; LLVM IR from TheAlgorithms/C-Plus-Plus :: numerical_methods/qr_eigen_values.ll (ZN12qr_algorithm12eigen_valuesEPSt8valarrayIS0_IdEEb)

; Unoptimized IR (clang -disable-llvm-passes):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }
%"class.std::valarray.0" = type { i64, ptr }
%"class.std::valarray" = type { i64, ptr }

@_ZSt4cout = external global %"class.std::basic_ostream", align 8
@.str.1 = external hidden unnamed_addr constant [2 x i8], align 1
@.str.2 = external hidden unnamed_addr constant [47 x i8], align 1
@.str.3 = external hidden unnamed_addr constant [26 x i8], align 1
@.str.4 = external hidden unnamed_addr constant [14 x i8], align 1
@.str.5 = external hidden unnamed_addr constant [3 x i8], align 1

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef i64 @_ZNKSt8valarrayIS_IdEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(16)) #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) #1 align 2

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z7mat_mulRKSt8valarrayIS_IdEES3_PS1_(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 8 dereferenceable(16), ptr noundef) #2

; Function Attrs: mustprogress uwtable
define dso_local void @_ZN12qr_algorithm12eigen_valuesEPSt8valarrayIS0_IdEEb(ptr dead_on_unwind noalias writable sret(%"class.std::valarray.0") align 8 %0, ptr noundef %1, i1 noundef zeroext %2) #2 personality ptr @__gxx_personality_v0 {
  %4 = alloca ptr, align 8
  %5 = alloca ptr, align 8
  %6 = alloca i8, align 1
  %7 = alloca i32, align 4
  %8 = alloca i32, align 4
  %9 = alloca i32, align 4
  %10 = alloca i32, align 4
  %11 = alloca double, align 8
  %12 = alloca %"class.std::valarray", align 8
  %13 = alloca %"class.std::valarray", align 8
  %14 = alloca ptr, align 8
  %15 = alloca i32, align 4
  %16 = alloca i1, align 1
  %17 = alloca i32, align 4
  %18 = alloca %"class.std::valarray.0", align 8
  %19 = alloca %"class.std::valarray.0", align 8
  %20 = alloca i32, align 4
  %21 = alloca i32, align 4
  store ptr %0, ptr %4, align 8
  store ptr %1, ptr %5, align 8, !tbaa !5
  %22 = zext i1 %2 to i8
  store i8 %22, ptr %6, align 1, !tbaa !9
  call void @llvm.lifetime.start.p0(i64 4, ptr %7) #6
  %23 = load ptr, ptr %5, align 8, !tbaa !5
  %24 = call noundef i64 @_ZNKSt8valarrayIS_IdEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(16) %23)
  %25 = trunc i64 %24 to i32
  store i32 %25, ptr %7, align 4, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 4, ptr %8) #6
  %26 = load i32, ptr %7, align 4, !tbaa !11
  store i32 %26, ptr %8, align 4, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 4, ptr %9) #6
  store i32 0, ptr %9, align 4, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 4, ptr %10) #6
  %27 = load i32, ptr %7, align 4, !tbaa !11
  %28 = sub nsw i32 %27, 1
  store i32 %28, ptr %10, align 4, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 8, ptr %11) #6
  store double 0.000000e+00, ptr %11, align 8, !tbaa !13
  call void @llvm.lifetime.start.p0(i64 16, ptr %12) #6
  %29 = load i32, ptr %7, align 4, !tbaa !11
  %30 = sext i32 %29 to i64
  call void @_ZNSt8valarrayIS_IdEEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %12, i64 noundef %30)
  call void @llvm.lifetime.start.p0(i64 16, ptr %13) #6
  %31 = load i32, ptr %8, align 4, !tbaa !11
  %32 = sext i32 %31 to i64
  invoke void @_ZNSt8valarrayIS_IdEEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %13, i64 noundef %32)
          to label %33 unwind label %42

33:                                               ; preds = %3
  store i1 false, ptr %16, align 1
  %34 = load i32, ptr %7, align 4, !tbaa !11
  %35 = sext i32 %34 to i64
  invoke void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %0, i64 noundef %35)
          to label %36 unwind label %46

36:                                               ; preds = %33
  call void @llvm.lifetime.start.p0(i64 4, ptr %17) #6
  store i32 0, ptr %17, align 4, !tbaa !11
  br label %37

37:                                               ; preds = %65, %36
  %38 = load i32, ptr %17, align 4, !tbaa !11
  %39 = load i32, ptr %7, align 4, !tbaa !11
  %40 = icmp slt i32 %38, %39
  br i1 %40, label %50, label %41

41:                                               ; preds = %37
  call void @llvm.lifetime.end.p0(i64 4, ptr %17) #6
  br label %77

42:                                               ; preds = %3
  %43 = landingpad { ptr, i32 }
          cleanup
  %44 = extractvalue { ptr, i32 } %43, 0
  store ptr %44, ptr %14, align 8
  %45 = extractvalue { ptr, i32 } %43, 1
  store i32 %45, ptr %15, align 4
  br label %228

