double __builtin_acos(double);
float __builtin_acosf(float);
double __builtin_acosh(double);
float __builtin_acoshf(float);
long double __builtin_acoshl(long double);
long double __builtin_acosl(long double);
double __builtin_asin(double);
float __builtin_asinf(float);
double __builtin_asinh(double);
float __builtin_asinhf(float);
long double __builtin_asinhl(long double);
long double __builtin_asinl(long double);
double __builtin_atan(double);
double __builtin_atan2(double, double);
float __builtin_atan2f(float, float);
long double __builtin_atan2l(long double, long double);
float __builtin_atanf(float);
double __builtin_atanh(double);
float __builtin_atanhf(float);
long double __builtin_atanhl(long double);
long double __builtin_atanl(long double);
double __builtin_cbrt(double);
float __builtin_cbrtf(float);
long double __builtin_cbrtl(long double);
double __builtin_ceil(double);
float __builtin_ceilf(float);
long double __builtin_ceill(long double);
double __builtin_copysign(double, double);
float __builtin_copysignf(float, float);
long double __builtin_copysignl(long double, long double);
double __builtin_cos(double);
float __builtin_cosf(float);
double __builtin_cosh(double);
float __builtin_coshf(float);
long double __builtin_coshl(long double);
long double __builtin_cosl(long double);
double __builtin_drem(double, double);
float __builtin_dremf(float, float);
long double __builtin_dreml(long double, long double);
double __builtin_erf(double);
double __builtin_erfc(double);
float __builtin_erfcf(float);
long double __builtin_erfcl(long double);
float __builtin_erff(float);
long double __builtin_erfl(long double);
double __builtin_exp(double);
double __builtin_exp10(double);
float __builtin_exp10f(float);
long double __builtin_exp10l(long double);
double __builtin_exp2(double);
float __builtin_exp2f(float);
long double __builtin_exp2l(long double);
float __builtin_expf(float);
long double __builtin_expl(long double);
double __builtin_expm1(double);
float __builtin_expm1f(float);
long double __builtin_expm1l(long double);
double __builtin_fabs(double);
float __builtin_fabsf(float);
long double __builtin_fabsl(long double);



double __builtin_fdim(double, double);
float __builtin_fdimf(float, float);
long double __builtin_fdiml(long double, long double);
double __builtin_floor(double);
float __builtin_floorf(float);
long double __builtin_floorl(long double);
double __builtin_fma(double, double, double);
float __builtin_fmaf(float, float, float);
long double __builtin_fmal(long double, long double, long double);
double __builtin_fmax(double, double);
float __builtin_fmaxf(float, float);
long double __builtin_fmaxl(long double, long double);
double __builtin_fmin(double, double);
float __builtin_fminf(float, float);
long double __builtin_fminl(long double, long double);
double __builtin_fmod(double, double);
float __builtin_fmodf(float, float);
long double __builtin_fmodl(long double, long double);
double __builtin_frexp(double, int *);
float __builtin_frexpf(float, int *);
long double __builtin_frexpl(long double, int *);
double __builtin_gamma(double);
float __builtin_gammaf(float);
long double __builtin_gammal(long double);
double __builtin_gamma_r(double, int *);
float __builtin_gammaf_r(float, int *);
long double __builtin_gammal_r(long double, int *);
double __builtin_huge_val();
float __builtin_huge_valf();
long double __builtin_huge_vall();
double __builtin_hypot(double, double);
float __builtin_hypotf(float, float);
long double __builtin_hypotl(long double, long double);
int __builtin_iceil(double);
int __builtin_iceilf(float);
int __builtin_iceill(long double);
int __builtin_ifloor(double);
int __builtin_ifloorf(float);
int __builtin_ifloorl(long double);
int __builtin_ilogb(double);
int __builtin_ilogbf(float);
int __builtin_ilogbl(long double);
double __builtin_inf();
float __builtin_inff();
long double __builtin_infl();



int __builtin_irint(double);
int __builtin_irintf(float);
