libguile/numbers.h

   1 /* classes: h_files */
   2
   3 #ifndef SCM_NUMBERS_H
   4 #define SCM_NUMBERS_H
   5
   6 /* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005, 2006 Free Software Foundation, Inc.
   7  *
   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.
  12  *
  13  * This library is distributed in the hope that it will be useful,
  14  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  16  * Lesser General Public License for more details.
  17  *
  18  * You should have received a copy of the GNU Lesser General Public
  19  * License along with this library; if not, write to the Free Software
  20  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  21  */
  22
  23 \f
  24
  25 #include <gmp.h>
  26
  27 #include "libguile/__scm.h"
  28 #include "libguile/print.h"
  29
  30 #if SCM_HAVE_FLOATINGPOINT_H
  31 # include <floatingpoint.h>
  32 #endif
  33
  34 #if SCM_HAVE_IEEEFP_H
  35 # include <ieeefp.h>
  36 #endif
  37
  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 */
  47
  48 \f
  49
  50 /* Immediate Numbers, also known as fixnums
  51  *
  52  * Inums are exact integer data that fits within an SCM word.  */
  53
  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
  59 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  60 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  61 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  62
  63 /* SCM_SRS is signed right shift */
  64 #if (-1 == (((-1) << 2) + 2) >> 2)
  65 # define SCM_SRS(x, y) ((x) >> (y))
  66 #else
  67 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  68 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  69
  70
  71 #define SCM_I_INUMP(x)  (2 & SCM_UNPACK (x))
  72 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
  73 #define SCM_I_MAKINUM(x) \
  74   (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
  75 #define SCM_I_INUM(x)   (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  76
  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)
  80 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
  81
  82
  83 /* A name for 0. */
  84 #define SCM_INUM0 (SCM_I_MAKINUM (0))
  85
  86 /* SCM_MAXEXP is the maximum double precision exponent
  87  * SCM_FLTMAX is less than or scm_equal the largest single precision float
  88  */
  89
  90 #if SCM_HAVE_STDC_HEADERS
  91 # ifndef GO32
  92 #  include <float.h>
  93 #  ifdef __MINGW32__
  94 #   define copysign _copysign
  95 #   define finite _finite
  96 #  endif /* __MINGW32__ */
  97 # endif /* ndef GO32 */
  98 #endif /* def STDC_HEADERS */
  99
 100 #ifdef DBL_MAX_10_EXP
 101 # define SCM_MAXEXP DBL_MAX_10_EXP
 102 #else
 103 # define SCM_MAXEXP 308         /* IEEE doubles */
 104 #endif /* def DBL_MAX_10_EXP */
 105
 106 #ifdef FLT_MAX
 107 # define SCM_FLTMAX FLT_MAX
 108 #else
 109 # define SCM_FLTMAX 1e+23
 110 #endif /* def FLT_MAX */
 111
 112
 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.
 117  */
 118 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
 119
 120 \f
 121
 122 /* Numbers
 123  */
 124
 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
 130 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 131  * and SCM_NUMP)  */
 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)
 135 #define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)
 136
 137 #define SCM_INEXACTP(x) \
 138   (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
 139 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 140 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 141
 142 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 143 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 144 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 145 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 146
 147 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
 148 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
 149 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
 150
 151 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
 152 #define SCM_NUMP(x) (!SCM_IMP(x) \
 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)
 158 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
 159 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
 160 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
 161 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
 162
 163   /* I think the left half word is free in the type, so I'll use bit 17 */
