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, 2008, 2009 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 License
  10  * as published by the Free Software Foundation; either version 3 of
  11  * the License, or (at your option) any later version.
  12  *
  13  * This library is distributed in the hope that it will be useful, but
  14  * 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
  21  * 02110-1301 USA
  22  */
  23
  24 \f
  25
  26 #include <gmp.h>
  27
  28 #include "libguile/__scm.h"
  29 #include "libguile/print.h"
  30
  31 #ifndef SCM_T_WCHAR_DEFINED
  32 typedef scm_t_int32 scm_t_wchar;
  33 #define SCM_T_WCHAR_DEFINED
  34 #endif /* SCM_T_WCHAR_DEFINED */
  35
  36 #if SCM_HAVE_FLOATINGPOINT_H
  37 # include <floatingpoint.h>
  38 #endif
  39
  40 #if SCM_HAVE_IEEEFP_H
  41 # include <ieeefp.h>
  42 #endif
  43
  44 #if SCM_HAVE_NAN_H
  45 # if defined (SCO)
  46 #   define _IEEE 1
  47 # endif
  48 # include <nan.h>
  49 # if defined (SCO)
  50 #   undef _IEEE
  51 # endif
  52 #endif /* SCM_HAVE_NAN_H */
  53
  54 \f
  55
  56 /* Immediate Numbers, also known as fixnums
  57  *
  58  * Inums are exact integer data that fits within an SCM word.  */
  59
  60 /* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
  61  * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
  62  * which is the same as                (/ (- (expt 2 n) 4) 4)
  63  */
  64
  65 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  66 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  67 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  68
  69 /* SCM_SRS is signed right shift */
  70 #if (-1 == (((-1) << 2) + 2) >> 2)
  71 # define SCM_SRS(x, y) ((x) >> (y))
  72 #else
  73 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  74 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  75
  76
  77 #define SCM_I_INUMP(x)  (2 & SCM_UNPACK (x))
  78 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
  79 #define SCM_I_MAKINUM(x) \
  80   (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
  81 #define SCM_I_INUM(x)   (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  82
  83 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
  84 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
  85 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
  86 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
  87
  88
  89 /* A name for 0. */
  90 #define SCM_INUM0 (SCM_I_MAKINUM (0))
  91
  92 /* SCM_MAXEXP is the maximum double precision exponent
  93  * SCM_FLTMAX is less than or scm_equal the largest single precision float
  94  */
  95
  96 #if SCM_HAVE_STDC_HEADERS
  97 # ifndef GO32
  98 #  include <float.h>
  99 #  ifdef __MINGW32__
 100 #   define copysign _copysign
 101 #   define finite _finite
 102 #  endif /* __MINGW32__ */
 103 # endif /* ndef GO32 */
 104 #endif /* def STDC_HEADERS */
 105
 106 #ifdef DBL_MAX_10_EXP
 107 # define SCM_MAXEXP DBL_MAX_10_EXP
 108 #else
 109 # define SCM_MAXEXP 308         /* IEEE doubles */
 110 #endif /* def DBL_MAX_10_EXP */
 111
 112 #ifdef FLT_MAX
 113 # define SCM_FLTMAX FLT_MAX
 114 #else
 115 # define SCM_FLTMAX 1e+23
 116 #endif /* def FLT_MAX */
 117
 118
 119 /* SCM_INTBUFLEN is the maximum number of characters neccessary for
 120  * the printed or scm_string representation of an scm_t_intmax in
 121  * radix 2.  The buffer passed to scm_iint2str and scm_iuint2str must
 122  * be of this size, for example.
