6 /* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005, 2006, 2010 Free Software Foundation, Inc.
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.
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.
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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
27 #include "libguile/__scm.h"
28 #include "libguile/print.h"
30 #if SCM_HAVE_FLOATINGPOINT_H
31 # include <floatingpoint.h>
46 #endif /* SCM_HAVE_NAN_H */
50 /* Immediate Numbers, also known as fixnums
52 * Inums are exact integer data that fits within an SCM word. */
54 /* SCM_T_SIGNED_MAX is (- (expt 2 n) 1),
55 * SCM_MOST_POSITIVE_FIXNUM should be (- (expt 2 (- n 2)) 1)
56 * which is the same as (/ (- (expt 2 n) 4) 4)
59 #define SCM_I_FIXNUM_BIT (SCM_LONG_BIT - 2)
60 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
61 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
63 /* SCM_SRS is signed right shift */
64 #if (-1 == (((-1) << 2) + 2) >> 2)
65 # define SCM_SRS(x, y) ((x) >> (y))
67 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
68 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
71 #define SCM_I_INUMP(x) (2 & SCM_UNPACK (x))
72 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
73 #define SCM_I_MAKINUM(x) \
74 (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
75 #define SCM_I_INUM(x) (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
77 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
78 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
79 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
80 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
84 #define SCM_INUM0 (SCM_I_MAKINUM (0))
86 /* SCM_MAXEXP is the maximum double precision exponent
87 * SCM_FLTMAX is less than or scm_equal the largest single precision float
90 #if SCM_HAVE_STDC_HEADERS
94 # define copysign _copysign
95 # define finite _finite
96 # endif /* __MINGW32__ */
97 # endif /* ndef GO32 */
98 #endif /* def STDC_HEADERS */
100 #ifdef DBL_MAX_10_EXP
101 # define SCM_MAXEXP DBL_MAX_10_EXP
103 # define SCM_MAXEXP 308 /* IEEE doubles */
104 #endif /* def DBL_MAX_10_EXP */
107 # define SCM_FLTMAX FLT_MAX
109 # define SCM_FLTMAX 1e+23
110 #endif /* def FLT_MAX */
113 /* SCM_INTBUFLEN is the maximum number of characters neccessary for
114 * the printed or scm_string representation of an scm_t_intmax in
115 * radix 2. The buffer passed to scm_iint2str and scm_iuint2str must
116 * be of this size, for example.
118 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
126 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
127 * differ in one bit: This way, checking if an object is an inexact number can
128 * be done quickly (using the TYP16S macro). */
130 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
132 #define scm_tc16_big (scm_tc7_number + 1 * 256L)
133 #define scm_tc16_real (scm_tc7_number + 2 * 256L)
134 #define scm_tc16_complex (scm_tc7_number + 3 * 256L)
135 #define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
137 #define SCM_INEXACTP(x) \
138 (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
139 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
140 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
142 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
143 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
144 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
145 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
147 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
148 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
149 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
151 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
152 #define SCM_NUMP(x) (!SCM_IMP(x) \
153 && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
154 || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
155 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
157 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
158 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
159 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
163 typedef struct scm_t_double
170 typedef struct scm_t_complex
178 SCM_API SCM scm_exact_p (SCM x);
179 SCM_API SCM scm_odd_p (SCM n);
180 SCM_API SCM scm_even_p (SCM n);
181 SCM_API SCM scm_inf_p (SCM n);
182 SCM_API SCM scm_nan_p (SCM n);
183 SCM_API SCM scm_inf (void);
184 SCM_API SCM scm_nan (void);
185 SCM_API SCM scm_abs (SCM x);
186 SCM_API SCM scm_quotient (SCM x, SCM y);
187 SCM_API SCM scm_remainder (SCM x, SCM y);
188 SCM_API SCM scm_modulo (SCM x, SCM y);
189 SCM_API SCM scm_gcd (SCM x, SCM y);
190 SCM_API SCM scm_lcm (SCM n1, SCM n2);
191 SCM_API SCM scm_logand (SCM n1, SCM n2);
192 SCM_API SCM scm_logior (SCM n1, SCM n2);
193 SCM_API SCM scm_logxor (SCM n1, SCM n2);
194 SCM_API SCM scm_logtest (SCM n1, SCM n2);
195 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
196 SCM_API SCM scm_lognot (SCM n);
197 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
198 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
199 SCM_API SCM scm_ash (SCM n, SCM cnt);
200 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
201 SCM_API SCM scm_logcount (SCM n);
202 SCM_API SCM scm_integer_length (SCM n);
204 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
205 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
206 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
207 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
