Commit | Line | Data |
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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 | ||
2e274311 MW |
501 | static int |
502 | double_is_non_negative_zero (double x) | |
503 | { | |
504 | static double zero = 0.0; | |
505 | ||
506 | return !memcmp (&x, &zero, sizeof(double)); | |
507 | } | |
508 | ||
2519490c MW |
509 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
510 | (SCM x), | |
942e5b91 MG |
511 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
512 | "otherwise.") | |
1bbd0b84 | 513 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 514 | { |
41df63cf MW |
515 | if (SCM_INEXACTP (x)) |
516 | return SCM_BOOL_F; | |
517 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 518 | return SCM_BOOL_T; |
41df63cf | 519 | else |
2519490c | 520 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
521 | } |
522 | #undef FUNC_NAME | |
523 | ||
524 | ||
2519490c | 525 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
526 | (SCM x), |
527 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
528 | "else.") | |
529 | #define FUNC_NAME s_scm_inexact_p | |
530 | { | |
531 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 532 | return SCM_BOOL_T; |
41df63cf | 533 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 534 | return SCM_BOOL_F; |
41df63cf | 535 | else |
2519490c | 536 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 537 | } |
1bbd0b84 | 538 | #undef FUNC_NAME |
0f2d19dd | 539 | |
4219f20d | 540 | |
2519490c | 541 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 542 | (SCM n), |
942e5b91 MG |
543 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
544 | "otherwise.") | |
1bbd0b84 | 545 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 546 | { |
e11e83f3 | 547 | if (SCM_I_INUMP (n)) |
0aacf84e | 548 | { |
e25f3727 | 549 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 550 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
551 | } |
552 | else if (SCM_BIGP (n)) | |
553 | { | |
554 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
555 | scm_remember_upto_here_1 (n); | |
73e4de09 | 556 | return scm_from_bool (odd_p); |
0aacf84e | 557 | } |
f92e85f7 MV |
558 | else if (SCM_REALP (n)) |
559 | { | |
2519490c MW |
560 | double val = SCM_REAL_VALUE (n); |
561 | if (DOUBLE_IS_FINITE (val)) | |
562 | { | |
563 | double rem = fabs (fmod (val, 2.0)); | |
564 | if (rem == 1.0) | |
565 | return SCM_BOOL_T; | |
566 | else if (rem == 0.0) | |
567 | return SCM_BOOL_F; | |
568 | } | |
f92e85f7 | 569 | } |
2519490c | 570 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 571 | } |
1bbd0b84 | 572 | #undef FUNC_NAME |
0f2d19dd | 573 | |
4219f20d | 574 | |
2519490c | 575 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 576 | (SCM n), |
942e5b91 MG |
577 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
578 | "otherwise.") | |
1bbd0b84 | 579 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 580 | { |
e11e83f3 | 581 | if (SCM_I_INUMP (n)) |
0aacf84e | 582 | { |
e25f3727 | 583 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 584 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
585 | } |
586 | else if (SCM_BIGP (n)) | |
587 | { | |
588 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
589 | scm_remember_upto_here_1 (n); | |
73e4de09 | 590 | return scm_from_bool (even_p); |
0aacf84e | 591 | } |
f92e85f7 MV |
592 | else if (SCM_REALP (n)) |
593 | { | |
2519490c MW |
594 | double val = SCM_REAL_VALUE (n); |
595 | if (DOUBLE_IS_FINITE (val)) | |
596 | { | |
597 | double rem = fabs (fmod (val, 2.0)); | |
598 | if (rem == 1.0) | |
599 | return SCM_BOOL_F; | |
600 | else if (rem == 0.0) | |
601 | return SCM_BOOL_T; | |
602 | } | |
f92e85f7 | 603 | } |
2519490c | 604 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 605 | } |
1bbd0b84 | 606 | #undef FUNC_NAME |
0f2d19dd | 607 | |
2519490c MW |
608 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
609 | (SCM x), | |
10391e06 AW |
610 | "Return @code{#t} if the real number @var{x} is neither\n" |
611 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
612 | #define FUNC_NAME s_scm_finite_p |
613 | { | |
614 | if (SCM_REALP (x)) | |
615 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 616 | else if (scm_is_real (x)) |
7112615f MW |
617 | return SCM_BOOL_T; |
618 | else | |
2519490c | 619 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
620 | } |
621 | #undef FUNC_NAME | |
622 | ||
2519490c MW |
623 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
624 | (SCM x), | |
625 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
626 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
627 | #define FUNC_NAME s_scm_inf_p |
628 | { | |
b1092b3a | 629 | if (SCM_REALP (x)) |
2e65b52f | 630 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 631 | else if (scm_is_real (x)) |
7351e207 | 632 | return SCM_BOOL_F; |
10391e06 | 633 | else |
2519490c | 634 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
635 | } |
636 | #undef FUNC_NAME | |
637 | ||
2519490c MW |
638 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
639 | (SCM x), | |
10391e06 AW |
640 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
641 | "or @code{#f} otherwise.") | |
7351e207 MV |
642 | #define FUNC_NAME s_scm_nan_p |
643 | { | |
10391e06 AW |
644 | if (SCM_REALP (x)) |
645 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
646 | else if (scm_is_real (x)) | |
7351e207 | 647 | return SCM_BOOL_F; |
10391e06 | 648 | else |
2519490c | 649 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
650 | } |
651 | #undef FUNC_NAME | |
652 | ||
653 | /* Guile's idea of infinity. */ | |
654 | static double guile_Inf; | |
655 | ||
656 | /* Guile's idea of not a number. */ | |
657 | static double guile_NaN; | |
658 | ||
659 | static void | |
660 | guile_ieee_init (void) | |
661 | { | |
7351e207 MV |
662 | /* Some version of gcc on some old version of Linux used to crash when |
663 | trying to make Inf and NaN. */ | |
664 | ||
240a27d2 KR |
665 | #ifdef INFINITY |
666 | /* C99 INFINITY, when available. | |
667 | FIXME: The standard allows for INFINITY to be something that overflows | |
668 | at compile time. We ought to have a configure test to check for that | |
669 | before trying to use it. (But in practice we believe this is not a | |
670 | problem on any system guile is likely to target.) */ | |
671 | guile_Inf = INFINITY; | |
56a3dcd4 | 672 | #elif defined HAVE_DINFINITY |
240a27d2 | 673 | /* OSF */ |
7351e207 | 674 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 675 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
676 | #else |
677 | double tmp = 1e+10; | |
678 | guile_Inf = tmp; | |
679 | for (;;) | |
680 | { | |
681 | guile_Inf *= 1e+10; | |
682 | if (guile_Inf == tmp) | |
683 | break; | |
684 | tmp = guile_Inf; | |
685 | } | |
686 | #endif | |
687 | ||
240a27d2 KR |
688 | #ifdef NAN |
689 | /* C99 NAN, when available */ | |
690 | guile_NaN = NAN; | |
56a3dcd4 | 691 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
692 | { |
693 | /* OSF */ | |
694 | extern unsigned int DQNAN[2]; | |
695 | guile_NaN = (*((double *)(DQNAN))); | |
696 | } | |
7351e207 MV |
697 | #else |
698 | guile_NaN = guile_Inf / guile_Inf; | |
699 | #endif | |
7351e207 MV |
700 | } |
701 | ||
702 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
703 | (void), | |
704 | "Return Inf.") | |
705 | #define FUNC_NAME s_scm_inf | |
706 | { | |
707 | static int initialized = 0; | |
708 | if (! initialized) | |
709 | { | |
710 | guile_ieee_init (); | |
711 | initialized = 1; | |
712 | } | |
55f26379 | 713 | return scm_from_double (guile_Inf); |
7351e207 MV |
714 | } |
715 | #undef FUNC_NAME | |
716 | ||
717 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
718 | (void), | |
719 | "Return NaN.") | |
720 | #define FUNC_NAME s_scm_nan | |
721 | { | |
722 | static int initialized = 0; | |
0aacf84e | 723 | if (!initialized) |
7351e207 MV |
724 | { |
725 | guile_ieee_init (); | |
726 | initialized = 1; | |
727 | } | |
55f26379 | 728 | return scm_from_double (guile_NaN); |
7351e207 MV |
729 | } |
730 | #undef FUNC_NAME | |
731 | ||
4219f20d | 732 | |
a48d60b1 MD |
733 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
734 | (SCM x), | |
735 | "Return the absolute value of @var{x}.") | |
2519490c | 736 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 737 | { |
e11e83f3 | 738 | if (SCM_I_INUMP (x)) |
0aacf84e | 739 | { |
e25f3727 | 740 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
741 | if (xx >= 0) |
742 | return x; | |
743 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 744 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 745 | else |
e25f3727 | 746 | return scm_i_inum2big (-xx); |
4219f20d | 747 | } |
9b9ef10c MW |
748 | else if (SCM_LIKELY (SCM_REALP (x))) |
749 | { | |
750 | double xx = SCM_REAL_VALUE (x); | |
751 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
752 | if (xx < 0.0) | |
753 | return scm_from_double (-xx); | |
754 | /* Handle signed zeroes properly */ | |
755 | else if (SCM_UNLIKELY (xx == 0.0)) | |
756 | return flo0; | |
757 | else | |
758 | return x; | |
759 | } | |
0aacf84e MD |
760 | else if (SCM_BIGP (x)) |
761 | { | |
762 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
763 | if (sgn < 0) | |
764 | return scm_i_clonebig (x, 0); | |
765 | else | |
766 | return x; | |
4219f20d | 767 | } |
f92e85f7 MV |
768 | else if (SCM_FRACTIONP (x)) |
769 | { | |
73e4de09 | 770 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 771 | return x; |
cba42c93 | 772 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
773 | SCM_FRACTION_DENOMINATOR (x)); |
774 | } | |
0aacf84e | 775 | else |
a48d60b1 | 776 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 777 | } |
a48d60b1 | 778 | #undef FUNC_NAME |
0f2d19dd | 779 | |
4219f20d | 780 | |
2519490c MW |
781 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
782 | (SCM x, SCM y), | |
783 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
784 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 785 | { |
a16982ca | 786 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 787 | { |
e25f3727 | 788 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 789 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 790 | { |
e25f3727 | 791 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 792 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 793 | scm_num_overflow (s_scm_quotient); |
0aacf84e MD |
794 | else |
795 | { | |
e25f3727 | 796 | scm_t_inum z = xx / yy; |
a16982ca | 797 | if (SCM_LIKELY (SCM_FIXABLE (z))) |
d956fa6f | 798 | return SCM_I_MAKINUM (z); |
0aacf84e | 799 | else |
e25f3727 | 800 | return scm_i_inum2big (z); |
0aacf84e | 801 | } |
828865c3 | 802 | } |
0aacf84e | 803 | else if (SCM_BIGP (y)) |
ac0c002c | 804 | { |
e11e83f3 | 805 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
806 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
807 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
808 | { | |
809 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
810 | scm_remember_upto_here_1 (y); | |
d956fa6f | 811 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 812 | } |
0aacf84e | 813 | else |
cff5fa33 | 814 | return SCM_INUM0; |
ac0c002c DH |
815 | } |
816 | else | |
2519490c | 817 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
828865c3 | 818 | } |
0aacf84e MD |
819 | else if (SCM_BIGP (x)) |
820 | { | |
a16982ca | 821 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 822 | { |
e25f3727 | 823 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 824 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 825 | scm_num_overflow (s_scm_quotient); |
a16982ca | 826 | else if (SCM_UNLIKELY (yy == 1)) |
0aacf84e MD |
827 | return x; |
828 | else | |
829 | { | |
830 | SCM result = scm_i_mkbig (); | |
831 | if (yy < 0) | |
832 | { | |
833 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
834 | SCM_I_BIG_MPZ (x), | |
835 | - yy); | |
836 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
837 | } | |
838 | else | |
839 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
840 | scm_remember_upto_here_1 (x); | |
841 | return scm_i_normbig (result); | |
842 | } | |
843 | } | |
844 | else if (SCM_BIGP (y)) | |
845 | { | |
846 | SCM result = scm_i_mkbig (); | |
847 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
848 | SCM_I_BIG_MPZ (x), | |
849 | SCM_I_BIG_MPZ (y)); | |
850 | scm_remember_upto_here_2 (x, y); | |
851 | return scm_i_normbig (result); | |
852 | } | |
853 | else | |
2519490c | 854 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 855 | } |
0aacf84e | 856 | else |
2519490c | 857 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 858 | } |
2519490c | 859 | #undef FUNC_NAME |
0f2d19dd | 860 | |
2519490c MW |
861 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
862 | (SCM x, SCM y), | |
863 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
864 | "@lisp\n" | |
865 | "(remainder 13 4) @result{} 1\n" | |
866 | "(remainder -13 4) @result{} -1\n" | |
867 | "@end lisp") | |
868 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 869 | { |
a16982ca | 870 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 871 | { |
a16982ca | 872 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 873 | { |
e25f3727 | 874 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 875 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 876 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
877 | else |
878 | { | |
a16982ca MW |
879 | /* C99 specifies that "%" is the remainder corresponding to a |
880 | quotient rounded towards zero, and that's also traditional | |
881 | for machine division, so z here should be well defined. */ | |
e25f3727 | 882 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 883 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
884 | } |
885 | } | |
886 | else if (SCM_BIGP (y)) | |
ac0c002c | 887 | { |
e11e83f3 | 888 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
889 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
890 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
891 | { | |
892 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
893 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 894 | return SCM_INUM0; |
4dc09ee4 | 895 | } |
0aacf84e MD |
896 | else |
897 | return x; | |
ac0c002c DH |
898 | } |
899 | else | |
2519490c | 900 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
89a7e495 | 901 | } |
0aacf84e MD |
902 | else if (SCM_BIGP (x)) |
903 | { | |
a16982ca | 904 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 905 | { |
e25f3727 | 906 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 907 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 908 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
909 | else |
910 | { | |
911 | SCM result = scm_i_mkbig (); | |
912 | if (yy < 0) | |
913 | yy = - yy; | |
914 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
915 | scm_remember_upto_here_1 (x); | |
916 | return scm_i_normbig (result); | |
917 | } | |
918 | } | |
919 | else if (SCM_BIGP (y)) | |
920 | { | |
921 | SCM result = scm_i_mkbig (); | |
922 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
923 | SCM_I_BIG_MPZ (x), | |
924 | SCM_I_BIG_MPZ (y)); | |
925 | scm_remember_upto_here_2 (x, y); | |
926 | return scm_i_normbig (result); | |
927 | } | |
928 | else | |
2519490c | 929 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 930 | } |
0aacf84e | 931 | else |
2519490c | 932 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 933 | } |
2519490c | 934 | #undef FUNC_NAME |
0f2d19dd | 935 | |
89a7e495 | 936 | |
2519490c MW |
937 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
938 | (SCM x, SCM y), | |
939 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
940 | "@lisp\n" | |
941 | "(modulo 13 4) @result{} 1\n" | |
942 | "(modulo -13 4) @result{} 3\n" | |
943 | "@end lisp") | |
944 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 945 | { |
a16982ca | 946 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 947 | { |
e25f3727 | 948 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 949 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 950 | { |
e25f3727 | 951 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 952 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 953 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
954 | else |
955 | { | |
66b1c775 KR |
956 | /* C99 specifies that "%" is the remainder corresponding to a |
957 | quotient rounded towards zero, and that's also traditional | |
958 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
959 | scm_t_inum z = xx % yy; |
960 | scm_t_inum result; | |
0aacf84e MD |
961 | |
962 | if (yy < 0) | |
963 | { | |
964 | if (z > 0) | |
965 | result = z + yy; | |
966 | else | |
967 | result = z; | |
968 | } | |
969 | else | |
970 | { | |
971 | if (z < 0) | |
972 | result = z + yy; | |
973 | else | |
974 | result = z; | |
975 | } | |
d956fa6f | 976 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
977 | } |
978 | } | |
979 | else if (SCM_BIGP (y)) | |
980 | { | |
981 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
982 | { |
983 | mpz_t z_x; | |
984 | SCM result; | |
985 | ||
986 | if (sgn_y < 0) | |
987 | { | |
988 | SCM pos_y = scm_i_clonebig (y, 0); | |
989 | /* do this after the last scm_op */ | |
990 | mpz_init_set_si (z_x, xx); | |
991 | result = pos_y; /* re-use this bignum */ | |
992 | mpz_mod (SCM_I_BIG_MPZ (result), | |
993 | z_x, | |
994 | SCM_I_BIG_MPZ (pos_y)); | |
995 | scm_remember_upto_here_1 (pos_y); | |
996 | } | |
997 | else | |
998 | { | |
999 | result = scm_i_mkbig (); | |
1000 | /* do this after the last scm_op */ | |
1001 | mpz_init_set_si (z_x, xx); | |
1002 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1003 | z_x, | |
1004 | SCM_I_BIG_MPZ (y)); | |
1005 | scm_remember_upto_here_1 (y); | |
1006 | } | |
ca46fb90 | 1007 | |
0aacf84e MD |
1008 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
1009 | mpz_add (SCM_I_BIG_MPZ (result), | |
1010 | SCM_I_BIG_MPZ (y), | |
1011 | SCM_I_BIG_MPZ (result)); | |
1012 | scm_remember_upto_here_1 (y); | |
1013 | /* and do this before the next one */ | |
1014 | mpz_clear (z_x); | |
1015 | return scm_i_normbig (result); | |
1016 | } | |
1017 | } | |
1018 | else | |
2519490c | 1019 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
f872b822 | 1020 | } |
0aacf84e MD |
1021 | else if (SCM_BIGP (x)) |
1022 | { | |
a16982ca | 1023 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 1024 | { |
e25f3727 | 1025 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 1026 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 1027 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
1028 | else |
1029 | { | |
1030 | SCM result = scm_i_mkbig (); | |
1031 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1032 | SCM_I_BIG_MPZ (x), | |
1033 | (yy < 0) ? - yy : yy); | |
1034 | scm_remember_upto_here_1 (x); | |
1035 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1036 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1037 | SCM_I_BIG_MPZ (result), | |
1038 | - yy); | |
1039 | return scm_i_normbig (result); | |
1040 | } | |
1041 | } | |
1042 | else if (SCM_BIGP (y)) | |
1043 | { | |
a16982ca MW |
1044 | SCM result = scm_i_mkbig (); |
1045 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1046 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1047 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1048 | SCM_I_BIG_MPZ (x), | |
1049 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1050 | |
a16982ca MW |
1051 | scm_remember_upto_here_1 (x); |
1052 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1053 | mpz_add (SCM_I_BIG_MPZ (result), | |
1054 | SCM_I_BIG_MPZ (y), | |
1055 | SCM_I_BIG_MPZ (result)); | |
1056 | scm_remember_upto_here_2 (y, pos_y); | |
1057 | return scm_i_normbig (result); | |
0aacf84e MD |
1058 | } |
1059 | else | |
2519490c | 1060 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 1061 | } |
0aacf84e | 1062 | else |
2519490c | 1063 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1064 | } |
2519490c | 1065 | #undef FUNC_NAME |
0f2d19dd | 1066 | |
ff62c168 MW |
1067 | static SCM scm_i_inexact_euclidean_quotient (double x, double y); |
1068 | static SCM scm_i_slow_exact_euclidean_quotient (SCM x, SCM y); | |
1069 | ||
1070 | SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, | |
1071 | (SCM x, SCM y), | |
1072 | "Return the integer @var{q} such that\n" | |
1073 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1074 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1075 | "@lisp\n" | |
1076 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1077 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1078 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1079 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1080 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1081 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1082 | "@end lisp") | |
1083 | #define FUNC_NAME s_scm_euclidean_quotient | |
1084 | { | |
1085 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1086 | { | |
1087 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1088 | { | |
1089 | scm_t_inum yy = SCM_I_INUM (y); | |
1090 | if (SCM_UNLIKELY (yy == 0)) | |
1091 | scm_num_overflow (s_scm_euclidean_quotient); | |
1092 | else | |
1093 | { | |
1094 | scm_t_inum xx = SCM_I_INUM (x); | |
1095 | scm_t_inum qq = xx / yy; | |
1096 | if (xx < qq * yy) | |
1097 | { | |
1098 | if (yy > 0) | |
1099 | qq--; | |
1100 | else | |
1101 | qq++; | |
1102 | } | |
1103 | return SCM_I_MAKINUM (qq); | |
1104 | } | |
1105 | } | |
1106 | else if (SCM_BIGP (y)) | |
1107 | { | |
1108 | if (SCM_I_INUM (x) >= 0) | |
1109 | return SCM_INUM0; | |
1110 | else | |
1111 | return SCM_I_MAKINUM (- mpz_sgn (SCM_I_BIG_MPZ (y))); | |
1112 | } | |
1113 | else if (SCM_REALP (y)) | |
1114 | return scm_i_inexact_euclidean_quotient | |
1115 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1116 | else if (SCM_FRACTIONP (y)) | |
1117 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1118 | else | |
1119 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1120 | s_scm_euclidean_quotient); | |
1121 | } | |
1122 | else if (SCM_BIGP (x)) | |
1123 | { | |
1124 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1125 | { | |
1126 | scm_t_inum yy = SCM_I_INUM (y); | |
1127 | if (SCM_UNLIKELY (yy == 0)) | |
1128 | scm_num_overflow (s_scm_euclidean_quotient); | |
1129 | else | |
1130 | { | |
1131 | SCM q = scm_i_mkbig (); | |
1132 | if (yy > 0) | |
1133 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1134 | else | |
1135 | { | |
1136 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1137 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1138 | } | |
1139 | scm_remember_upto_here_1 (x); | |
1140 | return scm_i_normbig (q); | |
1141 | } | |
1142 | } | |
1143 | else if (SCM_BIGP (y)) | |
1144 | { | |
1145 | SCM q = scm_i_mkbig (); | |
1146 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1147 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1148 | SCM_I_BIG_MPZ (x), | |
1149 | SCM_I_BIG_MPZ (y)); | |
1150 | else | |
1151 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1152 | SCM_I_BIG_MPZ (x), | |
1153 | SCM_I_BIG_MPZ (y)); | |
1154 | scm_remember_upto_here_2 (x, y); | |
1155 | return scm_i_normbig (q); | |
1156 | } | |
1157 | else if (SCM_REALP (y)) | |
1158 | return scm_i_inexact_euclidean_quotient | |
1159 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1160 | else if (SCM_FRACTIONP (y)) | |
1161 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1162 | else | |
1163 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1164 | s_scm_euclidean_quotient); | |
1165 | } | |
1166 | else if (SCM_REALP (x)) | |
1167 | { | |
1168 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1169 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1170 | return scm_i_inexact_euclidean_quotient | |
1171 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1172 | else | |
1173 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1174 | s_scm_euclidean_quotient); | |
1175 | } | |
1176 | else if (SCM_FRACTIONP (x)) | |
1177 | { | |
1178 | if (SCM_REALP (y)) | |
1179 | return scm_i_inexact_euclidean_quotient | |
1180 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1181 | else | |
1182 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1183 | } | |
1184 | else | |
1185 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1186 | s_scm_euclidean_quotient); | |
1187 | } | |
1188 | #undef FUNC_NAME | |
1189 | ||
1190 | static SCM | |
1191 | scm_i_inexact_euclidean_quotient (double x, double y) | |
1192 | { | |
1193 | if (SCM_LIKELY (y > 0)) | |
1194 | return scm_from_double (floor (x / y)); | |
1195 | else if (SCM_LIKELY (y < 0)) | |
1196 | return scm_from_double (ceil (x / y)); | |
1197 | else if (y == 0) | |
1198 | scm_num_overflow (s_scm_euclidean_quotient); /* or return a NaN? */ | |
1199 | else | |
1200 | return scm_nan (); | |
1201 | } | |
1202 | ||
1203 | /* Compute exact euclidean_quotient the slow way. | |
1204 | We use this only if both arguments are exact, | |
1205 | and at least one of them is a fraction */ | |
1206 | static SCM | |
1207 | scm_i_slow_exact_euclidean_quotient (SCM x, SCM y) | |
1208 | { | |
1209 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1210 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1211 | s_scm_euclidean_quotient); | |
1212 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1213 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1214 | s_scm_euclidean_quotient); | |
1215 | else if (scm_is_true (scm_positive_p (y))) | |
1216 | return scm_floor (scm_divide (x, y)); | |
1217 | else if (scm_is_true (scm_negative_p (y))) | |
1218 | return scm_ceiling (scm_divide (x, y)); | |
1219 | else | |
1220 | scm_num_overflow (s_scm_euclidean_quotient); | |
1221 | } | |
1222 | ||
1223 | static SCM scm_i_inexact_euclidean_remainder (double x, double y); | |
1224 | static SCM scm_i_slow_exact_euclidean_remainder (SCM x, SCM y); | |
1225 | ||
1226 | SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, | |
1227 | (SCM x, SCM y), | |
1228 | "Return the real number @var{r} such that\n" | |
1229 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1230 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1231 | "for some integer @var{q}.\n" | |
1232 | "@lisp\n" | |
1233 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1234 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1235 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1236 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1237 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1238 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1239 | "@end lisp") | |
1240 | #define FUNC_NAME s_scm_euclidean_remainder | |
1241 | { | |
1242 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1243 | { | |
1244 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1245 | { | |
1246 | scm_t_inum yy = SCM_I_INUM (y); | |
1247 | if (SCM_UNLIKELY (yy == 0)) | |
1248 | scm_num_overflow (s_scm_euclidean_remainder); | |
1249 | else | |
1250 | { | |
1251 | scm_t_inum rr = SCM_I_INUM (x) % yy; | |
1252 | if (rr >= 0) | |
1253 | return SCM_I_MAKINUM (rr); | |
1254 | else if (yy > 0) | |
1255 | return SCM_I_MAKINUM (rr + yy); | |
1256 | else | |
1257 | return SCM_I_MAKINUM (rr - yy); | |
1258 | } | |
1259 | } | |
1260 | else if (SCM_BIGP (y)) | |
1261 | { | |
1262 | scm_t_inum xx = SCM_I_INUM (x); | |
1263 | if (xx >= 0) | |
1264 | return x; | |
1265 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1266 | { | |
1267 | SCM r = scm_i_mkbig (); | |
1268 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1269 | scm_remember_upto_here_1 (y); | |
1270 | return scm_i_normbig (r); | |
1271 | } | |
1272 | else | |
1273 | { | |
1274 | SCM r = scm_i_mkbig (); | |
1275 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1276 | scm_remember_upto_here_1 (y); | |
1277 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1278 | return scm_i_normbig (r); | |
1279 | } | |
1280 | } | |
1281 | else if (SCM_REALP (y)) | |
1282 | return scm_i_inexact_euclidean_remainder | |
1283 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1284 | else if (SCM_FRACTIONP (y)) | |
1285 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1286 | else | |
1287 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1288 | s_scm_euclidean_remainder); | |
1289 | } | |
1290 | else if (SCM_BIGP (x)) | |
1291 | { | |
1292 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1293 | { | |
1294 | scm_t_inum yy = SCM_I_INUM (y); | |
1295 | if (SCM_UNLIKELY (yy == 0)) | |
1296 | scm_num_overflow (s_scm_euclidean_remainder); | |
1297 | else | |
1298 | { | |
1299 | scm_t_inum rr; | |
1300 | if (yy < 0) | |
1301 | yy = -yy; | |
1302 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1303 | scm_remember_upto_here_1 (x); | |
1304 | return SCM_I_MAKINUM (rr); | |
1305 | } | |
1306 | } | |
1307 | else if (SCM_BIGP (y)) | |
1308 | { | |
1309 | SCM r = scm_i_mkbig (); | |
1310 | mpz_mod (SCM_I_BIG_MPZ (r), | |
1311 | SCM_I_BIG_MPZ (x), | |
1312 | SCM_I_BIG_MPZ (y)); | |
1313 | scm_remember_upto_here_2 (x, y); | |
1314 | return scm_i_normbig (r); | |
1315 | } | |
1316 | else if (SCM_REALP (y)) | |
1317 | return scm_i_inexact_euclidean_remainder | |
1318 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1319 | else if (SCM_FRACTIONP (y)) | |
1320 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1321 | else | |
1322 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1323 | s_scm_euclidean_remainder); | |
1324 | } | |
1325 | else if (SCM_REALP (x)) | |
1326 | { | |
1327 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1328 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1329 | return scm_i_inexact_euclidean_remainder | |
1330 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1331 | else | |
1332 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1333 | s_scm_euclidean_remainder); | |
1334 | } | |
1335 | else if (SCM_FRACTIONP (x)) | |
1336 | { | |
1337 | if (SCM_REALP (y)) | |
1338 | return scm_i_inexact_euclidean_remainder | |
1339 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1340 | else | |
1341 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1342 | } | |
1343 | else | |
1344 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1345 | s_scm_euclidean_remainder); | |
1346 | } | |
1347 | #undef FUNC_NAME | |
1348 | ||
1349 | static SCM | |
1350 | scm_i_inexact_euclidean_remainder (double x, double y) | |
1351 | { | |
1352 | double q; | |
1353 | ||
1354 | /* Although it would be more efficient to use fmod here, we can't | |
1355 | because it would in some cases produce results inconsistent with | |
1356 | scm_i_inexact_euclidean_quotient, such that x != q * y + r (not | |
1357 | even close). In particular, when x is very close to a multiple of | |
1358 | y, then r might be either 0.0 or abs(y)-epsilon, but those two | |
1359 | cases must correspond to different choices of q. If r = 0.0 then q | |
1360 | must be x/y, and if r = abs(y) then q must be (x-r)/y. If quotient | |
1361 | chooses one and remainder chooses the other, it would be bad. This | |
1362 | problem was observed with x = 130.0 and y = 10/7. */ | |
1363 | if (SCM_LIKELY (y > 0)) | |
1364 | q = floor (x / y); | |
1365 | else if (SCM_LIKELY (y < 0)) | |
1366 | q = ceil (x / y); | |
1367 | else if (y == 0) | |
1368 | scm_num_overflow (s_scm_euclidean_remainder); /* or return a NaN? */ | |
1369 | else | |
1370 | return scm_nan (); | |
1371 | return scm_from_double (x - q * y); | |
1372 | } | |
1373 | ||
1374 | /* Compute exact euclidean_remainder the slow way. | |
1375 | We use this only if both arguments are exact, | |
1376 | and at least one of them is a fraction */ | |
1377 | static SCM | |
1378 | scm_i_slow_exact_euclidean_remainder (SCM x, SCM y) | |
1379 | { | |
1380 | SCM q; | |
1381 | ||
1382 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1383 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1384 | s_scm_euclidean_remainder); | |
1385 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1386 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1387 | s_scm_euclidean_remainder); | |
1388 | else if (scm_is_true (scm_positive_p (y))) | |
1389 | q = scm_floor (scm_divide (x, y)); | |
1390 | else if (scm_is_true (scm_negative_p (y))) | |
1391 | q = scm_ceiling (scm_divide (x, y)); | |
1392 | else | |
1393 | scm_num_overflow (s_scm_euclidean_remainder); | |
1394 | return scm_difference (x, scm_product (y, q)); | |
1395 | } | |
1396 | ||
1397 | ||
ac6ce16b MW |
1398 | static SCM scm_i_inexact_euclidean_divide (double x, double y); |
1399 | static SCM scm_i_slow_exact_euclidean_divide (SCM x, SCM y); | |
ff62c168 | 1400 | |
ac6ce16b | 1401 | SCM_PRIMITIVE_GENERIC (scm_euclidean_divide, "euclidean/", 2, 0, 0, |
ff62c168 MW |
1402 | (SCM x, SCM y), |
1403 | "Return the integer @var{q} and the real number @var{r}\n" | |
1404 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1405 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1406 | "@lisp\n" | |
1407 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1408 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1409 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1410 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1411 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1412 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1413 | "@end lisp") | |
ac6ce16b | 1414 | #define FUNC_NAME s_scm_euclidean_divide |
ff62c168 MW |
1415 | { |
1416 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1417 | { | |
1418 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1419 | { | |
1420 | scm_t_inum yy = SCM_I_INUM (y); | |
1421 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1422 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1423 | else |
1424 | { | |
1425 | scm_t_inum xx = SCM_I_INUM (x); | |
1426 | scm_t_inum qq = xx / yy; | |
1427 | scm_t_inum rr = xx - qq * yy; | |
1428 | if (rr < 0) | |
1429 | { | |
1430 | if (yy > 0) | |
1431 | { rr += yy; qq--; } | |
1432 | else | |
1433 | { rr -= yy; qq++; } | |
1434 | } | |
1435 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
1436 | SCM_I_MAKINUM (rr))); | |
1437 | } | |
1438 | } | |
1439 | else if (SCM_BIGP (y)) | |
1440 | { | |
1441 | scm_t_inum xx = SCM_I_INUM (x); | |
1442 | if (xx >= 0) | |
1443 | return scm_values (scm_list_2 (SCM_INUM0, x)); | |
