Replace a.lo with inf(a) and similarly for .hi and sup

examples/examples.jl

@@ -41,7 +41,7 @@ function cube0(X::IntervalBox)  # contractor for y=x^3, x>=0
     x = x ⊓ (0..∞)
 
     y = y ⊓ (x ^ 3)
-    x = x ⊓ Interval(y.lo ^ (1/3), y.hi^(1/3))   # not rigorous!
+    x = x ⊓ Interval(inf(y) ^ (1/3), sup(y)^(1/3))   # not rigorous!
 
     return x × y
 end

src/IntervalContractors.jl

@@ -15,11 +15,13 @@ export plus_rev, minus_rev, inv_rev,
         mul_rev_IEEE1788, mul_rev_to_pair,
         pow_rev1, pow_rev2
 
-using IntervalArithmetic
+using IntervalArithmetic, IntervalArithmetic.Symbols
+using IntervalBoxes
 
 const half_pi = ExactReal(0.5) * interval(pi)
 const two_pi = ExactReal(2.0) * interval(pi)
 
+const ∞ = Inf
 #
 # Base.:⊔(f::Function, g::Function) = X -> ( f(X) ⊔ g(X) )
 # Base.:⊓(f::Function, g::Function) = X -> ( f(X) ⊓ g(X) )  # or f(g(X)) for contractors

src/arithmetic.jl

@@ -129,7 +129,7 @@ The triplet `(a, b_new, n)` where
 - `a` and `n` are unchanged
 - `b_new` is the interval hull of the set ``{x ∈ b : xⁿ ∈ a}``
 """
-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)
+function power_rev(a::Interval{T}, b::Interval{T}, n::Integer) where T  # a = b^n,  log(a) = inf(n)g(b),  b = a^(1/n)
 
     if iszero(n)
         1 ∈ a && return (a, entireinterval(T) ⊓ b, n)

src/extrema.jl

@@ -3,13 +3,13 @@ Reverse max
 """
 function max_rev(a::Interval, b::Interval, c::Interval)  # a = max(b,c)
 
-    B_lo = b.lo;  B_hi = b.hi;
-    C_lo = c.lo;  C_hi = c.hi;
+    B_lo = inf(b);  B_hi = sup(b);
+    C_lo = inf(c);  C_hi = sup(c);
 
-    (b.lo > c.lo) && (B_lo = max(b.lo,a.lo))
-    (b.lo < c.lo) && (C_lo = max(c.lo,a.lo))
-    (b.hi > c.hi) && (B_hi = min(b.hi,a.hi))
-    (b.hi < c.hi) && (C_hi = min(c.hi,a.hi))
+    (inf(b) > sup(c)) && (B_lo = max(inf(b),inf(a)))
+    (inf(b) < inf(c)) && (C_lo = max(inf(c),inf(a)))
+    (sup(b) > sup(c)) && (B_hi = min(sup(b),sup(a)))
+    (sup(b) < sup(c)) && (C_hi = min(sup(c),sup(a)))
 
     if isempty(b)
         isempty(c) && (return a, ∅, ∅)
@@ -26,13 +26,13 @@ Reverse min
 """
 function min_rev(a::Interval, b::Interval, c::Interval)
 
-    B_lo = b.lo;  B_hi = b.hi;
-    C_lo = c.lo;  C_hi = c.hi;
+    B_lo = inf(b);  B_hi = sup(b);
+    C_lo = inf(c);  C_hi = sup(c);
 
-    (b.lo > c.lo) && (B_lo = max(c.lo,a.lo))
-    (b.lo < c.lo) && (C_lo = max(b.lo,a.lo))
-    (b.hi > c.hi) && (B_hi = min(c.hi,a.hi))
-    (b.hi < c.hi) && (C_hi = min(b.hi,a.hi))
+    (inf(b) > inf(c)) && (B_lo = max(inf(c),inf(a)))
+    (inf(b) < inf(c)) && (C_lo = max(inf(b),inf(a)))
+    (sup(b) > sup(c)) && (B_hi = min(sup(c),sup(a)))
+    (sup(b) < sup(c)) && (C_hi = min(sup(b),sup(a)))
 
     if isempty(b)
         isempty(c) && (return a, ∅, ∅)

src/inverse_trig.jl

@@ -1,7 +1,7 @@
 function asin!(X::IntervalBox)
     x, y = X
 
-    h = half_pi.lo
+    h = inf(half_pi)
     y_new = y ⊓ Interval(-h, h)  # range of asin
     x_new = sin(y_new)
 