int __builtin_irintl(long double);
int __builtin_iround(double);
int __builtin_iroundf(float);
int __builtin_iroundl(long double);
double __builtin_j0(double);
float __builtin_j0f(float);
long double __builtin_j0l(long double);
double __builtin_j1(double);
float __builtin_j1f(float);
long double __builtin_j1l(long double);
double __builtin_jn(int, double);
float __builtin_jnf(int, float);
long double __builtin_jnl(int, long double);
long __builtin_lceil(double);
long __builtin_lceilf(float);
long __builtin_lceill(long double);
double __builtin_ldexp(double, int);
float __builtin_ldexpf(float, int);
long double __builtin_ldexpl(long double, int);
long __builtin_lfloor(double);
long __builtin_lfloorf(float);
long __builtin_lfloorl(long double);
double __builtin_lgamma(double);
float __builtin_lgammaf(float);
long double __builtin_lgammal(long double);
double __builtin_lgamma_r(double, int *);
float __builtin_lgammaf_r(float, int *);
long double __builtin_lgammal_r(long double, int *);
long long __builtin_llceil(double);
long long __builtin_llceilf(float);
long long __builtin_llceill(long double);
long long __builtin_llfloor(double);
long long __builtin_llfloorf(float);
long long __builtin_llfloorl(long double);
long long __builtin_llrint(double);
long long __builtin_llrintf(float);
long long __builtin_llrintl(long double);
long long __builtin_llround(double);
long long __builtin_llroundf(float);
long long __builtin_llroundl(long double);
double __builtin_log(double);
double __builtin_log10(double);
float __builtin_log10f(float);
long double __builtin_log10l(long double);
double __builtin_log1p(double);
float __builtin_log1pf(float);
long double __builtin_log1pl(long double);
double __builtin_log2(double);
float __builtin_log2f(float);
long double __builtin_log2l(long double);
double __builtin_logb(double);
float __builtin_logbf(float);
long double __builtin_logbl(long double);
float __builtin_logf(float);
long double __builtin_logl(long double);
long __builtin_lrint(double);
long __builtin_lrintf(float);
long __builtin_lrintl(long double);
long __builtin_lround(double);
long __builtin_lroundf(float);
long __builtin_lroundl(long double);
double __builtin_modf(double, double *);
float __builtin_modff(float, float *);
long double __builtin_modfl(long double, long double *);
double __builtin_nan(const char *);
float __builtin_nanf(const char *);
long double __builtin_nanl(const char *);



double __builtin_nans(const char *);
float __builtin_nansf(const char *);
long double __builtin_nansl(const char *);
double __builtin_nearbyint(double);
float __builtin_nearbyintf(float);
long double __builtin_nearbyintl(long double);
double __builtin_nextafter(double, double);
float __builtin_nextafterf(float, float);
long double __builtin_nextafterl(long double, long double);
double __builtin_nexttoward(double, long double);
float __builtin_nexttowardf(float, long double);
long double __builtin_nexttowardl(long double, long double);
double __builtin_pow(double, double);
double __builtin_pow10(double);
float __builtin_pow10f(float);
long double __builtin_pow10l(long double);
float __builtin_powf(float, float);
double __builtin_powi(double, int);
float __builtin_powif(float, int);
long double __builtin_powil(long double, int);
long double __builtin_powl(long double, long double);
double __builtin_remainder(double, double);
float __builtin_remainderf(float, float);
long double __builtin_remainderl(long double, long double);
double __builtin_remquo(double, double, int *);
float __builtin_remquof(float, float, int *);
long double __builtin_remquol(long double, long double, int *);
double __builtin_rint(double);
float __builtin_rintf(float);
long double __builtin_rintl(long double);
double __builtin_round(double);
float __builtin_roundf(float);
long double __builtin_roundl(long double);
double __builtin_scalb(double, double);
float __builtin_scalbf(float, float);
long double __builtin_scalbl(long double, long double);
