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 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 expm1 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __expm1 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double log1p (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log1p (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double logb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __logb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double exp2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __exp2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double log2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double pow (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __pow (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double sqrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sqrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double hypot (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __hypot (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double cbrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cbrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double ceil (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __ceil (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double fabs (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fabs (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double floor (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __floor (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double fmod (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __fmod (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern int __isinf (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int __finite (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int isinf (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int finite (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double drem (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __drem (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double significand (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __significand (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double copysign (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __copysign (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int __isnan (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int isnan (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double j0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __j0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double j1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __j1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double jn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double __jn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double y0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __y0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double y1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __y1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double yn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double __yn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double erf (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __erf (double) __attribute__ ((__nothrow__ , __leaf__)); extern double erfc (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __erfc (double) __attribute__ ((__nothrow__ , __leaf__)); extern double lgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __lgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double tgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __tgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double gamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __gamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern double __lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern double rint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __rint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double nexttoward (double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __nexttoward (double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double remainder (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __remainder (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double scalbn (double __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalbn (double __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern int ilogb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double scalbln (double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalbln (double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double nearbyint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __nearbyint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double round (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __round (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double trunc (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __trunc (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double remquo (double __x, double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern double __remquo (double __x, double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern long int lrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int llrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int lround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int llround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double fdim (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __fdim (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double fmax (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmax (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double fmin (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmin (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int __fpclassify (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern int __signbit (double __value) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ , __leaf__)); extern double __fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ , __leaf__)); extern double scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__));