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 | 24 | /* General assumptions: |
ca46fb90 RB |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
c7218482 | 28 | * XXX What about infinities? They are equal to their own floor! -mhw |
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 | ||
bbec4602 LC |
48 | #include <verify.h> |
49 | ||
0f2d19dd | 50 | #include <math.h> |
fc194577 | 51 | #include <string.h> |
3f47e526 MG |
52 | #include <unicase.h> |
53 | #include <unictype.h> | |
f92e85f7 | 54 | |
8ab3d8a0 KR |
55 | #if HAVE_COMPLEX_H |
56 | #include <complex.h> | |
57 | #endif | |
58 | ||
a0599745 | 59 | #include "libguile/_scm.h" |
a0599745 MD |
60 | #include "libguile/feature.h" |
61 | #include "libguile/ports.h" | |
62 | #include "libguile/root.h" | |
63 | #include "libguile/smob.h" | |
64 | #include "libguile/strings.h" | |
864e7d42 | 65 | #include "libguile/bdw-gc.h" |
a0599745 MD |
66 | |
67 | #include "libguile/validate.h" | |
68 | #include "libguile/numbers.h" | |
1be6b49c | 69 | #include "libguile/deprecation.h" |
f4c627b3 | 70 | |
f92e85f7 MV |
71 | #include "libguile/eq.h" |
72 | ||
8ab3d8a0 KR |
73 | /* values per glibc, if not already defined */ |
74 | #ifndef M_LOG10E | |
75 | #define M_LOG10E 0.43429448190325182765 | |
76 | #endif | |
85bdb6ac MW |
77 | #ifndef M_LN2 |
78 | #define M_LN2 0.69314718055994530942 | |
79 | #endif | |
8ab3d8a0 KR |
80 | #ifndef M_PI |
81 | #define M_PI 3.14159265358979323846 | |
82 | #endif | |
83 | ||
e25f3727 AW |
84 | typedef scm_t_signed_bits scm_t_inum; |
85 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
86 | ||
7112615f MW |
87 | /* Tests to see if a C double is neither infinite nor a NaN. |
88 | TODO: if it's available, use C99's isfinite(x) instead */ | |
89 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
90 | ||
041fccf6 MW |
91 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
92 | of the infinity, but other platforms return a boolean only. */ | |
93 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
94 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
95 | ||
0f2d19dd | 96 | \f |
f4c627b3 | 97 | |
ca46fb90 RB |
98 | /* |
99 | Wonder if this might be faster for some of our code? A switch on | |
100 | the numtag would jump directly to the right case, and the | |
101 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
102 | ||
103 | #define SCM_I_NUMTAG_NOTNUM 0 | |
104 | #define SCM_I_NUMTAG_INUM 1 | |
105 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
106 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
107 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
108 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 109 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 110 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 111 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
112 | : SCM_I_NUMTAG_NOTNUM))) |
113 | */ | |
f92e85f7 | 114 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
115 | |
116 | ||
b57bf272 AW |
117 | /* Default to 1, because as we used to hard-code `free' as the |
118 | deallocator, we know that overriding these functions with | |
119 | instrumented `malloc' / `free' is OK. */ | |
120 | int scm_install_gmp_memory_functions = 1; | |
e7efe8e7 | 121 | static SCM flo0; |
ff62c168 | 122 | static SCM exactly_one_half; |
a5f6b751 | 123 | static SCM flo_log10e; |
e7efe8e7 | 124 | |
34d19ef6 | 125 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 126 | |
56e55ac7 | 127 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
128 | * printed or scm_string representation of an inexact number. |
129 | */ | |
0b799eea | 130 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 131 | |
b127c712 | 132 | |
ad79736c AW |
133 | #if !defined (HAVE_ASINH) |
134 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
135 | #endif | |
136 | #if !defined (HAVE_ACOSH) | |
137 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
138 | #endif | |
139 | #if !defined (HAVE_ATANH) | |
140 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
141 | #endif | |
142 | ||
18d78c5e MW |
143 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
144 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released | |
145 | in March 2006), mpz_cmp_d now handles infinities properly. */ | |
f8a8200b | 146 | #if 1 |
b127c712 | 147 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 148 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
149 | #else |
150 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
151 | #endif | |
152 | ||
f92e85f7 | 153 | |
4b26c03e | 154 | #if defined (GUILE_I) |
03976fee | 155 | #if defined HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
156 | |
157 | /* For an SCM object Z which is a complex number (ie. satisfies | |
158 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
159 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 160 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 161 | |
7a35784c | 162 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
163 | |
164 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 165 | static inline SCM |
8ab3d8a0 KR |
166 | scm_from_complex_double (complex double z) |
167 | { | |
168 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
169 | } | |
bca69a9f | 170 | |
8ab3d8a0 | 171 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 172 | #endif /* GUILE_I */ |
8ab3d8a0 | 173 | |
0f2d19dd JB |
174 | \f |
175 | ||
713a4259 | 176 | static mpz_t z_negative_one; |
ac0c002c DH |
177 | |
178 | \f | |
b57bf272 | 179 | |
864e7d42 LC |
180 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
181 | static void | |
182 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
183 | { | |
184 | SCM bignum; | |
185 | ||
186 | bignum = PTR2SCM (ptr); | |
187 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
188 | } | |
189 | ||
b57bf272 AW |
190 | /* The next three functions (custom_libgmp_*) are passed to |
191 | mp_set_memory_functions (in GMP) so that memory used by the digits | |
192 | themselves is known to the garbage collector. This is needed so | |
193 | that GC will be run at appropriate times. Otherwise, a program which | |
194 | creates many large bignums would malloc a huge amount of memory | |
195 | before the GC runs. */ | |
196 | static void * | |
197 | custom_gmp_malloc (size_t alloc_size) | |
198 | { | |
199 | return scm_malloc (alloc_size); | |
200 | } | |
201 | ||
202 | static void * | |
203 | custom_gmp_realloc (void *old_ptr, size_t old_size, size_t new_size) | |
204 | { | |
205 | return scm_realloc (old_ptr, new_size); | |
206 | } | |
207 | ||
208 | static void | |
209 | custom_gmp_free (void *ptr, size_t size) | |
210 | { | |
211 | free (ptr); | |
212 | } | |
213 | ||
214 | ||
d017fcdf LC |
215 | /* Return a new uninitialized bignum. */ |
216 | static inline SCM | |
217 | make_bignum (void) | |
218 | { | |
219 | scm_t_bits *p; | |
864e7d42 LC |
220 | GC_finalization_proc prev_finalizer; |
221 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
222 | |
223 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
224 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
225 | "bignum"); | |
226 | p[0] = scm_tc16_big; | |
227 | ||
864e7d42 LC |
228 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
229 | &prev_finalizer, | |
230 | &prev_finalizer_data); | |
231 | ||
d017fcdf LC |
232 | return SCM_PACK (p); |
233 | } | |
ac0c002c | 234 | |
864e7d42 | 235 | |
189171c5 | 236 | SCM |
ca46fb90 RB |
237 | scm_i_mkbig () |
238 | { | |
239 | /* Return a newly created bignum. */ | |
d017fcdf | 240 | SCM z = make_bignum (); |
ca46fb90 RB |
241 | mpz_init (SCM_I_BIG_MPZ (z)); |
242 | return z; | |
243 | } | |
244 | ||
e25f3727 AW |
245 | static SCM |
246 | scm_i_inum2big (scm_t_inum x) | |
247 | { | |
248 | /* Return a newly created bignum initialized to X. */ | |
249 | SCM z = make_bignum (); | |
250 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
251 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
252 | #else | |
253 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
254 | mpz_*_si invocations in Guile. */ | |
255 | #error creation of mpz not implemented for this inum size | |
256 | #endif | |
257 | return z; | |
258 | } | |
259 | ||
189171c5 | 260 | SCM |
c71b0706 MV |
261 | scm_i_long2big (long x) |
262 | { | |
263 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 264 | SCM z = make_bignum (); |
c71b0706 MV |
265 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
266 | return z; | |
267 | } | |
268 | ||
189171c5 | 269 | SCM |
c71b0706 MV |
270 | scm_i_ulong2big (unsigned long x) |
271 | { | |
272 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 273 | SCM z = make_bignum (); |
c71b0706 MV |
274 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
275 | return z; | |
276 | } | |
277 | ||
189171c5 | 278 | SCM |
ca46fb90 RB |
279 | scm_i_clonebig (SCM src_big, int same_sign_p) |
280 | { | |
281 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 282 | SCM z = make_bignum (); |
ca46fb90 | 283 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
284 | if (!same_sign_p) |
285 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
286 | return z; |
287 | } | |
288 | ||
189171c5 | 289 | int |
ca46fb90 RB |
290 | scm_i_bigcmp (SCM x, SCM y) |
291 | { | |
292 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
293 | /* presume we already know x and y are bignums */ | |
294 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
295 | scm_remember_upto_here_2 (x, y); | |
296 | return result; | |
297 | } | |
298 | ||
189171c5 | 299 | SCM |
ca46fb90 RB |
300 | scm_i_dbl2big (double d) |
301 | { | |
302 | /* results are only defined if d is an integer */ | |
d017fcdf | 303 | SCM z = make_bignum (); |
ca46fb90 RB |
304 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
305 | return z; | |
306 | } | |
307 | ||
f92e85f7 MV |
308 | /* Convert a integer in double representation to a SCM number. */ |
309 | ||
189171c5 | 310 | SCM |
f92e85f7 MV |
311 | scm_i_dbl2num (double u) |
312 | { | |
313 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
314 | powers of 2, so there's no rounding when making "double" values | |
315 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
316 | get rounded on a 64-bit machine, hence the "+1". | |
317 | ||
318 | The use of floor() to force to an integer value ensures we get a | |
319 | "numerically closest" value without depending on how a | |
320 | double->long cast or how mpz_set_d will round. For reference, | |
321 | double->long probably follows the hardware rounding mode, | |
322 | mpz_set_d truncates towards zero. */ | |
323 | ||
324 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
325 | representable as a double? */ | |
326 | ||
327 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
328 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 329 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
330 | else |
331 | return scm_i_dbl2big (u); | |
332 | } | |
333 | ||
089c9a59 KR |
334 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
335 | with R5RS exact->inexact. | |
336 | ||
337 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
338 | (ie. truncate towards zero), then adjust to get the closest double by |
339 | examining the next lower bit and adding 1 (to the absolute value) if | |
340 | necessary. | |
341 | ||
342 | Bignums exactly half way between representable doubles are rounded to the | |
343 | next higher absolute value (ie. away from zero). This seems like an | |
344 | adequate interpretation of R5RS "numerically closest", and it's easier | |
345 | and faster than a full "nearest-even" style. | |
346 | ||
347 | The bit test must be done on the absolute value of the mpz_t, which means | |
348 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
349 | negatives as twos complement. | |
350 | ||
18d78c5e MW |
351 | In GMP before 4.2, mpz_get_d rounding was unspecified. It ended up |
352 | following the hardware rounding mode, but applied to the absolute | |
353 | value of the mpz_t operand. This is not what we want so we put the | |
354 | high DBL_MANT_DIG bits into a temporary. Starting with GMP 4.2 | |
355 | (released in March 2006) mpz_get_d now always truncates towards zero. | |
f8a8200b | 356 | |
18d78c5e MW |
357 | ENHANCE-ME: The temporary init+clear to force the rounding in GMP |
358 | before 4.2 is a slowdown. It'd be faster to pick out the relevant | |
359 | high bits with mpz_getlimbn. */ | |
089c9a59 KR |
360 | |
361 | double | |
ca46fb90 RB |
362 | scm_i_big2dbl (SCM b) |
363 | { | |
089c9a59 KR |
364 | double result; |
365 | size_t bits; | |
366 | ||
367 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
368 | ||
f8a8200b | 369 | #if 1 |
089c9a59 | 370 | { |
18d78c5e MW |
371 | /* For GMP earlier than 4.2, force truncation towards zero */ |
372 | ||
373 | /* FIXME: DBL_MANT_DIG is the number of base-`FLT_RADIX' digits, | |
374 | _not_ the number of bits, so this code will break badly on a | |
375 | system with non-binary doubles. */ | |
376 | ||
089c9a59 KR |
377 | mpz_t tmp; |
378 | if (bits > DBL_MANT_DIG) | |
379 | { | |
380 | size_t shift = bits - DBL_MANT_DIG; | |
381 | mpz_init2 (tmp, DBL_MANT_DIG); | |
382 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
383 | result = ldexp (mpz_get_d (tmp), shift); | |
384 | mpz_clear (tmp); | |
385 | } | |
386 | else | |
387 | { | |
388 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
389 | } | |
390 | } | |
391 | #else | |
18d78c5e | 392 | /* GMP 4.2 or later */ |
089c9a59 KR |
393 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
394 | #endif | |
395 | ||
396 | if (bits > DBL_MANT_DIG) | |
397 | { | |
398 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
399 | /* test bit number "pos" in absolute value */ | |
400 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
401 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
402 | { | |
403 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
404 | } | |
405 | } | |
406 | ||
ca46fb90 RB |
407 | scm_remember_upto_here_1 (b); |
408 | return result; | |
409 | } | |
410 | ||
189171c5 | 411 | SCM |
ca46fb90 RB |
412 | scm_i_normbig (SCM b) |
413 | { | |
414 | /* convert a big back to a fixnum if it'll fit */ | |
415 | /* presume b is a bignum */ | |
416 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
417 | { | |
e25f3727 | 418 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 419 | if (SCM_FIXABLE (val)) |
d956fa6f | 420 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
421 | } |
422 | return b; | |
423 | } | |
f872b822 | 424 | |
f92e85f7 MV |
425 | static SCM_C_INLINE_KEYWORD SCM |
426 | scm_i_mpz2num (mpz_t b) | |
427 | { | |
428 | /* convert a mpz number to a SCM number. */ | |
429 | if (mpz_fits_slong_p (b)) | |
430 | { | |
e25f3727 | 431 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 432 | if (SCM_FIXABLE (val)) |
d956fa6f | 433 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
434 | } |
435 | ||
436 | { | |
d017fcdf | 437 | SCM z = make_bignum (); |
f92e85f7 MV |
438 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
439 | return z; | |
440 | } | |
441 | } | |
442 | ||
443 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
444 | static SCM scm_divide2real (SCM x, SCM y); | |
445 | ||
cba42c93 MV |
446 | static SCM |
447 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 448 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 449 | { |
c60e130c MV |
450 | /* First make sure the arguments are proper. |
451 | */ | |
e11e83f3 | 452 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 453 | { |
bc36d050 | 454 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 455 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 456 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
457 | return numerator; |
458 | } | |
459 | else | |
460 | { | |
461 | if (!(SCM_BIGP(denominator))) | |
462 | SCM_WRONG_TYPE_ARG (2, denominator); | |
463 | } | |
e11e83f3 | 464 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
465 | SCM_WRONG_TYPE_ARG (1, numerator); |
466 | ||
467 | /* Then flip signs so that the denominator is positive. | |
468 | */ | |
73e4de09 | 469 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
470 | { |
471 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
472 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
473 | } | |
474 | ||
475 | /* Now consider for each of the four fixnum/bignum combinations | |
476 | whether the rational number is really an integer. | |
477 | */ | |
e11e83f3 | 478 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 479 | { |
e25f3727 | 480 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 481 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 482 | return SCM_INUM0; |
e11e83f3 | 483 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 484 | { |
e25f3727 | 485 | scm_t_inum y; |
e11e83f3 | 486 | y = SCM_I_INUM (denominator); |
f92e85f7 | 487 | if (x == y) |
cff5fa33 | 488 | return SCM_INUM1; |
f92e85f7 | 489 | if ((x % y) == 0) |
d956fa6f | 490 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 491 | } |
dd5130ca KR |
492 | else |
493 | { | |
494 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
495 | of that value for the denominator, as a bignum. Apart from |
496 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
497 | integer. */ | |
498 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
499 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
500 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 501 | return SCM_I_MAKINUM(-1); |
dd5130ca | 502 | } |
f92e85f7 | 503 | } |
c60e130c | 504 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 505 | { |
e11e83f3 | 506 | if (SCM_I_INUMP (denominator)) |
c60e130c | 507 | { |
e25f3727 | 508 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
509 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
510 | return scm_divide (numerator, denominator); | |
511 | } | |
512 | else | |
f92e85f7 | 513 | { |
bc36d050 | 514 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 515 | return SCM_INUM1; |
c60e130c MV |
516 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
517 | SCM_I_BIG_MPZ (denominator))) | |
518 | return scm_divide(numerator, denominator); | |
f92e85f7 | 519 | } |
f92e85f7 | 520 | } |
c60e130c MV |
521 | |
522 | /* No, it's a proper fraction. | |
523 | */ | |
e2bf3b19 HWN |
524 | { |
525 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 526 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
527 | { |
528 | numerator = scm_divide (numerator, divisor); | |
529 | denominator = scm_divide (denominator, divisor); | |
530 | } | |
531 | ||
532 | return scm_double_cell (scm_tc16_fraction, | |
533 | SCM_UNPACK (numerator), | |
534 | SCM_UNPACK (denominator), 0); | |
535 | } | |
f92e85f7 | 536 | } |
c60e130c | 537 | #undef FUNC_NAME |