46:                                               ; preds = %33
  %47 = landingpad { ptr, i32 }
          cleanup
  %48 = extractvalue { ptr, i32 } %47, 0
  store ptr %48, ptr %14, align 8
  %49 = extractvalue { ptr, i32 } %47, 1
  store i32 %49, ptr %15, align 4
  br label %227

50:                                               ; preds = %37
  call void @llvm.lifetime.start.p0(i64 16, ptr %18) #6
  %51 = load i32, ptr %8, align 4, !tbaa !11
  %52 = sext i32 %51 to i64
  invoke void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %18, i64 noundef %52)
          to label %53 unwind label %68

53:                                               ; preds = %50
  %54 = load i32, ptr %17, align 4, !tbaa !11
  %55 = sext i32 %54 to i64
  %56 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %12, i64 noundef %55) #6
  %57 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIdEaSEOS0_(ptr noundef nonnull align 8 dereferenceable(16) %56, ptr noundef nonnull align 8 dereferenceable(16) %18) #6
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %18) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr %18) #6
  call void @llvm.lifetime.start.p0(i64 16, ptr %19) #6
  %58 = load i32, ptr %8, align 4, !tbaa !11
  %59 = sext i32 %58 to i64
  invoke void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %19, i64 noundef %59)
          to label %60 unwind label %72

60:                                               ; preds = %53
  %61 = load i32, ptr %17, align 4, !tbaa !11
  %62 = sext i32 %61 to i64
  %63 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %13, i64 noundef %62) #6
  %64 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIdEaSEOS0_(ptr noundef nonnull align 8 dereferenceable(16) %63, ptr noundef nonnull align 8 dereferenceable(16) %19) #6
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %19) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr %19) #6
  br label %65

65:                                               ; preds = %60
  %66 = load i32, ptr %17, align 4, !tbaa !11
  %67 = add nsw i32 %66, 1
  store i32 %67, ptr %17, align 4, !tbaa !11
  br label %37, !llvm.loop !15

68:                                               ; preds = %50
  %69 = landingpad { ptr, i32 }
          cleanup
  %70 = extractvalue { ptr, i32 } %69, 0
  store ptr %70, ptr %14, align 8
  %71 = extractvalue { ptr, i32 } %69, 1
  store i32 %71, ptr %15, align 4
  call void @llvm.lifetime.end.p0(i64 16, ptr %18) #6
  br label %76

72:                                               ; preds = %53
  %73 = landingpad { ptr, i32 }
          cleanup
  %74 = extractvalue { ptr, i32 } %73, 0
  store ptr %74, ptr %14, align 8
  %75 = extractvalue { ptr, i32 } %73, 1
  store i32 %75, ptr %15, align 4
  call void @llvm.lifetime.end.p0(i64 16, ptr %19) #6
  br label %76

76:                                               ; preds = %72, %68
  call void @llvm.lifetime.end.p0(i64 4, ptr %17) #6
  br label %226

77:                                               ; preds = %41
  br label %78

78:                                               ; preds = %197, %77
  %79 = load i32, ptr %10, align 4, !tbaa !11
  %80 = icmp sgt i32 %79, 0
  br i1 %80, label %81, label %204

81:                                               ; preds = %78
  br label %82

82:                                               ; preds = %177, %81
  %83 = load ptr, ptr %5, align 8, !tbaa !5
  %84 = getelementptr inbounds %"class.std::valarray", ptr %83, i64 0
  %85 = load i32, ptr %10, align 4, !tbaa !11
  %86 = sext i32 %85 to i64
  %87 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %84, i64 noundef %86) #6
  %88 = load i32, ptr %10, align 4, !tbaa !11
  %89 = sub nsw i32 %88, 1
  %90 = sext i32 %89 to i64
  %91 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %87, i64 noundef %90) #6
  %92 = load double, ptr %91, align 8, !tbaa !13
  %93 = invoke noundef double @_ZSt3absd(double noundef %92)
          to label %94 unwind label %112

94:                                               ; preds = %82
  %95 = call noundef double @_ZNSt14numeric_limitsIdE7epsilonEv() #6
  %96 = fcmp ogt double %93, %95
  br i1 %96, label %97, label %178

97:                                               ; preds = %94
  %98 = load ptr, ptr %5, align 8, !tbaa !5
  %99 = getelementptr inbounds %"class.std::valarray", ptr %98, i64 0
  %100 = load i32, ptr %10, align 4, !tbaa !11
  %101 = sext i32 %100 to i64
  %102 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %99, i64 noundef %101) #6
  %103 = load i32, ptr %10, align 4, !tbaa !11
  %104 = sext i32 %103 to i64
  %105 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %102, i64 noundef %104) #6
  %106 = load double, ptr %105, align 8, !tbaa !13
  store double %106, ptr %11, align 8, !tbaa !13
  call void @llvm.lifetime.start.p0(i64 4, ptr %20) #6
  store i32 0, ptr %20, align 4, !tbaa !11
  br label %107

