_PROTO
#ifndef _PROTO
extern void impn_mul_n_basecase _PROTO ((mp_ptr prodp, mp_srcptr up,
extern void impn_mul_n _PROTO ((mp_ptr prodp, mp_srcptr up, mp_srcptr vp,
extern void impn_sqr_n_basecase _PROTO ((mp_ptr prodp, mp_srcptr up,
extern void impn_sqr_n _PROTO ((mp_ptr prodp, mp_srcptr up, mp_size_t size,
#ifndef _PROTO
void mp_set_memory_functions _PROTO ((void *(*) (size_t),
void *_mpz_realloc _PROTO ((mpz_ptr, mp_size_t));
void mpz_abs _PROTO ((mpz_ptr, mpz_srcptr));
void mpz_add _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_add_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_and _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_array_init _PROTO ((mpz_ptr, mp_size_t, mp_size_t));
void mpz_cdiv_q _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
unsigned long int mpz_cdiv_q_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_cdiv_qr _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
unsigned long int mpz_cdiv_qr_ui _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_cdiv_r _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
unsigned long int mpz_cdiv_r_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
unsigned long int mpz_cdiv_ui _PROTO ((mpz_srcptr, unsigned long int));
void mpz_clear _PROTO ((mpz_ptr));
void mpz_clrbit _PROTO ((mpz_ptr, unsigned long int));
int mpz_cmp _PROTO ((mpz_srcptr, mpz_srcptr));
int mpz_cmp_si _PROTO ((mpz_srcptr, signed long int));
int mpz_cmp_ui _PROTO ((mpz_srcptr, unsigned long int));
void mpz_com _PROTO ((mpz_ptr, mpz_srcptr));
void mpz_divexact _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_fac_ui _PROTO ((mpz_ptr, unsigned long int));
void mpz_fdiv_q _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_fdiv_q_2exp _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
unsigned long int mpz_fdiv_q_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_fdiv_qr _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
unsigned long int mpz_fdiv_qr_ui _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_fdiv_r _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_fdiv_r_2exp _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
unsigned long int mpz_fdiv_r_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
unsigned long int mpz_fdiv_ui _PROTO ((mpz_srcptr, unsigned long int));
void mpz_gcd _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
unsigned long int mpz_gcd_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_gcdext _PROTO ((mpz_ptr, mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
/* signed */ long int mpz_get_si _PROTO ((mpz_srcptr));
char *mpz_get_str _PROTO ((char *, int, mpz_srcptr));
unsigned long int mpz_get_ui _PROTO ((mpz_srcptr));
mp_limb_t mpz_getlimbn _PROTO ((mpz_srcptr, mp_size_t));
unsigned long int mpz_hamdist _PROTO ((mpz_srcptr, mpz_srcptr));
void mpz_init _PROTO ((mpz_ptr));
size_t mpz_inp_binary _PROTO ((mpz_ptr, FILE *));
size_t mpz_inp_raw _PROTO ((mpz_ptr, FILE *));
size_t mpz_inp_str _PROTO ((mpz_ptr, FILE *, int));
void mpz_init_set _PROTO ((mpz_ptr, mpz_srcptr));
void mpz_init_set_d _PROTO ((mpz_ptr, double));
void mpz_init_set_si _PROTO ((mpz_ptr, signed long int));
int mpz_init_set_str _PROTO ((mpz_ptr, const char *, int));
void mpz_init_set_ui _PROTO ((mpz_ptr, unsigned long int));
int mpz_invert _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_ior _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
int mpz_jacobi _PROTO ((mpz_srcptr, mpz_srcptr));
int mpz_legendre _PROTO ((mpz_srcptr, mpz_srcptr));
void mpz_mod _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_mul _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_mul_2exp _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_mul_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_neg _PROTO ((mpz_ptr, mpz_srcptr));
size_t mpz_out_binary _PROTO ((FILE *, mpz_srcptr));
size_t mpz_out_raw _PROTO ((FILE *, mpz_srcptr));
