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diff --git a/test/Transforms/InstSimplify/implies.ll b/test/Transforms/InstSimplify/implies.ll
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+; RUN: opt -S %s -instsimplify | FileCheck %s
+
+; A ==> A -> true
+define i1 @test(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test
+; CHECK: ret i1 true
+ %var29 = icmp slt i32 %i, %length.i
+ %res = icmp uge i1 %var29, %var29
+ ret i1 %res
+}
+
+; i +_{nsw} C_{>0} <s L ==> i <s L -> true
+define i1 @test2(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2
+; CHECK: ret i1 true
+ %iplus1 = add nsw i32 %i, 1
+ %var29 = icmp slt i32 %i, %length.i
+ %var30 = icmp slt i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+; i + C_{>0} <s L ==> i <s L -> unknown without the nsw
+define i1 @test2_neg(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2_neg
+; CHECK: ret i1 %res
+ %iplus1 = add i32 %i, 1
+ %var29 = icmp slt i32 %i, %length.i
+ %var30 = icmp slt i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+; sle is not implication
+define i1 @test2_neg2(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2_neg2
+; CHECK: ret i1 %res
+ %iplus1 = add i32 %i, 1
+ %var29 = icmp slt i32 %i, %length.i
+ %var30 = icmp slt i32 %iplus1, %length.i
+ %res = icmp sle i1 %var30, %var29
+ ret i1 %res
+}
+
+; The binary operator has to be an add
+define i1 @test2_neg3(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test2_neg3
+; CHECK: ret i1 %res
+ %iplus1 = sub nsw i32 %i, 1
+ %var29 = icmp slt i32 %i, %length.i
+ %var30 = icmp slt i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+; i +_{nsw} C_{>0} <s L ==> i <s L -> true
+; With an inverted conditional (ule B A rather than canonical ugt A B
+define i1 @test3(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test3
+; CHECK: ret i1 true
+ %iplus1 = add nsw i32 %i, 1
+ %var29 = icmp slt i32 %i, %length.i
+ %var30 = icmp slt i32 %iplus1, %length.i
+ %res = icmp uge i1 %var29, %var30
+ ret i1 %res
+}
+
+; i +_{nuw} C <u L ==> i <u L
+define i1 @test4(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test4
+; CHECK: ret i1 true
+ %iplus1 = add nuw i32 %i, 1
+ %var29 = icmp ult i32 %i, %length.i
+ %var30 = icmp ult i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+; A ==> A for vectors
+define <4 x i1> @test5(<4 x i1> %vec) {
+; CHECK-LABEL: @test5
+; CHECK: ret <4 x i1> <i1 true, i1 true, i1 true, i1 true>
+ %res = icmp ule <4 x i1> %vec, %vec
+ ret <4 x i1> %res
+}
+
+; Don't crash on vector inputs - pr25040
+define <4 x i1> @test6(<4 x i1> %a, <4 x i1> %b) {
+; CHECK-LABEL: @test6
+; CHECK: ret <4 x i1> %res
+ %res = icmp ule <4 x i1> %a, %b
+ ret <4 x i1> %res
+}
+
+; i +_{nsw} 1 <s L ==> i < L +_{nsw} 1
+define i1 @test7(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test7(
+; CHECK: ret i1 true
+ %iplus1 = add nsw i32 %i, 1
+ %len.plus.one = add nsw i32 %length.i, 1
+ %var29 = icmp slt i32 %i, %len.plus.one
+ %var30 = icmp slt i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+; i +_{nuw} 1 <s L ==> i < L +_{nuw} 1