1444 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1445 | { | |
1446 | SCM r = scm_i_mkbig (); | |
1447 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1448 | scm_remember_upto_here_1 (y); | |
1449 | return scm_values | |
1450 | (scm_list_2 (SCM_I_MAKINUM (-1), scm_i_normbig (r))); | |
1451 | } | |
1452 | else | |
1453 | { | |
1454 | SCM r = scm_i_mkbig (); | |
1455 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1456 | scm_remember_upto_here_1 (y); | |
1457 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1458 | return scm_values (scm_list_2 (SCM_INUM1, scm_i_normbig (r))); | |
1459 | } | |
1460 | } | |
1461 | else if (SCM_REALP (y)) | |
ac6ce16b | 1462 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1463 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
1464 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1465 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1466 | else |
ac6ce16b MW |
1467 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1468 | s_scm_euclidean_divide); | |
ff62c168 MW |
1469 | } |
1470 | else if (SCM_BIGP (x)) | |
1471 | { | |
1472 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1473 | { | |
1474 | scm_t_inum yy = SCM_I_INUM (y); | |
1475 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1476 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1477 | else |
1478 | { | |
1479 | SCM q = scm_i_mkbig (); | |
1480 | SCM r = scm_i_mkbig (); | |
1481 | if (yy > 0) | |
1482 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1483 | SCM_I_BIG_MPZ (x), yy); | |
1484 | else | |
1485 | { | |
1486 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1487 | SCM_I_BIG_MPZ (x), -yy); | |
1488 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1489 | } | |
1490 | scm_remember_upto_here_1 (x); | |
1491 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1492 | scm_i_normbig (r))); | |
1493 | } | |
1494 | } | |
1495 | else if (SCM_BIGP (y)) | |
1496 | { | |
1497 | SCM q = scm_i_mkbig (); | |
1498 | SCM r = scm_i_mkbig (); | |
1499 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1500 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1501 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1502 | else | |
1503 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1504 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1505 | scm_remember_upto_here_2 (x, y); | |
1506 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1507 | scm_i_normbig (r))); | |
1508 | } | |
1509 | else if (SCM_REALP (y)) | |
ac6ce16b | 1510 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1511 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
1512 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1513 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1514 | else |
ac6ce16b MW |
1515 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1516 | s_scm_euclidean_divide); | |
ff62c168 MW |
1517 | } |
1518 | else if (SCM_REALP (x)) | |
1519 | { | |
1520 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1521 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 1522 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1523 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
1524 | else | |
ac6ce16b MW |
1525 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1526 | s_scm_euclidean_divide); | |
ff62c168 MW |
1527 | } |
1528 | else if (SCM_FRACTIONP (x)) | |
1529 | { | |
1530 | if (SCM_REALP (y)) | |
ac6ce16b | 1531 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1532 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
1533 | else | |
ac6ce16b | 1534 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 MW |
1535 | } |
1536 | else | |
ac6ce16b MW |
1537 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1538 | s_scm_euclidean_divide); | |
ff62c168 MW |
1539 | } |
1540 | #undef FUNC_NAME | |
1541 | ||
1542 | static SCM | |
ac6ce16b | 1543 | scm_i_inexact_euclidean_divide (double x, double y) |
ff62c168 MW |
1544 | { |
1545 | double q, r; | |
1546 | ||
1547 | if (SCM_LIKELY (y > 0)) | |
1548 | q = floor (x / y); | |
1549 | else if (SCM_LIKELY (y < 0)) | |
1550 | q = ceil (x / y); | |
1551 | else if (y == 0) | |
ac6ce16b | 1552 | scm_num_overflow (s_scm_euclidean_divide); /* or return a NaN? */ |
ff62c168 MW |
1553 | else |
1554 | q = guile_NaN; | |
1555 | r = x - q * y; | |
1556 | return scm_values (scm_list_2 (scm_from_double (q), | |
1557 | scm_from_double (r))); | |
1558 | } | |
1559 | ||
1560 | /* Compute exact euclidean quotient and remainder the slow way. | |
1561 | We use this only if both arguments are exact, | |
1562 | and at least one of them is a fraction */ | |
1563 | static SCM | |
ac6ce16b | 1564 | scm_i_slow_exact_euclidean_divide (SCM x, SCM y) |
ff62c168 MW |
1565 | { |
1566 | SCM q, r; | |
1567 | ||
1568 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
1569 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1570 | s_scm_euclidean_divide); | |
ff62c168 | 1571 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
1572 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1573 | s_scm_euclidean_divide); | |
ff62c168 MW |
1574 | else if (scm_is_true (scm_positive_p (y))) |
1575 | q = scm_floor (scm_divide (x, y)); | |
1576 | else if (scm_is_true (scm_negative_p (y))) | |
1577 | q = scm_ceiling (scm_divide (x, y)); | |
1578 | else | |
ac6ce16b | 1579 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1580 | r = scm_difference (x, scm_product (q, y)); |
1581 | return scm_values (scm_list_2 (q, r)); | |
1582 | } | |
1583 | ||
1584 | static SCM scm_i_inexact_centered_quotient (double x, double y); | |
1585 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
1586 | static SCM scm_i_slow_exact_centered_quotient (SCM x, SCM y); | |
1587 | ||
1588 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, | |
1589 | (SCM x, SCM y), | |
1590 | "Return the integer @var{q} such that\n" | |
1591 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
1592 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
1593 | "@lisp\n" | |
1594 | "(centered-quotient 123 10) @result{} 12\n" | |
1595 | "(centered-quotient 123 -10) @result{} -12\n" | |
1596 | "(centered-quotient -123 10) @result{} -12\n" | |
1597 | "(centered-quotient -123 -10) @result{} 12\n" | |
1598 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
1599 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
1600 | "@end lisp") | |
1601 | #define FUNC_NAME s_scm_centered_quotient | |
1602 | { | |
1603 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1604 | { | |
1605 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1606 | { | |
1607 | scm_t_inum yy = SCM_I_INUM (y); | |
1608 | if (SCM_UNLIKELY (yy == 0)) | |
1609 | scm_num_overflow (s_scm_centered_quotient); | |
1610 | else | |
1611 | { | |
1612 | scm_t_inum xx = SCM_I_INUM (x); | |
1613 | scm_t_inum qq = xx / yy; | |
1614 | scm_t_inum rr = xx - qq * yy; | |
1615 | if (SCM_LIKELY (xx > 0)) | |
1616 | { | |
1617 | if (SCM_LIKELY (yy > 0)) | |
1618 | { | |
1619 | if (rr >= (yy + 1) / 2) | |
1620 | qq++; | |
1621 | } | |
1622 | else | |
1623 | { | |
1624 | if (rr >= (1 - yy) / 2) | |
1625 | qq--; | |
1626 | } | |
1627 | } | |
1628 | else | |
1629 | { | |
1630 | if (SCM_LIKELY (yy > 0)) | |
1631 | { | |
1632 | if (rr < -yy / 2) | |
1633 | qq--; | |
1634 | } | |
1635 | else | |
1636 | { | |
1637 | if (rr < yy / 2) | |
1638 | qq++; | |
1639 | } | |
1640 | } | |
1641 | return SCM_I_MAKINUM (qq); | |
1642 | } | |
1643 | } | |
1644 | else if (SCM_BIGP (y)) | |
1645 | { | |
1646 | /* Pass a denormalized bignum version of x (even though it | |
1647 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
1648 | return scm_i_bigint_centered_quotient | |
1649 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1650 | } | |
1651 | else if (SCM_REALP (y)) | |
1652 | return scm_i_inexact_centered_quotient | |
1653 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1654 | else if (SCM_FRACTIONP (y)) | |
1655 | return scm_i_slow_exact_centered_quotient (x, y); | |
1656 | else | |
1657 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1658 | s_scm_centered_quotient); | |
1659 | } | |
1660 | else if (SCM_BIGP (x)) | |
1661 | { | |
1662 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1663 | { | |
1664 | scm_t_inum yy = SCM_I_INUM (y); | |
1665 | if (SCM_UNLIKELY (yy == 0)) | |
1666 | scm_num_overflow (s_scm_centered_quotient); | |
1667 | else | |
1668 | { | |
1669 | SCM q = scm_i_mkbig (); | |
1670 | scm_t_inum rr; | |
1671 | /* Arrange for rr to initially be non-positive, | |
1672 | because that simplifies the test to see | |
1673 | if it is within the needed bounds. */ | |
1674 | if (yy > 0) | |
1675 | { | |
1676 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1677 | SCM_I_BIG_MPZ (x), yy); | |
1678 | scm_remember_upto_here_1 (x); | |
1679 | if (rr < -yy / 2) | |
1680 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1681 | SCM_I_BIG_MPZ (q), 1); | |
1682 | } | |
1683 | else | |
1684 | { | |
1685 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1686 | SCM_I_BIG_MPZ (x), -yy); | |
1687 | scm_remember_upto_here_1 (x); | |
1688 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1689 | if (rr < yy / 2) | |
1690 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1691 | SCM_I_BIG_MPZ (q), 1); | |
1692 | } | |
1693 | return scm_i_normbig (q); | |
1694 | } | |
1695 | } | |
1696 | else if (SCM_BIGP (y)) | |
1697 | return scm_i_bigint_centered_quotient (x, y); | |
1698 | else if (SCM_REALP (y)) | |
1699 | return scm_i_inexact_centered_quotient | |
1700 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1701 | else if (SCM_FRACTIONP (y)) | |
1702 | return scm_i_slow_exact_centered_quotient (x, y); | |
1703 | else | |
1704 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1705 | s_scm_centered_quotient); | |
1706 | } | |
1707 | else if (SCM_REALP (x)) | |
1708 | { | |
1709 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1710 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1711 | return scm_i_inexact_centered_quotient | |
1712 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1713 | else | |
1714 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1715 | s_scm_centered_quotient); | |
1716 | } | |
1717 | else if (SCM_FRACTIONP (x)) | |
1718 | { | |
1719 | if (SCM_REALP (y)) | |
1720 | return scm_i_inexact_centered_quotient | |
1721 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1722 | else | |
1723 | return scm_i_slow_exact_centered_quotient (x, y); | |
1724 | } | |
1725 | else | |
1726 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1727 | s_scm_centered_quotient); | |
1728 | } | |
1729 | #undef FUNC_NAME | |
1730 | ||
1731 | static SCM | |
1732 | scm_i_inexact_centered_quotient (double x, double y) | |
1733 | { | |
1734 | if (SCM_LIKELY (y > 0)) | |
1735 | return scm_from_double (floor (x/y + 0.5)); | |
1736 | else if (SCM_LIKELY (y < 0)) | |
1737 | return scm_from_double (ceil (x/y - 0.5)); | |
1738 | else if (y == 0) | |
1739 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
1740 | else | |
1741 | return scm_nan (); | |
1742 | } | |
1743 | ||
1744 | /* Assumes that both x and y are bigints, though | |
1745 | x might be able to fit into a fixnum. */ | |
1746 | static SCM | |
1747 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
1748 | { | |
1749 | SCM q, r, min_r; | |
1750 | ||
1751 | /* Note that x might be small enough to fit into a | |
1752 | fixnum, so we must not let it escape into the wild */ | |
1753 | q = scm_i_mkbig (); | |
1754 | r = scm_i_mkbig (); | |
1755 | ||
1756 | /* min_r will eventually become -abs(y)/2 */ | |
1757 | min_r = scm_i_mkbig (); | |
1758 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1759 | SCM_I_BIG_MPZ (y), 1); | |
1760 | ||
1761 | /* Arrange for rr to initially be non-positive, | |
1762 | because that simplifies the test to see | |
1763 | if it is within the needed bounds. */ | |
1764 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1765 | { | |
1766 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1767 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1768 | scm_remember_upto_here_2 (x, y); | |
1769 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1770 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1771 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1772 | SCM_I_BIG_MPZ (q), 1); | |
1773 | } | |
1774 | else | |
1775 | { | |
1776 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1777 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1778 | scm_remember_upto_here_2 (x, y); | |
1779 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1780 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1781 | SCM_I_BIG_MPZ (q), 1); | |
1782 | } | |
1783 | scm_remember_upto_here_2 (r, min_r); | |
1784 | return scm_i_normbig (q); | |
1785 | } | |
1786 | ||
1787 | /* Compute exact centered quotient the slow way. | |
1788 | We use this only if both arguments are exact, | |
1789 | and at least one of them is a fraction */ | |
1790 | static SCM | |
1791 | scm_i_slow_exact_centered_quotient (SCM x, SCM y) | |
1792 | { | |
1793 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1794 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1795 | s_scm_centered_quotient); | |
1796 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1797 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1798 | s_scm_centered_quotient); | |
1799 | else if (scm_is_true (scm_positive_p (y))) | |
1800 | return scm_floor (scm_sum (scm_divide (x, y), | |
1801 | exactly_one_half)); | |
1802 | else if (scm_is_true (scm_negative_p (y))) | |
1803 | return scm_ceiling (scm_difference (scm_divide (x, y), | |
1804 | exactly_one_half)); | |
1805 | else | |
1806 | scm_num_overflow (s_scm_centered_quotient); | |
1807 | } | |
1808 | ||
1809 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
1810 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
1811 | static SCM scm_i_slow_exact_centered_remainder (SCM x, SCM y); | |
1812 | ||
1813 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
1814 | (SCM x, SCM y), | |
1815 | "Return the real number @var{r} such that\n" | |
1816 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
1817 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1818 | "for some integer @var{q}.\n" | |
1819 | "@lisp\n" | |
1820 | "(centered-remainder 123 10) @result{} 3\n" | |
1821 | "(centered-remainder 123 -10) @result{} 3\n" | |
1822 | "(centered-remainder -123 10) @result{} -3\n" | |
1823 | "(centered-remainder -123 -10) @result{} -3\n" | |
1824 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
1825 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
1826 | "@end lisp") | |
1827 | #define FUNC_NAME s_scm_centered_remainder | |
1828 | { | |
1829 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1830 | { | |
1831 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1832 | { | |
1833 | scm_t_inum yy = SCM_I_INUM (y); | |
1834 | if (SCM_UNLIKELY (yy == 0)) | |
1835 | scm_num_overflow (s_scm_centered_remainder); | |
1836 | else | |
1837 | { | |
1838 | scm_t_inum xx = SCM_I_INUM (x); | |
1839 | scm_t_inum rr = xx % yy; | |
1840 | if (SCM_LIKELY (xx > 0)) | |
1841 | { | |
1842 | if (SCM_LIKELY (yy > 0)) | |
1843 | { | |
1844 | if (rr >= (yy + 1) / 2) | |
1845 | rr -= yy; | |
1846 | } | |
1847 | else | |
1848 | { | |
1849 | if (rr >= (1 - yy) / 2) | |
1850 | rr += yy; | |
1851 | } | |
1852 | } | |
1853 | else | |
1854 | { | |
1855 | if (SCM_LIKELY (yy > 0)) | |
1856 | { | |
1857 | if (rr < -yy / 2) | |
1858 | rr += yy; | |
1859 | } | |
1860 | else | |
1861 | { | |
1862 | if (rr < yy / 2) | |
1863 | rr -= yy; | |
1864 | } | |
1865 | } | |
1866 | return SCM_I_MAKINUM (rr); | |
1867 | } | |
1868 | } | |
1869 | else if (SCM_BIGP (y)) | |
1870 | { | |
1871 | /* Pass a denormalized bignum version of x (even though it | |
1872 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
1873 | return scm_i_bigint_centered_remainder | |
1874 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1875 | } | |
1876 | else if (SCM_REALP (y)) | |
1877 | return scm_i_inexact_centered_remainder | |
1878 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1879 | else if (SCM_FRACTIONP (y)) | |
1880 | return scm_i_slow_exact_centered_remainder (x, y); | |
1881 | else | |
1882 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1883 | s_scm_centered_remainder); | |
1884 | } | |
1885 | else if (SCM_BIGP (x)) | |
1886 | { | |
1887 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1888 | { | |
1889 | scm_t_inum yy = SCM_I_INUM (y); | |
1890 | if (SCM_UNLIKELY (yy == 0)) | |
1891 | scm_num_overflow (s_scm_centered_remainder); | |
1892 | else | |
1893 | { | |
1894 | scm_t_inum rr; | |
1895 | /* Arrange for rr to initially be non-positive, | |
1896 | because that simplifies the test to see | |
1897 | if it is within the needed bounds. */ | |
1898 | if (yy > 0) | |
1899 | { | |
1900 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1901 | scm_remember_upto_here_1 (x); | |
1902 | if (rr < -yy / 2) | |
1903 | rr += yy; | |
1904 | } | |
1905 | else | |
1906 | { | |
1907 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1908 | scm_remember_upto_here_1 (x); | |
1909 | if (rr < yy / 2) | |
1910 | rr -= yy; | |
1911 | } | |
1912 | return SCM_I_MAKINUM (rr); | |
1913 | } | |
1914 | } | |
1915 | else if (SCM_BIGP (y)) | |
1916 | return scm_i_bigint_centered_remainder (x, y); | |
1917 | else if (SCM_REALP (y)) | |
1918 | return scm_i_inexact_centered_remainder | |
1919 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1920 | else if (SCM_FRACTIONP (y)) | |
1921 | return scm_i_slow_exact_centered_remainder (x, y); | |
1922 | else | |
1923 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1924 | s_scm_centered_remainder); | |
1925 | } | |
1926 | else if (SCM_REALP (x)) | |
1927 | { | |
1928 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1929 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1930 | return scm_i_inexact_centered_remainder | |
1931 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1932 | else | |
1933 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1934 | s_scm_centered_remainder); | |
1935 | } | |
1936 | else if (SCM_FRACTIONP (x)) | |
1937 | { | |
1938 | if (SCM_REALP (y)) | |
1939 | return scm_i_inexact_centered_remainder | |
1940 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1941 | else | |
1942 | return scm_i_slow_exact_centered_remainder (x, y); | |
1943 | } | |
1944 | else | |
1945 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
1946 | s_scm_centered_remainder); | |
1947 | } | |
1948 | #undef FUNC_NAME | |
1949 | ||
1950 | static SCM | |
1951 | scm_i_inexact_centered_remainder (double x, double y) | |
1952 | { | |
1953 | double q; | |
1954 | ||
1955 | /* Although it would be more efficient to use fmod here, we can't | |
1956 | because it would in some cases produce results inconsistent with | |
1957 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
1958 | close). In particular, when x-y/2 is very close to a multiple of | |
1959 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
1960 | two cases must correspond to different choices of q. If quotient | |
1961 | chooses one and remainder chooses the other, it would be bad. */ | |
1962 | if (SCM_LIKELY (y > 0)) | |
1963 | q = floor (x/y + 0.5); | |
1964 | else if (SCM_LIKELY (y < 0)) | |
1965 | q = ceil (x/y - 0.5); | |
1966 | else if (y == 0) | |
1967 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
1968 | else | |
1969 | return scm_nan (); | |
1970 | return scm_from_double (x - q * y); | |
1971 | } | |
1972 | ||
1973 | /* Assumes that both x and y are bigints, though | |
1974 | x might be able to fit into a fixnum. */ | |
1975 | static SCM | |
1976 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
1977 | { | |
1978 | SCM r, min_r; | |
1979 | ||
1980 | /* Note that x might be small enough to fit into a | |
1981 | fixnum, so we must not let it escape into the wild */ | |
1982 | r = scm_i_mkbig (); | |
1983 | ||
1984 | /* min_r will eventually become -abs(y)/2 */ | |
1985 | min_r = scm_i_mkbig (); | |
1986 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1987 | SCM_I_BIG_MPZ (y), 1); | |
1988 | ||
1989 | /* Arrange for rr to initially be non-positive, | |
1990 | because that simplifies the test to see | |
1991 | if it is within the needed bounds. */ | |
1992 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1993 | { | |
1994 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1995 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1996 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1997 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1998 | mpz_add (SCM_I_BIG_MPZ (r), | |
1999 | SCM_I_BIG_MPZ (r), | |
2000 | SCM_I_BIG_MPZ (y)); | |
2001 | } | |
2002 | else | |
2003 | { | |
2004 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2005 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2006 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2007 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2008 | SCM_I_BIG_MPZ (r), | |
2009 | SCM_I_BIG_MPZ (y)); | |
2010 | } | |
2011 | scm_remember_upto_here_2 (x, y); | |
2012 | return scm_i_normbig (r); | |
2013 | } | |
2014 | ||
2015 | /* Compute exact centered_remainder the slow way. | |
2016 | We use this only if both arguments are exact, | |
2017 | and at least one of them is a fraction */ | |
2018 | static SCM | |
2019 | scm_i_slow_exact_centered_remainder (SCM x, SCM y) | |
2020 | { | |
2021 | SCM q; | |
2022 | ||
2023 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
2024 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2025 | s_scm_centered_remainder); | |
2026 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
2027 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2028 | s_scm_centered_remainder); | |
2029 | else if (scm_is_true (scm_positive_p (y))) | |
2030 | q = scm_floor (scm_sum (scm_divide (x, y), exactly_one_half)); | |
2031 | else if (scm_is_true (scm_negative_p (y))) | |
2032 | q = scm_ceiling (scm_difference (scm_divide (x, y), exactly_one_half)); | |
2033 | else | |
2034 | scm_num_overflow (s_scm_centered_remainder); | |
2035 | return scm_difference (x, scm_product (y, q)); | |
2036 | } | |
2037 | ||
2038 | ||
ac6ce16b MW |
2039 | static SCM scm_i_inexact_centered_divide (double x, double y); |
2040 | static SCM scm_i_bigint_centered_divide (SCM x, SCM y); | |
2041 | static SCM scm_i_slow_exact_centered_divide (SCM x, SCM y); | |
ff62c168 | 2042 | |
ac6ce16b | 2043 | SCM_PRIMITIVE_GENERIC (scm_centered_divide, "centered/", 2, 0, 0, |
ff62c168 MW |
2044 | (SCM x, SCM y), |
2045 | "Return the integer @var{q} and the real number @var{r}\n" | |
2046 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2047 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2048 | "@lisp\n" | |
2049 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2050 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2051 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2052 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2053 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2054 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2055 | "@end lisp") | |
ac6ce16b | 2056 | #define FUNC_NAME s_scm_centered_divide |
ff62c168 MW |
2057 | { |
2058 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2059 | { | |
2060 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2061 | { | |
2062 | scm_t_inum yy = SCM_I_INUM (y); | |
2063 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2064 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2065 | else |
2066 | { | |
2067 | scm_t_inum xx = SCM_I_INUM (x); | |
2068 | scm_t_inum qq = xx / yy; | |
2069 | scm_t_inum rr = xx - qq * yy; | |
2070 | if (SCM_LIKELY (xx > 0)) | |
2071 | { | |
2072 | if (SCM_LIKELY (yy > 0)) | |
2073 | { | |
2074 | if (rr >= (yy + 1) / 2) | |
2075 | { qq++; rr -= yy; } | |
2076 | } | |
2077 | else | |
2078 | { | |
2079 | if (rr >= (1 - yy) / 2) | |
2080 | { qq--; rr += yy; } | |
2081 | } | |
2082 | } | |
2083 | else | |
2084 | { | |
2085 | if (SCM_LIKELY (yy > 0)) | |
2086 | { | |
2087 | if (rr < -yy / 2) | |
2088 | { qq--; rr += yy; } | |
2089 | } | |
2090 | else | |
2091 | { | |
2092 | if (rr < yy / 2) | |
2093 | { qq++; rr -= yy; } | |
2094 | } | |
2095 | } | |
2096 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
2097 | SCM_I_MAKINUM (rr))); | |
2098 | } | |
2099 | } | |
2100 | else if (SCM_BIGP (y)) | |
2101 | { | |
2102 | /* Pass a denormalized bignum version of x (even though it | |
ac6ce16b MW |
2103 | can fit in a fixnum) to scm_i_bigint_centered_divide */ |
2104 | return scm_i_bigint_centered_divide | |
ff62c168 MW |
2105 | (scm_i_long2big (SCM_I_INUM (x)), y); |
2106 | } | |
2107 | else if (SCM_REALP (y)) | |
ac6ce16b | 2108 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2109 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
2110 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2111 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2112 | else |
ac6ce16b MW |
2113 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2114 | s_scm_centered_divide); | |
ff62c168 MW |
2115 | } |
2116 | else if (SCM_BIGP (x)) | |
2117 | { | |
2118 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2119 | { | |
2120 | scm_t_inum yy = SCM_I_INUM (y); | |
2121 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2122 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2123 | else |
2124 | { | |
2125 | SCM q = scm_i_mkbig (); | |
2126 | scm_t_inum rr; | |
2127 | /* Arrange for rr to initially be non-positive, | |
2128 | because that simplifies the test to see | |
2129 | if it is within the needed bounds. */ | |
2130 | if (yy > 0) | |
2131 | { | |
2132 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2133 | SCM_I_BIG_MPZ (x), yy); | |
2134 | scm_remember_upto_here_1 (x); | |
2135 | if (rr < -yy / 2) | |
2136 | { | |
2137 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2138 | SCM_I_BIG_MPZ (q), 1); | |
2139 | rr += yy; | |
2140 | } | |
2141 | } | |
2142 | else | |
2143 | { | |
2144 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2145 | SCM_I_BIG_MPZ (x), -yy); | |
2146 | scm_remember_upto_here_1 (x); | |
2147 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2148 | if (rr < yy / 2) | |
2149 | { | |
2150 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2151 | SCM_I_BIG_MPZ (q), 1); | |
2152 | rr -= yy; | |
2153 | } | |
2154 | } | |
2155 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2156 | SCM_I_MAKINUM (rr))); | |
2157 | } | |
2158 | } | |
2159 | else if (SCM_BIGP (y)) | |
ac6ce16b | 2160 | return scm_i_bigint_centered_divide (x, y); |
ff62c168 | 2161 | else if (SCM_REALP (y)) |
ac6ce16b | 2162 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2163 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
2164 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2165 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2166 | else |
ac6ce16b MW |
2167 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2168 | s_scm_centered_divide); | |
ff62c168 MW |
2169 | } |
2170 | else if (SCM_REALP (x)) | |
2171 | { | |
2172 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2173 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 2174 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2175 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
2176 | else | |
ac6ce16b MW |
2177 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2178 | s_scm_centered_divide); | |
ff62c168 MW |
2179 | } |
2180 | else if (SCM_FRACTIONP (x)) | |
2181 | { | |
2182 | if (SCM_REALP (y)) | |
ac6ce16b | 2183 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2184 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
2185 | else | |
ac6ce16b | 2186 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 MW |
2187 | } |
2188 | else | |
ac6ce16b MW |
2189 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2190 | s_scm_centered_divide); | |
ff62c168 MW |
2191 | } |
2192 | #undef FUNC_NAME | |
2193 | ||
2194 | static SCM | |
ac6ce16b | 2195 | scm_i_inexact_centered_divide (double x, double y) |
ff62c168 MW |
2196 | { |
2197 | double q, r; | |
2198 | ||
2199 | if (SCM_LIKELY (y > 0)) | |
2200 | q = floor (x/y + 0.5); | |
2201 | else if (SCM_LIKELY (y < 0)) | |
2202 | q = ceil (x/y - 0.5); | |
2203 | else if (y == 0) | |
ac6ce16b | 2204 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ |
ff62c168 MW |
2205 | else |
2206 | q = guile_NaN; | |
2207 | r = x - q * y; | |
2208 | return scm_values (scm_list_2 (scm_from_double (q), | |
2209 | scm_from_double (r))); | |
2210 | } | |
2211 | ||
2212 | /* Assumes that both x and y are bigints, though | |
2213 | x might be able to fit into a fixnum. */ | |
2214 | static SCM | |
ac6ce16b | 2215 | scm_i_bigint_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2216 | { |
2217 | SCM q, r, min_r; | |
2218 | ||
2219 | /* Note that x might be small enough to fit into a | |
2220 | fixnum, so we must not let it escape into the wild */ | |
2221 | q = scm_i_mkbig (); | |
2222 | r = scm_i_mkbig (); | |
2223 | ||
2224 | /* min_r will eventually become -abs(y/2) */ | |
2225 | min_r = scm_i_mkbig (); | |
2226 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2227 | SCM_I_BIG_MPZ (y), 1); | |
2228 | ||
2229 | /* Arrange for rr to initially be non-positive, | |
2230 | because that simplifies the test to see | |
2231 | if it is within the needed bounds. */ | |
2232 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2233 | { | |
2234 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2235 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2236 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2237 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2238 | { | |
2239 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2240 | SCM_I_BIG_MPZ (q), 1); | |
2241 | mpz_add (SCM_I_BIG_MPZ (r), | |
2242 | SCM_I_BIG_MPZ (r), | |
2243 | SCM_I_BIG_MPZ (y)); | |
2244 | } | |
2245 | } | |
2246 | else | |
2247 | { | |
2248 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2249 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2250 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2251 | { | |
2252 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2253 | SCM_I_BIG_MPZ (q), 1); | |
2254 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2255 | SCM_I_BIG_MPZ (r), | |
2256 | SCM_I_BIG_MPZ (y)); | |
2257 | } | |
2258 | } | |
2259 | scm_remember_upto_here_2 (x, y); | |
2260 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2261 | scm_i_normbig (r))); | |
2262 | } | |
2263 | ||
2264 | /* Compute exact centered quotient and remainder the slow way. | |
2265 | We use this only if both arguments are exact, | |
2266 | and at least one of them is a fraction */ | |
2267 | static SCM | |
ac6ce16b | 2268 | scm_i_slow_exact_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2269 | { |
2270 | SCM q, r; | |
2271 | ||
2272 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
2273 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2274 | s_scm_centered_divide); | |
ff62c168 | 2275 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
2276 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2277 | s_scm_centered_divide); | |
ff62c168 MW |
2278 | else if (scm_is_true (scm_positive_p (y))) |
2279 | q = scm_floor (scm_sum (scm_divide (x, y), | |
2280 | exactly_one_half)); | |
2281 | else if (scm_is_true (scm_negative_p (y))) | |
2282 | q = scm_ceiling (scm_difference (scm_divide (x, y), | |
2283 | exactly_one_half)); | |
2284 | else | |
ac6ce16b | 2285 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2286 | r = scm_difference (x, scm_product (q, y)); |
2287 | return scm_values (scm_list_2 (q, r)); | |
2288 | } | |
2289 | ||
2290 | ||
78d3deb1 AW |
2291 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
2292 | (SCM x, SCM y, SCM rest), | |
2293 | "Return the greatest common divisor of all parameter values.\n" | |
2294 | "If called without arguments, 0 is returned.") | |
2295 | #define FUNC_NAME s_scm_i_gcd | |
2296 | { | |
2297 | while (!scm_is_null (rest)) | |
2298 | { x = scm_gcd (x, y); | |
2299 | y = scm_car (rest); | |
2300 | rest = scm_cdr (rest); | |
2301 | } | |
2302 | return scm_gcd (x, y); | |
2303 | } | |
2304 | #undef FUNC_NAME | |
2305 | ||
2306 | #define s_gcd s_scm_i_gcd | |
2307 | #define g_gcd g_scm_i_gcd | |
2308 | ||
0f2d19dd | 2309 | SCM |
6e8d25a6 | 2310 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 2311 | { |
ca46fb90 | 2312 | if (SCM_UNBNDP (y)) |
1dd79792 | 2313 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 2314 | |
e11e83f3 | 2315 | if (SCM_I_INUMP (x)) |
ca46fb90 | 2316 | { |
e11e83f3 | 2317 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2318 | { |
e25f3727 AW |
2319 | scm_t_inum xx = SCM_I_INUM (x); |
2320 | scm_t_inum yy = SCM_I_INUM (y); | |
2321 | scm_t_inum u = xx < 0 ? -xx : xx; | |
2322 | scm_t_inum v = yy < 0 ? -yy : yy; | |
2323 | scm_t_inum result; | |
0aacf84e MD |
2324 | if (xx == 0) |
2325 | result = v; | |
2326 | else if (yy == 0) | |
2327 | result = u; | |
2328 | else | |
2329 | { | |
e25f3727 AW |
2330 | scm_t_inum k = 1; |
2331 | scm_t_inum t; | |
0aacf84e MD |
2332 | /* Determine a common factor 2^k */ |
2333 | while (!(1 & (u | v))) | |
2334 | { | |
2335 | k <<= 1; | |
2336 | u >>= 1; | |
2337 | v >>= 1; | |
2338 | } | |
2339 | /* Now, any factor 2^n can be eliminated */ | |
2340 | if (u & 1) | |
2341 | t = -v; | |
2342 | else | |
2343 | { | |
2344 | t = u; | |
2345 | b3: | |
2346 | t = SCM_SRS (t, 1); | |
2347 | } | |
2348 | if (!(1 & t)) | |
2349 | goto b3; | |
2350 | if (t > 0) | |
2351 | u = t; | |
2352 | else | |
2353 | v = -t; | |
2354 | t = u - v; | |
2355 | if (t != 0) | |
2356 | goto b3; | |
2357 | result = u * k; | |
2358 | } | |
2359 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 2360 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2361 | : scm_i_inum2big (result)); |
ca46fb90 RB |
2362 | } |
2363 | else if (SCM_BIGP (y)) | |
2364 | { | |
0bff4dce KR |
2365 | SCM_SWAP (x, y); |
2366 | goto big_inum; | |
ca46fb90 RB |
2367 | } |
2368 | else | |
2369 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 2370 | } |
ca46fb90 RB |
2371 | else if (SCM_BIGP (x)) |
2372 | { | |
e11e83f3 | 2373 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2374 | { |
e25f3727 AW |
2375 | scm_t_bits result; |
2376 | scm_t_inum yy; | |
0bff4dce | 2377 | big_inum: |
e11e83f3 | 2378 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
