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 Free Software Foundation, Inc.
   7  *
   8  * This program is free software; you can redistribute it and/or modify
   9  * it under the terms of the GNU General Public License as published by
  10  * the Free Software Foundation; either version 2, or (at your option)
  11  * any later version.
  12  *
  13  * This program 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
  16  * GNU General Public License for more details.
  17  *
  18  * You should have received a copy of the GNU General Public License
  19  * along with this software; see the file COPYING.  If not, write to
  20  * the Free Software Foundation, Inc., 59 Temple Place, Suite 330,
  21  * Boston, MA 02111-1307 USA
  22  *
  23  * As a special exception, the Free Software Foundation gives permission
  24  * for additional uses of the text contained in its release of GUILE.
  25  *
  26  * The exception is that, if you link the GUILE library with other files
  27  * to produce an executable, this does not by itself cause the
  28  * resulting executable to be covered by the GNU General Public License.
  29  * Your use of that executable is in no way restricted on account of
  30  * linking the GUILE library code into it.
  31  *
  32  * This exception does not however invalidate any other reasons why
  33  * the executable file might be covered by the GNU General Public License.
  34  *
  35  * This exception applies only to the code released by the
  36  * Free Software Foundation under the name GUILE.  If you copy
  37  * code from other Free Software Foundation releases into a copy of
  38  * GUILE, as the General Public License permits, the exception does
  39  * not apply to the code that you add in this way.  To avoid misleading
  40  * anyone as to the status of such modified files, you must delete
  41  * this exception notice from them.
  42  *
  43  * If you write modifications of your own for GUILE, it is your choice
  44  * whether to permit this exception to apply to your modifications.
  45  * If you do not wish that, delete this exception notice.  */
  46
  47 \f
  48
  49 #include "libguile/__scm.h"
  50 #include "libguile/print.h"
  51
  52 #if SCM_HAVE_FLOATINGPOINT_H
  53 # include <floatingpoint.h>
  54 #endif
  55
  56 #if SCM_HAVE_IEEEFP_H
  57 # include <ieeefp.h>
  58 #endif
  59
  60 #if SCM_HAVE_NAN_H
  61 # if defined (SCO)
  62 #   define _IEEE 1
  63 # endif
  64 # include <nan.h>
  65 # if defined (SCO)
  66 #   undef _IEEE
  67 # endif
  68 #endif /* SCM_HAVE_NAN_H */
  69
  70 \f
  71
  72 /* Immediate Numbers, also known as fixnums
  73  *
  74  * Inums are exact integer data that fits within an SCM word.  */
  75
  76 /* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
  77  * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
  78  * which is the same as                (/ (- (expt 2 n) 4) 4)
  79  */
  80
  81 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  82 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  83 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  84
  85 /* SCM_SRS is signed right shift */
  86 #if (-1 == (((-1) << 2) + 2) >> 2)
  87 # define SCM_SRS(x, y) ((x) >> (y))
  88 #else
  89 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  90 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  91
  92
  93 #define SCM_INUMP(x)    (2 & SCM_UNPACK (x))
  94 #define SCM_NINUMP(x)   (!SCM_INUMP (x))
  95 #define SCM_MAKINUM(x)  (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + 2))
