Use fast path for sqrt and inv (#230)

* Use fast routes for sqrt and inv

* Fix inv and sqrt for BigFloat

* Fix sqrt and inv for BigFloat

* Uncomment Float32 test

* Add simple tests for sqrt and inv

Author: dpsanders

src/intervals/rounding.jl

@@ -92,6 +92,13 @@ for (op, f) in ( (:+, :add), (:-, :sub), (:*, :mul), (:/, :div) )
     end
 end
 
+# inv and sqrt:
+
+# inv(::IntervalRounding{:tight}, a::T, r::RoundingMode) where T<:Union{Float32, Float64} = inv_round(a, r)
+#
+# sqrt(::IntervalRounding{:tight}, a::T, r::RoundingMode) where T<:Union{Float32, Float64} = sqrt_round(a, r)
+
+
 for T in (Float32, Float64)
     for mode in (:Down, :Up)
 
@@ -103,7 +110,7 @@ for T in (Float32, Float64)
         @eval inv(::IntervalRounding{:tight},
                             a::$T, $mode1) = inv_round(a, $mode2)
 
-                @eval sqrt(::IntervalRounding{:tight},
+        @eval sqrt(::IntervalRounding{:tight},
                             a::$T, $mode1) = sqrt_round(a, $mode2)
         end
 end
@@ -175,13 +182,19 @@ for mode in (:Down, :Up)
     # functions not in CRlibm:
     for f in (:sqrt, :inv, :tanh, :asinh, :acosh, :atanh)
 
+
         @eval function $f(::IntervalRounding{:slow},
                           a::T, $mode1) where T<:AbstractFloat
                             setrounding(T, $mode2) do
                                 $f(a)
                             end
                end
 
+        @eval function $f(::IntervalRounding{:tight},
+                                 a::T, $mode1) where T<:AbstractFloat
+                                   $f(IntervalRounding{:slow}(), a, $mode2)
+                      end
+
 
         @eval $f(::IntervalRounding{:accurate},
                   a::T, $mode1) where {T<:AbstractFloat} = $directed($f(a))
@@ -229,10 +242,18 @@ function _setrounding(::Type{Interval}, rounding_type::Symbol)
         @eval $f(a::T, b::T, r::RoundingMode) where {T<:AbstractFloat} = $f($roundtype, a, b, r)
     end
 
+    # unary functions:
+
+    for f in (:sqrt, :inv)
+        @eval $f(a::T, r::RoundingMode) where {T<:AbstractFloat} = $f($roundtype, a, r)
+    end
+
+
     if rounding_type == :tight   # for remaining functions, use CRlibm
         roundtype = IntervalRounding{:slow}()
     end
 
+
     for f in (:^, :atan)
 
         @eval $f(a::T, b::T, r::RoundingMode) where {T<:AbstractFloat} = $f($roundtype, a, b, r)
@@ -242,7 +263,7 @@ function _setrounding(::Type{Interval}, rounding_type::Symbol)
 
     # unary functions:
     for f in vcat(CRlibm.functions,
-                [:sqrt, :inv, :tanh, :asinh, :acosh, :atanh])
+                    [:tanh, :asinh, :acosh, :atanh])
 
         @eval $f(a::T, r::RoundingMode) where {T<:AbstractFloat} = $f($roundtype, a, r)
 

test/interval_tests/numeric.jl

@@ -272,13 +272,24 @@ end
         @test pow(y, @interval(2.1)) == Interval(0.0, 10.045108566305146)
     end
 
-    # comment out for now:
-    #=
+    @testset "sqrt" begin
+        @test sqrt(2..3) == Interval(1.414213562373095, 1.7320508075688774)
+
+        @test sqrt(big(2..3)) == Interval(big"1.414213562373095048801688724209698078569671875376948073176679737990732478462102", big"1.732050807568877293527446341505872366942805253810380628055806979451933016908815")
+    end
+
+    @testset "inv" begin
+        @test inv(2..3) == Interval(0.3333333333333333, 0.5)
+        @test inv(big(2..3)) == Interval(big"3.333333333333333333333333333333333333333333333333333333333333333333333333333305e-01", big"5.0e-01")
+    end
+
     @testset "Float32 intervals" begin
 
         a = Interval{Float32}(1e38)
         b = Interval{Float32}(1e2)
         @test a * b == Interval{Float32}(floatmax(Float32), Inf)
     end
-    =#
+
+
+
 end