# 1 "/home/ubuntu/neovim/src/nvim/math.c"
# 1 "<built-in>"
# 1 "<command-line>"
# 1 "/usr/include/stdc-predef.h" 1 3 4
# 1 "<command-line>" 2
# 1 "/home/ubuntu/neovim/src/nvim/math.c"

# 1 "/usr/include/math.h" 1 3 4
# 27 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 33 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 3 4
# 1 "/usr/include/features.h" 1 3 4
# 461 "/usr/include/features.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 1 3 4
# 452 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
# 453 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/long-double.h" 1 3 4
# 454 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 2 3 4
# 462 "/usr/include/features.h" 2 3 4
# 485 "/usr/include/features.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/gnu/stubs.h" 1 3 4




# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
# 6 "/usr/include/aarch64-linux-gnu/gnu/stubs.h" 2 3 4


# 1 "/usr/include/aarch64-linux-gnu/gnu/stubs-lp64.h" 1 3 4
# 9 "/usr/include/aarch64-linux-gnu/gnu/stubs.h" 2 3 4
# 486 "/usr/include/features.h" 2 3 4
# 34 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 2 3 4
# 28 "/usr/include/math.h" 2 3 4









# 1 "/usr/include/aarch64-linux-gnu/bits/types.h" 1 3 4
# 27 "/usr/include/aarch64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
# 28 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/timesize.h" 1 3 4
# 19 "/usr/include/aarch64-linux-gnu/bits/timesize.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
# 20 "/usr/include/aarch64-linux-gnu/bits/timesize.h" 2 3 4
# 29 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4



# 31 "/usr/include/aarch64-linux-gnu/bits/types.h" 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 __int8_t __int_least8_t;
typedef __uint8_t __uint_least8_t;
typedef __int16_t __int_least16_t;
typedef __uint16_t __uint_least16_t;
typedef __int32_t __int_least32_t;
typedef __uint32_t __uint_least32_t;
typedef __int64_t __int_least64_t;
typedef __uint64_t __uint_least64_t;



typedef long int __quad_t;
typedef unsigned long int __u_quad_t;







typedef long int __intmax_t;
typedef unsigned long int __uintmax_t;
# 141 "/usr/include/aarch64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/typesizes.h" 1 3 4
# 142 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/time64.h" 1 3 4
# 143 "/usr/include/aarch64-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 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 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 char *__caddr_t;


typedef long int __intptr_t;


typedef unsigned int __socklen_t;




typedef int __sig_atomic_t;
# 38 "/usr/include/math.h" 2 3 4


# 1 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 1 3 4
# 27 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/libm-simd-decl-stubs.h" 1 3 4
# 27 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 2 3 4
# 41 "/usr/include/math.h" 2 3 4


# 1 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 1 3 4
# 23 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/long-double.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 2 3 4
# 95 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/floatn-common.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/floatn-common.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/long-double.h" 1 3 4
# 25 "/usr/include/aarch64-linux-gnu/bits/floatn-common.h" 2 3 4
# 96 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 2 3 4
# 44 "/usr/include/math.h" 2 3 4
# 138 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/flt-eval-method.h" 1 3 4
# 139 "/usr/include/math.h" 2 3 4
# 149 "/usr/include/math.h" 3 4
typedef float float_t;
typedef double double_t;
# 190 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/fp-logb.h" 1 3 4
# 191 "/usr/include/math.h" 2 3 4
# 233 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/fp-fast.h" 1 3 4
# 234 "/usr/include/math.h" 2 3 4



enum
  {
    FP_INT_UPWARD =

      0,
    FP_INT_DOWNWARD =

      1,
    FP_INT_TOWARDZERO =

      2,
    FP_INT_TONEARESTFROMZERO =

      3,
    FP_INT_TONEAREST =

      4,
  };
# 289 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
# 21 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
extern int __fpclassify (double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));


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


extern int __iseqsig (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));


extern int __issignaling (double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));
# 290 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-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__));



 extern void sincos (double __x, double *__sinx, double *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincos (double __x, double *__sinx, double *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




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)));



extern double exp10 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __exp10 (double __x) __attribute__ ((__nothrow__ , __leaf__));




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__));
# 177 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
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__)); extern double __nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 211 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
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__)); extern double __nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));

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




extern double nextdown (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __nextdown (double __x) __attribute__ ((__nothrow__ , __leaf__));

extern double nextup (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __nextup (double __x) __attribute__ ((__nothrow__ , __leaf__));



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 long int llogb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogb (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 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 roundeven (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __roundeven (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfp (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfp (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfp (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfp (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpx (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpx (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpx (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpx (double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern double fmaxmag (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmaxmag (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern double fminmag (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fminmag (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalize (double *__cx, const double *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorder (const double *__x, const double *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermag (const double *__x, const double *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern double getpayload (const double *__x) __attribute__ ((__nothrow__ , __leaf__)); extern double __getpayload (const double *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayload (double *__x, double __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsig (double *__x, double __payload) __attribute__ ((__nothrow__ , __leaf__));







extern double scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__));
# 291 "/usr/include/math.h" 2 3 4
# 306 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
# 21 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
extern int __fpclassifyf (float __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));


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


extern int __iseqsigf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));


extern int __issignalingf (float __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));
# 307 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-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__));



 extern void sincosf (float __x, float *__sinx, float *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosf (float __x, float *__sinx, float *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




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)));



extern float exp10f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __exp10f (float __x) __attribute__ ((__nothrow__ , __leaf__));




