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 "libguile/__scm.h"
  26 #include "libguile/print.h"
  27
  28 #if SCM_HAVE_FLOATINGPOINT_H
  29 # include <floatingpoint.h>
  30 #endif
  31
  32 #if SCM_HAVE_IEEEFP_H
  33 # include <ieeefp.h>
  34 #endif
  35
  36 #if SCM_HAVE_NAN_H
  37 # if defined (SCO)
  38 #   define _IEEE 1
  39 # endif
  40 # include <nan.h>
  41 # if defined (SCO)
  42 #   undef _IEEE
  43 # endif
  44 #endif /* SCM_HAVE_NAN_H */
  45
  46 \f
  47
  48 /* Immediate Numbers, also known as fixnums
  49  *
  50  * Inums are exact integer data that fits within an SCM word.  */
  51
  52 /* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
  53  * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
  54  * which is the same as                (/ (- (expt 2 n) 4) 4)
  55  */
  56
  57 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  58 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  59 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  60
  61 /* SCM_SRS is signed right shift */
  62 #if (-1 == (((-1) << 2) + 2) >> 2)
  63 # define SCM_SRS(x, y) ((x) >> (y))
  64 #else
  65 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  66 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  67
  68
  69 #define SCM_I_INUMP(x)  (2 & SCM_UNPACK (x))
  70 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
  71 #define SCM_I_MAKINUM(x) \
  72   (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
  73 #define SCM_I_INUM(x)   (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  74
  75 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
  76 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
  77 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
  78 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
  79
  80
  81 /* A name for 0. */
  82 #define SCM_INUM0 (SCM_I_MAKINUM (0))
  83
  84 /* SCM_MAXEXP is the maximum double precision exponent
  85  * SCM_FLTMAX is less than or scm_equal the largest single precision float
  86  */
  87
  88 #if SCM_HAVE_STDC_HEADERS
  89 # ifndef GO32
  90 #  include <float.h>
  91 #  ifdef __MINGW32__
  92 #   define copysign _copysign
  93 #   define isnan _isnan
  94 #   define finite _finite
  95 #  endif /* __MINGW32__ */
  96 # endif /* ndef GO32 */
  97 #endif /* def STDC_HEADERS */
  98
  99 #ifdef DBL_MAX_10_EXP
 100 # define SCM_MAXEXP DBL_MAX_10_EXP
 101 #else
 102 # define SCM_MAXEXP 308         /* IEEE doubles */
 103 #endif /* def DBL_MAX_10_EXP */
 104
 105 #ifdef FLT_MAX
 106 # define SCM_FLTMAX FLT_MAX
 107 #else
 108 # define SCM_FLTMAX 1e+23
 109 #endif /* def FLT_MAX */
 110
 111
 112 /* SCM_INTBUFLEN is the maximum number of characters neccessary for the
 113  * printed or scm_string representation of an exact immediate.
 114  */
 115 #define SCM_INTBUFLEN (5 + SCM_LONG_BIT)
 116
 117 \f
 118
 119 /* Numbers
 120  */
 121
 122
 123 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
 124  * differ in one bit: This way, checking if an object is an inexact number can
 125  * be done quickly (using the TYP16S macro).  */
 126
 127 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 128  * and SCM_NUMP)  */
 129 #define scm_tc16_big            (scm_tc7_number + 1 * 256L)
 130 #define scm_tc16_real           (scm_tc7_number + 2 * 256L)
 131 #define scm_tc16_complex        (scm_tc7_number + 3 * 256L)
 132 #define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)
 133
 134 #define SCM_INEXACTP(x) \
 135   (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
 136 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 137 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 138
 139 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 140 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 141 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 142 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 143
 144 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
 145 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
