libguile/numbers.h

   1 /* classes: h_files */
   2
   3 #ifndef SCM_NUMBERS_H
   4 #define SCM_NUMBERS_H
   5
   6 /* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004 Free Software Foundation, Inc.
   7  *
   8  * This library is free software; you can redistribute it and/or
   9  * modify it under the terms of the GNU Lesser General Public
  10  * License as published by the Free Software Foundation; either
  11  * version 2.1 of the License, or (at your option) any later version.
  12  *
  13  * This library 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 GNU
  16  * Lesser General Public License for more details.
  17  *
  18  * You should have received a copy of the GNU Lesser General Public
  19  * License along with this library; if not, write to the Free Software
  20  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
  21  */
  22
  23 \f
  24
  25 #include "libguile/__scm.h"
  26 #include "libguile/print.h"
  27
  28 #if SCM_HAVE_FLOATINGPOINT_H
  29 # include <floatingpoint.h>
  30 #endif
  31
  32 #if SCM_HAVE_IEEEFP_H
  33 # include <ieeefp.h>
  34 #endif
  35
  36 #if SCM_HAVE_NAN_H
  37 # if defined (SCO)
  38 #   define _IEEE 1
  39 # endif
  40 # include <nan.h>
  41 # if defined (SCO)
  42 #   undef _IEEE
  43 # endif
  44 #endif /* SCM_HAVE_NAN_H */
  45
  46 \f
  47
  48 /* Immediate Numbers, also known as fixnums
  49  *
  50  * Inums are exact integer data that fits within an SCM word.  */
  51
  52 /* SCM_T_SIGNED_MAX is                 (- (expt 2 n) 1),
  53  * SCM_MOST_POSITIVE_FIXNUM should be  (- (expt 2 (- n 2)) 1)
  54  * which is the same as                (/ (- (expt 2 n) 4) 4)
  55  */
  56
  57 #define SCM_I_FIXNUM_BIT         (SCM_LONG_BIT - 2)
  58 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
  59 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
  60
  61 /* SCM_SRS is signed right shift */
  62 #if (-1 == (((-1) << 2) + 2) >> 2)
  63 # define SCM_SRS(x, y) ((x) >> (y))
  64 #else
  65 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
  66 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
  67
  68
  69 #define SCM_INUMP(x)    (2 & SCM_UNPACK (x))
  70 #define SCM_NINUMP(x)   (!SCM_INUMP (x))
  71 #define SCM_MAKINUM(x) \
  72   (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
  73 #define SCM_INUM(x)     (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
  74
  75
  76 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
  77 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
  78 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
  79 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
  80
  81
  82 /* A name for 0. */
  83 #define SCM_INUM0 (SCM_MAKINUM (0))
  84
  85
  86 /* SCM_MAXEXP is the maximum double precision exponent
  87  * SCM_FLTMAX is less than or scm_equal the largest single precision float
  88  */
  89
  90 #if SCM_HAVE_STDC_HEADERS
  91 # ifndef GO32
  92 #  include <float.h>
  93 #  ifdef __MINGW32__
  94 #   define copysign _copysign
  95 #   define isnan _isnan
  96 #   define finite _finite
  97 #  endif /* __MINGW32__ */
  98 # endif /* ndef GO32 */
  99 #endif /* def STDC_HEADERS */
 100
 101 #ifdef DBL_MAX_10_EXP
 102 # define SCM_MAXEXP DBL_MAX_10_EXP
 103 #else
 104 # define SCM_MAXEXP 308         /* IEEE doubles */
 105 #endif /* def DBL_MAX_10_EXP */
 106
 107 #ifdef FLT_MAX
 108 # define SCM_FLTMAX FLT_MAX
 109 #else
 110 # define SCM_FLTMAX 1e+23
 111 #endif /* def FLT_MAX */
 112
 113
 114 /* SCM_INTBUFLEN is the maximum number of characters neccessary for the
 115  * printed or scm_string representation of an exact immediate.
