6 /* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005, 2006, 2008, 2009, 2010, 2011 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 License
10 * as published by the Free Software Foundation; either version 3 of
11 * the License, or (at your option) any later version.
13 * This library is distributed in the hope that it will be useful, but
14 * 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
28 #include "libguile/__scm.h"
29 #include "libguile/print.h"
31 #ifndef SCM_T_WCHAR_DEFINED
32 typedef scm_t_int32 scm_t_wchar
;
33 #define SCM_T_WCHAR_DEFINED
34 #endif /* SCM_T_WCHAR_DEFINED */
38 /* Immediate Numbers, also known as fixnums
40 * Inums are exact integer data that fits within an SCM word. */
42 /* SCM_T_SIGNED_MAX is (- (expt 2 n) 1),
43 * SCM_MOST_POSITIVE_FIXNUM should be (- (expt 2 (- n 2)) 1)
44 * which is the same as (/ (- (expt 2 n) 4) 4)
47 #define SCM_I_FIXNUM_BIT (SCM_LONG_BIT - 2)
48 #define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
49 #define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
51 /* SCM_SRS is signed right shift */
52 #if (-1 == (((-1) << 2) + 2) >> 2)
53 # define SCM_SRS(x, y) ((x) >> (y))
55 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
56 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
59 #define SCM_I_INUMP(x) (2 & SCM_UNPACK (x))
60 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
61 #define SCM_I_MAKINUM(x) \
62 (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
63 #define SCM_I_INUM(x) (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
65 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
66 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
67 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
68 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
71 #define SCM_INUM0 (SCM_I_MAKINUM (0)) /* A name for 0 */
72 #define SCM_INUM1 (SCM_I_MAKINUM (1)) /* A name for 1 */
75 /* SCM_MAXEXP is the maximum double precision exponent
76 * SCM_FLTMAX is less than or scm_equal the largest single precision float
79 #if SCM_HAVE_STDC_HEADERS
83 # define copysign _copysign
84 # define finite _finite
85 # endif /* __MINGW32__ */
86 # endif /* ndef GO32 */
87 #endif /* def STDC_HEADERS */
90 # define SCM_MAXEXP DBL_MAX_10_EXP
92 # define SCM_MAXEXP 308 /* IEEE doubles */
93 #endif /* def DBL_MAX_10_EXP */
96 # define SCM_FLTMAX FLT_MAX
98 # define SCM_FLTMAX 1e+23
99 #endif /* def FLT_MAX */
102 /* SCM_INTBUFLEN is the maximum number of characters neccessary for
103 * the printed or scm_string representation of an scm_t_intmax in
104 * radix 2. The buffer passed to scm_iint2str and scm_iuint2str must
105 * be of this size, for example.
107 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
115 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
116 * differ in one bit: This way, checking if an object is an inexact number can
117 * be done quickly (using the TYP16S macro). */
119 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
121 #define scm_tc16_big (scm_tc7_number + 1 * 256L)
122 #define scm_tc16_real (scm_tc7_number + 2 * 256L)
123 #define scm_tc16_complex (scm_tc7_number + 3 * 256L)
124 #define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
