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 | } |
0aacf84e MD |
748 | else if (SCM_BIGP (x)) |
749 | { | |
750 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
751 | if (sgn < 0) | |
752 | return scm_i_clonebig (x, 0); | |
753 | else | |
754 | return x; | |
4219f20d | 755 | } |
0aacf84e | 756 | else if (SCM_REALP (x)) |
ae38324d KR |
757 | { |
758 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
759 | double xx = SCM_REAL_VALUE (x); | |
760 | if (xx < 0.0) | |
55f26379 | 761 | return scm_from_double (-xx); |
ae38324d KR |
762 | else |
763 | return x; | |
764 | } | |
f92e85f7 MV |
765 | else if (SCM_FRACTIONP (x)) |
766 | { | |
73e4de09 | 767 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 768 | return x; |
cba42c93 | 769 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
770 | SCM_FRACTION_DENOMINATOR (x)); |
771 | } | |
0aacf84e | 772 | else |
a48d60b1 | 773 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 774 | } |
a48d60b1 | 775 | #undef FUNC_NAME |
0f2d19dd | 776 | |
4219f20d | 777 | |
2519490c MW |
778 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
779 | (SCM x, SCM y), | |
780 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
781 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 782 | { |
a16982ca | 783 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 784 | { |
e25f3727 | 785 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 786 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 787 | { |
e25f3727 | 788 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 789 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 790 | scm_num_overflow (s_scm_quotient); |
0aacf84e MD |
791 | else |
792 | { | |
e25f3727 | 793 | scm_t_inum z = xx / yy; |
a16982ca | 794 | if (SCM_LIKELY (SCM_FIXABLE (z))) |
d956fa6f | 795 | return SCM_I_MAKINUM (z); |
0aacf84e | 796 | else |
e25f3727 | 797 | return scm_i_inum2big (z); |
0aacf84e | 798 | } |
828865c3 | 799 | } |
0aacf84e | 800 | else if (SCM_BIGP (y)) |
ac0c002c | 801 | { |
e11e83f3 | 802 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
803 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
804 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
805 | { | |
806 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
807 | scm_remember_upto_here_1 (y); | |
d956fa6f | 808 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 809 | } |
0aacf84e | 810 | else |
cff5fa33 | 811 | return SCM_INUM0; |
ac0c002c DH |
812 | } |
813 | else | |
2519490c | 814 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
828865c3 | 815 | } |
0aacf84e MD |
816 | else if (SCM_BIGP (x)) |
817 | { | |
a16982ca | 818 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 819 | { |
e25f3727 | 820 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 821 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 822 | scm_num_overflow (s_scm_quotient); |
a16982ca | 823 | else if (SCM_UNLIKELY (yy == 1)) |
0aacf84e MD |
824 | return x; |
825 | else | |
826 | { | |
827 | SCM result = scm_i_mkbig (); | |
828 | if (yy < 0) | |
829 | { | |
830 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
831 | SCM_I_BIG_MPZ (x), | |
832 | - yy); | |
833 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
834 | } | |
835 | else | |
836 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
837 | scm_remember_upto_here_1 (x); | |
838 | return scm_i_normbig (result); | |
839 | } | |
840 | } | |
841 | else if (SCM_BIGP (y)) | |
842 | { | |
843 | SCM result = scm_i_mkbig (); | |
844 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
845 | SCM_I_BIG_MPZ (x), | |
846 | SCM_I_BIG_MPZ (y)); | |
847 | scm_remember_upto_here_2 (x, y); | |
848 | return scm_i_normbig (result); | |
849 | } | |
850 | else | |
2519490c | 851 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 852 | } |
0aacf84e | 853 | else |
2519490c | 854 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 855 | } |
2519490c | 856 | #undef FUNC_NAME |
0f2d19dd | 857 | |
2519490c MW |
858 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
859 | (SCM x, SCM y), | |
860 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
861 | "@lisp\n" | |
862 | "(remainder 13 4) @result{} 1\n" | |
863 | "(remainder -13 4) @result{} -1\n" | |
864 | "@end lisp") | |
865 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 866 | { |
a16982ca | 867 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 868 | { |
a16982ca | 869 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 870 | { |
e25f3727 | 871 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 872 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 873 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
874 | else |
875 | { | |
a16982ca MW |
876 | /* C99 specifies that "%" is the remainder corresponding to a |
877 | quotient rounded towards zero, and that's also traditional | |
878 | for machine division, so z here should be well defined. */ | |
e25f3727 | 879 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 880 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
881 | } |
882 | } | |
883 | else if (SCM_BIGP (y)) | |
ac0c002c | 884 | { |
e11e83f3 | 885 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
886 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
887 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
888 | { | |
889 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
890 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 891 | return SCM_INUM0; |
4dc09ee4 | 892 | } |
0aacf84e MD |
893 | else |
894 | return x; | |
ac0c002c DH |
895 | } |
896 | else | |
2519490c | 897 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
89a7e495 | 898 | } |
0aacf84e MD |
899 | else if (SCM_BIGP (x)) |
900 | { | |
a16982ca | 901 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 902 | { |
e25f3727 | 903 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 904 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 905 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
906 | else |
907 | { | |
908 | SCM result = scm_i_mkbig (); | |
909 | if (yy < 0) | |
910 | yy = - yy; | |
911 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
912 | scm_remember_upto_here_1 (x); | |
913 | return scm_i_normbig (result); | |
914 | } | |
915 | } | |
916 | else if (SCM_BIGP (y)) | |
917 | { | |
918 | SCM result = scm_i_mkbig (); | |
919 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
920 | SCM_I_BIG_MPZ (x), | |
921 | SCM_I_BIG_MPZ (y)); | |
922 | scm_remember_upto_here_2 (x, y); | |
923 | return scm_i_normbig (result); | |
924 | } | |
925 | else | |
2519490c | 926 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 927 | } |
0aacf84e | 928 | else |
2519490c | 929 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 930 | } |
2519490c | 931 | #undef FUNC_NAME |
0f2d19dd | 932 | |
89a7e495 | 933 | |
2519490c MW |
934 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
935 | (SCM x, SCM y), | |
936 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
937 | "@lisp\n" | |
938 | "(modulo 13 4) @result{} 1\n" | |
939 | "(modulo -13 4) @result{} 3\n" | |
940 | "@end lisp") | |
941 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 942 | { |
a16982ca | 943 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 944 | { |
e25f3727 | 945 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 946 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 947 | { |
e25f3727 | 948 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 949 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 950 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
951 | else |
952 | { | |
66b1c775 KR |
953 | /* C99 specifies that "%" is the remainder corresponding to a |
954 | quotient rounded towards zero, and that's also traditional | |
955 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
956 | scm_t_inum z = xx % yy; |
957 | scm_t_inum result; | |
0aacf84e MD |
958 | |
959 | if (yy < 0) | |
960 | { | |
961 | if (z > 0) | |
962 | result = z + yy; | |
963 | else | |
964 | result = z; | |
965 | } | |
966 | else | |
967 | { | |
968 | if (z < 0) | |
969 | result = z + yy; | |
970 | else | |
971 | result = z; | |
972 | } | |
d956fa6f | 973 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
974 | } |
975 | } | |
976 | else if (SCM_BIGP (y)) | |
977 | { | |
978 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
979 | { |
980 | mpz_t z_x; | |
981 | SCM result; | |
982 | ||
983 | if (sgn_y < 0) | |
984 | { | |
985 | SCM pos_y = scm_i_clonebig (y, 0); | |
986 | /* do this after the last scm_op */ | |
987 | mpz_init_set_si (z_x, xx); | |
988 | result = pos_y; /* re-use this bignum */ | |
989 | mpz_mod (SCM_I_BIG_MPZ (result), | |
990 | z_x, | |
991 | SCM_I_BIG_MPZ (pos_y)); | |
992 | scm_remember_upto_here_1 (pos_y); | |
993 | } | |
994 | else | |
995 | { | |
996 | result = scm_i_mkbig (); | |
997 | /* do this after the last scm_op */ | |
998 | mpz_init_set_si (z_x, xx); | |
999 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1000 | z_x, | |
1001 | SCM_I_BIG_MPZ (y)); | |
1002 | scm_remember_upto_here_1 (y); | |
1003 | } | |
ca46fb90 | 1004 | |
0aacf84e MD |
1005 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
1006 | mpz_add (SCM_I_BIG_MPZ (result), | |
1007 | SCM_I_BIG_MPZ (y), | |
1008 | SCM_I_BIG_MPZ (result)); | |
1009 | scm_remember_upto_here_1 (y); | |
1010 | /* and do this before the next one */ | |
1011 | mpz_clear (z_x); | |
1012 | return scm_i_normbig (result); | |
1013 | } | |
1014 | } | |
1015 | else | |
2519490c | 1016 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
f872b822 | 1017 | } |
0aacf84e MD |
1018 | else if (SCM_BIGP (x)) |
1019 | { | |
a16982ca | 1020 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 1021 | { |
e25f3727 | 1022 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 1023 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 1024 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
1025 | else |
1026 | { | |
1027 | SCM result = scm_i_mkbig (); | |
1028 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1029 | SCM_I_BIG_MPZ (x), | |
1030 | (yy < 0) ? - yy : yy); | |
1031 | scm_remember_upto_here_1 (x); | |
1032 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1033 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1034 | SCM_I_BIG_MPZ (result), | |
1035 | - yy); | |
1036 | return scm_i_normbig (result); | |
1037 | } | |
1038 | } | |
1039 | else if (SCM_BIGP (y)) | |
1040 | { | |
a16982ca MW |
1041 | SCM result = scm_i_mkbig (); |
1042 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1043 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1044 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1045 | SCM_I_BIG_MPZ (x), | |
1046 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1047 | |
a16982ca MW |
1048 | scm_remember_upto_here_1 (x); |
1049 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1050 | mpz_add (SCM_I_BIG_MPZ (result), | |
1051 | SCM_I_BIG_MPZ (y), | |
1052 | SCM_I_BIG_MPZ (result)); | |
1053 | scm_remember_upto_here_2 (y, pos_y); | |
1054 | return scm_i_normbig (result); | |
0aacf84e MD |
1055 | } |
1056 | else | |
2519490c | 1057 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 1058 | } |
0aacf84e | 1059 | else |
2519490c | 1060 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1061 | } |
2519490c | 1062 | #undef FUNC_NAME |
0f2d19dd | 1063 | |
ff62c168 MW |
1064 | static SCM scm_i_inexact_euclidean_quotient (double x, double y); |
1065 | static SCM scm_i_slow_exact_euclidean_quotient (SCM x, SCM y); | |
1066 | ||
1067 | SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, | |
1068 | (SCM x, SCM y), | |
1069 | "Return the integer @var{q} such that\n" | |
1070 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1071 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1072 | "@lisp\n" | |
1073 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1074 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1075 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1076 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1077 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1078 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1079 | "@end lisp") | |
1080 | #define FUNC_NAME s_scm_euclidean_quotient | |
1081 | { | |
1082 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1083 | { | |
1084 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1085 | { | |
1086 | scm_t_inum yy = SCM_I_INUM (y); | |
1087 | if (SCM_UNLIKELY (yy == 0)) | |
1088 | scm_num_overflow (s_scm_euclidean_quotient); | |
1089 | else | |
1090 | { | |
1091 | scm_t_inum xx = SCM_I_INUM (x); | |
1092 | scm_t_inum qq = xx / yy; | |
1093 | if (xx < qq * yy) | |
1094 | { | |
1095 | if (yy > 0) | |
1096 | qq--; | |
1097 | else | |
1098 | qq++; | |
1099 | } | |
1100 | return SCM_I_MAKINUM (qq); | |
1101 | } | |
1102 | } | |
1103 | else if (SCM_BIGP (y)) | |
1104 | { | |
1105 | if (SCM_I_INUM (x) >= 0) | |
1106 | return SCM_INUM0; | |
1107 | else | |
1108 | return SCM_I_MAKINUM (- mpz_sgn (SCM_I_BIG_MPZ (y))); | |
1109 | } | |
1110 | else if (SCM_REALP (y)) | |
1111 | return scm_i_inexact_euclidean_quotient | |
1112 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1113 | else if (SCM_FRACTIONP (y)) | |
1114 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1115 | else | |
1116 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1117 | s_scm_euclidean_quotient); | |
1118 | } | |
1119 | else if (SCM_BIGP (x)) | |
1120 | { | |
1121 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1122 | { | |
1123 | scm_t_inum yy = SCM_I_INUM (y); | |
1124 | if (SCM_UNLIKELY (yy == 0)) | |
1125 | scm_num_overflow (s_scm_euclidean_quotient); | |
1126 | else | |
1127 | { | |
1128 | SCM q = scm_i_mkbig (); | |
1129 | if (yy > 0) | |
1130 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1131 | else | |
1132 | { | |
1133 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1134 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1135 | } | |
1136 | scm_remember_upto_here_1 (x); | |
1137 | return scm_i_normbig (q); | |
1138 | } | |
1139 | } | |
1140 | else if (SCM_BIGP (y)) | |
1141 | { | |
1142 | SCM q = scm_i_mkbig (); | |
1143 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1144 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1145 | SCM_I_BIG_MPZ (x), | |
1146 | SCM_I_BIG_MPZ (y)); | |
1147 | else | |
1148 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1149 | SCM_I_BIG_MPZ (x), | |
1150 | SCM_I_BIG_MPZ (y)); | |
1151 | scm_remember_upto_here_2 (x, y); | |
1152 | return scm_i_normbig (q); | |
1153 | } | |
1154 | else if (SCM_REALP (y)) | |
1155 | return scm_i_inexact_euclidean_quotient | |
1156 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1157 | else if (SCM_FRACTIONP (y)) | |
1158 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1159 | else | |
1160 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1161 | s_scm_euclidean_quotient); | |
1162 | } | |
1163 | else if (SCM_REALP (x)) | |
1164 | { | |
1165 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1166 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1167 | return scm_i_inexact_euclidean_quotient | |
1168 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1169 | else | |
1170 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1171 | s_scm_euclidean_quotient); | |
1172 | } | |
1173 | else if (SCM_FRACTIONP (x)) | |
1174 | { | |
1175 | if (SCM_REALP (y)) | |
1176 | return scm_i_inexact_euclidean_quotient | |
1177 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1178 | else | |
1179 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1180 | } | |
1181 | else | |
1182 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1183 | s_scm_euclidean_quotient); | |
1184 | } | |
1185 | #undef FUNC_NAME | |
1186 | ||
1187 | static SCM | |
1188 | scm_i_inexact_euclidean_quotient (double x, double y) | |
1189 | { | |
1190 | if (SCM_LIKELY (y > 0)) | |
1191 | return scm_from_double (floor (x / y)); | |
1192 | else if (SCM_LIKELY (y < 0)) | |
1193 | return scm_from_double (ceil (x / y)); | |
1194 | else if (y == 0) | |
1195 | scm_num_overflow (s_scm_euclidean_quotient); /* or return a NaN? */ | |
1196 | else | |
1197 | return scm_nan (); | |
1198 | } | |
1199 | ||
1200 | /* Compute exact euclidean_quotient the slow way. | |
1201 | We use this only if both arguments are exact, | |
1202 | and at least one of them is a fraction */ | |
1203 | static SCM | |
1204 | scm_i_slow_exact_euclidean_quotient (SCM x, SCM y) | |
1205 | { | |
1206 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1207 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1208 | s_scm_euclidean_quotient); | |
1209 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1210 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1211 | s_scm_euclidean_quotient); | |
1212 | else if (scm_is_true (scm_positive_p (y))) | |
1213 | return scm_floor (scm_divide (x, y)); | |
1214 | else if (scm_is_true (scm_negative_p (y))) | |
1215 | return scm_ceiling (scm_divide (x, y)); | |
1216 | else | |
1217 | scm_num_overflow (s_scm_euclidean_quotient); | |
1218 | } | |
1219 | ||
1220 | static SCM scm_i_inexact_euclidean_remainder (double x, double y); | |
1221 | static SCM scm_i_slow_exact_euclidean_remainder (SCM x, SCM y); | |
1222 | ||
1223 | SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, | |
1224 | (SCM x, SCM y), | |
1225 | "Return the real number @var{r} such that\n" | |
1226 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1227 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1228 | "for some integer @var{q}.\n" | |
1229 | "@lisp\n" | |
1230 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1231 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1232 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1233 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1234 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1235 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1236 | "@end lisp") | |
1237 | #define FUNC_NAME s_scm_euclidean_remainder | |
1238 | { | |
1239 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1240 | { | |
1241 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1242 | { | |
1243 | scm_t_inum yy = SCM_I_INUM (y); | |
1244 | if (SCM_UNLIKELY (yy == 0)) | |
1245 | scm_num_overflow (s_scm_euclidean_remainder); | |
1246 | else | |
1247 | { | |
1248 | scm_t_inum rr = SCM_I_INUM (x) % yy; | |
1249 | if (rr >= 0) | |
1250 | return SCM_I_MAKINUM (rr); | |
1251 | else if (yy > 0) | |
1252 | return SCM_I_MAKINUM (rr + yy); | |
1253 | else | |
1254 | return SCM_I_MAKINUM (rr - yy); | |
1255 | } | |
1256 | } | |
1257 | else if (SCM_BIGP (y)) | |
1258 | { | |
1259 | scm_t_inum xx = SCM_I_INUM (x); | |
1260 | if (xx >= 0) | |
1261 | return x; | |
1262 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1263 | { | |
1264 | SCM r = scm_i_mkbig (); | |
1265 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1266 | scm_remember_upto_here_1 (y); | |
1267 | return scm_i_normbig (r); | |
1268 | } | |
1269 | else | |
1270 | { | |
1271 | SCM r = scm_i_mkbig (); | |
1272 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1273 | scm_remember_upto_here_1 (y); | |
1274 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1275 | return scm_i_normbig (r); | |
1276 | } | |
1277 | } | |
1278 | else if (SCM_REALP (y)) | |
1279 | return scm_i_inexact_euclidean_remainder | |
1280 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1281 | else if (SCM_FRACTIONP (y)) | |
1282 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1283 | else | |
1284 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1285 | s_scm_euclidean_remainder); | |
1286 | } | |
1287 | else if (SCM_BIGP (x)) | |
1288 | { | |
1289 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1290 | { | |
1291 | scm_t_inum yy = SCM_I_INUM (y); | |
1292 | if (SCM_UNLIKELY (yy == 0)) | |
1293 | scm_num_overflow (s_scm_euclidean_remainder); | |
1294 | else | |
1295 | { | |
1296 | scm_t_inum rr; | |
1297 | if (yy < 0) | |
1298 | yy = -yy; | |
1299 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1300 | scm_remember_upto_here_1 (x); | |
1301 | return SCM_I_MAKINUM (rr); | |
1302 | } | |
1303 | } | |
1304 | else if (SCM_BIGP (y)) | |
1305 | { | |
1306 | SCM r = scm_i_mkbig (); | |
1307 | mpz_mod (SCM_I_BIG_MPZ (r), | |
1308 | SCM_I_BIG_MPZ (x), | |
1309 | SCM_I_BIG_MPZ (y)); | |
1310 | scm_remember_upto_here_2 (x, y); | |
1311 | return scm_i_normbig (r); | |
1312 | } | |
1313 | else if (SCM_REALP (y)) | |
1314 | return scm_i_inexact_euclidean_remainder | |
1315 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1316 | else if (SCM_FRACTIONP (y)) | |
1317 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1318 | else | |
1319 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1320 | s_scm_euclidean_remainder); | |
1321 | } | |
1322 | else if (SCM_REALP (x)) | |
1323 | { | |
1324 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1325 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1326 | return scm_i_inexact_euclidean_remainder | |
1327 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1328 | else | |
1329 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1330 | s_scm_euclidean_remainder); | |
1331 | } | |
1332 | else if (SCM_FRACTIONP (x)) | |
1333 | { | |
1334 | if (SCM_REALP (y)) | |
1335 | return scm_i_inexact_euclidean_remainder | |
1336 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1337 | else | |
1338 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1339 | } | |
1340 | else | |
1341 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1342 | s_scm_euclidean_remainder); | |
1343 | } | |
1344 | #undef FUNC_NAME | |
1345 | ||
1346 | static SCM | |
1347 | scm_i_inexact_euclidean_remainder (double x, double y) | |
1348 | { | |
1349 | double q; | |
1350 | ||
1351 | /* Although it would be more efficient to use fmod here, we can't | |
1352 | because it would in some cases produce results inconsistent with | |
1353 | scm_i_inexact_euclidean_quotient, such that x != q * y + r (not | |
1354 | even close). In particular, when x is very close to a multiple of | |
1355 | y, then r might be either 0.0 or abs(y)-epsilon, but those two | |
1356 | cases must correspond to different choices of q. If r = 0.0 then q | |
1357 | must be x/y, and if r = abs(y) then q must be (x-r)/y. If quotient | |
1358 | chooses one and remainder chooses the other, it would be bad. This | |
1359 | problem was observed with x = 130.0 and y = 10/7. */ | |
1360 | if (SCM_LIKELY (y > 0)) | |
1361 | q = floor (x / y); | |
1362 | else if (SCM_LIKELY (y < 0)) | |
1363 | q = ceil (x / y); | |
1364 | else if (y == 0) | |
1365 | scm_num_overflow (s_scm_euclidean_remainder); /* or return a NaN? */ | |
1366 | else | |
1367 | return scm_nan (); | |
1368 | return scm_from_double (x - q * y); | |
1369 | } | |
1370 | ||
1371 | /* Compute exact euclidean_remainder the slow way. | |
1372 | We use this only if both arguments are exact, | |
1373 | and at least one of them is a fraction */ | |
1374 | static SCM | |
1375 | scm_i_slow_exact_euclidean_remainder (SCM x, SCM y) | |
1376 | { | |
1377 | SCM q; | |
1378 | ||
1379 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1380 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1381 | s_scm_euclidean_remainder); | |
1382 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1383 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1384 | s_scm_euclidean_remainder); | |
1385 | else if (scm_is_true (scm_positive_p (y))) | |
1386 | q = scm_floor (scm_divide (x, y)); | |
1387 | else if (scm_is_true (scm_negative_p (y))) | |
1388 | q = scm_ceiling (scm_divide (x, y)); | |
1389 | else | |
1390 | scm_num_overflow (s_scm_euclidean_remainder); | |
1391 | return scm_difference (x, scm_product (y, q)); | |
1392 | } | |
1393 | ||
1394 | ||
ac6ce16b MW |
1395 | static SCM scm_i_inexact_euclidean_divide (double x, double y); |
1396 | static SCM scm_i_slow_exact_euclidean_divide (SCM x, SCM y); | |
ff62c168 | 1397 | |
ac6ce16b | 1398 | SCM_PRIMITIVE_GENERIC (scm_euclidean_divide, "euclidean/", 2, 0, 0, |
ff62c168 MW |
1399 | (SCM x, SCM y), |
1400 | "Return the integer @var{q} and the real number @var{r}\n" | |
1401 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1402 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1403 | "@lisp\n" | |
1404 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1405 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1406 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1407 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1408 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1409 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1410 | "@end lisp") | |
ac6ce16b | 1411 | #define FUNC_NAME s_scm_euclidean_divide |
ff62c168 MW |
1412 | { |
1413 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1414 | { | |
1415 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1416 | { | |
1417 | scm_t_inum yy = SCM_I_INUM (y); | |
1418 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1419 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1420 | else |
1421 | { | |
1422 | scm_t_inum xx = SCM_I_INUM (x); | |
1423 | scm_t_inum qq = xx / yy; | |
1424 | scm_t_inum rr = xx - qq * yy; | |
1425 | if (rr < 0) | |
1426 | { | |
1427 | if (yy > 0) | |
1428 | { rr += yy; qq--; } | |
1429 | else | |
1430 | { rr -= yy; qq++; } | |
1431 | } | |
1432 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
1433 | SCM_I_MAKINUM (rr))); | |
1434 | } | |
1435 | } | |
1436 | else if (SCM_BIGP (y)) | |
1437 | { | |
1438 | scm_t_inum xx = SCM_I_INUM (x); | |
1439 | if (xx >= 0) | |
1440 | return scm_values (scm_list_2 (SCM_INUM0, x)); | |
1441 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1442 | { | |
1443 | SCM r = scm_i_mkbig (); | |
1444 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1445 | scm_remember_upto_here_1 (y); | |
1446 | return scm_values | |
1447 | (scm_list_2 (SCM_I_MAKINUM (-1), scm_i_normbig (r))); | |
1448 | } | |
1449 | else | |
1450 | { | |
1451 | SCM r = scm_i_mkbig (); | |
1452 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1453 | scm_remember_upto_here_1 (y); | |
1454 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1455 | return scm_values (scm_list_2 (SCM_INUM1, scm_i_normbig (r))); | |
1456 | } | |
1457 | } | |
1458 | else if (SCM_REALP (y)) | |
ac6ce16b | 1459 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1460 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
1461 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1462 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1463 | else |
ac6ce16b MW |
1464 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1465 | s_scm_euclidean_divide); | |
ff62c168 MW |
1466 | } |
1467 | else if (SCM_BIGP (x)) | |
1468 | { | |
1469 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1470 | { | |
1471 | scm_t_inum yy = SCM_I_INUM (y); | |
1472 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1473 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1474 | else |
1475 | { | |
1476 | SCM q = scm_i_mkbig (); | |
1477 | SCM r = scm_i_mkbig (); | |
1478 | if (yy > 0) | |
1479 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1480 | SCM_I_BIG_MPZ (x), yy); | |
1481 | else | |
1482 | { | |
1483 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1484 | SCM_I_BIG_MPZ (x), -yy); | |
1485 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1486 | } | |
1487 | scm_remember_upto_here_1 (x); | |
1488 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1489 | scm_i_normbig (r))); | |
1490 | } | |
1491 | } | |
1492 | else if (SCM_BIGP (y)) | |
1493 | { | |
1494 | SCM q = scm_i_mkbig (); | |
1495 | SCM r = scm_i_mkbig (); | |
1496 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1497 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1498 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1499 | else | |
1500 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1501 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1502 | scm_remember_upto_here_2 (x, y); | |
1503 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1504 | scm_i_normbig (r))); | |
1505 | } | |
1506 | else if (SCM_REALP (y)) | |
ac6ce16b | 1507 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1508 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
1509 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1510 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1511 | else |
ac6ce16b MW |
1512 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1513 | s_scm_euclidean_divide); | |
ff62c168 MW |
1514 | } |
1515 | else if (SCM_REALP (x)) | |
1516 | { | |
1517 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1518 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 1519 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1520 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
1521 | else | |
ac6ce16b MW |
1522 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1523 | s_scm_euclidean_divide); | |
ff62c168 MW |
1524 | } |
1525 | else if (SCM_FRACTIONP (x)) | |
1526 | { | |
1527 | if (SCM_REALP (y)) | |
ac6ce16b | 1528 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1529 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
1530 | else | |
ac6ce16b | 1531 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 MW |
1532 | } |
1533 | else | |
ac6ce16b MW |
1534 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1535 | s_scm_euclidean_divide); | |
ff62c168 MW |
1536 | } |
1537 | #undef FUNC_NAME | |
1538 | ||
1539 | static SCM | |
ac6ce16b | 1540 | scm_i_inexact_euclidean_divide (double x, double y) |
ff62c168 MW |
1541 | { |
1542 | double q, r; | |
1543 | ||
1544 | if (SCM_LIKELY (y > 0)) | |
1545 | q = floor (x / y); | |
1546 | else if (SCM_LIKELY (y < 0)) | |
1547 | q = ceil (x / y); | |
1548 | else if (y == 0) | |
ac6ce16b | 1549 | scm_num_overflow (s_scm_euclidean_divide); /* or return a NaN? */ |
ff62c168 MW |
1550 | else |
1551 | q = guile_NaN; | |
1552 | r = x - q * y; | |
1553 | return scm_values (scm_list_2 (scm_from_double (q), | |
1554 | scm_from_double (r))); | |
1555 | } | |
1556 | ||
1557 | /* Compute exact euclidean quotient and remainder the slow way. | |
1558 | We use this only if both arguments are exact, | |
1559 | and at least one of them is a fraction */ | |
1560 | static SCM | |
ac6ce16b | 1561 | scm_i_slow_exact_euclidean_divide (SCM x, SCM y) |
ff62c168 MW |
1562 | { |
1563 | SCM q, r; | |
1564 | ||
1565 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
1566 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1567 | s_scm_euclidean_divide); | |
ff62c168 | 1568 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
1569 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1570 | s_scm_euclidean_divide); | |
ff62c168 MW |
1571 | else if (scm_is_true (scm_positive_p (y))) |
1572 | q = scm_floor (scm_divide (x, y)); | |
1573 | else if (scm_is_true (scm_negative_p (y))) | |
1574 | q = scm_ceiling (scm_divide (x, y)); | |
1575 | else | |
ac6ce16b | 1576 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1577 | r = scm_difference (x, scm_product (q, y)); |
1578 | return scm_values (scm_list_2 (q, r)); | |
1579 | } | |
1580 | ||
1581 | static SCM scm_i_inexact_centered_quotient (double x, double y); | |
1582 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
1583 | static SCM scm_i_slow_exact_centered_quotient (SCM x, SCM y); | |
1584 | ||
1585 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, | |
1586 | (SCM x, SCM y), | |
1587 | "Return the integer @var{q} such that\n" | |
1588 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
1589 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
1590 | "@lisp\n" | |
1591 | "(centered-quotient 123 10) @result{} 12\n" | |
1592 | "(centered-quotient 123 -10) @result{} -12\n" | |
1593 | "(centered-quotient -123 10) @result{} -12\n" | |
1594 | "(centered-quotient -123 -10) @result{} 12\n" | |
1595 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
1596 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
1597 | "@end lisp") | |
1598 | #define FUNC_NAME s_scm_centered_quotient | |
1599 | { | |
1600 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1601 | { | |
1602 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1603 | { | |
1604 | scm_t_inum yy = SCM_I_INUM (y); | |
1605 | if (SCM_UNLIKELY (yy == 0)) | |
1606 | scm_num_overflow (s_scm_centered_quotient); | |
1607 | else | |
1608 | { | |
1609 | scm_t_inum xx = SCM_I_INUM (x); | |
1610 | scm_t_inum qq = xx / yy; | |
1611 | scm_t_inum rr = xx - qq * yy; | |
1612 | if (SCM_LIKELY (xx > 0)) | |
1613 | { | |
1614 | if (SCM_LIKELY (yy > 0)) | |
1615 | { | |
1616 | if (rr >= (yy + 1) / 2) | |
1617 | qq++; | |
1618 | } | |
1619 | else | |
1620 | { | |
1621 | if (rr >= (1 - yy) / 2) | |
1622 | qq--; | |
1623 | } | |
1624 | } | |
1625 | else | |
1626 | { | |
1627 | if (SCM_LIKELY (yy > 0)) | |
1628 | { | |
1629 | if (rr < -yy / 2) | |
1630 | qq--; | |
1631 | } | |
1632 | else | |
1633 | { | |
1634 | if (rr < yy / 2) | |
1635 | qq++; | |
1636 | } | |
1637 | } | |
1638 | return SCM_I_MAKINUM (qq); | |
1639 | } | |
1640 | } | |
1641 | else if (SCM_BIGP (y)) | |
1642 | { | |
1643 | /* Pass a denormalized bignum version of x (even though it | |
