str, \
GB_ ## op ## _idxunop_code, \
NULL, 0 \
} ; \
GrB_IndexUnaryOp GXB (GB_OP (op)) = & GB_OPAQUE (GB_OP (op))
//------------------------------------------------------------------------------
// built-in select operators
//------------------------------------------------------------------------------
#define GXB_SEL(op,str) \
struct GB_SelectOp_opaque GB_OPAQUE (op) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (BOOL), /* ztype */ \
NULL, /* xtype */ \
NULL, /* thunk type for GxB_SelectOp */ \
NULL, NULL, NULL, NULL, \
str, \
GB_ ## op ## _selop_code, \
NULL, 0 \
} ; \
GxB_SelectOp GXB (op) = & GB_OPAQUE (op)
GXB_SEL (TRIL , "tril" ) ;
GXB_SEL (TRIU , "triu" ) ;
GXB_SEL (DIAG , "diag" ) ;
GXB_SEL (OFFDIAG , "offdiag" ) ;
GXB_SEL (NONZERO , "nonzero" ) ;
GXB_SEL (EQ_ZERO , "eq_zero" ) ;
GXB_SEL (GT_ZERO , "gt_zero" ) ;
GXB_SEL (GE_ZERO , "ge_zero" ) ;
GXB_SEL (LT_ZERO , "lt_zero" ) ;
GXB_SEL (LE_ZERO , "le_zero" ) ;
GXB_SEL (NE_THUNK , "ne_thunk") ;
GXB_SEL (EQ_THUNK , "eq_thunk") ;
GXB_SEL (GT_THUNK , "gt_thunk") ;
GXB_SEL (GE_THUNK , "ge_thunk") ;
GXB_SEL (LT_THUNK , "lt_thunk") ;
GXB_SEL (LE_THUNK , "le_thunk") ;
//------------------------------------------------------------------------------
// define all built-in operators
//------------------------------------------------------------------------------
#define GB_TYPE bool
#define GB_XTYPE BOOL
#include "GB_ops_template.c"
#define GB_TYPE int8_t
#define GB_XTYPE INT8
#define GB_SIGNED_INT
#include "GB_ops_template.c"
#define GB_TYPE uint8_t
#define GB_XTYPE UINT8
#define GB_UNSIGNED_INT
#include "GB_ops_template.c"
#define GB_TYPE int16_t
#define GB_XTYPE INT16
#define GB_SIGNED_INT
#include "GB_ops_template.c"
#define GB_TYPE uint16_t
#define GB_XTYPE UINT16
#define GB_UNSIGNED_INT
#include "GB_ops_template.c"
#define GB_TYPE int32_t
#define GB_XTYPE INT32
#define GB_SIGNED_INT
#define GB_SIGNED_INDEX
#include "GB_ops_template.c"
#define GB_TYPE uint32_t
#define GB_XTYPE UINT32
#define GB_UNSIGNED_INT
#include "GB_ops_template.c"
#define GB_TYPE int64_t
#define GB_XTYPE INT64
#define GB_SIGNED_INT
#define GB_SIGNED_INDEX
#define GB_SIGNED_INDEX64
#include "GB_ops_template.c"
#define GB_TYPE uint64_t
#define GB_XTYPE UINT64
#define GB_UNSIGNED_INT
#include "GB_ops_template.c"
#define GB_TYPE float
#define GB_XTYPE FP32
#define GB_FLOAT
#define GB_FLOATING_POINT
#include "GB_ops_template.c"
#define GB_TYPE double
#define GB_XTYPE FP64
#define GB_DOUBLE
#define GB_FLOATING_POINT
#include "GB_ops_template.c"
#define GB_TYPE GxB_FC32_t
#define GB_XTYPE FC32
#define GB_FLOAT_COMPLEX
#define GB_COMPLEX
#define GB_FLOATING_POINT
#include "GB_ops_template.c"
#define GB_TYPE GxB_FC64_t
#define GB_XTYPE FC64
#define GB_DOUBLE_COMPLEX
#define GB_COMPLEX
#define GB_FLOATING_POINT
#include "GB_ops_template.c"
//------------------------------------------------------------------------------
// special cases for functions and operators
//------------------------------------------------------------------------------
// 5 special cases:
// purely boolean operators: these do not have _BOOL in their name
// They are not created by the templates above.
