Properly use typed math constants instead of impl. specific hacks

PI is not in the stdlib, neither is 1/pi, pi*2 and so on. Instead
of relying on implementations providing these, use properly typed
math constants.

Main benefits:
- portable and
- returns constexpr, for compile-time computation

References:
- http://www.boost.org/doc/libs/1_60_0/libs/math/doc/html/math_toolkit/constants_intro.html
- http://www.boost.org/doc/libs/1_60_0/libs/math/doc/html/math_toolkit/constants.html

CMakeLists.txt

@@ -163,7 +163,6 @@ elseif(${CMAKE_CXX_COMPILER_ID} STREQUAL "GNU")
   # using GCC
   set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wall -Wextra -pedantic -Wuninitialized -Wunreachable-code -Wstrict-overflow=1 -D_FORTIFY_SOURCE=2 ${COLOR_FLAG} -fPIC")
   if(WIN32) # using mingw
-    add_definitions(-D_USE_MATH_DEFINES) # define M_PI, M_1_PI etc.
     add_definitions(-DWIN32)
     set(OPTIONAL_SOCKET_LIBS ws2_32 wsock32)
   endif()
@@ -175,7 +174,6 @@ elseif(${CMAKE_CXX_COMPILER_ID} STREQUAL "MSVC")
   set(BOOST_COMPONENTS ${BOOST_COMPONENTS} date_time chrono zlib)
   add_definitions(-D_CRT_SECURE_NO_WARNINGS)
   add_definitions(-DNOMINMAX) # avoid min and max macros that can break compilation
-  add_definitions(-D_USE_MATH_DEFINES) # define M_PI
   add_definitions(-D_WIN32_WINNT=0x0501)
   add_definitions(-DXML_STATIC)
   find_library(ws2_32_LIBRARY_PATH ws2_32)

include/engine/map_matching/bayes_classifier.hpp

@@ -6,6 +6,8 @@
 #include <vector>
 #include <utility>
 
+#include <boost/math/constants/constants.hpp>
+
 namespace osrm
 {
 namespace engine
@@ -23,8 +25,10 @@ struct NormalDistribution
     // FIXME implement log-probability version since its faster
     double density_function(const double val) const
     {
+        using namespace boost::math::constants;
+
         const double x = val - mean;
-        return 1.0 / (std::sqrt(2. * M_PI) * standard_deviation) *
+        return 1.0 / (std::sqrt(two_pi<double>()) * standard_deviation) *
                std::exp(-x * x / (standard_deviation * standard_deviation));
     }
 

include/engine/map_matching/hidden_markov_model.hpp

@@ -4,6 +4,7 @@
 #include "util/integer_range.hpp"
 
 #include <boost/assert.hpp>
+#include <boost/math/constants/constants.hpp>
 
 #include <cmath>
 
@@ -17,7 +18,7 @@ namespace engine
 namespace map_matching
 {
 
-static const double log_2_pi = std::log(2. * M_PI);
+static const double log_2_pi = std::log(2. * boost::math::constants::pi<double>());
 static const double IMPOSSIBLE_LOG_PROB = -std::numeric_limits<double>::infinity();
 static const double MINIMAL_LOG_PROB = std::numeric_limits<double>::lowest();
 static const std::size_t INVALID_STATE = std::numeric_limits<std::size_t>::max();

include/util/trigonometry_table.hpp

@@ -6,6 +6,8 @@
 
 #include <limits>
 
+#include <boost/math/constants/constants.hpp>
+
 namespace osrm
 {
 namespace util
@@ -356,19 +358,22 @@ constexpr unsigned short atan_table[4096] = {
     0xffe0, 0xffea, 0xfff4, 0xffff};
 
 // max value is pi/4
-constexpr double SCALING_FACTOR = 4. / M_PI * 0xFFFF;
+const constexpr double SCALING_FACTOR = 4. / boost::math::constants::pi<double>() * 0xFFFF;
 
 inline double atan2_lookup(double y, double x)
 {
+
+    using namespace boost::math::constants;
+
     if (std::abs(x) < std::numeric_limits<double>::epsilon())
     {
         if (y >= 0.)
         {
-            return M_PI / 2.;
+            return half_pi<double>();
         }
         else
         {
-            return -M_PI / 2.;
+            return -half_pi<double>();
         }
     }
 
