Further performance improvements for FP math

src/h3lib/include/constants.h

@@ -50,6 +50,9 @@
 /** one third **/
 #define M_ONETHIRD 0.333333333333333333333333333333333333333
 
+/** one seventh (1/7) **/
+#define M_ONESEVENTH 0.14285714285714285714285714285714285
+
 /** rotation angle between Class II and Class III resolution axes
  * (asin(sqrt(3.0 / 28.0))) */
 #define M_AP7_ROT_RADS 0.333473172251832115336090755351601070065900389

src/h3lib/lib/bbox.c

@@ -57,10 +57,10 @@ bool bboxIsTransmeridian(const BBox *bbox) { return bbox->east < bbox->west; }
  * @param center Output center coordinate
  */
 void bboxCenter(const BBox *bbox, LatLng *center) {
-    center->lat = (bbox->north + bbox->south) / 2.0;
+    center->lat = (bbox->north + bbox->south) * 0.5;
     // If the bbox crosses the antimeridian, shift east 360 degrees
     double east = bboxIsTransmeridian(bbox) ? bbox->east + M_2PI : bbox->east;
-    center->lng = constrainLng((east + bbox->west) / 2.0);
+    center->lng = constrainLng((east + bbox->west) * 0.5);
 }
 
 /**
@@ -265,8 +265,8 @@ H3Error lineHexEstimate(const LatLng *origin, const LatLng *destination,
 void scaleBBox(BBox *bbox, double scale) {
     double width = bboxWidthRads(bbox);
     double height = bboxHeightRads(bbox);
-    double widthBuffer = (width * scale - width) / 2;
-    double heightBuffer = (height * scale - height) / 2;
+    double widthBuffer = (width * scale - width) * 0.5;
+    double heightBuffer = (height * scale - height) * 0.5;
     // Scale north and south, clamping to latitude domain
     bbox->north += heightBuffer;
     if (bbox->north > M_PI_2) bbox->north = M_PI_2;
@@ -308,4 +308,4 @@ void bboxNormalization(const BBox *a, const BBox *b,
                       : aIsTransmeridian ? NORMALIZE_EAST
                       : aToBTrendsEast   ? NORMALIZE_WEST
                                          : NORMALIZE_EAST;
-}
+}

src/h3lib/lib/coordijk.c

@@ -345,8 +345,8 @@ H3Error _upAp7Checked(CoordIJK *ijk) {
         }
     }
 
-    ijk->i = (int)lround(((i * 3) - j) / 7.0);
-    ijk->j = (int)lround((i + (j * 2)) / 7.0);
+    ijk->i = (int)lround(((i * 3) - j) * M_ONESEVENTH);
+    ijk->j = (int)lround((i + (j * 2)) * M_ONESEVENTH);
     ijk->k = 0;
 
     // Expected not to be reachable, because max + min or max - min would need
@@ -393,8 +393,8 @@ H3Error _upAp7rChecked(CoordIJK *ijk) {
         }
     }
 
-    ijk->i = (int)lround(((i * 2) + j) / 7.0);
-    ijk->j = (int)lround(((j * 3) - i) / 7.0);
+    ijk->i = (int)lround(((i * 2) + j) * M_ONESEVENTH);
+    ijk->j = (int)lround(((j * 3) - i) * M_ONESEVENTH);
     ijk->k = 0;
 
     // Expected not to be reachable, because max + min or max - min would need
@@ -417,8 +417,8 @@ void _upAp7(CoordIJK *ijk) {
     int i = ijk->i - ijk->k;
     int j = ijk->j - ijk->k;
 
-    ijk->i = (int)lround((3 * i - j) / 7.0);
-    ijk->j = (int)lround((i + 2 * j) / 7.0);
+    ijk->i = (int)lround((3 * i - j) * M_ONESEVENTH);
+    ijk->j = (int)lround((i + 2 * j) * M_ONESEVENTH);
     ijk->k = 0;
     _ijkNormalize(ijk);
 }
@@ -434,8 +434,8 @@ void _upAp7r(CoordIJK *ijk) {
     int i = ijk->i - ijk->k;
     int j = ijk->j - ijk->k;
 