1644 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
1645 | return scm_i_bigint_centered_quotient | |
1646 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1647 | } | |
1648 | else if (SCM_REALP (y)) | |
1649 | return scm_i_inexact_centered_quotient | |
1650 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1651 | else if (SCM_FRACTIONP (y)) | |
1652 | return scm_i_slow_exact_centered_quotient (x, y); | |
1653 | else | |
1654 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1655 | s_scm_centered_quotient); | |
1656 | } | |
1657 | else if (SCM_BIGP (x)) | |
1658 | { | |
1659 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1660 | { | |
1661 | scm_t_inum yy = SCM_I_INUM (y); | |
1662 | if (SCM_UNLIKELY (yy == 0)) | |
1663 | scm_num_overflow (s_scm_centered_quotient); | |
1664 | else | |
1665 | { | |
1666 | SCM q = scm_i_mkbig (); | |
1667 | scm_t_inum rr; | |
1668 | /* Arrange for rr to initially be non-positive, | |
1669 | because that simplifies the test to see | |
1670 | if it is within the needed bounds. */ | |
1671 | if (yy > 0) | |
1672 | { | |
1673 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1674 | SCM_I_BIG_MPZ (x), yy); | |
1675 | scm_remember_upto_here_1 (x); | |
1676 | if (rr < -yy / 2) | |
1677 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1678 | SCM_I_BIG_MPZ (q), 1); | |
1679 | } | |
1680 | else | |
1681 | { | |
1682 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1683 | SCM_I_BIG_MPZ (x), -yy); | |
1684 | scm_remember_upto_here_1 (x); | |
1685 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1686 | if (rr < yy / 2) | |
1687 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1688 | SCM_I_BIG_MPZ (q), 1); | |
1689 | } | |
1690 | return scm_i_normbig (q); | |
1691 | } | |
1692 | } | |
1693 | else if (SCM_BIGP (y)) | |
1694 | return scm_i_bigint_centered_quotient (x, y); | |
1695 | else if (SCM_REALP (y)) | |
1696 | return scm_i_inexact_centered_quotient | |
1697 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1698 | else if (SCM_FRACTIONP (y)) | |
1699 | return scm_i_slow_exact_centered_quotient (x, y); | |
1700 | else | |
1701 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1702 | s_scm_centered_quotient); | |
1703 | } | |
1704 | else if (SCM_REALP (x)) | |
1705 | { | |
1706 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1707 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1708 | return scm_i_inexact_centered_quotient | |
1709 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1710 | else | |
1711 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1712 | s_scm_centered_quotient); | |
1713 | } | |
1714 | else if (SCM_FRACTIONP (x)) | |
1715 | { | |
1716 | if (SCM_REALP (y)) | |
1717 | return scm_i_inexact_centered_quotient | |
1718 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1719 | else | |
1720 | return scm_i_slow_exact_centered_quotient (x, y); | |
1721 | } | |
1722 | else | |
1723 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1724 | s_scm_centered_quotient); | |
1725 | } | |
1726 | #undef FUNC_NAME | |
1727 | ||
1728 | static SCM | |
1729 | scm_i_inexact_centered_quotient (double x, double y) | |
1730 | { | |
1731 | if (SCM_LIKELY (y > 0)) | |
1732 | return scm_from_double (floor (x/y + 0.5)); | |
1733 | else if (SCM_LIKELY (y < 0)) | |
1734 | return scm_from_double (ceil (x/y - 0.5)); | |
1735 | else if (y == 0) | |
1736 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
1737 | else | |
1738 | return scm_nan (); | |
1739 | } | |
1740 | ||
1741 | /* Assumes that both x and y are bigints, though | |
1742 | x might be able to fit into a fixnum. */ | |
1743 | static SCM | |
1744 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
1745 | { | |
1746 | SCM q, r, min_r; | |
1747 | ||
1748 | /* Note that x might be small enough to fit into a | |
1749 | fixnum, so we must not let it escape into the wild */ | |
1750 | q = scm_i_mkbig (); | |
1751 | r = scm_i_mkbig (); | |
1752 | ||
1753 | /* min_r will eventually become -abs(y)/2 */ | |
1754 | min_r = scm_i_mkbig (); | |
1755 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1756 | SCM_I_BIG_MPZ (y), 1); | |
1757 | ||
1758 | /* Arrange for rr to initially be non-positive, | |
1759 | because that simplifies the test to see | |
1760 | if it is within the needed bounds. */ | |
1761 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1762 | { | |
1763 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1764 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1765 | scm_remember_upto_here_2 (x, y); | |
1766 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1767 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1768 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1769 | SCM_I_BIG_MPZ (q), 1); | |
1770 | } | |
1771 | else | |
1772 | { | |
1773 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1774 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1775 | scm_remember_upto_here_2 (x, y); | |
1776 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1777 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1778 | SCM_I_BIG_MPZ (q), 1); | |
1779 | } | |
1780 | scm_remember_upto_here_2 (r, min_r); | |
1781 | return scm_i_normbig (q); | |
1782 | } | |
1783 | ||
1784 | /* Compute exact centered quotient the slow way. | |
1785 | We use this only if both arguments are exact, | |
1786 | and at least one of them is a fraction */ | |
1787 | static SCM | |
1788 | scm_i_slow_exact_centered_quotient (SCM x, SCM y) | |
1789 | { | |
1790 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1791 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1792 | s_scm_centered_quotient); | |
1793 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1794 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1795 | s_scm_centered_quotient); | |
1796 | else if (scm_is_true (scm_positive_p (y))) | |
1797 | return scm_floor (scm_sum (scm_divide (x, y), | |
1798 | exactly_one_half)); | |
1799 | else if (scm_is_true (scm_negative_p (y))) | |
1800 | return scm_ceiling (scm_difference (scm_divide (x, y), | |
1801 | exactly_one_half)); | |
1802 | else | |
1803 | scm_num_overflow (s_scm_centered_quotient); | |
1804 | } | |
1805 | ||
1806 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
1807 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
1808 | static SCM scm_i_slow_exact_centered_remainder (SCM x, SCM y); | |
1809 | ||
1810 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
1811 | (SCM x, SCM y), | |
1812 | "Return the real number @var{r} such that\n" | |
1813 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
1814 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1815 | "for some integer @var{q}.\n" | |
1816 | "@lisp\n" | |
1817 | "(centered-remainder 123 10) @result{} 3\n" | |
1818 | "(centered-remainder 123 -10) @result{} 3\n" | |
1819 | "(centered-remainder -123 10) @result{} -3\n" | |
1820 | "(centered-remainder -123 -10) @result{} -3\n" | |
1821 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
1822 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
1823 | "@end lisp") | |
1824 | #define FUNC_NAME s_scm_centered_remainder | |
1825 | { | |
1826 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1827 | { | |
1828 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1829 | { | |
1830 | scm_t_inum yy = SCM_I_INUM (y); | |
1831 | if (SCM_UNLIKELY (yy == 0)) | |
1832 | scm_num_overflow (s_scm_centered_remainder); | |
1833 | else | |
1834 | { | |
1835 | scm_t_inum xx = SCM_I_INUM (x); | |
1836 | scm_t_inum rr = xx % yy; | |
1837 | if (SCM_LIKELY (xx > 0)) | |
1838 | { | |
1839 | if (SCM_LIKELY (yy > 0)) | |
1840 | { | |
1841 | if (rr >= (yy + 1) / 2) | |
1842 | rr -= yy; | |
1843 | } | |
1844 | else | |
1845 | { | |
1846 | if (rr >= (1 - yy) / 2) | |
1847 | rr += yy; | |
1848 | } | |
1849 | } | |
1850 | else | |
1851 | { | |
1852 | if (SCM_LIKELY (yy > 0)) | |
1853 | { | |
1854 | if (rr < -yy / 2) | |
1855 | rr += yy; | |
1856 | } | |
1857 | else | |
1858 | { | |
1859 | if (rr < yy / 2) | |
1860 | rr -= yy; | |
1861 | } | |
1862 | } | |
1863 | return SCM_I_MAKINUM (rr); | |
1864 | } | |
1865 | } | |
1866 | else if (SCM_BIGP (y)) | |
1867 | { | |
1868 | /* Pass a denormalized bignum version of x (even though it | |
1869 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
1870 | return scm_i_bigint_centered_remainder | |
1871 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1872 | } | |
1873 | else if (SCM_REALP (y)) | |
1874 | return scm_i_inexact_centered_remainder | |
1875 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1876 | else if (SCM_FRACTIONP (y)) | |
1877 | return scm_i_slow_exact_centered_remainder (x, y); | |
1878 | else | |
1879 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1880 | s_scm_centered_remainder); | |
1881 | } | |
1882 | else if (SCM_BIGP (x)) | |
1883 | { | |
1884 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1885 | { | |
1886 | scm_t_inum yy = SCM_I_INUM (y); | |
1887 | if (SCM_UNLIKELY (yy == 0)) | |
1888 | scm_num_overflow (s_scm_centered_remainder); | |
1889 | else | |
1890 | { | |
1891 | scm_t_inum rr; | |
1892 | /* Arrange for rr to initially be non-positive, | |
1893 | because that simplifies the test to see | |
1894 | if it is within the needed bounds. */ | |
1895 | if (yy > 0) | |
1896 | { | |
1897 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1898 | scm_remember_upto_here_1 (x); | |
1899 | if (rr < -yy / 2) | |
1900 | rr += yy; | |
1901 | } | |
1902 | else | |
1903 | { | |
1904 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1905 | scm_remember_upto_here_1 (x); | |
1906 | if (rr < yy / 2) | |
1907 | rr -= yy; | |
1908 | } | |
1909 | return SCM_I_MAKINUM (rr); | |
1910 | } | |
1911 | } | |
1912 | else if (SCM_BIGP (y)) | |
1913 | return scm_i_bigint_centered_remainder (x, y); | |
1914 | else if (SCM_REALP (y)) | |
1915 | return scm_i_inexact_centered_remainder | |
1916 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1917 | else if (SCM_FRACTIONP (y)) | |
1918 | return scm_i_slow_exact_centered_remainder (x, y); | |
1919 | else | |
1920 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1921 | s_scm_centered_remainder); | |
1922 | } | |
1923 | else if (SCM_REALP (x)) | |
1924 | { | |
1925 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1926 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1927 | return scm_i_inexact_centered_remainder | |
1928 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1929 | else | |
1930 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1931 | s_scm_centered_remainder); | |
1932 | } | |
1933 | else if (SCM_FRACTIONP (x)) | |
1934 | { | |
1935 | if (SCM_REALP (y)) | |
1936 | return scm_i_inexact_centered_remainder | |
1937 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1938 | else | |
1939 | return scm_i_slow_exact_centered_remainder (x, y); | |
1940 | } | |
1941 | else | |
1942 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
1943 | s_scm_centered_remainder); | |
1944 | } | |
1945 | #undef FUNC_NAME | |
1946 | ||
1947 | static SCM | |
1948 | scm_i_inexact_centered_remainder (double x, double y) | |
1949 | { | |
1950 | double q; | |
1951 | ||
1952 | /* Although it would be more efficient to use fmod here, we can't | |
1953 | because it would in some cases produce results inconsistent with | |
1954 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
1955 | close). In particular, when x-y/2 is very close to a multiple of | |
1956 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
1957 | two cases must correspond to different choices of q. If quotient | |
1958 | chooses one and remainder chooses the other, it would be bad. */ | |
1959 | if (SCM_LIKELY (y > 0)) | |
1960 | q = floor (x/y + 0.5); | |
1961 | else if (SCM_LIKELY (y < 0)) | |
1962 | q = ceil (x/y - 0.5); | |
1963 | else if (y == 0) | |
1964 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
1965 | else | |
1966 | return scm_nan (); | |
1967 | return scm_from_double (x - q * y); | |
1968 | } | |
1969 | ||
1970 | /* Assumes that both x and y are bigints, though | |
1971 | x might be able to fit into a fixnum. */ | |
1972 | static SCM | |
1973 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
1974 | { | |
1975 | SCM r, min_r; | |
1976 | ||
1977 | /* Note that x might be small enough to fit into a | |
1978 | fixnum, so we must not let it escape into the wild */ | |
1979 | r = scm_i_mkbig (); | |
1980 | ||
1981 | /* min_r will eventually become -abs(y)/2 */ | |
1982 | min_r = scm_i_mkbig (); | |
1983 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1984 | SCM_I_BIG_MPZ (y), 1); | |
1985 | ||
1986 | /* Arrange for rr to initially be non-positive, | |
1987 | because that simplifies the test to see | |
1988 | if it is within the needed bounds. */ | |
1989 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1990 | { | |
1991 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1992 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1993 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1994 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1995 | mpz_add (SCM_I_BIG_MPZ (r), | |
1996 | SCM_I_BIG_MPZ (r), | |
1997 | SCM_I_BIG_MPZ (y)); | |
1998 | } | |
1999 | else | |
2000 | { | |
2001 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2002 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2003 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2004 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2005 | SCM_I_BIG_MPZ (r), | |
2006 | SCM_I_BIG_MPZ (y)); | |
2007 | } | |
2008 | scm_remember_upto_here_2 (x, y); | |
2009 | return scm_i_normbig (r); | |
2010 | } | |
2011 | ||
2012 | /* Compute exact centered_remainder the slow way. | |
2013 | We use this only if both arguments are exact, | |
2014 | and at least one of them is a fraction */ | |
2015 | static SCM | |
2016 | scm_i_slow_exact_centered_remainder (SCM x, SCM y) | |
2017 | { | |
2018 | SCM q; | |
2019 | ||
2020 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
2021 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2022 | s_scm_centered_remainder); | |
2023 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
2024 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2025 | s_scm_centered_remainder); | |
2026 | else if (scm_is_true (scm_positive_p (y))) | |
2027 | q = scm_floor (scm_sum (scm_divide (x, y), exactly_one_half)); | |
2028 | else if (scm_is_true (scm_negative_p (y))) | |
2029 | q = scm_ceiling (scm_difference (scm_divide (x, y), exactly_one_half)); | |
2030 | else | |
2031 | scm_num_overflow (s_scm_centered_remainder); | |
2032 | return scm_difference (x, scm_product (y, q)); | |
2033 | } | |
2034 | ||
2035 | ||
ac6ce16b MW |
2036 | static SCM scm_i_inexact_centered_divide (double x, double y); |
2037 | static SCM scm_i_bigint_centered_divide (SCM x, SCM y); | |
2038 | static SCM scm_i_slow_exact_centered_divide (SCM x, SCM y); | |
ff62c168 | 2039 | |
ac6ce16b | 2040 | SCM_PRIMITIVE_GENERIC (scm_centered_divide, "centered/", 2, 0, 0, |
ff62c168 MW |
2041 | (SCM x, SCM y), |
2042 | "Return the integer @var{q} and the real number @var{r}\n" | |
2043 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2044 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2045 | "@lisp\n" | |
2046 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2047 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2048 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2049 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2050 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2051 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2052 | "@end lisp") | |
ac6ce16b | 2053 | #define FUNC_NAME s_scm_centered_divide |
ff62c168 MW |
2054 | { |
2055 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2056 | { | |
2057 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2058 | { | |
2059 | scm_t_inum yy = SCM_I_INUM (y); | |
2060 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2061 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2062 | else |
2063 | { | |
2064 | scm_t_inum xx = SCM_I_INUM (x); | |
2065 | scm_t_inum qq = xx / yy; | |
2066 | scm_t_inum rr = xx - qq * yy; | |
2067 | if (SCM_LIKELY (xx > 0)) | |
2068 | { | |
2069 | if (SCM_LIKELY (yy > 0)) | |
2070 | { | |
2071 | if (rr >= (yy + 1) / 2) | |
2072 | { qq++; rr -= yy; } | |
2073 | } | |
2074 | else | |
2075 | { | |
2076 | if (rr >= (1 - yy) / 2) | |
2077 | { qq--; rr += yy; } | |
2078 | } | |
2079 | } | |
2080 | else | |
2081 | { | |
2082 | if (SCM_LIKELY (yy > 0)) | |
2083 | { | |
2084 | if (rr < -yy / 2) | |
2085 | { qq--; rr += yy; } | |
2086 | } | |
2087 | else | |
2088 | { | |
2089 | if (rr < yy / 2) | |
2090 | { qq++; rr -= yy; } | |
2091 | } | |
2092 | } | |
2093 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
2094 | SCM_I_MAKINUM (rr))); | |
2095 | } | |
2096 | } | |
2097 | else if (SCM_BIGP (y)) | |
2098 | { | |
2099 | /* Pass a denormalized bignum version of x (even though it | |
ac6ce16b MW |
2100 | can fit in a fixnum) to scm_i_bigint_centered_divide */ |
2101 | return scm_i_bigint_centered_divide | |
ff62c168 MW |
2102 | (scm_i_long2big (SCM_I_INUM (x)), y); |
2103 | } | |
2104 | else if (SCM_REALP (y)) | |
ac6ce16b | 2105 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2106 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
2107 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2108 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2109 | else |
ac6ce16b MW |
2110 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2111 | s_scm_centered_divide); | |
ff62c168 MW |
2112 | } |
2113 | else if (SCM_BIGP (x)) | |
2114 | { | |
2115 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2116 | { | |
2117 | scm_t_inum yy = SCM_I_INUM (y); | |
2118 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2119 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2120 | else |
2121 | { | |
2122 | SCM q = scm_i_mkbig (); | |
2123 | scm_t_inum rr; | |
2124 | /* Arrange for rr to initially be non-positive, | |
2125 | because that simplifies the test to see | |
2126 | if it is within the needed bounds. */ | |
2127 | if (yy > 0) | |
2128 | { | |
2129 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2130 | SCM_I_BIG_MPZ (x), yy); | |
2131 | scm_remember_upto_here_1 (x); | |
2132 | if (rr < -yy / 2) | |
2133 | { | |
2134 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2135 | SCM_I_BIG_MPZ (q), 1); | |
2136 | rr += yy; | |
2137 | } | |
2138 | } | |
2139 | else | |
2140 | { | |
2141 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2142 | SCM_I_BIG_MPZ (x), -yy); | |
2143 | scm_remember_upto_here_1 (x); | |
2144 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2145 | if (rr < yy / 2) | |
2146 | { | |
2147 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2148 | SCM_I_BIG_MPZ (q), 1); | |
2149 | rr -= yy; | |
2150 | } | |
2151 | } | |
2152 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2153 | SCM_I_MAKINUM (rr))); | |
2154 | } | |
2155 | } | |
2156 | else if (SCM_BIGP (y)) | |
ac6ce16b | 2157 | return scm_i_bigint_centered_divide (x, y); |
ff62c168 | 2158 | else if (SCM_REALP (y)) |
ac6ce16b | 2159 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2160 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
2161 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2162 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2163 | else |
ac6ce16b MW |
2164 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2165 | s_scm_centered_divide); | |
ff62c168 MW |
2166 | } |
2167 | else if (SCM_REALP (x)) | |
2168 | { | |
2169 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2170 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 2171 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2172 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
2173 | else | |
ac6ce16b MW |
2174 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2175 | s_scm_centered_divide); | |
ff62c168 MW |
2176 | } |
2177 | else if (SCM_FRACTIONP (x)) | |
2178 | { | |
2179 | if (SCM_REALP (y)) | |
ac6ce16b | 2180 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2181 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
2182 | else | |
ac6ce16b | 2183 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 MW |
2184 | } |
2185 | else | |
ac6ce16b MW |
2186 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2187 | s_scm_centered_divide); | |
ff62c168 MW |
2188 | } |
2189 | #undef FUNC_NAME | |
2190 | ||
2191 | static SCM | |
ac6ce16b | 2192 | scm_i_inexact_centered_divide (double x, double y) |
ff62c168 MW |
2193 | { |
2194 | double q, r; | |
2195 | ||
2196 | if (SCM_LIKELY (y > 0)) | |
2197 | q = floor (x/y + 0.5); | |
2198 | else if (SCM_LIKELY (y < 0)) | |
2199 | q = ceil (x/y - 0.5); | |
2200 | else if (y == 0) | |
ac6ce16b | 2201 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ |
ff62c168 MW |
2202 | else |
2203 | q = guile_NaN; | |
2204 | r = x - q * y; | |
2205 | return scm_values (scm_list_2 (scm_from_double (q), | |
2206 | scm_from_double (r))); | |
2207 | } | |
2208 | ||
2209 | /* Assumes that both x and y are bigints, though | |
2210 | x might be able to fit into a fixnum. */ | |
2211 | static SCM | |
ac6ce16b | 2212 | scm_i_bigint_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2213 | { |
2214 | SCM q, r, min_r; | |
2215 | ||
2216 | /* Note that x might be small enough to fit into a | |
2217 | fixnum, so we must not let it escape into the wild */ | |
2218 | q = scm_i_mkbig (); | |
2219 | r = scm_i_mkbig (); | |
2220 | ||
2221 | /* min_r will eventually become -abs(y/2) */ | |
2222 | min_r = scm_i_mkbig (); | |
2223 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2224 | SCM_I_BIG_MPZ (y), 1); | |
2225 | ||
2226 | /* Arrange for rr to initially be non-positive, | |
2227 | because that simplifies the test to see | |
2228 | if it is within the needed bounds. */ | |
2229 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2230 | { | |
2231 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2232 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2233 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2234 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2235 | { | |
2236 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2237 | SCM_I_BIG_MPZ (q), 1); | |
2238 | mpz_add (SCM_I_BIG_MPZ (r), | |
2239 | SCM_I_BIG_MPZ (r), | |
2240 | SCM_I_BIG_MPZ (y)); | |
2241 | } | |
2242 | } | |
2243 | else | |
2244 | { | |
2245 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2246 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2247 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2248 | { | |
2249 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2250 | SCM_I_BIG_MPZ (q), 1); | |
2251 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2252 | SCM_I_BIG_MPZ (r), | |
2253 | SCM_I_BIG_MPZ (y)); | |
2254 | } | |
2255 | } | |
2256 | scm_remember_upto_here_2 (x, y); | |
2257 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2258 | scm_i_normbig (r))); | |
2259 | } | |
2260 | ||
2261 | /* Compute exact centered quotient and remainder the slow way. | |
2262 | We use this only if both arguments are exact, | |
2263 | and at least one of them is a fraction */ | |
2264 | static SCM | |
ac6ce16b | 2265 | scm_i_slow_exact_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2266 | { |
2267 | SCM q, r; | |
2268 | ||
2269 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
2270 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2271 | s_scm_centered_divide); | |
ff62c168 | 2272 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
2273 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2274 | s_scm_centered_divide); | |
ff62c168 MW |
2275 | else if (scm_is_true (scm_positive_p (y))) |
2276 | q = scm_floor (scm_sum (scm_divide (x, y), | |
2277 | exactly_one_half)); | |
2278 | else if (scm_is_true (scm_negative_p (y))) | |
2279 | q = scm_ceiling (scm_difference (scm_divide (x, y), | |
2280 | exactly_one_half)); | |
2281 | else | |
ac6ce16b | 2282 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2283 | r = scm_difference (x, scm_product (q, y)); |
2284 | return scm_values (scm_list_2 (q, r)); | |
2285 | } | |
2286 | ||
2287 | ||
78d3deb1 AW |
2288 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
2289 | (SCM x, SCM y, SCM rest), | |
2290 | "Return the greatest common divisor of all parameter values.\n" | |
2291 | "If called without arguments, 0 is returned.") | |
2292 | #define FUNC_NAME s_scm_i_gcd | |
2293 | { | |
2294 | while (!scm_is_null (rest)) | |
2295 | { x = scm_gcd (x, y); | |
2296 | y = scm_car (rest); | |
2297 | rest = scm_cdr (rest); | |
2298 | } | |
2299 | return scm_gcd (x, y); | |
2300 | } | |
2301 | #undef FUNC_NAME | |
2302 | ||
2303 | #define s_gcd s_scm_i_gcd | |
2304 | #define g_gcd g_scm_i_gcd | |
2305 | ||
0f2d19dd | 2306 | SCM |
6e8d25a6 | 2307 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 2308 | { |
ca46fb90 | 2309 | if (SCM_UNBNDP (y)) |
1dd79792 | 2310 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 2311 | |
e11e83f3 | 2312 | if (SCM_I_INUMP (x)) |
ca46fb90 | 2313 | { |
e11e83f3 | 2314 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2315 | { |
e25f3727 AW |
2316 | scm_t_inum xx = SCM_I_INUM (x); |
2317 | scm_t_inum yy = SCM_I_INUM (y); | |
2318 | scm_t_inum u = xx < 0 ? -xx : xx; | |
2319 | scm_t_inum v = yy < 0 ? -yy : yy; | |
2320 | scm_t_inum result; | |
0aacf84e MD |
2321 | if (xx == 0) |
2322 | result = v; | |
2323 | else if (yy == 0) | |
2324 | result = u; | |
2325 | else | |
2326 | { | |
e25f3727 AW |
2327 | scm_t_inum k = 1; |
2328 | scm_t_inum t; | |
0aacf84e MD |
2329 | /* Determine a common factor 2^k */ |
2330 | while (!(1 & (u | v))) | |
2331 | { | |
2332 | k <<= 1; | |
2333 | u >>= 1; | |
2334 | v >>= 1; | |
2335 | } | |
2336 | /* Now, any factor 2^n can be eliminated */ | |
2337 | if (u & 1) | |
2338 | t = -v; | |
2339 | else | |
2340 | { | |
2341 | t = u; | |
2342 | b3: | |
2343 | t = SCM_SRS (t, 1); | |
2344 | } | |
2345 | if (!(1 & t)) | |
2346 | goto b3; | |
2347 | if (t > 0) | |
2348 | u = t; | |
2349 | else | |
2350 | v = -t; | |
2351 | t = u - v; | |
2352 | if (t != 0) | |
2353 | goto b3; | |
2354 | result = u * k; | |
2355 | } | |
2356 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 2357 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2358 | : scm_i_inum2big (result)); |
ca46fb90 RB |
2359 | } |
2360 | else if (SCM_BIGP (y)) | |
2361 | { | |
0bff4dce KR |
2362 | SCM_SWAP (x, y); |
2363 | goto big_inum; | |
ca46fb90 RB |
2364 | } |
2365 | else | |
2366 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 2367 | } |
ca46fb90 RB |
2368 | else if (SCM_BIGP (x)) |
2369 | { | |
e11e83f3 | 2370 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2371 | { |
e25f3727 AW |
2372 | scm_t_bits result; |
2373 | scm_t_inum yy; | |
0bff4dce | 2374 | big_inum: |
e11e83f3 | 2375 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
2376 | if (yy == 0) |
2377 | return scm_abs (x); | |
0aacf84e MD |
2378 | if (yy < 0) |
2379 | yy = -yy; | |
ca46fb90 RB |
2380 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
2381 | scm_remember_upto_here_1 (x); | |
0aacf84e | 2382 | return (SCM_POSFIXABLE (result) |
d956fa6f | 2383 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2384 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
2385 | } |
2386 | else if (SCM_BIGP (y)) | |
2387 | { | |
2388 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
2389 | mpz_gcd (SCM_I_BIG_MPZ (result), |
2390 | SCM_I_BIG_MPZ (x), | |
2391 | SCM_I_BIG_MPZ (y)); | |
2392 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
2393 | return scm_i_normbig (result); |
2394 | } | |
2395 | else | |
2396 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 2397 | } |
ca46fb90 | 2398 | else |
09fb7599 | 2399 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
2400 | } |
2401 | ||
78d3deb1 AW |
2402 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
2403 | (SCM x, SCM y, SCM rest), | |
2404 | "Return the least common multiple of the arguments.\n" | |
2405 | "If called without arguments, 1 is returned.") | |
2406 | #define FUNC_NAME s_scm_i_lcm | |
2407 | { | |
2408 | while (!scm_is_null (rest)) | |
2409 | { x = scm_lcm (x, y); | |
2410 | y = scm_car (rest); | |
2411 | rest = scm_cdr (rest); | |
2412 | } | |
2413 | return scm_lcm (x, y); | |
2414 | } | |
2415 | #undef FUNC_NAME | |
2416 | ||
2417 | #define s_lcm s_scm_i_lcm | |
2418 | #define g_lcm g_scm_i_lcm | |
2419 | ||
0f2d19dd | 2420 | SCM |
6e8d25a6 | 2421 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 2422 | { |
ca46fb90 RB |
2423 | if (SCM_UNBNDP (n2)) |
2424 | { | |
2425 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
2426 | return SCM_I_MAKINUM (1L); |
2427 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 2428 | } |
09fb7599 | 2429 | |
e11e83f3 | 2430 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 2431 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 2432 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 2433 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 2434 | |
e11e83f3 | 2435 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 2436 | { |
e11e83f3 | 2437 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2438 | { |
2439 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 2440 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
2441 | return d; |
2442 | else | |
2443 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
2444 | } | |
2445 | else | |
2446 | { | |
2447 | /* inum n1, big n2 */ | |
2448 | inumbig: | |
2449 | { | |
2450 | SCM result = scm_i_mkbig (); | |
e25f3727 | 2451 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
2452 | if (nn1 == 0) return SCM_INUM0; |
2453 | if (nn1 < 0) nn1 = - nn1; | |
2454 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
2455 | scm_remember_upto_here_1 (n2); | |
2456 | return result; | |
2457 | } | |
2458 | } | |
2459 | } | |
2460 | else | |
2461 | { | |
2462 | /* big n1 */ | |
e11e83f3 | 2463 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2464 | { |
2465 | SCM_SWAP (n1, n2); | |
2466 | goto inumbig; | |
2467 | } | |
2468 | else | |
2469 | { | |
2470 | SCM result = scm_i_mkbig (); | |
2471 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
2472 | SCM_I_BIG_MPZ (n1), | |
2473 | SCM_I_BIG_MPZ (n2)); | |
2474 | scm_remember_upto_here_2(n1, n2); | |
2475 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
2476 | return result; | |
2477 | } | |
f872b822 | 2478 | } |
0f2d19dd JB |
2479 | } |
2480 | ||
8a525303 GB |
2481 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
2482 | ||
2483 | Logand: | |
2484 | X Y Result Method: | |
2485 | (len) | |
2486 | + + + x (map digit:logand X Y) | |
2487 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
2488 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
2489 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
2490 | ||
2491 | Logior: | |
2492 | X Y Result Method: | |
2493 | ||
2494 | + + + (map digit:logior X Y) | |
2495 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
2496 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
2497 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
2498 | ||
2499 | Logxor: | |
2500 | X Y Result Method: | |
2501 | ||
2502 | + + + (map digit:logxor X Y) | |
2503 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
2504 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
2505 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
2506 | ||
2507 | Logtest: | |
2508 | X Y Result | |
2509 | ||
2510 | + + (any digit:logand X Y) | |
2511 | + - (any digit:logand X (lognot (+ -1 Y))) | |
2512 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
2513 | - - #t | |
2514 | ||
2515 | */ | |
2516 | ||
78d3deb1 AW |
2517 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
2518 | (SCM x, SCM y, SCM rest), | |
2519 | "Return the bitwise AND of the integer arguments.\n\n" | |
2520 | "@lisp\n" | |
2521 | "(logand) @result{} -1\n" | |
2522 | "(logand 7) @result{} 7\n" | |
2523 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
2524 | "@end lisp") | |
2525 | #define FUNC_NAME s_scm_i_logand | |
2526 | { | |
2527 | while (!scm_is_null (rest)) | |
2528 | { x = scm_logand (x, y); | |
2529 | y = scm_car (rest); | |
2530 | rest = scm_cdr (rest); | |
2531 | } | |
2532 | return scm_logand (x, y); | |
2533 | } | |
2534 | #undef FUNC_NAME | |
2535 | ||
2536 | #define s_scm_logand s_scm_i_logand | |
2537 | ||
2538 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 2539 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 2540 | { |
e25f3727 | 2541 | scm_t_inum nn1; |
9a00c9fc | 2542 | |
0aacf84e MD |
2543 | if (SCM_UNBNDP (n2)) |
2544 | { | |
2545 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 2546 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
2547 | else if (!SCM_NUMBERP (n1)) |
2548 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
2549 | else if (SCM_NUMBERP (n1)) | |
2550 | return n1; | |
2551 | else | |
2552 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2553 | } |
09fb7599 | 2554 | |
e11e83f3 | 2555 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2556 | { |
e11e83f3 MV |
2557 | nn1 = SCM_I_INUM (n1); |
2558 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2559 | { |
