diff --git a/src/cmd/compile/internal/gc/const.go b/src/cmd/compile/internal/gc/const.go
index ef4b933f68..39adba0f07 100644
--- a/src/cmd/compile/internal/gc/const.go
+++ b/src/cmd/compile/internal/gc/const.go
@@ -838,15 +838,13 @@ Outer:
 		case ODIV:
 			if y.CmpInt64(0) == 0 {
 				yyerror("division by zero")
-				u.SetOverflow()
-				break
+				return Val{}
 			}
 			u.Quo(y)
 		case OMOD:
 			if y.CmpInt64(0) == 0 {
 				yyerror("division by zero")
-				u.SetOverflow()
-				break
+				return Val{}
 			}
 			u.Rem(y)
 		case OOR:
@@ -877,13 +875,13 @@ Outer:
 		case ODIV:
 			if y.CmpFloat64(0) == 0 {
 				yyerror("division by zero")
-				u.SetFloat64(1)
-				break
+				return Val{}
 			}
 			u.Quo(y)
-		case OMOD:
-			// TODO(mdempsky): Move to typecheck.
-			yyerror("illegal constant expression: floating-point %% operation")
+		case OMOD, OOR, OAND, OANDNOT, OXOR:
+			// TODO(mdempsky): Move to typecheck; see #31060.
+			yyerror("invalid operation: operator %v not defined on untyped float", op)
+			return Val{}
 		default:
 			break Outer
 		}
@@ -907,9 +905,12 @@ Outer:
 		case ODIV:
 			if !u.Div(y) {
 				yyerror("complex division by zero")
-				u.Real.SetFloat64(1)
-				u.Imag.SetFloat64(0)
+				return Val{}
 			}
+		case OMOD, OOR, OAND, OANDNOT, OXOR:
+			// TODO(mdempsky): Move to typecheck; see #31060.
+			yyerror("invalid operation: operator %v not defined on untyped complex", op)
+			return Val{}
 		default:
 			break Outer
 		}
@@ -956,19 +957,31 @@ func unaryOp(op Op, x Val, t *types.Type) Val {
 		}
 
 	case OBITNOT:
-		x := x.U.(*Mpint)
+		switch x.Ctype() {
+		case CTINT, CTRUNE:
+			x := x.U.(*Mpint)
 
-		u := new(Mpint)
-		u.Rune = x.Rune
-		if t.IsSigned() || t.IsUntyped() {
-			// Signed values change sign.
-			u.SetInt64(-1)
-		} else {
-			// Unsigned values invert their bits.
-			u.Set(maxintval[t.Etype])
+			u := new(Mpint)
+			u.Rune = x.Rune
+			if t.IsSigned() || t.IsUntyped() {
+				// Signed values change sign.
+				u.SetInt64(-1)
+			} else {
+				// Unsigned values invert their bits.
+				u.Set(maxintval[t.Etype])
+			}
+			u.Xor(x)
+			return Val{U: u}
+
+		case CTFLT:
+			// TODO(mdempsky): Move to typecheck; see #31060.
+			yyerror("invalid operation: operator %v not defined on untyped float", op)
+			return Val{}
+		case CTCPLX:
+			// TODO(mdempsky): Move to typecheck; see #31060.
+			yyerror("invalid operation: operator %v not defined on untyped complex", op)
+			return Val{}
 		}
-		u.Xor(x)
-		return Val{U: u}
 
 	case ONOT:
 		return Val{U: !x.U.(bool)}
@@ -1001,6 +1014,12 @@ func shiftOp(x Val, op Op, y Val) Val {
 
 // setconst rewrites n as an OLITERAL with value v.
 func setconst(n *Node, v Val) {
+	// If constant folding failed, mark n as broken and give up.
+	if v.U == nil {
+		n.Type = nil
+		return
+	}
+
 	// Ensure n.Orig still points to a semantically-equivalent
 	// expression after we rewrite n into a constant.
 	if n.Orig == n {
diff --git a/test/const1.go b/test/const1.go
index 62abe4145a..3fd5b55522 100644
--- a/test/const1.go
+++ b/test/const1.go
@@ -68,7 +68,7 @@ var (
 	c3 float64 = float64(Big) * Big // ERROR "overflow"
 	c4         = Big * Big          // ERROR "overflow"
 	c5         = Big / 0            // ERROR "division by zero"
-	c6         = 1000 % 1e3         // ERROR "floating-point % operation|expected integer type"
+	c6         = 1000 % 1e3         // ERROR "invalid operation|expected integer type"
 )
 
 func f(int)
diff --git a/test/fixedbugs/issue31060.go b/test/fixedbugs/issue31060.go
new file mode 100644
index 0000000000..a1ba705160
--- /dev/null
+++ b/test/fixedbugs/issue31060.go
@@ -0,0 +1,30 @@
+// errorcheck
+
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package p
+
+const (
+	f = 1.0
+	c = 1.0i
+
+	_ = ^f // ERROR "invalid operation|expected integer"
+	_ = ^c // ERROR "invalid operation|expected integer"
+
+	_ = f % f // ERROR "invalid operation|expected integer"
+	_ = c % c // ERROR "invalid operation|expected integer"
+
+	_ = f & f // ERROR "invalid operation|expected integer"
+	_ = c & c // ERROR "invalid operation|expected integer"
+
+	_ = f | f // ERROR "invalid operation|expected integer"
+	_ = c | c // ERROR "invalid operation|expected integer"
+
+	_ = f ^ f // ERROR "invalid operation|expected integer"
+	_ = c ^ c // ERROR "invalid operation|expected integer"
+
+	_ = f &^ f // ERROR "invalid operation|expected integer"
+	_ = c &^ c // ERROR "invalid operation|expected integer"
+)