Bug#702397: gcc-4.8: ICE with -O3 -ffast-math in propagate_op_to_single_use

To: Debian Bug Tracking System <submit@bugs.debian.org>
Subject: Bug#702397: gcc-4.8: ICE with -O3 -ffast-math in propagate_op_to_single_use
From: Xavier Andrade <xavier@tddft.org>
Date: Tue, 05 Mar 2013 20:37:05 -0500
Message-id: <[🔎] 20130306013705.21027.11540.reportbug@laja.chem.harvard.edu>
Reply-to: Xavier Andrade <xavier@tddft.org>, 702397@bugs.debian.org

Package: gcc-4.8
Version: 4.8-20130228-1
Severity: normal

Dear Maintainer,

Compiling the attached preprocessed source file with gcc-4.8 and the flags
'-O3 -ffast-math' produces an internal compiler error. This is the
error message:

xavier@laja:~/files/codes/octopus/trunk_clean/blds/gfortran$ gcc-4.8
-O3 -ffast-math  -c bug.c 
In file included from ../../../../libxc/src/gga_k_dk.c:158:0:
.../../../../libxc/src/work_gga_x.c: In function ‘work_gga_k’:
.../../../../libxc/src/work_gga_x.c:36:1: internal compiler error: in
propagate_op_to_single_use, at tree-ssa-reassoc.c:1057
Please submit a full bug report,
with preprocessed source if appropriate.
See <file:///usr/share/doc/gcc-4.8/README.Bugs> for instructions.

Please let me know if you need any additional information.

Thanks,

Xavier

-- System Information:
Debian Release: 7.0
  APT prefers unstable
  APT policy: (500, 'unstable'), (1, 'experimental')
Architecture: amd64 (x86_64)
Foreign Architectures: i386

Kernel: Linux 3.7.0-10.dmz.1-liquorix-amd64 (SMP w/4 CPU cores; PREEMPT)
Locale: LANG=en_US.UTF-8, LC_CTYPE=en_US.UTF-8 (charmap=UTF-8)
Shell: /bin/sh linked to /bin/dash

Versions of packages gcc-4.8 depends on:
ii  binutils        2.22-8
ii  cpp-4.8         4.8-20130228-1
ii  gcc-4.8-base    4.8-20130228-1
ii  libc6           2.17-0experimental2
ii  libcloog-isl4   0.18.0-1
ii  libgcc-4.8-dev  4.8-20130228-1
ii  libgmp10        2:5.0.5+dfsg-2
ii  libisl10        0.11.1-2
ii  libmpc2         0.9-4
ii  libmpfr4        3.1.1-1
ii  zlib1g          1:1.2.7.dfsg-13

Versions of packages gcc-4.8 recommends:
ii  libc6-dev  2.17-0experimental2

Versions of packages gcc-4.8 suggests:
pn  binutils-gold        <none>
pn  gcc-4.8-doc          <none>
pn  gcc-4.8-locales      <none>
pn  gcc-4.8-multilib     <none>
pn  libasan0-dbg         <none>
pn  libatomic1-dbg       <none>
pn  libbacktrace1-dbg    <none>
pn  libgcc1-dbg          <none>
pn  libgomp1-dbg         <none>
pn  libitm1-dbg          <none>
pn  libmudflap0-4.8-dev  <none>
pn  libmudflap0-dbg      <none>
pn  libquadmath0-dbg     <none>
pn  libtsan0-dbg         <none>

-- no debconf information

// /usr/lib/gcc/x86_64-linux-gnu/4.8/cc1 -quiet -I . -I ../../../../libxc/src -I .. -imultilib . -imultiarch x86_64-linux-gnu -MD libxc_la-gga_k_dk.d -MF .deps/libxc_la-gga_k_dk.Tpo -MP -MT libxc_la-gga_k_dk.lo -D HAVE_CONFIG_H ../../../../libxc/src/gga_k_dk.c -march=corei7-avx -mcx16 -msahf -mno-movbe -mno-aes -mpclmul -mpopcnt -mno-abm -mno-lwp -mno-fma -mno-fma4 -mno-xop -mno-bmi -mno-bmi2 -mno-tbm -mavx -mno-avx2 -msse4.2 -msse4.1 -mno-lzcnt -mno-rtm -mno-hle -mno-rdrnd -mno-f16c -mno-fsgsbase -mno-rdseed -mno-prfchw -mno-adx -mfxsr -mxsave -mxsaveopt --param l1-cache-size=32 --param l1-cache-line-size=64 --param l2-cache-size=3072 -mtune=corei7-avx -quiet -dumpbase gga_k_dk.c -auxbase-strip libxc_la-gga_k_dk.o -g -g -O3 -O3 -Wstrict-aliasing=2 -Wall -Wpedantic -Wstrict-aliasing=2 -p -funroll-loops -fgcse-lm -fgcse-sm -ffast-math -ftree-vectorize -o - -frandom-seed=0
# 1 "../../../../libxc/src/gga_k_dk.c"
# 1 "/home/xavier/files/codes/octopus/trunk_clean/blds/gfortran/libxc_build/src//"
# 1 "<command-line>"
# 1 "/usr/include/stdc-predef.h" 1 3 4
# 30 "/usr/include/stdc-predef.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/predefs.h" 1 3 4
# 31 "/usr/include/stdc-predef.h" 2 3 4
# 1 "<command-line>" 2
# 1 "../../../../libxc/src/gga_k_dk.c"
# 19 "../../../../libxc/src/gga_k_dk.c"
# 1 "/usr/include/stdio.h" 1 3 4
# 27 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/features.h" 1 3 4
# 371 "/usr/include/features.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 1 3 4
# 385 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 386 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 2 3 4
# 372 "/usr/include/features.h" 2 3 4
# 395 "/usr/include/features.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/gnu/stubs.h" 1 3 4
# 10 "/usr/include/x86_64-linux-gnu/gnu/stubs.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/gnu/stubs-64.h" 1 3 4
# 11 "/usr/include/x86_64-linux-gnu/gnu/stubs.h" 2 3 4
# 396 "/usr/include/features.h" 2 3 4
# 28 "/usr/include/stdio.h" 2 3 4





# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 1 3 4
# 212 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 3 4
typedef long unsigned int size_t;
# 34 "/usr/include/stdio.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/types.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 28 "/usr/include/x86_64-linux-gnu/bits/types.h" 2 3 4


typedef unsigned char __u_char;
typedef unsigned short int __u_short;
typedef unsigned int __u_int;
typedef unsigned long int __u_long;


typedef signed char __int8_t;
typedef unsigned char __uint8_t;
typedef signed short int __int16_t;
typedef unsigned short int __uint16_t;
typedef signed int __int32_t;
typedef unsigned int __uint32_t;

typedef signed long int __int64_t;
typedef unsigned long int __uint64_t;







typedef long int __quad_t;
typedef unsigned long int __u_quad_t;
# 130 "/usr/include/x86_64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/typesizes.h" 1 3 4
# 131 "/usr/include/x86_64-linux-gnu/bits/types.h" 2 3 4


typedef unsigned long int __dev_t;
typedef unsigned int __uid_t;
typedef unsigned int __gid_t;
typedef unsigned long int __ino_t;
typedef unsigned long int __ino64_t;
typedef unsigned int __mode_t;
typedef unsigned long int __nlink_t;
typedef long int __off_t;
typedef long int __off64_t;
typedef int __pid_t;
typedef struct { int __val[2]; } __fsid_t;
typedef long int __clock_t;
typedef unsigned long int __rlim_t;
typedef unsigned long int __rlim64_t;
typedef unsigned int __id_t;
typedef long int __time_t;
typedef unsigned int __useconds_t;
typedef long int __suseconds_t;

typedef int __daddr_t;
typedef int __key_t;


typedef int __clockid_t;


typedef void * __timer_t;


typedef long int __blksize_t;




typedef long int __blkcnt_t;
typedef long int __blkcnt64_t;


typedef unsigned long int __fsblkcnt_t;
typedef unsigned long int __fsblkcnt64_t;


typedef unsigned long int __fsfilcnt_t;
typedef unsigned long int __fsfilcnt64_t;


typedef long int __fsword_t;

typedef long int __ssize_t;


typedef long int __syscall_slong_t;

typedef unsigned long int __syscall_ulong_t;



typedef __off64_t __loff_t;
typedef __quad_t *__qaddr_t;
typedef char *__caddr_t;


typedef long int __intptr_t;


typedef unsigned int __socklen_t;
# 36 "/usr/include/stdio.h" 2 3 4
# 44 "/usr/include/stdio.h" 3 4
struct _IO_FILE;



typedef struct _IO_FILE FILE;





# 64 "/usr/include/stdio.h" 3 4
typedef struct _IO_FILE __FILE;
# 74 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/libio.h" 1 3 4
# 32 "/usr/include/libio.h" 3 4
# 1 "/usr/include/_G_config.h" 1 3 4
# 15 "/usr/include/_G_config.h" 3 4
# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 1 3 4
# 16 "/usr/include/_G_config.h" 2 3 4




# 1 "/usr/include/wchar.h" 1 3 4
# 82 "/usr/include/wchar.h" 3 4
typedef struct
{
  int __count;
  union
  {

    unsigned int __wch;



    char __wchb[4];
  } __value;
} __mbstate_t;
# 21 "/usr/include/_G_config.h" 2 3 4
typedef struct
{
  __off_t __pos;
  __mbstate_t __state;
} _G_fpos_t;
typedef struct
{
  __off64_t __pos;
  __mbstate_t __state;
} _G_fpos64_t;
# 33 "/usr/include/libio.h" 2 3 4
# 50 "/usr/include/libio.h" 3 4
# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stdarg.h" 1 3 4
# 40 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stdarg.h" 3 4
typedef __builtin_va_list __gnuc_va_list;
# 51 "/usr/include/libio.h" 2 3 4
# 145 "/usr/include/libio.h" 3 4
struct _IO_jump_t; struct _IO_FILE;
# 155 "/usr/include/libio.h" 3 4
typedef void _IO_lock_t;





struct _IO_marker {
  struct _IO_marker *_next;
  struct _IO_FILE *_sbuf;



  int _pos;
# 178 "/usr/include/libio.h" 3 4
};


enum __codecvt_result
{
  __codecvt_ok,
  __codecvt_partial,
  __codecvt_error,
  __codecvt_noconv
};
# 246 "/usr/include/libio.h" 3 4
struct _IO_FILE {
  int _flags;




  char* _IO_read_ptr;
  char* _IO_read_end;
  char* _IO_read_base;
  char* _IO_write_base;
  char* _IO_write_ptr;
  char* _IO_write_end;
  char* _IO_buf_base;
  char* _IO_buf_end;

  char *_IO_save_base;
  char *_IO_backup_base;
  char *_IO_save_end;

  struct _IO_marker *_markers;

  struct _IO_FILE *_chain;

  int _fileno;



  int _flags2;

  __off_t _old_offset;



  unsigned short _cur_column;
  signed char _vtable_offset;
  char _shortbuf[1];



  _IO_lock_t *_lock;
# 294 "/usr/include/libio.h" 3 4
  __off64_t _offset;
# 303 "/usr/include/libio.h" 3 4
  void *__pad1;
  void *__pad2;
  void *__pad3;
  void *__pad4;
  size_t __pad5;

  int _mode;

  char _unused2[15 * sizeof (int) - 4 * sizeof (void *) - sizeof (size_t)];