e25f3727 | 2560 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2561 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
2562 | } |
2563 | else if SCM_BIGP (n2) | |
2564 | { | |
2565 | intbig: | |
2566 | if (n1 == 0) | |
2567 | return SCM_INUM0; | |
2568 | { | |
2569 | SCM result_z = scm_i_mkbig (); | |
2570 | mpz_t nn1_z; | |
2571 | mpz_init_set_si (nn1_z, nn1); | |
2572 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2573 | scm_remember_upto_here_1 (n2); | |
2574 | mpz_clear (nn1_z); | |
2575 | return scm_i_normbig (result_z); | |
2576 | } | |
2577 | } | |
2578 | else | |
2579 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2580 | } | |
2581 | else if (SCM_BIGP (n1)) | |
2582 | { | |
e11e83f3 | 2583 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2584 | { |
2585 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2586 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2587 | goto intbig; |
2588 | } | |
2589 | else if (SCM_BIGP (n2)) | |
2590 | { | |
2591 | SCM result_z = scm_i_mkbig (); | |
2592 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
2593 | SCM_I_BIG_MPZ (n1), | |
2594 | SCM_I_BIG_MPZ (n2)); | |
2595 | scm_remember_upto_here_2 (n1, n2); | |
2596 | return scm_i_normbig (result_z); | |
2597 | } | |
2598 | else | |
2599 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2600 | } |
0aacf84e | 2601 | else |
09fb7599 | 2602 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2603 | } |
1bbd0b84 | 2604 | #undef FUNC_NAME |
0f2d19dd | 2605 | |
09fb7599 | 2606 | |
78d3deb1 AW |
2607 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
2608 | (SCM x, SCM y, SCM rest), | |
2609 | "Return the bitwise OR of the integer arguments.\n\n" | |
2610 | "@lisp\n" | |
2611 | "(logior) @result{} 0\n" | |
2612 | "(logior 7) @result{} 7\n" | |
2613 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
2614 | "@end lisp") | |
2615 | #define FUNC_NAME s_scm_i_logior | |
2616 | { | |
2617 | while (!scm_is_null (rest)) | |
2618 | { x = scm_logior (x, y); | |
2619 | y = scm_car (rest); | |
2620 | rest = scm_cdr (rest); | |
2621 | } | |
2622 | return scm_logior (x, y); | |
2623 | } | |
2624 | #undef FUNC_NAME | |
2625 | ||
2626 | #define s_scm_logior s_scm_i_logior | |
2627 | ||
2628 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 2629 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 2630 | { |
e25f3727 | 2631 | scm_t_inum nn1; |
9a00c9fc | 2632 | |
0aacf84e MD |
2633 | if (SCM_UNBNDP (n2)) |
2634 | { | |
2635 | if (SCM_UNBNDP (n1)) | |
2636 | return SCM_INUM0; | |
2637 | else if (SCM_NUMBERP (n1)) | |
2638 | return n1; | |
2639 | else | |
2640 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2641 | } |
09fb7599 | 2642 | |
e11e83f3 | 2643 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2644 | { |
e11e83f3 MV |
2645 | nn1 = SCM_I_INUM (n1); |
2646 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2647 | { |
e11e83f3 | 2648 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 2649 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
2650 | } |
2651 | else if (SCM_BIGP (n2)) | |
2652 | { | |
2653 | intbig: | |
2654 | if (nn1 == 0) | |
2655 | return n2; | |
2656 | { | |
2657 | SCM result_z = scm_i_mkbig (); | |
2658 | mpz_t nn1_z; | |
2659 | mpz_init_set_si (nn1_z, nn1); | |
2660 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2661 | scm_remember_upto_here_1 (n2); | |
2662 | mpz_clear (nn1_z); | |
9806de0d | 2663 | return scm_i_normbig (result_z); |
0aacf84e MD |
2664 | } |
2665 | } | |
2666 | else | |
2667 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2668 | } | |
2669 | else if (SCM_BIGP (n1)) | |
2670 | { | |
e11e83f3 | 2671 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2672 | { |
2673 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2674 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2675 | goto intbig; |
2676 | } | |
2677 | else if (SCM_BIGP (n2)) | |
2678 | { | |
2679 | SCM result_z = scm_i_mkbig (); | |
2680 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
2681 | SCM_I_BIG_MPZ (n1), | |
2682 | SCM_I_BIG_MPZ (n2)); | |
2683 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 2684 | return scm_i_normbig (result_z); |
0aacf84e MD |
2685 | } |
2686 | else | |
2687 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2688 | } |
0aacf84e | 2689 | else |
09fb7599 | 2690 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2691 | } |
1bbd0b84 | 2692 | #undef FUNC_NAME |
0f2d19dd | 2693 | |
09fb7599 | 2694 | |
78d3deb1 AW |
2695 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
2696 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
2697 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
2698 | "set in the result if it is set in an odd number of arguments.\n" | |
2699 | "@lisp\n" | |
2700 | "(logxor) @result{} 0\n" | |
2701 | "(logxor 7) @result{} 7\n" | |
2702 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
2703 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 2704 | "@end lisp") |
78d3deb1 AW |
2705 | #define FUNC_NAME s_scm_i_logxor |
2706 | { | |
2707 | while (!scm_is_null (rest)) | |
2708 | { x = scm_logxor (x, y); | |
2709 | y = scm_car (rest); | |
2710 | rest = scm_cdr (rest); | |
2711 | } | |
2712 | return scm_logxor (x, y); | |
2713 | } | |
2714 | #undef FUNC_NAME | |
2715 | ||
2716 | #define s_scm_logxor s_scm_i_logxor | |
2717 | ||
2718 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 2719 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 2720 | { |
e25f3727 | 2721 | scm_t_inum nn1; |
9a00c9fc | 2722 | |
0aacf84e MD |
2723 | if (SCM_UNBNDP (n2)) |
2724 | { | |
2725 | if (SCM_UNBNDP (n1)) | |
2726 | return SCM_INUM0; | |
2727 | else if (SCM_NUMBERP (n1)) | |
2728 | return n1; | |
2729 | else | |
2730 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2731 | } |
09fb7599 | 2732 | |
e11e83f3 | 2733 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2734 | { |
e11e83f3 MV |
2735 | nn1 = SCM_I_INUM (n1); |
2736 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2737 | { |
e25f3727 | 2738 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2739 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
2740 | } |
2741 | else if (SCM_BIGP (n2)) | |
2742 | { | |
2743 | intbig: | |
2744 | { | |
2745 | SCM result_z = scm_i_mkbig (); | |
2746 | mpz_t nn1_z; | |
2747 | mpz_init_set_si (nn1_z, nn1); | |
2748 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2749 | scm_remember_upto_here_1 (n2); | |
2750 | mpz_clear (nn1_z); | |
2751 | return scm_i_normbig (result_z); | |
2752 | } | |
2753 | } | |
2754 | else | |
2755 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2756 | } | |
2757 | else if (SCM_BIGP (n1)) | |
2758 | { | |
e11e83f3 | 2759 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2760 | { |
2761 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2762 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2763 | goto intbig; |
2764 | } | |
2765 | else if (SCM_BIGP (n2)) | |
2766 | { | |
2767 | SCM result_z = scm_i_mkbig (); | |
2768 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
2769 | SCM_I_BIG_MPZ (n1), | |
2770 | SCM_I_BIG_MPZ (n2)); | |
2771 | scm_remember_upto_here_2 (n1, n2); | |
2772 | return scm_i_normbig (result_z); | |
2773 | } | |
2774 | else | |
2775 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2776 | } |
0aacf84e | 2777 | else |
09fb7599 | 2778 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2779 | } |
1bbd0b84 | 2780 | #undef FUNC_NAME |
0f2d19dd | 2781 | |
09fb7599 | 2782 | |
a1ec6916 | 2783 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 2784 | (SCM j, SCM k), |
ba6e7231 KR |
2785 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
2786 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
2787 | "without actually calculating the @code{logand}, just testing\n" | |
2788 | "for non-zero.\n" | |
2789 | "\n" | |
1e6808ea | 2790 | "@lisp\n" |
b380b885 MD |
2791 | "(logtest #b0100 #b1011) @result{} #f\n" |
2792 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 2793 | "@end lisp") |
1bbd0b84 | 2794 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 2795 | { |
e25f3727 | 2796 | scm_t_inum nj; |
9a00c9fc | 2797 | |
e11e83f3 | 2798 | if (SCM_I_INUMP (j)) |
0aacf84e | 2799 | { |
e11e83f3 MV |
2800 | nj = SCM_I_INUM (j); |
2801 | if (SCM_I_INUMP (k)) | |
0aacf84e | 2802 | { |
e25f3727 | 2803 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 2804 | return scm_from_bool (nj & nk); |
0aacf84e MD |
2805 | } |
2806 | else if (SCM_BIGP (k)) | |
2807 | { | |
2808 | intbig: | |
2809 | if (nj == 0) | |
2810 | return SCM_BOOL_F; | |
2811 | { | |
2812 | SCM result; | |
2813 | mpz_t nj_z; | |
2814 | mpz_init_set_si (nj_z, nj); | |
2815 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
2816 | scm_remember_upto_here_1 (k); | |
73e4de09 | 2817 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
2818 | mpz_clear (nj_z); |
2819 | return result; | |
2820 | } | |
2821 | } | |
2822 | else | |
2823 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2824 | } | |
2825 | else if (SCM_BIGP (j)) | |
2826 | { | |
e11e83f3 | 2827 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
2828 | { |
2829 | SCM_SWAP (j, k); | |
e11e83f3 | 2830 | nj = SCM_I_INUM (j); |
0aacf84e MD |
2831 | goto intbig; |
2832 | } | |
2833 | else if (SCM_BIGP (k)) | |
2834 | { | |
2835 | SCM result; | |
2836 | mpz_t result_z; | |
2837 | mpz_init (result_z); | |
2838 | mpz_and (result_z, | |
2839 | SCM_I_BIG_MPZ (j), | |
2840 | SCM_I_BIG_MPZ (k)); | |
2841 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 2842 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
2843 | mpz_clear (result_z); |
2844 | return result; | |
2845 | } | |
2846 | else | |
2847 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2848 | } | |
2849 | else | |
2850 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 2851 | } |
1bbd0b84 | 2852 | #undef FUNC_NAME |
0f2d19dd | 2853 | |
c1bfcf60 | 2854 | |
a1ec6916 | 2855 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 2856 | (SCM index, SCM j), |
ba6e7231 KR |
2857 | "Test whether bit number @var{index} in @var{j} is set.\n" |
2858 | "@var{index} starts from 0 for the least significant bit.\n" | |
2859 | "\n" | |
1e6808ea | 2860 | "@lisp\n" |
b380b885 MD |
2861 | "(logbit? 0 #b1101) @result{} #t\n" |
2862 | "(logbit? 1 #b1101) @result{} #f\n" | |
2863 | "(logbit? 2 #b1101) @result{} #t\n" | |
2864 | "(logbit? 3 #b1101) @result{} #t\n" | |
2865 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 2866 | "@end lisp") |
1bbd0b84 | 2867 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 2868 | { |
78166ad5 | 2869 | unsigned long int iindex; |
5efd3c7d | 2870 | iindex = scm_to_ulong (index); |
78166ad5 | 2871 | |
e11e83f3 | 2872 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
2873 | { |
2874 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 2875 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 2876 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 2877 | } |
0aacf84e MD |
2878 | else if (SCM_BIGP (j)) |
2879 | { | |
2880 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
2881 | scm_remember_upto_here_1 (j); | |
73e4de09 | 2882 | return scm_from_bool (val); |
0aacf84e MD |
2883 | } |
2884 | else | |
78166ad5 | 2885 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 2886 | } |
1bbd0b84 | 2887 | #undef FUNC_NAME |
0f2d19dd | 2888 | |
78166ad5 | 2889 | |
a1ec6916 | 2890 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 2891 | (SCM n), |
4d814788 | 2892 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
2893 | "argument.\n" |
2894 | "\n" | |
b380b885 MD |
2895 | "@lisp\n" |
2896 | "(number->string (lognot #b10000000) 2)\n" | |
2897 | " @result{} \"-10000001\"\n" | |
2898 | "(number->string (lognot #b0) 2)\n" | |
2899 | " @result{} \"-1\"\n" | |
1e6808ea | 2900 | "@end lisp") |
1bbd0b84 | 2901 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 2902 | { |
e11e83f3 | 2903 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
2904 | /* No overflow here, just need to toggle all the bits making up the inum. |
2905 | Enhancement: No need to strip the tag and add it back, could just xor | |
2906 | a block of 1 bits, if that worked with the various debug versions of | |
2907 | the SCM typedef. */ | |
e11e83f3 | 2908 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
2909 | |
2910 | } else if (SCM_BIGP (n)) { | |
2911 | SCM result = scm_i_mkbig (); | |
2912 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
2913 | scm_remember_upto_here_1 (n); | |
2914 | return result; | |
2915 | ||
2916 | } else { | |
2917 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
2918 | } | |
0f2d19dd | 2919 | } |
1bbd0b84 | 2920 | #undef FUNC_NAME |
0f2d19dd | 2921 | |
518b7508 KR |
2922 | /* returns 0 if IN is not an integer. OUT must already be |
2923 | initialized. */ | |
2924 | static int | |
2925 | coerce_to_big (SCM in, mpz_t out) | |
2926 | { | |
2927 | if (SCM_BIGP (in)) | |
2928 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
2929 | else if (SCM_I_INUMP (in)) |
2930 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
2931 | else |
2932 | return 0; | |
2933 | ||
2934 | return 1; | |
2935 | } | |
2936 | ||
d885e204 | 2937 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
2938 | (SCM n, SCM k, SCM m), |
2939 | "Return @var{n} raised to the integer exponent\n" | |
2940 | "@var{k}, modulo @var{m}.\n" | |
2941 | "\n" | |
2942 | "@lisp\n" | |
2943 | "(modulo-expt 2 3 5)\n" | |
2944 | " @result{} 3\n" | |
2945 | "@end lisp") | |
d885e204 | 2946 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
2947 | { |
2948 | mpz_t n_tmp; | |
2949 | mpz_t k_tmp; | |
2950 | mpz_t m_tmp; | |
2951 | ||
2952 | /* There are two classes of error we might encounter -- | |
2953 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
2954 | and | |
2955 | 2) wrong-type errors, which of course we'll report by calling | |
2956 | SCM_WRONG_TYPE_ARG. | |
2957 | We don't report those errors immediately, however; instead we do | |
2958 | some cleanup first. These variables tell us which error (if | |
2959 | any) we should report after cleaning up. | |
2960 | */ | |
2961 | int report_overflow = 0; | |
2962 | ||
2963 | int position_of_wrong_type = 0; | |
2964 | SCM value_of_wrong_type = SCM_INUM0; | |
2965 | ||
2966 | SCM result = SCM_UNDEFINED; | |
2967 | ||
2968 | mpz_init (n_tmp); | |
2969 | mpz_init (k_tmp); | |
2970 | mpz_init (m_tmp); | |
2971 | ||
bc36d050 | 2972 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
2973 | { |
2974 | report_overflow = 1; | |
2975 | goto cleanup; | |
2976 | } | |
2977 | ||
2978 | if (!coerce_to_big (n, n_tmp)) | |
2979 | { | |
2980 | value_of_wrong_type = n; | |
2981 | position_of_wrong_type = 1; | |
2982 | goto cleanup; | |
2983 | } | |
2984 | ||
2985 | if (!coerce_to_big (k, k_tmp)) | |
2986 | { | |
2987 | value_of_wrong_type = k; | |
2988 | position_of_wrong_type = 2; | |
2989 | goto cleanup; | |
2990 | } | |
2991 | ||
2992 | if (!coerce_to_big (m, m_tmp)) | |
2993 | { | |
2994 | value_of_wrong_type = m; | |
2995 | position_of_wrong_type = 3; | |
2996 | goto cleanup; | |
2997 | } | |
2998 | ||
2999 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
3000 | will get a divide-by-zero exception when an inverse 1/n mod m | |
3001 | doesn't exist (or is not unique). Since exceptions are hard to | |
3002 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
3003 | a simple failure code, which is easy to handle. */ | |
3004 | ||
3005 | if (-1 == mpz_sgn (k_tmp)) | |
3006 | { | |
3007 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
3008 | { | |
3009 | report_overflow = 1; | |
3010 | goto cleanup; | |
3011 | } | |
3012 | mpz_neg (k_tmp, k_tmp); | |
3013 | } | |
3014 | ||
3015 | result = scm_i_mkbig (); | |
3016 | mpz_powm (SCM_I_BIG_MPZ (result), | |
3017 | n_tmp, | |
3018 | k_tmp, | |
3019 | m_tmp); | |
b7b8c575 KR |
3020 | |
3021 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
3022 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
3023 | ||
518b7508 KR |
3024 | cleanup: |
3025 | mpz_clear (m_tmp); | |
3026 | mpz_clear (k_tmp); | |
3027 | mpz_clear (n_tmp); | |
3028 | ||
3029 | if (report_overflow) | |
3030 | scm_num_overflow (FUNC_NAME); | |
3031 | ||
3032 | if (position_of_wrong_type) | |
3033 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
3034 | value_of_wrong_type); | |
3035 | ||
3036 | return scm_i_normbig (result); | |
3037 | } | |
3038 | #undef FUNC_NAME | |
3039 | ||
a1ec6916 | 3040 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 3041 | (SCM n, SCM k), |
ba6e7231 KR |
3042 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
3043 | "exact integer, @var{n} can be any number.\n" | |
3044 | "\n" | |
2519490c MW |
3045 | "Negative @var{k} is supported, and results in\n" |
3046 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
3047 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 3048 | "includes @math{0^0} is 1.\n" |
1e6808ea | 3049 | "\n" |
b380b885 | 3050 | "@lisp\n" |
ba6e7231 KR |
3051 | "(integer-expt 2 5) @result{} 32\n" |
3052 | "(integer-expt -3 3) @result{} -27\n" | |
3053 | "(integer-expt 5 -3) @result{} 1/125\n" | |
3054 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 3055 | "@end lisp") |
1bbd0b84 | 3056 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 3057 | { |
e25f3727 | 3058 | scm_t_inum i2 = 0; |
1c35cb19 RB |
3059 | SCM z_i2 = SCM_BOOL_F; |
3060 | int i2_is_big = 0; | |
d956fa6f | 3061 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 3062 | |
bfe1f03a MW |
3063 | /* Specifically refrain from checking the type of the first argument. |
3064 | This allows us to exponentiate any object that can be multiplied. | |
3065 | If we must raise to a negative power, we must also be able to | |
3066 | take its reciprocal. */ | |
3067 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 3068 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 3069 | |
bfe1f03a MW |
3070 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
3071 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
3072 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
3073 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
3074 | /* The next check is necessary only because R6RS specifies different | |
3075 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
3076 | we simply skip this case and move on. */ | |
3077 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
3078 | { | |
3079 | /* k cannot be 0 at this point, because we | |
3080 | have already checked for that case above */ | |
3081 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
3082 | return n; |
3083 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
3084 | return scm_nan (); | |
3085 | } | |
ca46fb90 | 3086 | |
e11e83f3 MV |
3087 | if (SCM_I_INUMP (k)) |
3088 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
3089 | else if (SCM_BIGP (k)) |
3090 | { | |
3091 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
3092 | scm_remember_upto_here_1 (k); |
3093 | i2_is_big = 1; | |
3094 | } | |
2830fd91 | 3095 | else |
ca46fb90 RB |
3096 | SCM_WRONG_TYPE_ARG (2, k); |
3097 | ||
3098 | if (i2_is_big) | |
f872b822 | 3099 | { |
ca46fb90 RB |
3100 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
3101 | { | |
3102 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
3103 | n = scm_divide (n, SCM_UNDEFINED); | |
3104 | } | |
3105 | while (1) | |
3106 | { | |
3107 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
3108 | { | |
ca46fb90 RB |
3109 | return acc; |
3110 | } | |
3111 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
3112 | { | |
ca46fb90 RB |
3113 | return scm_product (acc, n); |
3114 | } | |
3115 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
3116 | acc = scm_product (acc, n); | |
3117 | n = scm_product (n, n); | |
3118 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
3119 | } | |
f872b822 | 3120 | } |
ca46fb90 | 3121 | else |
f872b822 | 3122 | { |
ca46fb90 RB |
3123 | if (i2 < 0) |
3124 | { | |
3125 | i2 = -i2; | |
3126 | n = scm_divide (n, SCM_UNDEFINED); | |
3127 | } | |
3128 | while (1) | |
3129 | { | |
3130 | if (0 == i2) | |
3131 | return acc; | |
3132 | if (1 == i2) | |
3133 | return scm_product (acc, n); | |
3134 | if (i2 & 1) | |
3135 | acc = scm_product (acc, n); | |
3136 | n = scm_product (n, n); | |
3137 | i2 >>= 1; | |
3138 | } | |
f872b822 | 3139 | } |
0f2d19dd | 3140 | } |
1bbd0b84 | 3141 | #undef FUNC_NAME |
0f2d19dd | 3142 | |
a1ec6916 | 3143 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 3144 | (SCM n, SCM cnt), |
32f19569 KR |
3145 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
3146 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 3147 | "\n" |
e7644cb2 | 3148 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
3149 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
3150 | "infinity. (Note that this is not the same rounding as\n" | |
3151 | "@code{quotient} does.)\n" | |
3152 | "\n" | |
3153 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
3154 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
3155 | "shift dropping bits.\n" | |
1e6808ea | 3156 | "\n" |
b380b885 | 3157 | "@lisp\n" |
1e6808ea MG |
3158 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
3159 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
3160 | "\n" |
3161 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
3162 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 3163 | "@end lisp") |
1bbd0b84 | 3164 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 3165 | { |
3ab9f56e | 3166 | long bits_to_shift; |
5efd3c7d | 3167 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 3168 | |
788aca27 KR |
3169 | if (SCM_I_INUMP (n)) |
3170 | { | |
e25f3727 | 3171 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
3172 | |
3173 | if (bits_to_shift > 0) | |
3174 | { | |
3175 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
3176 | overflow a non-zero fixnum. For smaller shifts we check the | |
3177 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
3178 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
3179 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
3180 | bits_to_shift)". */ | |
3181 | ||
3182 | if (nn == 0) | |
3183 | return n; | |
3184 | ||
3185 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3186 | && ((scm_t_bits) |
788aca27 KR |
3187 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
3188 | <= 1)) | |
3189 | { | |
3190 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
3191 | } | |
3192 | else | |
3193 | { | |
e25f3727 | 3194 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
3195 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3196 | bits_to_shift); | |
3197 | return result; | |
3198 | } | |
3199 | } | |
3200 | else | |
3201 | { | |
3202 | bits_to_shift = -bits_to_shift; | |
3203 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 3204 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
3205 | else |
3206 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
3207 | } | |
3208 | ||
3209 | } | |
3210 | else if (SCM_BIGP (n)) | |
ca46fb90 | 3211 | { |
788aca27 KR |
3212 | SCM result; |
3213 | ||
3214 | if (bits_to_shift == 0) | |
3215 | return n; | |
3216 | ||
3217 | result = scm_i_mkbig (); | |
3218 | if (bits_to_shift >= 0) | |
3219 | { | |
3220 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3221 | bits_to_shift); | |
3222 | return result; | |
3223 | } | |
ca46fb90 | 3224 | else |
788aca27 KR |
3225 | { |
3226 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
3227 | we have to allocate a bignum even if the result is going to be a | |
3228 | fixnum. */ | |
3229 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3230 | -bits_to_shift); | |
3231 | return scm_i_normbig (result); | |
3232 | } | |
3233 | ||
ca46fb90 RB |
3234 | } |
3235 | else | |
788aca27 KR |
3236 | { |
3237 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
3238 | } | |
0f2d19dd | 3239 | } |
1bbd0b84 | 3240 | #undef FUNC_NAME |
0f2d19dd | 3241 | |
3c9f20f8 | 3242 | |
a1ec6916 | 3243 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 3244 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
3245 | "Return the integer composed of the @var{start} (inclusive)\n" |
3246 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
3247 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
3248 | "\n" | |
b380b885 MD |
3249 | "@lisp\n" |
3250 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
3251 | " @result{} \"1010\"\n" | |
3252 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
3253 | " @result{} \"10110\"\n" | |
3254 | "@end lisp") | |
1bbd0b84 | 3255 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 3256 | { |
7f848242 | 3257 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
3258 | istart = scm_to_ulong (start); |
3259 | iend = scm_to_ulong (end); | |
c1bfcf60 | 3260 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 3261 | |
7f848242 KR |
3262 | /* how many bits to keep */ |
3263 | bits = iend - istart; | |
3264 | ||
e11e83f3 | 3265 | if (SCM_I_INUMP (n)) |
0aacf84e | 3266 | { |
e25f3727 | 3267 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
3268 | |
3269 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 3270 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 3271 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 3272 | |
0aacf84e MD |
3273 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
3274 | { | |
3275 | /* Since we emulate two's complement encoded numbers, this | |
3276 | * special case requires us to produce a result that has | |
7f848242 | 3277 | * more bits than can be stored in a fixnum. |
0aacf84e | 3278 | */ |
e25f3727 | 3279 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
3280 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3281 | bits); | |
3282 | return result; | |
0aacf84e | 3283 | } |
ac0c002c | 3284 | |
7f848242 | 3285 | /* mask down to requisite bits */ |
857ae6af | 3286 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 3287 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
3288 | } |
3289 | else if (SCM_BIGP (n)) | |
ac0c002c | 3290 | { |
7f848242 KR |
3291 | SCM result; |
3292 | if (bits == 1) | |
3293 | { | |
d956fa6f | 3294 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
3295 | } |
3296 | else | |
3297 | { | |
3298 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
3299 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
3300 | such bits into a ulong. */ | |
3301 | result = scm_i_mkbig (); | |
3302 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
3303 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
3304 | result = scm_i_normbig (result); | |
3305 | } | |
3306 | scm_remember_upto_here_1 (n); | |
3307 | return result; | |
ac0c002c | 3308 | } |
0aacf84e | 3309 | else |
78166ad5 | 3310 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 3311 | } |
1bbd0b84 | 3312 | #undef FUNC_NAME |
0f2d19dd | 3313 | |
7f848242 | 3314 | |
e4755e5c JB |
3315 | static const char scm_logtab[] = { |
3316 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
3317 | }; | |
1cc91f1b | 3318 | |
a1ec6916 | 3319 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 3320 | (SCM n), |
1e6808ea MG |
3321 | "Return the number of bits in integer @var{n}. If integer is\n" |
3322 | "positive, the 1-bits in its binary representation are counted.\n" | |
3323 | "If negative, the 0-bits in its two's-complement binary\n" | |
3324 | "representation are counted. If 0, 0 is returned.\n" | |
3325 | "\n" | |
b380b885 MD |
3326 | "@lisp\n" |
3327 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
3328 | " @result{} 4\n" |
3329 | "(logcount 0)\n" | |
3330 | " @result{} 0\n" | |
3331 | "(logcount -2)\n" | |
3332 | " @result{} 1\n" | |
3333 | "@end lisp") | |
3334 | #define FUNC_NAME s_scm_logcount | |
3335 | { | |
e11e83f3 | 3336 | if (SCM_I_INUMP (n)) |
f872b822 | 3337 | { |
e25f3727 AW |
3338 | unsigned long c = 0; |
3339 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
3340 | if (nn < 0) |
3341 | nn = -1 - nn; | |
3342 | while (nn) | |
3343 | { | |
3344 | c += scm_logtab[15 & nn]; | |
3345 | nn >>= 4; | |
3346 | } | |
d956fa6f | 3347 | return SCM_I_MAKINUM (c); |
f872b822 | 3348 | } |
ca46fb90 | 3349 | else if (SCM_BIGP (n)) |
f872b822 | 3350 | { |
ca46fb90 | 3351 | unsigned long count; |
713a4259 KR |
3352 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
3353 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 3354 | else |
713a4259 KR |
3355 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
3356 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3357 | return SCM_I_MAKINUM (count); |
f872b822 | 3358 | } |
ca46fb90 RB |
3359 | else |
3360 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 3361 | } |
ca46fb90 | 3362 | #undef FUNC_NAME |
0f2d19dd JB |
3363 | |
3364 | ||
ca46fb90 RB |
3365 | static const char scm_ilentab[] = { |
3366 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
3367 | }; | |
3368 | ||
0f2d19dd | 3369 | |
ca46fb90 RB |
3370 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
3371 | (SCM n), | |
3372 | "Return the number of bits necessary to represent @var{n}.\n" | |
3373 | "\n" | |
3374 | "@lisp\n" | |
3375 | "(integer-length #b10101010)\n" | |
3376 | " @result{} 8\n" | |
3377 | "(integer-length 0)\n" | |
3378 | " @result{} 0\n" | |
3379 | "(integer-length #b1111)\n" | |
3380 | " @result{} 4\n" | |
3381 | "@end lisp") | |
3382 | #define FUNC_NAME s_scm_integer_length | |
3383 | { | |
e11e83f3 | 3384 | if (SCM_I_INUMP (n)) |
0aacf84e | 3385 | { |
e25f3727 | 3386 | unsigned long c = 0; |
0aacf84e | 3387 | unsigned int l = 4; |
e25f3727 | 3388 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
3389 | if (nn < 0) |
3390 | nn = -1 - nn; | |
3391 | while (nn) | |
3392 | { | |
3393 | c += 4; | |
3394 | l = scm_ilentab [15 & nn]; | |
3395 | nn >>= 4; | |
3396 | } | |
d956fa6f | 3397 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
3398 | } |
3399 | else if (SCM_BIGP (n)) | |
3400 | { | |
3401 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
3402 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
3403 | 1 too big, so check for that and adjust. */ | |
3404 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
3405 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
3406 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
3407 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
3408 | size--; | |
3409 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3410 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
3411 | } |
3412 | else | |
ca46fb90 | 3413 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
3414 | } |
3415 | #undef FUNC_NAME | |
0f2d19dd JB |
3416 | |
3417 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
3418 | #define SCM_MAX_DBL_PREC 60 |
3419 | #define SCM_MAX_DBL_RADIX 36 | |
3420 | ||
3421 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
3422 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
3423 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
3424 | ||
3425 | static | |
3426 | void init_dblprec(int *prec, int radix) { | |
3427 | /* determine floating point precision by adding successively | |
3428 | smaller increments to 1.0 until it is considered == 1.0 */ | |
3429 | double f = ((double)1.0)/radix; | |
3430 | double fsum = 1.0 + f; | |
3431 | ||
3432 | *prec = 0; | |
3433 | while (fsum != 1.0) | |
3434 | { | |
3435 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
3436 | fsum = 1.0; | |
3437 | else | |
3438 | { | |
3439 | f /= radix; | |
3440 | fsum = f + 1.0; | |
3441 | } | |
3442 | } | |
3443 | (*prec) -= 1; | |
3444 | } | |
3445 | ||
3446 | static | |
3447 | void init_fx_radix(double *fx_list, int radix) | |
3448 | { | |
3449 | /* initialize a per-radix list of tolerances. When added | |
3450 | to a number < 1.0, we can determine if we should raund | |
3451 | up and quit converting a number to a string. */ | |
3452 | int i; | |
3453 | fx_list[0] = 0.0; | |
3454 | fx_list[1] = 0.5; | |
3455 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
3456 | fx_list[i] = (fx_list[i-1] / radix); | |
3457 | } | |
3458 | ||
3459 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 3460 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 3461 | |
1be6b49c | 3462 | static size_t |
0b799eea | 3463 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 3464 | { |
0b799eea MV |
3465 | int efmt, dpt, d, i, wp; |
3466 | double *fx; | |
3467 | #ifdef DBL_MIN_10_EXP | |
3468 | double f_cpy; | |
3469 | int exp_cpy; | |
3470 | #endif /* DBL_MIN_10_EXP */ | |
3471 | size_t ch = 0; | |
3472 | int exp = 0; | |
3473 | ||
3474 | if(radix < 2 || | |
3475 | radix > SCM_MAX_DBL_RADIX) | |
3476 | { | |
3477 | /* revert to existing behavior */ | |
3478 | radix = 10; | |
3479 | } | |
3480 | ||
3481 | wp = scm_dblprec[radix-2]; | |
3482 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 3483 | |
f872b822 | 3484 | if (f == 0.0) |
abb7e44d MV |
3485 | { |
3486 | #ifdef HAVE_COPYSIGN | |
3487 | double sgn = copysign (1.0, f); | |
3488 | ||
3489 | if (sgn < 0.0) | |
3490 | a[ch++] = '-'; | |
3491 | #endif | |
abb7e44d MV |
3492 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
3493 | } | |
7351e207 | 3494 | |
2e65b52f | 3495 | if (isinf (f)) |
7351e207 MV |
3496 | { |
3497 | if (f < 0) | |
3498 | strcpy (a, "-inf.0"); | |
