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 the
 115  * printed or scm_string representation of an exact immediate.
 116  */
 117 #define SCM_INTBUFLEN (5 + SCM_LONG_BIT)
 118
 119 \f
 120
 121 /* Numbers
 122  */
 123
 124
 125 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
 126  * differ in one bit: This way, checking if an object is an inexact number can
 127  * be done quickly (using the TYP16S macro).  */
 128
 129 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 130  * and SCM_NUMP)  */
 131 #define scm_tc16_big            (scm_tc7_number + 1 * 256L)
 132 #define scm_tc16_real           (scm_tc7_number + 2 * 256L)
 133 #define scm_tc16_complex        (scm_tc7_number + 3 * 256L)
 134 #define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)
 135
 136 #define SCM_INEXACTP(x) \
 137   (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
 138 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 139 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 140
 141 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 142 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 143 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 144 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 145
 146 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
 147 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
 148 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
 149
 150 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
 151 #define SCM_NUMP(x) (!SCM_IMP(x) \
 152   && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
 153       || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
 154 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
 155
 156 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
 157 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
 158 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
 159 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
 160 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
 161
 162   /* I think the left half word is free in the type, so I'll use bit 17 */
 163 #define SCM_FRACTION_REDUCED_BIT 0x10000
 164 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
 165 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
 166 #define SCM_FRACTION_REDUCED(x)     (0x10000 & SCM_CELL_TYPE (x))
 167
 168 \f
 169
 170 typedef struct scm_t_double
 171 {
 172   SCM type;
 173   SCM pad;
 174   double real;
 175 } scm_t_double;
 176
 177 typedef struct scm_t_complex
 178 {
 179   double real;
 180   double imag;
 181 } scm_t_complex;
 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 (long num, int rad, char *p);
 212 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 213 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 214 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 215 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 216 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
 217 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 218 SCM_API SCM scm_bigequal (SCM x, SCM y);
 219 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 220 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 221 SCM_API SCM scm_number_p (SCM x);
 222 SCM_API SCM scm_complex_p (SCM x);
 223 SCM_API SCM scm_real_p (SCM x);
 224 SCM_API SCM scm_rational_p (SCM z);
 225 SCM_API SCM scm_integer_p (SCM x);
 226 SCM_API SCM scm_inexact_p (SCM x);
 227 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 228 SCM_API SCM scm_less_p (SCM x, SCM y);
 229 SCM_API SCM scm_gr_p (SCM x, SCM y);
 230 SCM_API SCM scm_leq_p (SCM x, SCM y);
 231 SCM_API SCM scm_geq_p (SCM x, SCM y);
 232 SCM_API SCM scm_zero_p (SCM z);
 233 SCM_API SCM scm_positive_p (SCM x);
 234 SCM_API SCM scm_negative_p (SCM x);
 235 SCM_API SCM scm_max (SCM x, SCM y);
 236 SCM_API SCM scm_min (SCM x, SCM y);
 237 SCM_API SCM scm_sum (SCM x, SCM y);
 238 SCM_API SCM scm_difference (SCM x, SCM y);
 239 SCM_API SCM scm_product (SCM x, SCM y);
 240 SCM_API SCM scm_divide (SCM x, SCM y);
 241 SCM_API SCM scm_floor (SCM x);
 242 SCM_API SCM scm_ceiling (SCM x);
 243 SCM_API double scm_asinh (double x);
 244 SCM_API double scm_acosh (double x);
 245 SCM_API double scm_atanh (double x);
 246 SCM_API double scm_c_truncate (double x);
 247 SCM_API double scm_c_round (double x);
 248 SCM_API SCM scm_truncate_number (SCM x);
 249 SCM_API SCM scm_round_number (SCM x);
 250 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 251 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 252 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 253 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 254 SCM_API SCM scm_real_part (SCM z);
