libguile/numbers.h

   1 /* classes: h_files */
   2
   3 #ifndef NUMBERSH
   4 #define NUMBERSH
   5 /*      Copyright (C) 1995, 1996, 1998 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 \f
  46
  47 #include "libguile/__scm.h"
  48
  49 #include "libguile/print.h"
  50
  51 \f
  52
  53
  54 /* Immediate Numbers
  55  *
  56  * Inums are exact integer data that fits within an SCM word.
  57  *
  58  * SCM_INUMP applies only to values known to be Scheme objects.
  59  * In particular, SCM_INUMP (SCM_CAR (x)) is valid only if x is known
  60  * to be a SCM_CONSP.  If x is only known to be a SCM_NIMP,
  61  * SCM_INUMP (SCM_CAR (x)) can give wrong answers.
  62  */
  63
  64 #define SCM_INUMP(x)    (2 & (int)(x))
  65 #define SCM_NINUMP(x)   (!SCM_INUMP(x))
  66
  67 #ifdef __TURBOC__
  68 /* shifts of more than one are done by a library call, single shifts are
  69  * performed in registers
  70  */
  71 # define SCM_MAKINUM(x) ((((x)<<1)<<1)+2L)
  72 #else
  73 # define SCM_MAKINUM(x) (((x)<<2)+2L)
  74 #endif /* def __TURBOC__ */
  75
  76
  77 /* SCM_SRS is signed right shift */
  78 /* Turbo C++ v1.0 has a bug with right shifts of signed longs!
  79  * It is believed to be fixed in Turbo C++ v1.01
  80  */
  81 #if (-1==(((-1)<<2)+2)>>2) && (__TURBOC__ != 0x295)
  82 # define SCM_SRS(x, y) ((x)>>y)
  83 # ifdef __TURBOC__
  84 #  define SCM_INUM(x) (((x)>>1)>>1)
  85 # else
  86 #  define SCM_INUM(x) SCM_SRS(x, 2)
  87 # endif /* def __TURBOC__ */
  88 #else
  89 # define SCM_SRS(x, y) (((x)<0) ? ~((~(x))>>y) : (x)>>y)
  90 # define SCM_INUM(x) SCM_SRS(x, 2)
  91 #endif /*  (-1==(((-1)<<2)+2)>>2) && (__TURBOC__ != 0x295) */
  92
  93
  94 /* A name for 0.
  95  */
  96 #define SCM_INUM0 ((SCM) 2)
  97
  98
  99
 100 /* SCM_FIXABLE is non-0 if its long argument can be encoded in an SCM_INUM.
 101  */
 102 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
 103 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
 104 #define SCM_UNEGFIXABLE(n) ((n) <= -SCM_MOST_NEGATIVE_FIXNUM)
 105 #define SCM_FIXABLE(n) (SCM_POSFIXABLE(n) && SCM_NEGFIXABLE(n))
 106
 107 /* SCM_INTBUFLEN is the maximum number of characters neccessary for the
 108  * printed or scm_string representation of an exact immediate.
 109  */
 110
 111 #ifndef SCM_CHAR_BIT
 112 # define SCM_CHAR_BIT 8
 113 #endif /* ndef SCM_CHAR_BIT */
 114 #ifndef SCM_LONG_BIT
 115 # define SCM_LONG_BIT (SCM_CHAR_BIT*sizeof(long)/sizeof(char))
 116 #endif /* ndef SCM_LONG_BIT */
 117 #define SCM_INTBUFLEN (5+SCM_LONG_BIT)
 118
 119 /* SCM_FLOBUFLEN is the maximum number of characters neccessary for the
 120  * printed or scm_string representation of an inexact number.
