[bpt/guile.git] / libguile / numbers.h

/* classes: h_files */

#ifndef SCM_NUMBERS_H
#define SCM_NUMBERS_H

/* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005, 2006 Free Software Foundation, Inc.
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 */

\f

#include <gmp.h>

#include "libguile/__scm.h"
#include "libguile/print.h"

#if SCM_HAVE_FLOATINGPOINT_H
# include <floatingpoint.h>
#endif

#if SCM_HAVE_IEEEFP_H
# include <ieeefp.h>
#endif

#if SCM_HAVE_NAN_H
# if defined (SCO)
#   define _IEEE 1
# endif
# include <nan.h>
# if defined (SCO)
#   undef _IEEE
# endif
#endif /* SCM_HAVE_NAN_H */

\f

/* Immediate Numbers, also known as fixnums
 *
 * Inums are exact integer data that fits within an SCM word.  */

/* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
 * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
 * which is the same as                (/ (- (expt 2 n) 4) 4)
 */

#define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
#define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
#define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)

/* SCM_SRS is signed right shift */
#if (-1 == (((-1) << 2) + 2) >> 2)
# define SCM_SRS(x, y) ((x) >> (y))
#else
# define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
#endif /* (-1 == (((-1) << 2) + 2) >> 2) */


#define SCM_I_INUMP(x)	(2 & SCM_UNPACK (x))
#define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
#define SCM_I_MAKINUM(x) \
  (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
#define SCM_I_INUM(x)   (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))

/* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
#define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
#define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
#define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))


/* A name for 0. */
#define SCM_INUM0 (SCM_I_MAKINUM (0))

/* SCM_MAXEXP is the maximum double precision exponent
 * SCM_FLTMAX is less than or scm_equal the largest single precision float
 */

#if SCM_HAVE_STDC_HEADERS
# ifndef GO32
#  include <float.h>
#  ifdef __MINGW32__
#   define copysign _copysign
#   define finite _finite
#  endif /* __MINGW32__ */
# endif /* ndef GO32 */
#endif /* def STDC_HEADERS */

#ifdef DBL_MAX_10_EXP
# define SCM_MAXEXP DBL_MAX_10_EXP
#else
# define SCM_MAXEXP 308		/* IEEE doubles */
#endif /* def DBL_MAX_10_EXP */

#ifdef FLT_MAX
# define SCM_FLTMAX FLT_MAX
#else
# define SCM_FLTMAX 1e+23
#endif /* def FLT_MAX */


/* SCM_INTBUFLEN is the maximum number of characters neccessary for
 * the printed or scm_string representation of an scm_t_intmax in
 * radix 2.  The buffer passed to scm_iint2str and scm_iuint2str must
 * be of this size, for example.
 */
#define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))

\f

/* Numbers 
 */


/* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
 * differ in one bit: This way, checking if an object is an inexact number can
 * be done quickly (using the TYP16S macro).  */

/* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 * and SCM_NUMP)  */
#define scm_tc16_big		(scm_tc7_number + 1 * 256L)
#define scm_tc16_real           (scm_tc7_number + 2 * 256L)
#define scm_tc16_complex        (scm_tc7_number + 3 * 256L)
#define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)

#define SCM_INEXACTP(x) \
  (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
#define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
#define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)

#define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
#define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
#define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
#define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)

/* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
#define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
#define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)

#define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
#define SCM_NUMP(x) (!SCM_IMP(x) \
  && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
      || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
/* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */

#define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
#define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
#define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))

\f

typedef struct scm_t_double
{
  SCM type;
  SCM pad;
  double real;
} scm_t_double;

typedef struct scm_t_complex
{
  double real;
  double imag;
} scm_t_complex;