107:                                              ; preds = %128, %97
  %108 = load i32, ptr %20, align 4, !tbaa !11
  %109 = load i32, ptr %7, align 4, !tbaa !11
  %110 = icmp slt i32 %108, %109
  br i1 %110, label %116, label %111

111:                                              ; preds = %107
  call void @llvm.lifetime.end.p0(i64 4, ptr %20) #6
  br label %131

112:                                              ; preds = %219, %217, %215, %213, %194, %192, %189, %187, %185, %154, %149, %147, %145, %143, %141, %139, %136, %131, %82
  %113 = landingpad { ptr, i32 }
          cleanup
  %114 = extractvalue { ptr, i32 } %113, 0
  store ptr %114, ptr %14, align 8
  %115 = extractvalue { ptr, i32 } %113, 1
  store i32 %115, ptr %15, align 4
  br label %226

116:                                              ; preds = %107
  %117 = load double, ptr %11, align 8, !tbaa !13
  %118 = load ptr, ptr %5, align 8, !tbaa !5
  %119 = getelementptr inbounds %"class.std::valarray", ptr %118, i64 0
  %120 = load i32, ptr %20, align 4, !tbaa !11
  %121 = sext i32 %120 to i64
  %122 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %119, i64 noundef %121) #6
  %123 = load i32, ptr %20, align 4, !tbaa !11
  %124 = sext i32 %123 to i64
  %125 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %122, i64 noundef %124) #6
  %126 = load double, ptr %125, align 8, !tbaa !13
  %127 = fsub double %126, %117
  store double %127, ptr %125, align 8, !tbaa !13
  br label %128

128:                                              ; preds = %116
  %129 = load i32, ptr %20, align 4, !tbaa !11
  %130 = add nsw i32 %129, 1
  store i32 %130, ptr %20, align 4, !tbaa !11
  br label %107, !llvm.loop !17

131:                                              ; preds = %111
  %132 = load ptr, ptr %5, align 8, !tbaa !5
  invoke void @_ZN12qr_algorithm12qr_decomposeIdEEvRKSt8valarrayIS1_IT_EEPS4_S7_(ptr noundef nonnull align 8 dereferenceable(16) %132, ptr noundef %12, ptr noundef %13)
          to label %133 unwind label %112

133:                                              ; preds = %131
  %134 = load i8, ptr %6, align 1, !tbaa !9, !range !18, !noundef !19
  %135 = trunc i8 %134 to i1
  br i1 %135, label %136, label %154

136:                                              ; preds = %133
  %137 = load ptr, ptr %5, align 8, !tbaa !5
  %138 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %137)
          to label %139 unwind label %112

139:                                              ; preds = %136
  %140 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %138, ptr noundef @.str.1)
          to label %141 unwind label %112

141:                                              ; preds = %139
  %142 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %12)
          to label %143 unwind label %112

143:                                              ; preds = %141
  %144 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %142, ptr noundef @.str.1)
          to label %145 unwind label %112

145:                                              ; preds = %143
  %146 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %13)
          to label %147 unwind label %112

147:                                              ; preds = %145
  %148 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %146, ptr noundef @.str.1)
          to label %149 unwind label %112

149:                                              ; preds = %147
  %150 = load i32, ptr %9, align 4, !tbaa !11
  %151 = add nsw i32 %150, 1
  store i32 %151, ptr %9, align 4, !tbaa !11
  %152 = invoke i32 (ptr, ...) @printf(ptr noundef @.str.2, i32 noundef %151)
          to label %153 unwind label %112

153:                                              ; preds = %149
  br label %154

154:                                              ; preds = %153, %133
  %155 = load ptr, ptr %5, align 8, !tbaa !5
  invoke void @_Z7mat_mulRKSt8valarrayIS_IdEES3_PS1_(ptr noundef nonnull align 8 dereferenceable(16) %13, ptr noundef nonnull align 8 dereferenceable(16) %12, ptr noundef %155)
          to label %156 unwind label %112

156:                                              ; preds = %154
  call void @llvm.lifetime.start.p0(i64 4, ptr %21) #6
  store i32 0, ptr %21, align 4, !tbaa !11
  br label %157

157:                                              ; preds = %174, %156
  %158 = load i32, ptr %21, align 4, !tbaa !11
  %159 = load i32, ptr %7, align 4, !tbaa !11
  %160 = icmp slt i32 %158, %159
  br i1 %160, label %162, label %161

161:                                              ; preds = %157
  call void @llvm.lifetime.end.p0(i64 4, ptr %21) #6
  br label %177