 121  */
 122
 123 #define SCM_FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10)
 124
 125
 126 \f
 127
 128 /* Numbers
 129  */
 130
 131 #define SCM_INEXP(x) (SCM_TYP16(x)==scm_tc16_flo)
 132 #define SCM_CPLXP(x) (SCM_CAR(x)==scm_tc_dblc)
 133 #define SCM_REAL(x) (*(((scm_dbl *) (SCM2PTR(x)))->real))
 134 #define SCM_IMAG(x) (*((double *)(SCM_CHARS(x)+sizeof(double))))
 135 /* ((&SCM_REAL(x))[1]) */
 136
 137
 138 #ifdef SCM_SINGLES
 139 #define SCM_REALP(x) ((~SCM_REAL_PART & SCM_CAR(x))==scm_tc_flo)
 140 #define SCM_SINGP(x) (SCM_CAR(x)==scm_tc_flo)
 141 #define SCM_FLO(x) (((scm_flo *)(SCM2PTR(x)))->num)
 142 #define SCM_REALPART(x) (SCM_SINGP(x)?0.0+SCM_FLO(x):SCM_REAL(x))
 143 #else /* SCM_SINGLES */
 144 #define SCM_REALP(x) (SCM_CAR(x)==scm_tc_dblr)
 145 #define SCM_REALPART SCM_REAL
 146 #endif /* SCM_SINGLES */
 147
 148
 149 /* Define SCM_BIGDIG to an integer type whose size is smaller than long if
 150  * you want bignums.  SCM_BIGRAD is one greater than the biggest SCM_BIGDIG.
 151  *
 152  * Define SCM_DIGSTOOBIG if the digits equivalent to a long won't fit in a long.
 153  */
 154 #ifdef BIGNUMS
 155 # ifdef _UNICOS
 156 #  define SCM_DIGSTOOBIG
 157 #  if (1L << 31) <= SCM_USHRT_MAX
 158 #   define SCM_BIGDIG unsigned  short
 159 #  else
 160 #   define SCM_BIGDIG unsigned int
 161 #  endif /*  (1L << 31) <= USHRT_MAX */
 162 #  define SCM_BITSPERDIG 32
 163 # else
 164 #  define SCM_BIGDIG unsigned short
 165 #  define SCM_BITSPERDIG (sizeof(SCM_BIGDIG)*SCM_CHAR_BIT)
 166 # endif /* def _UNICOS */
 167
 168 # define SCM_BIGRAD (1L << SCM_BITSPERDIG)
 169 # define SCM_DIGSPERLONG ((scm_sizet)((sizeof(long)*SCM_CHAR_BIT+SCM_BITSPERDIG-1)/SCM_BITSPERDIG))
 170 # define SCM_BIGUP(x) ((unsigned long)(x) << SCM_BITSPERDIG)
 171 # define SCM_LONGLONGBIGUP(x) ((ulong_long)(x) << SCM_BITSPERDIG)
 172 # define SCM_BIGDN(x) ((x) >> SCM_BITSPERDIG)
 173 # define SCM_BIGLO(x) ((x) & (SCM_BIGRAD-1))
 174
 175 #endif /* def BIGNUMS */
 176
 177 #ifndef SCM_BIGDIG
 178 /* Definition is not really used but helps various function
 179  * prototypes to compile with conditionalization.
 180  */
 181 # define SCM_BIGDIG unsigned short
 182 # define SCM_NO_BIGDIG
 183 # ifndef SCM_FLOATS
 184 #  define SCM_INUMS_ONLY
 185 # endif /* ndef SCM_FLOATS */
 186 #endif /* ndef SCM_BIGDIG */
 187
 188 #ifdef SCM_FLOATS
 189 #define SCM_NUMBERP(x) (SCM_INUMP(x) || (SCM_NIMP(x) && SCM_NUMP(x)))
 190 #ifdef SCM_BIGDIG
 191 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 192                         ? (double) SCM_INUM (x) \
 193                         : (SCM_REALP (x) \
 194                            ? SCM_REALPART (x) \
 195                            : scm_big2dbl (x)))
 196 #else
 197 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 198                         ? (double) SCM_INUM (x) \
 199                         : SCM_REALPART (x))
 200 #endif
 201 #else
 202 #ifdef SCM_BIGDIG
 203 #define SCM_NUMBERP(x) (SCM_INUMP(x) || (SCM_NIMP(x) && SCM_NUMP(x)))
 204 #define SCM_NUM2DBL(x) (SCM_INUMP (x) \
 205                         ? (double) SCM_INUM (x) \
 206                         : scm_big2dbl (x))
