6 /* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 #include "libguile/__scm.h"
26 #include "libguile/print.h"
28 #if SCM_HAVE_FLOATINGPOINT_H
29 # include <floatingpoint.h>
44 #endif /* SCM_HAVE_NAN_H */
48 /* Immediate Numbers, also known as fixnums
50 * Inums are exact integer data that fits within an SCM word. */
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)
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)
61 /* SCM_SRS is signed right shift */
62 #if (-1 == (((-1) << 2) + 2) >> 2)
63 # define SCM_SRS(x, y) ((x) >> (y))
65 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
66 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
69 #define SCM_I_INUMP(x) (2 & SCM_UNPACK (x))
70 #define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
71 #define SCM_I_MAKINUM(x) \
72 (SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
73 #define SCM_I_INUM(x) (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
75 /* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
76 #define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
77 #define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
78 #define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
82 #define SCM_INUM0 (SCM_I_MAKINUM (0))
84 /* SCM_MAXEXP is the maximum double precision exponent
85 * SCM_FLTMAX is less than or scm_equal the largest single precision float
88 #if SCM_HAVE_STDC_HEADERS
92 # define copysign _copysign
94 # define finite _finite
95 # endif /* __MINGW32__ */
96 # endif /* ndef GO32 */
97 #endif /* def STDC_HEADERS */
100 # define SCM_MAXEXP DBL_MAX_10_EXP
102 # define SCM_MAXEXP 308 /* IEEE doubles */
103 #endif /* def DBL_MAX_10_EXP */
106 # define SCM_FLTMAX FLT_MAX
108 # define SCM_FLTMAX 1e+23
109 #endif /* def FLT_MAX */
112 /* SCM_INTBUFLEN is the maximum number of characters neccessary for the
113 * printed or scm_string representation of an exact immediate.
115 #define SCM_INTBUFLEN (5 + SCM_LONG_BIT)
123 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
124 * differ in one bit: This way, checking if an object is an inexact number can
125 * be done quickly (using the TYP16S macro). */
127 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
129 #define scm_tc16_big (scm_tc7_number + 1 * 256L)
130 #define scm_tc16_real (scm_tc7_number + 2 * 256L)
131 #define scm_tc16_complex (scm_tc7_number + 3 * 256L)
132 #define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
134 #define SCM_INEXACTP(x) \
135 (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
136 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
137 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
139 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
140 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
141 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
142 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
144 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
145 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
146 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
148 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
149 #define SCM_NUMP(x) (!SCM_IMP(x) \
150 && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
151 || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
152 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
154 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
155 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
