Commit | Line | Data |
---|---|---|
8e43ed5d | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e | 7 | * This library is free software; you can redistribute it and/or |
53befeb7 NJ |
8 | * modify it under the terms of the GNU Lesser General Public License |
9 | * as published by the Free Software Foundation; either version 3 of | |
10 | * the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
53befeb7 NJ |
12 | * This library is distributed in the hope that it will be useful, but |
13 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |
73be1d9e MV |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
53befeb7 NJ |
19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
20 | * 02110-1301 USA | |
73be1d9e | 21 | */ |
1bbd0b84 | 22 | |
0f2d19dd | 23 | \f |
ca46fb90 RB |
24 | /* General assumptions: |
25 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
26 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
27 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
28 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 29 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
30 | */ |
31 | ||
32 | /* TODO: | |
33 | ||
34 | - see if special casing bignums and reals in integer-exponent when | |
35 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
36 | ||
37 | - look in to better short-circuiting of common cases in | |
38 | integer-expt and elsewhere. | |
39 | ||
40 | - see if direct mpz operations can help in ash and elsewhere. | |
41 | ||
42 | */ | |
0f2d19dd | 43 | |
dbb605f5 | 44 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
45 | # include <config.h> |
46 | #endif | |
47 | ||
0f2d19dd | 48 | #include <math.h> |
fc194577 | 49 | #include <string.h> |
3f47e526 MG |
50 | #include <unicase.h> |
51 | #include <unictype.h> | |
f92e85f7 | 52 | |
8ab3d8a0 KR |
53 | #if HAVE_COMPLEX_H |
54 | #include <complex.h> | |
55 | #endif | |
56 | ||
a0599745 | 57 | #include "libguile/_scm.h" |
a0599745 MD |
58 | #include "libguile/feature.h" |
59 | #include "libguile/ports.h" | |
60 | #include "libguile/root.h" | |
61 | #include "libguile/smob.h" | |
62 | #include "libguile/strings.h" | |
864e7d42 | 63 | #include "libguile/bdw-gc.h" |
a0599745 MD |
64 | |
65 | #include "libguile/validate.h" | |
66 | #include "libguile/numbers.h" | |
1be6b49c | 67 | #include "libguile/deprecation.h" |
f4c627b3 | 68 | |
f92e85f7 MV |
69 | #include "libguile/eq.h" |
70 | ||
8ab3d8a0 KR |
71 | /* values per glibc, if not already defined */ |
72 | #ifndef M_LOG10E | |
73 | #define M_LOG10E 0.43429448190325182765 | |
74 | #endif | |
75 | #ifndef M_PI | |
76 | #define M_PI 3.14159265358979323846 | |
77 | #endif | |
78 | ||
e25f3727 AW |
79 | typedef scm_t_signed_bits scm_t_inum; |
80 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
81 | ||
7112615f MW |
82 | /* Tests to see if a C double is neither infinite nor a NaN. |
83 | TODO: if it's available, use C99's isfinite(x) instead */ | |
84 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
85 | ||
0f2d19dd | 86 | \f |
f4c627b3 | 87 | |
ca46fb90 RB |
88 | /* |
89 | Wonder if this might be faster for some of our code? A switch on | |
90 | the numtag would jump directly to the right case, and the | |
91 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
92 | ||
93 | #define SCM_I_NUMTAG_NOTNUM 0 | |
94 | #define SCM_I_NUMTAG_INUM 1 | |
95 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
96 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
97 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
98 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 99 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 100 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 101 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
102 | : SCM_I_NUMTAG_NOTNUM))) |
103 | */ | |
f92e85f7 | 104 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
105 | |
106 | ||
e7efe8e7 | 107 | static SCM flo0; |
ff62c168 | 108 | static SCM exactly_one_half; |
e7efe8e7 | 109 | |
34d19ef6 | 110 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 111 | |
56e55ac7 | 112 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
113 | * printed or scm_string representation of an inexact number. |
114 | */ | |
0b799eea | 115 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 116 | |
b127c712 | 117 | |
ad79736c AW |
118 | #if !defined (HAVE_ASINH) |
119 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
120 | #endif | |
121 | #if !defined (HAVE_ACOSH) | |
122 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
123 | #endif | |
124 | #if !defined (HAVE_ATANH) | |
125 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
126 | #endif | |
127 | ||
f8a8200b KR |
128 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
129 | an explicit check. In some future gmp (don't know what version number), | |
130 | mpz_cmp_d is supposed to do this itself. */ | |
131 | #if 1 | |
b127c712 | 132 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 133 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
134 | #else |
135 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
136 | #endif | |
137 | ||
f92e85f7 | 138 | |
4b26c03e | 139 | #if defined (GUILE_I) |
bca69a9f | 140 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
141 | |
142 | /* For an SCM object Z which is a complex number (ie. satisfies | |
143 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
144 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 145 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 146 | |
7a35784c | 147 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
148 | |
149 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 150 | static inline SCM |
8ab3d8a0 KR |
151 | scm_from_complex_double (complex double z) |
152 | { | |
153 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
154 | } | |
bca69a9f | 155 | |
8ab3d8a0 | 156 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 157 | #endif /* GUILE_I */ |
8ab3d8a0 | 158 | |
0f2d19dd JB |
159 | \f |
160 | ||
713a4259 | 161 | static mpz_t z_negative_one; |
ac0c002c DH |
162 | |
163 | \f | |
864e7d42 LC |
164 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
165 | static void | |
166 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
167 | { | |
168 | SCM bignum; | |
169 | ||
170 | bignum = PTR2SCM (ptr); | |
171 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
172 | } | |
173 | ||
d017fcdf LC |
174 | /* Return a new uninitialized bignum. */ |
175 | static inline SCM | |
176 | make_bignum (void) | |
177 | { | |
178 | scm_t_bits *p; | |
864e7d42 LC |
179 | GC_finalization_proc prev_finalizer; |
180 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
181 | |
182 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
183 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
184 | "bignum"); | |
185 | p[0] = scm_tc16_big; | |
186 | ||
864e7d42 LC |
187 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
188 | &prev_finalizer, | |
189 | &prev_finalizer_data); | |
190 | ||
d017fcdf LC |
191 | return SCM_PACK (p); |
192 | } | |
ac0c002c | 193 | |
864e7d42 | 194 | |
189171c5 | 195 | SCM |
ca46fb90 RB |
196 | scm_i_mkbig () |
197 | { | |
198 | /* Return a newly created bignum. */ | |
d017fcdf | 199 | SCM z = make_bignum (); |
ca46fb90 RB |
200 | mpz_init (SCM_I_BIG_MPZ (z)); |
201 | return z; | |
202 | } | |
203 | ||
e25f3727 AW |
204 | static SCM |
205 | scm_i_inum2big (scm_t_inum x) | |
206 | { | |
207 | /* Return a newly created bignum initialized to X. */ | |
208 | SCM z = make_bignum (); | |
209 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
210 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
211 | #else | |
212 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
213 | mpz_*_si invocations in Guile. */ | |
214 | #error creation of mpz not implemented for this inum size | |
215 | #endif | |
216 | return z; | |
217 | } | |
218 | ||
189171c5 | 219 | SCM |
c71b0706 MV |
220 | scm_i_long2big (long x) |
221 | { | |
222 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 223 | SCM z = make_bignum (); |
c71b0706 MV |
224 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
225 | return z; | |
226 | } | |
227 | ||
189171c5 | 228 | SCM |
c71b0706 MV |
229 | scm_i_ulong2big (unsigned long x) |
230 | { | |
231 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 232 | SCM z = make_bignum (); |
c71b0706 MV |
233 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
234 | return z; | |
235 | } | |
236 | ||
189171c5 | 237 | SCM |
ca46fb90 RB |
238 | scm_i_clonebig (SCM src_big, int same_sign_p) |
239 | { | |
240 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 241 | SCM z = make_bignum (); |
ca46fb90 | 242 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
243 | if (!same_sign_p) |
244 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
245 | return z; |
246 | } | |
247 | ||
189171c5 | 248 | int |
ca46fb90 RB |
249 | scm_i_bigcmp (SCM x, SCM y) |
250 | { | |
251 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
252 | /* presume we already know x and y are bignums */ | |
253 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
254 | scm_remember_upto_here_2 (x, y); | |
255 | return result; | |
256 | } | |
257 | ||
189171c5 | 258 | SCM |
ca46fb90 RB |
259 | scm_i_dbl2big (double d) |
260 | { | |
261 | /* results are only defined if d is an integer */ | |
d017fcdf | 262 | SCM z = make_bignum (); |
ca46fb90 RB |
263 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
264 | return z; | |
265 | } | |
266 | ||
f92e85f7 MV |
267 | /* Convert a integer in double representation to a SCM number. */ |
268 | ||
189171c5 | 269 | SCM |
f92e85f7 MV |
270 | scm_i_dbl2num (double u) |
271 | { | |
272 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
273 | powers of 2, so there's no rounding when making "double" values | |
274 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
275 | get rounded on a 64-bit machine, hence the "+1". | |
276 | ||
277 | The use of floor() to force to an integer value ensures we get a | |
278 | "numerically closest" value without depending on how a | |
279 | double->long cast or how mpz_set_d will round. For reference, | |
280 | double->long probably follows the hardware rounding mode, | |
281 | mpz_set_d truncates towards zero. */ | |
282 | ||
283 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
284 | representable as a double? */ | |
285 | ||
286 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
287 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 288 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
289 | else |
290 | return scm_i_dbl2big (u); | |
291 | } | |
292 | ||
089c9a59 KR |
293 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
294 | with R5RS exact->inexact. | |
295 | ||
296 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
297 | (ie. truncate towards zero), then adjust to get the closest double by |
298 | examining the next lower bit and adding 1 (to the absolute value) if | |
299 | necessary. | |
300 | ||
301 | Bignums exactly half way between representable doubles are rounded to the | |
302 | next higher absolute value (ie. away from zero). This seems like an | |
303 | adequate interpretation of R5RS "numerically closest", and it's easier | |
304 | and faster than a full "nearest-even" style. | |
305 | ||
306 | The bit test must be done on the absolute value of the mpz_t, which means | |
307 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
308 | negatives as twos complement. | |
309 | ||
310 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
311 | following the hardware rounding mode, but applied to the absolute value | |
312 | of the mpz_t operand. This is not what we want so we put the high | |
313 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
314 | mpz_get_d is supposed to always truncate towards zero. | |
315 | ||
316 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
317 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
318 | mpz_getlimbn if we could be bothered coding that, and if the new | |
319 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
320 | |
321 | double | |
ca46fb90 RB |
322 | scm_i_big2dbl (SCM b) |
323 | { | |
089c9a59 KR |
324 | double result; |
325 | size_t bits; | |
326 | ||
327 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
328 | ||
f8a8200b | 329 | #if 1 |
089c9a59 | 330 | { |
f8a8200b | 331 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
332 | mpz_t tmp; |
333 | if (bits > DBL_MANT_DIG) | |
334 | { | |
335 | size_t shift = bits - DBL_MANT_DIG; | |
336 | mpz_init2 (tmp, DBL_MANT_DIG); | |
337 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
338 | result = ldexp (mpz_get_d (tmp), shift); | |
339 | mpz_clear (tmp); | |
340 | } | |
341 | else | |
342 | { | |
343 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
344 | } | |
345 | } | |
346 | #else | |
f8a8200b | 347 | /* Future GMP */ |
089c9a59 KR |
348 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
349 | #endif | |
350 | ||
351 | if (bits > DBL_MANT_DIG) | |
352 | { | |
353 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
354 | /* test bit number "pos" in absolute value */ | |
355 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
356 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
357 | { | |
358 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
359 | } | |
360 | } | |
361 | ||
ca46fb90 RB |
362 | scm_remember_upto_here_1 (b); |
363 | return result; | |
364 | } | |
365 | ||
189171c5 | 366 | SCM |
ca46fb90 RB |
367 | scm_i_normbig (SCM b) |
368 | { | |
369 | /* convert a big back to a fixnum if it'll fit */ | |
370 | /* presume b is a bignum */ | |
371 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
372 | { | |
e25f3727 | 373 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 374 | if (SCM_FIXABLE (val)) |
d956fa6f | 375 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
376 | } |
377 | return b; | |
378 | } | |
f872b822 | 379 | |
f92e85f7 MV |
380 | static SCM_C_INLINE_KEYWORD SCM |
381 | scm_i_mpz2num (mpz_t b) | |
382 | { | |
383 | /* convert a mpz number to a SCM number. */ | |
384 | if (mpz_fits_slong_p (b)) | |
385 | { | |
e25f3727 | 386 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 387 | if (SCM_FIXABLE (val)) |
d956fa6f | 388 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
389 | } |
390 | ||
391 | { | |
d017fcdf | 392 | SCM z = make_bignum (); |
f92e85f7 MV |
393 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
394 | return z; | |
395 | } | |
396 | } | |
397 | ||
398 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
399 | static SCM scm_divide2real (SCM x, SCM y); | |
400 | ||
cba42c93 MV |
401 | static SCM |
402 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 403 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 404 | { |
c60e130c MV |
405 | /* First make sure the arguments are proper. |
406 | */ | |
e11e83f3 | 407 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 408 | { |
bc36d050 | 409 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 410 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 411 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
412 | return numerator; |
413 | } | |
414 | else | |
415 | { | |
416 | if (!(SCM_BIGP(denominator))) | |
417 | SCM_WRONG_TYPE_ARG (2, denominator); | |
418 | } | |
e11e83f3 | 419 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
420 | SCM_WRONG_TYPE_ARG (1, numerator); |
421 | ||
422 | /* Then flip signs so that the denominator is positive. | |
423 | */ | |
73e4de09 | 424 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
425 | { |
426 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
427 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
428 | } | |
429 | ||
430 | /* Now consider for each of the four fixnum/bignum combinations | |
431 | whether the rational number is really an integer. | |
432 | */ | |
e11e83f3 | 433 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 434 | { |
e25f3727 | 435 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 436 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 437 | return SCM_INUM0; |
e11e83f3 | 438 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 439 | { |
e25f3727 | 440 | scm_t_inum y; |
e11e83f3 | 441 | y = SCM_I_INUM (denominator); |
f92e85f7 | 442 | if (x == y) |
cff5fa33 | 443 | return SCM_INUM1; |
f92e85f7 | 444 | if ((x % y) == 0) |
d956fa6f | 445 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 446 | } |
dd5130ca KR |
447 | else |
448 | { | |
449 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
450 | of that value for the denominator, as a bignum. Apart from |
451 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
452 | integer. */ | |
453 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
454 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
455 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 456 | return SCM_I_MAKINUM(-1); |
dd5130ca | 457 | } |
f92e85f7 | 458 | } |
c60e130c | 459 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 460 | { |
e11e83f3 | 461 | if (SCM_I_INUMP (denominator)) |
c60e130c | 462 | { |
e25f3727 | 463 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
464 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
465 | return scm_divide (numerator, denominator); | |
466 | } | |
467 | else | |
f92e85f7 | 468 | { |
bc36d050 | 469 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 470 | return SCM_INUM1; |
c60e130c MV |
471 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
472 | SCM_I_BIG_MPZ (denominator))) | |
473 | return scm_divide(numerator, denominator); | |
f92e85f7 | 474 | } |
f92e85f7 | 475 | } |
c60e130c MV |
476 | |
477 | /* No, it's a proper fraction. | |
478 | */ | |
e2bf3b19 HWN |
479 | { |
480 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 481 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
482 | { |
483 | numerator = scm_divide (numerator, divisor); | |
484 | denominator = scm_divide (denominator, divisor); | |
485 | } | |
486 | ||
487 | return scm_double_cell (scm_tc16_fraction, | |
488 | SCM_UNPACK (numerator), | |
489 | SCM_UNPACK (denominator), 0); | |
490 | } | |
f92e85f7 | 491 | } |
c60e130c | 492 | #undef FUNC_NAME |
f92e85f7 | 493 | |
f92e85f7 MV |
494 | double |
495 | scm_i_fraction2double (SCM z) | |
496 | { | |
55f26379 MV |
497 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
498 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
499 | } |
500 | ||
2519490c MW |
501 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
502 | (SCM x), | |
942e5b91 MG |
503 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
504 | "otherwise.") | |
1bbd0b84 | 505 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 506 | { |
41df63cf MW |
507 | if (SCM_INEXACTP (x)) |
508 | return SCM_BOOL_F; | |
509 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 510 | return SCM_BOOL_T; |
41df63cf | 511 | else |
2519490c | 512 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
513 | } |
514 | #undef FUNC_NAME | |
515 | ||
516 | ||
2519490c | 517 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
518 | (SCM x), |
519 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
520 | "else.") | |
521 | #define FUNC_NAME s_scm_inexact_p | |
522 | { | |
523 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 524 | return SCM_BOOL_T; |
41df63cf | 525 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 526 | return SCM_BOOL_F; |
41df63cf | 527 | else |
2519490c | 528 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 529 | } |
1bbd0b84 | 530 | #undef FUNC_NAME |
0f2d19dd | 531 | |
4219f20d | 532 | |
2519490c | 533 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 534 | (SCM n), |
942e5b91 MG |
535 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
536 | "otherwise.") | |
1bbd0b84 | 537 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 538 | { |
e11e83f3 | 539 | if (SCM_I_INUMP (n)) |
0aacf84e | 540 | { |
e25f3727 | 541 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 542 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
543 | } |
544 | else if (SCM_BIGP (n)) | |
545 | { | |
546 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
547 | scm_remember_upto_here_1 (n); | |
73e4de09 | 548 | return scm_from_bool (odd_p); |
0aacf84e | 549 | } |
f92e85f7 MV |
550 | else if (SCM_REALP (n)) |
551 | { | |
2519490c MW |
552 | double val = SCM_REAL_VALUE (n); |
553 | if (DOUBLE_IS_FINITE (val)) | |
554 | { | |
555 | double rem = fabs (fmod (val, 2.0)); | |
556 | if (rem == 1.0) | |
557 | return SCM_BOOL_T; | |
558 | else if (rem == 0.0) | |
559 | return SCM_BOOL_F; | |
560 | } | |
f92e85f7 | 561 | } |
2519490c | 562 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 563 | } |
1bbd0b84 | 564 | #undef FUNC_NAME |
0f2d19dd | 565 | |
4219f20d | 566 | |
2519490c | 567 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 568 | (SCM n), |
942e5b91 MG |
569 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
570 | "otherwise.") | |
1bbd0b84 | 571 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 572 | { |
e11e83f3 | 573 | if (SCM_I_INUMP (n)) |
0aacf84e | 574 | { |
e25f3727 | 575 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 576 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
577 | } |
578 | else if (SCM_BIGP (n)) | |
579 | { | |
580 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
581 | scm_remember_upto_here_1 (n); | |
73e4de09 | 582 | return scm_from_bool (even_p); |
0aacf84e | 583 | } |
f92e85f7 MV |
584 | else if (SCM_REALP (n)) |
585 | { | |
2519490c MW |
586 | double val = SCM_REAL_VALUE (n); |
587 | if (DOUBLE_IS_FINITE (val)) | |
588 | { | |
589 | double rem = fabs (fmod (val, 2.0)); | |
590 | if (rem == 1.0) | |
591 | return SCM_BOOL_F; | |
592 | else if (rem == 0.0) | |
593 | return SCM_BOOL_T; | |
594 | } | |
f92e85f7 | 595 | } |
2519490c | 596 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 597 | } |
1bbd0b84 | 598 | #undef FUNC_NAME |
0f2d19dd | 599 | |
2519490c MW |
600 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
601 | (SCM x), | |
10391e06 AW |
602 | "Return @code{#t} if the real number @var{x} is neither\n" |
603 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
604 | #define FUNC_NAME s_scm_finite_p |
605 | { | |
606 | if (SCM_REALP (x)) | |
607 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 608 | else if (scm_is_real (x)) |
7112615f MW |
609 | return SCM_BOOL_T; |
610 | else | |
2519490c | 611 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
612 | } |
613 | #undef FUNC_NAME | |
614 | ||
2519490c MW |
615 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
616 | (SCM x), | |
617 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
618 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
619 | #define FUNC_NAME s_scm_inf_p |
620 | { | |
b1092b3a | 621 | if (SCM_REALP (x)) |
2e65b52f | 622 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 623 | else if (scm_is_real (x)) |
7351e207 | 624 | return SCM_BOOL_F; |
10391e06 | 625 | else |
2519490c | 626 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
627 | } |
628 | #undef FUNC_NAME | |
629 | ||
2519490c MW |
630 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
631 | (SCM x), | |
10391e06 AW |
632 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
633 | "or @code{#f} otherwise.") | |
7351e207 MV |
634 | #define FUNC_NAME s_scm_nan_p |
635 | { | |
10391e06 AW |
636 | if (SCM_REALP (x)) |
637 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
638 | else if (scm_is_real (x)) | |
7351e207 | 639 | return SCM_BOOL_F; |
10391e06 | 640 | else |
2519490c | 641 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
642 | } |
643 | #undef FUNC_NAME | |
644 | ||
645 | /* Guile's idea of infinity. */ | |
646 | static double guile_Inf; | |
647 | ||
648 | /* Guile's idea of not a number. */ | |
649 | static double guile_NaN; | |
650 | ||
651 | static void | |
652 | guile_ieee_init (void) | |
653 | { | |
7351e207 MV |
654 | /* Some version of gcc on some old version of Linux used to crash when |
655 | trying to make Inf and NaN. */ | |
656 | ||
240a27d2 KR |
657 | #ifdef INFINITY |
658 | /* C99 INFINITY, when available. | |
659 | FIXME: The standard allows for INFINITY to be something that overflows | |
660 | at compile time. We ought to have a configure test to check for that | |
661 | before trying to use it. (But in practice we believe this is not a | |
662 | problem on any system guile is likely to target.) */ | |
663 | guile_Inf = INFINITY; | |
56a3dcd4 | 664 | #elif defined HAVE_DINFINITY |
240a27d2 | 665 | /* OSF */ |
7351e207 | 666 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 667 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
668 | #else |
669 | double tmp = 1e+10; | |
670 | guile_Inf = tmp; | |
671 | for (;;) | |
672 | { | |
673 | guile_Inf *= 1e+10; | |
674 | if (guile_Inf == tmp) | |
675 | break; | |
676 | tmp = guile_Inf; | |
677 | } | |
678 | #endif | |
679 | ||
240a27d2 KR |
680 | #ifdef NAN |
681 | /* C99 NAN, when available */ | |
682 | guile_NaN = NAN; | |
56a3dcd4 | 683 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
684 | { |
685 | /* OSF */ | |
686 | extern unsigned int DQNAN[2]; | |
687 | guile_NaN = (*((double *)(DQNAN))); | |
688 | } | |
7351e207 MV |
689 | #else |
690 | guile_NaN = guile_Inf / guile_Inf; | |
691 | #endif | |
7351e207 MV |
692 | } |
693 | ||
694 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
695 | (void), | |
696 | "Return Inf.") | |
697 | #define FUNC_NAME s_scm_inf | |
698 | { | |
699 | static int initialized = 0; | |
700 | if (! initialized) | |
701 | { | |
702 | guile_ieee_init (); | |
703 | initialized = 1; | |
704 | } | |
55f26379 | 705 | return scm_from_double (guile_Inf); |
7351e207 MV |
706 | } |
707 | #undef FUNC_NAME | |
708 | ||
709 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
710 | (void), | |
711 | "Return NaN.") | |
712 | #define FUNC_NAME s_scm_nan | |
713 | { | |
714 | static int initialized = 0; | |
0aacf84e | 715 | if (!initialized) |
7351e207 MV |
716 | { |
717 | guile_ieee_init (); | |
718 | initialized = 1; | |
719 | } | |
55f26379 | 720 | return scm_from_double (guile_NaN); |
7351e207 MV |
721 | } |
722 | #undef FUNC_NAME | |
723 | ||
4219f20d | 724 | |
a48d60b1 MD |
725 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
726 | (SCM x), | |
727 | "Return the absolute value of @var{x}.") | |
2519490c | 728 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 729 | { |
e11e83f3 | 730 | if (SCM_I_INUMP (x)) |
0aacf84e | 731 | { |
e25f3727 | 732 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
733 | if (xx >= 0) |
734 | return x; | |
735 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 736 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 737 | else |
e25f3727 | 738 | return scm_i_inum2big (-xx); |
4219f20d | 739 | } |
0aacf84e MD |
740 | else if (SCM_BIGP (x)) |
741 | { | |
742 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
743 | if (sgn < 0) | |
744 | return scm_i_clonebig (x, 0); | |
745 | else | |
746 | return x; | |
4219f20d | 747 | } |
0aacf84e | 748 | else if (SCM_REALP (x)) |
ae38324d KR |
749 | { |
750 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
751 | double xx = SCM_REAL_VALUE (x); | |
752 | if (xx < 0.0) | |
55f26379 | 753 | return scm_from_double (-xx); |
ae38324d KR |
754 | else |
755 | return x; | |
756 | } | |
f92e85f7 MV |
757 | else if (SCM_FRACTIONP (x)) |
758 | { | |
73e4de09 | 759 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 760 | return x; |
cba42c93 | 761 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
762 | SCM_FRACTION_DENOMINATOR (x)); |
763 | } | |
0aacf84e | 764 | else |
a48d60b1 | 765 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 766 | } |
a48d60b1 | 767 | #undef FUNC_NAME |
0f2d19dd | 768 | |
4219f20d | 769 | |
2519490c MW |
770 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
771 | (SCM x, SCM y), | |
772 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
773 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 774 | { |
a16982ca | 775 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 776 | { |
e25f3727 | 777 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 778 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 779 | { |
e25f3727 | 780 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 781 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 782 | scm_num_overflow (s_scm_quotient); |
0aacf84e MD |
783 | else |
784 | { | |
e25f3727 | 785 | scm_t_inum z = xx / yy; |
a16982ca | 786 | if (SCM_LIKELY (SCM_FIXABLE (z))) |
d956fa6f | 787 | return SCM_I_MAKINUM (z); |
0aacf84e | 788 | else |
e25f3727 | 789 | return scm_i_inum2big (z); |
0aacf84e | 790 | } |
828865c3 | 791 | } |
0aacf84e | 792 | else if (SCM_BIGP (y)) |
ac0c002c | 793 | { |
e11e83f3 | 794 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
795 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
796 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
797 | { | |
798 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
799 | scm_remember_upto_here_1 (y); | |
d956fa6f | 800 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 801 | } |
0aacf84e | 802 | else |
cff5fa33 | 803 | return SCM_INUM0; |
ac0c002c DH |
804 | } |
805 | else | |
2519490c | 806 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
828865c3 | 807 | } |
0aacf84e MD |
808 | else if (SCM_BIGP (x)) |
809 | { | |
a16982ca | 810 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 811 | { |
e25f3727 | 812 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 813 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 814 | scm_num_overflow (s_scm_quotient); |
a16982ca | 815 | else if (SCM_UNLIKELY (yy == 1)) |
0aacf84e MD |
816 | return x; |
817 | else | |
818 | { | |
819 | SCM result = scm_i_mkbig (); | |
820 | if (yy < 0) | |
821 | { | |
822 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
823 | SCM_I_BIG_MPZ (x), | |
824 | - yy); | |
825 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
826 | } | |
827 | else | |
828 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
829 | scm_remember_upto_here_1 (x); | |
830 | return scm_i_normbig (result); | |
831 | } | |
832 | } | |
833 | else if (SCM_BIGP (y)) | |
834 | { | |
835 | SCM result = scm_i_mkbig (); | |
836 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
837 | SCM_I_BIG_MPZ (x), | |
838 | SCM_I_BIG_MPZ (y)); | |
839 | scm_remember_upto_here_2 (x, y); | |
840 | return scm_i_normbig (result); | |
841 | } | |
842 | else | |
2519490c | 843 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 844 | } |
0aacf84e | 845 | else |
2519490c | 846 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 847 | } |
2519490c | 848 | #undef FUNC_NAME |
0f2d19dd | 849 | |
2519490c MW |
850 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
851 | (SCM x, SCM y), | |
852 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
853 | "@lisp\n" | |
854 | "(remainder 13 4) @result{} 1\n" | |
855 | "(remainder -13 4) @result{} -1\n" | |
856 | "@end lisp") | |
857 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 858 | { |
a16982ca | 859 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 860 | { |
a16982ca | 861 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 862 | { |
e25f3727 | 863 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 864 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 865 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
866 | else |
867 | { | |
a16982ca MW |
868 | /* C99 specifies that "%" is the remainder corresponding to a |
869 | quotient rounded towards zero, and that's also traditional | |
870 | for machine division, so z here should be well defined. */ | |
e25f3727 | 871 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 872 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
873 | } |
874 | } | |
875 | else if (SCM_BIGP (y)) | |
ac0c002c | 876 | { |
e11e83f3 | 877 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
878 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
879 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
880 | { | |
881 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
882 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 883 | return SCM_INUM0; |
4dc09ee4 | 884 | } |
0aacf84e MD |
885 | else |
886 | return x; | |
ac0c002c DH |
887 | } |
888 | else | |
2519490c | 889 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
89a7e495 | 890 | } |
0aacf84e MD |
891 | else if (SCM_BIGP (x)) |
892 | { | |
a16982ca | 893 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 894 | { |
e25f3727 | 895 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 896 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 897 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
898 | else |
899 | { | |
900 | SCM result = scm_i_mkbig (); | |
901 | if (yy < 0) | |
902 | yy = - yy; | |
903 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
904 | scm_remember_upto_here_1 (x); | |
905 | return scm_i_normbig (result); | |
906 | } | |
907 | } | |
908 | else if (SCM_BIGP (y)) | |
909 | { | |
910 | SCM result = scm_i_mkbig (); | |
911 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
912 | SCM_I_BIG_MPZ (x), | |
913 | SCM_I_BIG_MPZ (y)); | |
914 | scm_remember_upto_here_2 (x, y); | |
915 | return scm_i_normbig (result); | |
916 | } | |
917 | else | |
2519490c | 918 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 919 | } |
0aacf84e | 920 | else |
2519490c | 921 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 922 | } |
2519490c | 923 | #undef FUNC_NAME |
0f2d19dd | 924 | |
89a7e495 | 925 | |
2519490c MW |
926 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
927 | (SCM x, SCM y), | |
928 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
929 | "@lisp\n" | |
930 | "(modulo 13 4) @result{} 1\n" | |
931 | "(modulo -13 4) @result{} 3\n" | |
932 | "@end lisp") | |
933 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 934 | { |
a16982ca | 935 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 936 | { |
e25f3727 | 937 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 938 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 939 | { |
e25f3727 | 940 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 941 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 942 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
943 | else |
944 | { | |
66b1c775 KR |
945 | /* C99 specifies that "%" is the remainder corresponding to a |
946 | quotient rounded towards zero, and that's also traditional | |
947 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
948 | scm_t_inum z = xx % yy; |
949 | scm_t_inum result; | |
0aacf84e MD |
950 | |
951 | if (yy < 0) | |
952 | { | |
953 | if (z > 0) | |
954 | result = z + yy; | |
955 | else | |
956 | result = z; | |
957 | } | |
958 | else | |
959 | { | |
960 | if (z < 0) | |
961 | result = z + yy; | |
962 | else | |
963 | result = z; | |
964 | } | |
d956fa6f | 965 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
966 | } |
967 | } | |
968 | else if (SCM_BIGP (y)) | |
969 | { | |
970 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
971 | { |
972 | mpz_t z_x; | |
973 | SCM result; | |
974 | ||
975 | if (sgn_y < 0) | |
976 | { | |
977 | SCM pos_y = scm_i_clonebig (y, 0); | |
978 | /* do this after the last scm_op */ | |
979 | mpz_init_set_si (z_x, xx); | |
980 | result = pos_y; /* re-use this bignum */ | |
981 | mpz_mod (SCM_I_BIG_MPZ (result), | |
982 | z_x, | |
983 | SCM_I_BIG_MPZ (pos_y)); | |
984 | scm_remember_upto_here_1 (pos_y); | |
985 | } | |
986 | else | |
987 | { | |
988 | result = scm_i_mkbig (); | |
989 | /* do this after the last scm_op */ | |
990 | mpz_init_set_si (z_x, xx); | |
991 | mpz_mod (SCM_I_BIG_MPZ (result), | |
992 | z_x, | |
993 | SCM_I_BIG_MPZ (y)); | |
994 | scm_remember_upto_here_1 (y); | |
995 | } | |
ca46fb90 | 996 | |
0aacf84e MD |
997 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
998 | mpz_add (SCM_I_BIG_MPZ (result), | |
999 | SCM_I_BIG_MPZ (y), | |
1000 | SCM_I_BIG_MPZ (result)); | |
1001 | scm_remember_upto_here_1 (y); | |
1002 | /* and do this before the next one */ | |
1003 | mpz_clear (z_x); | |