126 #define SCM_INEXACTP(x) \
127 (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
128 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
129 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
131 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
132 #define SCM_COMPLEX_REAL(x) (((scm_t_complex *) SCM2PTR (x))->real)
133 #define SCM_COMPLEX_IMAG(x) (((scm_t_complex *) SCM2PTR (x))->imag)
135 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
136 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
137 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
139 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
140 #define SCM_NUMP(x) (!SCM_IMP(x) \
141 && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
142 || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
143 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
145 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
146 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
147 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
151 typedef struct scm_t_double
158 typedef struct scm_t_complex
169 SCM_API SCM
scm_exact_p (SCM x
);
170 SCM_API SCM
scm_odd_p (SCM n
);
171 SCM_API SCM
scm_even_p (SCM n
);
172 SCM_API SCM
scm_inf_p (SCM n
);
173 SCM_API SCM
scm_nan_p (SCM n
);
174 SCM_API SCM
scm_inf (void);
175 SCM_API SCM
scm_nan (void);
176 SCM_API SCM
scm_abs (SCM x
);
177 SCM_API SCM
scm_quotient (SCM x
, SCM y
);
178 SCM_API SCM
scm_remainder (SCM x
, SCM y
);
179 SCM_API SCM
scm_modulo (SCM x
, SCM y
);
180 SCM_API SCM
scm_euclidean_quo_and_rem (SCM x
, SCM y
);
181 SCM_API SCM
scm_euclidean_quotient (SCM x
, SCM y
);
182 SCM_API SCM
scm_euclidean_remainder (SCM x
, SCM y
);
183 SCM_API SCM
scm_centered_quo_and_rem (SCM x
, SCM y
);
184 SCM_API SCM
scm_centered_quotient (SCM x
, SCM y
);
185 SCM_API SCM
scm_centered_remainder (SCM x
, SCM y
);
186 SCM_API SCM
scm_gcd (SCM x
, SCM y
);
187 SCM_API SCM
scm_lcm (SCM n1
, SCM n2
);
188 SCM_API SCM
scm_logand (SCM n1
, SCM n2
);
189 SCM_API SCM
scm_logior (SCM n1
, SCM n2
);
190 SCM_API SCM
scm_logxor (SCM n1
, SCM n2
);
191 SCM_API SCM
scm_logtest (SCM n1
, SCM n2
);
192 SCM_API SCM
scm_logbit_p (SCM n1
, SCM n2
);
193 SCM_API SCM
scm_lognot (SCM n
);
194 SCM_API SCM
scm_modulo_expt (SCM n
, SCM k
, SCM m
);
195 SCM_API SCM
scm_integer_expt (SCM z1
, SCM z2
);
196 SCM_API SCM
scm_ash (SCM n
, SCM cnt
);
197 SCM_API SCM
scm_bit_extract (SCM n
, SCM start
, SCM end
);
198 SCM_API SCM
scm_logcount (SCM n
);
199 SCM_API SCM
scm_integer_length (SCM n
);
201 SCM_INTERNAL SCM
scm_i_gcd (SCM x
, SCM y
, SCM rest
);
202 SCM_INTERNAL SCM
scm_i_lcm (SCM x
, SCM y
, SCM rest
);
203 SCM_INTERNAL SCM
scm_i_logand (SCM x
, SCM y
, SCM rest
);
204 SCM_INTERNAL SCM
scm_i_logior (SCM x
, SCM y
, SCM rest
);
205 SCM_INTERNAL SCM
scm_i_logxor (SCM x
, SCM y
, SCM rest
);
207 SCM_API
size_t scm_iint2str (scm_t_intmax num
, int rad
, char *p
);
208 SCM_API
size_t scm_iuint2str (scm_t_uintmax num
, int rad
, char *p
);
209 SCM_API SCM
scm_number_to_string (SCM x
, SCM radix
);
210 SCM_API
int scm_print_real (SCM sexp
, SCM port
, scm_print_state
*pstate
);
211 SCM_API
int scm_print_complex (SCM sexp
, SCM port
, scm_print_state