162:                                              ; preds = %157
  %163 = load double, ptr %11, align 8, !tbaa !13
  %164 = load ptr, ptr %5, align 8, !tbaa !5
  %165 = getelementptr inbounds %"class.std::valarray", ptr %164, i64 0
  %166 = load i32, ptr %21, align 4, !tbaa !11
  %167 = sext i32 %166 to i64
  %168 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %165, i64 noundef %167) #6
  %169 = load i32, ptr %21, align 4, !tbaa !11
  %170 = sext i32 %169 to i64
  %171 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %168, i64 noundef %170) #6
  %172 = load double, ptr %171, align 8, !tbaa !13
  %173 = fadd double %172, %163
  store double %173, ptr %171, align 8, !tbaa !13
  br label %174

174:                                              ; preds = %162
  %175 = load i32, ptr %21, align 4, !tbaa !11
  %176 = add nsw i32 %175, 1
  store i32 %176, ptr %21, align 4, !tbaa !11
  br label %157, !llvm.loop !20

177:                                              ; preds = %161
  br label %82, !llvm.loop !21

178:                                              ; preds = %94
  %179 = load double, ptr %11, align 8, !tbaa !13
  %180 = load i32, ptr %10, align 4, !tbaa !11
  %181 = sext i32 %180 to i64
  %182 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %0, i64 noundef %181) #6
  store double %179, ptr %182, align 8, !tbaa !13
  %183 = load i8, ptr %6, align 1, !tbaa !9, !range !18, !noundef !19
  %184 = trunc i8 %183 to i1
  br i1 %184, label %185, label %197

185:                                              ; preds = %178
  %186 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef @.str.3)
          to label %187 unwind label %112

187:                                              ; preds = %185
  %188 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef @.str.4)
          to label %189 unwind label %112

189:                                              ; preds = %187
  %190 = load double, ptr %11, align 8, !tbaa !13
  %191 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8) %188, double noundef %190)
          to label %192 unwind label %112

192:                                              ; preds = %189
  %193 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %191, ptr noundef @.str.5)
          to label %194 unwind label %112

194:                                              ; preds = %192
  %195 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef @.str.3)
          to label %196 unwind label %112

196:                                              ; preds = %194
  br label %197

197:                                              ; preds = %196, %178
  %198 = load i32, ptr %10, align 4, !tbaa !11
  %199 = add nsw i32 %198, -1
  store i32 %199, ptr %10, align 4, !tbaa !11
  %200 = load i32, ptr %7, align 4, !tbaa !11
  %201 = add nsw i32 %200, -1
  store i32 %201, ptr %7, align 4, !tbaa !11
  %202 = load i32, ptr %8, align 4, !tbaa !11
  %203 = add nsw i32 %202, -1
  store i32 %203, ptr %8, align 4, !tbaa !11
  br label %78, !llvm.loop !22

204:                                              ; preds = %78
  %205 = load ptr, ptr %5, align 8, !tbaa !5
  %206 = getelementptr inbounds %"class.std::valarray", ptr %205, i64 0
  %207 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %206, i64 noundef 0) #6
  %208 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %207, i64 noundef 0) #6
  %209 = load double, ptr %208, align 8, !tbaa !13
  %210 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %0, i64 noundef 0) #6
  store double %209, ptr %210, align 8, !tbaa !13
  %211 = load i8, ptr %6, align 1, !tbaa !9, !range !18, !noundef !19
  %212 = trunc i8 %211 to i1
  br i1 %212, label %213, label %222

213:                                              ; preds = %204
  %214 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %12)
          to label %215 unwind label %112

215:                                              ; preds = %213
  %216 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %214, ptr noundef @.str.1)
          to label %217 unwind label %112

217:                                              ; preds = %215
  %218 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %13)
          to label %219 unwind label %112

219:                                              ; preds = %217
  %220 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %218, ptr noundef @.str.1)
          to label %221 unwind label %112

221:                                              ; preds = %219
  br label %222

222:                                              ; preds = %221, %204
  store i1 true, ptr %16, align 1
  %223 = load i1, ptr %16, align 1
  br i1 %223, label %225, label %224

224:                                              ; preds = %222
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %0) #6
  br label %225

225:                                              ; preds = %224, %222
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %13) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr %13) #6
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %12) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr %12) #6
  call void @llvm.lifetime.end.p0(i64 8, ptr %11) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %10) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %9) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %8) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %7) #6
  ret void

226:                                              ; preds = %112, %76
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %0) #6
  br label %227

227:                                              ; preds = %226, %46
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %13) #6
  br label %228

228:                                              ; preds = %227, %42
  call void @llvm.lifetime.end.p0(i64 16, ptr %13) #6
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %12) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr %12) #6
  call void @llvm.lifetime.end.p0(i64 8, ptr %11) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %10) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %9) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %8) #6
  call void @llvm.lifetime.end.p0(i64 4, ptr %7) #6
  br label %229

229:                                              ; preds = %228
  %230 = load ptr, ptr %14, align 8
  %231 = load i32, ptr %15, align 4
  %232 = insertvalue { ptr, i32 } poison, ptr %230, 0
  %233 = insertvalue { ptr, i32 } %232, i32 %231, 1
  resume { ptr, i32 } %233
}

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local void @_ZNSt8valarrayIS_IdEEC2Em(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) unnamed_addr #3 align 2

declare i32 @__gxx_personality_v0(...)

