diff --git a/CHANGELOG b/CHANGELOG
index 3b36c3182..638ce558b 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -66,6 +66,7 @@ Yosys 0.9 .. Yosys 0.9-dev
     - Added "design -delete"
     - Added "select -unset"
     - Use YosysHQ/abc instead of upstream berkeley-abc/abc
+    - Added $divfloor and $modfloor cells
 
 Yosys 0.8 .. Yosys 0.9
 ----------------------
diff --git a/backends/btor/btor.cc b/backends/btor/btor.cc
index 14c8484e8..2816d3246 100644
--- a/backends/btor/btor.cc
+++ b/backends/btor/btor.cc
@@ -266,20 +266,26 @@ struct BtorWorker
 			goto okay;
 		}
 
-		if (cell->type.in(ID($div), ID($mod)))
+		if (cell->type.in(ID($div), ID($mod), ID($modfloor)))
 		{
+			bool a_signed = cell->hasParam(ID::A_SIGNED) ? cell->getParam(ID::A_SIGNED).as_bool() : false;
+			bool b_signed = cell->hasParam(ID::B_SIGNED) ? cell->getParam(ID::B_SIGNED).as_bool() : false;
+
 			string btor_op;
 			if (cell->type == ID($div)) btor_op = "div";
+			// "rem" = truncating modulo
 			if (cell->type == ID($mod)) btor_op = "rem";
+			// "mod" = flooring modulo
+			if (cell->type == ID($modfloor)) {
+				// "umod" doesn't exist because it's the same as "urem"
+				btor_op = a_signed || b_signed ? "mod" : "rem";
+			}
 			log_assert(!btor_op.empty());
 
 			int width = GetSize(cell->getPort(ID::Y));
 			width = std::max(width, GetSize(cell->getPort(ID::A)));
 			width = std::max(width, GetSize(cell->getPort(ID::B)));
 
-			bool a_signed = cell->hasParam(ID::A_SIGNED) ? cell->getParam(ID::A_SIGNED).as_bool() : false;
-			bool b_signed = cell->hasParam(ID::B_SIGNED) ? cell->getParam(ID::B_SIGNED).as_bool() : false;
-
 			int nid_a = get_sig_nid(cell->getPort(ID::A), width, a_signed);
 			int nid_b = get_sig_nid(cell->getPort(ID::B), width, b_signed);
 
diff --git a/backends/btor/test_cells.sh b/backends/btor/test_cells.sh
index e0f1a0514..3f077201a 100644
--- a/backends/btor/test_cells.sh
+++ b/backends/btor/test_cells.sh
@@ -6,7 +6,7 @@ rm -rf test_cells.tmp
 mkdir -p test_cells.tmp
 cd test_cells.tmp
 
-../../../yosys -p 'test_cell -n 5 -w test all /$alu /$fa /$lcu /$lut /$sop /$macc /$mul /$div /$mod'
+../../../yosys -p 'test_cell -n 5 -w test all /$alu /$fa /$lcu /$lut /$sop /$macc /$mul /$div /$mod /$divfloor /$modfloor'
 
 for fn in test_*.il; do
 	../../../yosys -p "
diff --git a/backends/firrtl/firrtl.cc b/backends/firrtl/firrtl.cc
index a90b0b87a..b1d8500bb 100644
--- a/backends/firrtl/firrtl.cc
+++ b/backends/firrtl/firrtl.cc
@@ -585,6 +585,7 @@ struct FirrtlWorker
 					firrtl_is_signed = a_signed | b_signed;
 					firrtl_width = a_width;
 				} else if (cell->type == ID($mod)) {
+					// "rem" = truncating modulo
 					primop = "rem";
 					firrtl_width = min(a_width, b_width);
 				} else if (cell->type.in(ID($and), ID($_AND_))) {
diff --git a/backends/smt2/smt2.cc b/backends/smt2/smt2.cc
index 3e67e55f2..26f17bcb3 100644
--- a/backends/smt2/smt2.cc
+++ b/backends/smt2/smt2.cc
@@ -590,7 +590,17 @@ struct Smt2Worker
 			if (cell->type == ID($sub)) return export_bvop(cell, "(bvsub A B)");
 			if (cell->type == ID($mul)) return export_bvop(cell, "(bvmul A B)");
 			if (cell->type == ID($div)) return export_bvop(cell, "(bvUdiv A B)", 'd');
+			// "rem" = truncating modulo
 			if (cell->type == ID($mod)) return export_bvop(cell, "(bvUrem A B)", 'd');
+			// "mod" = flooring modulo
+			if (cell->type == ID($modfloor)) {
+				// bvumod doesn't exist because it's the same as bvurem
+				if (cell->getParam(ID::A_SIGNED).as_bool()) {
+					return export_bvop(cell, "(bvsmod A B)", 'd');
+				} else {
+					return export_bvop(cell, "(bvurem A B)", 'd');
+				}
+			}
 
 			if (cell->type.in(ID($reduce_and), ID($reduce_or), ID($reduce_bool)) &&
 					2*GetSize(cell->getPort(ID::A).chunks()) < GetSize(cell->getPort(ID::A))) {
diff --git a/backends/smv/smv.cc b/backends/smv/smv.cc
index 7113ebc97..2fc7099f4 100644
--- a/backends/smv/smv.cc
+++ b/backends/smv/smv.cc
@@ -358,7 +358,8 @@ struct SmvWorker
 				continue;
 			}
 
-			if (cell->type.in(ID($div), ID($mod)))
+			// SMV has a "mod" operator, but its semantics don't seem to be well-defined - to be safe, don't generate it at all
+			if (cell->type.in(ID($div)/*, ID($mod), ID($modfloor)*/))
 			{
 				int width_y = GetSize(cell->getPort(ID::Y));
 				int width = max(width_y, GetSize(cell->getPort(ID::A)));
@@ -366,7 +367,7 @@ struct SmvWorker
 				string expr_a, expr_b, op;
 
 				if (cell->type == ID($div))  op = "/";
-				if (cell->type == ID($mod))  op = "mod";
+				//if (cell->type == ID($mod))  op = "mod";
 
 				if (cell->getParam(ID::A_SIGNED).as_bool())
 				{
diff --git a/backends/smv/test_cells.sh b/backends/smv/test_cells.sh
index 63de465c0..145b9c33b 100644
--- a/backends/smv/test_cells.sh
+++ b/backends/smv/test_cells.sh
@@ -7,8 +7,8 @@ mkdir -p test_cells.tmp
 cd test_cells.tmp
 
 # don't test $mul to reduce runtime
-# don't test $div and $mod to reduce runtime and avoid "div by zero" message
-../../../yosys -p 'test_cell -n 5 -w test all /$alu /$fa /$lcu /$lut /$macc /$mul /$div /$mod'
+# don't test $div/$mod/$divfloor/$modfloor to reduce runtime and avoid "div by zero" message
+../../../yosys -p 'test_cell -n 5 -w test all /$alu /$fa /$lcu /$lut /$macc /$mul /$div /$mod /$divfloor /$modfloor'
 
 cat > template.txt << "EOT"
 %module main
diff --git a/backends/verilog/verilog_backend.cc b/backends/verilog/verilog_backend.cc
index 11b2ae10f..4f44a053a 100644
--- a/backends/verilog/verilog_backend.cc
+++ b/backends/verilog/verilog_backend.cc
@@ -740,6 +740,95 @@ bool dump_cell_expr(std::ostream &f, std::string indent, RTLIL::Cell *cell)
 #undef HANDLE_UNIOP
 #undef HANDLE_BINOP
 