\f

SCM_API SCM scm_exact_p (SCM x);
SCM_API SCM scm_odd_p (SCM n);
SCM_API SCM scm_even_p (SCM n);
SCM_API SCM scm_inf_p (SCM n);
SCM_API SCM scm_nan_p (SCM n);
SCM_API SCM scm_inf (void);
SCM_API SCM scm_nan (void);
SCM_API SCM scm_abs (SCM x);
SCM_API SCM scm_quotient (SCM x, SCM y);
SCM_API SCM scm_remainder (SCM x, SCM y);
SCM_API SCM scm_modulo (SCM x, SCM y);
SCM_API SCM scm_gcd (SCM x, SCM y);
SCM_API SCM scm_lcm (SCM n1, SCM n2);
SCM_API SCM scm_logand (SCM n1, SCM n2);
SCM_API SCM scm_logior (SCM n1, SCM n2);
SCM_API SCM scm_logxor (SCM n1, SCM n2);
SCM_API SCM scm_logtest (SCM n1, SCM n2);
SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
SCM_API SCM scm_lognot (SCM n);
SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
SCM_API SCM scm_ash (SCM n, SCM cnt);
SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
SCM_API SCM scm_logcount (SCM n);
SCM_API SCM scm_integer_length (SCM n);

SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
SCM_API size_t scm_iuint2str (scm_t_uintmax 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_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_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_inexact_p (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_asinh (double x);
SCM_API double scm_acosh (double x);
SCM_API double scm_atanh (double 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_sys_expt (SCM z1, SCM z2);
SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
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);

/* bignum internal functions */
SCM_API SCM scm_i_mkbig (void);
SCM_API SCM scm_i_normbig (SCM x);
SCM_API int scm_i_bigcmp (SCM a, SCM b);
SCM_API SCM scm_i_dbl2big (double d);
SCM_API SCM scm_i_dbl2num (double d);
SCM_API double scm_i_big2dbl (SCM b);
SCM_API SCM scm_i_long2big (long n);
SCM_API SCM scm_i_ulong2big (unsigned long n);
SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);

/* 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_API double scm_i_fraction2double (SCM z);
SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);

/* general internal functions */
SCM_API void scm_i_print_double (double val, SCM port);
SCM_API 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_signed_integer (SCM val,
				   scm_t_intmax min, scm_t_intmax max);
SCM_API int scm_is_unsigned_integer (SCM val,
				     scm_t_uintmax min, scm_t_uintmax max);

SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);

SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
					    scm_t_intmax min,
					    scm_t_intmax max);
SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
					       scm_t_uintmax min,
					       scm_t_uintmax max);

SCM_API scm_t_int8   scm_to_int8     (SCM x);
SCM_API SCM          scm_from_int8   (scm_t_int8 x);

SCM_API scm_t_uint8  scm_to_uint8    (SCM x);
SCM_API SCM          scm_from_uint8  (scm_t_uint8 x);

SCM_API scm_t_int16  scm_to_int16    (SCM x);
SCM_API SCM          scm_from_int16  (scm_t_int16 x);

SCM_API scm_t_uint16 scm_to_uint16   (SCM x);
SCM_API SCM          scm_from_uint16 (scm_t_uint16 x);

SCM_API scm_t_int32  scm_to_int32    (SCM x);
SCM_API SCM          scm_from_int32  (scm_t_int32 x);

SCM_API scm_t_uint32 scm_to_uint32   (SCM x);
SCM_API SCM          scm_from_uint32 (scm_t_uint32 x);

#if SCM_HAVE_T_INT64

SCM_API scm_t_int64  scm_to_int64    (SCM x);
SCM_API SCM          scm_from_int64  (scm_t_int64 x);

SCM_API scm_t_uint64 scm_to_uint64   (SCM x);
SCM_API SCM          scm_from_uint64 (scm_t_uint64 x);

#endif

SCM_API void scm_to_mpz (SCM x, mpz_t rop);
SCM_API SCM  scm_from_mpz (mpz_t rop);


/* 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(scm_t_intmax) 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

/* 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_API void scm_init_numbers (void);