1004 | return scm_i_normbig (result); | |
1005 | } | |
1006 | } | |
1007 | else | |
2519490c | 1008 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
f872b822 | 1009 | } |
0aacf84e MD |
1010 | else if (SCM_BIGP (x)) |
1011 | { | |
a16982ca | 1012 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 1013 | { |
e25f3727 | 1014 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 1015 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 1016 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
1017 | else |
1018 | { | |
1019 | SCM result = scm_i_mkbig (); | |
1020 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1021 | SCM_I_BIG_MPZ (x), | |
1022 | (yy < 0) ? - yy : yy); | |
1023 | scm_remember_upto_here_1 (x); | |
1024 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1025 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1026 | SCM_I_BIG_MPZ (result), | |
1027 | - yy); | |
1028 | return scm_i_normbig (result); | |
1029 | } | |
1030 | } | |
1031 | else if (SCM_BIGP (y)) | |
1032 | { | |
a16982ca MW |
1033 | SCM result = scm_i_mkbig (); |
1034 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1035 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1036 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1037 | SCM_I_BIG_MPZ (x), | |
1038 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1039 | |
a16982ca MW |
1040 | scm_remember_upto_here_1 (x); |
1041 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1042 | mpz_add (SCM_I_BIG_MPZ (result), | |
1043 | SCM_I_BIG_MPZ (y), | |
1044 | SCM_I_BIG_MPZ (result)); | |
1045 | scm_remember_upto_here_2 (y, pos_y); | |
1046 | return scm_i_normbig (result); | |
0aacf84e MD |
1047 | } |
1048 | else | |
2519490c | 1049 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 1050 | } |
0aacf84e | 1051 | else |
2519490c | 1052 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1053 | } |
2519490c | 1054 | #undef FUNC_NAME |
0f2d19dd | 1055 | |
ff62c168 MW |
1056 | static SCM scm_i_inexact_euclidean_quotient (double x, double y); |
1057 | static SCM scm_i_slow_exact_euclidean_quotient (SCM x, SCM y); | |
1058 | ||
1059 | SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, | |
1060 | (SCM x, SCM y), | |
1061 | "Return the integer @var{q} such that\n" | |
1062 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1063 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1064 | "@lisp\n" | |
1065 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1066 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1067 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1068 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1069 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1070 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1071 | "@end lisp") | |
1072 | #define FUNC_NAME s_scm_euclidean_quotient | |
1073 | { | |
1074 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1075 | { | |
1076 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1077 | { | |
1078 | scm_t_inum yy = SCM_I_INUM (y); | |
1079 | if (SCM_UNLIKELY (yy == 0)) | |
1080 | scm_num_overflow (s_scm_euclidean_quotient); | |
1081 | else | |
1082 | { | |
1083 | scm_t_inum xx = SCM_I_INUM (x); | |
1084 | scm_t_inum qq = xx / yy; | |
1085 | if (xx < qq * yy) | |
1086 | { | |
1087 | if (yy > 0) | |
1088 | qq--; | |
1089 | else | |
1090 | qq++; | |
1091 | } | |
1092 | return SCM_I_MAKINUM (qq); | |
1093 | } | |
1094 | } | |
1095 | else if (SCM_BIGP (y)) | |
1096 | { | |
1097 | if (SCM_I_INUM (x) >= 0) | |
1098 | return SCM_INUM0; | |
1099 | else | |
1100 | return SCM_I_MAKINUM (- mpz_sgn (SCM_I_BIG_MPZ (y))); | |
1101 | } | |
1102 | else if (SCM_REALP (y)) | |
1103 | return scm_i_inexact_euclidean_quotient | |
1104 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1105 | else if (SCM_FRACTIONP (y)) | |
1106 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1107 | else | |
1108 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1109 | s_scm_euclidean_quotient); | |
1110 | } | |
1111 | else if (SCM_BIGP (x)) | |
1112 | { | |
1113 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1114 | { | |
1115 | scm_t_inum yy = SCM_I_INUM (y); | |
1116 | if (SCM_UNLIKELY (yy == 0)) | |
1117 | scm_num_overflow (s_scm_euclidean_quotient); | |
1118 | else | |
1119 | { | |
1120 | SCM q = scm_i_mkbig (); | |
1121 | if (yy > 0) | |
1122 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1123 | else | |
1124 | { | |
1125 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1126 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1127 | } | |
1128 | scm_remember_upto_here_1 (x); | |
1129 | return scm_i_normbig (q); | |
1130 | } | |
1131 | } | |
1132 | else if (SCM_BIGP (y)) | |
1133 | { | |
1134 | SCM q = scm_i_mkbig (); | |
1135 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1136 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1137 | SCM_I_BIG_MPZ (x), | |
1138 | SCM_I_BIG_MPZ (y)); | |
1139 | else | |
1140 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1141 | SCM_I_BIG_MPZ (x), | |
1142 | SCM_I_BIG_MPZ (y)); | |
1143 | scm_remember_upto_here_2 (x, y); | |
1144 | return scm_i_normbig (q); | |
1145 | } | |
1146 | else if (SCM_REALP (y)) | |
1147 | return scm_i_inexact_euclidean_quotient | |
1148 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1149 | else if (SCM_FRACTIONP (y)) | |
1150 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1151 | else | |
1152 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1153 | s_scm_euclidean_quotient); | |
1154 | } | |
1155 | else if (SCM_REALP (x)) | |
1156 | { | |
1157 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1158 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1159 | return scm_i_inexact_euclidean_quotient | |
1160 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1161 | else | |
1162 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1163 | s_scm_euclidean_quotient); | |
1164 | } | |
1165 | else if (SCM_FRACTIONP (x)) | |
1166 | { | |
1167 | if (SCM_REALP (y)) | |
1168 | return scm_i_inexact_euclidean_quotient | |
1169 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1170 | else | |
1171 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1172 | } | |
1173 | else | |
1174 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1175 | s_scm_euclidean_quotient); | |
1176 | } | |
1177 | #undef FUNC_NAME | |
1178 | ||
1179 | static SCM | |
1180 | scm_i_inexact_euclidean_quotient (double x, double y) | |
1181 | { | |
1182 | if (SCM_LIKELY (y > 0)) | |
1183 | return scm_from_double (floor (x / y)); | |
1184 | else if (SCM_LIKELY (y < 0)) | |
1185 | return scm_from_double (ceil (x / y)); | |
1186 | else if (y == 0) | |
1187 | scm_num_overflow (s_scm_euclidean_quotient); /* or return a NaN? */ | |
1188 | else | |
1189 | return scm_nan (); | |
1190 | } | |
1191 | ||
1192 | /* Compute exact euclidean_quotient the slow way. | |
1193 | We use this only if both arguments are exact, | |
1194 | and at least one of them is a fraction */ | |
1195 | static SCM | |
1196 | scm_i_slow_exact_euclidean_quotient (SCM x, SCM y) | |
1197 | { | |
1198 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1199 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1200 | s_scm_euclidean_quotient); | |
1201 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1202 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1203 | s_scm_euclidean_quotient); | |
1204 | else if (scm_is_true (scm_positive_p (y))) | |
1205 | return scm_floor (scm_divide (x, y)); | |
1206 | else if (scm_is_true (scm_negative_p (y))) | |
1207 | return scm_ceiling (scm_divide (x, y)); | |
1208 | else | |
1209 | scm_num_overflow (s_scm_euclidean_quotient); | |
1210 | } | |
1211 | ||
1212 | static SCM scm_i_inexact_euclidean_remainder (double x, double y); | |
1213 | static SCM scm_i_slow_exact_euclidean_remainder (SCM x, SCM y); | |
1214 | ||
1215 | SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, | |
1216 | (SCM x, SCM y), | |
1217 | "Return the real number @var{r} such that\n" | |
1218 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1219 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1220 | "for some integer @var{q}.\n" | |
1221 | "@lisp\n" | |
1222 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1223 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1224 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1225 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1226 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1227 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1228 | "@end lisp") | |
1229 | #define FUNC_NAME s_scm_euclidean_remainder | |
1230 | { | |
1231 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1232 | { | |
1233 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1234 | { | |
1235 | scm_t_inum yy = SCM_I_INUM (y); | |
1236 | if (SCM_UNLIKELY (yy == 0)) | |
1237 | scm_num_overflow (s_scm_euclidean_remainder); | |
1238 | else | |
1239 | { | |
1240 | scm_t_inum rr = SCM_I_INUM (x) % yy; | |
1241 | if (rr >= 0) | |
1242 | return SCM_I_MAKINUM (rr); | |
1243 | else if (yy > 0) | |
1244 | return SCM_I_MAKINUM (rr + yy); | |
1245 | else | |
1246 | return SCM_I_MAKINUM (rr - yy); | |
1247 | } | |
1248 | } | |
1249 | else if (SCM_BIGP (y)) | |
1250 | { | |
1251 | scm_t_inum xx = SCM_I_INUM (x); | |
1252 | if (xx >= 0) | |
1253 | return x; | |
1254 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1255 | { | |
1256 | SCM r = scm_i_mkbig (); | |
1257 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1258 | scm_remember_upto_here_1 (y); | |
1259 | return scm_i_normbig (r); | |
1260 | } | |
1261 | else | |
1262 | { | |
1263 | SCM r = scm_i_mkbig (); | |
1264 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1265 | scm_remember_upto_here_1 (y); | |
1266 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1267 | return scm_i_normbig (r); | |
1268 | } | |
1269 | } | |
1270 | else if (SCM_REALP (y)) | |
1271 | return scm_i_inexact_euclidean_remainder | |
1272 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1273 | else if (SCM_FRACTIONP (y)) | |
1274 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1275 | else | |
1276 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1277 | s_scm_euclidean_remainder); | |
1278 | } | |
1279 | else if (SCM_BIGP (x)) | |
1280 | { | |
1281 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1282 | { | |
1283 | scm_t_inum yy = SCM_I_INUM (y); | |
1284 | if (SCM_UNLIKELY (yy == 0)) | |
1285 | scm_num_overflow (s_scm_euclidean_remainder); | |
1286 | else | |
1287 | { | |
1288 | scm_t_inum rr; | |
1289 | if (yy < 0) | |
1290 | yy = -yy; | |
1291 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1292 | scm_remember_upto_here_1 (x); | |
1293 | return SCM_I_MAKINUM (rr); | |
1294 | } | |
1295 | } | |
1296 | else if (SCM_BIGP (y)) | |
1297 | { | |
1298 | SCM r = scm_i_mkbig (); | |
1299 | mpz_mod (SCM_I_BIG_MPZ (r), | |
1300 | SCM_I_BIG_MPZ (x), | |
1301 | SCM_I_BIG_MPZ (y)); | |
1302 | scm_remember_upto_here_2 (x, y); | |
1303 | return scm_i_normbig (r); | |
1304 | } | |
1305 | else if (SCM_REALP (y)) | |
1306 | return scm_i_inexact_euclidean_remainder | |
1307 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1308 | else if (SCM_FRACTIONP (y)) | |
1309 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1310 | else | |
1311 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1312 | s_scm_euclidean_remainder); | |
1313 | } | |
1314 | else if (SCM_REALP (x)) | |
1315 | { | |
1316 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1317 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1318 | return scm_i_inexact_euclidean_remainder | |
1319 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1320 | else | |
1321 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1322 | s_scm_euclidean_remainder); | |
1323 | } | |
1324 | else if (SCM_FRACTIONP (x)) | |
1325 | { | |
1326 | if (SCM_REALP (y)) | |
1327 | return scm_i_inexact_euclidean_remainder | |
1328 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1329 | else | |
1330 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1331 | } | |
1332 | else | |
1333 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1334 | s_scm_euclidean_remainder); | |
1335 | } | |
1336 | #undef FUNC_NAME | |
1337 | ||
1338 | static SCM | |
1339 | scm_i_inexact_euclidean_remainder (double x, double y) | |
1340 | { | |
1341 | double q; | |
1342 | ||
1343 | /* Although it would be more efficient to use fmod here, we can't | |
1344 | because it would in some cases produce results inconsistent with | |
1345 | scm_i_inexact_euclidean_quotient, such that x != q * y + r (not | |
1346 | even close). In particular, when x is very close to a multiple of | |
1347 | y, then r might be either 0.0 or abs(y)-epsilon, but those two | |
1348 | cases must correspond to different choices of q. If r = 0.0 then q | |
1349 | must be x/y, and if r = abs(y) then q must be (x-r)/y. If quotient | |
1350 | chooses one and remainder chooses the other, it would be bad. This | |
1351 | problem was observed with x = 130.0 and y = 10/7. */ | |
1352 | if (SCM_LIKELY (y > 0)) | |
1353 | q = floor (x / y); | |
1354 | else if (SCM_LIKELY (y < 0)) | |
1355 | q = ceil (x / y); | |
1356 | else if (y == 0) | |
1357 | scm_num_overflow (s_scm_euclidean_remainder); /* or return a NaN? */ | |
1358 | else | |
1359 | return scm_nan (); | |
1360 | return scm_from_double (x - q * y); | |
1361 | } | |
1362 | ||
1363 | /* Compute exact euclidean_remainder the slow way. | |
1364 | We use this only if both arguments are exact, | |
1365 | and at least one of them is a fraction */ | |
1366 | static SCM | |
1367 | scm_i_slow_exact_euclidean_remainder (SCM x, SCM y) | |
1368 | { | |
1369 | SCM q; | |
1370 | ||
1371 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1372 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1373 | s_scm_euclidean_remainder); | |
1374 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1375 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1376 | s_scm_euclidean_remainder); | |
1377 | else if (scm_is_true (scm_positive_p (y))) | |
1378 | q = scm_floor (scm_divide (x, y)); | |
1379 | else if (scm_is_true (scm_negative_p (y))) | |
1380 | q = scm_ceiling (scm_divide (x, y)); | |
1381 | else | |
1382 | scm_num_overflow (s_scm_euclidean_remainder); | |
1383 | return scm_difference (x, scm_product (y, q)); | |
1384 | } | |
1385 | ||
1386 | ||
ac6ce16b MW |
1387 | static SCM scm_i_inexact_euclidean_divide (double x, double y); |
1388 | static SCM scm_i_slow_exact_euclidean_divide (SCM x, SCM y); | |
ff62c168 | 1389 | |
ac6ce16b | 1390 | SCM_PRIMITIVE_GENERIC (scm_euclidean_divide, "euclidean/", 2, 0, 0, |
ff62c168 MW |
1391 | (SCM x, SCM y), |
1392 | "Return the integer @var{q} and the real number @var{r}\n" | |
1393 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1394 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1395 | "@lisp\n" | |
1396 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1397 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1398 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1399 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1400 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1401 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1402 | "@end lisp") | |
ac6ce16b | 1403 | #define FUNC_NAME s_scm_euclidean_divide |
ff62c168 MW |
1404 | { |
1405 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1406 | { | |
1407 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1408 | { | |
1409 | scm_t_inum yy = SCM_I_INUM (y); | |
1410 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1411 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1412 | else |
1413 | { | |
1414 | scm_t_inum xx = SCM_I_INUM (x); | |
1415 | scm_t_inum qq = xx / yy; | |
1416 | scm_t_inum rr = xx - qq * yy; | |
1417 | if (rr < 0) | |
1418 | { | |
1419 | if (yy > 0) | |
1420 | { rr += yy; qq--; } | |
1421 | else | |
1422 | { rr -= yy; qq++; } | |
1423 | } | |
1424 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
1425 | SCM_I_MAKINUM (rr))); | |
1426 | } | |
1427 | } | |
1428 | else if (SCM_BIGP (y)) | |
1429 | { | |
1430 | scm_t_inum xx = SCM_I_INUM (x); | |
1431 | if (xx >= 0) | |
1432 | return scm_values (scm_list_2 (SCM_INUM0, x)); | |
1433 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1434 | { | |
1435 | SCM r = scm_i_mkbig (); | |
1436 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1437 | scm_remember_upto_here_1 (y); | |
1438 | return scm_values | |
1439 | (scm_list_2 (SCM_I_MAKINUM (-1), scm_i_normbig (r))); | |
1440 | } | |
1441 | else | |
1442 | { | |
1443 | SCM r = scm_i_mkbig (); | |
1444 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1445 | scm_remember_upto_here_1 (y); | |
1446 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1447 | return scm_values (scm_list_2 (SCM_INUM1, scm_i_normbig (r))); | |
1448 | } | |
1449 | } | |
1450 | else if (SCM_REALP (y)) | |
ac6ce16b | 1451 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1452 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
1453 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1454 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1455 | else |
ac6ce16b MW |
1456 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1457 | s_scm_euclidean_divide); | |
ff62c168 MW |
1458 | } |
1459 | else if (SCM_BIGP (x)) | |
1460 | { | |
1461 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1462 | { | |
1463 | scm_t_inum yy = SCM_I_INUM (y); | |
1464 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1465 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1466 | else |
1467 | { | |
1468 | SCM q = scm_i_mkbig (); | |
1469 | SCM r = scm_i_mkbig (); | |
1470 | if (yy > 0) | |
1471 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1472 | SCM_I_BIG_MPZ (x), yy); | |
1473 | else | |
1474 | { | |
1475 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1476 | SCM_I_BIG_MPZ (x), -yy); | |
1477 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1478 | } | |
1479 | scm_remember_upto_here_1 (x); | |
1480 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1481 | scm_i_normbig (r))); | |
1482 | } | |
1483 | } | |
1484 | else if (SCM_BIGP (y)) | |
1485 | { | |
1486 | SCM q = scm_i_mkbig (); | |
1487 | SCM r = scm_i_mkbig (); | |
1488 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1489 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1490 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1491 | else | |
1492 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1493 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1494 | scm_remember_upto_here_2 (x, y); | |
1495 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1496 | scm_i_normbig (r))); | |
1497 | } | |
1498 | else if (SCM_REALP (y)) | |
ac6ce16b | 1499 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1500 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
1501 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1502 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1503 | else |
ac6ce16b MW |
1504 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1505 | s_scm_euclidean_divide); | |
ff62c168 MW |
1506 | } |
1507 | else if (SCM_REALP (x)) | |
1508 | { | |
1509 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1510 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 1511 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1512 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
1513 | else | |
ac6ce16b MW |
1514 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1515 | s_scm_euclidean_divide); | |
ff62c168 MW |
1516 | } |
1517 | else if (SCM_FRACTIONP (x)) | |
1518 | { | |
1519 | if (SCM_REALP (y)) | |
ac6ce16b | 1520 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1521 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
1522 | else | |
ac6ce16b | 1523 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 MW |
1524 | } |
1525 | else | |
ac6ce16b MW |
1526 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1527 | s_scm_euclidean_divide); | |
ff62c168 MW |
1528 | } |
1529 | #undef FUNC_NAME | |
1530 | ||
1531 | static SCM | |
ac6ce16b | 1532 | scm_i_inexact_euclidean_divide (double x, double y) |
ff62c168 MW |
1533 | { |
1534 | double q, r; | |
1535 | ||
1536 | if (SCM_LIKELY (y > 0)) | |
1537 | q = floor (x / y); | |
1538 | else if (SCM_LIKELY (y < 0)) | |
1539 | q = ceil (x / y); | |
1540 | else if (y == 0) | |
ac6ce16b | 1541 | scm_num_overflow (s_scm_euclidean_divide); /* or return a NaN? */ |
ff62c168 MW |
1542 | else |
1543 | q = guile_NaN; | |
1544 | r = x - q * y; | |
1545 | return scm_values (scm_list_2 (scm_from_double (q), | |
1546 | scm_from_double (r))); | |
1547 | } | |
1548 | ||
1549 | /* Compute exact euclidean quotient and remainder the slow way. | |
1550 | We use this only if both arguments are exact, | |
1551 | and at least one of them is a fraction */ | |
1552 | static SCM | |
ac6ce16b | 1553 | scm_i_slow_exact_euclidean_divide (SCM x, SCM y) |
ff62c168 MW |
1554 | { |
1555 | SCM q, r; | |
1556 | ||
1557 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
1558 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1559 | s_scm_euclidean_divide); | |
ff62c168 | 1560 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
1561 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1562 | s_scm_euclidean_divide); | |
ff62c168 MW |
1563 | else if (scm_is_true (scm_positive_p (y))) |
1564 | q = scm_floor (scm_divide (x, y)); | |
1565 | else if (scm_is_true (scm_negative_p (y))) | |
1566 | q = scm_ceiling (scm_divide (x, y)); | |
1567 | else | |
ac6ce16b | 1568 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1569 | r = scm_difference (x, scm_product (q, y)); |
1570 | return scm_values (scm_list_2 (q, r)); | |
1571 | } | |
1572 | ||
1573 | static SCM scm_i_inexact_centered_quotient (double x, double y); | |
1574 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
1575 | static SCM scm_i_slow_exact_centered_quotient (SCM x, SCM y); | |
1576 | ||
1577 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, | |
1578 | (SCM x, SCM y), | |
1579 | "Return the integer @var{q} such that\n" | |
1580 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
1581 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
1582 | "@lisp\n" | |
1583 | "(centered-quotient 123 10) @result{} 12\n" | |
1584 | "(centered-quotient 123 -10) @result{} -12\n" | |
1585 | "(centered-quotient -123 10) @result{} -12\n" | |
1586 | "(centered-quotient -123 -10) @result{} 12\n" | |
1587 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
1588 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
1589 | "@end lisp") | |
1590 | #define FUNC_NAME s_scm_centered_quotient | |
1591 | { | |
1592 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1593 | { | |
1594 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1595 | { | |
1596 | scm_t_inum yy = SCM_I_INUM (y); | |
1597 | if (SCM_UNLIKELY (yy == 0)) | |
1598 | scm_num_overflow (s_scm_centered_quotient); | |
1599 | else | |
1600 | { | |
1601 | scm_t_inum xx = SCM_I_INUM (x); | |
1602 | scm_t_inum qq = xx / yy; | |
1603 | scm_t_inum rr = xx - qq * yy; | |
1604 | if (SCM_LIKELY (xx > 0)) | |
1605 | { | |
1606 | if (SCM_LIKELY (yy > 0)) | |
1607 | { | |
1608 | if (rr >= (yy + 1) / 2) | |
1609 | qq++; | |
1610 | } | |
1611 | else | |
1612 | { | |
1613 | if (rr >= (1 - yy) / 2) | |
1614 | qq--; | |
1615 | } | |
1616 | } | |
1617 | else | |
1618 | { | |
1619 | if (SCM_LIKELY (yy > 0)) | |
1620 | { | |
1621 | if (rr < -yy / 2) | |
1622 | qq--; | |
1623 | } | |
1624 | else | |
1625 | { | |
1626 | if (rr < yy / 2) | |
1627 | qq++; | |
1628 | } | |
1629 | } | |
1630 | return SCM_I_MAKINUM (qq); | |
1631 | } | |
1632 | } | |
1633 | else if (SCM_BIGP (y)) | |
1634 | { | |
1635 | /* Pass a denormalized bignum version of x (even though it | |
1636 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
1637 | return scm_i_bigint_centered_quotient | |
1638 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1639 | } | |
1640 | else if (SCM_REALP (y)) | |
1641 | return scm_i_inexact_centered_quotient | |
1642 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1643 | else if (SCM_FRACTIONP (y)) | |
1644 | return scm_i_slow_exact_centered_quotient (x, y); | |
1645 | else | |
1646 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1647 | s_scm_centered_quotient); | |
1648 | } | |
1649 | else if (SCM_BIGP (x)) | |
1650 | { | |
1651 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1652 | { | |
1653 | scm_t_inum yy = SCM_I_INUM (y); | |
1654 | if (SCM_UNLIKELY (yy == 0)) | |
1655 | scm_num_overflow (s_scm_centered_quotient); | |
1656 | else | |
1657 | { | |
1658 | SCM q = scm_i_mkbig (); | |
1659 | scm_t_inum rr; | |
1660 | /* Arrange for rr to initially be non-positive, | |
1661 | because that simplifies the test to see | |
1662 | if it is within the needed bounds. */ | |
1663 | if (yy > 0) | |
1664 | { | |
1665 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1666 | SCM_I_BIG_MPZ (x), yy); | |
1667 | scm_remember_upto_here_1 (x); | |
1668 | if (rr < -yy / 2) | |
1669 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1670 | SCM_I_BIG_MPZ (q), 1); | |
1671 | } | |
1672 | else | |
1673 | { | |
1674 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1675 | SCM_I_BIG_MPZ (x), -yy); | |
1676 | scm_remember_upto_here_1 (x); | |
1677 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1678 | if (rr < yy / 2) | |
1679 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1680 | SCM_I_BIG_MPZ (q), 1); | |
1681 | } | |
1682 | return scm_i_normbig (q); | |
1683 | } | |
1684 | } | |
1685 | else if (SCM_BIGP (y)) | |
1686 | return scm_i_bigint_centered_quotient (x, y); | |
1687 | else if (SCM_REALP (y)) | |
1688 | return scm_i_inexact_centered_quotient | |
1689 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1690 | else if (SCM_FRACTIONP (y)) | |
1691 | return scm_i_slow_exact_centered_quotient (x, y); | |
1692 | else | |
1693 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1694 | s_scm_centered_quotient); | |
1695 | } | |
1696 | else if (SCM_REALP (x)) | |
1697 | { | |
1698 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1699 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1700 | return scm_i_inexact_centered_quotient | |
1701 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1702 | else | |
1703 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1704 | s_scm_centered_quotient); | |
1705 | } | |
1706 | else if (SCM_FRACTIONP (x)) | |
1707 | { | |
1708 | if (SCM_REALP (y)) | |
1709 | return scm_i_inexact_centered_quotient | |
1710 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1711 | else | |
1712 | return scm_i_slow_exact_centered_quotient (x, y); | |
1713 | } | |
1714 | else | |
1715 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1716 | s_scm_centered_quotient); | |
1717 | } | |
1718 | #undef FUNC_NAME | |
1719 | ||
1720 | static SCM | |
1721 | scm_i_inexact_centered_quotient (double x, double y) | |
1722 | { | |
1723 | if (SCM_LIKELY (y > 0)) | |
1724 | return scm_from_double (floor (x/y + 0.5)); | |
1725 | else if (SCM_LIKELY (y < 0)) | |
1726 | return scm_from_double (ceil (x/y - 0.5)); | |
1727 | else if (y == 0) | |
1728 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
1729 | else | |
1730 | return scm_nan (); | |
1731 | } | |
1732 | ||
1733 | /* Assumes that both x and y are bigints, though | |
1734 | x might be able to fit into a fixnum. */ | |
1735 | static SCM | |
1736 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
1737 | { | |
1738 | SCM q, r, min_r; | |
1739 | ||
1740 | /* Note that x might be small enough to fit into a | |
1741 | fixnum, so we must not let it escape into the wild */ | |
1742 | q = scm_i_mkbig (); | |
1743 | r = scm_i_mkbig (); | |
1744 | ||
1745 | /* min_r will eventually become -abs(y)/2 */ | |
1746 | min_r = scm_i_mkbig (); | |
1747 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1748 | SCM_I_BIG_MPZ (y), 1); | |
1749 | ||
1750 | /* Arrange for rr to initially be non-positive, | |
1751 | because that simplifies the test to see | |
1752 | if it is within the needed bounds. */ | |
1753 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1754 | { | |
1755 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1756 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1757 | scm_remember_upto_here_2 (x, y); | |
1758 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1759 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1760 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1761 | SCM_I_BIG_MPZ (q), 1); | |
1762 | } | |
1763 | else | |
1764 | { | |
1765 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1766 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1767 | scm_remember_upto_here_2 (x, y); | |
1768 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1769 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1770 | SCM_I_BIG_MPZ (q), 1); | |
1771 | } | |
1772 | scm_remember_upto_here_2 (r, min_r); | |
1773 | return scm_i_normbig (q); | |
1774 | } | |
1775 | ||
1776 | /* Compute exact centered quotient the slow way. | |
1777 | We use this only if both arguments are exact, | |
1778 | and at least one of them is a fraction */ | |
1779 | static SCM | |
1780 | scm_i_slow_exact_centered_quotient (SCM x, SCM y) | |
1781 | { | |
1782 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1783 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1784 | s_scm_centered_quotient); | |
1785 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1786 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1787 | s_scm_centered_quotient); | |
1788 | else if (scm_is_true (scm_positive_p (y))) | |
1789 | return scm_floor (scm_sum (scm_divide (x, y), | |
1790 | exactly_one_half)); | |
1791 | else if (scm_is_true (scm_negative_p (y))) | |
1792 | return scm_ceiling (scm_difference (scm_divide (x, y), | |
1793 | exactly_one_half)); | |
1794 | else | |
1795 | scm_num_overflow (s_scm_centered_quotient); | |
1796 | } | |
1797 | ||
1798 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
1799 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
1800 | static SCM scm_i_slow_exact_centered_remainder (SCM x, SCM y); | |
1801 | ||
1802 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
1803 | (SCM x, SCM y), | |
1804 | "Return the real number @var{r} such that\n" | |
1805 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
1806 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1807 | "for some integer @var{q}.\n" | |
1808 | "@lisp\n" | |
1809 | "(centered-remainder 123 10) @result{} 3\n" | |
1810 | "(centered-remainder 123 -10) @result{} 3\n" | |
1811 | "(centered-remainder -123 10) @result{} -3\n" | |
1812 | "(centered-remainder -123 -10) @result{} -3\n" | |
1813 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
1814 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
1815 | "@end lisp") | |
1816 | #define FUNC_NAME s_scm_centered_remainder | |
1817 | { | |
1818 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1819 | { | |
1820 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1821 | { | |
1822 | scm_t_inum yy = SCM_I_INUM (y); | |
1823 | if (SCM_UNLIKELY (yy == 0)) | |
1824 | scm_num_overflow (s_scm_centered_remainder); | |
1825 | else | |
1826 | { | |
1827 | scm_t_inum xx = SCM_I_INUM (x); | |
1828 | scm_t_inum rr = xx % yy; | |
1829 | if (SCM_LIKELY (xx > 0)) | |
1830 | { | |
1831 | if (SCM_LIKELY (yy > 0)) | |
1832 | { | |
1833 | if (rr >= (yy + 1) / 2) | |
1834 | rr -= yy; | |
1835 | } | |
1836 | else | |
1837 | { | |
1838 | if (rr >= (1 - yy) / 2) | |
1839 | rr += yy; | |
1840 | } | |
1841 | } | |
1842 | else | |
1843 | { | |
1844 | if (SCM_LIKELY (yy > 0)) | |
1845 | { | |
1846 | if (rr < -yy / 2) | |
1847 | rr += yy; | |
1848 | } | |
1849 | else | |
1850 | { | |
1851 | if (rr < yy / 2) | |
1852 | rr -= yy; | |
1853 | } | |
1854 | } | |
1855 | return SCM_I_MAKINUM (rr); | |
1856 | } | |
1857 | } | |
1858 | else if (SCM_BIGP (y)) | |
1859 | { | |
1860 | /* Pass a denormalized bignum version of x (even though it | |
1861 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
1862 | return scm_i_bigint_centered_remainder | |
1863 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1864 | } | |
1865 | else if (SCM_REALP (y)) | |
1866 | return scm_i_inexact_centered_remainder | |
1867 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1868 | else if (SCM_FRACTIONP (y)) | |
1869 | return scm_i_slow_exact_centered_remainder (x, y); | |
1870 | else | |
1871 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1872 | s_scm_centered_remainder); | |
1873 | } | |
1874 | else if (SCM_BIGP (x)) | |
1875 | { | |
1876 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1877 | { | |
1878 | scm_t_inum yy = SCM_I_INUM (y); | |
1879 | if (SCM_UNLIKELY (yy == 0)) | |
1880 | scm_num_overflow (s_scm_centered_remainder); | |
1881 | else | |
1882 | { | |
1883 | scm_t_inum rr; | |
1884 | /* Arrange for rr to initially be non-positive, | |
1885 | because that simplifies the test to see | |
1886 | if it is within the needed bounds. */ | |
1887 | if (yy > 0) | |
1888 | { | |
1889 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1890 | scm_remember_upto_here_1 (x); | |
1891 | if (rr < -yy / 2) | |
1892 | rr += yy; | |
1893 | } | |
1894 | else | |
1895 | { | |
1896 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1897 | scm_remember_upto_here_1 (x); | |
1898 | if (rr < yy / 2) | |
1899 | rr -= yy; | |
1900 | } | |
1901 | return SCM_I_MAKINUM (rr); | |
1902 | } | |
1903 | } | |
1904 | else if (SCM_BIGP (y)) | |
1905 | return scm_i_bigint_centered_remainder (x, y); | |
1906 | else if (SCM_REALP (y)) | |
1907 | return scm_i_inexact_centered_remainder | |
1908 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1909 | else if (SCM_FRACTIONP (y)) | |
1910 | return scm_i_slow_exact_centered_remainder (x, y); | |
1911 | else | |
1912 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1913 | s_scm_centered_remainder); | |
1914 | } | |
1915 | else if (SCM_REALP (x)) | |
1916 | { | |
1917 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1918 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1919 | return scm_i_inexact_centered_remainder | |
1920 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1921 | else | |
1922 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1923 | s_scm_centered_remainder); | |
1924 | } | |
1925 | else if (SCM_FRACTIONP (x)) | |
1926 | { | |
1927 | if (SCM_REALP (y)) | |
1928 | return scm_i_inexact_centered_remainder | |
1929 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1930 | else | |
1931 | return scm_i_slow_exact_centered_remainder (x, y); | |
1932 | } | |
1933 | else | |
1934 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
1935 | s_scm_centered_remainder); | |
1936 | } | |
1937 | #undef FUNC_NAME | |
1938 | ||
1939 | static SCM | |
1940 | scm_i_inexact_centered_remainder (double x, double y) | |
1941 | { | |
1942 | double q; | |
1943 | ||
1944 | /* Although it would be more efficient to use fmod here, we can't | |
1945 | because it would in some cases produce results inconsistent with | |
1946 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
1947 | close). In particular, when x-y/2 is very close to a multiple of | |
1948 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
1949 | two cases must correspond to different choices of q. If quotient | |
1950 | chooses one and remainder chooses the other, it would be bad. */ | |
1951 | if (SCM_LIKELY (y > 0)) | |
1952 | q = floor (x/y + 0.5); | |
1953 | else if (SCM_LIKELY (y < 0)) | |
1954 | q = ceil (x/y - 0.5); | |
1955 | else if (y == 0) | |
1956 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
1957 | else | |
1958 | return scm_nan (); | |
1959 | return scm_from_double (x - q * y); | |
1960 | } | |
1961 | ||
1962 | /* Assumes that both x and y are bigints, though | |
1963 | x might be able to fit into a fixnum. */ | |
1964 | static SCM | |
1965 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
1966 | { | |
1967 | SCM r, min_r; | |
1968 | ||