+	if (cell->type == ID($divfloor))
+	{
+		// wire [MAXLEN+1:0] _0_, _1_, _2_;
+		// assign _0_ = $signed(A);
+		// assign _1_ = $signed(B);
+		// assign _2_ = (A[-1] == B[-1]) || A == 0 ? _0_ : $signed(_0_ - (B[-1] ? _1_ + 1 : _1_ - 1));
+		// assign Y = $signed(_2_) / $signed(_1_);
+
+		if (cell->getParam(ID::A_SIGNED).as_bool() && cell->getParam(ID::B_SIGNED).as_bool()) {
+			SigSpec sig_a = cell->getPort(ID::A);
+			SigSpec sig_b = cell->getPort(ID::B);
+
+			std::string buf_a = next_auto_id();
+			std::string buf_b = next_auto_id();
+			std::string buf_num = next_auto_id();
+			int size_a = GetSize(sig_a);
+			int size_b = GetSize(sig_b);
+			int size_y = GetSize(cell->getPort(ID::Y));
+			int size_max = std::max(size_a, std::max(size_b, size_y));
+
+			// intentionally one wider than maximum width
+			f << stringf("%s" "wire [%d:0] %s, %s, %s;\n", indent.c_str(), size_max, buf_a.c_str(), buf_b.c_str(), buf_num.c_str());
+			f << stringf("%s" "assign %s = ", indent.c_str(), buf_a.c_str());
+			dump_cell_expr_port(f, cell, "A", true);
+			f << stringf(";\n");
+			f << stringf("%s" "assign %s = ", indent.c_str(), buf_b.c_str());
+			dump_cell_expr_port(f, cell, "B", true);
+			f << stringf(";\n");
+
+			f << stringf("%s" "assign %s = ", indent.c_str(), buf_num.c_str());
+			f << stringf("(");
+			dump_sigspec(f, sig_a.extract(sig_a.size()-1));
+			f << stringf(" == ");
+			dump_sigspec(f, sig_b.extract(sig_b.size()-1));
+			f << stringf(") || ");
+			dump_sigspec(f, sig_a);
+			f << stringf(" == 0 ? %s : ", buf_a.c_str());
+			f << stringf("$signed(%s - (", buf_a.c_str());
+			dump_sigspec(f, sig_b.extract(sig_b.size()-1));
+			f << stringf(" ? %s + 1 : %s - 1));\n", buf_b.c_str(), buf_b.c_str());
+
+
+			f << stringf("%s" "assign ", indent.c_str());
+			dump_sigspec(f, cell->getPort(ID::Y));
+			f << stringf(" = $signed(%s) / ", buf_num.c_str());
+			dump_attributes(f, "", cell->attributes, ' ');
+			f << stringf("$signed(%s);\n", buf_b.c_str());
+			return true;
+		} else {
+			// same as truncating division
+			dump_cell_expr_binop(f, indent, cell, "/");
+			return true;
+		}
+	}
+
+	if (cell->type == ID($modfloor))
+	{
+		// wire truncated = $signed(A) % $signed(B);
+		// assign Y = (A[-1] == B[-1]) || truncated == 0 ? truncated : $signed(B) + $signed(truncated);
+
+		if (cell->getParam(ID::A_SIGNED).as_bool() && cell->getParam(ID::B_SIGNED).as_bool()) {
+			SigSpec sig_a = cell->getPort(ID::A);
+			SigSpec sig_b = cell->getPort(ID::B);
+
+			std::string temp_id = next_auto_id();
+			f << stringf("%s" "wire [%d:0] %s = ", indent.c_str(), GetSize(cell->getPort(ID::A))-1, temp_id.c_str());
+			dump_cell_expr_port(f, cell, "A", true);
+			f << stringf(" %% ");
+			dump_attributes(f, "", cell->attributes, ' ');
+			dump_cell_expr_port(f, cell, "B", true);
+			f << stringf(";\n");
+
+			f << stringf("%s" "assign ", indent.c_str());
+			dump_sigspec(f, cell->getPort(ID::Y));
+			f << stringf(" = (");
+			dump_sigspec(f, sig_a.extract(sig_a.size()-1));
+			f << stringf(" == ");
+			dump_sigspec(f, sig_b.extract(sig_b.size()-1));
+			f << stringf(") || %s == 0 ? %s : ", temp_id.c_str(), temp_id.c_str());
+			dump_cell_expr_port(f, cell, "B", true);
+			f << stringf(" + $signed(%s);\n", temp_id.c_str());
+			return true;
+		} else {
+			// same as truncating modulo
+			dump_cell_expr_binop(f, indent, cell, "%");
+			return true;
+		}
+	}
+
 	if (cell->type == ID($shift))
 	{
 		f << stringf("%s" "assign ", indent.c_str());
diff --git a/kernel/calc.cc b/kernel/calc.cc
index 4a4840771..ae18809d3 100644
--- a/kernel/calc.cc
+++ b/kernel/calc.cc
@@ -489,6 +489,7 @@ RTLIL::Const RTLIL::const_mul(const RTLIL::Const &arg1, const RTLIL::Const &arg2
 	return big2const(y, result_len >= 0 ? result_len : max(arg1.bits.size(), arg2.bits.size()), min(undef_bit_pos, 0));
 }
 
+// truncating division
 RTLIL::Const RTLIL::const_div(const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len)
 {
 	int undef_bit_pos = -1;
@@ -502,6 +503,7 @@ RTLIL::Const RTLIL::const_div(const RTLIL::Const &arg1, const RTLIL::Const &arg2
 	return big2const(result_neg ? -(a / b) : (a / b), result_len >= 0 ? result_len : max(arg1.bits.size(), arg2.bits.size()), min(undef_bit_pos, 0));
 }
 
+// truncating modulo
 RTLIL::Const RTLIL::const_mod(const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len)
 {
 	int undef_bit_pos = -1;
@@ -515,6 +517,51 @@ RTLIL::Const RTLIL::const_mod(const RTLIL::Const &arg1, const RTLIL::Const &arg2
 	return big2const(result_neg ? -(a % b) : (a % b), result_len >= 0 ? result_len : max(arg1.bits.size(), arg2.bits.size()), min(undef_bit_pos, 0));
 }
 
