LAProof.C.cholesky

From Coq Require Import String List ZArith.
From compcert Require Import Coqlib Integers Floats AST Ctypes Cop Clight Clightdefs.
Import Clightdefs.ClightNotations.
Local Open Scope Z_scope.
Local Open Scope string_scope.
Local Open Scope clight_scope.

Module Info.
  Definition version := "3.15".
  Definition build_number := "".
  Definition build_tag := "".
  Definition build_branch := "".
  Definition arch := "aarch64".
  Definition model := "default".
  Definition abi := "apple".
  Definition bitsize := 64.
  Definition big_endian := false.
  Definition source_file := "C/src/cholesky.c".
  Definition normalized := true.
End Info.

Definition _A : ident := $"A".
Definition _R : ident := $"R".
Definition ___builtin_annot : ident := $"__builtin_annot".
Definition ___builtin_annot_intval : ident := $"__builtin_annot_intval".
Definition ___builtin_bswap : ident := $"__builtin_bswap".
Definition ___builtin_bswap16 : ident := $"__builtin_bswap16".
Definition ___builtin_bswap32 : ident := $"__builtin_bswap32".
Definition ___builtin_bswap64 : ident := $"__builtin_bswap64".
Definition ___builtin_cls : ident := $"__builtin_cls".
Definition ___builtin_clsl : ident := $"__builtin_clsl".
Definition ___builtin_clsll : ident := $"__builtin_clsll".
Definition ___builtin_clz : ident := $"__builtin_clz".
Definition ___builtin_clzl : ident := $"__builtin_clzl".
Definition ___builtin_clzll : ident := $"__builtin_clzll".
Definition ___builtin_ctz : ident := $"__builtin_ctz".
Definition ___builtin_ctzl : ident := $"__builtin_ctzl".
Definition ___builtin_ctzll : ident := $"__builtin_ctzll".
Definition ___builtin_debug : ident := $"__builtin_debug".
Definition ___builtin_expect : ident := $"__builtin_expect".
Definition ___builtin_fabs : ident := $"__builtin_fabs".
Definition ___builtin_fabsf : ident := $"__builtin_fabsf".
Definition ___builtin_fmadd : ident := $"__builtin_fmadd".
Definition ___builtin_fmax : ident := $"__builtin_fmax".
Definition ___builtin_fmin : ident := $"__builtin_fmin".
Definition ___builtin_fmsub : ident := $"__builtin_fmsub".
Definition ___builtin_fnmadd : ident := $"__builtin_fnmadd".
Definition ___builtin_fnmsub : ident := $"__builtin_fnmsub".
Definition ___builtin_fsqrt : ident := $"__builtin_fsqrt".
Definition ___builtin_membar : ident := $"__builtin_membar".
Definition ___builtin_memcpy_aligned : ident := $"__builtin_memcpy_aligned".
Definition ___builtin_sel : ident := $"__builtin_sel".
Definition ___builtin_sqrt : ident := $"__builtin_sqrt".
Definition ___builtin_unreachable : ident := $"__builtin_unreachable".
Definition ___builtin_va_arg : ident := $"__builtin_va_arg".
Definition ___builtin_va_copy : ident := $"__builtin_va_copy".
Definition ___builtin_va_end : ident := $"__builtin_va_end".
Definition ___builtin_va_start : ident := $"__builtin_va_start".
Definition ___compcert_i64_dtos : ident := $"__compcert_i64_dtos".
Definition ___compcert_i64_dtou : ident := $"__compcert_i64_dtou".
Definition ___compcert_i64_sar : ident := $"__compcert_i64_sar".
Definition ___compcert_i64_sdiv : ident := $"__compcert_i64_sdiv".
Definition ___compcert_i64_shl : ident := $"__compcert_i64_shl".
Definition ___compcert_i64_shr : ident := $"__compcert_i64_shr".
Definition ___compcert_i64_smod : ident := $"__compcert_i64_smod".
Definition ___compcert_i64_smulh : ident := $"__compcert_i64_smulh".
