Merge pull request #227 from araujoms/power

fix precision of non-integer power

Author: JeffreySarnoff

src/math/elementary/explog.jl

@@ -120,16 +120,8 @@ function Base.:(^)(r::DoubleFloat{T}, n::Int) where {T<:IEEEFloat}
 end
 
 function Base.:(^)(r::DoubleFloat{T}, n::DoubleFloat{T}) where {T <: IEEEFloat}
-    if isinteger(n)
-        return r^Int64(Float64(n)) # convert n to Float64 first
-    else
-        return exp(n * log(r))
-    end
-end
-
-function Base.:(^)(r::Int, n::DoubleFloat{T}) where {T<:IEEEFloat}
-    if isinteger(n)
-        return DoubleFloat{T}(r)^Int64(Float64(n)) # convert n to Float64 first
+    if isinteger(n) && n ≤ min(2^20, maxintfloat(T, Int64))
+        return r^Int64(n.hi)
     else
         return exp(n * log(r))
     end

test/function_accuracy.jl

@@ -85,6 +85,12 @@ end
     @test test_atol(rand_bigf, rand_vals, atanh, 1.0e-31)
     @test test_rtol(rand_bigf, rand_vals, atanh, 1.0e-29)
 
+    @test test_atol(rand_bigf, rand_vals, x -> x^x, 1.0e-31)
+    @test test_rtol(rand_bigf, rand_vals, x -> x^x, 1.0e-31)
+
+    @test test_atol(rand_bigf, rand_vals, x -> 2^x, 1.0e-31)
+    @test test_rtol(rand_bigf, rand_vals, x -> 2^x, 1.0e-31)
+
 
     @test test_atol(rand1_bigf, rand1_vals, exp, 1.0e-30)
     @test test_rtol(rand1_bigf, rand1_vals, exp, 1.0e-31)
@@ -115,4 +121,10 @@ end
 
     @test test_atol(rand1_bigf, rand1_vals, asinh, 1.0e-31)
     @test test_rtol(rand1_bigf, rand1_vals, asinh, 1.0e-31)
+
+    @test test_atol(rand1_bigf, rand1_vals, x -> x^x, 1.0e-30)
+    @test test_rtol(rand1_bigf, rand1_vals, x -> x^x, 1.0e-31)
+
+    @test test_atol(rand1_bigf, rand1_vals, x -> 2^x, 1.0e-30)
+    @test test_rtol(rand1_bigf, rand1_vals, x -> 2^x, 1.0e-31)
 end