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__));
# 177 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
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__)); extern float __nanf (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 211 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
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__)); extern float __nextafterf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));

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




extern float nextdownf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __nextdownf (float __x) __attribute__ ((__nothrow__ , __leaf__));

extern float nextupf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __nextupf (float __x) __attribute__ ((__nothrow__ , __leaf__));



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 long int llogbf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbf (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 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 roundevenf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __roundevenf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxf (float __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern float fmaxmagf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fmaxmagf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern float fminmagf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fminmagf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizef (float *__cx, const float *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderf (const float *__x, const float *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagf (const float *__x, const float *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern float getpayloadf (const float *__x) __attribute__ ((__nothrow__ , __leaf__)); extern float __getpayloadf (const float *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadf (float *__x, float __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigf (float *__x, float __payload) __attribute__ ((__nothrow__ , __leaf__));







extern float scalbf (float __x, float __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalbf (float __x, float __n) __attribute__ ((__nothrow__ , __leaf__));
# 308 "/usr/include/math.h" 2 3 4
# 349 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
# 21 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
extern int __fpclassifyl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));


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


extern int __iseqsigl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


extern int __issignalingl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
     __attribute__ ((__const__));
# 350 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-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__));



 extern void sincosl (long double __x, long double *__sinx, long double *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosl (long double __x, long double *__sinx, long double *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




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)));



extern long double exp10l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __exp10l (long double __x) __attribute__ ((__nothrow__ , __leaf__));




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__));
# 177 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
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__)); extern long double __nanl (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 211 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
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__)); extern long double __nextafterl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));

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




extern long double nextdownl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nextdownl (long double __x) __attribute__ ((__nothrow__ , __leaf__));

extern long double nextupl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nextupl (long double __x) __attribute__ ((__nothrow__ , __leaf__));



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 int llogbl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbl (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 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 roundevenl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __roundevenl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxl (long double __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern long double fmaxmagl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fmaxmagl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern long double fminmagl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fminmagl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizel (long double *__cx, const long double *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderl (const long double *__x, const long double *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagl (const long double *__x, const long double *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern long double getpayloadl (const long double *__x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __getpayloadl (const long double *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadl (long double *__x, long double __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigl (long double *__x, long double __payload) __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__));
# 351 "/usr/include/math.h" 2 3 4
# 389 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 acosf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __acosf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 asinf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __asinf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 atanf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __atanf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 atan2f32 (_Float32 __y, _Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __atan2f32 (_Float32 __y, _Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float32 cosf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __cosf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

 extern _Float32 sinf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __sinf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 tanf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __tanf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 coshf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __coshf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 sinhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __sinhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 tanhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __tanhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));



 extern void sincosf32 (_Float32 __x, _Float32 *__sinx, _Float32 *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosf32 (_Float32 __x, _Float32 *__sinx, _Float32 *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




extern _Float32 acoshf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __acoshf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 asinhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __asinhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 atanhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __atanhf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));





 extern _Float32 expf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __expf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 frexpf32 (_Float32 __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __frexpf32 (_Float32 __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 ldexpf32 (_Float32 __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __ldexpf32 (_Float32 __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float32 logf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __logf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 log10f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __log10f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 modff32 (_Float32 __x, _Float32 *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __modff32 (_Float32 __x, _Float32 *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern _Float32 exp10f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __exp10f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 expm1f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __expm1f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 log1pf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __log1pf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 logbf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __logbf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 exp2f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __exp2f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 log2f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __log2f32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));






 extern _Float32 powf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __powf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 sqrtf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __sqrtf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32 hypotf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __hypotf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 cbrtf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __cbrtf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));






extern _Float32 ceilf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __ceilf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32 fabsf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __fabsf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32 floorf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __floorf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32 fmodf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __fmodf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__));
# 196 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 copysignf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __copysignf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float32 nanf32 (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __nanf32 (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 217 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 j0f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __j0f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 j1f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __j1f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 jnf32 (int, _Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __jnf32 (int, _Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 y0f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __y0f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 y1f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __y1f32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 ynf32 (int, _Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __ynf32 (int, _Float32) __attribute__ ((__nothrow__ , __leaf__));





extern _Float32 erff32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __erff32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 erfcf32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __erfcf32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32 lgammaf32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __lgammaf32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 tgammaf32 (_Float32) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __tgammaf32 (_Float32) __attribute__ ((__nothrow__ , __leaf__));
# 249 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 lgammaf32_r (_Float32, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __lgammaf32_r (_Float32, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));






extern _Float32 rintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __rintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 nextafterf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __nextafterf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__));






extern _Float32 nextdownf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __nextdownf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32 nextupf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __nextupf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32 remainderf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __remainderf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32 scalbnf32 (_Float32 __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __scalbnf32 (_Float32 __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));