f92e85f7 | 538 | |
f92e85f7 MV |
539 | double |
540 | scm_i_fraction2double (SCM z) | |
541 | { | |
55f26379 MV |
542 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
543 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
544 | } |
545 | ||
2e274311 MW |
546 | static int |
547 | double_is_non_negative_zero (double x) | |
548 | { | |
549 | static double zero = 0.0; | |
550 | ||
551 | return !memcmp (&x, &zero, sizeof(double)); | |
552 | } | |
553 | ||
2519490c MW |
554 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
555 | (SCM x), | |
942e5b91 MG |
556 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
557 | "otherwise.") | |
1bbd0b84 | 558 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 559 | { |
41df63cf MW |
560 | if (SCM_INEXACTP (x)) |
561 | return SCM_BOOL_F; | |
562 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 563 | return SCM_BOOL_T; |
41df63cf | 564 | else |
2519490c | 565 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
566 | } |
567 | #undef FUNC_NAME | |
568 | ||
022dda69 MG |
569 | int |
570 | scm_is_exact (SCM val) | |
571 | { | |
572 | return scm_is_true (scm_exact_p (val)); | |
573 | } | |
41df63cf | 574 | |
2519490c | 575 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
576 | (SCM x), |
577 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
578 | "else.") | |
579 | #define FUNC_NAME s_scm_inexact_p | |
580 | { | |
581 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 582 | return SCM_BOOL_T; |
41df63cf | 583 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 584 | return SCM_BOOL_F; |
41df63cf | 585 | else |
2519490c | 586 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 587 | } |
1bbd0b84 | 588 | #undef FUNC_NAME |
0f2d19dd | 589 | |
022dda69 MG |
590 | int |
591 | scm_is_inexact (SCM val) | |
592 | { | |
593 | return scm_is_true (scm_inexact_p (val)); | |
594 | } | |
4219f20d | 595 | |
2519490c | 596 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 597 | (SCM n), |
942e5b91 MG |
598 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
599 | "otherwise.") | |
1bbd0b84 | 600 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 601 | { |
e11e83f3 | 602 | if (SCM_I_INUMP (n)) |
0aacf84e | 603 | { |
e25f3727 | 604 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 605 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
606 | } |
607 | else if (SCM_BIGP (n)) | |
608 | { | |
609 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
610 | scm_remember_upto_here_1 (n); | |
73e4de09 | 611 | return scm_from_bool (odd_p); |
0aacf84e | 612 | } |
f92e85f7 MV |
613 | else if (SCM_REALP (n)) |
614 | { | |
2519490c MW |
615 | double val = SCM_REAL_VALUE (n); |
616 | if (DOUBLE_IS_FINITE (val)) | |
617 | { | |
618 | double rem = fabs (fmod (val, 2.0)); | |
619 | if (rem == 1.0) | |
620 | return SCM_BOOL_T; | |
621 | else if (rem == 0.0) | |
622 | return SCM_BOOL_F; | |
623 | } | |
f92e85f7 | 624 | } |
2519490c | 625 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 626 | } |
1bbd0b84 | 627 | #undef FUNC_NAME |
0f2d19dd | 628 | |
4219f20d | 629 | |
2519490c | 630 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 631 | (SCM n), |
942e5b91 MG |
632 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
633 | "otherwise.") | |
1bbd0b84 | 634 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 635 | { |
e11e83f3 | 636 | if (SCM_I_INUMP (n)) |
0aacf84e | 637 | { |
e25f3727 | 638 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 639 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
640 | } |
641 | else if (SCM_BIGP (n)) | |
642 | { | |
643 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
644 | scm_remember_upto_here_1 (n); | |
73e4de09 | 645 | return scm_from_bool (even_p); |
0aacf84e | 646 | } |
f92e85f7 MV |
647 | else if (SCM_REALP (n)) |
648 | { | |
2519490c MW |
649 | double val = SCM_REAL_VALUE (n); |
650 | if (DOUBLE_IS_FINITE (val)) | |
651 | { | |
652 | double rem = fabs (fmod (val, 2.0)); | |
653 | if (rem == 1.0) | |
654 | return SCM_BOOL_F; | |
655 | else if (rem == 0.0) | |
656 | return SCM_BOOL_T; | |
657 | } | |
f92e85f7 | 658 | } |
2519490c | 659 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 660 | } |
1bbd0b84 | 661 | #undef FUNC_NAME |
0f2d19dd | 662 | |
2519490c MW |
663 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
664 | (SCM x), | |
10391e06 AW |
665 | "Return @code{#t} if the real number @var{x} is neither\n" |
666 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
667 | #define FUNC_NAME s_scm_finite_p |
668 | { | |
669 | if (SCM_REALP (x)) | |
670 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 671 | else if (scm_is_real (x)) |
7112615f MW |
672 | return SCM_BOOL_T; |
673 | else | |
2519490c | 674 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
675 | } |
676 | #undef FUNC_NAME | |
677 | ||
2519490c MW |
678 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
679 | (SCM x), | |
680 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
681 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
682 | #define FUNC_NAME s_scm_inf_p |
683 | { | |
b1092b3a | 684 | if (SCM_REALP (x)) |
2e65b52f | 685 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 686 | else if (scm_is_real (x)) |
7351e207 | 687 | return SCM_BOOL_F; |
10391e06 | 688 | else |
2519490c | 689 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
690 | } |
691 | #undef FUNC_NAME | |
692 | ||
2519490c MW |
693 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
694 | (SCM x), | |
10391e06 AW |
695 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
696 | "or @code{#f} otherwise.") | |
7351e207 MV |
697 | #define FUNC_NAME s_scm_nan_p |
698 | { | |
10391e06 AW |
699 | if (SCM_REALP (x)) |
700 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
701 | else if (scm_is_real (x)) | |
7351e207 | 702 | return SCM_BOOL_F; |
10391e06 | 703 | else |
2519490c | 704 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
705 | } |
706 | #undef FUNC_NAME | |
707 | ||
708 | /* Guile's idea of infinity. */ | |
709 | static double guile_Inf; | |
710 | ||
711 | /* Guile's idea of not a number. */ | |
712 | static double guile_NaN; | |
713 | ||
714 | static void | |
715 | guile_ieee_init (void) | |
716 | { | |
7351e207 MV |
717 | /* Some version of gcc on some old version of Linux used to crash when |
718 | trying to make Inf and NaN. */ | |
719 | ||
240a27d2 KR |
720 | #ifdef INFINITY |
721 | /* C99 INFINITY, when available. | |
722 | FIXME: The standard allows for INFINITY to be something that overflows | |
723 | at compile time. We ought to have a configure test to check for that | |
724 | before trying to use it. (But in practice we believe this is not a | |
725 | problem on any system guile is likely to target.) */ | |
726 | guile_Inf = INFINITY; | |
56a3dcd4 | 727 | #elif defined HAVE_DINFINITY |
240a27d2 | 728 | /* OSF */ |
7351e207 | 729 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 730 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
731 | #else |
732 | double tmp = 1e+10; | |
733 | guile_Inf = tmp; | |
734 | for (;;) | |
735 | { | |
736 | guile_Inf *= 1e+10; | |
737 | if (guile_Inf == tmp) | |
738 | break; | |
739 | tmp = guile_Inf; | |
740 | } | |
741 | #endif | |
742 | ||
240a27d2 KR |
743 | #ifdef NAN |
744 | /* C99 NAN, when available */ | |
745 | guile_NaN = NAN; | |
56a3dcd4 | 746 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
747 | { |
748 | /* OSF */ | |
749 | extern unsigned int DQNAN[2]; | |
750 | guile_NaN = (*((double *)(DQNAN))); | |
751 | } | |
7351e207 MV |
752 | #else |
753 | guile_NaN = guile_Inf / guile_Inf; | |
754 | #endif | |
7351e207 MV |
755 | } |
756 | ||
757 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
758 | (void), | |
759 | "Return Inf.") | |
760 | #define FUNC_NAME s_scm_inf | |
761 | { | |
762 | static int initialized = 0; | |
763 | if (! initialized) | |
764 | { | |
765 | guile_ieee_init (); | |
766 | initialized = 1; | |
767 | } | |
55f26379 | 768 | return scm_from_double (guile_Inf); |
7351e207 MV |
769 | } |
770 | #undef FUNC_NAME | |
771 | ||
772 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
773 | (void), | |
774 | "Return NaN.") | |
775 | #define FUNC_NAME s_scm_nan | |
776 | { | |
777 | static int initialized = 0; | |
0aacf84e | 778 | if (!initialized) |
7351e207 MV |
779 | { |
780 | guile_ieee_init (); | |
781 | initialized = 1; | |
782 | } | |
55f26379 | 783 | return scm_from_double (guile_NaN); |
7351e207 MV |
784 | } |
785 | #undef FUNC_NAME | |
786 | ||
4219f20d | 787 | |
a48d60b1 MD |
788 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
789 | (SCM x), | |
790 | "Return the absolute value of @var{x}.") | |
2519490c | 791 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 792 | { |
e11e83f3 | 793 | if (SCM_I_INUMP (x)) |
0aacf84e | 794 | { |
e25f3727 | 795 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
796 | if (xx >= 0) |
797 | return x; | |
798 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 799 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 800 | else |
e25f3727 | 801 | return scm_i_inum2big (-xx); |
4219f20d | 802 | } |
9b9ef10c MW |
803 | else if (SCM_LIKELY (SCM_REALP (x))) |
804 | { | |
805 | double xx = SCM_REAL_VALUE (x); | |
806 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
807 | if (xx < 0.0) | |
808 | return scm_from_double (-xx); | |
809 | /* Handle signed zeroes properly */ | |
810 | else if (SCM_UNLIKELY (xx == 0.0)) | |
811 | return flo0; | |
812 | else | |
813 | return x; | |
814 | } | |
0aacf84e MD |
815 | else if (SCM_BIGP (x)) |
816 | { | |
817 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
818 | if (sgn < 0) | |
819 | return scm_i_clonebig (x, 0); | |
820 | else | |
821 | return x; | |
4219f20d | 822 | } |
f92e85f7 MV |
823 | else if (SCM_FRACTIONP (x)) |
824 | { | |
73e4de09 | 825 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 826 | return x; |
cba42c93 | 827 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
828 | SCM_FRACTION_DENOMINATOR (x)); |
829 | } | |
0aacf84e | 830 | else |
a48d60b1 | 831 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 832 | } |
a48d60b1 | 833 | #undef FUNC_NAME |
0f2d19dd | 834 | |
4219f20d | 835 | |
2519490c MW |
836 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
837 | (SCM x, SCM y), | |
838 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
839 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 840 | { |
495a39c4 | 841 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 842 | { |
495a39c4 | 843 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 844 | return scm_truncate_quotient (x, y); |
0aacf84e | 845 | else |
2519490c | 846 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 847 | } |
0aacf84e | 848 | else |
2519490c | 849 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 850 | } |
2519490c | 851 | #undef FUNC_NAME |
0f2d19dd | 852 | |
2519490c MW |
853 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
854 | (SCM x, SCM y), | |
855 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
856 | "@lisp\n" | |
857 | "(remainder 13 4) @result{} 1\n" | |
858 | "(remainder -13 4) @result{} -1\n" | |
859 | "@end lisp") | |
860 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 861 | { |
495a39c4 | 862 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 863 | { |
495a39c4 | 864 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 865 | return scm_truncate_remainder (x, y); |
0aacf84e | 866 | else |
2519490c | 867 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 868 | } |
0aacf84e | 869 | else |
2519490c | 870 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 871 | } |
2519490c | 872 | #undef FUNC_NAME |
0f2d19dd | 873 | |
89a7e495 | 874 | |
2519490c MW |
875 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
876 | (SCM x, SCM y), | |
877 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
878 | "@lisp\n" | |
879 | "(modulo 13 4) @result{} 1\n" | |
880 | "(modulo -13 4) @result{} 3\n" | |
881 | "@end lisp") | |
882 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 883 | { |
495a39c4 | 884 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 885 | { |
495a39c4 | 886 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 887 | return scm_floor_remainder (x, y); |
0aacf84e | 888 | else |
2519490c | 889 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 890 | } |
0aacf84e | 891 | else |
2519490c | 892 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 893 | } |
2519490c | 894 | #undef FUNC_NAME |
0f2d19dd | 895 | |
5fbf680b MW |
896 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
897 | two-valued functions. It is called from primitive generics that take | |
898 | two arguments and return two values, when the core procedure is | |
899 | unable to handle the given argument types. If there are GOOPS | |
900 | methods for this primitive generic, it dispatches to GOOPS and, if | |
901 | successful, expects two values to be returned, which are placed in | |
902 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
903 | wrong-type-arg exception. | |
904 | ||
905 | FIXME: This obviously belongs somewhere else, but until we decide on | |
906 | the right API, it is here as a static function, because it is needed | |
907 | by the *_divide functions below. | |
908 | */ | |
909 | static void | |
910 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
911 | const char *subr, SCM *rp1, SCM *rp2) | |
912 | { | |
913 | if (SCM_UNPACK (gf)) | |
914 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
915 | else | |
916 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
917 | } | |
918 | ||
a8da6d93 MW |
919 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
920 | (SCM x, SCM y), | |
921 | "Return the integer @var{q} such that\n" | |
922 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
923 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
924 | "@lisp\n" | |
925 | "(euclidean-quotient 123 10) @result{} 12\n" | |
926 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
927 | "(euclidean-quotient -123 10) @result{} -13\n" | |
928 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
929 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
930 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
931 | "@end lisp") | |
ff62c168 MW |
932 | #define FUNC_NAME s_scm_euclidean_quotient |
933 | { | |
a8da6d93 MW |
934 | if (scm_is_false (scm_negative_p (y))) |
935 | return scm_floor_quotient (x, y); | |
ff62c168 | 936 | else |
a8da6d93 | 937 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
938 | } |
939 | #undef FUNC_NAME | |
940 | ||
a8da6d93 MW |
941 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
942 | (SCM x, SCM y), | |
943 | "Return the real number @var{r} such that\n" | |
944 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
945 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
946 | "for some integer @var{q}.\n" | |
947 | "@lisp\n" | |
948 | "(euclidean-remainder 123 10) @result{} 3\n" | |
949 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
950 | "(euclidean-remainder -123 10) @result{} 7\n" | |
951 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
952 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
953 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
954 | "@end lisp") | |
ff62c168 MW |
955 | #define FUNC_NAME s_scm_euclidean_remainder |
956 | { | |
a8da6d93 MW |
957 | if (scm_is_false (scm_negative_p (y))) |
958 | return scm_floor_remainder (x, y); | |
ff62c168 | 959 | else |
a8da6d93 | 960 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
961 | } |
962 | #undef FUNC_NAME | |
963 | ||
a8da6d93 MW |
964 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
965 | (SCM x, SCM y), | |
966 | "Return the integer @var{q} and the real number @var{r}\n" | |
967 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
968 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
969 | "@lisp\n" | |
970 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
971 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
972 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
973 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
974 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
975 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
976 | "@end lisp") | |
5fbf680b MW |
977 | #define FUNC_NAME s_scm_i_euclidean_divide |
978 | { | |
a8da6d93 MW |
979 | if (scm_is_false (scm_negative_p (y))) |
980 | return scm_i_floor_divide (x, y); | |
981 | else | |
982 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
983 | } |
984 | #undef FUNC_NAME | |
985 | ||
5fbf680b MW |
986 | void |
987 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 988 | { |
a8da6d93 MW |
989 | if (scm_is_false (scm_negative_p (y))) |
990 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 991 | else |
a8da6d93 | 992 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
993 | } |
994 | ||
8f9da340 MW |
995 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
996 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
997 | ||
998 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
999 | (SCM x, SCM y), | |
1000 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1001 | "@lisp\n" | |
1002 | "(floor-quotient 123 10) @result{} 12\n" | |
1003 | "(floor-quotient 123 -10) @result{} -13\n" | |
1004 | "(floor-quotient -123 10) @result{} -13\n" | |
1005 | "(floor-quotient -123 -10) @result{} 12\n" | |
1006 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1007 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1008 | "@end lisp") | |
1009 | #define FUNC_NAME s_scm_floor_quotient | |
1010 | { | |
1011 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1012 | { | |
1013 | scm_t_inum xx = SCM_I_INUM (x); | |
1014 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1015 | { | |
1016 | scm_t_inum yy = SCM_I_INUM (y); | |
1017 | scm_t_inum xx1 = xx; | |
1018 | scm_t_inum qq; | |
1019 | if (SCM_LIKELY (yy > 0)) | |
1020 | { | |
1021 | if (SCM_UNLIKELY (xx < 0)) | |
1022 | xx1 = xx - yy + 1; | |
1023 | } | |
1024 | else if (SCM_UNLIKELY (yy == 0)) | |
1025 | scm_num_overflow (s_scm_floor_quotient); | |
1026 | else if (xx > 0) | |
1027 | xx1 = xx - yy - 1; | |
1028 | qq = xx1 / yy; | |
1029 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1030 | return SCM_I_MAKINUM (qq); | |
1031 | else | |
1032 | return scm_i_inum2big (qq); | |
1033 | } | |
1034 | else if (SCM_BIGP (y)) | |
1035 | { | |
1036 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1037 | scm_remember_upto_here_1 (y); | |
1038 | if (sign > 0) | |
1039 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1040 | else | |
1041 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1042 | } | |
1043 | else if (SCM_REALP (y)) | |
1044 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1045 | else if (SCM_FRACTIONP (y)) | |