GrB_UnaryOp GrB_LNOT = & GB_OPAQUE (LNOT_BOOL) ;
GrB_BinaryOp GrB_LOR = & GB_OPAQUE (LOR_BOOL) ;
GrB_BinaryOp GrB_LAND = & GB_OPAQUE (LAND_BOOL) ;
GrB_BinaryOp GrB_LXOR = & GB_OPAQUE (LXOR_BOOL) ;
GrB_BinaryOp GrB_LXNOR = & GB_OPAQUE (EQ_BOOL) ;
// Special case for GrB_Matrix_build and GrB_Vector_build: this operator is
// not valid to use in any other methods.
struct GB_BinaryOp_opaque GB_OPAQUE (IGNORE_DUP) =
{
GB_MAGIC2, 0,
NULL, NULL, NULL,
NULL, NULL, NULL, NULL,
"ignore_dup", GB_NOP_code, NULL, 0
} ;
GrB_BinaryOp GxB_IGNORE_DUP = & GB_OPAQUE (IGNORE_DUP) ;
// GrB_ONEB_T: identical to GxB_PAIR_T
GrB_BinaryOp GrB_ONEB_BOOL = & GB_OPAQUE (PAIR_BOOL) ;
GrB_BinaryOp GrB_ONEB_INT8 = & GB_OPAQUE (PAIR_INT8) ;
GrB_BinaryOp GrB_ONEB_INT16 = & GB_OPAQUE (PAIR_INT16) ;
GrB_BinaryOp GrB_ONEB_INT32 = & GB_OPAQUE (PAIR_INT32) ;
GrB_BinaryOp GrB_ONEB_INT64 = & GB_OPAQUE (PAIR_INT64) ;
GrB_BinaryOp GrB_ONEB_UINT8 = & GB_OPAQUE (PAIR_UINT8) ;
GrB_BinaryOp GrB_ONEB_UINT16 = & GB_OPAQUE (PAIR_UINT16) ;
GrB_BinaryOp GrB_ONEB_UINT32 = & GB_OPAQUE (PAIR_UINT32) ;
GrB_BinaryOp GrB_ONEB_UINT64 = & GB_OPAQUE (PAIR_UINT64) ;
GrB_BinaryOp GrB_ONEB_FP32 = & GB_OPAQUE (PAIR_FP32) ;
GrB_BinaryOp GrB_ONEB_FP64 = & GB_OPAQUE (PAIR_FP64) ;
GrB_BinaryOp GxB_ONEB_FC32 = & GB_OPAQUE (PAIR_FC32) ;
GrB_BinaryOp GxB_ONEB_FC64 = & GB_OPAQUE (PAIR_FC64) ;
//------------------------------------------------------------------------------
// GrB_ALL
//------------------------------------------------------------------------------
// The GrB_ALL pointer is never dereferenced. It is passed in as an argument to
// indicate that all indices are to be used, as in the colon in C = A(:,j).
GrB_Index GB_OPAQUE (ALL) = 0 ;
const GrB_Index *GrB_ALL = & GB_OPAQUE (ALL) ;
// the default hyper_switch is defined in GB_defaults.h
const double GxB_HYPER_DEFAULT = GB_HYPER_SWITCH_DEFAULT ;
// set GxB_HYPER_SWITCH to either of these to ensure matrix is always, or never,
// stored in hypersparse format, respectively.