 116  */
 117 #define SCM_INTBUFLEN (5 + SCM_LONG_BIT)
 118
 119 \f
 120
 121 /* Numbers
 122  */
 123
 124
 125 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
 126  * differ in one bit: This way, checking if an object is an inexact number can
 127  * be done quickly (using the TYP16S macro).  */
 128
 129 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
 130  * and SCM_NUMP)  */
 131 #define scm_tc16_big            (scm_tc7_number + 1 * 256L)
 132 #define scm_tc16_real           (scm_tc7_number + 2 * 256L)
 133 #define scm_tc16_complex        (scm_tc7_number + 3 * 256L)
 134 #define scm_tc16_fraction       (scm_tc7_number + 4 * 256L)
 135
 136 #define SCM_INEXACTP(x) \
 137   (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
 138 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
 139 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
 140
 141 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
 142 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
 143 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
 144 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
 145
 146 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
 147 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
 148 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
 149
 150 #define SCM_NUMBERP(x) (SCM_INUMP(x) || SCM_NUMP(x))
 151 #define SCM_NUMP(x) (!SCM_IMP(x) \
 152   && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
 153       || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
 154 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
 155
 156 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
 157 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
 158 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
 159 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
 160 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
 161
 162   /* I think the left half word is free in the type, so I'll use bit 17 */
 163 #define SCM_FRACTION_REDUCED_BIT 0x10000
 164 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
 165 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
 166 #define SCM_FRACTION_REDUCED(x)     (0x10000 & SCM_CELL_TYPE (x))
 167
 168 \f
 169
 170 typedef struct scm_t_double
 171 {
 172   SCM type;
 173   SCM pad;
 174   double real;
 175 } scm_t_double;
 176
 177 typedef struct scm_t_complex
 178 {
 179   double real;
 180   double imag;
 181 } scm_t_complex;
 182
 183 \f
 184
 185 SCM_API SCM scm_exact_p (SCM x);
 186 SCM_API SCM scm_odd_p (SCM n);
 187 SCM_API SCM scm_even_p (SCM n);
 188 SCM_API SCM scm_inf_p (SCM n);
 189 SCM_API SCM scm_nan_p (SCM n);
 190 SCM_API SCM scm_inf (void);
 191 SCM_API SCM scm_nan (void);
 192 SCM_API SCM scm_abs (SCM x);
 193 SCM_API SCM scm_quotient (SCM x, SCM y);
 194 SCM_API SCM scm_remainder (SCM x, SCM y);
 195 SCM_API SCM scm_modulo (SCM x, SCM y);
 196 SCM_API SCM scm_gcd (SCM x, SCM y);
 197 SCM_API SCM scm_lcm (SCM n1, SCM n2);
 198 SCM_API SCM scm_logand (SCM n1, SCM n2);
 199 SCM_API SCM scm_logior (SCM n1, SCM n2);
 200 SCM_API SCM scm_logxor (SCM n1, SCM n2);
 201 SCM_API SCM scm_logtest (SCM n1, SCM n2);
 202 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
 203 SCM_API SCM scm_lognot (SCM n);
 204 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
 205 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
 206 SCM_API SCM scm_ash (SCM n, SCM cnt);
 207 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
 208 SCM_API SCM scm_logcount (SCM n);
 209 SCM_API SCM scm_integer_length (SCM n);
 210
 211 SCM_API size_t scm_iint2str (long num, int rad, char *p);
 212 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
 213 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
 214 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
 215 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
 216 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
 217 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
 218 SCM_API SCM scm_make_real (double x);
 219 SCM_API SCM scm_make_complex (double x, double y);
 220 SCM_API SCM scm_bigequal (SCM x, SCM y);
 221 SCM_API SCM scm_real_equalp (SCM x, SCM y);
 222 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
 223 SCM_API SCM scm_number_p (SCM x);
 224 SCM_API SCM scm_real_p (SCM x);
 225 SCM_API SCM scm_integer_p (SCM x);
 226 SCM_API SCM scm_inexact_p (SCM x);
 227 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
 228 SCM_API SCM scm_less_p (SCM x, SCM y);
 229 SCM_API SCM scm_gr_p (SCM x, SCM y);
 230 SCM_API SCM scm_leq_p (SCM x, SCM y);
 231 SCM_API SCM scm_geq_p (SCM x, SCM y);
 232 SCM_API SCM scm_zero_p (SCM z);
 233 SCM_API SCM scm_positive_p (SCM x);
 234 SCM_API SCM scm_negative_p (SCM x);
 235 SCM_API SCM scm_max (SCM x, SCM y);
 236 SCM_API SCM scm_min (SCM x, SCM y);
 237 SCM_API SCM scm_sum (SCM x, SCM y);
