(next_fluid_num): [From Ludovic Courtès:] Don't trigger
[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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 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 finite _finite
96 # endif /* __MINGW32__ */
97 # endif /* ndef GO32 */
98 #endif /* def STDC_HEADERS */
99
100 #ifdef DBL_MAX_10_EXP
101 # define SCM_MAXEXP DBL_MAX_10_EXP
102 #else
103 # define SCM_MAXEXP 308 /* IEEE doubles */
104 #endif /* def DBL_MAX_10_EXP */
105
106 #ifdef FLT_MAX
107 # define SCM_FLTMAX FLT_MAX
108 #else
109 # define SCM_FLTMAX 1e+23
110 #endif /* def FLT_MAX */
111
112
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.
117 */
118 #define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
119
120 \f
121
122 /* Numbers
123 */
124
125
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). */
129
130 /* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
131 * and SCM_NUMP) */
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)
136
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)
141
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)
146
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)
150
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 */
156
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))
160 #define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
161 #define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
162
163 /* I think the left half word is free in the type, so I'll use bit 17 */
164 #define SCM_FRACTION_REDUCED_BIT 0x10000
165 #define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
166 #define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
167 #define SCM_FRACTION_REDUCED(x) (0x10000 & SCM_CELL_TYPE (x))
168
169 \f
170
171 typedef struct scm_t_double
172 {
173 SCM type;
174 SCM pad;
175 double real;
176 } scm_t_double;
177
178 typedef struct scm_t_complex
179 {
180 double real;
181 double imag;
182 } scm_t_complex;
183
184 \f
185
186 SCM_API SCM scm_exact_p (SCM x);
187 SCM_API SCM scm_odd_p (SCM n);
188 SCM_API SCM scm_even_p (SCM n);
189 SCM_API SCM scm_inf_p (SCM n);
190 SCM_API SCM scm_nan_p (SCM n);
191 SCM_API SCM scm_inf (void);
192 SCM_API SCM scm_nan (void);
193 SCM_API SCM scm_abs (SCM x);
194 SCM_API SCM scm_quotient (SCM x, SCM y);
195 SCM_API SCM scm_remainder (SCM x, SCM y);
196 SCM_API SCM scm_modulo (SCM x, SCM y);
197 SCM_API SCM scm_gcd (SCM x, SCM y);
198 SCM_API SCM scm_lcm (SCM n1, SCM n2);
199 SCM_API SCM scm_logand (SCM n1, SCM n2);
200 SCM_API SCM scm_logior (SCM n1, SCM n2);
201 SCM_API SCM scm_logxor (SCM n1, SCM n2);
202 SCM_API SCM scm_logtest (SCM n1, SCM n2);
203 SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
204 SCM_API SCM scm_lognot (SCM n);
205 SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
206 SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
207 SCM_API SCM scm_ash (SCM n, SCM cnt);
208 SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
209 SCM_API SCM scm_logcount (SCM n);
210 SCM_API SCM scm_integer_length (SCM n);
211
212 SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
213 SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
214 SCM_API SCM scm_number_to_string (SCM x, SCM radix);
215 SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
216 SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
217 SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
218 SCM_API SCM scm_i_mem2number (const char *mem, size_t len, unsigned int radix);
219 SCM_API SCM scm_string_to_number (SCM str, SCM radix);
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_complex_p (SCM x);
225 SCM_API SCM scm_real_p (SCM x);
226 SCM_API SCM scm_rational_p (SCM z);
227 SCM_API SCM scm_integer_p (SCM x);
228 SCM_API SCM scm_inexact_p (SCM x);
229 SCM_API SCM scm_num_eq_p (SCM x, SCM y);
230 SCM_API SCM scm_less_p (SCM x, SCM y);
231 SCM_API SCM scm_gr_p (SCM x, SCM y);
232 SCM_API SCM scm_leq_p (SCM x, SCM y);
233 SCM_API SCM scm_geq_p (SCM x, SCM y);
234 SCM_API SCM scm_zero_p (SCM z);
235 SCM_API SCM scm_positive_p (SCM x);
236 SCM_API SCM scm_negative_p (SCM x);
237 SCM_API SCM scm_max (SCM x, SCM y);
238 SCM_API SCM scm_min (SCM x, SCM y);
239 SCM_API SCM scm_sum (SCM x, SCM y);
240 SCM_API SCM scm_oneplus (SCM x);
241 SCM_API SCM scm_difference (SCM x, SCM y);
242 SCM_API SCM scm_oneminus (SCM x);
243 SCM_API SCM scm_product (SCM x, SCM y);
