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 \f
  53
  54 /* Immediate Numbers, also known as fixnums
  55  *
  56  * Inums are exact integer data that fits within an SCM word.  */
  57
  58 /* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
  59  * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
  60  * which is the same as                (/ (- (expt 2 n) 4) 4)
  61  */
  62
  63 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  64 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  65 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  66
  67 /* SCM_SRS is signed right shift */
  68 #if (-1 == (((-1) << 2) + 2) >> 2)
  69 # define SCM_SRS(x, y) ((x) >> (y))
  70 #else
  71 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  72 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  73
  74
  75 #define SCM_INUMP(x)    (2 & SCM_UNPACK (x))
  76 #define SCM_NINUMP(x)   (!SCM_INUMP (x))
  77 #define SCM_MAKINUM(x)  (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + 2))
  78 #define SCM_INUM(x)     (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  79
  80
  81 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
  82 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
  83 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
  84 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
  85
  86
  87 /* A name for 0. */
  88 #define SCM_INUM0 (SCM_MAKINUM (0))
  89
  90
  91 /* SCM_MAXEXP is the maximum double precision exponent
  92  * SCM_FLTMAX is less than or scm_equal the largest single precision float
  93  */
  94
  95 #ifdef STDC_HEADERS
  96 #ifndef GO32
  97 #include <float.h>
  98 #endif /* ndef GO32 */
  99 #endif /* def STDC_HEADERS */
 100 #ifdef DBL_MAX_10_EXP
 101 #define SCM_MAXEXP DBL_MAX_10_EXP
 102 #else
 103 #define SCM_MAXEXP 308          /* IEEE doubles */
 104 #endif /* def DBL_MAX_10_EXP */
 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 #define SCM_SLOPPY_INEXACTP(x) (SCM_TYP16S (x) == scm_tc16_real)
 123 #define SCM_SLOPPY_REALP(x) (SCM_TYP16 (x) == scm_tc16_real)
 124 #define SCM_SLOPPY_COMPLEXP(x) (SCM_TYP16 (x) == scm_tc16_complex)
 125 #define SCM_INEXACTP(x) (!SCM_IMP (x) && SCM_TYP16S (x) == scm_tc16_real)
 126 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 127 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 128
 129 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 130 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 131 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 132 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 133
 134 /* Define SCM_BIGDIG to an integer type whose size is smaller than long if
 135  * you want bignums.  SCM_BIGRAD is one greater than the biggest SCM_BIGDIG.
 136  *
 137  * Define SCM_DIGSTOOBIG if the digits equivalent to a long won't fit in a long.
 138  */
 139 #ifdef BIGNUMS
 140 # ifdef _UNICOS
 141 #  define SCM_DIGSTOOBIG
 142 #  if (1L << 31) <= SCM_USHRT_MAX
 143 #   define SCM_BIGDIG unsigned  short
 144 #  else
 145 #   define SCM_BIGDIG unsigned int
 146 #  endif /*  (1L << 31) <= USHRT_MAX */
 147 #  define SCM_BITSPERDIG 32
 148 # else
 149 #  define SCM_BIGDIG unsigned short
 150 #  define SCM_BITSPERDIG (sizeof(SCM_BIGDIG)*SCM_CHAR_BIT)
 151 # endif /* def _UNICOS */
 152
 153 # define SCM_BIGRAD (1L << SCM_BITSPERDIG)
 154 # define SCM_DIGSPERLONG ((size_t)((sizeof(long)*SCM_CHAR_BIT+SCM_BITSPERDIG-1)/SCM_BITSPERDIG))
 155 # define SCM_I_BIGUP(type, x) ((type)(x) << SCM_BITSPERDIG)
 156 # define SCM_BIGUP(x) SCM_I_BIGUP (unsigned long, x)
 157 # define SCM_LONGLONGBIGUP(x) SCM_I_BIGUP (unsigned long long, x)
 158 # define SCM_BIGDN(x) ((x) >> SCM_BITSPERDIG)
 159 # define SCM_BIGLO(x) ((x) & (SCM_BIGRAD-1))
 160 #endif /* def BIGNUMS */
 161
 162 #ifndef SCM_BIGDIG
 163 /* Definition is not really used but helps various function
 164  * prototypes to compile with conditionalization.