Definition ___compcert_i64_stod : ident := $"__compcert_i64_stod".
Definition ___compcert_i64_stof : ident := $"__compcert_i64_stof".
Definition ___compcert_i64_udiv : ident := $"__compcert_i64_udiv".
Definition ___compcert_i64_umod : ident := $"__compcert_i64_umod".
Definition ___compcert_i64_umulh : ident := $"__compcert_i64_umulh".
Definition ___compcert_i64_utod : ident := $"__compcert_i64_utod".
Definition ___compcert_i64_utof : ident := $"__compcert_i64_utof".
Definition ___compcert_va_composite : ident := $"__compcert_va_composite".
Definition ___compcert_va_float64 : ident := $"__compcert_va_float64".
Definition ___compcert_va_int32 : ident := $"__compcert_va_int32".
Definition ___compcert_va_int64 : ident := $"__compcert_va_int64".
Definition _cholesky : ident := $"cholesky".
Definition _i : ident := $"i".
Definition _j : ident := $"j".
Definition _k : ident := $"k".
Definition _main : ident := $"main".
Definition _n : ident := $"n".
Definition _rkj : ident := $"rkj".
Definition _s : ident := $"s".
Definition _sqrt : ident := $"sqrt".
Definition _t'1 : ident := 128%positive.
Definition _t'2 : ident := 129%positive.
Definition _t'3 : ident := 130%positive.
Definition _t'4 : ident := 131%positive.

Definition f_cholesky := {|
  fn_return := tvoid;
  fn_callconv := cc_default;
  fn_params := ((_n, tuint) :: (_A, (tptr (tarray tdouble 1000))) ::
                (_R, (tptr (tarray tdouble 1000))) :: nil);
  fn_vars := nil;
  fn_temps := ((_i, tuint) :: (_j, tuint) :: (_k, tuint) :: (_s, tdouble) ::
               (_rkj, tdouble) :: (_t'1, tdouble) :: (_t'4, tdouble) ::
               (_t'3, tdouble) :: (_t'2, tdouble) :: nil);
  fn_body :=
(Ssequence
  (Sset _j (Econst_int (Int.repr 0) tint))
  (Sloop
    (Ssequence
      (Sifthenelse (Ebinop Olt (Etempvar _j tuint) (Etempvar _n tuint) tint)
        Sskip
        Sbreak)
      (Ssequence
        (Ssequence
          (Sset _i (Econst_int (Int.repr 0) tint))
          (Sloop
            (Ssequence
              (Sifthenelse (Ebinop Olt (Etempvar _i tuint)
                             (Etempvar _j tuint) tint)
                Sskip
                Sbreak)
              (Ssequence
                (Sset _s
                  (Ederef
                    (Ebinop Oadd
                      (Ederef
                        (Ebinop Oadd
                          (Etempvar _A (tptr (tarray tdouble 1000)))
                          (Etempvar _i tuint) (tptr (tarray tdouble 1000)))
                        (tarray tdouble 1000)) (Etempvar _j tuint)
                      (tptr tdouble)) tdouble))
                (Ssequence
                  (Ssequence
                    (Sset _k (Econst_int (Int.repr 0) tint))
                    (Sloop
                      (Ssequence
                        (Sifthenelse (Ebinop Olt (Etempvar _k tuint)
                                       (Etempvar _i tuint) tint)
                          Sskip
                          Sbreak)
                        (Ssequence
                          (Sset _t'3
                            (Ederef
                              (Ebinop Oadd
                                (Ederef
                                  (Ebinop Oadd
                                    (Etempvar _R (tptr (tarray tdouble 1000)))
                                    (Etempvar _k tuint)
                                    (tptr (tarray tdouble 1000)))
                                  (tarray tdouble 1000)) (Etempvar _i tuint)
                                (tptr tdouble)) tdouble))
                          (Ssequence
                            (Sset _t'4
                              (Ederef
                                (Ebinop Oadd
                                  (Ederef
                                    (Ebinop Oadd
                                      (Etempvar _R (tptr (tarray tdouble 1000)))
                                      (Etempvar _k tuint)
                                      (tptr (tarray tdouble 1000)))
