Add sqrt (#19)

* Mention sqrt in index.md

* Add sqrt

* test sqrt

docs/src/index.md

@@ -8,7 +8,7 @@ Provides the [`ULogarithmic`](@ref) and [`Logarithmic`](@ref) subtypes of `Real`
 
 * `ULogarithmic(x)` and `Logarithmic(x)` represent the number `x`.
 * `exp(ULogarithmic, x)` and `exp(Logarithmic, x)` represent `exp(x)` (and `x` can be huge).
-* Arithmetic: plus, minus, times, divide, power, `inv`, `log`, `prod`, `sum`.
+* Arithmetic: plus, minus, times, divide, power, `sqrt`, `inv`, `log`, `prod`, `sum`.
 * Comparisons: equality and ordering.
 * Random: `rand(ULogarithmic)` and `rand(Logarithmic)` produces a random number in the unit interval.
 * Other functions: `float`, `big`, `unsigned` (converts `ULogarithmic` to `Logarithmic`), `signed` (vice versa), `widen`, `typemin`, `typemax`, `zero`, `one`, `iszero`, `isone`, `isinf`, `isfinite`, `isnan`, `sign`, `signbit`, `abs`, `nextfloat`, `prevfloat`, `write`, `read`.

src/LogarithmicNumbers.jl

@@ -605,6 +605,10 @@ function Base.exp(x::Logarithmic)
     x.signbit ? inv(exp(x.abs)) : exp(x.abs)
 end
 
+function Base.sqrt(x::AnyLogarithmic)
+    uexp(x.log/2)
+end
+
 ### Hash
 
 const _HASH = hash(ULogarithmic)

test/runtests.jl

@@ -14,6 +14,7 @@ _sub(args...) = @inferred -(args...)
 _mul(args...) = @inferred *(args...)
 _div(args...) = @inferred /(args...)
 _pow(args...) = @inferred ^(args...)
+_sqrt(args...) = @inferred sqrt(args...)
 _float(args...) = @inferred float(args...)
 _inv(args...) = @inferred inv(args...)
 _prod(args...) = @inferred prod(args...)
@@ -457,6 +458,13 @@ atypes2 = (ULogarithmic, ULogFloat32, Logarithmic, LogFloat32)
                 @test _approx(_float(_pow(A(x), n)), float(x)^n)
             end
         end
+
+        @testset "sqrt" begin
+            for A in atypes, x in vals
+                x < 0 && continue
+                @test _approx(_float(_sqrt(A(x))), sqrt(float(x)))
+            end
+        end
 
         @testset "inv" begin
             for A in atypes, x in vals