2379 | if (yy == 0) |
2380 | return scm_abs (x); | |
0aacf84e MD |
2381 | if (yy < 0) |
2382 | yy = -yy; | |
ca46fb90 RB |
2383 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
2384 | scm_remember_upto_here_1 (x); | |
0aacf84e | 2385 | return (SCM_POSFIXABLE (result) |
d956fa6f | 2386 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2387 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
2388 | } |
2389 | else if (SCM_BIGP (y)) | |
2390 | { | |
2391 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
2392 | mpz_gcd (SCM_I_BIG_MPZ (result), |
2393 | SCM_I_BIG_MPZ (x), | |
2394 | SCM_I_BIG_MPZ (y)); | |
2395 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
2396 | return scm_i_normbig (result); |
2397 | } | |
2398 | else | |
2399 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 2400 | } |
ca46fb90 | 2401 | else |
09fb7599 | 2402 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
2403 | } |
2404 | ||
78d3deb1 AW |
2405 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
2406 | (SCM x, SCM y, SCM rest), | |
2407 | "Return the least common multiple of the arguments.\n" | |
2408 | "If called without arguments, 1 is returned.") | |
2409 | #define FUNC_NAME s_scm_i_lcm | |
2410 | { | |
2411 | while (!scm_is_null (rest)) | |
2412 | { x = scm_lcm (x, y); | |
2413 | y = scm_car (rest); | |
2414 | rest = scm_cdr (rest); | |
2415 | } | |
2416 | return scm_lcm (x, y); | |
2417 | } | |
2418 | #undef FUNC_NAME | |
2419 | ||
2420 | #define s_lcm s_scm_i_lcm | |
2421 | #define g_lcm g_scm_i_lcm | |
2422 | ||
0f2d19dd | 2423 | SCM |
6e8d25a6 | 2424 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 2425 | { |
ca46fb90 RB |
2426 | if (SCM_UNBNDP (n2)) |
2427 | { | |
2428 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
2429 | return SCM_I_MAKINUM (1L); |
2430 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 2431 | } |
09fb7599 | 2432 | |
e11e83f3 | 2433 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 2434 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 2435 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 2436 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 2437 | |
e11e83f3 | 2438 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 2439 | { |
e11e83f3 | 2440 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2441 | { |
2442 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 2443 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
2444 | return d; |
2445 | else | |
2446 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
2447 | } | |
2448 | else | |
2449 | { | |
2450 | /* inum n1, big n2 */ | |
2451 | inumbig: | |
2452 | { | |
2453 | SCM result = scm_i_mkbig (); | |
e25f3727 | 2454 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
2455 | if (nn1 == 0) return SCM_INUM0; |
2456 | if (nn1 < 0) nn1 = - nn1; | |
2457 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
2458 | scm_remember_upto_here_1 (n2); | |
2459 | return result; | |
2460 | } | |
2461 | } | |
2462 | } | |
2463 | else | |
2464 | { | |
2465 | /* big n1 */ | |
e11e83f3 | 2466 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2467 | { |
2468 | SCM_SWAP (n1, n2); | |
2469 | goto inumbig; | |
2470 | } | |
2471 | else | |
2472 | { | |
2473 | SCM result = scm_i_mkbig (); | |
2474 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
2475 | SCM_I_BIG_MPZ (n1), | |
2476 | SCM_I_BIG_MPZ (n2)); | |
2477 | scm_remember_upto_here_2(n1, n2); | |
2478 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
2479 | return result; | |
2480 | } | |
f872b822 | 2481 | } |
0f2d19dd JB |
2482 | } |
2483 | ||
8a525303 GB |
2484 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
2485 | ||
2486 | Logand: | |
2487 | X Y Result Method: | |
2488 | (len) | |
2489 | + + + x (map digit:logand X Y) | |
2490 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
2491 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
2492 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
2493 | ||
2494 | Logior: | |
2495 | X Y Result Method: | |
2496 | ||
2497 | + + + (map digit:logior X Y) | |
2498 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
2499 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
2500 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
2501 | ||
2502 | Logxor: | |
2503 | X Y Result Method: | |
2504 | ||
2505 | + + + (map digit:logxor X Y) | |
2506 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
2507 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
2508 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
2509 | ||
2510 | Logtest: | |
2511 | X Y Result | |
2512 | ||
2513 | + + (any digit:logand X Y) | |
2514 | + - (any digit:logand X (lognot (+ -1 Y))) | |
2515 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
2516 | - - #t | |
2517 | ||
2518 | */ | |
2519 | ||
78d3deb1 AW |
2520 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
2521 | (SCM x, SCM y, SCM rest), | |
2522 | "Return the bitwise AND of the integer arguments.\n\n" | |
2523 | "@lisp\n" | |
2524 | "(logand) @result{} -1\n" | |
2525 | "(logand 7) @result{} 7\n" | |
2526 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
2527 | "@end lisp") | |
2528 | #define FUNC_NAME s_scm_i_logand | |
2529 | { | |
2530 | while (!scm_is_null (rest)) | |
2531 | { x = scm_logand (x, y); | |
2532 | y = scm_car (rest); | |
2533 | rest = scm_cdr (rest); | |
2534 | } | |
2535 | return scm_logand (x, y); | |
2536 | } | |
2537 | #undef FUNC_NAME | |
2538 | ||
2539 | #define s_scm_logand s_scm_i_logand | |
2540 | ||
2541 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 2542 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 2543 | { |
e25f3727 | 2544 | scm_t_inum nn1; |
9a00c9fc | 2545 | |
0aacf84e MD |
2546 | if (SCM_UNBNDP (n2)) |
2547 | { | |
2548 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 2549 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
2550 | else if (!SCM_NUMBERP (n1)) |
2551 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
2552 | else if (SCM_NUMBERP (n1)) | |
2553 | return n1; | |
2554 | else | |
2555 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2556 | } |
09fb7599 | 2557 | |
e11e83f3 | 2558 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2559 | { |
e11e83f3 MV |
2560 | nn1 = SCM_I_INUM (n1); |
2561 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2562 | { |
e25f3727 | 2563 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2564 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
2565 | } |
2566 | else if SCM_BIGP (n2) | |
2567 | { | |
2568 | intbig: | |
2569 | if (n1 == 0) | |
2570 | return SCM_INUM0; | |
2571 | { | |
2572 | SCM result_z = scm_i_mkbig (); | |
2573 | mpz_t nn1_z; | |
2574 | mpz_init_set_si (nn1_z, nn1); | |
2575 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2576 | scm_remember_upto_here_1 (n2); | |
2577 | mpz_clear (nn1_z); | |
2578 | return scm_i_normbig (result_z); | |
2579 | } | |
2580 | } | |
2581 | else | |
2582 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2583 | } | |
2584 | else if (SCM_BIGP (n1)) | |
2585 | { | |
e11e83f3 | 2586 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2587 | { |
2588 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2589 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2590 | goto intbig; |
2591 | } | |
2592 | else if (SCM_BIGP (n2)) | |
2593 | { | |
2594 | SCM result_z = scm_i_mkbig (); | |
2595 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
2596 | SCM_I_BIG_MPZ (n1), | |
2597 | SCM_I_BIG_MPZ (n2)); | |
2598 | scm_remember_upto_here_2 (n1, n2); | |
2599 | return scm_i_normbig (result_z); | |
2600 | } | |
2601 | else | |
2602 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2603 | } |
0aacf84e | 2604 | else |
09fb7599 | 2605 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2606 | } |
1bbd0b84 | 2607 | #undef FUNC_NAME |
0f2d19dd | 2608 | |
09fb7599 | 2609 | |
78d3deb1 AW |
2610 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
2611 | (SCM x, SCM y, SCM rest), | |
2612 | "Return the bitwise OR of the integer arguments.\n\n" | |
2613 | "@lisp\n" | |
2614 | "(logior) @result{} 0\n" | |
2615 | "(logior 7) @result{} 7\n" | |
2616 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
2617 | "@end lisp") | |
2618 | #define FUNC_NAME s_scm_i_logior | |
2619 | { | |
2620 | while (!scm_is_null (rest)) | |
2621 | { x = scm_logior (x, y); | |
2622 | y = scm_car (rest); | |
2623 | rest = scm_cdr (rest); | |
2624 | } | |
2625 | return scm_logior (x, y); | |
2626 | } | |
2627 | #undef FUNC_NAME | |
2628 | ||
2629 | #define s_scm_logior s_scm_i_logior | |
2630 | ||
2631 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 2632 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 2633 | { |
e25f3727 | 2634 | scm_t_inum nn1; |
9a00c9fc | 2635 | |
0aacf84e MD |
2636 | if (SCM_UNBNDP (n2)) |
2637 | { | |
2638 | if (SCM_UNBNDP (n1)) | |
2639 | return SCM_INUM0; | |
2640 | else if (SCM_NUMBERP (n1)) | |
2641 | return n1; | |
2642 | else | |
2643 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2644 | } |
09fb7599 | 2645 | |
e11e83f3 | 2646 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2647 | { |
e11e83f3 MV |
2648 | nn1 = SCM_I_INUM (n1); |
2649 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2650 | { |
e11e83f3 | 2651 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 2652 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
2653 | } |
2654 | else if (SCM_BIGP (n2)) | |
2655 | { | |
2656 | intbig: | |
2657 | if (nn1 == 0) | |
2658 | return n2; | |
2659 | { | |
2660 | SCM result_z = scm_i_mkbig (); | |
2661 | mpz_t nn1_z; | |
2662 | mpz_init_set_si (nn1_z, nn1); | |
2663 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2664 | scm_remember_upto_here_1 (n2); | |
2665 | mpz_clear (nn1_z); | |
9806de0d | 2666 | return scm_i_normbig (result_z); |
0aacf84e MD |
2667 | } |
2668 | } | |
2669 | else | |
2670 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2671 | } | |
2672 | else if (SCM_BIGP (n1)) | |
2673 | { | |
e11e83f3 | 2674 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2675 | { |
2676 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2677 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2678 | goto intbig; |
2679 | } | |
2680 | else if (SCM_BIGP (n2)) | |
2681 | { | |
2682 | SCM result_z = scm_i_mkbig (); | |
2683 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
2684 | SCM_I_BIG_MPZ (n1), | |
2685 | SCM_I_BIG_MPZ (n2)); | |
2686 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 2687 | return scm_i_normbig (result_z); |
0aacf84e MD |
2688 | } |
2689 | else | |
2690 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2691 | } |
0aacf84e | 2692 | else |
09fb7599 | 2693 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2694 | } |
1bbd0b84 | 2695 | #undef FUNC_NAME |
0f2d19dd | 2696 | |
09fb7599 | 2697 | |
78d3deb1 AW |
2698 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
2699 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
2700 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
2701 | "set in the result if it is set in an odd number of arguments.\n" | |
2702 | "@lisp\n" | |
2703 | "(logxor) @result{} 0\n" | |
2704 | "(logxor 7) @result{} 7\n" | |
2705 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
2706 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 2707 | "@end lisp") |
78d3deb1 AW |
2708 | #define FUNC_NAME s_scm_i_logxor |
2709 | { | |
2710 | while (!scm_is_null (rest)) | |
2711 | { x = scm_logxor (x, y); | |
2712 | y = scm_car (rest); | |
2713 | rest = scm_cdr (rest); | |
2714 | } | |
2715 | return scm_logxor (x, y); | |
2716 | } | |
2717 | #undef FUNC_NAME | |
2718 | ||
2719 | #define s_scm_logxor s_scm_i_logxor | |
2720 | ||
2721 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 2722 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 2723 | { |
e25f3727 | 2724 | scm_t_inum nn1; |
9a00c9fc | 2725 | |
0aacf84e MD |
2726 | if (SCM_UNBNDP (n2)) |
2727 | { | |
2728 | if (SCM_UNBNDP (n1)) | |
2729 | return SCM_INUM0; | |
2730 | else if (SCM_NUMBERP (n1)) | |
2731 | return n1; | |
2732 | else | |
2733 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2734 | } |
09fb7599 | 2735 | |
e11e83f3 | 2736 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2737 | { |
e11e83f3 MV |
2738 | nn1 = SCM_I_INUM (n1); |
2739 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2740 | { |
e25f3727 | 2741 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2742 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
2743 | } |
2744 | else if (SCM_BIGP (n2)) | |
2745 | { | |
2746 | intbig: | |
2747 | { | |
2748 | SCM result_z = scm_i_mkbig (); | |
2749 | mpz_t nn1_z; | |
2750 | mpz_init_set_si (nn1_z, nn1); | |
2751 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2752 | scm_remember_upto_here_1 (n2); | |
2753 | mpz_clear (nn1_z); | |
2754 | return scm_i_normbig (result_z); | |
2755 | } | |
2756 | } | |
2757 | else | |
2758 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2759 | } | |
2760 | else if (SCM_BIGP (n1)) | |
2761 | { | |
e11e83f3 | 2762 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2763 | { |
2764 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2765 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2766 | goto intbig; |
2767 | } | |
2768 | else if (SCM_BIGP (n2)) | |
2769 | { | |
2770 | SCM result_z = scm_i_mkbig (); | |
2771 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
2772 | SCM_I_BIG_MPZ (n1), | |
2773 | SCM_I_BIG_MPZ (n2)); | |
2774 | scm_remember_upto_here_2 (n1, n2); | |
2775 | return scm_i_normbig (result_z); | |
2776 | } | |
2777 | else | |
2778 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2779 | } |
0aacf84e | 2780 | else |
09fb7599 | 2781 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2782 | } |
1bbd0b84 | 2783 | #undef FUNC_NAME |
0f2d19dd | 2784 | |
09fb7599 | 2785 | |
a1ec6916 | 2786 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 2787 | (SCM j, SCM k), |
ba6e7231 KR |
2788 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
2789 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
2790 | "without actually calculating the @code{logand}, just testing\n" | |
2791 | "for non-zero.\n" | |
2792 | "\n" | |
1e6808ea | 2793 | "@lisp\n" |
b380b885 MD |
2794 | "(logtest #b0100 #b1011) @result{} #f\n" |
2795 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 2796 | "@end lisp") |
1bbd0b84 | 2797 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 2798 | { |
e25f3727 | 2799 | scm_t_inum nj; |
9a00c9fc | 2800 | |
e11e83f3 | 2801 | if (SCM_I_INUMP (j)) |
0aacf84e | 2802 | { |
e11e83f3 MV |
2803 | nj = SCM_I_INUM (j); |
2804 | if (SCM_I_INUMP (k)) | |
0aacf84e | 2805 | { |
e25f3727 | 2806 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 2807 | return scm_from_bool (nj & nk); |
0aacf84e MD |
2808 | } |
2809 | else if (SCM_BIGP (k)) | |
2810 | { | |
2811 | intbig: | |
2812 | if (nj == 0) | |
2813 | return SCM_BOOL_F; | |
2814 | { | |
2815 | SCM result; | |
2816 | mpz_t nj_z; | |
2817 | mpz_init_set_si (nj_z, nj); | |
2818 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
2819 | scm_remember_upto_here_1 (k); | |
73e4de09 | 2820 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
2821 | mpz_clear (nj_z); |
2822 | return result; | |
2823 | } | |
2824 | } | |
2825 | else | |
2826 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2827 | } | |
2828 | else if (SCM_BIGP (j)) | |
2829 | { | |
e11e83f3 | 2830 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
2831 | { |
2832 | SCM_SWAP (j, k); | |
e11e83f3 | 2833 | nj = SCM_I_INUM (j); |
0aacf84e MD |
2834 | goto intbig; |
2835 | } | |
2836 | else if (SCM_BIGP (k)) | |
2837 | { | |
2838 | SCM result; | |
2839 | mpz_t result_z; | |
2840 | mpz_init (result_z); | |
2841 | mpz_and (result_z, | |
2842 | SCM_I_BIG_MPZ (j), | |
2843 | SCM_I_BIG_MPZ (k)); | |
2844 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 2845 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
2846 | mpz_clear (result_z); |
2847 | return result; | |
2848 | } | |
2849 | else | |
2850 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2851 | } | |
2852 | else | |
2853 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 2854 | } |
1bbd0b84 | 2855 | #undef FUNC_NAME |
0f2d19dd | 2856 | |
c1bfcf60 | 2857 | |
a1ec6916 | 2858 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 2859 | (SCM index, SCM j), |
ba6e7231 KR |
2860 | "Test whether bit number @var{index} in @var{j} is set.\n" |
2861 | "@var{index} starts from 0 for the least significant bit.\n" | |
2862 | "\n" | |
1e6808ea | 2863 | "@lisp\n" |
b380b885 MD |
2864 | "(logbit? 0 #b1101) @result{} #t\n" |
2865 | "(logbit? 1 #b1101) @result{} #f\n" | |
2866 | "(logbit? 2 #b1101) @result{} #t\n" | |
2867 | "(logbit? 3 #b1101) @result{} #t\n" | |
2868 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 2869 | "@end lisp") |
1bbd0b84 | 2870 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 2871 | { |
78166ad5 | 2872 | unsigned long int iindex; |
5efd3c7d | 2873 | iindex = scm_to_ulong (index); |
78166ad5 | 2874 | |
e11e83f3 | 2875 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
2876 | { |
2877 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 2878 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 2879 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 2880 | } |
0aacf84e MD |
2881 | else if (SCM_BIGP (j)) |
2882 | { | |
2883 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
2884 | scm_remember_upto_here_1 (j); | |
73e4de09 | 2885 | return scm_from_bool (val); |
0aacf84e MD |
2886 | } |
2887 | else | |
78166ad5 | 2888 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 2889 | } |
1bbd0b84 | 2890 | #undef FUNC_NAME |
0f2d19dd | 2891 | |
78166ad5 | 2892 | |
a1ec6916 | 2893 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 2894 | (SCM n), |
4d814788 | 2895 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
2896 | "argument.\n" |
2897 | "\n" | |
b380b885 MD |
2898 | "@lisp\n" |
2899 | "(number->string (lognot #b10000000) 2)\n" | |
2900 | " @result{} \"-10000001\"\n" | |
2901 | "(number->string (lognot #b0) 2)\n" | |
2902 | " @result{} \"-1\"\n" | |
1e6808ea | 2903 | "@end lisp") |
1bbd0b84 | 2904 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 2905 | { |
e11e83f3 | 2906 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
2907 | /* No overflow here, just need to toggle all the bits making up the inum. |
2908 | Enhancement: No need to strip the tag and add it back, could just xor | |
2909 | a block of 1 bits, if that worked with the various debug versions of | |
2910 | the SCM typedef. */ | |
e11e83f3 | 2911 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
2912 | |
2913 | } else if (SCM_BIGP (n)) { | |
2914 | SCM result = scm_i_mkbig (); | |
2915 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
2916 | scm_remember_upto_here_1 (n); | |
2917 | return result; | |
2918 | ||
2919 | } else { | |
2920 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
2921 | } | |
0f2d19dd | 2922 | } |
1bbd0b84 | 2923 | #undef FUNC_NAME |
0f2d19dd | 2924 | |
518b7508 KR |
2925 | /* returns 0 if IN is not an integer. OUT must already be |
2926 | initialized. */ | |
2927 | static int | |
2928 | coerce_to_big (SCM in, mpz_t out) | |
2929 | { | |
2930 | if (SCM_BIGP (in)) | |
2931 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
2932 | else if (SCM_I_INUMP (in)) |
2933 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
2934 | else |
2935 | return 0; | |
2936 | ||
2937 | return 1; | |
2938 | } | |
2939 | ||
d885e204 | 2940 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
2941 | (SCM n, SCM k, SCM m), |
2942 | "Return @var{n} raised to the integer exponent\n" | |
2943 | "@var{k}, modulo @var{m}.\n" | |
2944 | "\n" | |
2945 | "@lisp\n" | |
2946 | "(modulo-expt 2 3 5)\n" | |
2947 | " @result{} 3\n" | |
2948 | "@end lisp") | |
d885e204 | 2949 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
2950 | { |
2951 | mpz_t n_tmp; | |
2952 | mpz_t k_tmp; | |
2953 | mpz_t m_tmp; | |
2954 | ||
2955 | /* There are two classes of error we might encounter -- | |
2956 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
2957 | and | |
2958 | 2) wrong-type errors, which of course we'll report by calling | |
2959 | SCM_WRONG_TYPE_ARG. | |
2960 | We don't report those errors immediately, however; instead we do | |
2961 | some cleanup first. These variables tell us which error (if | |
2962 | any) we should report after cleaning up. | |
2963 | */ | |
2964 | int report_overflow = 0; | |
2965 | ||
2966 | int position_of_wrong_type = 0; | |
2967 | SCM value_of_wrong_type = SCM_INUM0; | |
2968 | ||
2969 | SCM result = SCM_UNDEFINED; | |
2970 | ||
2971 | mpz_init (n_tmp); | |
2972 | mpz_init (k_tmp); | |
2973 | mpz_init (m_tmp); | |
2974 | ||
bc36d050 | 2975 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
2976 | { |
2977 | report_overflow = 1; | |
2978 | goto cleanup; | |
2979 | } | |
2980 | ||
2981 | if (!coerce_to_big (n, n_tmp)) | |
2982 | { | |
2983 | value_of_wrong_type = n; | |
2984 | position_of_wrong_type = 1; | |
2985 | goto cleanup; | |
2986 | } | |
2987 | ||
2988 | if (!coerce_to_big (k, k_tmp)) | |
2989 | { | |
2990 | value_of_wrong_type = k; | |
2991 | position_of_wrong_type = 2; | |
2992 | goto cleanup; | |
2993 | } | |
2994 | ||
2995 | if (!coerce_to_big (m, m_tmp)) | |
2996 | { | |
2997 | value_of_wrong_type = m; | |
2998 | position_of_wrong_type = 3; | |
2999 | goto cleanup; | |
3000 | } | |
3001 | ||
3002 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
3003 | will get a divide-by-zero exception when an inverse 1/n mod m | |
3004 | doesn't exist (or is not unique). Since exceptions are hard to | |
3005 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
3006 | a simple failure code, which is easy to handle. */ | |
3007 | ||
3008 | if (-1 == mpz_sgn (k_tmp)) | |
3009 | { | |
3010 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
3011 | { | |
3012 | report_overflow = 1; | |
3013 | goto cleanup; | |
3014 | } | |
3015 | mpz_neg (k_tmp, k_tmp); | |
3016 | } | |
3017 | ||
3018 | result = scm_i_mkbig (); | |
3019 | mpz_powm (SCM_I_BIG_MPZ (result), | |
3020 | n_tmp, | |
3021 | k_tmp, | |
3022 | m_tmp); | |
b7b8c575 KR |
3023 | |
3024 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
3025 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
3026 | ||
518b7508 KR |
3027 | cleanup: |
3028 | mpz_clear (m_tmp); | |
3029 | mpz_clear (k_tmp); | |
3030 | mpz_clear (n_tmp); | |
3031 | ||
3032 | if (report_overflow) | |
3033 | scm_num_overflow (FUNC_NAME); | |
3034 | ||
3035 | if (position_of_wrong_type) | |
3036 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
3037 | value_of_wrong_type); | |
3038 | ||
3039 | return scm_i_normbig (result); | |
3040 | } | |
3041 | #undef FUNC_NAME | |
3042 | ||
a1ec6916 | 3043 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 3044 | (SCM n, SCM k), |
ba6e7231 KR |
3045 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
3046 | "exact integer, @var{n} can be any number.\n" | |
3047 | "\n" | |
2519490c MW |
3048 | "Negative @var{k} is supported, and results in\n" |
3049 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
3050 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 3051 | "includes @math{0^0} is 1.\n" |
1e6808ea | 3052 | "\n" |
b380b885 | 3053 | "@lisp\n" |
ba6e7231 KR |
3054 | "(integer-expt 2 5) @result{} 32\n" |
3055 | "(integer-expt -3 3) @result{} -27\n" | |
3056 | "(integer-expt 5 -3) @result{} 1/125\n" | |
3057 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 3058 | "@end lisp") |
1bbd0b84 | 3059 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 3060 | { |
e25f3727 | 3061 | scm_t_inum i2 = 0; |
1c35cb19 RB |
3062 | SCM z_i2 = SCM_BOOL_F; |
3063 | int i2_is_big = 0; | |
d956fa6f | 3064 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 3065 | |
bfe1f03a MW |
3066 | /* Specifically refrain from checking the type of the first argument. |
3067 | This allows us to exponentiate any object that can be multiplied. | |
3068 | If we must raise to a negative power, we must also be able to | |
3069 | take its reciprocal. */ | |
3070 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 3071 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 3072 | |
bfe1f03a MW |
3073 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
3074 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
3075 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
3076 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
3077 | /* The next check is necessary only because R6RS specifies different | |
3078 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
3079 | we simply skip this case and move on. */ | |
3080 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
3081 | { | |
3082 | /* k cannot be 0 at this point, because we | |
3083 | have already checked for that case above */ | |
3084 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
3085 | return n; |
3086 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
3087 | return scm_nan (); | |
3088 | } | |
ca46fb90 | 3089 | |
e11e83f3 MV |
3090 | if (SCM_I_INUMP (k)) |
3091 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
3092 | else if (SCM_BIGP (k)) |
3093 | { | |
3094 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
3095 | scm_remember_upto_here_1 (k); |
3096 | i2_is_big = 1; | |
3097 | } | |
2830fd91 | 3098 | else |
ca46fb90 RB |
3099 | SCM_WRONG_TYPE_ARG (2, k); |
3100 | ||
3101 | if (i2_is_big) | |
f872b822 | 3102 | { |
ca46fb90 RB |
3103 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
3104 | { | |
3105 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
3106 | n = scm_divide (n, SCM_UNDEFINED); | |
3107 | } | |
3108 | while (1) | |
3109 | { | |
3110 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
3111 | { | |
ca46fb90 RB |
3112 | return acc; |
3113 | } | |
3114 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
3115 | { | |
ca46fb90 RB |
3116 | return scm_product (acc, n); |
3117 | } | |
3118 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
3119 | acc = scm_product (acc, n); | |
3120 | n = scm_product (n, n); | |
3121 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
3122 | } | |
f872b822 | 3123 | } |
ca46fb90 | 3124 | else |
f872b822 | 3125 | { |
ca46fb90 RB |
3126 | if (i2 < 0) |
3127 | { | |
3128 | i2 = -i2; | |
3129 | n = scm_divide (n, SCM_UNDEFINED); | |
3130 | } | |
3131 | while (1) | |
3132 | { | |
3133 | if (0 == i2) | |
3134 | return acc; | |
3135 | if (1 == i2) | |
3136 | return scm_product (acc, n); | |
3137 | if (i2 & 1) | |
3138 | acc = scm_product (acc, n); | |
3139 | n = scm_product (n, n); | |
3140 | i2 >>= 1; | |
3141 | } | |
f872b822 | 3142 | } |
0f2d19dd | 3143 | } |
1bbd0b84 | 3144 | #undef FUNC_NAME |
0f2d19dd | 3145 | |
a1ec6916 | 3146 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 3147 | (SCM n, SCM cnt), |
32f19569 KR |
3148 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
3149 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 3150 | "\n" |
e7644cb2 | 3151 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
3152 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
3153 | "infinity. (Note that this is not the same rounding as\n" | |
3154 | "@code{quotient} does.)\n" | |
3155 | "\n" | |
3156 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
3157 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
3158 | "shift dropping bits.\n" | |
1e6808ea | 3159 | "\n" |
b380b885 | 3160 | "@lisp\n" |
1e6808ea MG |
3161 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
3162 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
3163 | "\n" |
3164 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
3165 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 3166 | "@end lisp") |
1bbd0b84 | 3167 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 3168 | { |
3ab9f56e | 3169 | long bits_to_shift; |
5efd3c7d | 3170 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 3171 | |
788aca27 KR |
3172 | if (SCM_I_INUMP (n)) |
3173 | { | |
e25f3727 | 3174 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
3175 | |
3176 | if (bits_to_shift > 0) | |
3177 | { | |
3178 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
3179 | overflow a non-zero fixnum. For smaller shifts we check the | |
3180 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
3181 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
3182 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
3183 | bits_to_shift)". */ | |
3184 | ||
3185 | if (nn == 0) | |
3186 | return n; | |
3187 | ||
3188 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3189 | && ((scm_t_bits) |
788aca27 KR |
3190 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
3191 | <= 1)) | |
3192 | { | |
3193 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
3194 | } | |
3195 | else | |
3196 | { | |
e25f3727 | 3197 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
3198 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3199 | bits_to_shift); | |
3200 | return result; | |
3201 | } | |
3202 | } | |
3203 | else | |
3204 | { | |
3205 | bits_to_shift = -bits_to_shift; | |
3206 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 3207 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
3208 | else |
3209 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
3210 | } | |
3211 | ||
3212 | } | |
3213 | else if (SCM_BIGP (n)) | |
ca46fb90 | 3214 | { |
788aca27 KR |
3215 | SCM result; |
3216 | ||
3217 | if (bits_to_shift == 0) | |
3218 | return n; | |
3219 | ||
3220 | result = scm_i_mkbig (); | |
3221 | if (bits_to_shift >= 0) | |
3222 | { | |
3223 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3224 | bits_to_shift); | |
3225 | return result; | |
3226 | } | |
ca46fb90 | 3227 | else |
788aca27 KR |
3228 | { |
3229 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
3230 | we have to allocate a bignum even if the result is going to be a | |
3231 | fixnum. */ | |
3232 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3233 | -bits_to_shift); | |
3234 | return scm_i_normbig (result); | |
3235 | } | |
3236 | ||
ca46fb90 RB |
3237 | } |
3238 | else | |
788aca27 KR |
3239 | { |
3240 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
3241 | } | |
0f2d19dd | 3242 | } |
1bbd0b84 | 3243 | #undef FUNC_NAME |
0f2d19dd | 3244 | |
3c9f20f8 | 3245 | |
a1ec6916 | 3246 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 3247 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
3248 | "Return the integer composed of the @var{start} (inclusive)\n" |
3249 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
3250 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
3251 | "\n" | |
b380b885 MD |
3252 | "@lisp\n" |
3253 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
3254 | " @result{} \"1010\"\n" | |
3255 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
3256 | " @result{} \"10110\"\n" | |
3257 | "@end lisp") | |
1bbd0b84 | 3258 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 3259 | { |
7f848242 | 3260 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
3261 | istart = scm_to_ulong (start); |
3262 | iend = scm_to_ulong (end); | |
c1bfcf60 | 3263 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 3264 | |
7f848242 KR |
3265 | /* how many bits to keep */ |
3266 | bits = iend - istart; | |
3267 | ||
e11e83f3 | 3268 | if (SCM_I_INUMP (n)) |
0aacf84e | 3269 | { |
e25f3727 | 3270 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
3271 | |
3272 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 3273 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 3274 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 3275 | |
0aacf84e MD |
3276 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
3277 | { | |
3278 | /* Since we emulate two's complement encoded numbers, this | |
3279 | * special case requires us to produce a result that has | |
7f848242 | 3280 | * more bits than can be stored in a fixnum. |
0aacf84e | 3281 | */ |
e25f3727 | 3282 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
3283 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3284 | bits); | |
3285 | return result; | |
0aacf84e | 3286 | } |
ac0c002c | 3287 | |
7f848242 | 3288 | /* mask down to requisite bits */ |
857ae6af | 3289 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 3290 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
3291 | } |
3292 | else if (SCM_BIGP (n)) | |
ac0c002c | 3293 | { |
7f848242 KR |
3294 | SCM result; |
3295 | if (bits == 1) | |
3296 | { | |
d956fa6f | 3297 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
3298 | } |
3299 | else | |
3300 | { | |
3301 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
3302 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
3303 | such bits into a ulong. */ | |
3304 | result = scm_i_mkbig (); | |
3305 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
3306 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
3307 | result = scm_i_normbig (result); | |
3308 | } | |
3309 | scm_remember_upto_here_1 (n); | |
3310 | return result; | |
ac0c002c | 3311 | } |
0aacf84e | 3312 | else |
78166ad5 | 3313 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 3314 | } |
1bbd0b84 | 3315 | #undef FUNC_NAME |
0f2d19dd | 3316 | |
7f848242 | 3317 | |
e4755e5c JB |
3318 | static const char scm_logtab[] = { |
3319 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
3320 | }; | |
1cc91f1b | 3321 | |
a1ec6916 | 3322 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 3323 | (SCM n), |
1e6808ea MG |
3324 | "Return the number of bits in integer @var{n}. If integer is\n" |
3325 | "positive, the 1-bits in its binary representation are counted.\n" | |
3326 | "If negative, the 0-bits in its two's-complement binary\n" | |
3327 | "representation are counted. If 0, 0 is returned.\n" | |
3328 | "\n" | |
b380b885 MD |
3329 | "@lisp\n" |
3330 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
3331 | " @result{} 4\n" |
3332 | "(logcount 0)\n" | |
3333 | " @result{} 0\n" | |
3334 | "(logcount -2)\n" | |
3335 | " @result{} 1\n" | |
3336 | "@end lisp") | |
3337 | #define FUNC_NAME s_scm_logcount | |
3338 | { | |
e11e83f3 | 3339 | if (SCM_I_INUMP (n)) |
f872b822 | 3340 | { |
e25f3727 AW |
3341 | unsigned long c = 0; |
3342 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
3343 | if (nn < 0) |
3344 | nn = -1 - nn; | |
3345 | while (nn) | |
3346 | { | |
3347 | c += scm_logtab[15 & nn]; | |
3348 | nn >>= 4; | |
3349 | } | |
d956fa6f | 3350 | return SCM_I_MAKINUM (c); |