};


typedef struct _IO_FILE _IO_FILE;


struct _IO_FILE_plus;

extern struct _IO_FILE_plus _IO_2_1_stdin_;
extern struct _IO_FILE_plus _IO_2_1_stdout_;
extern struct _IO_FILE_plus _IO_2_1_stderr_;
# 339 "/usr/include/libio.h" 3 4
typedef __ssize_t __io_read_fn (void *__cookie, char *__buf, size_t __nbytes);







typedef __ssize_t __io_write_fn (void *__cookie, const char *__buf,
     size_t __n);







typedef int __io_seek_fn (void *__cookie, __off64_t *__pos, int __w);


typedef int __io_close_fn (void *__cookie);
# 391 "/usr/include/libio.h" 3 4
extern int __underflow (_IO_FILE *);
extern int __uflow (_IO_FILE *);
extern int __overflow (_IO_FILE *, int);
# 435 "/usr/include/libio.h" 3 4
extern int _IO_getc (_IO_FILE *__fp);
extern int _IO_putc (int __c, _IO_FILE *__fp);
extern int _IO_feof (_IO_FILE *__fp) __attribute__ ((__nothrow__ , __leaf__));
extern int _IO_ferror (_IO_FILE *__fp) __attribute__ ((__nothrow__ , __leaf__));

extern int _IO_peekc_locked (_IO_FILE *__fp);





extern void _IO_flockfile (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
extern void _IO_funlockfile (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
extern int _IO_ftrylockfile (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
# 465 "/usr/include/libio.h" 3 4
extern int _IO_vfscanf (_IO_FILE * __restrict, const char * __restrict,
   __gnuc_va_list, int *__restrict);
extern int _IO_vfprintf (_IO_FILE *__restrict, const char *__restrict,
    __gnuc_va_list);
extern __ssize_t _IO_padn (_IO_FILE *, int, __ssize_t);
extern size_t _IO_sgetn (_IO_FILE *, void *, size_t);

extern __off64_t _IO_seekoff (_IO_FILE *, __off64_t, int, int);
extern __off64_t _IO_seekpos (_IO_FILE *, __off64_t, int);

extern void _IO_free_backup_area (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
# 75 "/usr/include/stdio.h" 2 3 4




typedef __gnuc_va_list va_list;
# 90 "/usr/include/stdio.h" 3 4
typedef __off_t off_t;
# 102 "/usr/include/stdio.h" 3 4
typedef __ssize_t ssize_t;







typedef _G_fpos_t fpos_t;




# 164 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/stdio_lim.h" 1 3 4
# 165 "/usr/include/stdio.h" 2 3 4



extern struct _IO_FILE *stdin;
extern struct _IO_FILE *stdout;
extern struct _IO_FILE *stderr;







extern int remove (const char *__filename) __attribute__ ((__nothrow__ , __leaf__));

extern int rename (const char *__old, const char *__new) __attribute__ ((__nothrow__ , __leaf__));




extern int renameat (int __oldfd, const char *__old, int __newfd,
       const char *__new) __attribute__ ((__nothrow__ , __leaf__));








extern FILE *tmpfile (void) ;
# 209 "/usr/include/stdio.h" 3 4
extern char *tmpnam (char *__s) __attribute__ ((__nothrow__ , __leaf__)) ;





extern char *tmpnam_r (char *__s) __attribute__ ((__nothrow__ , __leaf__)) ;
# 227 "/usr/include/stdio.h" 3 4
extern char *tempnam (const char *__dir, const char *__pfx)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;








extern int fclose (FILE *__stream);




extern int fflush (FILE *__stream);

# 252 "/usr/include/stdio.h" 3 4
extern int fflush_unlocked (FILE *__stream);
# 266 "/usr/include/stdio.h" 3 4






extern FILE *fopen (const char *__restrict __filename,
      const char *__restrict __modes) ;




extern FILE *freopen (const char *__restrict __filename,
        const char *__restrict __modes,
        FILE *__restrict __stream) ;
# 295 "/usr/include/stdio.h" 3 4

# 306 "/usr/include/stdio.h" 3 4
extern FILE *fdopen (int __fd, const char *__modes) __attribute__ ((__nothrow__ , __leaf__)) ;
# 319 "/usr/include/stdio.h" 3 4
extern FILE *fmemopen (void *__s, size_t __len, const char *__modes)
  __attribute__ ((__nothrow__ , __leaf__)) ;




extern FILE *open_memstream (char **__bufloc, size_t *__sizeloc) __attribute__ ((__nothrow__ , __leaf__)) ;






extern void setbuf (FILE *__restrict __stream, char *__restrict __buf) __attribute__ ((__nothrow__ , __leaf__));



extern int setvbuf (FILE *__restrict __stream, char *__restrict __buf,
      int __modes, size_t __n) __attribute__ ((__nothrow__ , __leaf__));





extern void setbuffer (FILE *__restrict __stream, char *__restrict __buf,
         size_t __size) __attribute__ ((__nothrow__ , __leaf__));


extern void setlinebuf (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));








extern int fprintf (FILE *__restrict __stream,
      const char *__restrict __format, ...);




extern int printf (const char *__restrict __format, ...);

extern int sprintf (char *__restrict __s,
      const char *__restrict __format, ...) __attribute__ ((__nothrow__));





extern int vfprintf (FILE *__restrict __s, const char *__restrict __format,
       __gnuc_va_list __arg);




extern int vprintf (const char *__restrict __format, __gnuc_va_list __arg);

extern int vsprintf (char *__restrict __s, const char *__restrict __format,
       __gnuc_va_list __arg) __attribute__ ((__nothrow__));





extern int snprintf (char *__restrict __s, size_t __maxlen,
       const char *__restrict __format, ...)
     __attribute__ ((__nothrow__)) __attribute__ ((__format__ (__printf__, 3, 4)));

extern int vsnprintf (char *__restrict __s, size_t __maxlen,
        const char *__restrict __format, __gnuc_va_list __arg)
     __attribute__ ((__nothrow__)) __attribute__ ((__format__ (__printf__, 3, 0)));

# 412 "/usr/include/stdio.h" 3 4
extern int vdprintf (int __fd, const char *__restrict __fmt,
       __gnuc_va_list __arg)
     __attribute__ ((__format__ (__printf__, 2, 0)));
extern int dprintf (int __fd, const char *__restrict __fmt, ...)
     __attribute__ ((__format__ (__printf__, 2, 3)));








extern int fscanf (FILE *__restrict __stream,
     const char *__restrict __format, ...) ;




extern int scanf (const char *__restrict __format, ...) ;

extern int sscanf (const char *__restrict __s,
     const char *__restrict __format, ...) __attribute__ ((__nothrow__ , __leaf__));
# 443 "/usr/include/stdio.h" 3 4
extern int fscanf (FILE *__restrict __stream, const char *__restrict __format, ...) __asm__ ("" "__isoc99_fscanf")

                               ;
extern int scanf (const char *__restrict __format, ...) __asm__ ("" "__isoc99_scanf")
                              ;
extern int sscanf (const char *__restrict __s, const char *__restrict __format, ...) __asm__ ("" "__isoc99_sscanf") __attribute__ ((__nothrow__ , __leaf__))

                      ;
# 463 "/usr/include/stdio.h" 3 4








extern int vfscanf (FILE *__restrict __s, const char *__restrict __format,
      __gnuc_va_list __arg)
     __attribute__ ((__format__ (__scanf__, 2, 0))) ;





extern int vscanf (const char *__restrict __format, __gnuc_va_list __arg)
     __attribute__ ((__format__ (__scanf__, 1, 0))) ;


extern int vsscanf (const char *__restrict __s,
      const char *__restrict __format, __gnuc_va_list __arg)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__format__ (__scanf__, 2, 0)));
# 494 "/usr/include/stdio.h" 3 4
extern int vfscanf (FILE *__restrict __s, const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vfscanf")



     __attribute__ ((__format__ (__scanf__, 2, 0))) ;
extern int vscanf (const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vscanf")

     __attribute__ ((__format__ (__scanf__, 1, 0))) ;
extern int vsscanf (const char *__restrict __s, const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vsscanf") __attribute__ ((__nothrow__ , __leaf__))



     __attribute__ ((__format__ (__scanf__, 2, 0)));
# 522 "/usr/include/stdio.h" 3 4









extern int fgetc (FILE *__stream);
extern int getc (FILE *__stream);





extern int getchar (void);

# 550 "/usr/include/stdio.h" 3 4
extern int getc_unlocked (FILE *__stream);
extern int getchar_unlocked (void);
# 561 "/usr/include/stdio.h" 3 4
extern int fgetc_unlocked (FILE *__stream);











extern int fputc (int __c, FILE *__stream);
extern int putc (int __c, FILE *__stream);





extern int putchar (int __c);

# 594 "/usr/include/stdio.h" 3 4
extern int fputc_unlocked (int __c, FILE *__stream);







extern int putc_unlocked (int __c, FILE *__stream);
extern int putchar_unlocked (int __c);






extern int getw (FILE *__stream);


extern int putw (int __w, FILE *__stream);








extern char *fgets (char *__restrict __s, int __n, FILE *__restrict __stream)
     ;
# 638 "/usr/include/stdio.h" 3 4
extern char *gets (char *__s) __attribute__ ((__deprecated__));


# 665 "/usr/include/stdio.h" 3 4
extern __ssize_t __getdelim (char **__restrict __lineptr,
          size_t *__restrict __n, int __delimiter,
          FILE *__restrict __stream) ;
extern __ssize_t getdelim (char **__restrict __lineptr,
        size_t *__restrict __n, int __delimiter,
        FILE *__restrict __stream) ;







extern __ssize_t getline (char **__restrict __lineptr,
       size_t *__restrict __n,
       FILE *__restrict __stream) ;








extern int fputs (const char *__restrict __s, FILE *__restrict __stream);





extern int puts (const char *__s);






extern int ungetc (int __c, FILE *__stream);






extern size_t fread (void *__restrict __ptr, size_t __size,
       size_t __n, FILE *__restrict __stream) ;




extern size_t fwrite (const void *__restrict __ptr, size_t __size,
        size_t __n, FILE *__restrict __s);

# 737 "/usr/include/stdio.h" 3 4
extern size_t fread_unlocked (void *__restrict __ptr, size_t __size,
         size_t __n, FILE *__restrict __stream) ;
extern size_t fwrite_unlocked (const void *__restrict __ptr, size_t __size,
          size_t __n, FILE *__restrict __stream);








extern int fseek (FILE *__stream, long int __off, int __whence);




extern long int ftell (FILE *__stream) ;




extern void rewind (FILE *__stream);

# 773 "/usr/include/stdio.h" 3 4
extern int fseeko (FILE *__stream, __off_t __off, int __whence);




extern __off_t ftello (FILE *__stream) ;
# 792 "/usr/include/stdio.h" 3 4






extern int fgetpos (FILE *__restrict __stream, fpos_t *__restrict __pos);




extern int fsetpos (FILE *__stream, const fpos_t *__pos);
# 815 "/usr/include/stdio.h" 3 4

# 824 "/usr/include/stdio.h" 3 4


extern void clearerr (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));

extern int feof (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;

extern int ferror (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;




extern void clearerr_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
extern int feof_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int ferror_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;








extern void perror (const char *__s);