-    ijk->i = (int)lround((2 * i + j) / 7.0);
-    ijk->j = (int)lround((3 * j - i) / 7.0);
+    ijk->i = (int)lround((2 * i + j) * M_ONESEVENTH);
+    ijk->j = (int)lround((3 * j - i) * M_ONESEVENTH);
     ijk->k = 0;
     _ijkNormalize(ijk);
 }

src/h3lib/lib/faceijk.c

@@ -393,7 +393,7 @@ void _geoToHex2d(const LatLng *g, int res, int *face, Vec2d *v) {
     _geoToClosestFace(g, face, &sqd);
 
     // cos(r) = 1 - 2 * sin^2(r/2) = 1 - 2 * (sqd / 4) = 1 - sqd/2
-    double r = acos(1 - sqd / 2);
+    double r = acos(1 - sqd * 0.5);
 
     if (r < EPSILON) {
         v->x = v->y = 0.0;
@@ -413,7 +413,7 @@ void _geoToHex2d(const LatLng *g, int res, int *face, Vec2d *v) {
     r = tan(r);
 
     // scale for current resolution length u
-    r /= RES0_U_GNOMONIC;
+    r *= INV_RES0_U_GNOMONIC;
     for (int i = 0; i < res; i++) r *= M_SQRT7;
 
     // we now have (r, theta) in hex2d with theta ccw from x-axes

src/h3lib/lib/latLng.c

@@ -169,8 +169,8 @@ double normalizeLng(const double lng,
  * @return    the great circle distance in radians between a and b
  */
 double H3_EXPORT(greatCircleDistanceRads)(const LatLng *a, const LatLng *b) {
-    double sinLat = sin((b->lat - a->lat) / 2.0);
-    double sinLng = sin((b->lng - a->lng) / 2.0);
+    double sinLat = sin((b->lat - a->lat) * 0.5);
+    double sinLng = sin((b->lng - a->lng) * 0.5);
 
     double A = sinLat * sinLat + cos(a->lat) * cos(b->lat) * sinLng * sinLng;
 
@@ -355,12 +355,12 @@ H3Error H3_EXPORT(getNumCells)(int res, int64_t *out) {
  * @return     area in radians^2 of triangle on unit sphere
  */
 double triangleEdgeLengthsToArea(double a, double b, double c) {
-    double s = (a + b + c) / 2;
+    double s = (a + b + c) * 0.5;
 
-    a = (s - a) / 2;
-    b = (s - b) / 2;
-    c = (s - c) / 2;
-    s = s / 2;
+    a = (s - a) * 0.5;
+    b = (s - b) * 0.5;
+    c = (s - c) * 0.5;
+    s = s * 0.5;
 
     return 4 * atan(sqrt(tan(s) * tan(a) * tan(b) * tan(c)));
 }

src/h3lib/lib/localij.c

@@ -702,12 +702,10 @@ H3Error H3_EXPORT(gridPathCells)(H3Index start, H3Index end, H3Index *out) {
     ijkToCube(&startIjk);
     ijkToCube(&endIjk);
 
-    double iStep =
-        distance ? (double)(endIjk.i - startIjk.i) / (double)distance : 0;
-    double jStep =
-        distance ? (double)(endIjk.j - startIjk.j) / (double)distance : 0;
-    double kStep =
-        distance ? (double)(endIjk.k - startIjk.k) / (double)distance : 0;
+    double invDistance = distance ? 1.0 / (double)distance : 0;
+    double iStep = distance ? (double)(endIjk.i - startIjk.i) * invDistance : 0;
+    double jStep = distance ? (double)(endIjk.j - startIjk.j) * invDistance : 0;
+    double kStep = distance ? (double)(endIjk.k - startIjk.k) * invDistance : 0;
 
     CoordIJK currentIjk = {startIjk.i, startIjk.j, startIjk.k};
     for (int64_t n = 0; n <= distance; n++) {