+RTLIL::Const RTLIL::const_divfloor(const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len)
+{
+	int undef_bit_pos = -1;
+	BigInteger a = const2big(arg1, signed1, undef_bit_pos);
+	BigInteger b = const2big(arg2, signed2, undef_bit_pos);
+	if (b.isZero())
+		return RTLIL::Const(RTLIL::State::Sx, result_len);
+
+	bool result_pos = (a.getSign() == BigInteger::negative) == (b.getSign() == BigInteger::negative);
+	a = a.getSign() == BigInteger::negative ? -a : a;
+	b = b.getSign() == BigInteger::negative ? -b : b;
+	BigInteger result;
+
+	if (result_pos || a == 0) {
+		result = a / b;
+	} else {
+		// bigint division with negative numbers is wonky, make sure we only negate at the very end
+		result = -((a + b - 1) / b);
+	}
+	return big2const(result, result_len >= 0 ? result_len : max(arg1.bits.size(), arg2.bits.size()), min(undef_bit_pos, 0));
+}
+
+RTLIL::Const RTLIL::const_modfloor(const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len)
+{
+	int undef_bit_pos = -1;
+	BigInteger a = const2big(arg1, signed1, undef_bit_pos);
+	BigInteger b = const2big(arg2, signed2, undef_bit_pos);
+	if (b.isZero())
+		return RTLIL::Const(RTLIL::State::Sx, result_len);
+
+	BigInteger::Sign a_sign = a.getSign();
+	BigInteger::Sign b_sign = b.getSign();
+	a = a_sign == BigInteger::negative ? -a : a;
+	b = b_sign == BigInteger::negative ? -b : b;
+	BigInteger truncated = a_sign == BigInteger::negative ? -(a % b) : (a % b);
+	BigInteger modulo;
+
+	if (truncated == 0 || (a_sign == b_sign)) {
+		modulo = truncated;
+	} else {
+		modulo = b_sign == BigInteger::negative ? truncated - b : truncated + b;
+	}
+	return big2const(modulo, result_len >= 0 ? result_len : max(arg1.bits.size(), arg2.bits.size()), min(undef_bit_pos, 0));
+}
+
 RTLIL::Const RTLIL::const_pow(const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len)
 {
 	int undef_bit_pos = -1;
diff --git a/kernel/celledges.cc b/kernel/celledges.cc
index 54e0168e2..314e7c77e 100644
--- a/kernel/celledges.cc
+++ b/kernel/celledges.cc
@@ -187,7 +187,7 @@ bool YOSYS_NAMESPACE_PREFIX AbstractCellEdgesDatabase::add_edges_from_cell(RTLIL
 		return true;
 	}
 
-	// FIXME: $mul $div $mod $slice $concat
+	// FIXME: $mul $div $mod $divfloor $modfloor $slice $concat
 	// FIXME: $lut $sop $alu $lcu $macc $fa
 
 	return false;
diff --git a/kernel/celltypes.h b/kernel/celltypes.h
index 450865ce9..db54436cb 100644
--- a/kernel/celltypes.h
+++ b/kernel/celltypes.h
@@ -114,7 +114,7 @@ struct CellTypes
 			ID($and), ID($or), ID($xor), ID($xnor),
 			ID($shl), ID($shr), ID($sshl), ID($sshr), ID($shift), ID($shiftx),
 			ID($lt), ID($le), ID($eq), ID($ne), ID($eqx), ID($nex), ID($ge), ID($gt),
-			ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($pow),
+			ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($pow),
 			ID($logic_and), ID($logic_or), ID($concat), ID($macc)
 		};
 
@@ -304,6 +304,8 @@ struct CellTypes
 		HANDLE_CELL_TYPE(mul)
 		HANDLE_CELL_TYPE(div)
 		HANDLE_CELL_TYPE(mod)
+		HANDLE_CELL_TYPE(divfloor)
+		HANDLE_CELL_TYPE(modfloor)
 		HANDLE_CELL_TYPE(pow)
 		HANDLE_CELL_TYPE(pos)
 		HANDLE_CELL_TYPE(neg)
diff --git a/kernel/rtlil.cc b/kernel/rtlil.cc
index 196e301b6..ca4201b53 100644
--- a/kernel/rtlil.cc
+++ b/kernel/rtlil.cc
@@ -948,7 +948,7 @@ namespace {
 				return;
 			}
 
-			if (cell->type.in(ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($pow))) {
+			if (cell->type.in(ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($pow))) {
 				param_bool(ID::A_SIGNED);
 				param_bool(ID::B_SIGNED);
 				port(ID::A, param(ID::A_WIDTH));
@@ -1949,6 +1949,8 @@ DEF_METHOD(Sub,      max(sig_a.size(), sig_b.size()), ID($sub))
 DEF_METHOD(Mul,      max(sig_a.size(), sig_b.size()), ID($mul))
 DEF_METHOD(Div,      max(sig_a.size(), sig_b.size()), ID($div))
 DEF_METHOD(Mod,      max(sig_a.size(), sig_b.size()), ID($mod))
+DEF_METHOD(DivFloor, max(sig_a.size(), sig_b.size()), ID($divfloor))
+DEF_METHOD(ModFloor, max(sig_a.size(), sig_b.size()), ID($modfloor))
 DEF_METHOD(LogicAnd, 1, ID($logic_and))
 DEF_METHOD(LogicOr,  1, ID($logic_or))
 #undef DEF_METHOD
diff --git a/kernel/rtlil.h b/kernel/rtlil.h
index 91d6a9f77..8228523d5 100644
--- a/kernel/rtlil.h
+++ b/kernel/rtlil.h
@@ -468,6 +468,8 @@ namespace RTLIL
 	RTLIL::Const const_sub         (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
 	RTLIL::Const const_mul         (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
 	RTLIL::Const const_div         (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
+	RTLIL::Const const_divfloor    (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
+	RTLIL::Const const_modfloor    (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
 	RTLIL::Const const_mod         (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
 	RTLIL::Const const_pow         (const RTLIL::Const &arg1, const RTLIL::Const &arg2, bool signed1, bool signed2, int result_len);
 
@@ -1204,8 +1206,12 @@ public:
 	RTLIL::Cell* addAdd (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
 	RTLIL::Cell* addSub (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
 	RTLIL::Cell* addMul (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
+	// truncating division
 	RTLIL::Cell* addDiv (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
+	// truncating modulo
 	RTLIL::Cell* addMod (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
+	RTLIL::Cell* addDivFloor (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
+	RTLIL::Cell* addModFloor (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
 	RTLIL::Cell* addPow (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, const RTLIL::SigSpec &sig_y, bool a_signed = false, bool b_signed = false, const std::string &src = "");
 
 	RTLIL::Cell* addLogicNot (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_y, bool is_signed = false, const std::string &src = "");
@@ -1303,8 +1309,12 @@ public:
 	RTLIL::SigSpec Add (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
 	RTLIL::SigSpec Sub (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
 	RTLIL::SigSpec Mul (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
+	// truncating division
 	RTLIL::SigSpec Div (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
+	// truncating modulo
 	RTLIL::SigSpec Mod (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
+	RTLIL::SigSpec DivFloor (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
+	RTLIL::SigSpec ModFloor (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool is_signed = false, const std::string &src = "");
 	RTLIL::SigSpec Pow (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, const RTLIL::SigSpec &sig_b, bool a_signed = false, bool b_signed = false, const std::string &src = "");
 
 	RTLIL::SigSpec LogicNot (RTLIL::IdString name, const RTLIL::SigSpec &sig_a, bool is_signed = false, const std::string &src = "");
diff --git a/kernel/satgen.h b/kernel/satgen.h
index 88b84b7e6..3929a8708 100644
--- a/kernel/satgen.h
+++ b/kernel/satgen.h
@@ -279,7 +279,7 @@ struct SatGen
 		bool arith_undef_handled = false;
 		bool is_arith_compare = cell->type.in(ID($lt), ID($le), ID($ge), ID($gt));
 
-		if (model_undef && (cell->type.in(ID($add), ID($sub), ID($mul), ID($div), ID($mod)) || is_arith_compare))
+		if (model_undef && (cell->type.in(ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor)) || is_arith_compare))
 		{
 			std::vector<int> undef_a = importUndefSigSpec(cell->getPort(ID::A), timestep);
 			std::vector<int> undef_b = importUndefSigSpec(cell->getPort(ID::B), timestep);
@@ -293,7 +293,7 @@ struct SatGen
 			int undef_any_b = ez->expression(ezSAT::OpOr, undef_b);
 			int undef_y_bit = ez->OR(undef_any_a, undef_any_b);
 
