loor_divide (SCM x, SCM y);
SCM_INTERNAL SCM scm_i_ceiling_divide (SCM x, SCM y);
SCM_INTERNAL SCM scm_i_truncate_divide (SCM x, SCM y);
SCM_INTERNAL SCM scm_i_centered_divide (SCM x, SCM y);
SCM_INTERNAL SCM scm_i_round_divide (SCM x, SCM y);

SCM_INTERNAL SCM scm_i_gcd (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_lcm (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_logand (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_logior (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_logxor (SCM x, SCM y, SCM rest);

SCM_API size_t scm_iint2str (intmax_t num, int rad, char *p);
SCM_API size_t scm_iuint2str (uintmax_t num, int rad, char *p);
SCM_API SCM scm_number_to_string (SCM x, SCM radix);
SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
					    unsigned int radix);
SCM_INTERNAL SCM scm_i_string_to_number (SCM str, unsigned int radix);
SCM_API SCM scm_string_to_number (SCM str, SCM radix);
SCM_API SCM scm_bigequal (SCM x, SCM y);
SCM_API SCM scm_real_equalp (SCM x, SCM y);
SCM_API SCM scm_complex_equalp (SCM x, SCM y);
SCM_INTERNAL int scm_i_heap_numbers_equal_p (SCM x, SCM y);
SCM_API SCM scm_number_p (SCM x);
SCM_API SCM scm_complex_p (SCM x);
SCM_API SCM scm_real_p (SCM x);
SCM_API SCM scm_rational_p (SCM z);
SCM_API SCM scm_integer_p (SCM x);
SCM_API SCM scm_exact_integer_p (SCM x);
SCM_API SCM scm_inexact_p (SCM x);
SCM_API int scm_is_inexact (SCM x);
SCM_API SCM scm_num_eq_p (SCM x, SCM y);
SCM_API SCM scm_less_p (SCM x, SCM y);
SCM_API SCM scm_gr_p (SCM x, SCM y);
SCM_API SCM scm_leq_p (SCM x, SCM y);
SCM_API SCM scm_geq_p (SCM x, SCM y);
SCM_API SCM scm_zero_p (SCM z);
SCM_API SCM scm_positive_p (SCM x);
SCM_API SCM scm_negative_p (SCM x);
SCM_API SCM scm_max (SCM x, SCM y);
SCM_API SCM scm_min (SCM x, SCM y);
SCM_API SCM scm_sum (SCM x, SCM y);
SCM_API SCM scm_oneplus (SCM x);
SCM_API SCM scm_difference (SCM x, SCM y);
SCM_API SCM scm_oneminus (SCM x);
SCM_API SCM scm_product (SCM x, SCM y);
SCM_API SCM scm_divide (SCM x, SCM y);
SCM_API SCM scm_floor (SCM x);
SCM_API SCM scm_ceiling (SCM x);
SCM_API double scm_c_truncate (double x);
SCM_API double scm_c_round (double x);
SCM_API SCM scm_truncate_number (SCM x);
SCM_API SCM scm_round_number (SCM x);
SCM_API SCM scm_expt (SCM z1, SCM z2);
SCM_API SCM scm_sin (SCM z);
SCM_API SCM scm_cos (SCM z);
SCM_API SCM scm_tan (SCM z);
SCM_API SCM scm_sinh (SCM z);
SCM_API SCM scm_cosh (SCM z);
SCM_API SCM scm_tanh (SCM z);
SCM_API SCM scm_asin (SCM z);
SCM_API SCM scm_acos (SCM z);
SCM_API SCM scm_atan (SCM x, SCM y);
SCM_API SCM scm_sys_asinh (SCM z);
SCM_API SCM scm_sys_acosh (SCM z);
SCM_API SCM scm_sys_atanh (SCM z);
SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
SCM_API SCM scm_make_polar (SCM z1, SCM z2);
SCM_API SCM scm_real_part (SCM z);
SCM_API SCM scm_imag_part (SCM z);
SCM_API SCM scm_magnitude (SCM z);
SCM_API SCM scm_angle (SCM z);
SCM_API SCM scm_exact_to_inexact (SCM z);
SCM_API SCM scm_inexact_to_exact (SCM z);
SCM_API SCM scm_trunc (SCM x);
SCM_API SCM scm_log (SCM z);
SCM_API SCM scm_log10 (SCM z);
SCM_API SCM scm_exp (SCM z);
SCM_API SCM scm_sqrt (SCM z);
SCM_API void scm_exact_integer_sqrt (SCM k, SCM *s, SCM *r);

SCM_INTERNAL SCM scm_i_min (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_max (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_sum (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_difference (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_product (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_divide (SCM x, SCM y, SCM rest);
SCM_INTERNAL SCM scm_i_exact_integer_sqrt (SCM k);

/* ratio functions */
SCM_API SCM scm_rationalize (SCM x, SCM err);
SCM_API SCM scm_numerator (SCM z);
SCM_API SCM scm_denominator (SCM z);