#endif  /* SCM_NUMBERS_H */

/*
  Local Variables:
  c-file-style: "gnu"
  End:
*/
Commit	Line	Data
0f2d19dd JB	1	/* classes: h_files */
0f2d19dd JB	2
3c9a524f DH	3	#ifndef SCM_NUMBERS_H
3c9a524f DH	4	#define SCM_NUMBERS_H
dee01b01	5
2b829bbb	6	/* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005, 2006 Free Software Foundation, Inc.
dee01b01	7	*
73be1d9e MV	8	* This library is free software; you can redistribute it and/or
	9	* modify it under the terms of the GNU Lesser General Public
	10	* License as published by the Free Software Foundation; either
	11	* version 2.1 of the License, or (at your option) any later version.
dee01b01	12	*
73be1d9e	13	* This library is distributed in the hope that it will be useful,
0f2d19dd	14	* but WITHOUT ANY WARRANTY; without even the implied warranty of
73be1d9e MV	15	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
73be1d9e MV	16	* Lesser General Public License for more details.
dee01b01	17	*
73be1d9e MV	18	* You should have received a copy of the GNU Lesser General Public
73be1d9e MV	19	* License along with this library; if not, write to the Free Software
92205699	20	* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
73be1d9e	21	*/
d3a6bc94	22
0f2d19dd JB	23	\f
0f2d19dd JB	24
cd036260 MV	25	#include <gmp.h>
cd036260 MV	26
b4309c3c	27	#include "libguile/__scm.h"
34f74fe1 MD	28	#include "libguile/print.h"
34f74fe1 MD	29
f0ad7455 RB	30	#if SCM_HAVE_FLOATINGPOINT_H
f0ad7455 RB	31	# include <floatingpoint.h>
232898d9 MV	32	#endif
232898d9 MV	33
f0ad7455 RB	34	#if SCM_HAVE_IEEEFP_H
f0ad7455 RB	35	# include <ieeefp.h>
232898d9 MV	36	#endif
232898d9 MV	37
f0ad7455 RB	38	#if SCM_HAVE_NAN_H
	39	# if defined (SCO)
	40	# define _IEEE 1
	41	# endif
	42	# include <nan.h>
	43	# if defined (SCO)
	44	# undef _IEEE
	45	# endif
	46	#endif /* SCM_HAVE_NAN_H */
232898d9	47
0f2d19dd JB	48	\f
0f2d19dd JB	49
14282d0f	50	/* Immediate Numbers, also known as fixnums
0f2d19dd	51	*
14282d0f	52	* Inums are exact integer data that fits within an SCM word. */
0f2d19dd	53
c0060c95 MV	54	/* SCM_T_SIGNED_MAX is (- (expt 2 n) 1),
	55	* SCM_MOST_POSITIVE_FIXNUM should be (- (expt 2 (- n 2)) 1)
	56	* which is the same as (/ (- (expt 2 n) 4) 4)
	57	*/
	58
004c0902	59	#define SCM_I_FIXNUM_BIT (SCM_LONG_BIT - 2)
c0060c95	60	#define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
004c0902	61	#define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
5c75b29f	62
56100716 DH	63	/* SCM_SRS is signed right shift */
56100716 DH	64	#if (-1 == (((-1) << 2) + 2) >> 2)
14282d0f	65	# define SCM_SRS(x, y) ((x) >> (y))
0f2d19dd	66	#else
14282d0f	67	# define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
56100716	68	#endif /* (-1 == (((-1) << 2) + 2) >> 2) */
0f2d19dd JB	69
0f2d19dd JB	70
3aa13a05 MV	71	#define SCM_I_INUMP(x) (2 & SCM_UNPACK (x))
3aa13a05 MV	72	#define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
5a572ca1	73	#define SCM_I_MAKINUM(x) \
5d7d39ff	74	(SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
3aa13a05	75	#define SCM_I_INUM(x) (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
0f2d19dd	76
894a712b DH	77	/* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
	78	#define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
