diff --git a/internal/shader/expr.go b/internal/shader/expr.go
index f5a9425a7..5f2980647 100644
--- a/internal/shader/expr.go
+++ b/internal/shader/expr.go
@@ -105,7 +105,7 @@ func (cs *compileState) parseExpr(block *block, fname string, expr ast.Expr, mar
 		}
 
 		// Resolve untyped constants.
-		l, r, ok := shaderir.ResolveUntypedConstsForBinaryOp(lhs[0].Const, rhs[0].Const, lhst, rhst)
+		l, r, ok := shaderir.ResolveUntypedConstsForBinaryOp(op2, lhs[0].Const, rhs[0].Const, lhst, rhst)
 		if !ok {
 			// TODO: Show a better type name for untyped constants.
 			cs.addError(e.Pos(), fmt.Sprintf("types don't match: %s %s %s", lhst.String(), op, rhst.String()))
@@ -153,6 +153,13 @@ func (cs *compileState) parseExpr(block *block, fname string, expr ast.Expr, mar
 				v = gconstant.MakeBool(b)
 			case token.EQL, token.NEQ, token.LSS, token.LEQ, token.GTR, token.GEQ:
 				v = gconstant.MakeBool(gconstant.Compare(lhs[0].Const, op, rhs[0].Const))
+			case token.SHL, token.SHR:
+				shift, ok := gconstant.Int64Val(rhs[0].Const)
+				if !ok {
+					cs.addError(e.Pos(), fmt.Sprintf("unexpected %s type for: %s", rhs[0].Const.String(), e.Op))
+				} else {
+					v = gconstant.Shift(lhs[0].Const, op, uint(shift))
+				}
 			default:
 				v = gconstant.BinaryOp(lhs[0].Const, op, rhs[0].Const)
 			}
diff --git a/internal/shader/stmt.go b/internal/shader/stmt.go
index 42f0ddd13..6c07057da 100644
--- a/internal/shader/stmt.go
+++ b/internal/shader/stmt.go
@@ -60,7 +60,7 @@ func (cs *compileState) parseStmt(block *block, fname string, stmt ast.Stmt, inP
 				return nil, false
 			}
 			stmts = append(stmts, ss...)
-		case token.ADD_ASSIGN, token.SUB_ASSIGN, token.MUL_ASSIGN, token.QUO_ASSIGN, token.REM_ASSIGN, token.AND_ASSIGN, token.OR_ASSIGN, token.XOR_ASSIGN, token.AND_NOT_ASSIGN:
+		case token.ADD_ASSIGN, token.SUB_ASSIGN, token.MUL_ASSIGN, token.QUO_ASSIGN, token.REM_ASSIGN, token.AND_ASSIGN, token.OR_ASSIGN, token.XOR_ASSIGN, token.AND_NOT_ASSIGN, token.SHL_ASSIGN, token.SHR_ASSIGN:
 			rhs, rts, ss, ok := cs.parseExpr(block, fname, stmt.Rhs[0], true)
 			if !ok {
 				return nil, false
@@ -100,6 +100,10 @@ func (cs *compileState) parseStmt(block *block, fname string, stmt ast.Stmt, inP
 				op = shaderir.Or
 			case token.XOR_ASSIGN:
 				op = shaderir.Xor
+			case token.SHL_ASSIGN:
+				op = shaderir.LeftShift
+			case token.SHR_ASSIGN:
+				op = shaderir.RightShift
 			default:
 				cs.addError(stmt.Pos(), fmt.Sprintf("unexpected token: %s", stmt.Tok))
 				return nil, false
@@ -110,7 +114,7 @@ func (cs *compileState) parseStmt(block *block, fname string, stmt ast.Stmt, inP
 					cs.addError(stmt.Pos(), fmt.Sprintf("invalid operation: operator / not defined on %s", rts[0].String()))
 					return nil, false
 				}
-				if op == shaderir.And || op == shaderir.Or || op == shaderir.Xor {
+				if op == shaderir.And || op == shaderir.Or || op == shaderir.Xor || op == shaderir.LeftShift || op == shaderir.RightShift {
 					if lts[0].Main != shaderir.Int && !lts[0].IsIntVector() {
 						cs.addError(stmt.Pos(), fmt.Sprintf("invalid operation: operator %s not defined on %s", stmt.Tok, lts[0].String()))
 					}
@@ -137,7 +141,7 @@ func (cs *compileState) parseStmt(block *block, fname string, stmt ast.Stmt, inP
 						}
 					}
 				case shaderir.Float:
-					if op == shaderir.And || op == shaderir.Or || op == shaderir.Xor {
+					if op == shaderir.And || op == shaderir.Or || op == shaderir.Xor || op == shaderir.LeftShift || op == shaderir.RightShift {
