libguile/numbers.h

   1 /* classes: h_files */
   2
   3 #ifndef NUMBERSH
   4 #define NUMBERSH
   5 /*      Copyright (C) 1995, 1996, 1998, 2000 Free Software Foundation, Inc.
   6  *
   7  * This program is free software; you can redistribute it and/or modify
   8  * it under the terms of the GNU General Public License as published by
   9  * the Free Software Foundation; either version 2, or (at your option)
  10  * any later version.
  11  *
  12  * This program is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  * GNU General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU General Public License
  18  * along with this software; see the file COPYING.  If not, write to
  19  * the Free Software Foundation, Inc., 59 Temple Place, Suite 330,
  20  * Boston, MA 02111-1307 USA
  21  *
  22  * As a special exception, the Free Software Foundation gives permission
  23  * for additional uses of the text contained in its release of GUILE.
  24  *
  25  * The exception is that, if you link the GUILE library with other files
  26  * to produce an executable, this does not by itself cause the
  27  * resulting executable to be covered by the GNU General Public License.
  28  * Your use of that executable is in no way restricted on account of
  29  * linking the GUILE library code into it.
  30  *
  31  * This exception does not however invalidate any other reasons why
  32  * the executable file might be covered by the GNU General Public License.
  33  *
  34  * This exception applies only to the code released by the
  35  * Free Software Foundation under the name GUILE.  If you copy
  36  * code from other Free Software Foundation releases into a copy of
  37  * GUILE, as the General Public License permits, the exception does
  38  * not apply to the code that you add in this way.  To avoid misleading
  39  * anyone as to the status of such modified files, you must delete
  40  * this exception notice from them.
  41  *
  42  * If you write modifications of your own for GUILE, it is your choice
  43  * whether to permit this exception to apply to your modifications.
  44  * If you do not wish that, delete this exception notice.  */
  45
  46 /* Software engineering face-lift by Greg J. Badros, 11-Dec-1999,
  47    gjb@cs.washington.edu, http://www.cs.washington.edu/homes/gjb */
  48 \f
  49
  50 #include "libguile/__scm.h"
  51
  52 #include "libguile/print.h"
  53
  54 \f
  55
  56
  57 /* Immediate Numbers
  58  *
  59  * Inums are exact integer data that fits within an SCM word.
  60  *
  61  * SCM_INUMP applies only to values known to be Scheme objects.
  62  * In particular, SCM_INUMP (SCM_CAR (x)) is valid only if x is known
  63  * to be a SCM_CONSP.  If x is only known to be a SCM_NIMP,
  64  * SCM_INUMP (SCM_CAR (x)) can give wrong answers.
  65  */
  66
  67 #define SCM_INUMP(x)    (2 & SCM_UNPACK (x))
  68 #define SCM_NINUMP(x)   (!SCM_INUMP (x))
  69
  70 #ifdef __TURBOC__
  71 /* shifts of more than one are done by a library call, single shifts are
  72  * performed in registers
  73  */
  74 # define SCM_MAKINUM(x) (SCM_PACK ((((x) << 1) << 1) + 2L))
  75 #else
  76 # define SCM_MAKINUM(x) (SCM_PACK (((x) << 2) + 2L))
  77 #endif /* def __TURBOC__ */
  78
  79
  80 /* SCM_SRS is signed right shift */
  81 /* SCM_INUM makes a C int from an SCM immediate number. */
  82 /* Turbo C++ v1.0 has a bug with right shifts of signed longs!
  83  * It is believed to be fixed in Turbo C++ v1.01
  84  */
  85 #if (-1==(((-1)<<2)+2)>>2) && (__TURBOC__ != 0x295)
  86 # define SCM_SRS(x, y) ((x) >> y)
  87 # ifdef __TURBOC__
  88 #  define SCM_INUM(x) ((SCM_UNPACK (x) >>1) >>1)
  89 # else
  90 #  define SCM_INUM(x) SCM_SRS (SCM_UNPACK (x), 2)
  91 # endif /* def __TURBOC__ */
  92 #else
  93 # define SCM_SRS(x, y)\
  94  ((SCM_UNPACK (x) < 0) ? ~( (~SCM_UNPACK (x)) >> y) : (SCM_UNPACK (x) >> y))
  95 # define SCM_INUM(x) SCM_SRS (SCM_UNPACK (x), 2)
  96 #endif /*  (-1==(((-1)<<2)+2)>>2) && (__TURBOC__ != 0x295) */
  97
  98
  99 /* A name for 0.