1969 | /* Note that x might be small enough to fit into a | |
1970 | fixnum, so we must not let it escape into the wild */ | |
1971 | r = scm_i_mkbig (); | |
1972 | ||
1973 | /* min_r will eventually become -abs(y)/2 */ | |
1974 | min_r = scm_i_mkbig (); | |
1975 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1976 | SCM_I_BIG_MPZ (y), 1); | |
1977 | ||
1978 | /* Arrange for rr to initially be non-positive, | |
1979 | because that simplifies the test to see | |
1980 | if it is within the needed bounds. */ | |
1981 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1982 | { | |
1983 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1984 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1985 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1986 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1987 | mpz_add (SCM_I_BIG_MPZ (r), | |
1988 | SCM_I_BIG_MPZ (r), | |
1989 | SCM_I_BIG_MPZ (y)); | |
1990 | } | |
1991 | else | |
1992 | { | |
1993 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1994 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1995 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1996 | mpz_sub (SCM_I_BIG_MPZ (r), | |
1997 | SCM_I_BIG_MPZ (r), | |
1998 | SCM_I_BIG_MPZ (y)); | |
1999 | } | |
2000 | scm_remember_upto_here_2 (x, y); | |
2001 | return scm_i_normbig (r); | |
2002 | } | |
2003 | ||
2004 | /* Compute exact centered_remainder the slow way. | |
2005 | We use this only if both arguments are exact, | |
2006 | and at least one of them is a fraction */ | |
2007 | static SCM | |
2008 | scm_i_slow_exact_centered_remainder (SCM x, SCM y) | |
2009 | { | |
2010 | SCM q; | |
2011 | ||
2012 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
2013 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2014 | s_scm_centered_remainder); | |
2015 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
2016 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2017 | s_scm_centered_remainder); | |
2018 | else if (scm_is_true (scm_positive_p (y))) | |
2019 | q = scm_floor (scm_sum (scm_divide (x, y), exactly_one_half)); | |
2020 | else if (scm_is_true (scm_negative_p (y))) | |
2021 | q = scm_ceiling (scm_difference (scm_divide (x, y), exactly_one_half)); | |
2022 | else | |
2023 | scm_num_overflow (s_scm_centered_remainder); | |
2024 | return scm_difference (x, scm_product (y, q)); | |
2025 | } | |
2026 | ||
2027 | ||
ac6ce16b MW |
2028 | static SCM scm_i_inexact_centered_divide (double x, double y); |
2029 | static SCM scm_i_bigint_centered_divide (SCM x, SCM y); | |
2030 | static SCM scm_i_slow_exact_centered_divide (SCM x, SCM y); | |
ff62c168 | 2031 | |
ac6ce16b | 2032 | SCM_PRIMITIVE_GENERIC (scm_centered_divide, "centered/", 2, 0, 0, |
ff62c168 MW |
2033 | (SCM x, SCM y), |
2034 | "Return the integer @var{q} and the real number @var{r}\n" | |
2035 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2036 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2037 | "@lisp\n" | |
2038 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2039 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2040 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2041 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2042 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2043 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2044 | "@end lisp") | |
ac6ce16b | 2045 | #define FUNC_NAME s_scm_centered_divide |
ff62c168 MW |
2046 | { |
2047 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2048 | { | |
2049 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2050 | { | |
2051 | scm_t_inum yy = SCM_I_INUM (y); | |
2052 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2053 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2054 | else |
2055 | { | |
2056 | scm_t_inum xx = SCM_I_INUM (x); | |
2057 | scm_t_inum qq = xx / yy; | |
2058 | scm_t_inum rr = xx - qq * yy; | |
2059 | if (SCM_LIKELY (xx > 0)) | |
2060 | { | |
2061 | if (SCM_LIKELY (yy > 0)) | |
2062 | { | |
2063 | if (rr >= (yy + 1) / 2) | |
2064 | { qq++; rr -= yy; } | |
2065 | } | |
2066 | else | |
2067 | { | |
2068 | if (rr >= (1 - yy) / 2) | |
2069 | { qq--; rr += yy; } | |
2070 | } | |
2071 | } | |
2072 | else | |
2073 | { | |
2074 | if (SCM_LIKELY (yy > 0)) | |
2075 | { | |
2076 | if (rr < -yy / 2) | |
2077 | { qq--; rr += yy; } | |
2078 | } | |
2079 | else | |
2080 | { | |
2081 | if (rr < yy / 2) | |
2082 | { qq++; rr -= yy; } | |
2083 | } | |
2084 | } | |
2085 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
2086 | SCM_I_MAKINUM (rr))); | |
2087 | } | |
2088 | } | |
2089 | else if (SCM_BIGP (y)) | |
2090 | { | |
2091 | /* Pass a denormalized bignum version of x (even though it | |
ac6ce16b MW |
2092 | can fit in a fixnum) to scm_i_bigint_centered_divide */ |
2093 | return scm_i_bigint_centered_divide | |
ff62c168 MW |
2094 | (scm_i_long2big (SCM_I_INUM (x)), y); |
2095 | } | |
2096 | else if (SCM_REALP (y)) | |
ac6ce16b | 2097 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2098 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
2099 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2100 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2101 | else |
ac6ce16b MW |
2102 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2103 | s_scm_centered_divide); | |
ff62c168 MW |
2104 | } |
2105 | else if (SCM_BIGP (x)) | |
2106 | { | |
2107 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2108 | { | |
2109 | scm_t_inum yy = SCM_I_INUM (y); | |
2110 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2111 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2112 | else |
2113 | { | |
2114 | SCM q = scm_i_mkbig (); | |
2115 | scm_t_inum rr; | |
2116 | /* Arrange for rr to initially be non-positive, | |
2117 | because that simplifies the test to see | |
2118 | if it is within the needed bounds. */ | |
2119 | if (yy > 0) | |
2120 | { | |
2121 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2122 | SCM_I_BIG_MPZ (x), yy); | |
2123 | scm_remember_upto_here_1 (x); | |
2124 | if (rr < -yy / 2) | |
2125 | { | |
2126 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2127 | SCM_I_BIG_MPZ (q), 1); | |
2128 | rr += yy; | |
2129 | } | |
2130 | } | |
2131 | else | |
2132 | { | |
2133 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2134 | SCM_I_BIG_MPZ (x), -yy); | |
2135 | scm_remember_upto_here_1 (x); | |
2136 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2137 | if (rr < yy / 2) | |
2138 | { | |
2139 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2140 | SCM_I_BIG_MPZ (q), 1); | |
2141 | rr -= yy; | |
2142 | } | |
2143 | } | |
2144 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2145 | SCM_I_MAKINUM (rr))); | |
2146 | } | |
2147 | } | |
2148 | else if (SCM_BIGP (y)) | |
ac6ce16b | 2149 | return scm_i_bigint_centered_divide (x, y); |
ff62c168 | 2150 | else if (SCM_REALP (y)) |
ac6ce16b | 2151 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2152 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
2153 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2154 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2155 | else |
ac6ce16b MW |
2156 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2157 | s_scm_centered_divide); | |
ff62c168 MW |
2158 | } |
2159 | else if (SCM_REALP (x)) | |
2160 | { | |
2161 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2162 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 2163 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2164 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
2165 | else | |
ac6ce16b MW |
2166 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2167 | s_scm_centered_divide); | |
ff62c168 MW |
2168 | } |
2169 | else if (SCM_FRACTIONP (x)) | |
2170 | { | |
2171 | if (SCM_REALP (y)) | |
ac6ce16b | 2172 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2173 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
2174 | else | |
ac6ce16b | 2175 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 MW |
2176 | } |
2177 | else | |
ac6ce16b MW |
2178 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2179 | s_scm_centered_divide); | |
ff62c168 MW |
2180 | } |
2181 | #undef FUNC_NAME | |
2182 | ||
2183 | static SCM | |
ac6ce16b | 2184 | scm_i_inexact_centered_divide (double x, double y) |
ff62c168 MW |
2185 | { |
2186 | double q, r; | |
2187 | ||
2188 | if (SCM_LIKELY (y > 0)) | |
2189 | q = floor (x/y + 0.5); | |
2190 | else if (SCM_LIKELY (y < 0)) | |
2191 | q = ceil (x/y - 0.5); | |
2192 | else if (y == 0) | |
ac6ce16b | 2193 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ |
ff62c168 MW |
2194 | else |
2195 | q = guile_NaN; | |
2196 | r = x - q * y; | |
2197 | return scm_values (scm_list_2 (scm_from_double (q), | |
2198 | scm_from_double (r))); | |
2199 | } | |
2200 | ||
2201 | /* Assumes that both x and y are bigints, though | |
2202 | x might be able to fit into a fixnum. */ | |
2203 | static SCM | |
ac6ce16b | 2204 | scm_i_bigint_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2205 | { |
2206 | SCM q, r, min_r; | |
2207 | ||
2208 | /* Note that x might be small enough to fit into a | |
2209 | fixnum, so we must not let it escape into the wild */ | |
2210 | q = scm_i_mkbig (); | |
2211 | r = scm_i_mkbig (); | |
2212 | ||
2213 | /* min_r will eventually become -abs(y/2) */ | |
2214 | min_r = scm_i_mkbig (); | |
2215 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2216 | SCM_I_BIG_MPZ (y), 1); | |
2217 | ||
2218 | /* Arrange for rr to initially be non-positive, | |
2219 | because that simplifies the test to see | |
2220 | if it is within the needed bounds. */ | |
2221 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2222 | { | |
2223 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2224 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2225 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2226 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2227 | { | |
2228 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2229 | SCM_I_BIG_MPZ (q), 1); | |
2230 | mpz_add (SCM_I_BIG_MPZ (r), | |
2231 | SCM_I_BIG_MPZ (r), | |
2232 | SCM_I_BIG_MPZ (y)); | |
2233 | } | |
2234 | } | |
2235 | else | |
2236 | { | |
2237 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2238 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2239 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2240 | { | |
2241 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2242 | SCM_I_BIG_MPZ (q), 1); | |
2243 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2244 | SCM_I_BIG_MPZ (r), | |
2245 | SCM_I_BIG_MPZ (y)); | |
2246 | } | |
2247 | } | |
2248 | scm_remember_upto_here_2 (x, y); | |
2249 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2250 | scm_i_normbig (r))); | |
2251 | } | |
2252 | ||
2253 | /* Compute exact centered quotient and remainder the slow way. | |
2254 | We use this only if both arguments are exact, | |
2255 | and at least one of them is a fraction */ | |
2256 | static SCM | |
ac6ce16b | 2257 | scm_i_slow_exact_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2258 | { |
2259 | SCM q, r; | |
2260 | ||
2261 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
2262 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2263 | s_scm_centered_divide); | |
ff62c168 | 2264 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
2265 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2266 | s_scm_centered_divide); | |
ff62c168 MW |
2267 | else if (scm_is_true (scm_positive_p (y))) |
2268 | q = scm_floor (scm_sum (scm_divide (x, y), | |
2269 | exactly_one_half)); | |
2270 | else if (scm_is_true (scm_negative_p (y))) | |
2271 | q = scm_ceiling (scm_difference (scm_divide (x, y), | |
2272 | exactly_one_half)); | |
2273 | else | |
ac6ce16b | 2274 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2275 | r = scm_difference (x, scm_product (q, y)); |
2276 | return scm_values (scm_list_2 (q, r)); | |
2277 | } | |
2278 | ||
2279 | ||
78d3deb1 AW |
2280 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
2281 | (SCM x, SCM y, SCM rest), | |
2282 | "Return the greatest common divisor of all parameter values.\n" | |
2283 | "If called without arguments, 0 is returned.") | |
2284 | #define FUNC_NAME s_scm_i_gcd | |
2285 | { | |
2286 | while (!scm_is_null (rest)) | |
2287 | { x = scm_gcd (x, y); | |
2288 | y = scm_car (rest); | |
2289 | rest = scm_cdr (rest); | |
2290 | } | |
2291 | return scm_gcd (x, y); | |
2292 | } | |
2293 | #undef FUNC_NAME | |
2294 | ||
2295 | #define s_gcd s_scm_i_gcd | |
2296 | #define g_gcd g_scm_i_gcd | |
2297 | ||
0f2d19dd | 2298 | SCM |
6e8d25a6 | 2299 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 2300 | { |
ca46fb90 | 2301 | if (SCM_UNBNDP (y)) |
1dd79792 | 2302 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 2303 | |
e11e83f3 | 2304 | if (SCM_I_INUMP (x)) |
ca46fb90 | 2305 | { |
e11e83f3 | 2306 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2307 | { |
e25f3727 AW |
2308 | scm_t_inum xx = SCM_I_INUM (x); |
2309 | scm_t_inum yy = SCM_I_INUM (y); | |
2310 | scm_t_inum u = xx < 0 ? -xx : xx; | |
2311 | scm_t_inum v = yy < 0 ? -yy : yy; | |
2312 | scm_t_inum result; | |
0aacf84e MD |
2313 | if (xx == 0) |
2314 | result = v; | |
2315 | else if (yy == 0) | |
2316 | result = u; | |
2317 | else | |
2318 | { | |
e25f3727 AW |
2319 | scm_t_inum k = 1; |
2320 | scm_t_inum t; | |
0aacf84e MD |
2321 | /* Determine a common factor 2^k */ |
2322 | while (!(1 & (u | v))) | |
2323 | { | |
2324 | k <<= 1; | |
2325 | u >>= 1; | |
2326 | v >>= 1; | |
2327 | } | |
2328 | /* Now, any factor 2^n can be eliminated */ | |
2329 | if (u & 1) | |
2330 | t = -v; | |
2331 | else | |
2332 | { | |
2333 | t = u; | |
2334 | b3: | |
2335 | t = SCM_SRS (t, 1); | |
2336 | } | |
2337 | if (!(1 & t)) | |
2338 | goto b3; | |
2339 | if (t > 0) | |
2340 | u = t; | |
2341 | else | |
2342 | v = -t; | |
2343 | t = u - v; | |
2344 | if (t != 0) | |
2345 | goto b3; | |
2346 | result = u * k; | |
2347 | } | |
2348 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 2349 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2350 | : scm_i_inum2big (result)); |
ca46fb90 RB |
2351 | } |
2352 | else if (SCM_BIGP (y)) | |
2353 | { | |
0bff4dce KR |
2354 | SCM_SWAP (x, y); |
2355 | goto big_inum; | |
ca46fb90 RB |
2356 | } |
2357 | else | |
2358 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 2359 | } |
ca46fb90 RB |
2360 | else if (SCM_BIGP (x)) |
2361 | { | |
e11e83f3 | 2362 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2363 | { |
e25f3727 AW |
2364 | scm_t_bits result; |
2365 | scm_t_inum yy; | |
0bff4dce | 2366 | big_inum: |
e11e83f3 | 2367 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
2368 | if (yy == 0) |
2369 | return scm_abs (x); | |
0aacf84e MD |
2370 | if (yy < 0) |
2371 | yy = -yy; | |
ca46fb90 RB |
2372 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
2373 | scm_remember_upto_here_1 (x); | |
0aacf84e | 2374 | return (SCM_POSFIXABLE (result) |
d956fa6f | 2375 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2376 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
2377 | } |
2378 | else if (SCM_BIGP (y)) | |
2379 | { | |
2380 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
2381 | mpz_gcd (SCM_I_BIG_MPZ (result), |
2382 | SCM_I_BIG_MPZ (x), | |
2383 | SCM_I_BIG_MPZ (y)); | |
2384 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
2385 | return scm_i_normbig (result); |
2386 | } | |
2387 | else | |
2388 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 2389 | } |
ca46fb90 | 2390 | else |
09fb7599 | 2391 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
2392 | } |
2393 | ||
78d3deb1 AW |
2394 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
2395 | (SCM x, SCM y, SCM rest), | |
2396 | "Return the least common multiple of the arguments.\n" | |
2397 | "If called without arguments, 1 is returned.") | |
2398 | #define FUNC_NAME s_scm_i_lcm | |
2399 | { | |
2400 | while (!scm_is_null (rest)) | |
2401 | { x = scm_lcm (x, y); | |
2402 | y = scm_car (rest); | |
2403 | rest = scm_cdr (rest); | |
2404 | } | |
2405 | return scm_lcm (x, y); | |
2406 | } | |
2407 | #undef FUNC_NAME | |
2408 | ||
2409 | #define s_lcm s_scm_i_lcm | |
2410 | #define g_lcm g_scm_i_lcm | |
2411 | ||
0f2d19dd | 2412 | SCM |
6e8d25a6 | 2413 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 2414 | { |
ca46fb90 RB |
2415 | if (SCM_UNBNDP (n2)) |
2416 | { | |
2417 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
2418 | return SCM_I_MAKINUM (1L); |
2419 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 2420 | } |
09fb7599 | 2421 | |
e11e83f3 | 2422 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 2423 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 2424 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 2425 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 2426 | |
e11e83f3 | 2427 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 2428 | { |
e11e83f3 | 2429 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2430 | { |
2431 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 2432 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
2433 | return d; |
2434 | else | |
2435 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
2436 | } | |
2437 | else | |
2438 | { | |
2439 | /* inum n1, big n2 */ | |
2440 | inumbig: | |
2441 | { | |
2442 | SCM result = scm_i_mkbig (); | |
e25f3727 | 2443 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
2444 | if (nn1 == 0) return SCM_INUM0; |
2445 | if (nn1 < 0) nn1 = - nn1; | |
2446 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
2447 | scm_remember_upto_here_1 (n2); | |
2448 | return result; | |
2449 | } | |
2450 | } | |
2451 | } | |
2452 | else | |
2453 | { | |
2454 | /* big n1 */ | |
e11e83f3 | 2455 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2456 | { |
2457 | SCM_SWAP (n1, n2); | |
2458 | goto inumbig; | |
2459 | } | |
2460 | else | |
2461 | { | |
2462 | SCM result = scm_i_mkbig (); | |
2463 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
2464 | SCM_I_BIG_MPZ (n1), | |
2465 | SCM_I_BIG_MPZ (n2)); | |
2466 | scm_remember_upto_here_2(n1, n2); | |
2467 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
2468 | return result; | |
2469 | } | |
f872b822 | 2470 | } |
0f2d19dd JB |
2471 | } |
2472 | ||
8a525303 GB |
2473 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
2474 | ||
2475 | Logand: | |
2476 | X Y Result Method: | |
2477 | (len) | |
2478 | + + + x (map digit:logand X Y) | |
2479 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
2480 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
2481 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
2482 | ||
2483 | Logior: | |
2484 | X Y Result Method: | |
2485 | ||
2486 | + + + (map digit:logior X Y) | |
2487 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
2488 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
2489 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
2490 | ||
2491 | Logxor: | |
2492 | X Y Result Method: | |
2493 | ||
2494 | + + + (map digit:logxor X Y) | |
2495 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
2496 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
2497 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
2498 | ||
2499 | Logtest: | |
2500 | X Y Result | |
2501 | ||
2502 | + + (any digit:logand X Y) | |
2503 | + - (any digit:logand X (lognot (+ -1 Y))) | |
2504 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
2505 | - - #t | |
2506 | ||
2507 | */ | |
2508 | ||
78d3deb1 AW |
2509 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
2510 | (SCM x, SCM y, SCM rest), | |
2511 | "Return the bitwise AND of the integer arguments.\n\n" | |
2512 | "@lisp\n" | |
2513 | "(logand) @result{} -1\n" | |
2514 | "(logand 7) @result{} 7\n" | |
2515 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
2516 | "@end lisp") | |
2517 | #define FUNC_NAME s_scm_i_logand | |
2518 | { | |
2519 | while (!scm_is_null (rest)) | |
2520 | { x = scm_logand (x, y); | |
2521 | y = scm_car (rest); | |
2522 | rest = scm_cdr (rest); | |
2523 | } | |
2524 | return scm_logand (x, y); | |
2525 | } | |
2526 | #undef FUNC_NAME | |
2527 | ||
2528 | #define s_scm_logand s_scm_i_logand | |
2529 | ||
2530 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 2531 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 2532 | { |
e25f3727 | 2533 | scm_t_inum nn1; |
9a00c9fc | 2534 | |
0aacf84e MD |
2535 | if (SCM_UNBNDP (n2)) |
2536 | { | |
2537 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 2538 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
2539 | else if (!SCM_NUMBERP (n1)) |
2540 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
2541 | else if (SCM_NUMBERP (n1)) | |
2542 | return n1; | |
2543 | else | |
2544 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2545 | } |
09fb7599 | 2546 | |
e11e83f3 | 2547 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2548 | { |
e11e83f3 MV |
2549 | nn1 = SCM_I_INUM (n1); |
2550 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2551 | { |
e25f3727 | 2552 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2553 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
2554 | } |
2555 | else if SCM_BIGP (n2) | |
2556 | { | |
2557 | intbig: | |
2558 | if (n1 == 0) | |
2559 | return SCM_INUM0; | |
2560 | { | |
2561 | SCM result_z = scm_i_mkbig (); | |
2562 | mpz_t nn1_z; | |
2563 | mpz_init_set_si (nn1_z, nn1); | |
2564 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2565 | scm_remember_upto_here_1 (n2); | |
2566 | mpz_clear (nn1_z); | |
2567 | return scm_i_normbig (result_z); | |
2568 | } | |
2569 | } | |
2570 | else | |
2571 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2572 | } | |
2573 | else if (SCM_BIGP (n1)) | |
2574 | { | |
e11e83f3 | 2575 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2576 | { |
2577 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2578 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2579 | goto intbig; |
2580 | } | |
2581 | else if (SCM_BIGP (n2)) | |
2582 | { | |
2583 | SCM result_z = scm_i_mkbig (); | |
2584 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
2585 | SCM_I_BIG_MPZ (n1), | |
2586 | SCM_I_BIG_MPZ (n2)); | |
2587 | scm_remember_upto_here_2 (n1, n2); | |
2588 | return scm_i_normbig (result_z); | |
2589 | } | |
2590 | else | |
2591 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2592 | } |
0aacf84e | 2593 | else |
09fb7599 | 2594 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2595 | } |
1bbd0b84 | 2596 | #undef FUNC_NAME |
0f2d19dd | 2597 | |
09fb7599 | 2598 | |
78d3deb1 AW |
2599 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
2600 | (SCM x, SCM y, SCM rest), | |
2601 | "Return the bitwise OR of the integer arguments.\n\n" | |
2602 | "@lisp\n" | |
2603 | "(logior) @result{} 0\n" | |
2604 | "(logior 7) @result{} 7\n" | |
2605 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
2606 | "@end lisp") | |
2607 | #define FUNC_NAME s_scm_i_logior | |
2608 | { | |
2609 | while (!scm_is_null (rest)) | |
2610 | { x = scm_logior (x, y); | |
2611 | y = scm_car (rest); | |
2612 | rest = scm_cdr (rest); | |
2613 | } | |
2614 | return scm_logior (x, y); | |
2615 | } | |
2616 | #undef FUNC_NAME | |
2617 | ||
2618 | #define s_scm_logior s_scm_i_logior | |
2619 | ||
2620 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 2621 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 2622 | { |
e25f3727 | 2623 | scm_t_inum nn1; |
9a00c9fc | 2624 | |
0aacf84e MD |
2625 | if (SCM_UNBNDP (n2)) |
2626 | { | |
2627 | if (SCM_UNBNDP (n1)) | |
2628 | return SCM_INUM0; | |
2629 | else if (SCM_NUMBERP (n1)) | |
2630 | return n1; | |
2631 | else | |
2632 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2633 | } |
09fb7599 | 2634 | |
e11e83f3 | 2635 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2636 | { |
e11e83f3 MV |
2637 | nn1 = SCM_I_INUM (n1); |
2638 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2639 | { |
e11e83f3 | 2640 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 2641 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
2642 | } |
2643 | else if (SCM_BIGP (n2)) | |
2644 | { | |
2645 | intbig: | |
2646 | if (nn1 == 0) | |
2647 | return n2; | |
2648 | { | |
2649 | SCM result_z = scm_i_mkbig (); | |
2650 | mpz_t nn1_z; | |
2651 | mpz_init_set_si (nn1_z, nn1); | |
2652 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2653 | scm_remember_upto_here_1 (n2); | |
2654 | mpz_clear (nn1_z); | |
9806de0d | 2655 | return scm_i_normbig (result_z); |
0aacf84e MD |
2656 | } |
2657 | } | |
2658 | else | |
2659 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2660 | } | |
2661 | else if (SCM_BIGP (n1)) | |
2662 | { | |
e11e83f3 | 2663 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2664 | { |
2665 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2666 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2667 | goto intbig; |
2668 | } | |
2669 | else if (SCM_BIGP (n2)) | |
2670 | { | |
2671 | SCM result_z = scm_i_mkbig (); | |
2672 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
2673 | SCM_I_BIG_MPZ (n1), | |
2674 | SCM_I_BIG_MPZ (n2)); | |
2675 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 2676 | return scm_i_normbig (result_z); |
0aacf84e MD |
2677 | } |
2678 | else | |
2679 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2680 | } |
0aacf84e | 2681 | else |
09fb7599 | 2682 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2683 | } |
1bbd0b84 | 2684 | #undef FUNC_NAME |
0f2d19dd | 2685 | |
09fb7599 | 2686 | |
78d3deb1 AW |
2687 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
2688 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
2689 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
2690 | "set in the result if it is set in an odd number of arguments.\n" | |
2691 | "@lisp\n" | |
2692 | "(logxor) @result{} 0\n" | |
2693 | "(logxor 7) @result{} 7\n" | |
2694 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
2695 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 2696 | "@end lisp") |
78d3deb1 AW |
2697 | #define FUNC_NAME s_scm_i_logxor |
2698 | { | |
2699 | while (!scm_is_null (rest)) | |
2700 | { x = scm_logxor (x, y); | |
2701 | y = scm_car (rest); | |
2702 | rest = scm_cdr (rest); | |
2703 | } | |
2704 | return scm_logxor (x, y); | |
2705 | } | |
2706 | #undef FUNC_NAME | |
2707 | ||
2708 | #define s_scm_logxor s_scm_i_logxor | |
2709 | ||
2710 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 2711 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 2712 | { |
e25f3727 | 2713 | scm_t_inum nn1; |
9a00c9fc | 2714 | |
0aacf84e MD |
2715 | if (SCM_UNBNDP (n2)) |
2716 | { | |
2717 | if (SCM_UNBNDP (n1)) | |
2718 | return SCM_INUM0; | |
2719 | else if (SCM_NUMBERP (n1)) | |
2720 | return n1; | |
2721 | else | |
2722 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2723 | } |
09fb7599 | 2724 | |
e11e83f3 | 2725 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2726 | { |
e11e83f3 MV |
2727 | nn1 = SCM_I_INUM (n1); |
2728 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2729 | { |
e25f3727 | 2730 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2731 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
2732 | } |
2733 | else if (SCM_BIGP (n2)) | |
2734 | { | |
2735 | intbig: | |
2736 | { | |
2737 | SCM result_z = scm_i_mkbig (); | |
2738 | mpz_t nn1_z; | |
2739 | mpz_init_set_si (nn1_z, nn1); | |
2740 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2741 | scm_remember_upto_here_1 (n2); | |
2742 | mpz_clear (nn1_z); | |
2743 | return scm_i_normbig (result_z); | |
2744 | } | |
2745 | } | |
2746 | else | |
2747 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2748 | } | |
2749 | else if (SCM_BIGP (n1)) | |
2750 | { | |
e11e83f3 | 2751 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2752 | { |
2753 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2754 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2755 | goto intbig; |
2756 | } | |
2757 | else if (SCM_BIGP (n2)) | |
2758 | { | |
2759 | SCM result_z = scm_i_mkbig (); | |
2760 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
2761 | SCM_I_BIG_MPZ (n1), | |
2762 | SCM_I_BIG_MPZ (n2)); | |
2763 | scm_remember_upto_here_2 (n1, n2); | |
2764 | return scm_i_normbig (result_z); | |
2765 | } | |
2766 | else | |
2767 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2768 | } |
0aacf84e | 2769 | else |
09fb7599 | 2770 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2771 | } |
1bbd0b84 | 2772 | #undef FUNC_NAME |
0f2d19dd | 2773 | |
09fb7599 | 2774 | |
a1ec6916 | 2775 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 2776 | (SCM j, SCM k), |
ba6e7231 KR |
2777 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
2778 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
2779 | "without actually calculating the @code{logand}, just testing\n" | |
2780 | "for non-zero.\n" | |
2781 | "\n" | |
1e6808ea | 2782 | "@lisp\n" |
b380b885 MD |
2783 | "(logtest #b0100 #b1011) @result{} #f\n" |
2784 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 2785 | "@end lisp") |
1bbd0b84 | 2786 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 2787 | { |
e25f3727 | 2788 | scm_t_inum nj; |
9a00c9fc | 2789 | |
e11e83f3 | 2790 | if (SCM_I_INUMP (j)) |
0aacf84e | 2791 | { |
e11e83f3 MV |
2792 | nj = SCM_I_INUM (j); |
2793 | if (SCM_I_INUMP (k)) | |
0aacf84e | 2794 | { |
e25f3727 | 2795 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 2796 | return scm_from_bool (nj & nk); |
0aacf84e MD |
2797 | } |
2798 | else if (SCM_BIGP (k)) | |
2799 | { | |
2800 | intbig: | |
2801 | if (nj == 0) | |
2802 | return SCM_BOOL_F; | |
2803 | { | |
2804 | SCM result; | |
2805 | mpz_t nj_z; | |
2806 | mpz_init_set_si (nj_z, nj); | |
2807 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
2808 | scm_remember_upto_here_1 (k); | |
73e4de09 | 2809 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
2810 | mpz_clear (nj_z); |
2811 | return result; | |
2812 | } | |
2813 | } | |
2814 | else | |
2815 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2816 | } | |
2817 | else if (SCM_BIGP (j)) | |
2818 | { | |
e11e83f3 | 2819 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
2820 | { |
2821 | SCM_SWAP (j, k); | |
e11e83f3 | 2822 | nj = SCM_I_INUM (j); |
0aacf84e MD |
2823 | goto intbig; |
2824 | } | |
2825 | else if (SCM_BIGP (k)) | |
2826 | { | |
2827 | SCM result; | |
2828 | mpz_t result_z; | |
2829 | mpz_init (result_z); | |
2830 | mpz_and (result_z, | |
2831 | SCM_I_BIG_MPZ (j), | |
2832 | SCM_I_BIG_MPZ (k)); | |
2833 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 2834 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
2835 | mpz_clear (result_z); |
2836 | return result; | |
2837 | } | |
2838 | else | |
2839 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2840 | } | |
2841 | else | |
2842 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 2843 | } |
1bbd0b84 | 2844 | #undef FUNC_NAME |
0f2d19dd | 2845 | |
c1bfcf60 | 2846 | |
a1ec6916 | 2847 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 2848 | (SCM index, SCM j), |
ba6e7231 KR |
2849 | "Test whether bit number @var{index} in @var{j} is set.\n" |
2850 | "@var{index} starts from 0 for the least significant bit.\n" | |
2851 | "\n" | |
1e6808ea | 2852 | "@lisp\n" |
b380b885 MD |
2853 | "(logbit? 0 #b1101) @result{} #t\n" |
2854 | "(logbit? 1 #b1101) @result{} #f\n" | |
2855 | "(logbit? 2 #b1101) @result{} #t\n" | |
2856 | "(logbit? 3 #b1101) @result{} #t\n" | |
2857 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 2858 | "@end lisp") |
1bbd0b84 | 2859 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 2860 | { |
78166ad5 | 2861 | unsigned long int iindex; |
5efd3c7d | 2862 | iindex = scm_to_ulong (index); |
78166ad5 | 2863 | |
e11e83f3 | 2864 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
2865 | { |
2866 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 2867 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 2868 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 2869 | } |
0aacf84e MD |
2870 | else if (SCM_BIGP (j)) |
2871 | { | |
2872 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
2873 | scm_remember_upto_here_1 (j); | |
73e4de09 | 2874 | return scm_from_bool (val); |
0aacf84e MD |
2875 | } |
2876 | else | |
78166ad5 | 2877 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 2878 | } |
1bbd0b84 | 2879 | #undef FUNC_NAME |
0f2d19dd | 2880 | |
78166ad5 | 2881 | |
a1ec6916 | 2882 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 2883 | (SCM n), |
4d814788 | 2884 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
2885 | "argument.\n" |
2886 | "\n" | |
b380b885 MD |
2887 | "@lisp\n" |
2888 | "(number->string (lognot #b10000000) 2)\n" | |
2889 | " @result{} \"-10000001\"\n" | |
2890 | "(number->string (lognot #b0) 2)\n" | |
2891 | " @result{} \"-1\"\n" | |
1e6808ea | 2892 | "@end lisp") |
1bbd0b84 | 2893 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 2894 | { |
e11e83f3 | 2895 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
2896 | /* No overflow here, just need to toggle all the bits making up the inum. |
2897 | Enhancement: No need to strip the tag and add it back, could just xor | |
2898 | a block of 1 bits, if that worked with the various debug versions of | |
2899 | the SCM typedef. */ | |
e11e83f3 | 2900 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
2901 | |
2902 | } else if (SCM_BIGP (n)) { | |
2903 | SCM result = scm_i_mkbig (); | |
2904 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
2905 | scm_remember_upto_here_1 (n); | |
2906 | return result; | |
2907 | ||
2908 | } else { | |
2909 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
2910 | } | |
0f2d19dd | 2911 | } |
1bbd0b84 | 2912 | #undef FUNC_NAME |
0f2d19dd | 2913 | |
518b7508 KR |
2914 | /* returns 0 if IN is not an integer. OUT must already be |
2915 | initialized. */ | |
2916 | static int | |
2917 | coerce_to_big (SCM in, mpz_t out) | |
2918 | { | |
2919 | if (SCM_BIGP (in)) | |
2920 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
2921 | else if (SCM_I_INUMP (in)) |
2922 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
2923 | else |
2924 | return 0; | |
2925 | ||
2926 | return 1; | |
2927 | } | |
2928 | ||
d885e204 | 2929 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
2930 | (SCM n, SCM k, SCM m), |
2931 | "Return @var{n} raised to the integer exponent\n" | |
2932 | "@var{k}, modulo @var{m}.\n" | |
2933 | "\n" | |
2934 | "@lisp\n" | |
2935 | "(modulo-expt 2 3 5)\n" | |
2936 | " @result{} 3\n" | |
2937 | "@end lisp") | |
d885e204 | 2938 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
2939 | { |
2940 | mpz_t n_tmp; | |
2941 | mpz_t k_tmp; | |
2942 | mpz_t m_tmp; | |
2943 | ||
2944 | /* There are two classes of error we might encounter -- | |
2945 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
2946 | and | |
2947 | 2) wrong-type errors, which of course we'll report by calling | |
2948 | SCM_WRONG_TYPE_ARG. | |
2949 | We don't report those errors immediately, however; instead we do | |
2950 | some cleanup first. These variables tell us which error (if | |
2951 | any) we should report after cleaning up. | |
2952 | */ | |
2953 | int report_overflow = 0; | |
2954 | ||
2955 | int position_of_wrong_type = 0; | |
2956 | SCM value_of_wrong_type = SCM_INUM0; | |
2957 | ||
2958 | SCM result = SCM_UNDEFINED; | |
2959 | ||
2960 | mpz_init (n_tmp); | |
2961 | mpz_init (k_tmp); | |
2962 | mpz_init (m_tmp); | |
2963 | ||
bc36d050 | 2964 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
2965 | { |
2966 | report_overflow = 1; | |
2967 | goto cleanup; | |
2968 | } | |
2969 | ||
2970 | if (!coerce_to_big (n, n_tmp)) | |
2971 | { | |
2972 | value_of_wrong_type = n; | |
2973 | position_of_wrong_type = 1; | |
2974 | goto cleanup; | |
2975 | } | |
2976 | ||
2977 | if (!coerce_to_big (k, k_tmp)) | |
2978 | { | |
2979 | value_of_wrong_type = k; | |
2980 | position_of_wrong_type = 2; | |
2981 | goto cleanup; | |
2982 | } | |
2983 | ||
2984 | if (!coerce_to_big (m, m_tmp)) | |
2985 | { | |
2986 | value_of_wrong_type = m; | |
2987 | position_of_wrong_type = 3; | |
2988 | goto cleanup; | |
2989 | } | |
2990 | ||
2991 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
