Add decorations for reverse functions

src/IntervalContractors.jl

@@ -32,6 +32,7 @@ include("inverse_trig.jl")
 include("hyperbolic.jl")
 include("inverse_hyperbolic.jl")
 include("extrema.jl")
+include("decorations.jl")
 
 """
 Dictionary mapping functions to their reverse functions.

src/arithmetic.jl

@@ -97,6 +97,10 @@ function power_rev(a::Interval, b::Interval, n::Integer)  # a = b^n,  log(a) = n
         b1 = b ∩ root
         b2 = b ∩ (-root)
 
+    elseif n == 0
+        b_new = Interval(1, 1)
+        return(a, isempty(a ∩ b_new) ? ∅ : b, n)
+
     elseif iseven(n)
         root = a^(1//n)
 
@@ -133,7 +137,7 @@ end
 
 power_rev(a, b, c) = power_rev(promote(a, b, c)...)
 
-
+power_rev(a::Interval{T}, c) where T<:Real = power_rev(a, entireinterval(T), c)
 """
 Reverse square root
 """
@@ -162,7 +166,7 @@ function sqr_rev(c, x)   # c = x^2;  refine x
     return (c, hull(x1, x2))
 end
 
-sqr_rev(c) = sqr_rev(c, -∞..∞)
+sqr_rev(c::Interval{T}) where T<:Real = sqr_rev(c, entireinterval(T))
 
 """
 Reverse abs
@@ -176,6 +180,8 @@ function abs_rev(y, x)   # y = abs(x); refine x
 
     return (y, hull(x1, x2))
 end
+
+abs_rev(c::Interval{T}) where T<:Real = abs_rev(c, entireinterval(T))
 #=
 """
 Reverse sign
@@ -201,10 +207,13 @@ 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)
+function mul_rev_IEEE1788(b, c, x) 
+    temp = extended_div(c, b)  
+    return x ∩ (temp[1] ∪ temp[2])
 end
 
+mul_rev_IEEE1788(b::Interval{T}, c::Interval{T}) where T<:Real = mul_rev_IEEE1788(b, c, entireinterval(T))
+
 function pow_rev1(b, c, x)   # c = x^b
     return x ∩ c^(1/b)  # replace by 1//b
 end

src/decorations.jl

@@ -0,0 +1,60 @@
+"""
+Reverse Functions
+Decorated interval extension; the result is decorated as `trv`,
+following the IEEE-1788 Standard (see Sect. 11.7.1, pp 47).
+""" 
+reverse_functions =(
+    :sqr_rev , :abs_rev, :sin_rev, :cos_rev, :tan_rev, :cosh_rev)
+
+for f in reverse_functions
+    @eval function $(f)(xx::DecoratedInterval{T}) where T
+        x = xx.interval
+        r = $f(x)[2]
+        d = min(decoration(r), decoration(xx), trv)
+        DecoratedInterval(r, d)
+    end
+end
+
+
+for f in reverse_functions
+    @eval function $(f)(xx::DecoratedInterval, yy::DecoratedInterval)
+        x = xx.interval
+        y = yy.interval
+        r = $f(x,y)[2]
+        d = min(decoration(x), decoration(y), decoration(r), trv)
+        DecoratedInterval(r, d)
+    end
+end
+
+function mul_rev_IEEE1788(xx::DecoratedInterval, yy::DecoratedInterval)
+    x = xx.interval
+    y = yy.interval
+    r = mul_rev_IEEE1788(x, y)
+    d = min(decoration(x), decoration(y), decoration(r), trv)
+    DecoratedInterval(r, d)
+end
+
+
+function mul_rev_IEEE1788(xx::DecoratedInterval, yy::DecoratedInterval, zz::DecoratedInterval)
+    x = xx.interval
+    y = yy.interval
+    z = zz.interval
+    r = mul_rev_IEEE1788(x, y, z)
+    d = min(decoration(x), decoration(y), decoration(z), decoration(r), trv)
+    DecoratedInterval(r, d)
+end
+
+function power_rev(xx::DecoratedInterval, nn::Integer)
+    x = xx.interval
+    r = power_rev(x, nn)[2]
+    d = min(decoration(x), decoration(r), trv)
+    DecoratedInterval(r, d)
+end
+
+function power_rev(xx::DecoratedInterval, yy::DecoratedInterval, nn::Integer)
+    x = xx.interval
+    y = yy.interval
+    r = power_rev(x, y, nn)[2]
+    d = min(decoration(x), decoration(r), decoration(y), trv)
+    DecoratedInterval(r, d)
+end

src/hyperbolic.jl

@@ -10,13 +10,20 @@ end
 """
 Reverse function for `cosh`.
 """
-function cosh_rev(y::Interval,x::Interval)
-    y_new = y ∩ Interval(1.,∞)
-    x = x ∩ acosh(y)
+cosh_main(y::Interval,x::Interval) = x ∩ acosh(y)
 
-    return y_new, x
+function cosh_rev(x::Interval, y::Interval)
+    y1 = y ∩ Interval(-Inf,1)
+    y2 = y ∩ Interval(1,Inf)
+
+    x_new = x ∩ Interval(1.,∞)
+
+    z = -cosh_main(x,-y1) ∪ cosh_main(x,y2)
+    return x_new, z
 end
 
+cosh_rev(x::Interval{T}) where T<:Real = cosh_rev(x, entireinterval(T)) 
+
 """
 Reverse function for `tanh`.
 """

src/trig.jl

@@ -51,7 +51,7 @@ function sin_rev(y::Interval, x::Interval)
     return X_new[2], X_new[1]   # return in order y, x
 end
 
-
+sin_rev(y::Interval{T}) where T<:Real = sin_rev(y, entireinterval(T))
 ## cos contractor: alters x and y
 """
 Contractor for main branch of cos, from x = 0 to π.
@@ -104,6 +104,8 @@ function cos_rev(y::Interval, x::Interval)
     return X_new[2], X_new[1]   # return in order y, x
 end
 
+cos_rev(y::Interval{T}) where T<:Real = cos_rev(y, entireinterval(T))
+
 
 """
 Contractor for "main branch" of tan, from x = -π/2 to π/2.
@@ -141,3 +143,5 @@ function tan_rev(y::Interval, x::Interval)
 
     return X_new[2], X_new[1]   # return in order y, x
 end
+
+tan_rev(y::Interval{T}) where T<:Real = tan_rev(y, entireinterval(T))

test/Non1788tests/hyperbolic.jl

@@ -27,12 +27,12 @@ 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, Inf), -∞..∞)[2], Interval(-∞, ∞))
     @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))
+    @test isapprox(cosh_rev(Interval(0.0, 25.0), -∞..∞)[2], Interval(-3.91163, 3.91163))
+    @test isapprox(cosh_rev(Interval(-1.0, 25.0), -∞..∞)[2], Interval(-3.91163, 3.91163))
 end
 
 @testset "tanh_rev_test" begin