double __builtin_scalbln(double, long);
float __builtin_scalblnf(float, long);
long double __builtin_scalblnl(long double, long);
double __builtin_scalbn(double, int);
float __builtin_scalbnf(float, int);
long double __builtin_scalbnl(long double, int);
int __builtin_signbit(double);
int __builtin_signbitf(float);
int __builtin_signbitl(long double);



double __builtin_significand(double);
float __builtin_significandf(float);
long double __builtin_significandl(long double);
double __builtin_sin(double);
void __builtin_sincos(double, double *, double *);
void __builtin_sincosf(float, float *, float *);
void __builtin_sincosl(long double, long double *, long double *);
float __builtin_sinf(float);
double __builtin_sinh(double);
float __builtin_sinhf(float);
long double __builtin_sinhl(long double);
long double __builtin_sinl(long double);
double __builtin_sqrt(double);
float __builtin_sqrtf(float);
long double __builtin_sqrtl(long double);
double __builtin_tan(double);
float __builtin_tanf(float);
double __builtin_tanh(double);
float __builtin_tanhf(float);
long double __builtin_tanhl(long double);
long double __builtin_tanl(long double);
double __builtin_tgamma(double);
float __builtin_tgammaf(float);
long double __builtin_tgammal(long double);
double __builtin_trunc(double);
float __builtin_truncf(float);
long double __builtin_truncl(long double);
double __builtin_y0(double);
float __builtin_y0f(float);
long double __builtin_y0l(long double);
double __builtin_y1(double);
float __builtin_y1f(float);
long double __builtin_y1l(long double);
double __builtin_yn(int, double);
float __builtin_ynf(int, float);
long double __builtin_ynl(int, long double);
double __builtin_cabs(_Complex double);
float __builtin_cabsf(_Complex float);
long double __builtin_cabsl(_Complex long double);
_Complex double __builtin_cacos(_Complex double);
_Complex float __builtin_cacosf(_Complex float);
_Complex double __builtin_cacosh(_Complex double);
_Complex float __builtin_cacoshf(_Complex float);
_Complex long double __builtin_cacoshl(_Complex long double);
_Complex long double __builtin_cacosl(_Complex long double);
double __builtin_carg(_Complex double);
float __builtin_cargf(_Complex float);
long double __builtin_cargl(_Complex long double);
_Complex double __builtin_casin(_Complex double);
_Complex float __builtin_casinf(_Complex float);
_Complex double __builtin_casinh(_Complex double);
_Complex float __builtin_casinhf(_Complex float);
_Complex long double __builtin_casinhl(_Complex long double);
_Complex long double __builtin_casinl(_Complex long double);
_Complex double __builtin_catan(_Complex double);
_Complex float __builtin_catanf(_Complex float);
_Complex double __builtin_catanh(_Complex double);
_Complex float __builtin_catanhf(_Complex float);
_Complex long double __builtin_catanhl(_Complex long double);
_Complex long double __builtin_catanl(_Complex long double);
_Complex double __builtin_ccos(_Complex double);
_Complex float __builtin_ccosf(_Complex float);
_Complex double __builtin_ccosh(_Complex double);
_Complex float __builtin_ccoshf(_Complex float);
_Complex long double __builtin_ccoshl(_Complex long double);
_Complex long double __builtin_ccosl(_Complex long double);
_Complex double __builtin_cexp(_Complex double);
_Complex float __builtin_cexpf(_Complex float);
_Complex long double __builtin_cexpl(_Complex long double);
_Complex double __builtin_cexpi(double);
_Complex float __builtin_cexpif(float);
_Complex long double __builtin_cexpil(long double);
double __builtin_cimag(_Complex double);
float __builtin_cimagf(_Complex float);
long double __builtin_cimagl(_Complex long double);
_Complex double __builtin_clog(_Complex double);
_Complex float __builtin_clogf(_Complex float);
_Complex long double __builtin_clogl(_Complex long double);
_Complex double __builtin_clog10(_Complex double);
_Complex float __builtin_clog10f(_Complex float);
_Complex long double __builtin_clog10l(_Complex long double);
