From 0b4f8c3a338eea3906a3036b06265c191fac9471 Mon Sep 17 00:00:00 2001
From: yashrajgupta <yashrajgupta98@gmail.com>
Date: Tue, 12 Mar 2019 23:48:52 +0530
Subject: [PATCH 1/2] Add rsqrt function and test cases

---
 src/IntervalArithmetic.jl                     |  2 +-
 src/intervals/functions.jl                    |  8 ++++++++
 test/ITF1788_tests/libieeep1788_tests_elem.jl | 14 ++++++++++++++
 3 files changed, 23 insertions(+), 1 deletion(-)

diff --git a/src/IntervalArithmetic.jl b/src/IntervalArithmetic.jl
index c44bb1d55..ee372fe7f 100644
--- a/src/IntervalArithmetic.jl
+++ b/src/IntervalArithmetic.jl
@@ -62,7 +62,7 @@ export
     midpoint_radius, interval_from_midpoint_radius,
     RoundTiesToEven, RoundTiesToAway,
     cancelminus, cancelplus, isunbounded,
-    .., @I_str, ±,
+    .., @I_str, ±, rsqrt,
     pow, extended_div,
     setformat, @format
 
diff --git a/src/intervals/functions.jl b/src/intervals/functions.jl
index c27bbc9b1..eac8f3604 100644
--- a/src/intervals/functions.jl
+++ b/src/intervals/functions.jl
@@ -305,3 +305,11 @@ 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
diff --git a/test/ITF1788_tests/libieeep1788_tests_elem.jl b/test/ITF1788_tests/libieeep1788_tests_elem.jl
index e26df7722..bd8b8095e 100644
--- a/test/ITF1788_tests/libieeep1788_tests_elem.jl
+++ b/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), ∅, ∅) == ∅

From 5b302fb59839248b7feca64bf8b1aaa1357b9021 Mon Sep 17 00:00:00 2001
From: yashrajgupta <yashrajgupta98@gmail.com>
Date: Sat, 13 Apr 2019 02:06:22 +0530
Subject: [PATCH 2/2] Change name of rsqrt function and add doc string

---
 src/IntervalArithmetic.jl                     |  2 +-
 src/intervals/functions.jl                    |  3 ++-
 test/ITF1788_tests/libieeep1788_tests_elem.jl | 22 +++++++++----------
 3 files changed, 14 insertions(+), 13 deletions(-)

diff --git a/src/IntervalArithmetic.jl b/src/IntervalArithmetic.jl
index ee372fe7f..15e978fe2 100644
--- a/src/IntervalArithmetic.jl
+++ b/src/IntervalArithmetic.jl
@@ -62,7 +62,7 @@ export
     midpoint_radius, interval_from_midpoint_radius,
     RoundTiesToEven, RoundTiesToAway,
     cancelminus, cancelplus, isunbounded,
-    .., @I_str, ±, rsqrt,
+    .., @I_str, ±, reciprocal_sqrt,
     pow, extended_div,
     setformat, @format
 
diff --git a/src/intervals/functions.jl b/src/intervals/functions.jl
index eac8f3604..2664cb2ba 100644
--- a/src/intervals/functions.jl
+++ b/src/intervals/functions.jl
@@ -306,7 +306,8 @@ for f in (:log, :log2, :log10, :log1p)
         end
 end
 
-function rsqrt(a::Interval{T}) where T
+#computes the reciprocal of square root of an Interval
+function reciprocal_sqrt(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))
diff --git a/test/ITF1788_tests/libieeep1788_tests_elem.jl b/test/ITF1788_tests/libieeep1788_tests_elem.jl
index bd8b8095e..db03226a3 100644
--- a/test/ITF1788_tests/libieeep1788_tests_elem.jl
+++ b/test/ITF1788_tests/libieeep1788_tests_elem.jl
@@ -996,17 +996,17 @@ end
 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
+    @test reciprocal_sqrt(∅) == ∅
+    @test reciprocal_sqrt(Interval(-Inf, Inf)) == 0 .. Inf
+    @test reciprocal_sqrt(Interval(-Inf, -0x0.0000000000001p-1022)) == ∅
+    @test reciprocal_sqrt(Interval(-1.0, 1.0)) == 1.0 .. Inf
+    @test reciprocal_sqrt(Interval(0.0, 1.0)) == 1.0 .. Inf
+    @test reciprocal_sqrt(Interval(-0.0, 1.0)) == 1.0 .. Inf
+    @test reciprocal_sqrt(Interval(-5.0, 25.0)) == 0.2 .. Inf
+    @test reciprocal_sqrt(Interval(0.0, 25.0)) == 0.2 .. Inf
+    @test reciprocal_sqrt(Interval(-0.0, 25.0)) == 0.2 .. Inf
+    @test reciprocal_sqrt(Interval(-5.0, Inf)) == 0.0 .. Inf
+    @test reciprocal_sqrt(Interval(4.0, 25.0)) == 0.2 .. 0.5
 end
 
 @testset "minimal_fma_test" begin