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) unnamed_addr #3 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIdEaSEOS0_(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 8 dereferenceable(16)) #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16)) unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef double @_ZSt3absd(double noundef) #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef double @_ZNSt14numeric_limitsIdE7epsilonEv() #4 align 2

; Function Attrs: mustprogress uwtable
declare dso_local void @_ZN12qr_algorithm12qr_decomposeIdEEvRKSt8valarrayIS1_IT_EEPS4_S7_(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef, ptr noundef) #2

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8), ptr noundef) #3

; Function Attrs: mustprogress uwtable
declare dso_local noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8), ptr noundef nonnull align 8 dereferenceable(16)) #2

declare i32 @printf(ptr noundef, ...) #5

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8), double noundef) #2 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16)) unnamed_addr #1 align 2

attributes #0 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { inlinehint mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { inlinehint mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #4 = { mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #5 = { "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #6 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"any pointer", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}
!9 = !{!10, !10, i64 0}
!10 = !{!"bool", !7, i64 0}
!11 = !{!12, !12, i64 0}
!12 = !{!"int", !7, i64 0}
!13 = !{!14, !14, i64 0}
!14 = !{!"double", !7, i64 0}
!15 = distinct !{!15, !16}
!16 = !{!"llvm.loop.mustprogress"}
!17 = distinct !{!17, !16}
!18 = !{i8 0, i8 2}
!19 = !{}
!20 = distinct !{!20, !16}
!21 = distinct !{!21, !16}
!22 = distinct !{!22, !16}


; Optimized IR (opt -passes='default<O3>'):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }
%"class.std::valarray.0" = type { i64, ptr }
%"class.std::valarray" = type { i64, ptr }

@_ZSt4cout = external global %"class.std::basic_ostream", align 8
@.str.1 = external hidden unnamed_addr constant [2 x i8], align 1
@.str.2 = external hidden unnamed_addr constant [47 x i8], align 1
@.str.3 = external hidden unnamed_addr constant [26 x i8], align 1
@.str.4 = external hidden unnamed_addr constant [14 x i8], align 1
@.str.5 = external hidden unnamed_addr constant [3 x i8], align 1

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef i64 @_ZNKSt8valarrayIS_IdEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(16)) local_unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) local_unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) local_unnamed_addr #1 align 2

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z7mat_mulRKSt8valarrayIS_IdEES3_PS1_(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 8 dereferenceable(16), ptr noundef) local_unnamed_addr #2

; Function Attrs: mustprogress uwtable
define dso_local void @_ZN12qr_algorithm12eigen_valuesEPSt8valarrayIS0_IdEEb(ptr dead_on_unwind noalias writable sret(%"class.std::valarray.0") align 8 %0, ptr noundef nonnull %1, i1 noundef zeroext %2) local_unnamed_addr #2 personality ptr @__gxx_personality_v0 {
  %4 = alloca %"class.std::valarray", align 8
  %5 = alloca %"class.std::valarray", align 8
  %6 = alloca %"class.std::valarray.0", align 8
  %7 = alloca %"class.std::valarray.0", align 8
  %8 = tail call noundef i64 @_ZNKSt8valarrayIS_IdEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(16) %1)
  %9 = trunc i64 %8 to i32
  call void @llvm.lifetime.start.p0(i64 16, ptr nonnull %4) #6
  %sext = shl i64 %8, 32
  %10 = ashr exact i64 %sext, 32
  call void @_ZNSt8valarrayIS_IdEEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %4, i64 noundef %10)
  call void @llvm.lifetime.start.p0(i64 16, ptr nonnull %5) #6
  invoke void @_ZNSt8valarrayIS_IdEEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %5, i64 noundef %10)
          to label %11 unwind label %14

11:                                               ; preds = %3
  invoke void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %0, i64 noundef %10)
          to label %.preheader76 unwind label %16

.preheader76:                                     ; preds = %11
  %12 = icmp sgt i32 %9, 0
  br i1 %12, label %.lr.ph.preheader, label %._crit_edge96

.lr.ph.preheader:                                 ; preds = %.preheader76
  %wide.trip.count = and i64 %8, 2147483647
  br label %.lr.ph

.preheader72:                                     ; preds = %21
  %.not = icmp eq i32 %9, 1
  br i1 %.not, label %._crit_edge96, label %.preheader70.preheader

.preheader70.preheader:                           ; preds = %.preheader72
  %13 = and i64 %8, 2147483647
  br label %.preheader70

14:                                               ; preds = %3
  %15 = landingpad { ptr, i32 }
          cleanup
  br label %96