                                    (tarray tdouble 1000))
                                  (Etempvar _j tuint) (tptr tdouble))
                                tdouble))
                            (Sset _s
                              (Ebinop Osub (Etempvar _s tdouble)
                                (Ebinop Omul (Etempvar _t'3 tdouble)
                                  (Etempvar _t'4 tdouble) tdouble) tdouble)))))
                      (Sset _k
                        (Ebinop Oadd (Etempvar _k tuint)
                          (Econst_int (Int.repr 1) tint) tuint))))
                  (Ssequence
                    (Sset _t'2
                      (Ederef
                        (Ebinop Oadd
                          (Ederef
                            (Ebinop Oadd
                              (Etempvar _R (tptr (tarray tdouble 1000)))
                              (Etempvar _i tuint)
                              (tptr (tarray tdouble 1000)))
                            (tarray tdouble 1000)) (Etempvar _i tuint)
                          (tptr tdouble)) tdouble))
                    (Sassign
                      (Ederef
                        (Ebinop Oadd
                          (Ederef
                            (Ebinop Oadd
                              (Etempvar _R (tptr (tarray tdouble 1000)))
                              (Etempvar _i tuint)
                              (tptr (tarray tdouble 1000)))
                            (tarray tdouble 1000)) (Etempvar _j tuint)
                          (tptr tdouble)) tdouble)
                      (Ebinop Odiv (Etempvar _s tdouble)
                        (Etempvar _t'2 tdouble) tdouble))))))
            (Sset _i
              (Ebinop Oadd (Etempvar _i tuint) (Econst_int (Int.repr 1) tint)
                tuint))))
        (Ssequence
          (Sset _s
            (Ederef
              (Ebinop Oadd
                (Ederef
                  (Ebinop Oadd (Etempvar _A (tptr (tarray tdouble 1000)))
                    (Etempvar _j tuint) (tptr (tarray tdouble 1000)))
                  (tarray tdouble 1000)) (Etempvar _j tuint) (tptr tdouble))
              tdouble))
          (Ssequence
            (Ssequence
              (Sset _k (Econst_int (Int.repr 0) tint))
              (Sloop
                (Ssequence
                  (Sifthenelse (Ebinop Olt (Etempvar _k tuint)
                                 (Etempvar _j tuint) tint)
                    Sskip
                    Sbreak)
                  (Ssequence
                    (Sset _rkj
                      (Ederef
                        (Ebinop Oadd
                          (Ederef
                            (Ebinop Oadd
                              (Etempvar _R (tptr (tarray tdouble 1000)))
                              (Etempvar _k tuint)
                              (tptr (tarray tdouble 1000)))
                            (tarray tdouble 1000)) (Etempvar _j tuint)
                          (tptr tdouble)) tdouble))
                    (Sset _s
                      (Ebinop Osub (Etempvar _s tdouble)
                        (Ebinop Omul (Etempvar _rkj tdouble)
                          (Etempvar _rkj tdouble) tdouble) tdouble))))
                (Sset _k
                  (Ebinop Oadd (Etempvar _k tuint)
                    (Econst_int (Int.repr 1) tint) tuint))))
            (Ssequence
              (Scall (Some _t'1)
                (Evar _sqrt (Tfunction (tdouble :: nil) tdouble cc_default))
                ((Etempvar _s tdouble) :: nil))
              (Sassign
                (Ederef
                  (Ebinop Oadd
                    (Ederef
                      (Ebinop Oadd (Etempvar _R (tptr (tarray tdouble 1000)))
                        (Etempvar _j tuint) (tptr (tarray tdouble 1000)))
                      (tarray tdouble 1000)) (Etempvar _j tuint)
                    (tptr tdouble)) tdouble) (Etempvar _t'1 tdouble)))))))
    (Sset _j
      (Ebinop Oadd (Etempvar _j tuint) (Econst_int (Int.repr 1) tint) tuint))))
|}.

