ndarray: elementwise power (#293)

* ndarray: elementwise power

```julia
x.^2

2.^x

x.^y
```

* ndarray: elementwise power unfusion

* Update NEWS

NEWS.md

@@ -26,6 +26,12 @@
      2.0  4.0
     ```
 
+* Elementwise power of `NDArray`. (#293)
+    * `x.^2`
+    * `2.^x`
+    * `x.^y`
+    * where `x` and `y` are `NDArray`s.
+
 ## API Changes
 
 * `reshape` of NDArray shares the same interface with Base (#272).

src/ndarray.jl

@@ -689,6 +689,21 @@ broadcast_(::typeof(/), x::NDArray, y::NDArrayOrReal) =
 broadcast_(::typeof(/), x::Real, y::NDArray) =
   rdiv_from!(x, copy(y, context(y)))
 
+import Base: ^
+
+"""
+    .^(x::NDArray, y::NDArray)
+    .^(x::NDArray, s::Real)
+    .^(s::Real, x::NDArray)
+
+Elementwise power of NDArray.
+"""
+^
+
+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)
+
 """
     fill!(x, arr::NDArray)
 
@@ -713,7 +728,6 @@ end
 
 fill(x, dims::Integer...) = fill(x, dims)
 
-
 """
 Manipulating as Julia Arrays
 ----------------------------

test/unittest/ndarray.jl

@@ -380,6 +380,77 @@ function test_clip()
   @test all(clip_down .<= copy(clipped) .<= clip_up)
 end
 
+function test_power()
+  info("NDArray::power")
+  thresh = 1e8
+
+  info("NDArray::power::Int::x.^n")
+  let x = mx.NDArray([1 2; 3 4])
+    @test eltype(x) == Int
+    @test copy(x.^-1)  == [1 0; 0 0]
+    @test copy(x.^0)   == [1 1; 1 1]
+    @test copy(x.^1)   == [1 2; 3 4]
+    @test copy(x.^1.1) == [1 2; 3 4]
+    @test copy(x.^2)   == [1 4; 9 16]
+    @test copy(x.^2.9) == [1 4; 9 16]
+    @test copy(x.^3)   == [1 8; 27 64]
+  end
+
+  info("NDArray::power::Int::n.^x")
+  let x = mx.NDArray([1 2; 3 4])
+    @test eltype(x) == Int
+    @test copy(0.^x)   == [0 0; 0 0]
+    @test copy(1.^x)   == [1 1; 1 1]
+    @test copy(1.1.^x) == [1 1; 1 1]
+    @test copy(2.^x)   == [2 4; 8 16]
+    @test copy(2.9.^x) == [2 4; 8 16]
+    @test copy(3.^x)   == [3 9; 27 81]
+  end
+
+  info("NDArray::power::Int::x.^y")
+  let x = mx.NDArray([1 2; 3 4]), y = mx.NDArray([2 2; 2 2])
+    @test eltype(x) == Int
+    @test eltype(y) == Int
+    @test copy(x.^y) == [1 4; 9 16]
+    @test copy(y.^x) == [2 4; 8 16]
+  end
+
+  info("NDArray::power::Float32::x.^n")
+  let x = mx.NDArray(Float32[1 2; 3 4]), A = Float32[1 2; 3 4]
+    @test eltype(x) == Float32
+    @test copy(x.^0) == Float32[1 1; 1 1]
+    @test copy(x.^1) == Float32[1 2; 3 4]
+    @test copy(x.^2) == Float32[1 4; 9 16]
+    @test copy(x.^3) == Float32[1 8; 27 64]
+
+    @test reldiff(copy(x.^-1), A.^-1)   < thresh
+    @test reldiff(copy(x.^1.1), A.^1.1) < thresh
+    @test reldiff(copy(x.^2.9), A.^2.9) < thresh
+  end
+
+  info("NDArray::power::Float32::n.^x")
+  let x = mx.NDArray(Float32[1 2; 3 4]), A = Float32[1 2; 3 4]
+    @test eltype(x) == Float32
+    @test copy(0.^x) == Float32[0 0; 0 0]
+    @test copy(1.^x) == Float32[1 1; 1 1]
+    @test copy(2.^x) == Float32[2 4; 8 16]
+    @test copy(3.^x) == Float32[3 9; 27 81]
+
+    @test reldiff(copy(1.1.^x), 1.1.^A) < thresh
+    @test reldiff(copy(2.9.^x), 2.9.^A) < thresh
+  end
+
+  info("NDArray::power::Float32::x.^y")
+  let x = mx.NDArray(Float32[1 2; 3 4]), y = mx.NDArray(Float32[2 2; 2 2])
+    @test eltype(x) == Float32
+    @test eltype(y) == Float32
+    @test copy(x.^y) == Float32[1 4; 9 16]
+    @test copy(y.^x) == Float32[2 4; 8 16]
+  end
+
+  # TODO: Float64: wait for https://github.com/apache/incubator-mxnet/pull/8012
+end # function test_power
+
 function test_sqrt()
   dims = rand_dims()
   info("NDArray::sqrt::dims = $dims")
@@ -599,6 +670,7 @@ end
   test_gd()
   test_saveload()
   test_clip()
+  test_power()
   test_sqrt()
   test_eltype()
   test_nd_as_jl()