const double GxB_ALWAYS_HYPER = GB_ALWAYS_HYPER ;
const double GxB_NEVER_HYPER = GB_NEVER_HYPER ;
const GxB_Format_Value GxB_FORMAT_DEFAULT = GxB_BY_ROW ;
//------------------------------------------------------------------------------
// predefined built-in monoids
//------------------------------------------------------------------------------
#if GB_COMPILER_MSC
#define GB_FC32_ONE {1.0f, 0.0f}
#define GB_FC64_ONE {1.0 , 0.0 }
#define GB_FC32_ZERO {0.0f, 0.0f}
#define GB_FC64_ZERO {0.0 , 0.0 }
#else
#define GB_FC32_ONE GxB_CMPLXF (1,0)
#define GB_FC64_ONE GxB_CMPLX (1,0)
#define GB_FC32_ZERO GxB_CMPLXF (0,0)
#define GB_FC64_ZERO GxB_CMPLX (0,0)
#endif
// helper macro to define built-in monoids (no terminal value)
#define GB_MONOID_DEF(op,ztype,identity) \
ztype GB_OPAQUE (GB_EVAL2 (identity_, op)) = identity ; \
struct GB_Monoid_opaque GB_OPAQUE (GB_EVAL2 (op, _MONOID)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (op), \
& GB_OPAQUE (GB_EVAL2 (identity_, op)), \
NULL, \
0, 0 \
} ; \
GrB_Monoid GXB (GB_EVAL2 (op, _MONOID)) = \
& GB_OPAQUE (GB_EVAL2 (op, _MONOID)) ;
// helper macro to define built-in monoids (with terminal value)
#define GB_MONOID_DEFT(op,ztype,identity,terminal) \
ztype GB_OPAQUE (GB_EVAL2 (identity_, op)) = identity ; \
ztype GB_OPAQUE (GB_EVAL2 (terminal_, op)) = terminal ; \
struct GB_Monoid_opaque GB_OPAQUE (GB_EVAL2 (op, _MONOID)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (op), \
& GB_OPAQUE (GB_EVAL2 (identity_, op)), \
& GB_OPAQUE (GB_EVAL2 (terminal_, op)), \
0, 0 \
} ; \
GrB_Monoid GXB (GB_EVAL2 (op, _MONOID)) = \
& GB_OPAQUE (GB_EVAL2 (op, _MONOID)) ;
// macro to construct GrB_* monoids in the updated specification
#define GB_MONOID_GRB(op,type) \
GrB_Monoid GRB (GB_EVAL3 (op, _MONOID_, type)) = \
& GB_OPAQUE (GB_EVAL4 (op, _, type, _MONOID)) ;
// MIN monoids:
GB_MONOID_DEFT ( MIN_INT8 , int8_t , INT8_MAX , INT8_MIN )
GB_MONOID_DEFT ( MIN_INT16 , int16_t , INT16_MAX , INT16_MIN )
GB_MONOID_DEFT ( MIN_INT32 , int32_t , INT32_MAX , INT32_MIN )
GB_MONOID_DEFT ( MIN_INT64 , int64_t , INT64_MAX , INT64_MIN )
GB_MONOID_DEFT ( MIN_UINT8 , uint8_t , UINT8_MAX , 0 )
GB_MONOID_DEFT ( MIN_UINT16 , uint16_t , UINT16_MAX , 0 )
GB_MONOID_DEFT ( MIN_UINT32 , uint32_t , UINT32_MAX , 0 )
GB_MONOID_DEFT ( MIN_UINT64 , uint64_t , UINT64_MAX , 0 )
GB_MONOID_DEF ( MIN_FP32 , float , INFINITY )
GB_MONOID_DEF ( MIN_FP64 , double , INFINITY )
GB_MONOID_GRB ( MIN, INT8 )
GB_MONOID_GRB ( MIN, INT16 )
GB_MONOID_GRB ( MIN, INT32 )
GB_MONOID_GRB ( MIN, INT64 )