-			if (cell->type.in(ID($div), ID($mod))) {
+			if (cell->type.in(ID($div), ID($mod), ID($divfloor), ID($modfloor))) {
 				std::vector<int> b = importSigSpec(cell->getPort(ID::B), timestep);
 				undef_y_bit = ez->OR(undef_y_bit, ez->NOT(ez->expression(ezSAT::OpOr, b)));
 			}
@@ -935,7 +935,7 @@ struct SatGen
 			return true;
 		}
 
-		if (cell->type.in(ID($div), ID($mod)))
+		if (cell->type.in(ID($div), ID($mod), ID($divfloor), ID($modfloor)))
 		{
 			std::vector<int> a = importDefSigSpec(cell->getPort(ID::A), timestep);
 			std::vector<int> b = importDefSigSpec(cell->getPort(ID::B), timestep);
@@ -970,23 +970,48 @@ struct SatGen
 			}
 
 			std::vector<int> y_tmp = ignore_div_by_zero ? yy : ez->vec_var(y.size());
+
+			// modulo calculation
+			std::vector<int> modulo_trunc;
+			int floored_eq_trunc;
+			if (cell->parameters[ID::A_SIGNED].as_bool() && cell->parameters[ID::B_SIGNED].as_bool()) {
+				modulo_trunc = ez->vec_ite(a.back(), ez->vec_neg(chain_buf), chain_buf);
+				// floor == trunc when sgn(a) == sgn(b) or trunc == 0
+				floored_eq_trunc = ez->OR(ez->IFF(a.back(), b.back()), ez->NOT(ez->expression(ezSAT::OpOr, modulo_trunc)));
+			} else {
+				modulo_trunc = chain_buf;
+				floored_eq_trunc = ez->CONST_TRUE;
+			}
+
 			if (cell->type == ID($div)) {
 				if (cell->parameters[ID::A_SIGNED].as_bool() && cell->parameters[ID::B_SIGNED].as_bool())
 					ez->assume(ez->vec_eq(y_tmp, ez->vec_ite(ez->XOR(a.back(), b.back()), ez->vec_neg(y_u), y_u)));
 				else
 					ez->assume(ez->vec_eq(y_tmp, y_u));
-			} else {
+			} else if (cell->type == ID($mod)) {
+				ez->assume(ez->vec_eq(y_tmp, modulo_trunc));
+			} else if (cell->type == ID($divfloor)) {
 				if (cell->parameters[ID::A_SIGNED].as_bool() && cell->parameters[ID::B_SIGNED].as_bool())
-					ez->assume(ez->vec_eq(y_tmp, ez->vec_ite(a.back(), ez->vec_neg(chain_buf), chain_buf)));
+					ez->assume(ez->vec_eq(y_tmp, ez->vec_ite(
+						ez->XOR(a.back(), b.back()),
+						ez->vec_neg(ez->vec_ite(
+							ez->vec_reduce_or(modulo_trunc),
+							ez->vec_add(y_u, ez->vec_const_unsigned(1, y_u.size())),
+							y_u
+						)),
+						y_u
+					)));
 				else
-					ez->assume(ez->vec_eq(y_tmp, chain_buf));
+					ez->assume(ez->vec_eq(y_tmp, y_u));
+			} else if (cell->type == ID($modfloor)) {
+				ez->assume(ez->vec_eq(y_tmp, ez->vec_ite(floored_eq_trunc, modulo_trunc, ez->vec_add(modulo_trunc, b))));
 			}
 
 			if (ignore_div_by_zero) {
 				ez->assume(ez->expression(ezSAT::OpOr, b));
 			} else {
 				std::vector<int> div_zero_result;
-				if (cell->type == ID($div)) {
+				if (cell->type.in(ID($div), ID($divfloor))) {
 					if (cell->parameters[ID::A_SIGNED].as_bool() && cell->parameters[ID::B_SIGNED].as_bool()) {
 						std::vector<int> all_ones(y.size(), ez->CONST_TRUE);
 						std::vector<int> only_first_one(y.size(), ez->CONST_FALSE);
@@ -996,7 +1021,8 @@ struct SatGen
 						div_zero_result.insert(div_zero_result.end(), cell->getPort(ID::A).size(), ez->CONST_TRUE);
 						div_zero_result.insert(div_zero_result.end(), y.size() - div_zero_result.size(), ez->CONST_FALSE);
 					}
-				} else {
+				} else if (cell->type.in(ID($mod), ID($modfloor))) {
+					// a mod 0 = a
 					int copy_a_bits = min(cell->getPort(ID::A).size(), cell->getPort(ID::B).size());
 					div_zero_result.insert(div_zero_result.end(), a.begin(), a.begin() + copy_a_bits);
 					if (cell->parameters[ID::A_SIGNED].as_bool() && cell->parameters[ID::B_SIGNED].as_bool())
diff --git a/manual/CHAPTER_CellLib.tex b/manual/CHAPTER_CellLib.tex
index 55abd9b96..32c530582 100644
--- a/manual/CHAPTER_CellLib.tex
+++ b/manual/CHAPTER_CellLib.tex
@@ -139,6 +139,8 @@ Verilog & Cell Type \\
 \lstinline[language=Verilog]; Y = A  * B; & {\tt \$mul} \\
 \lstinline[language=Verilog]; Y = A  / B; & {\tt \$div} \\
 \lstinline[language=Verilog]; Y = A  % B; & {\tt \$mod} \\
+\multicolumn{1}{c}{\tt [N/A]} & {\tt \$divfloor} \\
+\multicolumn{1}{c}{\tt [N/A]} & {\tt \$modfoor} \\
 \lstinline[language=Verilog]; Y = A ** B; & {\tt \$pow} \\
 \end{tabular}
 \caption{Cell types for binary operators with their corresponding Verilog expressions.}
@@ -161,6 +163,27 @@ For the binary cells that output a logical value ({\tt \$logic\_and}, {\tt \$log
 {\tt \$gt}), when the \B{Y\_WIDTH} parameter is greater than 1, the output is zero-extended,
 and only the least significant bit varies.
 
+Division and modulo cells are available in two rounding modes. The original {\tt \$div} and {\tt \$mod}
+cells are based on truncating division, and correspond to the semantics of the verilog {\tt /} and
+{\tt \%} operators. The {\tt \$divfloor} and {\tt \$modfloor} cells represent flooring division and
+flooring modulo, the latter of which is also known as ``remainder'' in several languages. See
+table~\ref{tab:CellLib_divmod} for a side-by-side comparison between the different semantics.
+
+\begin{table}[h]
+\hfil
+\begin{tabular}{lr|rr|rr}
+\multirow{2}{*}{Division} & \multirow{2}{*}{Result} & \multicolumn{2}{c|}{Truncating} & \multicolumn{2}{c}{Flooring} \\
+               &            & {\tt \$div} & {\tt \$mod} & {\tt \$divfloor} & {\tt \$modfloor} \\
+\hline
+{\tt -10 / 3}  & {\tt -3.3} & {\tt -3}    & {\tt -1}    & {\tt -4}         & {\tt 2} \\
+{\tt 10 / -3}  & {\tt -3.3} & {\tt -3}    & {\tt 1}     & {\tt -4}         & {\tt -2} \\
+{\tt -10 / -3} & {\tt 3.3}  & {\tt 3}     & {\tt -1}    & {\tt 3}          & {\tt -1} \\
+{\tt 10 / 3}   & {\tt 3.3}  & {\tt 3}     & {\tt 1}     & {\tt 3}          & {\tt 1} \\
+\end{tabular}
+\caption{Comparison between different rounding modes for division and modulo cells.}
+\label{tab:CellLib_divmod}
+\end{table}
+
 \subsection{Multiplexers}
 