3499 | else | |
3500 | strcpy (a, "+inf.0"); | |
3501 | return ch+6; | |
3502 | } | |
2e65b52f | 3503 | else if (isnan (f)) |
7351e207 MV |
3504 | { |
3505 | strcpy (a, "+nan.0"); | |
3506 | return ch+6; | |
3507 | } | |
3508 | ||
f872b822 MD |
3509 | if (f < 0.0) |
3510 | { | |
3511 | f = -f; | |
3512 | a[ch++] = '-'; | |
3513 | } | |
7351e207 | 3514 | |
f872b822 MD |
3515 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
3516 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
3517 | /* just do the checking...if it passes, we do the conversion for our |
3518 | radix again below */ | |
3519 | f_cpy = f; | |
3520 | exp_cpy = exp; | |
3521 | ||
3522 | while (f_cpy < 1.0) | |
f872b822 | 3523 | { |
0b799eea MV |
3524 | f_cpy *= 10.0; |
3525 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
3526 | { |
3527 | a[ch++] = '#'; | |
3528 | a[ch++] = '.'; | |
3529 | a[ch++] = '#'; | |
3530 | return ch; | |
3531 | } | |
f872b822 | 3532 | } |
0b799eea | 3533 | while (f_cpy > 10.0) |
f872b822 | 3534 | { |
0b799eea MV |
3535 | f_cpy *= 0.10; |
3536 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
3537 | { |
3538 | a[ch++] = '#'; | |
3539 | a[ch++] = '.'; | |
3540 | a[ch++] = '#'; | |
3541 | return ch; | |
3542 | } | |
f872b822 | 3543 | } |
0b799eea MV |
3544 | #endif |
3545 | ||
f872b822 MD |
3546 | while (f < 1.0) |
3547 | { | |
0b799eea | 3548 | f *= radix; |
f872b822 MD |
3549 | exp--; |
3550 | } | |
0b799eea | 3551 | while (f > radix) |
f872b822 | 3552 | { |
0b799eea | 3553 | f /= radix; |
f872b822 MD |
3554 | exp++; |
3555 | } | |
0b799eea MV |
3556 | |
3557 | if (f + fx[wp] >= radix) | |
f872b822 MD |
3558 | { |
3559 | f = 1.0; | |
3560 | exp++; | |
3561 | } | |
0f2d19dd | 3562 | zero: |
0b799eea MV |
3563 | #ifdef ENGNOT |
3564 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 3565 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
3566 | exp -= dpt++; |
3567 | efmt = 1; | |
f872b822 MD |
3568 | #else |
3569 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 3570 | if (!efmt) |
cda139a7 MD |
3571 | { |
3572 | if (exp < 0) | |
3573 | { | |
3574 | a[ch++] = '0'; | |
3575 | a[ch++] = '.'; | |
3576 | dpt = exp; | |
f872b822 MD |
3577 | while (++dpt) |
3578 | a[ch++] = '0'; | |
cda139a7 MD |
3579 | } |
3580 | else | |
f872b822 | 3581 | dpt = exp + 1; |
cda139a7 | 3582 | } |
0f2d19dd JB |
3583 | else |
3584 | dpt = 1; | |
f872b822 MD |
3585 | #endif |
3586 | ||
3587 | do | |
3588 | { | |
3589 | d = f; | |
3590 | f -= d; | |
0b799eea | 3591 | a[ch++] = number_chars[d]; |
f872b822 MD |
3592 | if (f < fx[wp]) |
3593 | break; | |
3594 | if (f + fx[wp] >= 1.0) | |
3595 | { | |
0b799eea | 3596 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
3597 | break; |
3598 | } | |
0b799eea | 3599 | f *= radix; |
f872b822 MD |
3600 | if (!(--dpt)) |
3601 | a[ch++] = '.'; | |
0f2d19dd | 3602 | } |
f872b822 | 3603 | while (wp--); |
0f2d19dd JB |
3604 | |
3605 | if (dpt > 0) | |
cda139a7 | 3606 | { |
f872b822 | 3607 | #ifndef ENGNOT |
cda139a7 MD |
3608 | if ((dpt > 4) && (exp > 6)) |
3609 | { | |
f872b822 | 3610 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 3611 | for (i = ch++; i > d; i--) |
f872b822 | 3612 | a[i] = a[i - 1]; |
cda139a7 MD |
3613 | a[d] = '.'; |
3614 | efmt = 1; | |
3615 | } | |
3616 | else | |
f872b822 | 3617 | #endif |
cda139a7 | 3618 | { |
f872b822 MD |
3619 | while (--dpt) |
3620 | a[ch++] = '0'; | |
cda139a7 MD |
3621 | a[ch++] = '.'; |
3622 | } | |
3623 | } | |
f872b822 MD |
3624 | if (a[ch - 1] == '.') |
3625 | a[ch++] = '0'; /* trailing zero */ | |
3626 | if (efmt && exp) | |
3627 | { | |
3628 | a[ch++] = 'e'; | |
3629 | if (exp < 0) | |
3630 | { | |
3631 | exp = -exp; | |
3632 | a[ch++] = '-'; | |
3633 | } | |
0b799eea MV |
3634 | for (i = radix; i <= exp; i *= radix); |
3635 | for (i /= radix; i; i /= radix) | |
f872b822 | 3636 | { |
0b799eea | 3637 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
3638 | exp %= i; |
3639 | } | |
0f2d19dd | 3640 | } |
0f2d19dd JB |
3641 | return ch; |
3642 | } | |
3643 | ||
7a1aba42 MV |
3644 | |
3645 | static size_t | |
3646 | icmplx2str (double real, double imag, char *str, int radix) | |
3647 | { | |
3648 | size_t i; | |
3649 | ||
3650 | i = idbl2str (real, str, radix); | |
3651 | if (imag != 0.0) | |
3652 | { | |
3653 | /* Don't output a '+' for negative numbers or for Inf and | |
3654 | NaN. They will provide their own sign. */ | |
2e65b52f | 3655 | if (0 <= imag && !isinf (imag) && !isnan (imag)) |
7a1aba42 MV |
3656 | str[i++] = '+'; |
3657 | i += idbl2str (imag, &str[i], radix); | |
3658 | str[i++] = 'i'; | |
3659 | } | |
3660 | return i; | |
3661 | } | |
3662 | ||
1be6b49c | 3663 | static size_t |
0b799eea | 3664 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 3665 | { |
1be6b49c | 3666 | size_t i; |
3c9a524f | 3667 | if (SCM_REALP (flt)) |
0b799eea | 3668 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 3669 | else |
7a1aba42 MV |
3670 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
3671 | str, radix); | |
0f2d19dd JB |
3672 | return i; |
3673 | } | |
0f2d19dd | 3674 | |
2881e77b | 3675 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
3676 | characters in the result. |
3677 | rad is output base | |
3678 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 3679 | size_t |
2881e77b MV |
3680 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
3681 | { | |
3682 | if (num < 0) | |
3683 | { | |
3684 | *p++ = '-'; | |
3685 | return scm_iuint2str (-num, rad, p) + 1; | |
3686 | } | |
3687 | else | |
3688 | return scm_iuint2str (num, rad, p); | |
3689 | } | |
3690 | ||
3691 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
3692 | characters in the result. | |
3693 | rad is output base | |
3694 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
3695 | size_t | |
3696 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 3697 | { |
1be6b49c ML |
3698 | size_t j = 1; |
3699 | size_t i; | |
2881e77b | 3700 | scm_t_uintmax n = num; |
5c11cc9d | 3701 | |
a6f3af16 AW |
3702 | if (rad < 2 || rad > 36) |
3703 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
3704 | ||
f872b822 | 3705 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
3706 | j++; |
3707 | ||
3708 | i = j; | |
2881e77b | 3709 | n = num; |
f872b822 MD |
3710 | while (i--) |
3711 | { | |
5c11cc9d GH |
3712 | int d = n % rad; |
3713 | ||
f872b822 | 3714 | n /= rad; |
a6f3af16 | 3715 | p[i] = number_chars[d]; |
f872b822 | 3716 | } |
0f2d19dd JB |
3717 | return j; |
3718 | } | |
3719 | ||
a1ec6916 | 3720 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
3721 | (SCM n, SCM radix), |
3722 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
3723 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
3724 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 3725 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 3726 | { |
1bbd0b84 | 3727 | int base; |
98cb6e75 | 3728 | |
0aacf84e | 3729 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 3730 | base = 10; |
0aacf84e | 3731 | else |
5efd3c7d | 3732 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 3733 | |
e11e83f3 | 3734 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
3735 | { |
3736 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 3737 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 3738 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
3739 | } |
3740 | else if (SCM_BIGP (n)) | |
3741 | { | |
3742 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
3743 | scm_remember_upto_here_1 (n); | |
cc95e00a | 3744 | return scm_take_locale_string (str); |
0aacf84e | 3745 | } |
f92e85f7 MV |
3746 | else if (SCM_FRACTIONP (n)) |
3747 | { | |
f92e85f7 | 3748 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 3749 | scm_from_locale_string ("/"), |
f92e85f7 MV |
3750 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
3751 | } | |
0aacf84e MD |
3752 | else if (SCM_INEXACTP (n)) |
3753 | { | |
3754 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 3755 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
3756 | } |
3757 | else | |
bb628794 | 3758 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 3759 | } |
1bbd0b84 | 3760 | #undef FUNC_NAME |
0f2d19dd JB |
3761 | |
3762 | ||
ca46fb90 RB |
3763 | /* These print routines used to be stubbed here so that scm_repl.c |
3764 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 3765 | |
0f2d19dd | 3766 | int |
e81d98ec | 3767 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3768 | { |
56e55ac7 | 3769 | char num_buf[FLOBUFLEN]; |
0b799eea | 3770 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
3771 | return !0; |
3772 | } | |
3773 | ||
b479fe9a MV |
3774 | void |
3775 | scm_i_print_double (double val, SCM port) | |
3776 | { | |
3777 | char num_buf[FLOBUFLEN]; | |
3778 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
3779 | } | |
3780 | ||
f3ae5d60 | 3781 | int |
e81d98ec | 3782 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 3783 | |
f3ae5d60 | 3784 | { |
56e55ac7 | 3785 | char num_buf[FLOBUFLEN]; |
0b799eea | 3786 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
3787 | return !0; |
3788 | } | |
1cc91f1b | 3789 | |
7a1aba42 MV |
3790 | void |
3791 | scm_i_print_complex (double real, double imag, SCM port) | |
3792 | { | |
3793 | char num_buf[FLOBUFLEN]; | |
3794 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
3795 | } | |
3796 | ||
f92e85f7 MV |
3797 | int |
3798 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
3799 | { | |
3800 | SCM str; | |
f92e85f7 | 3801 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 3802 | scm_display (str, port); |
f92e85f7 MV |
3803 | scm_remember_upto_here_1 (str); |
3804 | return !0; | |
3805 | } | |
3806 | ||
0f2d19dd | 3807 | int |
e81d98ec | 3808 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3809 | { |
ca46fb90 RB |
3810 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
3811 | scm_remember_upto_here_1 (exp); | |
3812 | scm_lfwrite (str, (size_t) strlen (str), port); | |
3813 | free (str); | |
0f2d19dd JB |
3814 | return !0; |
3815 | } | |
3816 | /*** END nums->strs ***/ | |
3817 | ||
3c9a524f | 3818 | |
0f2d19dd | 3819 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 3820 | |
3c9a524f DH |
3821 | /* The following functions implement the conversion from strings to numbers. |
3822 | * The implementation somehow follows the grammar for numbers as it is given | |
3823 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
3824 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
3825 | * points should be noted about the implementation: | |
3826 | * * Each function keeps a local index variable 'idx' that points at the | |
3827 | * current position within the parsed string. The global index is only | |
3828 | * updated if the function could parse the corresponding syntactic unit | |
3829 | * successfully. | |
3830 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
3831 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
3832 | * global exactness information is only updated after each part has been | |
3833 | * successfully parsed. | |
3834 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
3835 | * Only if these fixnums would overflow, the result variables are updated | |
3836 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
3837 | * the temporary variables holding the fixnums are cleared, and the process | |
3838 | * starts over again. If for example fixnums were able to store five decimal | |
3839 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
3840 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
3841 | * only every five digits two bignum operations were performed. | |
3842 | */ | |
3843 | ||
3844 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
3845 | ||
3846 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
3847 | ||
a6f3af16 AW |
3848 | /* Caller is responsible for checking that the return value is in range |
3849 | for the given radix, which should be <= 36. */ | |
3850 | static unsigned int | |
3851 | char_decimal_value (scm_t_uint32 c) | |
3852 | { | |
3853 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
3854 | that's certainly above any valid decimal, so we take advantage of | |
3855 | that to elide some tests. */ | |
3856 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
3857 | ||
3858 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
3859 | hexadecimals. */ | |
3860 | if (d >= 10U) | |
3861 | { | |
3862 | c = uc_tolower (c); | |
3863 | if (c >= (scm_t_uint32) 'a') | |
3864 | d = c - (scm_t_uint32)'a' + 10U; | |
3865 | } | |
3866 | return d; | |
3867 | } | |
3c9a524f | 3868 | |
2a8fecee | 3869 | static SCM |
3f47e526 | 3870 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 3871 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 3872 | { |
3c9a524f DH |
3873 | unsigned int idx = *p_idx; |
3874 | unsigned int hash_seen = 0; | |
3875 | scm_t_bits shift = 1; | |
3876 | scm_t_bits add = 0; | |
3877 | unsigned int digit_value; | |
3878 | SCM result; | |
3879 | char c; | |
3f47e526 | 3880 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3881 | |
3882 | if (idx == len) | |
3883 | return SCM_BOOL_F; | |
2a8fecee | 3884 | |
3f47e526 | 3885 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3886 | digit_value = char_decimal_value (c); |
3c9a524f DH |
3887 | if (digit_value >= radix) |
3888 | return SCM_BOOL_F; | |
3889 | ||
3890 | idx++; | |
d956fa6f | 3891 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 3892 | while (idx != len) |
f872b822 | 3893 | { |
3f47e526 | 3894 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3895 | if (c == '#') |
3c9a524f DH |
3896 | { |
3897 | hash_seen = 1; | |
3898 | digit_value = 0; | |
3899 | } | |
a6f3af16 AW |
3900 | else if (hash_seen) |
3901 | break; | |
3c9a524f | 3902 | else |
a6f3af16 AW |
3903 | { |
3904 | digit_value = char_decimal_value (c); | |
3905 | /* This check catches non-decimals in addition to out-of-range | |
3906 | decimals. */ | |
3907 | if (digit_value >= radix) | |
3908 | break; | |
3909 | } | |
3c9a524f DH |
3910 | |
3911 | idx++; | |
3912 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
3913 | { | |
d956fa6f | 3914 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3915 | if (add > 0) |
d956fa6f | 3916 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3917 | |
3918 | shift = radix; | |
3919 | add = digit_value; | |
3920 | } | |
3921 | else | |
3922 | { | |
3923 | shift = shift * radix; | |
3924 | add = add * radix + digit_value; | |
3925 | } | |
3926 | }; | |
3927 | ||
3928 | if (shift > 1) | |
d956fa6f | 3929 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3930 | if (add > 0) |
d956fa6f | 3931 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3932 | |
3933 | *p_idx = idx; | |
3934 | if (hash_seen) | |
3935 | *p_exactness = INEXACT; | |
3936 | ||
3937 | return result; | |
2a8fecee JB |
3938 | } |
3939 | ||
3940 | ||
3c9a524f DH |
3941 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
3942 | * covers the parts of the rules that start at a potential point. The value | |
3943 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
3944 | * in variable result. The content of *p_exactness indicates, whether a hash |
3945 | * has already been seen in the digits before the point. | |
3c9a524f | 3946 | */ |
1cc91f1b | 3947 | |
3f47e526 | 3948 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
3949 | |
3950 | static SCM | |
3f47e526 | 3951 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 3952 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 3953 | { |
3c9a524f DH |
3954 | unsigned int idx = *p_idx; |
3955 | enum t_exactness x = *p_exactness; | |
3f47e526 | 3956 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3957 | |
3958 | if (idx == len) | |
79d34f68 | 3959 | return result; |
3c9a524f | 3960 | |
3f47e526 | 3961 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
3962 | { |
3963 | scm_t_bits shift = 1; | |
3964 | scm_t_bits add = 0; | |
3965 | unsigned int digit_value; | |
cff5fa33 | 3966 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
3967 | |
3968 | idx++; | |
3969 | while (idx != len) | |
3970 | { | |
3f47e526 MG |
3971 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
3972 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
3973 | { |
3974 | if (x == INEXACT) | |
3975 | return SCM_BOOL_F; | |
3976 | else | |
3977 | digit_value = DIGIT2UINT (c); | |
3978 | } | |
3979 | else if (c == '#') | |
3980 | { | |
3981 | x = INEXACT; | |
3982 | digit_value = 0; | |
3983 | } | |
3984 | else | |
3985 | break; | |
3986 | ||
3987 | idx++; | |
3988 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
3989 | { | |
d956fa6f MV |
3990 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
3991 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 3992 | if (add > 0) |
d956fa6f | 3993 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3994 | |
3995 | shift = 10; | |
3996 | add = digit_value; | |
3997 | } | |
3998 | else | |
3999 | { | |
4000 | shift = shift * 10; | |
4001 | add = add * 10 + digit_value; | |
4002 | } | |
4003 | }; | |
4004 | ||
4005 | if (add > 0) | |
4006 | { | |
d956fa6f MV |
4007 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4008 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
4009 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
4010 | } |
4011 | ||
d8592269 | 4012 | result = scm_divide (result, big_shift); |
79d34f68 | 4013 | |
3c9a524f DH |
4014 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
4015 | x = INEXACT; | |
f872b822 | 4016 | } |
3c9a524f | 4017 | |
3c9a524f | 4018 | if (idx != len) |
f872b822 | 4019 | { |
3c9a524f DH |
4020 | int sign = 1; |
4021 | unsigned int start; | |
3f47e526 | 4022 | scm_t_wchar c; |
3c9a524f DH |
4023 | int exponent; |
4024 | SCM e; | |
4025 | ||
4026 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
4027 | ||
3f47e526 | 4028 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 4029 | { |
3c9a524f DH |
4030 | case 'd': case 'D': |
4031 | case 'e': case 'E': | |
4032 | case 'f': case 'F': | |
4033 | case 'l': case 'L': | |
4034 | case 's': case 'S': | |
4035 | idx++; | |
ee0ddd21 AW |
4036 | if (idx == len) |
4037 | return SCM_BOOL_F; | |
4038 | ||
3c9a524f | 4039 | start = idx; |
3f47e526 | 4040 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4041 | if (c == '-') |
4042 | { | |
4043 | idx++; | |
ee0ddd21 AW |
4044 | if (idx == len) |
4045 | return SCM_BOOL_F; | |
4046 | ||
3c9a524f | 4047 | sign = -1; |
3f47e526 | 4048 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4049 | } |
4050 | else if (c == '+') | |
4051 | { | |
4052 | idx++; | |
ee0ddd21 AW |
4053 | if (idx == len) |
4054 | return SCM_BOOL_F; | |
4055 | ||
3c9a524f | 4056 | sign = 1; |
3f47e526 | 4057 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4058 | } |
4059 | else | |
4060 | sign = 1; | |
4061 | ||
3f47e526 | 4062 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
4063 | return SCM_BOOL_F; |
4064 | ||
4065 | idx++; | |
4066 | exponent = DIGIT2UINT (c); | |
4067 | while (idx != len) | |
f872b822 | 4068 | { |
3f47e526 MG |
4069 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
4070 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
4071 | { |
4072 | idx++; | |
4073 | if (exponent <= SCM_MAXEXP) | |
4074 | exponent = exponent * 10 + DIGIT2UINT (c); | |
4075 | } | |
4076 | else | |
4077 | break; | |
f872b822 | 4078 | } |
3c9a524f DH |
4079 | |
4080 | if (exponent > SCM_MAXEXP) | |
f872b822 | 4081 | { |
3c9a524f | 4082 | size_t exp_len = idx - start; |
3f47e526 | 4083 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
4084 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
4085 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 4086 | } |
3c9a524f | 4087 | |
d956fa6f | 4088 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
4089 | if (sign == 1) |
4090 | result = scm_product (result, e); | |
4091 | else | |
f92e85f7 | 4092 | result = scm_divide2real (result, e); |
3c9a524f DH |
4093 | |
4094 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
4095 | x = INEXACT; | |
4096 | ||
f872b822 | 4097 | break; |
3c9a524f | 4098 | |
f872b822 | 4099 | default: |
3c9a524f | 4100 | break; |
f872b822 | 4101 | } |
0f2d19dd | 4102 | } |
3c9a524f DH |
4103 | |
4104 | *p_idx = idx; | |
4105 | if (x == INEXACT) | |
4106 | *p_exactness = x; | |
4107 | ||
4108 | return result; | |
0f2d19dd | 4109 | } |
0f2d19dd | 4110 | |
3c9a524f DH |
4111 | |
4112 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
4113 | ||
4114 | static SCM | |
3f47e526 | 4115 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 4116 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 4117 | { |
3c9a524f | 4118 | unsigned int idx = *p_idx; |
164d2481 | 4119 | SCM result; |
3f47e526 | 4120 | size_t len = scm_i_string_length (mem); |
3c9a524f | 4121 | |
40f89215 NJ |
4122 | /* Start off believing that the number will be exact. This changes |
4123 | to INEXACT if we see a decimal point or a hash. */ | |
4124 | enum t_exactness x = EXACT; | |
4125 | ||
3c9a524f DH |
4126 | if (idx == len) |
4127 | return SCM_BOOL_F; | |
4128 | ||
3f47e526 | 4129 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
4130 | { |
4131 | *p_idx = idx+5; | |
4132 | return scm_inf (); | |
4133 | } | |
4134 | ||
3f47e526 | 4135 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 4136 | { |
d8592269 MV |
4137 | /* Cobble up the fractional part. We might want to set the |
4138 | NaN's mantissa from it. */ | |
7351e207 | 4139 | idx += 4; |
3f47e526 | 4140 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
4141 | *p_idx = idx; |
4142 | return scm_nan (); | |
4143 | } | |
4144 | ||
3f47e526 | 4145 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
4146 | { |
4147 | if (radix != 10) | |
4148 | return SCM_BOOL_F; | |
4149 | else if (idx + 1 == len) | |
4150 | return SCM_BOOL_F; | |
3f47e526 | 4151 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
4152 | return SCM_BOOL_F; |
4153 | else | |
cff5fa33 | 4154 | result = mem2decimal_from_point (SCM_INUM0, mem, |
40f89215 | 4155 | p_idx, &x); |
f872b822 | 4156 | } |
3c9a524f DH |
4157 | else |
4158 | { | |
3c9a524f | 4159 | SCM uinteger; |
3c9a524f | 4160 | |
3f47e526 | 4161 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 4162 | if (scm_is_false (uinteger)) |
3c9a524f DH |
4163 | return SCM_BOOL_F; |
4164 | ||
4165 | if (idx == len) | |
4166 | result = uinteger; | |
3f47e526 | 4167 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 4168 | { |
3c9a524f DH |
4169 | SCM divisor; |
4170 | ||
4171 | idx++; | |
ee0ddd21 AW |
4172 | if (idx == len) |
4173 | return SCM_BOOL_F; | |
3c9a524f | 4174 | |
3f47e526 | 4175 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 4176 | if (scm_is_false (divisor)) |
3c9a524f DH |
4177 | return SCM_BOOL_F; |
4178 | ||
f92e85f7 | 4179 | /* both are int/big here, I assume */ |
cba42c93 | 4180 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 4181 | } |
3c9a524f DH |
4182 | else if (radix == 10) |
4183 | { | |
3f47e526 | 4184 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 4185 | if (scm_is_false (result)) |
3c9a524f DH |
4186 | return SCM_BOOL_F; |
4187 | } | |
4188 | else | |
4189 | result = uinteger; | |
4190 | ||
4191 | *p_idx = idx; | |
f872b822 | 4192 | } |
164d2481 | 4193 | |
40f89215 NJ |
4194 | /* Update *p_exactness if the number just read was inexact. This is |
4195 | important for complex numbers, so that a complex number is | |
4196 | treated as inexact overall if either its real or imaginary part | |
4197 | is inexact. | |
4198 | */ | |
4199 | if (x == INEXACT) | |
4200 | *p_exactness = x; | |
4201 | ||
164d2481 MV |
4202 | /* When returning an inexact zero, make sure it is represented as a |
4203 | floating point value so that we can change its sign. | |
4204 | */ | |
cff5fa33 | 4205 | if (scm_is_eq (result, SCM_INUM0) && *p_exactness == INEXACT) |
55f26379 | 4206 | result = scm_from_double (0.0); |
164d2481 MV |
4207 | |
4208 | return result; | |
3c9a524f | 4209 | } |
0f2d19dd | 4210 | |
0f2d19dd | 4211 | |
3c9a524f | 4212 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 4213 | |
3c9a524f | 4214 | static SCM |
3f47e526 | 4215 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
4216 | unsigned int radix, enum t_exactness *p_exactness) |
4217 | { | |
3f47e526 | 4218 | scm_t_wchar c; |
3c9a524f DH |
4219 | int sign = 0; |
4220 | SCM ureal; | |
3f47e526 | 4221 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4222 | |
4223 | if (idx == len) | |
4224 | return SCM_BOOL_F; | |
4225 | ||
3f47e526 | 4226 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4227 | if (c == '+') |
4228 | { | |
4229 | idx++; | |
4230 | sign = 1; | |
4231 | } | |
4232 | else if (c == '-') | |
4233 | { | |
4234 | idx++; | |
4235 | sign = -1; | |
0f2d19dd | 4236 | } |
0f2d19dd | 4237 | |
3c9a524f DH |
4238 | if (idx == len) |
4239 | return SCM_BOOL_F; | |
4240 | ||
3f47e526 | 4241 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 4242 | if (scm_is_false (ureal)) |
f872b822 | 4243 | { |
3c9a524f DH |
4244 | /* input must be either +i or -i */ |
4245 | ||
4246 | if (sign == 0) | |
4247 | return SCM_BOOL_F; | |
4248 | ||
3f47e526 MG |
4249 | if (scm_i_string_ref (mem, idx) == 'i' |
4250 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 4251 | { |
3c9a524f DH |
4252 | idx++; |
4253 | if (idx != len) | |
4254 | return SCM_BOOL_F; | |
4255 | ||
cff5fa33 | 4256 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 4257 | } |
3c9a524f DH |
4258 | else |
4259 | return SCM_BOOL_F; | |
0f2d19dd | 4260 | } |
3c9a524f DH |
4261 | else |
4262 | { | |
73e4de09 | 4263 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 4264 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 4265 | |
3c9a524f DH |
4266 | if (idx == len) |
4267 | return ureal; | |
4268 | ||
3f47e526 | 4269 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 4270 | switch (c) |
f872b822 | 4271 | { |
3c9a524f DH |
4272 | case 'i': case 'I': |
4273 | /* either +<ureal>i or -<ureal>i */ | |
4274 | ||
4275 | idx++; | |
4276 | if (sign == 0) | |
4277 | return SCM_BOOL_F; | |
4278 | if (idx != len) | |
4279 | return SCM_BOOL_F; | |
cff5fa33 | 4280 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
4281 | |
4282 | case '@': | |
4283 | /* polar input: <real>@<real>. */ | |
4284 | ||
4285 | idx++; | |
4286 | if (idx == len) | |
4287 | return SCM_BOOL_F; | |
4288 | else | |
f872b822 | 4289 | { |
3c9a524f DH |
4290 | int sign; |
4291 | SCM angle; | |
4292 | SCM result; | |
4293 | ||
3f47e526 | 4294 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4295 | if (c == '+') |
4296 | { | |
4297 | idx++; | |
ee0ddd21 AW |
4298 | if (idx == len) |
4299 | return SCM_BOOL_F; | |
3c9a524f DH |
4300 | sign = 1; |
4301 | } | |
4302 | else if (c == '-') | |
4303 | { | |
4304 | idx++; | |
ee0ddd21 AW |
4305 | if (idx == len) |
4306 | return SCM_BOOL_F; | |
3c9a524f DH |
4307 | sign = -1; |
4308 | } | |
4309 | else | |
4310 | sign = 1; | |
4311 | ||
3f47e526 | 4312 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 4313 | if (scm_is_false (angle)) |
3c9a524f DH |
4314 | return SCM_BOOL_F; |
4315 | if (idx != len) | |
4316 | return SCM_BOOL_F; | |
4317 | ||
73e4de09 | 4318 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
4319 | angle = scm_difference (angle, SCM_UNDEFINED); |
4320 | ||
4321 | result = scm_make_polar (ureal, angle); | |
4322 | return result; | |
f872b822 | 4323 | } |
3c9a524f DH |
4324 | case '+': |
4325 | case '-': | |
4326 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 4327 | |
3c9a524f DH |
4328 | idx++; |
4329 | if (idx == len) | |
4330 | return SCM_BOOL_F; | |
4331 | else | |
4332 | { | |
4333 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 4334 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 4335 | |
73e4de09 | 4336 | if (scm_is_false (imag)) |
d956fa6f | 4337 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 4338 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 4339 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 4340 | |
3c9a524f DH |
4341 | if (idx == len) |
4342 | return SCM_BOOL_F; | |
3f47e526 MG |
4343 | if (scm_i_string_ref (mem, idx) != 'i' |
4344 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 4345 | return SCM_BOOL_F; |
0f2d19dd | 4346 | |
3c9a524f DH |
4347 | idx++; |
4348 | if (idx != len) | |
4349 | return SCM_BOOL_F; | |
0f2d19dd | 4350 | |
1fe5e088 | 4351 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
4352 | } |
4353 | default: | |
4354 | return SCM_BOOL_F; | |
4355 | } | |
4356 | } | |
0f2d19dd | 4357 | } |
0f2d19dd JB |
4358 | |
4359 | ||
3c9a524f DH |
4360 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
4361 | ||
4362 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 4363 | |
0f2d19dd | 4364 | SCM |
3f47e526 | 4365 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 4366 | { |
3c9a524f DH |
4367 | unsigned int idx = 0; |
4368 | unsigned int radix = NO_RADIX; | |
4369 | enum t_exactness forced_x = NO_EXACTNESS; | |
4370 | enum t_exactness implicit_x = EXACT; | |
4371 | SCM result; | |
3f47e526 | 4372 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4373 | |
4374 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 4375 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 4376 | { |
3f47e526 | 4377 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
4378 | { |
4379 | case 'b': case 'B': | |
4380 | if (radix != NO_RADIX) | |
4381 | return SCM_BOOL_F; | |
4382 | radix = DUAL; | |
4383 | break; | |
4384 | case 'd': case 'D': | |
4385 | if (radix != NO_RADIX) | |
4386 | return SCM_BOOL_F; | |
4387 | radix = DEC; | |
4388 | break; | |
4389 | case 'i': case 'I': | |
4390 | if (forced_x != NO_EXACTNESS) | |
4391 | return SCM_BOOL_F; | |
4392 | forced_x = INEXACT; | |
4393 | break; | |
4394 | case 'e': case 'E': | |
4395 | if (forced_x != NO_EXACTNESS) | |
4396 | return SCM_BOOL_F; | |
4397 | forced_x = EXACT; | |
4398 | break; | |
4399 | case 'o': case 'O': | |
4400 | if (radix != NO_RADIX) | |
4401 | return SCM_BOOL_F; | |
4402 | radix = OCT; | |
4403 | break; | |
4404 | case 'x': case 'X': | |
4405 | if (radix != NO_RADIX) | |
4406 | return SCM_BOOL_F; | |
4407 | radix = HEX; | |
4408 | break; | |
4409 | default: | |
f872b822 | 4410 | return SCM_BOOL_F; |
3c9a524f DH |
4411 | } |
4412 | idx += 2; | |
4413 | } | |
4414 | ||
4415 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
4416 | if (radix == NO_RADIX) | |
3f47e526 | 4417 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 4418 | else |
3f47e526 | 4419 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 4420 | |
73e4de09 | 4421 | if (scm_is_false (result)) |
3c9a524f | 4422 | return SCM_BOOL_F; |
f872b822 | 4423 | |
3c9a524f | 4424 | switch (forced_x) |
f872b822 | 4425 | { |
3c9a524f DH |
4426 | case EXACT: |
4427 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
4428 | return scm_inexact_to_exact (result); |
4429 | else | |
4430 | return result; | |
4431 | case INEXACT: | |
4432 | if (SCM_INEXACTP (result)) | |
4433 | return result; | |
4434 | else | |
4435 | return scm_exact_to_inexact (result); | |
4436 | case NO_EXACTNESS: | |
4437 | default: | |
4438 | if (implicit_x == INEXACT) | |
4439 | { | |
4440 | if (SCM_INEXACTP (result)) | |
4441 | return result; | |
4442 | else | |
4443 | return scm_exact_to_inexact (result); | |
4444 | } | |
4445 | else | |
4446 | return result; | |
f872b822 | 4447 | } |
0f2d19dd JB |
4448 | } |
4449 | ||
3f47e526 MG |
4450 | SCM |
4451 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
4452 | unsigned int default_radix) | |
4453 | { | |
4454 | SCM str = scm_from_locale_stringn (mem, len); | |
4455 | ||
4456 | return scm_i_string_to_number (str, default_radix); | |
4457 | } | |
4458 | ||
0f2d19dd | 4459 | |
a1ec6916 | 4460 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 4461 | (SCM string, SCM radix), |
1e6808ea | 4462 | "Return a number of the maximally precise representation\n" |
942e5b91 | 4463 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
4464 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
4465 | "is a default radix that may be overridden by an explicit radix\n" | |
4466 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
4467 | "supplied, then the default radix is 10. If string is not a\n" | |
4468 | "syntactically valid notation for a number, then\n" | |
4469 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 4470 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
4471 | { |
4472 | SCM answer; | |
5efd3c7d | 4473 | unsigned int base; |
a6d9e5ab | 4474 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
4475 | |
4476 | if (SCM_UNBNDP (radix)) | |
4477 | base = 10; | |
4478 | else | |
4479 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
4480 | ||
3f47e526 | 4481 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
4482 | scm_remember_upto_here_1 (string); |
4483 | return answer; | |
0f2d19dd | 4484 | } |
1bbd0b84 | 4485 | #undef FUNC_NAME |
3c9a524f DH |
4486 | |
4487 | ||
0f2d19dd JB |
4488 | /*** END strs->nums ***/ |
4489 | ||
5986c47d | 4490 | |
8507ec80 MV |
4491 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
4492 | (SCM x), | |
4493 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
4494 | "otherwise.") | |
4495 | #define FUNC_NAME s_scm_number_p | |
4496 | { | |