244 SCM_API SCM scm_divide (SCM x, SCM y);
245 SCM_API SCM scm_floor (SCM x);
246 SCM_API SCM scm_ceiling (SCM x);
247 SCM_API double scm_asinh (double x);
248 SCM_API double scm_acosh (double x);
249 SCM_API double scm_atanh (double x);
250 SCM_API double scm_c_truncate (double x);
251 SCM_API double scm_c_round (double x);
252 SCM_API SCM scm_truncate_number (SCM x);
253 SCM_API SCM scm_round_number (SCM x);
254 SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
255 SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
256 SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
257 SCM_API SCM scm_make_polar (SCM z1, SCM z2);
258 SCM_API SCM scm_real_part (SCM z);
259 SCM_API SCM scm_imag_part (SCM z);
260 SCM_API SCM scm_magnitude (SCM z);
261 SCM_API SCM scm_angle (SCM z);
262 SCM_API SCM scm_exact_to_inexact (SCM z);
263 SCM_API SCM scm_inexact_to_exact (SCM z);
264 SCM_API SCM scm_trunc (SCM x);
265
266 /* bignum internal functions */
267 SCM_API SCM scm_i_mkbig (void);
268 SCM_API SCM scm_i_normbig (SCM x);
269 SCM_API int scm_i_bigcmp (SCM a, SCM b);
270 SCM_API SCM scm_i_dbl2big (double d);
271 SCM_API SCM scm_i_dbl2num (double d);
272 SCM_API double scm_i_big2dbl (SCM b);
273 SCM_API SCM scm_i_long2big (long n);
274 SCM_API SCM scm_i_ulong2big (unsigned long n);
275 SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);
276
277 /* ratio functions */
278 SCM_API SCM scm_rationalize (SCM x, SCM err);
279 SCM_API SCM scm_numerator (SCM z);
280 SCM_API SCM scm_denominator (SCM z);
281
282 /* fraction internal functions */
283 SCM_API double scm_i_fraction2double (SCM z);
284 SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
285 SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
286
287 /* general internal functions */
288 SCM_API void scm_i_print_double (double val, SCM port);
289 SCM_API void scm_i_print_complex (double real, double imag, SCM port);
290
291 /* conversion functions for integers */
292
293 SCM_API int scm_is_integer (SCM val);
294 SCM_API int scm_is_signed_integer (SCM val,
295 scm_t_intmax min, scm_t_intmax max);
296 SCM_API int scm_is_unsigned_integer (SCM val,
297 scm_t_uintmax min, scm_t_uintmax max);
298
299 SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
300 SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
301
302 SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
303 scm_t_intmax min,
304 scm_t_intmax max);
305 SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
306 scm_t_uintmax min,
307 scm_t_uintmax max);
308
309 SCM_API scm_t_int8 scm_to_int8 (SCM x);
310 SCM_API SCM scm_from_int8 (scm_t_int8 x);
311
312 SCM_API scm_t_uint8 scm_to_uint8 (SCM x);
313 SCM_API SCM scm_from_uint8 (scm_t_uint8 x);
314
315 SCM_API scm_t_int16 scm_to_int16 (SCM x);
316 SCM_API SCM scm_from_int16 (scm_t_int16 x);
317
318 SCM_API scm_t_uint16 scm_to_uint16 (SCM x);
319 SCM_API SCM scm_from_uint16 (scm_t_uint16 x);
320
321 SCM_API scm_t_int32 scm_to_int32 (SCM x);
322 SCM_API SCM scm_from_int32 (scm_t_int32 x);
323
324 SCM_API scm_t_uint32 scm_to_uint32 (SCM x);
325 SCM_API SCM scm_from_uint32 (scm_t_uint32 x);
326
327 #if SCM_HAVE_T_INT64
328
329 SCM_API scm_t_int64 scm_to_int64 (SCM x);
330 SCM_API SCM scm_from_int64 (scm_t_int64 x);
331
332 SCM_API scm_t_uint64 scm_to_uint64 (SCM x);
333 SCM_API SCM scm_from_uint64 (scm_t_uint64 x);
334
335 #endif
336
337 SCM_API void scm_to_mpz (SCM x, mpz_t rop);
338 SCM_API SCM scm_from_mpz (mpz_t rop);
339
340
341 /* The conversion functions for other types are aliased to the
342 appropriate ones from above. We pick the right one based on the
343 size of the type.
344
345 Not each and every possibility is covered by the code below, and
346 while it is trivial to complete the tests, it might be better to
347 just test for the 'sane' possibilities. When one of the tests
348 below fails, chances are good that some silent assumption somewhere
349 else will also fail.
350 */
351
352 #if SCM_SIZEOF_CHAR == 1
353 #define scm_to_schar scm_to_int8
354 #define scm_from_schar scm_from_int8
355 #define scm_to_uchar scm_to_uint8
356 #define scm_from_uchar scm_from_uint8
357 #if CHAR_MIN == 0
358 #define scm_to_char scm_to_uint8
359 #define scm_from_char scm_from_uint8
360 #else
361 #define scm_to_char scm_to_int8
362 #define scm_from_char scm_from_int8
363 #endif
364 #else
365 #error sizeof(char) is not 1.