 Multiplexers are generated by the Verilog HDL frontend for {\tt
diff --git a/manual/PRESENTATION_Prog.tex b/manual/PRESENTATION_Prog.tex
index b85eda892..a9416f82a 100644
--- a/manual/PRESENTATION_Prog.tex
+++ b/manual/PRESENTATION_Prog.tex
@@ -307,7 +307,7 @@ cell name from the internal cell library:
 \begin{lstlisting}[xleftmargin=1cm, basicstyle=\ttfamily\fontsize{6pt}{7pt}\selectfont]
 $not $pos $neg $and $or $xor $xnor $reduce_and $reduce_or $reduce_xor $reduce_xnor
 $reduce_bool $shl $shr $sshl $sshr $lt $le $eq $ne $eqx $nex $ge $gt $add $sub $mul $div $mod
-$pow $logic_not $logic_and $logic_or $mux $pmux $slice $concat $lut $assert $sr $dff
+$divfloor $modfloor $pow $logic_not $logic_and $logic_or $mux $pmux $slice $concat $lut $assert $sr $dff
 $dffsr $adff $dlatch $dlatchsr $memrd $memwr $mem $fsm $_NOT_ $_AND_ $_OR_ $_XOR_ $_MUX_ $_SR_NN_
 $_SR_NP_ $_SR_PN_ $_SR_PP_ $_DFF_N_ $_DFF_P_ $_DFF_NN0_ $_DFF_NN1_ $_DFF_NP0_ $_DFF_NP1_ $_DFF_PN0_
 $_DFF_PN1_ $_DFF_PP0_ $_DFF_PP1_ $_DFFSR_NNN_ $_DFFSR_NNP_ $_DFFSR_NPN_ $_DFFSR_NPP_ $_DFFSR_PNN_
diff --git a/passes/cmds/stat.cc b/passes/cmds/stat.cc
index 6c4bc0e5b..30436d829 100644
--- a/passes/cmds/stat.cc
+++ b/passes/cmds/stat.cc
@@ -109,7 +109,7 @@ struct statdata_t
 						ID($lut), ID($and), ID($or), ID($xor), ID($xnor),
 						ID($shl), ID($shr), ID($sshl), ID($sshr), ID($shift), ID($shiftx),
 						ID($lt), ID($le), ID($eq), ID($ne), ID($eqx), ID($nex), ID($ge), ID($gt),
-						ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($pow), ID($alu))) {
+						ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($pow), ID($alu))) {
 					int width_a = cell->hasPort(ID::A) ? GetSize(cell->getPort(ID::A)) : 0;
 					int width_b = cell->hasPort(ID::B) ? GetSize(cell->getPort(ID::B)) : 0;
 					int width_y = cell->hasPort(ID::Y) ? GetSize(cell->getPort(ID::Y)) : 0;
diff --git a/passes/memory/memory_share.cc b/passes/memory/memory_share.cc
index 477246687..e11958bd6 100644
--- a/passes/memory/memory_share.cc
+++ b/passes/memory/memory_share.cc
@@ -715,6 +715,8 @@ struct MemoryShareWorker
 		cone_ct.cell_types.erase(ID($mul));
 		cone_ct.cell_types.erase(ID($mod));
 		cone_ct.cell_types.erase(ID($div));
+		cone_ct.cell_types.erase(ID($modfloor));
+		cone_ct.cell_types.erase(ID($divfloor));
 		cone_ct.cell_types.erase(ID($pow));
 		cone_ct.cell_types.erase(ID($shl));
 		cone_ct.cell_types.erase(ID($shr));
diff --git a/passes/opt/opt_expr.cc b/passes/opt/opt_expr.cc
index 777a24777..e5b8bda95 100644
--- a/passes/opt/opt_expr.cc
+++ b/passes/opt/opt_expr.cc
@@ -864,7 +864,7 @@ void replace_const_cells(RTLIL::Design *design, RTLIL::Module *module, bool cons
 skip_fine_alu:
 
 		if (cell->type.in(ID($reduce_xor), ID($reduce_xnor), ID($shift), ID($shiftx), ID($shl), ID($shr), ID($sshl), ID($sshr),
-					ID($lt), ID($le), ID($ge), ID($gt), ID($neg), ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($pow)))
+					ID($lt), ID($le), ID($ge), ID($gt), ID($neg), ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($pow)))
 		{
 			RTLIL::SigSpec sig_a = assign_map(cell->getPort(ID::A));
 			RTLIL::SigSpec sig_b = cell->hasPort(ID::B) ? assign_map(cell->getPort(ID::B)) : RTLIL::SigSpec();
@@ -883,7 +883,7 @@ skip_fine_alu:
 			if (0) {
 		found_the_x_bit:
 				cover_list("opt.opt_expr.xbit", "$reduce_xor", "$reduce_xnor", "$shl", "$shr", "$sshl", "$sshr", "$shift", "$shiftx",
-						"$lt", "$le", "$ge", "$gt", "$neg", "$add", "$sub", "$mul", "$div", "$mod", "$pow", cell->type.str());
+						"$lt", "$le", "$ge", "$gt", "$neg", "$add", "$sub", "$mul", "$div", "$mod", "$divfloor", "$modfloor", "$pow", cell->type.str());
 				if (cell->type.in(ID($reduce_xor), ID($reduce_xnor), ID($lt), ID($le), ID($ge), ID($gt)))
 					replace_cell(assign_map, module, cell, "x-bit in input", ID::Y, RTLIL::State::Sx);
 				else
@@ -1469,6 +1469,8 @@ skip_identity:
 		FOLD_2ARG_CELL(mul)
 		FOLD_2ARG_CELL(div)
 		FOLD_2ARG_CELL(mod)
+		FOLD_2ARG_CELL(divfloor)
+		FOLD_2ARG_CELL(modfloor)
 		FOLD_2ARG_CELL(pow)
 
 		FOLD_1ARG_CELL(pos)
@@ -1583,9 +1585,11 @@ skip_identity:
 			}
 		}
 
-		if (!keepdc && cell->type.in(ID($div), ID($mod)))
+		if (!keepdc && cell->type.in(ID($div), ID($mod), ID($divfloor), ID($modfloor)))
 		{
+			bool a_signed = cell->parameters[ID::A_SIGNED].as_bool();
 			bool b_signed = cell->parameters[ID::B_SIGNED].as_bool();
+			SigSpec sig_a = assign_map(cell->getPort(ID::A));
 			SigSpec sig_b = assign_map(cell->getPort(ID::B));
 			SigSpec sig_y = assign_map(cell->getPort(ID::Y));
 
@@ -1610,11 +1614,13 @@ skip_identity:
 				for (int i = 1; i < (b_signed ? sig_b.size()-1 : sig_b.size()); i++)
 					if (b_val == (1 << i))
 					{
-						if (cell->type == ID($div))
+						if (cell->type.in(ID($div), ID($divfloor)))
 						{
 							cover("opt.opt_expr.div_shift");
 