 164 #define SCM_FRACTION_REDUCED_BIT 0x10000
 165 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
 166 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
 167 #define SCM_FRACTION_REDUCED(x)     (0x10000 & SCM_CELL_TYPE (x))
 168
 169 \f
 170
 171 typedef struct scm_t_double
 172 {
 173   SCM type;
 174   SCM pad;
 175   double real;
 176 } scm_t_double;
 177
 178 typedef struct scm_t_complex
 179 {
 180   double real;
 181   double imag;
 182 } scm_t_complex;
 183
 184 \f
 185
 186 SCM_API SCM scm_exact_p (SCM x);
 187 SCM_API SCM scm_odd_p (SCM n);
 188 SCM_API SCM scm_even_p (SCM n);
 189 SCM_API SCM scm_inf_p (SCM n);
 190 SCM_API SCM scm_nan_p (SCM n);
 191 SCM_API SCM scm_inf (void);
 192 SCM_API SCM scm_nan (void);
 193 SCM_API SCM scm_abs (SCM x);
 194 SCM_API SCM scm_quotient (SCM x, SCM y);
 195 SCM_API SCM scm_remainder (SCM x, SCM y);
 196 SCM_API SCM scm_modulo (SCM x, SCM y);
 197 SCM_API SCM scm_gcd (SCM x, SCM y);
 198 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 199 SCM_API SCM scm_logand (SCM n1, SCM n2);
 200 SCM_API SCM scm_logior (SCM n1, SCM n2);
 201 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 202 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 203 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 204 SCM_API SCM scm_lognot (SCM n);
 205 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
 206 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 207 SCM_API SCM scm_ash (SCM n, SCM cnt);
 208 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 209 SCM_API SCM scm_logcount (SCM n);
 210 SCM_API SCM scm_integer_length (SCM n);
 211
 212 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
 213 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
 214 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 215 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 216 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 217 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 218 SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
 219                                             unsigned int radix);
 220 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 221 SCM_API SCM scm_bigequal (SCM x, SCM y);
 222 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 223 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 224 SCM_API SCM scm_number_p (SCM x);
 225 SCM_API SCM scm_complex_p (SCM x);
 226 SCM_API SCM scm_real_p (SCM x);
 227 SCM_API SCM scm_rational_p (SCM z);
 228 SCM_API SCM scm_integer_p (SCM x);
 229 SCM_API SCM scm_inexact_p (SCM x);
 230 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 231 SCM_API SCM scm_less_p (SCM x, SCM y);
 232 SCM_API SCM scm_gr_p (SCM x, SCM y);
 233 SCM_API SCM scm_leq_p (SCM x, SCM y);
 234 SCM_API SCM scm_geq_p (SCM x, SCM y);
 235 SCM_API SCM scm_zero_p (SCM z);
 236 SCM_API SCM scm_positive_p (SCM x);
 237 SCM_API SCM scm_negative_p (SCM x);
 238 SCM_API SCM scm_max (SCM x, SCM y);
 239 SCM_API SCM scm_min (SCM x, SCM y);
 240 SCM_API SCM scm_sum (SCM x, SCM y);
 241 SCM_API SCM scm_oneplus (SCM x);
 242 SCM_API SCM scm_difference (SCM x, SCM y);
 243 SCM_API SCM scm_oneminus (SCM x);
 244 SCM_API SCM scm_product (SCM x, SCM y);
 245 SCM_API SCM scm_divide (SCM x, SCM y);
 246 SCM_API SCM scm_floor (SCM x);
 247 SCM_API SCM scm_ceiling (SCM x);
 248 SCM_API double scm_asinh (double x);
 249 SCM_API double scm_acosh (double x);
 250 SCM_API double scm_atanh (double x);
 251 SCM_API double scm_c_truncate (double x);
 252 SCM_API double scm_c_round (double x);
 253 SCM_API SCM scm_truncate_number (SCM x);
 254 SCM_API SCM scm_round_number (SCM x);
 255 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 256 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 257 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 258 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 259 SCM_API SCM scm_real_part (SCM z);
 260 SCM_API SCM scm_imag_part (SCM z);
 261 SCM_API SCM scm_magnitude (SCM z);
 262 SCM_API SCM scm_angle (SCM z);
 263 SCM_API SCM scm_exact_to_inexact (SCM z);
 264 SCM_API SCM scm_inexact_to_exact (SCM z);
 265 SCM_API SCM scm_trunc (SCM x);
 266 SCM_API SCM scm_log (SCM z);
 267 SCM_API SCM scm_log10 (SCM z);
 268 SCM_API SCM scm_exp (SCM z);
 269 SCM_API SCM scm_sqrt (SCM z);
 270
 271 /* bignum internal functions */
 272 SCM_API SCM scm_i_mkbig (void);
 273 SCM_API SCM scm_i_normbig (SCM x);
 274 SCM_API int scm_i_bigcmp (SCM a, SCM b);