/* fraction internal functions */
SCM_INTERNAL double scm_i_fraction2double (SCM z);
SCM_INTERNAL SCM scm_i_fraction_equalp (SCM x, SCM y);
SCM_INTERNAL int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);

/* general internal functions */
SCM_INTERNAL void scm_i_print_double (double val, SCM port);
SCM_INTERNAL void scm_i_print_complex (double real, double imag, SCM port);

/* conversion functions for integers */

SCM_API int scm_is_integer (SCM val);
SCM_API int scm_is_exact_integer (SCM val);
SCM_API int scm_is_signed_integer (SCM val,
				   intmax_t min, intmax_t max);
SCM_API int scm_is_unsigned_integer (SCM val,
				     uintmax_t min, uintmax_t max);

SCM_API SCM scm_from_signed_integer (intmax_t val);
SCM_API SCM scm_from_unsigned_integer (uintmax_t val);

SCM_API intmax_t scm_to_signed_integer (SCM val,
                                        intmax_t min,
                                        intmax_t max);
SCM_API uintmax_t scm_to_unsigned_integer (SCM val,
                                           uintmax_t min,
                                           uintmax_t max);

SCM_API int8_t       scm_to_int8     (SCM x);
SCM_API SCM          scm_from_int8   (int8_t x);

SCM_API uint8_t      scm_to_uint8    (SCM x);
SCM_API SCM          scm_from_uint8  (uint8_t x);

SCM_API int16_t      scm_to_int16    (SCM x);
SCM_API SCM          scm_from_int16  (int16_t x);

SCM_API uint16_t     scm_to_uint16   (SCM x);
SCM_API SCM          scm_from_uint16 (uint16_t x);

SCM_API int32_t      scm_to_int32    (SCM x);
SCM_API SCM          scm_from_int32  (int32_t x);

SCM_API uint32_t     scm_to_uint32   (SCM x);
SCM_API SCM          scm_from_uint32 (uint32_t x);

SCM_API scm_t_wchar  scm_to_wchar    (SCM x);
SCM_API SCM          scm_from_wchar  (scm_t_wchar x);

SCM_API int64_t      scm_to_int64    (SCM x);
SCM_API SCM          scm_from_int64  (int64_t x);

SCM_API uint64_t     scm_to_uint64   (SCM x);
SCM_API SCM          scm_from_uint64 (uint64_t x);

#if defined BUILDING_LIBGUILE && SCM_ENABLE_MINI_GMP
SCM_INTERNAL void scm_to_mpz (SCM x, mpz_t rop);
SCM_INTERNAL SCM  scm_from_mpz (mpz_t rop);
#elif !SCM_ENABLE_MINI_GMP
SCM_API void scm_to_mpz (SCM x, mpz_t rop);
SCM_API SCM  scm_from_mpz (mpz_t rop);
#endif


/* The conversion functions for other types are aliased to the
   appropriate ones from above.  We pick the right one based on the
   size of the type.

   Not each and every possibility is covered by the code below, and
   while it is trivial to complete the tests, it might be better to
   just test for the 'sane' possibilities.  When one of the tests
   below fails, chances are good that some silent assumption somewhere
   else will also fail.
*/

#if SCM_SIZEOF_CHAR == 1
#define scm_to_schar   scm_to_int8
#define scm_from_schar scm_from_int8
#define scm_to_uchar   scm_to_uint8
#define scm_from_uchar scm_from_uint8
#if CHAR_MIN == 0
#define scm_to_char    scm_to_uint8
#define scm_from_char  scm_from_uint8
#else
#define scm_to_char    scm_to_int8
#define scm_from_char  scm_from_int8
#endif
#else
#error sizeof(char) is not 1.
#endif

#if SCM_SIZEOF_SHORT == 1
#define scm_to_short    scm_to_int8
#define scm_from_short  scm_from_int8
#define scm_to_ushort   scm_to_uint8
#define scm_from_ushort scm_from_uint8
#else
#if SCM_SIZEOF_SHORT == 2
#define scm_to_short    scm_to_int16
#define scm_from_short  scm_from_int16
#define scm_to_ushort   scm_to_uint16
#define scm_from_ushort scm_from_uint16
#else
#if SCM_SIZEOF_SHORT == 4
#define scm_to_short    scm_to_int32
#define scm_from_short  scm_from_int32
#define scm_to_ushort   scm_to_uint32
#define scm_from_ushort scm_from_uint32
#else
#error sizeof(short) is not 1, 2, or 4.
#endif
#endif
#endif

#if SCM_SIZEOF_INT == 4
#define scm_to_int    scm_to_int32
#define scm_from_int  scm_from_int32
#define scm_to_uint   scm_to_uint32
#define scm_from_uint scm_from_uint32
#else
#if SCM_SIZEOF_INT == 8
#define scm_to_int    scm_to_int64
#define scm_from_int  scm_from_int64
#define scm_to_uint   scm_to_uint64
#define scm_from_uint scm_from_uint64
#else
#error sizeof(int) is not 4 or 8.
#endif
#endif