16:                                               ; preds = %11
  %17 = landingpad { ptr, i32 }
          cleanup
  br label %95

.lr.ph:                                           ; preds = %.lr.ph.preheader, %21
  %indvars.iv = phi i64 [ 0, %.lr.ph.preheader ], [ %indvars.iv.next, %21 ]
  call void @llvm.lifetime.start.p0(i64 16, ptr nonnull %6) #6
  invoke void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %6, i64 noundef %10)
          to label %18 unwind label %24

18:                                               ; preds = %.lr.ph
  %19 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %4, i64 noundef %indvars.iv) #6
  %20 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIdEaSEOS0_(ptr noundef nonnull align 8 dereferenceable(16) %19, ptr noundef nonnull align 8 dereferenceable(16) %6) #6
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %6) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %6) #6
  call void @llvm.lifetime.start.p0(i64 16, ptr nonnull %7) #6
  invoke void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16) %7, i64 noundef %10)
          to label %21 unwind label %26

21:                                               ; preds = %18
  %22 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %5, i64 noundef %indvars.iv) #6
  %23 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIdEaSEOS0_(ptr noundef nonnull align 8 dereferenceable(16) %22, ptr noundef nonnull align 8 dereferenceable(16) %7) #6
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %7) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %7) #6
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %exitcond.not = icmp eq i64 %indvars.iv.next, %wide.trip.count
  br i1 %exitcond.not, label %.preheader72, label %.lr.ph, !llvm.loop !5

24:                                               ; preds = %.lr.ph
  %25 = landingpad { ptr, i32 }
          cleanup
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %6) #6
  br label %.loopexit.split-lp

26:                                               ; preds = %18
  %27 = landingpad { ptr, i32 }
          cleanup
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %7) #6
  br label %.loopexit.split-lp

.preheader70:                                     ; preds = %.preheader70.preheader, %80
  %indvars.iv109 = phi i64 [ %13, %.preheader70.preheader ], [ %indvars.iv.next110, %80 ]
  %.05794 = phi double [ 0.000000e+00, %.preheader70.preheader ], [ %.158.lcssa, %80 ]
  %.06092 = phi i32 [ 0, %.preheader70.preheader ], [ %.161.lcssa, %80 ]
  %indvars.iv.next110 = add nsw i64 %indvars.iv109, -1
  %28 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %1, i64 noundef %indvars.iv.next110) #6
  %29 = add nsw i64 %indvars.iv109, -2
  %30 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %28, i64 noundef %29) #6
  %31 = load double, ptr %30, align 8, !tbaa !7
  %32 = call noundef double @_ZSt3absd(double noundef %31)
  %33 = call noundef double @_ZNSt14numeric_limitsIdE7epsilonEv() #6
  %34 = fcmp ogt double %32, %33
  br i1 %34, label %.lr.ph82.preheader, label %._crit_edge87

.loopexit:                                        ; preds = %.lr.ph84
  %35 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %1, i64 noundef %indvars.iv.next110) #6
  %36 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %35, i64 noundef %29) #6
  %37 = load double, ptr %36, align 8, !tbaa !7
  %38 = call noundef double @_ZSt3absd(double noundef %37)
  %39 = call noundef double @_ZNSt14numeric_limitsIdE7epsilonEv() #6
  %40 = fcmp ogt double %38, %39
  br i1 %40, label %.lr.ph82.preheader, label %._crit_edge87, !llvm.loop !11

.lr.ph82.preheader:                               ; preds = %.preheader70, %.loopexit
  %.16185 = phi i32 [ %.262, %.loopexit ], [ %.06092, %.preheader70 ]
  %41 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %1, i64 noundef %indvars.iv.next110) #6
  %42 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %41, i64 noundef %indvars.iv.next110) #6
  %43 = load double, ptr %42, align 8, !tbaa !7
  br label %.lr.ph82

._crit_edge:                                      ; preds = %.lr.ph82
  invoke void @_ZN12qr_algorithm12qr_decomposeIdEEvRKSt8valarrayIS1_IT_EEPS4_S7_(ptr noundef nonnull align 8 dereferenceable(16) %1, ptr noundef nonnull %4, ptr noundef nonnull %5)
          to label %48 unwind label %.loopexit71

.loopexit71:                                      ; preds = %._crit_edge, %49, %51, %53, %55, %57, %59, %64
  %lpad.loopexit = landingpad { ptr, i32 }
          cleanup
  br label %.loopexit.split-lp

.loopexit.split-lp.loopexit:                      ; preds = %78, %76, %74, %72, %70
  %lpad.loopexit73 = landingpad { ptr, i32 }
          cleanup
  br label %.loopexit.split-lp

.loopexit.split-lp.loopexit.split-lp:             ; preds = %92, %90, %88, %86
  %lpad.loopexit.split-lp74 = landingpad { ptr, i32 }
          cleanup
  br label %.loopexit.split-lp