# 1 "/usr/include/x86_64-linux-gnu/bits/sys_errlist.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/sys_errlist.h" 3 4
extern int sys_nerr;
extern const char *const sys_errlist[];
# 854 "/usr/include/stdio.h" 2 3 4




extern int fileno (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;




extern int fileno_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
# 873 "/usr/include/stdio.h" 3 4
extern FILE *popen (const char *__command, const char *__modes) ;





extern int pclose (FILE *__stream);





extern char *ctermid (char *__s) __attribute__ ((__nothrow__ , __leaf__));
# 913 "/usr/include/stdio.h" 3 4
extern void flockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));



extern int ftrylockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;


extern void funlockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
# 934 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/stdio.h" 1 3 4
# 35 "/usr/include/x86_64-linux-gnu/bits/stdio.h" 3 4
extern __inline int
vprintf (const char *__restrict __fmt, __gnuc_va_list __arg)
{
  return vfprintf (stdout, __fmt, __arg);
}



extern __inline int
getchar (void)
{
  return _IO_getc (stdin);
}




extern __inline int
fgetc_unlocked (FILE *__fp)
{
  return (__builtin_expect (((__fp)->_IO_read_ptr >= (__fp)->_IO_read_end), 0) ? __uflow (__fp) : *(unsigned char *) (__fp)->_IO_read_ptr++);
}





extern __inline int
getc_unlocked (FILE *__fp)
{
  return (__builtin_expect (((__fp)->_IO_read_ptr >= (__fp)->_IO_read_end), 0) ? __uflow (__fp) : *(unsigned char *) (__fp)->_IO_read_ptr++);
}


extern __inline int
getchar_unlocked (void)
{
  return (__builtin_expect (((stdin)->_IO_read_ptr >= (stdin)->_IO_read_end), 0) ? __uflow (stdin) : *(unsigned char *) (stdin)->_IO_read_ptr++);
}




extern __inline int
putchar (int __c)
{
  return _IO_putc (__c, stdout);
}




extern __inline int
fputc_unlocked (int __c, FILE *__stream)
{
  return (__builtin_expect (((__stream)->_IO_write_ptr >= (__stream)->_IO_write_end), 0) ? __overflow (__stream, (unsigned char) (__c)) : (unsigned char) (*(__stream)->_IO_write_ptr++ = (__c)));
}





extern __inline int
putc_unlocked (int __c, FILE *__stream)
{
  return (__builtin_expect (((__stream)->_IO_write_ptr >= (__stream)->_IO_write_end), 0) ? __overflow (__stream, (unsigned char) (__c)) : (unsigned char) (*(__stream)->_IO_write_ptr++ = (__c)));
}


extern __inline int
putchar_unlocked (int __c)
{
  return (__builtin_expect (((stdout)->_IO_write_ptr >= (stdout)->_IO_write_end), 0) ? __overflow (stdout, (unsigned char) (__c)) : (unsigned char) (*(stdout)->_IO_write_ptr++ = (__c)));
}
# 124 "/usr/include/x86_64-linux-gnu/bits/stdio.h" 3 4
extern __inline int
__attribute__ ((__nothrow__ , __leaf__)) feof_unlocked (FILE *__stream)
{
  return (((__stream)->_flags & 0x10) != 0);
}


extern __inline int
__attribute__ ((__nothrow__ , __leaf__)) ferror_unlocked (FILE *__stream)
{
  return (((__stream)->_flags & 0x20) != 0);
}
# 935 "/usr/include/stdio.h" 2 3 4
# 943 "/usr/include/stdio.h" 3 4

# 20 "../../../../libxc/src/gga_k_dk.c" 2
# 1 "/usr/include/stdlib.h" 1 3 4
# 32 "/usr/include/stdlib.h" 3 4
# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 1 3 4
# 324 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 3 4
typedef int wchar_t;
# 33 "/usr/include/stdlib.h" 2 3 4








# 1 "/usr/include/x86_64-linux-gnu/bits/waitflags.h" 1 3 4
# 42 "/usr/include/stdlib.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/waitstatus.h" 1 3 4
# 64 "/usr/include/x86_64-linux-gnu/bits/waitstatus.h" 3 4
# 1 "/usr/include/endian.h" 1 3 4
# 36 "/usr/include/endian.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/endian.h" 1 3 4
# 37 "/usr/include/endian.h" 2 3 4
# 60 "/usr/include/endian.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 1 3 4
# 28 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 29 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 2 3 4






# 1 "/usr/include/x86_64-linux-gnu/bits/byteswap-16.h" 1 3 4
# 36 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 2 3 4
# 44 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 3 4
static __inline unsigned int
__bswap_32 (unsigned int __bsx)
{
  return __builtin_bswap32 (__bsx);
}
# 108 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 3 4
static __inline __uint64_t
__bswap_64 (__uint64_t __bsx)
{
  return __builtin_bswap64 (__bsx);
}
# 61 "/usr/include/endian.h" 2 3 4
# 65 "/usr/include/x86_64-linux-gnu/bits/waitstatus.h" 2 3 4

union wait
  {
    int w_status;
    struct
      {

 unsigned int __w_termsig:7;
 unsigned int __w_coredump:1;
 unsigned int __w_retcode:8;
 unsigned int:16;







      } __wait_terminated;
    struct
      {

 unsigned int __w_stopval:8;
 unsigned int __w_stopsig:8;
 unsigned int:16;






      } __wait_stopped;
  };
# 43 "/usr/include/stdlib.h" 2 3 4
# 67 "/usr/include/stdlib.h" 3 4
typedef union
  {
    union wait *__uptr;
    int *__iptr;
  } __WAIT_STATUS __attribute__ ((__transparent_union__));
# 95 "/usr/include/stdlib.h" 3 4


typedef struct
  {
    int quot;
    int rem;
  } div_t;



typedef struct
  {
    long int quot;
    long int rem;
  } ldiv_t;







__extension__ typedef struct
  {
    long long int quot;
    long long int rem;
  } lldiv_t;


# 139 "/usr/include/stdlib.h" 3 4
extern size_t __ctype_get_mb_cur_max (void) __attribute__ ((__nothrow__ , __leaf__)) ;




extern double atof (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

extern int atoi (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

extern long int atol (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;





__extension__ extern long long int atoll (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;





extern double strtod (const char *__restrict __nptr,
        char **__restrict __endptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));





extern float strtof (const char *__restrict __nptr,
       char **__restrict __endptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

extern long double strtold (const char *__restrict __nptr,
       char **__restrict __endptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));





extern long int strtol (const char *__restrict __nptr,
   char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

extern unsigned long int strtoul (const char *__restrict __nptr,
      char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));




__extension__
extern long long int strtoq (const char *__restrict __nptr,
        char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

__extension__
extern unsigned long long int strtouq (const char *__restrict __nptr,
           char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));





__extension__
extern long long int strtoll (const char *__restrict __nptr,
         char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

__extension__
extern unsigned long long int strtoull (const char *__restrict __nptr,
     char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

# 276 "/usr/include/stdlib.h" 3 4

extern __inline int
__attribute__ ((__nothrow__ , __leaf__)) atoi (const char *__nptr)
{
  return (int) strtol (__nptr, (char **) ((void *)0), 10);
}
extern __inline long int
__attribute__ ((__nothrow__ , __leaf__)) atol (const char *__nptr)
{
  return strtol (__nptr, (char **) ((void *)0), 10);
}




__extension__ extern __inline long long int
__attribute__ ((__nothrow__ , __leaf__)) atoll (const char *__nptr)
{
  return strtoll (__nptr, (char **) ((void *)0), 10);
}

# 305 "/usr/include/stdlib.h" 3 4
extern char *l64a (long int __n) __attribute__ ((__nothrow__ , __leaf__)) ;


extern long int a64l (const char *__s)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;




# 1 "/usr/include/x86_64-linux-gnu/sys/types.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4






typedef __u_char u_char;
typedef __u_short u_short;
typedef __u_int u_int;
typedef __u_long u_long;
typedef __quad_t quad_t;
typedef __u_quad_t u_quad_t;
typedef __fsid_t fsid_t;




typedef __loff_t loff_t;



typedef __ino_t ino_t;
# 60 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
typedef __dev_t dev_t;




typedef __gid_t gid_t;




typedef __mode_t mode_t;




typedef __nlink_t nlink_t;




typedef __uid_t uid_t;
# 98 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
typedef __pid_t pid_t;





typedef __id_t id_t;
# 115 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
typedef __daddr_t daddr_t;
typedef __caddr_t caddr_t;





typedef __key_t key_t;
# 132 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
# 1 "/usr/include/time.h" 1 3 4
# 57 "/usr/include/time.h" 3 4


typedef __clock_t clock_t;



# 73 "/usr/include/time.h" 3 4


typedef __time_t time_t;



# 91 "/usr/include/time.h" 3 4
typedef __clockid_t clockid_t;
# 103 "/usr/include/time.h" 3 4
typedef __timer_t timer_t;
# 133 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4
# 146 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 1 3 4
# 147 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4



typedef unsigned long int ulong;
typedef unsigned short int ushort;
typedef unsigned int uint;
# 194 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
typedef int int8_t __attribute__ ((__mode__ (__QI__)));
typedef int int16_t __attribute__ ((__mode__ (__HI__)));
typedef int int32_t __attribute__ ((__mode__ (__SI__)));
typedef int int64_t __attribute__ ((__mode__ (__DI__)));


typedef unsigned int u_int8_t __attribute__ ((__mode__ (__QI__)));
typedef unsigned int u_int16_t __attribute__ ((__mode__ (__HI__)));
typedef unsigned int u_int32_t __attribute__ ((__mode__ (__SI__)));
typedef unsigned int u_int64_t __attribute__ ((__mode__ (__DI__)));

typedef int register_t __attribute__ ((__mode__ (__word__)));
# 219 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/sys/select.h" 1 3 4
# 30 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/select.h" 1 3 4
# 22 "/usr/include/x86_64-linux-gnu/bits/select.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/select.h" 2 3 4
# 31 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/sigset.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/sigset.h" 3 4
typedef int __sig_atomic_t;




typedef struct
  {
    unsigned long int __val[(1024 / (8 * sizeof (unsigned long int)))];
  } __sigset_t;
# 34 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4



typedef __sigset_t sigset_t;





# 1 "/usr/include/time.h" 1 3 4
# 120 "/usr/include/time.h" 3 4
struct timespec
  {
    __time_t tv_sec;
    __syscall_slong_t tv_nsec;
  };
# 44 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/time.h" 1 3 4
# 30 "/usr/include/x86_64-linux-gnu/bits/time.h" 3 4
struct timeval
  {
    __time_t tv_sec;
    __suseconds_t tv_usec;
  };
# 46 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4


typedef __suseconds_t suseconds_t;





typedef long int __fd_mask;
# 64 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
typedef struct
  {






    __fd_mask __fds_bits[1024 / (8 * (int) sizeof (__fd_mask))];


  } fd_set;






typedef __fd_mask fd_mask;
# 96 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4

# 106 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
extern int select (int __nfds, fd_set *__restrict __readfds,
     fd_set *__restrict __writefds,
     fd_set *__restrict __exceptfds,
     struct timeval *__restrict __timeout);
# 118 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
extern int pselect (int __nfds, fd_set *__restrict __readfds,
      fd_set *__restrict __writefds,
      fd_set *__restrict __exceptfds,
      const struct timespec *__restrict __timeout,
      const __sigset_t *__restrict __sigmask);
# 131 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4

# 220 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/sys/sysmacros.h" 1 3 4
# 29 "/usr/include/x86_64-linux-gnu/sys/sysmacros.h" 3 4


__extension__
extern unsigned int gnu_dev_major (unsigned long long int __dev)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
__extension__
extern unsigned int gnu_dev_minor (unsigned long long int __dev)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
__extension__
extern unsigned long long int gnu_dev_makedev (unsigned int __major,
            unsigned int __minor)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


__extension__ extern __inline __attribute__ ((__const__)) unsigned int
__attribute__ ((__nothrow__ , __leaf__)) gnu_dev_major (unsigned long long int __dev)
{
  return ((__dev >> 8) & 0xfff) | ((unsigned int) (__dev >> 32) & ~0xfff);
}

__extension__ extern __inline __attribute__ ((__const__)) unsigned int
__attribute__ ((__nothrow__ , __leaf__)) gnu_dev_minor (unsigned long long int __dev)
{
  return (__dev & 0xff) | ((unsigned int) (__dev >> 12) & ~0xff);
}

__extension__ extern __inline __attribute__ ((__const__)) unsigned long long int
__attribute__ ((__nothrow__ , __leaf__)) gnu_dev_makedev (unsigned int __major, unsigned int __minor)
{
  return ((__minor & 0xff) | ((__major & 0xfff) << 8)
   | (((unsigned long long int) (__minor & ~0xff)) << 12)
   | (((unsigned long long int) (__major & ~0xfff)) << 32));
}