208 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
209 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
210 SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
212 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
213 SCM_API SCM scm_bigequal (SCM x, SCM y);
214 SCM_API SCM scm_real_equalp (SCM x, SCM y);
215 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
216 SCM_API SCM scm_number_p (SCM x);
217 SCM_API SCM scm_complex_p (SCM x);
218 SCM_API SCM scm_real_p (SCM x);
219 SCM_API SCM scm_rational_p (SCM z);
220 SCM_API SCM scm_integer_p (SCM x);
221 SCM_API SCM scm_inexact_p (SCM x);
222 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
223 SCM_API SCM scm_less_p (SCM x, SCM y);
224 SCM_API SCM scm_gr_p (SCM x, SCM y);
225 SCM_API SCM scm_leq_p (SCM x, SCM y);
226 SCM_API SCM scm_geq_p (SCM x, SCM y);
227 SCM_API SCM scm_zero_p (SCM z);
228 SCM_API SCM scm_positive_p (SCM x);
229 SCM_API SCM scm_negative_p (SCM x);
230 SCM_API SCM scm_max (SCM x, SCM y);
231 SCM_API SCM scm_min (SCM x, SCM y);
232 SCM_API SCM scm_sum (SCM x, SCM y);
233 SCM_API SCM scm_oneplus (SCM x);
234 SCM_API SCM scm_difference (SCM x, SCM y);
235 SCM_API SCM scm_oneminus (SCM x);
236 SCM_API SCM scm_product (SCM x, SCM y);
237 SCM_API SCM scm_divide (SCM x, SCM y);
238 SCM_API SCM scm_floor (SCM x);
239 SCM_API SCM scm_ceiling (SCM x);
240 SCM_API double scm_asinh (double x);
241 SCM_API double scm_acosh (double x);
242 SCM_API double scm_atanh (double x);
243 SCM_API double scm_c_truncate (double x);
244 SCM_API double scm_c_round (double x);
245 SCM_API SCM scm_truncate_number (SCM x);
246 SCM_API SCM scm_round_number (SCM x);
247 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
248 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
249 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
250 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
251 SCM_API SCM scm_real_part (SCM z);
252 SCM_API SCM scm_imag_part (SCM z);
253 SCM_API SCM scm_magnitude (SCM z);
254 SCM_API SCM scm_angle (SCM z);
255 SCM_API SCM scm_exact_to_inexact (SCM z);
256 SCM_API SCM scm_inexact_to_exact (SCM z);
257 SCM_API SCM scm_trunc (SCM x);
258 SCM_API SCM scm_log (SCM z);
259 SCM_API SCM scm_log10 (SCM z);
260 SCM_API SCM scm_exp (SCM z);
261 SCM_API SCM scm_sqrt (SCM z);
263 /* bignum internal functions */
264 SCM_API SCM scm_i_mkbig (void);
265 SCM_API SCM scm_i_normbig (SCM x);
266 SCM_API int scm_i_bigcmp (SCM a, SCM b);
267 SCM_API SCM scm_i_dbl2big (double d);
268 SCM_API SCM scm_i_dbl2num (double d);
269 SCM_API double scm_i_big2dbl (SCM b);
270 SCM_API SCM scm_i_long2big (long n);
271 SCM_API SCM scm_i_ulong2big (unsigned long n);
272 SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);
274 /* ratio functions */
275 SCM_API SCM scm_rationalize (SCM x, SCM err);
276 SCM_API SCM scm_numerator (SCM z);
277 SCM_API SCM scm_denominator (SCM z);
279 /* fraction internal functions */
280 SCM_API double scm_i_fraction2double (SCM z);
281 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
282 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
284 /* general internal functions */
285 SCM_API void scm_i_print_double (double val, SCM port);
286 SCM_API void scm_i_print_complex (double real, double imag, SCM port);
288 /* conversion functions for integers */
290 SCM_API int scm_is_integer (SCM val);
291 SCM_API int scm_is_signed_integer (SCM val,
292 scm_t_intmax min, scm_t_intmax max);
293 SCM_API int scm_is_unsigned_integer (SCM val,
294 scm_t_uintmax min, scm_t_uintmax max);
296 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
297 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
299 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
302 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
306 SCM_API scm_t_int8 scm_to_int8 (SCM x);
307 SCM_API SCM scm_from_int8 (scm_t_int8 x);
309 SCM_API scm_t_uint8 scm_to_uint8 (SCM x);
310 SCM_API SCM scm_from_uint8 (scm_t_uint8 x);
312 SCM_API scm_t_int16 scm_to_int16 (SCM x);
313 SCM_API SCM scm_from_int16 (scm_t_int16 x);
315 SCM_API scm_t_uint16 scm_to_uint16 (SCM x);
316 SCM_API SCM scm_from_uint16 (scm_t_uint16 x);
318 SCM_API scm_t_int32 scm_to_int32 (SCM x);
319 SCM_API SCM scm_from_int32 (scm_t_int32 x);
321 SCM_API scm_t_uint32 scm_to_uint32 (SCM x);
322 SCM_API SCM scm_from_uint32 (scm_t_uint32 x);
324 SCM_API scm_t_int64 scm_to_int64 (SCM x);
325 SCM_API SCM scm_from_int64 (scm_t_int64 x);
327 SCM_API scm_t_uint64 scm_to_uint64 (SCM x);
328 SCM_API SCM scm_from_uint64 (scm_t_uint64 x);
330 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
331 SCM_API SCM scm_from_mpz (mpz_t rop);
334 /* The conversion functions for other types are aliased to the
335 appropriate ones from above. We pick the right one based on the
338 Not each and every possibility is covered by the code below, and
339 while it is trivial to complete the tests, it might be better to
340 just test for the 'sane' possibilities. When one of the tests
341 below fails, chances are good that some silent assumption somewhere
345 #if SCM_SIZEOF_CHAR == 1
346 #define scm_to_schar scm_to_int8
347 #define scm_from_schar scm_from_int8
348 #define scm_to_uchar scm_to_uint8
349 #define scm_from_uchar scm_from_uint8
351 #define scm_to_char scm_to_uint8
352 #define scm_from_char scm_from_uint8
354 #define scm_to_char scm_to_int8
355 #define scm_from_char scm_from_int8
358 #error sizeof(char) is not 1.
