diff --git a/kernel/celledges.cc b/kernel/celledges.cc
index c43ba8db330..2ed0d503605 100644
--- a/kernel/celledges.cc
+++ b/kernel/celledges.cc
@@ -172,6 +172,141 @@ void demux_op(AbstractCellEdgesDatabase *db, RTLIL::Cell *cell)
 	}
 }
 
+void shift_op(AbstractCellEdgesDatabase *db, RTLIL::Cell *cell)
+{
+	bool is_signed = cell->getParam(ID::A_SIGNED).as_bool();
+	bool is_b_signed = cell->getParam(ID::B_SIGNED).as_bool();
+	int a_width = GetSize(cell->getPort(ID::A));
+	int b_width = GetSize(cell->getPort(ID::B));
+	int y_width = GetSize(cell->getPort(ID::Y));
+
+	// Behavior of the different shift cells:
+	//
+	//  $shl, $sshl -- shifts left by the amount on B port, B always unsigned
+	//  $shr, $sshr -- ditto right
+	//  $shift, $shiftx -- shifts right by the amount on B port, B optionally signed
+	//
+	// Sign extension (if A signed):
+	//
+	//  $shl, $shr, $shift -- only sign-extends up to size of Y, then shifts in zeroes
+	//  $sshl, $sshr -- fully sign-extends
+	//  $shiftx -- no sign extension
+	//
+	// Because $shl, $sshl only shift left, and $shl sign-extens up to size of Y, they
+	// are effectively the same.
+
+	// the cap below makes sure we don't overflow in the arithmetic further down, though
+	// it makes the edge data invalid once a_width approaches the order of 2**30
+	// (that ever happening is considered improbable)
+	int b_width_capped = min(b_width, 30);
+
+	int b_high, b_low;
+	if (!is_b_signed) {
+		b_high = (1 << b_width_capped) - 1;
+		b_low = 0;
+	} else {
+		b_high = (1 << (b_width_capped - 1)) - 1;
+		b_low = -(1 << (b_width_capped - 1));
+	}
+
+	for (int i = 0; i < y_width; i++){
+		// highest position of Y that can change with the value of B
+		int b_range_upper = 0;
+		// 1 + highest position of A that can be moved to Y[i]
+		int a_range_upper;
+		// lowest position of A that can be moved to Y[i]
+		int a_range_lower;
+
+		if (cell->type.in(ID($shl), ID($sshl))) {
+			b_range_upper = a_width + b_high;
+			if (is_signed) b_range_upper -= 1;
+			a_range_lower = max(0, i - b_high);
+			a_range_upper = min(i+1, a_width);
+		} else if (cell->type.in(ID($shr), ID($sshr)) || (cell->type.in(ID($shift), ID($shiftx)) && !is_b_signed)) {
+			b_range_upper = a_width;
+			a_range_lower = min(i, a_width - 1);
+			a_range_upper = min(i+1 + b_high, a_width);
+		} else if (cell->type.in(ID($shift), ID($shiftx)) && is_b_signed) {
+			// can go both ways depending on sign of B
+			// 2's complement range is different depending on direction
+			b_range_upper = a_width - b_low;
+			a_range_lower = max(0, i + b_low);
+			if (is_signed)
+				a_range_lower = min(a_range_lower, a_width - 1);
+			a_range_upper = min(i+1 + b_high, a_width);
+		} else {
+			log_assert(false && "unreachable");
+		}
+
+		if (i < b_range_upper) {
+			for (int k = a_range_lower; k < a_range_upper; k++)
+				db->add_edge(cell, ID::A, k, ID::Y, i, -1);
+		} else {
+			// only influence is through sign extension
+			if (is_signed)
+				db->add_edge(cell, ID::A, a_width - 1, ID::Y, i, -1);
+		}
+
+		for (int k = 0; k < b_width; k++) {
+			// left shifts
+			if (cell->type.in(ID($shl), ID($sshl))) {
+				if (a_width == 1 && is_signed) {
+					int skip = 1 << (k + 1);
+					int base = skip -1;
+					if (i % skip != base && i - a_width + 2 < 1 << b_width)
+						db->add_edge(cell, ID::B, k, ID::Y, i, -1);	
+				} else if (is_signed) {
+					if (i - a_width + 2 < 1 << b_width)
+						db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+				} else {
+					if (i - a_width + 1 < 1 << b_width)
+						db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+				}
+			// right shifts
+			} else if (cell->type.in(ID($shr), ID($sshr)) || (cell->type.in(ID($shift), ID($shiftx)) && !is_b_signed)) {
+				if (is_signed) {
+					bool shift_in_bulk = i < a_width - 1;
+					// can we jump into the zero-padding by toggling B[k]?
+					bool zpad_jump = (((y_width - i) & ((1 << (k + 1)) - 1)) != 0 \
+									&& (((y_width - i) & ~(1 << k)) < (1 << b_width)));
+
+					if (shift_in_bulk || (cell->type.in(ID($shr), ID($shift), ID($shiftx)) && zpad_jump))
+						db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+				} else {
+					if (i < a_width)
+						db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+				}
+			// bidirectional shifts (positive B shifts right, negative left)
+			} else if (cell->type.in(ID($shift), ID($shiftx)) && is_b_signed) {
+				if (is_signed) {
+					if (k != b_width - 1) {
+						bool r_shift_in_bulk = i < a_width - 1;
+						// assuming B is positive, can we jump into the upper zero-padding by toggling B[k]?
+						bool r_zpad_jump = (((y_width - i) & ((1 << (k + 1)) - 1)) != 0 \
+											&& (((y_width - i) & ~(1 << k)) <= b_high));
+						// assuming B is negative, can we influence Y[i] by toggling B[k]?
+						bool l = a_width - 2 - i >= b_low;
+						if (a_width == 1) {
+							// in case of a_width==1 we go into more detailed reasoning
+							l = l && (~(i - a_width) & ((1 << (k + 1)) - 1)) != 0;
+						}
+						if (r_shift_in_bulk || r_zpad_jump || l)
+							db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+					} else {
+						if (y_width - i <= b_high || a_width - 2 - i >= b_low)
+							db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+					}
+				} else {
+					if (a_width - 1 - i >= b_low)
+						db->add_edge(cell, ID::B, k, ID::Y, i, -1);
+				}
+			} else {
+				log_assert(false && "unreachable");
+			}
+		}
+	}
+}
+
 PRIVATE_NAMESPACE_END
 