 						cs.addError(stmt.Pos(), fmt.Sprintf("invalid operation: operator %s not defined on %s", stmt.Tok, lts[0].String()))
 					} else if rhs[0].Const != nil &&
 						(rts[0].Main == shaderir.None || rts[0].Main == shaderir.Float) &&
@@ -148,7 +152,7 @@ func (cs *compileState) parseStmt(block *block, fname string, stmt ast.Stmt, inP
 						return nil, false
 					}
 				case shaderir.Vec2, shaderir.Vec3, shaderir.Vec4, shaderir.Mat2, shaderir.Mat3, shaderir.Mat4:
-					if op == shaderir.And || op == shaderir.Or || op == shaderir.Xor {
+					if op == shaderir.And || op == shaderir.Or || op == shaderir.Xor || op == shaderir.LeftShift || op == shaderir.RightShift {
 						cs.addError(stmt.Pos(), fmt.Sprintf("invalid operation: operator %s not defined on %s", stmt.Tok, lts[0].String()))
 					} else if (op == shaderir.MatrixMul || op == shaderir.Div) &&
 						(rts[0].Main == shaderir.Float ||
diff --git a/internal/shader/syntax_test.go b/internal/shader/syntax_test.go
index a595c0c4a..f514daa08 100644
--- a/internal/shader/syntax_test.go
+++ b/internal/shader/syntax_test.go
@@ -1314,6 +1314,163 @@ func Fragment(dstPos vec4, srcPos vec2, color vec4) vec4 {
 	}
 }
 
+// Issue: #2755
+func TestSyntaxOperatorShift(t *testing.T) {
+	cases := []struct {
+		stmt string
+		err  bool
+	}{
+		{stmt: "a := 1 << 2; _ = a", err: false},
+		{stmt: "a := 1 << 2.0; _ = a", err: false},
+		{stmt: "a := 1.0 << 2; _ = a", err: false},
+		{stmt: "a := 1.0 << 2.0; _ = a", err: false},
+		{stmt: "var a = 1; b := a << 2.0; _ = b", err: false},
+		{stmt: "var a = 1; b := 2.0 << a; _ = b", err: false}, // PR: #2916
+		{stmt: "a := float(1.0) << 2; _ = a", err: true},
+		{stmt: "a := 1 << float(2.0); _ = a", err: true},
+		{stmt: "a := ivec2(1) << 2; _ = a", err: false},
+		{stmt: "a := 1 << ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) << float(2.0); _ = a", err: true},
+		{stmt: "a := float(1.0) << ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) << ivec2(2); _ = a", err: false},
+		{stmt: "a := ivec3(1) << ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) << ivec3(2); _ = a", err: true},
+		{stmt: "a := 1 << vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) << 2; _ = a", err: true},
+		{stmt: "a := float(1.0) << vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) << float(2.0); _ = a", err: true},
+		{stmt: "a := vec2(1) << vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) << vec3(2); _ = a", err: true},
+		{stmt: "a := vec3(1) << vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) << ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) << vec2(2); _ = a", err: true},
+		{stmt: "a := vec3(1) << ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) << vec3(2); _ = a", err: true},
+
+		{stmt: "a := 1 >> 2; _ = a", err: false},
+		{stmt: "a := 1 >> 2.0; _ = a", err: false},
+		{stmt: "a := 1.0 >> 2; _ = a", err: false},
+		{stmt: "a := 1.0 >> 2.0; _ = a", err: false},
+		{stmt: "var a = 1; b := a >> 2.0; _ = b", err: false},
+		{stmt: "var a = 1; b := 2.0 >> a; _ = b", err: false}, // PR: #2916
+		{stmt: "a := float(1.0) >> 2; _ = a", err: true},
+		{stmt: "a := 1 >> float(2.0); _ = a", err: true},
+		{stmt: "a := ivec2(1) >> 2; _ = a", err: false},
+		{stmt: "a := 1 >> ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) >> float(2.0); _ = a", err: true},
+		{stmt: "a := float(1.0) >> ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) >> ivec2(2); _ = a", err: false},
+		{stmt: "a := ivec3(1) >> ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) >> ivec3(2); _ = a", err: true},
