Replace some math function calls with constants, use inv_pi where applicable

Author: ajtribick

src/celengine/body.cpp

@@ -233,7 +233,7 @@ float Body::getBoundingRadius() const
     if (geometry == InvalidResource)
         return radius;
 
-    return radius * celestia::numbers::sqrt3_v<float>; // sqrt(3)
+    return radius * celestia::numbers::sqrt3_v<float>;
 }
 
 
@@ -354,7 +354,7 @@ float Body::getTemperature(double time) const
             float lum = square(s->getRadius()) * pow(s->getTemperature(), 4.0f);
             flux += lum / square(distFromSun);
         }
-        temp = (float) pow((1.0f - getBondAlbedo()) * flux, 0.25f) / sqrt(2.0f);
+        temp = std::pow((1.0f - getBondAlbedo()) * flux, 0.25f) * (celestia::numbers::sqrt2_v<float> * 0.5f);
     }
     return getTempDiscrepancy() + temp;
 }

src/celengine/render.cpp

@@ -48,6 +48,7 @@
 #include "orbitsampler.h"
 #include "rendcontext.h"
 #include "textlayout.h"
+#include <celcompat/numbers.h>
 #include <celengine/observer.h>
 #include <celmath/frustum.h>
 #include <celmath/distance.h>
@@ -347,7 +348,9 @@ static void BuildGaussianDiscMipLevel(unsigned char* mipPixels,
     unsigned int size = 1 << log2size;
     float sigma = fwhm / 2.3548f;
     float isig2 = 1.0f / (2.0f * sigma * sigma);
-    float s = 1.0f / (sigma * (float) sqrt(2.0 * celestia::numbers::pi));
+    // Store 1/sqrt(2*pi) in constexpr sfactor
+    constexpr auto sfactor = static_cast<float>(0.5 * celestia::numbers::sqrt2 * celestia::numbers::inv_sqrtpi);
+    float s = sfactor / sigma;
 
     for (unsigned int i = 0; i < size; i++)
     {
@@ -2381,7 +2384,7 @@ void Renderer::renderObject(const Vector3f& pos,
                 cloudNormalMap = atmosphere->cloudNormalMap.find(textureResolution);
         }
         if (atmosphere->cloudSpeed != 0.0f)
-            cloudTexOffset = (float) (-pfmod(now * atmosphere->cloudSpeed / (2 * celestia::numbers::pi), 1.0));
+            cloudTexOffset = (float) (-pfmod(now * atmosphere->cloudSpeed * 0.5 * celestia::numbers::inv_pi, 1.0));
     }
 
     if (obj.geometry == InvalidResource)

src/celengine/skygrid.cpp

@@ -475,10 +475,10 @@ SkyGrid::render(Renderer& renderer,
     int raIncrement  = meridianSpacing(idealMeridianSpacing);
     int decIncrement = parallelSpacing(idealParallelSpacing);
 
-    int startRa  = (int) std::ceil (totalLongitudeUnits * (minTheta / (celestia::numbers::pi * 2.0)) / (double) raIncrement) * raIncrement;
-    int endRa    = (int) std::floor(totalLongitudeUnits * (maxTheta / (celestia::numbers::pi * 2.0)) / (double) raIncrement) * raIncrement;
-    int startDec = (int) std::ceil (DEG_MIN_SEC_TOTAL  * (minDec / celestia::numbers::pi) / (double) decIncrement) * decIncrement;
-    int endDec   = (int) std::floor(DEG_MIN_SEC_TOTAL  * (maxDec / celestia::numbers::pi) / (double) decIncrement) * decIncrement;
+    int startRa  = (int) std::ceil (totalLongitudeUnits * (minTheta * 0.5 * celestia::numbers::inv_pi) / (double) raIncrement) * raIncrement;
+    int endRa    = (int) std::floor(totalLongitudeUnits * (maxTheta * 0.5 * celestia::numbers::inv_pi) / (double) raIncrement) * raIncrement;
+    int startDec = (int) std::ceil (DEG_MIN_SEC_TOTAL  * (minDec * celestia::numbers::inv_pi) / (double) decIncrement) * decIncrement;
+    int endDec   = (int) std::floor(DEG_MIN_SEC_TOTAL  * (maxDec * celestia::numbers::inv_pi) / (double) decIncrement) * decIncrement;
 
     // Get the orientation at single precision
     Quaterniond q = xrot90 * m_orientation * xrot90.conjugate();

src/celengine/stardb.cpp

@@ -26,6 +26,7 @@
 
 #include <celcompat/bit.h>
 #include <celcompat/charconv.h>
+#include <celcompat/numbers.h>
 #include <celutil/gettext.h>
 #include <celutil/intrusiveptr.h>
 #include <celutil/logger.h>
@@ -1622,7 +1623,7 @@ void StarDatabaseBuilder::buildOctree()
 
     GetLogger()->debug("Sorting stars into octree . . .\n");
     float absMag = astro::appToAbsMag(STAR_OCTREE_MAGNITUDE,
-                                      STAR_OCTREE_ROOT_SIZE * (float) sqrt(3.0));
+                                      STAR_OCTREE_ROOT_SIZE * celestia::numbers::sqrt3_v<float>);
     DynamicStarOctree* root = new DynamicStarOctree(Eigen::Vector3f(1000.0f, 1000.0f, 1000.0f),
                                                     absMag);
     for (unsigned int i = 0; i < unsortedStars.size(); ++i)

src/celengine/universe.cpp

@@ -214,8 +214,8 @@ ExactPlanetPickTraversal(Body* body, PlanetPickInfo& pickInfo)
     Eigen::Vector3d bodyMiss = bodyDir - pickInfo.pickRay.direction();
 
     if (double sinAngle2 = bodyMiss.norm() / 2.0;
-        sinAngle2 < std::sin(celestia::numbers::pi/4.0) && distance > 0.0 &&
-        distance <= pickInfo.closestDistance)
+        sinAngle2 < (celestia::numbers::sqrt2 * 0.5) && // sin(45 degrees) = sqrt(2)/2
+        distance > 0.0 && distance <= pickInfo.closestDistance)
     {
         pickInfo.closestDistance = distance;
         pickInfo.closestBody = body;