 bool YOSYS_NAMESPACE_PREFIX AbstractCellEdgesDatabase::add_edges_from_cell(RTLIL::Cell *cell)
@@ -201,11 +336,10 @@ bool YOSYS_NAMESPACE_PREFIX AbstractCellEdgesDatabase::add_edges_from_cell(RTLIL
 		return true;
 	}
 
-	// FIXME:
-	// if (cell->type.in(ID($shl), ID($shr), ID($sshl), ID($sshr), ID($shift), ID($shiftx))) {
-	// 	shift_op(this, cell);
-	// 	return true;
-	// }
+	if (cell->type.in(ID($shl), ID($shr), ID($sshl), ID($sshr), ID($shift), ID($shiftx))) {
+		shift_op(this, cell);
+		return true;
+	}
 
 	if (cell->type.in(ID($lt), ID($le), ID($eq), ID($ne), ID($eqx), ID($nex), ID($ge), ID($gt))) {
 		compare_op(this, cell);
@@ -227,8 +361,17 @@ bool YOSYS_NAMESPACE_PREFIX AbstractCellEdgesDatabase::add_edges_from_cell(RTLIL
 		return true;
 	}
 
-	// FIXME: $mul $div $mod $divfloor $modfloor $slice $concat
-	// FIXME: $lut $sop $alu $lcu $macc $fa
+	// FIXME: $mul $div $mod $divfloor $modfloor $pow $slice $concat $bweqx
+	// FIXME: $lut $sop $alu $lcu $macc $fa $logic_and $logic_or $bwmux
+
+	// FIXME: $_BUF_ $_NOT_ $_AND_ $_NAND_ $_OR_ $_NOR_ $_XOR_ $_XNOR_ $_ANDNOT_ $_ORNOT_
+	// FIXME: $_MUX_ $_NMUX_ $_MUX4_ $_MUX8_ $_MUX16_ $_AOI3_ $_OAI3_ $_AOI4_ $_OAI4_
+
+	// FIXME: $specify2 $specify3 $specrule ???
+	// FIXME: $equiv $set_tag $get_tag $overwrite_tag $original_tag
+
+	if (cell->type.in(ID($assert), ID($assume), ID($live), ID($fair), ID($cover), ID($initstate), ID($anyconst), ID($anyseq), ID($allconst), ID($allseq)))
+		return true; // no-op: these have either no inputs or no outputs
 
 	return false;
 }
diff --git a/passes/sat/eval.cc b/passes/sat/eval.cc
index 05879426e63..acebea6c568 100644
--- a/passes/sat/eval.cc
+++ b/passes/sat/eval.cc
@@ -543,13 +543,13 @@ struct EvalPass : public Pass {
 
 				int pos = 0;
 				for (auto &c : tabsigs.chunks()) {
-					tab_line.push_back(log_signal(RTLIL::SigSpec(tabvals).extract(pos, c.width)));
+					tab_line.push_back(log_signal(RTLIL::SigSpec(tabvals).extract(pos, c.width), false));
 					pos += c.width;
 				}
 
 				pos = 0;
 				for (auto &c : signal.chunks()) {
-					tab_line.push_back(log_signal(value.extract(pos, c.width)));
+					tab_line.push_back(log_signal(value.extract(pos, c.width), false));
 					pos += c.width;
 				}
 
diff --git a/tests/various/celledges_shift.ys b/tests/various/celledges_shift.ys
new file mode 100644
index 00000000000..753c8641e58
--- /dev/null
+++ b/tests/various/celledges_shift.ys
@@ -0,0 +1 @@
+test_cell -s 1705659041 -n 100 -edges $shift $shiftx $shl $shr $sshl $sshr