 207 #else
 208 #define SCM_NUMBERP SCM_INUMP
 209 #define SCM_NUM2DBL(x) ((double) SCM_INUM (x))
 210 #endif
 211 #endif
 212 #define SCM_NUMP(x) ((0xfcff & (int)SCM_CAR(x))==scm_tc7_smob)
 213 #define SCM_BIGP(x) (SCM_TYP16S(x)==scm_tc16_bigpos)
 214 #define SCM_BIGSIGN(x) (0x0100 & (int)SCM_CAR(x))
 215 #define SCM_BDIGITS(x) ((SCM_BIGDIG *)(SCM_CDR(x)))
 216 #define SCM_NUMDIGS(x) ((scm_sizet)(SCM_CAR(x)>>16))
 217 #define SCM_SETNUMDIGS(x, v, t) SCM_SETCAR(x, (((v)+0L)<<16)+(t))
 218 \f
 219
 220 #ifdef SCM_FLOATS
 221 typedef struct scm_dblproc
 222 {
 223   char *scm_string;
 224   double (*cproc) ();
 225 } scm_dblproc;
 226
 227 #ifdef SCM_SINGLES
 228 typedef struct scm_flo
 229 {
 230   SCM type;
 231   float num;
 232 } scm_flo;
 233 #endif
 234
 235 typedef struct scm_dbl
 236 {
 237   SCM type;
 238   double *real;
 239 } scm_dbl;
 240 #endif
 241
 242
 243
 244 \f
 245
 246 extern SCM scm_exact_p SCM_P ((SCM x));
 247 extern SCM scm_odd_p SCM_P ((SCM n));
 248 extern SCM scm_even_p SCM_P ((SCM n));
 249 extern SCM scm_abs SCM_P ((SCM x));
 250 extern SCM scm_quotient SCM_P ((SCM x, SCM y));
 251 extern SCM scm_remainder SCM_P ((SCM x, SCM y));
 252 extern SCM scm_modulo SCM_P ((SCM x, SCM y));
 253 extern SCM scm_gcd SCM_P ((SCM x, SCM y));
 254 extern SCM scm_lcm SCM_P ((SCM n1, SCM n2));
 255 extern SCM scm_logand SCM_P ((SCM n1, SCM n2));
 256 extern SCM scm_logior SCM_P ((SCM n1, SCM n2));
 257 extern SCM scm_logxor SCM_P ((SCM n1, SCM n2));
 258 extern SCM scm_logtest SCM_P ((SCM n1, SCM n2));
 259 extern SCM scm_logbit_p SCM_P ((SCM n1, SCM n2));
 260 extern SCM scm_lognot SCM_P ((SCM n));
 261 extern SCM scm_integer_expt SCM_P ((SCM z1, SCM z2));
 262 extern SCM scm_ash SCM_P ((SCM n, SCM cnt));
 263 extern SCM scm_bit_extract SCM_P ((SCM n, SCM start, SCM end));
 264 extern SCM scm_logcount SCM_P ((SCM n));
 265 extern SCM scm_integer_length SCM_P ((SCM n));
 266 extern SCM scm_mkbig SCM_P ((scm_sizet nlen, int sign));
 267 extern SCM scm_big2inum SCM_P ((SCM b, scm_sizet l));
 268 extern SCM scm_adjbig SCM_P ((SCM b, scm_sizet nlen));
 269 extern SCM scm_normbig SCM_P ((SCM b));
 270 extern SCM scm_copybig SCM_P ((SCM b, int sign));
 271 extern SCM scm_long2big SCM_P ((long n));
 272 extern SCM scm_long_long2big SCM_P ((long_long n));
 273 extern SCM scm_2ulong2big SCM_P ((unsigned long * np));
 274 extern SCM scm_ulong2big SCM_P ((unsigned long n));
 275 extern int scm_bigcomp SCM_P ((SCM x, SCM y));
 276 extern long scm_pseudolong SCM_P ((long x));
 277 extern void scm_longdigs SCM_P ((long x, SCM_BIGDIG digs[]));
 278 extern SCM scm_addbig SCM_P ((SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int sgny));
 279 extern SCM scm_mulbig SCM_P ((SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn));
 280 extern unsigned int scm_divbigdig SCM_P ((SCM_BIGDIG *ds, scm_sizet h, SCM_BIGDIG div));
 281 extern SCM scm_divbigint SCM_P ((SCM x, long z, int sgn, int mode));
 282 extern SCM scm_divbigbig SCM_P ((SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn, int modes));
 283 extern scm_sizet scm_iint2str SCM_P ((long num, int rad, char *p));