 100  */
 101 #define SCM_INUM0 (SCM_PACK (2))
 102
 103
 104 /* SCM_MAXEXP is the maximum double precision expontent
 105  * SCM_FLTMAX is less than or scm_equal the largest single precision float
 106  */
 107
 108 #ifdef STDC_HEADERS
 109 #ifndef GO32
 110 #include <float.h>
 111 #endif /* ndef GO32 */
 112 #endif /* def STDC_HEADERS */
 113 #ifdef DBL_MAX_10_EXP
 114 #define SCM_MAXEXP DBL_MAX_10_EXP
 115 #else
 116 #define SCM_MAXEXP 308          /* IEEE doubles */
 117 #endif /* def DBL_MAX_10_EXP */
 118 #ifdef FLT_MAX
 119 #define SCM_FLTMAX FLT_MAX
 120 #else
 121 #define SCM_FLTMAX 1e+23
 122 #endif /* def FLT_MAX */
 123
 124
 125 /* SCM_FIXABLE is non-0 if its long argument can be encoded in an SCM_INUM.
 126  */
 127 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
 128 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
 129 #define SCM_UNEGFIXABLE(n) ((n) <= -SCM_MOST_NEGATIVE_FIXNUM)
 130 #define SCM_FIXABLE(n) (SCM_POSFIXABLE(n) && SCM_NEGFIXABLE(n))
 131
 132 /* SCM_INTBUFLEN is the maximum number of characters neccessary for the
 133  * printed or scm_string representation of an exact immediate.
 134  */
 135
 136 #ifndef SCM_CHAR_BIT
 137 # define SCM_CHAR_BIT 8
 138 #endif /* ndef SCM_CHAR_BIT */
 139 #ifndef SCM_LONG_BIT
 140 # define SCM_LONG_BIT (SCM_CHAR_BIT*sizeof(long)/sizeof(char))
 141 #endif /* ndef SCM_LONG_BIT */
 142 #define SCM_INTBUFLEN (5+SCM_LONG_BIT)
 143
 144 /* SCM_FLOBUFLEN is the maximum number of characters neccessary for the
 145  * printed or scm_string representation of an inexact number.
 146  */
 147
 148 #define SCM_FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10)
 149
 150
 151 \f
 152
 153 /* Numbers
 154  */
 155
 156 #define SCM_NEWREAL(z, x) \
 157   do { \
 158     SCM_NEWCELL2 (z); \
 159     SCM_SET_CELL_TYPE (z, scm_tc16_real); \
 160     SCM_REAL_VALUE (z) = (x); \
 161   } while (0) \
 162
 163 #define SCM_NEWCOMPLEX(z, x, y) \
 164   do { \
 165     double __SCM_complex_tmp = (y); \
 166     if (__SCM_complex_tmp == 0.0) \
 167       SCM_NEWREAL (z, x); \
 168     else \
 169       { \
 170         SCM_NEWSMOB (z, scm_tc16_complex, \
 171                      scm_must_malloc (2L * sizeof (double), "complex")); \
 172         SCM_COMPLEX_REAL (z) = (x); \
 173         SCM_COMPLEX_IMAG (z) = __SCM_complex_tmp; \
 174       } \
 175   } while (0) \
 176
 177 #define SCM_SLOPPY_INEXACTP(x) (SCM_TYP16S (x) == scm_tc16_real)