.lr.ph82:                                         ; preds = %.lr.ph82.preheader, %.lr.ph82
  %indvars.iv99 = phi i64 [ 0, %.lr.ph82.preheader ], [ %indvars.iv.next100, %.lr.ph82 ]
  %44 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %1, i64 noundef %indvars.iv99) #6
  %45 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %44, i64 noundef %indvars.iv99) #6
  %46 = load double, ptr %45, align 8, !tbaa !7
  %47 = fsub double %46, %43
  store double %47, ptr %45, align 8, !tbaa !7
  %indvars.iv.next100 = add nuw nsw i64 %indvars.iv99, 1
  %exitcond103.not = icmp eq i64 %indvars.iv.next100, %indvars.iv109
  br i1 %exitcond103.not, label %._crit_edge, label %.lr.ph82, !llvm.loop !12

48:                                               ; preds = %._crit_edge
  br i1 %2, label %49, label %64

49:                                               ; preds = %48
  %50 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %1)
          to label %51 unwind label %.loopexit71

51:                                               ; preds = %49
  %52 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %50, ptr noundef nonnull @.str.1)
          to label %53 unwind label %.loopexit71

53:                                               ; preds = %51
  %54 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %4)
          to label %55 unwind label %.loopexit71

55:                                               ; preds = %53
  %56 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %54, ptr noundef nonnull @.str.1)
          to label %57 unwind label %.loopexit71

57:                                               ; preds = %55
  %58 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %5)
          to label %59 unwind label %.loopexit71

59:                                               ; preds = %57
  %60 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %58, ptr noundef nonnull @.str.1)
          to label %61 unwind label %.loopexit71

61:                                               ; preds = %59
  %62 = add nsw i32 %.16185, 1
  %63 = call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.2, i32 noundef %62)
  br label %64

64:                                               ; preds = %61, %48
  %.262 = phi i32 [ %62, %61 ], [ %.16185, %48 ]
  invoke void @_Z7mat_mulRKSt8valarrayIS_IdEES3_PS1_(ptr noundef nonnull align 8 dereferenceable(16) %5, ptr noundef nonnull align 8 dereferenceable(16) %4, ptr noundef nonnull %1)
          to label %.lr.ph84 unwind label %.loopexit71

.lr.ph84:                                         ; preds = %64, %.lr.ph84
  %indvars.iv104 = phi i64 [ %indvars.iv.next105, %.lr.ph84 ], [ 0, %64 ]
  %65 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %1, i64 noundef %indvars.iv104) #6
  %66 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %65, i64 noundef %indvars.iv104) #6
  %67 = load double, ptr %66, align 8, !tbaa !7
  %68 = fadd double %43, %67
  store double %68, ptr %66, align 8, !tbaa !7
  %indvars.iv.next105 = add nuw nsw i64 %indvars.iv104, 1
  %exitcond108.not = icmp eq i64 %indvars.iv.next105, %indvars.iv109
  br i1 %exitcond108.not, label %.loopexit, label %.lr.ph84, !llvm.loop !13

._crit_edge87:                                    ; preds = %.loopexit, %.preheader70
  %.161.lcssa = phi i32 [ %.06092, %.preheader70 ], [ %.262, %.loopexit ]
  %.158.lcssa = phi double [ %.05794, %.preheader70 ], [ %43, %.loopexit ]
  %69 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %0, i64 noundef %indvars.iv.next110) #6
  store double %.158.lcssa, ptr %69, align 8, !tbaa !7
  br i1 %2, label %70, label %80

70:                                               ; preds = %._crit_edge87
  %71 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull @.str.3)
          to label %72 unwind label %.loopexit.split-lp.loopexit

72:                                               ; preds = %70
  %73 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull @.str.4)
          to label %74 unwind label %.loopexit.split-lp.loopexit

74:                                               ; preds = %72
  %75 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8) %73, double noundef %.158.lcssa)
          to label %76 unwind label %.loopexit.split-lp.loopexit

76:                                               ; preds = %74
  %77 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %75, ptr noundef nonnull @.str.5)
          to label %78 unwind label %.loopexit.split-lp.loopexit

78:                                               ; preds = %76
  %79 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull @.str.3)
          to label %80 unwind label %.loopexit.split-lp.loopexit

80:                                               ; preds = %78, %._crit_edge87
  %81 = icmp sgt i64 %indvars.iv109, 2
  br i1 %81, label %.preheader70, label %._crit_edge96, !llvm.loop !14

._crit_edge96:                                    ; preds = %80, %.preheader76, %.preheader72
  %82 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIS_IdEEixEm(ptr noundef nonnull align 8 dereferenceable(16) %1, i64 noundef 0) #6
  %83 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %82, i64 noundef 0) #6
  %84 = load double, ptr %83, align 8, !tbaa !7
  %85 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSt8valarrayIdEixEm(ptr noundef nonnull align 8 dereferenceable(16) %0, i64 noundef 0) #6
  store double %84, ptr %85, align 8, !tbaa !7
  br i1 %2, label %86, label %94