GB_MONOID_GRB ( MIN, UINT8 )
GB_MONOID_GRB ( MIN, UINT16 )
GB_MONOID_GRB ( MIN, UINT32 )
GB_MONOID_GRB ( MIN, UINT64 )
GB_MONOID_GRB ( MIN, FP32 )
GB_MONOID_GRB ( MIN, FP64 )
// MAX monoids:
GB_MONOID_DEFT ( MAX_INT8 , int8_t , INT8_MIN , INT8_MAX )
GB_MONOID_DEFT ( MAX_INT16 , int16_t , INT16_MIN , INT16_MAX )
GB_MONOID_DEFT ( MAX_INT32 , int32_t , INT32_MIN , INT32_MAX )
GB_MONOID_DEFT ( MAX_INT64 , int64_t , INT64_MIN , INT64_MAX )
GB_MONOID_DEFT ( MAX_UINT8 , uint8_t , 0 , UINT8_MAX )
GB_MONOID_DEFT ( MAX_UINT16 , uint16_t , 0 , UINT16_MAX)
GB_MONOID_DEFT ( MAX_UINT32 , uint32_t , 0 , UINT32_MAX)
GB_MONOID_DEFT ( MAX_UINT64 , uint64_t , 0 , UINT64_MAX)
GB_MONOID_DEF ( MAX_FP32 , float , -INFINITY )
GB_MONOID_DEF ( MAX_FP64 , double , -INFINITY )
GB_MONOID_GRB ( MAX, INT8 )
GB_MONOID_GRB ( MAX, INT16 )
GB_MONOID_GRB ( MAX, INT32 )
GB_MONOID_GRB ( MAX, INT64 )
GB_MONOID_GRB ( MAX, UINT8 )
GB_MONOID_GRB ( MAX, UINT16 )
GB_MONOID_GRB ( MAX, UINT32 )
GB_MONOID_GRB ( MAX, UINT64 )
GB_MONOID_GRB ( MAX, FP32 )
GB_MONOID_GRB ( MAX, FP64 )
// PLUS monoids:
GB_MONOID_DEF ( PLUS_INT8 , int8_t , 0 )
GB_MONOID_DEF ( PLUS_INT16 , int16_t , 0 )
GB_MONOID_DEF ( PLUS_INT32 , int32_t , 0 )
GB_MONOID_DEF ( PLUS_INT64 , int64_t , 0 )
GB_MONOID_DEF ( PLUS_UINT8 , uint8_t , 0 )
GB_MONOID_DEF ( PLUS_UINT16 , uint16_t , 0 )
GB_MONOID_DEF ( PLUS_UINT32 , uint32_t , 0 )
GB_MONOID_DEF ( PLUS_UINT64 , uint64_t , 0 )
GB_MONOID_DEF ( PLUS_FP32 , float , 0 )
GB_MONOID_DEF ( PLUS_FP64 , double , 0 )
GB_MONOID_DEF ( PLUS_FC32 , GxB_FC32_t, GB_FC32_ZERO)
GB_MONOID_DEF ( PLUS_FC64 , GxB_FC64_t, GB_FC64_ZERO)
GB_MONOID_GRB ( PLUS, INT8 )
GB_MONOID_GRB ( PLUS, INT16 )
GB_MONOID_GRB ( PLUS, INT32 )
GB_MONOID_GRB ( PLUS, INT64 )
GB_MONOID_GRB ( PLUS, UINT8 )
GB_MONOID_GRB ( PLUS, UINT16 )
GB_MONOID_GRB ( PLUS, UINT32 )
GB_MONOID_GRB ( PLUS, UINT64 )
GB_MONOID_GRB ( PLUS, FP32 )
GB_MONOID_GRB ( PLUS, FP64 )
// TIMES monoids:
GB_MONOID_DEFT ( TIMES_INT8 , int8_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_INT16 , int16_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_INT32 , int32_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_INT64 , int64_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_UINT8 , uint8_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_UINT16 , uint16_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_UINT32 , uint32_t , 1 , 0)
GB_MONOID_DEFT ( TIMES_UINT64 , uint64_t , 1 , 0)
GB_MONOID_DEF ( TIMES_FP32 , float , 1 )
GB_MONOID_DEF ( TIMES_FP64 , double , 1 )
