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 & (int)(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) (((SCM_ASWORD(x)<<1)<<1)+2L))
  75 #else
  76 # define SCM_MAKINUM(x) ((SCM)((SCM_ASWORD(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_ASWORD (x) >>1) >>1)
  89 # else
  90 #  define SCM_INUM(x) SCM_SRS (SCM_ASWORD (x), 2)
  91 # endif /* def __TURBOC__ */
  92 #else
  93 # define SCM_SRS(x, y)\
  94  ((SCM_ASWORD (x) < 0) ? ~( (~SCM_ASWORD (x)) >> y) : (SCM_ASWORD (x) >> y))
  95 # define SCM_INUM(x) SCM_SRS (SCM_ASWORD (x), 2)
  96 #endif /*  (-1==(((-1)<<2)+2)>>2) && (__TURBOC__ != 0x295) */
  97
  98
  99 /* A name for 0.
 100  */
 101 #define SCM_INUM0 ((SCM) 2)
 102
 103
 104
 105 /* SCM_FIXABLE is non-0 if its long argument can be encoded in an SCM_INUM.
 106  */
 107 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
 108 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
 109 #define SCM_UNEGFIXABLE(n) ((n) <= -SCM_MOST_NEGATIVE_FIXNUM)
 110 #define SCM_FIXABLE(n) (SCM_POSFIXABLE(n) && SCM_NEGFIXABLE(n))
 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
 116 #ifndef SCM_CHAR_BIT
 117 # define SCM_CHAR_BIT 8
 118 #endif /* ndef SCM_CHAR_BIT */
 119 #ifndef SCM_LONG_BIT
 120 # define SCM_LONG_BIT (SCM_CHAR_BIT*sizeof(long)/sizeof(char))
 121 #endif /* ndef SCM_LONG_BIT */
 122 #define SCM_INTBUFLEN (5+SCM_LONG_BIT)
 123
 124 /* SCM_FLOBUFLEN is the maximum number of characters neccessary for the
 125  * printed or scm_string representation of an inexact number.
 126  */
 127
 128 #define SCM_FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10)
 129
 130
 131 \f
 132
 133 /* Numbers
 134  */
 135
 136 #define SCM_INEXP(x) (SCM_NIMP(x) && (SCM_TYP16(x)==scm_tc16_flo))
 137 #define SCM_CPLXP(x) (SCM_NIMP(x) && (SCM_CARW (x)==scm_tc_dblc))
 138 #define SCM_REAL(x) (*(((scm_dbl *) (SCM2PTR(x)))->real))
 139 #define SCM_IMAG(x) (*((double *)(SCM_CHARS(x)+sizeof(double))))
 140 /* ((&SCM_REAL(x))[1]) */
 141
 142
 143 #ifdef SCM_SINGLES
 144 #define SCM_REALP(x) (SCM_NIMP(x) && ((~SCM_REAL_PART & SCM_CARW (x))==scm_tc_flo))
 145 #define SCM_SINGP(x) (SCM_NIMP(x) && (SCM_CARW (x)==scm_tc_flo))
 146 #define SCM_FLO(x) (((scm_flo *)(SCM2PTR(x)))->num)
 147 #define SCM_REALPART(x) (SCM_SINGP(x)?0.0+SCM_FLO(x):SCM_REAL(x))
 148 #else /* SCM_SINGLES */
 149 #define SCM_REALP(x) (SCM_NIMP(x) && (SCM_CAR(x)==scm_tc_dblr))
 150 #define SCM_REALPART SCM_REAL
 151 #endif /* SCM_SINGLES */
 152
 153
 154 /* Define SCM_BIGDIG to an integer type whose size is smaller than long if
 155  * you want bignums.  SCM_BIGRAD is one greater than the biggest SCM_BIGDIG.
 156  *
 157  * Define SCM_DIGSTOOBIG if the digits equivalent to a long won't fit in a long.
 158  */
 159 #ifdef BIGNUMS
 160 # ifdef _UNICOS
 161 #  define SCM_DIGSTOOBIG
 162 #  if (1L << 31) <= SCM_USHRT_MAX
 163 #   define SCM_BIGDIG unsigned  short
 164 #  else
 165 #   define SCM_BIGDIG unsigned int
 166 #  endif /*  (1L << 31) <= USHRT_MAX */
 167 #  define SCM_BITSPERDIG 32
 168 # else
 169 #  define SCM_BIGDIG unsigned short
 170 #  define SCM_BITSPERDIG (sizeof(SCM_BIGDIG)*SCM_CHAR_BIT)
 171 # endif /* def _UNICOS */
 172
 173 # define SCM_BIGRAD (1L << SCM_BITSPERDIG)
 174 # define SCM_DIGSPERLONG ((scm_sizet)((sizeof(long)*SCM_CHAR_BIT+SCM_BITSPERDIG-1)/SCM_BITSPERDIG))
 175 # define SCM_BIGUP(x) ((unsigned long)(x) << SCM_BITSPERDIG)
 176 # define SCM_LONGLONGBIGUP(x) ((ulong_long)(x) << SCM_BITSPERDIG)
 177 # define SCM_BIGDN(x) ((x) >> SCM_BITSPERDIG)
 178 # define SCM_BIGLO(x) ((x) & (SCM_BIGRAD-1))
 179
 180 #endif /* def BIGNUMS */
 181
 182 #ifndef SCM_BIGDIG
 183 /* Definition is not really used but helps various function
 184  * prototypes to compile with conditionalization.
