Add rsqrt function and test cases

Author: yashrajgupta

src/IntervalArithmetic.jl

@@ -59,7 +59,7 @@ export
     midpoint_radius, interval_from_midpoint_radius,
     RoundTiesToEven, RoundTiesToAway,
     cancelminus, cancelplus, isunbounded,
-    .., @I_str, ±,
+    .., @I_str, ±, rsqrt,
     pow, extended_div,
     setformat, @format
 

src/intervals/functions.jl

@@ -269,3 +269,11 @@ for f in (:log, :log2, :log10, :log1p)
 
         end
 end
+
+function rsqrt(a::Interval{T}) where T
+    x = sqrt(a)
+    isempty(x) && return emptyinterval(x)
+    x.lo == zero(T) < x.hi && return @round(inv(x.hi), T(Inf))
+    x == zero(x) && return emptyinterval(T)
+    @round(inv(x.hi), inv(x.lo))
+end

test/ITF1788_tests/libieeep1788_tests_elem.jl

@@ -995,6 +995,20 @@ end
     @test decoration((DecoratedInterval(Interval(-5.0, Inf), dac))^(1//2)) == decoration(DecoratedInterval(Interval(0.0, Inf), trv))
 end
 
+@testset "minimal_rsqrt_test" begin
+    @test rsqrt(∅) == ∅
+    @test rsqrt(Interval(-Inf, Inf)) == 0 .. Inf
+    @test rsqrt(Interval(-Inf, -0x0.0000000000001p-1022)) == ∅
+    @test rsqrt(Interval(-1.0, 1.0)) == 1.0 .. Inf
+    @test rsqrt(Interval(0.0, 1.0)) == 1.0 .. Inf
+    @test rsqrt(Interval(-0.0, 1.0)) == 1.0 .. Inf
+    @test rsqrt(Interval(-5.0, 25.0)) == 0.2 .. Inf
+    @test rsqrt(Interval(0.0, 25.0)) == 0.2 .. Inf
+    @test rsqrt(Interval(-0.0, 25.0)) == 0.2 .. Inf
+    @test rsqrt(Interval(-5.0, Inf)) == 0.0 .. Inf
+    @test rsqrt(Interval(4.0, 25.0)) == 0.2 .. 0.5
+end
+
 @testset "minimal_fma_test" begin
     @test fma(∅, ∅, ∅) == ∅
     @test fma(Interval(-1.0, 1.0), ∅, ∅) == ∅