156 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
157 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
158 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
160 /* I think the left half word is free in the type, so I'll use bit 17 */
161 #define SCM_FRACTION_REDUCED_BIT 0x10000
162 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
163 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
164 #define SCM_FRACTION_REDUCED(x) (0x10000 & SCM_CELL_TYPE (x))
168 typedef struct scm_t_double
175 typedef struct scm_t_complex
183 SCM_API SCM
scm_exact_p (SCM x
);
184 SCM_API SCM
scm_odd_p (SCM n
);
185 SCM_API SCM
scm_even_p (SCM n
);
186 SCM_API SCM
scm_inf_p (SCM n
);
187 SCM_API SCM
scm_nan_p (SCM n
);
188 SCM_API SCM
scm_inf (void);
189 SCM_API SCM
scm_nan (void);
190 SCM_API SCM
scm_abs (SCM x
);
191 SCM_API SCM
scm_quotient (SCM x
, SCM y
);
192 SCM_API SCM
scm_remainder (SCM x
, SCM y
);
193 SCM_API SCM
scm_modulo (SCM x
, SCM y
);
194 SCM_API SCM
scm_gcd (SCM x
, SCM y
);
195 SCM_API SCM
scm_lcm (SCM n1
, SCM n2
);
196 SCM_API SCM
scm_logand (SCM n1
, SCM n2
);
197 SCM_API SCM
scm_logior (SCM n1
, SCM n2
);
198 SCM_API SCM
scm_logxor (SCM n1
, SCM n2
);
199 SCM_API SCM
scm_logtest (SCM n1
, SCM n2
);
200 SCM_API SCM
scm_logbit_p (SCM n1
, SCM n2
);
201 SCM_API SCM
scm_lognot (SCM n
);
202 SCM_API SCM
scm_modulo_expt (SCM n
, SCM k
, SCM m
);
203 SCM_API SCM
scm_integer_expt (SCM z1
, SCM z2
);
204 SCM_API SCM
scm_ash (SCM n
, SCM cnt
);
205 SCM_API SCM
scm_bit_extract (SCM n
, SCM start
, SCM end
);
206 SCM_API SCM
scm_logcount (SCM n
);
207 SCM_API SCM
scm_integer_length (SCM n
);
209 SCM_API
size_t scm_iint2str (long num
, int rad
, char *p
);
210 SCM_API SCM
scm_number_to_string (SCM x
, SCM radix
);
211 SCM_API
int scm_print_real (SCM sexp
, SCM port
, scm_print_state
*pstate
);
212 SCM_API
int scm_print_complex (SCM sexp
, SCM port
, scm_print_state
*pstate
);
213 SCM_API
int scm_bigprint (SCM exp
, SCM port
, scm_print_state
*pstate
);
214 SCM_API SCM
scm_i_mem2number (const char *mem
, size_t len
, unsigned int radix
);
215 SCM_API SCM
scm_string_to_number (SCM str
, SCM radix
);
216 SCM_API SCM
scm_bigequal (SCM x
, SCM y
);
217 SCM_API SCM
scm_real_equalp (SCM x
, SCM y
);
218 SCM_API SCM
scm_complex_equalp (SCM x
, SCM y
);
219 SCM_API SCM
scm_number_p (SCM x
);
220 SCM_API SCM
scm_complex_p (SCM x
);
221 SCM_API SCM
scm_real_p (SCM x
);
222 SCM_API SCM
scm_rational_p (SCM z
);
223 SCM_API SCM
scm_integer_p (SCM x
);
224 SCM_API SCM
scm_inexact_p (SCM x
);
225 SCM_API SCM
scm_num_eq_p (SCM x
, SCM y
);
226 SCM_API SCM
scm_less_p (SCM x
, SCM y
);
227 SCM_API SCM
scm_gr_p (SCM x
, SCM y
);
228 SCM_API SCM
scm_leq_p (SCM x
, SCM y
);
229 SCM_API SCM
scm_geq_p (SCM x
, SCM y
);
230 SCM_API SCM
scm_zero_p (SCM z
);
231 SCM_API SCM
scm_positive_p (SCM x
);
232 SCM_API SCM
scm_negative_p (SCM x
);
233 SCM_API SCM
scm_max (SCM x
, SCM y
);
234 SCM_API SCM
scm_min (SCM x
, SCM y
);
235 SCM_API SCM
scm_sum (SCM x
, SCM y
);
236 SCM_API SCM
scm_difference (SCM x
, SCM y
);
237 SCM_API SCM
scm_product (SCM x
, SCM y
);
238 SCM_API SCM
scm_divide (SCM x
, SCM y
);
239 SCM_API SCM
scm_floor (SCM x
);
240 SCM_API SCM
scm_ceiling (SCM x
);
241 SCM_API
double scm_asinh (double x
);
242 SCM_API
double scm_acosh (double x
);
243 SCM_API
double scm_atanh (double x
);
244 SCM_API
double scm_truncate (double x
);