 178 #define SCM_SLOPPY_REALP(x) (SCM_TYP16 (x) == scm_tc16_real)
 179 #define SCM_SLOPPY_COMPLEXP(x) (SCM_TYP16 (x) == scm_tc16_complex)
 180 #define SCM_INEXACTP(x) (SCM_NIMP (x) && SCM_TYP16S (x) == scm_tc16_real)
 181 #define SCM_REALP(x) (SCM_NIMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 182 #define SCM_COMPLEXP(x) (SCM_NIMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 183
 184 #define SCM_INEXP(x) SCM_INEXACTP(x) /* Deprecated */
 185 #define SCM_CPLXP(x) SCM_COMPLEXP(x) /* Deprecated */
 186
 187 #define SCM_REAL_VALUE(x) (((scm_double_t *) SCM2PTR (x))->real)
 188 #define SCM_COMPLEX_REAL(x) (((scm_complex_t *) SCM_CELL_WORD_1 (x))->real)
 189 #define SCM_COMPLEX_IMAG(x) (((scm_complex_t *) SCM_CELL_WORD_1 (x))->imag)
 190 #define SCM_REAL(x) \
 191  (SCM_SLOPPY_REALP (x) \
 192   ? SCM_REAL_VALUE (x) \
 193   : SCM_COMPLEX_REAL (x)) \
 194
 195 #define SCM_IMAG(x) \
 196   (SCM_SLOPPY_REALP (x) \
 197    ? 0.0 \
 198    : SCM_COMPLEX_IMAG (x)) \
 199
 200 #define SCM_REALPART(x) \
 201   (SCM_SLOPPY_REALP (x) ? SCM_REAL_VALUE (x) : SCM_COMPLEX_REAL (x))
 202
 203 #define scm_makdbl scm_make_complex /* Deprecated */
 204 #define SCM_SINGP(x) SCM_BOOL_F /* Deprecated */
 205
 206 /* Define SCM_BIGDIG to an integer type whose size is smaller than long if
 207  * you want bignums.  SCM_BIGRAD is one greater than the biggest SCM_BIGDIG.
 208  *
 209  * Define SCM_DIGSTOOBIG if the digits equivalent to a long won't fit in a long.
 210  */
 211 #ifdef BIGNUMS
 212 # ifdef _UNICOS
 213 #  define SCM_DIGSTOOBIG
 214 #  if (1L << 31) <= SCM_USHRT_MAX
 215 #   define SCM_BIGDIG unsigned  short
 216 #  else
 217 #   define SCM_BIGDIG unsigned int
 218 #  endif /*  (1L << 31) <= USHRT_MAX */
 219 #  define SCM_BITSPERDIG 32
 220 # else
 221 #  define SCM_BIGDIG unsigned short
 222 #  define SCM_BITSPERDIG (sizeof(SCM_BIGDIG)*SCM_CHAR_BIT)
 223 # endif /* def _UNICOS */
 224
 225 # define SCM_BIGRAD (1L << SCM_BITSPERDIG)
 226 # define SCM_DIGSPERLONG ((scm_sizet)((sizeof(long)*SCM_CHAR_BIT+SCM_BITSPERDIG-1)/SCM_BITSPERDIG))
 227 # define SCM_BIGUP(x) ((unsigned long)(x) << SCM_BITSPERDIG)
 228 # define SCM_LONGLONGBIGUP(x) ((ulong_long)(x) << SCM_BITSPERDIG)
 229 # define SCM_BIGDN(x) ((x) >> SCM_BITSPERDIG)
 230 # define SCM_BIGLO(x) ((x) & (SCM_BIGRAD-1))
 231
 232 #endif /* def BIGNUMS */
 233
 234 #ifndef SCM_BIGDIG
 235 /* Definition is not really used but helps various function
 236  * prototypes to compile with conditionalization.