2992 | will get a divide-by-zero exception when an inverse 1/n mod m | |
2993 | doesn't exist (or is not unique). Since exceptions are hard to | |
2994 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
2995 | a simple failure code, which is easy to handle. */ | |
2996 | ||
2997 | if (-1 == mpz_sgn (k_tmp)) | |
2998 | { | |
2999 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
3000 | { | |
3001 | report_overflow = 1; | |
3002 | goto cleanup; | |
3003 | } | |
3004 | mpz_neg (k_tmp, k_tmp); | |
3005 | } | |
3006 | ||
3007 | result = scm_i_mkbig (); | |
3008 | mpz_powm (SCM_I_BIG_MPZ (result), | |
3009 | n_tmp, | |
3010 | k_tmp, | |
3011 | m_tmp); | |
b7b8c575 KR |
3012 | |
3013 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
3014 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
3015 | ||
518b7508 KR |
3016 | cleanup: |
3017 | mpz_clear (m_tmp); | |
3018 | mpz_clear (k_tmp); | |
3019 | mpz_clear (n_tmp); | |
3020 | ||
3021 | if (report_overflow) | |
3022 | scm_num_overflow (FUNC_NAME); | |
3023 | ||
3024 | if (position_of_wrong_type) | |
3025 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
3026 | value_of_wrong_type); | |
3027 | ||
3028 | return scm_i_normbig (result); | |
3029 | } | |
3030 | #undef FUNC_NAME | |
3031 | ||
a1ec6916 | 3032 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 3033 | (SCM n, SCM k), |
ba6e7231 KR |
3034 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
3035 | "exact integer, @var{n} can be any number.\n" | |
3036 | "\n" | |
2519490c MW |
3037 | "Negative @var{k} is supported, and results in\n" |
3038 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
3039 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 3040 | "includes @math{0^0} is 1.\n" |
1e6808ea | 3041 | "\n" |
b380b885 | 3042 | "@lisp\n" |
ba6e7231 KR |
3043 | "(integer-expt 2 5) @result{} 32\n" |
3044 | "(integer-expt -3 3) @result{} -27\n" | |
3045 | "(integer-expt 5 -3) @result{} 1/125\n" | |
3046 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 3047 | "@end lisp") |
1bbd0b84 | 3048 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 3049 | { |
e25f3727 | 3050 | scm_t_inum i2 = 0; |
1c35cb19 RB |
3051 | SCM z_i2 = SCM_BOOL_F; |
3052 | int i2_is_big = 0; | |
d956fa6f | 3053 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 3054 | |
bfe1f03a MW |
3055 | /* Specifically refrain from checking the type of the first argument. |
3056 | This allows us to exponentiate any object that can be multiplied. | |
3057 | If we must raise to a negative power, we must also be able to | |
3058 | take its reciprocal. */ | |
3059 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 3060 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 3061 | |
bfe1f03a MW |
3062 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
3063 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
3064 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
3065 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
3066 | /* The next check is necessary only because R6RS specifies different | |
3067 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
3068 | we simply skip this case and move on. */ | |
3069 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
3070 | { | |
3071 | /* k cannot be 0 at this point, because we | |
3072 | have already checked for that case above */ | |
3073 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
3074 | return n; |
3075 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
3076 | return scm_nan (); | |
3077 | } | |
ca46fb90 | 3078 | |
e11e83f3 MV |
3079 | if (SCM_I_INUMP (k)) |
3080 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
3081 | else if (SCM_BIGP (k)) |
3082 | { | |
3083 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
3084 | scm_remember_upto_here_1 (k); |
3085 | i2_is_big = 1; | |
3086 | } | |
2830fd91 | 3087 | else |
ca46fb90 RB |
3088 | SCM_WRONG_TYPE_ARG (2, k); |
3089 | ||
3090 | if (i2_is_big) | |
f872b822 | 3091 | { |
ca46fb90 RB |
3092 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
3093 | { | |
3094 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
3095 | n = scm_divide (n, SCM_UNDEFINED); | |
3096 | } | |
3097 | while (1) | |
3098 | { | |
3099 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
3100 | { | |
ca46fb90 RB |
3101 | return acc; |
3102 | } | |
3103 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
3104 | { | |
ca46fb90 RB |
3105 | return scm_product (acc, n); |
3106 | } | |
3107 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
3108 | acc = scm_product (acc, n); | |
3109 | n = scm_product (n, n); | |
3110 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
3111 | } | |
f872b822 | 3112 | } |
ca46fb90 | 3113 | else |
f872b822 | 3114 | { |
ca46fb90 RB |
3115 | if (i2 < 0) |
3116 | { | |
3117 | i2 = -i2; | |
3118 | n = scm_divide (n, SCM_UNDEFINED); | |
3119 | } | |
3120 | while (1) | |
3121 | { | |
3122 | if (0 == i2) | |
3123 | return acc; | |
3124 | if (1 == i2) | |
3125 | return scm_product (acc, n); | |
3126 | if (i2 & 1) | |
3127 | acc = scm_product (acc, n); | |
3128 | n = scm_product (n, n); | |
3129 | i2 >>= 1; | |
3130 | } | |
f872b822 | 3131 | } |
0f2d19dd | 3132 | } |
1bbd0b84 | 3133 | #undef FUNC_NAME |
0f2d19dd | 3134 | |
a1ec6916 | 3135 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 3136 | (SCM n, SCM cnt), |
32f19569 KR |
3137 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
3138 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 3139 | "\n" |
e7644cb2 | 3140 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
3141 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
3142 | "infinity. (Note that this is not the same rounding as\n" | |
3143 | "@code{quotient} does.)\n" | |
3144 | "\n" | |
3145 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
3146 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
3147 | "shift dropping bits.\n" | |
1e6808ea | 3148 | "\n" |
b380b885 | 3149 | "@lisp\n" |
1e6808ea MG |
3150 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
3151 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
3152 | "\n" |
3153 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
3154 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 3155 | "@end lisp") |
1bbd0b84 | 3156 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 3157 | { |
3ab9f56e | 3158 | long bits_to_shift; |
5efd3c7d | 3159 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 3160 | |
788aca27 KR |
3161 | if (SCM_I_INUMP (n)) |
3162 | { | |
e25f3727 | 3163 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
3164 | |
3165 | if (bits_to_shift > 0) | |
3166 | { | |
3167 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
3168 | overflow a non-zero fixnum. For smaller shifts we check the | |
3169 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
3170 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
3171 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
3172 | bits_to_shift)". */ | |
3173 | ||
3174 | if (nn == 0) | |
3175 | return n; | |
3176 | ||
3177 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3178 | && ((scm_t_bits) |
788aca27 KR |
3179 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
3180 | <= 1)) | |
3181 | { | |
3182 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
3183 | } | |
3184 | else | |
3185 | { | |
e25f3727 | 3186 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
3187 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3188 | bits_to_shift); | |
3189 | return result; | |
3190 | } | |
3191 | } | |
3192 | else | |
3193 | { | |
3194 | bits_to_shift = -bits_to_shift; | |
3195 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 3196 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
3197 | else |
3198 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
3199 | } | |
3200 | ||
3201 | } | |
3202 | else if (SCM_BIGP (n)) | |
ca46fb90 | 3203 | { |
788aca27 KR |
3204 | SCM result; |
3205 | ||
3206 | if (bits_to_shift == 0) | |
3207 | return n; | |
3208 | ||
3209 | result = scm_i_mkbig (); | |
3210 | if (bits_to_shift >= 0) | |
3211 | { | |
3212 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3213 | bits_to_shift); | |
3214 | return result; | |
3215 | } | |
ca46fb90 | 3216 | else |
788aca27 KR |
3217 | { |
3218 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
3219 | we have to allocate a bignum even if the result is going to be a | |
3220 | fixnum. */ | |
3221 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3222 | -bits_to_shift); | |
3223 | return scm_i_normbig (result); | |
3224 | } | |
3225 | ||
ca46fb90 RB |
3226 | } |
3227 | else | |
788aca27 KR |
3228 | { |
3229 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
3230 | } | |
0f2d19dd | 3231 | } |
1bbd0b84 | 3232 | #undef FUNC_NAME |
0f2d19dd | 3233 | |
3c9f20f8 | 3234 | |
a1ec6916 | 3235 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 3236 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
3237 | "Return the integer composed of the @var{start} (inclusive)\n" |
3238 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
3239 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
3240 | "\n" | |
b380b885 MD |
3241 | "@lisp\n" |
3242 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
3243 | " @result{} \"1010\"\n" | |
3244 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
3245 | " @result{} \"10110\"\n" | |
3246 | "@end lisp") | |
1bbd0b84 | 3247 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 3248 | { |
7f848242 | 3249 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
3250 | istart = scm_to_ulong (start); |
3251 | iend = scm_to_ulong (end); | |
c1bfcf60 | 3252 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 3253 | |
7f848242 KR |
3254 | /* how many bits to keep */ |
3255 | bits = iend - istart; | |
3256 | ||
e11e83f3 | 3257 | if (SCM_I_INUMP (n)) |
0aacf84e | 3258 | { |
e25f3727 | 3259 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
3260 | |
3261 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 3262 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 3263 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 3264 | |
0aacf84e MD |
3265 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
3266 | { | |
3267 | /* Since we emulate two's complement encoded numbers, this | |
3268 | * special case requires us to produce a result that has | |
7f848242 | 3269 | * more bits than can be stored in a fixnum. |
0aacf84e | 3270 | */ |
e25f3727 | 3271 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
3272 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3273 | bits); | |
3274 | return result; | |
0aacf84e | 3275 | } |
ac0c002c | 3276 | |
7f848242 | 3277 | /* mask down to requisite bits */ |
857ae6af | 3278 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 3279 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
3280 | } |
3281 | else if (SCM_BIGP (n)) | |
ac0c002c | 3282 | { |
7f848242 KR |
3283 | SCM result; |
3284 | if (bits == 1) | |
3285 | { | |
d956fa6f | 3286 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
3287 | } |
3288 | else | |
3289 | { | |
3290 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
3291 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
3292 | such bits into a ulong. */ | |
3293 | result = scm_i_mkbig (); | |
3294 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
3295 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
3296 | result = scm_i_normbig (result); | |
3297 | } | |
3298 | scm_remember_upto_here_1 (n); | |
3299 | return result; | |
ac0c002c | 3300 | } |
0aacf84e | 3301 | else |
78166ad5 | 3302 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 3303 | } |
1bbd0b84 | 3304 | #undef FUNC_NAME |
0f2d19dd | 3305 | |
7f848242 | 3306 | |
e4755e5c JB |
3307 | static const char scm_logtab[] = { |
3308 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
3309 | }; | |
1cc91f1b | 3310 | |
a1ec6916 | 3311 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 3312 | (SCM n), |
1e6808ea MG |
3313 | "Return the number of bits in integer @var{n}. If integer is\n" |
3314 | "positive, the 1-bits in its binary representation are counted.\n" | |
3315 | "If negative, the 0-bits in its two's-complement binary\n" | |
3316 | "representation are counted. If 0, 0 is returned.\n" | |
3317 | "\n" | |
b380b885 MD |
3318 | "@lisp\n" |
3319 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
3320 | " @result{} 4\n" |
3321 | "(logcount 0)\n" | |
3322 | " @result{} 0\n" | |
3323 | "(logcount -2)\n" | |
3324 | " @result{} 1\n" | |
3325 | "@end lisp") | |
3326 | #define FUNC_NAME s_scm_logcount | |
3327 | { | |
e11e83f3 | 3328 | if (SCM_I_INUMP (n)) |
f872b822 | 3329 | { |
e25f3727 AW |
3330 | unsigned long c = 0; |
3331 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
3332 | if (nn < 0) |
3333 | nn = -1 - nn; | |
3334 | while (nn) | |
3335 | { | |
3336 | c += scm_logtab[15 & nn]; | |
3337 | nn >>= 4; | |
3338 | } | |
d956fa6f | 3339 | return SCM_I_MAKINUM (c); |
f872b822 | 3340 | } |
ca46fb90 | 3341 | else if (SCM_BIGP (n)) |
f872b822 | 3342 | { |
ca46fb90 | 3343 | unsigned long count; |
713a4259 KR |
3344 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
3345 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 3346 | else |
713a4259 KR |
3347 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
3348 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3349 | return SCM_I_MAKINUM (count); |
f872b822 | 3350 | } |
ca46fb90 RB |
3351 | else |
3352 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 3353 | } |
ca46fb90 | 3354 | #undef FUNC_NAME |
0f2d19dd JB |
3355 | |
3356 | ||
ca46fb90 RB |
3357 | static const char scm_ilentab[] = { |
3358 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
3359 | }; | |
3360 | ||
0f2d19dd | 3361 | |
ca46fb90 RB |
3362 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
3363 | (SCM n), | |
3364 | "Return the number of bits necessary to represent @var{n}.\n" | |
3365 | "\n" | |
3366 | "@lisp\n" | |
3367 | "(integer-length #b10101010)\n" | |
3368 | " @result{} 8\n" | |
3369 | "(integer-length 0)\n" | |
3370 | " @result{} 0\n" | |
3371 | "(integer-length #b1111)\n" | |
3372 | " @result{} 4\n" | |
3373 | "@end lisp") | |
3374 | #define FUNC_NAME s_scm_integer_length | |
3375 | { | |
e11e83f3 | 3376 | if (SCM_I_INUMP (n)) |
0aacf84e | 3377 | { |
e25f3727 | 3378 | unsigned long c = 0; |
0aacf84e | 3379 | unsigned int l = 4; |
e25f3727 | 3380 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
3381 | if (nn < 0) |
3382 | nn = -1 - nn; | |
3383 | while (nn) | |
3384 | { | |
3385 | c += 4; | |
3386 | l = scm_ilentab [15 & nn]; | |
3387 | nn >>= 4; | |
3388 | } | |
d956fa6f | 3389 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
3390 | } |
3391 | else if (SCM_BIGP (n)) | |
3392 | { | |
3393 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
3394 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
3395 | 1 too big, so check for that and adjust. */ | |
3396 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
3397 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
3398 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
3399 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
3400 | size--; | |
3401 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3402 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
3403 | } |
3404 | else | |
ca46fb90 | 3405 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
3406 | } |
3407 | #undef FUNC_NAME | |
0f2d19dd JB |
3408 | |
3409 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
3410 | #define SCM_MAX_DBL_PREC 60 |
3411 | #define SCM_MAX_DBL_RADIX 36 | |
3412 | ||
3413 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
3414 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
3415 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
3416 | ||
3417 | static | |
3418 | void init_dblprec(int *prec, int radix) { | |
3419 | /* determine floating point precision by adding successively | |
3420 | smaller increments to 1.0 until it is considered == 1.0 */ | |
3421 | double f = ((double)1.0)/radix; | |
3422 | double fsum = 1.0 + f; | |
3423 | ||
3424 | *prec = 0; | |
3425 | while (fsum != 1.0) | |
3426 | { | |
3427 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
3428 | fsum = 1.0; | |
3429 | else | |
3430 | { | |
3431 | f /= radix; | |
3432 | fsum = f + 1.0; | |
3433 | } | |
3434 | } | |
3435 | (*prec) -= 1; | |
3436 | } | |
3437 | ||
3438 | static | |
3439 | void init_fx_radix(double *fx_list, int radix) | |
3440 | { | |
3441 | /* initialize a per-radix list of tolerances. When added | |
3442 | to a number < 1.0, we can determine if we should raund | |
3443 | up and quit converting a number to a string. */ | |
3444 | int i; | |
3445 | fx_list[0] = 0.0; | |
3446 | fx_list[1] = 0.5; | |
3447 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
3448 | fx_list[i] = (fx_list[i-1] / radix); | |
3449 | } | |
3450 | ||
3451 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 3452 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 3453 | |
1be6b49c | 3454 | static size_t |
0b799eea | 3455 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 3456 | { |
0b799eea MV |
3457 | int efmt, dpt, d, i, wp; |
3458 | double *fx; | |
3459 | #ifdef DBL_MIN_10_EXP | |
3460 | double f_cpy; | |
3461 | int exp_cpy; | |
3462 | #endif /* DBL_MIN_10_EXP */ | |
3463 | size_t ch = 0; | |
3464 | int exp = 0; | |
3465 | ||
3466 | if(radix < 2 || | |
3467 | radix > SCM_MAX_DBL_RADIX) | |
3468 | { | |
3469 | /* revert to existing behavior */ | |
3470 | radix = 10; | |
3471 | } | |
3472 | ||
3473 | wp = scm_dblprec[radix-2]; | |
3474 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 3475 | |
f872b822 | 3476 | if (f == 0.0) |
abb7e44d MV |
3477 | { |
3478 | #ifdef HAVE_COPYSIGN | |
3479 | double sgn = copysign (1.0, f); | |
3480 | ||
3481 | if (sgn < 0.0) | |
3482 | a[ch++] = '-'; | |
3483 | #endif | |
abb7e44d MV |
3484 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
3485 | } | |
7351e207 | 3486 | |
2e65b52f | 3487 | if (isinf (f)) |
7351e207 MV |
3488 | { |
3489 | if (f < 0) | |
3490 | strcpy (a, "-inf.0"); | |
3491 | else | |
3492 | strcpy (a, "+inf.0"); | |
3493 | return ch+6; | |
3494 | } | |
2e65b52f | 3495 | else if (isnan (f)) |
7351e207 MV |
3496 | { |
3497 | strcpy (a, "+nan.0"); | |
3498 | return ch+6; | |
3499 | } | |
3500 | ||
f872b822 MD |
3501 | if (f < 0.0) |
3502 | { | |
3503 | f = -f; | |
3504 | a[ch++] = '-'; | |
3505 | } | |
7351e207 | 3506 | |
f872b822 MD |
3507 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
3508 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
3509 | /* just do the checking...if it passes, we do the conversion for our |
3510 | radix again below */ | |
3511 | f_cpy = f; | |
3512 | exp_cpy = exp; | |
3513 | ||
3514 | while (f_cpy < 1.0) | |
f872b822 | 3515 | { |
0b799eea MV |
3516 | f_cpy *= 10.0; |
3517 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
3518 | { |
3519 | a[ch++] = '#'; | |
3520 | a[ch++] = '.'; | |
3521 | a[ch++] = '#'; | |
3522 | return ch; | |
3523 | } | |
f872b822 | 3524 | } |
0b799eea | 3525 | while (f_cpy > 10.0) |
f872b822 | 3526 | { |
0b799eea MV |
3527 | f_cpy *= 0.10; |
3528 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
3529 | { |
3530 | a[ch++] = '#'; | |
3531 | a[ch++] = '.'; | |
3532 | a[ch++] = '#'; | |
3533 | return ch; | |
3534 | } | |
f872b822 | 3535 | } |
0b799eea MV |
3536 | #endif |
3537 | ||
f872b822 MD |
3538 | while (f < 1.0) |
3539 | { | |
0b799eea | 3540 | f *= radix; |
f872b822 MD |
3541 | exp--; |
3542 | } | |
0b799eea | 3543 | while (f > radix) |
f872b822 | 3544 | { |
0b799eea | 3545 | f /= radix; |
f872b822 MD |
3546 | exp++; |
3547 | } | |
0b799eea MV |
3548 | |
3549 | if (f + fx[wp] >= radix) | |
f872b822 MD |
3550 | { |
3551 | f = 1.0; | |
3552 | exp++; | |
3553 | } | |
0f2d19dd | 3554 | zero: |
0b799eea MV |
3555 | #ifdef ENGNOT |
3556 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 3557 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
3558 | exp -= dpt++; |
3559 | efmt = 1; | |
f872b822 MD |
3560 | #else |
3561 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 3562 | if (!efmt) |
cda139a7 MD |
3563 | { |
3564 | if (exp < 0) | |
3565 | { | |
3566 | a[ch++] = '0'; | |
3567 | a[ch++] = '.'; | |
3568 | dpt = exp; | |
f872b822 MD |
3569 | while (++dpt) |
3570 | a[ch++] = '0'; | |
cda139a7 MD |
3571 | } |
3572 | else | |
f872b822 | 3573 | dpt = exp + 1; |
cda139a7 | 3574 | } |
0f2d19dd JB |
3575 | else |
3576 | dpt = 1; | |
f872b822 MD |
3577 | #endif |
3578 | ||
3579 | do | |
3580 | { | |
3581 | d = f; | |
3582 | f -= d; | |
0b799eea | 3583 | a[ch++] = number_chars[d]; |
f872b822 MD |
3584 | if (f < fx[wp]) |
3585 | break; | |
3586 | if (f + fx[wp] >= 1.0) | |
3587 | { | |
0b799eea | 3588 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
3589 | break; |
3590 | } | |
0b799eea | 3591 | f *= radix; |
f872b822 MD |
3592 | if (!(--dpt)) |
3593 | a[ch++] = '.'; | |
0f2d19dd | 3594 | } |
f872b822 | 3595 | while (wp--); |
0f2d19dd JB |
3596 | |
3597 | if (dpt > 0) | |
cda139a7 | 3598 | { |
f872b822 | 3599 | #ifndef ENGNOT |
cda139a7 MD |
3600 | if ((dpt > 4) && (exp > 6)) |
3601 | { | |
f872b822 | 3602 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 3603 | for (i = ch++; i > d; i--) |
f872b822 | 3604 | a[i] = a[i - 1]; |
cda139a7 MD |
3605 | a[d] = '.'; |
3606 | efmt = 1; | |
3607 | } | |
3608 | else | |
f872b822 | 3609 | #endif |
cda139a7 | 3610 | { |
f872b822 MD |
3611 | while (--dpt) |
3612 | a[ch++] = '0'; | |
cda139a7 MD |
3613 | a[ch++] = '.'; |
3614 | } | |
3615 | } | |
f872b822 MD |
3616 | if (a[ch - 1] == '.') |
3617 | a[ch++] = '0'; /* trailing zero */ | |
3618 | if (efmt && exp) | |
3619 | { | |
3620 | a[ch++] = 'e'; | |
3621 | if (exp < 0) | |
3622 | { | |
3623 | exp = -exp; | |
3624 | a[ch++] = '-'; | |
3625 | } | |
0b799eea MV |
3626 | for (i = radix; i <= exp; i *= radix); |
3627 | for (i /= radix; i; i /= radix) | |
f872b822 | 3628 | { |
0b799eea | 3629 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
3630 | exp %= i; |
3631 | } | |
0f2d19dd | 3632 | } |
0f2d19dd JB |
3633 | return ch; |
3634 | } | |
3635 | ||
7a1aba42 MV |
3636 | |
3637 | static size_t | |
3638 | icmplx2str (double real, double imag, char *str, int radix) | |
3639 | { | |
3640 | size_t i; | |
3641 | ||
3642 | i = idbl2str (real, str, radix); | |
3643 | if (imag != 0.0) | |
3644 | { | |
3645 | /* Don't output a '+' for negative numbers or for Inf and | |
3646 | NaN. They will provide their own sign. */ | |
2e65b52f | 3647 | if (0 <= imag && !isinf (imag) && !isnan (imag)) |
7a1aba42 MV |
3648 | str[i++] = '+'; |
3649 | i += idbl2str (imag, &str[i], radix); | |
3650 | str[i++] = 'i'; | |
3651 | } | |
3652 | return i; | |
3653 | } | |
3654 | ||
1be6b49c | 3655 | static size_t |
0b799eea | 3656 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 3657 | { |
1be6b49c | 3658 | size_t i; |
3c9a524f | 3659 | if (SCM_REALP (flt)) |
0b799eea | 3660 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 3661 | else |
7a1aba42 MV |
3662 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
3663 | str, radix); | |
0f2d19dd JB |
3664 | return i; |
3665 | } | |
0f2d19dd | 3666 | |
2881e77b | 3667 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
3668 | characters in the result. |
3669 | rad is output base | |
3670 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 3671 | size_t |
2881e77b MV |
3672 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
3673 | { | |
3674 | if (num < 0) | |
3675 | { | |
3676 | *p++ = '-'; | |
3677 | return scm_iuint2str (-num, rad, p) + 1; | |
3678 | } | |
3679 | else | |
3680 | return scm_iuint2str (num, rad, p); | |
3681 | } | |
3682 | ||
3683 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
3684 | characters in the result. | |
3685 | rad is output base | |
3686 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
3687 | size_t | |
3688 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 3689 | { |
1be6b49c ML |
3690 | size_t j = 1; |
3691 | size_t i; | |
2881e77b | 3692 | scm_t_uintmax n = num; |
5c11cc9d | 3693 | |
a6f3af16 AW |
3694 | if (rad < 2 || rad > 36) |
3695 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
3696 | ||
f872b822 | 3697 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
3698 | j++; |
3699 | ||
3700 | i = j; | |
2881e77b | 3701 | n = num; |
f872b822 MD |
3702 | while (i--) |
3703 | { | |
5c11cc9d GH |
3704 | int d = n % rad; |
3705 | ||
f872b822 | 3706 | n /= rad; |
a6f3af16 | 3707 | p[i] = number_chars[d]; |
f872b822 | 3708 | } |
0f2d19dd JB |
3709 | return j; |
3710 | } | |
3711 | ||
a1ec6916 | 3712 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
3713 | (SCM n, SCM radix), |
3714 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
3715 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
3716 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 3717 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 3718 | { |
1bbd0b84 | 3719 | int base; |
98cb6e75 | 3720 | |
0aacf84e | 3721 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 3722 | base = 10; |
0aacf84e | 3723 | else |
5efd3c7d | 3724 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 3725 | |
e11e83f3 | 3726 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
3727 | { |
3728 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 3729 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 3730 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
3731 | } |
3732 | else if (SCM_BIGP (n)) | |
3733 | { | |
3734 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
3735 | scm_remember_upto_here_1 (n); | |
cc95e00a | 3736 | return scm_take_locale_string (str); |
0aacf84e | 3737 | } |
f92e85f7 MV |
3738 | else if (SCM_FRACTIONP (n)) |
3739 | { | |
f92e85f7 | 3740 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 3741 | scm_from_locale_string ("/"), |
f92e85f7 MV |
3742 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
3743 | } | |
0aacf84e MD |
3744 | else if (SCM_INEXACTP (n)) |
3745 | { | |
3746 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 3747 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
3748 | } |
3749 | else | |
bb628794 | 3750 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 3751 | } |
1bbd0b84 | 3752 | #undef FUNC_NAME |
0f2d19dd JB |
3753 | |
3754 | ||
ca46fb90 RB |
3755 | /* These print routines used to be stubbed here so that scm_repl.c |
3756 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 3757 | |
0f2d19dd | 3758 | int |
e81d98ec | 3759 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3760 | { |
56e55ac7 | 3761 | char num_buf[FLOBUFLEN]; |
0b799eea | 3762 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
3763 | return !0; |
3764 | } | |
3765 | ||
b479fe9a MV |
3766 | void |
3767 | scm_i_print_double (double val, SCM port) | |
3768 | { | |
3769 | char num_buf[FLOBUFLEN]; | |
3770 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
3771 | } | |
3772 | ||
f3ae5d60 | 3773 | int |
e81d98ec | 3774 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 3775 | |
f3ae5d60 | 3776 | { |
56e55ac7 | 3777 | char num_buf[FLOBUFLEN]; |
0b799eea | 3778 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
3779 | return !0; |
3780 | } | |
1cc91f1b | 3781 | |
7a1aba42 MV |
3782 | void |
3783 | scm_i_print_complex (double real, double imag, SCM port) | |
3784 | { | |
3785 | char num_buf[FLOBUFLEN]; | |
3786 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
3787 | } | |
3788 | ||
f92e85f7 MV |
3789 | int |
3790 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
3791 | { | |
3792 | SCM str; | |
f92e85f7 | 3793 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 3794 | scm_display (str, port); |
f92e85f7 MV |
3795 | scm_remember_upto_here_1 (str); |
3796 | return !0; | |
3797 | } | |
3798 | ||
0f2d19dd | 3799 | int |
e81d98ec | 3800 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3801 | { |
ca46fb90 RB |
3802 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
3803 | scm_remember_upto_here_1 (exp); | |
3804 | scm_lfwrite (str, (size_t) strlen (str), port); | |
3805 | free (str); | |
0f2d19dd JB |
3806 | return !0; |
3807 | } | |
3808 | /*** END nums->strs ***/ | |
3809 | ||
3c9a524f | 3810 | |
0f2d19dd | 3811 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 3812 | |
3c9a524f DH |
3813 | /* The following functions implement the conversion from strings to numbers. |
3814 | * The implementation somehow follows the grammar for numbers as it is given | |
3815 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
3816 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
3817 | * points should be noted about the implementation: | |
3818 | * * Each function keeps a local index variable 'idx' that points at the | |
3819 | * current position within the parsed string. The global index is only | |
3820 | * updated if the function could parse the corresponding syntactic unit | |
3821 | * successfully. | |
3822 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
3823 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
3824 | * global exactness information is only updated after each part has been | |
3825 | * successfully parsed. | |
3826 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
3827 | * Only if these fixnums would overflow, the result variables are updated | |
3828 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
3829 | * the temporary variables holding the fixnums are cleared, and the process | |
3830 | * starts over again. If for example fixnums were able to store five decimal | |
3831 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
3832 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
3833 | * only every five digits two bignum operations were performed. | |
3834 | */ | |
3835 | ||
3836 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
3837 | ||
3838 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
3839 | ||
a6f3af16 AW |
3840 | /* Caller is responsible for checking that the return value is in range |
3841 | for the given radix, which should be <= 36. */ | |
3842 | static unsigned int | |
3843 | char_decimal_value (scm_t_uint32 c) | |
3844 | { | |
3845 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
3846 | that's certainly above any valid decimal, so we take advantage of | |
3847 | that to elide some tests. */ | |
3848 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
3849 | ||
3850 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
3851 | hexadecimals. */ | |
3852 | if (d >= 10U) | |
3853 | { | |
3854 | c = uc_tolower (c); | |
3855 | if (c >= (scm_t_uint32) 'a') | |
3856 | d = c - (scm_t_uint32)'a' + 10U; | |
3857 | } | |
3858 | return d; | |
3859 | } | |
3c9a524f | 3860 | |
2a8fecee | 3861 | static SCM |
3f47e526 | 3862 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 3863 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 3864 | { |
3c9a524f DH |
3865 | unsigned int idx = *p_idx; |
3866 | unsigned int hash_seen = 0; | |
3867 | scm_t_bits shift = 1; | |
3868 | scm_t_bits add = 0; | |
3869 | unsigned int digit_value; | |
3870 | SCM result; | |
3871 | char c; | |
3f47e526 | 3872 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3873 | |
3874 | if (idx == len) | |
3875 | return SCM_BOOL_F; | |
2a8fecee | 3876 | |
3f47e526 | 3877 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3878 | digit_value = char_decimal_value (c); |
3c9a524f DH |
3879 | if (digit_value >= radix) |
3880 | return SCM_BOOL_F; | |
3881 | ||
3882 | idx++; | |
d956fa6f | 3883 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 3884 | while (idx != len) |
f872b822 | 3885 | { |
3f47e526 | 3886 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3887 | if (c == '#') |
3c9a524f DH |
3888 | { |
3889 | hash_seen = 1; | |
3890 | digit_value = 0; | |
3891 | } | |
a6f3af16 AW |
3892 | else if (hash_seen) |
3893 | break; | |
3c9a524f | 3894 | else |
a6f3af16 AW |
3895 | { |
3896 | digit_value = char_decimal_value (c); | |
3897 | /* This check catches non-decimals in addition to out-of-range | |
3898 | decimals. */ | |
3899 | if (digit_value >= radix) | |
3900 | break; | |
3901 | } | |
3c9a524f DH |
3902 | |
3903 | idx++; | |
3904 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
3905 | { | |
d956fa6f | 3906 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3907 | if (add > 0) |
d956fa6f | 3908 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3909 | |
3910 | shift = radix; | |
3911 | add = digit_value; | |
3912 | } | |
3913 | else | |
3914 | { | |
3915 | shift = shift * radix; | |
3916 | add = add * radix + digit_value; | |
3917 | } | |
3918 | }; | |
3919 | ||
3920 | if (shift > 1) | |
d956fa6f | 3921 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3922 | if (add > 0) |
d956fa6f | 3923 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3924 | |
3925 | *p_idx = idx; | |
3926 | if (hash_seen) | |
3927 | *p_exactness = INEXACT; | |
3928 | ||
3929 | return result; | |
2a8fecee JB |
3930 | } |
3931 | ||
3932 | ||
3c9a524f DH |
3933 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
3934 | * covers the parts of the rules that start at a potential point. The value | |
3935 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
3936 | * in variable result. The content of *p_exactness indicates, whether a hash |
3937 | * has already been seen in the digits before the point. | |
3c9a524f | 3938 | */ |
1cc91f1b | 3939 | |
3f47e526 | 3940 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
3941 | |
3942 | static SCM | |
3f47e526 | 3943 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 3944 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 3945 | { |
3c9a524f DH |
3946 | unsigned int idx = *p_idx; |
3947 | enum t_exactness x = *p_exactness; | |
3f47e526 | 3948 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3949 | |
3950 | if (idx == len) | |
79d34f68 | 3951 | return result; |
3c9a524f | 3952 | |
3f47e526 | 3953 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
3954 | { |
3955 | scm_t_bits shift = 1; | |
3956 | scm_t_bits add = 0; | |
3957 | unsigned int digit_value; | |
cff5fa33 | 3958 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
3959 | |
3960 | idx++; | |
3961 | while (idx != len) | |
3962 | { | |
3f47e526 MG |
3963 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
3964 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
3965 | { |
3966 | if (x == INEXACT) | |
3967 | return SCM_BOOL_F; | |
3968 | else | |
3969 | digit_value = DIGIT2UINT (c); | |
3970 | } | |
3971 | else if (c == '#') | |
3972 | { | |
3973 | x = INEXACT; | |
3974 | digit_value = 0; | |
3975 | } | |
3976 | else | |
3977 | break; | |
3978 | ||
3979 | idx++; | |
3980 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
3981 | { | |
d956fa6f MV |
3982 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
3983 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 3984 | if (add > 0) |
d956fa6f | 3985 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3986 | |
3987 | shift = 10; | |
3988 | add = digit_value; | |
3989 | } | |
3990 | else | |
3991 | { | |
3992 | shift = shift * 10; | |
3993 | add = add * 10 + digit_value; | |
3994 | } | |
3995 | }; | |
3996 | ||
3997 | if (add > 0) | |
3998 | { | |
d956fa6f MV |
3999 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4000 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
4001 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
4002 | } |
4003 | ||
d8592269 | 4004 | result = scm_divide (result, big_shift); |
79d34f68 | 4005 | |
3c9a524f DH |
4006 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
4007 | x = INEXACT; | |
f872b822 | 4008 | } |
3c9a524f | 4009 | |
3c9a524f | 4010 | if (idx != len) |
f872b822 | 4011 | { |
3c9a524f DH |
4012 | int sign = 1; |
4013 | unsigned int start; | |
3f47e526 | 4014 | scm_t_wchar c; |
3c9a524f DH |
4015 | int exponent; |
4016 | SCM e; | |
4017 | ||
4018 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
4019 | ||
3f47e526 | 4020 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 4021 | { |
3c9a524f DH |
4022 | case 'd': case 'D': |
4023 | case 'e': case 'E': | |
4024 | case 'f': case 'F': | |