1046 | return scm_i_exact_rational_floor_quotient (x, y); | |
1047 | else | |
1048 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1049 | s_scm_floor_quotient); | |
1050 | } | |
1051 | else if (SCM_BIGP (x)) | |
1052 | { | |
1053 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1054 | { | |
1055 | scm_t_inum yy = SCM_I_INUM (y); | |
1056 | if (SCM_UNLIKELY (yy == 0)) | |
1057 | scm_num_overflow (s_scm_floor_quotient); | |
1058 | else if (SCM_UNLIKELY (yy == 1)) | |
1059 | return x; | |
1060 | else | |
1061 | { | |
1062 | SCM q = scm_i_mkbig (); | |
1063 | if (yy > 0) | |
1064 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1065 | else | |
1066 | { | |
1067 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1068 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1069 | } | |
1070 | scm_remember_upto_here_1 (x); | |
1071 | return scm_i_normbig (q); | |
1072 | } | |
1073 | } | |
1074 | else if (SCM_BIGP (y)) | |
1075 | { | |
1076 | SCM q = scm_i_mkbig (); | |
1077 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1078 | SCM_I_BIG_MPZ (x), | |
1079 | SCM_I_BIG_MPZ (y)); | |
1080 | scm_remember_upto_here_2 (x, y); | |
1081 | return scm_i_normbig (q); | |
1082 | } | |
1083 | else if (SCM_REALP (y)) | |
1084 | return scm_i_inexact_floor_quotient | |
1085 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1086 | else if (SCM_FRACTIONP (y)) | |
1087 | return scm_i_exact_rational_floor_quotient (x, y); | |
1088 | else | |
1089 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1090 | s_scm_floor_quotient); | |
1091 | } | |
1092 | else if (SCM_REALP (x)) | |
1093 | { | |
1094 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1095 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1096 | return scm_i_inexact_floor_quotient | |
1097 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1098 | else | |
1099 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1100 | s_scm_floor_quotient); | |
1101 | } | |
1102 | else if (SCM_FRACTIONP (x)) | |
1103 | { | |
1104 | if (SCM_REALP (y)) | |
1105 | return scm_i_inexact_floor_quotient | |
1106 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1107 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1108 | return scm_i_exact_rational_floor_quotient (x, y); | |
1109 | else | |
1110 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1111 | s_scm_floor_quotient); | |
1112 | } | |
1113 | else | |
1114 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1115 | s_scm_floor_quotient); | |
1116 | } | |
1117 | #undef FUNC_NAME | |
1118 | ||
1119 | static SCM | |
1120 | scm_i_inexact_floor_quotient (double x, double y) | |
1121 | { | |
1122 | if (SCM_UNLIKELY (y == 0)) | |
1123 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1124 | else | |
1125 | return scm_from_double (floor (x / y)); | |
1126 | } | |
1127 | ||
1128 | static SCM | |
1129 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1130 | { | |
1131 | return scm_floor_quotient | |
1132 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1133 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1134 | } | |
1135 | ||
1136 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1137 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1138 | ||
1139 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1140 | (SCM x, SCM y), | |
1141 | "Return the real number @var{r} such that\n" | |
1142 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1143 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1144 | "@lisp\n" | |
1145 | "(floor-remainder 123 10) @result{} 3\n" | |
1146 | "(floor-remainder 123 -10) @result{} -7\n" | |
1147 | "(floor-remainder -123 10) @result{} 7\n" | |
1148 | "(floor-remainder -123 -10) @result{} -3\n" | |
1149 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1150 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1151 | "@end lisp") | |
1152 | #define FUNC_NAME s_scm_floor_remainder | |
1153 | { | |
1154 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1155 | { | |
1156 | scm_t_inum xx = SCM_I_INUM (x); | |
1157 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1158 | { | |
1159 | scm_t_inum yy = SCM_I_INUM (y); | |
1160 | if (SCM_UNLIKELY (yy == 0)) | |
1161 | scm_num_overflow (s_scm_floor_remainder); | |
1162 | else | |
1163 | { | |
1164 | scm_t_inum rr = xx % yy; | |
1165 | int needs_adjustment; | |
1166 | ||
1167 | if (SCM_LIKELY (yy > 0)) | |
1168 | needs_adjustment = (rr < 0); | |
1169 | else | |
1170 | needs_adjustment = (rr > 0); | |
1171 | ||
1172 | if (needs_adjustment) | |
1173 | rr += yy; | |
1174 | return SCM_I_MAKINUM (rr); | |
1175 | } | |
1176 | } | |
1177 | else if (SCM_BIGP (y)) | |
1178 | { | |
1179 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1180 | scm_remember_upto_here_1 (y); | |
1181 | if (sign > 0) | |
1182 | { | |
1183 | if (xx < 0) | |
1184 | { | |
1185 | SCM r = scm_i_mkbig (); | |
1186 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1187 | scm_remember_upto_here_1 (y); | |
1188 | return scm_i_normbig (r); | |
1189 | } | |
1190 | else | |
1191 | return x; | |
1192 | } | |
1193 | else if (xx <= 0) | |
1194 | return x; | |
1195 | else | |
1196 | { | |
1197 | SCM r = scm_i_mkbig (); | |
1198 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1199 | scm_remember_upto_here_1 (y); | |
1200 | return scm_i_normbig (r); | |
1201 | } | |
1202 | } | |
1203 | else if (SCM_REALP (y)) | |
1204 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1205 | else if (SCM_FRACTIONP (y)) | |
1206 | return scm_i_exact_rational_floor_remainder (x, y); | |
1207 | else | |
1208 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1209 | s_scm_floor_remainder); | |
1210 | } | |
1211 | else if (SCM_BIGP (x)) | |
1212 | { | |
1213 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1214 | { | |
1215 | scm_t_inum yy = SCM_I_INUM (y); | |
1216 | if (SCM_UNLIKELY (yy == 0)) | |
1217 | scm_num_overflow (s_scm_floor_remainder); | |
1218 | else | |
1219 | { | |
1220 | scm_t_inum rr; | |
1221 | if (yy > 0) | |
1222 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1223 | else | |
1224 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1225 | scm_remember_upto_here_1 (x); | |
1226 | return SCM_I_MAKINUM (rr); | |
1227 | } | |
1228 | } | |
1229 | else if (SCM_BIGP (y)) | |
1230 | { | |
1231 | SCM r = scm_i_mkbig (); | |
1232 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1233 | SCM_I_BIG_MPZ (x), | |
1234 | SCM_I_BIG_MPZ (y)); | |
1235 | scm_remember_upto_here_2 (x, y); | |
1236 | return scm_i_normbig (r); | |
1237 | } | |
1238 | else if (SCM_REALP (y)) | |
1239 | return scm_i_inexact_floor_remainder | |
1240 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1241 | else if (SCM_FRACTIONP (y)) | |
1242 | return scm_i_exact_rational_floor_remainder (x, y); | |
1243 | else | |
1244 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1245 | s_scm_floor_remainder); | |
1246 | } | |
1247 | else if (SCM_REALP (x)) | |
1248 | { | |
1249 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1250 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1251 | return scm_i_inexact_floor_remainder | |
1252 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1253 | else | |
1254 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1255 | s_scm_floor_remainder); | |
1256 | } | |
1257 | else if (SCM_FRACTIONP (x)) | |
1258 | { | |
1259 | if (SCM_REALP (y)) | |
1260 | return scm_i_inexact_floor_remainder | |
1261 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1262 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1263 | return scm_i_exact_rational_floor_remainder (x, y); | |
1264 | else | |
1265 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1266 | s_scm_floor_remainder); | |
1267 | } | |
1268 | else | |
1269 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1270 | s_scm_floor_remainder); | |
1271 | } | |
1272 | #undef FUNC_NAME | |
1273 | ||
1274 | static SCM | |
1275 | scm_i_inexact_floor_remainder (double x, double y) | |
1276 | { | |
1277 | /* Although it would be more efficient to use fmod here, we can't | |
1278 | because it would in some cases produce results inconsistent with | |
1279 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1280 | close). In particular, when x is very close to a multiple of y, | |
1281 | then r might be either 0.0 or y, but those two cases must | |
1282 | correspond to different choices of q. If r = 0.0 then q must be | |
1283 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1284 | and remainder chooses the other, it would be bad. */ | |
1285 | if (SCM_UNLIKELY (y == 0)) | |
1286 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1287 | else | |
1288 | return scm_from_double (x - y * floor (x / y)); | |
1289 | } | |
1290 | ||
1291 | static SCM | |
1292 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1293 | { | |
1294 | SCM xd = scm_denominator (x); | |
1295 | SCM yd = scm_denominator (y); | |
1296 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1297 | scm_product (scm_numerator (y), xd)); | |
1298 | return scm_divide (r1, scm_product (xd, yd)); | |
1299 | } | |
1300 | ||
1301 | ||
1302 | static void scm_i_inexact_floor_divide (double x, double y, | |
1303 | SCM *qp, SCM *rp); | |
1304 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1305 | SCM *qp, SCM *rp); | |
1306 | ||
1307 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1308 | (SCM x, SCM y), | |
1309 | "Return the integer @var{q} and the real number @var{r}\n" | |
1310 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1311 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1312 | "@lisp\n" | |
1313 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1314 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1315 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1316 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1317 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1318 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1319 | "@end lisp") | |
1320 | #define FUNC_NAME s_scm_i_floor_divide | |
1321 | { | |
1322 | SCM q, r; | |
1323 | ||
1324 | scm_floor_divide(x, y, &q, &r); | |
1325 | return scm_values (scm_list_2 (q, r)); | |
1326 | } | |
1327 | #undef FUNC_NAME | |
1328 | ||
1329 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1330 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1331 | ||
1332 | void | |
1333 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1334 | { | |
1335 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1336 | { | |
1337 | scm_t_inum xx = SCM_I_INUM (x); | |
1338 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1339 | { | |
1340 | scm_t_inum yy = SCM_I_INUM (y); | |
1341 | if (SCM_UNLIKELY (yy == 0)) | |
1342 | scm_num_overflow (s_scm_floor_divide); | |
1343 | else | |
1344 | { | |
1345 | scm_t_inum qq = xx / yy; | |
1346 | scm_t_inum rr = xx % yy; | |
1347 | int needs_adjustment; | |
1348 | ||
1349 | if (SCM_LIKELY (yy > 0)) | |
1350 | needs_adjustment = (rr < 0); | |
1351 | else | |
1352 | needs_adjustment = (rr > 0); | |
1353 | ||
1354 | if (needs_adjustment) | |
1355 | { | |
1356 | rr += yy; | |
1357 | qq--; | |
1358 | } | |
1359 | ||
1360 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1361 | *qp = SCM_I_MAKINUM (qq); | |
1362 | else | |
1363 | *qp = scm_i_inum2big (qq); | |
1364 | *rp = SCM_I_MAKINUM (rr); | |
1365 | } | |
1366 | return; | |
1367 | } | |
1368 | else if (SCM_BIGP (y)) | |
1369 | { | |
1370 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1371 | scm_remember_upto_here_1 (y); | |
1372 | if (sign > 0) | |
1373 | { | |
1374 | if (xx < 0) | |
1375 | { | |
1376 | SCM r = scm_i_mkbig (); | |
1377 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1378 | scm_remember_upto_here_1 (y); | |
1379 | *qp = SCM_I_MAKINUM (-1); | |
1380 | *rp = scm_i_normbig (r); | |
1381 | } | |
1382 | else | |
1383 | { | |
1384 | *qp = SCM_INUM0; | |
1385 | *rp = x; | |
1386 | } | |
1387 | } | |
1388 | else if (xx <= 0) | |
1389 | { | |
1390 | *qp = SCM_INUM0; | |
1391 | *rp = x; | |
1392 | } | |
1393 | else | |
1394 | { | |
1395 | SCM r = scm_i_mkbig (); | |
1396 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1397 | scm_remember_upto_here_1 (y); | |
1398 | *qp = SCM_I_MAKINUM (-1); | |
1399 | *rp = scm_i_normbig (r); | |
1400 | } | |
1401 | return; | |
1402 | } | |
1403 | else if (SCM_REALP (y)) | |
1404 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1405 | else if (SCM_FRACTIONP (y)) | |
1406 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1407 | else | |
1408 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1409 | s_scm_floor_divide, qp, rp); | |
1410 | } | |
1411 | else if (SCM_BIGP (x)) | |
1412 | { | |
1413 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1414 | { | |
1415 | scm_t_inum yy = SCM_I_INUM (y); | |
1416 | if (SCM_UNLIKELY (yy == 0)) | |
1417 | scm_num_overflow (s_scm_floor_divide); | |
1418 | else | |
1419 | { | |
1420 | SCM q = scm_i_mkbig (); | |
1421 | SCM r = scm_i_mkbig (); | |
1422 | if (yy > 0) | |
1423 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1424 | SCM_I_BIG_MPZ (x), yy); | |
1425 | else | |
1426 | { | |
1427 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1428 | SCM_I_BIG_MPZ (x), -yy); | |
1429 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1430 | } | |
1431 | scm_remember_upto_here_1 (x); | |
1432 | *qp = scm_i_normbig (q); | |
1433 | *rp = scm_i_normbig (r); | |
1434 | } | |
1435 | return; | |
1436 | } | |
1437 | else if (SCM_BIGP (y)) | |
1438 | { | |
1439 | SCM q = scm_i_mkbig (); | |
1440 | SCM r = scm_i_mkbig (); | |
1441 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1442 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1443 | scm_remember_upto_here_2 (x, y); | |
1444 | *qp = scm_i_normbig (q); | |
1445 | *rp = scm_i_normbig (r); | |
1446 | return; | |
1447 | } | |
1448 | else if (SCM_REALP (y)) | |
1449 | return scm_i_inexact_floor_divide | |
1450 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1451 | else if (SCM_FRACTIONP (y)) | |
1452 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1453 | else | |
1454 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1455 | s_scm_floor_divide, qp, rp); | |
1456 | } | |
1457 | else if (SCM_REALP (x)) | |
1458 | { | |
1459 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1460 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1461 | return scm_i_inexact_floor_divide | |
1462 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1463 | else | |
1464 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1465 | s_scm_floor_divide, qp, rp); | |
1466 | } | |
1467 | else if (SCM_FRACTIONP (x)) | |
1468 | { | |
1469 | if (SCM_REALP (y)) | |
1470 | return scm_i_inexact_floor_divide | |
1471 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1472 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1473 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1474 | else | |
1475 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1476 | s_scm_floor_divide, qp, rp); | |
1477 | } | |
1478 | else | |
1479 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1480 | s_scm_floor_divide, qp, rp); | |
1481 | } | |
1482 | ||
1483 | static void | |
1484 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1485 | { | |
1486 | if (SCM_UNLIKELY (y == 0)) | |
1487 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1488 | else | |
1489 | { | |
1490 | double q = floor (x / y); | |
1491 | double r = x - q * y; | |
1492 | *qp = scm_from_double (q); | |
1493 | *rp = scm_from_double (r); | |
1494 | } | |
1495 | } | |
1496 | ||
1497 | static void | |
1498 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1499 | { | |
1500 | SCM r1; | |
1501 | SCM xd = scm_denominator (x); | |
1502 | SCM yd = scm_denominator (y); | |
1503 | ||
1504 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1505 | scm_product (scm_numerator (y), xd), | |
1506 | qp, &r1); | |
1507 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1508 | } | |
1509 | ||
1510 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1511 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1512 | ||
1513 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1514 | (SCM x, SCM y), | |
1515 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1516 | "@lisp\n" | |
1517 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1518 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1519 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1520 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1521 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1522 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1523 | "@end lisp") | |
1524 | #define FUNC_NAME s_scm_ceiling_quotient | |
1525 | { | |
1526 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1527 | { | |
1528 | scm_t_inum xx = SCM_I_INUM (x); | |
1529 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1530 | { | |
1531 | scm_t_inum yy = SCM_I_INUM (y); | |
1532 | if (SCM_UNLIKELY (yy == 0)) | |
1533 | scm_num_overflow (s_scm_ceiling_quotient); | |
1534 | else | |
1535 | { | |
1536 | scm_t_inum xx1 = xx; | |
1537 | scm_t_inum qq; | |
1538 | if (SCM_LIKELY (yy > 0)) | |
1539 | { | |
1540 | if (SCM_LIKELY (xx >= 0)) | |
1541 | xx1 = xx + yy - 1; | |
1542 | } | |
8f9da340 MW |
1543 | else if (xx < 0) |
1544 | xx1 = xx + yy + 1; | |
1545 | qq = xx1 / yy; | |
1546 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1547 | return SCM_I_MAKINUM (qq); | |
1548 | else | |
1549 | return scm_i_inum2big (qq); | |
1550 | } | |
1551 | } | |
1552 | else if (SCM_BIGP (y)) | |
1553 | { | |
1554 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1555 | scm_remember_upto_here_1 (y); | |
1556 | if (SCM_LIKELY (sign > 0)) | |
1557 | { | |
1558 | if (SCM_LIKELY (xx > 0)) | |
1559 | return SCM_INUM1; | |
1560 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1561 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1562 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1563 | { | |
1564 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1565 | scm_remember_upto_here_1 (y); | |
1566 | return SCM_I_MAKINUM (-1); | |
1567 | } | |
1568 | else | |
1569 | return SCM_INUM0; | |
1570 | } | |
1571 | else if (xx >= 0) | |
1572 | return SCM_INUM0; | |
1573 | else | |
1574 | return SCM_INUM1; | |
1575 | } | |
1576 | else if (SCM_REALP (y)) | |
1577 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1578 | else if (SCM_FRACTIONP (y)) | |
1579 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1580 | else | |
1581 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1582 | s_scm_ceiling_quotient); | |
1583 | } | |
1584 | else if (SCM_BIGP (x)) | |
1585 | { | |
1586 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1587 | { | |
1588 | scm_t_inum yy = SCM_I_INUM (y); | |