size_t mpz_out_str _PROTO ((FILE *, int, mpz_srcptr));
int mpz_perfect_square_p _PROTO ((mpz_srcptr));
unsigned long int mpz_popcount _PROTO ((mpz_srcptr));
void mpz_pow_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_powm _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr));
void mpz_powm_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int, mpz_srcptr));
int mpz_probab_prime_p _PROTO ((mpz_srcptr, int));
void mpz_random _PROTO ((mpz_ptr, mp_size_t));
void mpz_random2 _PROTO ((mpz_ptr, mp_size_t));
unsigned long int mpz_scan0 _PROTO ((mpz_srcptr, unsigned long int));
unsigned long int mpz_scan1 _PROTO ((mpz_srcptr, unsigned long int));
void mpz_set _PROTO ((mpz_ptr, mpz_srcptr));
void mpz_set_d _PROTO ((mpz_ptr, double));
void mpz_set_si _PROTO ((mpz_ptr, signed long int));
int mpz_set_str _PROTO ((mpz_ptr, const char *, int));
void mpz_set_ui _PROTO ((mpz_ptr, unsigned long int));
void mpz_setbit _PROTO ((mpz_ptr, unsigned long int));
size_t mpz_size _PROTO ((mpz_srcptr));
size_t mpz_sizeinbase _PROTO ((mpz_srcptr, int));
void mpz_sqrt _PROTO ((mpz_ptr, mpz_srcptr));
void mpz_sqrtrem _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr));
void mpz_sub _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_sub_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_tdiv_q _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_tdiv_q_2exp _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_tdiv_q_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_tdiv_qr _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_tdiv_qr_ui _PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_tdiv_r _PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
void mpz_tdiv_r_2exp _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_tdiv_r_ui _PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
void mpz_ui_pow_ui _PROTO ((mpz_ptr, unsigned long int, unsigned long int));
void mpq_init _PROTO ((mpq_ptr));
void mpq_clear _PROTO ((mpq_ptr));
void mpq_set _PROTO ((mpq_ptr, mpq_srcptr));
void mpq_set_ui _PROTO ((mpq_ptr, unsigned long int, unsigned long int));
void mpq_set_si _PROTO ((mpq_ptr, signed long int, unsigned long int));
void mpq_add _PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
void mpq_sub _PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
void mpq_mul _PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
void mpq_div _PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
void mpq_neg _PROTO ((mpq_ptr, mpq_srcptr));
int mpq_cmp _PROTO ((mpq_srcptr, mpq_srcptr));
int mpq_cmp_ui _PROTO ((mpq_srcptr, unsigned long int, unsigned long int));
void mpq_inv _PROTO ((mpq_ptr, mpq_srcptr));
void mpq_set_num _PROTO ((mpq_ptr, mpz_srcptr));
void mpq_set_den _PROTO ((mpq_ptr, mpz_srcptr));
void mpq_get_num _PROTO ((mpz_ptr, mpq_srcptr));
void mpq_get_den _PROTO ((mpz_ptr, mpq_srcptr));
double mpq_get_d _PROTO ((mpq_srcptr));
void mpq_canonicalize _PROTO ((mpq_ptr));
void mpf_abs _PROTO ((mpf_ptr, mpf_srcptr));
void mpf_add _PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
void mpf_add_ui _PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
void mpf_clear _PROTO ((mpf_ptr));
int mpf_cmp _PROTO ((mpf_srcptr, mpf_srcptr));
int mpf_cmp_si _PROTO ((mpf_srcptr, signed long int));
int mpf_cmp_ui _PROTO ((mpf_srcptr, unsigned long int));
void mpf_div _PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
void mpf_div_2exp _PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
void mpf_div_ui _PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
void mpf_dump _PROTO ((mpf_srcptr));
int mpf_eq _PROTO ((mpf_srcptr, mpf_srcptr, unsigned long int));
unsigned long int mpf_get_prec _PROTO ((mpf_srcptr));
char *mpf_get_str _PROTO ((char *, mp_exp_t *, int, size_t, mpf_srcptr));
void mpf_init _PROTO ((mpf_ptr));
void mpf_init2 _PROTO ((mpf_ptr, unsigned long int));
size_t mpf_inp_str _PROTO ((mpf_ptr, FILE *, int));
void mpf_init_set _PROTO ((mpf_ptr, mpf_srcptr));
