ndarray: change internal api of mul/div to help autograd (#366)

address #274 (comment)

src/ndarray.jl

@@ -650,12 +650,12 @@ import Base: *
 
 Currently only multiplication a scalar with an `NDArray` is implemented.
 """
-*(x:: NDArray, y::Real) = x .* y
-*(x::Real, y::NDArray)  = y .* x
+*(x::NDArray, y::Real)  = _mul_scalar(x, scalar = y)
+*(y::Real, x::NDArray)  = _mul_scalar(x, scalar = y)
 
-broadcast_(::typeof(*), x::NDArray, y::NDArrayOrReal) =
-  mul_to!(copy(x, context(x)), y)
-broadcast_(::typeof(*), x::Real, y::NDArray) = y .* x
+broadcast_(::typeof(*), x::NDArray, y::Real)    = x * y
+broadcast_(::typeof(*), y::Real, x::NDArray)    = x * y
+broadcast_(::typeof(*), x::NDArray, y::NDArray) = _mul(x, y)
 
 """
     *(A::NDArray, B::NDArray)
@@ -703,25 +703,23 @@ of the same shape.
 
 * Matrix division (solving linear systems) is not implemented yet.
 """
-/(x::NDArray, y::Real) = x ./ y
+/(x::NDArray, y::Real) = _div_scalar(x, scalar = y)
 
-broadcast_(::typeof(/), x::NDArray, y::NDArrayOrReal) =
-  div_from!(copy(x, context(x)), y)
-
-broadcast_(::typeof(/), x::Real, y::NDArray) =
-  rdiv_from!(x, copy(y, context(y)))
+broadcast_(::typeof(/), x::NDArray, y::NDArray) = _div(x, y)
+broadcast_(::typeof(/), x::NDArray, y::Real)    = _div_scalar(x, scalar = y)
+broadcast_(::typeof(/), y::Real, x::NDArray)    = _rdiv_scalar(x, scalar = y)
 
 import Base: ^
 
 # document of `.^` is merged into SymbolicNode's
 
 broadcast_(::typeof(^), x::NDArray, y::NDArray) = _power(x, y)
-broadcast_(::typeof(^), x::NDArray, s::Real) = _power_scalar(x, scalar=s)
-broadcast_(::typeof(^), s::Real, x::NDArray) = _rpower_scalar(x, scalar=s)
+broadcast_(::typeof(^), x::NDArray, s::Real) = _power_scalar(x, scalar = s)
+broadcast_(::typeof(^), s::Real, x::NDArray) = _rpower_scalar(x, scalar = s)
 
 broadcast_(::typeof(^), ::Irrational{:e}, x::NDArray) = exp(x)
-broadcast_(::typeof(^), x::NDArray, s::Irrational) = _power_scalar(x, scalar=s)
-broadcast_(::typeof(^), s::Irrational, x::NDArray) = _rpower_scalar(x, scalar=s)
+broadcast_(::typeof(^), x::NDArray, s::Irrational) = _power_scalar(x, scalar = s)
+broadcast_(::typeof(^), s::Irrational, x::NDArray) = _rpower_scalar(x, scalar = s)
 
 """
     fill!(arr::NDArray, x)