4497 | return scm_from_bool (SCM_NUMBERP (x)); | |
4498 | } | |
4499 | #undef FUNC_NAME | |
4500 | ||
4501 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 4502 | (SCM x), |
942e5b91 | 4503 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 4504 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
4505 | "values form subsets of the set of complex numbers, i. e. the\n" |
4506 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
4507 | "rational or integer number.") | |
8507ec80 | 4508 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 4509 | { |
8507ec80 MV |
4510 | /* all numbers are complex. */ |
4511 | return scm_number_p (x); | |
0f2d19dd | 4512 | } |
1bbd0b84 | 4513 | #undef FUNC_NAME |
0f2d19dd | 4514 | |
f92e85f7 MV |
4515 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
4516 | (SCM x), | |
4517 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
4518 | "otherwise. Note that the set of integer values forms a subset of\n" | |
4519 | "the set of real numbers, i. e. the predicate will also be\n" | |
4520 | "fulfilled if @var{x} is an integer number.") | |
4521 | #define FUNC_NAME s_scm_real_p | |
4522 | { | |
c960e556 MW |
4523 | return scm_from_bool |
4524 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
4525 | } |
4526 | #undef FUNC_NAME | |
4527 | ||
4528 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 4529 | (SCM x), |
942e5b91 | 4530 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 4531 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 4532 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
4533 | "fulfilled if @var{x} is an integer number.") |
4534 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 4535 | { |
c960e556 | 4536 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
4537 | return SCM_BOOL_T; |
4538 | else if (SCM_REALP (x)) | |
c960e556 MW |
4539 | /* due to their limited precision, finite floating point numbers are |
4540 | rational as well. (finite means neither infinity nor a NaN) */ | |
4541 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 4542 | else |
bb628794 | 4543 | return SCM_BOOL_F; |
0f2d19dd | 4544 | } |
1bbd0b84 | 4545 | #undef FUNC_NAME |
0f2d19dd | 4546 | |
a1ec6916 | 4547 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 4548 | (SCM x), |
942e5b91 MG |
4549 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
4550 | "else.") | |
1bbd0b84 | 4551 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 4552 | { |
c960e556 | 4553 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 4554 | return SCM_BOOL_T; |
c960e556 MW |
4555 | else if (SCM_REALP (x)) |
4556 | { | |
4557 | double val = SCM_REAL_VALUE (x); | |
4558 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
4559 | } | |
4560 | else | |
8e43ed5d | 4561 | return SCM_BOOL_F; |
0f2d19dd | 4562 | } |
1bbd0b84 | 4563 | #undef FUNC_NAME |
0f2d19dd JB |
4564 | |
4565 | ||
8a1f4f98 AW |
4566 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
4567 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
4568 | (SCM x, SCM y, SCM rest), | |
4569 | "Return @code{#t} if all parameters are numerically equal.") | |
4570 | #define FUNC_NAME s_scm_i_num_eq_p | |
4571 | { | |
4572 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4573 | return SCM_BOOL_T; | |
4574 | while (!scm_is_null (rest)) | |
4575 | { | |
4576 | if (scm_is_false (scm_num_eq_p (x, y))) | |
4577 | return SCM_BOOL_F; | |
4578 | x = y; | |
4579 | y = scm_car (rest); | |
4580 | rest = scm_cdr (rest); | |
4581 | } | |
4582 | return scm_num_eq_p (x, y); | |
4583 | } | |
4584 | #undef FUNC_NAME | |
0f2d19dd | 4585 | SCM |
6e8d25a6 | 4586 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 4587 | { |
d8b95e27 | 4588 | again: |
e11e83f3 | 4589 | if (SCM_I_INUMP (x)) |
0aacf84e | 4590 | { |
e25f3727 | 4591 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 4592 | if (SCM_I_INUMP (y)) |
0aacf84e | 4593 | { |
e25f3727 | 4594 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 4595 | return scm_from_bool (xx == yy); |
0aacf84e MD |
4596 | } |
4597 | else if (SCM_BIGP (y)) | |
4598 | return SCM_BOOL_F; | |
4599 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
4600 | { |
4601 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
4602 | to a double and compare. | |
4603 | ||
4604 | But on a 64-bit system an inum is bigger than a double and | |
4605 | casting it to a double (call that dxx) will round. dxx is at | |
4606 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
4607 | an integer and fits a long. So we cast yy to a long and | |
4608 | compare with plain xx. | |
4609 | ||
4610 | An alternative (for any size system actually) would be to check | |
4611 | yy is an integer (with floor) and is in range of an inum | |
4612 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
4613 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
4614 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
4615 | |
4616 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
4617 | return scm_from_bool ((double) xx == yy |
4618 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4619 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 4620 | } |
0aacf84e | 4621 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4622 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4623 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
4624 | else if (SCM_FRACTIONP (y)) |
4625 | return SCM_BOOL_F; | |
0aacf84e | 4626 | else |
8a1f4f98 | 4627 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4628 | } |
0aacf84e MD |
4629 | else if (SCM_BIGP (x)) |
4630 | { | |
e11e83f3 | 4631 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4632 | return SCM_BOOL_F; |
4633 | else if (SCM_BIGP (y)) | |
4634 | { | |
4635 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4636 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4637 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4638 | } |
4639 | else if (SCM_REALP (y)) | |
4640 | { | |
4641 | int cmp; | |
2e65b52f | 4642 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4643 | return SCM_BOOL_F; |
4644 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4645 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4646 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4647 | } |
4648 | else if (SCM_COMPLEXP (y)) | |
4649 | { | |
4650 | int cmp; | |
4651 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
4652 | return SCM_BOOL_F; | |
2e65b52f | 4653 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
4654 | return SCM_BOOL_F; |
4655 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
4656 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4657 | return scm_from_bool (0 == cmp); |
0aacf84e | 4658 | } |
f92e85f7 MV |
4659 | else if (SCM_FRACTIONP (y)) |
4660 | return SCM_BOOL_F; | |
0aacf84e | 4661 | else |
8a1f4f98 | 4662 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4663 | } |
0aacf84e MD |
4664 | else if (SCM_REALP (x)) |
4665 | { | |
e8c5b1f2 | 4666 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 4667 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
4668 | { |
4669 | /* see comments with inum/real above */ | |
e25f3727 | 4670 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
4671 | return scm_from_bool (xx == (double) yy |
4672 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4673 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 4674 | } |
0aacf84e MD |
4675 | else if (SCM_BIGP (y)) |
4676 | { | |
4677 | int cmp; | |
2e65b52f | 4678 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4679 | return SCM_BOOL_F; |
4680 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4681 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4682 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4683 | } |
4684 | else if (SCM_REALP (y)) | |
73e4de09 | 4685 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 4686 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4687 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4688 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4689 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4690 | { |
4691 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4692 | if (isnan (xx)) |
d8b95e27 | 4693 | return SCM_BOOL_F; |
2e65b52f | 4694 | if (isinf (xx)) |
73e4de09 | 4695 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4696 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4697 | goto again; | |
4698 | } | |
0aacf84e | 4699 | else |
8a1f4f98 | 4700 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4701 | } |
0aacf84e MD |
4702 | else if (SCM_COMPLEXP (x)) |
4703 | { | |
e11e83f3 MV |
4704 | if (SCM_I_INUMP (y)) |
4705 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
4706 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4707 | else if (SCM_BIGP (y)) | |
4708 | { | |
4709 | int cmp; | |
4710 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
4711 | return SCM_BOOL_F; | |
2e65b52f | 4712 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
4713 | return SCM_BOOL_F; |
4714 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
4715 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4716 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4717 | } |
4718 | else if (SCM_REALP (y)) | |
73e4de09 | 4719 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
4720 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4721 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 4722 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4723 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4724 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4725 | { |
4726 | double xx; | |
4727 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
4728 | return SCM_BOOL_F; | |
4729 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 4730 | if (isnan (xx)) |
d8b95e27 | 4731 | return SCM_BOOL_F; |
2e65b52f | 4732 | if (isinf (xx)) |
73e4de09 | 4733 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4734 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4735 | goto again; | |
4736 | } | |
f92e85f7 | 4737 | else |
8a1f4f98 | 4738 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
4739 | } |
4740 | else if (SCM_FRACTIONP (x)) | |
4741 | { | |
e11e83f3 | 4742 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
4743 | return SCM_BOOL_F; |
4744 | else if (SCM_BIGP (y)) | |
4745 | return SCM_BOOL_F; | |
4746 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
4747 | { |
4748 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4749 | if (isnan (yy)) |
d8b95e27 | 4750 | return SCM_BOOL_F; |
2e65b52f | 4751 | if (isinf (yy)) |
73e4de09 | 4752 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4753 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4754 | goto again; | |
4755 | } | |
f92e85f7 | 4756 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
4757 | { |
4758 | double yy; | |
4759 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
4760 | return SCM_BOOL_F; | |
4761 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 4762 | if (isnan (yy)) |
d8b95e27 | 4763 | return SCM_BOOL_F; |
2e65b52f | 4764 | if (isinf (yy)) |
73e4de09 | 4765 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4766 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4767 | goto again; | |
4768 | } | |
f92e85f7 MV |
4769 | else if (SCM_FRACTIONP (y)) |
4770 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 4771 | else |
8a1f4f98 | 4772 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4773 | } |
0aacf84e | 4774 | else |
8a1f4f98 | 4775 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
4776 | } |
4777 | ||
4778 | ||
a5f0b599 KR |
4779 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
4780 | done are good for inums, but for bignums an answer can almost always be | |
4781 | had by just examining a few high bits of the operands, as done by GMP in | |
4782 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
4783 | of the float exponent to take into account. */ | |
4784 | ||
8c93b597 | 4785 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
4786 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
4787 | (SCM x, SCM y, SCM rest), | |
4788 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4789 | "increasing.") | |
4790 | #define FUNC_NAME s_scm_i_num_less_p | |
4791 | { | |
4792 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4793 | return SCM_BOOL_T; | |
4794 | while (!scm_is_null (rest)) | |
4795 | { | |
4796 | if (scm_is_false (scm_less_p (x, y))) | |
4797 | return SCM_BOOL_F; | |
4798 | x = y; | |
4799 | y = scm_car (rest); | |
4800 | rest = scm_cdr (rest); | |
4801 | } | |
4802 | return scm_less_p (x, y); | |
4803 | } | |
4804 | #undef FUNC_NAME | |
0f2d19dd | 4805 | SCM |
6e8d25a6 | 4806 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 4807 | { |
a5f0b599 | 4808 | again: |
e11e83f3 | 4809 | if (SCM_I_INUMP (x)) |
0aacf84e | 4810 | { |
e25f3727 | 4811 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4812 | if (SCM_I_INUMP (y)) |
0aacf84e | 4813 | { |
e25f3727 | 4814 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 4815 | return scm_from_bool (xx < yy); |
0aacf84e MD |
4816 | } |
4817 | else if (SCM_BIGP (y)) | |
4818 | { | |
4819 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4820 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4821 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
4822 | } |
4823 | else if (SCM_REALP (y)) | |
73e4de09 | 4824 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 4825 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4826 | { |
4827 | /* "x < a/b" becomes "x*b < a" */ | |
4828 | int_frac: | |
4829 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
4830 | y = SCM_FRACTION_NUMERATOR (y); | |
4831 | goto again; | |
4832 | } | |
0aacf84e | 4833 | else |
8a1f4f98 | 4834 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4835 | } |
0aacf84e MD |
4836 | else if (SCM_BIGP (x)) |
4837 | { | |
e11e83f3 | 4838 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4839 | { |
4840 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4841 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4842 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
4843 | } |
4844 | else if (SCM_BIGP (y)) | |
4845 | { | |
4846 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4847 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4848 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
4849 | } |
4850 | else if (SCM_REALP (y)) | |
4851 | { | |
4852 | int cmp; | |
2e65b52f | 4853 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4854 | return SCM_BOOL_F; |
4855 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4856 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4857 | return scm_from_bool (cmp < 0); |
0aacf84e | 4858 | } |
f92e85f7 | 4859 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 4860 | goto int_frac; |
0aacf84e | 4861 | else |
8a1f4f98 | 4862 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 4863 | } |
0aacf84e MD |
4864 | else if (SCM_REALP (x)) |
4865 | { | |
e11e83f3 MV |
4866 | if (SCM_I_INUMP (y)) |
4867 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
4868 | else if (SCM_BIGP (y)) |
4869 | { | |
4870 | int cmp; | |
2e65b52f | 4871 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4872 | return SCM_BOOL_F; |
4873 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4874 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4875 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
4876 | } |
4877 | else if (SCM_REALP (y)) | |
73e4de09 | 4878 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 4879 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4880 | { |
4881 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4882 | if (isnan (xx)) |
a5f0b599 | 4883 | return SCM_BOOL_F; |
2e65b52f | 4884 | if (isinf (xx)) |
73e4de09 | 4885 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
4886 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4887 | goto again; | |
4888 | } | |
f92e85f7 | 4889 | else |
8a1f4f98 | 4890 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
4891 | } |
4892 | else if (SCM_FRACTIONP (x)) | |
4893 | { | |
e11e83f3 | 4894 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
4895 | { |
4896 | /* "a/b < y" becomes "a < y*b" */ | |
4897 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
4898 | x = SCM_FRACTION_NUMERATOR (x); | |
4899 | goto again; | |
4900 | } | |
f92e85f7 | 4901 | else if (SCM_REALP (y)) |
a5f0b599 KR |
4902 | { |
4903 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4904 | if (isnan (yy)) |
a5f0b599 | 4905 | return SCM_BOOL_F; |
2e65b52f | 4906 | if (isinf (yy)) |
73e4de09 | 4907 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
4908 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4909 | goto again; | |
4910 | } | |
f92e85f7 | 4911 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4912 | { |
4913 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
4914 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
4915 | SCM_FRACTION_DENOMINATOR (y)); | |
4916 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
4917 | SCM_FRACTION_DENOMINATOR (x)); | |
4918 | x = new_x; | |
4919 | y = new_y; | |
4920 | goto again; | |
4921 | } | |
0aacf84e | 4922 | else |
8a1f4f98 | 4923 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4924 | } |
0aacf84e | 4925 | else |
8a1f4f98 | 4926 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
4927 | } |
4928 | ||
4929 | ||
8a1f4f98 AW |
4930 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
4931 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
4932 | (SCM x, SCM y, SCM rest), | |
4933 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4934 | "decreasing.") | |
4935 | #define FUNC_NAME s_scm_i_num_gr_p | |
4936 | { | |
4937 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4938 | return SCM_BOOL_T; | |
4939 | while (!scm_is_null (rest)) | |
4940 | { | |
4941 | if (scm_is_false (scm_gr_p (x, y))) | |
4942 | return SCM_BOOL_F; | |
4943 | x = y; | |
4944 | y = scm_car (rest); | |
4945 | rest = scm_cdr (rest); | |
4946 | } | |
4947 | return scm_gr_p (x, y); | |
4948 | } | |
4949 | #undef FUNC_NAME | |
4950 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
4951 | SCM |
4952 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 4953 | { |
c76b1eaf | 4954 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4955 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4956 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4957 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
4958 | else |
4959 | return scm_less_p (y, x); | |
0f2d19dd | 4960 | } |
1bbd0b84 | 4961 | #undef FUNC_NAME |
0f2d19dd JB |
4962 | |
4963 | ||
8a1f4f98 AW |
4964 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
4965 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
4966 | (SCM x, SCM y, SCM rest), | |
4967 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4968 | "non-decreasing.") | |
4969 | #define FUNC_NAME s_scm_i_num_leq_p | |
4970 | { | |
4971 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4972 | return SCM_BOOL_T; | |
4973 | while (!scm_is_null (rest)) | |
4974 | { | |
4975 | if (scm_is_false (scm_leq_p (x, y))) | |
4976 | return SCM_BOOL_F; | |
4977 | x = y; | |
4978 | y = scm_car (rest); | |
4979 | rest = scm_cdr (rest); | |
4980 | } | |
4981 | return scm_leq_p (x, y); | |
4982 | } | |
4983 | #undef FUNC_NAME | |
4984 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
4985 | SCM |
4986 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 4987 | { |
c76b1eaf | 4988 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4989 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4990 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4991 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 4992 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 4993 | return SCM_BOOL_F; |
c76b1eaf | 4994 | else |
73e4de09 | 4995 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 4996 | } |
1bbd0b84 | 4997 | #undef FUNC_NAME |
0f2d19dd JB |
4998 | |
4999 | ||
8a1f4f98 AW |
5000 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
5001 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
5002 | (SCM x, SCM y, SCM rest), | |
5003 | "Return @code{#t} if the list of parameters is monotonically\n" | |
5004 | "non-increasing.") | |
5005 | #define FUNC_NAME s_scm_i_num_geq_p | |
5006 | { | |
5007 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
5008 | return SCM_BOOL_T; | |
5009 | while (!scm_is_null (rest)) | |
5010 | { | |
5011 | if (scm_is_false (scm_geq_p (x, y))) | |
5012 | return SCM_BOOL_F; | |
5013 | x = y; | |
5014 | y = scm_car (rest); | |
5015 | rest = scm_cdr (rest); | |
5016 | } | |
5017 | return scm_geq_p (x, y); | |
5018 | } | |
5019 | #undef FUNC_NAME | |
5020 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
5021 | SCM |
5022 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 5023 | { |
c76b1eaf | 5024 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 5025 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 5026 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 5027 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 5028 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 5029 | return SCM_BOOL_F; |
c76b1eaf | 5030 | else |
73e4de09 | 5031 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 5032 | } |
1bbd0b84 | 5033 | #undef FUNC_NAME |
0f2d19dd JB |
5034 | |
5035 | ||
2519490c MW |
5036 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
5037 | (SCM z), | |
5038 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
5039 | "zero.") | |
5040 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 5041 | { |
e11e83f3 | 5042 | if (SCM_I_INUMP (z)) |
bc36d050 | 5043 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 5044 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5045 | return SCM_BOOL_F; |
0aacf84e | 5046 | else if (SCM_REALP (z)) |
73e4de09 | 5047 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 5048 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 5049 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 5050 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
5051 | else if (SCM_FRACTIONP (z)) |
5052 | return SCM_BOOL_F; | |
0aacf84e | 5053 | else |
2519490c | 5054 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 5055 | } |
2519490c | 5056 | #undef FUNC_NAME |
0f2d19dd JB |
5057 | |
5058 | ||
2519490c MW |
5059 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
5060 | (SCM x), | |
5061 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
5062 | "zero.") | |
5063 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 5064 | { |
e11e83f3 MV |
5065 | if (SCM_I_INUMP (x)) |
5066 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
5067 | else if (SCM_BIGP (x)) |
5068 | { | |
5069 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5070 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5071 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
5072 | } |
5073 | else if (SCM_REALP (x)) | |
73e4de09 | 5074 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
5075 | else if (SCM_FRACTIONP (x)) |
5076 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5077 | else |
2519490c | 5078 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 5079 | } |
2519490c | 5080 | #undef FUNC_NAME |
0f2d19dd JB |
5081 | |
5082 | ||
2519490c MW |
5083 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
5084 | (SCM x), | |
5085 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
5086 | "zero.") | |
5087 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 5088 | { |
e11e83f3 MV |
5089 | if (SCM_I_INUMP (x)) |
5090 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
5091 | else if (SCM_BIGP (x)) |
5092 | { | |
5093 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5094 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5095 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
5096 | } |
5097 | else if (SCM_REALP (x)) | |
73e4de09 | 5098 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
5099 | else if (SCM_FRACTIONP (x)) |
5100 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5101 | else |
2519490c | 5102 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 5103 | } |
2519490c | 5104 | #undef FUNC_NAME |
0f2d19dd JB |
5105 | |
5106 | ||
2a06f791 KR |
5107 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
5108 | required by r5rs. On that basis, for exact/inexact combinations the | |
5109 | exact is converted to inexact to compare and possibly return. This is | |
5110 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
5111 | its test, such trouble is not required for min and max. */ | |
5112 | ||
78d3deb1 AW |
5113 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
5114 | (SCM x, SCM y, SCM rest), | |
5115 | "Return the maximum of all parameter values.") | |
5116 | #define FUNC_NAME s_scm_i_max | |
5117 | { | |
5118 | while (!scm_is_null (rest)) | |
5119 | { x = scm_max (x, y); | |
5120 | y = scm_car (rest); | |
5121 | rest = scm_cdr (rest); | |
5122 | } | |
5123 | return scm_max (x, y); | |
5124 | } | |
5125 | #undef FUNC_NAME | |
5126 | ||
5127 | #define s_max s_scm_i_max | |
5128 | #define g_max g_scm_i_max | |
5129 | ||
0f2d19dd | 5130 | SCM |
6e8d25a6 | 5131 | scm_max (SCM x, SCM y) |
0f2d19dd | 5132 | { |
0aacf84e MD |
5133 | if (SCM_UNBNDP (y)) |
5134 | { | |
5135 | if (SCM_UNBNDP (x)) | |
5136 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 5137 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5138 | return x; |
5139 | else | |
5140 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 5141 | } |
f4c627b3 | 5142 | |
e11e83f3 | 5143 | if (SCM_I_INUMP (x)) |
0aacf84e | 5144 | { |
e25f3727 | 5145 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5146 | if (SCM_I_INUMP (y)) |
0aacf84e | 5147 | { |
e25f3727 | 5148 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5149 | return (xx < yy) ? y : x; |
5150 | } | |
5151 | else if (SCM_BIGP (y)) | |
5152 | { | |
5153 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5154 | scm_remember_upto_here_1 (y); | |
5155 | return (sgn < 0) ? x : y; | |
5156 | } | |
5157 | else if (SCM_REALP (y)) | |
5158 | { | |
2e274311 MW |
5159 | double xxd = xx; |
5160 | double yyd = SCM_REAL_VALUE (y); | |
5161 | ||
5162 | if (xxd > yyd) | |
5163 | return scm_from_double (xxd); | |
5164 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
5165 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5166 | return y; | |
5167 | /* Handle signed zeroes properly */ | |
5168 | else if (xx == 0) | |
5169 | return flo0; | |
5170 | else | |
5171 | return y; | |
0aacf84e | 5172 | } |
f92e85f7 MV |
5173 | else if (SCM_FRACTIONP (y)) |
5174 | { | |
e4bc5d6c | 5175 | use_less: |
73e4de09 | 5176 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 5177 | } |
0aacf84e MD |
5178 | else |
5179 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5180 | } |
0aacf84e MD |
5181 | else if (SCM_BIGP (x)) |
5182 | { | |
e11e83f3 | 5183 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5184 | { |
5185 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5186 | scm_remember_upto_here_1 (x); | |
5187 | return (sgn < 0) ? y : x; | |
5188 | } | |
5189 | else if (SCM_BIGP (y)) | |
5190 | { | |
5191 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5192 | scm_remember_upto_here_2 (x, y); | |
5193 | return (cmp > 0) ? x : y; | |
5194 | } | |
5195 | else if (SCM_REALP (y)) | |
5196 | { | |
2a06f791 KR |
5197 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
5198 | double xx, yy; | |
5199 | big_real: | |
5200 | xx = scm_i_big2dbl (x); | |
5201 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5202 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 5203 | } |
f92e85f7 MV |
5204 | else if (SCM_FRACTIONP (y)) |
5205 | { | |
e4bc5d6c | 5206 | goto use_less; |
f92e85f7 | 5207 | } |
0aacf84e MD |
5208 | else |
5209 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 5210 | } |
0aacf84e MD |
5211 | else if (SCM_REALP (x)) |
5212 | { | |
e11e83f3 | 5213 | if (SCM_I_INUMP (y)) |
0aacf84e | 5214 | { |
2e274311 MW |
5215 | scm_t_inum yy = SCM_I_INUM (y); |
5216 | double xxd = SCM_REAL_VALUE (x); | |
5217 | double yyd = yy; | |
5218 | ||
5219 | if (yyd > xxd) | |
5220 | return scm_from_double (yyd); | |
5221 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
5222 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5223 | return x; | |
5224 | /* Handle signed zeroes properly */ | |
5225 | else if (yy == 0) | |
5226 | return flo0; | |
5227 | else | |
5228 | return x; | |
0aacf84e MD |
5229 | } |
5230 | else if (SCM_BIGP (y)) | |
5231 | { | |
b6f8f763 | 5232 | SCM_SWAP (x, y); |
2a06f791 | 5233 | goto big_real; |
0aacf84e MD |
5234 | } |
5235 | else if (SCM_REALP (y)) | |
5236 | { | |
0aacf84e | 5237 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5238 | double yy = SCM_REAL_VALUE (y); |
5239 | ||
5240 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
5241 | if (xx > yy) | |
5242 | return x; | |
5243 | else if (SCM_LIKELY (xx < yy)) | |
5244 | return y; | |
5245 | /* If neither (xx > yy) nor (xx < yy), then | |
5246 | either they're equal or one is a NaN */ | |
5247 | else if (SCM_UNLIKELY (isnan (xx))) | |
5248 | return (isinf (yy) == 1) ? y : x; | |
5249 | else if (SCM_UNLIKELY (isnan (yy))) | |
5250 | return (isinf (xx) == 1) ? x : y; | |
5251 | /* xx == yy, but handle signed zeroes properly */ | |
5252 | else if (double_is_non_negative_zero (yy)) | |
5253 | return y; | |
5254 | else | |
5255 | return x; | |
0aacf84e | 5256 | } |
f92e85f7 MV |
5257 | else if (SCM_FRACTIONP (y)) |
5258 | { | |
5259 | double yy = scm_i_fraction2double (y); | |
5260 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5261 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
5262 | } |
5263 | else | |
5264 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
5265 | } | |
5266 | else if (SCM_FRACTIONP (x)) | |
5267 | { | |
e11e83f3 | 5268 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5269 | { |
e4bc5d6c | 5270 | goto use_less; |
f92e85f7 MV |
5271 | } |
5272 | else if (SCM_BIGP (y)) | |
5273 | { | |
e4bc5d6c | 5274 | goto use_less; |
f92e85f7 MV |
5275 | } |
5276 | else if (SCM_REALP (y)) | |
5277 | { | |
5278 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5279 | /* if y==NaN then ">" is false, so we return the NaN y */ |
5280 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5281 | } |
5282 | else if (SCM_FRACTIONP (y)) | |
5283 | { | |
e4bc5d6c | 5284 | goto use_less; |
f92e85f7 | 5285 | } |
0aacf84e MD |
5286 | else |
5287 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5288 | } |
0aacf84e | 5289 | else |
f4c627b3 | 5290 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
5291 | } |
5292 | ||
5293 | ||
78d3deb1 AW |
5294 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
5295 | (SCM x, SCM y, SCM rest), | |
5296 | "Return the minimum of all parameter values.") | |
5297 | #define FUNC_NAME s_scm_i_min | |
5298 | { | |
5299 | while (!scm_is_null (rest)) | |
5300 | { x = scm_min (x, y); | |
5301 | y = scm_car (rest); | |
5302 | rest = scm_cdr (rest); | |
5303 | } | |
5304 | return scm_min (x, y); | |
5305 | } | |
5306 | #undef FUNC_NAME | |
5307 | ||
5308 | #define s_min s_scm_i_min | |
5309 | #define g_min g_scm_i_min | |
5310 | ||
0f2d19dd | 5311 | SCM |
6e8d25a6 | 5312 | scm_min (SCM x, SCM y) |
0f2d19dd | 5313 | { |
0aacf84e MD |
5314 | if (SCM_UNBNDP (y)) |
5315 | { | |
5316 | if (SCM_UNBNDP (x)) | |
5317 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 5318 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5319 | return x; |
5320 | else | |
5321 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 5322 | } |
f4c627b3 | 5323 | |
e11e83f3 | 5324 | if (SCM_I_INUMP (x)) |
0aacf84e | 5325 | { |
e25f3727 | 5326 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5327 | if (SCM_I_INUMP (y)) |
0aacf84e | 5328 | { |
e25f3727 | 5329 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5330 | return (xx < yy) ? x : y; |
5331 | } | |
5332 | else if (SCM_BIGP (y)) | |
5333 | { | |
5334 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5335 | scm_remember_upto_here_1 (y); | |
5336 | return (sgn < 0) ? y : x; | |
5337 | } | |
5338 | else if (SCM_REALP (y)) | |
5339 | { | |
5340 | double z = xx; | |
5341 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 5342 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 5343 | } |
f92e85f7 MV |
5344 | else if (SCM_FRACTIONP (y)) |
5345 | { | |
e4bc5d6c | 5346 | use_less: |
73e4de09 | 5347 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 5348 | } |
0aacf84e MD |
5349 | else |
5350 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5351 | } |
0aacf84e MD |
5352 | else if (SCM_BIGP (x)) |
5353 | { | |
e11e83f3 | 5354 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5355 | { |
5356 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5357 | scm_remember_upto_here_1 (x); | |
5358 | return (sgn < 0) ? x : y; | |
5359 | } | |
5360 | else if (SCM_BIGP (y)) | |
5361 | { | |
5362 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5363 | scm_remember_upto_here_2 (x, y); | |
5364 | return (cmp > 0) ? y : x; | |
5365 | } | |
5366 | else if (SCM_REALP (y)) | |
5367 | { | |
2a06f791 KR |
5368 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
