(scm_i_clonebig): Remove static, so can use in srfi-60.
[bpt/guile.git] / libguile / numbers.h
1 /* classes: h_files */
2
3 #ifndef SCM_NUMBERS_H
4 #define SCM_NUMBERS_H
5
6 /* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005 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 <gmp.h>
26
27 #include "libguile/__scm.h"
28 #include "libguile/print.h"
29
30 #if SCM_HAVE_FLOATINGPOINT_H
31 # include <floatingpoint.h>
32 #endif
33
34 #if SCM_HAVE_IEEEFP_H
35 # include <ieeefp.h>
36 #endif
37
38 #if SCM_HAVE_NAN_H
39 # if defined (SCO)
40 # define _IEEE 1
41 # endif
42 # include <nan.h>
43 # if defined (SCO)
44 # undef _IEEE
45 # endif
46 #endif /* SCM_HAVE_NAN_H */
47
48 \f
49
50 /* Immediate Numbers, also known as fixnums
51 *
52 * Inums are exact integer data that fits within an SCM word. */
53
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)
57 */
58
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)
62
63 /* SCM_SRS is signed right shift */
64 #if (-1 == (((-1) << 2) + 2) >> 2)
65 # define SCM_SRS(x, y) ((x) >> (y))
66 #else
67 # define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
68 #endif /* (-1 == (((-1) << 2) + 2) >> 2) */
69
70
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))
76
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))
81
82
83 /* A name for 0. */
84 #define SCM_INUM0 (SCM_I_MAKINUM (0))
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
115 * the printed or scm_string representation of an scm_t_intmax in
116 * radix 2. The buffer passed to scm_iint2str and scm_iuint2str must
117 * be of this size, for example.
118 */
119 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
120
121 \f
122
123 /* Numbers
124 */
125
126
127 /* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
128 * differ in one bit: This way, checking if an object is an inexact number can
129 * be done quickly (using the TYP16S macro). */
130
131 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
132 * and SCM_NUMP) */
133 #define scm_tc16_big (scm_tc7_number + 1 * 256L)
134 #define scm_tc16_real (scm_tc7_number + 2 * 256L)
135 #define scm_tc16_complex (scm_tc7_number + 3 * 256L)
136 #define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
137
138 #define SCM_INEXACTP(x) \
139 (!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
140 #define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
141 #define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
142
143 #define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
144 #define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
145 #define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
146 #define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
147
148 /* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
149 #define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
150 #define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
151
152 #define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
153 #define SCM_NUMP(x) (!SCM_IMP(x) \
154 && (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
155 || ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
156 /* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
157
158 #define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
159 #define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
160 #define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
161 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
162 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
163
164 /* I think the left half word is free in the type, so I'll use bit 17 */
165 #define SCM_FRACTION_REDUCED_BIT 0x10000
166 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
167 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
168 #define SCM_FRACTION_REDUCED(x) (0x10000 & SCM_CELL_TYPE (x))
169
170 \f
171
172 typedef struct scm_t_double
