LAProof.C.sparse

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/sparse.c".
  Definition normalized := true.
End Info.

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 _col_ind : ident := $"col_ind".
Definition _cols : ident := $"cols".
Definition _crs_matrix : ident := $"crs_matrix".
Definition _crs_matrix_rows : ident := $"crs_matrix_rows".
Definition _crs_matrix_vector_multiply : ident := $"crs_matrix_vector_multiply".
Definition _crs_matrix_vector_multiply_byrows : ident := $"crs_matrix_vector_multiply_byrows".
Definition _crs_row_vector_multiply : ident := $"crs_row_vector_multiply".
Definition _fma : ident := $"fma".
Definition _h : ident := $"h".
Definition _hi : ident := $"hi".
Definition _i : ident := $"i".
Definition _j : ident := $"j".
Definition _m : ident := $"m".
Definition _main : ident := $"main".
Definition _next : ident := $"next".
Definition _p : ident := $"p".
Definition _row_ptr : ident := $"row_ptr".
Definition _rows : ident := $"rows".
Definition _s : ident := $"s".
Definition _v : ident := $"v".
Definition _val : ident := $"val".
Definition _x : ident := $"x".
Definition _y : ident := $"y".
Definition _t'1 : ident := 128%positive.
Definition _t'2 : ident := 129%positive.

Definition f_crs_row_vector_multiply := {|
  fn_return := tdouble;
  fn_callconv := cc_default;
  fn_params := ((_m, (tptr (Tstruct _crs_matrix noattr))) ::
                (_v, (tptr tdouble)) :: (_i, tuint) :: nil);
  fn_vars := nil;
  fn_temps := ((_val, (tptr tdouble)) :: (_col_ind, (tptr tuint)) ::
               (_row_ptr, (tptr tuint)) :: (_h, tuint) :: (_hi, tuint) ::
               (_s, tdouble) :: (_x, tdouble) :: (_j, tuint) ::
               (_y, tdouble) :: (_t'1, tdouble) :: nil);
  fn_body :=
(Ssequence
  (Sset _val
    (Efield
      (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
        (Tstruct _crs_matrix noattr)) _val (tptr tdouble)))
  (Ssequence
    (Sset _col_ind
      (Efield
        (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
          (Tstruct _crs_matrix noattr)) _col_ind (tptr tuint)))
    (Ssequence
      (Sset _row_ptr
        (Efield
          (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
            (Tstruct _crs_matrix noattr)) _row_ptr (tptr tuint)))
      (Ssequence
        (Sset _hi
          (Ederef
            (Ebinop Oadd (Etempvar _row_ptr (tptr tuint))
              (Ebinop Oadd (Etempvar _i tuint) (Econst_int (Int.repr 1) tint)
                tuint) (tptr tuint)) tuint))
        (Ssequence
          (Sset _s (Econst_float (Float.of_bits (Int64.repr 0)) tdouble))
          (Ssequence
            (Ssequence
              (Sset _h
                (Ederef
                  (Ebinop Oadd (Etempvar _row_ptr (tptr tuint))
                    (Etempvar _i tuint) (tptr tuint)) tuint))
              (Sloop
                (Ssequence
                  (Sifthenelse (Ebinop Olt (Etempvar _h tuint)
                                 (Etempvar _hi tuint) tint)
                    Sskip
                    Sbreak)
                  (Ssequence
                    (Sset _x
                      (Ederef
                        (Ebinop Oadd (Etempvar _val (tptr tdouble))
                          (Etempvar _h tuint) (tptr tdouble)) tdouble))
                    (Ssequence
                      (Sset _j
                        (Ederef
                          (Ebinop Oadd (Etempvar _col_ind (tptr tuint))
                            (Etempvar _h tuint) (tptr tuint)) tuint))
                      (Ssequence
                        (Sset _y
                          (Ederef
                            (Ebinop Oadd (Etempvar _v (tptr tdouble))
                              (Etempvar _j tuint) (tptr tdouble)) tdouble))
                        (Ssequence
                          (Scall (Some _t'1)
                            (Evar _fma (Tfunction
                                         (tdouble :: tdouble :: tdouble ::
                                          nil) tdouble cc_default))
                            ((Etempvar _x tdouble) ::
                             (Etempvar _y tdouble) ::
                             (Etempvar _s tdouble) :: nil))
                          (Sset _s (Etempvar _t'1 tdouble)))))))
                (Sset _h
                  (Ebinop Oadd (Etempvar _h tuint)
                    (Econst_int (Int.repr 1) tint) tuint))))
            (Sreturn (Some (Etempvar _s tdouble)))))))))
|}.