1589 | if (SCM_UNLIKELY (yy == 0)) | |
1590 | scm_num_overflow (s_scm_ceiling_quotient); | |
1591 | else if (SCM_UNLIKELY (yy == 1)) | |
1592 | return x; | |
1593 | else | |
1594 | { | |
1595 | SCM q = scm_i_mkbig (); | |
1596 | if (yy > 0) | |
1597 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1598 | else | |
1599 | { | |
1600 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1601 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1602 | } | |
1603 | scm_remember_upto_here_1 (x); | |
1604 | return scm_i_normbig (q); | |
1605 | } | |
1606 | } | |
1607 | else if (SCM_BIGP (y)) | |
1608 | { | |
1609 | SCM q = scm_i_mkbig (); | |
1610 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1611 | SCM_I_BIG_MPZ (x), | |
1612 | SCM_I_BIG_MPZ (y)); | |
1613 | scm_remember_upto_here_2 (x, y); | |
1614 | return scm_i_normbig (q); | |
1615 | } | |
1616 | else if (SCM_REALP (y)) | |
1617 | return scm_i_inexact_ceiling_quotient | |
1618 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1619 | else if (SCM_FRACTIONP (y)) | |
1620 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1621 | else | |
1622 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1623 | s_scm_ceiling_quotient); | |
1624 | } | |
1625 | else if (SCM_REALP (x)) | |
1626 | { | |
1627 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1628 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1629 | return scm_i_inexact_ceiling_quotient | |
1630 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1631 | else | |
1632 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1633 | s_scm_ceiling_quotient); | |
1634 | } | |
1635 | else if (SCM_FRACTIONP (x)) | |
1636 | { | |
1637 | if (SCM_REALP (y)) | |
1638 | return scm_i_inexact_ceiling_quotient | |
1639 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1640 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1641 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1642 | else | |
1643 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1644 | s_scm_ceiling_quotient); | |
1645 | } | |
1646 | else | |
1647 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1648 | s_scm_ceiling_quotient); | |
1649 | } | |
1650 | #undef FUNC_NAME | |
1651 | ||
1652 | static SCM | |
1653 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1654 | { | |
1655 | if (SCM_UNLIKELY (y == 0)) | |
1656 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1657 | else | |
1658 | return scm_from_double (ceil (x / y)); | |
1659 | } | |
1660 | ||
1661 | static SCM | |
1662 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1663 | { | |
1664 | return scm_ceiling_quotient | |
1665 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1666 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1667 | } | |
1668 | ||
1669 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1670 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1671 | ||
1672 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1673 | (SCM x, SCM y), | |
1674 | "Return the real number @var{r} such that\n" | |
1675 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1676 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1677 | "@lisp\n" | |
1678 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1679 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1680 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1681 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1682 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1683 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1684 | "@end lisp") | |
1685 | #define FUNC_NAME s_scm_ceiling_remainder | |
1686 | { | |
1687 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1688 | { | |
1689 | scm_t_inum xx = SCM_I_INUM (x); | |
1690 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1691 | { | |
1692 | scm_t_inum yy = SCM_I_INUM (y); | |
1693 | if (SCM_UNLIKELY (yy == 0)) | |
1694 | scm_num_overflow (s_scm_ceiling_remainder); | |
1695 | else | |
1696 | { | |
1697 | scm_t_inum rr = xx % yy; | |
1698 | int needs_adjustment; | |
1699 | ||
1700 | if (SCM_LIKELY (yy > 0)) | |
1701 | needs_adjustment = (rr > 0); | |
1702 | else | |
1703 | needs_adjustment = (rr < 0); | |
1704 | ||
1705 | if (needs_adjustment) | |
1706 | rr -= yy; | |
1707 | return SCM_I_MAKINUM (rr); | |
1708 | } | |
1709 | } | |
1710 | else if (SCM_BIGP (y)) | |
1711 | { | |
1712 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1713 | scm_remember_upto_here_1 (y); | |
1714 | if (SCM_LIKELY (sign > 0)) | |
1715 | { | |
1716 | if (SCM_LIKELY (xx > 0)) | |
1717 | { | |
1718 | SCM r = scm_i_mkbig (); | |
1719 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1720 | scm_remember_upto_here_1 (y); | |
1721 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1722 | return scm_i_normbig (r); | |
1723 | } | |
1724 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1725 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1726 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1727 | { | |
1728 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1729 | scm_remember_upto_here_1 (y); | |
1730 | return SCM_INUM0; | |
1731 | } | |
1732 | else | |
1733 | return x; | |
1734 | } | |
1735 | else if (xx >= 0) | |
1736 | return x; | |
1737 | else | |
1738 | { | |
1739 | SCM r = scm_i_mkbig (); | |
1740 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1741 | scm_remember_upto_here_1 (y); | |
1742 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1743 | return scm_i_normbig (r); | |
1744 | } | |
1745 | } | |
1746 | else if (SCM_REALP (y)) | |
1747 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1748 | else if (SCM_FRACTIONP (y)) | |
1749 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1750 | else | |
1751 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1752 | s_scm_ceiling_remainder); | |
1753 | } | |
1754 | else if (SCM_BIGP (x)) | |
1755 | { | |
1756 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1757 | { | |
1758 | scm_t_inum yy = SCM_I_INUM (y); | |
1759 | if (SCM_UNLIKELY (yy == 0)) | |
1760 | scm_num_overflow (s_scm_ceiling_remainder); | |
1761 | else | |
1762 | { | |
1763 | scm_t_inum rr; | |
1764 | if (yy > 0) | |
1765 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1766 | else | |
1767 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1768 | scm_remember_upto_here_1 (x); | |
1769 | return SCM_I_MAKINUM (rr); | |
1770 | } | |
1771 | } | |
1772 | else if (SCM_BIGP (y)) | |
1773 | { | |
1774 | SCM r = scm_i_mkbig (); | |
1775 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1776 | SCM_I_BIG_MPZ (x), | |
1777 | SCM_I_BIG_MPZ (y)); | |
1778 | scm_remember_upto_here_2 (x, y); | |
1779 | return scm_i_normbig (r); | |
1780 | } | |
1781 | else if (SCM_REALP (y)) | |
1782 | return scm_i_inexact_ceiling_remainder | |
1783 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1784 | else if (SCM_FRACTIONP (y)) | |
1785 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1786 | else | |
1787 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1788 | s_scm_ceiling_remainder); | |
1789 | } | |
1790 | else if (SCM_REALP (x)) | |
1791 | { | |
1792 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1793 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1794 | return scm_i_inexact_ceiling_remainder | |
1795 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1796 | else | |
1797 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1798 | s_scm_ceiling_remainder); | |
1799 | } | |
1800 | else if (SCM_FRACTIONP (x)) | |
1801 | { | |
1802 | if (SCM_REALP (y)) | |
1803 | return scm_i_inexact_ceiling_remainder | |
1804 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1805 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1806 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1807 | else | |
1808 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1809 | s_scm_ceiling_remainder); | |
1810 | } | |
1811 | else | |
1812 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1813 | s_scm_ceiling_remainder); | |
1814 | } | |
1815 | #undef FUNC_NAME | |
1816 | ||
1817 | static SCM | |
1818 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1819 | { | |
1820 | /* Although it would be more efficient to use fmod here, we can't | |
1821 | because it would in some cases produce results inconsistent with | |
1822 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1823 | close). In particular, when x is very close to a multiple of y, | |
1824 | then r might be either 0.0 or -y, but those two cases must | |
1825 | correspond to different choices of q. If r = 0.0 then q must be | |
1826 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1827 | and remainder chooses the other, it would be bad. */ | |
1828 | if (SCM_UNLIKELY (y == 0)) | |
1829 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1830 | else | |
1831 | return scm_from_double (x - y * ceil (x / y)); | |
1832 | } | |
1833 | ||
1834 | static SCM | |
1835 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1836 | { | |
1837 | SCM xd = scm_denominator (x); | |
1838 | SCM yd = scm_denominator (y); | |
1839 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1840 | scm_product (scm_numerator (y), xd)); | |
1841 | return scm_divide (r1, scm_product (xd, yd)); | |
1842 | } | |
1843 | ||
1844 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1845 | SCM *qp, SCM *rp); | |
1846 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1847 | SCM *qp, SCM *rp); | |
1848 | ||
1849 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1850 | (SCM x, SCM y), | |
1851 | "Return the integer @var{q} and the real number @var{r}\n" | |
1852 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1853 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1854 | "@lisp\n" | |
1855 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
1856 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
1857 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
1858 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
1859 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1860 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1861 | "@end lisp") | |
1862 | #define FUNC_NAME s_scm_i_ceiling_divide | |
1863 | { | |
1864 | SCM q, r; | |
1865 | ||
1866 | scm_ceiling_divide(x, y, &q, &r); | |
1867 | return scm_values (scm_list_2 (q, r)); | |
1868 | } | |
1869 | #undef FUNC_NAME | |
1870 | ||
1871 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
1872 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
1873 | ||
1874 | void | |
1875 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1876 | { | |
1877 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1878 | { | |
1879 | scm_t_inum xx = SCM_I_INUM (x); | |
1880 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1881 | { | |
1882 | scm_t_inum yy = SCM_I_INUM (y); | |
1883 | if (SCM_UNLIKELY (yy == 0)) | |
1884 | scm_num_overflow (s_scm_ceiling_divide); | |
1885 | else | |
1886 | { | |
1887 | scm_t_inum qq = xx / yy; | |
1888 | scm_t_inum rr = xx % yy; | |
1889 | int needs_adjustment; | |
1890 | ||
1891 | if (SCM_LIKELY (yy > 0)) | |
1892 | needs_adjustment = (rr > 0); | |
1893 | else | |
1894 | needs_adjustment = (rr < 0); | |
1895 | ||
1896 | if (needs_adjustment) | |
1897 | { | |
1898 | rr -= yy; | |
1899 | qq++; | |
1900 | } | |
1901 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1902 | *qp = SCM_I_MAKINUM (qq); | |
1903 | else | |
1904 | *qp = scm_i_inum2big (qq); | |
1905 | *rp = SCM_I_MAKINUM (rr); | |
1906 | } | |
1907 | return; | |
1908 | } | |
1909 | else if (SCM_BIGP (y)) | |
1910 | { | |
1911 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1912 | scm_remember_upto_here_1 (y); | |
1913 | if (SCM_LIKELY (sign > 0)) | |
1914 | { | |
1915 | if (SCM_LIKELY (xx > 0)) | |
1916 | { | |
1917 | SCM r = scm_i_mkbig (); | |
1918 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1919 | scm_remember_upto_here_1 (y); | |
1920 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1921 | *qp = SCM_INUM1; | |
1922 | *rp = scm_i_normbig (r); | |
1923 | } | |
1924 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1925 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1926 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1927 | { | |
1928 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1929 | scm_remember_upto_here_1 (y); | |
1930 | *qp = SCM_I_MAKINUM (-1); | |
1931 | *rp = SCM_INUM0; | |
1932 | } | |
1933 | else | |
1934 | { | |
1935 | *qp = SCM_INUM0; | |
1936 | *rp = x; | |
1937 | } | |
1938 | } | |
1939 | else if (xx >= 0) | |
1940 | { | |
1941 | *qp = SCM_INUM0; | |
1942 | *rp = x; | |
1943 | } | |
1944 | else | |
1945 | { | |
1946 | SCM r = scm_i_mkbig (); | |
1947 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1948 | scm_remember_upto_here_1 (y); | |
1949 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1950 | *qp = SCM_INUM1; | |
1951 | *rp = scm_i_normbig (r); | |
1952 | } | |
1953 | return; | |
1954 | } | |
1955 | else if (SCM_REALP (y)) | |
1956 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1957 | else if (SCM_FRACTIONP (y)) | |
1958 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1959 | else | |
1960 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1961 | s_scm_ceiling_divide, qp, rp); | |
1962 | } | |
1963 | else if (SCM_BIGP (x)) | |
1964 | { | |
1965 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1966 | { | |
1967 | scm_t_inum yy = SCM_I_INUM (y); | |
1968 | if (SCM_UNLIKELY (yy == 0)) | |
1969 | scm_num_overflow (s_scm_ceiling_divide); | |
1970 | else | |
1971 | { | |
1972 | SCM q = scm_i_mkbig (); | |
1973 | SCM r = scm_i_mkbig (); | |
1974 | if (yy > 0) | |
1975 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1976 | SCM_I_BIG_MPZ (x), yy); | |
1977 | else | |
1978 | { | |
1979 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1980 | SCM_I_BIG_MPZ (x), -yy); | |
1981 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1982 | } | |
1983 | scm_remember_upto_here_1 (x); | |
1984 | *qp = scm_i_normbig (q); | |
1985 | *rp = scm_i_normbig (r); | |
1986 | } | |
1987 | return; | |
1988 | } | |
1989 | else if (SCM_BIGP (y)) | |
1990 | { | |
1991 | SCM q = scm_i_mkbig (); | |
1992 | SCM r = scm_i_mkbig (); | |
1993 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1994 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1995 | scm_remember_upto_here_2 (x, y); | |
1996 | *qp = scm_i_normbig (q); | |
1997 | *rp = scm_i_normbig (r); | |
1998 | return; | |
1999 | } | |
2000 | else if (SCM_REALP (y)) | |
2001 | return scm_i_inexact_ceiling_divide | |
2002 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2003 | else if (SCM_FRACTIONP (y)) | |
2004 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2005 | else | |
2006 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2007 | s_scm_ceiling_divide, qp, rp); | |
2008 | } | |
2009 | else if (SCM_REALP (x)) | |
2010 | { | |
2011 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2012 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2013 | return scm_i_inexact_ceiling_divide | |
2014 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2015 | else | |
2016 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2017 | s_scm_ceiling_divide, qp, rp); | |
2018 | } | |
2019 | else if (SCM_FRACTIONP (x)) | |
2020 | { | |
2021 | if (SCM_REALP (y)) | |
2022 | return scm_i_inexact_ceiling_divide | |
2023 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2024 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2025 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2026 | else | |
2027 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2028 | s_scm_ceiling_divide, qp, rp); | |
2029 | } | |
2030 | else | |
2031 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2032 | s_scm_ceiling_divide, qp, rp); | |
2033 | } | |
2034 | ||
2035 | static void | |
2036 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2037 | { | |
2038 | if (SCM_UNLIKELY (y == 0)) | |
2039 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2040 | else | |
2041 | { | |
2042 | double q = ceil (x / y); | |
2043 | double r = x - q * y; | |
2044 | *qp = scm_from_double (q); | |
2045 | *rp = scm_from_double (r); | |
2046 | } | |
2047 | } | |
2048 | ||
2049 | static void | |
2050 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2051 | { | |
2052 | SCM r1; | |
2053 | SCM xd = scm_denominator (x); | |
2054 | SCM yd = scm_denominator (y); | |
2055 | ||
2056 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2057 | scm_product (scm_numerator (y), xd), | |
2058 | qp, &r1); | |
2059 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2060 | } | |
2061 | ||
2062 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2063 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2064 | ||
2065 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2066 | (SCM x, SCM y), | |
2067 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2068 | "@lisp\n" | |
2069 | "(truncate-quotient 123 10) @result{} 12\n" | |
2070 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2071 | "(truncate-quotient -123 10) @result{} -12\n" | |
2072 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2073 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2074 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2075 | "@end lisp") | |
2076 | #define FUNC_NAME s_scm_truncate_quotient | |
2077 | { | |
2078 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2079 | { | |
2080 | scm_t_inum xx = SCM_I_INUM (x); | |
2081 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2082 | { | |
2083 | scm_t_inum yy = SCM_I_INUM (y); | |
2084 | if (SCM_UNLIKELY (yy == 0)) | |
2085 | scm_num_overflow (s_scm_truncate_quotient); | |
2086 | else | |
2087 | { | |
2088 | scm_t_inum qq = xx / yy; | |
2089 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2090 | return SCM_I_MAKINUM (qq); | |
2091 | else | |
2092 | return scm_i_inum2big (qq); | |
2093 | } | |
2094 | } | |
2095 | else if (SCM_BIGP (y)) | |
2096 | { | |
2097 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2098 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2099 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2100 | { | |
2101 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2102 | scm_remember_upto_here_1 (y); | |
2103 | return SCM_I_MAKINUM (-1); | |
2104 | } | |
2105 | else | |
2106 | return SCM_INUM0; | |
2107 | } | |
2108 | else if (SCM_REALP (y)) | |
2109 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2110 | else if (SCM_FRACTIONP (y)) | |
2111 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2112 | else | |
2113 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2114 | s_scm_truncate_quotient); | |
2115 | } | |
2116 | else if (SCM_BIGP (x)) | |
2117 | { | |
2118 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2119 | { | |
2120 | scm_t_inum yy = SCM_I_INUM (y); | |