173 {
174 SCM type;
175 SCM pad;
176 double real;
177 } scm_t_double;
178
179 typedef struct scm_t_complex
180 {
181 double real;
182 double imag;
183 } scm_t_complex;
184
185 \f
186
187 SCM_API SCM scm_exact_p (SCM x);
188 SCM_API SCM scm_odd_p (SCM n);
189 SCM_API SCM scm_even_p (SCM n);
190 SCM_API SCM scm_inf_p (SCM n);
191 SCM_API SCM scm_nan_p (SCM n);
192 SCM_API SCM scm_inf (void);
193 SCM_API SCM scm_nan (void);
194 SCM_API SCM scm_abs (SCM x);
195 SCM_API SCM scm_quotient (SCM x, SCM y);
196 SCM_API SCM scm_remainder (SCM x, SCM y);
197 SCM_API SCM scm_modulo (SCM x, SCM y);
198 SCM_API SCM scm_gcd (SCM x, SCM y);
199 SCM_API SCM scm_lcm (SCM n1, SCM n2);
200 SCM_API SCM scm_logand (SCM n1, SCM n2);
201 SCM_API SCM scm_logior (SCM n1, SCM n2);
202 SCM_API SCM scm_logxor (SCM n1, SCM n2);
203 SCM_API SCM scm_logtest (SCM n1, SCM n2);
204 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
205 SCM_API SCM scm_lognot (SCM n);
206 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
207 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
208 SCM_API SCM scm_ash (SCM n, SCM cnt);
209 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
210 SCM_API SCM scm_logcount (SCM n);
211 SCM_API SCM scm_integer_length (SCM n);
212
213 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
214 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
215 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
216 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
217 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
218 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
219 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
220 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
221 SCM_API SCM scm_bigequal (SCM x, SCM y);
222 SCM_API SCM scm_real_equalp (SCM x, SCM y);
223 SCM_API SCM scm_complex_equalp (SCM x, SCM y);
224 SCM_API SCM scm_number_p (SCM x);
225 SCM_API SCM scm_complex_p (SCM x);
226 SCM_API SCM scm_real_p (SCM x);
227 SCM_API SCM scm_rational_p (SCM z);
228 SCM_API SCM scm_integer_p (SCM x);
229 SCM_API SCM scm_inexact_p (SCM x);
230 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
231 SCM_API SCM scm_less_p (SCM x, SCM y);
232 SCM_API SCM scm_gr_p (SCM x, SCM y);
233 SCM_API SCM scm_leq_p (SCM x, SCM y);
234 SCM_API SCM scm_geq_p (SCM x, SCM y);
235 SCM_API SCM scm_zero_p (SCM z);
236 SCM_API SCM scm_positive_p (SCM x);
237 SCM_API SCM scm_negative_p (SCM x);
238 SCM_API SCM scm_max (SCM x, SCM y);
239 SCM_API SCM scm_min (SCM x, SCM y);
240 SCM_API SCM scm_sum (SCM x, SCM y);
241 SCM_API SCM scm_difference (SCM x, SCM y);
242 SCM_API SCM scm_product (SCM x, SCM y);
243 SCM_API SCM scm_divide (SCM x, SCM y);
244 SCM_API SCM scm_floor (SCM x);
245 SCM_API SCM scm_ceiling (SCM x);
246 SCM_API double scm_asinh (double x);
247 SCM_API double scm_acosh (double x);
248 SCM_API double scm_atanh (double x);
249 SCM_API double scm_c_truncate (double x);
250 SCM_API double scm_c_round (double x);
251 SCM_API SCM scm_truncate_number (SCM x);
252 SCM_API SCM scm_round_number (SCM x);
253 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
254 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
255 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
256 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
257 SCM_API SCM scm_real_part (SCM z);
258 SCM_API SCM scm_imag_part (SCM z);
259 SCM_API SCM scm_magnitude (SCM z);
260 SCM_API SCM scm_angle (SCM z);
261 SCM_API SCM scm_exact_to_inexact (SCM z);
262 SCM_API SCM scm_inexact_to_exact (SCM z);
263 SCM_API SCM scm_trunc (SCM x);
264
265 /* bignum internal functions */
266 SCM_API SCM scm_i_mkbig (void);
267 SCM_API SCM scm_i_normbig (SCM x);
268 SCM_API int scm_i_bigcmp (SCM a, SCM b);
269 SCM_API SCM scm_i_dbl2big (double d);
270 SCM_API SCM scm_i_dbl2num (double d);