Definition composites : list composite_definition :=
nil.

Definition global_definitions : list (ident × globdef fundef type) :=
((___compcert_va_int32,
   Gfun(External (EF_runtime "__compcert_va_int32"
                   (mksignature (AST.Xptr :: nil) AST.Xint cc_default))
     ((tptr tvoid) :: nil) tuint cc_default)) ::
 (___compcert_va_int64,
   Gfun(External (EF_runtime "__compcert_va_int64"
                   (mksignature (AST.Xptr :: nil) AST.Xlong cc_default))
     ((tptr tvoid) :: nil) tulong cc_default)) ::
 (___compcert_va_float64,
   Gfun(External (EF_runtime "__compcert_va_float64"
                   (mksignature (AST.Xptr :: nil) AST.Xfloat cc_default))
     ((tptr tvoid) :: nil) tdouble cc_default)) ::
 (___compcert_va_composite,
   Gfun(External (EF_runtime "__compcert_va_composite"
                   (mksignature (AST.Xptr :: AST.Xlong :: nil) AST.Xptr
                     cc_default)) ((tptr tvoid) :: tulong :: nil)
     (tptr tvoid) cc_default)) ::
 (___compcert_i64_dtos,
   Gfun(External (EF_runtime "__compcert_i64_dtos"
                   (mksignature (AST.Xfloat :: nil) AST.Xlong cc_default))
     (tdouble :: nil) tlong cc_default)) ::
 (___compcert_i64_dtou,
   Gfun(External (EF_runtime "__compcert_i64_dtou"
                   (mksignature (AST.Xfloat :: nil) AST.Xlong cc_default))
     (tdouble :: nil) tulong cc_default)) ::
 (___compcert_i64_stod,
   Gfun(External (EF_runtime "__compcert_i64_stod"
                   (mksignature (AST.Xlong :: nil) AST.Xfloat cc_default))
     (tlong :: nil) tdouble cc_default)) ::
 (___compcert_i64_utod,
   Gfun(External (EF_runtime "__compcert_i64_utod"
                   (mksignature (AST.Xlong :: nil) AST.Xfloat cc_default))
     (tulong :: nil) tdouble cc_default)) ::
 (___compcert_i64_stof,
   Gfun(External (EF_runtime "__compcert_i64_stof"
                   (mksignature (AST.Xlong :: nil) AST.Xsingle cc_default))
     (tlong :: nil) tfloat cc_default)) ::
 (___compcert_i64_utof,
   Gfun(External (EF_runtime "__compcert_i64_utof"
                   (mksignature (AST.Xlong :: nil) AST.Xsingle cc_default))
     (tulong :: nil) tfloat cc_default)) ::
 (___compcert_i64_sdiv,
   Gfun(External (EF_runtime "__compcert_i64_sdiv"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tlong :: tlong :: nil) tlong cc_default)) ::
 (___compcert_i64_udiv,
   Gfun(External (EF_runtime "__compcert_i64_udiv"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tulong :: tulong :: nil) tulong
     cc_default)) ::
 (___compcert_i64_smod,
   Gfun(External (EF_runtime "__compcert_i64_smod"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tlong :: tlong :: nil) tlong cc_default)) ::
 (___compcert_i64_umod,
   Gfun(External (EF_runtime "__compcert_i64_umod"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tulong :: tulong :: nil) tulong
     cc_default)) ::
 (___compcert_i64_shl,
   Gfun(External (EF_runtime "__compcert_i64_shl"
                   (mksignature (AST.Xlong :: AST.Xint :: nil) AST.Xlong
                     cc_default)) (tlong :: tint :: nil) tlong cc_default)) ::
 (___compcert_i64_shr,
   Gfun(External (EF_runtime "__compcert_i64_shr"
                   (mksignature (AST.Xlong :: AST.Xint :: nil) AST.Xlong
                     cc_default)) (tulong :: tint :: nil) tulong cc_default)) ::