GB_MONOID_DEF ( TIMES_FC32 , GxB_FC32_t, GB_FC32_ONE )
GB_MONOID_DEF ( TIMES_FC64 , GxB_FC64_t, GB_FC64_ONE )
GB_MONOID_GRB ( TIMES, INT8 )
GB_MONOID_GRB ( TIMES, INT16 )
GB_MONOID_GRB ( TIMES, INT32 )
GB_MONOID_GRB ( TIMES, INT64 )
GB_MONOID_GRB ( TIMES, UINT8 )
GB_MONOID_GRB ( TIMES, UINT16 )
GB_MONOID_GRB ( TIMES, UINT32 )
GB_MONOID_GRB ( TIMES, UINT64 )
GB_MONOID_GRB ( TIMES, FP32 )
GB_MONOID_GRB ( TIMES, FP64 )
// ANY monoids:
GB_MONOID_DEFT ( ANY_INT8 , int8_t , 0 , 0)
GB_MONOID_DEFT ( ANY_INT16 , int16_t , 0 , 0)
GB_MONOID_DEFT ( ANY_INT32 , int32_t , 0 , 0)
GB_MONOID_DEFT ( ANY_INT64 , int64_t , 0 , 0)
GB_MONOID_DEFT ( ANY_UINT8 , uint8_t , 0 , 0)
GB_MONOID_DEFT ( ANY_UINT16 , uint16_t , 0 , 0)
GB_MONOID_DEFT ( ANY_UINT32 , uint32_t , 0 , 0)
GB_MONOID_DEFT ( ANY_UINT64 , uint64_t , 0 , 0)
GB_MONOID_DEFT ( ANY_FP32 , float , 0 , 0)
GB_MONOID_DEFT ( ANY_FP64 , double , 0 , 0)
GB_MONOID_DEFT ( ANY_FC32 , GxB_FC32_t, GB_FC32_ZERO, GB_FC32_ZERO)
GB_MONOID_DEFT ( ANY_FC64 , GxB_FC64_t, GB_FC64_ZERO, GB_FC64_ZERO)
// Boolean monoids:
GB_MONOID_DEFT ( ANY_BOOL , bool , false , false)
GB_MONOID_DEFT ( LOR_BOOL , bool , false , true )
GB_MONOID_DEFT ( LAND_BOOL , bool , true , false)
GB_MONOID_DEF ( LXOR_BOOL , bool , false )
GB_MONOID_DEF ( EQ_BOOL , bool , true )
// GrB_LXNOR_BOOL_MONIOD is the same as GrB_EQ_BOOL_MONIOD:
GrB_Monoid GxB_LXNOR_BOOL_MONOID = & GB_OPAQUE (EQ_BOOL_MONOID) ;
GB_MONOID_GRB ( LOR , BOOL )
GB_MONOID_GRB ( LAND , BOOL )
GB_MONOID_GRB ( LXOR , BOOL )
GrB_Monoid GrB_LXNOR_MONOID_BOOL = & GB_OPAQUE (EQ_BOOL_MONOID) ;
// BOR monoids (bitwise or):
GB_MONOID_DEFT ( BOR_UINT8 , uint8_t , 0, 0xFF )
GB_MONOID_DEFT ( BOR_UINT16 , uint16_t , 0, 0xFFFF )
GB_MONOID_DEFT ( BOR_UINT32 , uint32_t , 0, 0xFFFFFFFF )
GB_MONOID_DEFT ( BOR_UINT64 , uint64_t , 0, 0xFFFFFFFFFFFFFFFF )
// BAND monoids (bitwise and):
GB_MONOID_DEFT ( BAND_UINT8 , uint8_t , 0xFF , 0 )
GB_MONOID_DEFT ( BAND_UINT16 , uint16_t , 0xFFFF , 0 )
GB_MONOID_DEFT ( BAND_UINT32 , uint32_t , 0xFFFFFFFF , 0 )
GB_MONOID_DEFT ( BAND_UINT64 , uint64_t , 0xFFFFFFFFFFFFFFFF, 0 )
// BXOR monoids (bitwise xor):
GB_MONOID_DEF ( BXOR_UINT8 , uint8_t , 0)
GB_MONOID_DEF ( BXOR_UINT16 , uint16_t , 0)
GB_MONOID_DEF ( BXOR_UINT32 , uint32_t , 0)
GB_MONOID_DEF ( BXOR_UINT64 , uint64_t , 0)
// BXNOR monoids (bitwise xnor):
GB_MONOID_DEF ( BXNOR_UINT8 , uint8_t , 0xFF )
GB_MONOID_DEF ( BXNOR_UINT16 , uint16_t , 0xFFFF )
GB_MONOID_DEF ( BXNOR_UINT32 , uint32_t , 0xFFFFFFFF )
GB_MONOID_DEF ( BXNOR_UINT64 , uint64_t , 0xFFFFFFFFFFFFFFFF )