  96 #define SCM_INUM(x)     (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  97
  98
  99 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
 100 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
 101 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
 102 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
 103
 104
 105 /* A name for 0. */
 106 #define SCM_INUM0 (SCM_MAKINUM (0))
 107
 108
 109 /* SCM_MAXEXP is the maximum double precision exponent
 110  * SCM_FLTMAX is less than or scm_equal the largest single precision float
 111  */
 112
 113 #if SCM_HAVE_STDC_HEADERS
 114 # ifndef GO32
 115 #   include <float.h>
 116 # endif /* ndef GO32 */
 117 #endif /* def STDC_HEADERS */
 118
 119 #ifdef DBL_MAX_10_EXP
 120 # define SCM_MAXEXP DBL_MAX_10_EXP
 121 #else
 122 # define SCM_MAXEXP 308         /* IEEE doubles */
 123 #endif /* def DBL_MAX_10_EXP */
 124
 125 #ifdef FLT_MAX
 126 # define SCM_FLTMAX FLT_MAX
 127 #else
 128 # define SCM_FLTMAX 1e+23
 129 #endif /* def FLT_MAX */
 130
 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 #define SCM_INTBUFLEN (5 + SCM_LONG_BIT)
 136
 137 \f
 138
 139 /* Numbers
 140  */
 141
 142 #define SCM_SLOPPY_INEXACTP(x) (SCM_TYP16S (x) == scm_tc16_real)
 143 #define SCM_SLOPPY_REALP(x) (SCM_TYP16 (x) == scm_tc16_real)
 144 #define SCM_SLOPPY_COMPLEXP(x) (SCM_TYP16 (x) == scm_tc16_complex)
 145 #define SCM_INEXACTP(x) (!SCM_IMP (x) && SCM_TYP16S (x) == scm_tc16_real)
 146 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 147 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 148
 149 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 150 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 151 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 152 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 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 ((size_t)((sizeof(long)*SCM_CHAR_BIT+SCM_BITSPERDIG-1)/SCM_BITSPERDIG))
 175 # define SCM_I_BIGUP(type, x) ((type)(x) << SCM_BITSPERDIG)
 176 # define SCM_BIGUP(x) SCM_I_BIGUP (unsigned long, x)
 177 # define SCM_LONGLONGBIGUP(x) SCM_I_BIGUP (unsigned long long, x)
 178 # define SCM_BIGDN(x) ((x) >> SCM_BITSPERDIG)
 179 # define SCM_BIGLO(x) ((x) & (SCM_BIGRAD-1))
 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 #endif /* ndef SCM_BIGDIG */
 188
 189 #define SCM_NUMBERP(x) (SCM_INUMP(x) || SCM_NUMP(x))
 190 #define SCM_NUMP(x) (!SCM_IMP(x) && (0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_smob)
 191 #define SCM_BIGP(x) (!SCM_IMP (x) && (SCM_TYP16 (x) == scm_tc16_big))
 192 #define SCM_BIGSIGNFLAG 0x10000L
 193 #define SCM_BIGSIZEFIELD 17
 194 #define SCM_BIGSIGN(x) (SCM_CELL_WORD_0 (x) & SCM_BIGSIGNFLAG)
 195 #define SCM_BDIGITS(x) ((SCM_BIGDIG *) (SCM_CELL_WORD_1 (x)))
 196 #define SCM_SET_BIGNUM_BASE(n, b) (SCM_SET_CELL_WORD_1 ((n), (b)))
 197 #define SCM_NUMDIGS(x) ((size_t) (SCM_CELL_WORD_0 (x) >> SCM_BIGSIZEFIELD))
 198 #define SCM_MAKE_BIGNUM_TAG(v, sign)              \
 199               (scm_tc16_big                       \
 200                | ((sign) ? SCM_BIGSIGNFLAG : 0)   \
 201                | (((v) + 0L) << SCM_BIGSIZEFIELD))
 202 #define SCM_SETNUMDIGS(x, v, sign) \
 203   SCM_SET_CELL_WORD_0 (x, SCM_MAKE_BIGNUM_TAG (v, sign))
 204
 205 \f
 206
 207 typedef struct scm_t_double
 208 {
 209   SCM type;
 210   SCM pad;
 211   double real;
 212 } scm_t_double;
 213
 214 typedef struct scm_t_complex
 215 {
 216   double real;
 217   double imag;
 218 } scm_t_complex;
 219
 220 \f
 221