# 223 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4





typedef __blksize_t blksize_t;






typedef __blkcnt_t blkcnt_t;



typedef __fsblkcnt_t fsblkcnt_t;



typedef __fsfilcnt_t fsfilcnt_t;
# 270 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 1 3 4
# 21 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 22 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 2 3 4
# 60 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 3 4
typedef unsigned long int pthread_t;


union pthread_attr_t
{
  char __size[56];
  long int __align;
};

typedef union pthread_attr_t pthread_attr_t;





typedef struct __pthread_internal_list
{
  struct __pthread_internal_list *__prev;
  struct __pthread_internal_list *__next;
} __pthread_list_t;
# 90 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 3 4
typedef union
{
  struct __pthread_mutex_s
  {
    int __lock;
    unsigned int __count;
    int __owner;

    unsigned int __nusers;



    int __kind;

    int __spins;
    __pthread_list_t __list;
# 115 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 3 4
  } __data;
  char __size[40];
  long int __align;
} pthread_mutex_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_mutexattr_t;




typedef union
{
  struct
  {
    int __lock;
    unsigned int __futex;
    __extension__ unsigned long long int __total_seq;
    __extension__ unsigned long long int __wakeup_seq;
    __extension__ unsigned long long int __woken_seq;
    void *__mutex;
    unsigned int __nwaiters;
    unsigned int __broadcast_seq;
  } __data;
  char __size[48];
  __extension__ long long int __align;
} pthread_cond_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_condattr_t;



typedef unsigned int pthread_key_t;



typedef int pthread_once_t;





typedef union
{

  struct
  {
    int __lock;
    unsigned int __nr_readers;
    unsigned int __readers_wakeup;
    unsigned int __writer_wakeup;
    unsigned int __nr_readers_queued;
    unsigned int __nr_writers_queued;
    int __writer;
    int __shared;
    unsigned long int __pad1;
    unsigned long int __pad2;


    unsigned int __flags;

  } __data;
# 202 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 3 4
  char __size[56];
  long int __align;
} pthread_rwlock_t;

typedef union
{
  char __size[8];
  long int __align;
} pthread_rwlockattr_t;





typedef volatile int pthread_spinlock_t;




typedef union
{
  char __size[32];
  long int __align;
} pthread_barrier_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_barrierattr_t;
# 271 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4



# 315 "/usr/include/stdlib.h" 2 3 4






extern long int random (void) __attribute__ ((__nothrow__ , __leaf__));


extern void srandom (unsigned int __seed) __attribute__ ((__nothrow__ , __leaf__));





extern char *initstate (unsigned int __seed, char *__statebuf,
   size_t __statelen) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern char *setstate (char *__statebuf) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));







struct random_data
  {
    int32_t *fptr;
    int32_t *rptr;
    int32_t *state;
    int rand_type;
    int rand_deg;
    int rand_sep;
    int32_t *end_ptr;
  };

extern int random_r (struct random_data *__restrict __buf,
       int32_t *__restrict __result) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern int srandom_r (unsigned int __seed, struct random_data *__buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));

extern int initstate_r (unsigned int __seed, char *__restrict __statebuf,
   size_t __statelen,
   struct random_data *__restrict __buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 4)));

extern int setstate_r (char *__restrict __statebuf,
         struct random_data *__restrict __buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));






extern int rand (void) __attribute__ ((__nothrow__ , __leaf__));

extern void srand (unsigned int __seed) __attribute__ ((__nothrow__ , __leaf__));




extern int rand_r (unsigned int *__seed) __attribute__ ((__nothrow__ , __leaf__));







extern double drand48 (void) __attribute__ ((__nothrow__ , __leaf__));
extern double erand48 (unsigned short int __xsubi[3]) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern long int lrand48 (void) __attribute__ ((__nothrow__ , __leaf__));
extern long int nrand48 (unsigned short int __xsubi[3])
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern long int mrand48 (void) __attribute__ ((__nothrow__ , __leaf__));
extern long int jrand48 (unsigned short int __xsubi[3])
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern void srand48 (long int __seedval) __attribute__ ((__nothrow__ , __leaf__));
extern unsigned short int *seed48 (unsigned short int __seed16v[3])
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern void lcong48 (unsigned short int __param[7]) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));





struct drand48_data
  {
    unsigned short int __x[3];
    unsigned short int __old_x[3];
    unsigned short int __c;
    unsigned short int __init;
    unsigned long long int __a;
  };


extern int drand48_r (struct drand48_data *__restrict __buffer,
        double *__restrict __result) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int erand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        double *__restrict __result) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern int lrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int nrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern int mrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int jrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern int srand48_r (long int __seedval, struct drand48_data *__buffer)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));

extern int seed48_r (unsigned short int __seed16v[3],
       struct drand48_data *__buffer) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern int lcong48_r (unsigned short int __param[7],
        struct drand48_data *__buffer)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));









extern void *malloc (size_t __size) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;

extern void *calloc (size_t __nmemb, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;










extern void *realloc (void *__ptr, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__warn_unused_result__));

extern void free (void *__ptr) __attribute__ ((__nothrow__ , __leaf__));




extern void cfree (void *__ptr) __attribute__ ((__nothrow__ , __leaf__));



# 1 "/usr/include/alloca.h" 1 3 4
# 24 "/usr/include/alloca.h" 3 4
# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/stddef.h" 1 3 4
# 25 "/usr/include/alloca.h" 2 3 4







extern void *alloca (size_t __size) __attribute__ ((__nothrow__ , __leaf__));






# 492 "/usr/include/stdlib.h" 2 3 4





extern void *valloc (size_t __size) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;




extern int posix_memalign (void **__memptr, size_t __alignment, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;
# 512 "/usr/include/stdlib.h" 3 4


extern void abort (void) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));



extern int atexit (void (*__func) (void)) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
# 529 "/usr/include/stdlib.h" 3 4





extern int on_exit (void (*__func) (int __status, void *__arg), void *__arg)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));






extern void exit (int __status) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));













extern void _Exit (int __status) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));






extern char *getenv (const char *__name) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;

# 577 "/usr/include/stdlib.h" 3 4
extern int putenv (char *__string) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));





extern int setenv (const char *__name, const char *__value, int __replace)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));


extern int unsetenv (const char *__name) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));






extern int clearenv (void) __attribute__ ((__nothrow__ , __leaf__));
# 605 "/usr/include/stdlib.h" 3 4
extern char *mktemp (char *__template) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
# 619 "/usr/include/stdlib.h" 3 4
extern int mkstemp (char *__template) __attribute__ ((__nonnull__ (1))) ;
# 641 "/usr/include/stdlib.h" 3 4
extern int mkstemps (char *__template, int __suffixlen) __attribute__ ((__nonnull__ (1))) ;
# 662 "/usr/include/stdlib.h" 3 4
extern char *mkdtemp (char *__template) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;
# 711 "/usr/include/stdlib.h" 3 4





extern int system (const char *__command) ;

# 733 "/usr/include/stdlib.h" 3 4
extern char *realpath (const char *__restrict __name,
         char *__restrict __resolved) __attribute__ ((__nothrow__ , __leaf__)) ;






typedef int (*__compar_fn_t) (const void *, const void *);
# 751 "/usr/include/stdlib.h" 3 4



extern void *bsearch (const void *__key, const void *__base,
        size_t __nmemb, size_t __size, __compar_fn_t __compar)
     __attribute__ ((__nonnull__ (1, 2, 5))) ;



extern void qsort (void *__base, size_t __nmemb, size_t __size,
     __compar_fn_t __compar) __attribute__ ((__nonnull__ (1, 4)));
# 770 "/usr/include/stdlib.h" 3 4
extern int abs (int __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;
extern long int labs (long int __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;



__extension__ extern long long int llabs (long long int __x)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;







extern div_t div (int __numer, int __denom)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;
extern ldiv_t ldiv (long int __numer, long int __denom)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;




__extension__ extern lldiv_t lldiv (long long int __numer,
        long long int __denom)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;

# 807 "/usr/include/stdlib.h" 3 4
extern char *ecvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;




extern char *fcvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;




extern char *gcvt (double __value, int __ndigit, char *__buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3))) ;




extern char *qecvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qfcvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qgcvt (long double __value, int __ndigit, char *__buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3))) ;




extern int ecvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4, 5)));
extern int fcvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4, 5)));

extern int qecvt_r (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign,
      char *__restrict __buf, size_t __len)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4, 5)));
extern int qfcvt_r (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign,
      char *__restrict __buf, size_t __len)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4, 5)));







extern int mblen (const char *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) ;


extern int mbtowc (wchar_t *__restrict __pwc,
     const char *__restrict __s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) ;


extern int wctomb (char *__s, wchar_t __wchar) __attribute__ ((__nothrow__ , __leaf__)) ;



extern size_t mbstowcs (wchar_t *__restrict __pwcs,
   const char *__restrict __s, size_t __n) __attribute__ ((__nothrow__ , __leaf__));

extern size_t wcstombs (char *__restrict __s,
   const wchar_t *__restrict __pwcs, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__));








extern int rpmatch (const char *__response) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;
# 895 "/usr/include/stdlib.h" 3 4
extern int getsubopt (char **__restrict __optionp,
        char *const *__restrict __tokens,
        char **__restrict __valuep)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2, 3))) ;
# 947 "/usr/include/stdlib.h" 3 4
extern int getloadavg (double __loadavg[], int __nelem)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


# 1 "/usr/include/x86_64-linux-gnu/bits/stdlib-float.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/stdlib-float.h" 3 4

extern __inline double
__attribute__ ((__nothrow__ , __leaf__)) atof (const char *__nptr)
{
  return strtod (__nptr, (char **) ((void *)0));
}

# 952 "/usr/include/stdlib.h" 2 3 4
# 964 "/usr/include/stdlib.h" 3 4

# 21 "../../../../libxc/src/gga_k_dk.c" 2
# 1 "/usr/include/assert.h" 1 3 4
# 67 "/usr/include/assert.h" 3 4



extern void __assert_fail (const char *__assertion, const char *__file,
      unsigned int __line, const char *__function)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));


extern void __assert_perror_fail (int __errnum, const char *__file,
      unsigned int __line, const char *__function)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));




extern void __assert (const char *__assertion, const char *__file, int __line)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));



# 22 "../../../../libxc/src/gga_k_dk.c" 2
# 1 "../../../../libxc/src/util.h" 1
# 22 "../../../../libxc/src/util.h"
# 1 "/usr/include/math.h" 1 3 4
# 29 "/usr/include/math.h" 3 4




# 1 "/usr/include/x86_64-linux-gnu/bits/huge_val.h" 1 3 4
# 34 "/usr/include/math.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/huge_valf.h" 1 3 4
# 36 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/huge_vall.h" 1 3 4
# 37 "/usr/include/math.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/inf.h" 1 3 4
# 40 "/usr/include/math.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/nan.h" 1 3 4
# 43 "/usr/include/math.h" 2 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/mathdef.h" 1 3 4
# 28 "/usr/include/x86_64-linux-gnu/bits/mathdef.h" 3 4
typedef float float_t;
typedef double double_t;
# 47 "/usr/include/math.h" 2 3 4
# 70 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 52 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern double acos (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __acos (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double asin (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __asin (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double atan (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __atan (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double atan2 (double __y, double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __atan2 (double __y, double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double cos (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cos (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double sin (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sin (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double tan (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __tan (double __x) __attribute__ ((__nothrow__ , __leaf__));




extern double cosh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cosh (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double sinh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sinh (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double tanh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __tanh (double __x) __attribute__ ((__nothrow__ , __leaf__));

# 86 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern double acosh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __acosh (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double asinh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __asinh (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double atanh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __atanh (double __x) __attribute__ ((__nothrow__ , __leaf__));







extern double exp (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __exp (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double frexp (double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern double __frexp (double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern double ldexp (double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern double __ldexp (double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


extern double log (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double log10 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log10 (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double modf (double __x, double *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern double __modf (double __x, double *__iptr) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__nonnull__ (2)));