 238 SCM_API SCM scm_difference (SCM x, SCM y);
 239 SCM_API SCM scm_product (SCM x, SCM y);
 240 SCM_API double scm_num2dbl (SCM a, const char * why);
 241 SCM_API SCM scm_divide (SCM x, SCM y);
 242 SCM_API SCM scm_floor (SCM x);
 243 SCM_API SCM scm_ceiling (SCM x);
 244 SCM_API double scm_asinh (double x);
 245 SCM_API double scm_acosh (double x);
 246 SCM_API double scm_atanh (double x);
 247 SCM_API double scm_truncate (double x);
 248 SCM_API double scm_round (double x);
 249 SCM_API SCM scm_truncate_number (SCM x);
 250 SCM_API SCM scm_round_number (SCM x);
 251 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
 252 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
 253 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
 254 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
 255 SCM_API SCM scm_real_part (SCM z);
 256 SCM_API SCM scm_imag_part (SCM z);
 257 SCM_API SCM scm_magnitude (SCM z);
 258 SCM_API SCM scm_angle (SCM z);
 259 SCM_API SCM scm_exact_to_inexact (SCM z);
 260 SCM_API SCM scm_inexact_to_exact (SCM z);
 261 SCM_API SCM scm_trunc (SCM x);
 262
 263 SCM_API SCM scm_short2num (short n);
 264 SCM_API SCM scm_ushort2num (unsigned short n);
 265 SCM_API SCM scm_int2num (int n);
 266 SCM_API SCM scm_uint2num (unsigned int n);
 267 SCM_API SCM scm_long2num (long n);
 268 SCM_API SCM scm_ulong2num (unsigned long n);
 269 SCM_API SCM scm_size2num (size_t n);
 270 SCM_API SCM scm_ptrdiff2num (scm_t_ptrdiff n);
 271 SCM_API short scm_num2short (SCM num, unsigned long int pos,
 272                              const char *s_caller);
 273 SCM_API unsigned short scm_num2ushort (SCM num, unsigned long int pos,
 274                                        const char *s_caller);
 275 SCM_API int scm_num2int (SCM num, unsigned long int pos,
 276                          const char *s_caller);
 277 SCM_API unsigned int scm_num2uint (SCM num, unsigned long int pos,
 278                                    const char *s_caller);
 279 SCM_API long scm_num2long (SCM num, unsigned long int pos,
 280                            const char *s_caller);
 281 SCM_API unsigned long scm_num2ulong (SCM num, unsigned long int pos,
 282                                      const char *s_caller);
 283 SCM_API scm_t_ptrdiff scm_num2ptrdiff (SCM num, unsigned long int pos,
 284                                        const char *s_caller);
 285 SCM_API size_t scm_num2size (SCM num, unsigned long int pos,
 286                              const char *s_caller);
 287 #if SCM_SIZEOF_LONG_LONG != 0
 288 SCM_API SCM scm_long_long2num (long long sl);
 289 SCM_API SCM scm_ulong_long2num (unsigned long long sl);
 290 SCM_API long long scm_num2long_long (SCM num, unsigned long int pos,
 291                                      const char *s_caller);
 292 SCM_API unsigned long long scm_num2ulong_long (SCM num, unsigned long int pos,
 293                                                const char *s_caller);
 294 #endif
 295
 296 SCM_API SCM scm_float2num (float n);
 297 SCM_API SCM scm_double2num (double n);
 298 SCM_API float scm_num2float (SCM num, unsigned long int pos,
 299                              const char *s_caller);
 300 SCM_API double scm_num2double (SCM num, unsigned long int pos,
 301                                const char *s_caller);
 302
 303
 304 /* bignum internal functions */
 305 SCM_API SCM scm_i_mkbig (void);
 306 SCM_API SCM scm_i_normbig (SCM x);
 307 SCM_API int scm_i_bigcmp (SCM a, SCM b);
 308 SCM_API SCM scm_i_dbl2big (double d);
 309 SCM_API SCM scm_i_dbl2num (double d);
 310 SCM_API double scm_i_big2dbl (SCM b);
 311 SCM_API SCM scm_i_short2big (short n);
 312 SCM_API SCM scm_i_ushort2big (unsigned short n);
 313 SCM_API SCM scm_i_int2big (int n);
 314 SCM_API SCM scm_i_uint2big (unsigned int n);
 315 SCM_API SCM scm_i_long2big (long n);
 316 SCM_API SCM scm_i_ulong2big (unsigned long n);
 317 SCM_API SCM scm_i_size2big (size_t n);
 318 SCM_API SCM scm_i_ptrdiff2big (scm_t_ptrdiff n);
 319
 320 #if SCM_SIZEOF_LONG_LONG != 0
 321 SCM_API SCM scm_i_long_long2big (long long n);
 322 SCM_API SCM scm_i_ulong_long2big (unsigned long long n);
 323 #endif
 324
 325
 326 /* ratio functions */
 327 SCM_API SCM scm_make_ratio (SCM num, SCM den);
 328 SCM_API SCM scm_rationalize (SCM x, SCM err);
 329 SCM_API SCM scm_numerator (SCM z);
 330 SCM_API SCM scm_denominator (SCM z);
 331 SCM_API SCM scm_rational_p (SCM z);
 332
 333 /* fraction internal functions */
 334 SCM_API double scm_i_fraction2double (SCM z);
 335 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
 336 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
 337
 338
 339 #ifdef GUILE_DEBUG
 340 SCM_API SCM scm_sys_check_number_conversions (void);
 341 #endif
 342
 343 SCM_API void scm_init_numbers (void);
 344
 345 #endif  /* SCM_NUMBERS_H */
 346
 347 /*
 348   Local Variables:
 349   c-file-style: "gnu"
 350   End:
 351 */