//------------------------------------------------------------------------------
// predefined built-in semirings
//------------------------------------------------------------------------------
#define GB_SEMIRING_NAME(add,mult) \
GB_EVAL5 (add, _, mult, _, GB_XTYPE)
// helper macro to define semirings: all x,y,z types the same
#define GXB_SEMIRING(add,mult) \
struct GB_Semiring_opaque GB_OPAQUE (GB_SEMIRING_NAME(add, mult)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (GB_EVAL4 (add, _, GB_XTYPE, _MONOID)), \
& GB_OPAQUE (GB_EVAL3 (mult, _, GB_XTYPE)), \
} ; \
GrB_Semiring GXB (GB_SEMIRING_NAME (add, mult)) = \
& GB_OPAQUE (GB_SEMIRING_NAME (add, mult)) ;
// helper macro to define semirings: x,y types the same, z boolean
#define GB_SEMIRING_COMPARE_DEFINE(add,mult) \
struct GB_Semiring_opaque GB_OPAQUE (GB_SEMIRING_NAME(add, mult)) = \
{ \
GB_MAGIC, 0, \
& GB_OPAQUE (GB_EVAL2 (add, _BOOL_MONOID)), \
& GB_OPAQUE (GB_EVAL3 (mult, _, GB_XTYPE)), \
} ;
#define GXB_SEMIRING_COMPARE(add,mult) \
GB_SEMIRING_COMPARE_DEFINE (add, mult) \
GrB_Semiring GXB (GB_SEMIRING_NAME (add, mult)) = \
& GB_OPAQUE (GB_SEMIRING_NAME (add, mult)) ;
#define GB_XTYPE BOOL
#define GB_BOOLEAN
#include "GB_semiring_template.c"
#define GB_XTYPE INT8
#include "GB_semiring_template.c"
#define GB_XTYPE UINT8
#define GB_UNSIGNED_INT
#include "GB_semiring_template.c"
#define GB_XTYPE INT16
#include "GB_semiring_template.c"
#define GB_XTYPE UINT16
#define GB_UNSIGNED_INT
#include "GB_semiring_template.c"
#define GB_XTYPE INT32
#define GB_POSITIONAL
#include "GB_semiring_template.c"
#define GB_UNSIGNED_INT
#define GB_XTYPE UINT32
#include "GB_semiring_template.c"
#define GB_POSITIONAL
#define GB_XTYPE INT64
#include "GB_semiring_template.c"
#define GB_UNSIGNED_INT
#define GB_XTYPE UINT64
#include "GB_semiring_template.c"
#define GB_XTYPE FP32
#include "GB_semiring_template.c"
#define GB_XTYPE FP64
#include "GB_semiring_template.c"
#define GB_COMPLEX
#define GB_XTYPE FC32
#include "GB_semiring_template.c"
#define GB_COMPLEX
#define GB_XTYPE FC64
#include "GB_semiring_template.c"
//------------------------------------------------------------------------------
// 124 predefined built-in semirings in the v1.3 C API
//------------------------------------------------------------------------------
// These predefined semirings have been added to the spec, as of v1.3.
// They are identical to the GxB* semirings of the same name, except for
// GrB_LXNOR_LOR_SEMIRING_BOOL, which is identical to GxB_EQ_LOR_BOOL.