# 127 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern double expm1 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __expm1 (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double log1p (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log1p (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double logb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __logb (double __x) __attribute__ ((__nothrow__ , __leaf__));






extern double exp2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __exp2 (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double log2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log2 (double __x) __attribute__ ((__nothrow__ , __leaf__));








extern double pow (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __pow (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));


extern double sqrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sqrt (double __x) __attribute__ ((__nothrow__ , __leaf__));





extern double hypot (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __hypot (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));






extern double cbrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cbrt (double __x) __attribute__ ((__nothrow__ , __leaf__));








extern double ceil (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __ceil (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double fabs (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fabs (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double floor (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __floor (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double fmod (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __fmod (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));




extern int __isinf (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int __finite (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int isinf (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int finite (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double drem (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __drem (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));



extern double significand (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __significand (double __x) __attribute__ ((__nothrow__ , __leaf__));





extern double copysign (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __copysign (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));






extern double nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int __isnan (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int isnan (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double j0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __j0 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double j1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __j1 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double jn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double __jn (int, double) __attribute__ ((__nothrow__ , __leaf__));
extern double y0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __y0 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double y1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __y1 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double yn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double __yn (int, double) __attribute__ ((__nothrow__ , __leaf__));






extern double erf (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __erf (double) __attribute__ ((__nothrow__ , __leaf__));
extern double erfc (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __erfc (double) __attribute__ ((__nothrow__ , __leaf__));
extern double lgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __lgamma (double) __attribute__ ((__nothrow__ , __leaf__));






extern double tgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __tgamma (double) __attribute__ ((__nothrow__ , __leaf__));





extern double gamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __gamma (double) __attribute__ ((__nothrow__ , __leaf__));






extern double lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern double __lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));







extern double rint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __rint (double __x) __attribute__ ((__nothrow__ , __leaf__));


extern double nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));

extern double nexttoward (double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __nexttoward (double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern double remainder (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __remainder (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));



extern double scalbn (double __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalbn (double __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogb (double __x) __attribute__ ((__nothrow__ , __leaf__));




extern double scalbln (double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalbln (double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern double nearbyint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __nearbyint (double __x) __attribute__ ((__nothrow__ , __leaf__));



extern double round (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __round (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern double trunc (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __trunc (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern double remquo (double __x, double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern double __remquo (double __x, double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrint (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long long int llrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrint (double __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lround (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long long int llround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llround (double __x) __attribute__ ((__nothrow__ , __leaf__));



extern double fdim (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __fdim (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));


extern double fmax (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmax (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double fmin (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmin (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int __fpclassify (double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));


extern int __signbit (double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));



extern double fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ , __leaf__)); extern double __fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ , __leaf__));








extern double scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__));
# 71 "/usr/include/math.h" 2 3 4
# 89 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 52 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern float acosf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __acosf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float asinf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __asinf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float atanf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __atanf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float atan2f (float __y, float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __atan2f (float __y, float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float cosf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __cosf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float sinf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __sinf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float tanf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __tanf (float __x) __attribute__ ((__nothrow__ , __leaf__));




extern float coshf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __coshf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float sinhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __sinhf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float tanhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __tanhf (float __x) __attribute__ ((__nothrow__ , __leaf__));

# 86 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern float acoshf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __acoshf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float asinhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __asinhf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float atanhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __atanhf (float __x) __attribute__ ((__nothrow__ , __leaf__));







extern float expf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __expf (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float frexpf (float __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern float __frexpf (float __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern float ldexpf (float __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern float __ldexpf (float __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


extern float logf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __logf (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float log10f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __log10f (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float modff (float __x, float *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern float __modff (float __x, float *__iptr) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__nonnull__ (2)));

# 127 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern float expm1f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __expm1f (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float log1pf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __log1pf (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float logbf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __logbf (float __x) __attribute__ ((__nothrow__ , __leaf__));






extern float exp2f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __exp2f (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float log2f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __log2f (float __x) __attribute__ ((__nothrow__ , __leaf__));








extern float powf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __powf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));


extern float sqrtf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __sqrtf (float __x) __attribute__ ((__nothrow__ , __leaf__));





extern float hypotf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __hypotf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));






extern float cbrtf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __cbrtf (float __x) __attribute__ ((__nothrow__ , __leaf__));








extern float ceilf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __ceilf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float fabsf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fabsf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float floorf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __floorf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float fmodf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __fmodf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));




extern int __isinff (float __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int __finitef (float __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int isinff (float __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int finitef (float __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float dremf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __dremf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));



extern float significandf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __significandf (float __x) __attribute__ ((__nothrow__ , __leaf__));





extern float copysignf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __copysignf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));






extern float nanf (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __nanf (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int __isnanf (float __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int isnanf (float __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float j0f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __j0f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float j1f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __j1f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float jnf (int, float) __attribute__ ((__nothrow__ , __leaf__)); extern float __jnf (int, float) __attribute__ ((__nothrow__ , __leaf__));
extern float y0f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __y0f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float y1f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __y1f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float ynf (int, float) __attribute__ ((__nothrow__ , __leaf__)); extern float __ynf (int, float) __attribute__ ((__nothrow__ , __leaf__));






extern float erff (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __erff (float) __attribute__ ((__nothrow__ , __leaf__));
extern float erfcf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __erfcf (float) __attribute__ ((__nothrow__ , __leaf__));
extern float lgammaf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __lgammaf (float) __attribute__ ((__nothrow__ , __leaf__));






extern float tgammaf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __tgammaf (float) __attribute__ ((__nothrow__ , __leaf__));





extern float gammaf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __gammaf (float) __attribute__ ((__nothrow__ , __leaf__));






extern float lgammaf_r (float, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern float __lgammaf_r (float, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));







extern float rintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __rintf (float __x) __attribute__ ((__nothrow__ , __leaf__));


extern float nextafterf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __nextafterf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));

extern float nexttowardf (float __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __nexttowardf (float __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern float remainderf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __remainderf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));



extern float scalbnf (float __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalbnf (float __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf (float __x) __attribute__ ((__nothrow__ , __leaf__));




extern float scalblnf (float __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalblnf (float __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern float nearbyintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __nearbyintf (float __x) __attribute__ ((__nothrow__ , __leaf__));



extern float roundf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __roundf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern float truncf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __truncf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern float remquof (float __x, float __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern float __remquof (float __x, float __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern long long int llrintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf (float __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern long long int llroundf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf (float __x) __attribute__ ((__nothrow__ , __leaf__));



extern float fdimf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __fdimf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fmaxf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fmaxf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float fminf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fminf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int __fpclassifyf (float __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));


extern int __signbitf (float __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));



extern float fmaf (float __x, float __y, float __z) __attribute__ ((__nothrow__ , __leaf__)); extern float __fmaf (float __x, float __y, float __z) __attribute__ ((__nothrow__ , __leaf__));








extern float scalbf (float __x, float __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalbf (float __x, float __n) __attribute__ ((__nothrow__ , __leaf__));
# 90 "/usr/include/math.h" 2 3 4
# 136 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 52 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern long double acosl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __acosl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double asinl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __asinl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double atanl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __atanl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double atan2l (long double __y, long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __atan2l (long double __y, long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double cosl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __cosl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double sinl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __sinl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double tanl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __tanl (long double __x) __attribute__ ((__nothrow__ , __leaf__));




extern long double coshl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __coshl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double sinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __sinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double tanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __tanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

# 86 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern long double acoshl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __acoshl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double asinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __asinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double atanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __atanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));







extern long double expl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __expl (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double frexpl (long double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern long double __frexpl (long double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern long double ldexpl (long double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern long double __ldexpl (long double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


extern long double logl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __logl (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double log10l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __log10l (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double modfl (long double __x, long double *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern long double __modfl (long double __x, long double *__iptr) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__nonnull__ (2)));

# 127 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4


extern long double expm1l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __expm1l (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double log1pl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __log1pl (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double logbl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __logbl (long double __x) __attribute__ ((__nothrow__ , __leaf__));






extern long double exp2l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __exp2l (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double log2l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __log2l (long double __x) __attribute__ ((__nothrow__ , __leaf__));








extern long double powl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __powl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


extern long double sqrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __sqrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__));





extern long double hypotl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __hypotl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));






extern long double cbrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __cbrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__));








extern long double ceill (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __ceill (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double fabsl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fabsl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double floorl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __floorl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double fmodl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __fmodl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));




extern int __isinfl (long double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int __finitel (long double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int isinfl (long double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int finitel (long double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double dreml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __dreml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));



extern long double significandl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __significandl (long double __x) __attribute__ ((__nothrow__ , __leaf__));





extern long double copysignl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __copysignl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));






extern long double nanl (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __nanl (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int __isnanl (long double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int isnanl (long double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double j0l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __j0l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double j1l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __j1l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double jnl (int, long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __jnl (int, long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double y0l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __y0l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double y1l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __y1l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double ynl (int, long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __ynl (int, long double) __attribute__ ((__nothrow__ , __leaf__));






extern long double erfl (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __erfl (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double erfcl (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __erfcl (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double lgammal (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __lgammal (long double) __attribute__ ((__nothrow__ , __leaf__));






extern long double tgammal (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __tgammal (long double) __attribute__ ((__nothrow__ , __leaf__));





extern long double gammal (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __gammal (long double) __attribute__ ((__nothrow__ , __leaf__));






extern long double lgammal_r (long double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern long double __lgammal_r (long double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));







extern long double rintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __rintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));


extern long double nextafterl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __nextafterl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));

extern long double nexttowardl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __nexttowardl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern long double remainderl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __remainderl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));



extern long double scalbnl (long double __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern long double __scalbnl (long double __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbl (long double __x) __attribute__ ((__nothrow__ , __leaf__));




extern long double scalblnl (long double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern long double __scalblnl (long double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern long double nearbyintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nearbyintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));



extern long double roundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __roundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern long double truncl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __truncl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern long double remquol (long double __x, long double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern long double __remquol (long double __x, long double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long long int llrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long long int llroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__));



extern long double fdiml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __fdiml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


extern long double fmaxl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fmaxl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double fminl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fminl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int __fpclassifyl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));


extern int __signbitl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));



extern long double fmal (long double __x, long double __y, long double __z) __attribute__ ((__nothrow__ , __leaf__)); extern long double __fmal (long double __x, long double __y, long double __z) __attribute__ ((__nothrow__ , __leaf__));








extern long double scalbl (long double __x, long double __n) __attribute__ ((__nothrow__ , __leaf__)); extern long double __scalbl (long double __x, long double __n) __attribute__ ((__nothrow__ , __leaf__));
# 137 "/usr/include/math.h" 2 3 4
# 152 "/usr/include/math.h" 3 4
extern int signgam;
# 193 "/usr/include/math.h" 3 4
enum
  {
    FP_NAN =

      0,
    FP_INFINITE =

      1,
    FP_ZERO =

      2,
    FP_SUBNORMAL =

      3,
    FP_NORMAL =

      4
  };
# 291 "/usr/include/math.h" 3 4
typedef enum
{
  _IEEE_ = -1,
  _SVID_,
  _XOPEN_,
  _POSIX_,
  _ISOC_
} _LIB_VERSION_TYPE;




extern _LIB_VERSION_TYPE _LIB_VERSION;
# 316 "/usr/include/math.h" 3 4
struct exception

  {
    int type;
    char *name;
    double arg1;
    double arg2;
    double retval;
  };




extern int matherr (struct exception *__exc);
# 416 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathinline.h" 1 3 4
# 123 "/usr/include/x86_64-linux-gnu/bits/mathinline.h" 3 4



extern __inline __attribute__ ((__always_inline__)) int
__attribute__ ((__nothrow__ , __leaf__)) __signbitf (float __x)
{

  int __m;
  __asm ("pmovmskb %1, %0" : "=r" (__m) : "x" (__x));
  return (__m & 0x8) != 0;