+		{stmt: "a := 1 >> vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) >> 2; _ = a", err: true},
+		{stmt: "a := float(1.0) >> vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) >> float(2.0); _ = a", err: true},
+		{stmt: "a := vec2(1) >> vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) >> vec3(2); _ = a", err: true},
+		{stmt: "a := vec3(1) >> vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1) >> ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) >> vec2(2); _ = a", err: true},
+		{stmt: "a := vec3(1) >> ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1) >> vec3(2); _ = a", err: true},
+	}
+
+	for _, c := range cases {
+		_, err := compileToIR([]byte(fmt.Sprintf(`package main
+
+func Fragment(dstPos vec4, srcPos vec2, color vec4) vec4 {
+	%s
+	return dstPos
+}`, c.stmt)))
+		if err == nil && c.err {
+			t.Errorf("%s must return an error but does not", c.stmt)
+		} else if err != nil && !c.err {
+			t.Errorf("%s must not return nil but returned %v", c.stmt, err)
+		}
+	}
+}
+
+func TestSyntaxOperatorShiftAssign(t *testing.T) {
+	cases := []struct {
+		stmt string
+		err  bool
+	}{
+		{stmt: "a := 1; a <<= 2; _ = a", err: false},
+		{stmt: "a := 1; a <<= 2.0; _ = a", err: false},
+		{stmt: "a := float(1.0); a <<= 2; _ = a", err: true},
+		{stmt: "a := 1; a <<= float(2.0); _ = a", err: true},
+		{stmt: "a := ivec2(1); a <<= 2; _ = a", err: false},
+		{stmt: "a := 1;  a <<= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a <<= float(2.0); _ = a", err: true},
+		{stmt: "a := float(1.0); a <<= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a <<= ivec2(2); _ = a", err: false},
+		{stmt: "a := ivec3(1); a <<= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a <<= ivec3(2); _ = a", err: true},
+		{stmt: "a := 1; a <<= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a <<= 2; _ = a", err: true},
+		{stmt: "a := float(1.0); a <<= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a <<= float(2.0); _ = a", err: true},
+		{stmt: "a := vec2(1); a <<= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a <<= vec3(2); _ = a", err: true},
+		{stmt: "a := vec3(1); a <<= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a <<= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a <<= vec2(2); _ = a", err: true},
+		{stmt: "a := vec3(1); a <<= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a <<= vec3(2); _ = a", err: true},
+		{stmt: "const c = 2; a := 1; a <<= c; _ = a", err: false},
+		{stmt: "const c = 2.0; a := 1; a <<= c; _ = a", err: false},
+		{stmt: "const c = 2; a := float(1.0); a <<= c; _ = a", err: true},
+		{stmt: "const c float = 2; a := 1; a <<= c; _ = a", err: true},
+		{stmt: "const c float = 2.0; a := 1; a <<= c; _ = a", err: true},
+		{stmt: "const c int = 2; a := ivec2(1); a <<= c; _ = a", err: false},
+		{stmt: "const c int = 2; a := vec2(1); a <<= c; _ = a", err: true},
+
+		{stmt: "a := 1; a >>= 2; _ = a", err: false},
+		{stmt: "a := 1; a >>= 2.0; _ = a", err: false},
+		{stmt: "a := float(1.0); a >>= 2; _ = a", err: true},
+		{stmt: "a := 1; a >>= float(2.0); _ = a", err: true},
+		{stmt: "a := ivec2(1); a >>= 2; _ = a", err: false},
+		{stmt: "a := 1;  a >>= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a >>= float(2.0); _ = a", err: true},
+		{stmt: "a := float(1.0); a >>= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a >>= ivec2(2); _ = a", err: false},
+		{stmt: "a := ivec3(1); a >>= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a >>= ivec3(2); _ = a", err: true},