+define i1 @test8(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test8(
+; CHECK: ret i1 true
+ %iplus1 = add nuw i32 %i, 1
+ %len.plus.one = add nuw i32 %length.i, 1
+ %var29 = icmp ult i32 %i, %len.plus.one
+ %var30 = icmp ult i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+; i +_{nuw} C <s L ==> i < L, even if C is negative
+define i1 @test9(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test9(
+; CHECK: ret i1 true
+ %iplus1 = add nuw i32 %i, -100
+ %var29 = icmp ult i32 %i, %length.i
+ %var30 = icmp ult i32 %iplus1, %length.i
+ %res = icmp ule i1 %var30, %var29
+ ret i1 %res
+}
+
+define i1 @test10(i32 %length.i, i32 %x.full) {
+; CHECK-LABEL: @test10(
+; CHECK: ret i1 true
+
+ %x = and i32 %x.full, 4294901760 ;; 4294901760 == 0xffff0000
+ %large = or i32 %x, 100
+ %small = or i32 %x, 90
+ %known = icmp ult i32 %large, %length.i
+ %to.prove = icmp ult i32 %small, %length.i
+ %res = icmp ule i1 %known, %to.prove
+ ret i1 %res
+}
+
+define i1 @test11(i32 %length.i, i32 %x) {
+; CHECK-LABEL: @test11(
+; CHECK: %res = icmp ule i1 %known, %to.prove
+; CHECK: ret i1 %res
+
+ %large = or i32 %x, 100
+ %small = or i32 %x, 90
+ %known = icmp ult i32 %large, %length.i
+ %to.prove = icmp ult i32 %small, %length.i
+ %res = icmp ule i1 %known, %to.prove
+ ret i1 %res
+}
+
+define i1 @test12(i32 %length.i, i32 %x.full) {
+; CHECK-LABEL: @test12(
+; CHECK: %res = icmp ule i1 %known, %to.prove
+; CHECK: ret i1 %res
+
+ %x = and i32 %x.full, 4294901760 ;; 4294901760 == 0xffff0000
+ %large = or i32 %x, 65536 ;; 65536 == 0x00010000
+ %small = or i32 %x, 90
+ %known = icmp ult i32 %large, %length.i
+ %to.prove = icmp ult i32 %small, %length.i
+ %res = icmp ule i1 %known, %to.prove
+ ret i1 %res
+}
+
+define i1 @test13(i32 %length.i, i32 %x) {
+; CHECK-LABEL: @test13(
+; CHECK: ret i1 true
+
+ %large = add nuw i32 %x, 100
+ %small = add nuw i32 %x, 90
+ %known = icmp ult i32 %large, %length.i
+ %to.prove = icmp ult i32 %small, %length.i
+ %res = icmp ule i1 %known, %to.prove
+ ret i1 %res
+}
+
+define i1 @test14(i32 %length.i, i32 %x.full) {
+; CHECK-LABEL: @test14(
+; CHECK: ret i1 true
+
+ %x = and i32 %x.full, 4294905615 ;; 4294905615 == 0xffff0f0f
+ %large = or i32 %x, 8224 ;; == 0x2020
+ %small = or i32 %x, 4112 ;; == 0x1010
+ %known = icmp ult i32 %large, %length.i
+ %to.prove = icmp ult i32 %small, %length.i
+ %res = icmp ule i1 %known, %to.prove
+ ret i1 %res
+}
+
+define i1 @test15(i32 %length.i, i32 %x) {
+; CHECK-LABEL: @test15(
+; CHECK: %res = icmp ule i1 %known, %to.prove
+; CHECK: ret i1 %res
+
+ %large = add nuw i32 %x, 100
+ %small = add nuw i32 %x, 110
+ %known = icmp ult i32 %large, %length.i
+ %to.prove = icmp ult i32 %small, %length.i
+ %res = icmp ule i1 %known, %to.prove
+ ret i1 %res
+}
+
+; X >=(s) Y == X ==> Y (i1 1 becomes -1 for reasoning)
+define i1 @test_sge(i32 %length.i, i32 %i) {
+; CHECK-LABEL: @test_sge
+; CHECK: ret i1 true
+ %iplus1 = add nsw nuw i32 %i, 1
+ %var29 = icmp ult i32 %i, %length.i
+ %var30 = icmp ult i32 %iplus1, %length.i
+ %res = icmp sge i1 %var30, %var29
+ ret i1 %res
+}