	79	#define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
14282d0f	80	#define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
894a712b DH	81
894a712b DH	82
56100716	83	/* A name for 0. */
5a572ca1	84	#define SCM_INUM0 (SCM_I_MAKINUM (0))
0f2d19dd	85
c0060c95	86	/* SCM_MAXEXP is the maximum double precision exponent
88eb6852 MD	87	* SCM_FLTMAX is less than or scm_equal the largest single precision float
	88	*/
	89
f0ad7455 RB	90	#if SCM_HAVE_STDC_HEADERS
f0ad7455 RB	91	# ifndef GO32
1e498fbd SJ	92	# include <float.h>
	93	# ifdef __MINGW32__
	94	# define copysign _copysign
1e498fbd SJ	95	# define finite _finite
1e498fbd SJ	96	# endif /* __MINGW32__ */
f0ad7455	97	# endif /* ndef GO32 */
88eb6852	98	#endif /* def STDC_HEADERS */
f0ad7455	99
88eb6852	100	#ifdef DBL_MAX_10_EXP
f0ad7455	101	# define SCM_MAXEXP DBL_MAX_10_EXP
88eb6852	102	#else
f0ad7455	103	# define SCM_MAXEXP 308 /* IEEE doubles */
88eb6852	104	#endif /* def DBL_MAX_10_EXP */
f0ad7455	105
88eb6852	106	#ifdef FLT_MAX
f0ad7455	107	# define SCM_FLTMAX FLT_MAX
88eb6852	108	#else
f0ad7455	109	# define SCM_FLTMAX 1e+23
88eb6852 MD	110	#endif /* def FLT_MAX */
88eb6852 MD	111
0f2d19dd	112
2881e77b MV	113	/* SCM_INTBUFLEN is the maximum number of characters neccessary for
	114	* the printed or scm_string representation of an scm_t_intmax in
	115	* radix 2. The buffer passed to scm_iint2str and scm_iuint2str must
	116	* be of this size, for example.
0f2d19dd	117	*/
2881e77b	118	#define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
0f2d19dd JB	119
	120	\f
	121
	122	/* Numbers
	123	*/
	124
534c55a9 DH	125
	126	/* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
	127	* differ in one bit: This way, checking if an object is an inexact number can
	128	* be done quickly (using the TYP16S macro). */
	129
f03314f9 DH	130	/* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
f03314f9 DH	131	* and SCM_NUMP) */
534c55a9 DH	132	#define scm_tc16_big (scm_tc7_number + 1 * 256L)
	133	#define scm_tc16_real (scm_tc7_number + 2 * 256L)
	134	#define scm_tc16_complex (scm_tc7_number + 3 * 256L)
f92e85f7	135	#define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
534c55a9	136
f03314f9 DH	137	#define SCM_INEXACTP(x) \
f03314f9 DH	138	(!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
0d5e3480 DH	139	#define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
0d5e3480 DH	140	#define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
88eb6852	141
92c2555f MV	142	#define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
92c2555f MV	143	#define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
405aaef9 DH	144	#define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
405aaef9 DH	145	#define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
0f2d19dd	146
d3e7e88d	147	/* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
fba8fdc0	148	#define SCM_I_BIG_MPZ(x) (((mpz_t ) (SCM_CELL_OBJECT_LOC((x),1))))
d3e7e88d	149	#define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
0f2d19dd	150
3aa13a05	151	#define SCM_NUMBERP(x) (SCM_I_INUMP(x) \|\| SCM_NUMP(x))
d3e7e88d	152	#define SCM_NUMP(x) (!SCM_IMP(x) \