2121 | if (SCM_UNLIKELY (yy == 0)) | |
2122 | scm_num_overflow (s_scm_truncate_quotient); | |
2123 | else if (SCM_UNLIKELY (yy == 1)) | |
2124 | return x; | |
2125 | else | |
2126 | { | |
2127 | SCM q = scm_i_mkbig (); | |
2128 | if (yy > 0) | |
2129 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2130 | else | |
2131 | { | |
2132 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2133 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2134 | } | |
2135 | scm_remember_upto_here_1 (x); | |
2136 | return scm_i_normbig (q); | |
2137 | } | |
2138 | } | |
2139 | else if (SCM_BIGP (y)) | |
2140 | { | |
2141 | SCM q = scm_i_mkbig (); | |
2142 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2143 | SCM_I_BIG_MPZ (x), | |
2144 | SCM_I_BIG_MPZ (y)); | |
2145 | scm_remember_upto_here_2 (x, y); | |
2146 | return scm_i_normbig (q); | |
2147 | } | |
2148 | else if (SCM_REALP (y)) | |
2149 | return scm_i_inexact_truncate_quotient | |
2150 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2151 | else if (SCM_FRACTIONP (y)) | |
2152 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2153 | else | |
2154 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2155 | s_scm_truncate_quotient); | |
2156 | } | |
2157 | else if (SCM_REALP (x)) | |
2158 | { | |
2159 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2160 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2161 | return scm_i_inexact_truncate_quotient | |
2162 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2163 | else | |
2164 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2165 | s_scm_truncate_quotient); | |
2166 | } | |
2167 | else if (SCM_FRACTIONP (x)) | |
2168 | { | |
2169 | if (SCM_REALP (y)) | |
2170 | return scm_i_inexact_truncate_quotient | |
2171 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2172 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2173 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2174 | else | |
2175 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2176 | s_scm_truncate_quotient); | |
2177 | } | |
2178 | else | |
2179 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2180 | s_scm_truncate_quotient); | |
2181 | } | |
2182 | #undef FUNC_NAME | |
2183 | ||
2184 | static SCM | |
2185 | scm_i_inexact_truncate_quotient (double x, double y) | |
2186 | { | |
2187 | if (SCM_UNLIKELY (y == 0)) | |
2188 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2189 | else | |
c251ab63 | 2190 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2191 | } |
2192 | ||
2193 | static SCM | |
2194 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2195 | { | |
2196 | return scm_truncate_quotient | |
2197 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2198 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2199 | } | |
2200 | ||
2201 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2202 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2203 | ||
2204 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2205 | (SCM x, SCM y), | |
2206 | "Return the real number @var{r} such that\n" | |
2207 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2208 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2209 | "@lisp\n" | |
2210 | "(truncate-remainder 123 10) @result{} 3\n" | |
2211 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2212 | "(truncate-remainder -123 10) @result{} -3\n" | |
2213 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2214 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2215 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2216 | "@end lisp") | |
2217 | #define FUNC_NAME s_scm_truncate_remainder | |
2218 | { | |
2219 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2220 | { | |
2221 | scm_t_inum xx = SCM_I_INUM (x); | |
2222 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2223 | { | |
2224 | scm_t_inum yy = SCM_I_INUM (y); | |
2225 | if (SCM_UNLIKELY (yy == 0)) | |
2226 | scm_num_overflow (s_scm_truncate_remainder); | |
2227 | else | |
2228 | return SCM_I_MAKINUM (xx % yy); | |
2229 | } | |
2230 | else if (SCM_BIGP (y)) | |
2231 | { | |
2232 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2233 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2234 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2235 | { | |
2236 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2237 | scm_remember_upto_here_1 (y); | |
2238 | return SCM_INUM0; | |
2239 | } | |
2240 | else | |
2241 | return x; | |
2242 | } | |
2243 | else if (SCM_REALP (y)) | |
2244 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2245 | else if (SCM_FRACTIONP (y)) | |
2246 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2247 | else | |
2248 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2249 | s_scm_truncate_remainder); | |
2250 | } | |
2251 | else if (SCM_BIGP (x)) | |
2252 | { | |
2253 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2254 | { | |
2255 | scm_t_inum yy = SCM_I_INUM (y); | |
2256 | if (SCM_UNLIKELY (yy == 0)) | |
2257 | scm_num_overflow (s_scm_truncate_remainder); | |
2258 | else | |
2259 | { | |
2260 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2261 | (yy > 0) ? yy : -yy) | |
2262 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2263 | scm_remember_upto_here_1 (x); | |
2264 | return SCM_I_MAKINUM (rr); | |
2265 | } | |
2266 | } | |
2267 | else if (SCM_BIGP (y)) | |
2268 | { | |
2269 | SCM r = scm_i_mkbig (); | |
2270 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2271 | SCM_I_BIG_MPZ (x), | |
2272 | SCM_I_BIG_MPZ (y)); | |
2273 | scm_remember_upto_here_2 (x, y); | |
2274 | return scm_i_normbig (r); | |
2275 | } | |
2276 | else if (SCM_REALP (y)) | |
2277 | return scm_i_inexact_truncate_remainder | |
2278 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2279 | else if (SCM_FRACTIONP (y)) | |
2280 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2281 | else | |
2282 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2283 | s_scm_truncate_remainder); | |
2284 | } | |
2285 | else if (SCM_REALP (x)) | |
2286 | { | |
2287 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2288 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2289 | return scm_i_inexact_truncate_remainder | |
2290 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2291 | else | |
2292 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2293 | s_scm_truncate_remainder); | |
2294 | } | |
2295 | else if (SCM_FRACTIONP (x)) | |
2296 | { | |
2297 | if (SCM_REALP (y)) | |
2298 | return scm_i_inexact_truncate_remainder | |
2299 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2300 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2301 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2302 | else | |
2303 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2304 | s_scm_truncate_remainder); | |
2305 | } | |
2306 | else | |
2307 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2308 | s_scm_truncate_remainder); | |
2309 | } | |
2310 | #undef FUNC_NAME | |
2311 | ||
2312 | static SCM | |
2313 | scm_i_inexact_truncate_remainder (double x, double y) | |
2314 | { | |
2315 | /* Although it would be more efficient to use fmod here, we can't | |
2316 | because it would in some cases produce results inconsistent with | |
2317 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2318 | close). In particular, when x is very close to a multiple of y, | |
2319 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2320 | correspond to different choices of q. If quotient chooses one and | |
2321 | remainder chooses the other, it would be bad. */ | |
2322 | if (SCM_UNLIKELY (y == 0)) | |
2323 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2324 | else | |
c251ab63 | 2325 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2326 | } |
2327 | ||
2328 | static SCM | |
2329 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2330 | { | |
2331 | SCM xd = scm_denominator (x); | |
2332 | SCM yd = scm_denominator (y); | |
2333 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2334 | scm_product (scm_numerator (y), xd)); | |
2335 | return scm_divide (r1, scm_product (xd, yd)); | |
2336 | } | |
2337 | ||
2338 | ||
2339 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2340 | SCM *qp, SCM *rp); | |
2341 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2342 | SCM *qp, SCM *rp); | |
2343 | ||
2344 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2345 | (SCM x, SCM y), | |
2346 | "Return the integer @var{q} and the real number @var{r}\n" | |
2347 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2348 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2349 | "@lisp\n" | |
2350 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2351 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2352 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2353 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2354 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2355 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2356 | "@end lisp") | |
2357 | #define FUNC_NAME s_scm_i_truncate_divide | |
2358 | { | |
2359 | SCM q, r; | |
2360 | ||
2361 | scm_truncate_divide(x, y, &q, &r); | |
2362 | return scm_values (scm_list_2 (q, r)); | |
2363 | } | |
2364 | #undef FUNC_NAME | |
2365 | ||
2366 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2367 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2368 | ||
2369 | void | |
2370 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2371 | { | |
2372 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2373 | { | |
2374 | scm_t_inum xx = SCM_I_INUM (x); | |
2375 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2376 | { | |
2377 | scm_t_inum yy = SCM_I_INUM (y); | |
2378 | if (SCM_UNLIKELY (yy == 0)) | |
2379 | scm_num_overflow (s_scm_truncate_divide); | |
2380 | else | |
2381 | { | |
2382 | scm_t_inum qq = xx / yy; | |
2383 | scm_t_inum rr = xx % yy; | |
2384 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2385 | *qp = SCM_I_MAKINUM (qq); | |
2386 | else | |
2387 | *qp = scm_i_inum2big (qq); | |
2388 | *rp = SCM_I_MAKINUM (rr); | |
2389 | } | |
2390 | return; | |
2391 | } | |
2392 | else if (SCM_BIGP (y)) | |
2393 | { | |
2394 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2395 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2396 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2397 | { | |
2398 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2399 | scm_remember_upto_here_1 (y); | |
2400 | *qp = SCM_I_MAKINUM (-1); | |
2401 | *rp = SCM_INUM0; | |
2402 | } | |
2403 | else | |
2404 | { | |
2405 | *qp = SCM_INUM0; | |
2406 | *rp = x; | |
2407 | } | |
2408 | return; | |
2409 | } | |
2410 | else if (SCM_REALP (y)) | |
2411 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2412 | else if (SCM_FRACTIONP (y)) | |
2413 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2414 | else | |
2415 | return two_valued_wta_dispatch_2 | |
2416 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2417 | s_scm_truncate_divide, qp, rp); | |
2418 | } | |
2419 | else if (SCM_BIGP (x)) | |
2420 | { | |
2421 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2422 | { | |
2423 | scm_t_inum yy = SCM_I_INUM (y); | |
2424 | if (SCM_UNLIKELY (yy == 0)) | |
2425 | scm_num_overflow (s_scm_truncate_divide); | |
2426 | else | |
2427 | { | |
2428 | SCM q = scm_i_mkbig (); | |
2429 | scm_t_inum rr; | |
2430 | if (yy > 0) | |
2431 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2432 | SCM_I_BIG_MPZ (x), yy); | |
2433 | else | |
2434 | { | |
2435 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2436 | SCM_I_BIG_MPZ (x), -yy); | |
2437 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2438 | } | |
2439 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2440 | scm_remember_upto_here_1 (x); | |
2441 | *qp = scm_i_normbig (q); | |
2442 | *rp = SCM_I_MAKINUM (rr); | |
2443 | } | |
2444 | return; | |
2445 | } | |
2446 | else if (SCM_BIGP (y)) | |
2447 | { | |
2448 | SCM q = scm_i_mkbig (); | |
2449 | SCM r = scm_i_mkbig (); | |
2450 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2451 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2452 | scm_remember_upto_here_2 (x, y); | |
2453 | *qp = scm_i_normbig (q); | |
2454 | *rp = scm_i_normbig (r); | |
2455 | } | |
2456 | else if (SCM_REALP (y)) | |
2457 | return scm_i_inexact_truncate_divide | |
2458 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2459 | else if (SCM_FRACTIONP (y)) | |
2460 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2461 | else | |
2462 | return two_valued_wta_dispatch_2 | |
2463 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2464 | s_scm_truncate_divide, qp, rp); | |
2465 | } | |
2466 | else if (SCM_REALP (x)) | |
2467 | { | |
2468 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2469 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2470 | return scm_i_inexact_truncate_divide | |
2471 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2472 | else | |
2473 | return two_valued_wta_dispatch_2 | |
2474 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2475 | s_scm_truncate_divide, qp, rp); | |
2476 | } | |
2477 | else if (SCM_FRACTIONP (x)) | |
2478 | { | |
2479 | if (SCM_REALP (y)) | |
2480 | return scm_i_inexact_truncate_divide | |
2481 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2482 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2483 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2484 | else | |
2485 | return two_valued_wta_dispatch_2 | |
2486 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2487 | s_scm_truncate_divide, qp, rp); | |
2488 | } | |
2489 | else | |
2490 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2491 | s_scm_truncate_divide, qp, rp); | |
2492 | } | |
2493 | ||
2494 | static void | |
2495 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2496 | { | |
2497 | if (SCM_UNLIKELY (y == 0)) | |
2498 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2499 | else | |
2500 | { | |
c15fe499 MW |
2501 | double q = trunc (x / y); |
2502 | double r = x - q * y; | |
8f9da340 MW |
2503 | *qp = scm_from_double (q); |
2504 | *rp = scm_from_double (r); | |
2505 | } | |
2506 | } | |
2507 | ||
2508 | static void | |
2509 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2510 | { | |
2511 | SCM r1; | |
2512 | SCM xd = scm_denominator (x); | |
2513 | SCM yd = scm_denominator (y); | |
2514 | ||
2515 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2516 | scm_product (scm_numerator (y), xd), | |
2517 | qp, &r1); | |
2518 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2519 | } | |
2520 | ||
ff62c168 MW |
2521 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2522 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2523 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2524 | |
8f9da340 MW |
2525 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2526 | (SCM x, SCM y), | |
2527 | "Return the integer @var{q} such that\n" | |
2528 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2529 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2530 | "@lisp\n" | |
2531 | "(centered-quotient 123 10) @result{} 12\n" | |
2532 | "(centered-quotient 123 -10) @result{} -12\n" | |
2533 | "(centered-quotient -123 10) @result{} -12\n" | |
2534 | "(centered-quotient -123 -10) @result{} 12\n" | |
2535 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2536 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2537 | "@end lisp") | |
2538 | #define FUNC_NAME s_scm_centered_quotient | |
2539 | { | |
2540 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2541 | { | |
2542 | scm_t_inum xx = SCM_I_INUM (x); | |
2543 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2544 | { | |
2545 | scm_t_inum yy = SCM_I_INUM (y); | |
2546 | if (SCM_UNLIKELY (yy == 0)) | |
2547 | scm_num_overflow (s_scm_centered_quotient); | |
2548 | else | |
2549 | { | |
2550 | scm_t_inum qq = xx / yy; | |
2551 | scm_t_inum rr = xx % yy; | |
2552 | if (SCM_LIKELY (xx > 0)) | |
2553 | { | |
2554 | if (SCM_LIKELY (yy > 0)) | |
2555 | { | |
2556 | if (rr >= (yy + 1) / 2) | |
2557 | qq++; | |
2558 | } | |
2559 | else | |
2560 | { | |
2561 | if (rr >= (1 - yy) / 2) | |
2562 | qq--; | |
2563 | } | |
2564 | } | |
2565 | else | |
2566 | { | |
2567 | if (SCM_LIKELY (yy > 0)) | |
2568 | { | |
2569 | if (rr < -yy / 2) | |
2570 | qq--; | |
2571 | } | |
2572 | else | |
2573 | { | |
2574 | if (rr < yy / 2) | |
2575 | qq++; | |
2576 | } | |
2577 | } | |
2578 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2579 | return SCM_I_MAKINUM (qq); | |
2580 | else | |
2581 | return scm_i_inum2big (qq); | |
2582 | } | |
2583 | } | |
2584 | else if (SCM_BIGP (y)) | |
2585 | { | |
2586 | /* Pass a denormalized bignum version of x (even though it | |
2587 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2588 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2589 | } | |
2590 | else if (SCM_REALP (y)) | |
2591 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2592 | else if (SCM_FRACTIONP (y)) | |
2593 | return scm_i_exact_rational_centered_quotient (x, y); | |
2594 | else | |
2595 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2596 | s_scm_centered_quotient); | |
2597 | } | |
2598 | else if (SCM_BIGP (x)) | |
2599 | { | |
2600 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2601 | { | |
2602 | scm_t_inum yy = SCM_I_INUM (y); | |
2603 | if (SCM_UNLIKELY (yy == 0)) | |
2604 | scm_num_overflow (s_scm_centered_quotient); | |
2605 | else if (SCM_UNLIKELY (yy == 1)) | |
2606 | return x; | |
2607 | else | |
2608 | { | |
2609 | SCM q = scm_i_mkbig (); | |
2610 | scm_t_inum rr; | |
2611 | /* Arrange for rr to initially be non-positive, | |
2612 | because that simplifies the test to see | |
2613 | if it is within the needed bounds. */ | |
2614 | if (yy > 0) | |
2615 | { | |
2616 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2617 | SCM_I_BIG_MPZ (x), yy); | |
2618 | scm_remember_upto_here_1 (x); | |
2619 | if (rr < -yy / 2) | |
2620 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2621 | SCM_I_BIG_MPZ (q), 1); | |
2622 | } | |
2623 | else | |
2624 | { | |
2625 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2626 | SCM_I_BIG_MPZ (x), -yy); | |
2627 | scm_remember_upto_here_1 (x); | |
2628 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2629 | if (rr < yy / 2) | |
2630 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2631 | SCM_I_BIG_MPZ (q), 1); | |
2632 | } | |
2633 | return scm_i_normbig (q); | |
2634 | } | |
2635 | } | |
2636 | else if (SCM_BIGP (y)) | |
2637 | return scm_i_bigint_centered_quotient (x, y); | |
2638 | else if (SCM_REALP (y)) | |
2639 | return scm_i_inexact_centered_quotient | |
2640 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2641 | else if (SCM_FRACTIONP (y)) | |
2642 | return scm_i_exact_rational_centered_quotient (x, y); | |
