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 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 #if SCM_HAVE_FLOATINGPOINT_H
  32 # include <floatingpoint.h>
  33 #endif
  34
  35 #if SCM_HAVE_IEEEFP_H
  36 # include <ieeefp.h>
  37 #endif
  38
  39 #if SCM_HAVE_NAN_H
  40 # if defined (SCO)
  41 #   define _IEEE 1
  42 # endif
  43 # include <nan.h>
  44 # if defined (SCO)
  45 #   undef _IEEE
  46 # endif
  47 #endif /* SCM_HAVE_NAN_H */
  48
  49 \f
  50
  51 /* Immediate Numbers, also known as fixnums
  52  *
  53  * Inums are exact integer data that fits within an SCM word.  */
  54
  55 /* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
  56  * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
  57  * which is the same as                (/ (- (expt 2 n) 4) 4)
  58  */
  59
  60 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  61 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  62 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  63
  64 /* SCM_SRS is signed right shift */
  65 #if (-1 == (((-1) << 2) + 2) >> 2)
  66 # define SCM_SRS(x, y) ((x) >> (y))
  67 #else
  68 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  69 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  70
  71
  72 #define SCM_I_INUMP(x)  (2 & SCM_UNPACK (x))
  73 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
  74 #define SCM_I_MAKINUM(x) \
  75   (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
  76 #define SCM_I_INUM(x)   (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  77
  78 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
  79 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
  80 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
  81 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
  82
  83
  84 /* A name for 0. */
  85 #define SCM_INUM0 (SCM_I_MAKINUM (0))
  86
  87 /* SCM_MAXEXP is the maximum double precision exponent
  88  * SCM_FLTMAX is less than or scm_equal the largest single precision float
  89  */
  90
  91 #if SCM_HAVE_STDC_HEADERS
  92 # ifndef GO32
  93 #  include <float.h>
  94 #  ifdef __MINGW32__
  95 #   define copysign _copysign
  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
 162 \f
 163
 164 typedef struct scm_t_double
 165 {
 166   SCM type;
 167   SCM pad;
 168   double real;
 169 } scm_t_double;
 170
 171 typedef struct scm_t_complex
 172 {
 173   double real;
 174   double imag;
 175 } scm_t_complex;
 176
 177 \f
 178
 179 SCM_API SCM scm_exact_p (SCM x);
 180 SCM_API SCM scm_odd_p (SCM n);
 181 SCM_API SCM scm_even_p (SCM n);
 182 SCM_API SCM scm_inf_p (SCM n);
 183 SCM_API SCM scm_nan_p (SCM n);
 184 SCM_API SCM scm_inf (void);
 185 SCM_API SCM scm_nan (void);
 186 SCM_API SCM scm_abs (SCM x);
 187 SCM_API SCM scm_quotient (SCM x, SCM y);
 188 SCM_API SCM scm_remainder (SCM x, SCM y);
 189 SCM_API SCM scm_modulo (SCM x, SCM y);
 190 SCM_API SCM scm_gcd (SCM x, SCM y);
 191 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 192 SCM_API SCM scm_logand (SCM n1, SCM n2);
 193 SCM_API SCM scm_logior (SCM n1, SCM n2);
 194 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 195 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 196 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 197 SCM_API SCM scm_lognot (SCM n);
 198 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
 199 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 200 SCM_API SCM scm_ash (SCM n, SCM cnt);
 201 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 202 SCM_API SCM scm_logcount (SCM n);
 203 SCM_API SCM scm_integer_length (SCM n);
 204
 205 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
 206 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