@@ -13,7 +13,7 @@ Reverse `asin`.
 """
 function asin_rev(y::Interval, x::Interval)  # y = asin(x)
 
-    h = half_pi.lo
+    h = inf(half_pi)
     y_new = y ⊓ Interval(-h, h)  # range of asin
 
     x_new = sin(y_new)
@@ -25,7 +25,7 @@ end
 Reverse `acos`.
 """
 function acos_rev(y::Interval, x::Interval)
-        y_new = y ⊓ Interval(0.0,two_pi.hi)
+        y_new = y ⊓ Interval(0.0,sup(two_pi))
         x_new = x ⊓ cos(y_new)
 
         return y_new, x_new
@@ -38,7 +38,7 @@ Inverse of `y = atan(x)`.
 Returns the new `y` and `x`.
 """
 function atan_rev(y::Interval, x::Interval)
-        y_new = y ⊓ Interval(-half_pi.hi, half_pi.hi)
+        y_new = y ⊓ Interval(-sup(half_pi), sup(half_pi))
         x_new = x ⊓ tan(y_new)
 
         return y_new, x_new

src/powers.jl

@@ -30,7 +30,7 @@ function cube_pos(X::IntervalBox)  # contractor for y=x^3, x>=0
     x = x ⊓ (0..∞)
 
     y = y ⊓ (x ^ 3)
-    x = x ⊓ Interval(y.lo ^ (1/3), y.hi^(1/3))   # not rigorous!
+    x = x ⊓ Interval(inf(y) ^ (1/3), sup(y)^(1/3))   # not rigorous!
 
     return x × y
 end

src/transformations.jl

@@ -6,8 +6,8 @@ Return the integers enclosed in the interval `x`.
 """
 
 function integer_contractor(x::Interval)
-    a = floor(x.lo)+1
-    b = floor(x.hi)
+    a = floor(inf(x))+1
+    b = floor(sup(x))
 
     a > b && return emptyinterval(x)
 

src/trig.jl

@@ -8,7 +8,7 @@ function sin_main(X::IntervalBox)
 
     x, y = X
 
-    x_range = Interval(-half_pi.hi, half_pi.hi)
+    x_range = Interval(-sup(half_pi), sup(half_pi))
     y_range = -1..1
 
     x = x ⊓ x_range
@@ -126,7 +126,7 @@ function tan_main(X::IntervalBox)
 
     x, y = X
 
-    x_range = Interval(-half_pi.hi, half_pi.hi)
+    x_range = Interval(-sup(half_pi), sup(half_pi))
 
     x = x ⊓ x_range
 

test/Non1788tests/exponential.jl

@@ -11,7 +11,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 @testset "exp2_rev_test" begin
     @test exp2_rev(∅, entireinterval(Float64))[2] == ∅

test/Non1788tests/extrema.jl

@@ -10,7 +10,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 @testset "max_rev_test" begin
     @test max_rev(∅, entireinterval(Float64),entireinterval(Float64))[2] == Interval(-∞, ∞)

test/Non1788tests/hyperbolic.jl

@@ -11,7 +11,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 @testset "sinh_rev_test" begin
     @test isapprox(sinh_rev(∅, -∞..∞)[2], ∅)

test/Non1788tests/inv_hyperbolic.jl

@@ -11,7 +11,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 @testset "asinh_rev_test" begin
     @test asinh_rev(∅, -∞..∞)[2] == ∅

test/Non1788tests/inv_rev.jl

@@ -12,7 +12,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 @testset "inv_rev_test" begin
     @test inv_rev(∅, entireinterval(Float64))[2] == ∅

test/Non1788tests/inv_trig.jl

@@ -12,7 +12,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 @testset "acos_rev_test" begin
     @test acos_rev(∅, entireinterval(Float64))[2] == ∅

test/Non1788tests/script.jl

@@ -12,7 +12,7 @@ setprecision(Interval, Float64)
 
 # Using approximate checks for validaty update later?
 import Base.isapprox
-isapprox(x::Interval,y::Interval) = isapprox(x.lo,y.lo,atol=1E-4) && isapprox(x.hi,y.hi,atol=1E-4)
+isapprox(x::Interval,y::Interval) = isapprox(inf(x),inf(y),atol=1E-4) && isapprox(sup(x),sup(y),atol=1E-4)
 
 c = ∅
 d = entireinterval(Float64)