 237  */
 238 # define SCM_BIGDIG unsigned short
 239 # define SCM_NO_BIGDIG
 240 #endif /* ndef SCM_BIGDIG */
 241
 242 #define SCM_NUMBERP(x) (SCM_INUMP(x) || SCM_NUMP(x))
 243 #ifdef SCM_BIGDIG
 244 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 245                         ? (double) SCM_INUM (x) \
 246                         : (SCM_REALP (x) \
 247                            ? SCM_REALPART (x) \
 248                            : scm_big2dbl (x)))
 249 #else
 250 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 251                         ? (double) SCM_INUM (x) \
 252                         : SCM_REALPART (x))
 253 #endif
 254 #define SCM_NUMP(x) \
 255   (SCM_NIMP(x) && (0xfcff & SCM_UNPACK (SCM_CAR(x))) == scm_tc7_smob)
 256 #define SCM_BIGP(x) SCM_SMOB_PREDICATE (scm_tc16_big, x)
 257 #define SCM_BIGSIGNFLAG 0x10000L
 258 #define SCM_BIGSIZEFIELD 17
 259 #define SCM_BIGSIGN(x) (SCM_UNPACK_CAR (x) & SCM_BIGSIGNFLAG)
 260 #define SCM_BDIGITS(x) ((SCM_BIGDIG *) SCM_UNPACK (SCM_CDR (x)))
 261 #define SCM_NUMDIGS(x) ((scm_sizet) (SCM_UNPACK_CAR (x) >> SCM_BIGSIZEFIELD))
 262 #define SCM_SETNUMDIGS(x, v, sign) \
 263   SCM_SET_CELL_WORD_0 (x, \
 264               scm_tc16_big \
 265               | ((sign) ? SCM_BIGSIGNFLAG : 0) \
 266               | (((v) + 0L) << SCM_BIGSIZEFIELD))
 267
 268 \f
 269
 270 typedef struct scm_dblproc
 271 {
 272   char *scm_string;
 273   double (*cproc) ();
 274 } scm_dblproc;
 275
 276 typedef struct scm_double_t
 277 {
 278   SCM type;
 279   SCM pad;
 280   double real;
 281 } scm_double_t;
 282
 283 typedef struct scm_complex_t
 284 {
 285   double real;
 286   double imag;
 287 } scm_complex_t;
 288
 289
 290 \f
 291
 292 extern SCM scm_exact_p (SCM x);
 293 extern SCM scm_odd_p (SCM n);
 294 extern SCM scm_even_p (SCM n);
 295 extern SCM scm_abs (SCM x);
 296 extern SCM scm_quotient (SCM x, SCM y);
 297 extern SCM scm_remainder (SCM x, SCM y);
 298 extern SCM scm_modulo (SCM x, SCM y);
 299 extern SCM scm_gcd (SCM x, SCM y);
 300 extern SCM scm_lcm (SCM n1, SCM n2);
 301 extern SCM scm_logand (SCM n1, SCM n2);
 302 extern SCM scm_logior (SCM n1, SCM n2);
 303 extern SCM scm_logxor (SCM n1, SCM n2);
 304 extern SCM scm_logtest (SCM n1, SCM n2);
 305 extern SCM scm_logbit_p (SCM n1, SCM n2);
 306 extern SCM scm_lognot (SCM n);
 307 extern SCM scm_integer_expt (SCM z1, SCM z2);
 308 extern SCM scm_ash (SCM n, SCM cnt);
 309 extern SCM scm_bit_extract (SCM n, SCM start, SCM end);
 310 extern SCM scm_logcount (SCM n);
 311 extern SCM scm_integer_length (SCM n);
 312 extern SCM scm_mkbig (scm_sizet nlen, int sign);
 313 extern SCM scm_big2inum (SCM b, scm_sizet l);
 314 extern SCM scm_adjbig (SCM b, scm_sizet nlen);
 315 extern SCM scm_normbig (SCM b);
 316 extern SCM scm_copybig (SCM b, int sign);
 317 extern SCM scm_long2big (long n);
 318 extern SCM scm_long_long2big (long_long n);
 319 extern SCM scm_2ulong2big (unsigned long * np);
 320 extern SCM scm_ulong2big (unsigned long n);
 321 extern int scm_bigcomp (SCM x, SCM y);
 322 extern long scm_pseudolong (long x);
 323 extern void scm_longdigs (long x, SCM_BIGDIG digs[]);
 324 extern SCM scm_addbig (SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int sgny);