*pstate
);
212 SCM_API
int scm_bigprint (SCM exp
, SCM port
, scm_print_state
*pstate
);
213 SCM_API SCM
scm_c_locale_stringn_to_number (const char *mem
, size_t len
,
215 SCM_INTERNAL SCM
scm_i_string_to_number (SCM str
, unsigned int radix
);
216 SCM_API SCM
scm_string_to_number (SCM str
, SCM radix
);
217 SCM_API SCM
scm_bigequal (SCM x
, SCM y
);
218 SCM_API SCM
scm_real_equalp (SCM x
, SCM y
);
219 SCM_API SCM
scm_complex_equalp (SCM x
, SCM y
);
220 SCM_API SCM
scm_number_p (SCM x
);
221 SCM_API SCM
scm_complex_p (SCM x
);
222 SCM_API SCM
scm_real_p (SCM x
);
223 SCM_API SCM
scm_rational_p (SCM z
);
224 SCM_API SCM
scm_integer_p (SCM x
);
225 SCM_API SCM
scm_inexact_p (SCM x
);
226 SCM_API SCM
scm_num_eq_p (SCM x
, SCM y
);
227 SCM_API SCM
scm_less_p (SCM x
, SCM y
);
228 SCM_API SCM
scm_gr_p (SCM x
, SCM y
);
229 SCM_API SCM
scm_leq_p (SCM x
, SCM y
);
230 SCM_API SCM
scm_geq_p (SCM x
, SCM y
);
231 SCM_API SCM
scm_zero_p (SCM z
);
232 SCM_API SCM
scm_positive_p (SCM x
);
233 SCM_API SCM
scm_negative_p (SCM x
);
234 SCM_API SCM
scm_max (SCM x
, SCM y
);
235 SCM_API SCM
scm_min (SCM x
, SCM y
);
236 SCM_API SCM
scm_sum (SCM x
, SCM y
);
237 SCM_API SCM
scm_oneplus (SCM x
);
238 SCM_API SCM
scm_difference (SCM x
, SCM y
);
239 SCM_API SCM
scm_oneminus (SCM x
);
240 SCM_API SCM
scm_product (SCM x
, SCM y
);
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_c_truncate (double x
);
245 SCM_API
double scm_c_round (double x
);
246 SCM_API SCM
scm_truncate_number (SCM x
);
247 SCM_API SCM
scm_round_number (SCM x
);
248 SCM_API SCM
scm_expt (SCM z1
, SCM z2
);
249 SCM_API SCM
scm_sin (SCM z
);
250 SCM_API SCM
scm_cos (SCM z
);
251 SCM_API SCM
scm_tan (SCM z
);
252 SCM_API SCM
scm_sinh (SCM z
);
253 SCM_API SCM
scm_cosh (SCM z
);
254 SCM_API SCM
scm_tanh (SCM z
);
255 SCM_API SCM
scm_asin (SCM z
);
256 SCM_API SCM
scm_acos (SCM z
);
257 SCM_API SCM
scm_atan (SCM x
, SCM y
);
258 SCM_API SCM
scm_sys_asinh (SCM z
);
259 SCM_API SCM
scm_sys_acosh (SCM z
);
260 SCM_API SCM
scm_sys_atanh (SCM z
);
261 SCM_API SCM
scm_make_rectangular (SCM z1
, SCM z2
);
262 SCM_API SCM
scm_make_polar (SCM z1
, SCM z2
);
263 SCM_API SCM
scm_real_part (SCM z
);
264 SCM_API SCM
scm_imag_part (SCM z
);
265 SCM_API SCM
scm_magnitude (SCM z
);
266 SCM_API SCM
scm_angle (SCM z
);
267 SCM_API SCM
scm_exact_to_inexact (SCM z
);
268 SCM_API SCM
scm_inexact_to_exact (SCM z
);
269 SCM_API SCM
scm_trunc (SCM x
);
270 SCM_API SCM
scm_log (SCM z
);
271 SCM_API SCM
scm_log10 (SCM z
);
272 SCM_API SCM
scm_exp (SCM z
);
273 SCM_API SCM
scm_sqrt (SCM z
);
275 SCM_INTERNAL SCM
scm_i_min (SCM x
, SCM y
, SCM rest
);
276 SCM_INTERNAL SCM
scm_i_max (SCM x
, SCM y
, SCM rest
);
277 SCM_INTERNAL SCM
scm_i_sum (SCM x
, SCM y
, SCM rest
);
278 SCM_INTERNAL SCM
scm_i_difference (SCM x
, SCM y
, SCM rest
);
279 SCM_INTERNAL SCM
scm_i_product (SCM x
, SCM y
, SCM rest
);
280 SCM_INTERNAL SCM
scm_i_divide (SCM x
, SCM y
, SCM rest
);
282 /* bignum internal functions */
283 SCM_INTERNAL SCM
scm_i_mkbig (void);
284 SCM_API
/* FIXME: not internal */ SCM
scm_i_normbig (SCM x
);
285 SCM_INTERNAL
int scm_i_bigcmp (SCM a
, SCM b
);
286 SCM_INTERNAL SCM
scm_i_dbl2big (double d
);
287 SCM_INTERNAL SCM