366 #endif
367
368 #if SCM_SIZEOF_SHORT == 1
369 #define scm_to_short scm_to_int8
370 #define scm_from_short scm_from_int8
371 #define scm_to_ushort scm_to_uint8
372 #define scm_from_ushort scm_from_uint8
373 #else
374 #if SCM_SIZEOF_SHORT == 2
375 #define scm_to_short scm_to_int16
376 #define scm_from_short scm_from_int16
377 #define scm_to_ushort scm_to_uint16
378 #define scm_from_ushort scm_from_uint16
379 #else
380 #if SCM_SIZEOF_SHORT == 4
381 #define scm_to_short scm_to_int32
382 #define scm_from_short scm_from_int32
383 #define scm_to_ushort scm_to_uint32
384 #define scm_from_ushort scm_from_uint32
385 #else
386 #error sizeof(short) is not 1, 2, or 4.
387 #endif
388 #endif
389 #endif
390
391 #if SCM_SIZEOF_INT == 4
392 #define scm_to_int scm_to_int32
393 #define scm_from_int scm_from_int32
394 #define scm_to_uint scm_to_uint32
395 #define scm_from_uint scm_from_uint32
396 #else
397 #if SCM_SIZEOF_INT == 8
398 #define scm_to_int scm_to_int64
399 #define scm_from_int scm_from_int64
400 #define scm_to_uint scm_to_uint64
401 #define scm_from_uint scm_from_uint64
402 #else
403 #error sizeof(int) is not 4 or 8.
404 #endif
405 #endif
406
407 #if SCM_SIZEOF_LONG == 4
408 #define scm_to_long scm_to_int32
409 #define scm_from_long scm_from_int32
410 #define scm_to_ulong scm_to_uint32
411 #define scm_from_ulong scm_from_uint32
412 #else
413 #if SCM_SIZEOF_LONG == 8
414 #define scm_to_long scm_to_int64
415 #define scm_from_long scm_from_int64
416 #define scm_to_ulong scm_to_uint64
417 #define scm_from_ulong scm_from_uint64
418 #else
419 #error sizeof(long) is not 4 or 8.
420 #endif
421 #endif
422
423 #if SCM_SIZEOF_INTMAX == 4
424 #define scm_to_intmax scm_to_int32
425 #define scm_from_intmax scm_from_int32
426 #define scm_to_uintmax scm_to_uint32
427 #define scm_from_uintmax scm_from_uint32
428 #else
429 #if SCM_SIZEOF_INTMAX == 8
430 #define scm_to_intmax scm_to_int64
431 #define scm_from_intmax scm_from_int64
432 #define scm_to_uintmax scm_to_uint64
433 #define scm_from_uintmax scm_from_uint64
434 #else
435 #error sizeof(scm_t_intmax) is not 4 or 8.
436 #endif
437 #endif
438
439 #if SCM_SIZEOF_LONG_LONG == 0
440 #else
441 #if SCM_SIZEOF_LONG_LONG == 8
442 #define scm_to_long_long scm_to_int64
443 #define scm_from_long_long scm_from_int64
444 #define scm_to_ulong_long scm_to_uint64
445 #define scm_from_ulong_long scm_from_uint64
446 #else
447 #error sizeof(long long) is not 8.
448 #endif
449 #endif
450
451 #if SCM_SIZEOF_SIZE_T == 4
452 #define scm_to_ssize_t scm_to_int32
453 #define scm_from_ssize_t scm_from_int32
454 #define scm_to_size_t scm_to_uint32
455 #define scm_from_size_t scm_from_uint32
456 #else
457 #if SCM_SIZEOF_SIZE_T == 8
458 #define scm_to_ssize_t scm_to_int64
459 #define scm_from_ssize_t scm_from_int64
460 #define scm_to_size_t scm_to_uint64
461 #define scm_from_size_t scm_from_uint64
462 #else
463 #error sizeof(size_t) is not 4 or 8.
464 #endif
465 #endif
466
467 /* conversion functions for double */
468
469 SCM_API int scm_is_real (SCM val);
470 SCM_API int scm_is_rational (SCM val);
471 SCM_API double scm_to_double (SCM val);
472 SCM_API SCM scm_from_double (double val);
473
474 /* conversion functions for complex */
475
476 SCM_API int scm_is_complex (SCM val);
477 SCM_API SCM scm_c_make_rectangular (double re, double im);
478 SCM_API SCM scm_c_make_polar (double mag, double ang);
479 SCM_API double scm_c_real_part (SCM z);
480 SCM_API double scm_c_imag_part (SCM z);
481 SCM_API double scm_c_magnitude (SCM z);
482 SCM_API double scm_c_angle (SCM z);
483
484 SCM_API int scm_is_number (SCM val);
485
486 SCM_API void scm_init_numbers (void);
487
488 #endif /* SCM_NUMBERS_H */
489
490 /*
491 Local Variables:
492 c-file-style: "gnu"
493 End:
494 */