 (___compcert_i64_sar,
   Gfun(External (EF_runtime "__compcert_i64_sar"
                   (mksignature (AST.Xlong :: AST.Xint :: nil) AST.Xlong
                     cc_default)) (tlong :: tint :: nil) tlong cc_default)) ::
 (___compcert_i64_smulh,
   Gfun(External (EF_runtime "__compcert_i64_smulh"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tlong :: tlong :: nil) tlong cc_default)) ::
 (___compcert_i64_umulh,
   Gfun(External (EF_runtime "__compcert_i64_umulh"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tulong :: tulong :: nil) tulong
     cc_default)) ::
 (___builtin_bswap64,
   Gfun(External (EF_builtin "__builtin_bswap64"
                   (mksignature (AST.Xlong :: nil) AST.Xlong cc_default))
     (tulong :: nil) tulong cc_default)) ::
 (___builtin_bswap,
   Gfun(External (EF_builtin "__builtin_bswap"
                   (mksignature (AST.Xint :: nil) AST.Xint cc_default))
     (tuint :: nil) tuint cc_default)) ::
 (___builtin_bswap32,
   Gfun(External (EF_builtin "__builtin_bswap32"
                   (mksignature (AST.Xint :: nil) AST.Xint cc_default))
     (tuint :: nil) tuint cc_default)) ::
 (___builtin_bswap16,
   Gfun(External (EF_builtin "__builtin_bswap16"
                   (mksignature (AST.Xint16unsigned :: nil)
                     AST.Xint16unsigned cc_default)) (tushort :: nil) tushort
     cc_default)) ::
 (___builtin_clz,
   Gfun(External (EF_builtin "__builtin_clz"
                   (mksignature (AST.Xint :: nil) AST.Xint cc_default))
     (tuint :: nil) tint cc_default)) ::
 (___builtin_clzl,
   Gfun(External (EF_builtin "__builtin_clzl"
                   (mksignature (AST.Xlong :: nil) AST.Xint cc_default))
     (tulong :: nil) tint cc_default)) ::
 (___builtin_clzll,
   Gfun(External (EF_builtin "__builtin_clzll"
                   (mksignature (AST.Xlong :: nil) AST.Xint cc_default))
     (tulong :: nil) tint cc_default)) ::
 (___builtin_ctz,
   Gfun(External (EF_builtin "__builtin_ctz"
                   (mksignature (AST.Xint :: nil) AST.Xint cc_default))
     (tuint :: nil) tint cc_default)) ::
 (___builtin_ctzl,
   Gfun(External (EF_builtin "__builtin_ctzl"
                   (mksignature (AST.Xlong :: nil) AST.Xint cc_default))
     (tulong :: nil) tint cc_default)) ::
 (___builtin_ctzll,
   Gfun(External (EF_builtin "__builtin_ctzll"
                   (mksignature (AST.Xlong :: nil) AST.Xint cc_default))
     (tulong :: nil) tint cc_default)) ::
 (___builtin_fabs,
   Gfun(External (EF_builtin "__builtin_fabs"
                   (mksignature (AST.Xfloat :: nil) AST.Xfloat cc_default))
     (tdouble :: nil) tdouble cc_default)) ::
 (___builtin_fabsf,
   Gfun(External (EF_builtin "__builtin_fabsf"
                   (mksignature (AST.Xsingle :: nil) AST.Xsingle cc_default))
     (tfloat :: nil) tfloat cc_default)) ::
 (___builtin_fsqrt,
   Gfun(External (EF_builtin "__builtin_fsqrt"
                   (mksignature (AST.Xfloat :: nil) AST.Xfloat cc_default))
     (tdouble :: nil) tdouble cc_default)) ::
 (___builtin_sqrt,
   Gfun(External (EF_builtin "__builtin_sqrt"
                   (mksignature (AST.Xfloat :: nil) AST.Xfloat cc_default))
     (tdouble :: nil) tdouble cc_default)) ::
 (___builtin_memcpy_aligned,
