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Fix trig functions for large arguments #260

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merged 4 commits into from
Mar 20, 2017
Merged

Fix trig functions for large arguments #260

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16fe458
Do not truncate to Int in find_quadrants, to enable trig for large ar…
dpsanders Mar 18, 2017
9f171e7
Add tests for trig functions of large args
dpsanders Mar 18, 2017
b207ad2
Fix testsets
dpsanders Mar 18, 2017
d600820
Fix testset
dpsanders Mar 19, 2017
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2 changes: 1 addition & 1 deletion src/intervals/trigonometric.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -21,7 +21,7 @@ Tucker, *Validated Numerics*."""

function find_quadrants(x::AbstractFloat)
temp = x / half_pi(x)
(floor(Int, temp.lo), floor(Int, temp.hi))
(floor(temp.lo), floor(temp.hi))
end

function sin{T}(a::Interval{T})
Expand Down
27 changes: 25 additions & 2 deletions test/interval_tests/trig.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@ using Base.Test
setprecision(Interval, 128)
setprecision(Interval, Float64)

@testset "Trig tests" begin
@testset "sin" begin
@test sin(@interval(0.5)) == Interval(0.47942553860420295, 0.47942553860420301)
@test sin(@interval(0.5, 1.67)) == Interval(4.7942553860420295e-01, 1.0)
@test sin(@interval(1.67, 3.2)) == Interval(-5.8374143427580093e-02, 9.9508334981018021e-01)
Expand All @@ -22,7 +22,9 @@ setprecision(Interval, Float64)
@test sin(@biginterval(0.5, 8.5)) ⊆ sin(@interval(0.5, 8.5))
@test sin(@biginterval(-4.5, 0.1)) ⊆ sin(@interval(-4.5, 0.1))
@test sin(@biginterval(1.3, 6.3)) ⊆ sin(@interval(1.3, 6.3))
end

@testset "cos" begin
@test cos(@interval(0.5)) == Interval(0.87758256189037265, 0.87758256189037276)
@test cos(@interval(0.5, 1.67)) == Interval(-0.09904103659872825, 0.8775825618903728)
@test cos(@interval(2.1, 5.6)) == Interval(-1.0, 0.77556587851025016)
Expand All @@ -36,7 +38,9 @@ setprecision(Interval, Float64)
@test cos(@biginterval(0.5, 8.5)) ⊆ cos(@interval(0.5, 8.5))
@test cos(@biginterval(-4.5, 0.1)) ⊆ cos(@interval(-4.5, 0.1))
@test cos(@biginterval(1.3, 6.3)) ⊆ cos(@interval(1.3, 6.3))
end

@testset "tan" begin
@test tan(@interval(0.5)) == Interval(0.54630248984379048, 0.5463024898437906)
@test tan(@interval(0.5, 1.67)) == entireinterval()
@test tan(@interval(1.67, 3.2)) == Interval(-10.047182299210307, 0.05847385445957865)
Expand All @@ -49,8 +53,9 @@ setprecision(Interval, Float64)
@test tan(@biginterval(0.5, 8.5)) ⊆ tan(@interval(0.5, 8.5))
@test tan(@biginterval(-4.5, 0.1)) ⊆ tan(@interval(-4.5, 0.1))
@test tan(@biginterval(1.3, 6.3)) ⊆ tan(@interval(1.3, 6.3))
end


@testset "Inverse trig" begin
@test asin(@interval(1)) == @interval(pi/2)#pi_interval(Float64)/2
@test asin(@interval(0.9, 2)) == asin(@interval(0.9, 1))
@test asin(@interval(3, 4)) == ∅
Expand All @@ -71,7 +76,9 @@ setprecision(Interval, Float64)
Interval(-pi_interval(Float64).hi/4, pi_interval(Float64).hi/4)
@test atan(@interval(0)) == Interval(0.0, 0.0)
@test atan(@biginterval(-1, 1)) ⊆ atan(@interval(-1, 1))
end

@testset "atan2" begin
@test atan2(∅, entireinterval()) == ∅
@test atan2(entireinterval(), ∅) == ∅
@test atan2(@interval(0.0, 1.0), @biginterval(0.0)) == @biginterval(pi/2)
Expand Down Expand Up @@ -163,11 +170,27 @@ setprecision(Interval, Float64)
Interval(-1.5707963267948968, 1.5707963267948968)
@test atan2(@biginterval(-0.1, 0.1), @biginterval(-0.0, 0.1)) ⊆
atan2(@interval(-0.1, 0.1), @interval(0.0, 0.1))
end

@testset "Trig" begin
for a in ( @interval(17, 19), @interval(0.5, 1.2) )
@test tan(a) ⊆ sin(a)/cos(a)
end

@test sin(Interval(-pi/2, 3pi/2)) == Interval(-1, 1)
@test cos(Interval(-pi/2, 3pi/2)) == Interval(-1, 1)
end

@testset "Trig with large arguments" begin
x = Interval(2.)^1000 # this is a thin interval
@test diam(x) == 0.0

@test sin(x) == -1..1
@test cos(x) == -1..1
@test tan(x) == Interval(-0.16125837995065806, -0.16125837995065803)

x = Interval(prevfloat(∞), ∞)
@test sin(x) == -1..1
@test cos(x) == -1..1
@test tan(x) == -∞..∞
end