 146 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
 147
 148 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
 149 #define SCM_NUMP(x) (!SCM_IMP(x) \
 150   && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
 151       || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
 152 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
 153
 154 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
 155 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
 156 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
 157 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
 158 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
 159
 160   /* I think the left half word is free in the type, so I'll use bit 17 */
 161 #define SCM_FRACTION_REDUCED_BIT 0x10000
 162 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
 163 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
 164 #define SCM_FRACTION_REDUCED(x)     (0x10000 & SCM_CELL_TYPE (x))
 165
 166 \f
 167
 168 typedef struct scm_t_double
 169 {
 170   SCM type;
 171   SCM pad;
 172   double real;
 173 } scm_t_double;
 174
 175 typedef struct scm_t_complex
 176 {
 177   double real;
 178   double imag;
 179 } scm_t_complex;
 180
 181 \f
 182
 183 SCM_API SCM scm_exact_p (SCM x);
 184 SCM_API SCM scm_odd_p (SCM n);
 185 SCM_API SCM scm_even_p (SCM n);
 186 SCM_API SCM scm_inf_p (SCM n);
 187 SCM_API SCM scm_nan_p (SCM n);
 188 SCM_API SCM scm_inf (void);
 189 SCM_API SCM scm_nan (void);
 190 SCM_API SCM scm_abs (SCM x);
 191 SCM_API SCM scm_quotient (SCM x, SCM y);
 192 SCM_API SCM scm_remainder (SCM x, SCM y);
 193 SCM_API SCM scm_modulo (SCM x, SCM y);
 194 SCM_API SCM scm_gcd (SCM x, SCM y);
 195 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 196 SCM_API SCM scm_logand (SCM n1, SCM n2);
 197 SCM_API SCM scm_logior (SCM n1, SCM n2);
 198 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 199 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 200 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 201 SCM_API SCM scm_lognot (SCM n);
 202 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
 203 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 204 SCM_API SCM scm_ash (SCM n, SCM cnt);
 205 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 206 SCM_API SCM scm_logcount (SCM n);
 207 SCM_API SCM scm_integer_length (SCM n);
 208
 209 SCM_API size_t scm_iint2str (long num, int rad, char *p);
 210 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 211 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 212 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 213 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 214 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
 215 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 216 SCM_API SCM scm_bigequal (SCM x, SCM y);
 217 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 218 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 219 SCM_API SCM scm_number_p (SCM x);
 220 SCM_API SCM scm_complex_p (SCM x);
 221 SCM_API SCM scm_real_p (SCM x);
 222 SCM_API SCM scm_rational_p (SCM z);
 223 SCM_API SCM scm_integer_p (SCM x);
 224 SCM_API SCM scm_inexact_p (SCM x);
 225 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 226 SCM_API SCM scm_less_p (SCM x, SCM y);
 227 SCM_API SCM scm_gr_p (SCM x, SCM y);
 228 SCM_API SCM scm_leq_p (SCM x, SCM y);
 229 SCM_API SCM scm_geq_p (SCM x, SCM y);
 230 SCM_API SCM scm_zero_p (SCM z);
 231 SCM_API SCM scm_positive_p (SCM x);
 232 SCM_API SCM scm_negative_p (SCM x);
 233 SCM_API SCM scm_max (SCM x, SCM y);
 234 SCM_API SCM scm_min (SCM x, SCM y);
 235 SCM_API SCM scm_sum (SCM x, SCM y);
 236 SCM_API SCM scm_difference (SCM x, SCM y);
 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
 260 /* bignum internal functions */
 261 SCM_API SCM scm_i_mkbig (void);
 262 SCM_API SCM scm_i_normbig (SCM x);
 263 SCM_API int scm_i_bigcmp (SCM a, SCM b);
 264 SCM_API SCM scm_i_dbl2big (double d);
 265 SCM_API SCM scm_i_dbl2num (double d);
 266 SCM_API double scm_i_big2dbl (SCM b);
