diff --git a/go/internal/gcimporter/gcimporter_test.go b/go/internal/gcimporter/gcimporter_test.go
index b517bf1250..cfafbbf1c4 100644
--- a/go/internal/gcimporter/gcimporter_test.go
+++ b/go/internal/gcimporter/gcimporter_test.go
@@ -10,6 +10,7 @@ package gcimporter
 import (
 	"bytes"
 	"fmt"
+	"go/constant"
 	"go/types"
 	"io/ioutil"
 	"os"
@@ -320,26 +321,11 @@ func TestImportedTypes(t *testing.T) {
 	}
 
 	for _, test := range importedObjectTests {
-		s := strings.Split(test.name, ".")
-		if len(s) != 2 {
-			t.Fatal("inconsistent test data")
-		}
-		importPath := s[0]
-		objName := s[1]
-
-		pkg, err := Import(make(map[string]*types.Package), importPath, ".", nil)
-		if err != nil {
-			t.Error(err)
-			continue
-		}
-
-		obj := pkg.Scope().Lookup(objName)
+		obj := importObject(t, test.name)
 		if obj == nil {
-			t.Errorf("%s: object not found", test.name)
-			continue
+			continue // error reported elsewhere
 		}
-
-		got := types.ObjectString(obj, types.RelativeTo(pkg))
+		got := types.ObjectString(obj, types.RelativeTo(obj.Pkg()))
 		if got != test.want {
 			t.Errorf("%s: got %q; want %q", test.name, got, test.want)
 		}
@@ -350,6 +336,54 @@ func TestImportedTypes(t *testing.T) {
 	}
 }
 
+func TestImportedConsts(t *testing.T) {
+	testenv.NeedsGo1Point(t, 11)
+	skipSpecialPlatforms(t)
+
+	tests := []struct {
+		name string
+		want constant.Kind
+	}{
+		{"math.Pi", constant.Float},
+		{"math.MaxFloat64", constant.Float},
+		{"math.MaxInt64", constant.Int},
+	}
+
+	for _, test := range tests {
+		obj := importObject(t, test.name)
+		if got := obj.(*types.Const).Val().Kind(); got != test.want {
+			t.Errorf("%s: imported as constant.Kind(%v), want constant.Kind(%v)", test.name, got, test.want)
+		}
+	}
+}
+
+// importObject imports the object specified by a name of the form
+// <import path>.<object name>, e.g. go/types.Type.
+//
+// If any errors occur they are reported via t and the resulting object will
+// be nil.
+func importObject(t *testing.T, name string) types.Object {
+	s := strings.Split(name, ".")
+	if len(s) != 2 {
+		t.Fatal("inconsistent test data")
+	}
+	importPath := s[0]
+	objName := s[1]
+
+	pkg, err := Import(make(map[string]*types.Package), importPath, ".", nil)
+	if err != nil {
+		t.Error(err)
+		return nil
+	}
+
+	obj := pkg.Scope().Lookup(objName)
+	if obj == nil {
+		t.Errorf("%s: object not found", name)
+		return nil
+	}
+	return obj
+}
+
 // verifyInterfaceMethodRecvs verifies that method receiver types
 // are named if the methods belong to a named interface type.
 func verifyInterfaceMethodRecvs(t *testing.T, named *types.Named, level int) {
diff --git a/go/internal/gcimporter/iimport.go b/go/internal/gcimporter/iimport.go
index b236debad1..8ed8bc62d6 100644
--- a/go/internal/gcimporter/iimport.go
+++ b/go/internal/gcimporter/iimport.go
@@ -473,6 +473,14 @@ func (r *importReader) mpfloat(b *types.Basic) constant.Value {
 	switch {
 	case exp > 0:
 		x = constant.Shift(x, token.SHL, uint(exp))
+		// Ensure that the imported Kind is Float, else this constant may run into
+		// bitsize limits on overlarge integers. Eventually we can instead adopt
+		// the approach of CL 288632, but that CL relies on go/constant APIs that
+		// were introduced in go1.13.
+		//
+		// TODO(rFindley): sync the logic here with tip Go once we no longer
+		// support go1.12.
+		x = constant.ToFloat(x)
 	case exp < 0:
 		d := constant.Shift(constant.MakeInt64(1), token.SHL, uint(-exp))
 		x = constant.BinaryOp(x, token.QUO, d)