#if SCM_SIZEOF_LONG == 4
#define scm_to_long    scm_to_int32
#define scm_from_long  scm_from_int32
#define scm_to_ulong   scm_to_uint32
#define scm_from_ulong scm_from_uint32
#else
#if SCM_SIZEOF_LONG == 8
#define scm_to_long    scm_to_int64
#define scm_from_long  scm_from_int64
#define scm_to_ulong   scm_to_uint64
#define scm_from_ulong scm_from_uint64
#else
#error sizeof(long) is not 4 or 8.
#endif
#endif

#if SCM_SIZEOF_INTMAX == 4
#define scm_to_intmax    scm_to_int32
#define scm_from_intmax  scm_from_int32
#define scm_to_uintmax   scm_to_uint32
#define scm_from_uintmax scm_from_uint32
#else
#if SCM_SIZEOF_INTMAX == 8
#define scm_to_intmax    scm_to_int64
#define scm_from_intmax  scm_from_int64
#define scm_to_uintmax   scm_to_uint64
#define scm_from_uintmax scm_from_uint64
#else
#error sizeof(intmax_t) is not 4 or 8.
#endif
#endif

#if SCM_SIZEOF_LONG_LONG == 0
#else
#if SCM_SIZEOF_LONG_LONG == 8
#define scm_to_long_long    scm_to_int64
#define scm_from_long_long  scm_from_int64
#define scm_to_ulong_long   scm_to_uint64
#define scm_from_ulong_long scm_from_uint64
#else
#error sizeof(long long) is not 8.
#endif
#endif

#if SCM_SIZEOF_SIZE_T == 4
#define scm_to_ssize_t    scm_to_int32
#define scm_from_ssize_t  scm_from_int32
#define scm_to_size_t     scm_to_uint32
#define scm_from_size_t   scm_from_uint32
#else
#if SCM_SIZEOF_SIZE_T == 8
#define scm_to_ssize_t    scm_to_int64
#define scm_from_ssize_t  scm_from_int64
#define scm_to_size_t     scm_to_uint64
#define scm_from_size_t   scm_from_uint64
#else
#error sizeof(size_t) is not 4 or 8.
#endif
#endif

#if SCM_SIZEOF_SCM_T_PTRDIFF == 4
#define scm_to_ptrdiff_t    scm_to_int32
#define scm_from_ptrdiff_t  scm_from_int32
#else
#if SCM_SIZEOF_SCM_T_PTRDIFF == 8
#define scm_to_ptrdiff_t    scm_to_int64
#define scm_from_ptrdiff_t  scm_from_int64
#else
#error sizeof(ptrdiff_t) is not 4 or 8.
#endif
#endif

#if SCM_SIZEOF_INTPTR_T == 0
/* No intptr_t; use size_t functions. */
#define scm_to_intptr_t   scm_to_ssize_t
#define scm_from_intptr_t scm_from_ssize_t
#elif SCM_SIZEOF_INTPTR_T == 4
#define scm_to_intptr_t   scm_to_int32
#define scm_from_intptr_t scm_from_int32
#elif SCM_SIZEOF_INTPTR_T == 8
#define scm_to_intptr_t   scm_to_int64
#define scm_from_intptr_t scm_from_int64
#else
#error sizeof(intptr_t) is not 4 or 8.
#endif

#if SCM_SIZEOF_UINTPTR_T == 0
/* No uintptr_t; use size_t functions. */
#define scm_to_uintptr_t   scm_to_size_t
#define scm_from_uintptr_t scm_from_size_t
#elif SCM_SIZEOF_UINTPTR_T == 4
#define scm_to_uintptr_t   scm_to_uint32
#define scm_from_uintptr_t scm_from_uint32
#elif SCM_SIZEOF_UINTPTR_T == 8
#define scm_to_uintptr_t   scm_to_uint64
#define scm_from_uintptr_t scm_from_uint64
#else
#error sizeof(uintptr_t) is not 4 or 8.
#endif

/* conversion functions for double */

SCM_API int scm_is_real (SCM val);
SCM_API int scm_is_rational (SCM val);
SCM_API double scm_to_double (SCM val);
SCM_API SCM scm_from_double (double val);

/* conversion functions for complex */

SCM_API int scm_is_complex (SCM val);
SCM_API SCM scm_c_make_rectangular (double re, double im);
SCM_API SCM scm_c_make_polar (double mag, double ang);
SCM_API double scm_c_real_part (SCM z);
SCM_API double scm_c_imag_part (SCM z);
SCM_API double scm_c_magnitude (SCM z);
SCM_API double scm_c_angle (SCM z);

SCM_API int scm_is_number (SCM val);

SCM_INTERNAL void scm_init_numbers (void);