4025 | case 'l': case 'L': | |
4026 | case 's': case 'S': | |
4027 | idx++; | |
ee0ddd21 AW |
4028 | if (idx == len) |
4029 | return SCM_BOOL_F; | |
4030 | ||
3c9a524f | 4031 | start = idx; |
3f47e526 | 4032 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4033 | if (c == '-') |
4034 | { | |
4035 | idx++; | |
ee0ddd21 AW |
4036 | if (idx == len) |
4037 | return SCM_BOOL_F; | |
4038 | ||
3c9a524f | 4039 | sign = -1; |
3f47e526 | 4040 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4041 | } |
4042 | else if (c == '+') | |
4043 | { | |
4044 | idx++; | |
ee0ddd21 AW |
4045 | if (idx == len) |
4046 | return SCM_BOOL_F; | |
4047 | ||
3c9a524f | 4048 | sign = 1; |
3f47e526 | 4049 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4050 | } |
4051 | else | |
4052 | sign = 1; | |
4053 | ||
3f47e526 | 4054 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
4055 | return SCM_BOOL_F; |
4056 | ||
4057 | idx++; | |
4058 | exponent = DIGIT2UINT (c); | |
4059 | while (idx != len) | |
f872b822 | 4060 | { |
3f47e526 MG |
4061 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
4062 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
4063 | { |
4064 | idx++; | |
4065 | if (exponent <= SCM_MAXEXP) | |
4066 | exponent = exponent * 10 + DIGIT2UINT (c); | |
4067 | } | |
4068 | else | |
4069 | break; | |
f872b822 | 4070 | } |
3c9a524f DH |
4071 | |
4072 | if (exponent > SCM_MAXEXP) | |
f872b822 | 4073 | { |
3c9a524f | 4074 | size_t exp_len = idx - start; |
3f47e526 | 4075 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
4076 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
4077 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 4078 | } |
3c9a524f | 4079 | |
d956fa6f | 4080 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
4081 | if (sign == 1) |
4082 | result = scm_product (result, e); | |
4083 | else | |
f92e85f7 | 4084 | result = scm_divide2real (result, e); |
3c9a524f DH |
4085 | |
4086 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
4087 | x = INEXACT; | |
4088 | ||
f872b822 | 4089 | break; |
3c9a524f | 4090 | |
f872b822 | 4091 | default: |
3c9a524f | 4092 | break; |
f872b822 | 4093 | } |
0f2d19dd | 4094 | } |
3c9a524f DH |
4095 | |
4096 | *p_idx = idx; | |
4097 | if (x == INEXACT) | |
4098 | *p_exactness = x; | |
4099 | ||
4100 | return result; | |
0f2d19dd | 4101 | } |
0f2d19dd | 4102 | |
3c9a524f DH |
4103 | |
4104 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
4105 | ||
4106 | static SCM | |
3f47e526 | 4107 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 4108 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 4109 | { |
3c9a524f | 4110 | unsigned int idx = *p_idx; |
164d2481 | 4111 | SCM result; |
3f47e526 | 4112 | size_t len = scm_i_string_length (mem); |
3c9a524f | 4113 | |
40f89215 NJ |
4114 | /* Start off believing that the number will be exact. This changes |
4115 | to INEXACT if we see a decimal point or a hash. */ | |
4116 | enum t_exactness x = EXACT; | |
4117 | ||
3c9a524f DH |
4118 | if (idx == len) |
4119 | return SCM_BOOL_F; | |
4120 | ||
3f47e526 | 4121 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
4122 | { |
4123 | *p_idx = idx+5; | |
4124 | return scm_inf (); | |
4125 | } | |
4126 | ||
3f47e526 | 4127 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 4128 | { |
d8592269 MV |
4129 | /* Cobble up the fractional part. We might want to set the |
4130 | NaN's mantissa from it. */ | |
7351e207 | 4131 | idx += 4; |
3f47e526 | 4132 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
4133 | *p_idx = idx; |
4134 | return scm_nan (); | |
4135 | } | |
4136 | ||
3f47e526 | 4137 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
4138 | { |
4139 | if (radix != 10) | |
4140 | return SCM_BOOL_F; | |
4141 | else if (idx + 1 == len) | |
4142 | return SCM_BOOL_F; | |
3f47e526 | 4143 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
4144 | return SCM_BOOL_F; |
4145 | else | |
cff5fa33 | 4146 | result = mem2decimal_from_point (SCM_INUM0, mem, |
40f89215 | 4147 | p_idx, &x); |
f872b822 | 4148 | } |
3c9a524f DH |
4149 | else |
4150 | { | |
3c9a524f | 4151 | SCM uinteger; |
3c9a524f | 4152 | |
3f47e526 | 4153 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 4154 | if (scm_is_false (uinteger)) |
3c9a524f DH |
4155 | return SCM_BOOL_F; |
4156 | ||
4157 | if (idx == len) | |
4158 | result = uinteger; | |
3f47e526 | 4159 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 4160 | { |
3c9a524f DH |
4161 | SCM divisor; |
4162 | ||
4163 | idx++; | |
ee0ddd21 AW |
4164 | if (idx == len) |
4165 | return SCM_BOOL_F; | |
3c9a524f | 4166 | |
3f47e526 | 4167 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 4168 | if (scm_is_false (divisor)) |
3c9a524f DH |
4169 | return SCM_BOOL_F; |
4170 | ||
f92e85f7 | 4171 | /* both are int/big here, I assume */ |
cba42c93 | 4172 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 4173 | } |
3c9a524f DH |
4174 | else if (radix == 10) |
4175 | { | |
3f47e526 | 4176 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 4177 | if (scm_is_false (result)) |
3c9a524f DH |
4178 | return SCM_BOOL_F; |
4179 | } | |
4180 | else | |
4181 | result = uinteger; | |
4182 | ||
4183 | *p_idx = idx; | |
f872b822 | 4184 | } |
164d2481 | 4185 | |
40f89215 NJ |
4186 | /* Update *p_exactness if the number just read was inexact. This is |
4187 | important for complex numbers, so that a complex number is | |
4188 | treated as inexact overall if either its real or imaginary part | |
4189 | is inexact. | |
4190 | */ | |
4191 | if (x == INEXACT) | |
4192 | *p_exactness = x; | |
4193 | ||
164d2481 MV |
4194 | /* When returning an inexact zero, make sure it is represented as a |
4195 | floating point value so that we can change its sign. | |
4196 | */ | |
cff5fa33 | 4197 | if (scm_is_eq (result, SCM_INUM0) && *p_exactness == INEXACT) |
55f26379 | 4198 | result = scm_from_double (0.0); |
164d2481 MV |
4199 | |
4200 | return result; | |
3c9a524f | 4201 | } |
0f2d19dd | 4202 | |
0f2d19dd | 4203 | |
3c9a524f | 4204 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 4205 | |
3c9a524f | 4206 | static SCM |
3f47e526 | 4207 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
4208 | unsigned int radix, enum t_exactness *p_exactness) |
4209 | { | |
3f47e526 | 4210 | scm_t_wchar c; |
3c9a524f DH |
4211 | int sign = 0; |
4212 | SCM ureal; | |
3f47e526 | 4213 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4214 | |
4215 | if (idx == len) | |
4216 | return SCM_BOOL_F; | |
4217 | ||
3f47e526 | 4218 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4219 | if (c == '+') |
4220 | { | |
4221 | idx++; | |
4222 | sign = 1; | |
4223 | } | |
4224 | else if (c == '-') | |
4225 | { | |
4226 | idx++; | |
4227 | sign = -1; | |
0f2d19dd | 4228 | } |
0f2d19dd | 4229 | |
3c9a524f DH |
4230 | if (idx == len) |
4231 | return SCM_BOOL_F; | |
4232 | ||
3f47e526 | 4233 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 4234 | if (scm_is_false (ureal)) |
f872b822 | 4235 | { |
3c9a524f DH |
4236 | /* input must be either +i or -i */ |
4237 | ||
4238 | if (sign == 0) | |
4239 | return SCM_BOOL_F; | |
4240 | ||
3f47e526 MG |
4241 | if (scm_i_string_ref (mem, idx) == 'i' |
4242 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 4243 | { |
3c9a524f DH |
4244 | idx++; |
4245 | if (idx != len) | |
4246 | return SCM_BOOL_F; | |
4247 | ||
cff5fa33 | 4248 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 4249 | } |
3c9a524f DH |
4250 | else |
4251 | return SCM_BOOL_F; | |
0f2d19dd | 4252 | } |
3c9a524f DH |
4253 | else |
4254 | { | |
73e4de09 | 4255 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 4256 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 4257 | |
3c9a524f DH |
4258 | if (idx == len) |
4259 | return ureal; | |
4260 | ||
3f47e526 | 4261 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 4262 | switch (c) |
f872b822 | 4263 | { |
3c9a524f DH |
4264 | case 'i': case 'I': |
4265 | /* either +<ureal>i or -<ureal>i */ | |
4266 | ||
4267 | idx++; | |
4268 | if (sign == 0) | |
4269 | return SCM_BOOL_F; | |
4270 | if (idx != len) | |
4271 | return SCM_BOOL_F; | |
cff5fa33 | 4272 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
4273 | |
4274 | case '@': | |
4275 | /* polar input: <real>@<real>. */ | |
4276 | ||
4277 | idx++; | |
4278 | if (idx == len) | |
4279 | return SCM_BOOL_F; | |
4280 | else | |
f872b822 | 4281 | { |
3c9a524f DH |
4282 | int sign; |
4283 | SCM angle; | |
4284 | SCM result; | |
4285 | ||
3f47e526 | 4286 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4287 | if (c == '+') |
4288 | { | |
4289 | idx++; | |
ee0ddd21 AW |
4290 | if (idx == len) |
4291 | return SCM_BOOL_F; | |
3c9a524f DH |
4292 | sign = 1; |
4293 | } | |
4294 | else if (c == '-') | |
4295 | { | |
4296 | idx++; | |
ee0ddd21 AW |
4297 | if (idx == len) |
4298 | return SCM_BOOL_F; | |
3c9a524f DH |
4299 | sign = -1; |
4300 | } | |
4301 | else | |
4302 | sign = 1; | |
4303 | ||
3f47e526 | 4304 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 4305 | if (scm_is_false (angle)) |
3c9a524f DH |
4306 | return SCM_BOOL_F; |
4307 | if (idx != len) | |
4308 | return SCM_BOOL_F; | |
4309 | ||
73e4de09 | 4310 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
4311 | angle = scm_difference (angle, SCM_UNDEFINED); |
4312 | ||
4313 | result = scm_make_polar (ureal, angle); | |
4314 | return result; | |
f872b822 | 4315 | } |
3c9a524f DH |
4316 | case '+': |
4317 | case '-': | |
4318 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 4319 | |
3c9a524f DH |
4320 | idx++; |
4321 | if (idx == len) | |
4322 | return SCM_BOOL_F; | |
4323 | else | |
4324 | { | |
4325 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 4326 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 4327 | |
73e4de09 | 4328 | if (scm_is_false (imag)) |
d956fa6f | 4329 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 4330 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 4331 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 4332 | |
3c9a524f DH |
4333 | if (idx == len) |
4334 | return SCM_BOOL_F; | |
3f47e526 MG |
4335 | if (scm_i_string_ref (mem, idx) != 'i' |
4336 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 4337 | return SCM_BOOL_F; |
0f2d19dd | 4338 | |
3c9a524f DH |
4339 | idx++; |
4340 | if (idx != len) | |
4341 | return SCM_BOOL_F; | |
0f2d19dd | 4342 | |
1fe5e088 | 4343 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
4344 | } |
4345 | default: | |
4346 | return SCM_BOOL_F; | |
4347 | } | |
4348 | } | |
0f2d19dd | 4349 | } |
0f2d19dd JB |
4350 | |
4351 | ||
3c9a524f DH |
4352 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
4353 | ||
4354 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 4355 | |
0f2d19dd | 4356 | SCM |
3f47e526 | 4357 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 4358 | { |
3c9a524f DH |
4359 | unsigned int idx = 0; |
4360 | unsigned int radix = NO_RADIX; | |
4361 | enum t_exactness forced_x = NO_EXACTNESS; | |
4362 | enum t_exactness implicit_x = EXACT; | |
4363 | SCM result; | |
3f47e526 | 4364 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4365 | |
4366 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 4367 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 4368 | { |
3f47e526 | 4369 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
4370 | { |
4371 | case 'b': case 'B': | |
4372 | if (radix != NO_RADIX) | |
4373 | return SCM_BOOL_F; | |
4374 | radix = DUAL; | |
4375 | break; | |
4376 | case 'd': case 'D': | |
4377 | if (radix != NO_RADIX) | |
4378 | return SCM_BOOL_F; | |
4379 | radix = DEC; | |
4380 | break; | |
4381 | case 'i': case 'I': | |
4382 | if (forced_x != NO_EXACTNESS) | |
4383 | return SCM_BOOL_F; | |
4384 | forced_x = INEXACT; | |
4385 | break; | |
4386 | case 'e': case 'E': | |
4387 | if (forced_x != NO_EXACTNESS) | |
4388 | return SCM_BOOL_F; | |
4389 | forced_x = EXACT; | |
4390 | break; | |
4391 | case 'o': case 'O': | |
4392 | if (radix != NO_RADIX) | |
4393 | return SCM_BOOL_F; | |
4394 | radix = OCT; | |
4395 | break; | |
4396 | case 'x': case 'X': | |
4397 | if (radix != NO_RADIX) | |
4398 | return SCM_BOOL_F; | |
4399 | radix = HEX; | |
4400 | break; | |
4401 | default: | |
f872b822 | 4402 | return SCM_BOOL_F; |
3c9a524f DH |
4403 | } |
4404 | idx += 2; | |
4405 | } | |
4406 | ||
4407 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
4408 | if (radix == NO_RADIX) | |
3f47e526 | 4409 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 4410 | else |
3f47e526 | 4411 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 4412 | |
73e4de09 | 4413 | if (scm_is_false (result)) |
3c9a524f | 4414 | return SCM_BOOL_F; |
f872b822 | 4415 | |
3c9a524f | 4416 | switch (forced_x) |
f872b822 | 4417 | { |
3c9a524f DH |
4418 | case EXACT: |
4419 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
4420 | return scm_inexact_to_exact (result); |
4421 | else | |
4422 | return result; | |
4423 | case INEXACT: | |
4424 | if (SCM_INEXACTP (result)) | |
4425 | return result; | |
4426 | else | |
4427 | return scm_exact_to_inexact (result); | |
4428 | case NO_EXACTNESS: | |
4429 | default: | |
4430 | if (implicit_x == INEXACT) | |
4431 | { | |
4432 | if (SCM_INEXACTP (result)) | |
4433 | return result; | |
4434 | else | |
4435 | return scm_exact_to_inexact (result); | |
4436 | } | |
4437 | else | |
4438 | return result; | |
f872b822 | 4439 | } |
0f2d19dd JB |
4440 | } |
4441 | ||
3f47e526 MG |
4442 | SCM |
4443 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
4444 | unsigned int default_radix) | |
4445 | { | |
4446 | SCM str = scm_from_locale_stringn (mem, len); | |
4447 | ||
4448 | return scm_i_string_to_number (str, default_radix); | |
4449 | } | |
4450 | ||
0f2d19dd | 4451 | |
a1ec6916 | 4452 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 4453 | (SCM string, SCM radix), |
1e6808ea | 4454 | "Return a number of the maximally precise representation\n" |
942e5b91 | 4455 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
4456 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
4457 | "is a default radix that may be overridden by an explicit radix\n" | |
4458 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
4459 | "supplied, then the default radix is 10. If string is not a\n" | |
4460 | "syntactically valid notation for a number, then\n" | |
4461 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 4462 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
4463 | { |
4464 | SCM answer; | |
5efd3c7d | 4465 | unsigned int base; |
a6d9e5ab | 4466 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
4467 | |
4468 | if (SCM_UNBNDP (radix)) | |
4469 | base = 10; | |
4470 | else | |
4471 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
4472 | ||
3f47e526 | 4473 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
4474 | scm_remember_upto_here_1 (string); |
4475 | return answer; | |
0f2d19dd | 4476 | } |
1bbd0b84 | 4477 | #undef FUNC_NAME |
3c9a524f DH |
4478 | |
4479 | ||
0f2d19dd JB |
4480 | /*** END strs->nums ***/ |
4481 | ||
5986c47d | 4482 | |
8507ec80 MV |
4483 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
4484 | (SCM x), | |
4485 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
4486 | "otherwise.") | |
4487 | #define FUNC_NAME s_scm_number_p | |
4488 | { | |
4489 | return scm_from_bool (SCM_NUMBERP (x)); | |
4490 | } | |
4491 | #undef FUNC_NAME | |
4492 | ||
4493 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 4494 | (SCM x), |
942e5b91 | 4495 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 4496 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
4497 | "values form subsets of the set of complex numbers, i. e. the\n" |
4498 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
4499 | "rational or integer number.") | |
8507ec80 | 4500 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 4501 | { |
8507ec80 MV |
4502 | /* all numbers are complex. */ |
4503 | return scm_number_p (x); | |
0f2d19dd | 4504 | } |
1bbd0b84 | 4505 | #undef FUNC_NAME |
0f2d19dd | 4506 | |
f92e85f7 MV |
4507 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
4508 | (SCM x), | |
4509 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
4510 | "otherwise. Note that the set of integer values forms a subset of\n" | |
4511 | "the set of real numbers, i. e. the predicate will also be\n" | |
4512 | "fulfilled if @var{x} is an integer number.") | |
4513 | #define FUNC_NAME s_scm_real_p | |
4514 | { | |
c960e556 MW |
4515 | return scm_from_bool |
4516 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
4517 | } |
4518 | #undef FUNC_NAME | |
4519 | ||
4520 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 4521 | (SCM x), |
942e5b91 | 4522 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 4523 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 4524 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
4525 | "fulfilled if @var{x} is an integer number.") |
4526 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 4527 | { |
c960e556 | 4528 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
4529 | return SCM_BOOL_T; |
4530 | else if (SCM_REALP (x)) | |
c960e556 MW |
4531 | /* due to their limited precision, finite floating point numbers are |
4532 | rational as well. (finite means neither infinity nor a NaN) */ | |
4533 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 4534 | else |
bb628794 | 4535 | return SCM_BOOL_F; |
0f2d19dd | 4536 | } |
1bbd0b84 | 4537 | #undef FUNC_NAME |
0f2d19dd | 4538 | |
a1ec6916 | 4539 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 4540 | (SCM x), |
942e5b91 MG |
4541 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
4542 | "else.") | |
1bbd0b84 | 4543 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 4544 | { |
c960e556 | 4545 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 4546 | return SCM_BOOL_T; |
c960e556 MW |
4547 | else if (SCM_REALP (x)) |
4548 | { | |
4549 | double val = SCM_REAL_VALUE (x); | |
4550 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
4551 | } | |
4552 | else | |
8e43ed5d | 4553 | return SCM_BOOL_F; |
0f2d19dd | 4554 | } |
1bbd0b84 | 4555 | #undef FUNC_NAME |
0f2d19dd JB |
4556 | |
4557 | ||
8a1f4f98 AW |
4558 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
4559 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
4560 | (SCM x, SCM y, SCM rest), | |
4561 | "Return @code{#t} if all parameters are numerically equal.") | |
4562 | #define FUNC_NAME s_scm_i_num_eq_p | |
4563 | { | |
4564 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4565 | return SCM_BOOL_T; | |
4566 | while (!scm_is_null (rest)) | |
4567 | { | |
4568 | if (scm_is_false (scm_num_eq_p (x, y))) | |
4569 | return SCM_BOOL_F; | |
4570 | x = y; | |
4571 | y = scm_car (rest); | |
4572 | rest = scm_cdr (rest); | |
4573 | } | |
4574 | return scm_num_eq_p (x, y); | |
4575 | } | |
4576 | #undef FUNC_NAME | |
0f2d19dd | 4577 | SCM |
6e8d25a6 | 4578 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 4579 | { |
d8b95e27 | 4580 | again: |
e11e83f3 | 4581 | if (SCM_I_INUMP (x)) |
0aacf84e | 4582 | { |
e25f3727 | 4583 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 4584 | if (SCM_I_INUMP (y)) |
0aacf84e | 4585 | { |
e25f3727 | 4586 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 4587 | return scm_from_bool (xx == yy); |
0aacf84e MD |
4588 | } |
4589 | else if (SCM_BIGP (y)) | |
4590 | return SCM_BOOL_F; | |
4591 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
4592 | { |
4593 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
4594 | to a double and compare. | |
4595 | ||
4596 | But on a 64-bit system an inum is bigger than a double and | |
4597 | casting it to a double (call that dxx) will round. dxx is at | |
4598 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
4599 | an integer and fits a long. So we cast yy to a long and | |
4600 | compare with plain xx. | |
4601 | ||
4602 | An alternative (for any size system actually) would be to check | |
4603 | yy is an integer (with floor) and is in range of an inum | |
4604 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
4605 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
4606 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
4607 | |
4608 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
4609 | return scm_from_bool ((double) xx == yy |
4610 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4611 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 4612 | } |
0aacf84e | 4613 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4614 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4615 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
4616 | else if (SCM_FRACTIONP (y)) |
4617 | return SCM_BOOL_F; | |
0aacf84e | 4618 | else |
8a1f4f98 | 4619 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4620 | } |
0aacf84e MD |
4621 | else if (SCM_BIGP (x)) |
4622 | { | |
e11e83f3 | 4623 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4624 | return SCM_BOOL_F; |
4625 | else if (SCM_BIGP (y)) | |
4626 | { | |
4627 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4628 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4629 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4630 | } |
4631 | else if (SCM_REALP (y)) | |
4632 | { | |
4633 | int cmp; | |
2e65b52f | 4634 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4635 | return SCM_BOOL_F; |
4636 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4637 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4638 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4639 | } |
4640 | else if (SCM_COMPLEXP (y)) | |
4641 | { | |
4642 | int cmp; | |
4643 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
4644 | return SCM_BOOL_F; | |
2e65b52f | 4645 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
4646 | return SCM_BOOL_F; |
4647 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
4648 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4649 | return scm_from_bool (0 == cmp); |
0aacf84e | 4650 | } |
f92e85f7 MV |
4651 | else if (SCM_FRACTIONP (y)) |
4652 | return SCM_BOOL_F; | |
0aacf84e | 4653 | else |
8a1f4f98 | 4654 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4655 | } |
0aacf84e MD |
4656 | else if (SCM_REALP (x)) |
4657 | { | |
e8c5b1f2 | 4658 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 4659 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
4660 | { |
4661 | /* see comments with inum/real above */ | |
e25f3727 | 4662 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
4663 | return scm_from_bool (xx == (double) yy |
4664 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4665 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 4666 | } |
0aacf84e MD |
4667 | else if (SCM_BIGP (y)) |
4668 | { | |
4669 | int cmp; | |
2e65b52f | 4670 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4671 | return SCM_BOOL_F; |
4672 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4673 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4674 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4675 | } |
4676 | else if (SCM_REALP (y)) | |
73e4de09 | 4677 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 4678 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4679 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4680 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4681 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4682 | { |
4683 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4684 | if (isnan (xx)) |
d8b95e27 | 4685 | return SCM_BOOL_F; |
2e65b52f | 4686 | if (isinf (xx)) |
73e4de09 | 4687 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4688 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4689 | goto again; | |
4690 | } | |
0aacf84e | 4691 | else |
8a1f4f98 | 4692 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4693 | } |
0aacf84e MD |
4694 | else if (SCM_COMPLEXP (x)) |
4695 | { | |
e11e83f3 MV |
4696 | if (SCM_I_INUMP (y)) |
4697 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
4698 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4699 | else if (SCM_BIGP (y)) | |
4700 | { | |
4701 | int cmp; | |
4702 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
4703 | return SCM_BOOL_F; | |
2e65b52f | 4704 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
4705 | return SCM_BOOL_F; |
4706 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
4707 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4708 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4709 | } |
4710 | else if (SCM_REALP (y)) | |
73e4de09 | 4711 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
4712 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4713 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 4714 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4715 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4716 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4717 | { |
4718 | double xx; | |
4719 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
4720 | return SCM_BOOL_F; | |
4721 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 4722 | if (isnan (xx)) |
d8b95e27 | 4723 | return SCM_BOOL_F; |
2e65b52f | 4724 | if (isinf (xx)) |
73e4de09 | 4725 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4726 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4727 | goto again; | |
4728 | } | |
f92e85f7 | 4729 | else |
8a1f4f98 | 4730 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
4731 | } |
4732 | else if (SCM_FRACTIONP (x)) | |
4733 | { | |
e11e83f3 | 4734 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
4735 | return SCM_BOOL_F; |
4736 | else if (SCM_BIGP (y)) | |
4737 | return SCM_BOOL_F; | |
4738 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
4739 | { |
4740 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4741 | if (isnan (yy)) |
d8b95e27 | 4742 | return SCM_BOOL_F; |
2e65b52f | 4743 | if (isinf (yy)) |
73e4de09 | 4744 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4745 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4746 | goto again; | |
4747 | } | |
f92e85f7 | 4748 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
4749 | { |
4750 | double yy; | |
4751 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
4752 | return SCM_BOOL_F; | |
4753 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 4754 | if (isnan (yy)) |
d8b95e27 | 4755 | return SCM_BOOL_F; |
2e65b52f | 4756 | if (isinf (yy)) |
73e4de09 | 4757 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4758 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4759 | goto again; | |
4760 | } | |
f92e85f7 MV |
4761 | else if (SCM_FRACTIONP (y)) |
4762 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 4763 | else |
8a1f4f98 | 4764 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4765 | } |
0aacf84e | 4766 | else |
8a1f4f98 | 4767 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
4768 | } |
4769 | ||
4770 | ||
a5f0b599 KR |
4771 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
4772 | done are good for inums, but for bignums an answer can almost always be | |
4773 | had by just examining a few high bits of the operands, as done by GMP in | |
4774 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
4775 | of the float exponent to take into account. */ | |
4776 | ||
8c93b597 | 4777 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
4778 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
4779 | (SCM x, SCM y, SCM rest), | |
4780 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4781 | "increasing.") | |
4782 | #define FUNC_NAME s_scm_i_num_less_p | |
4783 | { | |
4784 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4785 | return SCM_BOOL_T; | |
4786 | while (!scm_is_null (rest)) | |
4787 | { | |
4788 | if (scm_is_false (scm_less_p (x, y))) | |
4789 | return SCM_BOOL_F; | |
4790 | x = y; | |
4791 | y = scm_car (rest); | |
4792 | rest = scm_cdr (rest); | |
4793 | } | |
4794 | return scm_less_p (x, y); | |
4795 | } | |
4796 | #undef FUNC_NAME | |
0f2d19dd | 4797 | SCM |
6e8d25a6 | 4798 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 4799 | { |
a5f0b599 | 4800 | again: |
e11e83f3 | 4801 | if (SCM_I_INUMP (x)) |
0aacf84e | 4802 | { |
e25f3727 | 4803 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4804 | if (SCM_I_INUMP (y)) |
0aacf84e | 4805 | { |
e25f3727 | 4806 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 4807 | return scm_from_bool (xx < yy); |
0aacf84e MD |
4808 | } |
4809 | else if (SCM_BIGP (y)) | |
4810 | { | |
4811 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4812 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4813 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
4814 | } |
4815 | else if (SCM_REALP (y)) | |
73e4de09 | 4816 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 4817 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4818 | { |
4819 | /* "x < a/b" becomes "x*b < a" */ | |
4820 | int_frac: | |
4821 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
4822 | y = SCM_FRACTION_NUMERATOR (y); | |
4823 | goto again; | |
4824 | } | |
0aacf84e | 4825 | else |
8a1f4f98 | 4826 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4827 | } |
0aacf84e MD |
4828 | else if (SCM_BIGP (x)) |
4829 | { | |
e11e83f3 | 4830 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4831 | { |
4832 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4833 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4834 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
4835 | } |
4836 | else if (SCM_BIGP (y)) | |
4837 | { | |
4838 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4839 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4840 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
4841 | } |
4842 | else if (SCM_REALP (y)) | |
4843 | { | |
4844 | int cmp; | |
2e65b52f | 4845 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4846 | return SCM_BOOL_F; |
4847 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4848 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4849 | return scm_from_bool (cmp < 0); |
0aacf84e | 4850 | } |
f92e85f7 | 4851 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 4852 | goto int_frac; |
0aacf84e | 4853 | else |
8a1f4f98 | 4854 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 4855 | } |
0aacf84e MD |
4856 | else if (SCM_REALP (x)) |
4857 | { | |
e11e83f3 MV |
4858 | if (SCM_I_INUMP (y)) |
4859 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
4860 | else if (SCM_BIGP (y)) |
4861 | { | |
4862 | int cmp; | |
2e65b52f | 4863 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4864 | return SCM_BOOL_F; |
4865 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4866 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4867 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
4868 | } |
4869 | else if (SCM_REALP (y)) | |
73e4de09 | 4870 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 4871 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4872 | { |
4873 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4874 | if (isnan (xx)) |
a5f0b599 | 4875 | return SCM_BOOL_F; |
2e65b52f | 4876 | if (isinf (xx)) |
73e4de09 | 4877 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
4878 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4879 | goto again; | |
4880 | } | |
f92e85f7 | 4881 | else |
8a1f4f98 | 4882 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
4883 | } |
4884 | else if (SCM_FRACTIONP (x)) | |
4885 | { | |
e11e83f3 | 4886 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
4887 | { |
4888 | /* "a/b < y" becomes "a < y*b" */ | |
4889 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
4890 | x = SCM_FRACTION_NUMERATOR (x); | |
4891 | goto again; | |
4892 | } | |
f92e85f7 | 4893 | else if (SCM_REALP (y)) |
a5f0b599 KR |
4894 | { |
4895 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4896 | if (isnan (yy)) |
a5f0b599 | 4897 | return SCM_BOOL_F; |
2e65b52f | 4898 | if (isinf (yy)) |
73e4de09 | 4899 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
4900 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4901 | goto again; | |
4902 | } | |
f92e85f7 | 4903 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4904 | { |
4905 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
4906 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
4907 | SCM_FRACTION_DENOMINATOR (y)); | |
4908 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
4909 | SCM_FRACTION_DENOMINATOR (x)); | |
4910 | x = new_x; | |
4911 | y = new_y; | |
4912 | goto again; | |
4913 | } | |
0aacf84e | 4914 | else |
8a1f4f98 | 4915 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4916 | } |
0aacf84e | 4917 | else |
8a1f4f98 | 4918 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
4919 | } |
4920 | ||
4921 | ||
8a1f4f98 AW |
4922 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
4923 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
4924 | (SCM x, SCM y, SCM rest), | |
4925 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4926 | "decreasing.") | |
4927 | #define FUNC_NAME s_scm_i_num_gr_p | |
4928 | { | |
4929 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4930 | return SCM_BOOL_T; | |
4931 | while (!scm_is_null (rest)) | |
4932 | { | |
4933 | if (scm_is_false (scm_gr_p (x, y))) | |
4934 | return SCM_BOOL_F; | |
4935 | x = y; | |
4936 | y = scm_car (rest); | |
4937 | rest = scm_cdr (rest); | |
4938 | } | |
4939 | return scm_gr_p (x, y); | |
4940 | } | |
4941 | #undef FUNC_NAME | |
4942 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
4943 | SCM |
4944 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 4945 | { |
c76b1eaf | 4946 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4947 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4948 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4949 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
4950 | else |
4951 | return scm_less_p (y, x); | |
0f2d19dd | 4952 | } |
1bbd0b84 | 4953 | #undef FUNC_NAME |
0f2d19dd JB |
4954 | |
4955 | ||
8a1f4f98 AW |
4956 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
4957 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
4958 | (SCM x, SCM y, SCM rest), | |
4959 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4960 | "non-decreasing.") | |
4961 | #define FUNC_NAME s_scm_i_num_leq_p | |
4962 | { | |
4963 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4964 | return SCM_BOOL_T; | |
4965 | while (!scm_is_null (rest)) | |
4966 | { | |
4967 | if (scm_is_false (scm_leq_p (x, y))) | |
4968 | return SCM_BOOL_F; | |
4969 | x = y; | |
4970 | y = scm_car (rest); | |
4971 | rest = scm_cdr (rest); | |
4972 | } | |
4973 | return scm_leq_p (x, y); | |
4974 | } | |
4975 | #undef FUNC_NAME | |
4976 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
4977 | SCM |
4978 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 4979 | { |
c76b1eaf | 4980 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4981 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4982 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4983 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 4984 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 4985 | return SCM_BOOL_F; |
c76b1eaf | 4986 | else |
73e4de09 | 4987 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 4988 | } |
1bbd0b84 | 4989 | #undef FUNC_NAME |
0f2d19dd JB |
4990 | |
4991 | ||
8a1f4f98 AW |
4992 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
4993 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
4994 | (SCM x, SCM y, SCM rest), | |
4995 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4996 | "non-increasing.") | |
4997 | #define FUNC_NAME s_scm_i_num_geq_p | |
4998 | { | |
4999 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
5000 | return SCM_BOOL_T; | |
5001 | while (!scm_is_null (rest)) | |
5002 | { | |
5003 | if (scm_is_false (scm_geq_p (x, y))) | |
5004 | return SCM_BOOL_F; | |
5005 | x = y; | |
5006 | y = scm_car (rest); | |
5007 | rest = scm_cdr (rest); | |
5008 | } | |
5009 | return scm_geq_p (x, y); | |
5010 | } | |
5011 | #undef FUNC_NAME | |
5012 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
5013 | SCM |
5014 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 5015 | { |