#define GRB_SEMIRING(add,mult,xtype) \
GrB_Semiring GRB (GB_EVAL5 (add, _, mult, _SEMIRING_, xtype)) = \
& GB_OPAQUE (GB_EVAL5 (add, _, mult, _, xtype)) ;
//--------------------------------------------------------------------------
// 4 boolean semirings
//--------------------------------------------------------------------------
GRB_SEMIRING (LOR, LAND, BOOL)
GRB_SEMIRING (LAND, LOR, BOOL)
GRB_SEMIRING (LXOR, LAND, BOOL)
GrB_Semiring GRB (LXNOR_LOR_SEMIRING_BOOL) = & GB_OPAQUE (EQ_LOR_BOOL) ;
//--------------------------------------------------------------------------
// 20 semirings with PLUS monoids
//--------------------------------------------------------------------------
GRB_SEMIRING (PLUS, TIMES, INT8)
GRB_SEMIRING (PLUS, TIMES, INT16)
GRB_SEMIRING (PLUS, TIMES, INT32)
GRB_SEMIRING (PLUS, TIMES, INT64)
GRB_SEMIRING (PLUS, TIMES, UINT8)
GRB_SEMIRING (PLUS, TIMES, UINT16)
GRB_SEMIRING (PLUS, TIMES, UINT32)
GRB_SEMIRING (PLUS, TIMES, UINT64)
GRB_SEMIRING (PLUS, TIMES, FP32)
GRB_SEMIRING (PLUS, TIMES, FP64)
GRB_SEMIRING (PLUS, MIN, INT8)
GRB_SEMIRING (PLUS, MIN, INT16)
GRB_SEMIRING (PLUS, MIN, INT32)
GRB_SEMIRING (PLUS, MIN, INT64)
GRB_SEMIRING (PLUS, MIN, UINT8)
GRB_SEMIRING (PLUS, MIN, UINT16)
GRB_SEMIRING (PLUS, MIN, UINT32)
GRB_SEMIRING (PLUS, MIN, UINT64)
GRB_SEMIRING (PLUS, MIN, FP32)
GRB_SEMIRING (PLUS, MIN, FP64)
//--------------------------------------------------------------------------
// 50 semirings with MIN monoids
//--------------------------------------------------------------------------
GRB_SEMIRING (MIN, PLUS, INT8)
GRB_SEMIRING (MIN, PLUS, INT16)
GRB_SEMIRING (MIN, PLUS, INT32)
GRB_SEMIRING (MIN, PLUS, INT64)
GRB_SEMIRING (MIN, PLUS, UINT8)
GRB_SEMIRING (MIN, PLUS, UINT16)
GRB_SEMIRING (MIN, PLUS, UINT32)
GRB_SEMIRING (MIN, PLUS, UINT64)
GRB_SEMIRING (MIN, PLUS, FP32)
GRB_SEMIRING (MIN, PLUS, FP64)
GRB_SEMIRING (MIN, TIMES, INT8)
GRB_SEMIRING (MIN, TIMES, INT16)
GRB_SEMIRING (MIN, TIMES, INT32)
GRB_SEMIRING (MIN, TIMES, INT64)
GRB_SEMIRING (MIN, TIMES, UINT8)
GRB_SEMIRING (MIN, TIMES, UINT16)
GRB_SEMIRING (MIN, TIMES, UINT32)
GRB_SEMIRING (MIN, TIMES, UINT64)
GRB_SEMIRING (MIN, TIMES, FP32)
GRB_SEMIRING (MIN, TIMES, FP64)
GRB_SEMIRING (MIN, FIRST, INT8)
GRB_SEMIRING (MIN, FIRST, INT16)
GRB_SEMIRING (MIN, FIRST, INT32)
GRB_SEMIRING (MIN, FIRST, INT64)
GRB_SEMIRING (MIN, FIRST, UINT8)
GRB_SEMIRING (MIN, FIRST, UINT16)
GRB_SEMIRING (MIN, FIRST, UINT32)
GRB_SEMIRING (MIN, FIRST, UINT64)
GRB_SEMIRING (MIN, FIRST, FP32)
GRB_SEMIRING (MIN, FIRST, FP64)