 207 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 208 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 209 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 210 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 211 SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
 212                                             unsigned int radix);
 213 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 214 SCM_API SCM scm_bigequal (SCM x, SCM y);
 215 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 216 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 217 SCM_API SCM scm_number_p (SCM x);
 218 SCM_API SCM scm_complex_p (SCM x);
 219 SCM_API SCM scm_real_p (SCM x);
 220 SCM_API SCM scm_rational_p (SCM z);
 221 SCM_API SCM scm_integer_p (SCM x);
 222 SCM_API SCM scm_inexact_p (SCM x);
 223 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 224 SCM_API SCM scm_less_p (SCM x, SCM y);
 225 SCM_API SCM scm_gr_p (SCM x, SCM y);
 226 SCM_API SCM scm_leq_p (SCM x, SCM y);
 227 SCM_API SCM scm_geq_p (SCM x, SCM y);
 228 SCM_API SCM scm_zero_p (SCM z);
 229 SCM_API SCM scm_positive_p (SCM x);
 230 SCM_API SCM scm_negative_p (SCM x);
 231 SCM_API SCM scm_max (SCM x, SCM y);
 232 SCM_API SCM scm_min (SCM x, SCM y);
 233 SCM_API SCM scm_sum (SCM x, SCM y);
 234 SCM_API SCM scm_oneplus (SCM x);
 235 SCM_API SCM scm_difference (SCM x, SCM y);
 236 SCM_API SCM scm_oneminus (SCM x);
 237 SCM_API SCM scm_product (SCM x, SCM y);
 238 SCM_API SCM scm_divide (SCM x, SCM y);
 239 SCM_API SCM scm_floor (SCM x);
 240 SCM_API SCM scm_ceiling (SCM x);
 241 SCM_API double scm_asinh (double x);
 242 SCM_API double scm_acosh (double x);
 243 SCM_API double scm_atanh (double x);
 244 SCM_API double scm_c_truncate (double x);
 245 SCM_API double scm_c_round (double x);
 246 SCM_API SCM scm_truncate_number (SCM x);
 247 SCM_API SCM scm_round_number (SCM x);
 248 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 249 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 250 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 251 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 252 SCM_API SCM scm_real_part (SCM z);
 253 SCM_API SCM scm_imag_part (SCM z);
 254 SCM_API SCM scm_magnitude (SCM z);
 255 SCM_API SCM scm_angle (SCM z);
 256 SCM_API SCM scm_exact_to_inexact (SCM z);
 257 SCM_API SCM scm_inexact_to_exact (SCM z);
 258 SCM_API SCM scm_trunc (SCM x);
 259 SCM_API SCM scm_log (SCM z);
 260 SCM_API SCM scm_log10 (SCM z);
 261 SCM_API SCM scm_exp (SCM z);
 262 SCM_API SCM scm_sqrt (SCM z);
 263
 264 /* bignum internal functions */
 265 SCM_INTERNAL SCM scm_i_mkbig (void);
 266 SCM_API /* FIXME: not internal */ SCM scm_i_normbig (SCM x);
 267 SCM_INTERNAL int scm_i_bigcmp (SCM a, SCM b);
 268 SCM_INTERNAL SCM scm_i_dbl2big (double d);
 269 SCM_INTERNAL SCM scm_i_dbl2num (double d);
 270 SCM_API /* FIXME: not internal */ double scm_i_big2dbl (SCM b);
 271 SCM_API /* FIXME: not internal */ SCM scm_i_long2big (long n);
 272 SCM_API /* FIXME: not internal */ SCM scm_i_ulong2big (unsigned long n);
 273 SCM_API /* FIXME: not internal */ SCM scm_i_clonebig (SCM src_big, int same_sign_p);
 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_INTERNAL double scm_i_fraction2double (SCM z);
 282 SCM_INTERNAL SCM scm_i_fraction_equalp (SCM x, SCM y);
 283 SCM_INTERNAL int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 284
 285 /* general internal functions */
 286 SCM_INTERNAL void scm_i_print_double (double val, SCM port);
 287 SCM_INTERNAL void scm_i_print_complex (double real, double imag, SCM port);
 288
 289 /* conversion functions for integers */
 290
 291 SCM_API int scm_is_integer (SCM val);
 292 SCM_API int scm_is_signed_integer (SCM val,
 293                                    scm_t_intmax min, scm_t_intmax max);
 294 SCM_API int scm_is_unsigned_integer (SCM val,
 295                                      scm_t_uintmax min, scm_t_uintmax max);