c76b1eaf | 5016 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 5017 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 5018 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 5019 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 5020 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 5021 | return SCM_BOOL_F; |
c76b1eaf | 5022 | else |
73e4de09 | 5023 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 5024 | } |
1bbd0b84 | 5025 | #undef FUNC_NAME |
0f2d19dd JB |
5026 | |
5027 | ||
2519490c MW |
5028 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
5029 | (SCM z), | |
5030 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
5031 | "zero.") | |
5032 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 5033 | { |
e11e83f3 | 5034 | if (SCM_I_INUMP (z)) |
bc36d050 | 5035 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 5036 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5037 | return SCM_BOOL_F; |
0aacf84e | 5038 | else if (SCM_REALP (z)) |
73e4de09 | 5039 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 5040 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 5041 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 5042 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
5043 | else if (SCM_FRACTIONP (z)) |
5044 | return SCM_BOOL_F; | |
0aacf84e | 5045 | else |
2519490c | 5046 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 5047 | } |
2519490c | 5048 | #undef FUNC_NAME |
0f2d19dd JB |
5049 | |
5050 | ||
2519490c MW |
5051 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
5052 | (SCM x), | |
5053 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
5054 | "zero.") | |
5055 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 5056 | { |
e11e83f3 MV |
5057 | if (SCM_I_INUMP (x)) |
5058 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
5059 | else if (SCM_BIGP (x)) |
5060 | { | |
5061 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5062 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5063 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
5064 | } |
5065 | else if (SCM_REALP (x)) | |
73e4de09 | 5066 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
5067 | else if (SCM_FRACTIONP (x)) |
5068 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5069 | else |
2519490c | 5070 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 5071 | } |
2519490c | 5072 | #undef FUNC_NAME |
0f2d19dd JB |
5073 | |
5074 | ||
2519490c MW |
5075 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
5076 | (SCM x), | |
5077 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
5078 | "zero.") | |
5079 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 5080 | { |
e11e83f3 MV |
5081 | if (SCM_I_INUMP (x)) |
5082 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
5083 | else if (SCM_BIGP (x)) |
5084 | { | |
5085 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5086 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5087 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
5088 | } |
5089 | else if (SCM_REALP (x)) | |
73e4de09 | 5090 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
5091 | else if (SCM_FRACTIONP (x)) |
5092 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5093 | else |
2519490c | 5094 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 5095 | } |
2519490c | 5096 | #undef FUNC_NAME |
0f2d19dd JB |
5097 | |
5098 | ||
2a06f791 KR |
5099 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
5100 | required by r5rs. On that basis, for exact/inexact combinations the | |
5101 | exact is converted to inexact to compare and possibly return. This is | |
5102 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
5103 | its test, such trouble is not required for min and max. */ | |
5104 | ||
78d3deb1 AW |
5105 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
5106 | (SCM x, SCM y, SCM rest), | |
5107 | "Return the maximum of all parameter values.") | |
5108 | #define FUNC_NAME s_scm_i_max | |
5109 | { | |
5110 | while (!scm_is_null (rest)) | |
5111 | { x = scm_max (x, y); | |
5112 | y = scm_car (rest); | |
5113 | rest = scm_cdr (rest); | |
5114 | } | |
5115 | return scm_max (x, y); | |
5116 | } | |
5117 | #undef FUNC_NAME | |
5118 | ||
5119 | #define s_max s_scm_i_max | |
5120 | #define g_max g_scm_i_max | |
5121 | ||
0f2d19dd | 5122 | SCM |
6e8d25a6 | 5123 | scm_max (SCM x, SCM y) |
0f2d19dd | 5124 | { |
0aacf84e MD |
5125 | if (SCM_UNBNDP (y)) |
5126 | { | |
5127 | if (SCM_UNBNDP (x)) | |
5128 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 5129 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5130 | return x; |
5131 | else | |
5132 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 5133 | } |
f4c627b3 | 5134 | |
e11e83f3 | 5135 | if (SCM_I_INUMP (x)) |
0aacf84e | 5136 | { |
e25f3727 | 5137 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5138 | if (SCM_I_INUMP (y)) |
0aacf84e | 5139 | { |
e25f3727 | 5140 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5141 | return (xx < yy) ? y : x; |
5142 | } | |
5143 | else if (SCM_BIGP (y)) | |
5144 | { | |
5145 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5146 | scm_remember_upto_here_1 (y); | |
5147 | return (sgn < 0) ? x : y; | |
5148 | } | |
5149 | else if (SCM_REALP (y)) | |
5150 | { | |
5151 | double z = xx; | |
5152 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 5153 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 5154 | } |
f92e85f7 MV |
5155 | else if (SCM_FRACTIONP (y)) |
5156 | { | |
e4bc5d6c | 5157 | use_less: |
73e4de09 | 5158 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 5159 | } |
0aacf84e MD |
5160 | else |
5161 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5162 | } |
0aacf84e MD |
5163 | else if (SCM_BIGP (x)) |
5164 | { | |
e11e83f3 | 5165 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5166 | { |
5167 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5168 | scm_remember_upto_here_1 (x); | |
5169 | return (sgn < 0) ? y : x; | |
5170 | } | |
5171 | else if (SCM_BIGP (y)) | |
5172 | { | |
5173 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5174 | scm_remember_upto_here_2 (x, y); | |
5175 | return (cmp > 0) ? x : y; | |
5176 | } | |
5177 | else if (SCM_REALP (y)) | |
5178 | { | |
2a06f791 KR |
5179 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
5180 | double xx, yy; | |
5181 | big_real: | |
5182 | xx = scm_i_big2dbl (x); | |
5183 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5184 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 5185 | } |
f92e85f7 MV |
5186 | else if (SCM_FRACTIONP (y)) |
5187 | { | |
e4bc5d6c | 5188 | goto use_less; |
f92e85f7 | 5189 | } |
0aacf84e MD |
5190 | else |
5191 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 5192 | } |
0aacf84e MD |
5193 | else if (SCM_REALP (x)) |
5194 | { | |
e11e83f3 | 5195 | if (SCM_I_INUMP (y)) |
0aacf84e | 5196 | { |
e11e83f3 | 5197 | double z = SCM_I_INUM (y); |
0aacf84e | 5198 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 5199 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
5200 | } |
5201 | else if (SCM_BIGP (y)) | |
5202 | { | |
b6f8f763 | 5203 | SCM_SWAP (x, y); |
2a06f791 | 5204 | goto big_real; |
0aacf84e MD |
5205 | } |
5206 | else if (SCM_REALP (y)) | |
5207 | { | |
5208 | /* if x==NaN then our explicit check means we return NaN | |
5209 | if y==NaN then ">" is false and we return NaN | |
5210 | calling isnan is unavoidable, since it's the only way to know | |
5211 | which of x or y causes any compares to be false */ | |
5212 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 5213 | return (isnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 5214 | } |
f92e85f7 MV |
5215 | else if (SCM_FRACTIONP (y)) |
5216 | { | |
5217 | double yy = scm_i_fraction2double (y); | |
5218 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5219 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
5220 | } |
5221 | else | |
5222 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
5223 | } | |
5224 | else if (SCM_FRACTIONP (x)) | |
5225 | { | |
e11e83f3 | 5226 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5227 | { |
e4bc5d6c | 5228 | goto use_less; |
f92e85f7 MV |
5229 | } |
5230 | else if (SCM_BIGP (y)) | |
5231 | { | |
e4bc5d6c | 5232 | goto use_less; |
f92e85f7 MV |
5233 | } |
5234 | else if (SCM_REALP (y)) | |
5235 | { | |
5236 | double xx = scm_i_fraction2double (x); | |
55f26379 | 5237 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
5238 | } |
5239 | else if (SCM_FRACTIONP (y)) | |
5240 | { | |
e4bc5d6c | 5241 | goto use_less; |
f92e85f7 | 5242 | } |
0aacf84e MD |
5243 | else |
5244 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5245 | } |
0aacf84e | 5246 | else |
f4c627b3 | 5247 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
5248 | } |
5249 | ||
5250 | ||
78d3deb1 AW |
5251 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
5252 | (SCM x, SCM y, SCM rest), | |
5253 | "Return the minimum of all parameter values.") | |
5254 | #define FUNC_NAME s_scm_i_min | |
5255 | { | |
5256 | while (!scm_is_null (rest)) | |
5257 | { x = scm_min (x, y); | |
5258 | y = scm_car (rest); | |
5259 | rest = scm_cdr (rest); | |
5260 | } | |
5261 | return scm_min (x, y); | |
5262 | } | |
5263 | #undef FUNC_NAME | |
5264 | ||
5265 | #define s_min s_scm_i_min | |
5266 | #define g_min g_scm_i_min | |
5267 | ||
0f2d19dd | 5268 | SCM |
6e8d25a6 | 5269 | scm_min (SCM x, SCM y) |
0f2d19dd | 5270 | { |
0aacf84e MD |
5271 | if (SCM_UNBNDP (y)) |
5272 | { | |
5273 | if (SCM_UNBNDP (x)) | |
5274 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 5275 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5276 | return x; |
5277 | else | |
5278 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 5279 | } |
f4c627b3 | 5280 | |
e11e83f3 | 5281 | if (SCM_I_INUMP (x)) |
0aacf84e | 5282 | { |
e25f3727 | 5283 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5284 | if (SCM_I_INUMP (y)) |
0aacf84e | 5285 | { |
e25f3727 | 5286 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5287 | return (xx < yy) ? x : y; |
5288 | } | |
5289 | else if (SCM_BIGP (y)) | |
5290 | { | |
5291 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5292 | scm_remember_upto_here_1 (y); | |
5293 | return (sgn < 0) ? y : x; | |
5294 | } | |
5295 | else if (SCM_REALP (y)) | |
5296 | { | |
5297 | double z = xx; | |
5298 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 5299 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 5300 | } |
f92e85f7 MV |
5301 | else if (SCM_FRACTIONP (y)) |
5302 | { | |
e4bc5d6c | 5303 | use_less: |
73e4de09 | 5304 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 5305 | } |
0aacf84e MD |
5306 | else |
5307 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5308 | } |
0aacf84e MD |
5309 | else if (SCM_BIGP (x)) |
5310 | { | |
e11e83f3 | 5311 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5312 | { |
5313 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5314 | scm_remember_upto_here_1 (x); | |
5315 | return (sgn < 0) ? x : y; | |
5316 | } | |
5317 | else if (SCM_BIGP (y)) | |
5318 | { | |
5319 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5320 | scm_remember_upto_here_2 (x, y); | |
5321 | return (cmp > 0) ? y : x; | |
5322 | } | |
5323 | else if (SCM_REALP (y)) | |
5324 | { | |
2a06f791 KR |
5325 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
5326 | double xx, yy; | |
5327 | big_real: | |
5328 | xx = scm_i_big2dbl (x); | |
5329 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5330 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 5331 | } |
f92e85f7 MV |
5332 | else if (SCM_FRACTIONP (y)) |
5333 | { | |
e4bc5d6c | 5334 | goto use_less; |
f92e85f7 | 5335 | } |
0aacf84e MD |
5336 | else |
5337 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 5338 | } |
0aacf84e MD |
5339 | else if (SCM_REALP (x)) |
5340 | { | |
e11e83f3 | 5341 | if (SCM_I_INUMP (y)) |
0aacf84e | 5342 | { |
e11e83f3 | 5343 | double z = SCM_I_INUM (y); |
0aacf84e | 5344 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 5345 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
5346 | } |
5347 | else if (SCM_BIGP (y)) | |
5348 | { | |
b6f8f763 | 5349 | SCM_SWAP (x, y); |
2a06f791 | 5350 | goto big_real; |
0aacf84e MD |
5351 | } |
5352 | else if (SCM_REALP (y)) | |
5353 | { | |
5354 | /* if x==NaN then our explicit check means we return NaN | |
5355 | if y==NaN then "<" is false and we return NaN | |
5356 | calling isnan is unavoidable, since it's the only way to know | |
5357 | which of x or y causes any compares to be false */ | |
5358 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 5359 | return (isnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 5360 | } |
f92e85f7 MV |
5361 | else if (SCM_FRACTIONP (y)) |
5362 | { | |
5363 | double yy = scm_i_fraction2double (y); | |
5364 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5365 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 5366 | } |
0aacf84e MD |
5367 | else |
5368 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5369 | } |
f92e85f7 MV |
5370 | else if (SCM_FRACTIONP (x)) |
5371 | { | |
e11e83f3 | 5372 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5373 | { |
e4bc5d6c | 5374 | goto use_less; |
f92e85f7 MV |
5375 | } |
5376 | else if (SCM_BIGP (y)) | |
5377 | { | |
e4bc5d6c | 5378 | goto use_less; |
f92e85f7 MV |
5379 | } |
5380 | else if (SCM_REALP (y)) | |
5381 | { | |
5382 | double xx = scm_i_fraction2double (x); | |
55f26379 | 5383 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
5384 | } |
5385 | else if (SCM_FRACTIONP (y)) | |
5386 | { | |
e4bc5d6c | 5387 | goto use_less; |
f92e85f7 MV |
5388 | } |
5389 | else | |
78d3deb1 | 5390 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 5391 | } |
0aacf84e | 5392 | else |
f4c627b3 | 5393 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
5394 | } |
5395 | ||
5396 | ||
8ccd24f7 AW |
5397 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
5398 | (SCM x, SCM y, SCM rest), | |
5399 | "Return the sum of all parameter values. Return 0 if called without\n" | |
5400 | "any parameters." ) | |
5401 | #define FUNC_NAME s_scm_i_sum | |
5402 | { | |
5403 | while (!scm_is_null (rest)) | |
5404 | { x = scm_sum (x, y); | |
5405 | y = scm_car (rest); | |
5406 | rest = scm_cdr (rest); | |
5407 | } | |
5408 | return scm_sum (x, y); | |
5409 | } | |
5410 | #undef FUNC_NAME | |
5411 | ||
5412 | #define s_sum s_scm_i_sum | |
5413 | #define g_sum g_scm_i_sum | |
5414 | ||
0f2d19dd | 5415 | SCM |
6e8d25a6 | 5416 | scm_sum (SCM x, SCM y) |
0f2d19dd | 5417 | { |
9cc37597 | 5418 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5419 | { |
5420 | if (SCM_NUMBERP (x)) return x; | |
5421 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 5422 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 5423 | } |
c209c88e | 5424 | |
9cc37597 | 5425 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 5426 | { |
9cc37597 | 5427 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 5428 | { |
e25f3727 AW |
5429 | scm_t_inum xx = SCM_I_INUM (x); |
5430 | scm_t_inum yy = SCM_I_INUM (y); | |
5431 | scm_t_inum z = xx + yy; | |
5432 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
5433 | } |
5434 | else if (SCM_BIGP (y)) | |
5435 | { | |
5436 | SCM_SWAP (x, y); | |
5437 | goto add_big_inum; | |
5438 | } | |
5439 | else if (SCM_REALP (y)) | |
5440 | { | |
e25f3727 | 5441 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5442 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
5443 | } |
5444 | else if (SCM_COMPLEXP (y)) | |
5445 | { | |
e25f3727 | 5446 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5447 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
5448 | SCM_COMPLEX_IMAG (y)); |
5449 | } | |
f92e85f7 | 5450 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5451 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5452 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5453 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
5454 | else |
5455 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
5456 | } else if (SCM_BIGP (x)) |
5457 | { | |
e11e83f3 | 5458 | if (SCM_I_INUMP (y)) |
0aacf84e | 5459 | { |
e25f3727 | 5460 | scm_t_inum inum; |
0aacf84e MD |
5461 | int bigsgn; |
5462 | add_big_inum: | |
e11e83f3 | 5463 | inum = SCM_I_INUM (y); |
0aacf84e MD |
5464 | if (inum == 0) |
5465 | return x; | |
5466 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5467 | if (inum < 0) | |
5468 | { | |
5469 | SCM result = scm_i_mkbig (); | |
5470 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
5471 | scm_remember_upto_here_1 (x); | |
5472 | /* we know the result will have to be a bignum */ | |
5473 | if (bigsgn == -1) | |
5474 | return result; | |
5475 | return scm_i_normbig (result); | |
5476 | } | |
5477 | else | |
5478 | { | |
5479 | SCM result = scm_i_mkbig (); | |
5480 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
5481 | scm_remember_upto_here_1 (x); | |
5482 | /* we know the result will have to be a bignum */ | |
5483 | if (bigsgn == 1) | |
5484 | return result; | |
5485 | return scm_i_normbig (result); | |
5486 | } | |
5487 | } | |
5488 | else if (SCM_BIGP (y)) | |
5489 | { | |
5490 | SCM result = scm_i_mkbig (); | |
5491 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5492 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5493 | mpz_add (SCM_I_BIG_MPZ (result), | |
5494 | SCM_I_BIG_MPZ (x), | |
5495 | SCM_I_BIG_MPZ (y)); | |
5496 | scm_remember_upto_here_2 (x, y); | |
5497 | /* we know the result will have to be a bignum */ | |
5498 | if (sgn_x == sgn_y) | |
5499 | return result; | |
5500 | return scm_i_normbig (result); | |
5501 | } | |
5502 | else if (SCM_REALP (y)) | |
5503 | { | |
5504 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
5505 | scm_remember_upto_here_1 (x); | |
55f26379 | 5506 | return scm_from_double (result); |
0aacf84e MD |
5507 | } |
5508 | else if (SCM_COMPLEXP (y)) | |
5509 | { | |
5510 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5511 | + SCM_COMPLEX_REAL (y)); | |
5512 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5513 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5514 | } |
f92e85f7 | 5515 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5516 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5517 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5518 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5519 | else |
5520 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 5521 | } |
0aacf84e MD |
5522 | else if (SCM_REALP (x)) |
5523 | { | |
e11e83f3 | 5524 | if (SCM_I_INUMP (y)) |
55f26379 | 5525 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
5526 | else if (SCM_BIGP (y)) |
5527 | { | |
5528 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
5529 | scm_remember_upto_here_1 (y); | |
55f26379 | 5530 | return scm_from_double (result); |
0aacf84e MD |
5531 | } |
5532 | else if (SCM_REALP (y)) | |
55f26379 | 5533 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 5534 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5535 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5536 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5537 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5538 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
5539 | else |
5540 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 5541 | } |
0aacf84e MD |
5542 | else if (SCM_COMPLEXP (x)) |
5543 | { | |
e11e83f3 | 5544 | if (SCM_I_INUMP (y)) |
8507ec80 | 5545 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
5546 | SCM_COMPLEX_IMAG (x)); |
5547 | else if (SCM_BIGP (y)) | |
5548 | { | |
5549 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
5550 | + SCM_COMPLEX_REAL (x)); | |
5551 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5552 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
5553 | } |
5554 | else if (SCM_REALP (y)) | |
8507ec80 | 5555 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
5556 | SCM_COMPLEX_IMAG (x)); |
5557 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5558 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5559 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5560 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5561 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
5562 | SCM_COMPLEX_IMAG (x)); |
5563 | else | |
5564 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
5565 | } | |
5566 | else if (SCM_FRACTIONP (x)) | |
5567 | { | |
e11e83f3 | 5568 | if (SCM_I_INUMP (y)) |
cba42c93 | 5569 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5570 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5571 | SCM_FRACTION_DENOMINATOR (x)); | |
5572 | else if (SCM_BIGP (y)) | |
cba42c93 | 5573 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5574 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5575 | SCM_FRACTION_DENOMINATOR (x)); | |
5576 | else if (SCM_REALP (y)) | |
55f26379 | 5577 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 5578 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5579 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
5580 | SCM_COMPLEX_IMAG (y)); |
5581 | else if (SCM_FRACTIONP (y)) | |
5582 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 5583 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5584 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5585 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5586 | else |
5587 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 5588 | } |
0aacf84e | 5589 | else |
98cb6e75 | 5590 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
5591 | } |
5592 | ||
5593 | ||
40882e3d KR |
5594 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
5595 | (SCM x), | |
5596 | "Return @math{@var{x}+1}.") | |
5597 | #define FUNC_NAME s_scm_oneplus | |
5598 | { | |
cff5fa33 | 5599 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
5600 | } |
5601 | #undef FUNC_NAME | |
5602 | ||
5603 | ||
78d3deb1 AW |
5604 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
5605 | (SCM x, SCM y, SCM rest), | |
5606 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
5607 | "the sum of all but the first argument are subtracted from the first\n" | |
5608 | "argument.") | |
5609 | #define FUNC_NAME s_scm_i_difference | |
5610 | { | |
5611 | while (!scm_is_null (rest)) | |
5612 | { x = scm_difference (x, y); | |
5613 | y = scm_car (rest); | |
5614 | rest = scm_cdr (rest); | |
5615 | } | |
5616 | return scm_difference (x, y); | |
5617 | } | |
5618 | #undef FUNC_NAME | |
5619 | ||
5620 | #define s_difference s_scm_i_difference | |
5621 | #define g_difference g_scm_i_difference | |
5622 | ||
0f2d19dd | 5623 | SCM |
6e8d25a6 | 5624 | scm_difference (SCM x, SCM y) |
78d3deb1 | 5625 | #define FUNC_NAME s_difference |
0f2d19dd | 5626 | { |
9cc37597 | 5627 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5628 | { |
5629 | if (SCM_UNBNDP (x)) | |
5630 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
5631 | else | |
e11e83f3 | 5632 | if (SCM_I_INUMP (x)) |
ca46fb90 | 5633 | { |
e25f3727 | 5634 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 5635 | if (SCM_FIXABLE (xx)) |
d956fa6f | 5636 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 5637 | else |
e25f3727 | 5638 | return scm_i_inum2big (xx); |
ca46fb90 RB |
5639 | } |
5640 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
5641 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
5642 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
5643 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
5644 | else if (SCM_REALP (x)) | |
55f26379 | 5645 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 5646 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 5647 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 5648 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 5649 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 5650 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 5651 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
5652 | else |
5653 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 5654 | } |
ca46fb90 | 5655 | |
9cc37597 | 5656 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5657 | { |
9cc37597 | 5658 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5659 | { |
e25f3727 AW |
5660 | scm_t_inum xx = SCM_I_INUM (x); |
5661 | scm_t_inum yy = SCM_I_INUM (y); | |
5662 | scm_t_inum z = xx - yy; | |
0aacf84e | 5663 | if (SCM_FIXABLE (z)) |
d956fa6f | 5664 | return SCM_I_MAKINUM (z); |
0aacf84e | 5665 | else |
e25f3727 | 5666 | return scm_i_inum2big (z); |
0aacf84e MD |
5667 | } |
5668 | else if (SCM_BIGP (y)) | |
5669 | { | |
5670 | /* inum-x - big-y */ | |
e25f3727 | 5671 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 5672 | |
0aacf84e | 5673 | if (xx == 0) |
b5c40589 MW |
5674 | { |
5675 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
5676 | bignum, but negating that gives a fixnum. */ | |
5677 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
5678 | } | |
0aacf84e MD |
5679 | else |
5680 | { | |
5681 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5682 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5683 | |
0aacf84e MD |
5684 | if (xx >= 0) |
5685 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
5686 | else | |
5687 | { | |
5688 | /* x - y == -(y + -x) */ | |
5689 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
5690 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5691 | } | |
5692 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 5693 | |
0aacf84e MD |
5694 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
5695 | /* we know the result will have to be a bignum */ | |
5696 | return result; | |
5697 | else | |
5698 | return scm_i_normbig (result); | |
5699 | } | |
5700 | } | |
5701 | else if (SCM_REALP (y)) | |
5702 | { | |
e25f3727 | 5703 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5704 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
5705 | } |
5706 | else if (SCM_COMPLEXP (y)) | |
5707 | { | |
e25f3727 | 5708 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5709 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
5710 | - SCM_COMPLEX_IMAG (y)); |
5711 | } | |
f92e85f7 MV |
5712 | else if (SCM_FRACTIONP (y)) |
5713 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 5714 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5715 | SCM_FRACTION_NUMERATOR (y)), |
5716 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5717 | else |
5718 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 5719 | } |
0aacf84e MD |
5720 | else if (SCM_BIGP (x)) |
5721 | { | |
e11e83f3 | 5722 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5723 | { |
5724 | /* big-x - inum-y */ | |
e25f3727 | 5725 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 5726 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 5727 | |
0aacf84e MD |
5728 | scm_remember_upto_here_1 (x); |
5729 | if (sgn_x == 0) | |
c71b0706 | 5730 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 5731 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
5732 | else |
5733 | { | |
5734 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5735 | |
708f22c6 KR |
5736 | if (yy >= 0) |
5737 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
5738 | else | |
5739 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 5740 | scm_remember_upto_here_1 (x); |
ca46fb90 | 5741 | |
0aacf84e MD |
5742 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
5743 | /* we know the result will have to be a bignum */ | |
5744 | return result; | |
5745 | else | |
5746 | return scm_i_normbig (result); | |
5747 | } | |
5748 | } | |
5749 | else if (SCM_BIGP (y)) | |
5750 | { | |
5751 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5752 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5753 | SCM result = scm_i_mkbig (); | |
5754 | mpz_sub (SCM_I_BIG_MPZ (result), | |
5755 | SCM_I_BIG_MPZ (x), | |
5756 | SCM_I_BIG_MPZ (y)); | |
5757 | scm_remember_upto_here_2 (x, y); | |
5758 | /* we know the result will have to be a bignum */ | |
5759 | if ((sgn_x == 1) && (sgn_y == -1)) | |
5760 | return result; | |
5761 | if ((sgn_x == -1) && (sgn_y == 1)) | |
5762 | return result; | |
5763 | return scm_i_normbig (result); | |
5764 | } | |
5765 | else if (SCM_REALP (y)) | |
5766 | { | |
5767 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
5768 | scm_remember_upto_here_1 (x); | |
55f26379 | 5769 | return scm_from_double (result); |
0aacf84e MD |
5770 | } |
5771 | else if (SCM_COMPLEXP (y)) | |
5772 | { | |
5773 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5774 | - SCM_COMPLEX_REAL (y)); | |
5775 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5776 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5777 | } |
f92e85f7 | 5778 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5779 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5780 | SCM_FRACTION_NUMERATOR (y)), |
5781 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 5782 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 5783 | } |
0aacf84e MD |
5784 | else if (SCM_REALP (x)) |
5785 | { | |
e11e83f3 | 5786 | if (SCM_I_INUMP (y)) |
55f26379 | 5787 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
5788 | else if (SCM_BIGP (y)) |
5789 | { | |
5790 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5791 | scm_remember_upto_here_1 (x); | |
55f26379 | 5792 | return scm_from_double (result); |
0aacf84e MD |
5793 | } |
5794 | else if (SCM_REALP (y)) | |
55f26379 | 5795 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 5796 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5797 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5798 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5799 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5800 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
5801 | else |
5802 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5803 | } |
0aacf84e MD |
5804 | else if (SCM_COMPLEXP (x)) |
5805 | { | |
e11e83f3 | 5806 | if (SCM_I_INUMP (y)) |
8507ec80 | 5807 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
5808 | SCM_COMPLEX_IMAG (x)); |
5809 | else if (SCM_BIGP (y)) | |
5810 | { | |
5811 | double real_part = (SCM_COMPLEX_REAL (x) | |
5812 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
5813 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5814 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
5815 | } |
5816 | else if (SCM_REALP (y)) | |
8507ec80 | 5817 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
5818 | SCM_COMPLEX_IMAG (x)); |
5819 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5820 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5821 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5822 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5823 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
5824 | SCM_COMPLEX_IMAG (x)); |
5825 | else | |
5826 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
5827 | } | |
5828 | else if (SCM_FRACTIONP (x)) | |
5829 | { | |
e11e83f3 | 5830 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5831 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 5832 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5833 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5834 | SCM_FRACTION_DENOMINATOR (x)); | |
5835 | else if (SCM_BIGP (y)) | |
cba42c93 | 5836 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5837 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5838 | SCM_FRACTION_DENOMINATOR (x)); | |
5839 | else if (SCM_REALP (y)) | |
55f26379 | 5840 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 5841 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5842 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
5843 | -SCM_COMPLEX_IMAG (y)); |
5844 | else if (SCM_FRACTIONP (y)) | |
5845 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 5846 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5847 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5848 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5849 | else |
5850 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5851 | } |
0aacf84e | 5852 | else |
98cb6e75 | 5853 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 5854 | } |
c05e97b7 | 5855 | #undef FUNC_NAME |
0f2d19dd | 5856 | |
ca46fb90 | 5857 | |
40882e3d KR |
5858 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
5859 | (SCM x), | |
5860 | "Return @math{@var{x}-1}.") | |
5861 | #define FUNC_NAME s_scm_oneminus | |
5862 | { | |
cff5fa33 | 5863 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
5864 | } |
5865 | #undef FUNC_NAME | |
5866 | ||
5867 | ||
78d3deb1 AW |
5868 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
5869 | (SCM x, SCM y, SCM rest), | |
5870 | "Return the product of all arguments. If called without arguments,\n" | |
5871 | "1 is returned.") | |
5872 | #define FUNC_NAME s_scm_i_product | |
5873 | { | |
5874 | while (!scm_is_null (rest)) | |
5875 | { x = scm_product (x, y); | |
5876 | y = scm_car (rest); | |
5877 | rest = scm_cdr (rest); | |
5878 | } | |
5879 | return scm_product (x, y); | |
5880 | } | |
5881 | #undef FUNC_NAME | |
5882 | ||
5883 | #define s_product s_scm_i_product | |
5884 | #define g_product g_scm_i_product | |
5885 | ||
0f2d19dd | 5886 | SCM |
6e8d25a6 | 5887 | scm_product (SCM x, SCM y) |
0f2d19dd | 5888 | { |
9cc37597 | 5889 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
5890 | { |
5891 | if (SCM_UNBNDP (x)) | |
d956fa6f | 5892 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
5893 | else if (SCM_NUMBERP (x)) |
5894 | return x; | |
5895 | else | |
5896 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 5897 | } |
ca46fb90 | 5898 | |
9cc37597 | 5899 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5900 | { |
e25f3727 | 5901 | scm_t_inum xx; |
f4c627b3 | 5902 | |
0aacf84e | 5903 | intbig: |
e11e83f3 | 5904 | xx = SCM_I_INUM (x); |
f4c627b3 | 5905 | |
0aacf84e MD |
5906 | switch (xx) |
5907 | { | |
ca46fb90 RB |
5908 | case 0: return x; break; |
5909 | case 1: return y; break; | |
b5c40589 MW |
5910 | /* |
5911 | * The following case (x = -1) is important for more than | |
5912 | * just optimization. It handles the case of negating | |
5913 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), | |
5914 | * which is a bignum that must be changed back into a fixnum. | |
5915 | * Failure to do so will cause the following to return #f: | |
5916 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
5917 | */ | |
5918 | case -1: | |
5919 | return scm_difference(y, SCM_UNDEFINED); | |
5920 | break; | |
0aacf84e | 5921 | } |
f4c627b3 | 5922 | |
9cc37597 | 5923 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5924 | { |
e25f3727 AW |
5925 | scm_t_inum yy = SCM_I_INUM (y); |
5926 | scm_t_inum kk = xx * yy; | |
d956fa6f | 5927 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 5928 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
5929 | return k; |
5930 | else | |
5931 | { | |
e25f3727 | 5932 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
5933 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
5934 | return scm_i_normbig (result); | |
5935 | } | |
5936 | } | |
5937 | else if (SCM_BIGP (y)) | |
5938 | { | |
5939 | SCM result = scm_i_mkbig (); | |
5940 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
5941 | scm_remember_upto_here_1 (y); | |
5942 | return result; | |
5943 | } | |
5944 | else if (SCM_REALP (y)) | |
55f26379 | 5945 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 5946 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5947 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 5948 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5949 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5950 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 5951 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
5952 | else |
5953 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 5954 | } |
0aacf84e MD |
5955 | else if (SCM_BIGP (x)) |
5956 | { | |
e11e83f3 | 5957 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5958 | { |
5959 | SCM_SWAP (x, y); | |
5960 | goto intbig; | |
5961 | } | |
5962 | else if (SCM_BIGP (y)) | |
5963 | { | |
5964 | SCM result = scm_i_mkbig (); | |
5965 | mpz_mul (SCM_I_BIG_MPZ (result), | |