245 SCM_API
double scm_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_sys_expt (SCM z1
, SCM z2
);
249 SCM_API SCM
scm_sys_atan2 (SCM z1
, SCM z2
);
250 SCM_API SCM
scm_make_rectangular (SCM z1
, SCM z2
);
251 SCM_API SCM
scm_make_polar (SCM z1
, SCM z2
);
252 SCM_API SCM
scm_real_part (SCM z
);
253 SCM_API SCM
scm_imag_part (SCM z
);
254 SCM_API SCM
scm_magnitude (SCM z
);
255 SCM_API SCM
scm_angle (SCM z
);
256 SCM_API SCM
scm_exact_to_inexact (SCM z
);
257 SCM_API SCM
scm_inexact_to_exact (SCM z
);
258 SCM_API SCM
scm_trunc (SCM x
);
260 /* bignum internal functions */
261 SCM_API SCM
scm_i_mkbig (void);
262 SCM_API SCM
scm_i_normbig (SCM x
);
263 SCM_API
int scm_i_bigcmp (SCM a
, SCM b
);
264 SCM_API SCM
scm_i_dbl2big (double d
);
265 SCM_API SCM
scm_i_dbl2num (double d
);
266 SCM_API
double scm_i_big2dbl (SCM b
);
267 SCM_API SCM
scm_i_long2big (long n
);
268 SCM_API SCM
scm_i_ulong2big (unsigned long n
);
270 /* ratio functions */
271 SCM_API SCM
scm_rationalize (SCM x
, SCM err
);
272 SCM_API SCM
scm_numerator (SCM z
);
273 SCM_API SCM
scm_denominator (SCM z
);
275 /* fraction internal functions */
276 SCM_API
double scm_i_fraction2double (SCM z
);
277 SCM_API SCM
scm_i_fraction_equalp (SCM x
, SCM y
);
278 SCM_API
int scm_i_print_fraction (SCM sexp
, SCM port
, scm_print_state
*pstate
);
280 /* conversion functions for integers */
282 SCM_API
int scm_is_integer (SCM val
);
283 SCM_API
int scm_is_signed_integer (SCM val
,
284 scm_t_intmax min
, scm_t_intmax max
);
285 SCM_API
int scm_is_unsigned_integer (SCM val
,
286 scm_t_uintmax min
, scm_t_uintmax max
);
288 SCM_API SCM
scm_from_signed_integer (scm_t_intmax val
);
289 SCM_API SCM
scm_from_unsigned_integer (scm_t_uintmax val
);
291 SCM_API scm_t_intmax
scm_to_signed_integer (SCM val
,
294 SCM_API scm_t_uintmax
scm_to_unsigned_integer (SCM val
,
298 SCM_API scm_t_int8
scm_to_int8 (SCM x
);
299 SCM_API SCM
scm_from_int8 (scm_t_int8 x
);
301 SCM_API scm_t_uint8
scm_to_uint8 (SCM x
);
302 SCM_API SCM
scm_from_uint8 (scm_t_uint8 x
);
304 SCM_API scm_t_int16
scm_to_int16 (SCM x
);
305 SCM_API SCM
scm_from_int16 (scm_t_int16 x
);
307 SCM_API scm_t_uint16
scm_to_uint16 (SCM x
);
308 SCM_API SCM
scm_from_uint16 (scm_t_uint16 x
);
310 SCM_API scm_t_int32
scm_to_int32 (SCM x
);
311 SCM_API SCM
scm_from_int32 (scm_t_int32 x
);
313 SCM_API scm_t_uint32
scm_to_uint32 (SCM x
);
314 SCM_API SCM
scm_from_uint32 (scm_t_uint32 x
);
318 SCM_API scm_t_int64
scm_to_int64 (SCM x
);
319 SCM_API SCM
scm_from_int64 (scm_t_int64 x
);
321 SCM_API scm_t_uint64
scm_to_uint64 (SCM x
);
322 SCM_API SCM
scm_from_uint64 (scm_t_uint64 x
);
326 /* The conversion functions for other types are aliased to the
327 appropriate ones from above. We pick the right one based on the
330 Not each and every possibility is covered by the code below, and
331 while it is trivial to complete the tests, it might be better to
332 just test for the 'sane' possibilities. When one of the tests
333 below fails, chances are good that some silent assumption somewhere
337 #if SCM_SIZEOF_CHAR == 1
338 #define scm_to_schar scm_to_int8
339 #define scm_from_schar scm_from_int8
340 #define scm_to_uchar scm_to_uint8
341 #define scm_from_uchar scm_from_uint8
343 #define scm_to_char scm_to_uint8
344 #define scm_from_char scm_from_uint8
346 #define scm_to_char scm_to_int8
347 #define scm_from_char scm_from_int8
350 #error sizeof(char) is not 1.