271 SCM_API double scm_i_big2dbl (SCM b);
272 SCM_API SCM scm_i_long2big (long n);
273 SCM_API SCM scm_i_ulong2big (unsigned long n);
274 SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);
275
276 /* ratio functions */
277 SCM_API SCM scm_rationalize (SCM x, SCM err);
278 SCM_API SCM scm_numerator (SCM z);
279 SCM_API SCM scm_denominator (SCM z);
280
281 /* fraction internal functions */
282 SCM_API double scm_i_fraction2double (SCM z);
283 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
284 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
285
286 /* general internal functions */
287 SCM_API void scm_i_print_double (double val, SCM port);
288 SCM_API void scm_i_print_complex (double real, double imag, SCM port);
289
290 /* conversion functions for integers */
291
292 SCM_API int scm_is_integer (SCM val);
293 SCM_API int scm_is_signed_integer (SCM val,
294 scm_t_intmax min, scm_t_intmax max);
295 SCM_API int scm_is_unsigned_integer (SCM val,
296 scm_t_uintmax min, scm_t_uintmax max);
297
298 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
299 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
300
301 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
302 scm_t_intmax min,
303 scm_t_intmax max);
304 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
305 scm_t_uintmax min,
306 scm_t_uintmax max);
307
308 SCM_API scm_t_int8 scm_to_int8 (SCM x);
309 SCM_API SCM scm_from_int8 (scm_t_int8 x);
310
311 SCM_API scm_t_uint8 scm_to_uint8 (SCM x);
312 SCM_API SCM scm_from_uint8 (scm_t_uint8 x);
313
314 SCM_API scm_t_int16 scm_to_int16 (SCM x);
315 SCM_API SCM scm_from_int16 (scm_t_int16 x);
316
317 SCM_API scm_t_uint16 scm_to_uint16 (SCM x);
318 SCM_API SCM scm_from_uint16 (scm_t_uint16 x);
319
320 SCM_API scm_t_int32 scm_to_int32 (SCM x);
321 SCM_API SCM scm_from_int32 (scm_t_int32 x);
322
323 SCM_API scm_t_uint32 scm_to_uint32 (SCM x);
324 SCM_API SCM scm_from_uint32 (scm_t_uint32 x);
325
326 #if SCM_HAVE_T_INT64
327
328 SCM_API scm_t_int64 scm_to_int64 (SCM x);
329 SCM_API SCM scm_from_int64 (scm_t_int64 x);
330
331 SCM_API scm_t_uint64 scm_to_uint64 (SCM x);
332 SCM_API SCM scm_from_uint64 (scm_t_uint64 x);
333
334 #endif
335
336 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
337 SCM_API SCM scm_from_mpz (mpz_t rop);
338
339
340 /* The conversion functions for other types are aliased to the
341 appropriate ones from above. We pick the right one based on the
342 size of the type.
343
344 Not each and every possibility is covered by the code below, and
345 while it is trivial to complete the tests, it might be better to
346 just test for the 'sane' possibilities. When one of the tests
347 below fails, chances are good that some silent assumption somewhere
348 else will also fail.
349 */
350
351 #if SCM_SIZEOF_CHAR == 1
352 #define scm_to_schar scm_to_int8
353 #define scm_from_schar scm_from_int8
354 #define scm_to_uchar scm_to_uint8
355 #define scm_from_uchar scm_from_uint8
356 #if CHAR_MIN == 0
357 #define scm_to_char scm_to_uint8
358 #define scm_from_char scm_from_uint8
359 #else
360 #define scm_to_char scm_to_int8
361 #define scm_from_char scm_from_int8
362 #endif
363 #else
364 #error sizeof(char) is not 1.
365 #endif
366
367 #if SCM_SIZEOF_SHORT == 1
368 #define scm_to_short scm_to_int8
369 #define scm_from_short scm_from_int8
370 #define scm_to_ushort scm_to_uint8
371 #define scm_from_ushort scm_from_uint8
372 #else
373 #if SCM_SIZEOF_SHORT == 2
374 #define scm_to_short scm_to_int16
375 #define scm_from_short scm_from_int16
376 #define scm_to_ushort scm_to_uint16
377 #define scm_from_ushort scm_from_uint16
378 #else
379 #if SCM_SIZEOF_SHORT == 4
380 #define scm_to_short scm_to_int32
381 #define scm_from_short scm_from_int32
382 #define scm_to_ushort scm_to_uint32
383 #define scm_from_ushort scm_from_uint32
384 #else
385 #error sizeof(short) is not 1, 2, or 4.