extern long int llogbf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 scalblnf32 (_Float32 __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __scalblnf32 (_Float32 __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32 nearbyintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __nearbyintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32 roundf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __roundf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern _Float32 truncf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __truncf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float32 remquof32 (_Float32 __x, _Float32 __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __remquof32 (_Float32 __x, _Float32 __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32 fdimf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __fdimf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 fmaxf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __fmaxf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32 fminf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __fminf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32 fmaf32 (_Float32 __x, _Float32 __y, _Float32 __z) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __fmaf32 (_Float32 __x, _Float32 __y, _Float32 __z) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32 roundevenf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __roundevenf32 (_Float32 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxf32 (_Float32 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern _Float32 fmaxmagf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __fmaxmagf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32 fminmagf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32 __fminmagf32 (_Float32 __x, _Float32 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizef32 (_Float32 *__cx, const _Float32 *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderf32 (const _Float32 *__x, const _Float32 *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagf32 (const _Float32 *__x, const _Float32 *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern _Float32 getpayloadf32 (const _Float32 *__x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32 __getpayloadf32 (const _Float32 *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadf32 (_Float32 *__x, _Float32 __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigf32 (_Float32 *__x, _Float32 __payload) __attribute__ ((__nothrow__ , __leaf__));
# 390 "/usr/include/math.h" 2 3 4
# 406 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 acosf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __acosf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 asinf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __asinf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 atanf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __atanf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 atan2f64 (_Float64 __y, _Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __atan2f64 (_Float64 __y, _Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float64 cosf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __cosf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

 extern _Float64 sinf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __sinf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 tanf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __tanf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 coshf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __coshf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 sinhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __sinhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 tanhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __tanhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));



 extern void sincosf64 (_Float64 __x, _Float64 *__sinx, _Float64 *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosf64 (_Float64 __x, _Float64 *__sinx, _Float64 *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




extern _Float64 acoshf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __acoshf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 asinhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __asinhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 atanhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __atanhf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));





 extern _Float64 expf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __expf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 frexpf64 (_Float64 __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __frexpf64 (_Float64 __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 ldexpf64 (_Float64 __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __ldexpf64 (_Float64 __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float64 logf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __logf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 log10f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __log10f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 modff64 (_Float64 __x, _Float64 *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __modff64 (_Float64 __x, _Float64 *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern _Float64 exp10f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __exp10f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 expm1f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __expm1f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 log1pf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __log1pf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 logbf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __logbf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 exp2f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __exp2f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 log2f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __log2f64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));






 extern _Float64 powf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __powf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 sqrtf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __sqrtf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64 hypotf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __hypotf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 cbrtf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __cbrtf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));






extern _Float64 ceilf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __ceilf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64 fabsf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __fabsf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64 floorf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __floorf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64 fmodf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __fmodf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));
# 196 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 copysignf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __copysignf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float64 nanf64 (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __nanf64 (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 217 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 j0f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __j0f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 j1f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __j1f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 jnf64 (int, _Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __jnf64 (int, _Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 y0f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __y0f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 y1f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __y1f64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 ynf64 (int, _Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __ynf64 (int, _Float64) __attribute__ ((__nothrow__ , __leaf__));





extern _Float64 erff64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __erff64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 erfcf64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __erfcf64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64 lgammaf64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __lgammaf64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 tgammaf64 (_Float64) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __tgammaf64 (_Float64) __attribute__ ((__nothrow__ , __leaf__));
# 249 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 lgammaf64_r (_Float64, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __lgammaf64_r (_Float64, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));






extern _Float64 rintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __rintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 nextafterf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __nextafterf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));






extern _Float64 nextdownf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __nextdownf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64 nextupf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __nextupf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64 remainderf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __remainderf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64 scalbnf64 (_Float64 __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __scalbnf64 (_Float64 __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));




extern long int llogbf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 scalblnf64 (_Float64 __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __scalblnf64 (_Float64 __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64 nearbyintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __nearbyintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64 roundf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __roundf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern _Float64 truncf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __truncf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float64 remquof64 (_Float64 __x, _Float64 __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __remquof64 (_Float64 __x, _Float64 __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64 fdimf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __fdimf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 fmaxf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __fmaxf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64 fminf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __fminf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64 fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64 roundevenf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __roundevenf64 (_Float64 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxf64 (_Float64 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern _Float64 fmaxmagf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __fmaxmagf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64 fminmagf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64 __fminmagf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizef64 (_Float64 *__cx, const _Float64 *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderf64 (const _Float64 *__x, const _Float64 *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagf64 (const _Float64 *__x, const _Float64 *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern _Float64 getpayloadf64 (const _Float64 *__x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64 __getpayloadf64 (const _Float64 *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadf64 (_Float64 *__x, _Float64 __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigf64 (_Float64 *__x, _Float64 __payload) __attribute__ ((__nothrow__ , __leaf__));
# 407 "/usr/include/math.h" 2 3 4
# 423 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float128 acosf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __acosf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 asinf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __asinf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 atanf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __atanf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 atan2f128 (_Float128 __y, _Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __atan2f128 (_Float128 __y, _Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float128 cosf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __cosf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

 extern _Float128 sinf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __sinf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 tanf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __tanf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 coshf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __coshf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 sinhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __sinhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 tanhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __tanhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));



 extern void sincosf128 (_Float128 __x, _Float128 *__sinx, _Float128 *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosf128 (_Float128 __x, _Float128 *__sinx, _Float128 *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




extern _Float128 acoshf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __acoshf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 asinhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __asinhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 atanhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __atanhf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));





 extern _Float128 expf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __expf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 frexpf128 (_Float128 __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __frexpf128 (_Float128 __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 ldexpf128 (_Float128 __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __ldexpf128 (_Float128 __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float128 logf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __logf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 log10f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __log10f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 modff128 (_Float128 __x, _Float128 *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __modff128 (_Float128 __x, _Float128 *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern _Float128 exp10f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __exp10f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 expm1f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __expm1f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 log1pf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __log1pf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 logbf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __logbf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 exp2f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __exp2f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 log2f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __log2f128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));






 extern _Float128 powf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __powf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 sqrtf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __sqrtf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float128 hypotf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __hypotf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 cbrtf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __cbrtf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));