f92e85f7 MV	153	&& (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
	154	\|\| ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
	155	/* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
	156
	157	#define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
651f07f8 DH	158	#define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
651f07f8 DH	159	#define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
88eb6852	160
0f2d19dd JB	161	\f
0f2d19dd JB	162
92c2555f	163	typedef struct scm_t_double
0f2d19dd JB	164	{
0f2d19dd JB	165	SCM type;
88eb6852 MD	166	SCM pad;
88eb6852 MD	167	double real;
92c2555f	168	} scm_t_double;
0f2d19dd	169
92c2555f	170	typedef struct scm_t_complex
0f2d19dd	171	{
88eb6852 MD	172	double real;
88eb6852 MD	173	double imag;
92c2555f	174	} scm_t_complex;
0f2d19dd	175
0f2d19dd	176	\f
0f2d19dd	177
33b001fd MV	178	SCM_API SCM scm_exact_p (SCM x);
	179	SCM_API SCM scm_odd_p (SCM n);
	180	SCM_API SCM scm_even_p (SCM n);
232898d9 MV	181	SCM_API SCM scm_inf_p (SCM n);
	182	SCM_API SCM scm_nan_p (SCM n);
	183	SCM_API SCM scm_inf (void);
	184	SCM_API SCM scm_nan (void);
33b001fd MV	185	SCM_API SCM scm_abs (SCM x);
	186	SCM_API SCM scm_quotient (SCM x, SCM y);
	187	SCM_API SCM scm_remainder (SCM x, SCM y);
	188	SCM_API SCM scm_modulo (SCM x, SCM y);
	189	SCM_API SCM scm_gcd (SCM x, SCM y);
	190	SCM_API SCM scm_lcm (SCM n1, SCM n2);
	191	SCM_API SCM scm_logand (SCM n1, SCM n2);
	192	SCM_API SCM scm_logior (SCM n1, SCM n2);
	193	SCM_API SCM scm_logxor (SCM n1, SCM n2);
	194	SCM_API SCM scm_logtest (SCM n1, SCM n2);
	195	SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
	196	SCM_API SCM scm_lognot (SCM n);
d885e204	197	SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
33b001fd MV	198	SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
	199	SCM_API SCM scm_ash (SCM n, SCM cnt);
	200	SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
	201	SCM_API SCM scm_logcount (SCM n);
	202	SCM_API SCM scm_integer_length (SCM n);
1be6b49c	203
2881e77b MV	204	SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
2881e77b MV	205	SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
33b001fd MV	206	SCM_API SCM scm_number_to_string (SCM x, SCM radix);
	207	SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
	208	SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
	209	SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
2b829bbb KR	210	SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
2b829bbb KR	211	unsigned int radix);
33b001fd	212	SCM_API SCM scm_string_to_number (SCM str, SCM radix);
33b001fd MV	213	SCM_API SCM scm_bigequal (SCM x, SCM y);
	214	SCM_API SCM scm_real_equalp (SCM x, SCM y);
	215	SCM_API SCM scm_complex_equalp (SCM x, SCM y);
	216	SCM_API SCM scm_number_p (SCM x);
8507ec80	217	SCM_API SCM scm_complex_p (SCM x);
33b001fd	218	SCM_API SCM scm_real_p (SCM x);
8507ec80	219	SCM_API SCM scm_rational_p (SCM z);
33b001fd MV	220	SCM_API SCM scm_integer_p (SCM x);
	221	SCM_API SCM scm_inexact_p (SCM x);
	222	SCM_API SCM scm_num_eq_p (SCM x, SCM y);
	223	SCM_API SCM scm_less_p (SCM x, SCM y);
	224	SCM_API SCM scm_gr_p (SCM x, SCM y);
	225	SCM_API SCM scm_leq_p (SCM x, SCM y);
	226	SCM_API SCM scm_geq_p (SCM x, SCM y);
	227	SCM_API SCM scm_zero_p (SCM z);