 275 SCM_API SCM scm_i_dbl2big (double d);
 276 SCM_API SCM scm_i_dbl2num (double d);
 277 SCM_API double scm_i_big2dbl (SCM b);
 278 SCM_API SCM scm_i_long2big (long n);
 279 SCM_API SCM scm_i_ulong2big (unsigned long n);
 280 SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);
 281
 282 /* ratio functions */
 283 SCM_API SCM scm_rationalize (SCM x, SCM err);
 284 SCM_API SCM scm_numerator (SCM z);
 285 SCM_API SCM scm_denominator (SCM z);
 286
 287 /* fraction internal functions */
 288 SCM_API double scm_i_fraction2double (SCM z);
 289 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
 290 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 291
 292 /* general internal functions */
 293 SCM_API void scm_i_print_double (double val, SCM port);
 294 SCM_API void scm_i_print_complex (double real, double imag, SCM port);
 295
 296 /* conversion functions for integers */
 297
 298 SCM_API int scm_is_integer (SCM val);
 299 SCM_API int scm_is_signed_integer (SCM val,
 300                                    scm_t_intmax min, scm_t_intmax max);
 301 SCM_API int scm_is_unsigned_integer (SCM val,
 302                                      scm_t_uintmax min, scm_t_uintmax max);
 303
 304 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
 305 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
 306
 307 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
 308                                             scm_t_intmax min,
 309                                             scm_t_intmax max);
 310 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
 311                                                scm_t_uintmax min,
 312                                                scm_t_uintmax max);
 313
 314 SCM_API scm_t_int8   scm_to_int8     (SCM x);
 315 SCM_API SCM          scm_from_int8   (scm_t_int8 x);
 316
 317 SCM_API scm_t_uint8  scm_to_uint8    (SCM x);
 318 SCM_API SCM          scm_from_uint8  (scm_t_uint8 x);
 319
 320 SCM_API scm_t_int16  scm_to_int16    (SCM x);
 321 SCM_API SCM          scm_from_int16  (scm_t_int16 x);
 322
 323 SCM_API scm_t_uint16 scm_to_uint16   (SCM x);
 324 SCM_API SCM          scm_from_uint16 (scm_t_uint16 x);
 325
 326 SCM_API scm_t_int32  scm_to_int32    (SCM x);
 327 SCM_API SCM          scm_from_int32  (scm_t_int32 x);
 328
 329 SCM_API scm_t_uint32 scm_to_uint32   (SCM x);
 330 SCM_API SCM          scm_from_uint32 (scm_t_uint32 x);
 331
 332 #if SCM_HAVE_T_INT64
 333
 334 SCM_API scm_t_int64  scm_to_int64    (SCM x);
 335 SCM_API SCM          scm_from_int64  (scm_t_int64 x);
 336
 337 SCM_API scm_t_uint64 scm_to_uint64   (SCM x);
 338 SCM_API SCM          scm_from_uint64 (scm_t_uint64 x);
 339
 340 #endif
 341
 342 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
 343 SCM_API SCM  scm_from_mpz (mpz_t rop);
 344
 345
 346 /* The conversion functions for other types are aliased to the
 347    appropriate ones from above.  We pick the right one based on the
 348    size of the type.
 349
 350    Not each and every possibility is covered by the code below, and
 351    while it is trivial to complete the tests, it might be better to
 352    just test for the 'sane' possibilities.  When one of the tests
 353    below fails, chances are good that some silent assumption somewhere
 354    else will also fail.
 355 */
 356
 357 #if SCM_SIZEOF_CHAR == 1
 358 #define scm_to_schar   scm_to_int8
 359 #define scm_from_schar scm_from_int8
 360 #define scm_to_uchar   scm_to_uint8
 361 #define scm_from_uchar scm_from_uint8
 362 #if CHAR_MIN == 0
 363 #define scm_to_char    scm_to_uint8
 364 #define scm_from_char  scm_from_uint8
 365 #else
 366 #define scm_to_char    scm_to_int8
 367 #define scm_from_char  scm_from_int8
 368 #endif
 369 #else
 370 #error sizeof(char) is not 1.
 371 #endif
 372
 373 #if SCM_SIZEOF_SHORT == 1
 374 #define scm_to_short    scm_to_int8
 375 #define scm_from_short  scm_from_int8
 376 #define scm_to_ushort   scm_to_uint8
 377 #define scm_from_ushort scm_from_uint8
 378 #else
 379 #if SCM_SIZEOF_SHORT == 2
 380 #define scm_to_short    scm_to_int16
 381 #define scm_from_short  scm_from_int16
 382 #define scm_to_ushort   scm_to_uint16
 383 #define scm_from_ushort scm_from_uint16
 384 #else
 385 #if SCM_SIZEOF_SHORT == 4
 386 #define scm_to_short    scm_to_int32
 387 #define scm_from_short  scm_from_int32
 388 #define scm_to_ushort   scm_to_uint32
 389 #define scm_from_ushort scm_from_uint32
 390 #else
 391 #error sizeof(short) is not 1, 2, or 4.
