From b440c98b3389d1d379e717e96aba8dae6d84e6d9 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Thu, 23 Feb 2023 00:53:32 +0100
Subject: [PATCH 1/6] Add trigonometric functions for special irrationals

---
 Project.toml               |  2 +-
 src/IrrationalConstants.jl |  1 +
 src/trigonometric.jl       | 29 +++++++++++++++++++++++++++++
 test/runtests.jl           | 25 +++++++++++++++++++++++++
 4 files changed, 56 insertions(+), 1 deletion(-)
 create mode 100644 src/trigonometric.jl

diff --git a/Project.toml b/Project.toml
index 53e9b18..b3acd5f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "IrrationalConstants"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 authors = ["JuliaMath"]
-version = "0.2.0"
+version = "0.2.1"
 
 [compat]
 julia = "1"
diff --git a/src/IrrationalConstants.jl b/src/IrrationalConstants.jl
index 3d9e8ee..691be93 100644
--- a/src/IrrationalConstants.jl
+++ b/src/IrrationalConstants.jl
@@ -28,5 +28,6 @@ export
 
 include("macro.jl")
 include("stats.jl")
+include("trigonometric.jl")
 
 end # module
diff --git a/src/trigonometric.jl b/src/trigonometric.jl
new file mode 100644
index 0000000..6cafe93
--- /dev/null
+++ b/src/trigonometric.jl
@@ -0,0 +1,29 @@
+# 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
diff --git a/test/runtests.jl b/test/runtests.jl
index 3863cfd..b702173 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -135,3 +135,28 @@ end
   @test twoπ/ComplexF32(2) isa ComplexF32
   @test log(twoπ, ComplexF32(2)) isa ComplexF32
 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 ((1 // 2, halfπ), (1 // 4, quartπ))
+    @test sin(x) === sinpi(r)
+    @test cos(x) === cospi(r)
+  end
+
+  for x in (twoπ, fourπ, halfπ, quartπ)
+    # Check consistency of definitions
+    @test sincos(x) === (sin(x), cos(x))
+    @test tan(x) === sin(x) / cos(x)
+
+    # These are defined automatically via sin, cos, and tan
+    @test csc(x) === inv(sin(x)) === csc(0.0)
+    @test sec(x) === inv(cos(x)) === sec(0.0)
+    @test cot(x) === inv(tan(x)) === cot(0.0)
+  end
+end

From 807c15f095c51e980c05b53118a3de0581e63d4e Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Thu, 23 Feb 2023 16:06:30 +0100
Subject: [PATCH 2/6] Fix tests

---
 test/runtests.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/runtests.jl b/test/runtests.jl
index b702173..543b2e9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -155,8 +155,8 @@ end
     @test tan(x) === sin(x) / cos(x)
 
     # These are defined automatically via sin, cos, and tan
-    @test csc(x) === inv(sin(x)) === csc(0.0)
-    @test sec(x) === inv(cos(x)) === sec(0.0)
-    @test cot(x) === inv(tan(x)) === cot(0.0)
+    @test csc(x) === inv(sin(x))
+    @test sec(x) === inv(cos(x))
+    @test cot(x) === inv(tan(x))
   end
 end

From c5cd49fa749a356da12b6449dddc143d458f7c75 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Thu, 23 Feb 2023 16:22:51 +0100
Subject: [PATCH 3/6] Try to fix tests on Julia nightly

---
 test/runtests.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/runtests.jl b/test/runtests.jl
index 543b2e9..cce7386 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -144,9 +144,9 @@ end
   end
 
   # halfπ, quartπ
-  for (r, x) in ((1 // 2, halfπ), (1 // 4, quartπ))
-    @test sin(x) === sinpi(r)
-    @test cos(x) === cospi(r)
+  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
 
   for x in (twoπ, fourπ, halfπ, quartπ)

From 6565ece706ba04bf09916e72534a6c39fd39a18f Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Fri, 24 Feb 2023 14:08:47 +0100
Subject: [PATCH 4/6] Bump version

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index b3acd5f..c16d012 100644
--- a/Project.toml
+++ b/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"

From c24139b2ca512fa3d60446cc2d0c510537982224 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Fri, 24 Feb 2023 15:48:53 +0100
Subject: [PATCH 5/6] Improve definition for quartpi

---
 src/trigonometric.jl |  5 +++++
 test/runtests.jl     | 44 ++++++++++++++++++++++----------------------
 2 files changed, 27 insertions(+), 22 deletions(-)

diff --git a/src/trigonometric.jl b/src/trigonometric.jl
index 6cafe93..7f84548 100644
--- a/src/trigonometric.jl
+++ b/src/trigonometric.jl
@@ -27,3 +27,8 @@ 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)
diff --git a/test/runtests.jl b/test/runtests.jl
index ce3a238..493250e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -152,26 +152,26 @@ 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
-
-  for x in (twoπ, fourπ, halfπ, quartπ)
-    # Check consistency of definitions
-    @test sincos(x) === (sin(x), cos(x))
-    @test tan(x) === sin(x) / cos(x)
-
-    # These are defined automatically via sin, cos, and tan
-    @test csc(x) === inv(sin(x))
-    @test sec(x) === inv(cos(x))
-    @test cot(x) === inv(tan(x))
-  end
+    # 2π, 4π
+    for (n, x) in ((2, twoπ), (4, fourπ))
+        @test sin(x) === sinpi(n) === sin(0.0) === Float64(sin(big(x)))
+        @test cos(x) === cospi(n) === cos(0.0) === Float64(cos(big(x)))
+    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
+
+    for x in (twoπ, fourπ, halfπ, quartπ)
+        # Check consistency of definitions
+        @test sincos(x) === (sin(x), cos(x))
+        @test tan(x) === sin(x) / cos(x)
+
+        # These are defined automatically via sin, cos, and tan
+        @test csc(x) === Float64(csc(big(x)))
+        @test sec(x) === Float64(sec(big(x)))
+        @test cot(x) === csc(x) / sec(x)
+    end
 end

From dd8b35532e5ca96ad8ee8b8d071b20e8ff664859 Mon Sep 17 00:00:00 2001
From: David Widmann <david.widmann@it.uu.se>
Date: Sun, 26 Feb 2023 03:21:58 +0100
Subject: [PATCH 6/6] Update tests

---
 test/runtests.jl | 16 +++++++++++-----
 1 file changed, 11 insertions(+), 5 deletions(-)

diff --git a/test/runtests.jl b/test/runtests.jl
index 493250e..a529a5e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -154,8 +154,8 @@ end
 @testset "trigonometric functions" begin
     # 2π, 4π
     for (n, x) in ((2, twoπ), (4, fourπ))
-        @test sin(x) === sinpi(n) === sin(0.0) === Float64(sin(big(x)))
-        @test cos(x) === cospi(n) === cos(0.0) === Float64(cos(big(x)))
+        @test sin(x) === sinpi(n) === sin(0.0)
+        @test cos(x) === cospi(n) === cos(0.0)
     end
 
     # halfπ, quartπ
@@ -164,14 +164,20 @@ end
         @test cos(x) === Float64(cospi(r))
     end
 
+    # Check consistency of definitions
     for x in (twoπ, fourπ, halfπ, quartπ)
-        # Check consistency of definitions
         @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) === Float64(csc(big(x)))
-        @test sec(x) === Float64(sec(big(x)))
+        @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