From 076144886a58b7ff5aafe1a7c846321702069b32 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Thu, 1 Jan 2015 14:18:57 +0100
Subject: [PATCH] Math: added half pi and Euler's number to constants.

Constants::piHalf() is not longer to write than doing the division
manually and it has significantly smaller mental overhead. Also I chose
piHalf() instead of halfPi() to make it more discoverable through
autocompletion.

    Float a = Constants::pi()*0.5f;
    Float a = Constants::piHalf();

    Float b = Constants::pi()/(2*countOfSomething);
    Float b = Constants::piHalf()/countOfSomething;
---
 doc/transformations.dox                |  2 +-
 src/Magnum/Math/Constants.h            | 16 ++++++++++++++--
 src/Magnum/Math/Test/ConstantsTest.cpp | 10 ++++++++++
 3 files changed, 25 insertions(+), 3 deletions(-)

diff --git a/doc/transformations.dox b/doc/transformations.dox
index 02ebbd29b..1594b646f 100644
--- a/doc/transformations.dox
+++ b/doc/transformations.dox
@@ -90,7 +90,7 @@ and rotation transformation can be created by calling @ref Matrix3::rotation(),
 @ref Complex::rotation() or @ref DualComplex::rotation(), for example:
 @code
 auto a = Matrix3::rotation(23.0_degf);
-auto b = Complex::rotation(Rad(Constants::pi()/2));
+auto b = Complex::rotation(Rad(Constants::piHalf()));
 auto c = DualComplex::rotation(-1.57_radf);
 @endcode
 
diff --git a/src/Magnum/Math/Constants.h b/src/Magnum/Math/Constants.h
index 17b873340..212da2cd4 100644
--- a/src/Magnum/Math/Constants.h
+++ b/src/Magnum/Math/Constants.h
@@ -46,18 +46,26 @@ template<class T> struct Constants {
     /**
      * @brief Pi
      *
-     * @see @ref tau(), @ref Deg, @ref Rad
+     * @see @ref piHalf(), @ref tau(), @ref Deg, @ref Rad
      */
     static constexpr T pi();
 
+    /**
+     * @brief Half pi
+     *
+     * @see @ref pi(), @ref tau(), @ref Deg, @ref Rad
+     */
+    static constexpr T piHalf();
+
     /**
      * @brief Tau
      *
      * Or two pi.
-     * @see @ref pi(), @ref Deg, @ref Rad
+     * @see @ref pi(), @ref piHalf(), @ref Deg, @ref Rad
      */
     static constexpr T tau();
 
+    static constexpr T e();     /**< @brief Euler's number */
     static constexpr T sqrt2(); /**< @brief Square root of 2 */
     static constexpr T sqrt3(); /**< @brief Square root of 3 */
     #endif
@@ -69,7 +77,9 @@ template<> struct Constants<Double> {
     Constants() = delete;
 
     static constexpr Double pi()        { return 3.141592653589793; }
+    static constexpr Double piHalf()    { return 1.570796326794897; }
     static constexpr Double tau()       { return 6.283185307179586; }
+    static constexpr Double e()         { return 2.718281828459045; }
     static constexpr Double sqrt2()     { return 1.414213562373095; }
     static constexpr Double sqrt3()     { return 1.732050807568877; }
 };
@@ -78,7 +88,9 @@ template<> struct Constants<Float> {
     Constants() = delete;
 
     static constexpr Float pi()         { return 3.141592654f; }
+    static constexpr Float piHalf()     { return 1.570796327f; }
     static constexpr Float tau()        { return 6.283185307f; }
+    static constexpr Float e()          { return 2.718281828f; }
     static constexpr Float sqrt2()      { return 1.414213562f; }
     static constexpr Float sqrt3()      { return 1.732050808f; }
 };
diff --git a/src/Magnum/Math/Test/ConstantsTest.cpp b/src/Magnum/Math/Test/ConstantsTest.cpp
index 813c99aab..2331e477e 100644
--- a/src/Magnum/Math/Test/ConstantsTest.cpp
+++ b/src/Magnum/Math/Test/ConstantsTest.cpp
@@ -50,8 +50,13 @@ void ConstantsTest::constantsFloat() {
     CORRADE_COMPARE(Math::pow<2>(b), 3.0f);
 
     constexpr Float c = Constants<Float>::pi();
+    constexpr Float d = Constants<Float>::piHalf();
     constexpr Float e = Constants<Float>::tau();
+    CORRADE_COMPARE(0.5f*c, d);
     CORRADE_COMPARE(2.0f*c, e);
+
+    constexpr Float f = Constants<Float>::e();
+    CORRADE_COMPARE(std::log(f), 1.0f);
 }
 
 void ConstantsTest::constantsDouble() {
@@ -62,8 +67,13 @@ void ConstantsTest::constantsDouble() {
     CORRADE_COMPARE(Math::pow<2>(b), 3.0);
 
     constexpr Double c = Constants<Double>::pi();
+    constexpr Double d = Constants<Double>::piHalf();
     constexpr Double e = Constants<Double>::tau();
+    CORRADE_COMPARE(0.5*c, d);
     CORRADE_COMPARE(2.0*c, e);
+
+    constexpr Double f = Constants<Double>::e();
+    CORRADE_COMPARE(std::log(f), 1.0);
     #else
     CORRADE_SKIP("Double precision is not supported when targeting OpenGL ES.");
     #endif