2643 | else | |
2644 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2645 | s_scm_centered_quotient); | |
2646 | } | |
2647 | else if (SCM_REALP (x)) | |
2648 | { | |
2649 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2650 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2651 | return scm_i_inexact_centered_quotient | |
2652 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2653 | else | |
2654 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2655 | s_scm_centered_quotient); | |
2656 | } | |
2657 | else if (SCM_FRACTIONP (x)) | |
2658 | { | |
2659 | if (SCM_REALP (y)) | |
2660 | return scm_i_inexact_centered_quotient | |
2661 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2662 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2663 | return scm_i_exact_rational_centered_quotient (x, y); | |
2664 | else | |
2665 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2666 | s_scm_centered_quotient); | |
2667 | } | |
2668 | else | |
2669 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2670 | s_scm_centered_quotient); | |
2671 | } | |
2672 | #undef FUNC_NAME | |
2673 | ||
2674 | static SCM | |
2675 | scm_i_inexact_centered_quotient (double x, double y) | |
2676 | { | |
2677 | if (SCM_LIKELY (y > 0)) | |
2678 | return scm_from_double (floor (x/y + 0.5)); | |
2679 | else if (SCM_LIKELY (y < 0)) | |
2680 | return scm_from_double (ceil (x/y - 0.5)); | |
2681 | else if (y == 0) | |
2682 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2683 | else | |
2684 | return scm_nan (); | |
2685 | } | |
2686 | ||
2687 | /* Assumes that both x and y are bigints, though | |
2688 | x might be able to fit into a fixnum. */ | |
2689 | static SCM | |
2690 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2691 | { | |
2692 | SCM q, r, min_r; | |
2693 | ||
2694 | /* Note that x might be small enough to fit into a | |
2695 | fixnum, so we must not let it escape into the wild */ | |
2696 | q = scm_i_mkbig (); | |
2697 | r = scm_i_mkbig (); | |
2698 | ||
2699 | /* min_r will eventually become -abs(y)/2 */ | |
2700 | min_r = scm_i_mkbig (); | |
2701 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2702 | SCM_I_BIG_MPZ (y), 1); | |
2703 | ||
2704 | /* Arrange for rr to initially be non-positive, | |
2705 | because that simplifies the test to see | |
2706 | if it is within the needed bounds. */ | |
2707 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2708 | { | |
2709 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2710 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2711 | scm_remember_upto_here_2 (x, y); | |
2712 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2713 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2714 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2715 | SCM_I_BIG_MPZ (q), 1); | |
2716 | } | |
2717 | else | |
2718 | { | |
2719 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2720 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2721 | scm_remember_upto_here_2 (x, y); | |
2722 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2723 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2724 | SCM_I_BIG_MPZ (q), 1); | |
2725 | } | |
2726 | scm_remember_upto_here_2 (r, min_r); | |
2727 | return scm_i_normbig (q); | |
2728 | } | |
2729 | ||
2730 | static SCM | |
2731 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2732 | { | |
2733 | return scm_centered_quotient | |
2734 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2735 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2736 | } | |
2737 | ||
2738 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2739 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2740 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2741 | ||
2742 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2743 | (SCM x, SCM y), | |
2744 | "Return the real number @var{r} such that\n" | |
2745 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2746 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2747 | "for some integer @var{q}.\n" | |
2748 | "@lisp\n" | |
2749 | "(centered-remainder 123 10) @result{} 3\n" | |
2750 | "(centered-remainder 123 -10) @result{} 3\n" | |
2751 | "(centered-remainder -123 10) @result{} -3\n" | |
2752 | "(centered-remainder -123 -10) @result{} -3\n" | |
2753 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2754 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2755 | "@end lisp") | |
2756 | #define FUNC_NAME s_scm_centered_remainder | |
2757 | { | |
2758 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2759 | { | |
2760 | scm_t_inum xx = SCM_I_INUM (x); | |
2761 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2762 | { | |
2763 | scm_t_inum yy = SCM_I_INUM (y); | |
2764 | if (SCM_UNLIKELY (yy == 0)) | |
2765 | scm_num_overflow (s_scm_centered_remainder); | |
2766 | else | |
2767 | { | |
2768 | scm_t_inum rr = xx % yy; | |
2769 | if (SCM_LIKELY (xx > 0)) | |
2770 | { | |
2771 | if (SCM_LIKELY (yy > 0)) | |
2772 | { | |
2773 | if (rr >= (yy + 1) / 2) | |
2774 | rr -= yy; | |
2775 | } | |
2776 | else | |
2777 | { | |
2778 | if (rr >= (1 - yy) / 2) | |
2779 | rr += yy; | |
2780 | } | |
2781 | } | |
2782 | else | |
2783 | { | |
2784 | if (SCM_LIKELY (yy > 0)) | |
2785 | { | |
2786 | if (rr < -yy / 2) | |
2787 | rr += yy; | |
2788 | } | |
2789 | else | |
2790 | { | |
2791 | if (rr < yy / 2) | |
2792 | rr -= yy; | |
2793 | } | |
2794 | } | |
2795 | return SCM_I_MAKINUM (rr); | |
2796 | } | |
2797 | } | |
2798 | else if (SCM_BIGP (y)) | |
2799 | { | |
2800 | /* Pass a denormalized bignum version of x (even though it | |
2801 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2802 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2803 | } | |
2804 | else if (SCM_REALP (y)) | |
2805 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2806 | else if (SCM_FRACTIONP (y)) | |
2807 | return scm_i_exact_rational_centered_remainder (x, y); | |
2808 | else | |
2809 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2810 | s_scm_centered_remainder); | |
2811 | } | |
2812 | else if (SCM_BIGP (x)) | |
2813 | { | |
2814 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2815 | { | |
2816 | scm_t_inum yy = SCM_I_INUM (y); | |
2817 | if (SCM_UNLIKELY (yy == 0)) | |
2818 | scm_num_overflow (s_scm_centered_remainder); | |
2819 | else | |
2820 | { | |
2821 | scm_t_inum rr; | |
2822 | /* Arrange for rr to initially be non-positive, | |
2823 | because that simplifies the test to see | |
2824 | if it is within the needed bounds. */ | |
2825 | if (yy > 0) | |
2826 | { | |
2827 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2828 | scm_remember_upto_here_1 (x); | |
2829 | if (rr < -yy / 2) | |
2830 | rr += yy; | |
2831 | } | |
2832 | else | |
2833 | { | |
2834 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2835 | scm_remember_upto_here_1 (x); | |
2836 | if (rr < yy / 2) | |
2837 | rr -= yy; | |
2838 | } | |
2839 | return SCM_I_MAKINUM (rr); | |
2840 | } | |
2841 | } | |
2842 | else if (SCM_BIGP (y)) | |
2843 | return scm_i_bigint_centered_remainder (x, y); | |
2844 | else if (SCM_REALP (y)) | |
2845 | return scm_i_inexact_centered_remainder | |
2846 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2847 | else if (SCM_FRACTIONP (y)) | |
2848 | return scm_i_exact_rational_centered_remainder (x, y); | |
2849 | else | |
2850 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2851 | s_scm_centered_remainder); | |
2852 | } | |
2853 | else if (SCM_REALP (x)) | |
2854 | { | |
2855 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2856 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2857 | return scm_i_inexact_centered_remainder | |
2858 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2859 | else | |
2860 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2861 | s_scm_centered_remainder); | |
2862 | } | |
2863 | else if (SCM_FRACTIONP (x)) | |
2864 | { | |
2865 | if (SCM_REALP (y)) | |
2866 | return scm_i_inexact_centered_remainder | |
2867 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2868 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2869 | return scm_i_exact_rational_centered_remainder (x, y); | |
2870 | else | |
2871 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2872 | s_scm_centered_remainder); | |
2873 | } | |
2874 | else | |
2875 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2876 | s_scm_centered_remainder); | |
2877 | } | |
2878 | #undef FUNC_NAME | |
2879 | ||
2880 | static SCM | |
2881 | scm_i_inexact_centered_remainder (double x, double y) | |
2882 | { | |
2883 | double q; | |
2884 | ||
2885 | /* Although it would be more efficient to use fmod here, we can't | |
2886 | because it would in some cases produce results inconsistent with | |
2887 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
2888 | close). In particular, when x-y/2 is very close to a multiple of | |
2889 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
2890 | two cases must correspond to different choices of q. If quotient | |
2891 | chooses one and remainder chooses the other, it would be bad. */ | |
2892 | if (SCM_LIKELY (y > 0)) | |
2893 | q = floor (x/y + 0.5); | |
2894 | else if (SCM_LIKELY (y < 0)) | |
2895 | q = ceil (x/y - 0.5); | |
2896 | else if (y == 0) | |
2897 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
2898 | else | |
2899 | return scm_nan (); | |
2900 | return scm_from_double (x - q * y); | |
2901 | } | |
2902 | ||
2903 | /* Assumes that both x and y are bigints, though | |
2904 | x might be able to fit into a fixnum. */ | |
2905 | static SCM | |
2906 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2907 | { | |
2908 | SCM r, min_r; | |
2909 | ||
2910 | /* Note that x might be small enough to fit into a | |
2911 | fixnum, so we must not let it escape into the wild */ | |
2912 | r = scm_i_mkbig (); | |
2913 | ||
2914 | /* min_r will eventually become -abs(y)/2 */ | |
2915 | min_r = scm_i_mkbig (); | |
2916 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2917 | SCM_I_BIG_MPZ (y), 1); | |
2918 | ||
2919 | /* Arrange for rr to initially be non-positive, | |
2920 | because that simplifies the test to see | |
2921 | if it is within the needed bounds. */ | |
2922 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2923 | { | |
2924 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2925 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2926 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2927 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2928 | mpz_add (SCM_I_BIG_MPZ (r), | |
2929 | SCM_I_BIG_MPZ (r), | |
2930 | SCM_I_BIG_MPZ (y)); | |
2931 | } | |
2932 | else | |
2933 | { | |
2934 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2935 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2936 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2937 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2938 | SCM_I_BIG_MPZ (r), | |
2939 | SCM_I_BIG_MPZ (y)); | |
2940 | } | |
2941 | scm_remember_upto_here_2 (x, y); | |
2942 | return scm_i_normbig (r); | |
2943 | } | |
2944 | ||
2945 | static SCM | |
2946 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
2947 | { | |
2948 | SCM xd = scm_denominator (x); | |
2949 | SCM yd = scm_denominator (y); | |
2950 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2951 | scm_product (scm_numerator (y), xd)); | |
2952 | return scm_divide (r1, scm_product (xd, yd)); | |
2953 | } | |
2954 | ||
2955 | ||
2956 | static void scm_i_inexact_centered_divide (double x, double y, | |
2957 | SCM *qp, SCM *rp); | |
2958 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
2959 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
2960 | SCM *qp, SCM *rp); | |
2961 | ||
2962 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
2963 | (SCM x, SCM y), | |
2964 | "Return the integer @var{q} and the real number @var{r}\n" | |
2965 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2966 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2967 | "@lisp\n" | |
2968 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2969 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2970 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2971 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2972 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2973 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2974 | "@end lisp") | |
2975 | #define FUNC_NAME s_scm_i_centered_divide | |
2976 | { | |
2977 | SCM q, r; | |
2978 | ||
2979 | scm_centered_divide(x, y, &q, &r); | |
2980 | return scm_values (scm_list_2 (q, r)); | |
2981 | } | |
2982 | #undef FUNC_NAME | |
2983 | ||
2984 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2985 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2986 | ||
2987 | void | |
2988 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2989 | { | |
2990 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2991 | { | |
2992 | scm_t_inum xx = SCM_I_INUM (x); | |
2993 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2994 | { | |
2995 | scm_t_inum yy = SCM_I_INUM (y); | |
2996 | if (SCM_UNLIKELY (yy == 0)) | |
2997 | scm_num_overflow (s_scm_centered_divide); | |
2998 | else | |
2999 | { | |
3000 | scm_t_inum qq = xx / yy; | |
3001 | scm_t_inum rr = xx % yy; | |
3002 | if (SCM_LIKELY (xx > 0)) | |
3003 | { | |
3004 | if (SCM_LIKELY (yy > 0)) | |
3005 | { | |
3006 | if (rr >= (yy + 1) / 2) | |
3007 | { qq++; rr -= yy; } | |
3008 | } | |
3009 | else | |
3010 | { | |
3011 | if (rr >= (1 - yy) / 2) | |
3012 | { qq--; rr += yy; } | |
3013 | } | |
3014 | } | |
3015 | else | |
3016 | { | |
3017 | if (SCM_LIKELY (yy > 0)) | |
3018 | { | |
3019 | if (rr < -yy / 2) | |
3020 | { qq--; rr += yy; } | |
3021 | } | |
3022 | else | |
3023 | { | |
3024 | if (rr < yy / 2) | |
3025 | { qq++; rr -= yy; } | |
3026 | } | |
3027 | } | |
3028 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3029 | *qp = SCM_I_MAKINUM (qq); | |
3030 | else | |
3031 | *qp = scm_i_inum2big (qq); | |
3032 | *rp = SCM_I_MAKINUM (rr); | |
3033 | } | |
3034 | return; | |
3035 | } | |
3036 | else if (SCM_BIGP (y)) | |
3037 | { | |
3038 | /* Pass a denormalized bignum version of x (even though it | |
3039 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3040 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3041 | } | |
3042 | else if (SCM_REALP (y)) | |
3043 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3044 | else if (SCM_FRACTIONP (y)) | |
3045 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3046 | else | |
3047 | return two_valued_wta_dispatch_2 | |
3048 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3049 | s_scm_centered_divide, qp, rp); | |
3050 | } | |
3051 | else if (SCM_BIGP (x)) | |
3052 | { | |
3053 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3054 | { | |
3055 | scm_t_inum yy = SCM_I_INUM (y); | |
3056 | if (SCM_UNLIKELY (yy == 0)) | |
3057 | scm_num_overflow (s_scm_centered_divide); | |
3058 | else | |
3059 | { | |
3060 | SCM q = scm_i_mkbig (); | |
3061 | scm_t_inum rr; | |
3062 | /* Arrange for rr to initially be non-positive, | |
3063 | because that simplifies the test to see | |
3064 | if it is within the needed bounds. */ | |
3065 | if (yy > 0) | |
3066 | { | |
3067 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3068 | SCM_I_BIG_MPZ (x), yy); | |
3069 | scm_remember_upto_here_1 (x); | |
3070 | if (rr < -yy / 2) | |
3071 | { | |
3072 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3073 | SCM_I_BIG_MPZ (q), 1); | |
3074 | rr += yy; | |
3075 | } | |
3076 | } | |
3077 | else | |
3078 | { | |
3079 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3080 | SCM_I_BIG_MPZ (x), -yy); | |
3081 | scm_remember_upto_here_1 (x); | |
3082 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3083 | if (rr < yy / 2) | |
3084 | { | |
3085 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3086 | SCM_I_BIG_MPZ (q), 1); | |
3087 | rr -= yy; | |
3088 | } | |
3089 | } | |
3090 | *qp = scm_i_normbig (q); | |
3091 | *rp = SCM_I_MAKINUM (rr); | |
3092 | } | |
3093 | return; | |
3094 | } | |
3095 | else if (SCM_BIGP (y)) | |
3096 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3097 | else if (SCM_REALP (y)) | |
3098 | return scm_i_inexact_centered_divide | |
3099 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3100 | else if (SCM_FRACTIONP (y)) | |
3101 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3102 | else | |
3103 | return two_valued_wta_dispatch_2 | |
3104 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3105 | s_scm_centered_divide, qp, rp); | |
3106 | } | |
3107 | else if (SCM_REALP (x)) | |
3108 | { | |
3109 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3110 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3111 | return scm_i_inexact_centered_divide | |
3112 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3113 | else | |
3114 | return two_valued_wta_dispatch_2 | |
3115 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3116 | s_scm_centered_divide, qp, rp); | |
3117 | } | |
3118 | else if (SCM_FRACTIONP (x)) | |
3119 | { | |
3120 | if (SCM_REALP (y)) | |
3121 | return scm_i_inexact_centered_divide | |
3122 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3123 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3124 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3125 | else | |
3126 | return two_valued_wta_dispatch_2 | |
3127 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3128 | s_scm_centered_divide, qp, rp); | |
3129 | } | |
3130 | else | |
3131 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3132 | s_scm_centered_divide, qp, rp); | |
3133 | } | |
3134 | ||
3135 | static void | |
3136 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3137 | { | |
3138 | double q, r; | |
3139 | ||
3140 | if (SCM_LIKELY (y > 0)) | |
3141 | q = floor (x/y + 0.5); | |
3142 | else if (SCM_LIKELY (y < 0)) | |
3143 | q = ceil (x/y - 0.5); | |
3144 | else if (y == 0) | |
3145 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3146 | else | |
3147 | q = guile_NaN; | |
3148 | r = x - q * y; | |
3149 | *qp = scm_from_double (q); | |
3150 | *rp = scm_from_double (r); | |
3151 | } | |
3152 | ||
3153 | /* Assumes that both x and y are bigints, though | |
3154 | x might be able to fit into a fixnum. */ | |
3155 | static void | |
3156 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3157 | { | |
3158 | SCM q, r, min_r; | |
3159 | ||
3160 | /* Note that x might be small enough to fit into a | |
3161 | fixnum, so we must not let it escape into the wild */ | |
3162 | q = scm_i_mkbig (); | |
3163 | r = scm_i_mkbig (); | |
3164 | ||
3165 | /* min_r will eventually become -abs(y/2) */ | |
3166 | min_r = scm_i_mkbig (); | |
3167 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3168 | SCM_I_BIG_MPZ (y), 1); | |
3169 | ||
3170 | /* Arrange for rr to initially be non-positive, | |
