diff --git a/src/g_doom/a_painelemental.cpp b/src/g_doom/a_painelemental.cpp
index b52224c0c..f361fb78d 100644
--- a/src/g_doom/a_painelemental.cpp
+++ b/src/g_doom/a_painelemental.cpp
@@ -103,7 +103,7 @@ void A_PainShootSkull (AActor *self, angle_t angle, const PClass *spawntype, int
 				  box.Top()    < ld->bbox[BOXBOTTOM] ||
 				  box.Bottom() > ld->bbox[BOXTOP]))
 			{
-				if (P_PointOnLineSide(self->x,self->y,ld) != P_PointOnLineSide(x,y,ld))
+				if (P_PointOnLineSidePrecise(self->x,self->y,ld) != P_PointOnLineSidePrecise(x,y,ld))
 					return;  // line blocks trajectory				//   ^
 			}
 		}
diff --git a/src/p_local.h b/src/p_local.h
index fd5064f3c..e8cc5fde0 100644
--- a/src/p_local.h
+++ b/src/p_local.h
@@ -249,6 +249,12 @@ inline int P_PointOnLineSide (fixed_t x, fixed_t y, const line_t *line)
 		: DMulScale32 (y-line->v1->y, line->dx, line->v1->x-x, line->dy) > 0;
 }
 
+inline int P_PointOnLineSidePrecise (fixed_t x, fixed_t y, const line_t *line)
+{
+	return DMulScale32 (y-line->v1->y, line->dx, line->v1->x-x, line->dy) > 0;
+}
+
+
 //==========================================================================
 //
 // P_PointOnDivlineSide
@@ -267,6 +273,12 @@ inline int P_PointOnDivlineSide (fixed_t x, fixed_t y, const divline_t *line)
 		: (DMulScale32 (y-line->y, line->dx, line->x-x, line->dy) > 0);
 }
 
+inline int P_PointOnDivlineSidePrecise (fixed_t x, fixed_t y, const divline_t *line)
+{
+	return DMulScale32 (y-line->y, line->dx, line->x-x, line->dy) > 0;
+}
+
+
 //==========================================================================
 //
 // P_MakeDivline
diff --git a/src/p_maputl.cpp b/src/p_maputl.cpp
index e6d5a99e6..1d806d044 100644
--- a/src/p_maputl.cpp
+++ b/src/p_maputl.cpp
@@ -1056,13 +1056,13 @@ void FPathTraverse::AddThingIntercepts (int bx, int by, FBlockThingsIterator &it
 					break;
 				}
 				// Check if this side is facing the trace origin
-				if (P_PointOnDivlineSide (trace.x, trace.y, &line) == 0)
+				if (P_PointOnDivlineSidePrecise (trace.x, trace.y, &line) == 0)
 				{
 					numfronts++;
 
 					// If it is, see if the trace crosses it
-					if (P_PointOnDivlineSide (line.x, line.y, &trace) !=
-						P_PointOnDivlineSide (line.x + line.dx, line.y + line.dy, &trace))
+					if (P_PointOnDivlineSidePrecise (line.x, line.y, &trace) !=
+						P_PointOnDivlineSidePrecise (line.x + line.dx, line.y + line.dy, &trace))
 					{
 						// It's a hit
 						fixed_t frac = P_InterceptVector (&trace, &line);
diff --git a/src/p_mobj.cpp b/src/p_mobj.cpp
index 750cc18fb..bcaa77855 100644
--- a/src/p_mobj.cpp
+++ b/src/p_mobj.cpp
@@ -1284,7 +1284,7 @@ void P_ExplodeMissile (AActor *mo, line_t *line, AActor *target)
 
 	if (line != NULL && cl_missiledecals)
 	{
-		int side = P_PointOnLineSide (mo->x, mo->y, line);
+		int side = P_PointOnLineSidePrecise (mo->x, mo->y, line);
 		if (line->sidedef[side] == NULL)
 			side ^= 1;
 		if (line->sidedef[side] != NULL)
diff --git a/src/p_sight.cpp b/src/p_sight.cpp
index 135698b8b..2d465aab5 100644
--- a/src/p_sight.cpp
+++ b/src/p_sight.cpp
@@ -132,7 +132,7 @@ bool SightCheck::PTR_SightTraverse (intercept_t *in)
 	{
 		int  frontflag;
 		