extern _Float128 ceilf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __ceilf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float128 fabsf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __fabsf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float128 floorf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __floorf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float128 fmodf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __fmodf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));
# 196 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float128 copysignf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __copysignf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float128 nanf128 (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __nanf128 (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 217 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float128 j0f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __j0f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 j1f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __j1f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 jnf128 (int, _Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __jnf128 (int, _Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 y0f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __y0f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 y1f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __y1f128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 ynf128 (int, _Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __ynf128 (int, _Float128) __attribute__ ((__nothrow__ , __leaf__));





extern _Float128 erff128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __erff128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 erfcf128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __erfcf128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
extern _Float128 lgammaf128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __lgammaf128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 tgammaf128 (_Float128) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __tgammaf128 (_Float128) __attribute__ ((__nothrow__ , __leaf__));
# 249 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float128 lgammaf128_r (_Float128, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __lgammaf128_r (_Float128, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));






extern _Float128 rintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __rintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 nextafterf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __nextafterf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));






extern _Float128 nextdownf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __nextdownf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float128 nextupf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __nextupf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float128 remainderf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __remainderf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));



extern _Float128 scalbnf128 (_Float128 __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __scalbnf128 (_Float128 __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));




extern long int llogbf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 scalblnf128 (_Float128 __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __scalblnf128 (_Float128 __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern _Float128 nearbyintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __nearbyintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float128 roundf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __roundf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern _Float128 truncf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __truncf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float128 remquof128 (_Float128 __x, _Float128 __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __remquof128 (_Float128 __x, _Float128 __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float128 fdimf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __fdimf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float128 fmaxf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __fmaxf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float128 fminf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __fminf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float128 fmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __fmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) __attribute__ ((__nothrow__ , __leaf__));




extern _Float128 roundevenf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __roundevenf128 (_Float128 __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxf128 (_Float128 __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern _Float128 fmaxmagf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __fmaxmagf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float128 fminmagf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float128 __fminmagf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizef128 (_Float128 *__cx, const _Float128 *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderf128 (const _Float128 *__x, const _Float128 *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagf128 (const _Float128 *__x, const _Float128 *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern _Float128 getpayloadf128 (const _Float128 *__x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float128 __getpayloadf128 (const _Float128 *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadf128 (_Float128 *__x, _Float128 __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigf128 (_Float128 *__x, _Float128 __payload) __attribute__ ((__nothrow__ , __leaf__));
# 424 "/usr/include/math.h" 2 3 4
# 440 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x acosf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __acosf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x asinf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __asinf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x atanf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __atanf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x atan2f32x (_Float32x __y, _Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __atan2f32x (_Float32x __y, _Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float32x cosf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __cosf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

 extern _Float32x sinf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __sinf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x tanf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __tanf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x coshf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __coshf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x sinhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __sinhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x tanhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __tanhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));



 extern void sincosf32x (_Float32x __x, _Float32x *__sinx, _Float32x *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosf32x (_Float32x __x, _Float32x *__sinx, _Float32x *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




extern _Float32x acoshf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __acoshf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x asinhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __asinhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x atanhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __atanhf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));





 extern _Float32x expf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __expf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x frexpf32x (_Float32x __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __frexpf32x (_Float32x __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x ldexpf32x (_Float32x __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __ldexpf32x (_Float32x __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float32x logf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __logf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x log10f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __log10f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x modff32x (_Float32x __x, _Float32x *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __modff32x (_Float32x __x, _Float32x *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern _Float32x exp10f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __exp10f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x expm1f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __expm1f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x log1pf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __log1pf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x logbf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __logbf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x exp2f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __exp2f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x log2f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __log2f32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));






 extern _Float32x powf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __powf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x sqrtf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __sqrtf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32x hypotf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __hypotf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x cbrtf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __cbrtf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));






extern _Float32x ceilf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __ceilf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32x fabsf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __fabsf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32x floorf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __floorf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32x fmodf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __fmodf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));
# 196 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x copysignf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __copysignf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float32x nanf32x (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __nanf32x (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 217 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x j0f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __j0f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x j1f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __j1f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x jnf32x (int, _Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __jnf32x (int, _Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x y0f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __y0f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x y1f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __y1f32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x ynf32x (int, _Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __ynf32x (int, _Float32x) __attribute__ ((__nothrow__ , __leaf__));





extern _Float32x erff32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __erff32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x erfcf32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __erfcf32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float32x lgammaf32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __lgammaf32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x tgammaf32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __tgammaf32x (_Float32x) __attribute__ ((__nothrow__ , __leaf__));
# 249 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x lgammaf32x_r (_Float32x, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __lgammaf32x_r (_Float32x, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));






extern _Float32x rintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __rintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x nextafterf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __nextafterf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));






extern _Float32x nextdownf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __nextdownf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float32x nextupf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __nextupf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32x remainderf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __remainderf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32x scalbnf32x (_Float32x __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __scalbnf32x (_Float32x __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));




extern long int llogbf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x scalblnf32x (_Float32x __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __scalblnf32x (_Float32x __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32x nearbyintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __nearbyintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32x roundf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __roundf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern _Float32x truncf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __truncf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float32x remquof32x (_Float32x __x, _Float32x __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __remquof32x (_Float32x __x, _Float32x __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float32x fdimf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __fdimf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x fmaxf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __fmaxf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32x fminf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __fminf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32x fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) __attribute__ ((__nothrow__ , __leaf__));