	228	SCM_API SCM scm_positive_p (SCM x);
	229	SCM_API SCM scm_negative_p (SCM x);
	230	SCM_API SCM scm_max (SCM x, SCM y);
	231	SCM_API SCM scm_min (SCM x, SCM y);
	232	SCM_API SCM scm_sum (SCM x, SCM y);
40882e3d	233	SCM_API SCM scm_oneplus (SCM x);
33b001fd	234	SCM_API SCM scm_difference (SCM x, SCM y);
40882e3d	235	SCM_API SCM scm_oneminus (SCM x);
33b001fd	236	SCM_API SCM scm_product (SCM x, SCM y);
33b001fd	237	SCM_API SCM scm_divide (SCM x, SCM y);
f92e85f7 MV	238	SCM_API SCM scm_floor (SCM x);
f92e85f7 MV	239	SCM_API SCM scm_ceiling (SCM x);
33b001fd MV	240	SCM_API double scm_asinh (double x);
	241	SCM_API double scm_acosh (double x);
	242	SCM_API double scm_atanh (double x);
3101f40f MV	243	SCM_API double scm_c_truncate (double x);
3101f40f MV	244	SCM_API double scm_c_round (double x);
f92e85f7 MV	245	SCM_API SCM scm_truncate_number (SCM x);
f92e85f7 MV	246	SCM_API SCM scm_round_number (SCM x);
33b001fd MV	247	SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
	248	SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
	249	SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
	250	SCM_API SCM scm_make_polar (SCM z1, SCM z2);
	251	SCM_API SCM scm_real_part (SCM z);
	252	SCM_API SCM scm_imag_part (SCM z);
	253	SCM_API SCM scm_magnitude (SCM z);
	254	SCM_API SCM scm_angle (SCM z);
	255	SCM_API SCM scm_exact_to_inexact (SCM z);
	256	SCM_API SCM scm_inexact_to_exact (SCM z);
	257	SCM_API SCM scm_trunc (SCM x);
8ab3d8a0 KR	258	SCM_API SCM scm_log (SCM z);
	259	SCM_API SCM scm_log10 (SCM z);
	260	SCM_API SCM scm_exp (SCM z);
	261	SCM_API SCM scm_sqrt (SCM z);
33b001fd	262
d3e7e88d RB	263	/* bignum internal functions */
	264	SCM_API SCM scm_i_mkbig (void);
	265	SCM_API SCM scm_i_normbig (SCM x);
	266	SCM_API int scm_i_bigcmp (SCM a, SCM b);
	267	SCM_API SCM scm_i_dbl2big (double d);
f92e85f7	268	SCM_API SCM scm_i_dbl2num (double d);
d3e7e88d	269	SCM_API double scm_i_big2dbl (SCM b);
d3e7e88d RB	270	SCM_API SCM scm_i_long2big (long n);
d3e7e88d RB	271	SCM_API SCM scm_i_ulong2big (unsigned long n);
23c3b605	272	SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);
d3e7e88d	273
f92e85f7	274	/* ratio functions */
f92e85f7 MV	275	SCM_API SCM scm_rationalize (SCM x, SCM err);
	276	SCM_API SCM scm_numerator (SCM z);
	277	SCM_API SCM scm_denominator (SCM z);
f92e85f7 MV	278
	279	/* fraction internal functions */
	280	SCM_API double scm_i_fraction2double (SCM z);
	281	SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
	282	SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
	283
b479fe9a MV	284	/* general internal functions */
b479fe9a MV	285	SCM_API void scm_i_print_double (double val, SCM port);
7a1aba42	286	SCM_API void scm_i_print_complex (double real, double imag, SCM port);
b479fe9a	287
d1b5b400	288	/* conversion functions for integers */
73e4de09 MV	289
	290	SCM_API int scm_is_integer (SCM val);
	291	SCM_API int scm_is_signed_integer (SCM val,
	292	scm_t_intmax min, scm_t_intmax max);
	293	SCM_API int scm_is_unsigned_integer (SCM val,
	294	scm_t_uintmax min, scm_t_uintmax max);
	295
	296	SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
	297	SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
	298