_Complex double __builtin_conj(_Complex double);
_Complex float __builtin_conjf(_Complex float);
_Complex long double __builtin_conjl(_Complex long double);
_Complex double __builtin_cpow(_Complex double, _Complex double);
_Complex float __builtin_cpowf(_Complex float, _Complex float);
_Complex long double __builtin_cpowl(_Complex long double, _Complex long double);
_Complex double __builtin_cproj(_Complex double);
_Complex float __builtin_cprojf(_Complex float);
_Complex long double __builtin_cprojl(_Complex long double);
double __builtin_creal(_Complex double);
float __builtin_crealf(_Complex float);
long double __builtin_creall(_Complex long double);
_Complex double __builtin_csin(_Complex double);
_Complex float __builtin_csinf(_Complex float);
_Complex double __builtin_csinh(_Complex double);
_Complex float __builtin_csinhf(_Complex float);
_Complex long double __builtin_csinhl(_Complex long double);
_Complex long double __builtin_csinl(_Complex long double);
_Complex double __builtin_csqrt(_Complex double);
_Complex float __builtin_csqrtf(_Complex float);
_Complex long double __builtin_csqrtl(_Complex long double);
_Complex double __builtin_ctan(_Complex double);
_Complex float __builtin_ctanf(_Complex float);
_Complex double __builtin_ctanh(_Complex double);
_Complex float __builtin_ctanhf(_Complex float);
_Complex long double __builtin_ctanhl(_Complex long double);
_Complex long double __builtin_ctanl(_Complex long double);
int __builtin_bcmp(const void *, const void *, unsigned long);
void __builtin_bcopy(const void *, void *, unsigned long);
void __builtin_bzero(void *, unsigned long);
char * __builtin_index(const char *, int);
void * __builtin_memchr(const void *, int, unsigned long);
int __builtin_memcmp(const void *, const void *, unsigned long);
void * __builtin_memcpy(void *, const void *, unsigned long);
void * __builtin_memmove(void *, const void *, unsigned long);
void * __builtin_mempcpy(void *, const void *, unsigned long);
void * __builtin_memset(void *, int, unsigned long);
char * __builtin_rindex(const char *, int);
char * __builtin_stpcpy(char *, const char *);
char * __builtin_stpncpy(char *, const char *, unsigned long);
int __builtin_strcasecmp(const char *, const char *);
char * __builtin_strcat(char *, const char *);
char * __builtin_strchr(const char *, int);
int __builtin_strcmp(const char *, const char *);
char * __builtin_strcpy(char *, const char *);
unsigned long __builtin_strcspn(const char *, const char *);
char * __builtin_strdup(const char *);
char * __builtin_strndup(const char *, unsigned long);
unsigned long __builtin_strlen(const char *);
int __builtin_strncasecmp(const char *, const char *, unsigned long);
char * __builtin_strncat(char *, const char *, unsigned long);
int __builtin_strncmp(const char *, const char *, unsigned long);
char * __builtin_strncpy(char *, const char *, unsigned long);
char * __builtin_strpbrk(const char *, const char *);
char * __builtin_strrchr(const char *, int);
unsigned long __builtin_strspn(const char *, const char *);
char * __builtin_strstr(const char *, const char *);
int __builtin_fprintf(struct _IO_FILE *, const char *, ...);
int __builtin_fprintf_unlocked(struct _IO_FILE *, const char *, ...);
int __builtin_putc(int, struct _IO_FILE *);
int __builtin_putc_unlocked(int, struct _IO_FILE *);
int __builtin_fputc(int, struct _IO_FILE *);
int __builtin_fputc_unlocked(int, struct _IO_FILE *);
int __builtin_fputs(const char *, struct _IO_FILE *);
int __builtin_fputs_unlocked(const char *, struct _IO_FILE *);
int __builtin_fscanf(struct _IO_FILE *, const char *, ...);
unsigned long __builtin_fwrite(const void *, unsigned long, unsigned long, struct _IO_FILE *);
unsigned long __builtin_fwrite_unlocked(const void *, unsigned long, unsigned long, struct _IO_FILE *);
int __builtin_printf(const char *, ...);
int __builtin_printf_unlocked(const char *, ...);
int __builtin_putchar(int);
int __builtin_putchar_unlocked(int);