+		{stmt: "a := 1; a >>= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a >>= 2; _ = a", err: true},
+		{stmt: "a := float(1.0); a >>= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a >>= float(2.0); _ = a", err: true},
+		{stmt: "a := vec2(1); a >>= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a >>= vec3(2); _ = a", err: true},
+		{stmt: "a := vec3(1); a >>= vec2(2); _ = a", err: true},
+		{stmt: "a := vec2(1); a >>= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a >>= vec2(2); _ = a", err: true},
+		{stmt: "a := vec3(1); a >>= ivec2(2); _ = a", err: true},
+		{stmt: "a := ivec2(1); a >>= vec3(2); _ = a", err: true},
+		{stmt: "const c = 2; a := 1; a >>= c; _ = a", err: false},
+		{stmt: "const c = 2.0; a := 1; a >>= c; _ = a", err: false},
+		{stmt: "const c = 2; a := float(1.0); a >>= c; _ = a", err: true},
+		{stmt: "const c float = 2; a := 1; a >>= c; _ = a", err: true},
+		{stmt: "const c float = 2.0; a := 1; a >>= c; _ = a", err: true},
+		{stmt: "const c int = 2; a := ivec2(1); a >>= c; _ = a", err: false},
+		{stmt: "const c int = 2; a := vec2(1); a >>= c; _ = a", err: true},
+	}
+
+	for _, c := range cases {
+		_, err := compileToIR([]byte(fmt.Sprintf(`package main
+
+func Fragment(dstPos vec4, srcPos vec2, color vec4) vec4 {
+	%s
+	return dstPos
+}`, c.stmt)))
+		if err == nil && c.err {
+			t.Errorf("%s must return an error but does not", c.stmt)
+		} else if err != nil && !c.err {
+			t.Errorf("%s must not return nil but returned %v", c.stmt, err)
+		}
+	}
+}
+
 // Issue #1971
 func TestSyntaxOperatorMultiplyAssign(t *testing.T) {
 	cases := []struct {
diff --git a/internal/shaderir/check.go b/internal/shaderir/check.go
index 857bd1e2a..88fa18d49 100644
--- a/internal/shaderir/check.go
+++ b/internal/shaderir/check.go
@@ -18,8 +18,21 @@ import (
 	"go/constant"
 )
 
-func ResolveUntypedConstsForBinaryOp(lhs, rhs constant.Value, lhst, rhst Type) (newLhs, newRhs constant.Value, ok bool) {
+func ResolveUntypedConstsForBinaryOp(op Op, lhs, rhs constant.Value, lhst, rhst Type) (newLhs, newRhs constant.Value, ok bool) {
 	if lhst.Main == None && rhst.Main == None {
+		if op == LeftShift || op == RightShift {
+			newLhs = constant.ToInt(lhs)
+			newRhs = constant.ToInt(rhs)
+
+			if newLhs.Kind() == constant.Unknown {
+				return nil, nil, false
+			}
+			if newRhs.Kind() == constant.Unknown {
+				return nil, nil, false
+			}
+			return newLhs, newRhs, true
+		}
+
 		if lhs.Kind() == rhs.Kind() {
 			return lhs, rhs, true
 		}
@@ -98,6 +111,13 @@ func TypeFromBinaryOp(op Op, lhst, rhst Type, lhsConst, rhsConst constant.Value)
 			return Type{}, false
 		}
 
+		if op == LeftShift || op == RightShift {
+			if lhsConst.Kind() == constant.Int && rhsConst.Kind() == constant.Int {
+				return Type{Main: Int}, true
+			}
+			return Type{}, false
+		}
+
 		if op == EqualOp || op == NotEqualOp || op == LessThanOp || op == LessThanEqualOp || op == GreaterThanOp || op == GreaterThanEqualOp {
 			return Type{Main: Bool}, true
 		}
@@ -195,6 +215,16 @@ func TypeFromBinaryOp(op Op, lhst, rhst Type, lhsConst, rhsConst constant.Value)
 		return Type{}, false
 	}
 
+	if op == LeftShift || op == RightShift {
+		if (lhst.Main == Int || lhst.IsIntVector()) && rhst.Main == Int {
+			return lhst, true
+		}
+		if lhst.IsIntVector() && rhst.IsIntVector() && lhst.VectorElementCount() == rhst.VectorElementCount() {
+			return lhst, true
+		}
+		return Type{}, false
+	}
+
 	if lhst.Equal(&rhst) {
 		if lhst.Main == None {
 			return rhst, true