Add correctly rounded hyperbolic functions and their inverses

Only sinh and cosh are covered in CRlibm

src/ValidatedNumerics.jl

@@ -20,6 +20,7 @@ import Base:
     in, zero, one, abs, real, show, min, max,
     sqrt, exp, log, sin, cos, tan, inv,
     asin, acos, atan,
+    sinh, cosh, tanh, asinh, acosh, atanh,
     union, intersect, isempty,
     convert, promote_rule, eltype,
     BigFloat, float,

src/intervals/hyperbolic_functions.jl

@@ -0,0 +1,91 @@
+# This file is part of the ValidatedNumerics.jl package; MIT licensed
+
+
+function sinh(a::Interval{Float64})
+    isempty(a) && return a
+    return Interval(sinh(a.lo, RoundDown), sinh(a.hi, RoundUp))
+end
+
+function sinh(a::Interval{BigFloat})
+    isempty(a) && return a
+    return @controlled_round(BigFloat, sinh(a.lo), sinh(a.hi))
+end
+
+
+function cosh(a::Interval{Float64})
+    isempty(a) && return a
+    return Interval(cosh(mig(a), RoundDown), cosh(mag(a), RoundUp))
+end
+
+function cosh(a::Interval{BigFloat})
+    isempty(a) && return a
+    return @controlled_round(BigFloat, cosh(mig(a)), cosh(mag(a)))
+end
+
+
+function tanh(a::Interval{Float64})
+    isempty(a) && return a
+    res = with_bigfloat_precision(53) do
+        aa = Interval(big(a.lo), big(a.hi))
+        float( tanh(aa) )
+    end
+    return res
+end
+
+function tanh(a::Interval{BigFloat})
+    isempty(a) && return a
+    return @controlled_round(BigFloat, tanh(a.lo), tanh(a.hi))
+end
+
+
+function asinh(a::Interval{Float64})
+    isempty(a) && return a
+    res = with_bigfloat_precision(53) do
+        aa = Interval(big(a.lo), big(a.hi))
+        float( asinh(aa) )
+    end
+    return res
+end
+
+function asinh(a::Interval{BigFloat})
+    isempty(a) && return a
+    @controlled_round(BigFloat, asinh(a.lo), asinh(a.hi))
+end
+
+
+function acosh(a::Interval{Float64})
+    domain = Interval(one(eltype(a)), Inf)
+    a = a ∩ domain
+    isempty(a) && return a
+    res = with_bigfloat_precision(53) do
+        aa = Interval(big(a.lo), big(a.hi))
+        float( acosh(aa) )
+    end
+    return res
+end
+
+function acosh(a::Interval{BigFloat})
+    domain = Interval(one(eltype(a)), Inf)
+    a = a ∩ domain
+    isempty(a) && return a
+    @controlled_round(BigFloat, acosh(a.lo), acosh(a.hi))
+end
+
+
+function atanh(a::Interval{Float64})
+    domain = Interval(-one(eltype(a)), one(eltype(a)))
+    a = a ∩ domain
+    (isempty(a) || abs(a) == one(a)) && return emptyinterval(a)
+    res = with_bigfloat_precision(53) do
+        aa = Interval(big(a.lo), big(a.hi))
+        float( atanh(aa) )
+    end
+    return res
+end
+
+function atanh(a::Interval{BigFloat})
+    domain = Interval(-one(eltype(a)), one(eltype(a)))
+    a = a ∩ domain
+    isempty(a) && return a
+    @controlled_round(BigFloat, atanh(a.lo), atanh(a.hi))
+end

src/intervals/intervals.jl

@@ -46,5 +46,6 @@ include("macro_definitions.jl")
 include("conversion_promotion.jl")
 include("arithmetic.jl")
 include("precision.jl")
-include("trigonometric_functions.jl")
 include("functions.jl")
+include("trigonometric_functions.jl")
+include("hyperbolic_functions.jl")