 222 SCM_API SCM scm_exact_p (SCM x);
 223 SCM_API SCM scm_odd_p (SCM n);
 224 SCM_API SCM scm_even_p (SCM n);
 225 SCM_API SCM scm_inf_p (SCM n);
 226 SCM_API SCM scm_nan_p (SCM n);
 227 SCM_API SCM scm_inf (void);
 228 SCM_API SCM scm_nan (void);
 229 SCM_API SCM scm_abs (SCM x);
 230 SCM_API SCM scm_quotient (SCM x, SCM y);
 231 SCM_API SCM scm_remainder (SCM x, SCM y);
 232 SCM_API SCM scm_modulo (SCM x, SCM y);
 233 SCM_API SCM scm_gcd (SCM x, SCM y);
 234 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 235 SCM_API SCM scm_logand (SCM n1, SCM n2);
 236 SCM_API SCM scm_logior (SCM n1, SCM n2);
 237 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 238 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 239 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 240 SCM_API SCM scm_lognot (SCM n);
 241 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 242 SCM_API SCM scm_ash (SCM n, SCM cnt);
 243 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 244 SCM_API SCM scm_logcount (SCM n);
 245 SCM_API SCM scm_integer_length (SCM n);
 246 SCM_API SCM scm_i_mkbig (size_t nlen, int sign);
 247 SCM_API SCM scm_i_big2inum (SCM b, size_t l);
 248 SCM_API SCM scm_i_adjbig (SCM b, size_t nlen);
 249 SCM_API SCM scm_i_normbig (SCM b);
 250 SCM_API SCM scm_i_copybig (SCM b, int sign);
 251 SCM_API SCM scm_i_short2big (short n);
 252 SCM_API SCM scm_i_ushort2big (unsigned short n);
 253 SCM_API SCM scm_i_int2big (int n);
 254 SCM_API SCM scm_i_uint2big (unsigned int n);
 255 SCM_API SCM scm_i_long2big (long n);
 256 SCM_API SCM scm_i_ulong2big (unsigned long n);
 257 SCM_API SCM scm_i_size2big (size_t n);
 258 SCM_API SCM scm_i_ptrdiff2big (scm_t_ptrdiff n);
 259
 260 #if SCM_SIZEOF_LONG_LONG != 0
 261 SCM_API SCM scm_i_long_long2big (long long n);
 262 SCM_API SCM scm_i_ulong_long2big (unsigned long long n);
 263 #endif
 264
 265 SCM_API int scm_bigcomp (SCM x, SCM y);
 266 SCM_API long scm_pseudolong (long x);
 267 SCM_API void scm_longdigs (long x, SCM_BIGDIG digs[]);
 268 SCM_API SCM scm_addbig (SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int sgny);
 269 SCM_API SCM scm_mulbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn);
 270 SCM_API unsigned int scm_divbigdig (SCM_BIGDIG *ds, size_t h, SCM_BIGDIG div);
 271 SCM_API size_t scm_iint2str (long num, int rad, char *p);
 272 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 273 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 274 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 275 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 276 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
 277 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 278 SCM_API SCM scm_make_real (double x);
 279 SCM_API SCM scm_make_complex (double x, double y);
 280 SCM_API SCM scm_bigequal (SCM x, SCM y);
 281 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 282 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 283 SCM_API SCM scm_number_p (SCM x);
 284 SCM_API SCM scm_real_p (SCM x);
 285 SCM_API SCM scm_integer_p (SCM x);
 286 SCM_API SCM scm_inexact_p (SCM x);
 287 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 288 SCM_API SCM scm_less_p (SCM x, SCM y);
 289 SCM_API SCM scm_gr_p (SCM x, SCM y);
 290 SCM_API SCM scm_leq_p (SCM x, SCM y);
 291 SCM_API SCM scm_geq_p (SCM x, SCM y);
 292 SCM_API SCM scm_zero_p (SCM z);
 293 SCM_API SCM scm_positive_p (SCM x);
 294 SCM_API SCM scm_negative_p (SCM x);
 295 SCM_API SCM scm_max (SCM x, SCM y);
 296 SCM_API SCM scm_min (SCM x, SCM y);