 165  */
 166 # define SCM_BIGDIG unsigned short
 167 #endif /* ndef SCM_BIGDIG */
 168
 169 #define SCM_NUMBERP(x) (SCM_INUMP(x) || SCM_NUMP(x))
 170 #define SCM_NUMP(x) (!SCM_IMP(x) && (0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_smob)
 171 #define SCM_BIGP(x) (!SCM_IMP (x) && (SCM_TYP16 (x) == scm_tc16_big))
 172 #define SCM_BIGSIGNFLAG 0x10000L
 173 #define SCM_BIGSIZEFIELD 17
 174 #define SCM_BIGSIGN(x) (SCM_CELL_WORD_0 (x) & SCM_BIGSIGNFLAG)
 175 #define SCM_BDIGITS(x) ((SCM_BIGDIG *) (SCM_CELL_WORD_1 (x)))
 176 #define SCM_SET_BIGNUM_BASE(n, b) (SCM_SET_CELL_WORD_1 ((n), (b)))
 177 #define SCM_NUMDIGS(x) ((size_t) (SCM_CELL_WORD_0 (x) >> SCM_BIGSIZEFIELD))
 178 #define SCM_MAKE_BIGNUM_TAG(v, sign)              \
 179               (scm_tc16_big                       \
 180                | ((sign) ? SCM_BIGSIGNFLAG : 0)   \
 181                | (((v) + 0L) << SCM_BIGSIZEFIELD))
 182 #define SCM_SETNUMDIGS(x, v, sign) \
 183   SCM_SET_CELL_WORD_0 (x, SCM_MAKE_BIGNUM_TAG (v, sign))
 184
 185 \f
 186
 187 typedef struct scm_t_double
 188 {
 189   SCM type;
 190   SCM pad;
 191   double real;
 192 } scm_t_double;
 193
 194 typedef struct scm_t_complex
 195 {
 196   double real;
 197   double imag;
 198 } scm_t_complex;
 199
 200 \f
 201
 202 SCM_API SCM scm_exact_p (SCM x);
 203 SCM_API SCM scm_odd_p (SCM n);
 204 SCM_API SCM scm_even_p (SCM n);
 205 SCM_API SCM scm_abs (SCM x);
 206 SCM_API SCM scm_quotient (SCM x, SCM y);
 207 SCM_API SCM scm_remainder (SCM x, SCM y);
 208 SCM_API SCM scm_modulo (SCM x, SCM y);
 209 SCM_API SCM scm_gcd (SCM x, SCM y);
 210 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 211 SCM_API SCM scm_logand (SCM n1, SCM n2);
 212 SCM_API SCM scm_logior (SCM n1, SCM n2);
 213 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 214 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 215 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 216 SCM_API SCM scm_lognot (SCM n);
 217 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 218 SCM_API SCM scm_ash (SCM n, SCM cnt);
 219 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 220 SCM_API SCM scm_logcount (SCM n);
 221 SCM_API SCM scm_integer_length (SCM n);
 222 SCM_API SCM scm_i_mkbig (size_t nlen, int sign);
 223 SCM_API SCM scm_i_big2inum (SCM b, size_t l);
 224 SCM_API SCM scm_i_adjbig (SCM b, size_t nlen);
 225 SCM_API SCM scm_i_normbig (SCM b);
 226 SCM_API SCM scm_i_copybig (SCM b, int sign);
 227 SCM_API SCM scm_i_short2big (short n);
 228 SCM_API SCM scm_i_ushort2big (unsigned short n);
 229 SCM_API SCM scm_i_int2big (int n);
 230 SCM_API SCM scm_i_uint2big (unsigned int n);
 231 SCM_API SCM scm_i_long2big (long n);
 232 SCM_API SCM scm_i_ulong2big (unsigned long n);
 233 SCM_API SCM scm_i_size2big (size_t n);
 234 SCM_API SCM scm_i_ptrdiff2big (ptrdiff_t n);
 235
 236 #ifdef HAVE_LONG_LONGS
 237 SCM_API SCM scm_i_long_long2big (long long n);
 238 SCM_API SCM scm_i_ulong_long2big (unsigned long long n);
 239 #endif
 240
 241 SCM_API int scm_bigcomp (SCM x, SCM y);
 242 SCM_API long scm_pseudolong (long x);
 243 SCM_API void scm_longdigs (long x, SCM_BIGDIG digs[]);
 244 SCM_API SCM scm_addbig (SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int sgny);
 245 SCM_API SCM scm_mulbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn);
 246 SCM_API unsigned int scm_divbigdig (SCM_BIGDIG *ds, size_t h, SCM_BIGDIG div);
 247 SCM_API size_t scm_iint2str (long num, int rad, char *p);
 248 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 249 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 250 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 251 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 252 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
 253 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 254 SCM_API SCM scm_make_real (double x);
 255 SCM_API SCM scm_make_complex (double x, double y);
 256 SCM_API SCM scm_bigequal (SCM x, SCM y);
 257 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 258 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 259 SCM_API SCM scm_number_p (SCM x);