f872b822 | 3351 | } |
ca46fb90 | 3352 | else if (SCM_BIGP (n)) |
f872b822 | 3353 | { |
ca46fb90 | 3354 | unsigned long count; |
713a4259 KR |
3355 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
3356 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 3357 | else |
713a4259 KR |
3358 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
3359 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3360 | return SCM_I_MAKINUM (count); |
f872b822 | 3361 | } |
ca46fb90 RB |
3362 | else |
3363 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 3364 | } |
ca46fb90 | 3365 | #undef FUNC_NAME |
0f2d19dd JB |
3366 | |
3367 | ||
ca46fb90 RB |
3368 | static const char scm_ilentab[] = { |
3369 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
3370 | }; | |
3371 | ||
0f2d19dd | 3372 | |
ca46fb90 RB |
3373 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
3374 | (SCM n), | |
3375 | "Return the number of bits necessary to represent @var{n}.\n" | |
3376 | "\n" | |
3377 | "@lisp\n" | |
3378 | "(integer-length #b10101010)\n" | |
3379 | " @result{} 8\n" | |
3380 | "(integer-length 0)\n" | |
3381 | " @result{} 0\n" | |
3382 | "(integer-length #b1111)\n" | |
3383 | " @result{} 4\n" | |
3384 | "@end lisp") | |
3385 | #define FUNC_NAME s_scm_integer_length | |
3386 | { | |
e11e83f3 | 3387 | if (SCM_I_INUMP (n)) |
0aacf84e | 3388 | { |
e25f3727 | 3389 | unsigned long c = 0; |
0aacf84e | 3390 | unsigned int l = 4; |
e25f3727 | 3391 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
3392 | if (nn < 0) |
3393 | nn = -1 - nn; | |
3394 | while (nn) | |
3395 | { | |
3396 | c += 4; | |
3397 | l = scm_ilentab [15 & nn]; | |
3398 | nn >>= 4; | |
3399 | } | |
d956fa6f | 3400 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
3401 | } |
3402 | else if (SCM_BIGP (n)) | |
3403 | { | |
3404 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
3405 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
3406 | 1 too big, so check for that and adjust. */ | |
3407 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
3408 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
3409 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
3410 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
3411 | size--; | |
3412 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3413 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
3414 | } |
3415 | else | |
ca46fb90 | 3416 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
3417 | } |
3418 | #undef FUNC_NAME | |
0f2d19dd JB |
3419 | |
3420 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
3421 | #define SCM_MAX_DBL_PREC 60 |
3422 | #define SCM_MAX_DBL_RADIX 36 | |
3423 | ||
3424 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
3425 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
3426 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
3427 | ||
3428 | static | |
3429 | void init_dblprec(int *prec, int radix) { | |
3430 | /* determine floating point precision by adding successively | |
3431 | smaller increments to 1.0 until it is considered == 1.0 */ | |
3432 | double f = ((double)1.0)/radix; | |
3433 | double fsum = 1.0 + f; | |
3434 | ||
3435 | *prec = 0; | |
3436 | while (fsum != 1.0) | |
3437 | { | |
3438 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
3439 | fsum = 1.0; | |
3440 | else | |
3441 | { | |
3442 | f /= radix; | |
3443 | fsum = f + 1.0; | |
3444 | } | |
3445 | } | |
3446 | (*prec) -= 1; | |
3447 | } | |
3448 | ||
3449 | static | |
3450 | void init_fx_radix(double *fx_list, int radix) | |
3451 | { | |
3452 | /* initialize a per-radix list of tolerances. When added | |
3453 | to a number < 1.0, we can determine if we should raund | |
3454 | up and quit converting a number to a string. */ | |
3455 | int i; | |
3456 | fx_list[0] = 0.0; | |
3457 | fx_list[1] = 0.5; | |
3458 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
3459 | fx_list[i] = (fx_list[i-1] / radix); | |
3460 | } | |
3461 | ||
3462 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 3463 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 3464 | |
1be6b49c | 3465 | static size_t |
0b799eea | 3466 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 3467 | { |
0b799eea MV |
3468 | int efmt, dpt, d, i, wp; |
3469 | double *fx; | |
3470 | #ifdef DBL_MIN_10_EXP | |
3471 | double f_cpy; | |
3472 | int exp_cpy; | |
3473 | #endif /* DBL_MIN_10_EXP */ | |
3474 | size_t ch = 0; | |
3475 | int exp = 0; | |
3476 | ||
3477 | if(radix < 2 || | |
3478 | radix > SCM_MAX_DBL_RADIX) | |
3479 | { | |
3480 | /* revert to existing behavior */ | |
3481 | radix = 10; | |
3482 | } | |
3483 | ||
3484 | wp = scm_dblprec[radix-2]; | |
3485 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 3486 | |
f872b822 | 3487 | if (f == 0.0) |
abb7e44d MV |
3488 | { |
3489 | #ifdef HAVE_COPYSIGN | |
3490 | double sgn = copysign (1.0, f); | |
3491 | ||
3492 | if (sgn < 0.0) | |
3493 | a[ch++] = '-'; | |
3494 | #endif | |
abb7e44d MV |
3495 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
3496 | } | |
7351e207 | 3497 | |
2e65b52f | 3498 | if (isinf (f)) |
7351e207 MV |
3499 | { |
3500 | if (f < 0) | |
3501 | strcpy (a, "-inf.0"); | |
3502 | else | |
3503 | strcpy (a, "+inf.0"); | |
3504 | return ch+6; | |
3505 | } | |
2e65b52f | 3506 | else if (isnan (f)) |
7351e207 MV |
3507 | { |
3508 | strcpy (a, "+nan.0"); | |
3509 | return ch+6; | |
3510 | } | |
3511 | ||
f872b822 MD |
3512 | if (f < 0.0) |
3513 | { | |
3514 | f = -f; | |
3515 | a[ch++] = '-'; | |
3516 | } | |
7351e207 | 3517 | |
f872b822 MD |
3518 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
3519 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
3520 | /* just do the checking...if it passes, we do the conversion for our |
3521 | radix again below */ | |
3522 | f_cpy = f; | |
3523 | exp_cpy = exp; | |
3524 | ||
3525 | while (f_cpy < 1.0) | |
f872b822 | 3526 | { |
0b799eea MV |
3527 | f_cpy *= 10.0; |
3528 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
3529 | { |
3530 | a[ch++] = '#'; | |
3531 | a[ch++] = '.'; | |
3532 | a[ch++] = '#'; | |
3533 | return ch; | |
3534 | } | |
f872b822 | 3535 | } |
0b799eea | 3536 | while (f_cpy > 10.0) |
f872b822 | 3537 | { |
0b799eea MV |
3538 | f_cpy *= 0.10; |
3539 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
3540 | { |
3541 | a[ch++] = '#'; | |
3542 | a[ch++] = '.'; | |
3543 | a[ch++] = '#'; | |
3544 | return ch; | |
3545 | } | |
f872b822 | 3546 | } |
0b799eea MV |
3547 | #endif |
3548 | ||
f872b822 MD |
3549 | while (f < 1.0) |
3550 | { | |
0b799eea | 3551 | f *= radix; |
f872b822 MD |
3552 | exp--; |
3553 | } | |
0b799eea | 3554 | while (f > radix) |
f872b822 | 3555 | { |
0b799eea | 3556 | f /= radix; |
f872b822 MD |
3557 | exp++; |
3558 | } | |
0b799eea MV |
3559 | |
3560 | if (f + fx[wp] >= radix) | |
f872b822 MD |
3561 | { |
3562 | f = 1.0; | |
3563 | exp++; | |
3564 | } | |
0f2d19dd | 3565 | zero: |
0b799eea MV |
3566 | #ifdef ENGNOT |
3567 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 3568 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
3569 | exp -= dpt++; |
3570 | efmt = 1; | |
f872b822 MD |
3571 | #else |
3572 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 3573 | if (!efmt) |
cda139a7 MD |
3574 | { |
3575 | if (exp < 0) | |
3576 | { | |
3577 | a[ch++] = '0'; | |
3578 | a[ch++] = '.'; | |
3579 | dpt = exp; | |
f872b822 MD |
3580 | while (++dpt) |
3581 | a[ch++] = '0'; | |
cda139a7 MD |
3582 | } |
3583 | else | |
f872b822 | 3584 | dpt = exp + 1; |
cda139a7 | 3585 | } |
0f2d19dd JB |
3586 | else |
3587 | dpt = 1; | |
f872b822 MD |
3588 | #endif |
3589 | ||
3590 | do | |
3591 | { | |
3592 | d = f; | |
3593 | f -= d; | |
0b799eea | 3594 | a[ch++] = number_chars[d]; |
f872b822 MD |
3595 | if (f < fx[wp]) |
3596 | break; | |
3597 | if (f + fx[wp] >= 1.0) | |
3598 | { | |
0b799eea | 3599 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
3600 | break; |
3601 | } | |
0b799eea | 3602 | f *= radix; |
f872b822 MD |
3603 | if (!(--dpt)) |
3604 | a[ch++] = '.'; | |
0f2d19dd | 3605 | } |
f872b822 | 3606 | while (wp--); |
0f2d19dd JB |
3607 | |
3608 | if (dpt > 0) | |
cda139a7 | 3609 | { |
f872b822 | 3610 | #ifndef ENGNOT |
cda139a7 MD |
3611 | if ((dpt > 4) && (exp > 6)) |
3612 | { | |
f872b822 | 3613 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 3614 | for (i = ch++; i > d; i--) |
f872b822 | 3615 | a[i] = a[i - 1]; |
cda139a7 MD |
3616 | a[d] = '.'; |
3617 | efmt = 1; | |
3618 | } | |
3619 | else | |
f872b822 | 3620 | #endif |
cda139a7 | 3621 | { |
f872b822 MD |
3622 | while (--dpt) |
3623 | a[ch++] = '0'; | |
cda139a7 MD |
3624 | a[ch++] = '.'; |
3625 | } | |
3626 | } | |
f872b822 MD |
3627 | if (a[ch - 1] == '.') |
3628 | a[ch++] = '0'; /* trailing zero */ | |
3629 | if (efmt && exp) | |
3630 | { | |
3631 | a[ch++] = 'e'; | |
3632 | if (exp < 0) | |
3633 | { | |
3634 | exp = -exp; | |
3635 | a[ch++] = '-'; | |
3636 | } | |
0b799eea MV |
3637 | for (i = radix; i <= exp; i *= radix); |
3638 | for (i /= radix; i; i /= radix) | |
f872b822 | 3639 | { |
0b799eea | 3640 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
3641 | exp %= i; |
3642 | } | |
0f2d19dd | 3643 | } |
0f2d19dd JB |
3644 | return ch; |
3645 | } | |
3646 | ||
7a1aba42 MV |
3647 | |
3648 | static size_t | |
3649 | icmplx2str (double real, double imag, char *str, int radix) | |
3650 | { | |
3651 | size_t i; | |
3652 | ||
3653 | i = idbl2str (real, str, radix); | |
3654 | if (imag != 0.0) | |
3655 | { | |
3656 | /* Don't output a '+' for negative numbers or for Inf and | |
3657 | NaN. They will provide their own sign. */ | |
2e65b52f | 3658 | if (0 <= imag && !isinf (imag) && !isnan (imag)) |
7a1aba42 MV |
3659 | str[i++] = '+'; |
3660 | i += idbl2str (imag, &str[i], radix); | |
3661 | str[i++] = 'i'; | |
3662 | } | |
3663 | return i; | |
3664 | } | |
3665 | ||
1be6b49c | 3666 | static size_t |
0b799eea | 3667 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 3668 | { |
1be6b49c | 3669 | size_t i; |
3c9a524f | 3670 | if (SCM_REALP (flt)) |
0b799eea | 3671 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 3672 | else |
7a1aba42 MV |
3673 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
3674 | str, radix); | |
0f2d19dd JB |
3675 | return i; |
3676 | } | |
0f2d19dd | 3677 | |
2881e77b | 3678 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
3679 | characters in the result. |
3680 | rad is output base | |
3681 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 3682 | size_t |
2881e77b MV |
3683 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
3684 | { | |
3685 | if (num < 0) | |
3686 | { | |
3687 | *p++ = '-'; | |
3688 | return scm_iuint2str (-num, rad, p) + 1; | |
3689 | } | |
3690 | else | |
3691 | return scm_iuint2str (num, rad, p); | |
3692 | } | |
3693 | ||
3694 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
3695 | characters in the result. | |
3696 | rad is output base | |
3697 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
3698 | size_t | |
3699 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 3700 | { |
1be6b49c ML |
3701 | size_t j = 1; |
3702 | size_t i; | |
2881e77b | 3703 | scm_t_uintmax n = num; |
5c11cc9d | 3704 | |
a6f3af16 AW |
3705 | if (rad < 2 || rad > 36) |
3706 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
3707 | ||
f872b822 | 3708 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
3709 | j++; |
3710 | ||
3711 | i = j; | |
2881e77b | 3712 | n = num; |
f872b822 MD |
3713 | while (i--) |
3714 | { | |
5c11cc9d GH |
3715 | int d = n % rad; |
3716 | ||
f872b822 | 3717 | n /= rad; |
a6f3af16 | 3718 | p[i] = number_chars[d]; |
f872b822 | 3719 | } |
0f2d19dd JB |
3720 | return j; |
3721 | } | |
3722 | ||
a1ec6916 | 3723 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
3724 | (SCM n, SCM radix), |
3725 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
3726 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
3727 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 3728 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 3729 | { |
1bbd0b84 | 3730 | int base; |
98cb6e75 | 3731 | |
0aacf84e | 3732 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 3733 | base = 10; |
0aacf84e | 3734 | else |
5efd3c7d | 3735 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 3736 | |
e11e83f3 | 3737 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
3738 | { |
3739 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 3740 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 3741 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
3742 | } |
3743 | else if (SCM_BIGP (n)) | |
3744 | { | |
3745 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
3746 | scm_remember_upto_here_1 (n); | |
cc95e00a | 3747 | return scm_take_locale_string (str); |
0aacf84e | 3748 | } |
f92e85f7 MV |
3749 | else if (SCM_FRACTIONP (n)) |
3750 | { | |
f92e85f7 | 3751 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 3752 | scm_from_locale_string ("/"), |
f92e85f7 MV |
3753 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
3754 | } | |
0aacf84e MD |
3755 | else if (SCM_INEXACTP (n)) |
3756 | { | |
3757 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 3758 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
3759 | } |
3760 | else | |
bb628794 | 3761 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 3762 | } |
1bbd0b84 | 3763 | #undef FUNC_NAME |
0f2d19dd JB |
3764 | |
3765 | ||
ca46fb90 RB |
3766 | /* These print routines used to be stubbed here so that scm_repl.c |
3767 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 3768 | |
0f2d19dd | 3769 | int |
e81d98ec | 3770 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3771 | { |
56e55ac7 | 3772 | char num_buf[FLOBUFLEN]; |
0b799eea | 3773 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
3774 | return !0; |
3775 | } | |
3776 | ||
b479fe9a MV |
3777 | void |
3778 | scm_i_print_double (double val, SCM port) | |
3779 | { | |
3780 | char num_buf[FLOBUFLEN]; | |
3781 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
3782 | } | |
3783 | ||
f3ae5d60 | 3784 | int |
e81d98ec | 3785 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 3786 | |
f3ae5d60 | 3787 | { |
56e55ac7 | 3788 | char num_buf[FLOBUFLEN]; |
0b799eea | 3789 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
3790 | return !0; |
3791 | } | |
1cc91f1b | 3792 | |
7a1aba42 MV |
3793 | void |
3794 | scm_i_print_complex (double real, double imag, SCM port) | |
3795 | { | |
3796 | char num_buf[FLOBUFLEN]; | |
3797 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
3798 | } | |
3799 | ||
f92e85f7 MV |
3800 | int |
3801 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
3802 | { | |
3803 | SCM str; | |
f92e85f7 | 3804 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 3805 | scm_display (str, port); |
f92e85f7 MV |
3806 | scm_remember_upto_here_1 (str); |
3807 | return !0; | |
3808 | } | |
3809 | ||
0f2d19dd | 3810 | int |
e81d98ec | 3811 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3812 | { |
ca46fb90 RB |
3813 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
3814 | scm_remember_upto_here_1 (exp); | |
3815 | scm_lfwrite (str, (size_t) strlen (str), port); | |
3816 | free (str); | |
0f2d19dd JB |
3817 | return !0; |
3818 | } | |
3819 | /*** END nums->strs ***/ | |
3820 | ||
3c9a524f | 3821 | |
0f2d19dd | 3822 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 3823 | |
3c9a524f DH |
3824 | /* The following functions implement the conversion from strings to numbers. |
3825 | * The implementation somehow follows the grammar for numbers as it is given | |
3826 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
3827 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
3828 | * points should be noted about the implementation: | |
3829 | * * Each function keeps a local index variable 'idx' that points at the | |
3830 | * current position within the parsed string. The global index is only | |
3831 | * updated if the function could parse the corresponding syntactic unit | |
3832 | * successfully. | |
3833 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
3834 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
3835 | * global exactness information is only updated after each part has been | |
3836 | * successfully parsed. | |
3837 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
3838 | * Only if these fixnums would overflow, the result variables are updated | |
3839 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
3840 | * the temporary variables holding the fixnums are cleared, and the process | |
3841 | * starts over again. If for example fixnums were able to store five decimal | |
3842 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
3843 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
3844 | * only every five digits two bignum operations were performed. | |
3845 | */ | |
3846 | ||
3847 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
3848 | ||
3849 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
3850 | ||
a6f3af16 AW |
3851 | /* Caller is responsible for checking that the return value is in range |
3852 | for the given radix, which should be <= 36. */ | |
3853 | static unsigned int | |
3854 | char_decimal_value (scm_t_uint32 c) | |
3855 | { | |
3856 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
3857 | that's certainly above any valid decimal, so we take advantage of | |
3858 | that to elide some tests. */ | |
3859 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
3860 | ||
3861 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
3862 | hexadecimals. */ | |
3863 | if (d >= 10U) | |
3864 | { | |
3865 | c = uc_tolower (c); | |
3866 | if (c >= (scm_t_uint32) 'a') | |
3867 | d = c - (scm_t_uint32)'a' + 10U; | |
3868 | } | |
3869 | return d; | |
3870 | } | |
3c9a524f | 3871 | |
2a8fecee | 3872 | static SCM |
3f47e526 | 3873 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 3874 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 3875 | { |
3c9a524f DH |
3876 | unsigned int idx = *p_idx; |
3877 | unsigned int hash_seen = 0; | |
3878 | scm_t_bits shift = 1; | |
3879 | scm_t_bits add = 0; | |
3880 | unsigned int digit_value; | |
3881 | SCM result; | |
3882 | char c; | |
3f47e526 | 3883 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3884 | |
3885 | if (idx == len) | |
3886 | return SCM_BOOL_F; | |
2a8fecee | 3887 | |
3f47e526 | 3888 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3889 | digit_value = char_decimal_value (c); |
3c9a524f DH |
3890 | if (digit_value >= radix) |
3891 | return SCM_BOOL_F; | |
3892 | ||
3893 | idx++; | |
d956fa6f | 3894 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 3895 | while (idx != len) |
f872b822 | 3896 | { |
3f47e526 | 3897 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3898 | if (c == '#') |
3c9a524f DH |
3899 | { |
3900 | hash_seen = 1; | |
3901 | digit_value = 0; | |
3902 | } | |
a6f3af16 AW |
3903 | else if (hash_seen) |
3904 | break; | |
3c9a524f | 3905 | else |
a6f3af16 AW |
3906 | { |
3907 | digit_value = char_decimal_value (c); | |
3908 | /* This check catches non-decimals in addition to out-of-range | |
3909 | decimals. */ | |
3910 | if (digit_value >= radix) | |
3911 | break; | |
3912 | } | |
3c9a524f DH |
3913 | |
3914 | idx++; | |
3915 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
3916 | { | |
d956fa6f | 3917 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3918 | if (add > 0) |
d956fa6f | 3919 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3920 | |
3921 | shift = radix; | |
3922 | add = digit_value; | |
3923 | } | |
3924 | else | |
3925 | { | |
3926 | shift = shift * radix; | |
3927 | add = add * radix + digit_value; | |
3928 | } | |
3929 | }; | |
3930 | ||
3931 | if (shift > 1) | |
d956fa6f | 3932 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3933 | if (add > 0) |
d956fa6f | 3934 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3935 | |
3936 | *p_idx = idx; | |
3937 | if (hash_seen) | |
3938 | *p_exactness = INEXACT; | |
3939 | ||
3940 | return result; | |
2a8fecee JB |
3941 | } |
3942 | ||
3943 | ||
3c9a524f DH |
3944 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
3945 | * covers the parts of the rules that start at a potential point. The value | |
3946 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
3947 | * in variable result. The content of *p_exactness indicates, whether a hash |
3948 | * has already been seen in the digits before the point. | |
3c9a524f | 3949 | */ |
1cc91f1b | 3950 | |
3f47e526 | 3951 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
3952 | |
3953 | static SCM | |
3f47e526 | 3954 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 3955 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 3956 | { |
3c9a524f DH |
3957 | unsigned int idx = *p_idx; |
3958 | enum t_exactness x = *p_exactness; | |
3f47e526 | 3959 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3960 | |
3961 | if (idx == len) | |
79d34f68 | 3962 | return result; |
3c9a524f | 3963 | |
3f47e526 | 3964 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
3965 | { |
3966 | scm_t_bits shift = 1; | |
3967 | scm_t_bits add = 0; | |
3968 | unsigned int digit_value; | |
cff5fa33 | 3969 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
3970 | |
3971 | idx++; | |
3972 | while (idx != len) | |
3973 | { | |
3f47e526 MG |
3974 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
3975 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
3976 | { |
3977 | if (x == INEXACT) | |
3978 | return SCM_BOOL_F; | |
3979 | else | |
3980 | digit_value = DIGIT2UINT (c); | |
3981 | } | |
3982 | else if (c == '#') | |
3983 | { | |
3984 | x = INEXACT; | |
3985 | digit_value = 0; | |
3986 | } | |
3987 | else | |
3988 | break; | |
3989 | ||
3990 | idx++; | |
3991 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
3992 | { | |
d956fa6f MV |
3993 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
3994 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 3995 | if (add > 0) |
d956fa6f | 3996 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3997 | |
3998 | shift = 10; | |
3999 | add = digit_value; | |
4000 | } | |
4001 | else | |
4002 | { | |
4003 | shift = shift * 10; | |
4004 | add = add * 10 + digit_value; | |
4005 | } | |
4006 | }; | |
4007 | ||
4008 | if (add > 0) | |
4009 | { | |
d956fa6f MV |
4010 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4011 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
4012 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
4013 | } |
4014 | ||
d8592269 | 4015 | result = scm_divide (result, big_shift); |
79d34f68 | 4016 | |
3c9a524f DH |
4017 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
4018 | x = INEXACT; | |
f872b822 | 4019 | } |
3c9a524f | 4020 | |
3c9a524f | 4021 | if (idx != len) |
f872b822 | 4022 | { |
3c9a524f DH |
4023 | int sign = 1; |
4024 | unsigned int start; | |
3f47e526 | 4025 | scm_t_wchar c; |
3c9a524f DH |
4026 | int exponent; |
4027 | SCM e; | |
4028 | ||
4029 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
4030 | ||
3f47e526 | 4031 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 4032 | { |
3c9a524f DH |
4033 | case 'd': case 'D': |
4034 | case 'e': case 'E': | |
4035 | case 'f': case 'F': | |
4036 | case 'l': case 'L': | |
4037 | case 's': case 'S': | |
4038 | idx++; | |
ee0ddd21 AW |
4039 | if (idx == len) |
4040 | return SCM_BOOL_F; | |
4041 | ||
3c9a524f | 4042 | start = idx; |
3f47e526 | 4043 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4044 | if (c == '-') |
4045 | { | |
4046 | idx++; | |
ee0ddd21 AW |
4047 | if (idx == len) |
4048 | return SCM_BOOL_F; | |
4049 | ||
3c9a524f | 4050 | sign = -1; |
3f47e526 | 4051 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4052 | } |
4053 | else if (c == '+') | |
4054 | { | |
4055 | idx++; | |
ee0ddd21 AW |
4056 | if (idx == len) |
4057 | return SCM_BOOL_F; | |
4058 | ||
3c9a524f | 4059 | sign = 1; |
3f47e526 | 4060 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4061 | } |
4062 | else | |
4063 | sign = 1; | |
4064 | ||
3f47e526 | 4065 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
4066 | return SCM_BOOL_F; |
4067 | ||
4068 | idx++; | |
4069 | exponent = DIGIT2UINT (c); | |
4070 | while (idx != len) | |
f872b822 | 4071 | { |
3f47e526 MG |
4072 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
4073 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
4074 | { |
4075 | idx++; | |
4076 | if (exponent <= SCM_MAXEXP) | |
4077 | exponent = exponent * 10 + DIGIT2UINT (c); | |
4078 | } | |
4079 | else | |
4080 | break; | |
f872b822 | 4081 | } |
3c9a524f DH |
4082 | |
4083 | if (exponent > SCM_MAXEXP) | |
f872b822 | 4084 | { |
3c9a524f | 4085 | size_t exp_len = idx - start; |
3f47e526 | 4086 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
4087 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
4088 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 4089 | } |
3c9a524f | 4090 | |
d956fa6f | 4091 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
4092 | if (sign == 1) |
4093 | result = scm_product (result, e); | |
4094 | else | |
f92e85f7 | 4095 | result = scm_divide2real (result, e); |
3c9a524f DH |
4096 | |
4097 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
4098 | x = INEXACT; | |
4099 | ||
f872b822 | 4100 | break; |
3c9a524f | 4101 | |
f872b822 | 4102 | default: |
3c9a524f | 4103 | break; |
f872b822 | 4104 | } |
0f2d19dd | 4105 | } |
3c9a524f DH |
4106 | |
4107 | *p_idx = idx; | |
4108 | if (x == INEXACT) | |
4109 | *p_exactness = x; | |
4110 | ||
4111 | return result; | |
0f2d19dd | 4112 | } |
0f2d19dd | 4113 | |
3c9a524f DH |
4114 | |
4115 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
4116 | ||
4117 | static SCM | |
3f47e526 | 4118 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 4119 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 4120 | { |
3c9a524f | 4121 | unsigned int idx = *p_idx; |
164d2481 | 4122 | SCM result; |
3f47e526 | 4123 | size_t len = scm_i_string_length (mem); |
3c9a524f | 4124 | |
40f89215 NJ |
4125 | /* Start off believing that the number will be exact. This changes |
4126 | to INEXACT if we see a decimal point or a hash. */ | |
4127 | enum t_exactness x = EXACT; | |
4128 | ||
3c9a524f DH |
4129 | if (idx == len) |
4130 | return SCM_BOOL_F; | |
4131 | ||
3f47e526 | 4132 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
4133 | { |
4134 | *p_idx = idx+5; | |
4135 | return scm_inf (); | |
4136 | } | |
4137 | ||
3f47e526 | 4138 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 4139 | { |
d8592269 MV |
4140 | /* Cobble up the fractional part. We might want to set the |
4141 | NaN's mantissa from it. */ | |
7351e207 | 4142 | idx += 4; |
3f47e526 | 4143 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
4144 | *p_idx = idx; |
4145 | return scm_nan (); | |
4146 | } | |
4147 | ||
3f47e526 | 4148 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
4149 | { |
4150 | if (radix != 10) | |
4151 | return SCM_BOOL_F; | |
4152 | else if (idx + 1 == len) | |
4153 | return SCM_BOOL_F; | |
3f47e526 | 4154 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
4155 | return SCM_BOOL_F; |
4156 | else | |
cff5fa33 | 4157 | result = mem2decimal_from_point (SCM_INUM0, mem, |
40f89215 | 4158 | p_idx, &x); |
f872b822 | 4159 | } |
3c9a524f DH |
4160 | else |
4161 | { | |
3c9a524f | 4162 | SCM uinteger; |
3c9a524f | 4163 | |
3f47e526 | 4164 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 4165 | if (scm_is_false (uinteger)) |
3c9a524f DH |
4166 | return SCM_BOOL_F; |
4167 | ||
4168 | if (idx == len) | |
4169 | result = uinteger; | |
3f47e526 | 4170 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 4171 | { |
3c9a524f DH |
4172 | SCM divisor; |
4173 | ||
4174 | idx++; | |
ee0ddd21 AW |
4175 | if (idx == len) |
4176 | return SCM_BOOL_F; | |
3c9a524f | 4177 | |
3f47e526 | 4178 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 4179 | if (scm_is_false (divisor)) |
3c9a524f DH |
4180 | return SCM_BOOL_F; |
4181 | ||
f92e85f7 | 4182 | /* both are int/big here, I assume */ |
cba42c93 | 4183 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 4184 | } |
3c9a524f DH |
4185 | else if (radix == 10) |
4186 | { | |
3f47e526 | 4187 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 4188 | if (scm_is_false (result)) |
3c9a524f DH |
4189 | return SCM_BOOL_F; |
4190 | } | |
4191 | else | |
4192 | result = uinteger; | |
4193 | ||
4194 | *p_idx = idx; | |
f872b822 | 4195 | } |
164d2481 | 4196 | |
40f89215 NJ |
4197 | /* Update *p_exactness if the number just read was inexact. This is |
4198 | important for complex numbers, so that a complex number is | |
4199 | treated as inexact overall if either its real or imaginary part | |
4200 | is inexact. | |
4201 | */ | |
4202 | if (x == INEXACT) | |
4203 | *p_exactness = x; | |
4204 | ||
164d2481 MV |
4205 | /* When returning an inexact zero, make sure it is represented as a |
4206 | floating point value so that we can change its sign. | |
4207 | */ | |
cff5fa33 | 4208 | if (scm_is_eq (result, SCM_INUM0) && *p_exactness == INEXACT) |
55f26379 | 4209 | result = scm_from_double (0.0); |
164d2481 MV |
4210 | |
4211 | return result; | |
3c9a524f | 4212 | } |
0f2d19dd | 4213 | |
0f2d19dd | 4214 | |
3c9a524f | 4215 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 4216 | |
3c9a524f | 4217 | static SCM |
3f47e526 | 4218 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
4219 | unsigned int radix, enum t_exactness *p_exactness) |
4220 | { | |
3f47e526 | 4221 | scm_t_wchar c; |
3c9a524f DH |
4222 | int sign = 0; |
4223 | SCM ureal; | |
3f47e526 | 4224 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4225 | |
4226 | if (idx == len) | |
4227 | return SCM_BOOL_F; | |
4228 | ||
3f47e526 | 4229 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4230 | if (c == '+') |
4231 | { | |
4232 | idx++; | |
4233 | sign = 1; | |
4234 | } | |
4235 | else if (c == '-') | |
4236 | { | |
4237 | idx++; | |
4238 | sign = -1; | |
0f2d19dd | 4239 | } |
0f2d19dd | 4240 | |
3c9a524f DH |
4241 | if (idx == len) |
4242 | return SCM_BOOL_F; | |
4243 | ||
3f47e526 | 4244 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 4245 | if (scm_is_false (ureal)) |
f872b822 | 4246 | { |
3c9a524f DH |
4247 | /* input must be either +i or -i */ |
4248 | ||
4249 | if (sign == 0) | |
4250 | return SCM_BOOL_F; | |
4251 | ||
3f47e526 MG |
4252 | if (scm_i_string_ref (mem, idx) == 'i' |
4253 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 4254 | { |
3c9a524f DH |
4255 | idx++; |
4256 | if (idx != len) | |
4257 | return SCM_BOOL_F; | |
4258 | ||
cff5fa33 | 4259 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 4260 | } |
3c9a524f DH |
4261 | else |
4262 | return SCM_BOOL_F; | |
0f2d19dd | 4263 | } |
3c9a524f DH |
4264 | else |
4265 | { | |
73e4de09 | 4266 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 4267 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 4268 | |
3c9a524f DH |
4269 | if (idx == len) |
4270 | return ureal; | |
4271 | ||
3f47e526 | 4272 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 4273 | switch (c) |
f872b822 | 4274 | { |
3c9a524f DH |
4275 | case 'i': case 'I': |
4276 | /* either +<ureal>i or -<ureal>i */ | |
4277 | ||
4278 | idx++; | |
4279 | if (sign == 0) | |
4280 | return SCM_BOOL_F; | |
4281 | if (idx != len) | |
4282 | return SCM_BOOL_F; | |
cff5fa33 | 4283 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
4284 | |
4285 | case '@': | |
4286 | /* polar input: <real>@<real>. */ | |
4287 | ||
4288 | idx++; | |
4289 | if (idx == len) | |
4290 | return SCM_BOOL_F; | |
4291 | else | |
f872b822 | 4292 | { |
3c9a524f DH |
4293 | int sign; |
4294 | SCM angle; | |
4295 | SCM result; | |
4296 | ||
3f47e526 | 4297 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4298 | if (c == '+') |
4299 | { | |
4300 | idx++; | |
ee0ddd21 AW |
4301 | if (idx == len) |
4302 | return SCM_BOOL_F; | |
3c9a524f DH |
4303 | sign = 1; |
4304 | } | |
4305 | else if (c == '-') | |
4306 | { | |
4307 | idx++; | |
ee0ddd21 AW |
4308 | if (idx == len) |
4309 | return SCM_BOOL_F; | |
3c9a524f DH |
4310 | sign = -1; |
4311 | } | |
4312 | else | |
4313 | sign = 1; | |
4314 | ||
3f47e526 | 4315 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 4316 | if (scm_is_false (angle)) |
3c9a524f DH |
4317 | return SCM_BOOL_F; |
4318 | if (idx != len) | |
4319 | return SCM_BOOL_F; | |
4320 | ||
73e4de09 | 4321 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
4322 | angle = scm_difference (angle, SCM_UNDEFINED); |
4323 | ||
4324 | result = scm_make_polar (ureal, angle); | |
4325 | return result; | |
f872b822 | 4326 | } |
3c9a524f DH |
4327 | case '+': |
4328 | case '-': | |
4329 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 4330 | |
3c9a524f DH |
4331 | idx++; |
4332 | if (idx == len) | |
4333 | return SCM_BOOL_F; | |
4334 | else | |
4335 | { | |
4336 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 4337 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 4338 | |
73e4de09 | 4339 | if (scm_is_false (imag)) |
d956fa6f | 4340 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 4341 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 4342 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 4343 | |
3c9a524f DH |
4344 | if (idx == len) |
4345 | return SCM_BOOL_F; | |
3f47e526 MG |
4346 | if (scm_i_string_ref (mem, idx) != 'i' |
4347 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 4348 | return SCM_BOOL_F; |
0f2d19dd | 4349 | |
3c9a524f DH |
4350 | idx++; |
4351 | if (idx != len) | |
4352 | return SCM_BOOL_F; | |
0f2d19dd | 4353 | |
1fe5e088 | 4354 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
4355 | } |
4356 | default: | |
4357 | return SCM_BOOL_F; | |
4358 | } | |
4359 | } | |
0f2d19dd | 4360 | } |
0f2d19dd JB |
4361 | |
4362 | ||
3c9a524f DH |
4363 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
4364 | ||
4365 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 4366 | |
0f2d19dd | 4367 | SCM |
3f47e526 | 4368 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 4369 | { |
3c9a524f DH |
4370 | unsigned int idx = 0; |
4371 | unsigned int radix = NO_RADIX; | |
4372 | enum t_exactness forced_x = NO_EXACTNESS; | |
4373 | enum t_exactness implicit_x = EXACT; | |
4374 | SCM result; | |
3f47e526 | 4375 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4376 | |
4377 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 4378 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 4379 | { |
3f47e526 | 4380 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
4381 | { |
