[skip ci] Rephrased the API docs in terms of adding new types

Missing two commits in StaticRTree changes

docs/http.md

@@ -421,7 +421,8 @@ step.
   direction of travel immediately before the maneuver.
 - `bearing_after`: The clockwise angle from true north to the
   direction of travel immediately after the maneuver.
-- `type` A string indicating the type of maneuver
+- `type` A string indicating the type of maneuver. **new identifiers might be introduced without API change**
+   Types  unknown to the client should be handled like the `turn` type, the existance of correct `modifier` values is guranteed.
   
   | `type`            | Description                                                  |
   |-------------------|--------------------------------------------------------------|
@@ -476,7 +477,7 @@ step.
   | `turn` or `end of road`| Indicates the number of intersections passed until the turn. Example instruction: `at the fourth intersection, turn left` |
   
 
-New maneuver `type` and `modifier` and new properties (potentially depending on `type`) may be introduced in the future without an API version change.
+New properties (potentially depending on `type`) may be introduced in the future without an API version change.
 
 ### Waypoint
 

include/util/static_rtree.hpp

@@ -74,9 +74,9 @@ class StaticRTree
     struct LeafNode
     {
         LeafNode() : object_count(0), objects() {}
-        uint32_t object_count;
+        std::uint32_t object_count;
         std::array<EdgeDataT, LEAF_NODE_SIZE> objects;
-        unsigned char leaf_page_padding[LEAF_PAGE_SIZE - sizeof(object_count) - sizeof(objects)];
+        unsigned char leaf_page_padding[LEAF_PAGE_SIZE - sizeof(std::uint32_t) - sizeof(std::array<EdgeDataT, LEAF_NODE_SIZE>)];
     };
     static_assert(sizeof(LeafNode) == LEAF_PAGE_SIZE, "LeafNode size does not fit the page size");
 

include/util/web_mercator.hpp

@@ -35,7 +35,7 @@ inline FloatLatitude yToLat(const double y)
     const double normalized_lat =
         detail::RAD_TO_DEGREE * 2. * std::atan(std::exp(clamped_y * detail::DEGREE_TO_RAD));
 
-    return FloatLatitude(normalized_lat - 90.);
+    return FloatLatitude(std::round(normalized_lat * COORDINATE_PRECISION) / COORDINATE_PRECISION - 90.);
 }
 
 inline double latToY(const FloatLatitude latitude)
@@ -47,6 +47,31 @@ inline double latToY(const FloatLatitude latitude)
     return clamped_y;
 }
 
+template<typename T>
+constexpr double horner(double, T an) { return an; }
+
+template<typename T, typename... U>
+constexpr double horner(double x, T an, U ...a) { return horner(x, a...) * x + an; }
+
+inline double latToYapprox(const FloatLatitude latitude)
+{
+    if (latitude < FloatLatitude(-70.) || latitude > FloatLatitude(70.))
+        return latToY(latitude);
+
+    // Approximate the inverse Gudermannian function with the Padé approximant [11/11]: deg → deg
+    // Coefficients are computed for the argument range [-70°,70°] by Remez algorithm |err|_∞=3.387e-12
+    const auto x = static_cast<double>(latitude);
+    return
+        horner(x, 0.00000000000000000000000000e+00,  1.00000000000089108431373566e+00,  2.34439410386997223035693483e-06,
+                 -3.21291701673364717170998957e-04, -6.62778508496089940141103135e-10,  3.68188055470304769936079078e-08,
+                  6.31192702320492485752941578e-14, -1.77274453235716299127325443e-12, -2.24563810831776747318521450e-18,
+                  3.13524754818073129982475171e-17,  2.09014225025314211415458228e-23, -9.82938075991732185095509716e-23) /
+        horner(x, 1.00000000000000000000000000e+00,  2.34439410398970701719081061e-06, -3.72061271627251952928813333e-04,
+                 -7.81802389685429267252612620e-10,  5.18418724186576447072888605e-08,  9.37468561198098681003717477e-14,
+                 -3.30833288607921773936702558e-12, -4.78446279888774903983338274e-18,  9.32999229169156878168234191e-17,
+                  9.17695141954265959600965170e-23, -8.72130728982012387640166055e-22, -3.23083224835967391884404730e-28);
+}
+
 inline FloatLatitude clamp(const FloatLatitude lat)
 {
     return std::max(std::min(lat, FloatLatitude(detail::MAX_LATITUDE)),
@@ -87,7 +112,7 @@ inline double degreeToPixel(FloatLatitude lat, unsigned zoom)
 
 inline FloatCoordinate fromWGS84(const FloatCoordinate &wgs84_coordinate)
 {
-    return {wgs84_coordinate.lon, FloatLatitude{latToY(wgs84_coordinate.lat)}};
+    return {wgs84_coordinate.lon, FloatLatitude{latToYapprox(wgs84_coordinate.lat)}};
 }
 
 inline FloatCoordinate toWGS84(const FloatCoordinate &mercator_coordinate)