 123  */
 124 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
 125
 126 \f
 127
 128 /* Numbers
 129  */
 130
 131
 132 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
 133  * differ in one bit: This way, checking if an object is an inexact number can
 134  * be done quickly (using the TYP16S macro).  */
 135
 136 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 137  * and SCM_NUMP)  */
 138 #define scm_tc16_big            (scm_tc7_number + 1 * 256L)
 139 #define scm_tc16_real           (scm_tc7_number + 2 * 256L)
 140 #define scm_tc16_complex        (scm_tc7_number + 3 * 256L)
 141 #define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)
 142
 143 #define SCM_INEXACTP(x) \
 144   (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
 145 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 146 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 147
 148 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 149 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 150 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 151 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 152
 153 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
 154 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
 155 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
 156
 157 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
 158 #define SCM_NUMP(x) (!SCM_IMP(x) \
 159   && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
 160       || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
 161 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
 162
 163 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
 164 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
 165 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
 166
 167 \f
 168
 169 typedef struct scm_t_double
 170 {
 171   SCM type;
 172   SCM pad;
 173   double real;
 174 } scm_t_double;
 175
 176 typedef struct scm_t_complex
 177 {
 178   double real;
 179   double imag;
 180 } scm_t_complex;
 181
 182
 183 \f
 184
 185 SCM_API SCM scm_exact_p (SCM x);
 186 SCM_API SCM scm_odd_p (SCM n);
 187 SCM_API SCM scm_even_p (SCM n);
 188 SCM_API SCM scm_inf_p (SCM n);
 189 SCM_API SCM scm_nan_p (SCM n);
 190 SCM_API SCM scm_inf (void);
 191 SCM_API SCM scm_nan (void);
 192 SCM_API SCM scm_abs (SCM x);
 193 SCM_API SCM scm_quotient (SCM x, SCM y);
 194 SCM_API SCM scm_remainder (SCM x, SCM y);
 195 SCM_API SCM scm_modulo (SCM x, SCM y);
 196 SCM_API SCM scm_gcd (SCM x, SCM y);
 197 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 198 SCM_API SCM scm_logand (SCM n1, SCM n2);
 199 SCM_API SCM scm_logior (SCM n1, SCM n2);
 200 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 201 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 202 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 203 SCM_API SCM scm_lognot (SCM n);
 204 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
 205 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 206 SCM_API SCM scm_ash (SCM n, SCM cnt);
 207 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 208 SCM_API SCM scm_logcount (SCM n);
 209 SCM_API SCM scm_integer_length (SCM n);
 210
 211 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
 212 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
 213 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 214 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 215 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 216 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 217 SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
 218                                             unsigned int radix);
 219 SCM_INTERNAL SCM scm_i_string_to_number (SCM str, 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_c_truncate (double x);
 249 SCM_API double scm_c_round (double x);
 250 SCM_API SCM scm_truncate_number (SCM x);
 251 SCM_API SCM scm_round_number (SCM x);
 252 SCM_API SCM scm_expt (SCM z1, SCM z2);
 253 SCM_API SCM scm_sin (SCM z);
 254 SCM_API SCM scm_cos (SCM z);
 255 SCM_API SCM scm_tan (SCM z);
 256 SCM_API SCM scm_sinh (SCM z);
 257 SCM_API SCM scm_cosh (SCM z);
 258 SCM_API SCM scm_tanh (SCM z);
 259 SCM_API SCM scm_asin (SCM z);
 260 SCM_API SCM scm_acos (SCM z);
 261 SCM_API SCM scm_atan (SCM x, SCM y);
 262 SCM_API SCM scm_sys_asinh (SCM z);
 263 SCM_API SCM scm_sys_acosh (SCM z);
 264 SCM_API SCM scm_sys_atanh (SCM z);
 265 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 266 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 267 SCM_API SCM scm_real_part (SCM z);
 268 SCM_API SCM scm_imag_part (SCM z);
 269 SCM_API SCM scm_magnitude (SCM z);
 270 SCM_API SCM scm_angle (SCM z);
 271 SCM_API SCM scm_exact_to_inexact (SCM z);
 272 SCM_API SCM scm_inexact_to_exact (SCM z);
 273 SCM_API SCM scm_trunc (SCM x);
 274 SCM_API SCM scm_log (SCM z);
 275 SCM_API SCM scm_log10 (SCM z);
 276 SCM_API SCM scm_exp (SCM z);
 277 SCM_API SCM scm_sqrt (SCM z);