extern _Float32x roundevenf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __roundevenf32x (_Float32x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxf32x (_Float32x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern _Float32x fmaxmagf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __fmaxmagf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float32x fminmagf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float32x __fminmagf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizef32x (_Float32x *__cx, const _Float32x *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderf32x (const _Float32x *__x, const _Float32x *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagf32x (const _Float32x *__x, const _Float32x *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern _Float32x getpayloadf32x (const _Float32x *__x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float32x __getpayloadf32x (const _Float32x *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadf32x (_Float32x *__x, _Float32x __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigf32x (_Float32x *__x, _Float32x __payload) __attribute__ ((__nothrow__ , __leaf__));
# 441 "/usr/include/math.h" 2 3 4
# 457 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x acosf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __acosf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x asinf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __asinf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x atanf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __atanf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x atan2f64x (_Float64x __y, _Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __atan2f64x (_Float64x __y, _Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float64x cosf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __cosf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

 extern _Float64x sinf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __sinf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x tanf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __tanf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x coshf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __coshf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x sinhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __sinhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x tanhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __tanhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));



 extern void sincosf64x (_Float64x __x, _Float64x *__sinx, _Float64x *__cosx) __attribute__ ((__nothrow__ , __leaf__)); extern void __sincosf64x (_Float64x __x, _Float64x *__sinx, _Float64x *__cosx) __attribute__ ((__nothrow__ , __leaf__))
                                                        ;




extern _Float64x acoshf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __acoshf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x asinhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __asinhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x atanhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __atanhf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));





 extern _Float64x expf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __expf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x frexpf64x (_Float64x __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __frexpf64x (_Float64x __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x ldexpf64x (_Float64x __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __ldexpf64x (_Float64x __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));


 extern _Float64x logf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __logf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x log10f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __log10f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x modff64x (_Float64x __x, _Float64x *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __modff64x (_Float64x __x, _Float64x *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern _Float64x exp10f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __exp10f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x expm1f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __expm1f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x log1pf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __log1pf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x logbf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __logbf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x exp2f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __exp2f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x log2f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __log2f64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));






 extern _Float64x powf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __powf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x sqrtf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __sqrtf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64x hypotf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __hypotf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x cbrtf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __cbrtf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));






extern _Float64x ceilf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __ceilf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64x fabsf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __fabsf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64x floorf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __floorf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64x fmodf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __fmodf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));
# 196 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x copysignf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __copysignf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float64x nanf64x (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __nanf64x (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
# 217 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x j0f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __j0f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x j1f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __j1f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x jnf64x (int, _Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __jnf64x (int, _Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x y0f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __y0f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x y1f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __y1f64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x ynf64x (int, _Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __ynf64x (int, _Float64x) __attribute__ ((__nothrow__ , __leaf__));





extern _Float64x erff64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __erff64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x erfcf64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __erfcf64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
extern _Float64x lgammaf64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __lgammaf64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x tgammaf64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __tgammaf64x (_Float64x) __attribute__ ((__nothrow__ , __leaf__));
# 249 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x lgammaf64x_r (_Float64x, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __lgammaf64x_r (_Float64x, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));






extern _Float64x rintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __rintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x nextafterf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __nextafterf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));






extern _Float64x nextdownf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __nextdownf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));

extern _Float64x nextupf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __nextupf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64x remainderf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __remainderf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64x scalbnf64x (_Float64x __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __scalbnf64x (_Float64x __x, int __n) __attribute__ ((__nothrow__ , __leaf__));



extern int ilogbf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));




extern long int llogbf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __llogbf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x scalblnf64x (_Float64x __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __scalblnf64x (_Float64x __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64x nearbyintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __nearbyintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64x roundf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __roundf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern _Float64x truncf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __truncf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));




extern _Float64x remquof64x (_Float64x __x, _Float64x __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __remquof64x (_Float64x __x, _Float64x __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));






extern long int lrintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));



extern long int lroundf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__));



extern _Float64x fdimf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __fdimf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x fmaxf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __fmaxf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64x fminf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __fminf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64x fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) __attribute__ ((__nothrow__ , __leaf__));




extern _Float64x roundevenf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __roundevenf64x (_Float64x __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern __intmax_t fromfpf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                            ;



extern __uintmax_t ufromfpf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                              ;




extern __intmax_t fromfpxf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __intmax_t __fromfpxf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                             ;




extern __uintmax_t ufromfpxf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__)); extern __uintmax_t __ufromfpxf64x (_Float64x __x, int __round, unsigned int __width) __attribute__ ((__nothrow__ , __leaf__))
                               ;


extern _Float64x fmaxmagf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __fmaxmagf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern _Float64x fminmagf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern _Float64x __fminmagf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));


extern int canonicalizef64x (_Float64x *__cx, const _Float64x *__x) __attribute__ ((__nothrow__ , __leaf__));




extern int totalorderf64x (const _Float64x *__x, const _Float64x *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern int totalordermagf64x (const _Float64x *__x, const _Float64x *__y) __attribute__ ((__nothrow__ , __leaf__))

     __attribute__ ((__pure__));


extern _Float64x getpayloadf64x (const _Float64x *__x) __attribute__ ((__nothrow__ , __leaf__)); extern _Float64x __getpayloadf64x (const _Float64x *__x) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadf64x (_Float64x *__x, _Float64x __payload) __attribute__ ((__nothrow__ , __leaf__));


extern int setpayloadsigf64x (_Float64x *__x, _Float64x __payload) __attribute__ ((__nothrow__ , __leaf__));
# 458 "/usr/include/math.h" 2 3 4
# 503 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern float fadd (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fdiv (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fmul (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fsub (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
# 504 "/usr/include/math.h" 2 3 4
# 517 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern float faddl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fdivl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fmull (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


extern float fsubl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
# 518 "/usr/include/math.h" 2 3 4
# 537 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern double daddl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));


