diff --git a/src/p_map.cpp b/src/p_map.cpp
index c0e5c3baa7..b3718ce718 100644
--- a/src/p_map.cpp
+++ b/src/p_map.cpp
@@ -737,18 +737,50 @@ bool PIT_CheckLine(line_t *ld, const FBoundingBox &box, FCheckPosition &tm)
 	{ // Find the point on the line closest to the actor's center, and use
 		// that to calculate openings
 		// [EP] Use 64 bit integers in order to keep the exact result of the
-		// multiplication, because in the worst case, which is by the map limit
-		// (32767 units, which is 2147418112 in fixed_t notation), the result
-		// would occupy 62 bits (if I consider also the addition with another
-		// and possible 62 bit value, it's 63 bits).
-		// This privilege could not be available if the starting data would be
-		// 64 bit long.
-		// With this, the division is exact as the 32 bit float counterpart,
-		// though I don't know why I had to discard the first 24 bits from the
-		// divisor.
-		SQWORD r_num = ((SQWORD(tm.x - ld->v1->x)*ld->dx) + (SQWORD(tm.y - ld->v1->y)*ld->dy));
-		SQWORD r_den = (SQWORD(ld->dx)*ld->dx + SQWORD(ld->dy)*ld->dy) / (1 << 24);
-		fixed_t r = (fixed_t)(r_num / r_den);
+		// multiplication, because in the case the vertexes have both the
+		// distance coordinates equal to the map limit (32767 units, which is
+		// 2147418112 in fixed_t notation), the product result would occupy
+		// 62 bits and the sum of two products would occupy 63 bits
+		// in the worst case. If instead the vertexes are very close (1 in
+		// fixed_t notation, which is 1.52587890625e-05 in float notation), the
+		// product and the sum can be 1 in the worst case, which is very tiny.
+		SQWORD r_num = ((SQWORD(tm.x - ld->v1->x)*ld->dx) +
+						(SQWORD(tm.y - ld->v1->y)*ld->dy));
+		// The denominator is always positive. Use this to avoid useless
+		// calculations.
+		SQWORD r_den = (SQWORD(ld->dx)*ld->dx + SQWORD(ld->dy)*ld->dy);
+		fixed_t r = 0;
+		if (r_num <= 0) {
+			// [EP] The numerator is less or equal to zero, hence the closest
+			// point on the line is the first vertex. Truncate the result to 0.
+			r = 0;
+		} else if (r_num >= r_den) {
+			// [EP] The division is greater or equal to 1, hence the closest
+			// point on the line is the second vertex. Truncate the result to
+			// 1 << 24.
+			r = (1 << 24);
+		} else {
+			// [EP] Deal with the limited bits. The original formula is:
+			// r = (r_num << 24) / r_den,
+			// but r_num might be big enough to make the shift overflow.
+			// Since the numerator can't be saved in a 128bit integer,
+			// the denominator must be right shifted. If the denominator is
+			// less than (1 << 24), there would be a division by zero.
+			// Thanks to the fact that in this code path the denominator is less
+			// than the numerator, it's possible to avoid this bad situation by
+			// just checking the last 24 bits of the numerator.
+			if ((r_num >> (63-24)) != 0) {
+				// [EP] In fact, if the numerator is greater than
+				// (1 << (63-24)), the denominator must be greater than
+				// (1 << (63-24)), hence the denominator won't be zero after
+				// the right shift by 24 places.
+				r = (r_num)/(r_den >> 24);
+			} else {
+				// [EP] Having the last 24 bits all zero allows right shifting
+				// the numerator by 24 bits.
+				r = (r_num << 24)/r_den;
+			}
+		}
 		/*		Printf ("%d:%d: %d  (%d %d %d %d)  (%d %d %d %d)\n", level.time, ld-lines, r,
 		ld->frontsector->floorplane.a,
 		ld->frontsector->floorplane.b,