Add trigonometric functions for special irrationals (#21)

* Add trigonometric functions for special irrationals

* Fix tests

* Try to fix tests on Julia nightly

* Bump version

* Improve definition for quartpi

* Update tests

Project.toml

@@ -1,7 +1,7 @@
 name = "IrrationalConstants"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 authors = ["JuliaMath"]
-version = "0.2.1"
+version = "0.2.2"
 
 [compat]
 julia = "1"

src/IrrationalConstants.jl

@@ -28,5 +28,6 @@ export
 
 include("macro.jl")
 include("stats.jl")
+include("trigonometric.jl")
 
 end # module

src/trigonometric.jl

@@ -0,0 +1,34 @@
+# Functions return `Float64`, consistent with Base
+# https://github.com/JuliaLang/julia/pull/42595
+# Values at poles are defined to be consistent with `cot(0)` and `cot(π)`
+# https://github.com/JuliaLang/julia/issues/7123
+# https://github.com/JuliaLang/julia/blob/e3d366f1966595ba737220df49e220610823b331/base/mathconstants.jl#L130
+
+# `sin`
+Base.sin(::Twoπ) = 0.0
+Base.sin(::Fourπ) = 0.0
+Base.sin(::Halfπ) = 1.0
+Base.sin(::Quartπ) = Float64(invsqrt2)
+
+# `cos`
+Base.cos(::Twoπ) = 1.0
+Base.cos(::Fourπ) = 1.0
+Base.cos(::Halfπ) = 0.0
+Base.cos(::Quartπ) = Float64(invsqrt2)
+
+# `sincos`
+Base.sincos(::Twoπ) = (0.0, 1.0)
+Base.sincos(::Fourπ) = (0.0, 1.0)
+Base.sincos(::Halfπ) = (1.0, 0.0)
+Base.sincos(::Quartπ) = (Float64(invsqrt2), Float64(invsqrt2))
+
+# `tan`
+Base.tan(::Twoπ) = 0.0
+Base.tan(::Fourπ) = 0.0
+Base.tan(::Halfπ) = 1/0
+Base.tan(::Quartπ) = 1.0
+
+# `csc`, `sec`, and `cot` are defined automatically, so we do not define them
+# there is one exception where we can improve accuracy:
+Base.csc(::Quartπ) = Float64(sqrt2)
+Base.sec(::Quartπ) = Float64(sqrt2)

test/runtests.jl

@@ -150,3 +150,34 @@ end
         @test @inferred(round(loghalf, mode)) == 0.0
     end
 end
+
+@testset "trigonometric functions" begin
+    # 2π, 4π
+    for (n, x) in ((2, twoπ), (4, fourπ))
+        @test sin(x) === sinpi(n) === sin(0.0)
+        @test cos(x) === cospi(n) === cos(0.0)
+    end
+
+    # halfπ, quartπ
+    for (r, x) in ((big"0.5", halfπ), (big"0.25", quartπ))
+        @test sin(x) === Float64(sinpi(r))
+        @test cos(x) === Float64(cospi(r))
+    end
+
+    # Check consistency of definitions
+    for x in (twoπ, fourπ, halfπ, quartπ)
+        @test sincos(x) === (sin(x), cos(x))
+        @test tan(x) === sin(x) / cos(x)
+    end
+
+    # Check `csc`, `sec`, and `cot`
+    for x in (twoπ, fourπ, halfπ)
+        # These are defined automatically via sin, cos, and tan
+        @test csc(x) === 1 / sin(x)
+        @test sec(x) === 1 / cos(x)
+        @test cot(x) === csc(x) / sec(x)
+    end
+    @test csc(quartπ) === Float64(csc(big(quartπ)))
+    @test sec(quartπ) === Float64(sec(big(quartπ)))
+    @test cot(quartπ) === Float64(cot(big(quartπ)))
+end