@@ -399,25 +404,25 @@ inline double atan2_lookup(double y, double x)
     case 0:
         break;
     case 1:
-        angle = M_PI - angle;
+        angle = pi<double>() - angle;
         break;
     case 2:
         angle = -angle;
         break;
     case 3:
-        angle = -M_PI + angle;
+        angle = -pi<double>() + angle;
         break;
     case 4:
-        angle = M_PI / 2.0 - angle;
+        angle = half_pi<double>() - angle;
         break;
     case 5:
-        angle = M_PI / 2.0 + angle;
+        angle = half_pi<double>() + angle;
         break;
     case 6:
-        angle = -M_PI / 2.0 + angle;
+        angle = -half_pi<double>() + angle;
         break;
     case 7:
-        angle = -M_PI / 2.0 - angle;
+        angle = -half_pi<double>() - angle;
         break;
     }
     return angle;

include/util/typedefs.hpp

@@ -6,14 +6,6 @@
 #include <limits>
 #include <cstddef>
 
-// Necessary workaround for Windows as VS doesn't implement C99
-#ifdef _MSC_VER
-#define WIN32_LEAN_AND_MEAN
-#ifndef M_PI
-#define M_PI 3.14159265358979323846
-#endif
-#endif
-
 // OpenStreetMap node ids are higher than 2^32
 OSRM_STRONG_TYPEDEF(uint64_t, OSMNodeID)
 OSRM_STRONG_TYPEDEF(uint32_t, OSMWayID)

src/util/coordinate_calculation.cpp

@@ -4,6 +4,7 @@
 #include "util/trigonometry_table.hpp"
 
 #include <boost/assert.hpp>
+#include <boost/math/constants/constants.hpp>
 
 #include <cmath>
 
@@ -193,9 +194,17 @@ perpendicularDistanceFromProjectedCoordinate(const FixedPointCoordinate segment_
     return approximate_distance;
 }
 
-double degToRad(const double degree) { return degree * (static_cast<double>(M_PI) / 180.0); }
+double degToRad(const double degree)
+{
+    using namespace boost::math::constants;
+    return degree * (pi<double>() / 180.0);
+}
 
-double radToDeg(const double radian) { return radian * (180.0 * static_cast<double>(M_1_PI)); }
+double radToDeg(const double radian)
+{
+    using namespace boost::math::constants;
+    return radian * (180.0 * (1. / pi<double>()));
+}
 
 double bearing(const FixedPointCoordinate first_coordinate,
                const FixedPointCoordinate second_coordinate)
@@ -225,6 +234,7 @@ double computeAngle(const FixedPointCoordinate first,
                     const FixedPointCoordinate second,
                     const FixedPointCoordinate third)
 {
+    using namespace boost::math::constants;
     using namespace coordinate_calculation;
 
     const double v1x = (first.lon - second.lon) / COORDINATE_PRECISION;
@@ -234,7 +244,7 @@ double computeAngle(const FixedPointCoordinate first,
     const double v2y = mercator::latToY(third.lat / COORDINATE_PRECISION) -
                        mercator::latToY(second.lat / COORDINATE_PRECISION);
 
-    double angle = (atan2_lookup(v2y, v2x) - atan2_lookup(v1y, v1x)) * 180. / M_PI;
+    double angle = (atan2_lookup(v2y, v2x) - atan2_lookup(v1y, v1x)) * 180. / pi<double>();
 
     while (angle < 0.)
     {
@@ -248,12 +258,18 @@ namespace mercator
 {
 double yToLat(const double value)
 {
-    return 180. * M_1_PI * (2. * std::atan(std::exp(value * M_PI / 180.)) - M_PI_2);
+    using namespace boost::math::constants;
+
+    return 180. * (1. / pi<long double>()) *
+           (2. * std::atan(std::exp(value * pi<double>() / 180.)) - half_pi<double>());
 }
 
 double latToY(const double latitude)
 {
-    return 180. * M_1_PI * std::log(std::tan(M_PI_4 + latitude * (M_PI / 180.) / 2.));
+    using namespace boost::math::constants;
+
+    return 180. * (1. / pi<double>()) *
+           std::log(std::tan((pi<double>() / 4.) + latitude * (pi<double>() / 180.) / 2.));
 }
 } // ns mercato // ns mercatorr
 } // ns coordinate_calculation