[Bug c/79884] New: Math functions with variable argument fail

[tino.calancha at gmail dot com]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=79884

            Bug ID: 79884
           Summary: Math functions with variable argument fail
           Product: gcc
           Version: 6.3.0
            Status: UNCONFIRMED
          Severity: normal
          Priority: P3
         Component: c
          Assignee: unassigned at gcc dot gnu.org
          Reporter: tino.calancha at gmail dot com
  Target Milestone: ---

Consider the following snippet code:

#include <stdio.h>
#include <math.h>

int main ()
{
  double param = 1024.0;
  double result = sqrt (param);
  printf ("sqrt(%.1f) = %.1f\n", param, result );
  return 0;
}

$> gcc  -Wall -Wextra file.c

file.o: In function `main':
file.c:(.text+0x23): undefined reference to `sqrt'
collect2: error: ld returned 1 exit status


*) If i use:
double result = sqrt (1024.0);
instead of
double result = sqrt (param);

then, the program compiles.


System type:
Linux 4.9.0-1-amd64 #1 SMP Debian 4.9.6-3 (2017-01-28) x86_64 GNU/Linux

$> gcc -v 
Using built-in specs.
COLLECT_GCC=gcc
COLLECT_LTO_WRAPPER=/usr/lib/gcc/x86_64-linux-gnu/6/lto-wrapper
Target: x86_64-linux-gnu
Configured with: ../src/configure -v --with-pkgversion='Debian 6.3.0-6'
--with-bugurl=file:///usr/share/doc/gcc-6/README.Bugs
--enable-languages=c,ada,c++,java,go,d,fortran,objc,obj-c++ --prefix=/usr
--program-suffix=-6 --program-prefix=x86_64-linux-gnu- --enable-shared
--enable-linker-build-id --libexecdir=/usr/lib --without-included-gettext
--enable-threads=posix --libdir=/usr/lib --enable-nls --with-sysroot=/
--enable-clocale=gnu --enable-libstdcxx-debug --enable-libstdcxx-time=yes
--with-default-libstdcxx-abi=new --enable-gnu-unique-object
--disable-vtable-verify --enable-libmpx --enable-plugin --enable-default-pie
--with-system-zlib --disable-browser-plugin --enable-java-awt=gtk
--enable-gtk-cairo --with-java-home=/usr/lib/jvm/java-1.5.0-gcj-6-amd64/jre
--enable-java-home --with-jvm-root-dir=/usr/lib/jvm/java-1.5.0-gcj-6-amd64
--with-jvm-jar-dir=/usr/lib/jvm-exports/java-1.5.0-gcj-6-amd64
--with-arch-directory=amd64 --with-ecj-jar=/usr/share/java/eclipse-ecj.jar
--with-target-system-zlib --enable-objc-gc=auto --enable-multiarch
--with-arch-32=i686 --with-abi=m64 --with-multilib-list=m32,m64,mx32
--enable-multilib --with-tune=generic --enable-checking=release
--build=x86_64-linux-gnu --host=x86_64-linux-gnu --target=x86_64-linux-gnu
Thread model: posix
gcc version 6.3.0 20170205 (Debian 6.3.0-6) 


preprocessed file.i:

# 1 "file.c"
# 1 "<built-in>"
# 1 "<command-line>"
# 31 "<command-line>"
# 1 "/usr/include/stdc-predef.h" 1 3 4
# 32 "<command-line>" 2
# 1 "file.c"

# 1 "/usr/include/stdio.h" 1 3 4
# 27 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/features.h" 1 3 4
# 364 "/usr/include/features.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 1 3 4
# 415 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 416 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 2 3 4
# 365 "/usr/include/features.h" 2 3 4
# 388 "/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
# 389 "/usr/include/features.h" 2 3 4
# 28 "/usr/include/stdio.h" 2 3 4





# 1 "/usr/lib/gcc/x86_64-linux-gnu/6/include/stddef.h" 1 3 4
# 216 "/usr/lib/gcc/x86_64-linux-gnu/6/include/stddef.h" 3 4

# 216 "/usr/lib/gcc/x86_64-linux-gnu/6/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;
# 121 "/usr/include/x86_64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/typesizes.h" 1 3 4
# 122 "/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
# 31 "/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/6/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;
# 32 "/usr/include/libio.h" 2 3 4
# 49 "/usr/include/libio.h" 3 4
# 1 "/usr/lib/gcc/x86_64-linux-gnu/6/include/stdarg.h" 1 3 4
# 40 "/usr/lib/gcc/x86_64-linux-gnu/6/include/stdarg.h" 3 4
typedef __builtin_va_list __gnuc_va_list;
# 50 "/usr/include/libio.h" 2 3 4
# 144 "/usr/include/libio.h" 3 4
struct _IO_jump_t; struct _IO_FILE;





typedef void _IO_lock_t;





