From 07408e302de1ad9cda6d1b114b5f2d2c9ce6d719 Mon Sep 17 00:00:00 2001
From: jatin <jatinchowdhury18@gmail.com>
Date: Sun, 14 Jan 2024 11:27:04 -0800
Subject: [PATCH] Updating docs

---
 .gitignore                              |  1 +
 README.md                               | 35 ++++++++++++++++++++++---
 include/math_approx/src/trig_approx.hpp |  4 ++-
 3 files changed, 35 insertions(+), 5 deletions(-)

diff --git a/.gitignore b/.gitignore
index 48854f7..5463156 100644
--- a/.gitignore
+++ b/.gitignore
@@ -2,5 +2,6 @@
 .vscode/
 
 build*/
+*.zip
 
 .DS_Store
diff --git a/README.md b/README.md
index dcb4c9b..2c4ef3d 100644
--- a/README.md
+++ b/README.md
@@ -13,9 +13,9 @@ Currently supported:
 - log/log2/log10/log1p
 - sinh/cosh/tanh
 - arcsinh/arccosh/arctanh
-- sigmoid
-- Wright-Omega function
-- Dilogarithm function
+- [Sigmoid function](https://en.wikipedia.org/wiki/Sigmoid_function)
+- [Wright-Omega function](https://en.wikipedia.org/wiki/Wright_omega_function)
+- [Dilogarithm function](https://en.wikipedia.org/wiki/Dilogarithm)
 
 At the moment, most of these implementations have been "good enough"
 for my own use cases (both in terms of performance and accuracy). That
@@ -27,6 +27,33 @@ approximations, either by:
 
 then please get in touch with a GitHub issue or pull request!
 
+## Usage
+
+### With CMake
+
+`math_approx` is set up as a CMake `INTERFACE` library. To use it as
+such, you'll need to add the following to your `CMakeLists.txt` file:
+
+```cmake
+add_subdirectory(math_approx)
+target_link_libraries(<your_target> math_approx)
+```
+
+And then in your C++ code, you can use the approximations like so:
+
+```cpp
+#include <math_approx/math_approx.hpp>
+
+constexpr auto sin_half = math_approx::sin<5> (0.5f);
+```
+
+### Without CMake
+
+To use `math_approx` without CMake, you'll need to add
+`/path/to/repo/include` to your include path. If you're
+compiling your program with MSVC, you may also need to
+add the pre-processor definition `_USE_MATH_DEFINES`.
+
 ## A few other thoughts
 
 ### Accuracy vs. Performance
@@ -44,7 +71,7 @@ polynomial approximations, I've tried to provide the details
 for how those polynomials were derived, by providing a zipped
 folder containing the Mathematica notebooks that were used to
 derive the polynomials. Since not everyone has access to
-Mathematica, the folder also contains a PDF version of the
+Mathematica, the folder also contains a PDF version of each
 notebook. At the moment, I'm planning to upload an updated
 copy of the zipped folder with each release of the library,
 but if I can think of a better method of distribution, that
diff --git a/include/math_approx/src/trig_approx.hpp b/include/math_approx/src/trig_approx.hpp
index e93257b..8dba67a 100644
--- a/include/math_approx/src/trig_approx.hpp
+++ b/include/math_approx/src/trig_approx.hpp
@@ -48,7 +48,9 @@ namespace trig_detail
         return select (x >= (T) 0, mod, mod + pi) - half_pi;
     }
 
-    // for polynomial derivations, see notebooks/sin_approx.nb
+    // Polynomials were derived using the method presented in
+    // https://mooooo.ooo/chebyshev-sine-approximation/
+    // and then adapted for various (odd) orders.
 
     template <typename T>
     constexpr T sin_poly_9 (T x, T x_sq)