-							log_debug("Replacing divide-by-%d cell `%s' in module `%s' with shift-by-%d.\n",
+							bool is_truncating = cell->type == ID($div);
+							log_debug("Replacing %s-divide-by-%d cell `%s' in module `%s' with shift-by-%d.\n",
+									is_truncating ? "truncating" : "flooring",
 									b_val, cell->name.c_str(), module->name.c_str(), i);
 
 							std::vector<RTLIL::SigBit> new_b = RTLIL::SigSpec(i, 6);
@@ -1622,17 +1628,35 @@ skip_identity:
 							while (GetSize(new_b) > 1 && new_b.back() == RTLIL::State::S0)
 								new_b.pop_back();
 
-							cell->type = ID($shr);
+							cell->type = ID($sshr);
 							cell->parameters[ID::B_WIDTH] = GetSize(new_b);
 							cell->parameters[ID::B_SIGNED] = false;
 							cell->setPort(ID::B, new_b);
+
+							// Truncating division is the same as flooring division, except when
+							// the result is negative and there is a remainder - then trunc = floor + 1
+							if (is_truncating && a_signed) {
+								Wire *flooring = module->addWire(NEW_ID, sig_y.size());
+								cell->setPort(ID::Y, flooring);
+
+								Wire *result_neg = module->addWire(NEW_ID);
+								module->addXor(NEW_ID, sig_a[sig_a.size()-1], sig_b[sig_b.size()-1], result_neg);
+								Wire *rem_nonzero = module->addWire(NEW_ID);
+								module->addReduceOr(NEW_ID, sig_a.extract(0, i), rem_nonzero);
+								Wire *should_add = module->addWire(NEW_ID);
+								module->addAnd(NEW_ID, result_neg, rem_nonzero, should_add);
+								module->addAdd(NEW_ID, flooring, should_add, sig_y);
+							}
+
 							cell->check();
 						}
-						else
+						else if (cell->type.in(ID($mod), ID($modfloor)))
 						{
 							cover("opt.opt_expr.mod_mask");
 
-							log_debug("Replacing modulo-by-%d cell `%s' in module `%s' with bitmask.\n",
+							bool is_truncating = cell->type == ID($mod);
+							log_debug("Replacing %s-modulo-by-%d cell `%s' in module `%s' with bitmask.\n",
+									is_truncating ? "truncating" : "flooring",
 									b_val, cell->name.c_str(), module->name.c_str());
 
 							std::vector<RTLIL::SigBit> new_b = RTLIL::SigSpec(State::S1, i);
@@ -1643,6 +1667,24 @@ skip_identity:
 							cell->type = ID($and);
 							cell->parameters[ID::B_WIDTH] = GetSize(new_b);
 							cell->setPort(ID::B, new_b);
+
+							// truncating modulo has the same masked bits as flooring modulo, but
+							// the sign bits are those of A (except when R=0)
+							if (is_truncating && a_signed) {
+								Wire *flooring = module->addWire(NEW_ID, sig_y.size());
+								cell->setPort(ID::Y, flooring);
+								SigSpec truncating = SigSpec(flooring).extract(0, i);
+
+								Wire *rem_nonzero = module->addWire(NEW_ID);
+								module->addReduceOr(NEW_ID, truncating, rem_nonzero);
+								SigSpec a_sign = sig_a[sig_a.size()-1];
+								Wire *extend_bit = module->addWire(NEW_ID);
+								module->addAnd(NEW_ID, a_sign, rem_nonzero, extend_bit);
+
+								truncating.append(extend_bit);
+								module->addPos(NEW_ID, truncating, sig_y, true);
+							}
+
 							cell->check();
 						}
 
diff --git a/passes/opt/opt_share.cc b/passes/opt/opt_share.cc
index 1f69c98f4..cbace7bac 100644
--- a/passes/opt/opt_share.cc
+++ b/passes/opt/opt_share.cc
@@ -103,7 +103,7 @@ bool cell_supported(RTLIL::Cell *cell)
 
 		if (sig_bi.is_fully_const() && sig_ci.is_fully_const() && sig_bi == sig_ci)
 			return true;
-	} else if (cell->type.in(LOGICAL_OPS, SHIFT_OPS, BITWISE_OPS, RELATIONAL_OPS, ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($concat))) {
+	} else if (cell->type.in(LOGICAL_OPS, SHIFT_OPS, BITWISE_OPS, RELATIONAL_OPS, ID($add), ID($sub), ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($concat))) {
 		return true;
 	}
 
@@ -130,7 +130,7 @@ bool mergeable(RTLIL::Cell *a, RTLIL::Cell *b)
 
 RTLIL::IdString decode_port_semantics(RTLIL::Cell *cell, RTLIL::IdString port_name)
 {
-	if (cell->type.in(ID($lt), ID($le), ID($ge), ID($gt), ID($div), ID($mod), ID($concat), SHIFT_OPS) && port_name == ID::B)
+	if (cell->type.in(ID($lt), ID($le), ID($ge), ID($gt), ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($concat), SHIFT_OPS) && port_name == ID::B)
 		return port_name;
 
 	return "";
diff --git a/passes/opt/share.cc b/passes/opt/share.cc
index 2839507b0..988253edf 100644
--- a/passes/opt/share.cc
+++ b/passes/opt/share.cc
@@ -376,7 +376,7 @@ struct ShareWorker
 				continue;
 			}
 
-			if (cell->type.in(ID($mul), ID($div), ID($mod))) {
+			if (cell->type.in(ID($mul), ID($div), ID($mod), ID($divfloor), ID($modfloor))) {
 				if (config.opt_aggressive || cell->parameters.at(ID::Y_WIDTH).as_int() >= 4)
 					shareable_cells.insert(cell);
 				continue;
@@ -1133,6 +1133,8 @@ struct ShareWorker
 		cone_ct.cell_types.erase(ID($mul));
 		cone_ct.cell_types.erase(ID($mod));
 		cone_ct.cell_types.erase(ID($div));
+		cone_ct.cell_types.erase(ID($modfloor));
+		cone_ct.cell_types.erase(ID($divfloor));
 		cone_ct.cell_types.erase(ID($pow));
 		cone_ct.cell_types.erase(ID($shl));
 		cone_ct.cell_types.erase(ID($shr));
@@ -1512,6 +1514,8 @@ struct SharePass : public Pass {
 		config.generic_bin_ops.insert(ID($sub));
 		config.generic_bin_ops.insert(ID($div));
 		config.generic_bin_ops.insert(ID($mod));
+		config.generic_bin_ops.insert(ID($divfloor));
+		config.generic_bin_ops.insert(ID($modfloor));
 		// config.generic_bin_ops.insert(ID($pow));
 
 		config.generic_uni_ops.insert(ID($logic_not));
diff --git a/passes/opt/wreduce.cc b/passes/opt/wreduce.cc
index 195400bf0..f60f2f8a8 100644
--- a/passes/opt/wreduce.cc
+++ b/passes/opt/wreduce.cc
@@ -37,7 +37,7 @@ struct WreduceConfig
 			ID($and), ID($or), ID($xor), ID($xnor),
 			ID($shl), ID($shr), ID($sshl), ID($sshr), ID($shift), ID($shiftx),
 			ID($lt), ID($le), ID($eq), ID($ne), ID($eqx), ID($nex), ID($ge), ID($gt),
-			ID($add), ID($sub), ID($mul), // ID($div), ID($mod), ID($pow),
+			ID($add), ID($sub), ID($mul), // ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($pow),
 			ID($mux), ID($pmux),
 			ID($dff), ID($adff)
 		});
@@ -545,7 +545,7 @@ struct WreducePass : public Pass {
 					}
 				}
 
