binaryops.md

Binary Operators

Binary operators are defined on three domains $D_1 \times D_2 \rightarrow D_3$. However, the vast majority of binary operators are defined on a single domain.

BinaryOps are in almost every GraphBLAS operation. They are the primary op argument for emul, eadd, and apply. BinaryOps which are also monoids may be used in reduce. And every GraphBLAS operation which takes an accum keyword argument accepts a BinaryOp.

In almost all cases you should pass Julia functions, which will be mapped to built-in operators, or used to create a new user-defined operator.

using SuiteSparseGraphBLAS

x = GBMatrix([[1,2] [3,4]])

x .+ x
eadd(x, x, +)

x .^ x
emul(x, x, ^)

x2 = Float64.(x)
eadd!(x2, x, x, +; accum=/)

Internally functions are lowered like this:

using SuiteSparseGraphBLAS

typedop = binaryop(+, Int64, Int64)

eadd(GBVector([1,2]), GBVector([3,4]), typedop)

Built-Ins

All built-in binary operators can be found below:

Julia Function	GraphBLAS Name	Notes
first	FIRST	first(x, y) = x
second	SECOND	second(x, y) = y
any	ANY	any(x, y) can return either x or y. The result is non-deterministic.
pair	PAIR	pair(x, y) = 1 if x and y are stored values
+	PLUS
-	MINUS
rminus	RMINUS
*	TIMES
/	DIV
\	RDIV
^	POW
iseq	ISEQ	iseq(x::T, y::T) = T(x == y)
isne	ISNE	isne(x::T, y::T) = T(x != y)
min	MIN
max	MAX
isgt	ISGT	isgt(x::T, y::T) = T(x > y)
islt	ISLT	islt(x::T, y::T) = T(x < y)
isge	ISGE	isge(x::T, y::T) = T(x >= y)
isle	ISLE	isle(x::T, y::T) = T(x <= y)
∨	LOR
∧	LAND
lxor	LXOR
==	EQ
!=	NE
>	GT
<	LT
>=	GE
<=	LE
xnor	LXNOR
atan	ATAN2
hypot	HYPOT
fmod	FMOD
rem	REMAINDER
ldexp	LDEXP
copysign	COPYSIGN
complex	CMPLX
|	BOR
&	BAND
⊻	BXOR
bget	BGET
bset	BSET
bclr	BCLR
>>	BSHIFT
firsti0	FIRSTI	firsti0(A[i,j], B[k,l]) = i - 1
firsti	FIRSTI1	firsti(A[i,j], B[k,l]) = i
firstj0	FIRSTJ	firstj0(A[i,j], B[k,l]) = j - 1
firstj	FIRSTJ1	firstj(A[i,j], B[k,l]) = j
secondi0	SECONDI	secondi0(A[i,j], B[k,l]) = k - 1
secondi	SECONDI1	secondi(A[i,j], B[k,l]) = k
secondj0	SECONDJ	secondj0(A[i,j], B[k,l]) = l - 1
secondj	SECONDJ1	secondj(A[i,j], B[k,l]) = l