scm_i_dbl2num (double d
);
288 SCM_API
/* FIXME: not internal */ double scm_i_big2dbl (SCM b
);
289 SCM_API
/* FIXME: not internal */ SCM
scm_i_long2big (long n
);
290 SCM_API
/* FIXME: not internal */ SCM
scm_i_ulong2big (unsigned long n
);
291 SCM_API
/* FIXME: not internal */ SCM
scm_i_clonebig (SCM src_big
, int same_sign_p
);
293 /* ratio functions */
294 SCM_API SCM
scm_rationalize (SCM x
, SCM err
);
295 SCM_API SCM
scm_numerator (SCM z
);
296 SCM_API SCM
scm_denominator (SCM z
);
298 /* fraction internal functions */
299 SCM_INTERNAL
double scm_i_fraction2double (SCM z
);
300 SCM_INTERNAL SCM
scm_i_fraction_equalp (SCM x
, SCM y
);
301 SCM_INTERNAL
int scm_i_print_fraction (SCM sexp
, SCM port
, scm_print_state
*pstate
);
303 /* general internal functions */
304 SCM_INTERNAL
void scm_i_print_double (double val
, SCM port
);
305 SCM_INTERNAL
void scm_i_print_complex (double real
, double imag
, SCM port
);
307 /* conversion functions for integers */
309 SCM_API
int scm_is_integer (SCM val
);
310 SCM_API
int scm_is_signed_integer (SCM val
,
311 scm_t_intmax min
, scm_t_intmax max
);
312 SCM_API
int scm_is_unsigned_integer (SCM val
,
313 scm_t_uintmax min
, scm_t_uintmax max
);
315 SCM_API SCM
scm_from_signed_integer (scm_t_intmax val
);
316 SCM_API SCM
scm_from_unsigned_integer (scm_t_uintmax val
);
318 SCM_API scm_t_intmax
scm_to_signed_integer (SCM val
,
321 SCM_API scm_t_uintmax
scm_to_unsigned_integer (SCM val
,
325 SCM_API scm_t_int8
scm_to_int8 (SCM x
);
326 SCM_API SCM
scm_from_int8 (scm_t_int8 x
);
328 SCM_API scm_t_uint8
scm_to_uint8 (SCM x
);
329 SCM_API SCM
scm_from_uint8 (scm_t_uint8 x
);
331 SCM_API scm_t_int16
scm_to_int16 (SCM x
);
332 SCM_API SCM
scm_from_int16 (scm_t_int16 x
);
334 SCM_API scm_t_uint16
scm_to_uint16 (SCM x
);
335 SCM_API SCM
scm_from_uint16 (scm_t_uint16 x
);
337 SCM_API scm_t_int32
scm_to_int32 (SCM x
);
338 SCM_API SCM
scm_from_int32 (scm_t_int32 x
);
340 SCM_API scm_t_uint32
scm_to_uint32 (SCM x
);
341 SCM_API SCM
scm_from_uint32 (scm_t_uint32 x
);
343 SCM_API scm_t_wchar
scm_to_wchar (SCM x
);
344 SCM_API SCM
scm_from_wchar (scm_t_wchar x
);
346 SCM_API scm_t_int64
scm_to_int64 (SCM x
);
347 SCM_API SCM
scm_from_int64 (scm_t_int64 x
);
349 SCM_API scm_t_uint64
scm_to_uint64 (SCM x
);
350 SCM_API SCM
scm_from_uint64 (scm_t_uint64 x
);
352 SCM_API
void scm_to_mpz (SCM x
, mpz_t rop
);
353 SCM_API SCM
scm_from_mpz (mpz_t rop
);
356 /* The conversion functions for other types are aliased to the
357 appropriate ones from above. We pick the right one based on the
360 Not each and every possibility is covered by the code below, and
361 while it is trivial to complete the tests, it might be better to
362 just test for the 'sane' possibilities. When one of the tests
363 below fails, chances are good that some silent assumption somewhere
367 #if SCM_SIZEOF_CHAR == 1
368 #define scm_to_schar scm_to_int8
369 #define scm_from_schar scm_from_int8
370 #define scm_to_uchar scm_to_uint8
371 #define scm_from_uchar scm_from_uint8
373 #define scm_to_char scm_to_uint8
374 #define scm_from_char scm_from_uint8
376 #define scm_to_char scm_to_int8
377 #define scm_from_char scm_from_int8
380 #error sizeof(char) is not 1.
