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 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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 isnan _isnan
  96 #   define finite _finite
  97 #  endif /* __MINGW32__ */
  98 # endif /* ndef GO32 */
  99 #endif /* def STDC_HEADERS */
 100
 101 #ifdef DBL_MAX_10_EXP
 102 # define SCM_MAXEXP DBL_MAX_10_EXP
 103 #else
 104 # define SCM_MAXEXP 308         /* IEEE doubles */
 105 #endif /* def DBL_MAX_10_EXP */
 106
 107 #ifdef FLT_MAX
 108 # define SCM_FLTMAX FLT_MAX
 109 #else
 110 # define SCM_FLTMAX 1e+23
 111 #endif /* def FLT_MAX */
 112
 113
 114 /* SCM_INTBUFLEN is the maximum number of characters neccessary for
 115  * the printed or scm_string representation of an scm_t_intmax in
 116  * radix 2.  The buffer passed to scm_iint2str and scm_iuint2str must
 117  * be of this size, for example.
 118  */
 119 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
 120
 121 \f
 122
 123 /* Numbers
 124  */
 125
 126
 127 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
 128  * differ in one bit: This way, checking if an object is an inexact number can
 129  * be done quickly (using the TYP16S macro).  */
 130
 131 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 132  * and SCM_NUMP)  */
 133 #define scm_tc16_big            (scm_tc7_number + 1 * 256L)
 134 #define scm_tc16_real           (scm_tc7_number + 2 * 256L)
 135 #define scm_tc16_complex        (scm_tc7_number + 3 * 256L)
 136 #define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)
 137
 138 #define SCM_INEXACTP(x) \
 139   (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
 140 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 141 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 142
 143 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 144 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 145 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 146 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 147
 148 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
 149 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
 150 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
 151
 152 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
 153 #define SCM_NUMP(x) (!SCM_IMP(x) \
 154   && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
 155       || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
 156 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
 157
 158 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
 159 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
 160 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
 161 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
 162 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
 163
 164   /* I think the left half word is free in the type, so I'll use bit 17 */
 165 #define SCM_FRACTION_REDUCED_BIT 0x10000
 166 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
 167 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
 168 #define SCM_FRACTION_REDUCED(x)     (0x10000 & SCM_CELL_TYPE (x))
 169
 170 \f
 171
 172 typedef struct scm_t_double
 173 {
 174   SCM type;
 175   SCM pad;
 176   double real;
 177 } scm_t_double;
 178
 179 typedef struct scm_t_complex
 180 {
 181   double real;
 182   double imag;
 183 } scm_t_complex;
 184
 185 \f
 186
 187 SCM_API SCM scm_exact_p (SCM x);
 188 SCM_API SCM scm_odd_p (SCM n);
 189 SCM_API SCM scm_even_p (SCM n);
 190 SCM_API SCM scm_inf_p (SCM n);
 191 SCM_API SCM scm_nan_p (SCM n);
 192 SCM_API SCM scm_inf (void);
 193 SCM_API SCM scm_nan (void);
 194 SCM_API SCM scm_abs (SCM x);
 195 SCM_API SCM scm_quotient (SCM x, SCM y);
 196 SCM_API SCM scm_remainder (SCM x, SCM y);
 197 SCM_API SCM scm_modulo (SCM x, SCM y);
 198 SCM_API SCM scm_gcd (SCM x, SCM y);
 199 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 200 SCM_API SCM scm_logand (SCM n1, SCM n2);
 201 SCM_API SCM scm_logior (SCM n1, SCM n2);
 202 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 203 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 204 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 205 SCM_API SCM scm_lognot (SCM n);
 206 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
 207 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 208 SCM_API SCM scm_ash (SCM n, SCM cnt);
 209 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 210 SCM_API SCM scm_logcount (SCM n);
 211 SCM_API SCM scm_integer_length (SCM n);
 212
 213 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
 214 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
 215 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 216 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 217 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 218 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 219 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, 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_difference (SCM x, SCM y);
 242 SCM_API SCM scm_product (SCM x, SCM y);
 243 SCM_API SCM scm_divide (SCM x, SCM y);
 244 SCM_API SCM scm_floor (SCM x);
 245 SCM_API SCM scm_ceiling (SCM x);
 246 SCM_API double scm_asinh (double x);
 247 SCM_API double scm_acosh (double x);
 248 SCM_API double scm_atanh (double x);
 249 SCM_API double scm_c_truncate (double x);
 250 SCM_API double scm_c_round (double x);
 251 SCM_API SCM scm_truncate_number (SCM x);
 252 SCM_API SCM scm_round_number (SCM x);
 253 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 254 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 255 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 256 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 257 SCM_API SCM scm_real_part (SCM z);
 258 SCM_API SCM scm_imag_part (SCM z);
 259 SCM_API SCM scm_magnitude (SCM z);
 260 SCM_API SCM scm_angle (SCM z);
 261 SCM_API SCM scm_exact_to_inexact (SCM z);
 262 SCM_API SCM scm_inexact_to_exact (SCM z);
 263 SCM_API SCM scm_trunc (SCM x);
 264
 265 /* bignum internal functions */
 266 SCM_API SCM scm_i_mkbig (void);
 267 SCM_API SCM scm_i_normbig (SCM x);
 268 SCM_API int scm_i_bigcmp (SCM a, SCM b);
 269 SCM_API SCM scm_i_dbl2big (double d);
 270 SCM_API SCM scm_i_dbl2num (double d);
 271 SCM_API double scm_i_big2dbl (SCM b);
 272 SCM_API SCM scm_i_long2big (long n);
 273 SCM_API SCM scm_i_ulong2big (unsigned long n);
 274
 275 /* ratio functions */
 276 SCM_API SCM scm_rationalize (SCM x, SCM err);
 277 SCM_API SCM scm_numerator (SCM z);
 278 SCM_API SCM scm_denominator (SCM z);
 279
 280 /* fraction internal functions */
 281 SCM_API double scm_i_fraction2double (SCM z);
 282 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
 283 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 284
 285 /* general internal functions */
 286 SCM_API void scm_i_print_double (double val, SCM port);
 287
 288 /* conversion functions for integers */
 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
 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
 334 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
 335 SCM_API SCM  scm_from_mpz (mpz_t rop);
 336
 337
 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
 354 #if CHAR_MIN == 0
 355 #define scm_to_char    scm_to_uint8
 356 #define scm_from_char  scm_from_uint8
 357 #else
 358 #define scm_to_char    scm_to_int8
 359 #define scm_from_char  scm_from_int8
 360 #endif
 361 #else
 362 #error sizeof(char) is not 1.
 363 #endif
 364
 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
 382 #else
 383 #error sizeof(short) is not 1, 2, or 4.
 384 #endif
 385 #endif
 386 #endif
 387
 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
 403
 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
 419
 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
 432 #error sizeof(scm_t_intmax) is not 4 or 8.
 433 #endif
 434 #endif
 435
 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
 447
 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
 462 #endif
 463
 464 /* conversion functions for double */
 465
 466 SCM_API int scm_is_real (SCM val);
 467 SCM_API int scm_is_rational (SCM val);
 468 SCM_API double scm_to_double (SCM val);
 469 SCM_API SCM scm_from_double (double val);
 470
 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
 483 SCM_API void scm_init_numbers (void);
 484
 485 #endif  /* SCM_NUMBERS_H */
 486
 487 /*
 488   Local Variables:
 489   c-file-style: "gnu"
 490   End:
 491 */