 260 SCM_API SCM scm_real_p (SCM x);
 261 SCM_API SCM scm_integer_p (SCM x);
 262 SCM_API SCM scm_inexact_p (SCM x);
 263 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 264 SCM_API SCM scm_less_p (SCM x, SCM y);
 265 SCM_API SCM scm_gr_p (SCM x, SCM y);
 266 SCM_API SCM scm_leq_p (SCM x, SCM y);
 267 SCM_API SCM scm_geq_p (SCM x, SCM y);
 268 SCM_API SCM scm_zero_p (SCM z);
 269 SCM_API SCM scm_positive_p (SCM x);
 270 SCM_API SCM scm_negative_p (SCM x);
 271 SCM_API SCM scm_max (SCM x, SCM y);
 272 SCM_API SCM scm_min (SCM x, SCM y);
 273 SCM_API SCM scm_sum (SCM x, SCM y);
 274 SCM_API SCM scm_difference (SCM x, SCM y);
 275 SCM_API SCM scm_product (SCM x, SCM y);
 276 SCM_API double scm_num2dbl (SCM a, const char * why);
 277 SCM_API SCM scm_divide (SCM x, SCM y);
 278 SCM_API double scm_asinh (double x);
 279 SCM_API double scm_acosh (double x);
 280 SCM_API double scm_atanh (double x);
 281 SCM_API double scm_truncate (double x);
 282 SCM_API double scm_round (double x);
 283 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 284 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 285 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 286 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 287 SCM_API SCM scm_real_part (SCM z);
 288 SCM_API SCM scm_imag_part (SCM z);
 289 SCM_API SCM scm_magnitude (SCM z);
 290 SCM_API SCM scm_angle (SCM z);
 291 SCM_API SCM scm_exact_to_inexact (SCM z);
 292 SCM_API SCM scm_inexact_to_exact (SCM z);
 293 SCM_API SCM scm_trunc (SCM x);
 294 SCM_API SCM scm_i_dbl2big (double d);
 295 SCM_API double scm_i_big2dbl (SCM b);
 296
 297 SCM_API SCM scm_short2num (short n);
 298 SCM_API SCM scm_ushort2num (unsigned short n);
 299 SCM_API SCM scm_int2num (int n);
 300 SCM_API SCM scm_uint2num (unsigned int n);
 301 SCM_API SCM scm_long2num (long n);
 302 SCM_API SCM scm_ulong2num (unsigned long n);
 303 SCM_API SCM scm_size2num (size_t n);
 304 SCM_API SCM scm_ptrdiff2num (ptrdiff_t n);
 305 SCM_API short scm_num2short (SCM num, unsigned long int pos,
 306                              const char *s_caller);
 307 SCM_API unsigned short scm_num2ushort (SCM num, unsigned long int pos,
 308                                        const char *s_caller);
 309 SCM_API int scm_num2int (SCM num, unsigned long int pos,
 310                          const char *s_caller);
 311 SCM_API unsigned int scm_num2uint (SCM num, unsigned long int pos,
 312                                    const char *s_caller);
 313 SCM_API long scm_num2long (SCM num, unsigned long int pos,
 314                            const char *s_caller);
 315 SCM_API unsigned long scm_num2ulong (SCM num, unsigned long int pos,
 316                                      const char *s_caller);
 317 SCM_API ptrdiff_t scm_num2ptrdiff (SCM num, unsigned long int pos,
 318                                    const char *s_caller);
 319 SCM_API size_t scm_num2size (SCM num, unsigned long int pos,
 320                              const char *s_caller);
 321 #ifdef HAVE_LONG_LONGS
 322 SCM_API SCM scm_long_long2num (long long sl);
 323 SCM_API SCM scm_ulong_long2num (unsigned long long sl);
 324 SCM_API long long scm_num2long_long (SCM num, unsigned long int pos,
 325                                      const char *s_caller);
 326 SCM_API unsigned long long scm_num2ulong_long (SCM num, unsigned long int pos,
 327                                                const char *s_caller);
 328 #endif
 329
 330 SCM_API SCM scm_float2num (float n);
 331 SCM_API SCM scm_double2num (double n);
 332 SCM_API float scm_num2float (SCM num, unsigned long int pos,
 333                              const char *s_caller);
 334 SCM_API double scm_num2double (SCM num, unsigned long int pos,
 335                                const char *s_caller);
 336
 337 #ifdef GUILE_DEBUG
 338 SCM_API SCM scm_sys_check_number_conversions (void);
 339 #endif
 340
 341 SCM_API void scm_init_numbers (void);
 342
 343 #endif  /* SCM_NUMBERS_H */
 344
 345 /*
 346   Local Variables:
 347   c-file-style: "gnu"
 348   End:
 349 */