-				if (c->type.in(ID($div), ID($mod), ID($pow)))
+				if (c->type.in(ID($div), ID($mod), ID($divfloor), ID($modfloor), ID($pow)))
 				{
 					SigSpec A = c->getPort(ID::A);
 					int original_a_width = GetSize(A);
diff --git a/passes/tests/test_cell.cc b/passes/tests/test_cell.cc
index cdbe922b2..c6801007d 100644
--- a/passes/tests/test_cell.cc
+++ b/passes/tests/test_cell.cc
@@ -264,7 +264,7 @@ static void create_gold_module(RTLIL::Design *design, RTLIL::IdString cell_type,
 		cell->setPort(ID::Y, wire);
 	}
 
-	if (muxdiv && cell_type.in(ID($div), ID($mod))) {
+	if (muxdiv && cell_type.in(ID($div), ID($mod), ID($divfloor), ID($modfloor))) {
 		auto b_not_zero = module->ReduceBool(NEW_ID, cell->getPort(ID::B));
 		auto div_out = module->addWire(NEW_ID, GetSize(cell->getPort(ID::Y)));
 		module->addMux(NEW_ID, RTLIL::SigSpec(0, GetSize(div_out)), div_out, b_not_zero, cell->getPort(ID::Y));
@@ -839,6 +839,8 @@ struct TestCellPass : public Pass {
 		cell_types[ID($mul)] = "ABSY";
 		cell_types[ID($div)] = "ABSY";
 		cell_types[ID($mod)] = "ABSY";
+		cell_types[ID($divfloor)] = "ABSY";
+		cell_types[ID($modfloor)] = "ABSY";
 		// cell_types[ID($pow)] = "ABsY";
 
 		cell_types[ID($logic_not)] = "ASY";
diff --git a/techlibs/common/simlib.v b/techlibs/common/simlib.v
index 2cdddeabb..125b8e013 100644
--- a/techlibs/common/simlib.v
+++ b/techlibs/common/simlib.v
@@ -997,6 +997,12 @@ endmodule
 
 // --------------------------------------------------------
 
+//  |---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|
+//-
+//-     $div (A, B, Y)
+//-
+//- Division with truncated result (rounded towards 0).
+//-
 module \$div (A, B, Y);
 
 parameter A_SIGNED = 0;
@@ -1021,6 +1027,14 @@ endmodule
 
 // --------------------------------------------------------
 
+//  |---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|
+//-
+//-     $mod (A, B, Y)
+//-
+//- Modulo/remainder of division with truncated result (rounded towards 0).
+//-
+//- Invariant: $div(A, B) * B + $mod(A, B) == A
+//-
 module \$mod (A, B, Y);
 
 parameter A_SIGNED = 0;
@@ -1043,6 +1057,83 @@ endgenerate
 
 endmodule
 
+// --------------------------------------------------------
+
+//  |---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|
+//-
+//-     $divfloor (A, B, Y)
+//-
+//- Division with floored result (rounded towards negative infinity).
+//-
+module \$divfloor (A, B, Y);
+
+parameter A_SIGNED = 0;
+parameter B_SIGNED = 0;
+parameter A_WIDTH = 0;
+parameter B_WIDTH = 0;
+parameter Y_WIDTH = 0;
+
+input [A_WIDTH-1:0] A;
+input [B_WIDTH-1:0] B;
+output [Y_WIDTH-1:0] Y;
+
+generate
+	if (A_SIGNED && B_SIGNED) begin:BLOCK1
+		localparam WIDTH =
+				A_WIDTH >= B_WIDTH && A_WIDTH >= Y_WIDTH ? A_WIDTH :
+				B_WIDTH >= A_WIDTH && B_WIDTH >= Y_WIDTH ? B_WIDTH : Y_WIDTH;
+		wire [WIDTH:0] A_buf, B_buf, N_buf;
+		assign A_buf = $signed(A);
+		assign B_buf = $signed(B);
+		assign N_buf = (A[A_WIDTH-1] == B[B_WIDTH-1]) || A == 0 ? A_buf : $signed(A_buf - (B[B_WIDTH-1] ? B_buf+1 : B_buf-1));
+		assign Y = $signed(N_buf) / $signed(B_buf);
+	end else begin:BLOCK2
+		assign Y = A / B;
+	end
+endgenerate
+
+endmodule
+
+// --------------------------------------------------------
+
+//  |---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|
+//-
+//-     $modfloor (A, B, Y)
+//-
+//- Modulo/remainder of division with floored result (rounded towards negative infinity).
+//-
+//- Invariant: $divfloor(A, B) * B + $modfloor(A, B) == A
+//-
+module \$modfloor (A, B, Y);
+
+parameter A_SIGNED = 0;
+parameter B_SIGNED = 0;
+parameter A_WIDTH = 0;
+parameter B_WIDTH = 0;
+parameter Y_WIDTH = 0;
+
+input [A_WIDTH-1:0] A;
+input [B_WIDTH-1:0] B;
+output [Y_WIDTH-1:0] Y;
+
+generate
+	if (A_SIGNED && B_SIGNED) begin:BLOCK1
+		localparam WIDTH = B_WIDTH >= Y_WIDTH ? B_WIDTH : Y_WIDTH;
+		wire [WIDTH-1:0] B_buf, Y_trunc;
+		assign B_buf = $signed(B);
+		assign Y_trunc = $signed(A) % $signed(B);
+		// flooring mod is the same as truncating mod for positive division results (A and B have
+		// the same sign), as well as when there's no remainder.
+		// For all other cases, they behave as `floor - trunc = B`
+		assign Y = (A[A_WIDTH-1] == B[B_WIDTH-1]) || Y_trunc == 0 ? Y_trunc : $signed(B_buf) + $signed(Y_trunc);
+	end else begin:BLOCK2
+		// no difference between truncating and flooring for unsigned
+		assign Y = A % B;
+	end
+endgenerate
+
+endmodule
+
 // --------------------------------------------------------
 `ifndef SIMLIB_NOPOW
 
diff --git a/techlibs/common/techmap.v b/techlibs/common/techmap.v
index c1efc378b..eafe8d4da 100644
--- a/techlibs/common/techmap.v
+++ b/techlibs/common/techmap.v
@@ -364,7 +364,8 @@ module \$__div_mod_u (A, B, Y, R);
 	end endgenerate
 endmodule
 
-module \$__div_mod (A, B, Y, R);
+// truncating signed division/modulo
+module \$__div_mod_trunc (A, B, Y, R);
 	parameter A_SIGNED = 0;
 	parameter B_SIGNED = 0;
 	parameter A_WIDTH = 1;
@@ -420,7 +421,7 @@ module _90_div (A, B, Y);
 	(* force_downto *)
 	output [Y_WIDTH-1:0] Y;
 
-	\$__div_mod #(
+	\$__div_mod_trunc #(
 		.A_SIGNED(A_SIGNED),
 		.B_SIGNED(B_SIGNED),
 		.A_WIDTH(A_WIDTH),
@@ -448,7 +449,107 @@ module _90_mod (A, B, Y);
 	(* force_downto *)
 	output [Y_WIDTH-1:0] Y;
 
