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

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)