 255 SCM_API SCM scm_imag_part (SCM z);
 256 SCM_API SCM scm_magnitude (SCM z);
 257 SCM_API SCM scm_angle (SCM z);
 258 SCM_API SCM scm_exact_to_inexact (SCM z);
 259 SCM_API SCM scm_inexact_to_exact (SCM z);
 260 SCM_API SCM scm_trunc (SCM x);
 261
 262 /* bignum internal functions */
 263 SCM_API SCM scm_i_mkbig (void);
 264 SCM_API SCM scm_i_normbig (SCM x);
 265 SCM_API int scm_i_bigcmp (SCM a, SCM b);
 266 SCM_API SCM scm_i_dbl2big (double d);
 267 SCM_API SCM scm_i_dbl2num (double d);
 268 SCM_API double scm_i_big2dbl (SCM b);
 269 SCM_API SCM scm_i_long2big (long n);
 270 SCM_API SCM scm_i_ulong2big (unsigned long n);
 271
 272 /* ratio functions */
 273 SCM_API SCM scm_rationalize (SCM x, SCM err);
 274 SCM_API SCM scm_numerator (SCM z);
 275 SCM_API SCM scm_denominator (SCM z);
 276
 277 /* fraction internal functions */
 278 SCM_API double scm_i_fraction2double (SCM z);
 279 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
 280 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 281
 282 /* conversion functions for integers */
 283
 284 SCM_API int scm_is_integer (SCM val);
 285 SCM_API int scm_is_signed_integer (SCM val,
 286                                    scm_t_intmax min, scm_t_intmax max);
 287 SCM_API int scm_is_unsigned_integer (SCM val,
 288                                      scm_t_uintmax min, scm_t_uintmax max);
 289
 290 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
 291 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
 292
 293 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
 294                                             scm_t_intmax min,
 295                                             scm_t_intmax max);
 296 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
 297                                                scm_t_uintmax min,
 298                                                scm_t_uintmax max);
 299
 300 SCM_API scm_t_int8   scm_to_int8     (SCM x);
 301 SCM_API SCM          scm_from_int8   (scm_t_int8 x);
 302
 303 SCM_API scm_t_uint8  scm_to_uint8    (SCM x);
 304 SCM_API SCM          scm_from_uint8  (scm_t_uint8 x);
 305
 306 SCM_API scm_t_int16  scm_to_int16    (SCM x);
 307 SCM_API SCM          scm_from_int16  (scm_t_int16 x);
 308
 309 SCM_API scm_t_uint16 scm_to_uint16   (SCM x);
 310 SCM_API SCM          scm_from_uint16 (scm_t_uint16 x);
 311
 312 SCM_API scm_t_int32  scm_to_int32    (SCM x);
 313 SCM_API SCM          scm_from_int32  (scm_t_int32 x);
 314
 315 SCM_API scm_t_uint32 scm_to_uint32   (SCM x);
 316 SCM_API SCM          scm_from_uint32 (scm_t_uint32 x);
 317
 318 #if SCM_HAVE_T_INT64
 319
 320 SCM_API scm_t_int64  scm_to_int64    (SCM x);
 321 SCM_API SCM          scm_from_int64  (scm_t_int64 x);
 322
 323 SCM_API scm_t_uint64 scm_to_uint64   (SCM x);
 324 SCM_API SCM          scm_from_uint64 (scm_t_uint64 x);
 325
 326 #endif
 327
 328 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
 329 SCM_API SCM  scm_from_mpz (mpz_t rop);
 330
 331
 332 /* The conversion functions for other types are aliased to the
 333    appropriate ones from above.  We pick the right one based on the
 334    size of the type.
 335
 336    Not each and every possibility is covered by the code below, and
 337    while it is trivial to complete the tests, it might be better to
 338    just test for the 'sane' possibilities.  When one of the tests
 339    below fails, chances are good that some silent assumption somewhere
 340    else will also fail.
 341 */
 342
 343 #if SCM_SIZEOF_CHAR == 1
 344 #define scm_to_schar   scm_to_int8
 345 #define scm_from_schar scm_from_int8
 346 #define scm_to_uchar   scm_to_uint8
 347 #define scm_from_uchar scm_from_uint8
 348 #if CHAR_MIN == 0
 349 #define scm_to_char    scm_to_uint8
 350 #define scm_from_char  scm_from_uint8
 351 #else
 352 #define scm_to_char    scm_to_int8
 353 #define scm_from_char  scm_from_int8
 354 #endif
 355 #else
 356 #error sizeof(char) is not 1.
 357 #endif
 358
 359 #if SCM_SIZEOF_SHORT == 1
 360 #define scm_to_short    scm_to_int8
 361 #define scm_from_short  scm_from_int8
 362 #define scm_to_ushort   scm_to_uint8
 363 #define scm_from_ushort scm_from_uint8
 364 #else
 365 #if SCM_SIZEOF_SHORT == 2
 366 #define scm_to_short    scm_to_int16
 367 #define scm_from_short  scm_from_int16
 368 #define scm_to_ushort   scm_to_uint16
 369 #define scm_from_ushort scm_from_uint16
 370 #else
 371 #if SCM_SIZEOF_SHORT == 4
 372 #define scm_to_short    scm_to_int32
 373 #define scm_from_short  scm_from_int32
 374 #define scm_to_ushort   scm_to_uint32
 375 #define scm_from_ushort scm_from_uint32
 376 #else
 377 #error sizeof(short) is not 1, 2, or 4.