}
extern __inline __attribute__ ((__always_inline__)) int
__attribute__ ((__nothrow__ , __leaf__)) __signbit (double __x)
{

  int __m;
  __asm ("pmovmskb %1, %0" : "=r" (__m) : "x" (__x));
  return (__m & 0x80) != 0;




}
extern __inline __attribute__ ((__always_inline__)) int
__attribute__ ((__nothrow__ , __leaf__)) __signbitl (long double __x)
{
  __extension__ union { long double __l; int __i[3]; } __u = { __l: __x };
  return (__u.__i[2] & 0x8000) != 0;
}


# 417 "/usr/include/math.h" 2 3 4





# 1 "/usr/include/x86_64-linux-gnu/bits/math-finite.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/math-finite.h" 3 4
extern double acos (double) __asm__ ("" "__acos_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float acosf (float) __asm__ ("" "__acosf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double acosl (long double) __asm__ ("" "__acosl_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double acosh (double) __asm__ ("" "__acosh_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float acoshf (float) __asm__ ("" "__acoshf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double acoshl (long double) __asm__ ("" "__acoshl_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double asin (double) __asm__ ("" "__asin_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float asinf (float) __asm__ ("" "__asinf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double asinl (long double) __asm__ ("" "__asinl_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double atan2 (double, double) __asm__ ("" "__atan2_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float atan2f (float, float) __asm__ ("" "__atan2f_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double atan2l (long double, long double) __asm__ ("" "__atan2l_finite") __attribute__ ((__nothrow__ , __leaf__))
                       ;





extern double atanh (double) __asm__ ("" "__atanh_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float atanhf (float) __asm__ ("" "__atanhf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double atanhl (long double) __asm__ ("" "__atanhl_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double cosh (double) __asm__ ("" "__cosh_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float coshf (float) __asm__ ("" "__coshf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double coshl (long double) __asm__ ("" "__coshl_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double exp (double) __asm__ ("" "__exp_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float expf (float) __asm__ ("" "__expf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double expl (long double) __asm__ ("" "__expl_finite") __attribute__ ((__nothrow__ , __leaf__));
# 132 "/usr/include/x86_64-linux-gnu/bits/math-finite.h" 3 4
extern double exp2 (double) __asm__ ("" "__exp2_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float exp2f (float) __asm__ ("" "__exp2f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double exp2l (long double) __asm__ ("" "__exp2l_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double fmod (double, double) __asm__ ("" "__fmod_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float fmodf (float, float) __asm__ ("" "__fmodf_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double fmodl (long double, long double) __asm__ ("" "__fmodl_finite") __attribute__ ((__nothrow__ , __leaf__))
                      ;





extern double hypot (double, double) __asm__ ("" "__hypot_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float hypotf (float, float) __asm__ ("" "__hypotf_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double hypotl (long double, long double) __asm__ ("" "__hypotl_finite") __attribute__ ((__nothrow__ , __leaf__))
                       ;






extern double j0 (double) __asm__ ("" "__j0_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float j0f (float) __asm__ ("" "__j0f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double j0l (long double) __asm__ ("" "__j0l_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double y0 (double) __asm__ ("" "__y0_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float y0f (float) __asm__ ("" "__y0f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double y0l (long double) __asm__ ("" "__y0l_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double j1 (double) __asm__ ("" "__j1_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float j1f (float) __asm__ ("" "__j1f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double j1l (long double) __asm__ ("" "__j1l_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double y1 (double) __asm__ ("" "__y1_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float y1f (float) __asm__ ("" "__y1f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double y1l (long double) __asm__ ("" "__y1l_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double jn (int, double) __asm__ ("" "__jn_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float jnf (int, float) __asm__ ("" "__jnf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double jnl (int, long double) __asm__ ("" "__jnl_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double yn (int, double) __asm__ ("" "__yn_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float ynf (int, float) __asm__ ("" "__ynf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double ynl (int, long double) __asm__ ("" "__ynl_finite") __attribute__ ((__nothrow__ , __leaf__));






extern double lgamma_r (double, int *) __asm__ ("" "__lgamma_r_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float lgammaf_r (float, int *) __asm__ ("" "__lgammaf_r_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double lgammal_r (long double, int *) __asm__ ("" "__lgammal_r_finite") __attribute__ ((__nothrow__ , __leaf__))
                          ;






extern __inline __attribute__ ((__always_inline__)) double __attribute__ ((__nothrow__ , __leaf__)) lgamma (double __d)
{

  int __local_signgam = 0;
  return lgamma_r (__d, &__local_signgam);



}
extern __inline __attribute__ ((__always_inline__)) float __attribute__ ((__nothrow__ , __leaf__)) lgammaf (float __d)
{

  int __local_signgam = 0;
  return lgammaf_r (__d, &__local_signgam);



}

extern __inline __attribute__ ((__always_inline__)) long double __attribute__ ((__nothrow__ , __leaf__)) lgammal (long double __d)
{

  int __local_signgam = 0;
  return lgammal_r (__d, &__local_signgam);



}





extern __inline __attribute__ ((__always_inline__)) double __attribute__ ((__nothrow__ , __leaf__)) gamma (double __d)
{

  int __local_signgam = 0;
  return lgamma_r (__d, &__local_signgam);



}
extern __inline __attribute__ ((__always_inline__)) float __attribute__ ((__nothrow__ , __leaf__)) gammaf (float __d)
{

  int __local_signgam = 0;
  return lgammaf_r (__d, &__local_signgam);



}

extern __inline __attribute__ ((__always_inline__)) long double __attribute__ ((__nothrow__ , __leaf__)) gammal (long double __d)
{

  int __local_signgam = 0;
  return lgammal_r (__d, &__local_signgam);



}




extern double log (double) __asm__ ("" "__log_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float logf (float) __asm__ ("" "__logf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double logl (long double) __asm__ ("" "__logl_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double log10 (double) __asm__ ("" "__log10_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float log10f (float) __asm__ ("" "__log10f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double log10l (long double) __asm__ ("" "__log10l_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double log2 (double) __asm__ ("" "__log2_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float log2f (float) __asm__ ("" "__log2f_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double log2l (long double) __asm__ ("" "__log2l_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double ldexp (double, int) __asm__ ("" "scalbn") __attribute__ ((__nothrow__ , __leaf__));
extern float ldexpf (float, int) __asm__ ("" "scalbnf") __attribute__ ((__nothrow__ , __leaf__));

extern long double ldexpl (long double, int) __asm__ ("" "scalbnl") __attribute__ ((__nothrow__ , __leaf__));



extern double pow (double, double) __asm__ ("" "__pow_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float powf (float, float) __asm__ ("" "__powf_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double powl (long double, long double) __asm__ ("" "__powl_finite") __attribute__ ((__nothrow__ , __leaf__))
                     ;




extern double remainder (double, double) __asm__ ("" "__remainder_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float remainderf (float, float) __asm__ ("" "__remainderf_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double remainderl (long double, long double) __asm__ ("" "__remainderl_finite") __attribute__ ((__nothrow__ , __leaf__))
                           ;





extern double scalb (double, double) __asm__ ("" "__scalb_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float scalbf (float, float) __asm__ ("" "__scalbf_finite") __attribute__ ((__nothrow__ , __leaf__));





extern long double scalbl (long double, long double) __asm__ ("" "__scalbl_finite") __attribute__ ((__nothrow__ , __leaf__))
                       ;





extern double sinh (double) __asm__ ("" "__sinh_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float sinhf (float) __asm__ ("" "__sinhf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double sinhl (long double) __asm__ ("" "__sinhl_finite") __attribute__ ((__nothrow__ , __leaf__));




extern double sqrt (double) __asm__ ("" "__sqrt_finite") __attribute__ ((__nothrow__ , __leaf__));
extern float sqrtf (float) __asm__ ("" "__sqrtf_finite") __attribute__ ((__nothrow__ , __leaf__));




extern long double sqrtl (long double) __asm__ ("" "__sqrtl_finite") __attribute__ ((__nothrow__ , __leaf__));





extern double __gamma_r_finite (double, int *);
extern __inline __attribute__ ((__always_inline__)) double __attribute__ ((__nothrow__ , __leaf__)) tgamma (double __d)
{
  int __local_signgam = 0;
  double __res = __gamma_r_finite (__d, &__local_signgam);
  return __local_signgam < 0 ? -__res : __res;
}
extern float __gammaf_r_finite (float, int *);
extern __inline __attribute__ ((__always_inline__)) float __attribute__ ((__nothrow__ , __leaf__)) tgammaf (float __d)
{
  int __local_signgam = 0;
  float __res = __gammaf_r_finite (__d, &__local_signgam);
  return __local_signgam < 0 ? -__res : __res;
}

extern long double __gammal_r_finite (long double, int *);
extern __inline __attribute__ ((__always_inline__)) long double __attribute__ ((__nothrow__ , __leaf__)) tgammal (long double __d)
{
  int __local_signgam = 0;



  long double __res = __gammal_r_finite (__d, &__local_signgam);

  return __local_signgam < 0 ? -__res : __res;
}
# 423 "/usr/include/math.h" 2 3 4
# 478 "/usr/include/math.h" 3 4

# 23 "../../../../libxc/src/util.h" 2
# 1 "/usr/lib/gcc/x86_64-linux-gnu/4.8/include/float.h" 1 3 4
# 24 "../../../../libxc/src/util.h" 2
# 1 "../../../../libxc/src/xc_config.h" 1
# 25 "../../../../libxc/src/util.h" 2
# 50 "../../../../libxc/src/util.h"
double lambert_w(double z);


static inline double
cheb_eval(const double x, const double *cs, const int N)
{
  int i;
  double twox, b0, b1, b2;

  b2 = b1 = b0 = 0.0;

  twox = 2.0*x;
  for(i=N-1; i>=0; i--){
    b2 = b1;
    b1 = b0;
    b0 = twox*b1 - b2 + cs[i];
  }

  return 0.5*(b0 - b2);
}

double bessel_I0_scaled(const double x);
double bessel_I0(const double x);
double bessel_K0_scaled(const double x);
double bessel_K0(const double x);
double bessel_K1_scaled(const double x);
double bessel_K1(const double x);

double expint_e1_impl(const double x, const int scale);
static inline double expint_e1(const double x) { return expint_e1_impl( x, 0); }
static inline double expint_e1_scaled(const double x) { return expint_e1_impl( x, 1); }
static inline double expint_Ei(const double x) { return -expint_e1_impl(-x, 0); }
static inline double expint_Ei_scaled(const double x) { return -expint_e1_impl(-x, 1); }


typedef void integr_fn(double *x, int n, void *ex);
double integrate(integr_fn func, void *ex, double a, double b);
void rdqagse(integr_fn f, void *ex, double *a, double *b,
      double *epsabs, double *epsrel, int *limit, double *result,
      double *abserr, int *neval, int *ier, double *alist__,
      double *blist, double *rlist, double *elist, int *iord, int *last);

typedef struct xc_functional_key_t {
  char name[256];
  int number;
} xc_functional_key_t;
# 119 "../../../../libxc/src/util.h"
# 1 "../../../../libxc/src/xc.h" 1
# 26 "../../../../libxc/src/xc.h"
# 1 "../xc_version.h" 1
# 27 "../../../../libxc/src/xc.h" 2
# 1 "../../../../libxc/src/xc_config.h" 1
# 28 "../../../../libxc/src/xc.h" 2
# 69 "../../../../libxc/src/xc.h"
void xc_version(int *major, int *minor);

struct xc_func_type;

typedef struct{
  int number;
  int kind;

  char *name;
  int family;
  char *refs;

  int flags;

  double min_dens;
  double min_grad;
  double min_tau;
  double min_zeta;

  void (*init)(struct xc_func_type *p);
  void (*end) (struct xc_func_type *p);
  void (*lda) (const struct xc_func_type *p, int np,
        const double *rho,
        double *zk, double *vrho, double *v2rho2, double *v3rho3);
  void (*gga) (const struct xc_func_type *p, int np,
        const double *rho, const double *sigma,
        double *zk, double *vrho, double *vsigma,
        double *v2rho2, double *v2rhosigma, double *v2sigma2);
  void (*mgga)(const struct xc_func_type *p, int np,
        const double *rho, const double *sigma, const double *lapl_rho, const double *tau,
        double *zk, double *vrho, double *vsigma, double *vlapl_rho, double *vtau,
        double *v2rho2, double *v2sigma2, double *v2tau2, double *v2lapl2,
        double *v2rhosigma, double *v2rhotau, double *v2rholapl,
        double *v2sigmatau, double *v2sigmalapl, double *v2taulapl);
} xc_func_info_type;


struct xc_func_type{
  const xc_func_info_type *info;
  int nspin;

  int n_func_aux;
  struct xc_func_type **func_aux;
  double *mix_coef;

  double cam_omega;
  double cam_alpha;
  double cam_beta;

  int func;
  int n_rho, n_sigma, n_tau, n_lapl;
  int n_zk;
  int n_vrho, n_vsigma, n_vtau, n_vlapl;
  int n_v2rho2, n_v2sigma2, n_v2tau2, n_v2lapl2,
    n_v2rhosigma, n_v2rhotau, n_v2rholapl,
    n_v2sigmatau, n_v2sigmalapl, n_v2lapltau;
  int n_v3rho3;

  void *params;
};

typedef struct xc_func_type xc_func_type;


int xc_functional_get_number(const char *name);
char *xc_functional_get_name(int number);
int xc_family_from_id(int id, int *family, int *number);
int xc_func_init(xc_func_type *p, int functional, int nspin);
void xc_func_end(xc_func_type *p);