 278
 279 /* bignum internal functions */
 280 SCM_INTERNAL SCM scm_i_mkbig (void);
 281 SCM_API /* FIXME: not internal */ SCM scm_i_normbig (SCM x);
 282 SCM_INTERNAL int scm_i_bigcmp (SCM a, SCM b);
 283 SCM_INTERNAL SCM scm_i_dbl2big (double d);
 284 SCM_INTERNAL SCM scm_i_dbl2num (double d);
 285 SCM_API /* FIXME: not internal */ double scm_i_big2dbl (SCM b);
 286 SCM_API /* FIXME: not internal */ SCM scm_i_long2big (long n);
 287 SCM_API /* FIXME: not internal */ SCM scm_i_ulong2big (unsigned long n);
 288 SCM_API /* FIXME: not internal */ SCM scm_i_clonebig (SCM src_big, int same_sign_p);
 289
 290 /* ratio functions */
 291 SCM_API SCM scm_rationalize (SCM x, SCM err);
 292 SCM_API SCM scm_numerator (SCM z);
 293 SCM_API SCM scm_denominator (SCM z);
 294
 295 /* fraction internal functions */
 296 SCM_INTERNAL double scm_i_fraction2double (SCM z);
 297 SCM_INTERNAL SCM scm_i_fraction_equalp (SCM x, SCM y);
 298 SCM_INTERNAL int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 299
 300 /* general internal functions */
 301 SCM_INTERNAL void scm_i_print_double (double val, SCM port);
 302 SCM_INTERNAL void scm_i_print_complex (double real, double imag, SCM port);
 303
 304 /* conversion functions for integers */
 305
 306 SCM_API int scm_is_integer (SCM val);
 307 SCM_API int scm_is_signed_integer (SCM val,
 308                                    scm_t_intmax min, scm_t_intmax max);
 309 SCM_API int scm_is_unsigned_integer (SCM val,
 310                                      scm_t_uintmax min, scm_t_uintmax max);
 311
 312 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
 313 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
 314
 315 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
 316                                             scm_t_intmax min,
 317                                             scm_t_intmax max);
 318 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
 319                                                scm_t_uintmax min,
 320                                                scm_t_uintmax max);
 321
 322 SCM_API scm_t_int8   scm_to_int8     (SCM x);
 323 SCM_API SCM          scm_from_int8   (scm_t_int8 x);
 324
 325 SCM_API scm_t_uint8  scm_to_uint8    (SCM x);
 326 SCM_API SCM          scm_from_uint8  (scm_t_uint8 x);
 327
 328 SCM_API scm_t_int16  scm_to_int16    (SCM x);
 329 SCM_API SCM          scm_from_int16  (scm_t_int16 x);
 330
 331 SCM_API scm_t_uint16 scm_to_uint16   (SCM x);
 332 SCM_API SCM          scm_from_uint16 (scm_t_uint16 x);
 333
 334 SCM_API scm_t_int32  scm_to_int32    (SCM x);
 335 SCM_API SCM          scm_from_int32  (scm_t_int32 x);
 336
 337 SCM_API scm_t_uint32 scm_to_uint32   (SCM x);
 338 SCM_API SCM          scm_from_uint32 (scm_t_uint32 x);
 339
 340 SCM_API scm_t_wchar  scm_to_wchar    (SCM x);
 341 SCM_API SCM          scm_from_wchar  (scm_t_wchar x);
 342
 343 #if SCM_HAVE_T_INT64
 344
 345 SCM_API scm_t_int64  scm_to_int64    (SCM x);
 346 SCM_API SCM          scm_from_int64  (scm_t_int64 x);
 347
 348 SCM_API scm_t_uint64 scm_to_uint64   (SCM x);
 349 SCM_API SCM          scm_from_uint64 (scm_t_uint64 x);
 350
 351 #endif
 352
 353 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
 354 SCM_API SCM  scm_from_mpz (mpz_t rop);
 355
 356
 357 /* The conversion functions for other types are aliased to the
 358    appropriate ones from above.  We pick the right one based on the
 359    size of the type.
 360
 361    Not each and every possibility is covered by the code below, and
 362    while it is trivial to complete the tests, it might be better to
 363    just test for the 'sane' possibilities.  When one of the tests
 364    below fails, chances are good that some silent assumption somewhere
 365    else will also fail.
 366 */
 367
 368 #if SCM_SIZEOF_CHAR == 1
 369 #define scm_to_schar   scm_to_int8
 370 #define scm_from_schar scm_from_int8
 371 #define scm_to_uchar   scm_to_uint8
 372 #define scm_from_uchar scm_from_uint8
 373 #if CHAR_MIN == 0
 374 #define scm_to_char    scm_to_uint8
 375 #define scm_from_char  scm_from_uint8
 376 #else
 377 #define scm_to_char    scm_to_int8
 378 #define scm_from_char  scm_from_int8
 379 #endif
 380 #else
 381 #error sizeof(char) is not 1.
 382 #endif
 383
 384 #if SCM_SIZEOF_SHORT == 1
 385 #define scm_to_short    scm_to_int8
 386 #define scm_from_short  scm_from_int8
 387 #define scm_to_ushort   scm_to_uint8
 388 #define scm_from_ushort scm_from_uint8
 389 #else
 390 #if SCM_SIZEOF_SHORT == 2
 391 #define scm_to_short    scm_to_int16
 392 #define scm_from_short  scm_from_int16
 393 #define scm_to_ushort   scm_to_uint16
 394 #define scm_from_ushort scm_from_uint16
 395 #else
 396 #if SCM_SIZEOF_SHORT == 4
 397 #define scm_to_short    scm_to_int32
 398 #define scm_from_short  scm_from_int32
 399 #define scm_to_ushort   scm_to_uint32
 400 #define scm_from_ushort scm_from_uint32
 401 #else
 402 #error sizeof(short) is not 1, 2, or 4.