5369 | double xx, yy; | |
5370 | big_real: | |
5371 | xx = scm_i_big2dbl (x); | |
5372 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5373 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 5374 | } |
f92e85f7 MV |
5375 | else if (SCM_FRACTIONP (y)) |
5376 | { | |
e4bc5d6c | 5377 | goto use_less; |
f92e85f7 | 5378 | } |
0aacf84e MD |
5379 | else |
5380 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 5381 | } |
0aacf84e MD |
5382 | else if (SCM_REALP (x)) |
5383 | { | |
e11e83f3 | 5384 | if (SCM_I_INUMP (y)) |
0aacf84e | 5385 | { |
e11e83f3 | 5386 | double z = SCM_I_INUM (y); |
0aacf84e | 5387 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 5388 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
5389 | } |
5390 | else if (SCM_BIGP (y)) | |
5391 | { | |
b6f8f763 | 5392 | SCM_SWAP (x, y); |
2a06f791 | 5393 | goto big_real; |
0aacf84e MD |
5394 | } |
5395 | else if (SCM_REALP (y)) | |
5396 | { | |
0aacf84e | 5397 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5398 | double yy = SCM_REAL_VALUE (y); |
5399 | ||
5400 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
5401 | if (xx < yy) | |
5402 | return x; | |
5403 | else if (SCM_LIKELY (xx > yy)) | |
5404 | return y; | |
5405 | /* If neither (xx < yy) nor (xx > yy), then | |
5406 | either they're equal or one is a NaN */ | |
5407 | else if (SCM_UNLIKELY (isnan (xx))) | |
5408 | return (isinf (yy) == -1) ? y : x; | |
5409 | else if (SCM_UNLIKELY (isnan (yy))) | |
5410 | return (isinf (xx) == -1) ? x : y; | |
5411 | /* xx == yy, but handle signed zeroes properly */ | |
5412 | else if (double_is_non_negative_zero (xx)) | |
5413 | return y; | |
5414 | else | |
5415 | return x; | |
0aacf84e | 5416 | } |
f92e85f7 MV |
5417 | else if (SCM_FRACTIONP (y)) |
5418 | { | |
5419 | double yy = scm_i_fraction2double (y); | |
5420 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5421 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 5422 | } |
0aacf84e MD |
5423 | else |
5424 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5425 | } |
f92e85f7 MV |
5426 | else if (SCM_FRACTIONP (x)) |
5427 | { | |
e11e83f3 | 5428 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5429 | { |
e4bc5d6c | 5430 | goto use_less; |
f92e85f7 MV |
5431 | } |
5432 | else if (SCM_BIGP (y)) | |
5433 | { | |
e4bc5d6c | 5434 | goto use_less; |
f92e85f7 MV |
5435 | } |
5436 | else if (SCM_REALP (y)) | |
5437 | { | |
5438 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5439 | /* if y==NaN then "<" is false, so we return the NaN y */ |
5440 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5441 | } |
5442 | else if (SCM_FRACTIONP (y)) | |
5443 | { | |
e4bc5d6c | 5444 | goto use_less; |
f92e85f7 MV |
5445 | } |
5446 | else | |
78d3deb1 | 5447 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 5448 | } |
0aacf84e | 5449 | else |
f4c627b3 | 5450 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
5451 | } |
5452 | ||
5453 | ||
8ccd24f7 AW |
5454 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
5455 | (SCM x, SCM y, SCM rest), | |
5456 | "Return the sum of all parameter values. Return 0 if called without\n" | |
5457 | "any parameters." ) | |
5458 | #define FUNC_NAME s_scm_i_sum | |
5459 | { | |
5460 | while (!scm_is_null (rest)) | |
5461 | { x = scm_sum (x, y); | |
5462 | y = scm_car (rest); | |
5463 | rest = scm_cdr (rest); | |
5464 | } | |
5465 | return scm_sum (x, y); | |
5466 | } | |
5467 | #undef FUNC_NAME | |
5468 | ||
5469 | #define s_sum s_scm_i_sum | |
5470 | #define g_sum g_scm_i_sum | |
5471 | ||
0f2d19dd | 5472 | SCM |
6e8d25a6 | 5473 | scm_sum (SCM x, SCM y) |
0f2d19dd | 5474 | { |
9cc37597 | 5475 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5476 | { |
5477 | if (SCM_NUMBERP (x)) return x; | |
5478 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 5479 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 5480 | } |
c209c88e | 5481 | |
9cc37597 | 5482 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 5483 | { |
9cc37597 | 5484 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 5485 | { |
e25f3727 AW |
5486 | scm_t_inum xx = SCM_I_INUM (x); |
5487 | scm_t_inum yy = SCM_I_INUM (y); | |
5488 | scm_t_inum z = xx + yy; | |
5489 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
5490 | } |
5491 | else if (SCM_BIGP (y)) | |
5492 | { | |
5493 | SCM_SWAP (x, y); | |
5494 | goto add_big_inum; | |
5495 | } | |
5496 | else if (SCM_REALP (y)) | |
5497 | { | |
e25f3727 | 5498 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5499 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
5500 | } |
5501 | else if (SCM_COMPLEXP (y)) | |
5502 | { | |
e25f3727 | 5503 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5504 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
5505 | SCM_COMPLEX_IMAG (y)); |
5506 | } | |
f92e85f7 | 5507 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5508 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5509 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5510 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
5511 | else |
5512 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
5513 | } else if (SCM_BIGP (x)) |
5514 | { | |
e11e83f3 | 5515 | if (SCM_I_INUMP (y)) |
0aacf84e | 5516 | { |
e25f3727 | 5517 | scm_t_inum inum; |
0aacf84e MD |
5518 | int bigsgn; |
5519 | add_big_inum: | |
e11e83f3 | 5520 | inum = SCM_I_INUM (y); |
0aacf84e MD |
5521 | if (inum == 0) |
5522 | return x; | |
5523 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5524 | if (inum < 0) | |
5525 | { | |
5526 | SCM result = scm_i_mkbig (); | |
5527 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
5528 | scm_remember_upto_here_1 (x); | |
5529 | /* we know the result will have to be a bignum */ | |
5530 | if (bigsgn == -1) | |
5531 | return result; | |
5532 | return scm_i_normbig (result); | |
5533 | } | |
5534 | else | |
5535 | { | |
5536 | SCM result = scm_i_mkbig (); | |
5537 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
5538 | scm_remember_upto_here_1 (x); | |
5539 | /* we know the result will have to be a bignum */ | |
5540 | if (bigsgn == 1) | |
5541 | return result; | |
5542 | return scm_i_normbig (result); | |
5543 | } | |
5544 | } | |
5545 | else if (SCM_BIGP (y)) | |
5546 | { | |
5547 | SCM result = scm_i_mkbig (); | |
5548 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5549 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5550 | mpz_add (SCM_I_BIG_MPZ (result), | |
5551 | SCM_I_BIG_MPZ (x), | |
5552 | SCM_I_BIG_MPZ (y)); | |
5553 | scm_remember_upto_here_2 (x, y); | |
5554 | /* we know the result will have to be a bignum */ | |
5555 | if (sgn_x == sgn_y) | |
5556 | return result; | |
5557 | return scm_i_normbig (result); | |
5558 | } | |
5559 | else if (SCM_REALP (y)) | |
5560 | { | |
5561 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
5562 | scm_remember_upto_here_1 (x); | |
55f26379 | 5563 | return scm_from_double (result); |
0aacf84e MD |
5564 | } |
5565 | else if (SCM_COMPLEXP (y)) | |
5566 | { | |
5567 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5568 | + SCM_COMPLEX_REAL (y)); | |
5569 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5570 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5571 | } |
f92e85f7 | 5572 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5573 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5574 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5575 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5576 | else |
5577 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 5578 | } |
0aacf84e MD |
5579 | else if (SCM_REALP (x)) |
5580 | { | |
e11e83f3 | 5581 | if (SCM_I_INUMP (y)) |
55f26379 | 5582 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
5583 | else if (SCM_BIGP (y)) |
5584 | { | |
5585 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
5586 | scm_remember_upto_here_1 (y); | |
55f26379 | 5587 | return scm_from_double (result); |
0aacf84e MD |
5588 | } |
5589 | else if (SCM_REALP (y)) | |
55f26379 | 5590 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 5591 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5592 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5593 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5594 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5595 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
5596 | else |
5597 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 5598 | } |
0aacf84e MD |
5599 | else if (SCM_COMPLEXP (x)) |
5600 | { | |
e11e83f3 | 5601 | if (SCM_I_INUMP (y)) |
8507ec80 | 5602 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
5603 | SCM_COMPLEX_IMAG (x)); |
5604 | else if (SCM_BIGP (y)) | |
5605 | { | |
5606 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
5607 | + SCM_COMPLEX_REAL (x)); | |
5608 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5609 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
5610 | } |
5611 | else if (SCM_REALP (y)) | |
8507ec80 | 5612 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
5613 | SCM_COMPLEX_IMAG (x)); |
5614 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5615 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5616 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5617 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5618 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
5619 | SCM_COMPLEX_IMAG (x)); |
5620 | else | |
5621 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
5622 | } | |
5623 | else if (SCM_FRACTIONP (x)) | |
5624 | { | |
e11e83f3 | 5625 | if (SCM_I_INUMP (y)) |
cba42c93 | 5626 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5627 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5628 | SCM_FRACTION_DENOMINATOR (x)); | |
5629 | else if (SCM_BIGP (y)) | |
cba42c93 | 5630 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5631 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5632 | SCM_FRACTION_DENOMINATOR (x)); | |
5633 | else if (SCM_REALP (y)) | |
55f26379 | 5634 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 5635 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5636 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
5637 | SCM_COMPLEX_IMAG (y)); |
5638 | else if (SCM_FRACTIONP (y)) | |
5639 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 5640 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5641 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5642 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5643 | else |
5644 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 5645 | } |
0aacf84e | 5646 | else |
98cb6e75 | 5647 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
5648 | } |
5649 | ||
5650 | ||
40882e3d KR |
5651 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
5652 | (SCM x), | |
5653 | "Return @math{@var{x}+1}.") | |
5654 | #define FUNC_NAME s_scm_oneplus | |
5655 | { | |
cff5fa33 | 5656 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
5657 | } |
5658 | #undef FUNC_NAME | |
5659 | ||
5660 | ||
78d3deb1 AW |
5661 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
5662 | (SCM x, SCM y, SCM rest), | |
5663 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
5664 | "the sum of all but the first argument are subtracted from the first\n" | |
5665 | "argument.") | |
5666 | #define FUNC_NAME s_scm_i_difference | |
5667 | { | |
5668 | while (!scm_is_null (rest)) | |
5669 | { x = scm_difference (x, y); | |
5670 | y = scm_car (rest); | |
5671 | rest = scm_cdr (rest); | |
5672 | } | |
5673 | return scm_difference (x, y); | |
5674 | } | |
5675 | #undef FUNC_NAME | |
5676 | ||
5677 | #define s_difference s_scm_i_difference | |
5678 | #define g_difference g_scm_i_difference | |
5679 | ||
0f2d19dd | 5680 | SCM |
6e8d25a6 | 5681 | scm_difference (SCM x, SCM y) |
78d3deb1 | 5682 | #define FUNC_NAME s_difference |
0f2d19dd | 5683 | { |
9cc37597 | 5684 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5685 | { |
5686 | if (SCM_UNBNDP (x)) | |
5687 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
5688 | else | |
e11e83f3 | 5689 | if (SCM_I_INUMP (x)) |
ca46fb90 | 5690 | { |
e25f3727 | 5691 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 5692 | if (SCM_FIXABLE (xx)) |
d956fa6f | 5693 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 5694 | else |
e25f3727 | 5695 | return scm_i_inum2big (xx); |
ca46fb90 RB |
5696 | } |
5697 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
5698 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
5699 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
5700 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
5701 | else if (SCM_REALP (x)) | |
55f26379 | 5702 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 5703 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 5704 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 5705 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 5706 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 5707 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 5708 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
5709 | else |
5710 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 5711 | } |
ca46fb90 | 5712 | |
9cc37597 | 5713 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5714 | { |
9cc37597 | 5715 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5716 | { |
e25f3727 AW |
5717 | scm_t_inum xx = SCM_I_INUM (x); |
5718 | scm_t_inum yy = SCM_I_INUM (y); | |
5719 | scm_t_inum z = xx - yy; | |
0aacf84e | 5720 | if (SCM_FIXABLE (z)) |
d956fa6f | 5721 | return SCM_I_MAKINUM (z); |
0aacf84e | 5722 | else |
e25f3727 | 5723 | return scm_i_inum2big (z); |
0aacf84e MD |
5724 | } |
5725 | else if (SCM_BIGP (y)) | |
5726 | { | |
5727 | /* inum-x - big-y */ | |
e25f3727 | 5728 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 5729 | |
0aacf84e | 5730 | if (xx == 0) |
b5c40589 MW |
5731 | { |
5732 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
5733 | bignum, but negating that gives a fixnum. */ | |
5734 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
5735 | } | |
0aacf84e MD |
5736 | else |
5737 | { | |
5738 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5739 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5740 | |
0aacf84e MD |
5741 | if (xx >= 0) |
5742 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
5743 | else | |
5744 | { | |
5745 | /* x - y == -(y + -x) */ | |
5746 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
5747 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5748 | } | |
5749 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 5750 | |
0aacf84e MD |
5751 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
5752 | /* we know the result will have to be a bignum */ | |
5753 | return result; | |
5754 | else | |
5755 | return scm_i_normbig (result); | |
5756 | } | |
5757 | } | |
5758 | else if (SCM_REALP (y)) | |
5759 | { | |
e25f3727 | 5760 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5761 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
5762 | } |
5763 | else if (SCM_COMPLEXP (y)) | |
5764 | { | |
e25f3727 | 5765 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5766 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
5767 | - SCM_COMPLEX_IMAG (y)); |
5768 | } | |
f92e85f7 MV |
5769 | else if (SCM_FRACTIONP (y)) |
5770 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 5771 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5772 | SCM_FRACTION_NUMERATOR (y)), |
5773 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5774 | else |
5775 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 5776 | } |
0aacf84e MD |
5777 | else if (SCM_BIGP (x)) |
5778 | { | |
e11e83f3 | 5779 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5780 | { |
5781 | /* big-x - inum-y */ | |
e25f3727 | 5782 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 5783 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 5784 | |
0aacf84e MD |
5785 | scm_remember_upto_here_1 (x); |
5786 | if (sgn_x == 0) | |
c71b0706 | 5787 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 5788 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
5789 | else |
5790 | { | |
5791 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5792 | |
708f22c6 KR |
5793 | if (yy >= 0) |
5794 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
5795 | else | |
5796 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 5797 | scm_remember_upto_here_1 (x); |
ca46fb90 | 5798 | |
0aacf84e MD |
5799 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
5800 | /* we know the result will have to be a bignum */ | |
5801 | return result; | |
5802 | else | |
5803 | return scm_i_normbig (result); | |
5804 | } | |
5805 | } | |
5806 | else if (SCM_BIGP (y)) | |
5807 | { | |
5808 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5809 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5810 | SCM result = scm_i_mkbig (); | |
5811 | mpz_sub (SCM_I_BIG_MPZ (result), | |
5812 | SCM_I_BIG_MPZ (x), | |
5813 | SCM_I_BIG_MPZ (y)); | |
5814 | scm_remember_upto_here_2 (x, y); | |
5815 | /* we know the result will have to be a bignum */ | |
5816 | if ((sgn_x == 1) && (sgn_y == -1)) | |
5817 | return result; | |
5818 | if ((sgn_x == -1) && (sgn_y == 1)) | |
5819 | return result; | |
5820 | return scm_i_normbig (result); | |
5821 | } | |
5822 | else if (SCM_REALP (y)) | |
5823 | { | |
5824 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
5825 | scm_remember_upto_here_1 (x); | |
55f26379 | 5826 | return scm_from_double (result); |
0aacf84e MD |
5827 | } |
5828 | else if (SCM_COMPLEXP (y)) | |
5829 | { | |
5830 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5831 | - SCM_COMPLEX_REAL (y)); | |
5832 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5833 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5834 | } |
f92e85f7 | 5835 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5836 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5837 | SCM_FRACTION_NUMERATOR (y)), |
5838 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 5839 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 5840 | } |
0aacf84e MD |
5841 | else if (SCM_REALP (x)) |
5842 | { | |
e11e83f3 | 5843 | if (SCM_I_INUMP (y)) |
55f26379 | 5844 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
5845 | else if (SCM_BIGP (y)) |
5846 | { | |
5847 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5848 | scm_remember_upto_here_1 (x); | |
55f26379 | 5849 | return scm_from_double (result); |
0aacf84e MD |
5850 | } |
5851 | else if (SCM_REALP (y)) | |
55f26379 | 5852 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 5853 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5854 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5855 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5856 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5857 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
5858 | else |
5859 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5860 | } |
0aacf84e MD |
5861 | else if (SCM_COMPLEXP (x)) |
5862 | { | |
e11e83f3 | 5863 | if (SCM_I_INUMP (y)) |
8507ec80 | 5864 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
5865 | SCM_COMPLEX_IMAG (x)); |
5866 | else if (SCM_BIGP (y)) | |
5867 | { | |
5868 | double real_part = (SCM_COMPLEX_REAL (x) | |
5869 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
5870 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5871 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
5872 | } |
5873 | else if (SCM_REALP (y)) | |
8507ec80 | 5874 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
5875 | SCM_COMPLEX_IMAG (x)); |
5876 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5877 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5878 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5879 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5880 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
5881 | SCM_COMPLEX_IMAG (x)); |
5882 | else | |
5883 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
5884 | } | |
5885 | else if (SCM_FRACTIONP (x)) | |
5886 | { | |
e11e83f3 | 5887 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5888 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 5889 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5890 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5891 | SCM_FRACTION_DENOMINATOR (x)); | |
5892 | else if (SCM_BIGP (y)) | |
cba42c93 | 5893 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5894 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5895 | SCM_FRACTION_DENOMINATOR (x)); | |
5896 | else if (SCM_REALP (y)) | |
55f26379 | 5897 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 5898 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5899 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
5900 | -SCM_COMPLEX_IMAG (y)); |
5901 | else if (SCM_FRACTIONP (y)) | |
5902 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 5903 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5904 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5905 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5906 | else |
5907 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5908 | } |
0aacf84e | 5909 | else |
98cb6e75 | 5910 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 5911 | } |
c05e97b7 | 5912 | #undef FUNC_NAME |
0f2d19dd | 5913 | |
ca46fb90 | 5914 | |
40882e3d KR |
5915 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
5916 | (SCM x), | |
5917 | "Return @math{@var{x}-1}.") | |
5918 | #define FUNC_NAME s_scm_oneminus | |
5919 | { | |
cff5fa33 | 5920 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
5921 | } |
5922 | #undef FUNC_NAME | |
5923 | ||
5924 | ||
78d3deb1 AW |
5925 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
5926 | (SCM x, SCM y, SCM rest), | |
5927 | "Return the product of all arguments. If called without arguments,\n" | |
5928 | "1 is returned.") | |
5929 | #define FUNC_NAME s_scm_i_product | |
5930 | { | |
5931 | while (!scm_is_null (rest)) | |
5932 | { x = scm_product (x, y); | |
5933 | y = scm_car (rest); | |
5934 | rest = scm_cdr (rest); | |
5935 | } | |
5936 | return scm_product (x, y); | |
5937 | } | |
5938 | #undef FUNC_NAME | |
5939 | ||
5940 | #define s_product s_scm_i_product | |
5941 | #define g_product g_scm_i_product | |
5942 | ||
0f2d19dd | 5943 | SCM |
6e8d25a6 | 5944 | scm_product (SCM x, SCM y) |
0f2d19dd | 5945 | { |
9cc37597 | 5946 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
5947 | { |
5948 | if (SCM_UNBNDP (x)) | |
d956fa6f | 5949 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
5950 | else if (SCM_NUMBERP (x)) |
5951 | return x; | |
5952 | else | |
5953 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 5954 | } |
ca46fb90 | 5955 | |
9cc37597 | 5956 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5957 | { |
e25f3727 | 5958 | scm_t_inum xx; |
f4c627b3 | 5959 | |
5e791807 | 5960 | xinum: |
e11e83f3 | 5961 | xx = SCM_I_INUM (x); |
f4c627b3 | 5962 | |
0aacf84e MD |
5963 | switch (xx) |
5964 | { | |
5e791807 MW |
5965 | case 1: |
5966 | /* exact1 is the universal multiplicative identity */ | |
5967 | return y; | |
5968 | break; | |
5969 | case 0: | |
5970 | /* exact0 times a fixnum is exact0: optimize this case */ | |
5971 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
5972 | return SCM_INUM0; | |
5973 | /* if the other argument is inexact, the result is inexact, | |
5974 | and we must do the multiplication in order to handle | |
5975 | infinities and NaNs properly. */ | |
5976 | else if (SCM_REALP (y)) | |
5977 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
5978 | else if (SCM_COMPLEXP (y)) | |
5979 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
5980 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
5981 | /* we've already handled inexact numbers, | |
5982 | so y must be exact, and we return exact0 */ | |
5983 | else if (SCM_NUMP (y)) | |
5984 | return SCM_INUM0; | |
5985 | else | |
5986 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
5987 | break; | |
5988 | case -1: | |
b5c40589 | 5989 | /* |
5e791807 MW |
5990 | * This case is important for more than just optimization. |
5991 | * It handles the case of negating | |
b5c40589 MW |
5992 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
5993 | * which is a bignum that must be changed back into a fixnum. | |
5994 | * Failure to do so will cause the following to return #f: | |
5995 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
5996 | */ | |
b5c40589 MW |
5997 | return scm_difference(y, SCM_UNDEFINED); |
5998 | break; | |
0aacf84e | 5999 | } |
f4c627b3 | 6000 | |
9cc37597 | 6001 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6002 | { |
e25f3727 AW |
6003 | scm_t_inum yy = SCM_I_INUM (y); |
6004 | scm_t_inum kk = xx * yy; | |
d956fa6f | 6005 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 6006 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
6007 | return k; |
6008 | else | |
6009 | { | |
e25f3727 | 6010 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
6011 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
6012 | return scm_i_normbig (result); | |
6013 | } | |
6014 | } | |
6015 | else if (SCM_BIGP (y)) | |
6016 | { | |
6017 | SCM result = scm_i_mkbig (); | |
6018 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
6019 | scm_remember_upto_here_1 (y); | |
6020 | return result; | |
6021 | } | |
6022 | else if (SCM_REALP (y)) | |
55f26379 | 6023 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 6024 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6025 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 6026 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6027 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6028 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6029 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6030 | else |
6031 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6032 | } |
0aacf84e MD |
6033 | else if (SCM_BIGP (x)) |
6034 | { | |
e11e83f3 | 6035 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6036 | { |
6037 | SCM_SWAP (x, y); | |
5e791807 | 6038 | goto xinum; |
0aacf84e MD |
6039 | } |
6040 | else if (SCM_BIGP (y)) | |
6041 | { | |
6042 | SCM result = scm_i_mkbig (); | |
6043 | mpz_mul (SCM_I_BIG_MPZ (result), | |
6044 | SCM_I_BIG_MPZ (x), | |
6045 | SCM_I_BIG_MPZ (y)); | |
6046 | scm_remember_upto_here_2 (x, y); | |
6047 | return result; | |
6048 | } | |
6049 | else if (SCM_REALP (y)) | |
6050 | { | |
6051 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
6052 | scm_remember_upto_here_1 (x); | |
55f26379 | 6053 | return scm_from_double (result); |
0aacf84e MD |
6054 | } |
6055 | else if (SCM_COMPLEXP (y)) | |
6056 | { | |
6057 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
6058 | scm_remember_upto_here_1 (x); | |
8507ec80 | 6059 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
6060 | z * SCM_COMPLEX_IMAG (y)); |
6061 | } | |
f92e85f7 | 6062 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6063 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6064 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6065 | else |
6066 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6067 | } |
0aacf84e MD |
6068 | else if (SCM_REALP (x)) |
6069 | { | |
e11e83f3 | 6070 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6071 | { |
6072 | SCM_SWAP (x, y); | |
6073 | goto xinum; | |
6074 | } | |
0aacf84e MD |
6075 | else if (SCM_BIGP (y)) |
6076 | { | |
6077 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
6078 | scm_remember_upto_here_1 (y); | |
55f26379 | 6079 | return scm_from_double (result); |
0aacf84e MD |
6080 | } |
6081 | else if (SCM_REALP (y)) | |
55f26379 | 6082 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 6083 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6084 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 6085 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6086 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6087 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
6088 | else |
6089 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6090 | } |
0aacf84e MD |
6091 | else if (SCM_COMPLEXP (x)) |
6092 | { | |
e11e83f3 | 6093 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6094 | { |
6095 | SCM_SWAP (x, y); | |
6096 | goto xinum; | |
6097 | } | |
0aacf84e MD |
6098 | else if (SCM_BIGP (y)) |
6099 | { | |
6100 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6101 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6102 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 6103 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
6104 | } |
6105 | else if (SCM_REALP (y)) | |
8507ec80 | 6106 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
6107 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
6108 | else if (SCM_COMPLEXP (y)) | |
6109 | { | |
8507ec80 | 6110 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
6111 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
6112 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
6113 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
6114 | } | |
f92e85f7 MV |
6115 | else if (SCM_FRACTIONP (y)) |
6116 | { | |
6117 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6118 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
6119 | yy * SCM_COMPLEX_IMAG (x)); |
6120 | } | |
6121 | else | |
6122 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6123 | } | |
6124 | else if (SCM_FRACTIONP (x)) | |
6125 | { | |
e11e83f3 | 6126 | if (SCM_I_INUMP (y)) |
cba42c93 | 6127 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6128 | SCM_FRACTION_DENOMINATOR (x)); |
6129 | else if (SCM_BIGP (y)) | |
cba42c93 | 6130 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6131 | SCM_FRACTION_DENOMINATOR (x)); |
6132 | else if (SCM_REALP (y)) | |
55f26379 | 6133 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
6134 | else if (SCM_COMPLEXP (y)) |
6135 | { | |
6136 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 6137 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
6138 | xx * SCM_COMPLEX_IMAG (y)); |
6139 | } | |
6140 | else if (SCM_FRACTIONP (y)) | |
6141 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 6142 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6143 | SCM_FRACTION_NUMERATOR (y)), |
6144 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
6145 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
6146 | else |
6147 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6148 | } |
0aacf84e | 6149 | else |
f4c627b3 | 6150 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
6151 | } |
6152 | ||
7351e207 MV |
6153 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
6154 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
6155 | #define ALLOW_DIVIDE_BY_ZERO | |
6156 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
6157 | #endif | |
0f2d19dd | 6158 | |
ba74ef4e MV |
6159 | /* The code below for complex division is adapted from the GNU |
6160 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
6161 | this copyright: */ | |
6162 | ||
6163 | /**************************************************************** | |
6164 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
6165 | ||
6166 | Permission to use, copy, modify, and distribute this software | |
6167 | and its documentation for any purpose and without fee is hereby | |
6168 | granted, provided that the above copyright notice appear in all | |
6169 | copies and that both that the copyright notice and this | |
6170 | permission notice and warranty disclaimer appear in supporting | |
6171 | documentation, and that the names of AT&T Bell Laboratories or | |
6172 | Bellcore or any of their entities not be used in advertising or | |
6173 | publicity pertaining to distribution of the software without | |
6174 | specific, written prior permission. | |
6175 | ||
6176 | AT&T and Bellcore disclaim all warranties with regard to this | |
6177 | software, including all implied warranties of merchantability | |
6178 | and fitness. In no event shall AT&T or Bellcore be liable for | |
6179 | any special, indirect or consequential damages or any damages | |
6180 | whatsoever resulting from loss of use, data or profits, whether | |
6181 | in an action of contract, negligence or other tortious action, | |
6182 | arising out of or in connection with the use or performance of | |
6183 | this software. | |
6184 | ****************************************************************/ | |
6185 | ||
78d3deb1 AW |
6186 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
6187 | (SCM x, SCM y, SCM rest), | |
6188 | "Divide the first argument by the product of the remaining\n" | |
6189 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
6190 | "returned.") | |
6191 | #define FUNC_NAME s_scm_i_divide | |
6192 | { | |
6193 | while (!scm_is_null (rest)) | |
6194 | { x = scm_divide (x, y); | |
6195 | y = scm_car (rest); | |
6196 | rest = scm_cdr (rest); | |
6197 | } | |
6198 | return scm_divide (x, y); | |
6199 | } | |
6200 | #undef FUNC_NAME | |
6201 | ||
6202 | #define s_divide s_scm_i_divide | |
6203 | #define g_divide g_scm_i_divide | |
6204 | ||
f92e85f7 | 6205 | static SCM |
78d3deb1 AW |
6206 | do_divide (SCM x, SCM y, int inexact) |
6207 | #define FUNC_NAME s_divide | |
0f2d19dd | 6208 | { |
f8de44c1 DH |
6209 | double a; |
6210 | ||