 392 #endif
 393 #endif
 394 #endif
 395
 396 #if SCM_SIZEOF_INT == 4
 397 #define scm_to_int    scm_to_int32
 398 #define scm_from_int  scm_from_int32
 399 #define scm_to_uint   scm_to_uint32
 400 #define scm_from_uint scm_from_uint32
 401 #else
 402 #if SCM_SIZEOF_INT == 8
 403 #define scm_to_int    scm_to_int64
 404 #define scm_from_int  scm_from_int64
 405 #define scm_to_uint   scm_to_uint64
 406 #define scm_from_uint scm_from_uint64
 407 #else
 408 #error sizeof(int) is not 4 or 8.
 409 #endif
 410 #endif
 411
 412 #if SCM_SIZEOF_LONG == 4
 413 #define scm_to_long    scm_to_int32
 414 #define scm_from_long  scm_from_int32
 415 #define scm_to_ulong   scm_to_uint32
 416 #define scm_from_ulong scm_from_uint32
 417 #else
 418 #if SCM_SIZEOF_LONG == 8
 419 #define scm_to_long    scm_to_int64
 420 #define scm_from_long  scm_from_int64
 421 #define scm_to_ulong   scm_to_uint64
 422 #define scm_from_ulong scm_from_uint64
 423 #else
 424 #error sizeof(long) is not 4 or 8.
 425 #endif
 426 #endif
 427
 428 #if SCM_SIZEOF_INTMAX == 4
 429 #define scm_to_intmax    scm_to_int32
 430 #define scm_from_intmax  scm_from_int32
 431 #define scm_to_uintmax   scm_to_uint32
 432 #define scm_from_uintmax scm_from_uint32
 433 #else
 434 #if SCM_SIZEOF_INTMAX == 8
 435 #define scm_to_intmax    scm_to_int64
 436 #define scm_from_intmax  scm_from_int64
 437 #define scm_to_uintmax   scm_to_uint64
 438 #define scm_from_uintmax scm_from_uint64
 439 #else
 440 #error sizeof(scm_t_intmax) is not 4 or 8.
 441 #endif
 442 #endif
 443
 444 #if SCM_SIZEOF_LONG_LONG == 0
 445 #else
 446 #if SCM_SIZEOF_LONG_LONG == 8
 447 #define scm_to_long_long    scm_to_int64
 448 #define scm_from_long_long  scm_from_int64
 449 #define scm_to_ulong_long   scm_to_uint64
 450 #define scm_from_ulong_long scm_from_uint64
 451 #else
 452 #error sizeof(long long) is not 8.
 453 #endif
 454 #endif
 455
 456 #if SCM_SIZEOF_SIZE_T == 4
 457 #define scm_to_ssize_t    scm_to_int32
 458 #define scm_from_ssize_t  scm_from_int32
 459 #define scm_to_size_t     scm_to_uint32
 460 #define scm_from_size_t   scm_from_uint32
 461 #else
 462 #if SCM_SIZEOF_SIZE_T == 8
 463 #define scm_to_ssize_t    scm_to_int64
 464 #define scm_from_ssize_t  scm_from_int64
 465 #define scm_to_size_t     scm_to_uint64
 466 #define scm_from_size_t   scm_from_uint64
 467 #else
 468 #error sizeof(size_t) is not 4 or 8.
 469 #endif
 470 #endif
 471
 472 /* conversion functions for double */
 473
 474 SCM_API int scm_is_real (SCM val);
 475 SCM_API int scm_is_rational (SCM val);
 476 SCM_API double scm_to_double (SCM val);
 477 SCM_API SCM scm_from_double (double val);
 478
 479 /* conversion functions for complex */
 480
 481 SCM_API int scm_is_complex (SCM val);
 482 SCM_API SCM scm_c_make_rectangular (double re, double im);
 483 SCM_API SCM scm_c_make_polar (double mag, double ang);
 484 SCM_API double scm_c_real_part (SCM z);
 485 SCM_API double scm_c_imag_part (SCM z);
 486 SCM_API double scm_c_magnitude (SCM z);
 487 SCM_API double scm_c_angle (SCM z);
 488
 489 SCM_API int scm_is_number (SCM val);
 490
 491 SCM_API void scm_init_numbers (void);
 492
 493 #endif  /* SCM_NUMBERS_H */
 494
 495 /*
 496   Local Variables:
 497   c-file-style: "gnu"
 498   End:
 499 */