4382 | case 'b': case 'B': | |
4383 | if (radix != NO_RADIX) | |
4384 | return SCM_BOOL_F; | |
4385 | radix = DUAL; | |
4386 | break; | |
4387 | case 'd': case 'D': | |
4388 | if (radix != NO_RADIX) | |
4389 | return SCM_BOOL_F; | |
4390 | radix = DEC; | |
4391 | break; | |
4392 | case 'i': case 'I': | |
4393 | if (forced_x != NO_EXACTNESS) | |
4394 | return SCM_BOOL_F; | |
4395 | forced_x = INEXACT; | |
4396 | break; | |
4397 | case 'e': case 'E': | |
4398 | if (forced_x != NO_EXACTNESS) | |
4399 | return SCM_BOOL_F; | |
4400 | forced_x = EXACT; | |
4401 | break; | |
4402 | case 'o': case 'O': | |
4403 | if (radix != NO_RADIX) | |
4404 | return SCM_BOOL_F; | |
4405 | radix = OCT; | |
4406 | break; | |
4407 | case 'x': case 'X': | |
4408 | if (radix != NO_RADIX) | |
4409 | return SCM_BOOL_F; | |
4410 | radix = HEX; | |
4411 | break; | |
4412 | default: | |
f872b822 | 4413 | return SCM_BOOL_F; |
3c9a524f DH |
4414 | } |
4415 | idx += 2; | |
4416 | } | |
4417 | ||
4418 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
4419 | if (radix == NO_RADIX) | |
3f47e526 | 4420 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 4421 | else |
3f47e526 | 4422 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 4423 | |
73e4de09 | 4424 | if (scm_is_false (result)) |
3c9a524f | 4425 | return SCM_BOOL_F; |
f872b822 | 4426 | |
3c9a524f | 4427 | switch (forced_x) |
f872b822 | 4428 | { |
3c9a524f DH |
4429 | case EXACT: |
4430 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
4431 | return scm_inexact_to_exact (result); |
4432 | else | |
4433 | return result; | |
4434 | case INEXACT: | |
4435 | if (SCM_INEXACTP (result)) | |
4436 | return result; | |
4437 | else | |
4438 | return scm_exact_to_inexact (result); | |
4439 | case NO_EXACTNESS: | |
4440 | default: | |
4441 | if (implicit_x == INEXACT) | |
4442 | { | |
4443 | if (SCM_INEXACTP (result)) | |
4444 | return result; | |
4445 | else | |
4446 | return scm_exact_to_inexact (result); | |
4447 | } | |
4448 | else | |
4449 | return result; | |
f872b822 | 4450 | } |
0f2d19dd JB |
4451 | } |
4452 | ||
3f47e526 MG |
4453 | SCM |
4454 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
4455 | unsigned int default_radix) | |
4456 | { | |
4457 | SCM str = scm_from_locale_stringn (mem, len); | |
4458 | ||
4459 | return scm_i_string_to_number (str, default_radix); | |
4460 | } | |
4461 | ||
0f2d19dd | 4462 | |
a1ec6916 | 4463 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 4464 | (SCM string, SCM radix), |
1e6808ea | 4465 | "Return a number of the maximally precise representation\n" |
942e5b91 | 4466 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
4467 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
4468 | "is a default radix that may be overridden by an explicit radix\n" | |
4469 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
4470 | "supplied, then the default radix is 10. If string is not a\n" | |
4471 | "syntactically valid notation for a number, then\n" | |
4472 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 4473 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
4474 | { |
4475 | SCM answer; | |
5efd3c7d | 4476 | unsigned int base; |
a6d9e5ab | 4477 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
4478 | |
4479 | if (SCM_UNBNDP (radix)) | |
4480 | base = 10; | |
4481 | else | |
4482 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
4483 | ||
3f47e526 | 4484 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
4485 | scm_remember_upto_here_1 (string); |
4486 | return answer; | |
0f2d19dd | 4487 | } |
1bbd0b84 | 4488 | #undef FUNC_NAME |
3c9a524f DH |
4489 | |
4490 | ||
0f2d19dd JB |
4491 | /*** END strs->nums ***/ |
4492 | ||
5986c47d | 4493 | |
8507ec80 MV |
4494 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
4495 | (SCM x), | |
4496 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
4497 | "otherwise.") | |
4498 | #define FUNC_NAME s_scm_number_p | |
4499 | { | |
4500 | return scm_from_bool (SCM_NUMBERP (x)); | |
4501 | } | |
4502 | #undef FUNC_NAME | |
4503 | ||
4504 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 4505 | (SCM x), |
942e5b91 | 4506 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 4507 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
4508 | "values form subsets of the set of complex numbers, i. e. the\n" |
4509 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
4510 | "rational or integer number.") | |
8507ec80 | 4511 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 4512 | { |
8507ec80 MV |
4513 | /* all numbers are complex. */ |
4514 | return scm_number_p (x); | |
0f2d19dd | 4515 | } |
1bbd0b84 | 4516 | #undef FUNC_NAME |
0f2d19dd | 4517 | |
f92e85f7 MV |
4518 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
4519 | (SCM x), | |
4520 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
4521 | "otherwise. Note that the set of integer values forms a subset of\n" | |
4522 | "the set of real numbers, i. e. the predicate will also be\n" | |
4523 | "fulfilled if @var{x} is an integer number.") | |
4524 | #define FUNC_NAME s_scm_real_p | |
4525 | { | |
c960e556 MW |
4526 | return scm_from_bool |
4527 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
4528 | } |
4529 | #undef FUNC_NAME | |
4530 | ||
4531 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 4532 | (SCM x), |
942e5b91 | 4533 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 4534 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 4535 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
4536 | "fulfilled if @var{x} is an integer number.") |
4537 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 4538 | { |
c960e556 | 4539 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
4540 | return SCM_BOOL_T; |
4541 | else if (SCM_REALP (x)) | |
c960e556 MW |
4542 | /* due to their limited precision, finite floating point numbers are |
4543 | rational as well. (finite means neither infinity nor a NaN) */ | |
4544 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 4545 | else |
bb628794 | 4546 | return SCM_BOOL_F; |
0f2d19dd | 4547 | } |
1bbd0b84 | 4548 | #undef FUNC_NAME |
0f2d19dd | 4549 | |
a1ec6916 | 4550 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 4551 | (SCM x), |
942e5b91 MG |
4552 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
4553 | "else.") | |
1bbd0b84 | 4554 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 4555 | { |
c960e556 | 4556 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 4557 | return SCM_BOOL_T; |
c960e556 MW |
4558 | else if (SCM_REALP (x)) |
4559 | { | |
4560 | double val = SCM_REAL_VALUE (x); | |
4561 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
4562 | } | |
4563 | else | |
8e43ed5d | 4564 | return SCM_BOOL_F; |
0f2d19dd | 4565 | } |
1bbd0b84 | 4566 | #undef FUNC_NAME |
0f2d19dd JB |
4567 | |
4568 | ||
8a1f4f98 AW |
4569 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
4570 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
4571 | (SCM x, SCM y, SCM rest), | |
4572 | "Return @code{#t} if all parameters are numerically equal.") | |
4573 | #define FUNC_NAME s_scm_i_num_eq_p | |
4574 | { | |
4575 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4576 | return SCM_BOOL_T; | |
4577 | while (!scm_is_null (rest)) | |
4578 | { | |
4579 | if (scm_is_false (scm_num_eq_p (x, y))) | |
4580 | return SCM_BOOL_F; | |
4581 | x = y; | |
4582 | y = scm_car (rest); | |
4583 | rest = scm_cdr (rest); | |
4584 | } | |
4585 | return scm_num_eq_p (x, y); | |
4586 | } | |
4587 | #undef FUNC_NAME | |
0f2d19dd | 4588 | SCM |
6e8d25a6 | 4589 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 4590 | { |
d8b95e27 | 4591 | again: |
e11e83f3 | 4592 | if (SCM_I_INUMP (x)) |
0aacf84e | 4593 | { |
e25f3727 | 4594 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 4595 | if (SCM_I_INUMP (y)) |
0aacf84e | 4596 | { |
e25f3727 | 4597 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 4598 | return scm_from_bool (xx == yy); |
0aacf84e MD |
4599 | } |
4600 | else if (SCM_BIGP (y)) | |
4601 | return SCM_BOOL_F; | |
4602 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
4603 | { |
4604 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
4605 | to a double and compare. | |
4606 | ||
4607 | But on a 64-bit system an inum is bigger than a double and | |
4608 | casting it to a double (call that dxx) will round. dxx is at | |
4609 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
4610 | an integer and fits a long. So we cast yy to a long and | |
4611 | compare with plain xx. | |
4612 | ||
4613 | An alternative (for any size system actually) would be to check | |
4614 | yy is an integer (with floor) and is in range of an inum | |
4615 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
4616 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
4617 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
4618 | |
4619 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
4620 | return scm_from_bool ((double) xx == yy |
4621 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4622 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 4623 | } |
0aacf84e | 4624 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4625 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4626 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
4627 | else if (SCM_FRACTIONP (y)) |
4628 | return SCM_BOOL_F; | |
0aacf84e | 4629 | else |
8a1f4f98 | 4630 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4631 | } |
0aacf84e MD |
4632 | else if (SCM_BIGP (x)) |
4633 | { | |
e11e83f3 | 4634 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4635 | return SCM_BOOL_F; |
4636 | else if (SCM_BIGP (y)) | |
4637 | { | |
4638 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4639 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4640 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4641 | } |
4642 | else if (SCM_REALP (y)) | |
4643 | { | |
4644 | int cmp; | |
2e65b52f | 4645 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4646 | return SCM_BOOL_F; |
4647 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4648 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4649 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4650 | } |
4651 | else if (SCM_COMPLEXP (y)) | |
4652 | { | |
4653 | int cmp; | |
4654 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
4655 | return SCM_BOOL_F; | |
2e65b52f | 4656 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
4657 | return SCM_BOOL_F; |
4658 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
4659 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4660 | return scm_from_bool (0 == cmp); |
0aacf84e | 4661 | } |
f92e85f7 MV |
4662 | else if (SCM_FRACTIONP (y)) |
4663 | return SCM_BOOL_F; | |
0aacf84e | 4664 | else |
8a1f4f98 | 4665 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4666 | } |
0aacf84e MD |
4667 | else if (SCM_REALP (x)) |
4668 | { | |
e8c5b1f2 | 4669 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 4670 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
4671 | { |
4672 | /* see comments with inum/real above */ | |
e25f3727 | 4673 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
4674 | return scm_from_bool (xx == (double) yy |
4675 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4676 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 4677 | } |
0aacf84e MD |
4678 | else if (SCM_BIGP (y)) |
4679 | { | |
4680 | int cmp; | |
2e65b52f | 4681 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4682 | return SCM_BOOL_F; |
4683 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4684 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4685 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4686 | } |
4687 | else if (SCM_REALP (y)) | |
73e4de09 | 4688 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 4689 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4690 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4691 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4692 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4693 | { |
4694 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4695 | if (isnan (xx)) |
d8b95e27 | 4696 | return SCM_BOOL_F; |
2e65b52f | 4697 | if (isinf (xx)) |
73e4de09 | 4698 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4699 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4700 | goto again; | |
4701 | } | |
0aacf84e | 4702 | else |
8a1f4f98 | 4703 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4704 | } |
0aacf84e MD |
4705 | else if (SCM_COMPLEXP (x)) |
4706 | { | |
e11e83f3 MV |
4707 | if (SCM_I_INUMP (y)) |
4708 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
4709 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4710 | else if (SCM_BIGP (y)) | |
4711 | { | |
4712 | int cmp; | |
4713 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
4714 | return SCM_BOOL_F; | |
2e65b52f | 4715 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
4716 | return SCM_BOOL_F; |
4717 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
4718 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4719 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4720 | } |
4721 | else if (SCM_REALP (y)) | |
73e4de09 | 4722 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
4723 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4724 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 4725 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4726 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4727 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4728 | { |
4729 | double xx; | |
4730 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
4731 | return SCM_BOOL_F; | |
4732 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 4733 | if (isnan (xx)) |
d8b95e27 | 4734 | return SCM_BOOL_F; |
2e65b52f | 4735 | if (isinf (xx)) |
73e4de09 | 4736 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4737 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4738 | goto again; | |
4739 | } | |
f92e85f7 | 4740 | else |
8a1f4f98 | 4741 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
4742 | } |
4743 | else if (SCM_FRACTIONP (x)) | |
4744 | { | |
e11e83f3 | 4745 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
4746 | return SCM_BOOL_F; |
4747 | else if (SCM_BIGP (y)) | |
4748 | return SCM_BOOL_F; | |
4749 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
4750 | { |
4751 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4752 | if (isnan (yy)) |
d8b95e27 | 4753 | return SCM_BOOL_F; |
2e65b52f | 4754 | if (isinf (yy)) |
73e4de09 | 4755 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4756 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4757 | goto again; | |
4758 | } | |
f92e85f7 | 4759 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
4760 | { |
4761 | double yy; | |
4762 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
4763 | return SCM_BOOL_F; | |
4764 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 4765 | if (isnan (yy)) |
d8b95e27 | 4766 | return SCM_BOOL_F; |
2e65b52f | 4767 | if (isinf (yy)) |
73e4de09 | 4768 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4769 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4770 | goto again; | |
4771 | } | |
f92e85f7 MV |
4772 | else if (SCM_FRACTIONP (y)) |
4773 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 4774 | else |
8a1f4f98 | 4775 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4776 | } |
0aacf84e | 4777 | else |
8a1f4f98 | 4778 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
4779 | } |
4780 | ||
4781 | ||
a5f0b599 KR |
4782 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
4783 | done are good for inums, but for bignums an answer can almost always be | |
4784 | had by just examining a few high bits of the operands, as done by GMP in | |
4785 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
4786 | of the float exponent to take into account. */ | |
4787 | ||
8c93b597 | 4788 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
4789 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
4790 | (SCM x, SCM y, SCM rest), | |
4791 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4792 | "increasing.") | |
4793 | #define FUNC_NAME s_scm_i_num_less_p | |
4794 | { | |
4795 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4796 | return SCM_BOOL_T; | |
4797 | while (!scm_is_null (rest)) | |
4798 | { | |
4799 | if (scm_is_false (scm_less_p (x, y))) | |
4800 | return SCM_BOOL_F; | |
4801 | x = y; | |
4802 | y = scm_car (rest); | |
4803 | rest = scm_cdr (rest); | |
4804 | } | |
4805 | return scm_less_p (x, y); | |
4806 | } | |
4807 | #undef FUNC_NAME | |
0f2d19dd | 4808 | SCM |
6e8d25a6 | 4809 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 4810 | { |
a5f0b599 | 4811 | again: |
e11e83f3 | 4812 | if (SCM_I_INUMP (x)) |
0aacf84e | 4813 | { |
e25f3727 | 4814 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4815 | if (SCM_I_INUMP (y)) |
0aacf84e | 4816 | { |
e25f3727 | 4817 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 4818 | return scm_from_bool (xx < yy); |
0aacf84e MD |
4819 | } |
4820 | else if (SCM_BIGP (y)) | |
4821 | { | |
4822 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4823 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4824 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
4825 | } |
4826 | else if (SCM_REALP (y)) | |
73e4de09 | 4827 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 4828 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4829 | { |
4830 | /* "x < a/b" becomes "x*b < a" */ | |
4831 | int_frac: | |
4832 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
4833 | y = SCM_FRACTION_NUMERATOR (y); | |
4834 | goto again; | |
4835 | } | |
0aacf84e | 4836 | else |
8a1f4f98 | 4837 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4838 | } |
0aacf84e MD |
4839 | else if (SCM_BIGP (x)) |
4840 | { | |
e11e83f3 | 4841 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4842 | { |
4843 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4844 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4845 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
4846 | } |
4847 | else if (SCM_BIGP (y)) | |
4848 | { | |
4849 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4850 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4851 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
4852 | } |
4853 | else if (SCM_REALP (y)) | |
4854 | { | |
4855 | int cmp; | |
2e65b52f | 4856 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4857 | return SCM_BOOL_F; |
4858 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4859 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4860 | return scm_from_bool (cmp < 0); |
0aacf84e | 4861 | } |
f92e85f7 | 4862 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 4863 | goto int_frac; |
0aacf84e | 4864 | else |
8a1f4f98 | 4865 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 4866 | } |
0aacf84e MD |
4867 | else if (SCM_REALP (x)) |
4868 | { | |
e11e83f3 MV |
4869 | if (SCM_I_INUMP (y)) |
4870 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
4871 | else if (SCM_BIGP (y)) |
4872 | { | |
4873 | int cmp; | |
2e65b52f | 4874 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4875 | return SCM_BOOL_F; |
4876 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4877 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4878 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
4879 | } |
4880 | else if (SCM_REALP (y)) | |
73e4de09 | 4881 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 4882 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4883 | { |
4884 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4885 | if (isnan (xx)) |
a5f0b599 | 4886 | return SCM_BOOL_F; |
2e65b52f | 4887 | if (isinf (xx)) |
73e4de09 | 4888 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
4889 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4890 | goto again; | |
4891 | } | |
f92e85f7 | 4892 | else |
8a1f4f98 | 4893 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
4894 | } |
4895 | else if (SCM_FRACTIONP (x)) | |
4896 | { | |
e11e83f3 | 4897 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
4898 | { |
4899 | /* "a/b < y" becomes "a < y*b" */ | |
4900 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
4901 | x = SCM_FRACTION_NUMERATOR (x); | |
4902 | goto again; | |
4903 | } | |
f92e85f7 | 4904 | else if (SCM_REALP (y)) |
a5f0b599 KR |
4905 | { |
4906 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4907 | if (isnan (yy)) |
a5f0b599 | 4908 | return SCM_BOOL_F; |
2e65b52f | 4909 | if (isinf (yy)) |
73e4de09 | 4910 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
4911 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4912 | goto again; | |
4913 | } | |
f92e85f7 | 4914 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4915 | { |
4916 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
4917 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
4918 | SCM_FRACTION_DENOMINATOR (y)); | |
4919 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
4920 | SCM_FRACTION_DENOMINATOR (x)); | |
4921 | x = new_x; | |
4922 | y = new_y; | |
4923 | goto again; | |
4924 | } | |
0aacf84e | 4925 | else |
8a1f4f98 | 4926 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4927 | } |
0aacf84e | 4928 | else |
8a1f4f98 | 4929 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
4930 | } |
4931 | ||
4932 | ||
8a1f4f98 AW |
4933 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
4934 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
4935 | (SCM x, SCM y, SCM rest), | |
4936 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4937 | "decreasing.") | |
4938 | #define FUNC_NAME s_scm_i_num_gr_p | |
4939 | { | |
4940 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4941 | return SCM_BOOL_T; | |
4942 | while (!scm_is_null (rest)) | |
4943 | { | |
4944 | if (scm_is_false (scm_gr_p (x, y))) | |
4945 | return SCM_BOOL_F; | |
4946 | x = y; | |
4947 | y = scm_car (rest); | |
4948 | rest = scm_cdr (rest); | |
4949 | } | |
4950 | return scm_gr_p (x, y); | |
4951 | } | |
4952 | #undef FUNC_NAME | |
4953 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
4954 | SCM |
4955 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 4956 | { |
c76b1eaf | 4957 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4958 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4959 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4960 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
4961 | else |
4962 | return scm_less_p (y, x); | |
0f2d19dd | 4963 | } |
1bbd0b84 | 4964 | #undef FUNC_NAME |
0f2d19dd JB |
4965 | |
4966 | ||
8a1f4f98 AW |
4967 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
4968 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
4969 | (SCM x, SCM y, SCM rest), | |
4970 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4971 | "non-decreasing.") | |
4972 | #define FUNC_NAME s_scm_i_num_leq_p | |
4973 | { | |
4974 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4975 | return SCM_BOOL_T; | |
4976 | while (!scm_is_null (rest)) | |
4977 | { | |
4978 | if (scm_is_false (scm_leq_p (x, y))) | |
4979 | return SCM_BOOL_F; | |
4980 | x = y; | |
4981 | y = scm_car (rest); | |
4982 | rest = scm_cdr (rest); | |
4983 | } | |
4984 | return scm_leq_p (x, y); | |
4985 | } | |
4986 | #undef FUNC_NAME | |
4987 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
4988 | SCM |
4989 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 4990 | { |
c76b1eaf | 4991 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4992 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4993 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4994 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 4995 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 4996 | return SCM_BOOL_F; |
c76b1eaf | 4997 | else |
73e4de09 | 4998 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 4999 | } |
1bbd0b84 | 5000 | #undef FUNC_NAME |
0f2d19dd JB |
5001 | |
5002 | ||
8a1f4f98 AW |
5003 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
5004 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
5005 | (SCM x, SCM y, SCM rest), | |
5006 | "Return @code{#t} if the list of parameters is monotonically\n" | |
5007 | "non-increasing.") | |
5008 | #define FUNC_NAME s_scm_i_num_geq_p | |
5009 | { | |
5010 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
5011 | return SCM_BOOL_T; | |
5012 | while (!scm_is_null (rest)) | |
5013 | { | |
5014 | if (scm_is_false (scm_geq_p (x, y))) | |
5015 | return SCM_BOOL_F; | |
5016 | x = y; | |
5017 | y = scm_car (rest); | |
5018 | rest = scm_cdr (rest); | |
5019 | } | |
5020 | return scm_geq_p (x, y); | |
5021 | } | |
5022 | #undef FUNC_NAME | |
5023 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
5024 | SCM |
5025 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 5026 | { |
c76b1eaf | 5027 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 5028 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 5029 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 5030 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 5031 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 5032 | return SCM_BOOL_F; |
c76b1eaf | 5033 | else |
73e4de09 | 5034 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 5035 | } |
1bbd0b84 | 5036 | #undef FUNC_NAME |
0f2d19dd JB |
5037 | |
5038 | ||
2519490c MW |
5039 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
5040 | (SCM z), | |
5041 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
5042 | "zero.") | |
5043 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 5044 | { |
e11e83f3 | 5045 | if (SCM_I_INUMP (z)) |
bc36d050 | 5046 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 5047 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5048 | return SCM_BOOL_F; |
0aacf84e | 5049 | else if (SCM_REALP (z)) |
73e4de09 | 5050 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 5051 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 5052 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 5053 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
5054 | else if (SCM_FRACTIONP (z)) |
5055 | return SCM_BOOL_F; | |
0aacf84e | 5056 | else |
2519490c | 5057 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 5058 | } |
2519490c | 5059 | #undef FUNC_NAME |
0f2d19dd JB |
5060 | |
5061 | ||
2519490c MW |
5062 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
5063 | (SCM x), | |
5064 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
5065 | "zero.") | |
5066 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 5067 | { |
e11e83f3 MV |
5068 | if (SCM_I_INUMP (x)) |
5069 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
5070 | else if (SCM_BIGP (x)) |
5071 | { | |
5072 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5073 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5074 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
5075 | } |
5076 | else if (SCM_REALP (x)) | |
73e4de09 | 5077 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
5078 | else if (SCM_FRACTIONP (x)) |
5079 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5080 | else |
2519490c | 5081 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 5082 | } |
2519490c | 5083 | #undef FUNC_NAME |
0f2d19dd JB |
5084 | |
5085 | ||
2519490c MW |
5086 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
5087 | (SCM x), | |
5088 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
5089 | "zero.") | |
5090 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 5091 | { |
e11e83f3 MV |
5092 | if (SCM_I_INUMP (x)) |
5093 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
5094 | else if (SCM_BIGP (x)) |
5095 | { | |
5096 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5097 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5098 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
5099 | } |
5100 | else if (SCM_REALP (x)) | |
73e4de09 | 5101 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
5102 | else if (SCM_FRACTIONP (x)) |
5103 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5104 | else |
2519490c | 5105 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 5106 | } |
2519490c | 5107 | #undef FUNC_NAME |
0f2d19dd JB |
5108 | |
5109 | ||
2a06f791 KR |
5110 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
5111 | required by r5rs. On that basis, for exact/inexact combinations the | |
5112 | exact is converted to inexact to compare and possibly return. This is | |
5113 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
5114 | its test, such trouble is not required for min and max. */ | |
5115 | ||
78d3deb1 AW |
5116 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
5117 | (SCM x, SCM y, SCM rest), | |
5118 | "Return the maximum of all parameter values.") | |
5119 | #define FUNC_NAME s_scm_i_max | |
5120 | { | |
5121 | while (!scm_is_null (rest)) | |
5122 | { x = scm_max (x, y); | |
5123 | y = scm_car (rest); | |
5124 | rest = scm_cdr (rest); | |
5125 | } | |
5126 | return scm_max (x, y); | |
5127 | } | |
5128 | #undef FUNC_NAME | |
5129 | ||
5130 | #define s_max s_scm_i_max | |
5131 | #define g_max g_scm_i_max | |
5132 | ||
0f2d19dd | 5133 | SCM |
6e8d25a6 | 5134 | scm_max (SCM x, SCM y) |
0f2d19dd | 5135 | { |
0aacf84e MD |
5136 | if (SCM_UNBNDP (y)) |
5137 | { | |
5138 | if (SCM_UNBNDP (x)) | |
5139 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 5140 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5141 | return x; |
5142 | else | |
5143 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 5144 | } |
f4c627b3 | 5145 | |
e11e83f3 | 5146 | if (SCM_I_INUMP (x)) |
0aacf84e | 5147 | { |
e25f3727 | 5148 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5149 | if (SCM_I_INUMP (y)) |
0aacf84e | 5150 | { |
e25f3727 | 5151 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5152 | return (xx < yy) ? y : x; |
5153 | } | |
5154 | else if (SCM_BIGP (y)) | |
5155 | { | |
5156 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5157 | scm_remember_upto_here_1 (y); | |
5158 | return (sgn < 0) ? x : y; | |
5159 | } | |
5160 | else if (SCM_REALP (y)) | |
5161 | { | |
2e274311 MW |
5162 | double xxd = xx; |
5163 | double yyd = SCM_REAL_VALUE (y); | |
5164 | ||
5165 | if (xxd > yyd) | |
5166 | return scm_from_double (xxd); | |
5167 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
5168 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5169 | return y; | |
5170 | /* Handle signed zeroes properly */ | |
5171 | else if (xx == 0) | |
5172 | return flo0; | |
5173 | else | |
5174 | return y; | |
0aacf84e | 5175 | } |
f92e85f7 MV |
5176 | else if (SCM_FRACTIONP (y)) |
5177 | { | |
e4bc5d6c | 5178 | use_less: |
73e4de09 | 5179 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 5180 | } |
0aacf84e MD |
5181 | else |
5182 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5183 | } |
0aacf84e MD |
5184 | else if (SCM_BIGP (x)) |
5185 | { | |
e11e83f3 | 5186 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5187 | { |
5188 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5189 | scm_remember_upto_here_1 (x); | |
5190 | return (sgn < 0) ? y : x; | |
5191 | } | |
5192 | else if (SCM_BIGP (y)) | |
5193 | { | |
5194 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5195 | scm_remember_upto_here_2 (x, y); | |
5196 | return (cmp > 0) ? x : y; | |
5197 | } | |
5198 | else if (SCM_REALP (y)) | |
5199 | { | |
2a06f791 KR |
5200 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
5201 | double xx, yy; | |
5202 | big_real: | |
5203 | xx = scm_i_big2dbl (x); | |
5204 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5205 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 5206 | } |
f92e85f7 MV |
5207 | else if (SCM_FRACTIONP (y)) |
5208 | { | |
e4bc5d6c | 5209 | goto use_less; |
f92e85f7 | 5210 | } |
0aacf84e MD |
5211 | else |
5212 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 5213 | } |
0aacf84e MD |
5214 | else if (SCM_REALP (x)) |
5215 | { | |
e11e83f3 | 5216 | if (SCM_I_INUMP (y)) |
0aacf84e | 5217 | { |
2e274311 MW |
5218 | scm_t_inum yy = SCM_I_INUM (y); |
5219 | double xxd = SCM_REAL_VALUE (x); | |
5220 | double yyd = yy; | |
5221 | ||
5222 | if (yyd > xxd) | |
5223 | return scm_from_double (yyd); | |
5224 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
5225 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5226 | return x; | |
5227 | /* Handle signed zeroes properly */ | |
5228 | else if (yy == 0) | |
5229 | return flo0; | |
5230 | else | |
5231 | return x; | |
0aacf84e MD |
5232 | } |
5233 | else if (SCM_BIGP (y)) | |
5234 | { | |
b6f8f763 | 5235 | SCM_SWAP (x, y); |
2a06f791 | 5236 | goto big_real; |
0aacf84e MD |
5237 | } |
5238 | else if (SCM_REALP (y)) | |
5239 | { | |
0aacf84e | 5240 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5241 | double yy = SCM_REAL_VALUE (y); |
5242 | ||
5243 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
5244 | if (xx > yy) | |
5245 | return x; | |
5246 | else if (SCM_LIKELY (xx < yy)) | |
5247 | return y; | |
5248 | /* If neither (xx > yy) nor (xx < yy), then | |
5249 | either they're equal or one is a NaN */ | |
5250 | else if (SCM_UNLIKELY (isnan (xx))) | |
5251 | return (isinf (yy) == 1) ? y : x; | |
5252 | else if (SCM_UNLIKELY (isnan (yy))) | |
5253 | return (isinf (xx) == 1) ? x : y; | |
5254 | /* xx == yy, but handle signed zeroes properly */ | |
5255 | else if (double_is_non_negative_zero (yy)) | |
5256 | return y; | |
5257 | else | |
5258 | return x; | |
0aacf84e | 5259 | } |
f92e85f7 MV |
5260 | else if (SCM_FRACTIONP (y)) |
5261 | { | |
5262 | double yy = scm_i_fraction2double (y); | |
5263 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5264 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
5265 | } |
5266 | else | |
5267 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
5268 | } | |
5269 | else if (SCM_FRACTIONP (x)) | |
5270 | { | |
e11e83f3 | 5271 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5272 | { |
e4bc5d6c | 5273 | goto use_less; |
f92e85f7 MV |
5274 | } |
5275 | else if (SCM_BIGP (y)) | |
5276 | { | |
e4bc5d6c | 5277 | goto use_less; |
f92e85f7 MV |
5278 | } |
5279 | else if (SCM_REALP (y)) | |
5280 | { | |
5281 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5282 | /* if y==NaN then ">" is false, so we return the NaN y */ |
5283 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5284 | } |
5285 | else if (SCM_FRACTIONP (y)) | |
5286 | { | |
e4bc5d6c | 5287 | goto use_less; |
f92e85f7 | 5288 | } |
0aacf84e MD |