 296
 297 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
 298 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
 299
 300 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
 301                                             scm_t_intmax min,
 302                                             scm_t_intmax max);
 303 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
 304                                                scm_t_uintmax min,
 305                                                scm_t_uintmax max);
 306
 307 SCM_API scm_t_int8   scm_to_int8     (SCM x);
 308 SCM_API SCM          scm_from_int8   (scm_t_int8 x);
 309
 310 SCM_API scm_t_uint8  scm_to_uint8    (SCM x);
 311 SCM_API SCM          scm_from_uint8  (scm_t_uint8 x);
 312
 313 SCM_API scm_t_int16  scm_to_int16    (SCM x);
 314 SCM_API SCM          scm_from_int16  (scm_t_int16 x);
 315
 316 SCM_API scm_t_uint16 scm_to_uint16   (SCM x);
 317 SCM_API SCM          scm_from_uint16 (scm_t_uint16 x);
 318
 319 SCM_API scm_t_int32  scm_to_int32    (SCM x);
 320 SCM_API SCM          scm_from_int32  (scm_t_int32 x);
 321
 322 SCM_API scm_t_uint32 scm_to_uint32   (SCM x);
 323 SCM_API SCM          scm_from_uint32 (scm_t_uint32 x);
 324
 325 #if SCM_HAVE_T_INT64
 326
 327 SCM_API scm_t_int64  scm_to_int64    (SCM x);
 328 SCM_API SCM          scm_from_int64  (scm_t_int64 x);
 329
 330 SCM_API scm_t_uint64 scm_to_uint64   (SCM x);
 331 SCM_API SCM          scm_from_uint64 (scm_t_uint64 x);
 332
 333 #endif
 334
 335 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
 336 SCM_API SCM  scm_from_mpz (mpz_t rop);
 337
 338
 339 /* The conversion functions for other types are aliased to the
 340    appropriate ones from above.  We pick the right one based on the
 341    size of the type.
 342
 343    Not each and every possibility is covered by the code below, and
 344    while it is trivial to complete the tests, it might be better to
 345    just test for the 'sane' possibilities.  When one of the tests
 346    below fails, chances are good that some silent assumption somewhere
 347    else will also fail.
 348 */
 349
 350 #if SCM_SIZEOF_CHAR == 1
 351 #define scm_to_schar   scm_to_int8
 352 #define scm_from_schar scm_from_int8
 353 #define scm_to_uchar   scm_to_uint8
 354 #define scm_from_uchar scm_from_uint8
 355 #if CHAR_MIN == 0
 356 #define scm_to_char    scm_to_uint8
 357 #define scm_from_char  scm_from_uint8
 358 #else
 359 #define scm_to_char    scm_to_int8
 360 #define scm_from_char  scm_from_int8
 361 #endif
 362 #else
 363 #error sizeof(char) is not 1.
 364 #endif
 365
 366 #if SCM_SIZEOF_SHORT == 1
 367 #define scm_to_short    scm_to_int8
 368 #define scm_from_short  scm_from_int8
 369 #define scm_to_ushort   scm_to_uint8
 370 #define scm_from_ushort scm_from_uint8
 371 #else
 372 #if SCM_SIZEOF_SHORT == 2
 373 #define scm_to_short    scm_to_int16
 374 #define scm_from_short  scm_from_int16
 375 #define scm_to_ushort   scm_to_uint16
 376 #define scm_from_ushort scm_from_uint16
 377 #else
 378 #if SCM_SIZEOF_SHORT == 4
 379 #define scm_to_short    scm_to_int32
 380 #define scm_from_short  scm_from_int32
 381 #define scm_to_ushort   scm_to_uint32
 382 #define scm_from_ushort scm_from_uint32
 383 #else
 384 #error sizeof(short) is not 1, 2, or 4.
 385 #endif
 386 #endif
 387 #endif
 388
 389 #if SCM_SIZEOF_INT == 4
 390 #define scm_to_int    scm_to_int32
 391 #define scm_from_int  scm_from_int32
 392 #define scm_to_uint   scm_to_uint32
 393 #define scm_from_uint scm_from_uint32
 394 #else
 395 #if SCM_SIZEOF_INT == 8
 396 #define scm_to_int    scm_to_int64
 397 #define scm_from_int  scm_from_int64
 398 #define scm_to_uint   scm_to_uint64
 399 #define scm_from_uint scm_from_uint64
 400 #else
 401 #error sizeof(int) is not 4 or 8.
