[NFC][InstSimplify] Some tests for dropping null check after uadd.with.overflow of...

https://rise4fun.com/Alive/WRzq

Name: C <= Y && Y != 0  -->  C <= Y  iff C != 0
Pre: C != 0
  %y_is_nonnull = icmp ne i64 %y, 0
  %no_overflow = icmp ule i64 C, %y
  %r = and i1 %y_is_nonnull, %no_overflow
=>
  %r = %no_overflow

Name: C <= Y || Y != 0  -->  Y != 0  iff C != 0
Pre: C != 0
  %y_is_nonnull = icmp ne i64 %y, 0
  %no_overflow = icmp ule i64 C, %y
  %r = or i1 %y_is_nonnull, %no_overflow
=>
  %r = %y_is_nonnull

Name: C > Y || Y == 0  -->  C > Y  iff C != 0
Pre: C != 0
  %y_is_null = icmp eq i64 %y, 0
  %overflow = icmp ugt i64 C, %y
  %r = or i1 %y_is_null, %overflow
=>
  %r = %overflow

Name: C > Y && Y == 0  -->  Y == 0  iff C != 0
Pre: C != 0
  %y_is_null = icmp eq i64 %y, 0
  %overflow = icmp ugt i64 C, %y
  %r = and i1 %y_is_null, %overflow
=>
  %r = %y_is_null

https://bugs.llvm.org/show_bug.cgi?id=43246

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@371339 91177308-0d34-0410-b5e6-96231b3b80d8

diff --git a/test/Transforms/InstSimplify/redundant-null-check-in-uadd_with_overflow-of-nonnull-ptr.ll b/test/Transforms/InstSimplify/redundant-null-check-in-uadd_with_overflow-of-nonnull-ptr.ll
new file mode 100644 (file)
index 0000000..87f15c3
--- /dev/null
+++ b/test/Transforms/InstSimplify/redundant-null-check-in-uadd_with_overflow-of-nonnull-ptr.ll
@@ -0,0 +1,278 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt %s -instsimplify -S | FileCheck %s
+
+; Here we have add some offset to a non-null pointer,
+; and check that the result does not overflow and is not a null pointer.
+; But since the base pointer is already non-null, and we check for overflow,
+; that will already catch the get null pointer,
+; so the separate null check is redundant and can be dropped.
+
+define i1 @t0(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t0(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp uge i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp uge i64 %adjusted, %base_int
+  %res = and i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t1(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t1(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ule i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ule i64 %base_int, %adjusted ; swapped
+  %res = and i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t2(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t2(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp uge i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp uge i64 %adjusted, %base_int
+  %res = and i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+define i1 @t3(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t3(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ule i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ule i64 %base_int, %adjusted ; swapped
+  %res = and i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+
+; If the joining operator was 'or', i.e. we check that either we produced null
+; pointer, or no overflow happened, then the overflow check itself is redundant.
+
+define i1 @t4(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t4(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp uge i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp uge i64 %adjusted, %base_int
+  %res = or i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t5(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t5(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ule i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ule i64 %base_int, %adjusted ; swapped
+  %res = or i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t6(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t6(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp uge i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp uge i64 %adjusted, %base_int
+  %res = or i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+define i1 @t7(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t7(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp ne i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ule i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp ne i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ule i64 %base_int, %adjusted ; swapped
+  %res = or i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+
+; Or, we could be checking the reverse condition, that we either get null pointer,
+; or overflow happens, then again, the standalone null check is redundant and
+; can be dropped.
+
+define i1 @t8(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t8(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ult i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ult i64 %adjusted, %base_int
+  %res = or i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t9(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t9(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ugt i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ugt i64 %base_int, %adjusted ; swapped
+  %res = or i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t10(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t10(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ult i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ult i64 %adjusted, %base_int
+  %res = or i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+define i1 @t11(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t11(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ugt i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = or i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ugt i64 %base_int, %adjusted ; swapped
+  %res = or i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+
+; If the joining operator was 'and', i.e. we check that we both get null pointer
+; AND overflow happens, then the overflow check is redundant.
+
+define i1 @t12(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t12(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ult i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ult i64 %adjusted, %base_int
+  %res = and i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t13(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t13(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ugt i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NON_NULL_AFTER_ADJUSTMENT]], [[NO_OVERFLOW_DURING_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ugt i64 %base_int, %adjusted ; swapped
+  %res = and i1 %non_null_after_adjustment, %no_overflow_during_adjustment
+  ret i1 %res
+}
+define i1 @t14(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t14(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ult i64 [[ADJUSTED]], [[BASE_INT]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ult i64 %adjusted, %base_int
+  %res = and i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}
+define i1 @t15(i8* nonnull %base, i64 %offset) {
+; CHECK-LABEL: @t15(
+; CHECK-NEXT:    [[BASE_INT:%.*]] = ptrtoint i8* [[BASE:%.*]] to i64
+; CHECK-NEXT:    [[ADJUSTED:%.*]] = add i64 [[BASE_INT]], [[OFFSET:%.*]]
+; CHECK-NEXT:    [[NON_NULL_AFTER_ADJUSTMENT:%.*]] = icmp eq i64 [[ADJUSTED]], 0
+; CHECK-NEXT:    [[NO_OVERFLOW_DURING_ADJUSTMENT:%.*]] = icmp ugt i64 [[BASE_INT]], [[ADJUSTED]]
+; CHECK-NEXT:    [[RES:%.*]] = and i1 [[NO_OVERFLOW_DURING_ADJUSTMENT]], [[NON_NULL_AFTER_ADJUSTMENT]]
+; CHECK-NEXT:    ret i1 [[RES]]
+;
+  %base_int = ptrtoint i8* %base to i64
+  %adjusted = add i64 %base_int, %offset
+  %non_null_after_adjustment = icmp eq i64 %adjusted, 0
+  %no_overflow_during_adjustment = icmp ugt i64 %base_int, %adjusted ; swapped
+  %res = and i1 %no_overflow_during_adjustment, %non_null_after_adjustment ; swapped
+  ret i1 %res
+}