	299	SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
	300	scm_t_intmax min,
	301	scm_t_intmax max);
	302	SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
	303	scm_t_uintmax min,
	304	scm_t_uintmax max);
	305
bfd7932e MV	306	SCM_API scm_t_int8 scm_to_int8 (SCM x);
	307	SCM_API SCM scm_from_int8 (scm_t_int8 x);
	308
	309	SCM_API scm_t_uint8 scm_to_uint8 (SCM x);
	310	SCM_API SCM scm_from_uint8 (scm_t_uint8 x);
	311
	312	SCM_API scm_t_int16 scm_to_int16 (SCM x);
	313	SCM_API SCM scm_from_int16 (scm_t_int16 x);
	314
	315	SCM_API scm_t_uint16 scm_to_uint16 (SCM x);
	316	SCM_API SCM scm_from_uint16 (scm_t_uint16 x);
	317
	318	SCM_API scm_t_int32 scm_to_int32 (SCM x);
	319	SCM_API SCM scm_from_int32 (scm_t_int32 x);
	320
	321	SCM_API scm_t_uint32 scm_to_uint32 (SCM x);
	322	SCM_API SCM scm_from_uint32 (scm_t_uint32 x);
	323
	324	#if SCM_HAVE_T_INT64
	325
	326	SCM_API scm_t_int64 scm_to_int64 (SCM x);
	327	SCM_API SCM scm_from_int64 (scm_t_int64 x);
	328
	329	SCM_API scm_t_uint64 scm_to_uint64 (SCM x);
	330	SCM_API SCM scm_from_uint64 (scm_t_uint64 x);
	331
	332	#endif
	333
cd036260 MV	334	SCM_API void scm_to_mpz (SCM x, mpz_t rop);
	335	SCM_API SCM scm_from_mpz (mpz_t rop);
	336
	337
d1b5b400 MV	338	/* The conversion functions for other types are aliased to the
	339	appropriate ones from above. We pick the right one based on the
	340	size of the type.
	341
	342	Not each and every possibility is covered by the code below, and
	343	while it is trivial to complete the tests, it might be better to
	344	just test for the 'sane' possibilities. When one of the tests
	345	below fails, chances are good that some silent assumption somewhere
	346	else will also fail.
	347	*/
	348
	349	#if SCM_SIZEOF_CHAR == 1
	350	#define scm_to_schar scm_to_int8
	351	#define scm_from_schar scm_from_int8
	352	#define scm_to_uchar scm_to_uint8
	353	#define scm_from_uchar scm_from_uint8
73e4de09	354	#if CHAR_MIN == 0
d1b5b400 MV	355	#define scm_to_char scm_to_uint8
d1b5b400 MV	356	#define scm_from_char scm_from_uint8
73e4de09	357	#else
d1b5b400 MV	358	#define scm_to_char scm_to_int8
d1b5b400 MV	359	#define scm_from_char scm_from_int8
73e4de09	360	#endif
d1b5b400 MV	361	#else
d1b5b400 MV	362	#error sizeof(char) is not 1.
22008a78 MV	363	#endif
22008a78 MV	364
d1b5b400 MV	365	#if SCM_SIZEOF_SHORT == 1
	366	#define scm_to_short scm_to_int8
	367	#define scm_from_short scm_from_int8
	368	#define scm_to_ushort scm_to_uint8
	369	#define scm_from_ushort scm_from_uint8
	370	#else
	371	#if SCM_SIZEOF_SHORT == 2
	372	#define scm_to_short scm_to_int16
	373	#define scm_from_short scm_from_int16
	374	#define scm_to_ushort scm_to_uint16
	375	#define scm_from_ushort scm_from_uint16
	376	#else
	377	#if SCM_SIZEOF_SHORT == 4
	378	#define scm_to_short scm_to_int32
	379	#define scm_from_short scm_from_int32
	380	#define scm_to_ushort scm_to_uint32
	381	#define scm_from_ushort scm_from_uint32
73e4de09	382	#else
d1b5b400 MV	383	#error sizeof(short) is not 1, 2, or 4.
	384	#endif
	385	#endif
73e4de09 MV	386	#endif
73e4de09 MV	387
d1b5b400 MV	388	#if SCM_SIZEOF_INT == 4
	389	#define scm_to_int scm_to_int32
	390	#define scm_from_int scm_from_int32
	391	#define scm_to_uint scm_to_uint32