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


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


extern double dsubl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
# 538 "/usr/include/math.h" 2 3 4
# 616 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32divf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32mulf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32subf32x (_Float32x __x, _Float32x __y) __attribute__ ((__nothrow__ , __leaf__));
# 617 "/usr/include/math.h" 2 3 4
# 626 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32divf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32mulf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32subf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));
# 627 "/usr/include/math.h" 2 3 4
# 636 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32divf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32mulf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32subf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));
# 637 "/usr/include/math.h" 2 3 4
# 646 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32divf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32mulf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32 f32subf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));
# 647 "/usr/include/math.h" 2 3 4
# 666 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32x f32xaddf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xdivf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xmulf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xsubf64 (_Float64 __x, _Float64 __y) __attribute__ ((__nothrow__ , __leaf__));
# 667 "/usr/include/math.h" 2 3 4
# 676 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32x f32xaddf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xdivf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xmulf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xsubf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));
# 677 "/usr/include/math.h" 2 3 4
# 686 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32x f32xaddf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xdivf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xmulf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float32x f32xsubf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));
# 687 "/usr/include/math.h" 2 3 4
# 706 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float64 f64addf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 f64divf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 f64mulf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 f64subf64x (_Float64x __x, _Float64x __y) __attribute__ ((__nothrow__ , __leaf__));
# 707 "/usr/include/math.h" 2 3 4
# 716 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float64 f64addf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 f64divf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 f64mulf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64 f64subf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));
# 717 "/usr/include/math.h" 2 3 4
# 736 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float64x f64xaddf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x f64xdivf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x f64xmulf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));


extern _Float64x f64xsubf128 (_Float128 __x, _Float128 __y) __attribute__ ((__nothrow__ , __leaf__));
# 737 "/usr/include/math.h" 2 3 4
# 773 "/usr/include/math.h" 3 4
extern int signgam;
# 853 "/usr/include/math.h" 3 4
enum
  {
    FP_NAN =

      0,
    FP_INFINITE =

      1,
    FP_ZERO =

      2,
    FP_SUBNORMAL =

      3,
    FP_NORMAL =

      4
  };
# 973 "/usr/include/math.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/iscanonical.h" 1 3 4
# 974 "/usr/include/math.h" 2 3 4
# 1338 "/usr/include/math.h" 3 4

# 3 "/home/ubuntu/neovim/src/nvim/math.c" 2

# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/limits.h" 1 3 4
# 34 "/usr/lib/gcc/aarch64-linux-gnu/9/include/limits.h" 3 4
# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/syslimits.h" 1 3 4






# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/limits.h" 1 3 4
# 194 "/usr/lib/gcc/aarch64-linux-gnu/9/include/limits.h" 3 4
# 1 "/usr/include/limits.h" 1 3 4
# 26 "/usr/include/limits.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 27 "/usr/include/limits.h" 2 3 4
# 183 "/usr/include/limits.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 1 3 4
# 27 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
# 28 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 2 3 4
# 161 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 1 3 4
# 39 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 3 4
# 1 "/usr/include/linux/limits.h" 1 3 4
# 40 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 2 3 4
# 162 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 2 3 4
# 184 "/usr/include/limits.h" 2 3 4



# 1 "/usr/include/aarch64-linux-gnu/bits/posix2_lim.h" 1 3 4
# 188 "/usr/include/limits.h" 2 3 4



# 1 "/usr/include/aarch64-linux-gnu/bits/xopen_lim.h" 1 3 4
# 64 "/usr/include/aarch64-linux-gnu/bits/xopen_lim.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/uio_lim.h" 1 3 4
# 65 "/usr/include/aarch64-linux-gnu/bits/xopen_lim.h" 2 3 4
# 192 "/usr/include/limits.h" 2 3 4
# 195 "/usr/lib/gcc/aarch64-linux-gnu/9/include/limits.h" 2 3 4
# 8 "/usr/lib/gcc/aarch64-linux-gnu/9/include/syslimits.h" 2 3 4
# 35 "/usr/lib/gcc/aarch64-linux-gnu/9/include/limits.h" 2 3 4
# 5 "/home/ubuntu/neovim/src/nvim/math.c" 2
# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stdint.h" 1 3 4
# 9 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stdint.h" 3 4
# 1 "/usr/include/stdint.h" 1 3 4
# 26 "/usr/include/stdint.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 27 "/usr/include/stdint.h" 2 3 4

# 1 "/usr/include/aarch64-linux-gnu/bits/wchar.h" 1 3 4
# 29 "/usr/include/stdint.h" 2 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
# 30 "/usr/include/stdint.h" 2 3 4




# 1 "/usr/include/aarch64-linux-gnu/bits/stdint-intn.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/stdint-intn.h" 3 4
typedef __int8_t int8_t;
typedef __int16_t int16_t;
typedef __int32_t int32_t;
typedef __int64_t int64_t;
# 35 "/usr/include/stdint.h" 2 3 4