 325 extern SCM scm_mulbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn);
 326 extern unsigned int scm_divbigdig (SCM_BIGDIG *ds, scm_sizet h, SCM_BIGDIG div);
 327 extern scm_sizet scm_iint2str (long num, int rad, char *p);
 328 extern SCM scm_number_to_string (SCM x, SCM radix);
 329 extern int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 330 extern int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 331 extern int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 332 extern SCM scm_istr2int (char *str, long len, long radix);
 333 extern SCM scm_istr2flo (char *str, long len, long radix);
 334 extern SCM scm_istring2number (char *str, long len, long radix);
 335 extern SCM scm_string_to_number (SCM str, SCM radix);
 336 extern SCM scm_make_real (double x);
 337 extern SCM scm_make_complex (double x, double y);
 338 extern SCM scm_makdbl (double x, double y); /* Deprecated */
 339 extern SCM scm_bigequal (SCM x, SCM y);
 340 extern SCM scm_real_equalp (SCM x, SCM y);
 341 extern SCM scm_complex_equalp (SCM x, SCM y);
 342 extern SCM scm_number_p (SCM x);
 343 extern SCM scm_real_p (SCM x);
 344 extern SCM scm_integer_p (SCM x);
 345 extern SCM scm_inexact_p (SCM x);
 346 extern SCM scm_num_eq_p (SCM x, SCM y);
 347 extern SCM scm_less_p (SCM x, SCM y);
 348 extern SCM scm_gr_p (SCM x, SCM y);
 349 extern SCM scm_leq_p (SCM x, SCM y);
 350 extern SCM scm_geq_p (SCM x, SCM y);
 351 extern SCM scm_zero_p (SCM z);
 352 extern SCM scm_positive_p (SCM x);
 353 extern SCM scm_negative_p (SCM x);
 354 extern SCM scm_max (SCM x, SCM y);
 355 extern SCM scm_min (SCM x, SCM y);
 356 extern SCM scm_sum (SCM x, SCM y);
 357 extern SCM scm_difference (SCM x, SCM y);
 358 extern SCM scm_product (SCM x, SCM y);
 359 extern double scm_num2dbl (SCM a, const char * why);
 360 extern SCM scm_divide (SCM x, SCM y);
 361 extern double scm_asinh (double x);
 362 extern double scm_acosh (double x);
 363 extern double scm_atanh (double x);
 364 extern double scm_truncate (double x);
 365 extern double scm_round (double x);
 366 extern double scm_exact_to_inexact (double z);
 367 extern SCM scm_sys_expt (SCM z1, SCM z2);
 368 extern SCM scm_sys_atan2 (SCM z1, SCM z2);
 369 extern SCM scm_make_rectangular (SCM z1, SCM z2);
 370 extern SCM scm_make_polar (SCM z1, SCM z2);
 371 extern SCM scm_real_part (SCM z);
 372 extern SCM scm_imag_part (SCM z);
 373 extern SCM scm_magnitude (SCM z);
 374 extern SCM scm_angle (SCM z);
 375 extern SCM scm_inexact_to_exact (SCM z);
 376 extern SCM scm_trunc (SCM x);
 377 extern SCM scm_dbl2big (double d);
 378 extern double scm_big2dbl (SCM b);
 379 extern SCM scm_long2num (long sl);
 380 extern SCM scm_long_long2num (long_long sl);
 381 extern SCM scm_ulong2num (unsigned long sl);
 382 extern long scm_num2long (SCM num, char *pos, const char *s_caller);
 383 extern long_long scm_num2long_long (SCM num, char *pos,
 384                                     const char *s_caller);
 385 extern unsigned long scm_num2ulong (SCM num, char *pos,
 386                                     const char *s_caller);
 387 extern void scm_init_numbers (void);
 388
 389 #endif  /* NUMBERSH */
 390
 391 /*
 392   Local Variables:
 393   c-file-style: "gnu"
 394   End:
 395 */