5966 | SCM_I_BIG_MPZ (x), | |
5967 | SCM_I_BIG_MPZ (y)); | |
5968 | scm_remember_upto_here_2 (x, y); | |
5969 | return result; | |
5970 | } | |
5971 | else if (SCM_REALP (y)) | |
5972 | { | |
5973 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
5974 | scm_remember_upto_here_1 (x); | |
55f26379 | 5975 | return scm_from_double (result); |
0aacf84e MD |
5976 | } |
5977 | else if (SCM_COMPLEXP (y)) | |
5978 | { | |
5979 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
5980 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5981 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
5982 | z * SCM_COMPLEX_IMAG (y)); |
5983 | } | |
f92e85f7 | 5984 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5985 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 5986 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
5987 | else |
5988 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 5989 | } |
0aacf84e MD |
5990 | else if (SCM_REALP (x)) |
5991 | { | |
e11e83f3 | 5992 | if (SCM_I_INUMP (y)) |
23d72566 KR |
5993 | { |
5994 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
5995 | if (scm_is_eq (y, SCM_INUM0)) | |
5996 | return y; | |
5997 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
5998 | } | |
0aacf84e MD |
5999 | else if (SCM_BIGP (y)) |
6000 | { | |
6001 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
6002 | scm_remember_upto_here_1 (y); | |
55f26379 | 6003 | return scm_from_double (result); |
0aacf84e MD |
6004 | } |
6005 | else if (SCM_REALP (y)) | |
55f26379 | 6006 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 6007 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6008 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 6009 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6010 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6011 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
6012 | else |
6013 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6014 | } |
0aacf84e MD |
6015 | else if (SCM_COMPLEXP (x)) |
6016 | { | |
e11e83f3 | 6017 | if (SCM_I_INUMP (y)) |
23d72566 KR |
6018 | { |
6019 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
6020 | if (scm_is_eq (y, SCM_INUM0)) | |
6021 | return y; | |
6022 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
6023 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
6024 | } | |
0aacf84e MD |
6025 | else if (SCM_BIGP (y)) |
6026 | { | |
6027 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6028 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6029 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 6030 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
6031 | } |
6032 | else if (SCM_REALP (y)) | |
8507ec80 | 6033 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
6034 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
6035 | else if (SCM_COMPLEXP (y)) | |
6036 | { | |
8507ec80 | 6037 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
6038 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
6039 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
6040 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
6041 | } | |
f92e85f7 MV |
6042 | else if (SCM_FRACTIONP (y)) |
6043 | { | |
6044 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6045 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
6046 | yy * SCM_COMPLEX_IMAG (x)); |
6047 | } | |
6048 | else | |
6049 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6050 | } | |
6051 | else if (SCM_FRACTIONP (x)) | |
6052 | { | |
e11e83f3 | 6053 | if (SCM_I_INUMP (y)) |
cba42c93 | 6054 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6055 | SCM_FRACTION_DENOMINATOR (x)); |
6056 | else if (SCM_BIGP (y)) | |
cba42c93 | 6057 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6058 | SCM_FRACTION_DENOMINATOR (x)); |
6059 | else if (SCM_REALP (y)) | |
55f26379 | 6060 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
6061 | else if (SCM_COMPLEXP (y)) |
6062 | { | |
6063 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 6064 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
6065 | xx * SCM_COMPLEX_IMAG (y)); |
6066 | } | |
6067 | else if (SCM_FRACTIONP (y)) | |
6068 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 6069 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6070 | SCM_FRACTION_NUMERATOR (y)), |
6071 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
6072 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
6073 | else |
6074 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6075 | } |
0aacf84e | 6076 | else |
f4c627b3 | 6077 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
6078 | } |
6079 | ||
7351e207 MV |
6080 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
6081 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
6082 | #define ALLOW_DIVIDE_BY_ZERO | |
6083 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
6084 | #endif | |
0f2d19dd | 6085 | |
ba74ef4e MV |
6086 | /* The code below for complex division is adapted from the GNU |
6087 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
6088 | this copyright: */ | |
6089 | ||
6090 | /**************************************************************** | |
6091 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
6092 | ||
6093 | Permission to use, copy, modify, and distribute this software | |
6094 | and its documentation for any purpose and without fee is hereby | |
6095 | granted, provided that the above copyright notice appear in all | |
6096 | copies and that both that the copyright notice and this | |
6097 | permission notice and warranty disclaimer appear in supporting | |
6098 | documentation, and that the names of AT&T Bell Laboratories or | |
6099 | Bellcore or any of their entities not be used in advertising or | |
6100 | publicity pertaining to distribution of the software without | |
6101 | specific, written prior permission. | |
6102 | ||
6103 | AT&T and Bellcore disclaim all warranties with regard to this | |
6104 | software, including all implied warranties of merchantability | |
6105 | and fitness. In no event shall AT&T or Bellcore be liable for | |
6106 | any special, indirect or consequential damages or any damages | |
6107 | whatsoever resulting from loss of use, data or profits, whether | |
6108 | in an action of contract, negligence or other tortious action, | |
6109 | arising out of or in connection with the use or performance of | |
6110 | this software. | |
6111 | ****************************************************************/ | |
6112 | ||
78d3deb1 AW |
6113 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
6114 | (SCM x, SCM y, SCM rest), | |
6115 | "Divide the first argument by the product of the remaining\n" | |
6116 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
6117 | "returned.") | |
6118 | #define FUNC_NAME s_scm_i_divide | |
6119 | { | |
6120 | while (!scm_is_null (rest)) | |
6121 | { x = scm_divide (x, y); | |
6122 | y = scm_car (rest); | |
6123 | rest = scm_cdr (rest); | |
6124 | } | |
6125 | return scm_divide (x, y); | |
6126 | } | |
6127 | #undef FUNC_NAME | |
6128 | ||
6129 | #define s_divide s_scm_i_divide | |
6130 | #define g_divide g_scm_i_divide | |
6131 | ||
f92e85f7 | 6132 | static SCM |
78d3deb1 AW |
6133 | do_divide (SCM x, SCM y, int inexact) |
6134 | #define FUNC_NAME s_divide | |
0f2d19dd | 6135 | { |
f8de44c1 DH |
6136 | double a; |
6137 | ||
9cc37597 | 6138 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
6139 | { |
6140 | if (SCM_UNBNDP (x)) | |
6141 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 6142 | else if (SCM_I_INUMP (x)) |
0aacf84e | 6143 | { |
e25f3727 | 6144 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
6145 | if (xx == 1 || xx == -1) |
6146 | return x; | |
7351e207 | 6147 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6148 | else if (xx == 0) |
6149 | scm_num_overflow (s_divide); | |
7351e207 | 6150 | #endif |
0aacf84e | 6151 | else |
f92e85f7 MV |
6152 | { |
6153 | if (inexact) | |
55f26379 | 6154 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 6155 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6156 | } |
0aacf84e MD |
6157 | } |
6158 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
6159 | { |
6160 | if (inexact) | |
55f26379 | 6161 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 6162 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6163 | } |
0aacf84e MD |
6164 | else if (SCM_REALP (x)) |
6165 | { | |
6166 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 6167 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6168 | if (xx == 0.0) |
6169 | scm_num_overflow (s_divide); | |
6170 | else | |
7351e207 | 6171 | #endif |
55f26379 | 6172 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
6173 | } |
6174 | else if (SCM_COMPLEXP (x)) | |
6175 | { | |
6176 | double r = SCM_COMPLEX_REAL (x); | |
6177 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 6178 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6179 | { |
6180 | double t = r / i; | |
6181 | double d = i * (1.0 + t * t); | |
8507ec80 | 6182 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
6183 | } |
6184 | else | |
6185 | { | |
6186 | double t = i / r; | |
6187 | double d = r * (1.0 + t * t); | |
8507ec80 | 6188 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
6189 | } |
6190 | } | |
f92e85f7 | 6191 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 6192 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 6193 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
6194 | else |
6195 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 6196 | } |
f8de44c1 | 6197 | |
9cc37597 | 6198 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 6199 | { |
e25f3727 | 6200 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 6201 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6202 | { |
e25f3727 | 6203 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6204 | if (yy == 0) |
6205 | { | |
7351e207 | 6206 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6207 | scm_num_overflow (s_divide); |
7351e207 | 6208 | #else |
55f26379 | 6209 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 6210 | #endif |
0aacf84e MD |
6211 | } |
6212 | else if (xx % yy != 0) | |
f92e85f7 MV |
6213 | { |
6214 | if (inexact) | |
55f26379 | 6215 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 6216 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6217 | } |
0aacf84e MD |
6218 | else |
6219 | { | |
e25f3727 | 6220 | scm_t_inum z = xx / yy; |
0aacf84e | 6221 | if (SCM_FIXABLE (z)) |
d956fa6f | 6222 | return SCM_I_MAKINUM (z); |
0aacf84e | 6223 | else |
e25f3727 | 6224 | return scm_i_inum2big (z); |
0aacf84e | 6225 | } |
f872b822 | 6226 | } |
0aacf84e | 6227 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
6228 | { |
6229 | if (inexact) | |
55f26379 | 6230 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 6231 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6232 | } |
0aacf84e MD |
6233 | else if (SCM_REALP (y)) |
6234 | { | |
6235 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6236 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6237 | if (yy == 0.0) |
6238 | scm_num_overflow (s_divide); | |
6239 | else | |
7351e207 | 6240 | #endif |
55f26379 | 6241 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 6242 | } |
0aacf84e MD |
6243 | else if (SCM_COMPLEXP (y)) |
6244 | { | |
6245 | a = xx; | |
6246 | complex_div: /* y _must_ be a complex number */ | |
6247 | { | |
6248 | double r = SCM_COMPLEX_REAL (y); | |
6249 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6250 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6251 | { |
6252 | double t = r / i; | |
6253 | double d = i * (1.0 + t * t); | |
8507ec80 | 6254 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
6255 | } |
6256 | else | |
6257 | { | |
6258 | double t = i / r; | |
6259 | double d = r * (1.0 + t * t); | |
8507ec80 | 6260 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
6261 | } |
6262 | } | |
6263 | } | |
f92e85f7 MV |
6264 | else if (SCM_FRACTIONP (y)) |
6265 | /* a / b/c = ac / b */ | |
cba42c93 | 6266 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6267 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6268 | else |
6269 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6270 | } |
0aacf84e MD |
6271 | else if (SCM_BIGP (x)) |
6272 | { | |
e11e83f3 | 6273 | if (SCM_I_INUMP (y)) |
0aacf84e | 6274 | { |
e25f3727 | 6275 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6276 | if (yy == 0) |
6277 | { | |
7351e207 | 6278 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6279 | scm_num_overflow (s_divide); |
7351e207 | 6280 | #else |
0aacf84e MD |
6281 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
6282 | scm_remember_upto_here_1 (x); | |
6283 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 6284 | #endif |
0aacf84e MD |
6285 | } |
6286 | else if (yy == 1) | |
6287 | return x; | |
6288 | else | |
6289 | { | |
6290 | /* FIXME: HMM, what are the relative performance issues here? | |
6291 | We need to test. Is it faster on average to test | |
6292 | divisible_p, then perform whichever operation, or is it | |
6293 | faster to perform the integer div opportunistically and | |
6294 | switch to real if there's a remainder? For now we take the | |
6295 | middle ground: test, then if divisible, use the faster div | |
6296 | func. */ | |
6297 | ||
e25f3727 | 6298 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
6299 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
6300 | ||
6301 | if (divisible_p) | |
6302 | { | |
6303 | SCM result = scm_i_mkbig (); | |
6304 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
6305 | scm_remember_upto_here_1 (x); | |
6306 | if (yy < 0) | |
6307 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
6308 | return scm_i_normbig (result); | |
6309 | } | |
6310 | else | |
f92e85f7 MV |
6311 | { |
6312 | if (inexact) | |
55f26379 | 6313 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 6314 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6315 | } |
0aacf84e MD |
6316 | } |
6317 | } | |
6318 | else if (SCM_BIGP (y)) | |
6319 | { | |
a4955a04 MW |
6320 | /* big_x / big_y */ |
6321 | if (inexact) | |
0aacf84e | 6322 | { |
a4955a04 MW |
6323 | /* It's easily possible for the ratio x/y to fit a double |
6324 | but one or both x and y be too big to fit a double, | |
6325 | hence the use of mpq_get_d rather than converting and | |
6326 | dividing. */ | |
6327 | mpq_t q; | |
6328 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
6329 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
6330 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
6331 | } |
6332 | else | |
6333 | { | |
a4955a04 MW |
6334 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
6335 | SCM_I_BIG_MPZ (y)); | |
6336 | if (divisible_p) | |
6337 | { | |
6338 | SCM result = scm_i_mkbig (); | |
6339 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
6340 | SCM_I_BIG_MPZ (x), | |
6341 | SCM_I_BIG_MPZ (y)); | |
6342 | scm_remember_upto_here_2 (x, y); | |
6343 | return scm_i_normbig (result); | |
6344 | } | |
6345 | else | |
6346 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
6347 | } |
6348 | } | |
6349 | else if (SCM_REALP (y)) | |
6350 | { | |
6351 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6352 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6353 | if (yy == 0.0) |
6354 | scm_num_overflow (s_divide); | |
6355 | else | |
7351e207 | 6356 | #endif |
55f26379 | 6357 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
6358 | } |
6359 | else if (SCM_COMPLEXP (y)) | |
6360 | { | |
6361 | a = scm_i_big2dbl (x); | |
6362 | goto complex_div; | |
6363 | } | |
f92e85f7 | 6364 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6365 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6366 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6367 | else |
6368 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6369 | } |
0aacf84e MD |
6370 | else if (SCM_REALP (x)) |
6371 | { | |
6372 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 6373 | if (SCM_I_INUMP (y)) |
0aacf84e | 6374 | { |
e25f3727 | 6375 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6376 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6377 | if (yy == 0) |
6378 | scm_num_overflow (s_divide); | |
6379 | else | |
7351e207 | 6380 | #endif |
55f26379 | 6381 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
6382 | } |
6383 | else if (SCM_BIGP (y)) | |
6384 | { | |
6385 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6386 | scm_remember_upto_here_1 (y); | |
55f26379 | 6387 | return scm_from_double (rx / dby); |
0aacf84e MD |
6388 | } |
6389 | else if (SCM_REALP (y)) | |
6390 | { | |
6391 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6392 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6393 | if (yy == 0.0) |
6394 | scm_num_overflow (s_divide); | |
6395 | else | |
7351e207 | 6396 | #endif |
55f26379 | 6397 | return scm_from_double (rx / yy); |
0aacf84e MD |
6398 | } |
6399 | else if (SCM_COMPLEXP (y)) | |
6400 | { | |
6401 | a = rx; | |
6402 | goto complex_div; | |
6403 | } | |
f92e85f7 | 6404 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6405 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
6406 | else |
6407 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6408 | } |
0aacf84e MD |
6409 | else if (SCM_COMPLEXP (x)) |
6410 | { | |
6411 | double rx = SCM_COMPLEX_REAL (x); | |
6412 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 6413 | if (SCM_I_INUMP (y)) |
0aacf84e | 6414 | { |
e25f3727 | 6415 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6416 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6417 | if (yy == 0) |
6418 | scm_num_overflow (s_divide); | |
6419 | else | |
7351e207 | 6420 | #endif |
0aacf84e MD |
6421 | { |
6422 | double d = yy; | |
8507ec80 | 6423 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
6424 | } |
6425 | } | |
6426 | else if (SCM_BIGP (y)) | |
6427 | { | |
6428 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6429 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6430 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
6431 | } |
6432 | else if (SCM_REALP (y)) | |
6433 | { | |
6434 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6435 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6436 | if (yy == 0.0) |
6437 | scm_num_overflow (s_divide); | |
6438 | else | |
7351e207 | 6439 | #endif |
8507ec80 | 6440 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
6441 | } |
6442 | else if (SCM_COMPLEXP (y)) | |
6443 | { | |
6444 | double ry = SCM_COMPLEX_REAL (y); | |
6445 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6446 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
6447 | { |
6448 | double t = ry / iy; | |
6449 | double d = iy * (1.0 + t * t); | |
8507ec80 | 6450 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
6451 | } |
6452 | else | |
6453 | { | |
6454 | double t = iy / ry; | |
6455 | double d = ry * (1.0 + t * t); | |
8507ec80 | 6456 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
6457 | } |
6458 | } | |
f92e85f7 MV |
6459 | else if (SCM_FRACTIONP (y)) |
6460 | { | |
6461 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6462 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 6463 | } |
0aacf84e MD |
6464 | else |
6465 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6466 | } |
f92e85f7 MV |
6467 | else if (SCM_FRACTIONP (x)) |
6468 | { | |
e11e83f3 | 6469 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6470 | { |
e25f3727 | 6471 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
6472 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
6473 | if (yy == 0) | |
6474 | scm_num_overflow (s_divide); | |
6475 | else | |
6476 | #endif | |
cba42c93 | 6477 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6478 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6479 | } | |
6480 | else if (SCM_BIGP (y)) | |
6481 | { | |
cba42c93 | 6482 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6483 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6484 | } | |
6485 | else if (SCM_REALP (y)) | |
6486 | { | |
6487 | double yy = SCM_REAL_VALUE (y); | |
6488 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6489 | if (yy == 0.0) | |
6490 | scm_num_overflow (s_divide); | |
6491 | else | |
6492 | #endif | |
55f26379 | 6493 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
6494 | } |
6495 | else if (SCM_COMPLEXP (y)) | |
6496 | { | |
6497 | a = scm_i_fraction2double (x); | |
6498 | goto complex_div; | |
6499 | } | |
6500 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 6501 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
6502 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
6503 | else | |
6504 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
6505 | } | |
0aacf84e | 6506 | else |
f8de44c1 | 6507 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 6508 | } |
f92e85f7 MV |
6509 | |
6510 | SCM | |
6511 | scm_divide (SCM x, SCM y) | |
6512 | { | |
78d3deb1 | 6513 | return do_divide (x, y, 0); |
f92e85f7 MV |
6514 | } |
6515 | ||
6516 | static SCM scm_divide2real (SCM x, SCM y) | |
6517 | { | |
78d3deb1 | 6518 | return do_divide (x, y, 1); |
f92e85f7 | 6519 | } |
c05e97b7 | 6520 | #undef FUNC_NAME |
0f2d19dd | 6521 | |
fa605590 | 6522 | |
0f2d19dd | 6523 | double |
3101f40f | 6524 | scm_c_truncate (double x) |
0f2d19dd | 6525 | { |
fa605590 KR |
6526 | #if HAVE_TRUNC |
6527 | return trunc (x); | |
6528 | #else | |
f872b822 MD |
6529 | if (x < 0.0) |
6530 | return -floor (-x); | |
6531 | return floor (x); | |
fa605590 | 6532 | #endif |
0f2d19dd | 6533 | } |
0f2d19dd | 6534 | |
3101f40f MV |
6535 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
6536 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
6537 | Then half-way cases are identified and adjusted down if the | |
6538 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
6539 | |
6540 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
6541 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
6542 | ||
6543 | An odd "result" value is identified with result/2 != floor(result/2). | |
6544 | This is done with plus_half, since that value is ready for use sooner in | |
6545 | a pipelined cpu, and we're already requiring plus_half == result. | |
6546 | ||
6547 | Note however that we need to be careful when x is big and already an | |
6548 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
6549 | us to return such a value, incorrectly. For instance if the hardware is | |
6550 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
6551 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
6552 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
6553 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
6554 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
6555 | ||
6556 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
6557 | x is already an integer. If it is then clearly that's the desired result | |
6558 | already. And if it's not then the exponent must be small enough to allow | |
6559 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
6560 | ||
0f2d19dd | 6561 | double |
3101f40f | 6562 | scm_c_round (double x) |
0f2d19dd | 6563 | { |
6187f48b KR |
6564 | double plus_half, result; |
6565 | ||
6566 | if (x == floor (x)) | |
6567 | return x; | |
6568 | ||
6569 | plus_half = x + 0.5; | |
6570 | result = floor (plus_half); | |
3101f40f | 6571 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
6572 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
6573 | ? result - 1 | |
6574 | : result); | |
0f2d19dd JB |
6575 | } |
6576 | ||
f92e85f7 MV |
6577 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
6578 | (SCM x), | |
6579 | "Round the number @var{x} towards zero.") | |
6580 | #define FUNC_NAME s_scm_truncate_number | |
6581 | { | |
73e4de09 | 6582 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6583 | return scm_floor (x); |
6584 | else | |
6585 | return scm_ceiling (x); | |
6586 | } | |
6587 | #undef FUNC_NAME | |
6588 | ||
f92e85f7 MV |
6589 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, |
6590 | (SCM x), | |
6591 | "Round the number @var{x} towards the nearest integer. " | |
6592 | "When it is exactly halfway between two integers, " | |
6593 | "round towards the even one.") | |
6594 | #define FUNC_NAME s_scm_round_number | |
6595 | { | |
e11e83f3 | 6596 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
6597 | return x; |
6598 | else if (SCM_REALP (x)) | |
3101f40f | 6599 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 6600 | else |
bae30667 KR |
6601 | { |
6602 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
6603 | single quotient+remainder division then examining to see which way | |
6604 | the rounding should go. */ | |
6605 | SCM plus_half = scm_sum (x, exactly_one_half); | |
6606 | SCM result = scm_floor (plus_half); | |
3101f40f | 6607 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
6608 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
6609 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 6610 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
6611 | else |
6612 | return result; | |
6613 | } | |
f92e85f7 MV |
6614 | } |
6615 | #undef FUNC_NAME | |
6616 | ||
6617 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
6618 | (SCM x), | |
6619 | "Round the number @var{x} towards minus infinity.") | |
6620 | #define FUNC_NAME s_scm_floor | |
6621 | { | |
e11e83f3 | 6622 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6623 | return x; |
6624 | else if (SCM_REALP (x)) | |
55f26379 | 6625 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6626 | else if (SCM_FRACTIONP (x)) |
6627 | { | |
6628 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6629 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6630 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6631 | { |
6632 | /* For positive x, rounding towards zero is correct. */ | |
6633 | return q; | |
6634 | } | |
6635 | else | |
6636 | { | |
6637 | /* For negative x, we need to return q-1 unless x is an | |
6638 | integer. But fractions are never integer, per our | |
6639 | assumptions. */ | |
cff5fa33 | 6640 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
6641 | } |
6642 | } | |
6643 | else | |
6644 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
6645 | } | |
6646 | #undef FUNC_NAME | |
6647 | ||
6648 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
6649 | (SCM x), | |
6650 | "Round the number @var{x} towards infinity.") | |
6651 | #define FUNC_NAME s_scm_ceiling | |
6652 | { | |
e11e83f3 | 6653 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6654 | return x; |
6655 | else if (SCM_REALP (x)) | |
55f26379 | 6656 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6657 | else if (SCM_FRACTIONP (x)) |
6658 | { | |
6659 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6660 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6661 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
6662 | { |
6663 | /* For negative x, rounding towards zero is correct. */ | |
6664 | return q; | |
6665 | } | |
6666 | else | |
6667 | { | |
6668 | /* For positive x, we need to return q+1 unless x is an | |
6669 | integer. But fractions are never integer, per our | |
6670 | assumptions. */ | |
cff5fa33 | 6671 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
6672 | } |
6673 | } | |
6674 | else | |
6675 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
6676 | } | |
6677 | #undef FUNC_NAME | |
0f2d19dd | 6678 | |
ad79736c AW |
6679 | /* sin/cos/tan/asin/acos/atan |
6680 | sinh/cosh/tanh/asinh/acosh/atanh | |
6681 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
6682 | Written by Jerry D. Hedden, (C) FSF. | |
6683 | See the file `COPYING' for terms applying to this program. */ | |
0f2d19dd | 6684 | |
2519490c MW |
6685 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
6686 | (SCM x, SCM y), | |
6687 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 6688 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 6689 | { |
01c7284a MW |
6690 | if (scm_is_integer (y)) |
6691 | { | |
6692 | if (scm_is_true (scm_exact_p (y))) | |
6693 | return scm_integer_expt (x, y); | |
6694 | else | |
6695 | { | |
6696 | /* Here we handle the case where the exponent is an inexact | |
6697 | integer. We make the exponent exact in order to use | |
6698 | scm_integer_expt, and thus avoid the spurious imaginary | |
6699 | parts that may result from round-off errors in the general | |
6700 | e^(y log x) method below (for example when squaring a large | |
6701 | negative number). In this case, we must return an inexact | |
6702 | result for correctness. We also make the base inexact so | |
6703 | that scm_integer_expt will use fast inexact arithmetic | |
6704 | internally. Note that making the base inexact is not | |
6705 | sufficient to guarantee an inexact result, because | |
6706 | scm_integer_expt will return an exact 1 when the exponent | |
6707 | is 0, even if the base is inexact. */ | |
6708 | return scm_exact_to_inexact | |
6709 | (scm_integer_expt (scm_exact_to_inexact (x), | |
6710 | scm_inexact_to_exact (y))); | |
6711 | } | |
6712 | } | |
6fc4d012 AW |
6713 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
6714 | { | |
6715 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
6716 | } | |
2519490c | 6717 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 6718 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
6719 | else if (scm_is_complex (x)) |
6720 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
6721 | else | |
6722 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 6723 | } |
1bbd0b84 | 6724 | #undef FUNC_NAME |
0f2d19dd | 6725 | |
ad79736c AW |
6726 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
6727 | (SCM z), | |
6728 | "Compute the sine of @var{z}.") | |
6729 | #define FUNC_NAME s_scm_sin | |
6730 | { | |
6731 | if (scm_is_real (z)) | |
6732 | return scm_from_double (sin (scm_to_double (z))); | |
6733 | else if (SCM_COMPLEXP (z)) | |
6734 | { double x, y; | |
6735 | x = SCM_COMPLEX_REAL (z); | |
6736 | y = SCM_COMPLEX_IMAG (z); | |
6737 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
6738 | cos (x) * sinh (y)); | |
6739 | } | |
6740 | else | |
6741 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
6742 | } | |
6743 | #undef FUNC_NAME | |
0f2d19dd | 6744 | |
ad79736c AW |
6745 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
6746 | (SCM z), | |
6747 | "Compute the cosine of @var{z}.") | |
6748 | #define FUNC_NAME s_scm_cos | |
6749 | { | |
6750 | if (scm_is_real (z)) | |
6751 | return scm_from_double (cos (scm_to_double (z))); | |
6752 | else if (SCM_COMPLEXP (z)) | |
6753 | { double x, y; | |
6754 | x = SCM_COMPLEX_REAL (z); | |
6755 | y = SCM_COMPLEX_IMAG (z); | |
6756 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
6757 | -sin (x) * sinh (y)); | |
6758 | } | |
6759 | else | |
6760 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
6761 | } | |
6762 | #undef FUNC_NAME | |
6763 | ||
6764 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
6765 | (SCM z), | |
6766 | "Compute the tangent of @var{z}.") | |
6767 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 6768 | { |
ad79736c AW |
6769 | if (scm_is_real (z)) |
6770 | return scm_from_double (tan (scm_to_double (z))); | |
6771 | else if (SCM_COMPLEXP (z)) | |
6772 | { double x, y, w; | |
6773 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6774 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6775 | w = cos (x) + cosh (y); | |
6776 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6777 | if (w == 0.0) | |
6778 | scm_num_overflow (s_scm_tan); | |
6779 | #endif | |
6780 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
6781 | } | |
6782 | else | |
6783 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
6784 | } | |
6785 | #undef FUNC_NAME | |
6786 | ||
6787 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
6788 | (SCM z), | |
6789 | "Compute the hyperbolic sine of @var{z}.") | |
6790 | #define FUNC_NAME s_scm_sinh | |
6791 | { | |
6792 | if (scm_is_real (z)) | |
6793 | return scm_from_double (sinh (scm_to_double (z))); | |
6794 | else if (SCM_COMPLEXP (z)) | |
6795 | { double x, y; | |
6796 | x = SCM_COMPLEX_REAL (z); | |
6797 | y = SCM_COMPLEX_IMAG (z); | |
6798 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
6799 | cosh (x) * sin (y)); | |
6800 | } | |
6801 | else | |
6802 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
6803 | } | |
6804 | #undef FUNC_NAME | |
6805 | ||
6806 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
6807 | (SCM z), | |
6808 | "Compute the hyperbolic cosine of @var{z}.") | |
6809 | #define FUNC_NAME s_scm_cosh | |
6810 | { | |
6811 | if (scm_is_real (z)) | |
6812 | return scm_from_double (cosh (scm_to_double (z))); | |
6813 | else if (SCM_COMPLEXP (z)) | |
6814 | { double x, y; | |
6815 | x = SCM_COMPLEX_REAL (z); | |
6816 | y = SCM_COMPLEX_IMAG (z); | |
6817 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
6818 | sinh (x) * sin (y)); | |
6819 | } | |
6820 | else | |
6821 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
6822 | } | |
6823 | #undef FUNC_NAME | |
6824 | ||
6825 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
6826 | (SCM z), | |
6827 | "Compute the hyperbolic tangent of @var{z}.") | |
6828 | #define FUNC_NAME s_scm_tanh | |
6829 | { | |
6830 | if (scm_is_real (z)) | |
6831 | return scm_from_double (tanh (scm_to_double (z))); | |
6832 | else if (SCM_COMPLEXP (z)) | |
6833 | { double x, y, w; | |
6834 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6835 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6836 | w = cosh (x) + cos (y); | |
6837 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6838 | if (w == 0.0) | |
6839 | scm_num_overflow (s_scm_tanh); | |
6840 | #endif | |
6841 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
6842 | } | |
6843 | else | |
6844 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
6845 | } | |
6846 | #undef FUNC_NAME | |
6847 | ||
6848 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
6849 | (SCM z), | |
6850 | "Compute the arc sine of @var{z}.") | |
6851 | #define FUNC_NAME s_scm_asin | |
6852 | { | |
6853 | if (scm_is_real (z)) | |
6854 | { | |
6855 | double w = scm_to_double (z); | |
6856 | if (w >= -1.0 && w <= 1.0) | |
6857 | return scm_from_double (asin (w)); | |
6858 | else | |
6859 | return scm_product (scm_c_make_rectangular (0, -1), | |
6860 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
6861 | } | |
6862 | else if (SCM_COMPLEXP (z)) | |
6863 | { double x, y; | |
6864 | x = SCM_COMPLEX_REAL (z); | |
6865 | y = SCM_COMPLEX_IMAG (z); | |
6866 | return scm_product (scm_c_make_rectangular (0, -1), | |
6867 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
6868 | } | |
6869 | else | |
6870 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
6871 | } | |
6872 | #undef FUNC_NAME | |
6873 | ||
6874 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
6875 | (SCM z), | |
6876 | "Compute the arc cosine of @var{z}.") | |
6877 | #define FUNC_NAME s_scm_acos | |
6878 | { | |
6879 | if (scm_is_real (z)) | |
6880 | { | |
6881 | double w = scm_to_double (z); | |
6882 | if (w >= -1.0 && w <= 1.0) | |
6883 | return scm_from_double (acos (w)); | |
6884 | else | |
6885 | return scm_sum (scm_from_double (acos (0.0)), | |
6886 | scm_product (scm_c_make_rectangular (0, 1), | |
6887 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
6888 | } | |
6889 | else if (SCM_COMPLEXP (z)) | |
6890 | { double x, y; | |
6891 | x = SCM_COMPLEX_REAL (z); | |
6892 | y = SCM_COMPLEX_IMAG (z); | |
6893 | return scm_sum (scm_from_double (acos (0.0)), | |
6894 | scm_product (scm_c_make_rectangular (0, 1), | |
6895 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
6896 | } | |
6897 | else | |
6898 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
6899 | } | |
6900 | #undef FUNC_NAME | |
6901 | ||
6902 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
6903 | (SCM z, SCM y), | |
6904 | "With one argument, compute the arc tangent of @var{z}.\n" | |
6905 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