	392	#define scm_from_uint scm_from_uint32
	393	#else
	394	#if SCM_SIZEOF_INT == 8
	395	#define scm_to_int scm_to_int64
	396	#define scm_from_int scm_from_int64
	397	#define scm_to_uint scm_to_uint64
	398	#define scm_from_uint scm_from_uint64
	399	#else
	400	#error sizeof(int) is not 4 or 8.
	401	#endif
	402	#endif
73e4de09	403
d1b5b400 MV	404	#if SCM_SIZEOF_LONG == 4
	405	#define scm_to_long scm_to_int32
	406	#define scm_from_long scm_from_int32
	407	#define scm_to_ulong scm_to_uint32
	408	#define scm_from_ulong scm_from_uint32
	409	#else
	410	#if SCM_SIZEOF_LONG == 8
	411	#define scm_to_long scm_to_int64
	412	#define scm_from_long scm_from_int64
	413	#define scm_to_ulong scm_to_uint64
	414	#define scm_from_ulong scm_from_uint64
	415	#else
	416	#error sizeof(long) is not 4 or 8.
	417	#endif
	418	#endif
73e4de09	419
d1b5b400 MV	420	#if SCM_SIZEOF_INTMAX == 4
	421	#define scm_to_intmax scm_to_int32
	422	#define scm_from_intmax scm_from_int32
	423	#define scm_to_uintmax scm_to_uint32
	424	#define scm_from_uintmax scm_from_uint32
	425	#else
	426	#if SCM_SIZEOF_INTMAX == 8
	427	#define scm_to_intmax scm_to_int64
	428	#define scm_from_intmax scm_from_int64
	429	#define scm_to_uintmax scm_to_uint64
	430	#define scm_from_uintmax scm_from_uint64
	431	#else
55f26379	432	#error sizeof(scm_t_intmax) is not 4 or 8.
d1b5b400 MV	433	#endif
d1b5b400 MV	434	#endif
73e4de09	435
d1b5b400 MV	436	#if SCM_SIZEOF_LONG_LONG == 0
	437	#else
	438	#if SCM_SIZEOF_LONG_LONG == 8
	439	#define scm_to_long_long scm_to_int64
	440	#define scm_from_long_long scm_from_int64
	441	#define scm_to_ulong_long scm_to_uint64
	442	#define scm_from_ulong_long scm_from_uint64
	443	#else
	444	#error sizeof(long long) is not 8.
	445	#endif
	446	#endif
73e4de09	447
d1b5b400 MV	448	#if SCM_SIZEOF_SIZE_T == 4
	449	#define scm_to_ssize_t scm_to_int32
	450	#define scm_from_ssize_t scm_from_int32
	451	#define scm_to_size_t scm_to_uint32
	452	#define scm_from_size_t scm_from_uint32
	453	#else
	454	#if SCM_SIZEOF_SIZE_T == 8
	455	#define scm_to_ssize_t scm_to_int64
	456	#define scm_from_ssize_t scm_from_int64
	457	#define scm_to_size_t scm_to_uint64
	458	#define scm_from_size_t scm_from_uint64
	459	#else
	460	#error sizeof(size_t) is not 4 or 8.
	461	#endif
22008a78 MV	462	#endif
22008a78 MV	463
8507ec80	464	/* conversion functions for double */
22008a78	465
73e4de09	466	SCM_API int scm_is_real (SCM val);
55f26379	467	SCM_API int scm_is_rational (SCM val);
73e4de09 MV	468	SCM_API double scm_to_double (SCM val);
	469	SCM_API SCM scm_from_double (double val);
	470
8507ec80 MV	471	/* conversion functions for complex */
	472
	473	SCM_API int scm_is_complex (SCM val);
	474	SCM_API SCM scm_c_make_rectangular (double re, double im);
	475	SCM_API SCM scm_c_make_polar (double mag, double ang);
	476	SCM_API double scm_c_real_part (SCM z);
	477	SCM_API double scm_c_imag_part (SCM z);
	478	SCM_API double scm_c_magnitude (SCM z);
	479	SCM_API double scm_c_angle (SCM z);
	480
	481	SCM_API int scm_is_number (SCM val);
	482
33b001fd	483	SCM_API void scm_init_numbers (void);
0f2d19dd	484
3c9a524f	485	#endif /* SCM_NUMBERS_H */
89e00824 ML	486
	487	/*
	488	Local Variables:
	489	c-file-style: "gnu"
	490	End:
	491	*/