5289 | else |
5290 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5291 | } |
0aacf84e | 5292 | else |
f4c627b3 | 5293 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
5294 | } |
5295 | ||
5296 | ||
78d3deb1 AW |
5297 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
5298 | (SCM x, SCM y, SCM rest), | |
5299 | "Return the minimum of all parameter values.") | |
5300 | #define FUNC_NAME s_scm_i_min | |
5301 | { | |
5302 | while (!scm_is_null (rest)) | |
5303 | { x = scm_min (x, y); | |
5304 | y = scm_car (rest); | |
5305 | rest = scm_cdr (rest); | |
5306 | } | |
5307 | return scm_min (x, y); | |
5308 | } | |
5309 | #undef FUNC_NAME | |
5310 | ||
5311 | #define s_min s_scm_i_min | |
5312 | #define g_min g_scm_i_min | |
5313 | ||
0f2d19dd | 5314 | SCM |
6e8d25a6 | 5315 | scm_min (SCM x, SCM y) |
0f2d19dd | 5316 | { |
0aacf84e MD |
5317 | if (SCM_UNBNDP (y)) |
5318 | { | |
5319 | if (SCM_UNBNDP (x)) | |
5320 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 5321 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5322 | return x; |
5323 | else | |
5324 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 5325 | } |
f4c627b3 | 5326 | |
e11e83f3 | 5327 | if (SCM_I_INUMP (x)) |
0aacf84e | 5328 | { |
e25f3727 | 5329 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5330 | if (SCM_I_INUMP (y)) |
0aacf84e | 5331 | { |
e25f3727 | 5332 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5333 | return (xx < yy) ? x : y; |
5334 | } | |
5335 | else if (SCM_BIGP (y)) | |
5336 | { | |
5337 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5338 | scm_remember_upto_here_1 (y); | |
5339 | return (sgn < 0) ? y : x; | |
5340 | } | |
5341 | else if (SCM_REALP (y)) | |
5342 | { | |
5343 | double z = xx; | |
5344 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 5345 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 5346 | } |
f92e85f7 MV |
5347 | else if (SCM_FRACTIONP (y)) |
5348 | { | |
e4bc5d6c | 5349 | use_less: |
73e4de09 | 5350 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 5351 | } |
0aacf84e MD |
5352 | else |
5353 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5354 | } |
0aacf84e MD |
5355 | else if (SCM_BIGP (x)) |
5356 | { | |
e11e83f3 | 5357 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5358 | { |
5359 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5360 | scm_remember_upto_here_1 (x); | |
5361 | return (sgn < 0) ? x : y; | |
5362 | } | |
5363 | else if (SCM_BIGP (y)) | |
5364 | { | |
5365 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5366 | scm_remember_upto_here_2 (x, y); | |
5367 | return (cmp > 0) ? y : x; | |
5368 | } | |
5369 | else if (SCM_REALP (y)) | |
5370 | { | |
2a06f791 KR |
5371 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
5372 | double xx, yy; | |
5373 | big_real: | |
5374 | xx = scm_i_big2dbl (x); | |
5375 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5376 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 5377 | } |
f92e85f7 MV |
5378 | else if (SCM_FRACTIONP (y)) |
5379 | { | |
e4bc5d6c | 5380 | goto use_less; |
f92e85f7 | 5381 | } |
0aacf84e MD |
5382 | else |
5383 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 5384 | } |
0aacf84e MD |
5385 | else if (SCM_REALP (x)) |
5386 | { | |
e11e83f3 | 5387 | if (SCM_I_INUMP (y)) |
0aacf84e | 5388 | { |
e11e83f3 | 5389 | double z = SCM_I_INUM (y); |
0aacf84e | 5390 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 5391 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
5392 | } |
5393 | else if (SCM_BIGP (y)) | |
5394 | { | |
b6f8f763 | 5395 | SCM_SWAP (x, y); |
2a06f791 | 5396 | goto big_real; |
0aacf84e MD |
5397 | } |
5398 | else if (SCM_REALP (y)) | |
5399 | { | |
0aacf84e | 5400 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5401 | double yy = SCM_REAL_VALUE (y); |
5402 | ||
5403 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
5404 | if (xx < yy) | |
5405 | return x; | |
5406 | else if (SCM_LIKELY (xx > yy)) | |
5407 | return y; | |
5408 | /* If neither (xx < yy) nor (xx > yy), then | |
5409 | either they're equal or one is a NaN */ | |
5410 | else if (SCM_UNLIKELY (isnan (xx))) | |
5411 | return (isinf (yy) == -1) ? y : x; | |
5412 | else if (SCM_UNLIKELY (isnan (yy))) | |
5413 | return (isinf (xx) == -1) ? x : y; | |
5414 | /* xx == yy, but handle signed zeroes properly */ | |
5415 | else if (double_is_non_negative_zero (xx)) | |
5416 | return y; | |
5417 | else | |
5418 | return x; | |
0aacf84e | 5419 | } |
f92e85f7 MV |
5420 | else if (SCM_FRACTIONP (y)) |
5421 | { | |
5422 | double yy = scm_i_fraction2double (y); | |
5423 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5424 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 5425 | } |
0aacf84e MD |
5426 | else |
5427 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5428 | } |
f92e85f7 MV |
5429 | else if (SCM_FRACTIONP (x)) |
5430 | { | |
e11e83f3 | 5431 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5432 | { |
e4bc5d6c | 5433 | goto use_less; |
f92e85f7 MV |
5434 | } |
5435 | else if (SCM_BIGP (y)) | |
5436 | { | |
e4bc5d6c | 5437 | goto use_less; |
f92e85f7 MV |
5438 | } |
5439 | else if (SCM_REALP (y)) | |
5440 | { | |
5441 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5442 | /* if y==NaN then "<" is false, so we return the NaN y */ |
5443 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5444 | } |
5445 | else if (SCM_FRACTIONP (y)) | |
5446 | { | |
e4bc5d6c | 5447 | goto use_less; |
f92e85f7 MV |
5448 | } |
5449 | else | |
78d3deb1 | 5450 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 5451 | } |
0aacf84e | 5452 | else |
f4c627b3 | 5453 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
5454 | } |
5455 | ||
5456 | ||
8ccd24f7 AW |
5457 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
5458 | (SCM x, SCM y, SCM rest), | |
5459 | "Return the sum of all parameter values. Return 0 if called without\n" | |
5460 | "any parameters." ) | |
5461 | #define FUNC_NAME s_scm_i_sum | |
5462 | { | |
5463 | while (!scm_is_null (rest)) | |
5464 | { x = scm_sum (x, y); | |
5465 | y = scm_car (rest); | |
5466 | rest = scm_cdr (rest); | |
5467 | } | |
5468 | return scm_sum (x, y); | |
5469 | } | |
5470 | #undef FUNC_NAME | |
5471 | ||
5472 | #define s_sum s_scm_i_sum | |
5473 | #define g_sum g_scm_i_sum | |
5474 | ||
0f2d19dd | 5475 | SCM |
6e8d25a6 | 5476 | scm_sum (SCM x, SCM y) |
0f2d19dd | 5477 | { |
9cc37597 | 5478 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5479 | { |
5480 | if (SCM_NUMBERP (x)) return x; | |
5481 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 5482 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 5483 | } |
c209c88e | 5484 | |
9cc37597 | 5485 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 5486 | { |
9cc37597 | 5487 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 5488 | { |
e25f3727 AW |
5489 | scm_t_inum xx = SCM_I_INUM (x); |
5490 | scm_t_inum yy = SCM_I_INUM (y); | |
5491 | scm_t_inum z = xx + yy; | |
5492 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
5493 | } |
5494 | else if (SCM_BIGP (y)) | |
5495 | { | |
5496 | SCM_SWAP (x, y); | |
5497 | goto add_big_inum; | |
5498 | } | |
5499 | else if (SCM_REALP (y)) | |
5500 | { | |
e25f3727 | 5501 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5502 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
5503 | } |
5504 | else if (SCM_COMPLEXP (y)) | |
5505 | { | |
e25f3727 | 5506 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5507 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
5508 | SCM_COMPLEX_IMAG (y)); |
5509 | } | |
f92e85f7 | 5510 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5511 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5512 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5513 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
5514 | else |
5515 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
5516 | } else if (SCM_BIGP (x)) |
5517 | { | |
e11e83f3 | 5518 | if (SCM_I_INUMP (y)) |
0aacf84e | 5519 | { |
e25f3727 | 5520 | scm_t_inum inum; |
0aacf84e MD |
5521 | int bigsgn; |
5522 | add_big_inum: | |
e11e83f3 | 5523 | inum = SCM_I_INUM (y); |
0aacf84e MD |
5524 | if (inum == 0) |
5525 | return x; | |
5526 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5527 | if (inum < 0) | |
5528 | { | |
5529 | SCM result = scm_i_mkbig (); | |
5530 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
5531 | scm_remember_upto_here_1 (x); | |
5532 | /* we know the result will have to be a bignum */ | |
5533 | if (bigsgn == -1) | |
5534 | return result; | |
5535 | return scm_i_normbig (result); | |
5536 | } | |
5537 | else | |
5538 | { | |
5539 | SCM result = scm_i_mkbig (); | |
5540 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
5541 | scm_remember_upto_here_1 (x); | |
5542 | /* we know the result will have to be a bignum */ | |
5543 | if (bigsgn == 1) | |
5544 | return result; | |
5545 | return scm_i_normbig (result); | |
5546 | } | |
5547 | } | |
5548 | else if (SCM_BIGP (y)) | |
5549 | { | |
5550 | SCM result = scm_i_mkbig (); | |
5551 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5552 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5553 | mpz_add (SCM_I_BIG_MPZ (result), | |
5554 | SCM_I_BIG_MPZ (x), | |
5555 | SCM_I_BIG_MPZ (y)); | |
5556 | scm_remember_upto_here_2 (x, y); | |
5557 | /* we know the result will have to be a bignum */ | |
5558 | if (sgn_x == sgn_y) | |
5559 | return result; | |
5560 | return scm_i_normbig (result); | |
5561 | } | |
5562 | else if (SCM_REALP (y)) | |
5563 | { | |
5564 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
5565 | scm_remember_upto_here_1 (x); | |
55f26379 | 5566 | return scm_from_double (result); |
0aacf84e MD |
5567 | } |
5568 | else if (SCM_COMPLEXP (y)) | |
5569 | { | |
5570 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5571 | + SCM_COMPLEX_REAL (y)); | |
5572 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5573 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5574 | } |
f92e85f7 | 5575 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5576 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5577 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5578 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5579 | else |
5580 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 5581 | } |
0aacf84e MD |
5582 | else if (SCM_REALP (x)) |
5583 | { | |
e11e83f3 | 5584 | if (SCM_I_INUMP (y)) |
55f26379 | 5585 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
5586 | else if (SCM_BIGP (y)) |
5587 | { | |
5588 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
5589 | scm_remember_upto_here_1 (y); | |
55f26379 | 5590 | return scm_from_double (result); |
0aacf84e MD |
5591 | } |
5592 | else if (SCM_REALP (y)) | |
55f26379 | 5593 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 5594 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5595 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5596 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5597 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5598 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
5599 | else |
5600 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 5601 | } |
0aacf84e MD |
5602 | else if (SCM_COMPLEXP (x)) |
5603 | { | |
e11e83f3 | 5604 | if (SCM_I_INUMP (y)) |
8507ec80 | 5605 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
5606 | SCM_COMPLEX_IMAG (x)); |
5607 | else if (SCM_BIGP (y)) | |
5608 | { | |
5609 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
5610 | + SCM_COMPLEX_REAL (x)); | |
5611 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5612 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
5613 | } |
5614 | else if (SCM_REALP (y)) | |
8507ec80 | 5615 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
5616 | SCM_COMPLEX_IMAG (x)); |
5617 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5618 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5619 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5620 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5621 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
5622 | SCM_COMPLEX_IMAG (x)); |
5623 | else | |
5624 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
5625 | } | |
5626 | else if (SCM_FRACTIONP (x)) | |
5627 | { | |
e11e83f3 | 5628 | if (SCM_I_INUMP (y)) |
cba42c93 | 5629 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5630 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5631 | SCM_FRACTION_DENOMINATOR (x)); | |
5632 | else if (SCM_BIGP (y)) | |
cba42c93 | 5633 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5634 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5635 | SCM_FRACTION_DENOMINATOR (x)); | |
5636 | else if (SCM_REALP (y)) | |
55f26379 | 5637 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 5638 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5639 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
5640 | SCM_COMPLEX_IMAG (y)); |
5641 | else if (SCM_FRACTIONP (y)) | |
5642 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 5643 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5644 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5645 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5646 | else |
5647 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 5648 | } |
0aacf84e | 5649 | else |
98cb6e75 | 5650 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
5651 | } |
5652 | ||
5653 | ||
40882e3d KR |
5654 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
5655 | (SCM x), | |
5656 | "Return @math{@var{x}+1}.") | |
5657 | #define FUNC_NAME s_scm_oneplus | |
5658 | { | |
cff5fa33 | 5659 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
5660 | } |
5661 | #undef FUNC_NAME | |
5662 | ||
5663 | ||
78d3deb1 AW |
5664 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
5665 | (SCM x, SCM y, SCM rest), | |
5666 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
5667 | "the sum of all but the first argument are subtracted from the first\n" | |
5668 | "argument.") | |
5669 | #define FUNC_NAME s_scm_i_difference | |
5670 | { | |
5671 | while (!scm_is_null (rest)) | |
5672 | { x = scm_difference (x, y); | |
5673 | y = scm_car (rest); | |
5674 | rest = scm_cdr (rest); | |
5675 | } | |
5676 | return scm_difference (x, y); | |
5677 | } | |
5678 | #undef FUNC_NAME | |
5679 | ||
5680 | #define s_difference s_scm_i_difference | |
5681 | #define g_difference g_scm_i_difference | |
5682 | ||
0f2d19dd | 5683 | SCM |
6e8d25a6 | 5684 | scm_difference (SCM x, SCM y) |
78d3deb1 | 5685 | #define FUNC_NAME s_difference |
0f2d19dd | 5686 | { |
9cc37597 | 5687 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5688 | { |
5689 | if (SCM_UNBNDP (x)) | |
5690 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
5691 | else | |
e11e83f3 | 5692 | if (SCM_I_INUMP (x)) |
ca46fb90 | 5693 | { |
e25f3727 | 5694 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 5695 | if (SCM_FIXABLE (xx)) |
d956fa6f | 5696 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 5697 | else |
e25f3727 | 5698 | return scm_i_inum2big (xx); |
ca46fb90 RB |
5699 | } |
5700 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
5701 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
5702 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
5703 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
5704 | else if (SCM_REALP (x)) | |
55f26379 | 5705 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 5706 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 5707 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 5708 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 5709 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 5710 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 5711 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
5712 | else |
5713 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 5714 | } |
ca46fb90 | 5715 | |
9cc37597 | 5716 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5717 | { |
9cc37597 | 5718 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5719 | { |
e25f3727 AW |
5720 | scm_t_inum xx = SCM_I_INUM (x); |
5721 | scm_t_inum yy = SCM_I_INUM (y); | |
5722 | scm_t_inum z = xx - yy; | |
0aacf84e | 5723 | if (SCM_FIXABLE (z)) |
d956fa6f | 5724 | return SCM_I_MAKINUM (z); |
0aacf84e | 5725 | else |
e25f3727 | 5726 | return scm_i_inum2big (z); |
0aacf84e MD |
5727 | } |
5728 | else if (SCM_BIGP (y)) | |
5729 | { | |
5730 | /* inum-x - big-y */ | |
e25f3727 | 5731 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 5732 | |
0aacf84e | 5733 | if (xx == 0) |
b5c40589 MW |
5734 | { |
5735 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
5736 | bignum, but negating that gives a fixnum. */ | |
5737 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
5738 | } | |
0aacf84e MD |
5739 | else |
5740 | { | |
5741 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5742 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5743 | |
0aacf84e MD |
5744 | if (xx >= 0) |
5745 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
5746 | else | |
5747 | { | |
5748 | /* x - y == -(y + -x) */ | |
5749 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
5750 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5751 | } | |
5752 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 5753 | |
0aacf84e MD |
5754 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
5755 | /* we know the result will have to be a bignum */ | |
5756 | return result; | |
5757 | else | |
5758 | return scm_i_normbig (result); | |
5759 | } | |
5760 | } | |
5761 | else if (SCM_REALP (y)) | |
5762 | { | |
e25f3727 | 5763 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
5764 | |
5765 | /* | |
5766 | * We need to handle x == exact 0 | |
5767 | * specially because R6RS states that: | |
5768 | * (- 0.0) ==> -0.0 and | |
5769 | * (- 0.0 0.0) ==> 0.0 | |
5770 | * and the scheme compiler changes | |
5771 | * (- 0.0) into (- 0 0.0) | |
5772 | * So we need to treat (- 0 0.0) like (- 0.0). | |
5773 | * At the C level, (-x) is different than (0.0 - x). | |
5774 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
5775 | */ | |
5776 | if (xx == 0) | |
5777 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
5778 | else | |
5779 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
5780 | } |
5781 | else if (SCM_COMPLEXP (y)) | |
5782 | { | |
e25f3727 | 5783 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
5784 | |
5785 | /* We need to handle x == exact 0 specially. | |
5786 | See the comment above (for SCM_REALP (y)) */ | |
5787 | if (xx == 0) | |
5788 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
5789 | - SCM_COMPLEX_IMAG (y)); | |
5790 | else | |
5791 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
5792 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 5793 | } |
f92e85f7 MV |
5794 | else if (SCM_FRACTIONP (y)) |
5795 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 5796 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5797 | SCM_FRACTION_NUMERATOR (y)), |
5798 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5799 | else |
5800 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 5801 | } |
0aacf84e MD |
5802 | else if (SCM_BIGP (x)) |
5803 | { | |
e11e83f3 | 5804 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5805 | { |
5806 | /* big-x - inum-y */ | |
e25f3727 | 5807 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 5808 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 5809 | |
0aacf84e MD |
5810 | scm_remember_upto_here_1 (x); |
5811 | if (sgn_x == 0) | |
c71b0706 | 5812 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 5813 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
5814 | else |
5815 | { | |
5816 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5817 | |
708f22c6 KR |
5818 | if (yy >= 0) |
5819 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
5820 | else | |
5821 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 5822 | scm_remember_upto_here_1 (x); |
ca46fb90 | 5823 | |
0aacf84e MD |
5824 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
5825 | /* we know the result will have to be a bignum */ | |
5826 | return result; | |
5827 | else | |
5828 | return scm_i_normbig (result); | |
5829 | } | |
5830 | } | |
5831 | else if (SCM_BIGP (y)) | |
5832 | { | |
5833 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5834 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5835 | SCM result = scm_i_mkbig (); | |
5836 | mpz_sub (SCM_I_BIG_MPZ (result), | |
5837 | SCM_I_BIG_MPZ (x), | |
5838 | SCM_I_BIG_MPZ (y)); | |
5839 | scm_remember_upto_here_2 (x, y); | |
5840 | /* we know the result will have to be a bignum */ | |
5841 | if ((sgn_x == 1) && (sgn_y == -1)) | |
5842 | return result; | |
5843 | if ((sgn_x == -1) && (sgn_y == 1)) | |
5844 | return result; | |
5845 | return scm_i_normbig (result); | |
5846 | } | |
5847 | else if (SCM_REALP (y)) | |
5848 | { | |
5849 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
5850 | scm_remember_upto_here_1 (x); | |
55f26379 | 5851 | return scm_from_double (result); |
0aacf84e MD |
5852 | } |
5853 | else if (SCM_COMPLEXP (y)) | |
5854 | { | |
5855 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5856 | - SCM_COMPLEX_REAL (y)); | |
5857 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5858 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5859 | } |
f92e85f7 | 5860 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5861 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5862 | SCM_FRACTION_NUMERATOR (y)), |
5863 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 5864 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 5865 | } |
0aacf84e MD |
5866 | else if (SCM_REALP (x)) |
5867 | { | |
e11e83f3 | 5868 | if (SCM_I_INUMP (y)) |
55f26379 | 5869 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
5870 | else if (SCM_BIGP (y)) |
5871 | { | |
5872 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5873 | scm_remember_upto_here_1 (x); | |
55f26379 | 5874 | return scm_from_double (result); |
0aacf84e MD |
5875 | } |
5876 | else if (SCM_REALP (y)) | |
55f26379 | 5877 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 5878 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5879 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5880 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5881 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5882 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
5883 | else |
5884 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5885 | } |
0aacf84e MD |
5886 | else if (SCM_COMPLEXP (x)) |
5887 | { | |
e11e83f3 | 5888 | if (SCM_I_INUMP (y)) |
8507ec80 | 5889 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
5890 | SCM_COMPLEX_IMAG (x)); |
5891 | else if (SCM_BIGP (y)) | |
5892 | { | |
5893 | double real_part = (SCM_COMPLEX_REAL (x) | |
5894 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
5895 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5896 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
5897 | } |
5898 | else if (SCM_REALP (y)) | |
8507ec80 | 5899 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
5900 | SCM_COMPLEX_IMAG (x)); |
5901 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5902 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5903 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5904 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5905 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
5906 | SCM_COMPLEX_IMAG (x)); |
5907 | else | |
5908 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
5909 | } | |
5910 | else if (SCM_FRACTIONP (x)) | |
5911 | { | |
e11e83f3 | 5912 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5913 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 5914 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5915 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5916 | SCM_FRACTION_DENOMINATOR (x)); | |
5917 | else if (SCM_BIGP (y)) | |
cba42c93 | 5918 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5919 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5920 | SCM_FRACTION_DENOMINATOR (x)); | |
5921 | else if (SCM_REALP (y)) | |
55f26379 | 5922 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 5923 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5924 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
5925 | -SCM_COMPLEX_IMAG (y)); |
5926 | else if (SCM_FRACTIONP (y)) | |
5927 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 5928 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5929 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5930 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5931 | else |
5932 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5933 | } |
0aacf84e | 5934 | else |
98cb6e75 | 5935 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 5936 | } |
c05e97b7 | 5937 | #undef FUNC_NAME |
0f2d19dd | 5938 | |
ca46fb90 | 5939 | |
40882e3d KR |
5940 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
5941 | (SCM x), | |
5942 | "Return @math{@var{x}-1}.") | |
5943 | #define FUNC_NAME s_scm_oneminus | |
5944 | { | |
cff5fa33 | 5945 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
5946 | } |
5947 | #undef FUNC_NAME | |
5948 | ||
5949 | ||
78d3deb1 AW |
5950 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
5951 | (SCM x, SCM y, SCM rest), | |
5952 | "Return the product of all arguments. If called without arguments,\n" | |
5953 | "1 is returned.") | |
5954 | #define FUNC_NAME s_scm_i_product | |
5955 | { | |
5956 | while (!scm_is_null (rest)) | |
5957 | { x = scm_product (x, y); | |
5958 | y = scm_car (rest); | |
5959 | rest = scm_cdr (rest); | |
5960 | } | |
5961 | return scm_product (x, y); | |
5962 | } | |
5963 | #undef FUNC_NAME | |
5964 | ||
5965 | #define s_product s_scm_i_product | |
5966 | #define g_product g_scm_i_product | |
5967 | ||
0f2d19dd | 5968 | SCM |
6e8d25a6 | 5969 | scm_product (SCM x, SCM y) |
0f2d19dd | 5970 | { |
9cc37597 | 5971 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
5972 | { |
5973 | if (SCM_UNBNDP (x)) | |
d956fa6f | 5974 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
5975 | else if (SCM_NUMBERP (x)) |
5976 | return x; | |
5977 | else | |
5978 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 5979 | } |
ca46fb90 | 5980 | |
9cc37597 | 5981 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5982 | { |
e25f3727 | 5983 | scm_t_inum xx; |
f4c627b3 | 5984 | |
5e791807 | 5985 | xinum: |
e11e83f3 | 5986 | xx = SCM_I_INUM (x); |
f4c627b3 | 5987 | |
0aacf84e MD |
5988 | switch (xx) |
5989 | { | |
5e791807 MW |
5990 | case 1: |
5991 | /* exact1 is the universal multiplicative identity */ | |
5992 | return y; | |
5993 | break; | |
5994 | case 0: | |
5995 | /* exact0 times a fixnum is exact0: optimize this case */ | |
5996 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
5997 | return SCM_INUM0; | |
5998 | /* if the other argument is inexact, the result is inexact, | |
5999 | and we must do the multiplication in order to handle | |
6000 | infinities and NaNs properly. */ | |
6001 | else if (SCM_REALP (y)) | |
6002 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
6003 | else if (SCM_COMPLEXP (y)) | |
6004 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
6005 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
6006 | /* we've already handled inexact numbers, | |
6007 | so y must be exact, and we return exact0 */ | |
6008 | else if (SCM_NUMP (y)) | |
6009 | return SCM_INUM0; | |
6010 | else | |
6011 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6012 | break; | |
6013 | case -1: | |
b5c40589 | 6014 | /* |
5e791807 MW |
6015 | * This case is important for more than just optimization. |
6016 | * It handles the case of negating | |
b5c40589 MW |
6017 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
6018 | * which is a bignum that must be changed back into a fixnum. | |
6019 | * Failure to do so will cause the following to return #f: | |
6020 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
6021 | */ | |
b5c40589 MW |
6022 | return scm_difference(y, SCM_UNDEFINED); |
6023 | break; | |
0aacf84e | 6024 | } |
f4c627b3 | 6025 | |
9cc37597 | 6026 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6027 | { |
e25f3727 AW |
6028 | scm_t_inum yy = SCM_I_INUM (y); |
6029 | scm_t_inum kk = xx * yy; | |
d956fa6f | 6030 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 6031 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
6032 | return k; |
6033 | else | |
6034 | { | |
e25f3727 | 6035 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
6036 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
6037 | return scm_i_normbig (result); | |
6038 | } | |
6039 | } | |
6040 | else if (SCM_BIGP (y)) | |
6041 | { | |
6042 | SCM result = scm_i_mkbig (); | |
6043 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
6044 | scm_remember_upto_here_1 (y); | |
6045 | return result; | |
6046 | } | |
6047 | else if (SCM_REALP (y)) | |
55f26379 | 6048 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 6049 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6050 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 6051 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6052 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6053 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6054 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6055 | else |
6056 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6057 | } |
0aacf84e MD |
6058 | else if (SCM_BIGP (x)) |
6059 | { | |
e11e83f3 | 6060 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6061 | { |
6062 | SCM_SWAP (x, y); | |
5e791807 | 6063 | goto xinum; |
0aacf84e MD |
6064 | } |
6065 | else if (SCM_BIGP (y)) | |
6066 | { | |
6067 | SCM result = scm_i_mkbig (); | |
6068 | mpz_mul (SCM_I_BIG_MPZ (result), | |
6069 | SCM_I_BIG_MPZ (x), | |
6070 | SCM_I_BIG_MPZ (y)); | |
6071 | scm_remember_upto_here_2 (x, y); | |
6072 | return result; | |
6073 | } | |
6074 | else if (SCM_REALP (y)) | |
6075 | { | |
6076 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
6077 | scm_remember_upto_here_1 (x); | |
55f26379 | 6078 | return scm_from_double (result); |
0aacf84e MD |
6079 | } |
6080 | else if (SCM_COMPLEXP (y)) | |
6081 | { | |
6082 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
6083 | scm_remember_upto_here_1 (x); | |
8507ec80 | 6084 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
6085 | z * SCM_COMPLEX_IMAG (y)); |
6086 | } | |
f92e85f7 | 6087 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6088 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6089 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6090 | else |
6091 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6092 | } |
0aacf84e MD |
6093 | else if (SCM_REALP (x)) |
6094 | { | |
e11e83f3 | 6095 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6096 | { |
6097 | SCM_SWAP (x, y); | |
6098 | goto xinum; | |
6099 | } | |
0aacf84e MD |
6100 | else if (SCM_BIGP (y)) |
6101 | { | |
6102 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
6103 | scm_remember_upto_here_1 (y); | |
55f26379 | 6104 | return scm_from_double (result); |
0aacf84e MD |
6105 | } |
6106 | else if (SCM_REALP (y)) | |
55f26379 | 6107 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 6108 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6109 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 6110 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6111 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6112 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
6113 | else |
6114 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6115 | } |
0aacf84e MD |
6116 | else if (SCM_COMPLEXP (x)) |
6117 | { | |
e11e83f3 | 6118 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6119 | { |
6120 | SCM_SWAP (x, y); | |
6121 | goto xinum; | |
6122 | } | |
0aacf84e MD |
6123 | else if (SCM_BIGP (y)) |
6124 | { | |
6125 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6126 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6127 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 6128 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
6129 | } |
6130 | else if (SCM_REALP (y)) | |
8507ec80 | 6131 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
6132 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
6133 | else if (SCM_COMPLEXP (y)) | |
6134 | { | |
8507ec80 | 6135 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
6136 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
6137 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
6138 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
6139 | } | |
f92e85f7 MV |
6140 | else if (SCM_FRACTIONP (y)) |
6141 | { | |
6142 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6143 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
6144 | yy * SCM_COMPLEX_IMAG (x)); |
6145 | } | |
6146 | else | |
6147 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6148 | } | |
6149 | else if (SCM_FRACTIONP (x)) | |
6150 | { | |
e11e83f3 | 6151 | if (SCM_I_INUMP (y)) |
cba42c93 | 6152 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6153 | SCM_FRACTION_DENOMINATOR (x)); |
6154 | else if (SCM_BIGP (y)) | |
cba42c93 | 6155 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6156 | SCM_FRACTION_DENOMINATOR (x)); |
6157 | else if (SCM_REALP (y)) | |
55f26379 | 6158 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
6159 | else if (SCM_COMPLEXP (y)) |
6160 | { | |
6161 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 6162 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
6163 | xx * SCM_COMPLEX_IMAG (y)); |
6164 | } | |
6165 | else if (SCM_FRACTIONP (y)) | |
6166 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 6167 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6168 | SCM_FRACTION_NUMERATOR (y)), |
6169 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
6170 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
6171 | else |
6172 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6173 | } |
0aacf84e | 6174 | else |
f4c627b3 | 6175 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
6176 | } |
6177 | ||
7351e207 MV |
6178 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
6179 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
6180 | #define ALLOW_DIVIDE_BY_ZERO | |
6181 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
6182 | #endif | |
0f2d19dd | 6183 | |
ba74ef4e MV |
6184 | /* The code below for complex division is adapted from the GNU |