Definition f_crs_matrix_vector_multiply_byrows := {|
  fn_return := tvoid;
  fn_callconv := cc_default;
  fn_params := ((_m, (tptr (Tstruct _crs_matrix noattr))) ::
                (_v, (tptr tdouble)) :: (_p, (tptr tdouble)) :: nil);
  fn_vars := nil;
  fn_temps := ((_i, tuint) :: (_rows, tuint) :: (_t'2, tdouble) ::
               (_t'1, tuint) :: nil);
  fn_body :=
(Ssequence
  (Ssequence
    (Scall (Some _t'1)
      (Evar _crs_matrix_rows (Tfunction
                               ((tptr (Tstruct _crs_matrix noattr)) :: nil)
                               tuint cc_default))
      ((Etempvar _m (tptr (Tstruct _crs_matrix noattr))) :: nil))
    (Sset _rows (Etempvar _t'1 tuint)))
  (Ssequence
    (Sset _i (Econst_int (Int.repr 0) tint))
    (Sloop
      (Ssequence
        (Sifthenelse (Ebinop Olt (Etempvar _i tuint) (Etempvar _rows tuint)
                       tint)
          Sskip
          Sbreak)
        (Ssequence
          (Scall (Some _t'2)
            (Evar _crs_row_vector_multiply (Tfunction
                                             ((tptr (Tstruct _crs_matrix noattr)) ::
                                              (tptr tdouble) :: tuint :: nil)
                                             tdouble cc_default))
            ((Etempvar _m (tptr (Tstruct _crs_matrix noattr))) ::
             (Etempvar _v (tptr tdouble)) :: (Etempvar _i tuint) :: nil))
          (Sassign
            (Ederef
              (Ebinop Oadd (Etempvar _p (tptr tdouble)) (Etempvar _i tuint)
                (tptr tdouble)) tdouble) (Etempvar _t'2 tdouble))))
      (Sset _i
        (Ebinop Oadd (Etempvar _i tuint) (Econst_int (Int.repr 1) tint)
          tuint)))))
|}.

