fixed bugs towards ITF1788 compliance

src/IntervalContractors.jl

@@ -12,7 +12,8 @@ export plus_rev, minus_rev, inv_rev,
         asin_rev, acos_rev, atan_rev,
         sinh_rev, cosh_rev, tanh_rev,
         asinh_rev, acosh_rev, atanh_rev,
-        mul_rev_IEEE1788
+        mul_rev_IEEE1788, mul_rev_to_pair,
+        pow_rev1, pow_rev2
 
 using IntervalArithmetic
 
@@ -32,6 +33,7 @@ include("inverse_trig.jl")
 include("hyperbolic.jl")
 include("inverse_hyperbolic.jl")
 include("extrema.jl")
+include("decorated.jl")
 
 """
 Dictionary mapping functions to their reverse functions.

src/arithmetic.jl

@@ -90,7 +90,12 @@ inv_rev(a,b) = inv_rev(promote(a,b)...)
 """
 Reverse power
 """
-function power_rev(a::Interval, b::Interval, n::Integer)  # a = b^n,  log(a) = n.log(b),  b = a^(1/n)
+function power_rev(a::Interval{T}, b::Interval{T}, n::Integer) where T  # a = b^n,  log(a) = n.log(b),  b = a^(1/n)
+
+    if iszero(n)
+        1 ∈ a && return (a, entireinterval(T) ∩ b, n)
+        return (a, emptyinterval(T), n)
+    end
 
     if n == 2  # a = b^2
         root = √a
@@ -117,6 +122,7 @@ function power_rev(a::Interval, b::Interval, n::Integer)  # a = b^n,  log(a) = n
     return (a, b, n)
 end
 
+power_rev(a::Interval{T}, n::Integer) where T = power_rev(a, entireinterval(T), n)
 
 function power_rev(a::Interval, b::Interval, c::Interval)  # a = b^c
 
@@ -162,8 +168,6 @@ function sqr_rev(c, x)   # c = x^2;  refine x
     return (c, hull(x1, x2))
 end
 
-sqr_rev(c) = sqr_rev(c, -∞..∞)
-
 """
 Reverse abs
 """
@@ -201,14 +205,24 @@ According to the IEEE-1788 standard:
 When `∘` is commutative, these agree and we write `∘_rev(b, c, x)`.
 """
 
-function mul_rev_IEEE1788(b, c, x)   # c = b*x
-    return x ∩ (c / b)
-end
+mul_rev_IEEE1788(b, c, x) = mul_rev(c, x, b)[2]
 
 function pow_rev1(b, c, x)   # c = x^b
     return x ∩ c^(1/b)  # replace by 1//b
 end
 
 function pow_rev2(a, c, x)   # c = a^x
-    return x ∩ (log(c) / lob(a))
+    return x ∩ (log(c) / log(a))
 end
+
+mul_rev_to_pair(b::Interval, c::Interval) = extended_div(c, b)
+
+function mul_rev_to_pair(b::DecoratedInterval{T}, c::DecoratedInterval{T}) where T
+    (isnai(b) || isnai(c)) && return (nai(T), nai(T))
+
+    0 ∉ b && return (c/b, DecoratedInterval(emptyinterval(T), trv))
+
+    x1, x2 = extended_div(interval(c), interval(b))
+    return (DecoratedInterval(x1, trv), DecoratedInterval(x2, trv))
+end
+

src/decorated.jl

@@ -0,0 +1,35 @@
+entiredecorated(T) = DecoratedInterval(entireinterval(T))
+
+for op in (:sqr_rev, :abs_rev, :sin_rev, :cos_rev, :tan_rev, :cosh_rev, :sinh_rev, :tanh_rev)
+    @eval begin 
+        function $op(a::DecoratedInterval{T}, x::DecoratedInterval{T}) where T 
+            ( isnai(a) || isnai(x) ) && return nai(T)
+            bare = $op(interval(a), interval(x))
+            return (DecoratedInterval(bare[1], trv), DecoratedInterval(bare[2], trv))
+        end
+    end 
+    @eval $op(a::Interval{T}) where T = $op(a, entireinterval(T))
+    @eval $op(a::DecoratedInterval{T}) where T = $op(a, entiredecorated(T)) 
+end
+
+function power_rev(a::DecoratedInterval{T}, x::DecoratedInterval{T}, n::Integer) where T
+    ( isnai(a) || isnai(x) ) && return nai(T)
+    bare = power_rev(interval(a), interval(x), n)
+    return (DecoratedInterval(bare[1], trv), DecoratedInterval(bare[2], trv), n)
+end
+
+power_rev(a::DecoratedInterval{T}, n::Integer) where T = power_rev(a, entiredecorated(T), n)
+
+for op in (:mul_rev_IEEE1788, :pow_rev1, :pow_rev2)
+    @eval begin
+        function $op(b::DecoratedInterval{T}, c::DecoratedInterval{T}, x::DecoratedInterval{T}) where T
+            (isnai(b) || isnai(c) || isnai(x) ) && return nai(T)
+            bare = $op(interval(b), interval(c), interval(x))
+            return DecoratedInterval(bare, trv)
+        end
+    end
+
+    @eval $op(a::Interval{T}, b::Interval{T}) where T = $op(a, b, entireinterval(T))
+    @eval $op(a::DecoratedInterval{T}, b::DecoratedInterval{T}) where T = $op(a, b, entiredecorated(T))
+
+end

src/hyperbolic.jl

@@ -12,7 +12,7 @@ Reverse function for `cosh`.
 """
 function cosh_rev(y::Interval,x::Interval)
     y_new = y ∩ Interval(1.,∞)
-    x = x ∩ acosh(y)
+    x = (x ∩ acosh(y)) ∪ (x ∩ -acosh(y))
 
     return y_new, x
 end

test/Non1788tests/hyperbolic.jl

@@ -24,17 +24,6 @@ isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.
     @test isapprox(sinh_rev(Interval(-1.0, 25.0), -∞..∞)[2], Interval(-0.881374, 3.91243))
 end
 
-@testset "cosh_rev_test" begin
-    @test isapprox(cosh_rev(∅, -∞..∞)[2], ∅)
-    @test isapprox(cosh_rev(Interval(-10.0, -1.0), -∞..∞)[2], ∅)
-    @test isapprox(cosh_rev(Interval(0.0, Inf), -∞..∞)[2], Interval(0.0, ∞))
-    @test isapprox(cosh_rev(Interval(0.0, 1.0), -∞..∞)[2], Interval(0, 0))
-    @test isapprox(cosh_rev(Interval(-0.5, 1.0), -∞..∞)[2], Interval(0, 0))
-    @test isapprox(cosh_rev(Interval(-1000.0, 1.0), -∞..∞)[2], Interval(0, 0))
-    @test isapprox(cosh_rev(Interval(0.0, 25.0), -∞..∞)[2], Interval(0, 3.91163))
-    @test isapprox(cosh_rev(Interval(-1.0, 25.0), -∞..∞)[2], Interval(0, 3.91163))
-end
-
 @testset "tanh_rev_test" begin
     @test tanh_rev(∅, -∞..∞)[2] == ∅
     @test tanh_rev(Interval(-10.0, -1.0), -∞..∞)[2] == ∅