9cc37597 | 6211 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
6212 | { |
6213 | if (SCM_UNBNDP (x)) | |
6214 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 6215 | else if (SCM_I_INUMP (x)) |
0aacf84e | 6216 | { |
e25f3727 | 6217 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
6218 | if (xx == 1 || xx == -1) |
6219 | return x; | |
7351e207 | 6220 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6221 | else if (xx == 0) |
6222 | scm_num_overflow (s_divide); | |
7351e207 | 6223 | #endif |
0aacf84e | 6224 | else |
f92e85f7 MV |
6225 | { |
6226 | if (inexact) | |
55f26379 | 6227 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 6228 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6229 | } |
0aacf84e MD |
6230 | } |
6231 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
6232 | { |
6233 | if (inexact) | |
55f26379 | 6234 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 6235 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6236 | } |
0aacf84e MD |
6237 | else if (SCM_REALP (x)) |
6238 | { | |
6239 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 6240 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6241 | if (xx == 0.0) |
6242 | scm_num_overflow (s_divide); | |
6243 | else | |
7351e207 | 6244 | #endif |
55f26379 | 6245 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
6246 | } |
6247 | else if (SCM_COMPLEXP (x)) | |
6248 | { | |
6249 | double r = SCM_COMPLEX_REAL (x); | |
6250 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 6251 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6252 | { |
6253 | double t = r / i; | |
6254 | double d = i * (1.0 + t * t); | |
8507ec80 | 6255 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
6256 | } |
6257 | else | |
6258 | { | |
6259 | double t = i / r; | |
6260 | double d = r * (1.0 + t * t); | |
8507ec80 | 6261 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
6262 | } |
6263 | } | |
f92e85f7 | 6264 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 6265 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 6266 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
6267 | else |
6268 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 6269 | } |
f8de44c1 | 6270 | |
9cc37597 | 6271 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 6272 | { |
e25f3727 | 6273 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 6274 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6275 | { |
e25f3727 | 6276 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6277 | if (yy == 0) |
6278 | { | |
7351e207 | 6279 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6280 | scm_num_overflow (s_divide); |
7351e207 | 6281 | #else |
55f26379 | 6282 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 6283 | #endif |
0aacf84e MD |
6284 | } |
6285 | else if (xx % yy != 0) | |
f92e85f7 MV |
6286 | { |
6287 | if (inexact) | |
55f26379 | 6288 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 6289 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6290 | } |
0aacf84e MD |
6291 | else |
6292 | { | |
e25f3727 | 6293 | scm_t_inum z = xx / yy; |
0aacf84e | 6294 | if (SCM_FIXABLE (z)) |
d956fa6f | 6295 | return SCM_I_MAKINUM (z); |
0aacf84e | 6296 | else |
e25f3727 | 6297 | return scm_i_inum2big (z); |
0aacf84e | 6298 | } |
f872b822 | 6299 | } |
0aacf84e | 6300 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
6301 | { |
6302 | if (inexact) | |
55f26379 | 6303 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 6304 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6305 | } |
0aacf84e MD |
6306 | else if (SCM_REALP (y)) |
6307 | { | |
6308 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6309 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6310 | if (yy == 0.0) |
6311 | scm_num_overflow (s_divide); | |
6312 | else | |
7351e207 | 6313 | #endif |
55f26379 | 6314 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 6315 | } |
0aacf84e MD |
6316 | else if (SCM_COMPLEXP (y)) |
6317 | { | |
6318 | a = xx; | |
6319 | complex_div: /* y _must_ be a complex number */ | |
6320 | { | |
6321 | double r = SCM_COMPLEX_REAL (y); | |
6322 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6323 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6324 | { |
6325 | double t = r / i; | |
6326 | double d = i * (1.0 + t * t); | |
8507ec80 | 6327 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
6328 | } |
6329 | else | |
6330 | { | |
6331 | double t = i / r; | |
6332 | double d = r * (1.0 + t * t); | |
8507ec80 | 6333 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
6334 | } |
6335 | } | |
6336 | } | |
f92e85f7 MV |
6337 | else if (SCM_FRACTIONP (y)) |
6338 | /* a / b/c = ac / b */ | |
cba42c93 | 6339 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6340 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6341 | else |
6342 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6343 | } |
0aacf84e MD |
6344 | else if (SCM_BIGP (x)) |
6345 | { | |
e11e83f3 | 6346 | if (SCM_I_INUMP (y)) |
0aacf84e | 6347 | { |
e25f3727 | 6348 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6349 | if (yy == 0) |
6350 | { | |
7351e207 | 6351 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6352 | scm_num_overflow (s_divide); |
7351e207 | 6353 | #else |
0aacf84e MD |
6354 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
6355 | scm_remember_upto_here_1 (x); | |
6356 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 6357 | #endif |
0aacf84e MD |
6358 | } |
6359 | else if (yy == 1) | |
6360 | return x; | |
6361 | else | |
6362 | { | |
6363 | /* FIXME: HMM, what are the relative performance issues here? | |
6364 | We need to test. Is it faster on average to test | |
6365 | divisible_p, then perform whichever operation, or is it | |
6366 | faster to perform the integer div opportunistically and | |
6367 | switch to real if there's a remainder? For now we take the | |
6368 | middle ground: test, then if divisible, use the faster div | |
6369 | func. */ | |
6370 | ||
e25f3727 | 6371 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
6372 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
6373 | ||
6374 | if (divisible_p) | |
6375 | { | |
6376 | SCM result = scm_i_mkbig (); | |
6377 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
6378 | scm_remember_upto_here_1 (x); | |
6379 | if (yy < 0) | |
6380 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
6381 | return scm_i_normbig (result); | |
6382 | } | |
6383 | else | |
f92e85f7 MV |
6384 | { |
6385 | if (inexact) | |
55f26379 | 6386 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 6387 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6388 | } |
0aacf84e MD |
6389 | } |
6390 | } | |
6391 | else if (SCM_BIGP (y)) | |
6392 | { | |
a4955a04 MW |
6393 | /* big_x / big_y */ |
6394 | if (inexact) | |
0aacf84e | 6395 | { |
a4955a04 MW |
6396 | /* It's easily possible for the ratio x/y to fit a double |
6397 | but one or both x and y be too big to fit a double, | |
6398 | hence the use of mpq_get_d rather than converting and | |
6399 | dividing. */ | |
6400 | mpq_t q; | |
6401 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
6402 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
6403 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
6404 | } |
6405 | else | |
6406 | { | |
a4955a04 MW |
6407 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
6408 | SCM_I_BIG_MPZ (y)); | |
6409 | if (divisible_p) | |
6410 | { | |
6411 | SCM result = scm_i_mkbig (); | |
6412 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
6413 | SCM_I_BIG_MPZ (x), | |
6414 | SCM_I_BIG_MPZ (y)); | |
6415 | scm_remember_upto_here_2 (x, y); | |
6416 | return scm_i_normbig (result); | |
6417 | } | |
6418 | else | |
6419 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
6420 | } |
6421 | } | |
6422 | else if (SCM_REALP (y)) | |
6423 | { | |
6424 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6425 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6426 | if (yy == 0.0) |
6427 | scm_num_overflow (s_divide); | |
6428 | else | |
7351e207 | 6429 | #endif |
55f26379 | 6430 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
6431 | } |
6432 | else if (SCM_COMPLEXP (y)) | |
6433 | { | |
6434 | a = scm_i_big2dbl (x); | |
6435 | goto complex_div; | |
6436 | } | |
f92e85f7 | 6437 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6438 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6439 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6440 | else |
6441 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6442 | } |
0aacf84e MD |
6443 | else if (SCM_REALP (x)) |
6444 | { | |
6445 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 6446 | if (SCM_I_INUMP (y)) |
0aacf84e | 6447 | { |
e25f3727 | 6448 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6449 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6450 | if (yy == 0) |
6451 | scm_num_overflow (s_divide); | |
6452 | else | |
7351e207 | 6453 | #endif |
55f26379 | 6454 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
6455 | } |
6456 | else if (SCM_BIGP (y)) | |
6457 | { | |
6458 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6459 | scm_remember_upto_here_1 (y); | |
55f26379 | 6460 | return scm_from_double (rx / dby); |
0aacf84e MD |
6461 | } |
6462 | else if (SCM_REALP (y)) | |
6463 | { | |
6464 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6465 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6466 | if (yy == 0.0) |
6467 | scm_num_overflow (s_divide); | |
6468 | else | |
7351e207 | 6469 | #endif |
55f26379 | 6470 | return scm_from_double (rx / yy); |
0aacf84e MD |
6471 | } |
6472 | else if (SCM_COMPLEXP (y)) | |
6473 | { | |
6474 | a = rx; | |
6475 | goto complex_div; | |
6476 | } | |
f92e85f7 | 6477 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6478 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
6479 | else |
6480 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6481 | } |
0aacf84e MD |
6482 | else if (SCM_COMPLEXP (x)) |
6483 | { | |
6484 | double rx = SCM_COMPLEX_REAL (x); | |
6485 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 6486 | if (SCM_I_INUMP (y)) |
0aacf84e | 6487 | { |
e25f3727 | 6488 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6489 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6490 | if (yy == 0) |
6491 | scm_num_overflow (s_divide); | |
6492 | else | |
7351e207 | 6493 | #endif |
0aacf84e MD |
6494 | { |
6495 | double d = yy; | |
8507ec80 | 6496 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
6497 | } |
6498 | } | |
6499 | else if (SCM_BIGP (y)) | |
6500 | { | |
6501 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6502 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6503 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
6504 | } |
6505 | else if (SCM_REALP (y)) | |
6506 | { | |
6507 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6508 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6509 | if (yy == 0.0) |
6510 | scm_num_overflow (s_divide); | |
6511 | else | |
7351e207 | 6512 | #endif |
8507ec80 | 6513 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
6514 | } |
6515 | else if (SCM_COMPLEXP (y)) | |
6516 | { | |
6517 | double ry = SCM_COMPLEX_REAL (y); | |
6518 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6519 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
6520 | { |
6521 | double t = ry / iy; | |
6522 | double d = iy * (1.0 + t * t); | |
8507ec80 | 6523 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
6524 | } |
6525 | else | |
6526 | { | |
6527 | double t = iy / ry; | |
6528 | double d = ry * (1.0 + t * t); | |
8507ec80 | 6529 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
6530 | } |
6531 | } | |
f92e85f7 MV |
6532 | else if (SCM_FRACTIONP (y)) |
6533 | { | |
6534 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6535 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 6536 | } |
0aacf84e MD |
6537 | else |
6538 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6539 | } |
f92e85f7 MV |
6540 | else if (SCM_FRACTIONP (x)) |
6541 | { | |
e11e83f3 | 6542 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6543 | { |
e25f3727 | 6544 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
6545 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
6546 | if (yy == 0) | |
6547 | scm_num_overflow (s_divide); | |
6548 | else | |
6549 | #endif | |
cba42c93 | 6550 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6551 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6552 | } | |
6553 | else if (SCM_BIGP (y)) | |
6554 | { | |
cba42c93 | 6555 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6556 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6557 | } | |
6558 | else if (SCM_REALP (y)) | |
6559 | { | |
6560 | double yy = SCM_REAL_VALUE (y); | |
6561 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6562 | if (yy == 0.0) | |
6563 | scm_num_overflow (s_divide); | |
6564 | else | |
6565 | #endif | |
55f26379 | 6566 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
6567 | } |
6568 | else if (SCM_COMPLEXP (y)) | |
6569 | { | |
6570 | a = scm_i_fraction2double (x); | |
6571 | goto complex_div; | |
6572 | } | |
6573 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 6574 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
6575 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
6576 | else | |
6577 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
6578 | } | |
0aacf84e | 6579 | else |
f8de44c1 | 6580 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 6581 | } |
f92e85f7 MV |
6582 | |
6583 | SCM | |
6584 | scm_divide (SCM x, SCM y) | |
6585 | { | |
78d3deb1 | 6586 | return do_divide (x, y, 0); |
f92e85f7 MV |
6587 | } |
6588 | ||
6589 | static SCM scm_divide2real (SCM x, SCM y) | |
6590 | { | |
78d3deb1 | 6591 | return do_divide (x, y, 1); |
f92e85f7 | 6592 | } |
c05e97b7 | 6593 | #undef FUNC_NAME |
0f2d19dd | 6594 | |
fa605590 | 6595 | |
0f2d19dd | 6596 | double |
3101f40f | 6597 | scm_c_truncate (double x) |
0f2d19dd | 6598 | { |
fa605590 KR |
6599 | #if HAVE_TRUNC |
6600 | return trunc (x); | |
6601 | #else | |
f872b822 MD |
6602 | if (x < 0.0) |
6603 | return -floor (-x); | |
6604 | return floor (x); | |
fa605590 | 6605 | #endif |
0f2d19dd | 6606 | } |
0f2d19dd | 6607 | |
3101f40f MV |
6608 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
6609 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
6610 | Then half-way cases are identified and adjusted down if the | |
6611 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
6612 | |
6613 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
6614 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
6615 | ||
6616 | An odd "result" value is identified with result/2 != floor(result/2). | |
6617 | This is done with plus_half, since that value is ready for use sooner in | |
6618 | a pipelined cpu, and we're already requiring plus_half == result. | |
6619 | ||
6620 | Note however that we need to be careful when x is big and already an | |
6621 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
6622 | us to return such a value, incorrectly. For instance if the hardware is | |
6623 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
6624 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
6625 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
6626 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
6627 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
6628 | ||
6629 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
6630 | x is already an integer. If it is then clearly that's the desired result | |
6631 | already. And if it's not then the exponent must be small enough to allow | |
6632 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
6633 | ||
0f2d19dd | 6634 | double |
3101f40f | 6635 | scm_c_round (double x) |
0f2d19dd | 6636 | { |
6187f48b KR |
6637 | double plus_half, result; |
6638 | ||
6639 | if (x == floor (x)) | |
6640 | return x; | |
6641 | ||
6642 | plus_half = x + 0.5; | |
6643 | result = floor (plus_half); | |
3101f40f | 6644 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
6645 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
6646 | ? result - 1 | |
6647 | : result); | |
0f2d19dd JB |
6648 | } |
6649 | ||
f92e85f7 MV |
6650 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
6651 | (SCM x), | |
6652 | "Round the number @var{x} towards zero.") | |
6653 | #define FUNC_NAME s_scm_truncate_number | |
6654 | { | |
73e4de09 | 6655 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6656 | return scm_floor (x); |
6657 | else | |
6658 | return scm_ceiling (x); | |
6659 | } | |
6660 | #undef FUNC_NAME | |
6661 | ||
f92e85f7 MV |
6662 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, |
6663 | (SCM x), | |
6664 | "Round the number @var{x} towards the nearest integer. " | |
6665 | "When it is exactly halfway between two integers, " | |
6666 | "round towards the even one.") | |
6667 | #define FUNC_NAME s_scm_round_number | |
6668 | { | |
e11e83f3 | 6669 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
6670 | return x; |
6671 | else if (SCM_REALP (x)) | |
3101f40f | 6672 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 6673 | else |
bae30667 KR |
6674 | { |
6675 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
6676 | single quotient+remainder division then examining to see which way | |
6677 | the rounding should go. */ | |
6678 | SCM plus_half = scm_sum (x, exactly_one_half); | |
6679 | SCM result = scm_floor (plus_half); | |
3101f40f | 6680 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
6681 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
6682 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 6683 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
6684 | else |
6685 | return result; | |
6686 | } | |
f92e85f7 MV |
6687 | } |
6688 | #undef FUNC_NAME | |
6689 | ||
6690 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
6691 | (SCM x), | |
6692 | "Round the number @var{x} towards minus infinity.") | |
6693 | #define FUNC_NAME s_scm_floor | |
6694 | { | |
e11e83f3 | 6695 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6696 | return x; |
6697 | else if (SCM_REALP (x)) | |
55f26379 | 6698 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6699 | else if (SCM_FRACTIONP (x)) |
6700 | { | |
6701 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6702 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6703 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6704 | { |
6705 | /* For positive x, rounding towards zero is correct. */ | |
6706 | return q; | |
6707 | } | |
6708 | else | |
6709 | { | |
6710 | /* For negative x, we need to return q-1 unless x is an | |
6711 | integer. But fractions are never integer, per our | |
6712 | assumptions. */ | |
cff5fa33 | 6713 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
6714 | } |
6715 | } | |
6716 | else | |
6717 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
6718 | } | |
6719 | #undef FUNC_NAME | |
6720 | ||
6721 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
6722 | (SCM x), | |
6723 | "Round the number @var{x} towards infinity.") | |
6724 | #define FUNC_NAME s_scm_ceiling | |
6725 | { | |
e11e83f3 | 6726 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6727 | return x; |
6728 | else if (SCM_REALP (x)) | |
55f26379 | 6729 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6730 | else if (SCM_FRACTIONP (x)) |
6731 | { | |
6732 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6733 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6734 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
6735 | { |
6736 | /* For negative x, rounding towards zero is correct. */ | |
6737 | return q; | |
6738 | } | |
6739 | else | |
6740 | { | |
6741 | /* For positive x, we need to return q+1 unless x is an | |
6742 | integer. But fractions are never integer, per our | |
6743 | assumptions. */ | |
cff5fa33 | 6744 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
6745 | } |
6746 | } | |
6747 | else | |
6748 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
6749 | } | |
6750 | #undef FUNC_NAME | |
0f2d19dd | 6751 | |
2519490c MW |
6752 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
6753 | (SCM x, SCM y), | |
6754 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 6755 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 6756 | { |
01c7284a MW |
6757 | if (scm_is_integer (y)) |
6758 | { | |
6759 | if (scm_is_true (scm_exact_p (y))) | |
6760 | return scm_integer_expt (x, y); | |
6761 | else | |
6762 | { | |
6763 | /* Here we handle the case where the exponent is an inexact | |
6764 | integer. We make the exponent exact in order to use | |
6765 | scm_integer_expt, and thus avoid the spurious imaginary | |
6766 | parts that may result from round-off errors in the general | |
6767 | e^(y log x) method below (for example when squaring a large | |
6768 | negative number). In this case, we must return an inexact | |
6769 | result for correctness. We also make the base inexact so | |
6770 | that scm_integer_expt will use fast inexact arithmetic | |
6771 | internally. Note that making the base inexact is not | |
6772 | sufficient to guarantee an inexact result, because | |
6773 | scm_integer_expt will return an exact 1 when the exponent | |
6774 | is 0, even if the base is inexact. */ | |
6775 | return scm_exact_to_inexact | |
6776 | (scm_integer_expt (scm_exact_to_inexact (x), | |
6777 | scm_inexact_to_exact (y))); | |
6778 | } | |
6779 | } | |
6fc4d012 AW |
6780 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
6781 | { | |
6782 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
6783 | } | |
2519490c | 6784 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 6785 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
6786 | else if (scm_is_complex (x)) |
6787 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
6788 | else | |
6789 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 6790 | } |
1bbd0b84 | 6791 | #undef FUNC_NAME |
0f2d19dd | 6792 | |
7f41099e MW |
6793 | /* sin/cos/tan/asin/acos/atan |
6794 | sinh/cosh/tanh/asinh/acosh/atanh | |
6795 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
6796 | Written by Jerry D. Hedden, (C) FSF. | |
6797 | See the file `COPYING' for terms applying to this program. */ | |
6798 | ||
ad79736c AW |
6799 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
6800 | (SCM z), | |
6801 | "Compute the sine of @var{z}.") | |
6802 | #define FUNC_NAME s_scm_sin | |
6803 | { | |
8deddc94 MW |
6804 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6805 | return z; /* sin(exact0) = exact0 */ | |
6806 | else if (scm_is_real (z)) | |
ad79736c AW |
6807 | return scm_from_double (sin (scm_to_double (z))); |
6808 | else if (SCM_COMPLEXP (z)) | |
6809 | { double x, y; | |
6810 | x = SCM_COMPLEX_REAL (z); | |
6811 | y = SCM_COMPLEX_IMAG (z); | |
6812 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
6813 | cos (x) * sinh (y)); | |
6814 | } | |
6815 | else | |
6816 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
6817 | } | |
6818 | #undef FUNC_NAME | |
0f2d19dd | 6819 | |
ad79736c AW |
6820 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
6821 | (SCM z), | |
6822 | "Compute the cosine of @var{z}.") | |
6823 | #define FUNC_NAME s_scm_cos | |
6824 | { | |
8deddc94 MW |
6825 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6826 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
6827 | else if (scm_is_real (z)) | |
ad79736c AW |
6828 | return scm_from_double (cos (scm_to_double (z))); |
6829 | else if (SCM_COMPLEXP (z)) | |
6830 | { double x, y; | |
6831 | x = SCM_COMPLEX_REAL (z); | |
6832 | y = SCM_COMPLEX_IMAG (z); | |
6833 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
6834 | -sin (x) * sinh (y)); | |
6835 | } | |
6836 | else | |
6837 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
6838 | } | |
6839 | #undef FUNC_NAME | |
6840 | ||
6841 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
6842 | (SCM z), | |
6843 | "Compute the tangent of @var{z}.") | |
6844 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 6845 | { |
8deddc94 MW |
6846 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6847 | return z; /* tan(exact0) = exact0 */ | |
6848 | else if (scm_is_real (z)) | |
ad79736c AW |
6849 | return scm_from_double (tan (scm_to_double (z))); |
6850 | else if (SCM_COMPLEXP (z)) | |
6851 | { double x, y, w; | |
6852 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6853 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6854 | w = cos (x) + cosh (y); | |
6855 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6856 | if (w == 0.0) | |
6857 | scm_num_overflow (s_scm_tan); | |
6858 | #endif | |
6859 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
6860 | } | |
6861 | else | |
6862 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
6863 | } | |
6864 | #undef FUNC_NAME | |
6865 | ||
6866 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
6867 | (SCM z), | |
6868 | "Compute the hyperbolic sine of @var{z}.") | |
6869 | #define FUNC_NAME s_scm_sinh | |
6870 | { | |
8deddc94 MW |
6871 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6872 | return z; /* sinh(exact0) = exact0 */ | |
6873 | else if (scm_is_real (z)) | |
ad79736c AW |
6874 | return scm_from_double (sinh (scm_to_double (z))); |
6875 | else if (SCM_COMPLEXP (z)) | |
6876 | { double x, y; | |
6877 | x = SCM_COMPLEX_REAL (z); | |
6878 | y = SCM_COMPLEX_IMAG (z); | |
6879 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
6880 | cosh (x) * sin (y)); | |
6881 | } | |
6882 | else | |
6883 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
6884 | } | |
6885 | #undef FUNC_NAME | |
6886 | ||
6887 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
6888 | (SCM z), | |
6889 | "Compute the hyperbolic cosine of @var{z}.") | |
6890 | #define FUNC_NAME s_scm_cosh | |
6891 | { | |
8deddc94 MW |
6892 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6893 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
6894 | else if (scm_is_real (z)) | |
ad79736c AW |
6895 | return scm_from_double (cosh (scm_to_double (z))); |
6896 | else if (SCM_COMPLEXP (z)) | |
6897 | { double x, y; | |
6898 | x = SCM_COMPLEX_REAL (z); | |
6899 | y = SCM_COMPLEX_IMAG (z); | |
6900 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
6901 | sinh (x) * sin (y)); | |
6902 | } | |
6903 | else | |
6904 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
6905 | } | |
6906 | #undef FUNC_NAME | |
6907 | ||
6908 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
6909 | (SCM z), | |
6910 | "Compute the hyperbolic tangent of @var{z}.") | |
6911 | #define FUNC_NAME s_scm_tanh | |
6912 | { | |
8deddc94 MW |
6913 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6914 | return z; /* tanh(exact0) = exact0 */ | |
6915 | else if (scm_is_real (z)) | |
ad79736c AW |
6916 | return scm_from_double (tanh (scm_to_double (z))); |
6917 | else if (SCM_COMPLEXP (z)) | |
6918 | { double x, y, w; | |
6919 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6920 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6921 | w = cosh (x) + cos (y); | |
6922 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6923 | if (w == 0.0) | |
6924 | scm_num_overflow (s_scm_tanh); | |
6925 | #endif | |
6926 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
6927 | } | |
6928 | else | |
6929 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
6930 | } | |
6931 | #undef FUNC_NAME | |
6932 | ||
6933 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
6934 | (SCM z), | |
6935 | "Compute the arc sine of @var{z}.") | |
6936 | #define FUNC_NAME s_scm_asin | |
6937 | { | |
8deddc94 MW |
6938 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6939 | return z; /* asin(exact0) = exact0 */ | |
6940 | else if (scm_is_real (z)) | |
ad79736c AW |
6941 | { |
6942 | double w = scm_to_double (z); | |
6943 | if (w >= -1.0 && w <= 1.0) | |
6944 | return scm_from_double (asin (w)); | |
6945 | else | |
6946 | return scm_product (scm_c_make_rectangular (0, -1), | |
6947 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
6948 | } | |
6949 | else if (SCM_COMPLEXP (z)) | |
6950 | { double x, y; | |
6951 | x = SCM_COMPLEX_REAL (z); | |
6952 | y = SCM_COMPLEX_IMAG (z); | |
6953 | return scm_product (scm_c_make_rectangular (0, -1), | |
6954 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
6955 | } | |
6956 | else | |
6957 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
6958 | } | |
6959 | #undef FUNC_NAME | |
6960 | ||
6961 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
6962 | (SCM z), | |
6963 | "Compute the arc cosine of @var{z}.") | |
6964 | #define FUNC_NAME s_scm_acos | |
6965 | { | |
8deddc94 MW |
6966 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
6967 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
6968 | else if (scm_is_real (z)) | |
ad79736c AW |
6969 | { |
6970 | double w = scm_to_double (z); | |
6971 | if (w >= -1.0 && w <= 1.0) | |
6972 | return scm_from_double (acos (w)); | |
6973 | else | |
6974 | return scm_sum (scm_from_double (acos (0.0)), | |
6975 | scm_product (scm_c_make_rectangular (0, 1), | |
6976 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
6977 | } | |
6978 | else if (SCM_COMPLEXP (z)) | |
6979 | { double x, y; | |
6980 | x = SCM_COMPLEX_REAL (z); | |
6981 | y = SCM_COMPLEX_IMAG (z); | |
6982 | return scm_sum (scm_from_double (acos (0.0)), | |
6983 | scm_product (scm_c_make_rectangular (0, 1), | |
6984 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
6985 | } | |
6986 | else | |
6987 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
6988 | } | |
6989 | #undef FUNC_NAME | |
6990 | ||
6991 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
6992 | (SCM z, SCM y), | |
6993 | "With one argument, compute the arc tangent of @var{z}.\n" | |
6994 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
6995 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
6996 | #define FUNC_NAME s_scm_atan | |
6997 | { | |
6998 | if (SCM_UNBNDP (y)) | |
6999 | { | |
8deddc94 MW |
7000 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7001 | return z; /* atan(exact0) = exact0 */ | |
7002 | else if (scm_is_real (z)) | |
ad79736c AW |
7003 | return scm_from_double (atan (scm_to_double (z))); |
7004 | else if (SCM_COMPLEXP (z)) | |
7005 | { | |
7006 | double v, w; | |
7007 | v = SCM_COMPLEX_REAL (z); | |
7008 | w = SCM_COMPLEX_IMAG (z); | |
7009 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
7010 | scm_c_make_rectangular (v, w + 1.0))), | |
7011 | scm_c_make_rectangular (0, 2)); | |
7012 | } | |
7013 | else | |
7014 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7015 | } | |
7016 | else if (scm_is_real (z)) | |
7017 | { | |
7018 | if (scm_is_real (y)) | |
7019 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
7020 | else | |
7021 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
7022 | } | |
7023 | else | |
7024 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7025 | } | |
7026 | #undef FUNC_NAME | |
7027 | ||
7028 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
7029 | (SCM z), | |
7030 | "Compute the inverse hyperbolic sine of @var{z}.") | |
7031 | #define FUNC_NAME s_scm_sys_asinh | |
7032 | { | |
8deddc94 MW |
7033 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7034 | return z; /* asinh(exact0) = exact0 */ | |
7035 | else if (scm_is_real (z)) | |
ad79736c AW |
7036 | return scm_from_double (asinh (scm_to_double (z))); |
7037 | else if (scm_is_number (z)) | |
7038 | return scm_log (scm_sum (z, | |
7039 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 7040 | SCM_INUM1)))); |
ad79736c AW |
7041 | else |
7042 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
7043 | } | |
7044 | #undef FUNC_NAME | |
7045 | ||
7046 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
7047 | (SCM z), | |
7048 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
7049 | #define FUNC_NAME s_scm_sys_acosh | |
7050 | { | |
8deddc94 MW |
7051 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
7052 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
7053 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
7054 | return scm_from_double (acosh (scm_to_double (z))); |
7055 | else if (scm_is_number (z)) | |
7056 | return scm_log (scm_sum (z, | |
7057 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 7058 | SCM_INUM1)))); |
ad79736c AW |
7059 | else |
7060 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
7061 | } | |
7062 | #undef FUNC_NAME | |
7063 | ||
7064 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
7065 | (SCM z), | |
7066 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
7067 | #define FUNC_NAME s_scm_sys_atanh | |
7068 | { | |
8deddc94 MW |
7069 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7070 | return z; /* atanh(exact0) = exact0 */ | |
7071 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
7072 | return scm_from_double (atanh (scm_to_double (z))); |
7073 | else if (scm_is_number (z)) | |
cff5fa33 MW |
7074 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
7075 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
7076 | SCM_I_MAKINUM (2)); |
7077 | else | |
7078 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 7079 | } |
1bbd0b84 | 7080 | #undef FUNC_NAME |
