Add sinpi and cospi function (#284)

Author: yashrajgupta

src/IntervalArithmetic.jl

@@ -24,7 +24,7 @@ import Base:
     sqrt, exp, log, sin, cos, tan, inv,
     exp2, exp10, log2, log10,
     asin, acos, atan,
-    sinh, cosh, tanh, asinh, acosh, atanh,
+    sinh, cosh, tanh, asinh, acosh, atanh, sinpi, cospi,
     union, intersect, isempty,
     convert, promote_rule, eltype, size,
     BigFloat, float, widen, big,

src/intervals/trigonometric.jl

@@ -137,6 +137,11 @@ function sin(a::Interval{Float64})
     end
 end
 
+function sinpi(a::Interval{T}) where T
+    isempty(a) && return a
+    w = a * pi_interval(T)
+    return(sin(w))
+end
 
 function cos(a::Interval{T}) where T
     isempty(a) && return a
@@ -222,6 +227,11 @@ function cos(a::Interval{Float64})
     end
 end
 
+function cospi(a::Interval{T}) where T
+    isempty(a) && return a
+    w = a * pi_interval(T)
+    return(cos(w))
+end
 
 function find_quadrants_tan(x::T) where {T}
     temp = atomic(Interval{T}, x) / half_pi(x)

test/interval_tests/trig.jl

@@ -40,6 +40,22 @@ end
     @test cos(@biginterval(1.3, 6.3)) ⊆ cos(@interval(1.3, 6.3))
 end
 
+@testset "sinpi" begin
+    @test sinpi(∅) == ∅
+    @test sinpi(0.5 .. 1.5) == Interval(-1 , 1)
+    @test sinpi(1 .. 2) ⊇ Interval(-1 , 0)
+    @test sinpi(0.25 .. 0.75) ⊇ Interval(1/sqrt(2) , 1)
+    @test sinpi(-0.25 .. 0.25) ⊇ Interval(-1/sqrt(2) , 1/sqrt(2))
+end
+
+@testset "cospi" begin
+    @test cospi(∅) == ∅
+    @test cospi(1 .. 2) == Interval(-1 , 1)
+    @test cospi(0.5 .. 1.5) ⊇ Interval(-1 , 0)
+    @test cospi(0.25 .. 0.75) ⊇ Interval(-1/sqrt(2) , 1/sqrt(2))
+    @test cospi(-0.25 .. 0.25) == Interval(1/sqrt(2) , 1)
+end
+
 @testset "tan" begin
     @test tan(@interval(0.5)) == Interval(0.54630248984379048, 0.5463024898437906)
     @test tan(@interval(0.5, 1.67)) == entireinterval()