-	\$__div_mod #(
+	\$__div_mod_trunc #(
+		.A_SIGNED(A_SIGNED),
+		.B_SIGNED(B_SIGNED),
+		.A_WIDTH(A_WIDTH),
+		.B_WIDTH(B_WIDTH),
+		.Y_WIDTH(Y_WIDTH)
+	) div_mod (
+		.A(A),
+		.B(B),
+		.R(Y)
+	);
+endmodule
+
+// flooring signed division/modulo
+module \$__div_mod_floor (A, B, Y, R);
+	parameter A_SIGNED = 0;
+	parameter B_SIGNED = 0;
+	parameter A_WIDTH = 1;
+	parameter B_WIDTH = 1;
+	parameter Y_WIDTH = 1;
+
+	localparam WIDTH =
+			A_WIDTH >= B_WIDTH && A_WIDTH >= Y_WIDTH ? A_WIDTH :
+			B_WIDTH >= A_WIDTH && B_WIDTH >= Y_WIDTH ? B_WIDTH : Y_WIDTH;
+
+	input [A_WIDTH-1:0] A;
+	input [B_WIDTH-1:0] B;
+	output [Y_WIDTH-1:0] Y, R;
+
+	wire [WIDTH-1:0] A_buf, B_buf;
+	\$pos #(.A_SIGNED(A_SIGNED), .A_WIDTH(A_WIDTH), .Y_WIDTH(WIDTH)) A_conv (.A(A), .Y(A_buf));
+	\$pos #(.A_SIGNED(B_SIGNED), .A_WIDTH(B_WIDTH), .Y_WIDTH(WIDTH)) B_conv (.A(B), .Y(B_buf));
+
+	wire [WIDTH-1:0] A_buf_u, B_buf_u, Y_u, R_u, R_s;
+	assign A_buf_u = A_SIGNED && A_buf[WIDTH-1] ? -A_buf : A_buf;
+	assign B_buf_u = B_SIGNED && B_buf[WIDTH-1] ? -B_buf : B_buf;
+
+	\$__div_mod_u #(
+		.WIDTH(WIDTH)
+	) div_mod_u (
+		.A(A_buf_u),
+		.B(B_buf_u),
+		.Y(Y_u),
+		.R(R_u)
+	);
+
+	// For negative results, if there was a remainder, subtract one to turn
+	// the round towards 0 into a round towards -inf
+	assign Y = A_SIGNED && B_SIGNED && (A_buf[WIDTH-1] != B_buf[WIDTH-1]) ? (R_u == 0 ? -Y_u : -Y_u-1) : Y_u;
+
+	// truncating modulo
+	assign R_s = A_SIGNED && B_SIGNED && A_buf[WIDTH-1] ? -R_u : R_u;
+	// Flooring modulo differs from truncating modulo only if it is nonzero and
+	// A and B have different signs - then `floor - trunc = B`
+	assign R = (R_s != 0) && A_SIGNED && B_SIGNED && (A_buf[WIDTH-1] != B_buf[WIDTH-1]) ? $signed(B_buf) + $signed(R_s) : R_s;
+endmodule
+
+(* techmap_celltype = "$divfloor" *)
+module _90_divfloor (A, B, Y);
+	parameter A_SIGNED = 0;
+	parameter B_SIGNED = 0;
+	parameter A_WIDTH = 1;
+	parameter B_WIDTH = 1;
+	parameter Y_WIDTH = 1;
+
+	(* force_downto *)
+	input [A_WIDTH-1:0] A;
+	(* force_downto *)
+	input [B_WIDTH-1:0] B;
+	(* force_downto *)
+	output [Y_WIDTH-1:0] Y;
+
+	\$__div_mod_floor #(
+		.A_SIGNED(A_SIGNED),
+		.B_SIGNED(B_SIGNED),
+		.A_WIDTH(A_WIDTH),
+		.B_WIDTH(B_WIDTH),
+		.Y_WIDTH(Y_WIDTH)
+	) div_mod (
+		.A(A),
+		.B(B),
+		.Y(Y)
+	);
+endmodule
+
+(* techmap_celltype = "$modfloor" *)
+module _90_modfloor (A, B, Y);
+	parameter A_SIGNED = 0;
+	parameter B_SIGNED = 0;
+	parameter A_WIDTH = 1;
+	parameter B_WIDTH = 1;
+	parameter Y_WIDTH = 1;
+
+	(* force_downto *)
+	input [A_WIDTH-1:0] A;
+	(* force_downto *)
+	input [B_WIDTH-1:0] B;
+	(* force_downto *)
+	output [Y_WIDTH-1:0] Y;
+
+	\$__div_mod_floor #(
 		.A_SIGNED(A_SIGNED),
 		.B_SIGNED(B_SIGNED),
 		.A_WIDTH(A_WIDTH),
diff --git a/tests/simple/constmuldivmod.v b/tests/simple/constmuldivmod.v
index d1d8be862..5dd8f9295 100644
--- a/tests/simple/constmuldivmod.v
+++ b/tests/simple/constmuldivmod.v
@@ -1,4 +1,4 @@
-module constmuldivmod(input [7:0] A, input [2:0] mode, output reg [7:0] Y);
+module constmuldivmod(input [7:0] A, input [5:0] mode, output reg [7:0] Y);
 	always @* begin
 		case (mode)
 			0: Y = A / 8'd0;
@@ -21,6 +21,46 @@ module constmuldivmod(input [7:0] A, input [2:0] mode, output reg [7:0] Y);
 			13: Y = A % 8'd8;
 			14: Y = A * 8'd8;
 
+			15: Y = $signed(A) / $signed(8'd0);
+			16: Y = $signed(A) % $signed(8'd0);
+			17: Y = $signed(A) * $signed(8'd0);
+
+			18: Y = $signed(A) / $signed(8'd1);
+			19: Y = $signed(A) % $signed(8'd1);
+			20: Y = $signed(A) * $signed(8'd1);
+
+			21: Y = $signed(A) / $signed(8'd2);
+			22: Y = $signed(A) % $signed(8'd2);
+			23: Y = $signed(A) * $signed(8'd2);
+
+			24: Y = $signed(A) / $signed(8'd4);
+			25: Y = $signed(A) % $signed(8'd4);
+			26: Y = $signed(A) * $signed(8'd4);
+
+			27: Y = $signed(A) / $signed(8'd8);
+			28: Y = $signed(A) % $signed(8'd8);
+			29: Y = $signed(A) * $signed(8'd8);
+
+			30: Y = $signed(A) / $signed(-8'd0);
+			31: Y = $signed(A) % $signed(-8'd0);
+			32: Y = $signed(A) * $signed(-8'd0);
+
+			33: Y = $signed(A) / $signed(-8'd1);
+			34: Y = $signed(A) % $signed(-8'd1);
+			35: Y = $signed(A) * $signed(-8'd1);
+
+			36: Y = $signed(A) / $signed(-8'd2);
+			37: Y = $signed(A) % $signed(-8'd2);
+			38: Y = $signed(A) * $signed(-8'd2);
+
+			39: Y = $signed(A) / $signed(-8'd4);
+			40: Y = $signed(A) % $signed(-8'd4);
+			41: Y = $signed(A) * $signed(-8'd4);
+
+			42: Y = $signed(A) / $signed(-8'd8);
+			43: Y = $signed(A) % $signed(-8'd8);
+			44: Y = $signed(A) * $signed(-8'd8);
+
 			default: Y = 8'd16 * A;
 		endcase
 	end