 185  */
 186 # define SCM_BIGDIG unsigned short
 187 # define SCM_NO_BIGDIG
 188 # ifndef SCM_FLOATS
 189 #  define SCM_INUMS_ONLY
 190 # endif /* ndef SCM_FLOATS */
 191 #endif /* ndef SCM_BIGDIG */
 192
 193 #ifdef SCM_FLOATS
 194 #define SCM_NUMBERP(x) (SCM_INUMP(x) || (SCM_NIMP(x) && SCM_NUMP(x)))
 195 #ifdef SCM_BIGDIG
 196 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 197                         ? (double) SCM_INUM (x) \
 198                         : (SCM_REALP (x) \
 199                            ? SCM_REALPART (x) \
 200                            : scm_big2dbl (x)))
 201 #else
 202 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 203                         ? (double) SCM_INUM (x) \
 204                         : SCM_REALPART (x))
 205 #endif
 206 #else
 207 #ifdef SCM_BIGDIG
 208 #define SCM_NUMBERP(x) (SCM_INUMP(x) || (SCM_NIMP(x) && SCM_NUMP(x)))
 209 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 210                         ? (double) SCM_INUM (x) \
 211                         : scm_big2dbl (x))
 212 #else
 213 #define SCM_NUMBERP SCM_INUMP
 214 #define SCM_NUM2DBL(x) ((double) SCM_INUM (x))
 215 #endif
 216 #endif
 217 #define SCM_NUMP(x) (SCM_NIMP(x) && (0xfcff & (int)SCM_CAR(x))==scm_tc7_smob)
 218 #define SCM_BIGP(x) (SCM_NIMP(x) && SCM_TYP16S(x)==scm_tc16_bigpos)
 219 #define SCM_BIGSIGN(x) (0x0100 & (int)SCM_CAR(x))
 220 #define SCM_BDIGITS(x) ((SCM_BIGDIG *)(SCM_CDR(x)))
 221 #define SCM_NUMDIGS(x) ((scm_sizet)(SCM_CARW (x)>>16))
 222 #define SCM_SETNUMDIGS(x, v, t) SCM_SETCAR(x, (((v)+0L)<<16)+(t))
 223 \f
 224
 225 #ifdef SCM_FLOATS
 226 typedef struct scm_dblproc
 227 {
 228   char *scm_string;
 229   double (*cproc) ();
 230 } scm_dblproc;
 231
 232 #ifdef SCM_SINGLES
 233 typedef struct scm_flo
 234 {
 235   SCM type;
 236   float num;
 237 } scm_flo;
 238 #endif
 239
 240 typedef struct scm_dbl
 241 {
 242   SCM type;
 243   double *real;
 244 } scm_dbl;
 245 #endif
 246
 247
 248
 249 \f
 250
 251 extern SCM scm_exact_p (SCM x);
 252 extern SCM scm_odd_p (SCM n);
 253 extern SCM scm_even_p (SCM n);
 254 extern SCM scm_abs (SCM x);
 255 extern SCM scm_quotient (SCM x, SCM y);
 256 extern SCM scm_remainder (SCM x, SCM y);
 257 extern SCM scm_modulo (SCM x, SCM y);
 258 extern SCM scm_gcd (SCM x, SCM y);
 259 extern SCM scm_lcm (SCM n1, SCM n2);
 260 extern SCM scm_logand (SCM n1, SCM n2);
 261 extern SCM scm_logior (SCM n1, SCM n2);
 262 extern SCM scm_logxor (SCM n1, SCM n2);
 263 extern SCM scm_logtest (SCM n1, SCM n2);
 264 extern SCM scm_logbit_p (SCM n1, SCM n2);
 265 extern SCM scm_lognot (SCM n);
 266 extern SCM scm_integer_expt (SCM z1, SCM z2);
 267 extern SCM scm_ash (SCM n, SCM cnt);
 268 extern SCM scm_bit_extract (SCM n, SCM start, SCM end);
 269 extern SCM scm_logcount (SCM n);
 270 extern SCM scm_integer_length (SCM n);
 271 extern SCM scm_mkbig (scm_sizet nlen, int sign);
 272 extern SCM scm_big2inum (SCM b, scm_sizet l);
 273 extern SCM scm_adjbig (SCM b, scm_sizet nlen);
 274 extern SCM scm_normbig (SCM b);
 275 extern SCM scm_copybig (SCM b, int sign);
 276 extern SCM scm_long2big (long n);
 277 extern SCM scm_long_long2big (long_long n);
 278 extern SCM scm_2ulong2big (unsigned long * np);
 279 extern SCM scm_ulong2big (unsigned long n);
 280 extern int scm_bigcomp (SCM x, SCM y);
