From 36ad0dc069d6f9cf4d8287cda74a20b413801ca5 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Thu, 23 Feb 2023 23:47:16 +0100
Subject: [PATCH 1/2] Add documentation

---
 README.md  | 10 ++++++++--
 src/Tau.jl | 45 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 53 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index a8b4965..842a841 100644
--- a/README.md
+++ b/README.md
@@ -29,7 +29,7 @@ Irrational{:twoπ}
 
 Note: to input the τ character, type `\tau` then press <kbd>Tab</kbd>.
 
-The tau variants of `sinpi`, `cospi`, and `mod2pi` are also defined:
+The tau variants of `sinpi`, `cospi`, `sincospi`, `cispi`, and `mod2pi` are also defined:
 
 ```julia
 julia> sintau(1//4)
@@ -38,11 +38,17 @@ julia> sintau(1//4)
 julia> costau(1//2)
 -1.0
 
+julia> sincostau(1//2)
+(0.0, -1.0)
+
+julia> cistau(1//2)
+-1.0 + 0.0im
+
 julia> modtau(9*pi/4)
 0.7853981633974481
 ```
 
-Alternatively, one can use the Unicode aliases `sinτ`, `cosτ`, and `modτ`.
+Alternatively, one can use the Unicode aliases `sinτ`, `cosτ`, `sincosτ`, `cisτ`, and `modτ`.
 
 ## The tau != 2pi inequality
 
diff --git a/src/Tau.jl b/src/Tau.jl
index af91e98..010b415 100644
--- a/src/Tau.jl
+++ b/src/Tau.jl
@@ -45,9 +45,54 @@ function cisτ(x::Integer)
     return complex(one(y), zero(y))
 end
 
+# Aliases
 const sintau = sinτ
 const costau = cosτ
 const sincostau = sincosτ
 const cistau = cisτ
 
+# Documentation
+
+"""
+    sinτ(x)
+    sintau(x)
+
+Compute ``\\sin(\\tau x)`` more accurately than `sin(tau*x)`, especially for large `x`.
+
+See also: `costau`, `sincostau`.
+"""
+function sintau end
+
+"""
+    cosτ(x)
+    costau(x)
+
+Compute ``\\cos(\\tau x)`` more accurately than `cos(tau*x)`, especially for large `x`.
+
+See also: `sintau`, `sincostau`.
+"""
+function costau end
+
+"""
+    sincosτ(x)
+    costau(x)
+
+Simultaneously compute `sintau(x)` and `costau(x)` (the sine and cosine of `tau*x`,
+where `x` is in radians), returning a tuple `(sine, cosine)`.
+
+See also: `sintau`, `costau`.
+"""
+function sincostau end
+
+
+"""
+    cisτ(x)
+    cistau(x)
+
+Compute ``\\exp(\\tau i x)`` more accurately than `cis(tau*x)`, especially for large `x`.
+
+See also: `cis`, `sincostau`.
+"""
+function cistau end
+
 end

From c0eb0216f8740cadc7ee9e80617e3b12da592879 Mon Sep 17 00:00:00 2001
From: David Widmann <david.widmann@it.uu.se>
Date: Sun, 26 Feb 2023 03:11:43 +0100
Subject: [PATCH 2/2] Fix docstrings

---
 src/Tau.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/Tau.jl b/src/Tau.jl
index 010b415..edc20fc 100644
--- a/src/Tau.jl
+++ b/src/Tau.jl
@@ -61,7 +61,7 @@ Compute ``\\sin(\\tau x)`` more accurately than `sin(tau*x)`, especially for lar
 
 See also: `costau`, `sincostau`.
 """
-function sintau end
+function sinτ end
 
 """
     cosτ(x)
@@ -71,7 +71,7 @@ Compute ``\\cos(\\tau x)`` more accurately than `cos(tau*x)`, especially for lar
 
 See also: `sintau`, `sincostau`.
 """
-function costau end
+function cosτ end
 
 """
     sincosτ(x)
@@ -82,7 +82,7 @@ where `x` is in radians), returning a tuple `(sine, cosine)`.
 
 See also: `sintau`, `costau`.
 """
-function sincostau end
+function sincosτ end
 
 
 """
@@ -93,6 +93,6 @@ Compute ``\\exp(\\tau i x)`` more accurately than `cis(tau*x)`, especially for l
 
 See also: `cis`, `sincostau`.
 """
-function cistau end
+function cisτ end
 
 end