void mpf_init_set_d _PROTO ((mpf_ptr, double));
void mpf_init_set_si _PROTO ((mpf_ptr, signed long int));
int mpf_init_set_str _PROTO ((mpf_ptr, char *, int));
void mpf_init_set_ui _PROTO ((mpf_ptr, unsigned long int));
void mpf_mul _PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
void mpf_mul_2exp _PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
void mpf_mul_ui _PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
void mpf_neg _PROTO ((mpf_ptr, mpf_srcptr));
size_t mpf_out_str _PROTO ((FILE *, int, size_t, mpf_srcptr));
void mpf_random2 _PROTO ((mpf_ptr, mp_size_t, mp_exp_t));
void mpf_reldiff _PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
void mpf_set _PROTO ((mpf_ptr, mpf_srcptr));
void mpf_set_d _PROTO ((mpf_ptr, double));
void mpf_set_default_prec _PROTO ((unsigned long int));
void mpf_set_prec _PROTO ((mpf_ptr, unsigned long int));
void mpf_set_prec_raw _PROTO ((mpf_ptr, unsigned long int));
void mpf_set_si _PROTO ((mpf_ptr, signed long int));
int mpf_set_str _PROTO ((mpf_ptr, const char *, int));
void mpf_set_ui _PROTO ((mpf_ptr, unsigned long int));
size_t mpf_size _PROTO ((mpf_srcptr));
void mpf_sqrt _PROTO ((mpf_ptr, mpf_srcptr));
void mpf_sqrt_ui _PROTO ((mpf_ptr, unsigned long int));
void mpf_sub _PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
void mpf_sub_ui _PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
void mpf_ui_div _PROTO ((mpf_ptr, unsigned long int, mpf_srcptr));
void mpf_ui_sub _PROTO ((mpf_ptr, unsigned long int, mpf_srcptr));
mp_limb_t mpn_add _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t));
mp_limb_t mpn_add_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
mp_limb_t mpn_add_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
mp_limb_t mpn_addmul_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
mp_limb_t mpn_bdivmod _PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, unsigned long int));
int mpn_cmp _PROTO ((mp_srcptr, mp_srcptr, mp_size_t));
mp_limb_t mpn_divmod_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
mp_limb_t mpn_divrem _PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr, mp_size_t));
mp_limb_t mpn_divrem_1 _PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
void mpn_dump _PROTO ((mp_srcptr, mp_size_t));
mp_size_t mpn_gcd _PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t));
mp_limb_t mpn_gcd_1 _PROTO ((mp_srcptr, mp_size_t, mp_limb_t));
mp_size_t mpn_gcdext _PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t));
size_t mpn_get_str _PROTO ((unsigned char *, int, mp_ptr, mp_size_t));
unsigned long int mpn_hamdist _PROTO ((mp_srcptr, mp_srcptr, mp_size_t));
mp_limb_t mpn_lshift _PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int));
mp_limb_t mpn_mod_1 _PROTO ((mp_srcptr, mp_size_t, mp_limb_t));
mp_limb_t mpn_mul _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
mp_limb_t mpn_mul_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
void mpn_mul_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
int mpn_perfect_square_p _PROTO ((mp_srcptr, mp_size_t));
unsigned long int mpn_popcount _PROTO ((mp_srcptr, mp_size_t));
mp_limb_t mpn_preinv_mod_1 _PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
void mpn_random2 _PROTO ((mp_ptr, mp_size_t));
mp_limb_t mpn_rshift _PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int));
unsigned long int mpn_scan0 _PROTO ((mp_srcptr, unsigned long int));
unsigned long int mpn_scan1 _PROTO ((mp_srcptr, unsigned long int));
mp_size_t mpn_set_str _PROTO ((mp_ptr, const unsigned char *, size_t, int));
mp_size_t mpn_sqrtrem _PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t));
mp_limb_t mpn_sub _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t));
mp_limb_t mpn_sub_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
mp_limb_t mpn_sub_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
mp_limb_t mpn_submul_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));