3171 | because that simplifies the test to see | |
3172 | if it is within the needed bounds. */ | |
3173 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3174 | { | |
3175 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3176 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3177 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3178 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3179 | { | |
3180 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3181 | SCM_I_BIG_MPZ (q), 1); | |
3182 | mpz_add (SCM_I_BIG_MPZ (r), | |
3183 | SCM_I_BIG_MPZ (r), | |
3184 | SCM_I_BIG_MPZ (y)); | |
3185 | } | |
3186 | } | |
3187 | else | |
3188 | { | |
3189 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3190 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3191 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3192 | { | |
3193 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3194 | SCM_I_BIG_MPZ (q), 1); | |
3195 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3196 | SCM_I_BIG_MPZ (r), | |
3197 | SCM_I_BIG_MPZ (y)); | |
3198 | } | |
3199 | } | |
3200 | scm_remember_upto_here_2 (x, y); | |
3201 | *qp = scm_i_normbig (q); | |
3202 | *rp = scm_i_normbig (r); | |
3203 | } | |
3204 | ||
3205 | static void | |
3206 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3207 | { | |
3208 | SCM r1; | |
3209 | SCM xd = scm_denominator (x); | |
3210 | SCM yd = scm_denominator (y); | |
3211 | ||
3212 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3213 | scm_product (scm_numerator (y), xd), | |
3214 | qp, &r1); | |
3215 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3216 | } | |
3217 | ||
3218 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3219 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3220 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3221 | ||
3222 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3223 | (SCM x, SCM y), |
8f9da340 MW |
3224 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3225 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3226 | "@lisp\n" |
8f9da340 MW |
3227 | "(round-quotient 123 10) @result{} 12\n" |
3228 | "(round-quotient 123 -10) @result{} -12\n" | |
3229 | "(round-quotient -123 10) @result{} -12\n" | |
3230 | "(round-quotient -123 -10) @result{} 12\n" | |
3231 | "(round-quotient 125 10) @result{} 12\n" | |
3232 | "(round-quotient 127 10) @result{} 13\n" | |
3233 | "(round-quotient 135 10) @result{} 14\n" | |
3234 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3235 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3236 | "@end lisp") |
8f9da340 | 3237 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3238 | { |
3239 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3240 | { | |
4a46bc2a | 3241 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3242 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3243 | { | |
3244 | scm_t_inum yy = SCM_I_INUM (y); | |
3245 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3246 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3247 | else |
3248 | { | |
ff62c168 | 3249 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3250 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3251 | scm_t_inum ay = yy; |
3252 | scm_t_inum r2 = 2 * rr; | |
3253 | ||
3254 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3255 | { |
8f9da340 MW |
3256 | ay = -ay; |
3257 | r2 = -r2; | |
3258 | } | |
3259 | ||
3260 | if (qq & 1L) | |
3261 | { | |
3262 | if (r2 >= ay) | |
3263 | qq++; | |
3264 | else if (r2 <= -ay) | |
3265 | qq--; | |
ff62c168 MW |
3266 | } |
3267 | else | |
3268 | { | |
8f9da340 MW |
3269 | if (r2 > ay) |
3270 | qq++; | |
3271 | else if (r2 < -ay) | |
3272 | qq--; | |
ff62c168 | 3273 | } |
4a46bc2a MW |
3274 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3275 | return SCM_I_MAKINUM (qq); | |
3276 | else | |
3277 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3278 | } |
3279 | } | |
3280 | else if (SCM_BIGP (y)) | |
3281 | { | |
3282 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3283 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3284 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3285 | } |
3286 | else if (SCM_REALP (y)) | |
8f9da340 | 3287 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3288 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3289 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3290 | else |
8f9da340 MW |
3291 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3292 | s_scm_round_quotient); | |
ff62c168 MW |
3293 | } |
3294 | else if (SCM_BIGP (x)) | |
3295 | { | |
3296 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3297 | { | |
3298 | scm_t_inum yy = SCM_I_INUM (y); | |
3299 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3300 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3301 | else if (SCM_UNLIKELY (yy == 1)) |
3302 | return x; | |
ff62c168 MW |
3303 | else |
3304 | { | |
3305 | SCM q = scm_i_mkbig (); | |
3306 | scm_t_inum rr; | |
8f9da340 MW |
3307 | int needs_adjustment; |
3308 | ||
ff62c168 MW |
3309 | if (yy > 0) |
3310 | { | |
8f9da340 MW |
3311 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3312 | SCM_I_BIG_MPZ (x), yy); | |
3313 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3314 | needs_adjustment = (2*rr >= yy); | |
3315 | else | |
3316 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3317 | } |
3318 | else | |
3319 | { | |
3320 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3321 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3322 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3323 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3324 | needs_adjustment = (2*rr <= yy); | |
3325 | else | |
3326 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3327 | } |
8f9da340 MW |
3328 | scm_remember_upto_here_1 (x); |
3329 | if (needs_adjustment) | |
3330 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3331 | return scm_i_normbig (q); |
3332 | } | |
3333 | } | |
3334 | else if (SCM_BIGP (y)) | |
8f9da340 | 3335 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3336 | else if (SCM_REALP (y)) |
8f9da340 | 3337 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3338 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3339 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3340 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3341 | else |
8f9da340 MW |
3342 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3343 | s_scm_round_quotient); | |
ff62c168 MW |
3344 | } |
3345 | else if (SCM_REALP (x)) | |
3346 | { | |
3347 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3348 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3349 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3350 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3351 | else | |
8f9da340 MW |
3352 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3353 | s_scm_round_quotient); | |
ff62c168 MW |
3354 | } |
3355 | else if (SCM_FRACTIONP (x)) | |
3356 | { | |
3357 | if (SCM_REALP (y)) | |
8f9da340 | 3358 | return scm_i_inexact_round_quotient |
ff62c168 | 3359 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3360 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3361 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3362 | else |
8f9da340 MW |
3363 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3364 | s_scm_round_quotient); | |
ff62c168 MW |
3365 | } |
3366 | else | |
8f9da340 MW |
3367 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3368 | s_scm_round_quotient); | |
ff62c168 MW |
3369 | } |
3370 | #undef FUNC_NAME | |
3371 | ||
3372 | static SCM | |
8f9da340 | 3373 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3374 | { |
8f9da340 MW |
3375 | if (SCM_UNLIKELY (y == 0)) |
3376 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3377 | else |
8f9da340 | 3378 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3379 | } |
3380 | ||
3381 | /* Assumes that both x and y are bigints, though | |
3382 | x might be able to fit into a fixnum. */ | |
3383 | static SCM | |
8f9da340 | 3384 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3385 | { |
8f9da340 MW |
3386 | SCM q, r, r2; |
3387 | int cmp, needs_adjustment; | |
ff62c168 MW |
3388 | |
3389 | /* Note that x might be small enough to fit into a | |
3390 | fixnum, so we must not let it escape into the wild */ | |
3391 | q = scm_i_mkbig (); | |
3392 | r = scm_i_mkbig (); | |
8f9da340 | 3393 | r2 = scm_i_mkbig (); |
ff62c168 | 3394 | |
8f9da340 MW |
3395 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3396 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3397 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3398 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3399 | |
8f9da340 MW |
3400 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3401 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3402 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3403 | else |
8f9da340 MW |
3404 | needs_adjustment = (cmp > 0); |
3405 | scm_remember_upto_here_2 (r2, y); | |
3406 | ||
3407 | if (needs_adjustment) | |
3408 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3409 | ||
ff62c168 MW |
3410 | return scm_i_normbig (q); |
3411 | } | |
3412 | ||
ff62c168 | 3413 | static SCM |
8f9da340 | 3414 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3415 | { |
8f9da340 | 3416 | return scm_round_quotient |
03ddd15b MW |
3417 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3418 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3419 | } |
3420 | ||
8f9da340 MW |
3421 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3422 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3423 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3424 | |
8f9da340 | 3425 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3426 | (SCM x, SCM y), |
3427 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3428 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3429 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3430 | "nearest integer, with ties going to the nearest\n" | |
3431 | "even integer.\n" | |
ff62c168 | 3432 | "@lisp\n" |
8f9da340 MW |
3433 | "(round-remainder 123 10) @result{} 3\n" |
3434 | "(round-remainder 123 -10) @result{} 3\n" | |
3435 | "(round-remainder -123 10) @result{} -3\n" | |
3436 | "(round-remainder -123 -10) @result{} -3\n" | |
3437 | "(round-remainder 125 10) @result{} 5\n" | |
3438 | "(round-remainder 127 10) @result{} -3\n" | |
3439 | "(round-remainder 135 10) @result{} -5\n" | |
3440 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3441 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3442 | "@end lisp") |
8f9da340 | 3443 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3444 | { |
3445 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3446 | { | |
4a46bc2a | 3447 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3448 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3449 | { | |
3450 | scm_t_inum yy = SCM_I_INUM (y); | |
3451 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3452 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3453 | else |
3454 | { | |
8f9da340 | 3455 | scm_t_inum qq = xx / yy; |
ff62c168 | 3456 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3457 | scm_t_inum ay = yy; |
3458 | scm_t_inum r2 = 2 * rr; | |
3459 | ||
3460 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3461 | { |
8f9da340 MW |
3462 | ay = -ay; |
3463 | r2 = -r2; | |
3464 | } | |
3465 | ||
3466 | if (qq & 1L) | |
3467 | { | |
3468 | if (r2 >= ay) | |
3469 | rr -= yy; | |
3470 | else if (r2 <= -ay) | |
3471 | rr += yy; | |
ff62c168 MW |
3472 | } |
3473 | else | |
3474 | { | |
8f9da340 MW |
3475 | if (r2 > ay) |
3476 | rr -= yy; | |
3477 | else if (r2 < -ay) | |
3478 | rr += yy; | |
ff62c168 MW |
3479 | } |
3480 | return SCM_I_MAKINUM (rr); | |
3481 | } | |
3482 | } | |
3483 | else if (SCM_BIGP (y)) | |
3484 | { | |
3485 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3486 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3487 | return scm_i_bigint_round_remainder | |
3488 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3489 | } |
3490 | else if (SCM_REALP (y)) | |
8f9da340 | 3491 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3492 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3493 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3494 | else |
8f9da340 MW |
3495 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3496 | s_scm_round_remainder); | |
ff62c168 MW |
3497 | } |
3498 | else if (SCM_BIGP (x)) | |
3499 | { | |
3500 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3501 | { | |
3502 | scm_t_inum yy = SCM_I_INUM (y); | |
3503 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3504 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3505 | else |
3506 | { | |
8f9da340 | 3507 | SCM q = scm_i_mkbig (); |
ff62c168 | 3508 | scm_t_inum rr; |
8f9da340 MW |
3509 | int needs_adjustment; |
3510 | ||
ff62c168 MW |
3511 | if (yy > 0) |
3512 | { | |
8f9da340 MW |
3513 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3514 | SCM_I_BIG_MPZ (x), yy); | |
3515 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3516 | needs_adjustment = (2*rr >= yy); | |
3517 | else | |
3518 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3519 | } |
3520 | else | |
3521 | { | |
8f9da340 MW |
3522 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3523 | SCM_I_BIG_MPZ (x), -yy); | |
3524 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3525 | needs_adjustment = (2*rr <= yy); | |
3526 | else | |
3527 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3528 | } |
8f9da340 MW |
3529 | scm_remember_upto_here_2 (x, q); |
3530 | if (needs_adjustment) | |
3531 | rr -= yy; | |
ff62c168 MW |
3532 | return SCM_I_MAKINUM (rr); |
3533 | } | |
3534 | } | |
3535 | else if (SCM_BIGP (y)) | |
8f9da340 | 3536 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3537 | else if (SCM_REALP (y)) |
8f9da340 | 3538 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3539 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3540 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3541 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3542 | else |
8f9da340 MW |
3543 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3544 | s_scm_round_remainder); | |
ff62c168 MW |
3545 | } |
3546 | else if (SCM_REALP (x)) | |
3547 | { | |
3548 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3549 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3550 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3551 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3552 | else | |
8f9da340 MW |
3553 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3554 | s_scm_round_remainder); | |
ff62c168 MW |
3555 | } |
3556 | else if (SCM_FRACTIONP (x)) | |
3557 | { | |
3558 | if (SCM_REALP (y)) | |
8f9da340 | 3559 | return scm_i_inexact_round_remainder |
ff62c168 | 3560 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3561 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3562 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3563 | else |
8f9da340 MW |
3564 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3565 | s_scm_round_remainder); | |
ff62c168 MW |
3566 | } |
3567 | else | |
8f9da340 MW |
3568 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3569 | s_scm_round_remainder); | |
ff62c168 MW |
3570 | } |
3571 | #undef FUNC_NAME | |
3572 | ||
3573 | static SCM | |
8f9da340 | 3574 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3575 | { |
ff62c168 MW |
3576 | /* Although it would be more efficient to use fmod here, we can't |
3577 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3578 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3579 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3580 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3581 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3582 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3583 | |
3584 | if (SCM_UNLIKELY (y == 0)) | |
3585 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3586 | else |
8f9da340 MW |
3587 | { |
3588 | double q = scm_c_round (x / y); | |
3589 | return scm_from_double (x - q * y); | |
3590 | } | |
ff62c168 MW |
3591 | } |
3592 | ||
3593 | /* Assumes that both x and y are bigints, though | |
3594 | x might be able to fit into a fixnum. */ | |
3595 | static SCM | |
8f9da340 | 3596 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3597 | { |
8f9da340 MW |
3598 | SCM q, r, r2; |
3599 | int cmp, needs_adjustment; | |
ff62c168 MW |
3600 | |
3601 | /* Note that x might be small enough to fit into a | |
3602 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3603 | q = scm_i_mkbig (); |
ff62c168 | 3604 | r = scm_i_mkbig (); |
8f9da340 | 3605 | r2 = scm_i_mkbig (); |
ff62c168 | 3606 | |
8f9da340 MW |
3607 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3608 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3609 | scm_remember_upto_here_1 (x); | |
3610 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3611 | |
8f9da340 MW |
3612 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3613 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3614 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3615 | else |
8f9da340 MW |
3616 | needs_adjustment = (cmp > 0); |
3617 | scm_remember_upto_here_2 (q, r2); | |
3618 | ||
3619 | if (needs_adjustment) | |
3620 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3621 | ||
3622 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3623 | return scm_i_normbig (r); |
3624 | } | |
3625 | ||
ff62c168 | 3626 | static SCM |
8f9da340 | 3627 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3628 | { |
03ddd15b MW |
3629 | SCM xd = scm_denominator (x); |
3630 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3631 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3632 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3633 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3634 | } |
3635 | ||
3636 | ||
8f9da340 MW |
3637 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3638 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3639 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3640 | |
8f9da340 | 3641 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3642 | (SCM x, SCM y), |
3643 | "Return the integer @var{q} and the real number @var{r}\n" | |
3644 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3645 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3646 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3647 | "@lisp\n" |
8f9da340 MW |
3648 | "(round/ 123 10) @result{} 12 and 3\n" |
3649 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3650 | "(round/ -123 10) @result{} -12 and -3\n" | |
3651 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3652 | "(round/ 125 10) @result{} 12 and 5\n" | |