353 #if SCM_SIZEOF_SHORT == 1
354 #define scm_to_short scm_to_int8
355 #define scm_from_short scm_from_int8
356 #define scm_to_ushort scm_to_uint8
357 #define scm_from_ushort scm_from_uint8
359 #if SCM_SIZEOF_SHORT == 2
360 #define scm_to_short scm_to_int16
361 #define scm_from_short scm_from_int16
362 #define scm_to_ushort scm_to_uint16
363 #define scm_from_ushort scm_from_uint16
365 #if SCM_SIZEOF_SHORT == 4
366 #define scm_to_short scm_to_int32
367 #define scm_from_short scm_from_int32
368 #define scm_to_ushort scm_to_uint32
369 #define scm_from_ushort scm_from_uint32
371 #error sizeof(short) is not 1, 2, or 4.
376 #if SCM_SIZEOF_INT == 4
377 #define scm_to_int scm_to_int32
378 #define scm_from_int scm_from_int32
379 #define scm_to_uint scm_to_uint32
380 #define scm_from_uint scm_from_uint32
382 #if SCM_SIZEOF_INT == 8
383 #define scm_to_int scm_to_int64
384 #define scm_from_int scm_from_int64
385 #define scm_to_uint scm_to_uint64
386 #define scm_from_uint scm_from_uint64
388 #error sizeof(int) is not 4 or 8.
392 #if SCM_SIZEOF_LONG == 4
393 #define scm_to_long scm_to_int32
394 #define scm_from_long scm_from_int32
395 #define scm_to_ulong scm_to_uint32
396 #define scm_from_ulong scm_from_uint32
398 #if SCM_SIZEOF_LONG == 8
399 #define scm_to_long scm_to_int64
400 #define scm_from_long scm_from_int64
401 #define scm_to_ulong scm_to_uint64
402 #define scm_from_ulong scm_from_uint64
404 #error sizeof(long) is not 4 or 8.
408 #if SCM_SIZEOF_INTMAX == 4
409 #define scm_to_intmax scm_to_int32
410 #define scm_from_intmax scm_from_int32
411 #define scm_to_uintmax scm_to_uint32
412 #define scm_from_uintmax scm_from_uint32
414 #if SCM_SIZEOF_INTMAX == 8
415 #define scm_to_intmax scm_to_int64
416 #define scm_from_intmax scm_from_int64
417 #define scm_to_uintmax scm_to_uint64
418 #define scm_from_uintmax scm_from_uint64
420 #error sizeof(scm_t_intmax) is not 4 or 8.
424 #if SCM_SIZEOF_LONG_LONG == 0
426 #if SCM_SIZEOF_LONG_LONG == 8
427 #define scm_to_long_long scm_to_int64
428 #define scm_from_long_long scm_from_int64
429 #define scm_to_ulong_long scm_to_uint64
430 #define scm_from_ulong_long scm_from_uint64
432 #error sizeof(long long) is not 8.
436 #if SCM_SIZEOF_SIZE_T == 4
437 #define scm_to_ssize_t scm_to_int32
438 #define scm_from_ssize_t scm_from_int32
439 #define scm_to_size_t scm_to_uint32
440 #define scm_from_size_t scm_from_uint32
442 #if SCM_SIZEOF_SIZE_T == 8
443 #define scm_to_ssize_t scm_to_int64
444 #define scm_from_ssize_t scm_from_int64
445 #define scm_to_size_t scm_to_uint64
446 #define scm_from_size_t scm_from_uint64
448 #error sizeof(size_t) is not 4 or 8.
452 /* conversion functions for double */
454 SCM_API
int scm_is_real (SCM val
);
455 SCM_API
int scm_is_rational (SCM val
);
456 SCM_API
double scm_to_double (SCM val
);
457 SCM_API SCM
scm_from_double (double val
);
459 /* conversion functions for complex */
461 SCM_API
int scm_is_complex (SCM val
);
462 SCM_API SCM
scm_c_make_rectangular (double re
, double im
);
463 SCM_API SCM
scm_c_make_polar (double mag
, double ang
);
464 SCM_API
double scm_c_real_part (SCM z
);
465 SCM_API
double scm_c_imag_part (SCM z
);
466 SCM_API
double scm_c_magnitude (SCM z
);
467 SCM_API
double scm_c_angle (SCM z
);
469 SCM_API
int scm_is_number (SCM val
);
471 SCM_API
void scm_init_numbers (void);
473 #endif /* SCM_NUMBERS_H */