Definition f_crs_matrix_vector_multiply := {|
  fn_return := tvoid;
  fn_callconv := cc_default;
  fn_params := ((_m, (tptr (Tstruct _crs_matrix noattr))) ::
                (_v, (tptr tdouble)) :: (_p, (tptr tdouble)) :: nil);
  fn_vars := nil;
  fn_temps := ((_i, tuint) :: (_rows, tuint) :: (_val, (tptr tdouble)) ::
               (_col_ind, (tptr tuint)) :: (_row_ptr, (tptr tuint)) ::
               (_next, tuint) :: (_s, tdouble) :: (_h, tuint) ::
               (_x, tdouble) :: (_j, tuint) :: (_y, tdouble) ::
               (_t'1, tdouble) :: nil);
  fn_body :=
(Ssequence
  (Sset _rows
    (Efield
      (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
        (Tstruct _crs_matrix noattr)) _rows tuint))
  (Ssequence
    (Sset _val
      (Efield
        (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
          (Tstruct _crs_matrix noattr)) _val (tptr tdouble)))
    (Ssequence
      (Sset _col_ind
        (Efield
          (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
            (Tstruct _crs_matrix noattr)) _col_ind (tptr tuint)))
      (Ssequence
        (Sset _row_ptr
          (Efield
            (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
              (Tstruct _crs_matrix noattr)) _row_ptr (tptr tuint)))
        (Ssequence
          (Sset _next
            (Ederef
              (Ebinop Oadd (Etempvar _row_ptr (tptr tuint))
                (Econst_int (Int.repr 0) tint) (tptr tuint)) tuint))
          (Ssequence
            (Sset _i (Econst_int (Int.repr 0) tint))
            (Sloop
              (Ssequence
                (Sifthenelse (Ebinop Olt (Etempvar _i tuint)
                               (Etempvar _rows tuint) tint)
                  Sskip
                  Sbreak)
                (Ssequence
                  (Sset _s
                    (Econst_float (Float.of_bits (Int64.repr 0)) tdouble))
                  (Ssequence
                    (Sset _h (Etempvar _next tuint))
                    (Ssequence
                      (Sset _next
                        (Ederef
                          (Ebinop Oadd (Etempvar _row_ptr (tptr tuint))
                            (Ebinop Oadd (Etempvar _i tuint)
                              (Econst_int (Int.repr 1) tint) tuint)
                            (tptr tuint)) tuint))
                      (Ssequence
                        (Sloop
                          (Ssequence
                            (Sifthenelse (Ebinop Olt (Etempvar _h tuint)
                                           (Etempvar _next tuint) tint)
                              Sskip
                              Sbreak)
                            (Ssequence
                              (Sset _x
                                (Ederef
                                  (Ebinop Oadd (Etempvar _val (tptr tdouble))
                                    (Etempvar _h tuint) (tptr tdouble))
                                  tdouble))
                              (Ssequence
                                (Sset _j
                                  (Ederef
                                    (Ebinop Oadd
                                      (Etempvar _col_ind (tptr tuint))
                                      (Etempvar _h tuint) (tptr tuint))
                                    tuint))
                                (Ssequence
                                  (Sset _y
                                    (Ederef
                                      (Ebinop Oadd
                                        (Etempvar _v (tptr tdouble))
                                        (Etempvar _j tuint) (tptr tdouble))
                                      tdouble))
                                  (Ssequence
                                    (Scall (Some _t'1)
                                      (Evar _fma (Tfunction
                                                   (tdouble :: tdouble ::
                                                    tdouble :: nil) tdouble
                                                   cc_default))
                                      ((Etempvar _x tdouble) ::
                                       (Etempvar _y tdouble) ::
                                       (Etempvar _s tdouble) :: nil))
                                    (Sset _s (Etempvar _t'1 tdouble)))))))
                          (Sset _h
                            (Ebinop Oadd (Etempvar _h tuint)
                              (Econst_int (Int.repr 1) tint) tuint)))
                        (Sassign
                          (Ederef
                            (Ebinop Oadd (Etempvar _p (tptr tdouble))
                              (Etempvar _i tuint) (tptr tdouble)) tdouble)
                          (Etempvar _s tdouble)))))))
              (Sset _i
                (Ebinop Oadd (Etempvar _i tuint)
                  (Econst_int (Int.repr 1) tint) tuint)))))))))
|}.

Definition f_crs_matrix_rows := {|
  fn_return := tuint;
  fn_callconv := cc_default;
  fn_params := ((_m, (tptr (Tstruct _crs_matrix noattr))) :: nil);
  fn_vars := nil;
  fn_temps := ((_t'1, tuint) :: nil);
  fn_body :=
(Ssequence
  (Sset _t'1
    (Efield
      (Ederef (Etempvar _m (tptr (Tstruct _crs_matrix noattr)))
        (Tstruct _crs_matrix noattr)) _rows tuint))
  (Sreturn (Some (Etempvar _t'1 tuint))))
|}.

Definition composites : list composite_definition :=
(Composite _crs_matrix Struct
   (Member_plain _val (tptr tdouble) :: Member_plain _col_ind (tptr tuint) ::
    Member_plain _row_ptr (tptr tuint) :: Member_plain _rows tuint ::
    Member_plain _cols tuint :: nil)
   noattr :: 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|})) ::
 (_fma,
   Gfun(External (EF_external "fma"
                   (mksignature
                     (AST.Xfloat :: AST.Xfloat :: AST.Xfloat :: nil)
                     AST.Xfloat cc_default))
     (tdouble :: tdouble :: tdouble :: nil) tdouble cc_default)) ::
 (_crs_row_vector_multiply, Gfun(Internal f_crs_row_vector_multiply)) ::
 (_crs_matrix_vector_multiply_byrows, Gfun(Internal f_crs_matrix_vector_multiply_byrows)) ::
 (_crs_matrix_vector_multiply, Gfun(Internal f_crs_matrix_vector_multiply)) ::
 (_crs_matrix_rows, Gfun(Internal f_crs_matrix_rows)) :: nil).

Definition public_idents : list ident :=
(_crs_matrix_rows :: _crs_matrix_vector_multiply ::
 _crs_matrix_vector_multiply_byrows :: _crs_row_vector_multiply :: _fma ::
 ___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.