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function identity = GB_spec_identity (arg1,arg2)
%GB_SPEC_IDENTITY the additive identity of a monoid
%
% identity = GB_spec_identity (add) ;
% or
% identity = GB_spec_identity (add_op, add_type) ; % both strings
%
% Returns the additive identity of an operator of a monoid.
%
% The identity is that value such that x == add (x,identity) == add
% (identity,x). For example, for 'plus', the value is zero. for 'max' the
% value of identity is -infinity.
%
% The addititive monoids supported are 'min', 'max', 'plus', 'times', 'or',
% 'and', 'xor', 'eq', 'bitor', 'bitand', 'bitxor', and 'bitxnor'.
% For the 'or', 'and', 'xor', and 'eq' the add_type must be 'logical'.
% For the 'bit*' operators, the add_type must be unsigned integer.
% SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
% SPDX-License-Identifier: Apache-2.0
if (nargin == 1)
add = arg1 ;
[add_operator add_type ztype xtype ytype] = GB_spec_operator (add) ;
else
add_operator = arg1 ;
add_type = arg2 ;
end
switch add_operator
case 'min'
% x == min (x, inf)
switch add_type
case 'logical'
identity = true ;
case 'int8'
identity = int8 (inf) ;
case 'uint8'
identity = uint8 (inf) ;
case 'int16'
identity = int16 (inf) ;
case 'uint16'
identity = uint16 (inf) ;
case 'int32'
identity = int32 (inf) ;
case 'uint32'
identity = uint32 (inf) ;
case 'int64'
identity = int64 (inf) ;
case 'uint64'
identity = uint64 (inf) ;
case 'single'
identity = single (inf) ;
case 'double'
identity = inf ;
end
case 'max'
% x == max (x, -inf)
switch add_type
case 'logical'
identity = false ;
case 'int8'
identity = int8 (-inf) ;
case 'uint8'
identity = 0 ;
case 'int16'
identity = int16 (-inf) ;
case 'uint16'
identity = 0 ;
case 'int32'
identity = int32 (-inf) ;
case 'uint32'
identity = 0 ;
case 'int64'
identity = int64 (-inf) ;
case 'uint64'
identity = 0 ;
case 'single'
identity = single (-inf) ;
case 'double'
identity = -inf ;
end
case 'plus'
% x == x + 0
identity = 0 ;
case 'times'
% x == x * 1
identity = 1 ;
case 'any'
identity = [ ] ;
case { 'or', 'lor'}
% x == x or false
identity = false ;
if (~isequal (add_type, 'logical'))
error ('OR monoid must be logical') ;
end
case { 'and', 'land' }
% x == x and true
identity = true ;
if (~isequal (add_type, 'logical'))
error ('AND monoid must be logical') ;
end
case { 'xor', 'lxor' }
% x == x xor false
identity = false ;
if (~isequal (add_type, 'logical'))
error ('XOR monoid must be logical') ;
end
case { 'eq', 'lxnor'}
% x == (x == true)
identity = true ;
if (~isequal (add_type, 'logical'))
error ('EQ monoid must be logical') ;
end
case { 'iseq', 'eq' }
% x == (x == true)
identity = true ;
if (~isequal (add_type, 'logical'))
error ('ISEQ monoid must be logical') ;
end
case { 'bitor', 'bor' }
switch add_type
case { 'uint8', 'uint16', 'uint32', 'uint64' }
identity = 0 ;
otherwise
error ('BIT* monoids must be unsigned int') ;
end
case { 'bitand', 'band' }
switch add_type
case { 'uint8', 'uint16', 'uint32', 'uint64' }
identity = intmax (add_type) ;
otherwise
error ('BIT* monoids must be unsigned int') ;
end
case { 'bitxor', 'bxor' }
switch add_type
case { 'uint8', 'uint16', 'uint32', 'uint64' }
identity = 0 ;
otherwise
error ('BIT* monoids must be unsigned int') ;
end
case { 'bitxnor', 'bxnor' }
switch add_type
case { 'uint8', 'uint16', 'uint32', 'uint64' }
identity = intmax (add_type) ;
otherwise
error ('BIT* monoids must be unsigned int') ;
end
otherwise
error ('unsupported additive monoid') ;
end
identity = GB_mex_cast (identity, add_type) ;
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