0f2d19dd | 7081 | |
8507ec80 MV |
7082 | SCM |
7083 | scm_c_make_rectangular (double re, double im) | |
7084 | { | |
7085 | if (im == 0.0) | |
7086 | return scm_from_double (re); | |
7087 | else | |
7088 | { | |
7089 | SCM z; | |
03604fcf LC |
7090 | |
7091 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
92d8fd32 | 7092 | "complex")); |
03604fcf | 7093 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
8507ec80 MV |
7094 | SCM_COMPLEX_REAL (z) = re; |
7095 | SCM_COMPLEX_IMAG (z) = im; | |
7096 | return z; | |
7097 | } | |
7098 | } | |
0f2d19dd | 7099 | |
a1ec6916 | 7100 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
7101 | (SCM real_part, SCM imaginary_part), |
7102 | "Return a complex number constructed of the given @var{real-part} " | |
7103 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 7104 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 7105 | { |
ad79736c AW |
7106 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
7107 | SCM_ARG1, FUNC_NAME, "real"); | |
7108 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
7109 | SCM_ARG2, FUNC_NAME, "real"); | |
7110 | return scm_c_make_rectangular (scm_to_double (real_part), | |
7111 | scm_to_double (imaginary_part)); | |
0f2d19dd | 7112 | } |
1bbd0b84 | 7113 | #undef FUNC_NAME |
0f2d19dd | 7114 | |
8507ec80 MV |
7115 | SCM |
7116 | scm_c_make_polar (double mag, double ang) | |
7117 | { | |
7118 | double s, c; | |
5e647d08 LC |
7119 | |
7120 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
7121 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
7122 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
7123 | details. */ | |
7124 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
7125 | sincos (ang, &s, &c); |
7126 | #else | |
7127 | s = sin (ang); | |
7128 | c = cos (ang); | |
7129 | #endif | |
7130 | return scm_c_make_rectangular (mag * c, mag * s); | |
7131 | } | |
0f2d19dd | 7132 | |
a1ec6916 | 7133 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 7134 | (SCM x, SCM y), |
942e5b91 | 7135 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 7136 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 7137 | { |
ad79736c AW |
7138 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7139 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
7140 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 7141 | } |
1bbd0b84 | 7142 | #undef FUNC_NAME |
0f2d19dd JB |
7143 | |
7144 | ||
2519490c MW |
7145 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
7146 | (SCM z), | |
7147 | "Return the real part of the number @var{z}.") | |
7148 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 7149 | { |
2519490c | 7150 | if (SCM_COMPLEXP (z)) |
55f26379 | 7151 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 7152 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 7153 | return z; |
0aacf84e | 7154 | else |
2519490c | 7155 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 7156 | } |
2519490c | 7157 | #undef FUNC_NAME |
0f2d19dd JB |
7158 | |
7159 | ||
2519490c MW |
7160 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
7161 | (SCM z), | |
7162 | "Return the imaginary part of the number @var{z}.") | |
7163 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 7164 | { |
2519490c MW |
7165 | if (SCM_COMPLEXP (z)) |
7166 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
0aacf84e | 7167 | else if (SCM_REALP (z)) |
e7efe8e7 | 7168 | return flo0; |
2519490c | 7169 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 7170 | return SCM_INUM0; |
0aacf84e | 7171 | else |
2519490c | 7172 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 7173 | } |
2519490c | 7174 | #undef FUNC_NAME |
0f2d19dd | 7175 | |
2519490c MW |
7176 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
7177 | (SCM z), | |
7178 | "Return the numerator of the number @var{z}.") | |
7179 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 7180 | { |
2519490c | 7181 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
7182 | return z; |
7183 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 7184 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
7185 | else if (SCM_REALP (z)) |
7186 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
7187 | else | |
2519490c | 7188 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 7189 | } |
2519490c | 7190 | #undef FUNC_NAME |
f92e85f7 MV |
7191 | |
7192 | ||
2519490c MW |
7193 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
7194 | (SCM z), | |
7195 | "Return the denominator of the number @var{z}.") | |
7196 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 7197 | { |
2519490c | 7198 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 7199 | return SCM_INUM1; |
f92e85f7 | 7200 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 7201 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
7202 | else if (SCM_REALP (z)) |
7203 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
7204 | else | |
2519490c | 7205 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 7206 | } |
2519490c | 7207 | #undef FUNC_NAME |
0f2d19dd | 7208 | |
2519490c MW |
7209 | |
7210 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
7211 | (SCM z), | |
7212 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
7213 | "@code{abs} for real arguments, but also allows complex numbers.") | |
7214 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 7215 | { |
e11e83f3 | 7216 | if (SCM_I_INUMP (z)) |
0aacf84e | 7217 | { |
e25f3727 | 7218 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
7219 | if (zz >= 0) |
7220 | return z; | |
7221 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 7222 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 7223 | else |
e25f3727 | 7224 | return scm_i_inum2big (-zz); |
5986c47d | 7225 | } |
0aacf84e MD |
7226 | else if (SCM_BIGP (z)) |
7227 | { | |
7228 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7229 | scm_remember_upto_here_1 (z); | |
7230 | if (sgn < 0) | |
7231 | return scm_i_clonebig (z, 0); | |
7232 | else | |
7233 | return z; | |
5986c47d | 7234 | } |
0aacf84e | 7235 | else if (SCM_REALP (z)) |
55f26379 | 7236 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 7237 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7238 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
7239 | else if (SCM_FRACTIONP (z)) |
7240 | { | |
73e4de09 | 7241 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 7242 | return z; |
cba42c93 | 7243 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
7244 | SCM_FRACTION_DENOMINATOR (z)); |
7245 | } | |
0aacf84e | 7246 | else |
2519490c | 7247 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 7248 | } |
2519490c | 7249 | #undef FUNC_NAME |
0f2d19dd JB |
7250 | |
7251 | ||
2519490c MW |
7252 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
7253 | (SCM z), | |
7254 | "Return the angle of the complex number @var{z}.") | |
7255 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 7256 | { |
c8ae173e | 7257 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 7258 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
7259 | But if atan2 follows the floating point rounding mode, then the value |
7260 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 7261 | if (SCM_I_INUMP (z)) |
0aacf84e | 7262 | { |
e11e83f3 | 7263 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 7264 | return flo0; |
0aacf84e | 7265 | else |
55f26379 | 7266 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 7267 | } |
0aacf84e MD |
7268 | else if (SCM_BIGP (z)) |
7269 | { | |
7270 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7271 | scm_remember_upto_here_1 (z); | |
7272 | if (sgn < 0) | |
55f26379 | 7273 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 7274 | else |
e7efe8e7 | 7275 | return flo0; |
0f2d19dd | 7276 | } |
0aacf84e | 7277 | else if (SCM_REALP (z)) |
c8ae173e KR |
7278 | { |
7279 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 7280 | return flo0; |
c8ae173e | 7281 | else |
55f26379 | 7282 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 7283 | } |
0aacf84e | 7284 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7285 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
7286 | else if (SCM_FRACTIONP (z)) |
7287 | { | |
73e4de09 | 7288 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 7289 | return flo0; |
55f26379 | 7290 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 7291 | } |
0aacf84e | 7292 | else |
2519490c | 7293 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 7294 | } |
2519490c | 7295 | #undef FUNC_NAME |
0f2d19dd JB |
7296 | |
7297 | ||
2519490c MW |
7298 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
7299 | (SCM z), | |
7300 | "Convert the number @var{z} to its inexact representation.\n") | |
7301 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 7302 | { |
e11e83f3 | 7303 | if (SCM_I_INUMP (z)) |
55f26379 | 7304 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 7305 | else if (SCM_BIGP (z)) |
55f26379 | 7306 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 7307 | else if (SCM_FRACTIONP (z)) |
55f26379 | 7308 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
7309 | else if (SCM_INEXACTP (z)) |
7310 | return z; | |
7311 | else | |
2519490c | 7312 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 7313 | } |
2519490c | 7314 | #undef FUNC_NAME |
3c9a524f DH |
7315 | |
7316 | ||
2519490c MW |
7317 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
7318 | (SCM z), | |
7319 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 7320 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 7321 | { |
2519490c | 7322 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f872b822 | 7323 | return z; |
0aacf84e MD |
7324 | else if (SCM_REALP (z)) |
7325 | { | |
2519490c | 7326 | if (!DOUBLE_IS_FINITE (SCM_REAL_VALUE (z))) |
f92e85f7 | 7327 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 7328 | else |
f92e85f7 MV |
7329 | { |
7330 | mpq_t frac; | |
7331 | SCM q; | |
7332 | ||
7333 | mpq_init (frac); | |
7334 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 7335 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
7336 | scm_i_mpz2num (mpq_denref (frac))); |
7337 | ||
cba42c93 | 7338 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
7339 | for frac... |
7340 | */ | |
7341 | mpq_clear (frac); | |
7342 | return q; | |
7343 | } | |
c2ff8ab0 | 7344 | } |
f92e85f7 MV |
7345 | else if (SCM_FRACTIONP (z)) |
7346 | return z; | |
0aacf84e | 7347 | else |
2519490c | 7348 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); |
0f2d19dd | 7349 | } |
1bbd0b84 | 7350 | #undef FUNC_NAME |
0f2d19dd | 7351 | |
f92e85f7 | 7352 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
7353 | (SCM x, SCM eps), |
7354 | "Returns the @emph{simplest} rational number differing\n" | |
7355 | "from @var{x} by no more than @var{eps}.\n" | |
7356 | "\n" | |
7357 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
7358 | "exact result when both its arguments are exact. Thus, you might need\n" | |
7359 | "to use @code{inexact->exact} on the arguments.\n" | |
7360 | "\n" | |
7361 | "@lisp\n" | |
7362 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
7363 | "@result{} 6/5\n" | |
7364 | "@end lisp") | |
f92e85f7 MV |
7365 | #define FUNC_NAME s_scm_rationalize |
7366 | { | |
605f6980 MW |
7367 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7368 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
7369 | eps = scm_abs (eps); | |
7370 | if (scm_is_false (scm_positive_p (eps))) | |
7371 | { | |
7372 | /* eps is either zero or a NaN */ | |
7373 | if (scm_is_true (scm_nan_p (eps))) | |
7374 | return scm_nan (); | |
7375 | else if (SCM_INEXACTP (eps)) | |
7376 | return scm_exact_to_inexact (x); | |
7377 | else | |
7378 | return x; | |
7379 | } | |
7380 | else if (scm_is_false (scm_finite_p (eps))) | |
7381 | { | |
7382 | if (scm_is_true (scm_finite_p (x))) | |
7383 | return flo0; | |
7384 | else | |
7385 | return scm_nan (); | |
7386 | } | |
7387 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 7388 | return x; |
605f6980 MW |
7389 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
7390 | scm_ceiling (scm_difference (x, eps))))) | |
7391 | { | |
7392 | /* There's an integer within range; we want the one closest to zero */ | |
7393 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
7394 | { | |
7395 | /* zero is within range */ | |
7396 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
7397 | return flo0; | |
7398 | else | |
7399 | return SCM_INUM0; | |
7400 | } | |
7401 | else if (scm_is_true (scm_positive_p (x))) | |
7402 | return scm_ceiling (scm_difference (x, eps)); | |
7403 | else | |
7404 | return scm_floor (scm_sum (x, eps)); | |
7405 | } | |
7406 | else | |
f92e85f7 MV |
7407 | { |
7408 | /* Use continued fractions to find closest ratio. All | |
7409 | arithmetic is done with exact numbers. | |
7410 | */ | |
7411 | ||
7412 | SCM ex = scm_inexact_to_exact (x); | |
7413 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
7414 | SCM tt = SCM_INUM1; |
7415 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
7416 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
7417 | SCM rx; |
7418 | int i = 0; | |
7419 | ||
f92e85f7 MV |
7420 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
7421 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
7422 | ||
7423 | /* We stop after a million iterations just to be absolutely sure | |
7424 | that we don't go into an infinite loop. The process normally | |
7425 | converges after less than a dozen iterations. | |
7426 | */ | |
7427 | ||
f92e85f7 MV |
7428 | while (++i < 1000000) |
7429 | { | |
7430 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
7431 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
7432 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
7433 | scm_is_false | |
f92e85f7 | 7434 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 7435 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
7436 | { |
7437 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 7438 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
7439 | return scm_exact_to_inexact (res); |
7440 | else | |
7441 | return res; | |
7442 | } | |
f92e85f7 MV |
7443 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
7444 | SCM_UNDEFINED); | |
7445 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
7446 | a2 = a1; | |
7447 | b2 = b1; | |
7448 | a1 = a; | |
7449 | b1 = b; | |
7450 | } | |
7451 | scm_num_overflow (s_scm_rationalize); | |
7452 | } | |
f92e85f7 MV |
7453 | } |
7454 | #undef FUNC_NAME | |
7455 | ||
73e4de09 MV |
7456 | /* conversion functions */ |
7457 | ||
7458 | int | |
7459 | scm_is_integer (SCM val) | |
7460 | { | |
7461 | return scm_is_true (scm_integer_p (val)); | |
7462 | } | |
7463 | ||
7464 | int | |
7465 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
7466 | { | |
e11e83f3 | 7467 | if (SCM_I_INUMP (val)) |
73e4de09 | 7468 | { |
e11e83f3 | 7469 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7470 | return n >= min && n <= max; |
7471 | } | |
7472 | else if (SCM_BIGP (val)) | |
7473 | { | |
7474 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
7475 | return 0; | |
7476 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
7477 | { |
7478 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
7479 | { | |
7480 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
7481 | return n >= min && n <= max; | |
7482 | } | |
7483 | else | |
7484 | return 0; | |
7485 | } | |
73e4de09 MV |
7486 | else |
7487 | { | |
d956fa6f MV |
7488 | scm_t_intmax n; |
7489 | size_t count; | |
73e4de09 | 7490 | |
d956fa6f MV |
7491 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7492 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
7493 | return 0; | |
7494 | ||
7495 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7496 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7497 | |
d956fa6f | 7498 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 7499 | { |
d956fa6f MV |
7500 | if (n < 0) |
7501 | return 0; | |
73e4de09 | 7502 | } |
73e4de09 MV |
7503 | else |
7504 | { | |
d956fa6f MV |
7505 | n = -n; |
7506 | if (n >= 0) | |
7507 | return 0; | |
73e4de09 | 7508 | } |
d956fa6f MV |
7509 | |
7510 | return n >= min && n <= max; | |
73e4de09 MV |
7511 | } |
7512 | } | |
73e4de09 MV |
7513 | else |
7514 | return 0; | |
7515 | } | |
7516 | ||
7517 | int | |
7518 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
7519 | { | |
e11e83f3 | 7520 | if (SCM_I_INUMP (val)) |
73e4de09 | 7521 | { |
e11e83f3 | 7522 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7523 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
7524 | } | |
7525 | else if (SCM_BIGP (val)) | |
7526 | { | |
7527 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
7528 | return 0; | |
7529 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
7530 | { |
7531 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
7532 | { | |
7533 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
7534 | return n >= min && n <= max; | |
7535 | } | |
7536 | else | |
7537 | return 0; | |
7538 | } | |
73e4de09 MV |
7539 | else |
7540 | { | |
d956fa6f MV |
7541 | scm_t_uintmax n; |
7542 | size_t count; | |
73e4de09 | 7543 | |
d956fa6f MV |
7544 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
7545 | return 0; | |
73e4de09 | 7546 | |
d956fa6f MV |
7547 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7548 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 7549 | return 0; |
d956fa6f MV |
7550 | |
7551 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7552 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7553 | |
d956fa6f | 7554 | return n >= min && n <= max; |
73e4de09 MV |
7555 | } |
7556 | } | |
73e4de09 MV |
7557 | else |
7558 | return 0; | |
7559 | } | |
7560 | ||
1713d319 MV |
7561 | static void |
7562 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
7563 | { | |
7564 | scm_error (scm_out_of_range_key, | |
7565 | NULL, | |
7566 | "Value out of range ~S to ~S: ~S", | |
7567 | scm_list_3 (min, max, bad_val), | |
7568 | scm_list_1 (bad_val)); | |
7569 | } | |
7570 | ||
bfd7932e MV |
7571 | #define TYPE scm_t_intmax |
7572 | #define TYPE_MIN min | |
7573 | #define TYPE_MAX max | |
7574 | #define SIZEOF_TYPE 0 | |
7575 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
7576 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
7577 | #include "libguile/conv-integer.i.c" | |
7578 | ||
7579 | #define TYPE scm_t_uintmax | |
7580 | #define TYPE_MIN min | |
7581 | #define TYPE_MAX max | |
7582 | #define SIZEOF_TYPE 0 | |
7583 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
7584 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
7585 | #include "libguile/conv-uinteger.i.c" | |
7586 | ||
7587 | #define TYPE scm_t_int8 | |
7588 | #define TYPE_MIN SCM_T_INT8_MIN | |
7589 | #define TYPE_MAX SCM_T_INT8_MAX | |
7590 | #define SIZEOF_TYPE 1 | |
7591 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
7592 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
7593 | #include "libguile/conv-integer.i.c" | |
7594 | ||
7595 | #define TYPE scm_t_uint8 | |
7596 | #define TYPE_MIN 0 | |
7597 | #define TYPE_MAX SCM_T_UINT8_MAX | |
7598 | #define SIZEOF_TYPE 1 | |
7599 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
7600 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
7601 | #include "libguile/conv-uinteger.i.c" | |
7602 | ||
7603 | #define TYPE scm_t_int16 | |
7604 | #define TYPE_MIN SCM_T_INT16_MIN | |
7605 | #define TYPE_MAX SCM_T_INT16_MAX | |
7606 | #define SIZEOF_TYPE 2 | |
7607 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
7608 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
7609 | #include "libguile/conv-integer.i.c" | |
7610 | ||
7611 | #define TYPE scm_t_uint16 | |
7612 | #define TYPE_MIN 0 | |
7613 | #define TYPE_MAX SCM_T_UINT16_MAX | |
7614 | #define SIZEOF_TYPE 2 | |
7615 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
7616 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
7617 | #include "libguile/conv-uinteger.i.c" | |
7618 | ||
7619 | #define TYPE scm_t_int32 | |
7620 | #define TYPE_MIN SCM_T_INT32_MIN | |
7621 | #define TYPE_MAX SCM_T_INT32_MAX | |
7622 | #define SIZEOF_TYPE 4 | |
7623 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
7624 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
7625 | #include "libguile/conv-integer.i.c" | |
7626 | ||
7627 | #define TYPE scm_t_uint32 | |
7628 | #define TYPE_MIN 0 | |
7629 | #define TYPE_MAX SCM_T_UINT32_MAX | |
7630 | #define SIZEOF_TYPE 4 | |
7631 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
7632 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
7633 | #include "libguile/conv-uinteger.i.c" | |
7634 | ||
904a78f1 MG |
7635 | #define TYPE scm_t_wchar |
7636 | #define TYPE_MIN (scm_t_int32)-1 | |
7637 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
7638 | #define SIZEOF_TYPE 4 | |
7639 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
7640 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
7641 | #include "libguile/conv-integer.i.c" | |
7642 | ||
bfd7932e MV |
7643 | #define TYPE scm_t_int64 |
7644 | #define TYPE_MIN SCM_T_INT64_MIN | |
7645 | #define TYPE_MAX SCM_T_INT64_MAX | |
7646 | #define SIZEOF_TYPE 8 | |
7647 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
7648 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
7649 | #include "libguile/conv-integer.i.c" | |
7650 | ||
7651 | #define TYPE scm_t_uint64 | |
7652 | #define TYPE_MIN 0 | |
7653 | #define TYPE_MAX SCM_T_UINT64_MAX | |
7654 | #define SIZEOF_TYPE 8 | |
7655 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
7656 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
7657 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 7658 | |
cd036260 MV |
7659 | void |
7660 | scm_to_mpz (SCM val, mpz_t rop) | |
7661 | { | |
7662 | if (SCM_I_INUMP (val)) | |
7663 | mpz_set_si (rop, SCM_I_INUM (val)); | |
7664 | else if (SCM_BIGP (val)) | |
7665 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
7666 | else | |
7667 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
7668 | } | |
7669 | ||
7670 | SCM | |
7671 | scm_from_mpz (mpz_t val) | |
7672 | { | |
7673 | return scm_i_mpz2num (val); | |
7674 | } | |
7675 | ||
73e4de09 MV |
7676 | int |
7677 | scm_is_real (SCM val) | |
7678 | { | |
7679 | return scm_is_true (scm_real_p (val)); | |
7680 | } | |
7681 | ||
55f26379 MV |
7682 | int |
7683 | scm_is_rational (SCM val) | |
7684 | { | |
7685 | return scm_is_true (scm_rational_p (val)); | |
7686 | } | |
7687 | ||
73e4de09 MV |
7688 | double |
7689 | scm_to_double (SCM val) | |
7690 | { | |
55f26379 MV |
7691 | if (SCM_I_INUMP (val)) |
7692 | return SCM_I_INUM (val); | |
7693 | else if (SCM_BIGP (val)) | |
7694 | return scm_i_big2dbl (val); | |
7695 | else if (SCM_FRACTIONP (val)) | |
7696 | return scm_i_fraction2double (val); | |
7697 | else if (SCM_REALP (val)) | |
7698 | return SCM_REAL_VALUE (val); | |
7699 | else | |
7a1aba42 | 7700 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
7701 | } |
7702 | ||
7703 | SCM | |
7704 | scm_from_double (double val) | |
7705 | { | |
978c52d1 LC |
7706 | SCM z; |
7707 | ||
7708 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
7709 | ||
7710 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 7711 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 7712 | |
55f26379 | 7713 | return z; |
73e4de09 MV |
7714 | } |
7715 | ||
220058a8 | 7716 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
7717 | |
7718 | float | |
e25f3727 | 7719 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7720 | { |
220058a8 AW |
7721 | scm_c_issue_deprecation_warning |
7722 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
7723 | ||
55f26379 MV |
7724 | if (SCM_BIGP (num)) |
7725 | { | |
7726 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7727 | if (!isinf (res)) |
55f26379 MV |
7728 | return res; |
7729 | else | |
7730 | scm_out_of_range (NULL, num); | |
7731 | } | |
7732 | else | |
7733 | return scm_to_double (num); | |
7734 | } | |
7735 | ||
7736 | double | |
e25f3727 | 7737 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7738 | { |
220058a8 AW |
7739 | scm_c_issue_deprecation_warning |
7740 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
7741 | ||
55f26379 MV |
7742 | if (SCM_BIGP (num)) |
7743 | { | |
7744 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7745 | if (!isinf (res)) |
55f26379 MV |
7746 | return res; |
7747 | else | |
7748 | scm_out_of_range (NULL, num); | |
7749 | } | |
7750 | else | |
7751 | return scm_to_double (num); | |
7752 | } | |
7753 | ||
7754 | #endif | |
7755 | ||
8507ec80 MV |
7756 | int |
7757 | scm_is_complex (SCM val) | |
7758 | { | |
7759 | return scm_is_true (scm_complex_p (val)); | |
7760 | } | |
7761 | ||
7762 | double | |
7763 | scm_c_real_part (SCM z) | |
7764 | { | |
7765 | if (SCM_COMPLEXP (z)) | |
7766 | return SCM_COMPLEX_REAL (z); | |
7767 | else | |
7768 | { | |
7769 | /* Use the scm_real_part to get proper error checking and | |
7770 | dispatching. | |
7771 | */ | |
7772 | return scm_to_double (scm_real_part (z)); | |
7773 | } | |
7774 | } | |
7775 | ||
7776 | double | |
7777 | scm_c_imag_part (SCM z) | |
7778 | { | |
7779 | if (SCM_COMPLEXP (z)) | |
7780 | return SCM_COMPLEX_IMAG (z); | |
7781 | else | |
7782 | { | |
7783 | /* Use the scm_imag_part to get proper error checking and | |
7784 | dispatching. The result will almost always be 0.0, but not | |
7785 | always. | |
7786 | */ | |
7787 | return scm_to_double (scm_imag_part (z)); | |
7788 | } | |
7789 | } | |
7790 | ||
7791 | double | |
7792 | scm_c_magnitude (SCM z) | |
7793 | { | |
7794 | return scm_to_double (scm_magnitude (z)); | |
7795 | } | |
7796 | ||
7797 | double | |
7798 | scm_c_angle (SCM z) | |
7799 | { | |
7800 | return scm_to_double (scm_angle (z)); | |
7801 | } | |
7802 | ||
7803 | int | |
7804 | scm_is_number (SCM z) | |
7805 | { | |
7806 | return scm_is_true (scm_number_p (z)); | |
7807 | } | |
7808 | ||
8ab3d8a0 KR |
7809 | |
7810 | /* In the following functions we dispatch to the real-arg funcs like log() | |
7811 | when we know the arg is real, instead of just handing everything to | |
7812 | clog() for instance. This is in case clog() doesn't optimize for a | |
7813 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
7814 | well use it to go straight to the applicable C func. */ | |
7815 | ||
2519490c MW |
7816 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
7817 | (SCM z), | |
7818 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
7819 | #define FUNC_NAME s_scm_log |
7820 | { | |
7821 | if (SCM_COMPLEXP (z)) | |
7822 | { | |
4b26c03e | 7823 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7824 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
7825 | #else | |
7826 | double re = SCM_COMPLEX_REAL (z); | |
7827 | double im = SCM_COMPLEX_IMAG (z); | |
7828 | return scm_c_make_rectangular (log (hypot (re, im)), | |
7829 | atan2 (im, re)); | |
7830 | #endif | |
7831 | } | |
2519490c | 7832 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7833 | { |
7834 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7835 | although the value itself overflows. */ | |
7836 | double re = scm_to_double (z); | |
7837 | double l = log (fabs (re)); | |
7838 | if (re >= 0.0) | |
7839 | return scm_from_double (l); | |
7840 | else | |
7841 | return scm_c_make_rectangular (l, M_PI); | |
7842 | } | |
2519490c MW |
7843 | else |
7844 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
7845 | } |
7846 | #undef FUNC_NAME | |
7847 | ||
7848 | ||
2519490c MW |
7849 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
7850 | (SCM z), | |
7851 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
7852 | #define FUNC_NAME s_scm_log10 |
7853 | { | |
7854 | if (SCM_COMPLEXP (z)) | |
7855 | { | |
7856 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
7857 | clog() and a multiply by M_LOG10E, rather than the fallback | |
7858 | log10+hypot+atan2.) */ | |
f328f862 LC |
7859 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
7860 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
7861 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
7862 | #else | |
7863 | double re = SCM_COMPLEX_REAL (z); | |
7864 | double im = SCM_COMPLEX_IMAG (z); | |
7865 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
7866 | M_LOG10E * atan2 (im, re)); | |
7867 | #endif | |
7868 | } | |
2519490c | 7869 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7870 | { |
7871 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7872 | although the value itself overflows. */ | |
7873 | double re = scm_to_double (z); | |
7874 | double l = log10 (fabs (re)); | |
7875 | if (re >= 0.0) | |
7876 | return scm_from_double (l); | |
7877 | else | |
7878 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
7879 | } | |
2519490c MW |
7880 | else |
7881 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
7882 | } |
7883 | #undef FUNC_NAME | |
7884 | ||
7885 | ||
2519490c MW |
7886 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
7887 | (SCM z), | |
7888 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
7889 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
7890 | #define FUNC_NAME s_scm_exp |
7891 | { | |
7892 | if (SCM_COMPLEXP (z)) | |
7893 | { | |
4b26c03e | 7894 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7895 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
7896 | #else | |
7897 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
7898 | SCM_COMPLEX_IMAG (z)); | |
7899 | #endif | |
7900 | } | |
2519490c | 7901 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7902 | { |
7903 | /* When z is a negative bignum the conversion to double overflows, | |
7904 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
7905 | return scm_from_double (exp (scm_to_double (z))); | |
7906 | } | |
2519490c MW |
7907 | else |
7908 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
7909 | } |
7910 | #undef FUNC_NAME | |
7911 | ||
7912 | ||
2519490c MW |
7913 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
7914 | (SCM z), | |
7915 | "Return the square root of @var{z}. Of the two possible roots\n" | |
7916 | "(positive and negative), the one with the a positive real part\n" | |
7917 | "is returned, or if that's zero then a positive imaginary part.\n" | |
7918 | "Thus,\n" | |
7919 | "\n" | |
7920 | "@example\n" | |
7921 | "(sqrt 9.0) @result{} 3.0\n" | |
7922 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
7923 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
7924 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
7925 | "@end example") | |
8ab3d8a0 KR |
7926 | #define FUNC_NAME s_scm_sqrt |
7927 | { | |
2519490c | 7928 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 7929 | { |
f328f862 LC |
7930 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
7931 | && defined SCM_COMPLEX_VALUE | |
2519490c | 7932 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 7933 | #else |
2519490c MW |
7934 | double re = SCM_COMPLEX_REAL (z); |
7935 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
7936 | return scm_c_make_polar (sqrt (hypot (re, im)), |
7937 | 0.5 * atan2 (im, re)); | |
7938 | #endif | |
7939 | } | |
2519490c | 7940 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 7941 | { |
2519490c | 7942 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
7943 | if (xx < 0) |
7944 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
7945 | else | |
7946 | return scm_from_double (sqrt (xx)); | |
7947 | } | |
2519490c MW |
7948 | else |
7949 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
7950 | } |
7951 | #undef FUNC_NAME | |
7952 | ||
7953 | ||
7954 | ||
0f2d19dd JB |
7955 | void |
7956 | scm_init_numbers () | |
0f2d19dd | 7957 | { |
0b799eea MV |
7958 | int i; |
7959 | ||
713a4259 KR |
7960 | mpz_init_set_si (z_negative_one, -1); |
7961 | ||
a261c0e9 DH |
7962 | /* It may be possible to tune the performance of some algorithms by using |
7963 | * the following constants to avoid the creation of bignums. Please, before | |
7964 | * using these values, remember the two rules of program optimization: | |
7965 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 7966 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 7967 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 7968 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 7969 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 7970 | |
f3ae5d60 MD |
7971 | scm_add_feature ("complex"); |
7972 | scm_add_feature ("inexact"); | |
e7efe8e7 | 7973 | flo0 = scm_from_double (0.0); |
0b799eea MV |
7974 | |
7975 | /* determine floating point precision */ | |
55f26379 | 7976 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
7977 | { |
7978 | init_dblprec(&scm_dblprec[i-2],i); | |
7979 | init_fx_radix(fx_per_radix[i-2],i); | |
7980 | } | |
f872b822 | 7981 | #ifdef DBL_DIG |
0b799eea | 7982 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 7983 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 7984 | #endif |
1be6b49c | 7985 | |
cff5fa33 | 7986 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 7987 | #include "libguile/numbers.x" |
0f2d19dd | 7988 | } |
89e00824 ML |
7989 | |
7990 | /* | |
7991 | Local Variables: | |
7992 | c-file-style: "gnu" | |
7993 | End: | |
7994 | */ |