int __builtin_puts(const char *);
int __builtin_puts_unlocked(const char *);
int __builtin_scanf(const char *, ...);
int __builtin_snprintf(char *, unsigned long, const char *, ...);
int __builtin_sprintf(char *, const char *, ...);
int __builtin_sscanf(const char *, const char *, ...);
int __builtin_vfprintf(struct _IO_FILE *, const char *, void **);
int __builtin_vfscanf(struct _IO_FILE *, const char *, void **);
int __builtin_vprintf(const char *, void **);
int __builtin_vscanf(const char *, void **);
int __builtin_vsnprintf(char *, unsigned long, const char *, void **);
int __builtin_vsprintf(char *, const char *, void **);
int __builtin_vsscanf(const char *, const char *, void **);
int __builtin_isalnum(int);
int __builtin_isalpha(int);
int __builtin_isascii(int);
int __builtin_isblank(int);
int __builtin_iscntrl(int);
int __builtin_isdigit(int);
int __builtin_isgraph(int);
int __builtin_islower(int);
int __builtin_isprint(int);
int __builtin_ispunct(int);
int __builtin_isspace(int);
int __builtin_isupper(int);
int __builtin_isxdigit(int);
int __builtin_toascii(int);
int __builtin_tolower(int);
int __builtin_toupper(int);
int __builtin_iswalnum(unsigned int);
int __builtin_iswalpha(unsigned int);
int __builtin_iswblank(unsigned int);
int __builtin_iswcntrl(unsigned int);
int __builtin_iswdigit(unsigned int);
int __builtin_iswgraph(unsigned int);
int __builtin_iswlower(unsigned int);
int __builtin_iswprint(unsigned int);
int __builtin_iswpunct(unsigned int);
int __builtin_iswspace(unsigned int);
int __builtin_iswupper(unsigned int);
int __builtin_iswxdigit(unsigned int);
unsigned int __builtin_towlower(unsigned int);
unsigned int __builtin_towupper(unsigned int);
void __builtin_abort();
int __builtin_abs(int);
void * __builtin_aggregate_incoming_address();
void * __builtin_alloca(unsigned long);
void * __builtin_apply();
void * __builtin_apply_args();
short int __builtin_bswap16(short int);
int __builtin_bswap32(int);
long long int __builtin_bswap64(long long int);
void __builtin___clear_cache(void *, void *);
void * __builtin_calloc(unsigned long, unsigned long);
int __builtin_classify_type();
int __builtin_clz(unsigned int);
int __builtin_clzimax(unsigned long int);
int __builtin_clzl(unsigned long);
int __builtin_clzll(unsigned long long);
int __builtin_constant_p();
int __builtin_ctz(unsigned int);
int __builtin_ctzimax(unsigned long int);
int __builtin_ctzl(unsigned long);
int __builtin_ctzll(unsigned long long);
int __builtin_clrsb(int);
int __builtin_clrsbimax(long int);
int __builtin_clrsbl(long);
int __builtin_clrsbll(long long);
char * __builtin_dcgettext(const char *, const char *, int);
char * __builtin_dgettext(const char *, const char *);
void * __builtin_dwarf_cfa();
unsigned int __builtin_dwarf_sp_column();
void __builtin_eh_return();
int __builtin_eh_return_data_regno(int);
int __builtin_execl(const char *, const char *, ...);
int __builtin_execlp(const char *, const char *, ...);
int __builtin_execle(const char *, const char *, ...);
int __builtin_execv(const char *, char *const);
int __builtin_execvp(const char *, char *const);
int __builtin_execve(const char *, char *const, char *const);
void __builtin_exit(int);
long __builtin_expect(long, long);
void * __builtin_assume_aligned(const void *, unsigned long, ...);
void * __builtin_extend_pointer(void *);
void * __builtin_extract_return_addr(void *);
int __builtin_ffs(int);
int __builtin_ffsimax(long int);
int __builtin_ffsl(long);
int __builtin_ffsll(long long);
int __builtin_fork();
void * __builtin_frame_address(unsigned int);
void __builtin_free(void *);
void * __builtin_frob_return_addr(void *);
char * __builtin_gettext(const char *);
long int __builtin_imaxabs(long int);
void __builtin_init_dwarf_reg_size_table(void *);
int __builtin_finite(double);
int __builtin_finitef(float);
int __builtin_finitel(long double);



int __builtin_fpclassify(int, int, int, int, int, ...);
int __builtin_isfinite();
int __builtin_isinf_sign();