 403 #endif
 404 #endif
 405 #endif
 406
 407 #if SCM_SIZEOF_INT == 4
 408 #define scm_to_int    scm_to_int32
 409 #define scm_from_int  scm_from_int32
 410 #define scm_to_uint   scm_to_uint32
 411 #define scm_from_uint scm_from_uint32
 412 #else
 413 #if SCM_SIZEOF_INT == 8
 414 #define scm_to_int    scm_to_int64
 415 #define scm_from_int  scm_from_int64
 416 #define scm_to_uint   scm_to_uint64
 417 #define scm_from_uint scm_from_uint64
 418 #else
 419 #error sizeof(int) is not 4 or 8.
 420 #endif
 421 #endif
 422
 423 #if SCM_SIZEOF_LONG == 4
 424 #define scm_to_long    scm_to_int32
 425 #define scm_from_long  scm_from_int32
 426 #define scm_to_ulong   scm_to_uint32
 427 #define scm_from_ulong scm_from_uint32
 428 #else
 429 #if SCM_SIZEOF_LONG == 8
 430 #define scm_to_long    scm_to_int64
 431 #define scm_from_long  scm_from_int64
 432 #define scm_to_ulong   scm_to_uint64
 433 #define scm_from_ulong scm_from_uint64
 434 #else
 435 #error sizeof(long) is not 4 or 8.
 436 #endif
 437 #endif
 438
 439 #if SCM_SIZEOF_INTMAX == 4
 440 #define scm_to_intmax    scm_to_int32
 441 #define scm_from_intmax  scm_from_int32
 442 #define scm_to_uintmax   scm_to_uint32
 443 #define scm_from_uintmax scm_from_uint32
 444 #else
 445 #if SCM_SIZEOF_INTMAX == 8
 446 #define scm_to_intmax    scm_to_int64
 447 #define scm_from_intmax  scm_from_int64
 448 #define scm_to_uintmax   scm_to_uint64
 449 #define scm_from_uintmax scm_from_uint64
 450 #else
 451 #error sizeof(scm_t_intmax) is not 4 or 8.
 452 #endif
 453 #endif
 454
 455 #if SCM_SIZEOF_LONG_LONG == 0
 456 #else
 457 #if SCM_SIZEOF_LONG_LONG == 8
 458 #define scm_to_long_long    scm_to_int64
 459 #define scm_from_long_long  scm_from_int64
 460 #define scm_to_ulong_long   scm_to_uint64
 461 #define scm_from_ulong_long scm_from_uint64
 462 #else
 463 #error sizeof(long long) is not 8.
 464 #endif
 465 #endif
 466
 467 #if SCM_SIZEOF_SIZE_T == 4
 468 #define scm_to_ssize_t    scm_to_int32
 469 #define scm_from_ssize_t  scm_from_int32
 470 #define scm_to_size_t     scm_to_uint32
 471 #define scm_from_size_t   scm_from_uint32
 472 #else
 473 #if SCM_SIZEOF_SIZE_T == 8
 474 #define scm_to_ssize_t    scm_to_int64
 475 #define scm_from_ssize_t  scm_from_int64
 476 #define scm_to_size_t     scm_to_uint64
 477 #define scm_from_size_t   scm_from_uint64
 478 #else
 479 #error sizeof(size_t) is not 4 or 8.
 480 #endif
 481 #endif
 482
 483 /* conversion functions for double */
 484
 485 SCM_API int scm_is_real (SCM val);
 486 SCM_API int scm_is_rational (SCM val);
 487 SCM_API double scm_to_double (SCM val);
 488 SCM_API SCM scm_from_double (double val);
 489
 490 /* conversion functions for complex */
 491
 492 SCM_API int scm_is_complex (SCM val);
 493 SCM_API SCM scm_c_make_rectangular (double re, double im);
 494 SCM_API SCM scm_c_make_polar (double mag, double ang);
 495 SCM_API double scm_c_real_part (SCM z);
 496 SCM_API double scm_c_imag_part (SCM z);
 497 SCM_API double scm_c_magnitude (SCM z);
 498 SCM_API double scm_c_angle (SCM z);
 499
 500 SCM_API int scm_is_number (SCM val);
 501
 502 SCM_INTERNAL void scm_init_numbers (void);
 503
 504 #endif  /* SCM_NUMBERS_H */
 505
 506 /*
 507   Local Variables:
 508   c-file-style: "gnu"
 509   End:
 510 */