# 1 "/usr/include/aarch64-linux-gnu/bits/stdint-uintn.h" 1 3 4
# 24 "/usr/include/aarch64-linux-gnu/bits/stdint-uintn.h" 3 4
typedef __uint8_t uint8_t;
typedef __uint16_t uint16_t;
typedef __uint32_t uint32_t;
typedef __uint64_t uint64_t;
# 38 "/usr/include/stdint.h" 2 3 4





typedef __int_least8_t int_least8_t;
typedef __int_least16_t int_least16_t;
typedef __int_least32_t int_least32_t;
typedef __int_least64_t int_least64_t;


typedef __uint_least8_t uint_least8_t;
typedef __uint_least16_t uint_least16_t;
typedef __uint_least32_t uint_least32_t;
typedef __uint_least64_t uint_least64_t;





typedef signed char int_fast8_t;

typedef long int int_fast16_t;
typedef long int int_fast32_t;
typedef long int int_fast64_t;
# 71 "/usr/include/stdint.h" 3 4
typedef unsigned char uint_fast8_t;

typedef unsigned long int uint_fast16_t;
typedef unsigned long int uint_fast32_t;
typedef unsigned long int uint_fast64_t;
# 87 "/usr/include/stdint.h" 3 4
typedef long int intptr_t;


typedef unsigned long int uintptr_t;
# 101 "/usr/include/stdint.h" 3 4
typedef __intmax_t intmax_t;
typedef __uintmax_t uintmax_t;
# 10 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stdint.h" 2 3 4
# 6 "/home/ubuntu/neovim/src/nvim/math.c" 2
# 1 "/usr/include/string.h" 1 3 4
# 26 "/usr/include/string.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 27 "/usr/include/string.h" 2 3 4






# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stddef.h" 1 3 4
# 209 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stddef.h" 3 4
typedef long unsigned int size_t;
# 34 "/usr/include/string.h" 2 3 4
# 43 "/usr/include/string.h" 3 4
extern void *memcpy (void *__restrict __dest, const void *__restrict __src,
       size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern void *memmove (void *__dest, const void *__src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));





extern void *memccpy (void *__restrict __dest, const void *__restrict __src,
        int __c, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));




extern void *memset (void *__s, int __c, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern int memcmp (const void *__s1, const void *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
# 91 "/usr/include/string.h" 3 4
extern void *memchr (const void *__s, int __c, size_t __n)
      __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
# 104 "/usr/include/string.h" 3 4
extern void *rawmemchr (const void *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
# 115 "/usr/include/string.h" 3 4
extern void *memrchr (const void *__s, int __c, size_t __n)
      __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));





extern char *strcpy (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern char *strncpy (char *__restrict __dest,
        const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern char *strcat (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern char *strncat (char *__restrict __dest, const char *__restrict __src,
        size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern int strcmp (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));

extern int strncmp (const char *__s1, const char *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern int strcoll (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));

extern size_t strxfrm (char *__restrict __dest,
         const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



# 1 "/usr/include/aarch64-linux-gnu/bits/types/locale_t.h" 1 3 4
# 22 "/usr/include/aarch64-linux-gnu/bits/types/locale_t.h" 3 4
# 1 "/usr/include/aarch64-linux-gnu/bits/types/__locale_t.h" 1 3 4
# 28 "/usr/include/aarch64-linux-gnu/bits/types/__locale_t.h" 3 4
struct __locale_struct
{

  struct __locale_data *__locales[13];


  const unsigned short int *__ctype_b;
  const int *__ctype_tolower;
  const int *__ctype_toupper;


  const char *__names[13];
};

typedef struct __locale_struct *__locale_t;
# 23 "/usr/include/aarch64-linux-gnu/bits/types/locale_t.h" 2 3 4

typedef __locale_t locale_t;
# 154 "/usr/include/string.h" 2 3 4


extern int strcoll_l (const char *__s1, const char *__s2, locale_t __l)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));


extern size_t strxfrm_l (char *__dest, const char *__src, size_t __n,
    locale_t __l) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 4)));





extern char *strdup (const char *__s)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));






extern char *strndup (const char *__string, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));
# 226 "/usr/include/string.h" 3 4
extern char *strchr (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
# 253 "/usr/include/string.h" 3 4
extern char *strrchr (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
# 266 "/usr/include/string.h" 3 4
extern char *strchrnul (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));





extern size_t strcspn (const char *__s, const char *__reject)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern size_t strspn (const char *__s, const char *__accept)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
# 303 "/usr/include/string.h" 3 4
extern char *strpbrk (const char *__s, const char *__accept)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
# 330 "/usr/include/string.h" 3 4
extern char *strstr (const char *__haystack, const char *__needle)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));




extern char *strtok (char *__restrict __s, const char *__restrict __delim)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));



extern char *__strtok_r (char *__restrict __s,
    const char *__restrict __delim,
    char **__restrict __save_ptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 3)));

extern char *strtok_r (char *__restrict __s, const char *__restrict __delim,
         char **__restrict __save_ptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 3)));
# 360 "/usr/include/string.h" 3 4
extern char *strcasestr (const char *__haystack, const char *__needle)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));







extern void *memmem (const void *__haystack, size_t __haystacklen,
       const void *__needle, size_t __needlelen)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 3)));



extern void *__mempcpy (void *__restrict __dest,
   const void *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern void *mempcpy (void *__restrict __dest,
        const void *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));




extern size_t strlen (const char *__s)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));




extern size_t strnlen (const char *__string, size_t __maxlen)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));




extern char *strerror (int __errnum) __attribute__ ((__nothrow__ , __leaf__));
# 421 "/usr/include/string.h" 3 4
extern char *strerror_r (int __errnum, char *__buf, size_t __buflen)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2))) ;





extern char *strerror_l (int __errnum, locale_t __l) __attribute__ ((__nothrow__ , __leaf__));