6185 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
6186 | this copyright: */ | |
6187 | ||
6188 | /**************************************************************** | |
6189 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
6190 | ||
6191 | Permission to use, copy, modify, and distribute this software | |
6192 | and its documentation for any purpose and without fee is hereby | |
6193 | granted, provided that the above copyright notice appear in all | |
6194 | copies and that both that the copyright notice and this | |
6195 | permission notice and warranty disclaimer appear in supporting | |
6196 | documentation, and that the names of AT&T Bell Laboratories or | |
6197 | Bellcore or any of their entities not be used in advertising or | |
6198 | publicity pertaining to distribution of the software without | |
6199 | specific, written prior permission. | |
6200 | ||
6201 | AT&T and Bellcore disclaim all warranties with regard to this | |
6202 | software, including all implied warranties of merchantability | |
6203 | and fitness. In no event shall AT&T or Bellcore be liable for | |
6204 | any special, indirect or consequential damages or any damages | |
6205 | whatsoever resulting from loss of use, data or profits, whether | |
6206 | in an action of contract, negligence or other tortious action, | |
6207 | arising out of or in connection with the use or performance of | |
6208 | this software. | |
6209 | ****************************************************************/ | |
6210 | ||
78d3deb1 AW |
6211 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
6212 | (SCM x, SCM y, SCM rest), | |
6213 | "Divide the first argument by the product of the remaining\n" | |
6214 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
6215 | "returned.") | |
6216 | #define FUNC_NAME s_scm_i_divide | |
6217 | { | |
6218 | while (!scm_is_null (rest)) | |
6219 | { x = scm_divide (x, y); | |
6220 | y = scm_car (rest); | |
6221 | rest = scm_cdr (rest); | |
6222 | } | |
6223 | return scm_divide (x, y); | |
6224 | } | |
6225 | #undef FUNC_NAME | |
6226 | ||
6227 | #define s_divide s_scm_i_divide | |
6228 | #define g_divide g_scm_i_divide | |
6229 | ||
f92e85f7 | 6230 | static SCM |
78d3deb1 AW |
6231 | do_divide (SCM x, SCM y, int inexact) |
6232 | #define FUNC_NAME s_divide | |
0f2d19dd | 6233 | { |
f8de44c1 DH |
6234 | double a; |
6235 | ||
9cc37597 | 6236 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
6237 | { |
6238 | if (SCM_UNBNDP (x)) | |
6239 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 6240 | else if (SCM_I_INUMP (x)) |
0aacf84e | 6241 | { |
e25f3727 | 6242 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
6243 | if (xx == 1 || xx == -1) |
6244 | return x; | |
7351e207 | 6245 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6246 | else if (xx == 0) |
6247 | scm_num_overflow (s_divide); | |
7351e207 | 6248 | #endif |
0aacf84e | 6249 | else |
f92e85f7 MV |
6250 | { |
6251 | if (inexact) | |
55f26379 | 6252 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 6253 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6254 | } |
0aacf84e MD |
6255 | } |
6256 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
6257 | { |
6258 | if (inexact) | |
55f26379 | 6259 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 6260 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6261 | } |
0aacf84e MD |
6262 | else if (SCM_REALP (x)) |
6263 | { | |
6264 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 6265 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6266 | if (xx == 0.0) |
6267 | scm_num_overflow (s_divide); | |
6268 | else | |
7351e207 | 6269 | #endif |
55f26379 | 6270 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
6271 | } |
6272 | else if (SCM_COMPLEXP (x)) | |
6273 | { | |
6274 | double r = SCM_COMPLEX_REAL (x); | |
6275 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 6276 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6277 | { |
6278 | double t = r / i; | |
6279 | double d = i * (1.0 + t * t); | |
8507ec80 | 6280 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
6281 | } |
6282 | else | |
6283 | { | |
6284 | double t = i / r; | |
6285 | double d = r * (1.0 + t * t); | |
8507ec80 | 6286 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
6287 | } |
6288 | } | |
f92e85f7 | 6289 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 6290 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 6291 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
6292 | else |
6293 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 6294 | } |
f8de44c1 | 6295 | |
9cc37597 | 6296 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 6297 | { |
e25f3727 | 6298 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 6299 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6300 | { |
e25f3727 | 6301 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6302 | if (yy == 0) |
6303 | { | |
7351e207 | 6304 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6305 | scm_num_overflow (s_divide); |
7351e207 | 6306 | #else |
55f26379 | 6307 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 6308 | #endif |
0aacf84e MD |
6309 | } |
6310 | else if (xx % yy != 0) | |
f92e85f7 MV |
6311 | { |
6312 | if (inexact) | |
55f26379 | 6313 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 6314 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6315 | } |
0aacf84e MD |
6316 | else |
6317 | { | |
e25f3727 | 6318 | scm_t_inum z = xx / yy; |
0aacf84e | 6319 | if (SCM_FIXABLE (z)) |
d956fa6f | 6320 | return SCM_I_MAKINUM (z); |
0aacf84e | 6321 | else |
e25f3727 | 6322 | return scm_i_inum2big (z); |
0aacf84e | 6323 | } |
f872b822 | 6324 | } |
0aacf84e | 6325 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
6326 | { |
6327 | if (inexact) | |
55f26379 | 6328 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 6329 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6330 | } |
0aacf84e MD |
6331 | else if (SCM_REALP (y)) |
6332 | { | |
6333 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6334 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6335 | if (yy == 0.0) |
6336 | scm_num_overflow (s_divide); | |
6337 | else | |
7351e207 | 6338 | #endif |
55f26379 | 6339 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 6340 | } |
0aacf84e MD |
6341 | else if (SCM_COMPLEXP (y)) |
6342 | { | |
6343 | a = xx; | |
6344 | complex_div: /* y _must_ be a complex number */ | |
6345 | { | |
6346 | double r = SCM_COMPLEX_REAL (y); | |
6347 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6348 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6349 | { |
6350 | double t = r / i; | |
6351 | double d = i * (1.0 + t * t); | |
8507ec80 | 6352 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
6353 | } |
6354 | else | |
6355 | { | |
6356 | double t = i / r; | |
6357 | double d = r * (1.0 + t * t); | |
8507ec80 | 6358 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
6359 | } |
6360 | } | |
6361 | } | |
f92e85f7 MV |
6362 | else if (SCM_FRACTIONP (y)) |
6363 | /* a / b/c = ac / b */ | |
cba42c93 | 6364 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6365 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6366 | else |
6367 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6368 | } |
0aacf84e MD |
6369 | else if (SCM_BIGP (x)) |
6370 | { | |
e11e83f3 | 6371 | if (SCM_I_INUMP (y)) |
0aacf84e | 6372 | { |
e25f3727 | 6373 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6374 | if (yy == 0) |
6375 | { | |
7351e207 | 6376 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6377 | scm_num_overflow (s_divide); |
7351e207 | 6378 | #else |
0aacf84e MD |
6379 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
6380 | scm_remember_upto_here_1 (x); | |
6381 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 6382 | #endif |
0aacf84e MD |
6383 | } |
6384 | else if (yy == 1) | |
6385 | return x; | |
6386 | else | |
6387 | { | |
6388 | /* FIXME: HMM, what are the relative performance issues here? | |
6389 | We need to test. Is it faster on average to test | |
6390 | divisible_p, then perform whichever operation, or is it | |
6391 | faster to perform the integer div opportunistically and | |
6392 | switch to real if there's a remainder? For now we take the | |
6393 | middle ground: test, then if divisible, use the faster div | |
6394 | func. */ | |
6395 | ||
e25f3727 | 6396 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
6397 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
6398 | ||
6399 | if (divisible_p) | |
6400 | { | |
6401 | SCM result = scm_i_mkbig (); | |
6402 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
6403 | scm_remember_upto_here_1 (x); | |
6404 | if (yy < 0) | |
6405 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
6406 | return scm_i_normbig (result); | |
6407 | } | |
6408 | else | |
f92e85f7 MV |
6409 | { |
6410 | if (inexact) | |
55f26379 | 6411 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 6412 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6413 | } |
0aacf84e MD |
6414 | } |
6415 | } | |
6416 | else if (SCM_BIGP (y)) | |
6417 | { | |
a4955a04 MW |
6418 | /* big_x / big_y */ |
6419 | if (inexact) | |
0aacf84e | 6420 | { |
a4955a04 MW |
6421 | /* It's easily possible for the ratio x/y to fit a double |
6422 | but one or both x and y be too big to fit a double, | |
6423 | hence the use of mpq_get_d rather than converting and | |
6424 | dividing. */ | |
6425 | mpq_t q; | |
6426 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
6427 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
6428 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
6429 | } |
6430 | else | |
6431 | { | |
a4955a04 MW |
6432 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
6433 | SCM_I_BIG_MPZ (y)); | |
6434 | if (divisible_p) | |
6435 | { | |
6436 | SCM result = scm_i_mkbig (); | |
6437 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
6438 | SCM_I_BIG_MPZ (x), | |
6439 | SCM_I_BIG_MPZ (y)); | |
6440 | scm_remember_upto_here_2 (x, y); | |
6441 | return scm_i_normbig (result); | |
6442 | } | |
6443 | else | |
6444 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
6445 | } |
6446 | } | |
6447 | else if (SCM_REALP (y)) | |
6448 | { | |
6449 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6450 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6451 | if (yy == 0.0) |
6452 | scm_num_overflow (s_divide); | |
6453 | else | |
7351e207 | 6454 | #endif |
55f26379 | 6455 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
6456 | } |
6457 | else if (SCM_COMPLEXP (y)) | |
6458 | { | |
6459 | a = scm_i_big2dbl (x); | |
6460 | goto complex_div; | |
6461 | } | |
f92e85f7 | 6462 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6463 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6464 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6465 | else |
6466 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6467 | } |
0aacf84e MD |
6468 | else if (SCM_REALP (x)) |
6469 | { | |
6470 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 6471 | if (SCM_I_INUMP (y)) |
0aacf84e | 6472 | { |
e25f3727 | 6473 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6474 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6475 | if (yy == 0) |
6476 | scm_num_overflow (s_divide); | |
6477 | else | |
7351e207 | 6478 | #endif |
55f26379 | 6479 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
6480 | } |
6481 | else if (SCM_BIGP (y)) | |
6482 | { | |
6483 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6484 | scm_remember_upto_here_1 (y); | |
55f26379 | 6485 | return scm_from_double (rx / dby); |
0aacf84e MD |
6486 | } |
6487 | else if (SCM_REALP (y)) | |
6488 | { | |
6489 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6490 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6491 | if (yy == 0.0) |
6492 | scm_num_overflow (s_divide); | |
6493 | else | |
7351e207 | 6494 | #endif |
55f26379 | 6495 | return scm_from_double (rx / yy); |
0aacf84e MD |
6496 | } |
6497 | else if (SCM_COMPLEXP (y)) | |
6498 | { | |
6499 | a = rx; | |
6500 | goto complex_div; | |
6501 | } | |
f92e85f7 | 6502 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6503 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
6504 | else |
6505 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6506 | } |
0aacf84e MD |
6507 | else if (SCM_COMPLEXP (x)) |
6508 | { | |
6509 | double rx = SCM_COMPLEX_REAL (x); | |
6510 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 6511 | if (SCM_I_INUMP (y)) |
0aacf84e | 6512 | { |
e25f3727 | 6513 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6514 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6515 | if (yy == 0) |
6516 | scm_num_overflow (s_divide); | |
6517 | else | |
7351e207 | 6518 | #endif |
0aacf84e MD |
6519 | { |
6520 | double d = yy; | |
8507ec80 | 6521 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
6522 | } |
6523 | } | |
6524 | else if (SCM_BIGP (y)) | |
6525 | { | |
6526 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6527 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6528 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
6529 | } |
6530 | else if (SCM_REALP (y)) | |
6531 | { | |
6532 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6533 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6534 | if (yy == 0.0) |
6535 | scm_num_overflow (s_divide); | |
6536 | else | |
7351e207 | 6537 | #endif |
8507ec80 | 6538 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
6539 | } |
6540 | else if (SCM_COMPLEXP (y)) | |
6541 | { | |
6542 | double ry = SCM_COMPLEX_REAL (y); | |
6543 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6544 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
6545 | { |
6546 | double t = ry / iy; | |
6547 | double d = iy * (1.0 + t * t); | |
8507ec80 | 6548 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
6549 | } |
6550 | else | |
6551 | { | |
6552 | double t = iy / ry; | |
6553 | double d = ry * (1.0 + t * t); | |
8507ec80 | 6554 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
6555 | } |
6556 | } | |
f92e85f7 MV |
6557 | else if (SCM_FRACTIONP (y)) |
6558 | { | |
6559 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6560 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 6561 | } |
0aacf84e MD |
6562 | else |
6563 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6564 | } |
f92e85f7 MV |
6565 | else if (SCM_FRACTIONP (x)) |
6566 | { | |
e11e83f3 | 6567 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6568 | { |
e25f3727 | 6569 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
6570 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
6571 | if (yy == 0) | |
6572 | scm_num_overflow (s_divide); | |
6573 | else | |
6574 | #endif | |
cba42c93 | 6575 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6576 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6577 | } | |
6578 | else if (SCM_BIGP (y)) | |
6579 | { | |
cba42c93 | 6580 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6581 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6582 | } | |
6583 | else if (SCM_REALP (y)) | |
6584 | { | |
6585 | double yy = SCM_REAL_VALUE (y); | |
6586 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6587 | if (yy == 0.0) | |
6588 | scm_num_overflow (s_divide); | |
6589 | else | |
6590 | #endif | |
55f26379 | 6591 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
6592 | } |
6593 | else if (SCM_COMPLEXP (y)) | |
6594 | { | |
6595 | a = scm_i_fraction2double (x); | |
6596 | goto complex_div; | |
6597 | } | |
6598 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 6599 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
6600 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
6601 | else | |
6602 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
6603 | } | |
0aacf84e | 6604 | else |
f8de44c1 | 6605 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 6606 | } |
f92e85f7 MV |
6607 | |
6608 | SCM | |
6609 | scm_divide (SCM x, SCM y) | |
6610 | { | |
78d3deb1 | 6611 | return do_divide (x, y, 0); |
f92e85f7 MV |
6612 | } |
6613 | ||
6614 | static SCM scm_divide2real (SCM x, SCM y) | |
6615 | { | |
78d3deb1 | 6616 | return do_divide (x, y, 1); |
f92e85f7 | 6617 | } |
c05e97b7 | 6618 | #undef FUNC_NAME |
0f2d19dd | 6619 | |
fa605590 | 6620 | |
0f2d19dd | 6621 | double |
3101f40f | 6622 | scm_c_truncate (double x) |
0f2d19dd | 6623 | { |
fa605590 KR |
6624 | #if HAVE_TRUNC |
6625 | return trunc (x); | |
6626 | #else | |
f872b822 MD |
6627 | if (x < 0.0) |
6628 | return -floor (-x); | |
6629 | return floor (x); | |
fa605590 | 6630 | #endif |
0f2d19dd | 6631 | } |
0f2d19dd | 6632 | |
3101f40f MV |
6633 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
6634 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
6635 | Then half-way cases are identified and adjusted down if the | |
6636 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
6637 | |
6638 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
6639 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
6640 | ||
6641 | An odd "result" value is identified with result/2 != floor(result/2). | |
6642 | This is done with plus_half, since that value is ready for use sooner in | |
6643 | a pipelined cpu, and we're already requiring plus_half == result. | |
6644 | ||
6645 | Note however that we need to be careful when x is big and already an | |
6646 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
6647 | us to return such a value, incorrectly. For instance if the hardware is | |
6648 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
6649 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
6650 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
6651 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
6652 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
6653 | ||
6654 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
6655 | x is already an integer. If it is then clearly that's the desired result | |
6656 | already. And if it's not then the exponent must be small enough to allow | |
6657 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
6658 | ||
0f2d19dd | 6659 | double |
3101f40f | 6660 | scm_c_round (double x) |
0f2d19dd | 6661 | { |
6187f48b KR |
6662 | double plus_half, result; |
6663 | ||
6664 | if (x == floor (x)) | |
6665 | return x; | |
6666 | ||
6667 | plus_half = x + 0.5; | |
6668 | result = floor (plus_half); | |
3101f40f | 6669 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
6670 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
6671 | ? result - 1 | |
6672 | : result); | |
0f2d19dd JB |
6673 | } |
6674 | ||
f92e85f7 MV |
6675 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
6676 | (SCM x), | |
6677 | "Round the number @var{x} towards zero.") | |
6678 | #define FUNC_NAME s_scm_truncate_number | |
6679 | { | |
73e4de09 | 6680 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6681 | return scm_floor (x); |
6682 | else | |
6683 | return scm_ceiling (x); | |
6684 | } | |
6685 | #undef FUNC_NAME | |
6686 | ||
f92e85f7 MV |
6687 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, |
6688 | (SCM x), | |
6689 | "Round the number @var{x} towards the nearest integer. " | |
6690 | "When it is exactly halfway between two integers, " | |
6691 | "round towards the even one.") | |
6692 | #define FUNC_NAME s_scm_round_number | |
6693 | { | |
e11e83f3 | 6694 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
6695 | return x; |
6696 | else if (SCM_REALP (x)) | |
3101f40f | 6697 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 6698 | else |
bae30667 KR |
6699 | { |
6700 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
6701 | single quotient+remainder division then examining to see which way | |
6702 | the rounding should go. */ | |
6703 | SCM plus_half = scm_sum (x, exactly_one_half); | |
6704 | SCM result = scm_floor (plus_half); | |
3101f40f | 6705 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
6706 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
6707 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 6708 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
6709 | else |
6710 | return result; | |
6711 | } | |
f92e85f7 MV |
6712 | } |
6713 | #undef FUNC_NAME | |
6714 | ||
6715 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
6716 | (SCM x), | |
6717 | "Round the number @var{x} towards minus infinity.") | |
6718 | #define FUNC_NAME s_scm_floor | |
6719 | { | |
e11e83f3 | 6720 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6721 | return x; |
6722 | else if (SCM_REALP (x)) | |
55f26379 | 6723 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6724 | else if (SCM_FRACTIONP (x)) |
6725 | { | |
6726 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6727 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6728 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6729 | { |
6730 | /* For positive x, rounding towards zero is correct. */ | |
6731 | return q; | |
6732 | } | |
6733 | else | |
6734 | { | |
6735 | /* For negative x, we need to return q-1 unless x is an | |
6736 | integer. But fractions are never integer, per our | |
6737 | assumptions. */ | |
cff5fa33 | 6738 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
6739 | } |
6740 | } | |
6741 | else | |
6742 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
6743 | } | |
6744 | #undef FUNC_NAME | |
6745 | ||
6746 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
6747 | (SCM x), | |
6748 | "Round the number @var{x} towards infinity.") | |
6749 | #define FUNC_NAME s_scm_ceiling | |
6750 | { | |
e11e83f3 | 6751 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6752 | return x; |
6753 | else if (SCM_REALP (x)) | |
55f26379 | 6754 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6755 | else if (SCM_FRACTIONP (x)) |
6756 | { | |
6757 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6758 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6759 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
6760 | { |
6761 | /* For negative x, rounding towards zero is correct. */ | |
6762 | return q; | |
6763 | } | |
6764 | else | |
6765 | { | |
6766 | /* For positive x, we need to return q+1 unless x is an | |
6767 | integer. But fractions are never integer, per our | |
6768 | assumptions. */ | |
cff5fa33 | 6769 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
6770 | } |
6771 | } | |
6772 | else | |
6773 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
6774 | } | |
6775 | #undef FUNC_NAME | |
0f2d19dd | 6776 | |
2519490c MW |
6777 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
6778 | (SCM x, SCM y), | |
6779 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 6780 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 6781 | { |
01c7284a MW |
6782 | if (scm_is_integer (y)) |
6783 | { | |
6784 | if (scm_is_true (scm_exact_p (y))) | |
6785 | return scm_integer_expt (x, y); | |
6786 | else | |
6787 | { | |
6788 | /* Here we handle the case where the exponent is an inexact | |
6789 | integer. We make the exponent exact in order to use | |
6790 | scm_integer_expt, and thus avoid the spurious imaginary | |
6791 | parts that may result from round-off errors in the general | |
6792 | e^(y log x) method below (for example when squaring a large | |
6793 | negative number). In this case, we must return an inexact | |
6794 | result for correctness. We also make the base inexact so | |
6795 | that scm_integer_expt will use fast inexact arithmetic | |
6796 | internally. Note that making the base inexact is not | |
6797 | sufficient to guarantee an inexact result, because | |
6798 | scm_integer_expt will return an exact 1 when the exponent | |
6799 | is 0, even if the base is inexact. */ | |
6800 | return scm_exact_to_inexact | |
6801 | (scm_integer_expt (scm_exact_to_inexact (x), | |
6802 | scm_inexact_to_exact (y))); | |
6803 | } | |
6804 | } | |
6fc4d012 AW |
6805 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
6806 | { | |
6807 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
6808 | } | |
2519490c | 6809 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 6810 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
6811 | else if (scm_is_complex (x)) |
6812 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
6813 | else | |
6814 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 6815 | } |
1bbd0b84 | 6816 | #undef FUNC_NAME |
0f2d19dd | 6817 | |
7f41099e MW |
6818 | /* sin/cos/tan/asin/acos/atan |
6819 | sinh/cosh/tanh/asinh/acosh/atanh | |
6820 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
6821 | Written by Jerry D. Hedden, (C) FSF. | |
6822 | See the file `COPYING' for terms applying to this program. */ | |
6823 | ||
ad79736c AW |
6824 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
6825 | (SCM z), | |
6826 | "Compute the sine of @var{z}.") | |
6827 | #define FUNC_NAME s_scm_sin | |
6828 | { | |
8deddc94 MW |
6829 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6830 | return z; /* sin(exact0) = exact0 */ | |
6831 | else if (scm_is_real (z)) | |
ad79736c AW |
6832 | return scm_from_double (sin (scm_to_double (z))); |
6833 | else if (SCM_COMPLEXP (z)) | |
6834 | { double x, y; | |
6835 | x = SCM_COMPLEX_REAL (z); | |
6836 | y = SCM_COMPLEX_IMAG (z); | |
6837 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
6838 | cos (x) * sinh (y)); | |
6839 | } | |
6840 | else | |
6841 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
6842 | } | |
6843 | #undef FUNC_NAME | |
0f2d19dd | 6844 | |
ad79736c AW |
6845 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
6846 | (SCM z), | |
6847 | "Compute the cosine of @var{z}.") | |
6848 | #define FUNC_NAME s_scm_cos | |
6849 | { | |
8deddc94 MW |
6850 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6851 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
6852 | else if (scm_is_real (z)) | |
ad79736c AW |
6853 | return scm_from_double (cos (scm_to_double (z))); |
6854 | else if (SCM_COMPLEXP (z)) | |
6855 | { double x, y; | |
6856 | x = SCM_COMPLEX_REAL (z); | |
6857 | y = SCM_COMPLEX_IMAG (z); | |
6858 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
6859 | -sin (x) * sinh (y)); | |
6860 | } | |
6861 | else | |
6862 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
6863 | } | |
6864 | #undef FUNC_NAME | |
6865 | ||
6866 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
6867 | (SCM z), | |
6868 | "Compute the tangent of @var{z}.") | |
6869 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 6870 | { |
8deddc94 MW |
6871 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6872 | return z; /* tan(exact0) = exact0 */ | |
6873 | else if (scm_is_real (z)) | |
ad79736c AW |
6874 | return scm_from_double (tan (scm_to_double (z))); |
6875 | else if (SCM_COMPLEXP (z)) | |
6876 | { double x, y, w; | |
6877 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6878 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6879 | w = cos (x) + cosh (y); | |
6880 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6881 | if (w == 0.0) | |
6882 | scm_num_overflow (s_scm_tan); | |
6883 | #endif | |
6884 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
6885 | } | |
6886 | else | |
6887 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
6888 | } | |
6889 | #undef FUNC_NAME | |
6890 | ||
6891 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
6892 | (SCM z), | |
6893 | "Compute the hyperbolic sine of @var{z}.") | |
6894 | #define FUNC_NAME s_scm_sinh | |
6895 | { | |
8deddc94 MW |
6896 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6897 | return z; /* sinh(exact0) = exact0 */ | |
6898 | else if (scm_is_real (z)) | |
ad79736c AW |
6899 | return scm_from_double (sinh (scm_to_double (z))); |
6900 | else if (SCM_COMPLEXP (z)) | |
6901 | { double x, y; | |
6902 | x = SCM_COMPLEX_REAL (z); | |
6903 | y = SCM_COMPLEX_IMAG (z); | |
6904 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
6905 | cosh (x) * sin (y)); | |
6906 | } | |
6907 | else | |
6908 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
6909 | } | |
6910 | #undef FUNC_NAME | |
6911 | ||
6912 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
6913 | (SCM z), | |
6914 | "Compute the hyperbolic cosine of @var{z}.") | |
6915 | #define FUNC_NAME s_scm_cosh | |
6916 | { | |
8deddc94 MW |
6917 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6918 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
6919 | else if (scm_is_real (z)) | |
ad79736c AW |
6920 | return scm_from_double (cosh (scm_to_double (z))); |
6921 | else if (SCM_COMPLEXP (z)) | |
6922 | { double x, y; | |
6923 | x = SCM_COMPLEX_REAL (z); | |
6924 | y = SCM_COMPLEX_IMAG (z); | |
6925 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
6926 | sinh (x) * sin (y)); | |
6927 | } | |
6928 | else | |
6929 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
6930 | } | |
6931 | #undef FUNC_NAME | |
6932 | ||
6933 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
6934 | (SCM z), | |
6935 | "Compute the hyperbolic tangent of @var{z}.") | |
6936 | #define FUNC_NAME s_scm_tanh | |
6937 | { | |
8deddc94 MW |
6938 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6939 | return z; /* tanh(exact0) = exact0 */ | |
6940 | else if (scm_is_real (z)) | |
ad79736c AW |
6941 | return scm_from_double (tanh (scm_to_double (z))); |
6942 | else if (SCM_COMPLEXP (z)) | |
6943 | { double x, y, w; | |
6944 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6945 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6946 | w = cosh (x) + cos (y); | |
6947 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6948 | if (w == 0.0) | |
6949 | scm_num_overflow (s_scm_tanh); | |
6950 | #endif | |
6951 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
6952 | } | |
6953 | else | |
6954 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
6955 | } | |
6956 | #undef FUNC_NAME | |
6957 | ||
6958 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
6959 | (SCM z), | |
6960 | "Compute the arc sine of @var{z}.") | |
6961 | #define FUNC_NAME s_scm_asin | |
6962 | { | |
8deddc94 MW |
6963 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6964 | return z; /* asin(exact0) = exact0 */ | |
6965 | else if (scm_is_real (z)) | |
ad79736c AW |
6966 | { |
6967 | double w = scm_to_double (z); | |
6968 | if (w >= -1.0 && w <= 1.0) | |
6969 | return scm_from_double (asin (w)); | |
6970 | else | |
6971 | return scm_product (scm_c_make_rectangular (0, -1), | |
6972 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
6973 | } | |
6974 | else if (SCM_COMPLEXP (z)) | |
6975 | { double x, y; | |
6976 | x = SCM_COMPLEX_REAL (z); | |
6977 | y = SCM_COMPLEX_IMAG (z); | |
6978 | return scm_product (scm_c_make_rectangular (0, -1), | |
6979 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
6980 | } | |
6981 | else | |
6982 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
6983 | } | |
6984 | #undef FUNC_NAME | |
6985 | ||
6986 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
6987 | (SCM z), | |
6988 | "Compute the arc cosine of @var{z}.") | |
6989 | #define FUNC_NAME s_scm_acos | |
6990 | { | |
8deddc94 MW |
6991 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
6992 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
6993 | else if (scm_is_real (z)) | |
ad79736c AW |
6994 | { |
6995 | double w = scm_to_double (z); | |
6996 | if (w >= -1.0 && w <= 1.0) | |
6997 | return scm_from_double (acos (w)); | |
6998 | else | |
6999 | return scm_sum (scm_from_double (acos (0.0)), | |
7000 | scm_product (scm_c_make_rectangular (0, 1), | |
7001 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
7002 | } | |
7003 | else if (SCM_COMPLEXP (z)) | |
7004 | { double x, y; | |
7005 | x = SCM_COMPLEX_REAL (z); | |
7006 | y = SCM_COMPLEX_IMAG (z); | |
7007 | return scm_sum (scm_from_double (acos (0.0)), | |
7008 | scm_product (scm_c_make_rectangular (0, 1), | |
7009 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
7010 | } | |
7011 | else | |
7012 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
7013 | } | |
7014 | #undef FUNC_NAME | |
7015 | ||
7016 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
7017 | (SCM z, SCM y), | |
7018 | "With one argument, compute the arc tangent of @var{z}.\n" | |
7019 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
7020 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
7021 | #define FUNC_NAME s_scm_atan | |
7022 | { | |
7023 | if (SCM_UNBNDP (y)) | |
7024 | { | |
8deddc94 MW |
7025 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7026 | return z; /* atan(exact0) = exact0 */ | |
7027 | else if (scm_is_real (z)) | |
ad79736c AW |
7028 | return scm_from_double (atan (scm_to_double (z))); |
7029 | else if (SCM_COMPLEXP (z)) | |
7030 | { | |
7031 | double v, w; | |
7032 | v = SCM_COMPLEX_REAL (z); | |
7033 | w = SCM_COMPLEX_IMAG (z); | |
7034 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
7035 | scm_c_make_rectangular (v, w + 1.0))), | |
7036 | scm_c_make_rectangular (0, 2)); | |
7037 | } | |
7038 | else | |
7039 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7040 | } | |
7041 | else if (scm_is_real (z)) | |
7042 | { | |
7043 | if (scm_is_real (y)) | |
7044 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
7045 | else | |
7046 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
7047 | } | |
7048 | else | |
7049 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7050 | } | |
7051 | #undef FUNC_NAME | |
7052 | ||
7053 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
7054 | (SCM z), | |
7055 | "Compute the inverse hyperbolic sine of @var{z}.") | |
7056 | #define FUNC_NAME s_scm_sys_asinh | |
7057 | { | |
8deddc94 MW |
7058 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7059 | return z; /* asinh(exact0) = exact0 */ | |
7060 | else if (scm_is_real (z)) | |
ad79736c AW |
7061 | return scm_from_double (asinh (scm_to_double (z))); |
7062 | else if (scm_is_number (z)) | |
7063 | return scm_log (scm_sum (z, | |
7064 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 7065 | SCM_INUM1)))); |
ad79736c AW |
7066 | else |
7067 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
7068 | } | |
7069 | #undef FUNC_NAME | |
7070 | ||
7071 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
7072 | (SCM z), | |
7073 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
7074 | #define FUNC_NAME s_scm_sys_acosh | |
7075 | { | |
8deddc94 MW |
7076 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
7077 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