   Gfun(External (EF_builtin "__builtin_memcpy_aligned"
                   (mksignature
                     (AST.Xptr :: AST.Xptr :: AST.Xlong :: AST.Xlong :: nil)
                     AST.Xvoid cc_default))
     ((tptr tvoid) :: (tptr tvoid) :: tulong :: tulong :: nil) tvoid
     cc_default)) ::
 (___builtin_sel,
   Gfun(External (EF_builtin "__builtin_sel"
                   (mksignature (AST.Xbool :: nil) AST.Xvoid
                     {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|}))
     (tbool :: nil) tvoid
     {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) ::
 (___builtin_annot,
   Gfun(External (EF_builtin "__builtin_annot"
                   (mksignature (AST.Xptr :: nil) AST.Xvoid
                     {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|}))
     ((tptr tschar) :: nil) tvoid
     {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) ::
 (___builtin_annot_intval,
   Gfun(External (EF_builtin "__builtin_annot_intval"
                   (mksignature (AST.Xptr :: AST.Xint :: nil) AST.Xint
                     cc_default)) ((tptr tschar) :: tint :: nil) tint
     cc_default)) ::
 (___builtin_membar,
   Gfun(External (EF_builtin "__builtin_membar"
                   (mksignature nil AST.Xvoid cc_default)) nil tvoid
     cc_default)) ::
 (___builtin_va_start,
   Gfun(External (EF_builtin "__builtin_va_start"
                   (mksignature (AST.Xptr :: nil) AST.Xvoid cc_default))
     ((tptr tvoid) :: nil) tvoid cc_default)) ::
 (___builtin_va_arg,
   Gfun(External (EF_builtin "__builtin_va_arg"
                   (mksignature (AST.Xptr :: AST.Xint :: nil) AST.Xvoid
                     cc_default)) ((tptr tvoid) :: tuint :: nil) tvoid
     cc_default)) ::
 (___builtin_va_copy,
   Gfun(External (EF_builtin "__builtin_va_copy"
                   (mksignature (AST.Xptr :: AST.Xptr :: nil) AST.Xvoid
                     cc_default)) ((tptr tvoid) :: (tptr tvoid) :: nil) tvoid
     cc_default)) ::
 (___builtin_va_end,
   Gfun(External (EF_builtin "__builtin_va_end"
                   (mksignature (AST.Xptr :: nil) AST.Xvoid cc_default))
     ((tptr tvoid) :: nil) tvoid cc_default)) ::
 (___builtin_unreachable,
   Gfun(External (EF_builtin "__builtin_unreachable"
                   (mksignature nil AST.Xvoid cc_default)) nil tvoid
     cc_default)) ::
 (___builtin_expect,
   Gfun(External (EF_builtin "__builtin_expect"
                   (mksignature (AST.Xlong :: AST.Xlong :: nil) AST.Xlong
                     cc_default)) (tlong :: tlong :: nil) tlong cc_default)) ::
 (___builtin_cls,
   Gfun(External (EF_builtin "__builtin_cls"
                   (mksignature (AST.Xint :: nil) AST.Xint cc_default))
     (tint :: nil) tint cc_default)) ::
 (___builtin_clsl,
   Gfun(External (EF_builtin "__builtin_clsl"
                   (mksignature (AST.Xlong :: nil) AST.Xint cc_default))
     (tlong :: nil) tint cc_default)) ::
 (___builtin_clsll,
   Gfun(External (EF_builtin "__builtin_clsll"
                   (mksignature (AST.Xlong :: nil) AST.Xint cc_default))
     (tlong :: nil) tint cc_default)) ::
 (___builtin_fmadd,
   Gfun(External (EF_builtin "__builtin_fmadd"
                   (mksignature
                     (AST.Xfloat :: AST.Xfloat :: AST.Xfloat :: nil)
                     AST.Xfloat cc_default))