361 #if SCM_SIZEOF_SHORT == 1
362 #define scm_to_short scm_to_int8
363 #define scm_from_short scm_from_int8
364 #define scm_to_ushort scm_to_uint8
365 #define scm_from_ushort scm_from_uint8
367 #if SCM_SIZEOF_SHORT == 2
368 #define scm_to_short scm_to_int16
369 #define scm_from_short scm_from_int16
370 #define scm_to_ushort scm_to_uint16
371 #define scm_from_ushort scm_from_uint16
373 #if SCM_SIZEOF_SHORT == 4
374 #define scm_to_short scm_to_int32
375 #define scm_from_short scm_from_int32
376 #define scm_to_ushort scm_to_uint32
377 #define scm_from_ushort scm_from_uint32
379 #error sizeof(short) is not 1, 2, or 4.
384 #if SCM_SIZEOF_INT == 4
385 #define scm_to_int scm_to_int32
386 #define scm_from_int scm_from_int32
387 #define scm_to_uint scm_to_uint32
388 #define scm_from_uint scm_from_uint32
390 #if SCM_SIZEOF_INT == 8
391 #define scm_to_int scm_to_int64
392 #define scm_from_int scm_from_int64
393 #define scm_to_uint scm_to_uint64
394 #define scm_from_uint scm_from_uint64
396 #error sizeof(int) is not 4 or 8.
400 #if SCM_SIZEOF_LONG == 4
401 #define scm_to_long scm_to_int32
402 #define scm_from_long scm_from_int32
403 #define scm_to_ulong scm_to_uint32
404 #define scm_from_ulong scm_from_uint32
406 #if SCM_SIZEOF_LONG == 8
407 #define scm_to_long scm_to_int64
408 #define scm_from_long scm_from_int64
409 #define scm_to_ulong scm_to_uint64
410 #define scm_from_ulong scm_from_uint64
412 #error sizeof(long) is not 4 or 8.
416 #if SCM_SIZEOF_INTMAX == 4
417 #define scm_to_intmax scm_to_int32
418 #define scm_from_intmax scm_from_int32
419 #define scm_to_uintmax scm_to_uint32
420 #define scm_from_uintmax scm_from_uint32
422 #if SCM_SIZEOF_INTMAX == 8
423 #define scm_to_intmax scm_to_int64
424 #define scm_from_intmax scm_from_int64
425 #define scm_to_uintmax scm_to_uint64
426 #define scm_from_uintmax scm_from_uint64
428 #error sizeof(scm_t_intmax) is not 4 or 8.
432 #if SCM_SIZEOF_LONG_LONG == 0
434 #if SCM_SIZEOF_LONG_LONG == 8
435 #define scm_to_long_long scm_to_int64
436 #define scm_from_long_long scm_from_int64
437 #define scm_to_ulong_long scm_to_uint64
438 #define scm_from_ulong_long scm_from_uint64
440 #error sizeof(long long) is not 8.
444 #if SCM_SIZEOF_SIZE_T == 4
445 #define scm_to_ssize_t scm_to_int32
446 #define scm_from_ssize_t scm_from_int32
447 #define scm_to_size_t scm_to_uint32
448 #define scm_from_size_t scm_from_uint32
450 #if SCM_SIZEOF_SIZE_T == 8
451 #define scm_to_ssize_t scm_to_int64
452 #define scm_from_ssize_t scm_from_int64
453 #define scm_to_size_t scm_to_uint64
454 #define scm_from_size_t scm_from_uint64
456 #error sizeof(size_t) is not 4 or 8.
460 /* conversion functions for double */
462 SCM_API int scm_is_real (SCM val);
463 SCM_API int scm_is_rational (SCM val);
464 SCM_API double scm_to_double (SCM val);
465 SCM_API SCM scm_from_double (double val);
467 /* conversion functions for complex */
469 SCM_API int scm_is_complex (SCM val);
470 SCM_API SCM scm_c_make_rectangular (double re, double im);
471 SCM_API SCM scm_c_make_polar (double mag, double ang);
472 SCM_API double scm_c_real_part (SCM z);
473 SCM_API double scm_c_imag_part (SCM z);
474 SCM_API double scm_c_magnitude (SCM z);
475 SCM_API double scm_c_angle (SCM z);
477 SCM_API int scm_is_number (SCM val);
479 SCM_API void scm_init_numbers (void);
481 #endif /* SCM_NUMBERS_H */