 267 SCM_API SCM scm_i_long2big (long n);
 268 SCM_API SCM scm_i_ulong2big (unsigned long n);
 269
 270 /* ratio functions */
 271 SCM_API SCM scm_rationalize (SCM x, SCM err);
 272 SCM_API SCM scm_numerator (SCM z);
 273 SCM_API SCM scm_denominator (SCM z);
 274
 275 /* fraction internal functions */
 276 SCM_API double scm_i_fraction2double (SCM z);
 277 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
 278 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 279
 280 /* conversion functions for integers */
 281
 282 SCM_API int scm_is_integer (SCM val);
 283 SCM_API int scm_is_signed_integer (SCM val,
 284                                    scm_t_intmax min, scm_t_intmax max);
 285 SCM_API int scm_is_unsigned_integer (SCM val,
 286                                      scm_t_uintmax min, scm_t_uintmax max);
 287
 288 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
 289 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
 290
 291 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
 292                                             scm_t_intmax min,
 293                                             scm_t_intmax max);
 294 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
 295                                                scm_t_uintmax min,
 296                                                scm_t_uintmax max);
 297
 298 SCM_API scm_t_int8   scm_to_int8     (SCM x);
 299 SCM_API SCM          scm_from_int8   (scm_t_int8 x);
 300
 301 SCM_API scm_t_uint8  scm_to_uint8    (SCM x);
 302 SCM_API SCM          scm_from_uint8  (scm_t_uint8 x);
 303
 304 SCM_API scm_t_int16  scm_to_int16    (SCM x);
 305 SCM_API SCM          scm_from_int16  (scm_t_int16 x);
 306
 307 SCM_API scm_t_uint16 scm_to_uint16   (SCM x);
 308 SCM_API SCM          scm_from_uint16 (scm_t_uint16 x);
 309
 310 SCM_API scm_t_int32  scm_to_int32    (SCM x);
 311 SCM_API SCM          scm_from_int32  (scm_t_int32 x);
 312
 313 SCM_API scm_t_uint32 scm_to_uint32   (SCM x);
 314 SCM_API SCM          scm_from_uint32 (scm_t_uint32 x);
 315
 316 #if SCM_HAVE_T_INT64
 317
 318 SCM_API scm_t_int64  scm_to_int64    (SCM x);
 319 SCM_API SCM          scm_from_int64  (scm_t_int64 x);
 320
 321 SCM_API scm_t_uint64 scm_to_uint64   (SCM x);
 322 SCM_API SCM          scm_from_uint64 (scm_t_uint64 x);
 323
 324 #endif
 325
 326 /* The conversion functions for other types are aliased to the
 327    appropriate ones from above.  We pick the right one based on the
 328    size of the type.
 329
 330    Not each and every possibility is covered by the code below, and
 331    while it is trivial to complete the tests, it might be better to
 332    just test for the 'sane' possibilities.  When one of the tests
 333    below fails, chances are good that some silent assumption somewhere
 334    else will also fail.
 335 */
 336
 337 #if SCM_SIZEOF_CHAR == 1
 338 #define scm_to_schar   scm_to_int8
 339 #define scm_from_schar scm_from_int8
 340 #define scm_to_uchar   scm_to_uint8
 341 #define scm_from_uchar scm_from_uint8
 342 #if CHAR_MIN == 0
 343 #define scm_to_char    scm_to_uint8
 344 #define scm_from_char  scm_from_uint8
 345 #else
 346 #define scm_to_char    scm_to_int8
 347 #define scm_from_char  scm_from_int8
 348 #endif
 349 #else
 350 #error sizeof(char) is not 1.
 351 #endif
 352
 353 #if SCM_SIZEOF_SHORT == 1
 354 #define scm_to_short    scm_to_int8
 355 #define scm_from_short  scm_from_int8
 356 #define scm_to_ushort   scm_to_uint8
 357 #define scm_from_ushort scm_from_uint8
 358 #else
 359 #if SCM_SIZEOF_SHORT == 2
 360 #define scm_to_short    scm_to_int16
 361 #define scm_from_short  scm_from_int16
 362 #define scm_to_ushort   scm_to_uint16
 363 #define scm_from_ushort scm_from_uint16
 364 #else
 365 #if SCM_SIZEOF_SHORT == 4
 366 #define scm_to_short    scm_to_int32
 367 #define scm_from_short  scm_from_int32
 368 #define scm_to_ushort   scm_to_uint32
 369 #define scm_from_ushort scm_from_uint32
 370 #else
 371 #error sizeof(short) is not 1, 2, or 4.