     (tdouble :: tdouble :: tdouble :: nil) tdouble cc_default)) ::
 (___builtin_fmsub,
   Gfun(External (EF_builtin "__builtin_fmsub"
                   (mksignature
                     (AST.Xfloat :: AST.Xfloat :: AST.Xfloat :: nil)
                     AST.Xfloat cc_default))
     (tdouble :: tdouble :: tdouble :: nil) tdouble cc_default)) ::
 (___builtin_fnmadd,
   Gfun(External (EF_builtin "__builtin_fnmadd"
                   (mksignature
                     (AST.Xfloat :: AST.Xfloat :: AST.Xfloat :: nil)
                     AST.Xfloat cc_default))
     (tdouble :: tdouble :: tdouble :: nil) tdouble cc_default)) ::
 (___builtin_fnmsub,
   Gfun(External (EF_builtin "__builtin_fnmsub"
                   (mksignature
                     (AST.Xfloat :: AST.Xfloat :: AST.Xfloat :: nil)
                     AST.Xfloat cc_default))
     (tdouble :: tdouble :: tdouble :: nil) tdouble cc_default)) ::
 (___builtin_fmax,
   Gfun(External (EF_builtin "__builtin_fmax"
                   (mksignature (AST.Xfloat :: AST.Xfloat :: nil) AST.Xfloat
                     cc_default)) (tdouble :: tdouble :: nil) tdouble
     cc_default)) ::
 (___builtin_fmin,
   Gfun(External (EF_builtin "__builtin_fmin"
                   (mksignature (AST.Xfloat :: AST.Xfloat :: nil) AST.Xfloat
                     cc_default)) (tdouble :: tdouble :: nil) tdouble
     cc_default)) ::
 (___builtin_debug,
   Gfun(External (EF_external "__builtin_debug"
                   (mksignature (AST.Xint :: nil) AST.Xvoid
                     {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|}))
     (tint :: nil) tvoid
     {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) ::
 (_sqrt,
   Gfun(External (EF_external "sqrt"
                   (mksignature (AST.Xfloat :: nil) AST.Xfloat cc_default))
     (tdouble :: nil) tdouble cc_default)) ::
 (_cholesky, Gfun(Internal f_cholesky)) :: nil).

Definition public_idents : list ident :=
(_cholesky :: _sqrt :: ___builtin_debug :: ___builtin_fmin ::
 ___builtin_fmax :: ___builtin_fnmsub :: ___builtin_fnmadd ::
 ___builtin_fmsub :: ___builtin_fmadd :: ___builtin_clsll ::
 ___builtin_clsl :: ___builtin_cls :: ___builtin_expect ::
 ___builtin_unreachable :: ___builtin_va_end :: ___builtin_va_copy ::
 ___builtin_va_arg :: ___builtin_va_start :: ___builtin_membar ::
 ___builtin_annot_intval :: ___builtin_annot :: ___builtin_sel ::
 ___builtin_memcpy_aligned :: ___builtin_sqrt :: ___builtin_fsqrt ::
 ___builtin_fabsf :: ___builtin_fabs :: ___builtin_ctzll ::
 ___builtin_ctzl :: ___builtin_ctz :: ___builtin_clzll :: ___builtin_clzl ::
 ___builtin_clz :: ___builtin_bswap16 :: ___builtin_bswap32 ::
 ___builtin_bswap :: ___builtin_bswap64 :: ___compcert_i64_umulh ::
 ___compcert_i64_smulh :: ___compcert_i64_sar :: ___compcert_i64_shr ::
 ___compcert_i64_shl :: ___compcert_i64_umod :: ___compcert_i64_smod ::
 ___compcert_i64_udiv :: ___compcert_i64_sdiv :: ___compcert_i64_utof ::
 ___compcert_i64_stof :: ___compcert_i64_utod :: ___compcert_i64_stod ::
 ___compcert_i64_dtou :: ___compcert_i64_dtos :: ___compcert_va_composite ::
 ___compcert_va_float64 :: ___compcert_va_int64 :: ___compcert_va_int32 ::
 nil).

Definition prog : Clight.program :=
  mkprogram composites global_definitions public_idents _main Logic.I.