 284 extern SCM scm_number_to_string SCM_P ((SCM x, SCM radix));
 285 extern int scm_floprint SCM_P ((SCM sexp, SCM port, scm_print_state *pstate));
 286 extern int scm_bigprint SCM_P ((SCM exp, SCM port, scm_print_state *pstate));
 287 extern SCM scm_istr2int SCM_P ((char *str, long len, long radix));
 288 extern SCM scm_istr2flo SCM_P ((char *str, long len, long radix));
 289 extern SCM scm_istring2number SCM_P ((char *str, long len, long radix));
 290 extern SCM scm_string_to_number SCM_P ((SCM str, SCM radix));
 291 extern SCM scm_makdbl SCM_P ((double x, double y));
 292 extern SCM scm_bigequal SCM_P ((SCM x, SCM y));
 293 extern SCM scm_floequal SCM_P ((SCM x, SCM y));
 294 extern SCM scm_number_p SCM_P ((SCM x));
 295 extern SCM scm_real_p SCM_P ((SCM x));
 296 extern SCM scm_integer_p SCM_P ((SCM x));
 297 extern SCM scm_inexact_p SCM_P ((SCM x));
 298 extern SCM scm_num_eq_p SCM_P ((SCM x, SCM y));
 299 extern SCM scm_less_p SCM_P ((SCM x, SCM y));
 300 extern SCM scm_gr_p SCM_P ((SCM x, SCM y));
 301 extern SCM scm_leq_p SCM_P ((SCM x, SCM y));
 302 extern SCM scm_geq_p SCM_P ((SCM x, SCM y));
 303 extern SCM scm_zero_p SCM_P ((SCM z));
 304 extern SCM scm_positive_p SCM_P ((SCM x));
 305 extern SCM scm_negative_p SCM_P ((SCM x));
 306 extern SCM scm_max SCM_P ((SCM x, SCM y));
 307 extern SCM scm_min SCM_P ((SCM x, SCM y));
 308 extern SCM scm_sum SCM_P ((SCM x, SCM y));
 309 extern SCM scm_difference SCM_P ((SCM x, SCM y));
 310 extern SCM scm_product SCM_P ((SCM x, SCM y));
 311 extern double scm_num2dbl SCM_P ((SCM a, const char * why));
 312 extern SCM scm_divide SCM_P ((SCM x, SCM y));
 313 extern double scm_asinh SCM_P ((double x));
 314 extern double scm_acosh SCM_P ((double x));
 315 extern double scm_atanh SCM_P ((double x));
 316 extern double scm_truncate SCM_P ((double x));
 317 extern double scm_round SCM_P ((double x));
 318 extern double scm_exact_to_inexact SCM_P ((double z));
 319 extern SCM scm_sys_expt SCM_P ((SCM z1, SCM z2));
 320 extern SCM scm_sys_atan2 SCM_P ((SCM z1, SCM z2));
 321 extern SCM scm_make_rectangular SCM_P ((SCM z1, SCM z2));
 322 extern SCM scm_make_polar SCM_P ((SCM z1, SCM z2));
 323 extern SCM scm_real_part SCM_P ((SCM z));
 324 extern SCM scm_imag_part SCM_P ((SCM z));
 325 extern SCM scm_magnitude SCM_P ((SCM z));
 326 extern SCM scm_angle SCM_P ((SCM z));
 327 extern SCM scm_inexact_to_exact SCM_P ((SCM z));
 328 extern SCM scm_trunc SCM_P ((SCM x));
 329 extern SCM scm_dbl2big SCM_P ((double d));
 330 extern double scm_big2dbl SCM_P ((SCM b));
 331 extern SCM scm_long2num SCM_P ((long sl));
 332 extern SCM scm_long_long2num SCM_P ((long_long sl));
 333 extern SCM scm_ulong2num SCM_P ((unsigned long sl));
 334 extern long scm_num2long SCM_P ((SCM num, char *pos, const char *s_caller));
 335 extern long_long scm_num2long_long SCM_P ((SCM num, char *pos,
 336                                            const char *s_caller));
 337 extern unsigned long scm_num2ulong SCM_P ((SCM num, char *pos,
 338                                            const char *s_caller));
 339 extern void scm_init_numbers SCM_P ((void));
 340
 341 #endif  /* NUMBERSH */