 281 extern long scm_pseudolong (long x);
 282 extern void scm_longdigs (long x, SCM_BIGDIG digs[]);
 283 extern SCM scm_addbig (SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int sgny);
 284 extern SCM scm_mulbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn);
 285 extern unsigned int scm_divbigdig (SCM_BIGDIG *ds, scm_sizet h, SCM_BIGDIG div);
 286 extern SCM scm_divbigint (SCM x, long z, int sgn, int mode);
 287 extern SCM scm_divbigbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn, int modes);
 288 extern scm_sizet scm_iint2str (long num, int rad, char *p);
 289 extern SCM scm_number_to_string (SCM x, SCM radix);
 290 extern int scm_floprint (SCM sexp, SCM port, scm_print_state *pstate);
 291 extern int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 292 extern SCM scm_istr2int (char *str, long len, long radix);
 293 extern SCM scm_istr2flo (char *str, long len, long radix);
 294 extern SCM scm_istring2number (char *str, long len, long radix);
 295 extern SCM scm_string_to_number (SCM str, SCM radix);
 296 extern SCM scm_makdbl (double x, double y);
 297 extern SCM scm_bigequal (SCM x, SCM y);
 298 extern SCM scm_floequal (SCM x, SCM y);
 299 extern SCM scm_number_p (SCM x);
 300 extern SCM scm_real_p (SCM x);
 301 extern SCM scm_integer_p (SCM x);
 302 extern SCM scm_inexact_p (SCM x);
 303 extern SCM scm_num_eq_p (SCM x, SCM y);
 304 extern SCM scm_less_p (SCM x, SCM y);
 305 extern SCM scm_gr_p (SCM x, SCM y);
 306 extern SCM scm_leq_p (SCM x, SCM y);
 307 extern SCM scm_geq_p (SCM x, SCM y);
 308 extern SCM scm_zero_p (SCM z);
 309 extern SCM scm_positive_p (SCM x);
 310 extern SCM scm_negative_p (SCM x);
 311 extern SCM scm_max (SCM x, SCM y);
 312 extern SCM scm_min (SCM x, SCM y);
 313 extern SCM scm_sum (SCM x, SCM y);
 314 extern SCM scm_difference (SCM x, SCM y);
 315 extern SCM scm_product (SCM x, SCM y);
 316 extern double scm_num2dbl (SCM a, const char * why);
 317 extern SCM scm_divide (SCM x, SCM y);
 318 extern double scm_asinh (double x);
 319 extern double scm_acosh (double x);
 320 extern double scm_atanh (double x);
 321 extern double scm_truncate (double x);
 322 extern double scm_round (double x);
 323 extern double scm_exact_to_inexact (double z);
 324 extern SCM scm_sys_expt (SCM z1, SCM z2);
 325 extern SCM scm_sys_atan2 (SCM z1, SCM z2);
 326 extern SCM scm_make_rectangular (SCM z1, SCM z2);
 327 extern SCM scm_make_polar (SCM z1, SCM z2);
 328 extern SCM scm_real_part (SCM z);
 329 extern SCM scm_imag_part (SCM z);
 330 extern SCM scm_magnitude (SCM z);
 331 extern SCM scm_angle (SCM z);
 332 extern SCM scm_inexact_to_exact (SCM z);
 333 extern SCM scm_trunc (SCM x);
 334 extern SCM scm_dbl2big (double d);
 335 extern double scm_big2dbl (SCM b);
 336 extern SCM scm_long2num (long sl);
 337 extern SCM scm_long_long2num (long_long sl);
 338 extern SCM scm_ulong2num (unsigned long sl);
 339 extern long scm_num2long (SCM num, char *pos, const char *s_caller);
 340 extern long_long scm_num2long_long (SCM num, char *pos,
 341                                     const char *s_caller);
 342 extern unsigned long scm_num2ulong (SCM num, char *pos,
 343                                     const char *s_caller);
 344 extern void scm_init_numbers (void);
 345
 346 #endif  /* NUMBERSH */