 402 #endif
 403 #endif
 404
 405 #if SCM_SIZEOF_LONG == 4
 406 #define scm_to_long    scm_to_int32
 407 #define scm_from_long  scm_from_int32
 408 #define scm_to_ulong   scm_to_uint32
 409 #define scm_from_ulong scm_from_uint32
 410 #else
 411 #if SCM_SIZEOF_LONG == 8
 412 #define scm_to_long    scm_to_int64
 413 #define scm_from_long  scm_from_int64
 414 #define scm_to_ulong   scm_to_uint64
 415 #define scm_from_ulong scm_from_uint64
 416 #else
 417 #error sizeof(long) is not 4 or 8.
 418 #endif
 419 #endif
 420
 421 #if SCM_SIZEOF_INTMAX == 4
 422 #define scm_to_intmax    scm_to_int32
 423 #define scm_from_intmax  scm_from_int32
 424 #define scm_to_uintmax   scm_to_uint32
 425 #define scm_from_uintmax scm_from_uint32
 426 #else
 427 #if SCM_SIZEOF_INTMAX == 8
 428 #define scm_to_intmax    scm_to_int64
 429 #define scm_from_intmax  scm_from_int64
 430 #define scm_to_uintmax   scm_to_uint64
 431 #define scm_from_uintmax scm_from_uint64
 432 #else
 433 #error sizeof(scm_t_intmax) is not 4 or 8.
 434 #endif
 435 #endif
 436
 437 #if SCM_SIZEOF_LONG_LONG == 0
 438 #else
 439 #if SCM_SIZEOF_LONG_LONG == 8
 440 #define scm_to_long_long    scm_to_int64
 441 #define scm_from_long_long  scm_from_int64
 442 #define scm_to_ulong_long   scm_to_uint64
 443 #define scm_from_ulong_long scm_from_uint64
 444 #else
 445 #error sizeof(long long) is not 8.
 446 #endif
 447 #endif
 448
 449 #if SCM_SIZEOF_SIZE_T == 4
 450 #define scm_to_ssize_t    scm_to_int32
 451 #define scm_from_ssize_t  scm_from_int32
 452 #define scm_to_size_t     scm_to_uint32
 453 #define scm_from_size_t   scm_from_uint32
 454 #else
 455 #if SCM_SIZEOF_SIZE_T == 8
 456 #define scm_to_ssize_t    scm_to_int64
 457 #define scm_from_ssize_t  scm_from_int64
 458 #define scm_to_size_t     scm_to_uint64
 459 #define scm_from_size_t   scm_from_uint64
 460 #else
 461 #error sizeof(size_t) is not 4 or 8.
 462 #endif
 463 #endif
 464
 465 /* conversion functions for double */
 466
 467 SCM_API int scm_is_real (SCM val);
 468 SCM_API int scm_is_rational (SCM val);
 469 SCM_API double scm_to_double (SCM val);
 470 SCM_API SCM scm_from_double (double val);
 471
 472 /* conversion functions for complex */
 473
 474 SCM_API int scm_is_complex (SCM val);
 475 SCM_API SCM scm_c_make_rectangular (double re, double im);
 476 SCM_API SCM scm_c_make_polar (double mag, double ang);
 477 SCM_API double scm_c_real_part (SCM z);
 478 SCM_API double scm_c_imag_part (SCM z);
 479 SCM_API double scm_c_magnitude (SCM z);
 480 SCM_API double scm_c_angle (SCM z);
 481
 482 SCM_API int scm_is_number (SCM val);
 483
 484 SCM_INTERNAL void scm_init_numbers (void);
 485
 486 #endif  /* SCM_NUMBERS_H */
 487
 488 /*
 489   Local Variables:
 490   c-file-style: "gnu"
 491   End:
 492 */