int __builtin_isinf();
int __builtin_isinff(float);
int __builtin_isinfl(long double);



int __builtin_isnan();
int __builtin_isnanf(float);
int __builtin_isnanl(long double);



int __builtin_isnormal();
int __builtin_isgreater();
int __builtin_isgreaterequal();
int __builtin_isless();
int __builtin_islessequal();
int __builtin_islessgreater();
int __builtin_isunordered();
long __builtin_labs(long);
long long __builtin_llabs(long long);
void __builtin_longjmp(void *, int);
void * __builtin_malloc(unsigned long);
void * __builtin_next_arg();
int __builtin_parity(unsigned int);
int __builtin_parityimax(unsigned long int);
int __builtin_parityl(unsigned long);
int __builtin_parityll(unsigned long long);
int __builtin_popcount(unsigned int);
int __builtin_popcountimax(unsigned long int);
int __builtin_popcountl(unsigned long);
int __builtin_popcountll(unsigned long long);
int __builtin_posix_memalign(void **, unsigned long, unsigned long);
void __builtin_prefetch(const void *, ...);
void * __builtin_realloc(void *, unsigned long);
void __builtin_return(void *);
void * __builtin_return_address(unsigned int);
void * __builtin_saveregs();
int __builtin_setjmp(void *);
long int __builtin_strfmon(char *, unsigned long, const char *, ...);
unsigned long __builtin_strftime(char *, unsigned long, const char *, const void *);
void __builtin_trap();
void __builtin_unreachable();
void __builtin_unwind_init();
void __builtin_update_setjmp_buf(void *, int);
void __builtin_va_copy(void **, void **);
void __builtin_va_end(void **);
void __builtin_va_start(void **, ...);
int __builtin_va_arg_pack();
int __builtin_va_arg_pack_len();
void __builtin__exit(int);
void __builtin__Exit(int);
void __builtin_init_trampoline();
void __builtin_init_heap_trampoline();
void __builtin_adjust_trampoline();
void __builtin_nonlocal_goto();
void __builtin_setjmp_setup();
void __builtin_setjmp_receiver();
void __builtin_stack_save();
void __builtin_stack_restore();
void __builtin_alloca_with_align();
unsigned long __builtin_object_size(const void *, int);
void * __builtin___memcpy_chk(void *, const void *, unsigned long, unsigned long);
void * __builtin___memmove_chk(void *, const void *, unsigned long, unsigned long);
void * __builtin___mempcpy_chk(void *, const void *, unsigned long, unsigned long);
void * __builtin___memset_chk(void *, int, unsigned long, unsigned long);
char * __builtin___stpcpy_chk(char *, const char *, unsigned long);
char * __builtin___stpncpy_chk(char *, const char *, unsigned long, unsigned long);
char * __builtin___strcat_chk(char *, const char *, unsigned long);
char * __builtin___strcpy_chk(char *, const char *, unsigned long);
char * __builtin___strncat_chk(char *, const char *, unsigned long, unsigned long);
char * __builtin___strncpy_chk(char *, const char *, unsigned long, unsigned long);
int __builtin___snprintf_chk(char *, unsigned long, int, unsigned long, const char *, ...);
int __builtin___sprintf_chk(char *, int, unsigned long, const char *, ...);
int __builtin___vsnprintf_chk(char *, unsigned long, int, unsigned long, const char *, void **);
int __builtin___vsprintf_chk(char *, int, unsigned long, const char *, void **);
int __builtin___fprintf_chk(struct _IO_FILE *, int, const char *, ...);
int __builtin___printf_chk(int, const char *, ...);
int __builtin___vfprintf_chk(struct _IO_FILE *, int, const char *, void **);
int __builtin___vprintf_chk(int, const char *, void **);
void __cyg_profile_func_enter(void *, void *);
void __cyg_profile_func_exit(void *, void *);
void * __builtin_thread_pointer();
void __builtin_set_thread_pointer(void *);


void __builtin_unwind_resume();
void __builtin_cxa_end_cleanup();
void __builtin_eh_pointer();
void __builtin_eh_filter();
void __builtin_eh_copy_values();
const char * __builtin_FILE();
const char * __builtin_FUNCTION();
int __builtin_LINE();
typedef void ** __builtin_va_list;
extern const char *__PRETTY_FUNCTION__;
typedef int wchar_t;