# 1 "/usr/include/strings.h" 1 3 4
# 23 "/usr/include/strings.h" 3 4
# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stddef.h" 1 3 4
# 24 "/usr/include/strings.h" 2 3 4










extern int bcmp (const void *__s1, const void *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern void bcopy (const void *__src, void *__dest, size_t __n)
  __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern void bzero (void *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
# 68 "/usr/include/strings.h" 3 4
extern char *index (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
# 96 "/usr/include/strings.h" 3 4
extern char *rindex (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));






extern int ffs (int __i) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));





extern int ffsl (long int __l) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
__extension__ extern int ffsll (long long int __ll)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));



extern int strcasecmp (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern int strncasecmp (const char *__s1, const char *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));






extern int strcasecmp_l (const char *__s1, const char *__s2, locale_t __loc)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));



extern int strncasecmp_l (const char *__s1, const char *__s2,
     size_t __n, locale_t __loc)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 4)));



# 433 "/usr/include/string.h" 2 3 4



extern void explicit_bzero (void *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));



extern char *strsep (char **__restrict __stringp,
       const char *__restrict __delim)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));




extern char *strsignal (int __sig) __attribute__ ((__nothrow__ , __leaf__));


extern char *__stpcpy (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *stpcpy (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));



extern char *__stpncpy (char *__restrict __dest,
   const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *stpncpy (char *__restrict __dest,
        const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));




extern int strverscmp (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern char *strfry (char *__string) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern void *memfrob (void *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
# 487 "/usr/include/string.h" 3 4
extern char *basename (const char *__filename) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
# 499 "/usr/include/string.h" 3 4

# 7 "/home/ubuntu/neovim/src/nvim/math.c" 2





# 1 "/home/ubuntu/neovim/src/nvim/math.h" 1
       

# 1 "/usr/lib/gcc/aarch64-linux-gnu/9/include/stdbool.h" 1 3 4
# 4 "/home/ubuntu/neovim/src/nvim/math.h" 2




# 7 "/home/ubuntu/neovim/src/nvim/math.h"
static inline 
# 7 "/home/ubuntu/neovim/src/nvim/math.h" 3 4
             _Bool 
# 7 "/home/ubuntu/neovim/src/nvim/math.h"
                  is_power_of_two(uint64_t x)
{
  return x != 0 && ((x & (x - 1)) == 0);
}
# 13 "/home/ubuntu/neovim/src/nvim/math.c" 2
# 1 "/home/ubuntu/neovim/src/nvim/vim_defs.h" 1
       







enum {

  NUMBUFLEN = 65,
};




typedef enum {
  kDirectionNotSet = 0,
  FORWARD = 1,
  BACKWARD = -1,
  FORWARD_FILE = 3,
  BACKWARD_FILE = -3,
} Direction;



typedef enum {
  kUnknown,
  kWorking,
  kBroken,
} WorkingStatus;







typedef enum {
  kCdScopeInvalid = -1,
  kCdScopeWindow,
  kCdScopeTabpage,
  kCdScopeGlobal,
} CdScope;





typedef enum {
  kCdCauseOther = -1,
  kCdCauseManual,
  kCdCauseWindow,
  kCdCauseAuto,
} CdCause;
# 14 "/home/ubuntu/neovim/src/nvim/math.c" 2





int xfpclassify(double d)
  FUNC_ATTR_CONST
{
  uint64_t m;

  memcpy(&m, &d, sizeof(m));
  int e = 0x7ff & (m >> 52);
  m = 0xfffffffffffffULL & m;

  switch (e) {
  default:
    return 
# 30 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
          4
# 30 "/home/ubuntu/neovim/src/nvim/math.c"
                   ;
  case 0x000:
    return m ? 
# 32 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
              3 
# 32 "/home/ubuntu/neovim/src/nvim/math.c"
                           : 
# 32 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
                             2
# 32 "/home/ubuntu/neovim/src/nvim/math.c"
                                    ;
  case 0x7ff:
    return m ? 
# 34 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
              0 
# 34 "/home/ubuntu/neovim/src/nvim/math.c"
                     : 
# 34 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
                       1
# 34 "/home/ubuntu/neovim/src/nvim/math.c"
                                  ;
  }
}

int xisinf(double d)
  FUNC_ATTR_CONST
{
  return 
# 41 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
        1 
# 41 "/home/ubuntu/neovim/src/nvim/math.c"
                    == xfpclassify(d);
}

int xisnan(double d)
  FUNC_ATTR_CONST
{
  return 
# 47 "/home/ubuntu/neovim/src/nvim/math.c" 3 4
        0 
# 47 "/home/ubuntu/neovim/src/nvim/math.c"
               == xfpclassify(d);
}


int xctz(uint64_t x)
{

  if (x == 0) {
    return 8 * sizeof(x);
  }



  return __builtin_ctzll(x);
# 78 "/home/ubuntu/neovim/src/nvim/math.c"
}


unsigned xpopcount(uint64_t x)
{




  return (unsigned)__builtin_popcountll(x);
# 97 "/home/ubuntu/neovim/src/nvim/math.c"
}


int vim_append_digit_int(int *value, int digit)
{
  int x = *value;
  if (x > ((0x7fffffff - digit) / 10)) {
    return 0;
  }
  *value = x * 10 + digit;
  return 1;
}