7078 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
7079 | return scm_from_double (acosh (scm_to_double (z))); |
7080 | else if (scm_is_number (z)) | |
7081 | return scm_log (scm_sum (z, | |
7082 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 7083 | SCM_INUM1)))); |
ad79736c AW |
7084 | else |
7085 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
7086 | } | |
7087 | #undef FUNC_NAME | |
7088 | ||
7089 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
7090 | (SCM z), | |
7091 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
7092 | #define FUNC_NAME s_scm_sys_atanh | |
7093 | { | |
8deddc94 MW |
7094 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7095 | return z; /* atanh(exact0) = exact0 */ | |
7096 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
7097 | return scm_from_double (atanh (scm_to_double (z))); |
7098 | else if (scm_is_number (z)) | |
cff5fa33 MW |
7099 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
7100 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
7101 | SCM_I_MAKINUM (2)); |
7102 | else | |
7103 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 7104 | } |
1bbd0b84 | 7105 | #undef FUNC_NAME |
0f2d19dd | 7106 | |
8507ec80 MV |
7107 | SCM |
7108 | scm_c_make_rectangular (double re, double im) | |
7109 | { | |
7110 | if (im == 0.0) | |
7111 | return scm_from_double (re); | |
7112 | else | |
7113 | { | |
7114 | SCM z; | |
03604fcf LC |
7115 | |
7116 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
92d8fd32 | 7117 | "complex")); |
03604fcf | 7118 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
8507ec80 MV |
7119 | SCM_COMPLEX_REAL (z) = re; |
7120 | SCM_COMPLEX_IMAG (z) = im; | |
7121 | return z; | |
7122 | } | |
7123 | } | |
0f2d19dd | 7124 | |
a1ec6916 | 7125 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
7126 | (SCM real_part, SCM imaginary_part), |
7127 | "Return a complex number constructed of the given @var{real-part} " | |
7128 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 7129 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 7130 | { |
ad79736c AW |
7131 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
7132 | SCM_ARG1, FUNC_NAME, "real"); | |
7133 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
7134 | SCM_ARG2, FUNC_NAME, "real"); | |
7135 | return scm_c_make_rectangular (scm_to_double (real_part), | |
7136 | scm_to_double (imaginary_part)); | |
0f2d19dd | 7137 | } |
1bbd0b84 | 7138 | #undef FUNC_NAME |
0f2d19dd | 7139 | |
8507ec80 MV |
7140 | SCM |
7141 | scm_c_make_polar (double mag, double ang) | |
7142 | { | |
7143 | double s, c; | |
5e647d08 LC |
7144 | |
7145 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
7146 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
7147 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
7148 | details. */ | |
7149 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
7150 | sincos (ang, &s, &c); |
7151 | #else | |
7152 | s = sin (ang); | |
7153 | c = cos (ang); | |
7154 | #endif | |
7155 | return scm_c_make_rectangular (mag * c, mag * s); | |
7156 | } | |
0f2d19dd | 7157 | |
a1ec6916 | 7158 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 7159 | (SCM x, SCM y), |
942e5b91 | 7160 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 7161 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 7162 | { |
ad79736c AW |
7163 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7164 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
7165 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 7166 | } |
1bbd0b84 | 7167 | #undef FUNC_NAME |
0f2d19dd JB |
7168 | |
7169 | ||
2519490c MW |
7170 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
7171 | (SCM z), | |
7172 | "Return the real part of the number @var{z}.") | |
7173 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 7174 | { |
2519490c | 7175 | if (SCM_COMPLEXP (z)) |
55f26379 | 7176 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 7177 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 7178 | return z; |
0aacf84e | 7179 | else |
2519490c | 7180 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 7181 | } |
2519490c | 7182 | #undef FUNC_NAME |
0f2d19dd JB |
7183 | |
7184 | ||
2519490c MW |
7185 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
7186 | (SCM z), | |
7187 | "Return the imaginary part of the number @var{z}.") | |
7188 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 7189 | { |
2519490c MW |
7190 | if (SCM_COMPLEXP (z)) |
7191 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
0aacf84e | 7192 | else if (SCM_REALP (z)) |
e7efe8e7 | 7193 | return flo0; |
2519490c | 7194 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 7195 | return SCM_INUM0; |
0aacf84e | 7196 | else |
2519490c | 7197 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 7198 | } |
2519490c | 7199 | #undef FUNC_NAME |
0f2d19dd | 7200 | |
2519490c MW |
7201 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
7202 | (SCM z), | |
7203 | "Return the numerator of the number @var{z}.") | |
7204 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 7205 | { |
2519490c | 7206 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
7207 | return z; |
7208 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 7209 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
7210 | else if (SCM_REALP (z)) |
7211 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
7212 | else | |
2519490c | 7213 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 7214 | } |
2519490c | 7215 | #undef FUNC_NAME |
f92e85f7 MV |
7216 | |
7217 | ||
2519490c MW |
7218 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
7219 | (SCM z), | |
7220 | "Return the denominator of the number @var{z}.") | |
7221 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 7222 | { |
2519490c | 7223 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 7224 | return SCM_INUM1; |
f92e85f7 | 7225 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 7226 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
7227 | else if (SCM_REALP (z)) |
7228 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
7229 | else | |
2519490c | 7230 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 7231 | } |
2519490c | 7232 | #undef FUNC_NAME |
0f2d19dd | 7233 | |
2519490c MW |
7234 | |
7235 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
7236 | (SCM z), | |
7237 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
7238 | "@code{abs} for real arguments, but also allows complex numbers.") | |
7239 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 7240 | { |
e11e83f3 | 7241 | if (SCM_I_INUMP (z)) |
0aacf84e | 7242 | { |
e25f3727 | 7243 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
7244 | if (zz >= 0) |
7245 | return z; | |
7246 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 7247 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 7248 | else |
e25f3727 | 7249 | return scm_i_inum2big (-zz); |
5986c47d | 7250 | } |
0aacf84e MD |
7251 | else if (SCM_BIGP (z)) |
7252 | { | |
7253 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7254 | scm_remember_upto_here_1 (z); | |
7255 | if (sgn < 0) | |
7256 | return scm_i_clonebig (z, 0); | |
7257 | else | |
7258 | return z; | |
5986c47d | 7259 | } |
0aacf84e | 7260 | else if (SCM_REALP (z)) |
55f26379 | 7261 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 7262 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7263 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
7264 | else if (SCM_FRACTIONP (z)) |
7265 | { | |
73e4de09 | 7266 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 7267 | return z; |
cba42c93 | 7268 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
7269 | SCM_FRACTION_DENOMINATOR (z)); |
7270 | } | |
0aacf84e | 7271 | else |
2519490c | 7272 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 7273 | } |
2519490c | 7274 | #undef FUNC_NAME |
0f2d19dd JB |
7275 | |
7276 | ||
2519490c MW |
7277 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
7278 | (SCM z), | |
7279 | "Return the angle of the complex number @var{z}.") | |
7280 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 7281 | { |
c8ae173e | 7282 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 7283 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
7284 | But if atan2 follows the floating point rounding mode, then the value |
7285 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 7286 | if (SCM_I_INUMP (z)) |
0aacf84e | 7287 | { |
e11e83f3 | 7288 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 7289 | return flo0; |
0aacf84e | 7290 | else |
55f26379 | 7291 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 7292 | } |
0aacf84e MD |
7293 | else if (SCM_BIGP (z)) |
7294 | { | |
7295 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7296 | scm_remember_upto_here_1 (z); | |
7297 | if (sgn < 0) | |
55f26379 | 7298 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 7299 | else |
e7efe8e7 | 7300 | return flo0; |
0f2d19dd | 7301 | } |
0aacf84e | 7302 | else if (SCM_REALP (z)) |
c8ae173e KR |
7303 | { |
7304 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 7305 | return flo0; |
c8ae173e | 7306 | else |
55f26379 | 7307 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 7308 | } |
0aacf84e | 7309 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7310 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
7311 | else if (SCM_FRACTIONP (z)) |
7312 | { | |
73e4de09 | 7313 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 7314 | return flo0; |
55f26379 | 7315 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 7316 | } |
0aacf84e | 7317 | else |
2519490c | 7318 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 7319 | } |
2519490c | 7320 | #undef FUNC_NAME |
0f2d19dd JB |
7321 | |
7322 | ||
2519490c MW |
7323 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
7324 | (SCM z), | |
7325 | "Convert the number @var{z} to its inexact representation.\n") | |
7326 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 7327 | { |
e11e83f3 | 7328 | if (SCM_I_INUMP (z)) |
55f26379 | 7329 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 7330 | else if (SCM_BIGP (z)) |
55f26379 | 7331 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 7332 | else if (SCM_FRACTIONP (z)) |
55f26379 | 7333 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
7334 | else if (SCM_INEXACTP (z)) |
7335 | return z; | |
7336 | else | |
2519490c | 7337 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 7338 | } |
2519490c | 7339 | #undef FUNC_NAME |
3c9a524f DH |
7340 | |
7341 | ||
2519490c MW |
7342 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
7343 | (SCM z), | |
7344 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 7345 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 7346 | { |
2519490c | 7347 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f872b822 | 7348 | return z; |
0aacf84e MD |
7349 | else if (SCM_REALP (z)) |
7350 | { | |
2519490c | 7351 | if (!DOUBLE_IS_FINITE (SCM_REAL_VALUE (z))) |
f92e85f7 | 7352 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 7353 | else |
f92e85f7 MV |
7354 | { |
7355 | mpq_t frac; | |
7356 | SCM q; | |
7357 | ||
7358 | mpq_init (frac); | |
7359 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 7360 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
7361 | scm_i_mpz2num (mpq_denref (frac))); |
7362 | ||
cba42c93 | 7363 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
7364 | for frac... |
7365 | */ | |
7366 | mpq_clear (frac); | |
7367 | return q; | |
7368 | } | |
c2ff8ab0 | 7369 | } |
f92e85f7 MV |
7370 | else if (SCM_FRACTIONP (z)) |
7371 | return z; | |
0aacf84e | 7372 | else |
2519490c | 7373 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); |
0f2d19dd | 7374 | } |
1bbd0b84 | 7375 | #undef FUNC_NAME |
0f2d19dd | 7376 | |
f92e85f7 | 7377 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
7378 | (SCM x, SCM eps), |
7379 | "Returns the @emph{simplest} rational number differing\n" | |
7380 | "from @var{x} by no more than @var{eps}.\n" | |
7381 | "\n" | |
7382 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
7383 | "exact result when both its arguments are exact. Thus, you might need\n" | |
7384 | "to use @code{inexact->exact} on the arguments.\n" | |
7385 | "\n" | |
7386 | "@lisp\n" | |
7387 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
7388 | "@result{} 6/5\n" | |
7389 | "@end lisp") | |
f92e85f7 MV |
7390 | #define FUNC_NAME s_scm_rationalize |
7391 | { | |
605f6980 MW |
7392 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7393 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
7394 | eps = scm_abs (eps); | |
7395 | if (scm_is_false (scm_positive_p (eps))) | |
7396 | { | |
7397 | /* eps is either zero or a NaN */ | |
7398 | if (scm_is_true (scm_nan_p (eps))) | |
7399 | return scm_nan (); | |
7400 | else if (SCM_INEXACTP (eps)) | |
7401 | return scm_exact_to_inexact (x); | |
7402 | else | |
7403 | return x; | |
7404 | } | |
7405 | else if (scm_is_false (scm_finite_p (eps))) | |
7406 | { | |
7407 | if (scm_is_true (scm_finite_p (x))) | |
7408 | return flo0; | |
7409 | else | |
7410 | return scm_nan (); | |
7411 | } | |
7412 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 7413 | return x; |
605f6980 MW |
7414 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
7415 | scm_ceiling (scm_difference (x, eps))))) | |
7416 | { | |
7417 | /* There's an integer within range; we want the one closest to zero */ | |
7418 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
7419 | { | |
7420 | /* zero is within range */ | |
7421 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
7422 | return flo0; | |
7423 | else | |
7424 | return SCM_INUM0; | |
7425 | } | |
7426 | else if (scm_is_true (scm_positive_p (x))) | |
7427 | return scm_ceiling (scm_difference (x, eps)); | |
7428 | else | |
7429 | return scm_floor (scm_sum (x, eps)); | |
7430 | } | |
7431 | else | |
f92e85f7 MV |
7432 | { |
7433 | /* Use continued fractions to find closest ratio. All | |
7434 | arithmetic is done with exact numbers. | |
7435 | */ | |
7436 | ||
7437 | SCM ex = scm_inexact_to_exact (x); | |
7438 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
7439 | SCM tt = SCM_INUM1; |
7440 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
7441 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
7442 | SCM rx; |
7443 | int i = 0; | |
7444 | ||
f92e85f7 MV |
7445 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
7446 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
7447 | ||
7448 | /* We stop after a million iterations just to be absolutely sure | |
7449 | that we don't go into an infinite loop. The process normally | |
7450 | converges after less than a dozen iterations. | |
7451 | */ | |
7452 | ||
f92e85f7 MV |
7453 | while (++i < 1000000) |
7454 | { | |
7455 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
7456 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
7457 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
7458 | scm_is_false | |
f92e85f7 | 7459 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 7460 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
7461 | { |
7462 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 7463 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
7464 | return scm_exact_to_inexact (res); |
7465 | else | |
7466 | return res; | |
7467 | } | |
f92e85f7 MV |
7468 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
7469 | SCM_UNDEFINED); | |
7470 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
7471 | a2 = a1; | |
7472 | b2 = b1; | |
7473 | a1 = a; | |
7474 | b1 = b; | |
7475 | } | |
7476 | scm_num_overflow (s_scm_rationalize); | |
7477 | } | |
f92e85f7 MV |
7478 | } |
7479 | #undef FUNC_NAME | |
7480 | ||
73e4de09 MV |
7481 | /* conversion functions */ |
7482 | ||
7483 | int | |
7484 | scm_is_integer (SCM val) | |
7485 | { | |
7486 | return scm_is_true (scm_integer_p (val)); | |
7487 | } | |
7488 | ||
7489 | int | |
7490 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
7491 | { | |
e11e83f3 | 7492 | if (SCM_I_INUMP (val)) |
73e4de09 | 7493 | { |
e11e83f3 | 7494 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7495 | return n >= min && n <= max; |
7496 | } | |
7497 | else if (SCM_BIGP (val)) | |
7498 | { | |
7499 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
7500 | return 0; | |
7501 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
7502 | { |
7503 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
7504 | { | |
7505 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
7506 | return n >= min && n <= max; | |
7507 | } | |
7508 | else | |
7509 | return 0; | |
7510 | } | |
73e4de09 MV |
7511 | else |
7512 | { | |
d956fa6f MV |
7513 | scm_t_intmax n; |
7514 | size_t count; | |
73e4de09 | 7515 | |
d956fa6f MV |
7516 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7517 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
7518 | return 0; | |
7519 | ||
7520 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7521 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7522 | |
d956fa6f | 7523 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 7524 | { |
d956fa6f MV |
7525 | if (n < 0) |
7526 | return 0; | |
73e4de09 | 7527 | } |
73e4de09 MV |
7528 | else |
7529 | { | |
d956fa6f MV |
7530 | n = -n; |
7531 | if (n >= 0) | |
7532 | return 0; | |
73e4de09 | 7533 | } |
d956fa6f MV |
7534 | |
7535 | return n >= min && n <= max; | |
73e4de09 MV |
7536 | } |
7537 | } | |
73e4de09 MV |
7538 | else |
7539 | return 0; | |
7540 | } | |
7541 | ||
7542 | int | |
7543 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
7544 | { | |
e11e83f3 | 7545 | if (SCM_I_INUMP (val)) |
73e4de09 | 7546 | { |
e11e83f3 | 7547 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7548 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
7549 | } | |
7550 | else if (SCM_BIGP (val)) | |
7551 | { | |
7552 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
7553 | return 0; | |
7554 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
7555 | { |
7556 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
7557 | { | |
7558 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
7559 | return n >= min && n <= max; | |
7560 | } | |
7561 | else | |
7562 | return 0; | |
7563 | } | |
73e4de09 MV |
7564 | else |
7565 | { | |
d956fa6f MV |
7566 | scm_t_uintmax n; |
7567 | size_t count; | |
73e4de09 | 7568 | |
d956fa6f MV |
7569 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
7570 | return 0; | |
73e4de09 | 7571 | |
d956fa6f MV |
7572 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7573 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 7574 | return 0; |
d956fa6f MV |
7575 | |
7576 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7577 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7578 | |
d956fa6f | 7579 | return n >= min && n <= max; |
73e4de09 MV |
7580 | } |
7581 | } | |
73e4de09 MV |
7582 | else |
7583 | return 0; | |
7584 | } | |
7585 | ||
1713d319 MV |
7586 | static void |
7587 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
7588 | { | |
7589 | scm_error (scm_out_of_range_key, | |
7590 | NULL, | |
7591 | "Value out of range ~S to ~S: ~S", | |
7592 | scm_list_3 (min, max, bad_val), | |
7593 | scm_list_1 (bad_val)); | |
7594 | } | |
7595 | ||
bfd7932e MV |
7596 | #define TYPE scm_t_intmax |
7597 | #define TYPE_MIN min | |
7598 | #define TYPE_MAX max | |
7599 | #define SIZEOF_TYPE 0 | |
7600 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
7601 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
7602 | #include "libguile/conv-integer.i.c" | |
7603 | ||
7604 | #define TYPE scm_t_uintmax | |
7605 | #define TYPE_MIN min | |
7606 | #define TYPE_MAX max | |
7607 | #define SIZEOF_TYPE 0 | |
7608 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
7609 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
7610 | #include "libguile/conv-uinteger.i.c" | |
7611 | ||
7612 | #define TYPE scm_t_int8 | |
7613 | #define TYPE_MIN SCM_T_INT8_MIN | |
7614 | #define TYPE_MAX SCM_T_INT8_MAX | |
7615 | #define SIZEOF_TYPE 1 | |
7616 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
7617 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
7618 | #include "libguile/conv-integer.i.c" | |
7619 | ||
7620 | #define TYPE scm_t_uint8 | |
7621 | #define TYPE_MIN 0 | |
7622 | #define TYPE_MAX SCM_T_UINT8_MAX | |
7623 | #define SIZEOF_TYPE 1 | |
7624 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
7625 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
7626 | #include "libguile/conv-uinteger.i.c" | |
7627 | ||
7628 | #define TYPE scm_t_int16 | |
7629 | #define TYPE_MIN SCM_T_INT16_MIN | |
7630 | #define TYPE_MAX SCM_T_INT16_MAX | |
7631 | #define SIZEOF_TYPE 2 | |
7632 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
7633 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
7634 | #include "libguile/conv-integer.i.c" | |
7635 | ||
7636 | #define TYPE scm_t_uint16 | |
7637 | #define TYPE_MIN 0 | |
7638 | #define TYPE_MAX SCM_T_UINT16_MAX | |
7639 | #define SIZEOF_TYPE 2 | |
7640 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
7641 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
7642 | #include "libguile/conv-uinteger.i.c" | |
7643 | ||
7644 | #define TYPE scm_t_int32 | |
7645 | #define TYPE_MIN SCM_T_INT32_MIN | |
7646 | #define TYPE_MAX SCM_T_INT32_MAX | |
7647 | #define SIZEOF_TYPE 4 | |
7648 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
7649 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
7650 | #include "libguile/conv-integer.i.c" | |
7651 | ||
7652 | #define TYPE scm_t_uint32 | |
7653 | #define TYPE_MIN 0 | |
7654 | #define TYPE_MAX SCM_T_UINT32_MAX | |
7655 | #define SIZEOF_TYPE 4 | |
7656 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
7657 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
7658 | #include "libguile/conv-uinteger.i.c" | |
7659 | ||
904a78f1 MG |
7660 | #define TYPE scm_t_wchar |
7661 | #define TYPE_MIN (scm_t_int32)-1 | |
7662 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
7663 | #define SIZEOF_TYPE 4 | |
7664 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
7665 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
7666 | #include "libguile/conv-integer.i.c" | |
7667 | ||
bfd7932e MV |
7668 | #define TYPE scm_t_int64 |
7669 | #define TYPE_MIN SCM_T_INT64_MIN | |
7670 | #define TYPE_MAX SCM_T_INT64_MAX | |
7671 | #define SIZEOF_TYPE 8 | |
7672 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
7673 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
7674 | #include "libguile/conv-integer.i.c" | |
7675 | ||
7676 | #define TYPE scm_t_uint64 | |
7677 | #define TYPE_MIN 0 | |
7678 | #define TYPE_MAX SCM_T_UINT64_MAX | |
7679 | #define SIZEOF_TYPE 8 | |
7680 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
7681 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
7682 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 7683 | |
cd036260 MV |
7684 | void |
7685 | scm_to_mpz (SCM val, mpz_t rop) | |
7686 | { | |
7687 | if (SCM_I_INUMP (val)) | |
7688 | mpz_set_si (rop, SCM_I_INUM (val)); | |
7689 | else if (SCM_BIGP (val)) | |
7690 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
7691 | else | |
7692 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
7693 | } | |
7694 | ||
7695 | SCM | |
7696 | scm_from_mpz (mpz_t val) | |
7697 | { | |
7698 | return scm_i_mpz2num (val); | |
7699 | } | |
7700 | ||
73e4de09 MV |
7701 | int |
7702 | scm_is_real (SCM val) | |
7703 | { | |
7704 | return scm_is_true (scm_real_p (val)); | |
7705 | } | |
7706 | ||
55f26379 MV |
7707 | int |
7708 | scm_is_rational (SCM val) | |
7709 | { | |
7710 | return scm_is_true (scm_rational_p (val)); | |
7711 | } | |
7712 | ||
73e4de09 MV |
7713 | double |
7714 | scm_to_double (SCM val) | |
7715 | { | |
55f26379 MV |
7716 | if (SCM_I_INUMP (val)) |
7717 | return SCM_I_INUM (val); | |
7718 | else if (SCM_BIGP (val)) | |
7719 | return scm_i_big2dbl (val); | |
7720 | else if (SCM_FRACTIONP (val)) | |
7721 | return scm_i_fraction2double (val); | |
7722 | else if (SCM_REALP (val)) | |
7723 | return SCM_REAL_VALUE (val); | |
7724 | else | |
7a1aba42 | 7725 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
7726 | } |
7727 | ||
7728 | SCM | |
7729 | scm_from_double (double val) | |
7730 | { | |
978c52d1 LC |
7731 | SCM z; |
7732 | ||
7733 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
7734 | ||
7735 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 7736 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 7737 | |
55f26379 | 7738 | return z; |
73e4de09 MV |
7739 | } |
7740 | ||
220058a8 | 7741 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
7742 | |
7743 | float | |
e25f3727 | 7744 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7745 | { |
220058a8 AW |
7746 | scm_c_issue_deprecation_warning |
7747 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
7748 | ||
55f26379 MV |
7749 | if (SCM_BIGP (num)) |
7750 | { | |
7751 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7752 | if (!isinf (res)) |
55f26379 MV |
7753 | return res; |
7754 | else | |
7755 | scm_out_of_range (NULL, num); | |
7756 | } | |
7757 | else | |
7758 | return scm_to_double (num); | |
7759 | } | |
7760 | ||
7761 | double | |
e25f3727 | 7762 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7763 | { |
220058a8 AW |
7764 | scm_c_issue_deprecation_warning |
7765 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
7766 | ||
55f26379 MV |
7767 | if (SCM_BIGP (num)) |
7768 | { | |
7769 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7770 | if (!isinf (res)) |
55f26379 MV |
7771 | return res; |
7772 | else | |
7773 | scm_out_of_range (NULL, num); | |
7774 | } | |
7775 | else | |
7776 | return scm_to_double (num); | |
7777 | } | |
7778 | ||
7779 | #endif | |
7780 | ||
8507ec80 MV |
7781 | int |
7782 | scm_is_complex (SCM val) | |
7783 | { | |
7784 | return scm_is_true (scm_complex_p (val)); | |
7785 | } | |
7786 | ||
7787 | double | |
7788 | scm_c_real_part (SCM z) | |
7789 | { | |
7790 | if (SCM_COMPLEXP (z)) | |
7791 | return SCM_COMPLEX_REAL (z); | |
7792 | else | |
7793 | { | |
7794 | /* Use the scm_real_part to get proper error checking and | |
7795 | dispatching. | |
7796 | */ | |
7797 | return scm_to_double (scm_real_part (z)); | |
7798 | } | |
7799 | } | |
7800 | ||
7801 | double | |
7802 | scm_c_imag_part (SCM z) | |
7803 | { | |
7804 | if (SCM_COMPLEXP (z)) | |
7805 | return SCM_COMPLEX_IMAG (z); | |
7806 | else | |
7807 | { | |
7808 | /* Use the scm_imag_part to get proper error checking and | |
7809 | dispatching. The result will almost always be 0.0, but not | |
7810 | always. | |
7811 | */ | |
7812 | return scm_to_double (scm_imag_part (z)); | |
7813 | } | |
7814 | } | |
7815 | ||
7816 | double | |
7817 | scm_c_magnitude (SCM z) | |
7818 | { | |
7819 | return scm_to_double (scm_magnitude (z)); | |
7820 | } | |
7821 | ||
7822 | double | |
7823 | scm_c_angle (SCM z) | |
7824 | { | |
7825 | return scm_to_double (scm_angle (z)); | |
7826 | } | |
7827 | ||
7828 | int | |
7829 | scm_is_number (SCM z) | |
7830 | { | |
7831 | return scm_is_true (scm_number_p (z)); | |
7832 | } | |
7833 | ||
8ab3d8a0 KR |
7834 | |
7835 | /* In the following functions we dispatch to the real-arg funcs like log() | |
7836 | when we know the arg is real, instead of just handing everything to | |
7837 | clog() for instance. This is in case clog() doesn't optimize for a | |
7838 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
7839 | well use it to go straight to the applicable C func. */ | |
7840 | ||
2519490c MW |
7841 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
7842 | (SCM z), | |
7843 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
7844 | #define FUNC_NAME s_scm_log |
7845 | { | |
7846 | if (SCM_COMPLEXP (z)) | |
7847 | { | |
4b26c03e | 7848 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7849 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
7850 | #else | |
7851 | double re = SCM_COMPLEX_REAL (z); | |
7852 | double im = SCM_COMPLEX_IMAG (z); | |
7853 | return scm_c_make_rectangular (log (hypot (re, im)), | |
7854 | atan2 (im, re)); | |
7855 | #endif | |
7856 | } | |
2519490c | 7857 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7858 | { |
7859 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7860 | although the value itself overflows. */ | |
7861 | double re = scm_to_double (z); | |
7862 | double l = log (fabs (re)); | |
7863 | if (re >= 0.0) | |
7864 | return scm_from_double (l); | |
7865 | else | |
7866 | return scm_c_make_rectangular (l, M_PI); | |
7867 | } | |
2519490c MW |
7868 | else |
7869 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
7870 | } |
7871 | #undef FUNC_NAME | |
7872 | ||
7873 | ||
2519490c MW |
7874 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
7875 | (SCM z), | |
7876 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
7877 | #define FUNC_NAME s_scm_log10 |
7878 | { | |
7879 | if (SCM_COMPLEXP (z)) | |
7880 | { | |
7881 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
7882 | clog() and a multiply by M_LOG10E, rather than the fallback | |
7883 | log10+hypot+atan2.) */ | |
f328f862 LC |
7884 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
7885 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
7886 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
7887 | #else | |
7888 | double re = SCM_COMPLEX_REAL (z); | |
7889 | double im = SCM_COMPLEX_IMAG (z); | |
7890 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
7891 | M_LOG10E * atan2 (im, re)); | |
7892 | #endif | |
7893 | } | |
2519490c | 7894 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7895 | { |
7896 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7897 | although the value itself overflows. */ | |
7898 | double re = scm_to_double (z); | |
7899 | double l = log10 (fabs (re)); | |
7900 | if (re >= 0.0) | |
7901 | return scm_from_double (l); | |
7902 | else | |
7903 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
7904 | } | |
2519490c MW |
7905 | else |
7906 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
7907 | } |
7908 | #undef FUNC_NAME | |
7909 | ||
7910 | ||
2519490c MW |
7911 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
7912 | (SCM z), | |
7913 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
7914 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
7915 | #define FUNC_NAME s_scm_exp |
7916 | { | |
7917 | if (SCM_COMPLEXP (z)) | |
7918 | { | |
4b26c03e | 7919 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7920 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
7921 | #else | |
7922 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
7923 | SCM_COMPLEX_IMAG (z)); | |
7924 | #endif | |
7925 | } | |
2519490c | 7926 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7927 | { |
7928 | /* When z is a negative bignum the conversion to double overflows, | |
7929 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
7930 | return scm_from_double (exp (scm_to_double (z))); | |
7931 | } | |
2519490c MW |
7932 | else |
7933 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
7934 | } |
7935 | #undef FUNC_NAME | |
7936 | ||
7937 | ||
2519490c MW |
7938 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
7939 | (SCM z), | |
7940 | "Return the square root of @var{z}. Of the two possible roots\n" | |
7941 | "(positive and negative), the one with the a positive real part\n" | |
7942 | "is returned, or if that's zero then a positive imaginary part.\n" | |
7943 | "Thus,\n" | |
7944 | "\n" | |
7945 | "@example\n" | |
7946 | "(sqrt 9.0) @result{} 3.0\n" | |
7947 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
7948 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
7949 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
7950 | "@end example") | |
8ab3d8a0 KR |
7951 | #define FUNC_NAME s_scm_sqrt |
7952 | { | |
2519490c | 7953 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 7954 | { |
f328f862 LC |
7955 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
7956 | && defined SCM_COMPLEX_VALUE | |
2519490c | 7957 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 7958 | #else |
2519490c MW |
7959 | double re = SCM_COMPLEX_REAL (z); |
7960 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
7961 | return scm_c_make_polar (sqrt (hypot (re, im)), |
7962 | 0.5 * atan2 (im, re)); | |
7963 | #endif | |
7964 | } | |
2519490c | 7965 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 7966 | { |
2519490c | 7967 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
7968 | if (xx < 0) |
7969 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
7970 | else | |
7971 | return scm_from_double (sqrt (xx)); | |
7972 | } | |
2519490c MW |
7973 | else |
7974 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
7975 | } |
7976 | #undef FUNC_NAME | |
7977 | ||
7978 | ||
7979 | ||
0f2d19dd JB |
7980 | void |
7981 | scm_init_numbers () | |
0f2d19dd | 7982 | { |
0b799eea MV |
7983 | int i; |
7984 | ||
713a4259 KR |
7985 | mpz_init_set_si (z_negative_one, -1); |
7986 | ||
a261c0e9 DH |
7987 | /* It may be possible to tune the performance of some algorithms by using |
7988 | * the following constants to avoid the creation of bignums. Please, before | |
7989 | * using these values, remember the two rules of program optimization: | |
7990 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 7991 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 7992 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 7993 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 7994 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 7995 | |
f3ae5d60 MD |
7996 | scm_add_feature ("complex"); |
7997 | scm_add_feature ("inexact"); | |
e7efe8e7 | 7998 | flo0 = scm_from_double (0.0); |
0b799eea MV |
7999 | |
8000 | /* determine floating point precision */ | |
55f26379 | 8001 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
8002 | { |
8003 | init_dblprec(&scm_dblprec[i-2],i); | |
8004 | init_fx_radix(fx_per_radix[i-2],i); | |
8005 | } | |
f872b822 | 8006 | #ifdef DBL_DIG |
0b799eea | 8007 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 8008 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 8009 | #endif |
1be6b49c | 8010 | |
cff5fa33 | 8011 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 8012 | #include "libguile/numbers.x" |
0f2d19dd | 8013 | } |
89e00824 ML |
8014 | |
8015 | /* | |
8016 | Local Variables: | |
8017 | c-file-style: "gnu" | |
8018 | End: | |
8019 | */ |