 297 SCM_API SCM scm_sum (SCM x, SCM y);
 298 SCM_API SCM scm_difference (SCM x, SCM y);
 299 SCM_API SCM scm_product (SCM x, SCM y);
 300 SCM_API double scm_num2dbl (SCM a, const char * why);
 301 SCM_API SCM scm_divide (SCM x, SCM y);
 302 SCM_API double scm_asinh (double x);
 303 SCM_API double scm_acosh (double x);
 304 SCM_API double scm_atanh (double x);
 305 SCM_API double scm_truncate (double x);
 306 SCM_API double scm_round (double x);
 307 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 308 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 309 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 310 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 311 SCM_API SCM scm_real_part (SCM z);
 312 SCM_API SCM scm_imag_part (SCM z);
 313 SCM_API SCM scm_magnitude (SCM z);
 314 SCM_API SCM scm_angle (SCM z);
 315 SCM_API SCM scm_exact_to_inexact (SCM z);
 316 SCM_API SCM scm_inexact_to_exact (SCM z);
 317 SCM_API SCM scm_trunc (SCM x);
 318 SCM_API SCM scm_i_dbl2big (double d);
 319 SCM_API double scm_i_big2dbl (SCM b);
 320
 321 SCM_API SCM scm_short2num (short n);
 322 SCM_API SCM scm_ushort2num (unsigned short n);
 323 SCM_API SCM scm_int2num (int n);
 324 SCM_API SCM scm_uint2num (unsigned int n);
 325 SCM_API SCM scm_long2num (long n);
 326 SCM_API SCM scm_ulong2num (unsigned long n);
 327 SCM_API SCM scm_size2num (size_t n);
 328 SCM_API SCM scm_ptrdiff2num (scm_t_ptrdiff n);
 329 SCM_API short scm_num2short (SCM num, unsigned long int pos,
 330                              const char *s_caller);
 331 SCM_API unsigned short scm_num2ushort (SCM num, unsigned long int pos,
 332                                        const char *s_caller);
 333 SCM_API int scm_num2int (SCM num, unsigned long int pos,
 334                          const char *s_caller);
 335 SCM_API unsigned int scm_num2uint (SCM num, unsigned long int pos,
 336                                    const char *s_caller);
 337 SCM_API long scm_num2long (SCM num, unsigned long int pos,
 338                            const char *s_caller);
 339 SCM_API unsigned long scm_num2ulong (SCM num, unsigned long int pos,
 340                                      const char *s_caller);
 341 SCM_API scm_t_ptrdiff scm_num2ptrdiff (SCM num, unsigned long int pos,
 342                                        const char *s_caller);
 343 SCM_API size_t scm_num2size (SCM num, unsigned long int pos,
 344                              const char *s_caller);
 345 #if SCM_SIZEOF_LONG_LONG != 0
 346 SCM_API SCM scm_long_long2num (long long sl);
 347 SCM_API SCM scm_ulong_long2num (unsigned long long sl);
 348 SCM_API long long scm_num2long_long (SCM num, unsigned long int pos,
 349                                      const char *s_caller);
 350 SCM_API unsigned long long scm_num2ulong_long (SCM num, unsigned long int pos,
 351                                                const char *s_caller);
 352 #endif
 353
 354 SCM_API SCM scm_float2num (float n);
 355 SCM_API SCM scm_double2num (double n);
 356 SCM_API float scm_num2float (SCM num, unsigned long int pos,
 357                              const char *s_caller);
 358 SCM_API double scm_num2double (SCM num, unsigned long int pos,
 359                                const char *s_caller);
 360
 361 #ifdef GUILE_DEBUG
 362 SCM_API SCM scm_sys_check_number_conversions (void);
 363 #endif
 364
 365 SCM_API void scm_init_numbers (void);
 366
 367 #endif  /* SCM_NUMBERS_H */
 368
 369 /*
 370   Local Variables:
 371   c-file-style: "gnu"
 372   End:
 373 */