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



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


enum __codecvt_result
{
  __codecvt_ok,
  __codecvt_partial,
  __codecvt_error,
  __codecvt_noconv
};
# 241 "/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;
# 289 "/usr/include/libio.h" 3 4
  __off64_t _offset;







  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_;
# 333 "/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);
# 385 "/usr/include/libio.h" 3 4
extern int __underflow (_IO_FILE *);
extern int __uflow (_IO_FILE *);
extern int __overflow (_IO_FILE *, int);
# 429 "/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__));
# 459 "/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;
# 104 "/usr/include/stdio.h" 3 4
typedef __ssize_t ssize_t;







typedef _G_fpos_t fpos_t;




# 166 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/stdio_lim.h" 1 3 4
# 167 "/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) ;
# 211 "/usr/include/stdio.h" 3 4
extern char *tmpnam (char *__s) __attribute__ ((__nothrow__ , __leaf__)) ;





extern char *tmpnam_r (char *__s) __attribute__ ((__nothrow__ , __leaf__)) ;
# 229 "/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);

# 254 "/usr/include/stdio.h" 3 4
extern int fflush_unlocked (FILE *__stream);
# 268 "/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) ;
# 297 "/usr/include/stdio.h" 3 4

# 308 "/usr/include/stdio.h" 3 4
extern FILE *fdopen (int __fd, const char *__modes) __attribute__ ((__nothrow__
, __leaf__)) ;
# 321 "/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)));

# 414 "/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__));
# 445 "/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__))

                      ;
# 465 "/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)));
# 496 "/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)));
# 524 "/usr/include/stdio.h" 3 4









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





extern int getchar (void);

# 552 "/usr/include/stdio.h" 3 4
extern int getc_unlocked (FILE *__stream);
extern int getchar_unlocked (void);
# 563 "/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);

# 596 "/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)
     ;
# 642 "/usr/include/stdio.h" 3 4

# 667 "/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);

# 739 "/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);

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




extern __off_t ftello (FILE *__stream) ;
# 794 "/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);
# 817 "/usr/include/stdio.h" 3 4

# 826 "/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[];
# 856 "/usr/include/stdio.h" 2 3 4




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




extern int fileno_unlocked (FILE *__stream) __attribute__ ((__nothrow__ ,
__leaf__)) ;
# 874 "/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__));
# 914 "/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__));
# 944 "/usr/include/stdio.h" 3 4

# 3 "file.c" 2
# 1 "/usr/include/math.h" 1 3 4
# 28 "/usr/include/math.h" 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/math-vector.h" 1 3 4
# 25 "/usr/include/x86_64-linux-gnu/bits/math-vector.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libm-simd-decl-stubs.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/math-vector.h" 2 3 4
# 32 "/usr/include/math.h" 2 3 4



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

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


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


# 1 "/usr/include/x86_64-linux-gnu/bits/nan.h" 1 3 4
# 45 "/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;
# 49 "/usr/include/math.h" 2 3 4
# 83 "/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)));

# 126 "/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__));
# 305 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
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__));
__extension__
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__));
__extension__
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__));




# 390 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern double scalb (double __x, double __n) __attribute__ ((__nothrow__ ,
__leaf__)); extern double __scalb (double __x, double __n) __attribute__
((__nothrow__ , __leaf__));
# 84 "/usr/include/math.h" 2 3 4
# 104 "/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)));

# 126 "/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__));
# 305 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
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__));
__extension__
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__));
__extension__
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__));




# 390 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern float scalbf (float __x, float __n) __attribute__ ((__nothrow__ ,
__leaf__)); extern float __scalbf (float __x, float __n) __attribute__
((__nothrow__ , __leaf__));
# 105 "/usr/include/math.h" 2 3 4
# 151 "/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)));

# 126 "/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__));
# 305 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
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__));
__extension__
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__));
__extension__
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__));




# 390 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
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__));
# 152 "/usr/include/math.h" 2 3 4
# 168 "/usr/include/math.h" 3 4
extern int signgam;
# 209 "/usr/include/math.h" 3 4
enum
  {
    FP_NAN =

      0,
    FP_INFINITE =

      1,
    FP_ZERO =

      2,
    FP_SUBNORMAL =

      3,
    FP_NORMAL =

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




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

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




extern int matherr (struct exception *__exc);
# 534 "/usr/include/math.h" 3 4

# 4 "file.c" 2


# 5 "file.c"
int main ()
{
  double param = 1024.0;
  double result = sqrt (param);
  printf ("sqrt(%.1f) = %.1f\n", param, result );
  return 0;
}