-		frontflag = P_PointOnLineSide(sightthing->x, sightthing->y, li);
+		frontflag = P_PointOnLineSidePrecise(sightthing->x, sightthing->y, li);
 		
 		//Check 3D FLOORS!
 		for(int i=1;i<=2;i++)
@@ -241,14 +241,14 @@ bool SightCheck::P_SightCheckLine (line_t *ld)
 		return true;
 	}
 	ld->validcount = validcount;
-	if (P_PointOnDivlineSide (ld->v1->x, ld->v1->y, &trace) ==
-		P_PointOnDivlineSide (ld->v2->x, ld->v2->y, &trace))
+	if (P_PointOnDivlineSidePrecise (ld->v1->x, ld->v1->y, &trace) ==
+		P_PointOnDivlineSidePrecise (ld->v2->x, ld->v2->y, &trace))
 	{
 		return true;		// line isn't crossed
 	}
 	P_MakeDivline (ld, &dl);
-	if (P_PointOnDivlineSide (trace.x, trace.y, &dl) ==
-		P_PointOnDivlineSide (trace.x+trace.dx, trace.y+trace.dy, &dl))
+	if (P_PointOnDivlineSidePrecise (trace.x, trace.y, &dl) ==
+		P_PointOnDivlineSidePrecise (trace.x+trace.dx, trace.y+trace.dy, &dl))
 	{
 		return true;		// line isn't crossed
 	}
diff --git a/src/p_slopes.cpp b/src/p_slopes.cpp
index c0b9b5ef0..a3db26526 100644
--- a/src/p_slopes.cpp
+++ b/src/p_slopes.cpp
@@ -54,7 +54,7 @@ static void P_SlopeLineToPoint (int lineid, fixed_t x, fixed_t y, fixed_t z, boo
 		sector_t *sec;
 		secplane_t *plane;
 		
-		if (P_PointOnLineSide (x, y, line) == 0)
+		if (P_PointOnLineSidePrecise (x, y, line) == 0)
 		{
 			sec = line->frontsector;
 		}
@@ -363,7 +363,7 @@ static void P_SetSlopesFromVertexHeights(FMapThing *firstmt, FMapThing *lastmt,
 				z3 = h3? *h3 : j==0? sec->GetPlaneTexZ(sector_t::floor) : sec->GetPlaneTexZ(sector_t::ceiling);
 				vt3.Z = FIXED2FLOAT(z3);
 
-				if (P_PointOnLineSide(vertexes[vi3].x, vertexes[vi3].y, sec->lines[0]) == 0)
+				if (P_PointOnLineSidePrecise(vertexes[vi3].x, vertexes[vi3].y, sec->lines[0]) == 0)
 				{
 					vec1 = vt2 - vt3;
 					vec2 = vt1 - vt3;
diff --git a/src/p_teleport.cpp b/src/p_teleport.cpp
index 040aca9f4..380f5572d 100644
--- a/src/p_teleport.cpp
+++ b/src/p_teleport.cpp
@@ -530,7 +530,7 @@ bool EV_SilentLineTeleport (line_t *line, int side, AActor *thing, int id, INTBO
 			int fudge = FUDGEFACTOR;
 
 			// Make sure we are on correct side of exit linedef.
-			while (P_PointOnLineSide(x, y, l) != side && --fudge >= 0)
+			while (P_PointOnLineSidePrecise(x, y, l) != side && --fudge >= 0)
 			{
 				if (abs(l->dx) > abs(l->dy))
 					y -= (l->dx < 0) != side ? -1 : 1;
diff --git a/src/po_man.cpp b/src/po_man.cpp
index 727591bd5..98fbbcbcb 100644
--- a/src/po_man.cpp
+++ b/src/po_man.cpp
@@ -1231,7 +1231,7 @@ bool FPolyObj::CheckMobjBlocking (side_t *sd)
 						// Best use the one facing the player and ignore the back side.
 						if (ld->sidedef[1] != NULL)
 						{
-							int side = P_PointOnLineSide(mobj->x, mobj->y, ld);
+							int side = P_PointOnLineSidePrecise(mobj->x, mobj->y, ld);
 							if (ld->sidedef[side] != sd)
 							{
 								continue;