# 1 "./xc_funcs.h" 1
# 140 "../../../../libxc/src/xc.h" 2

int xc_lda_init(xc_func_type *p, const xc_func_info_type *info, int nspin);
void xc_lda_end (xc_func_type *p);

void xc_lda (const xc_func_type *p, int np, const double *rho, double *zk, double *vrho, double *v2rho2, double *v3rho3);
void xc_lda_exc (const xc_func_type *p, int np, const double *rho, double *zk);
void xc_lda_exc_vxc(const xc_func_type *p, int np, const double *rho, double *zk, double *vrho);
void xc_lda_vxc (const xc_func_type *p, int np, const double *rho, double *vrho);
void xc_lda_fxc (const xc_func_type *p, int np, const double *rho, double *v2rho2);
void xc_lda_kxc (const xc_func_type *p, int np, const double *rho, double *v3rho3);

void xc_lda_x_set_params (xc_func_type *p, double alpha, int relativistic, double omega);
void xc_lda_x_1d_set_params (xc_func_type *p, int interaction, double bb);
void xc_lda_c_1d_csc_set_params (xc_func_type *p, int interaction, double bb);
void xc_lda_c_xalpha_set_params (xc_func_type *p, double alpha);
void xc_lda_c_2d_prm_set_params (xc_func_type *p, double N);
void xc_lda_c_vwn_set_params (xc_func_type *p, int spin_interpolation);


int xc_gga_init(xc_func_type *p, const xc_func_info_type *info, int nspin);
void xc_gga_end (xc_func_type *p);
void xc_gga (const xc_func_type *p, int np, const double *rho, const double *sigma,
    double *zk, double *vrho, double *vsigma,
    double *v2rho2, double *v2rhosigma, double *v2sigma2);
void xc_gga_exc(const xc_func_type *p, int np, const double *rho, const double *sigma,
   double *zk);
void xc_gga_exc_vxc(const xc_func_type *p, int np, const double *rho, const double *sigma,
       double *zk, double *vrho, double *vsigma);
void xc_gga_vxc(const xc_func_type *p, int np, const double *rho, const double *sigma,
   double *vrho, double *vsigma);
void xc_gga_fxc(const xc_func_type *p, int np, const double *rho, const double *sigma,
   double *v2rho2, double *v2rhosigma, double *v2sigma2);

void xc_gga_lb_modified (const xc_func_type *p, int np, const double *rho, const double *sigma,
      double r, double *vrho);

void xc_gga_x_b88_set_params (xc_func_type *p, double beta, double gamma);
void xc_gga_x_pbe_set_params (xc_func_type *p, double kappa, double mu);
void xc_gga_x_pw91_set_params (xc_func_type *p, double a, double b, double c, double d, double f, double alpha, double expo);
void xc_gga_x_pw91_set_params2 (xc_func_type *p, double bt, double alpha, double expo);
void xc_gga_x_rpbe_set_params (xc_func_type *p, double kappa, double mu);
void xc_gga_x_optx_set_params (xc_func_type *p, double a, double b, double gamma);
void xc_gga_c_lyp_set_params (xc_func_type *p, double A, double B, double c, double d);
void xc_gga_lb_set_params (xc_func_type *p, int modified, double threshold, double ip, double qtot);
void xc_gga_k_tflw_set_params (xc_func_type *p, double gamma, double lambda, double N);
void xc_gga_x_2d_b88_set_params (xc_func_type *p, double beta);
void xc_gga_x_wpbeh_set_params (xc_func_type *p, double omega);
void xc_gga_x_hjs_set_params (xc_func_type *p, double omega);
void xc_gga_x_ityh_set_params (xc_func_type *p, int func_id, double omega);
void xc_gga_x_ssb_sw_set_params (xc_func_type *p, double A, double B, double C, double D, double E);
void xc_gga_x_kt_set_params (xc_func_type *p, double gamma, double delta);

double xc_hyb_exx_coef(const xc_func_type *p);
void xc_hyb_cam_coef(const xc_func_type *p, double *omega, double *alpha, double *beta);

void xc_hyb_gga_xc_hse_set_params (xc_func_type *p, double alpha, double omega);
void xc_hyb_gga_xc_pbeh_set_params(xc_func_type *p, double alpha);


int xc_mgga_init(xc_func_type *p, const xc_func_info_type *info, int nspin);
void xc_mgga_end (xc_func_type *p);
void xc_mgga (const xc_func_type *p, int np,
        const double *rho, const double *sigma, const double *lapl, const double *tau,
        double *zk, double *vrho, double *vsigma, double *vlapl, double *vtau,
        double *v2rho2, double *v2sigma2, double *v2lapl2, double *v2tau2,
        double *v2rhosigma, double *v2rholapl, double *v2rhotau,
        double *v2sigmalapl, double *v2sigmatau, double *v2lapltau);
void xc_mgga_exc (const xc_func_type *p, int np,
        const double *rho, const double *sigma, const double *lapl, const double *tau,
        double *zk);
void xc_mgga_exc_vxc(const xc_func_type *p, int np,
        const double *rho, const double *sigma, const double *lapl, const double *tau,
        double *zk, double *vrho, double *vsigma, double *vlapl, double *vtau);
void xc_mgga_vxc (const xc_func_type *p, int np,
        const double *rho, const double *sigma, const double *lapl, const double *tau,
        double *vrho, double *vsigma, double *vlapl, double *vtau);
void xc_mgga_fxc (const xc_func_type *p, int np,
        const double *rho, const double *sigma, const double *lapl, const double *tau,
        double *v2rho2, double *v2sigma2, double *v2lapl2, double *v2tau2,
        double *v2rhosigma, double *v2rholapl, double *v2rhotau,
        double *v2sigmalapl, double *v2sigmatau, double *v2lapltau);

void xc_mgga_x_tb09_set_params(xc_func_type *p, double c);
void xc_mgga_c_bc95_set_params(xc_func_type *p, double css, double copp);


void xc_mix_func
  (const xc_func_type *func, int np,
   const double *rho, const double *sigma, const double *lapl, const double *tau,
   double *zk, double *vrho, double *vsigma, double *vlapl, double *vtau,
   double *v2rho2, double *v2sigma2, double *v2lapl2, double *v2tau2,
   double *v2rhosigma, double *v2rholapl, double *v2rhotau,
   double *v2sigmalapl, double *v2sigmatau, double *v2lapltau);
# 120 "../../../../libxc/src/util.h" 2


void xc_rho2dzeta(int nspin, const double *rho, double *d, double *zeta);
void xc_fast_fzeta(const double x, const int nspin, const int order, double * fz);
void xc_mix_init(xc_func_type *p, int n_funcs, const int *funcs_id, const double *mix_coef);


typedef struct xc_lda_work_t {
  int order;
  double rs[3], zeta;

  double zk;
  double dedrs, dedz;
  double d2edrs2, d2edrsz, d2edz2;
  double d3edrs3, d3edrs2z, d3edrsz2, d3edz3;
} xc_lda_work_t;

void xc_lda_fxc_fd(const xc_func_type *p, int np, const double *rho, double *fxc);
void xc_lda_kxc_fd(const xc_func_type *p, int np, const double *rho, double *kxc);

void xc_lda_x_attenuation_function(int interaction, int order, double aa, double *f, double *df, double *d2f, double *d3f);
void xc_lda_stoll(const xc_func_type *pw, double dens, double zeta, int order, xc_lda_work_t res[3]);


void xc_lda_c_hl_func (const xc_func_type *p, xc_lda_work_t *r);
void xc_lda_c_pw_func (const xc_func_type *p, xc_lda_work_t *r);
void xc_lda_c_pz_func (const xc_func_type *p, xc_lda_work_t *r);
void xc_lda_c_rc04_func(const xc_func_type *p, xc_lda_work_t *r);


void work_gga_becke_init(xc_func_type *p);


void xc_gga_x_wc_enhance (const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);
void xc_gga_x_pbe_enhance (const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);
void xc_gga_x_pw91_enhance(const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);
void xc_gga_x_rpbe_enhance(const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);
void xc_gga_x_htbs_enhance(const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);
void xc_gga_x_b88_enhance (const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);
void xc_gga_x_g96_enhance (const xc_func_type *p, int order, double x, double *f, double *dfdx, double *d2fdx2);



typedef struct xc_gga_work_c_t {
  int order;

  double dens, ds[2], sigmat, sigmas[3];
  double rs, zeta, xt, xs[2];

  double f;
  double dfdrs, dfdz, dfdxt, dfdxs[2];
  double d2fdrs2, d2fdrsz, d2fdrsxt, d2fdrsxs[2], d2fdz2,
    d2fdzxt, d2fdzxs[2], d2fdxt2, d2fdxtxs[2], d2fdxs2[3];
} xc_gga_work_c_t;

void xc_gga_c_pw91_func(const xc_func_type *p, xc_gga_work_c_t *r);
void xc_gga_c_pbe_func (const xc_func_type *p, xc_gga_work_c_t *r);


typedef struct xc_mgga_work_x_t {
  int order;
  double rs, zeta, x, t, u;

  double f;
  double dfdrs, dfdx, dfdt, dfdu;
  double d2fdrs2, d2fdx2, d2fdt2, d2fdu2;
  double d2fdrsx, d2fdrst, d2fdrsu, d2fdxt, d2fdxu, d2fdtu;
} xc_mgga_work_x_t;

typedef struct xc_mgga_work_c_t {
  int order;

  double dens, ds[2], sigmat, sigmas[3];
  double rs, zeta, xt, xs[2], ts[2], us[2];

  double f;
  double dfdrs, dfdz, dfdxt, dfdxs[2], dfdts[2], dfdus[2];
  double d2fdrs2, d2fdrsz, d2fdrsxt, d2fdrsxs[2], d2fdrsts[2], d2fdrsus[2];
  double d2fdz2, d2fdzxt, d2fdzxs[2], d2fdzts[2], d2fdzus[2];
  double d2fdxt2, d2fdxtxs[2], d2fdxtts[2], d2fdxtus[2];
  double d2fdxs2[3], d2fxsts[4], d2fxsus[4];
  double d2dts2[3], d2fdtsus[4];
  double d2fdus2[3];
} xc_mgga_work_c_t;


void xc_pbe_c_stoll (const xc_func_type *pbe, int get_max, const xc_mgga_work_c_t *in, xc_gga_work_c_t out[3]);

void xc_mgga_series_w(int order, int n, const double *a, double t, double *fw, double *dfwdt);
void xc_mgga_b97_func_g(const double *cc, double gamma, double s, int order, double *g, double *dgds, double *d2gds2);
void xc_mgga_x_gvt4_func(int order, double x, double z, double alpha, const double *d, double *h, double *dhdx, double *dhdz);
# 23 "../../../../libxc/src/gga_k_dk.c" 2







typedef struct{
  double aa[5], bb[5];
} gga_k_dk_params;

static void
gga_k_dk_init(xc_func_type *p)
{
  int i;
  double ff, *aa, *bb;