 372 #endif
 373 #endif
 374 #endif
 375
 376 #if SCM_SIZEOF_INT == 4
 377 #define scm_to_int    scm_to_int32
 378 #define scm_from_int  scm_from_int32
 379 #define scm_to_uint   scm_to_uint32
 380 #define scm_from_uint scm_from_uint32
 381 #else
 382 #if SCM_SIZEOF_INT == 8
 383 #define scm_to_int    scm_to_int64
 384 #define scm_from_int  scm_from_int64
 385 #define scm_to_uint   scm_to_uint64
 386 #define scm_from_uint scm_from_uint64
 387 #else
 388 #error sizeof(int) is not 4 or 8.
 389 #endif
 390 #endif
 391
 392 #if SCM_SIZEOF_LONG == 4
 393 #define scm_to_long    scm_to_int32
 394 #define scm_from_long  scm_from_int32
 395 #define scm_to_ulong   scm_to_uint32
 396 #define scm_from_ulong scm_from_uint32
 397 #else
 398 #if SCM_SIZEOF_LONG == 8
 399 #define scm_to_long    scm_to_int64
 400 #define scm_from_long  scm_from_int64
 401 #define scm_to_ulong   scm_to_uint64
 402 #define scm_from_ulong scm_from_uint64
 403 #else
 404 #error sizeof(long) is not 4 or 8.
 405 #endif
 406 #endif
 407
 408 #if SCM_SIZEOF_INTMAX == 4
 409 #define scm_to_intmax    scm_to_int32
 410 #define scm_from_intmax  scm_from_int32
 411 #define scm_to_uintmax   scm_to_uint32
 412 #define scm_from_uintmax scm_from_uint32
 413 #else
 414 #if SCM_SIZEOF_INTMAX == 8
 415 #define scm_to_intmax    scm_to_int64
 416 #define scm_from_intmax  scm_from_int64
 417 #define scm_to_uintmax   scm_to_uint64
 418 #define scm_from_uintmax scm_from_uint64
 419 #else
 420 #error sizeof(scm_t_intmax) is not 4 or 8.
 421 #endif
 422 #endif
 423
 424 #if SCM_SIZEOF_LONG_LONG == 0
 425 #else
 426 #if SCM_SIZEOF_LONG_LONG == 8
 427 #define scm_to_long_long    scm_to_int64
 428 #define scm_from_long_long  scm_from_int64
 429 #define scm_to_ulong_long   scm_to_uint64
 430 #define scm_from_ulong_long scm_from_uint64
 431 #else
 432 #error sizeof(long long) is not 8.
 433 #endif
 434 #endif
 435
 436 #if SCM_SIZEOF_SIZE_T == 4
 437 #define scm_to_ssize_t    scm_to_int32
 438 #define scm_from_ssize_t  scm_from_int32
 439 #define scm_to_size_t     scm_to_uint32
 440 #define scm_from_size_t   scm_from_uint32
 441 #else
 442 #if SCM_SIZEOF_SIZE_T == 8
 443 #define scm_to_ssize_t    scm_to_int64
 444 #define scm_from_ssize_t  scm_from_int64
 445 #define scm_to_size_t     scm_to_uint64
 446 #define scm_from_size_t   scm_from_uint64
 447 #else
 448 #error sizeof(size_t) is not 4 or 8.
 449 #endif
 450 #endif
 451
 452 /* conversion functions for double */
 453
 454 SCM_API int scm_is_real (SCM val);
 455 SCM_API int scm_is_rational (SCM val);
 456 SCM_API double scm_to_double (SCM val);
 457 SCM_API SCM scm_from_double (double val);
 458
 459 /* conversion functions for complex */
 460
 461 SCM_API int scm_is_complex (SCM val);
 462 SCM_API SCM scm_c_make_rectangular (double re, double im);
 463 SCM_API SCM scm_c_make_polar (double mag, double ang);
 464 SCM_API double scm_c_real_part (SCM z);
 465 SCM_API double scm_c_imag_part (SCM z);
 466 SCM_API double scm_c_magnitude (SCM z);
 467 SCM_API double scm_c_angle (SCM z);
 468
 469 SCM_API int scm_is_number (SCM val);
 470
 471 SCM_API void scm_init_numbers (void);
 472
 473 #endif  /* SCM_NUMBERS_H */
 474
 475 /*
 476   Local Variables:
 477   c-file-style: "gnu"
 478   End:
 479 */