86:                                               ; preds = %._crit_edge96
  %87 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %4)
          to label %88 unwind label %.loopexit.split-lp.loopexit.split-lp

88:                                               ; preds = %86
  %89 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %87, ptr noundef nonnull @.str.1)
          to label %90 unwind label %.loopexit.split-lp.loopexit.split-lp

90:                                               ; preds = %88
  %91 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull align 8 dereferenceable(16) %5)
          to label %92 unwind label %.loopexit.split-lp.loopexit.split-lp

92:                                               ; preds = %90
  %93 = invoke noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %91, ptr noundef nonnull @.str.1)
          to label %94 unwind label %.loopexit.split-lp.loopexit.split-lp

94:                                               ; preds = %._crit_edge96, %92
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %5) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %5) #6
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %4) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %4) #6
  ret void

.loopexit.split-lp:                               ; preds = %.loopexit71, %.loopexit.split-lp.loopexit.split-lp, %.loopexit.split-lp.loopexit, %24, %26
  %.pn.pn = phi { ptr, i32 } [ %27, %26 ], [ %25, %24 ], [ %lpad.loopexit, %.loopexit71 ], [ %lpad.loopexit73, %.loopexit.split-lp.loopexit ], [ %lpad.loopexit.split-lp74, %.loopexit.split-lp.loopexit.split-lp ]
  call void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %0) #6
  br label %95

95:                                               ; preds = %.loopexit.split-lp, %16
  %.pn.pn.pn = phi { ptr, i32 } [ %.pn.pn, %.loopexit.split-lp ], [ %17, %16 ]
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %5) #6
  br label %96

96:                                               ; preds = %95, %14
  %.pn.pn.pn.pn = phi { ptr, i32 } [ %.pn.pn.pn, %95 ], [ %15, %14 ]
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %5) #6
  call void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16) %4) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %4) #6
  resume { ptr, i32 } %.pn.pn.pn.pn
}

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local void @_ZNSt8valarrayIS_IdEEC2Em(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) unnamed_addr #3 align 2

declare i32 @__gxx_personality_v0(...)

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local void @_ZNSt8valarrayIdEC2Em(ptr noundef nonnull align 8 dereferenceable(16), i64 noundef) unnamed_addr #3 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(16) ptr @_ZNSt8valarrayIdEaSEOS0_(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 8 dereferenceable(16)) local_unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local void @_ZNSt8valarrayIdED2Ev(ptr noundef nonnull align 8 dereferenceable(16)) unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local noundef double @_ZSt3absd(double noundef) local_unnamed_addr #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef double @_ZNSt14numeric_limitsIdE7epsilonEv() local_unnamed_addr #4 align 2

; Function Attrs: mustprogress uwtable
declare dso_local void @_ZN12qr_algorithm12qr_decomposeIdEEvRKSt8valarrayIS1_IT_EEPS4_S7_(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef, ptr noundef) local_unnamed_addr #2

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8), ptr noundef) local_unnamed_addr #3

; Function Attrs: mustprogress uwtable
declare dso_local noundef nonnull align 8 dereferenceable(8) ptr @_ZN12qr_algorithmlsIdEERSoS1_RKSt8valarrayIS2_IT_EE(ptr noundef nonnull align 8 dereferenceable(8), ptr noundef nonnull align 8 dereferenceable(16)) local_unnamed_addr #2

; Function Attrs: nofree nounwind
declare noundef i32 @printf(ptr nocapture noundef readonly, ...) local_unnamed_addr #5

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8), double noundef) local_unnamed_addr #2 align 2

; Function Attrs: inlinehint mustprogress nounwind uwtable
declare dso_local void @_ZNSt8valarrayIS_IdEED2Ev(ptr noundef nonnull align 8 dereferenceable(16)) unnamed_addr #1 align 2

attributes #0 = { mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { inlinehint mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { inlinehint mustprogress uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #4 = { mustprogress nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #5 = { nofree nounwind "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #6 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = distinct !{!5, !6}
!6 = !{!"llvm.loop.mustprogress"}
!7 = !{!8, !8, i64 0}
!8 = !{!"double", !9, i64 0}
!9 = !{!"omnipotent char", !10, i64 0}
!10 = !{!"Simple C++ TBAA"}
!11 = distinct !{!11, !6}
!12 = distinct !{!12, !6}
!13 = distinct !{!13, !6}
!14 = distinct !{!14, !6}


; Effective O3 passes: EarlyCSEPass,GVNPass,GlobalOptPass,IPSCCPPass,IndVarSimplifyPass,InferFunctionAttrsPass,InstCombinePass,InstSimplifyPass,JumpThreadingPass,LCSSAPass,LICMPass,LoopInstSimplifyPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,PostOrderFunctionAttrsPass,ReassociatePass,SCCPPass,SROAPass,SimplifyCFGPass,TailCallElimPass