6906 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
6907 | #define FUNC_NAME s_scm_atan | |
6908 | { | |
6909 | if (SCM_UNBNDP (y)) | |
6910 | { | |
6911 | if (scm_is_real (z)) | |
6912 | return scm_from_double (atan (scm_to_double (z))); | |
6913 | else if (SCM_COMPLEXP (z)) | |
6914 | { | |
6915 | double v, w; | |
6916 | v = SCM_COMPLEX_REAL (z); | |
6917 | w = SCM_COMPLEX_IMAG (z); | |
6918 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
6919 | scm_c_make_rectangular (v, w + 1.0))), | |
6920 | scm_c_make_rectangular (0, 2)); | |
6921 | } | |
6922 | else | |
6923 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
6924 | } | |
6925 | else if (scm_is_real (z)) | |
6926 | { | |
6927 | if (scm_is_real (y)) | |
6928 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
6929 | else | |
6930 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
6931 | } | |
6932 | else | |
6933 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
6934 | } | |
6935 | #undef FUNC_NAME | |
6936 | ||
6937 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
6938 | (SCM z), | |
6939 | "Compute the inverse hyperbolic sine of @var{z}.") | |
6940 | #define FUNC_NAME s_scm_sys_asinh | |
6941 | { | |
6942 | if (scm_is_real (z)) | |
6943 | return scm_from_double (asinh (scm_to_double (z))); | |
6944 | else if (scm_is_number (z)) | |
6945 | return scm_log (scm_sum (z, | |
6946 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 6947 | SCM_INUM1)))); |
ad79736c AW |
6948 | else |
6949 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
6950 | } | |
6951 | #undef FUNC_NAME | |
6952 | ||
6953 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
6954 | (SCM z), | |
6955 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
6956 | #define FUNC_NAME s_scm_sys_acosh | |
6957 | { | |
6958 | if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
6959 | return scm_from_double (acosh (scm_to_double (z))); | |
6960 | else if (scm_is_number (z)) | |
6961 | return scm_log (scm_sum (z, | |
6962 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 6963 | SCM_INUM1)))); |
ad79736c AW |
6964 | else |
6965 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
6966 | } | |
6967 | #undef FUNC_NAME | |
6968 | ||
6969 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
6970 | (SCM z), | |
6971 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
6972 | #define FUNC_NAME s_scm_sys_atanh | |
6973 | { | |
6974 | if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
6975 | return scm_from_double (atanh (scm_to_double (z))); | |
6976 | else if (scm_is_number (z)) | |
cff5fa33 MW |
6977 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
6978 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
6979 | SCM_I_MAKINUM (2)); |
6980 | else | |
6981 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 6982 | } |
1bbd0b84 | 6983 | #undef FUNC_NAME |
0f2d19dd | 6984 | |
8507ec80 MV |
6985 | SCM |
6986 | scm_c_make_rectangular (double re, double im) | |
6987 | { | |
6988 | if (im == 0.0) | |
6989 | return scm_from_double (re); | |
6990 | else | |
6991 | { | |
6992 | SCM z; | |
03604fcf LC |
6993 | |
6994 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
92d8fd32 | 6995 | "complex")); |
03604fcf | 6996 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
8507ec80 MV |
6997 | SCM_COMPLEX_REAL (z) = re; |
6998 | SCM_COMPLEX_IMAG (z) = im; | |
6999 | return z; | |
7000 | } | |
7001 | } | |
0f2d19dd | 7002 | |
a1ec6916 | 7003 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
7004 | (SCM real_part, SCM imaginary_part), |
7005 | "Return a complex number constructed of the given @var{real-part} " | |
7006 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 7007 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 7008 | { |
ad79736c AW |
7009 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
7010 | SCM_ARG1, FUNC_NAME, "real"); | |
7011 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
7012 | SCM_ARG2, FUNC_NAME, "real"); | |
7013 | return scm_c_make_rectangular (scm_to_double (real_part), | |
7014 | scm_to_double (imaginary_part)); | |
0f2d19dd | 7015 | } |
1bbd0b84 | 7016 | #undef FUNC_NAME |
0f2d19dd | 7017 | |
8507ec80 MV |
7018 | SCM |
7019 | scm_c_make_polar (double mag, double ang) | |
7020 | { | |
7021 | double s, c; | |
5e647d08 LC |
7022 | |
7023 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
7024 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
7025 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
7026 | details. */ | |
7027 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
7028 | sincos (ang, &s, &c); |
7029 | #else | |
7030 | s = sin (ang); | |
7031 | c = cos (ang); | |
7032 | #endif | |
7033 | return scm_c_make_rectangular (mag * c, mag * s); | |
7034 | } | |
0f2d19dd | 7035 | |
a1ec6916 | 7036 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 7037 | (SCM x, SCM y), |
942e5b91 | 7038 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 7039 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 7040 | { |
ad79736c AW |
7041 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7042 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
7043 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 7044 | } |
1bbd0b84 | 7045 | #undef FUNC_NAME |
0f2d19dd JB |
7046 | |
7047 | ||
2519490c MW |
7048 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
7049 | (SCM z), | |
7050 | "Return the real part of the number @var{z}.") | |
7051 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 7052 | { |
2519490c | 7053 | if (SCM_COMPLEXP (z)) |
55f26379 | 7054 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 7055 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 7056 | return z; |
0aacf84e | 7057 | else |
2519490c | 7058 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 7059 | } |
2519490c | 7060 | #undef FUNC_NAME |
0f2d19dd JB |
7061 | |
7062 | ||
2519490c MW |
7063 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
7064 | (SCM z), | |
7065 | "Return the imaginary part of the number @var{z}.") | |
7066 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 7067 | { |
2519490c MW |
7068 | if (SCM_COMPLEXP (z)) |
7069 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
0aacf84e | 7070 | else if (SCM_REALP (z)) |
e7efe8e7 | 7071 | return flo0; |
2519490c | 7072 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 7073 | return SCM_INUM0; |
0aacf84e | 7074 | else |
2519490c | 7075 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 7076 | } |
2519490c | 7077 | #undef FUNC_NAME |
0f2d19dd | 7078 | |
2519490c MW |
7079 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
7080 | (SCM z), | |
7081 | "Return the numerator of the number @var{z}.") | |
7082 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 7083 | { |
2519490c | 7084 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
7085 | return z; |
7086 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 7087 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
7088 | else if (SCM_REALP (z)) |
7089 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
7090 | else | |
2519490c | 7091 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 7092 | } |
2519490c | 7093 | #undef FUNC_NAME |
f92e85f7 MV |
7094 | |
7095 | ||
2519490c MW |
7096 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
7097 | (SCM z), | |
7098 | "Return the denominator of the number @var{z}.") | |
7099 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 7100 | { |
2519490c | 7101 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 7102 | return SCM_INUM1; |
f92e85f7 | 7103 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 7104 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
7105 | else if (SCM_REALP (z)) |
7106 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
7107 | else | |
2519490c | 7108 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 7109 | } |
2519490c | 7110 | #undef FUNC_NAME |
0f2d19dd | 7111 | |
2519490c MW |
7112 | |
7113 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
7114 | (SCM z), | |
7115 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
7116 | "@code{abs} for real arguments, but also allows complex numbers.") | |
7117 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 7118 | { |
e11e83f3 | 7119 | if (SCM_I_INUMP (z)) |
0aacf84e | 7120 | { |
e25f3727 | 7121 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
7122 | if (zz >= 0) |
7123 | return z; | |
7124 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 7125 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 7126 | else |
e25f3727 | 7127 | return scm_i_inum2big (-zz); |
5986c47d | 7128 | } |
0aacf84e MD |
7129 | else if (SCM_BIGP (z)) |
7130 | { | |
7131 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7132 | scm_remember_upto_here_1 (z); | |
7133 | if (sgn < 0) | |
7134 | return scm_i_clonebig (z, 0); | |
7135 | else | |
7136 | return z; | |
5986c47d | 7137 | } |
0aacf84e | 7138 | else if (SCM_REALP (z)) |
55f26379 | 7139 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 7140 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7141 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
7142 | else if (SCM_FRACTIONP (z)) |
7143 | { | |
73e4de09 | 7144 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 7145 | return z; |
cba42c93 | 7146 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
7147 | SCM_FRACTION_DENOMINATOR (z)); |
7148 | } | |
0aacf84e | 7149 | else |
2519490c | 7150 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 7151 | } |
2519490c | 7152 | #undef FUNC_NAME |
0f2d19dd JB |
7153 | |
7154 | ||
2519490c MW |
7155 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
7156 | (SCM z), | |
7157 | "Return the angle of the complex number @var{z}.") | |
7158 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 7159 | { |
c8ae173e | 7160 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 7161 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
7162 | But if atan2 follows the floating point rounding mode, then the value |
7163 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 7164 | if (SCM_I_INUMP (z)) |
0aacf84e | 7165 | { |
e11e83f3 | 7166 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 7167 | return flo0; |
0aacf84e | 7168 | else |
55f26379 | 7169 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 7170 | } |
0aacf84e MD |
7171 | else if (SCM_BIGP (z)) |
7172 | { | |
7173 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7174 | scm_remember_upto_here_1 (z); | |
7175 | if (sgn < 0) | |
55f26379 | 7176 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 7177 | else |
e7efe8e7 | 7178 | return flo0; |
0f2d19dd | 7179 | } |
0aacf84e | 7180 | else if (SCM_REALP (z)) |
c8ae173e KR |
7181 | { |
7182 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 7183 | return flo0; |
c8ae173e | 7184 | else |
55f26379 | 7185 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 7186 | } |
0aacf84e | 7187 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7188 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
7189 | else if (SCM_FRACTIONP (z)) |
7190 | { | |
73e4de09 | 7191 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 7192 | return flo0; |
55f26379 | 7193 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 7194 | } |
0aacf84e | 7195 | else |
2519490c | 7196 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 7197 | } |
2519490c | 7198 | #undef FUNC_NAME |
0f2d19dd JB |
7199 | |
7200 | ||
2519490c MW |
7201 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
7202 | (SCM z), | |
7203 | "Convert the number @var{z} to its inexact representation.\n") | |
7204 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 7205 | { |
e11e83f3 | 7206 | if (SCM_I_INUMP (z)) |
55f26379 | 7207 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 7208 | else if (SCM_BIGP (z)) |
55f26379 | 7209 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 7210 | else if (SCM_FRACTIONP (z)) |
55f26379 | 7211 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
7212 | else if (SCM_INEXACTP (z)) |
7213 | return z; | |
7214 | else | |
2519490c | 7215 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 7216 | } |
2519490c | 7217 | #undef FUNC_NAME |
3c9a524f DH |
7218 | |
7219 | ||
2519490c MW |
7220 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
7221 | (SCM z), | |
7222 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 7223 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 7224 | { |
2519490c | 7225 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f872b822 | 7226 | return z; |
0aacf84e MD |
7227 | else if (SCM_REALP (z)) |
7228 | { | |
2519490c | 7229 | if (!DOUBLE_IS_FINITE (SCM_REAL_VALUE (z))) |
f92e85f7 | 7230 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 7231 | else |
f92e85f7 MV |
7232 | { |
7233 | mpq_t frac; | |
7234 | SCM q; | |
7235 | ||
7236 | mpq_init (frac); | |
7237 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 7238 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
7239 | scm_i_mpz2num (mpq_denref (frac))); |
7240 | ||
cba42c93 | 7241 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
7242 | for frac... |
7243 | */ | |
7244 | mpq_clear (frac); | |
7245 | return q; | |
7246 | } | |
c2ff8ab0 | 7247 | } |
f92e85f7 MV |
7248 | else if (SCM_FRACTIONP (z)) |
7249 | return z; | |
0aacf84e | 7250 | else |
2519490c | 7251 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); |
0f2d19dd | 7252 | } |
1bbd0b84 | 7253 | #undef FUNC_NAME |
0f2d19dd | 7254 | |
f92e85f7 | 7255 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
7256 | (SCM x, SCM eps), |
7257 | "Returns the @emph{simplest} rational number differing\n" | |
7258 | "from @var{x} by no more than @var{eps}.\n" | |
7259 | "\n" | |
7260 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
7261 | "exact result when both its arguments are exact. Thus, you might need\n" | |
7262 | "to use @code{inexact->exact} on the arguments.\n" | |
7263 | "\n" | |
7264 | "@lisp\n" | |
7265 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
7266 | "@result{} 6/5\n" | |
7267 | "@end lisp") | |
f92e85f7 MV |
7268 | #define FUNC_NAME s_scm_rationalize |
7269 | { | |
605f6980 MW |
7270 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7271 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
7272 | eps = scm_abs (eps); | |
7273 | if (scm_is_false (scm_positive_p (eps))) | |
7274 | { | |
7275 | /* eps is either zero or a NaN */ | |
7276 | if (scm_is_true (scm_nan_p (eps))) | |
7277 | return scm_nan (); | |
7278 | else if (SCM_INEXACTP (eps)) | |
7279 | return scm_exact_to_inexact (x); | |
7280 | else | |
7281 | return x; | |
7282 | } | |
7283 | else if (scm_is_false (scm_finite_p (eps))) | |
7284 | { | |
7285 | if (scm_is_true (scm_finite_p (x))) | |
7286 | return flo0; | |
7287 | else | |
7288 | return scm_nan (); | |
7289 | } | |
7290 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 7291 | return x; |
605f6980 MW |
7292 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
7293 | scm_ceiling (scm_difference (x, eps))))) | |
7294 | { | |
7295 | /* There's an integer within range; we want the one closest to zero */ | |
7296 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
7297 | { | |
7298 | /* zero is within range */ | |
7299 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
7300 | return flo0; | |
7301 | else | |
7302 | return SCM_INUM0; | |
7303 | } | |
7304 | else if (scm_is_true (scm_positive_p (x))) | |
7305 | return scm_ceiling (scm_difference (x, eps)); | |
7306 | else | |
7307 | return scm_floor (scm_sum (x, eps)); | |
7308 | } | |
7309 | else | |
f92e85f7 MV |
7310 | { |
7311 | /* Use continued fractions to find closest ratio. All | |
7312 | arithmetic is done with exact numbers. | |
7313 | */ | |
7314 | ||
7315 | SCM ex = scm_inexact_to_exact (x); | |
7316 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
7317 | SCM tt = SCM_INUM1; |
7318 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
7319 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
7320 | SCM rx; |
7321 | int i = 0; | |
7322 | ||
f92e85f7 MV |
7323 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
7324 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
7325 | ||
7326 | /* We stop after a million iterations just to be absolutely sure | |
7327 | that we don't go into an infinite loop. The process normally | |
7328 | converges after less than a dozen iterations. | |
7329 | */ | |
7330 | ||
f92e85f7 MV |
7331 | while (++i < 1000000) |
7332 | { | |
7333 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
7334 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
7335 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
7336 | scm_is_false | |
f92e85f7 | 7337 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 7338 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
7339 | { |
7340 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 7341 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
7342 | return scm_exact_to_inexact (res); |
7343 | else | |
7344 | return res; | |
7345 | } | |
f92e85f7 MV |
7346 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
7347 | SCM_UNDEFINED); | |
7348 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
7349 | a2 = a1; | |
7350 | b2 = b1; | |
7351 | a1 = a; | |
7352 | b1 = b; | |
7353 | } | |
7354 | scm_num_overflow (s_scm_rationalize); | |
7355 | } | |
f92e85f7 MV |
7356 | } |
7357 | #undef FUNC_NAME | |
7358 | ||
73e4de09 MV |
7359 | /* conversion functions */ |
7360 | ||
7361 | int | |
7362 | scm_is_integer (SCM val) | |
7363 | { | |
7364 | return scm_is_true (scm_integer_p (val)); | |
7365 | } | |
7366 | ||
7367 | int | |
7368 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
7369 | { | |
e11e83f3 | 7370 | if (SCM_I_INUMP (val)) |
73e4de09 | 7371 | { |
e11e83f3 | 7372 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7373 | return n >= min && n <= max; |
7374 | } | |
7375 | else if (SCM_BIGP (val)) | |
7376 | { | |
7377 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
7378 | return 0; | |
7379 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
7380 | { |
7381 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
7382 | { | |
7383 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
7384 | return n >= min && n <= max; | |
7385 | } | |
7386 | else | |
7387 | return 0; | |
7388 | } | |
73e4de09 MV |
7389 | else |
7390 | { | |
d956fa6f MV |
7391 | scm_t_intmax n; |
7392 | size_t count; | |
73e4de09 | 7393 | |
d956fa6f MV |
7394 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7395 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
7396 | return 0; | |
7397 | ||
7398 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7399 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7400 | |
d956fa6f | 7401 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 7402 | { |
d956fa6f MV |
7403 | if (n < 0) |
7404 | return 0; | |
73e4de09 | 7405 | } |
73e4de09 MV |
7406 | else |
7407 | { | |
d956fa6f MV |
7408 | n = -n; |
7409 | if (n >= 0) | |
7410 | return 0; | |
73e4de09 | 7411 | } |
d956fa6f MV |
7412 | |
7413 | return n >= min && n <= max; | |
73e4de09 MV |
7414 | } |
7415 | } | |
73e4de09 MV |
7416 | else |
7417 | return 0; | |
7418 | } | |
7419 | ||
7420 | int | |
7421 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
7422 | { | |
e11e83f3 | 7423 | if (SCM_I_INUMP (val)) |
73e4de09 | 7424 | { |
e11e83f3 | 7425 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7426 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
7427 | } | |
7428 | else if (SCM_BIGP (val)) | |
7429 | { | |
7430 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
7431 | return 0; | |
7432 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
7433 | { |
7434 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
7435 | { | |
7436 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
7437 | return n >= min && n <= max; | |
7438 | } | |
7439 | else | |
7440 | return 0; | |
7441 | } | |
73e4de09 MV |
7442 | else |
7443 | { | |
d956fa6f MV |
7444 | scm_t_uintmax n; |
7445 | size_t count; | |
73e4de09 | 7446 | |
d956fa6f MV |
7447 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
7448 | return 0; | |
73e4de09 | 7449 | |
d956fa6f MV |
7450 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7451 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 7452 | return 0; |
d956fa6f MV |
7453 | |
7454 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7455 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7456 | |
d956fa6f | 7457 | return n >= min && n <= max; |
73e4de09 MV |
7458 | } |
7459 | } | |
73e4de09 MV |
7460 | else |
7461 | return 0; | |
7462 | } | |
7463 | ||
1713d319 MV |
7464 | static void |
7465 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
7466 | { | |
7467 | scm_error (scm_out_of_range_key, | |
7468 | NULL, | |
7469 | "Value out of range ~S to ~S: ~S", | |
7470 | scm_list_3 (min, max, bad_val), | |
7471 | scm_list_1 (bad_val)); | |
7472 | } | |
7473 | ||
bfd7932e MV |
7474 | #define TYPE scm_t_intmax |
7475 | #define TYPE_MIN min | |
7476 | #define TYPE_MAX max | |
7477 | #define SIZEOF_TYPE 0 | |
7478 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
7479 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
7480 | #include "libguile/conv-integer.i.c" | |
7481 | ||
7482 | #define TYPE scm_t_uintmax | |
7483 | #define TYPE_MIN min | |
7484 | #define TYPE_MAX max | |
7485 | #define SIZEOF_TYPE 0 | |
7486 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
7487 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
7488 | #include "libguile/conv-uinteger.i.c" | |
7489 | ||
7490 | #define TYPE scm_t_int8 | |
7491 | #define TYPE_MIN SCM_T_INT8_MIN | |
7492 | #define TYPE_MAX SCM_T_INT8_MAX | |
7493 | #define SIZEOF_TYPE 1 | |
7494 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
7495 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
7496 | #include "libguile/conv-integer.i.c" | |
7497 | ||
7498 | #define TYPE scm_t_uint8 | |
7499 | #define TYPE_MIN 0 | |
7500 | #define TYPE_MAX SCM_T_UINT8_MAX | |
7501 | #define SIZEOF_TYPE 1 | |
7502 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
7503 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
7504 | #include "libguile/conv-uinteger.i.c" | |
7505 | ||
7506 | #define TYPE scm_t_int16 | |
7507 | #define TYPE_MIN SCM_T_INT16_MIN | |
7508 | #define TYPE_MAX SCM_T_INT16_MAX | |
7509 | #define SIZEOF_TYPE 2 | |
7510 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
7511 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
7512 | #include "libguile/conv-integer.i.c" | |
7513 | ||
7514 | #define TYPE scm_t_uint16 | |
7515 | #define TYPE_MIN 0 | |
7516 | #define TYPE_MAX SCM_T_UINT16_MAX | |
7517 | #define SIZEOF_TYPE 2 | |
7518 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
7519 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
7520 | #include "libguile/conv-uinteger.i.c" | |
7521 | ||
7522 | #define TYPE scm_t_int32 | |
7523 | #define TYPE_MIN SCM_T_INT32_MIN | |
7524 | #define TYPE_MAX SCM_T_INT32_MAX | |
7525 | #define SIZEOF_TYPE 4 | |
7526 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
7527 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
7528 | #include "libguile/conv-integer.i.c" | |
7529 | ||
7530 | #define TYPE scm_t_uint32 | |
7531 | #define TYPE_MIN 0 | |
7532 | #define TYPE_MAX SCM_T_UINT32_MAX | |
7533 | #define SIZEOF_TYPE 4 | |
7534 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
7535 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
7536 | #include "libguile/conv-uinteger.i.c" | |
7537 | ||
904a78f1 MG |
7538 | #define TYPE scm_t_wchar |
7539 | #define TYPE_MIN (scm_t_int32)-1 | |
7540 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
7541 | #define SIZEOF_TYPE 4 | |
7542 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
7543 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
7544 | #include "libguile/conv-integer.i.c" | |
7545 | ||
bfd7932e MV |
7546 | #define TYPE scm_t_int64 |
7547 | #define TYPE_MIN SCM_T_INT64_MIN | |
7548 | #define TYPE_MAX SCM_T_INT64_MAX | |
7549 | #define SIZEOF_TYPE 8 | |
7550 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
7551 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
7552 | #include "libguile/conv-integer.i.c" | |
7553 | ||
7554 | #define TYPE scm_t_uint64 | |
7555 | #define TYPE_MIN 0 | |
7556 | #define TYPE_MAX SCM_T_UINT64_MAX | |
7557 | #define SIZEOF_TYPE 8 | |
7558 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
7559 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
7560 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 7561 | |
cd036260 MV |
7562 | void |
7563 | scm_to_mpz (SCM val, mpz_t rop) | |
7564 | { | |
7565 | if (SCM_I_INUMP (val)) | |
7566 | mpz_set_si (rop, SCM_I_INUM (val)); | |
7567 | else if (SCM_BIGP (val)) | |
7568 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
7569 | else | |
7570 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
7571 | } | |
7572 | ||
7573 | SCM | |
7574 | scm_from_mpz (mpz_t val) | |
7575 | { | |
7576 | return scm_i_mpz2num (val); | |
7577 | } | |
7578 | ||
73e4de09 MV |
7579 | int |
7580 | scm_is_real (SCM val) | |
7581 | { | |
7582 | return scm_is_true (scm_real_p (val)); | |
7583 | } | |
7584 | ||
55f26379 MV |
7585 | int |
7586 | scm_is_rational (SCM val) | |
7587 | { | |
7588 | return scm_is_true (scm_rational_p (val)); | |
7589 | } | |
7590 | ||
73e4de09 MV |
7591 | double |
7592 | scm_to_double (SCM val) | |
7593 | { | |
55f26379 MV |
7594 | if (SCM_I_INUMP (val)) |
7595 | return SCM_I_INUM (val); | |
7596 | else if (SCM_BIGP (val)) | |
7597 | return scm_i_big2dbl (val); | |
7598 | else if (SCM_FRACTIONP (val)) | |
7599 | return scm_i_fraction2double (val); | |
7600 | else if (SCM_REALP (val)) | |
7601 | return SCM_REAL_VALUE (val); | |
7602 | else | |
7a1aba42 | 7603 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
7604 | } |
7605 | ||
7606 | SCM | |
7607 | scm_from_double (double val) | |
7608 | { | |
978c52d1 LC |
7609 | SCM z; |
7610 | ||
7611 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
7612 | ||
7613 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 7614 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 7615 | |
55f26379 | 7616 | return z; |
73e4de09 MV |
7617 | } |
7618 | ||
220058a8 | 7619 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
7620 | |
7621 | float | |
e25f3727 | 7622 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7623 | { |
220058a8 AW |
7624 | scm_c_issue_deprecation_warning |
7625 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
7626 | ||
55f26379 MV |
7627 | if (SCM_BIGP (num)) |
7628 | { | |
7629 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7630 | if (!isinf (res)) |
55f26379 MV |
7631 | return res; |
7632 | else | |
7633 | scm_out_of_range (NULL, num); | |
7634 | } | |
7635 | else | |
7636 | return scm_to_double (num); | |
7637 | } | |
7638 | ||
7639 | double | |
e25f3727 | 7640 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7641 | { |
220058a8 AW |
7642 | scm_c_issue_deprecation_warning |
7643 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
7644 | ||
55f26379 MV |
7645 | if (SCM_BIGP (num)) |
7646 | { | |
7647 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7648 | if (!isinf (res)) |
55f26379 MV |
7649 | return res; |
7650 | else | |
7651 | scm_out_of_range (NULL, num); | |
7652 | } | |
7653 | else | |
7654 | return scm_to_double (num); | |
7655 | } | |
7656 | ||
7657 | #endif | |
7658 | ||
8507ec80 MV |
7659 | int |
7660 | scm_is_complex (SCM val) | |
7661 | { | |
7662 | return scm_is_true (scm_complex_p (val)); | |
7663 | } | |
7664 | ||
7665 | double | |
7666 | scm_c_real_part (SCM z) | |
7667 | { | |
7668 | if (SCM_COMPLEXP (z)) | |
7669 | return SCM_COMPLEX_REAL (z); | |
7670 | else | |
7671 | { | |
7672 | /* Use the scm_real_part to get proper error checking and | |
7673 | dispatching. | |
7674 | */ | |
7675 | return scm_to_double (scm_real_part (z)); | |
7676 | } | |
7677 | } | |
7678 | ||
7679 | double | |
7680 | scm_c_imag_part (SCM z) | |
7681 | { | |
7682 | if (SCM_COMPLEXP (z)) | |
7683 | return SCM_COMPLEX_IMAG (z); | |
7684 | else | |
7685 | { | |
7686 | /* Use the scm_imag_part to get proper error checking and | |
7687 | dispatching. The result will almost always be 0.0, but not | |
7688 | always. | |
7689 | */ | |
7690 | return scm_to_double (scm_imag_part (z)); | |
7691 | } | |
7692 | } | |
7693 | ||
7694 | double | |
7695 | scm_c_magnitude (SCM z) | |
7696 | { | |
7697 | return scm_to_double (scm_magnitude (z)); | |
7698 | } | |
7699 | ||
7700 | double | |
7701 | scm_c_angle (SCM z) | |
7702 | { | |
7703 | return scm_to_double (scm_angle (z)); | |
7704 | } | |
7705 | ||
7706 | int | |
7707 | scm_is_number (SCM z) | |
7708 | { | |
7709 | return scm_is_true (scm_number_p (z)); | |
7710 | } | |
7711 | ||
8ab3d8a0 KR |
7712 | |
7713 | /* In the following functions we dispatch to the real-arg funcs like log() | |
7714 | when we know the arg is real, instead of just handing everything to | |
7715 | clog() for instance. This is in case clog() doesn't optimize for a | |
7716 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
7717 | well use it to go straight to the applicable C func. */ | |
7718 | ||
2519490c MW |
7719 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
7720 | (SCM z), | |
7721 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
7722 | #define FUNC_NAME s_scm_log |
7723 | { | |
7724 | if (SCM_COMPLEXP (z)) | |
7725 | { | |
4b26c03e | 7726 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7727 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
7728 | #else | |
7729 | double re = SCM_COMPLEX_REAL (z); | |
7730 | double im = SCM_COMPLEX_IMAG (z); | |
7731 | return scm_c_make_rectangular (log (hypot (re, im)), | |
7732 | atan2 (im, re)); | |
7733 | #endif | |
7734 | } | |
2519490c | 7735 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7736 | { |
7737 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7738 | although the value itself overflows. */ | |
7739 | double re = scm_to_double (z); | |
7740 | double l = log (fabs (re)); | |
7741 | if (re >= 0.0) | |
7742 | return scm_from_double (l); | |
7743 | else | |
7744 | return scm_c_make_rectangular (l, M_PI); | |
7745 | } | |
2519490c MW |
7746 | else |
7747 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
7748 | } |
7749 | #undef FUNC_NAME | |
7750 | ||
7751 | ||
2519490c MW |
7752 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
7753 | (SCM z), | |
7754 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
7755 | #define FUNC_NAME s_scm_log10 |
7756 | { | |
7757 | if (SCM_COMPLEXP (z)) | |
7758 | { | |
7759 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
7760 | clog() and a multiply by M_LOG10E, rather than the fallback | |
7761 | log10+hypot+atan2.) */ | |
f328f862 LC |
7762 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
7763 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
7764 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
7765 | #else | |
7766 | double re = SCM_COMPLEX_REAL (z); | |
7767 | double im = SCM_COMPLEX_IMAG (z); | |
7768 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
7769 | M_LOG10E * atan2 (im, re)); | |
7770 | #endif | |
7771 | } | |
2519490c | 7772 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7773 | { |
7774 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7775 | although the value itself overflows. */ | |
7776 | double re = scm_to_double (z); | |
7777 | double l = log10 (fabs (re)); | |
7778 | if (re >= 0.0) | |
7779 | return scm_from_double (l); | |
7780 | else | |
7781 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
7782 | } | |
2519490c MW |
7783 | else |
7784 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
7785 | } |
7786 | #undef FUNC_NAME | |
7787 | ||
7788 | ||
2519490c MW |
7789 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
7790 | (SCM z), | |
7791 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
7792 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
7793 | #define FUNC_NAME s_scm_exp |
7794 | { | |
7795 | if (SCM_COMPLEXP (z)) | |
7796 | { | |
4b26c03e | 7797 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7798 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
7799 | #else | |
7800 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
7801 | SCM_COMPLEX_IMAG (z)); | |
7802 | #endif | |
7803 | } | |
2519490c | 7804 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7805 | { |
7806 | /* When z is a negative bignum the conversion to double overflows, | |
7807 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
7808 | return scm_from_double (exp (scm_to_double (z))); | |
7809 | } | |
2519490c MW |
7810 | else |
7811 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
7812 | } |
7813 | #undef FUNC_NAME | |
7814 | ||
7815 | ||
2519490c MW |
7816 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
7817 | (SCM z), | |
7818 | "Return the square root of @var{z}. Of the two possible roots\n" | |
7819 | "(positive and negative), the one with the a positive real part\n" | |
7820 | "is returned, or if that's zero then a positive imaginary part.\n" | |
7821 | "Thus,\n" | |
7822 | "\n" | |
7823 | "@example\n" | |
7824 | "(sqrt 9.0) @result{} 3.0\n" | |
7825 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
7826 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
7827 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
7828 | "@end example") | |
8ab3d8a0 KR |
7829 | #define FUNC_NAME s_scm_sqrt |
7830 | { | |
2519490c | 7831 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 7832 | { |
f328f862 LC |
7833 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
7834 | && defined SCM_COMPLEX_VALUE | |
2519490c | 7835 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 7836 | #else |
2519490c MW |
7837 | double re = SCM_COMPLEX_REAL (z); |
7838 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
7839 | return scm_c_make_polar (sqrt (hypot (re, im)), |
7840 | 0.5 * atan2 (im, re)); | |
7841 | #endif | |
7842 | } | |
2519490c | 7843 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 7844 | { |
2519490c | 7845 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
7846 | if (xx < 0) |
7847 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
7848 | else | |
7849 | return scm_from_double (sqrt (xx)); | |
7850 | } | |
2519490c MW |
7851 | else |
7852 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
7853 | } |
7854 | #undef FUNC_NAME | |
7855 | ||
7856 | ||
7857 | ||
0f2d19dd JB |
7858 | void |
7859 | scm_init_numbers () | |
0f2d19dd | 7860 | { |
0b799eea MV |
7861 | int i; |
7862 | ||
713a4259 KR |
7863 | mpz_init_set_si (z_negative_one, -1); |
7864 | ||
a261c0e9 DH |
7865 | /* It may be possible to tune the performance of some algorithms by using |
7866 | * the following constants to avoid the creation of bignums. Please, before | |
7867 | * using these values, remember the two rules of program optimization: | |
7868 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 7869 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 7870 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 7871 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 7872 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 7873 | |
f3ae5d60 MD |
7874 | scm_add_feature ("complex"); |
7875 | scm_add_feature ("inexact"); | |
e7efe8e7 | 7876 | flo0 = scm_from_double (0.0); |
0b799eea MV |
7877 | |
7878 | /* determine floating point precision */ | |
55f26379 | 7879 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
7880 | { |
7881 | init_dblprec(&scm_dblprec[i-2],i); | |
7882 | init_fx_radix(fx_per_radix[i-2],i); | |
7883 | } | |
f872b822 | 7884 | #ifdef DBL_DIG |
0b799eea | 7885 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 7886 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 7887 | #endif |
1be6b49c | 7888 | |
cff5fa33 | 7889 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 7890 | #include "libguile/numbers.x" |
0f2d19dd | 7891 | } |
89e00824 ML |
7892 | |
7893 | /* | |
7894 | Local Variables: | |
7895 | c-file-style: "gnu" | |
7896 | End: | |
7897 | */ |