test/interval_tests/hyperb_tests.jl

@@ -0,0 +1,55 @@
+# This file is part of the ValidatedNumerics.jl package; MIT licensed
+
+using ValidatedNumerics
+using FactCheck
+
+facts("Hyperb tests") do
+    @fact sinh(emptyinterval()) --> emptyinterval()
+    @fact sinh(Interval(0.5)) --> Interval(0.5210953054937473, 0.5210953054937474)
+    @fact sinh(Interval(0.5, 1.67)) --> Interval(0.5210953054937473, 2.5619603657712102)
+    @fact sinh(Interval(-4.5, 0.1)) --> Interval(-45.00301115199179, 0.10016675001984404)
+    @fact sinh(@biginterval(0.5)) ⊆ sinh(@interval(0.5)) --> true
+    @fact sinh(@biginterval(0.5, 1.67)) ⊆ sinh(@interval(0.5, 1.67)) --> true
+    @fact sinh(@biginterval(1.67, 3.2)) ⊆ sinh(@interval(1.67, 3.2)) --> true
+    @fact sinh(@biginterval(2.1, 5.6)) ⊆ sinh(@interval(2.1, 5.6)) --> true
+    @fact sinh(@biginterval(0.5, 8.5)) ⊆ sinh(@interval(0.5, 8.5)) --> true
+    @fact sinh(@biginterval(-4.5, 0.1)) ⊆ sinh(@interval(-4.5, 0.1)) --> true
+    @fact sinh(@biginterval(1.3, 6.3)) ⊆ sinh(@interval(1.3, 6.3)) --> true
+
+    @fact cosh(emptyinterval()) --> emptyinterval()
+    @fact cosh(Interval(0.5)) --> Interval(1.1276259652063807, 1.127625965206381)
+    @fact cosh(Interval(0.5, 1.67)) --> Interval(1.1276259652063807, 2.750207431409957)
+    @fact cosh(Interval(-4.5, 0.1)) --> Interval(1.0, 45.01412014853003)
+    @fact cosh(@biginterval(0.5)) ⊆ cosh(@interval(0.5)) --> true
+    @fact cosh(@biginterval(0.5, 1.67)) ⊆ cosh(@interval(0.5, 1.67)) --> true
+    @fact cosh(@biginterval(1.67, 3.2)) ⊆ cosh(@interval(1.67, 3.2)) --> true
+    @fact cosh(@biginterval(2.1, 5.6)) ⊆ cosh(@interval(2.1, 5.6)) --> true
+    @fact cosh(@biginterval(0.5, 8.5)) ⊆ cosh(@interval(0.5, 8.5)) --> true
+    @fact cosh(@biginterval(-4.5, 0.1)) ⊆ cosh(@interval(-4.5, 0.1)) --> true
+    @fact cosh(@biginterval(1.3, 6.3)) ⊆ cosh(@interval(1.3, 6.3)) --> true
+
+    @fact tanh(emptyinterval()) --> emptyinterval()
+    @fact tanh(Interval(0.5)) --> Interval(0.46211715726000974, 0.4621171572600098)
+    @fact tanh(Interval(0.5, 1.67)) --> Interval(0.46211715726000974, 0.9315516846152083)
+    @fact tanh(Interval(-4.5, 0.1)) --> Interval(-0.9997532108480276, 0.09966799462495583)
+    @fact tanh(@biginterval(0.5)) ⊆ tanh(@interval(0.5)) --> true
+    @fact tanh(@biginterval(0.5, 1.67)) ⊆ tanh(@interval(0.5, 1.67)) --> true
+    @fact tanh(@biginterval(1.67, 3.2)) ⊆ tanh(@interval(1.67, 3.2)) --> true
+    @fact tanh(@biginterval(2.1, 5.6)) ⊆ tanh(@interval(2.1, 5.6)) --> true
+    @fact tanh(@biginterval(0.5, 8.5)) ⊆ tanh(@interval(0.5, 8.5)) --> true
+    @fact tanh(@biginterval(-4.5, 0.1)) ⊆ tanh(@interval(-4.5, 0.1)) --> true
+    @fact tanh(@biginterval(1.3, 6.3)) ⊆ tanh(@interval(1.3, 6.3)) --> true
+
+    @fact asinh(@biginterval(1)) ⊆ asinh(@interval(1)) --> true
+    @fact asinh(@biginterval(0.9, 2)) ⊆ asinh(@interval(0.9, 2)) --> true
+    @fact asinh(@biginterval(3, 4)) ⊆ asinh(@interval(3, 4)) --> true
+
+    @fact acosh(@biginterval(1)) ⊆ acosh(@interval(1)) --> true
+    @fact acosh(@biginterval(-2, -0.9)) ⊆ acosh(@interval(-2, -0.9)) --> true
+    @fact acosh(@biginterval(3, 4)) ⊆ acosh(@interval(3, 4)) --> true
+
+    for a in ( Interval(17, 19), Interval(0.5, 1.2) )
+        @fact tanh(a) ⊆ sinh(a)/cosh(a) --> true
+    end
+
+end

test/interval_tests/interval_tests.jl

@@ -4,6 +4,7 @@ include("construct_tests.jl")
 include("consistency_tests.jl")
 include("numeric_tests.jl")
 include("trig_tests.jl")
+include("hyperb_tests.jl")
 include("non_BigFloat_tests.jl")
 include("lin_alg_tests.jl")
 include("loop_tests.jl")