GRB_SEMIRING (MIN, SECOND, INT8)
GRB_SEMIRING (MIN, SECOND, INT16)
GRB_SEMIRING (MIN, SECOND, INT32)
GRB_SEMIRING (MIN, SECOND, INT64)
GRB_SEMIRING (MIN, SECOND, UINT8)
GRB_SEMIRING (MIN, SECOND, UINT16)
GRB_SEMIRING (MIN, SECOND, UINT32)
GRB_SEMIRING (MIN, SECOND, UINT64)
GRB_SEMIRING (MIN, SECOND, FP32)
GRB_SEMIRING (MIN, SECOND, FP64)
GRB_SEMIRING (MIN, MAX, INT8)
GRB_SEMIRING (MIN, MAX, INT16)
GRB_SEMIRING (MIN, MAX, INT32)
GRB_SEMIRING (MIN, MAX, INT64)
GRB_SEMIRING (MIN, MAX, UINT8)
GRB_SEMIRING (MIN, MAX, UINT16)
GRB_SEMIRING (MIN, MAX, UINT32)
GRB_SEMIRING (MIN, MAX, UINT64)
GRB_SEMIRING (MIN, MAX, FP32)
GRB_SEMIRING (MIN, MAX, FP64)
//--------------------------------------------------------------------------
// 50 semirings with MAX monoids
//--------------------------------------------------------------------------
GRB_SEMIRING (MAX, PLUS, INT8)
GRB_SEMIRING (MAX, PLUS, INT16)
GRB_SEMIRING (MAX, PLUS, INT32)
GRB_SEMIRING (MAX, PLUS, INT64)
GRB_SEMIRING (MAX, PLUS, UINT8)
GRB_SEMIRING (MAX, PLUS, UINT16)
GRB_SEMIRING (MAX, PLUS, UINT32)
GRB_SEMIRING (MAX, PLUS, UINT64)
GRB_SEMIRING (MAX, PLUS, FP32)
GRB_SEMIRING (MAX, PLUS, FP64)
GRB_SEMIRING (MAX, TIMES, INT8)
GRB_SEMIRING (MAX, TIMES, INT16)
GRB_SEMIRING (MAX, TIMES, INT32)
GRB_SEMIRING (MAX, TIMES, INT64)
GRB_SEMIRING (MAX, TIMES, UINT8)
GRB_SEMIRING (MAX, TIMES, UINT16)
GRB_SEMIRING (MAX, TIMES, UINT32)
GRB_SEMIRING (MAX, TIMES, UINT64)
GRB_SEMIRING (MAX, TIMES, FP32)
GRB_SEMIRING (MAX, TIMES, FP64)
GRB_SEMIRING (MAX, FIRST, INT8)
GRB_SEMIRING (MAX, FIRST, INT16)
GRB_SEMIRING (MAX, FIRST, INT32)
GRB_SEMIRING (MAX, FIRST, INT64)
GRB_SEMIRING (MAX, FIRST, UINT8)
GRB_SEMIRING (MAX, FIRST, UINT16)
GRB_SEMIRING (MAX, FIRST, UINT32)
GRB_SEMIRING (MAX, FIRST, UINT64)
GRB_SEMIRING (MAX, FIRST, FP32)
GRB_SEMIRING (MAX, FIRST, FP64)
GRB_SEMIRING (MAX, SECOND, INT8)
GRB_SEMIRING (MAX, SECOND, INT16)
GRB_SEMIRING (MAX, SECOND, INT32)
GRB_SEMIRING (MAX, SECOND, INT64)
GRB_SEMIRING (MAX, SECOND, UINT8)
GRB_SEMIRING (MAX, SECOND, UINT16)
GRB_SEMIRING (MAX, SECOND, UINT32)
GRB_SEMIRING (MAX, SECOND, UINT64)
GRB_SEMIRING (MAX, SECOND, FP32)
GRB_SEMIRING (MAX, SECOND, FP64)
GRB_SEMIRING (MAX, MIN, INT8)
GRB_SEMIRING (MAX, MIN, INT16)
GRB_SEMIRING (MAX, MIN, INT32)
GRB_SEMIRING (MAX, MIN, INT64)
GRB_SEMIRING (MAX, MIN, UINT8)
GRB_SEMIRING (MAX, MIN, UINT16)
GRB_SEMIRING (MAX, MIN, UINT32)
GRB_SEMIRING (MAX, MIN, UINT64)
GRB_SEMIRING (MAX, MIN, FP32)
GRB_SEMIRING (MAX, MIN, FP64)
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