diff --git a/src/p_map.c b/src/p_map.c
index 1116ae06a..98a85e614 100644
--- a/src/p_map.c
+++ b/src/p_map.c
@@ -2021,7 +2021,7 @@ static boolean PIT_CheckLine(line_t *ld)
 boolean P_CheckPosition(mobj_t *thing, fixed_t x, fixed_t y)
 {
 	INT32 xl, xh, yl, yh, bx, by;
-	subsector_t *newsubsec;
+	subsector_t *newsubsec = thing->subsector;
 	boolean blockval = true;
 
 	ps_checkposition_calls.value.i++;
@@ -2043,7 +2043,8 @@ boolean P_CheckPosition(mobj_t *thing, fixed_t x, fixed_t y)
 	tmbbox[BOXRIGHT] = x + tmthing->radius;
 	tmbbox[BOXLEFT] = x - tmthing->radius;
 
-	newsubsec = R_PointInSubsector(x, y);
+	if (thing->x != x || thing->y != y)
+		newsubsec = R_PointInSubsector(x, y);
 	ceilingline = blockingline = NULL;
 
 	// The base floor / ceiling is from the subsector
diff --git a/src/r_main.c b/src/r_main.c
index 32e3138eb..c0b97616a 100644
--- a/src/r_main.c
+++ b/src/r_main.c
@@ -246,55 +246,6 @@ static void FlipCam2_OnChange(void)
 	SendWeaponPref2();
 }
 
-//
-// R_PointOnSide
-// Traverse BSP (sub) tree,
-// check point against partition plane.
-// Returns side 0 (front) or 1 (back).
-//
-// killough 5/2/98: reformatted
-//
-INT32 R_PointOnSide(fixed_t x, fixed_t y, node_t *restrict node)
-{
-	if (!node->dx)
-		return x <= node->x ? node->dy > 0 : node->dy < 0;
-
-	if (!node->dy)
-		return y <= node->y ? node->dx < 0 : node->dx > 0;
-
-	fixed_t dx = (x >> 1) - (node->x >> 1);
-	fixed_t dy = (y >> 1) - (node->y >> 1);
-
-	// Try to quickly decide by looking at sign bits.
-	// also use a mask to avoid branch prediction
-	INT32 mask = (node->dy ^ node->dx ^ dx ^ dy) >> 31;
-	return (mask & ((node->dy ^ dx) < 0)) |  // (left is negative)
-		(~mask & (FixedMul(dy, node->dx>>FRACBITS) >= FixedMul(node->dy>>FRACBITS, dx)));
-}
-
-// killough 5/2/98: reformatted
-INT32 R_PointOnSegSide(fixed_t x, fixed_t y, seg_t *line)
-{
-	fixed_t lx = line->v1->x;
-	fixed_t ly = line->v1->y;
-	fixed_t ldx = line->v2->x - lx;
-	fixed_t ldy = line->v2->y - ly;
-
-	if (!ldx)
-		return x <= lx ? ldy > 0 : ldy < 0;
-
-	if (!ldy)
-		return y <= ly ? ldx < 0 : ldx > 0;
-
-	fixed_t dx = (x >> 1) - (lx >> 1);
-	fixed_t dy = (y >> 1) - (ly >> 1);
-
-	// Try to quickly decide by looking at sign bits.
-	if ((ldy ^ ldx ^ dx ^ dy) < 0)
-		return (ldy ^ dx) < 0;          // (left is negative)
-	return FixedMul(dy, ldx>>FRACBITS) >= FixedMul(ldy>>FRACBITS, dx);
-}
-
 //
 // R_PointToAngle
 // To get a global angle from cartesian coordinates,
diff --git a/src/r_main.h b/src/r_main.h
index af7086e83..164952769 100644
--- a/src/r_main.h
+++ b/src/r_main.h
@@ -72,8 +72,23 @@ extern lighttable_t *zlight[LIGHTLEVELS][MAXLIGHTZ];
 #define NUMCOLORMAPS 32
 
 // Utility functions.
-INT32 R_PointOnSide(fixed_t x, fixed_t y, node_t *node);
-INT32 R_PointOnSegSide(fixed_t x, fixed_t y, seg_t *line);
+static inline INT32 R_PointOnSide(fixed_t x, fixed_t y, node_t *node)
+{
+	// heavily optimized version of R_PointOnSide, stolen from GZDoom.
+	return (INT64)(y - node->y) * node->dx + (INT64)(node->x - x) * node->dy > 0;
+}
+
+static inline INT32 R_PointOnSegSide(fixed_t x, fixed_t y, seg_t *line)
+{
+	fixed_t lx = line->v1->x;
+	fixed_t ly = line->v1->y;
+	fixed_t ldx = line->v2->x - lx;
+	fixed_t ldy = line->v2->y - ly;
+
+	// heavily optimized version of R_PointOnSide, stolen from GZDoom.
+	return (INT64)(y - ly) * ldx + (INT64)(lx - x) * ldy > 0;
+}
+
 angle_t R_PointToAngle(fixed_t x, fixed_t y);
 angle_t R_PointToAngle64(INT64 x, INT64 y);
 angle_t R_PointToAngle2(fixed_t px2, fixed_t py2, fixed_t px1, fixed_t py1);