386 #endif
387 #endif
388 #endif
389
390 #if SCM_SIZEOF_INT == 4
391 #define scm_to_int scm_to_int32
392 #define scm_from_int scm_from_int32
393 #define scm_to_uint scm_to_uint32
394 #define scm_from_uint scm_from_uint32
395 #else
396 #if SCM_SIZEOF_INT == 8
397 #define scm_to_int scm_to_int64
398 #define scm_from_int scm_from_int64
399 #define scm_to_uint scm_to_uint64
400 #define scm_from_uint scm_from_uint64
401 #else
402 #error sizeof(int) is not 4 or 8.
403 #endif
404 #endif
405
406 #if SCM_SIZEOF_LONG == 4
407 #define scm_to_long scm_to_int32
408 #define scm_from_long scm_from_int32
409 #define scm_to_ulong scm_to_uint32
410 #define scm_from_ulong scm_from_uint32
411 #else
412 #if SCM_SIZEOF_LONG == 8
413 #define scm_to_long scm_to_int64
414 #define scm_from_long scm_from_int64
415 #define scm_to_ulong scm_to_uint64
416 #define scm_from_ulong scm_from_uint64
417 #else
418 #error sizeof(long) is not 4 or 8.
419 #endif
420 #endif
421
422 #if SCM_SIZEOF_INTMAX == 4
423 #define scm_to_intmax scm_to_int32
424 #define scm_from_intmax scm_from_int32
425 #define scm_to_uintmax scm_to_uint32
426 #define scm_from_uintmax scm_from_uint32
427 #else
428 #if SCM_SIZEOF_INTMAX == 8
429 #define scm_to_intmax scm_to_int64
430 #define scm_from_intmax scm_from_int64
431 #define scm_to_uintmax scm_to_uint64
432 #define scm_from_uintmax scm_from_uint64
433 #else
434 #error sizeof(scm_t_intmax) is not 4 or 8.
435 #endif
436 #endif
437
438 #if SCM_SIZEOF_LONG_LONG == 0
439 #else
440 #if SCM_SIZEOF_LONG_LONG == 8
441 #define scm_to_long_long scm_to_int64
442 #define scm_from_long_long scm_from_int64
443 #define scm_to_ulong_long scm_to_uint64
444 #define scm_from_ulong_long scm_from_uint64
445 #else
446 #error sizeof(long long) is not 8.
447 #endif
448 #endif
449
450 #if SCM_SIZEOF_SIZE_T == 4
451 #define scm_to_ssize_t scm_to_int32
452 #define scm_from_ssize_t scm_from_int32
453 #define scm_to_size_t scm_to_uint32
454 #define scm_from_size_t scm_from_uint32
455 #else
456 #if SCM_SIZEOF_SIZE_T == 8
457 #define scm_to_ssize_t scm_to_int64
458 #define scm_from_ssize_t scm_from_int64
459 #define scm_to_size_t scm_to_uint64
460 #define scm_from_size_t scm_from_uint64
461 #else
462 #error sizeof(size_t) is not 4 or 8.
463 #endif
464 #endif
465
466 /* conversion functions for double */
467
468 SCM_API int scm_is_real (SCM val);
469 SCM_API int scm_is_rational (SCM val);
470 SCM_API double scm_to_double (SCM val);
471 SCM_API SCM scm_from_double (double val);
472
473 /* conversion functions for complex */
474
475 SCM_API int scm_is_complex (SCM val);
476 SCM_API SCM scm_c_make_rectangular (double re, double im);
477 SCM_API SCM scm_c_make_polar (double mag, double ang);
478 SCM_API double scm_c_real_part (SCM z);
479 SCM_API double scm_c_imag_part (SCM z);
480 SCM_API double scm_c_magnitude (SCM z);
481 SCM_API double scm_c_angle (SCM z);
482
483 SCM_API int scm_is_number (SCM val);
484
485 SCM_API void scm_init_numbers (void);
486
487 #endif /* SCM_NUMBERS_H */
488
489 /*
490 Local Variables:
491 c-file-style: "gnu"
492 End:
493 */