383 #if SCM_SIZEOF_SHORT == 1
384 #define scm_to_short scm_to_int8
385 #define scm_from_short scm_from_int8
386 #define scm_to_ushort scm_to_uint8
387 #define scm_from_ushort scm_from_uint8
389 #if SCM_SIZEOF_SHORT == 2
390 #define scm_to_short scm_to_int16
391 #define scm_from_short scm_from_int16
392 #define scm_to_ushort scm_to_uint16
393 #define scm_from_ushort scm_from_uint16
395 #if SCM_SIZEOF_SHORT == 4
396 #define scm_to_short scm_to_int32
397 #define scm_from_short scm_from_int32
398 #define scm_to_ushort scm_to_uint32
399 #define scm_from_ushort scm_from_uint32
401 #error sizeof(short) is not 1, 2, or 4.
406 #if SCM_SIZEOF_INT == 4
407 #define scm_to_int scm_to_int32
408 #define scm_from_int scm_from_int32
409 #define scm_to_uint scm_to_uint32
410 #define scm_from_uint scm_from_uint32
412 #if SCM_SIZEOF_INT == 8
413 #define scm_to_int scm_to_int64
414 #define scm_from_int scm_from_int64
415 #define scm_to_uint scm_to_uint64
416 #define scm_from_uint scm_from_uint64
418 #error sizeof(int) is not 4 or 8.
422 #if SCM_SIZEOF_LONG == 4
423 #define scm_to_long scm_to_int32
424 #define scm_from_long scm_from_int32
425 #define scm_to_ulong scm_to_uint32
426 #define scm_from_ulong scm_from_uint32
428 #if SCM_SIZEOF_LONG == 8
429 #define scm_to_long scm_to_int64
430 #define scm_from_long scm_from_int64
431 #define scm_to_ulong scm_to_uint64
432 #define scm_from_ulong scm_from_uint64
434 #error sizeof(long) is not 4 or 8.
438 #if SCM_SIZEOF_INTMAX == 4
439 #define scm_to_intmax scm_to_int32
440 #define scm_from_intmax scm_from_int32
441 #define scm_to_uintmax scm_to_uint32
442 #define scm_from_uintmax scm_from_uint32
444 #if SCM_SIZEOF_INTMAX == 8
445 #define scm_to_intmax scm_to_int64
446 #define scm_from_intmax scm_from_int64
447 #define scm_to_uintmax scm_to_uint64
448 #define scm_from_uintmax scm_from_uint64
450 #error sizeof(scm_t_intmax) is not 4 or 8.
454 #if SCM_SIZEOF_LONG_LONG == 0
456 #if SCM_SIZEOF_LONG_LONG == 8
457 #define scm_to_long_long scm_to_int64
458 #define scm_from_long_long scm_from_int64
459 #define scm_to_ulong_long scm_to_uint64
460 #define scm_from_ulong_long scm_from_uint64
462 #error sizeof(long long) is not 8.
466 #if SCM_SIZEOF_SIZE_T == 4
467 #define scm_to_ssize_t scm_to_int32
468 #define scm_from_ssize_t scm_from_int32
469 #define scm_to_size_t scm_to_uint32
470 #define scm_from_size_t scm_from_uint32
472 #if SCM_SIZEOF_SIZE_T == 8
473 #define scm_to_ssize_t scm_to_int64
474 #define scm_from_ssize_t scm_from_int64
475 #define scm_to_size_t scm_to_uint64
476 #define scm_from_size_t scm_from_uint64
478 #error sizeof(size_t) is not 4 or 8.
482 /* conversion functions for double */
484 SCM_API
int scm_is_real (SCM val
);
485 SCM_API
int scm_is_rational (SCM val
);
486 SCM_API
double scm_to_double (SCM val
);
487 SCM_API SCM
scm_from_double (double val
);
489 /* conversion functions for complex */
491 SCM_API
int scm_is_complex (SCM val
);
492 SCM_API SCM
scm_c_make_rectangular (double re
, double im
);
493 SCM_API SCM
scm_c_make_polar (double mag
, double ang
);
494 SCM_API
double scm_c_real_part (SCM z
);
495 SCM_API
double scm_c_imag_part (SCM z
);
496 SCM_API
double scm_c_magnitude (SCM z
);
497 SCM_API
double scm_c_angle (SCM z
);
499 SCM_API
int scm_is_number (SCM val
);
501 SCM_INTERNAL
void scm_init_numbers (void);
503 #endif /* SCM_NUMBERS_H */