  ((p->params == ((void *)0)) ? (void) (0) : __assert_fail ("p->params == ((void *)0)", "../../../../libxc/src/gga_k_dk.c", 40, __PRETTY_FUNCTION__));
  p->params = malloc(sizeof(gga_k_dk_params));


  aa = ((gga_k_dk_params *) (p->params))->aa;
  bb = ((gga_k_dk_params *) (p->params))->bb;


  for(i=0; i<5; i++){
    aa[i] = 0.0;
    bb[i] = 0.0;
  }

  switch(p->info->number){
  case 516:
    ff = 5.0*0.1282782438530421943003109254455883701296*0.1282782438530421943003109254455883701296/27.0;

    bb[0] = 1.0;
    bb[1] = -0.05 *ff;
    bb[2] = 9.99802*(ff*ff);
    bb[3] = 2.96085*(ff*ff*ff);

    aa[0] = 1.0;
    aa[1] = 0.95 *ff;
    aa[2] = 14.28111*(ff*ff);
    aa[3] = -19.57962*(ff*ff*ff);
    aa[4] = 9.0*bb[3]*ff;

    break;

  case 517:
    ff = 0.1282782438530421943003109254455883701296*0.1282782438530421943003109254455883701296;

    bb[0] = 1.0;
    bb[1] = 88.3960*ff;
    bb[2] = 16.3683*(ff*ff);

    aa[0] = 1.0;
    aa[1] = 88.2108*ff;

    break;

  case 518:
    ff = 5.0*0.1282782438530421943003109254455883701296*0.1282782438530421943003109254455883701296/27.0;

    bb[0] = 1.0;
    bb[1] = -0.05 *ff;
    bb[2] = 0.396 *(ff*ff);

    aa[0] = 1.0;
    aa[1] = 0.95 *ff;
    aa[3] = 9.0*bb[2]*ff;

    break;

  case 519:
    ff = 0.1282782438530421943003109254455883701296*0.1282782438530421943003109254455883701296;

    bb[0] = 1.0;
    bb[1] = 0.6511 *ff;
    bb[2] = 0.0431 *(ff*ff);

    aa[0] = 1.0;
    aa[1] = 0.8944 *ff;
    aa[3] = -bb[2] *ff;

    break;

  case 520:
    ff = 0.1282782438530421943003109254455883701296*0.1282782438530421943003109254455883701296;

    bb[0] = 135.0;
    bb[1] = 3.0*ff;

    aa[0] = 135.0;
    aa[1] = 28.0*ff;
    aa[2] = 5.0*(ff*ff);

    break;
  }
}


static inline void
func(const xc_func_type *p, int order, double x,
     double *f, double *dfdx, double *d2fdx2)
{
  double xx2, xx4, num, denom, dnum, ddenom, d2num, d2denom;
  double *aa, *bb;

  ((p->params != ((void *)0)) ? (void) (0) : __assert_fail ("p->params != ((void *)0)", "../../../../libxc/src/gga_k_dk.c", 130, __PRETTY_FUNCTION__));
  aa = ((gga_k_dk_params *) (p->params))->aa;
  bb = ((gga_k_dk_params *) (p->params))->bb;

  xx2 = x*x;
  xx4 = xx2*xx2;

  num = aa[0] + aa[1]*xx2 + aa[2]*xx4 + aa[3]*xx2*xx4 + aa[4]*xx4*xx4;
  denom = bb[0] + bb[1]*xx2 + bb[2]*xx4 + bb[3]*xx2*xx4 + bb[4]*xx4*xx4;

  *f = num/denom;

  if(order < 1) return;

  dnum = 2.0*aa[1]*x + 4.0*aa[2]*x*xx2 + 6.0*aa[3]*x*xx4 + 8.0*aa[4]*x*xx2*xx4;
  ddenom = 2.0*bb[1]*x + 4.0*bb[2]*x*xx2 + 6.0*bb[3]*x*xx4 + 8.0*bb[4]*x*xx2*xx4;

  *dfdx = (dnum*denom - num*ddenom)/(denom*denom);

  if(order < 2) return;

  d2num = 2.0*aa[1] + 4.0*3.0*aa[2]*xx2 + 6.0*5.0*aa[3]*xx4 + 8.0*7.0*aa[4]*xx2*xx4;
  d2denom = 2.0*bb[1] + 4.0*3.0*bb[2]*xx2 + 6.0*5.0*bb[3]*xx4 + 8.0*7.0*bb[4]*xx2*xx4;

  *d2fdx2 = ((d2num*denom - num*d2denom)*denom - 2.0*ddenom*(dnum*denom - ddenom*num))/(denom*denom*denom);
}


# 1 "../../../../libxc/src/work_gga_x.c" 1
# 34 "../../../../libxc/src/work_gga_x.c"
static void

work_gga_k



(const xc_func_type *p, int np, const double *rho, const double *sigma,
 double *zk, double *vrho, double *vsigma,
 double *v2rho2, double *v2rhosigma, double *v2sigma2)
{
  double sfact, x_factor_c, alpha, beta, dens;
  int is, ip, order;






  beta = 1.0 + 1.0/3;
# 67 "../../../../libxc/src/work_gga_x.c"
  alpha = 5.0/3.0;
  x_factor_c = 4.557799872345597137288163759599305358515;




  sfact = (p->nspin == 2) ? 1.0 : 2.0;




  order = -1;
  if(zk != ((void *)0)) order = 0;
  if(vrho != ((void *)0)) order = 1;
  if(v2rho2 != ((void *)0)) order = 2;
  if(order < 0) return;

  for(ip = 0; ip < np; ip++){
    dens = (p->nspin == 1) ? rho[0] : rho[0] + rho[1];
    if(dens < p->info->min_dens) goto end_ip_loop;

    for(is=0; is<p->nspin; is++){
      double gdm, ds, rhoLDA;
      double x, f, dfdx, d2fdx2, lvsigma, lv2sigma2, lvsigmax, lvrho;
      int js = (is == 0) ? 0 : 2;
      int ks = (is == 0) ? 0 : 5;

      if(rho[is] < p->info->min_dens) continue;

      gdm = ((sqrt(sigma[js])/sfact<p->info->min_grad) ? (p->info->min_grad) : (sqrt(sigma[js])/sfact));
      ds = rho[is]/sfact;
      rhoLDA = pow(ds, alpha);
      x = gdm/pow(ds, beta);

      dfdx = d2fdx2 = 0.0;
      lvsigma = lv2sigma2 = lvsigmax = lvrho = 0.0;


      func(p, order, x, &f, &dfdx, &d2fdx2);
# 120 "../../../../libxc/src/work_gga_x.c"
      if(zk != ((void *)0) && (p->info->flags & (1 << 0)))
 *zk += sfact*x_factor_c*rhoLDA*f;

      if(vrho != ((void *)0) && (p->info->flags & (1 << 1))){
 vrho[is] += x_factor_c*(rhoLDA/ds)*(alpha*f - beta*dfdx*x)
   + x_factor_c*rhoLDA*lvrho;

 if(gdm>p->info->min_grad)
   vsigma[js] = sfact*x_factor_c*rhoLDA*(lvsigma + dfdx*x/(2.0*sigma[js]));
      }

      if(v2rho2 != ((void *)0) && (p->info->flags & (1 << 2))){
 v2rho2[js] = x_factor_c*rhoLDA/(ds*ds) *
   ((alpha - 1.0)*alpha*f + beta*(beta - 2.0*alpha + 1.0)*x*dfdx + beta*beta*x*x*d2fdx2)/sfact;

 if(gdm>p->info->min_grad){
   v2rhosigma[ks] = x_factor_c*(rhoLDA/ds) *
     (alpha*lvsigma - beta*x*lvsigmax + ((alpha - beta)*x*dfdx - beta*x*x*d2fdx2)/(2.0*sigma[js]));
   v2sigma2 [ks] = sfact*x_factor_c*rhoLDA*
     (lv2sigma2 + lvsigmax*x/sigma[js] + (d2fdx2*x - dfdx)*x/(4.0*sigma[js]*sigma[js]));
 }

      }
    }

    if(zk != ((void *)0) && (p->info->flags & (1 << 0)))
      *zk /= dens;

  end_ip_loop:

    rho += p->n_rho;
    sigma += p->n_sigma;

    if(zk != ((void *)0))
      zk += p->n_zk;

    if(vrho != ((void *)0)){
      vrho += p->n_vrho;
      vsigma += p->n_vsigma;
    }

    if(v2rho2 != ((void *)0)){
      v2rho2 += p->n_v2rho2;
      v2rhosigma += p->n_v2rhosigma;
      v2sigma2 += p->n_v2sigma2;
    }
  }
}
# 159 "../../../../libxc/src/gga_k_dk.c" 2

const xc_func_info_type xc_func_info_gga_k_dk = {
  516,
  3,
  "DePristo and Kress",
  2,
  "AE DePristo and JD Kress, Phys. Rev. A 35, 438-441 (1987)",
  (1 << 7) | (1 << 0) | (1 << 1) | (1 << 2),
  1e-32, 1e-32, 0.0, 1e-32,
  gga_k_dk_init,
  ((void *)0), ((void *)0),
  work_gga_k
};

const xc_func_info_type xc_func_info_gga_k_perdew = {
  517,
  3,
  "Perdew",
  2,
  "JP Perdew, Phys. Lett. A 165, 79 (1992)",
  (1 << 7) | (1 << 0) | (1 << 1) | (1 << 2),
  1e-32, 1e-32, 0.0, 1e-32,
  gga_k_dk_init,
  ((void *)0), ((void *)0),
  work_gga_k
};

const xc_func_info_type xc_func_info_gga_k_vsk = {
  518,
  3,
  "Vitos, Skriver, and Kollar",
  2,
  "L Vitos, HL Skriver, and J. KollÃ¡r, Phys. Rev. B 57, 12611-12615 (1998)",
  (1 << 7) | (1 << 0) | (1 << 1) | (1 << 2),
  1e-32, 1e-32, 0.0, 1e-32,
  gga_k_dk_init,
  ((void *)0), ((void *)0),
  work_gga_k
};

const xc_func_info_type xc_func_info_gga_k_vjks = {
  519,
  3,
  "Vitos, Johansson, Kollar, and Skriver",
  2,
  "L Vitos, B Johansson, J. KollÃ¡r, and HL Skriver, Phys. Rev. A 61, 052511 (2000)",
  (1 << 7) | (1 << 0) | (1 << 1) | (1 << 2),
  1e-32, 1e-32, 0.0, 1e-32,
  gga_k_dk_init,
  ((void *)0), ((void *)0),
  work_gga_k
};

const xc_func_info_type xc_func_info_gga_k_ernzerhof = {
  520,
  3,
  "Ernzerhof",
  2,
  "M Ernzerhof, J. Mol. Struct.:THEOCHEM 501-502, 59 (2000)",
  (1 << 7) | (1 << 0) | (1 << 1) | (1 << 2),
  1e-32, 1e-32, 0.0, 1e-32,
  gga_k_dk_init,
  ((void *)0), ((void *)0),
  work_gga_k
};

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