; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 4
; RUN: opt -passes=constraint-elimination -S %s | FileCheck %s

; n < m  /\  r = urem x, n  ==>  r < n < m  ==>  r < m
define i1 @urem_ult_divisor_bound(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
; CHECK-LABEL: define i1 @urem_ult_divisor_bound(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    ret i1 true
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ult i32 %n, %m
  br i1 %cmp, label %mid, label %else

mid:
  %r = urem i32 %x, %n
  br label %check

check:
  %v = icmp ult i32 %r, %m
  ret i1 %v

else:
  ret i1 false
}

; n <= m  /\  r = urem x, n  ==>  r < n <= m  ==>  r ule m
define i1 @urem_ule_divisor_bound(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
; CHECK-LABEL: define i1 @urem_ule_divisor_bound(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[N]], [[M]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    ret i1 true
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ule i32 %n, %m
  br i1 %cmp, label %mid, label %else

mid:
  %r = urem i32 %x, %n
  br label %check

check:
  %v = icmp ule i32 %r, %m
  ret i1 %v

else:
  ret i1 false
}

; x <= limit  /\  r = urem x, n  ==>  r <= x <= limit
define i1 @urem_ule_dividend_bound(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
; CHECK-LABEL: define i1 @urem_ule_dividend_bound(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    ret i1 true
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ule i32 %x, %limit
  br i1 %cmp, label %mid, label %else

mid:
  %r = urem i32 %x, %n
  br label %check

check:
  %v = icmp ule i32 %r, %limit
  ret i1 %v

else:
  ret i1 false
}

; x <= limit  /\  q = udiv x, n  ==>  q <= x <= limit
define i1 @udiv_ule_dividend_bound(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
; CHECK-LABEL: define i1 @udiv_ule_dividend_bound(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[Q:%.*]] = udiv i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    ret i1 true
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ule i32 %x, %limit
  br i1 %cmp, label %mid, label %else

mid:
  %q = udiv i32 %x, %n
  br label %check

check:
  %v = icmp ule i32 %q, %limit
  ret i1 %v

else:
  ret i1 false
}

; n < m  /\  m < k  /\  r = urem x, n  ==>  r < n < m < k  ==>  r < k
define i1 @urem_chain_three_hops(i32 noundef %x, i32 noundef %n, i32 noundef %m, i32 noundef %k) {
; CHECK-LABEL: define i1 @urem_chain_three_hops(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]], i32 noundef [[K:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[C1:%.*]] = icmp ult i32 [[N]], [[M]]
; CHECK-NEXT:    br i1 [[C1]], label [[BB1:%.*]], label [[OUT:%.*]]
; CHECK:       bb1:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    [[C2:%.*]] = icmp ult i32 [[M]], [[K]]
; CHECK-NEXT:    br i1 [[C2]], label [[BB2:%.*]], label [[OUT]]
; CHECK:       bb2:
; CHECK-NEXT:    ret i1 true
; CHECK:       out:
; CHECK-NEXT:    ret i1 false
;
entry:
  %c1 = icmp ult i32 %n, %m
  br i1 %c1, label %bb1, label %out

bb1:
  %r = urem i32 %x, %n
  %c2 = icmp ult i32 %m, %k
  br i1 %c2, label %bb2, label %out

bb2:
  %v = icmp ult i32 %r, %k
  ret i1 %v

out:
  ret i1 false
}

define i1 @udiv_urem_combined(i32 noundef %x, i32 noundef %n, i32 noundef %limit) {
; CHECK-LABEL: define i1 @udiv_urem_combined(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[LIMIT:%.*]]) {
; CHECK-NEXT:    [[CMP1:%.*]] = icmp ult i32 [[N]], [[LIMIT]]
; CHECK-NEXT:    [[CMP2:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
; CHECK-NEXT:    [[AND:%.*]] = and i1 [[CMP1]], [[CMP2]]
; CHECK-NEXT:    br i1 [[AND]], label [[THEN:%.*]], label [[ELSE:%.*]]
; CHECK:       then:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    [[Q:%.*]] = udiv i32 [[X]], [[N]]
; CHECK-NEXT:    [[RES:%.*]] = and i1 true, true
; CHECK-NEXT:    ret i1 [[RES]]
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
  %cmp1 = icmp ult i32 %n, %limit
  %cmp2 = icmp ule i32 %x, %limit
  %and = and i1 %cmp1, %cmp2
  br i1 %and, label %then, label %else