 378 #endif
 379 #endif
 380 #endif
 381
 382 #if SCM_SIZEOF_INT == 4
 383 #define scm_to_int    scm_to_int32
 384 #define scm_from_int  scm_from_int32
 385 #define scm_to_uint   scm_to_uint32
 386 #define scm_from_uint scm_from_uint32
 387 #else
 388 #if SCM_SIZEOF_INT == 8
 389 #define scm_to_int    scm_to_int64
 390 #define scm_from_int  scm_from_int64
 391 #define scm_to_uint   scm_to_uint64
 392 #define scm_from_uint scm_from_uint64
 393 #else
 394 #error sizeof(int) is not 4 or 8.
 395 #endif
 396 #endif
 397
 398 #if SCM_SIZEOF_LONG == 4
 399 #define scm_to_long    scm_to_int32
 400 #define scm_from_long  scm_from_int32
 401 #define scm_to_ulong   scm_to_uint32
 402 #define scm_from_ulong scm_from_uint32
 403 #else
 404 #if SCM_SIZEOF_LONG == 8
 405 #define scm_to_long    scm_to_int64
 406 #define scm_from_long  scm_from_int64
 407 #define scm_to_ulong   scm_to_uint64
 408 #define scm_from_ulong scm_from_uint64
 409 #else
 410 #error sizeof(long) is not 4 or 8.
 411 #endif
 412 #endif
 413
 414 #if SCM_SIZEOF_INTMAX == 4
 415 #define scm_to_intmax    scm_to_int32
 416 #define scm_from_intmax  scm_from_int32
 417 #define scm_to_uintmax   scm_to_uint32
 418 #define scm_from_uintmax scm_from_uint32
 419 #else
 420 #if SCM_SIZEOF_INTMAX == 8
 421 #define scm_to_intmax    scm_to_int64
 422 #define scm_from_intmax  scm_from_int64
 423 #define scm_to_uintmax   scm_to_uint64
 424 #define scm_from_uintmax scm_from_uint64
 425 #else
 426 #error sizeof(scm_t_intmax) is not 4 or 8.
 427 #endif
 428 #endif
 429
 430 #if SCM_SIZEOF_LONG_LONG == 0
 431 #else
 432 #if SCM_SIZEOF_LONG_LONG == 8
 433 #define scm_to_long_long    scm_to_int64
 434 #define scm_from_long_long  scm_from_int64
 435 #define scm_to_ulong_long   scm_to_uint64
 436 #define scm_from_ulong_long scm_from_uint64
 437 #else
 438 #error sizeof(long long) is not 8.
 439 #endif
 440 #endif
 441
 442 #if SCM_SIZEOF_SIZE_T == 4
 443 #define scm_to_ssize_t    scm_to_int32
 444 #define scm_from_ssize_t  scm_from_int32
 445 #define scm_to_size_t     scm_to_uint32
 446 #define scm_from_size_t   scm_from_uint32
 447 #else
 448 #if SCM_SIZEOF_SIZE_T == 8
 449 #define scm_to_ssize_t    scm_to_int64
 450 #define scm_from_ssize_t  scm_from_int64
 451 #define scm_to_size_t     scm_to_uint64
 452 #define scm_from_size_t   scm_from_uint64
 453 #else
 454 #error sizeof(size_t) is not 4 or 8.
 455 #endif
 456 #endif
 457
 458 /* conversion functions for double */
 459
 460 SCM_API int scm_is_real (SCM val);
 461 SCM_API int scm_is_rational (SCM val);
 462 SCM_API double scm_to_double (SCM val);
 463 SCM_API SCM scm_from_double (double val);
 464
 465 /* conversion functions for complex */
 466
 467 SCM_API int scm_is_complex (SCM val);
 468 SCM_API SCM scm_c_make_rectangular (double re, double im);
 469 SCM_API SCM scm_c_make_polar (double mag, double ang);
 470 SCM_API double scm_c_real_part (SCM z);
 471 SCM_API double scm_c_imag_part (SCM z);
 472 SCM_API double scm_c_magnitude (SCM z);
 473 SCM_API double scm_c_angle (SCM z);
 474
 475 SCM_API int scm_is_number (SCM val);
 476
 477 SCM_API void scm_init_numbers (void);
 478
 479 #endif  /* SCM_NUMBERS_H */
 480
 481 /*
 482   Local Variables:
 483   c-file-style: "gnu"
 484   End:
 485 */