then:
  %r = urem i32 %x, %n
  %q = udiv i32 %x, %n
  %cmp3 = icmp ule i32 %r, %limit
  %cmp4 = icmp ule i32 %q, %limit
  %res = and i1 %cmp3, %cmp4
  ret i1 %res

else:
  ret i1 false
}

define i1 @urem_i64(i64 noundef %x, i64 noundef %n, i64 noundef %m) {
; CHECK-LABEL: define i1 @urem_i64(
; CHECK-SAME: i64 noundef [[X:%.*]], i64 noundef [[N:%.*]], i64 noundef [[M:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i64 [[N]], [[M]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = urem i64 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    ret i1 true
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ult i64 %n, %m
  br i1 %cmp, label %mid, label %else

mid:
  %r = urem i64 %x, %n
  br label %check

check:
  %v = icmp ult i64 %r, %m
  ret i1 %v

else:
  ret i1 false
}

; Without noundef, isGuaranteedNotToBePoison may fail; don't add facts.
define i1 @neg_urem_no_noundef(i32 %x, i32 %n, i32 %m) {
; CHECK-LABEL: define i1 @neg_urem_no_noundef(
; CHECK-SAME: i32 [[X:%.*]], i32 [[N:%.*]], i32 [[M:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
; CHECK-NEXT:    ret i1 [[V]]
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ult i32 %n, %m
  br i1 %cmp, label %mid, label %else

mid:
  %r = urem i32 %x, %n
  br label %check

check:
  %v = icmp ult i32 %r, %m
  ret i1 %v

else:
  ret i1 false
}

define i1 @neg_udiv_no_noundef(i32 %x, i32 %n, i32 %limit) {
; CHECK-LABEL: define i1 @neg_udiv_no_noundef(
; CHECK-SAME: i32 [[X:%.*]], i32 [[N:%.*]], i32 [[LIMIT:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[X]], [[LIMIT]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[Q:%.*]] = udiv i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    [[V:%.*]] = icmp ule i32 [[Q]], [[LIMIT]]
; CHECK-NEXT:    ret i1 [[V]]
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ule i32 %x, %limit
  br i1 %cmp, label %mid, label %else

mid:
  %q = udiv i32 %x, %n
  br label %check

check:
  %v = icmp ule i32 %q, %limit
  ret i1 %v

else:
  ret i1 false
}

; srem/sdiv are NOT handled.
define i1 @neg_srem_not_handled(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
; CHECK-LABEL: define i1 @neg_srem_not_handled(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[N]], [[M]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = srem i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
; CHECK-NEXT:    ret i1 [[V]]
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ult i32 %n, %m
  br i1 %cmp, label %mid, label %else

mid:
  %r = srem i32 %x, %n
  br label %check

check:
  %v = icmp ult i32 %r, %m
  ret i1 %v

else:
  ret i1 false
}

; No dominating constraint relating n to m; can't simplify.
define i1 @neg_no_dominating_fact(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
; CHECK-LABEL: define i1 @neg_no_dominating_fact(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
; CHECK-NEXT:    ret i1 [[V]]
;
  %r = urem i32 %x, %n
  %v = icmp ult i32 %r, %m
  ret i1 %v
}

; Wrong direction: m < n, r < n, but r < m is NOT implied.
define i1 @neg_wrong_direction(i32 noundef %x, i32 noundef %n, i32 noundef %m) {
; CHECK-LABEL: define i1 @neg_wrong_direction(
; CHECK-SAME: i32 noundef [[X:%.*]], i32 noundef [[N:%.*]], i32 noundef [[M:%.*]]) {
; CHECK-NEXT:  entry:
; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 [[M]], [[N]]
; CHECK-NEXT:    br i1 [[CMP]], label [[MID:%.*]], label [[ELSE:%.*]]
; CHECK:       mid:
; CHECK-NEXT:    [[R:%.*]] = urem i32 [[X]], [[N]]
; CHECK-NEXT:    br label [[CHECK:%.*]]
; CHECK:       check:
; CHECK-NEXT:    [[V:%.*]] = icmp ult i32 [[R]], [[M]]
; CHECK-NEXT:    ret i1 [[V]]
; CHECK:       else:
; CHECK-NEXT:    ret i1 false
;
entry:
  %cmp = icmp ult i32 %m, %n
  br i1 %cmp, label %mid, label %else

mid:
  %r = urem i32 %x, %n
  br label %check

check:
  %v = icmp ult i32 %r, %m
  ret i1 %v

else:
  ret i1 false
}