3653 | "(round/ 127 10) @result{} 13 and -3\n" | |
3654 | "(round/ 135 10) @result{} 14 and -5\n" | |
3655 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3656 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3657 | "@end lisp") |
8f9da340 | 3658 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3659 | { |
3660 | SCM q, r; | |
3661 | ||
8f9da340 | 3662 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3663 | return scm_values (scm_list_2 (q, r)); |
3664 | } | |
3665 | #undef FUNC_NAME | |
3666 | ||
8f9da340 MW |
3667 | #define s_scm_round_divide s_scm_i_round_divide |
3668 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3669 | |
3670 | void | |
8f9da340 | 3671 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3672 | { |
3673 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3674 | { | |
4a46bc2a | 3675 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3676 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3677 | { | |
3678 | scm_t_inum yy = SCM_I_INUM (y); | |
3679 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3680 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3681 | else |
3682 | { | |
ff62c168 | 3683 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3684 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3685 | scm_t_inum ay = yy; |
3686 | scm_t_inum r2 = 2 * rr; | |
3687 | ||
3688 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3689 | { |
8f9da340 MW |
3690 | ay = -ay; |
3691 | r2 = -r2; | |
3692 | } | |
3693 | ||
3694 | if (qq & 1L) | |
3695 | { | |
3696 | if (r2 >= ay) | |
3697 | { qq++; rr -= yy; } | |
3698 | else if (r2 <= -ay) | |
3699 | { qq--; rr += yy; } | |
ff62c168 MW |
3700 | } |
3701 | else | |
3702 | { | |
8f9da340 MW |
3703 | if (r2 > ay) |
3704 | { qq++; rr -= yy; } | |
3705 | else if (r2 < -ay) | |
3706 | { qq--; rr += yy; } | |
ff62c168 | 3707 | } |
4a46bc2a | 3708 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3709 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3710 | else |
5fbf680b MW |
3711 | *qp = scm_i_inum2big (qq); |
3712 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3713 | } |
5fbf680b | 3714 | return; |
ff62c168 MW |
3715 | } |
3716 | else if (SCM_BIGP (y)) | |
3717 | { | |
3718 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3719 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3720 | return scm_i_bigint_round_divide | |
3721 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3722 | } |
3723 | else if (SCM_REALP (y)) | |
8f9da340 | 3724 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3725 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3726 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3727 | else |
8f9da340 MW |
3728 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3729 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3730 | } |
3731 | else if (SCM_BIGP (x)) | |
3732 | { | |
3733 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3734 | { | |
3735 | scm_t_inum yy = SCM_I_INUM (y); | |
3736 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3737 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3738 | else |
3739 | { | |
3740 | SCM q = scm_i_mkbig (); | |
3741 | scm_t_inum rr; | |
8f9da340 MW |
3742 | int needs_adjustment; |
3743 | ||
ff62c168 MW |
3744 | if (yy > 0) |
3745 | { | |
8f9da340 MW |
3746 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3747 | SCM_I_BIG_MPZ (x), yy); | |
3748 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3749 | needs_adjustment = (2*rr >= yy); | |
3750 | else | |
3751 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3752 | } |
3753 | else | |
3754 | { | |
3755 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3756 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3757 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3758 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3759 | needs_adjustment = (2*rr <= yy); | |
3760 | else | |
3761 | needs_adjustment = (2*rr < yy); | |
3762 | } | |
3763 | scm_remember_upto_here_1 (x); | |
3764 | if (needs_adjustment) | |
3765 | { | |
3766 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3767 | rr -= yy; | |
ff62c168 | 3768 | } |
5fbf680b MW |
3769 | *qp = scm_i_normbig (q); |
3770 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3771 | } |
5fbf680b | 3772 | return; |
ff62c168 MW |
3773 | } |
3774 | else if (SCM_BIGP (y)) | |
8f9da340 | 3775 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3776 | else if (SCM_REALP (y)) |
8f9da340 | 3777 | return scm_i_inexact_round_divide |
5fbf680b | 3778 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3779 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3780 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3781 | else |
8f9da340 MW |
3782 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3783 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3784 | } |
3785 | else if (SCM_REALP (x)) | |
3786 | { | |
3787 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3788 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3789 | return scm_i_inexact_round_divide |
5fbf680b | 3790 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3791 | else |
8f9da340 MW |
3792 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3793 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3794 | } |
3795 | else if (SCM_FRACTIONP (x)) | |
3796 | { | |
3797 | if (SCM_REALP (y)) | |
8f9da340 | 3798 | return scm_i_inexact_round_divide |
5fbf680b | 3799 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3800 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3801 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3802 | else |
8f9da340 MW |
3803 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3804 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3805 | } |
3806 | else | |
8f9da340 MW |
3807 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3808 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3809 | } |
ff62c168 | 3810 | |
5fbf680b | 3811 | static void |
8f9da340 | 3812 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3813 | { |
8f9da340 MW |
3814 | if (SCM_UNLIKELY (y == 0)) |
3815 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3816 | else |
8f9da340 MW |
3817 | { |
3818 | double q = scm_c_round (x / y); | |
3819 | double r = x - q * y; | |
3820 | *qp = scm_from_double (q); | |
3821 | *rp = scm_from_double (r); | |
3822 | } | |
ff62c168 MW |
3823 | } |
3824 | ||
3825 | /* Assumes that both x and y are bigints, though | |
3826 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3827 | static void |
8f9da340 | 3828 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3829 | { |
8f9da340 MW |
3830 | SCM q, r, r2; |
3831 | int cmp, needs_adjustment; | |
ff62c168 MW |
3832 | |
3833 | /* Note that x might be small enough to fit into a | |
3834 | fixnum, so we must not let it escape into the wild */ | |
3835 | q = scm_i_mkbig (); | |
3836 | r = scm_i_mkbig (); | |
8f9da340 | 3837 | r2 = scm_i_mkbig (); |
ff62c168 | 3838 | |
8f9da340 MW |
3839 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3840 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3841 | scm_remember_upto_here_1 (x); | |
3842 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3843 | |
8f9da340 MW |
3844 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3845 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3846 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3847 | else |
8f9da340 MW |
3848 | needs_adjustment = (cmp > 0); |
3849 | ||
3850 | if (needs_adjustment) | |
ff62c168 | 3851 | { |
8f9da340 MW |
3852 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3853 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3854 | } |
8f9da340 MW |
3855 | |
3856 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
3857 | *qp = scm_i_normbig (q); |
3858 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
3859 | } |
3860 | ||
5fbf680b | 3861 | static void |
8f9da340 | 3862 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3863 | { |
03ddd15b MW |
3864 | SCM r1; |
3865 | SCM xd = scm_denominator (x); | |
3866 | SCM yd = scm_denominator (y); | |
3867 | ||
8f9da340 MW |
3868 | scm_round_divide (scm_product (scm_numerator (x), yd), |
3869 | scm_product (scm_numerator (y), xd), | |
3870 | qp, &r1); | |
03ddd15b | 3871 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3872 | } |
3873 | ||
3874 | ||
78d3deb1 AW |
3875 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
3876 | (SCM x, SCM y, SCM rest), | |
3877 | "Return the greatest common divisor of all parameter values.\n" | |
3878 | "If called without arguments, 0 is returned.") | |
3879 | #define FUNC_NAME s_scm_i_gcd | |
3880 | { | |
3881 | while (!scm_is_null (rest)) | |
3882 | { x = scm_gcd (x, y); | |
3883 | y = scm_car (rest); | |
3884 | rest = scm_cdr (rest); | |
3885 | } | |
3886 | return scm_gcd (x, y); | |
3887 | } | |
3888 | #undef FUNC_NAME | |
3889 | ||
3890 | #define s_gcd s_scm_i_gcd | |
3891 | #define g_gcd g_scm_i_gcd | |
3892 | ||
0f2d19dd | 3893 | SCM |
6e8d25a6 | 3894 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 3895 | { |
ca46fb90 | 3896 | if (SCM_UNBNDP (y)) |
1dd79792 | 3897 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 3898 | |
e11e83f3 | 3899 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3900 | { |
e11e83f3 | 3901 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3902 | { |
e25f3727 AW |
3903 | scm_t_inum xx = SCM_I_INUM (x); |
3904 | scm_t_inum yy = SCM_I_INUM (y); | |
3905 | scm_t_inum u = xx < 0 ? -xx : xx; | |
3906 | scm_t_inum v = yy < 0 ? -yy : yy; | |
3907 | scm_t_inum result; | |
0aacf84e MD |
3908 | if (xx == 0) |
3909 | result = v; | |
3910 | else if (yy == 0) | |
3911 | result = u; | |
3912 | else | |
3913 | { | |
e25f3727 AW |
3914 | scm_t_inum k = 1; |
3915 | scm_t_inum t; | |
0aacf84e MD |
3916 | /* Determine a common factor 2^k */ |
3917 | while (!(1 & (u | v))) | |
3918 | { | |
3919 | k <<= 1; | |
3920 | u >>= 1; | |
3921 | v >>= 1; | |
3922 | } | |
3923 | /* Now, any factor 2^n can be eliminated */ | |
3924 | if (u & 1) | |
3925 | t = -v; | |
3926 | else | |
3927 | { | |
3928 | t = u; | |
3929 | b3: | |
3930 | t = SCM_SRS (t, 1); | |
3931 | } | |
3932 | if (!(1 & t)) | |
3933 | goto b3; | |
3934 | if (t > 0) | |
3935 | u = t; | |
3936 | else | |
3937 | v = -t; | |
3938 | t = u - v; | |
3939 | if (t != 0) | |
3940 | goto b3; | |
3941 | result = u * k; | |
3942 | } | |
3943 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 3944 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3945 | : scm_i_inum2big (result)); |
ca46fb90 RB |
3946 | } |
3947 | else if (SCM_BIGP (y)) | |
3948 | { | |
0bff4dce KR |
3949 | SCM_SWAP (x, y); |
3950 | goto big_inum; | |
ca46fb90 RB |
3951 | } |
3952 | else | |
3953 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 3954 | } |
ca46fb90 RB |
3955 | else if (SCM_BIGP (x)) |
3956 | { | |
e11e83f3 | 3957 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3958 | { |
e25f3727 AW |
3959 | scm_t_bits result; |
3960 | scm_t_inum yy; | |
0bff4dce | 3961 | big_inum: |
e11e83f3 | 3962 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
3963 | if (yy == 0) |
3964 | return scm_abs (x); | |
0aacf84e MD |
3965 | if (yy < 0) |
3966 | yy = -yy; | |
ca46fb90 RB |
3967 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
3968 | scm_remember_upto_here_1 (x); | |
0aacf84e | 3969 | return (SCM_POSFIXABLE (result) |
d956fa6f | 3970 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3971 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
3972 | } |
3973 | else if (SCM_BIGP (y)) | |
3974 | { | |
3975 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
3976 | mpz_gcd (SCM_I_BIG_MPZ (result), |
3977 | SCM_I_BIG_MPZ (x), | |
3978 | SCM_I_BIG_MPZ (y)); | |
3979 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
3980 | return scm_i_normbig (result); |
3981 | } | |
3982 | else | |
3983 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 3984 | } |
ca46fb90 | 3985 | else |
09fb7599 | 3986 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
3987 | } |
3988 | ||
78d3deb1 AW |
3989 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
3990 | (SCM x, SCM y, SCM rest), | |
3991 | "Return the least common multiple of the arguments.\n" | |
3992 | "If called without arguments, 1 is returned.") | |
3993 | #define FUNC_NAME s_scm_i_lcm | |
3994 | { | |
3995 | while (!scm_is_null (rest)) | |
3996 | { x = scm_lcm (x, y); | |
3997 | y = scm_car (rest); | |
3998 | rest = scm_cdr (rest); | |
3999 | } | |
4000 | return scm_lcm (x, y); | |
4001 | } | |
4002 | #undef FUNC_NAME | |
4003 | ||
4004 | #define s_lcm s_scm_i_lcm | |
4005 | #define g_lcm g_scm_i_lcm | |
4006 | ||
0f2d19dd | 4007 | SCM |
6e8d25a6 | 4008 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4009 | { |
ca46fb90 RB |
4010 | if (SCM_UNBNDP (n2)) |
4011 | { | |
4012 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
4013 | return SCM_I_MAKINUM (1L); |
4014 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 4015 | } |
09fb7599 | 4016 | |
e11e83f3 | 4017 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 4018 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 4019 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 4020 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 4021 | |
e11e83f3 | 4022 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 4023 | { |
e11e83f3 | 4024 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4025 | { |
4026 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4027 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4028 | return d; |
4029 | else | |
4030 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4031 | } | |
4032 | else | |
4033 | { | |
4034 | /* inum n1, big n2 */ | |
4035 | inumbig: | |
4036 | { | |
4037 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4038 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4039 | if (nn1 == 0) return SCM_INUM0; |
4040 | if (nn1 < 0) nn1 = - nn1; | |
4041 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4042 | scm_remember_upto_here_1 (n2); | |
4043 | return result; | |
4044 | } | |
4045 | } | |
4046 | } | |
4047 | else | |
4048 | { | |
4049 | /* big n1 */ | |
e11e83f3 | 4050 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4051 | { |
4052 | SCM_SWAP (n1, n2); | |
4053 | goto inumbig; | |
4054 | } | |
4055 | else | |
4056 | { | |
4057 | SCM result = scm_i_mkbig (); | |
4058 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4059 | SCM_I_BIG_MPZ (n1), | |
4060 | SCM_I_BIG_MPZ (n2)); | |
4061 | scm_remember_upto_here_2(n1, n2); | |
4062 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4063 | return result; | |
4064 | } | |
f872b822 | 4065 | } |
0f2d19dd JB |
4066 | } |
4067 | ||
8a525303 GB |
4068 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4069 | ||
4070 | Logand: | |
4071 | X Y Result Method: | |
4072 | (len) | |
4073 | + + + x (map digit:logand X Y) | |
4074 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4075 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4076 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4077 | ||
4078 | Logior: | |
4079 | X Y Result Method: | |
4080 | ||
4081 | + + + (map digit:logior X Y) | |
4082 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4083 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4084 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4085 | ||
4086 | Logxor: | |
4087 | X Y Result Method: | |
4088 | ||
4089 | + + + (map digit:logxor X Y) | |
4090 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4091 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4092 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4093 | ||
4094 | Logtest: | |
4095 | X Y Result | |
4096 | ||
4097 | + + (any digit:logand X Y) | |
4098 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4099 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4100 | - - #t | |
4101 | ||
4102 | */ | |
4103 | ||
78d3deb1 AW |
4104 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4105 | (SCM x, SCM y, SCM rest), | |
4106 | "Return the bitwise AND of the integer arguments.\n\n" | |
4107 | "@lisp\n" | |
4108 | "(logand) @result{} -1\n" | |
4109 | "(logand 7) @result{} 7\n" | |
4110 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4111 | "@end lisp") | |
4112 | #define FUNC_NAME s_scm_i_logand | |
4113 | { | |
4114 | while (!scm_is_null (rest)) | |
4115 | { x = scm_logand (x, y); | |
4116 | y = scm_car (rest); | |
4117 | rest = scm_cdr (rest); | |
4118 | } | |
4119 | return scm_logand (x, y); | |
4120 | } | |
4121 | #undef FUNC_NAME | |
4122 | ||
4123 | #define s_scm_logand s_scm_i_logand | |
4124 | ||
4125 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4126 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4127 | { |
e25f3727 | 4128 | scm_t_inum nn1; |
9a00c9fc | 4129 | |
0aacf84e MD |
4130 | if (SCM_UNBNDP (n2)) |
4131 | { | |
4132 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4133 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4134 | else if (!SCM_NUMBERP (n1)) |
4135 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4136 | else if (SCM_NUMBERP (n1)) | |
4137 | return n1; | |
4138 | else | |
4139 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4140 | } |
09fb7599 | 4141 | |
e11e83f3 | 4142 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4143 | { |
e11e83f3 MV |
4144 | nn1 = SCM_I_INUM (n1); |
4145 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4146 | { |
e25f3727 | 4147 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4148 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4149 | } |
4150 | else if SCM_BIGP (n2) | |
4151 | { | |
4152 | intbig: | |
2e16a342 | 4153 | if (nn1 == 0) |
0aacf84e MD |
4154 | return SCM_INUM0; |
4155 | { | |
4156 | SCM result_z = scm_i_mkbig (); | |
4157 | mpz_t nn1_z; | |
4158 | mpz_init_set_si (nn1_z, nn1); | |
4159 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4160 | scm_remember_upto_here_1 (n2); | |
4161 | mpz_clear (nn1_z); | |
4162 | return scm_i_normbig (result_z); | |
4163 | } | |
4164 | } | |
4165 | else | |
4166 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4167 | } | |
4168 | else if (SCM_BIGP (n1)) | |
4169 | { | |
e11e83f3 | 4170 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4171 | { |
4172 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4173 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4174 | goto intbig; |
4175 | } | |
4176 | else if (SCM_BIGP (n2)) | |
4177 | { | |
4178 | SCM result_z = scm_i_mkbig (); | |
4179 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4180 | SCM_I_BIG_MPZ (n1), | |
4181 | SCM_I_BIG_MPZ (n2)); | |
4182 | scm_remember_upto_here_2 (n1, n2); | |
4183 | return scm_i_normbig (result_z); | |
4184 | } | |
4185 | else | |
4186 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4187 | } |
0aacf84e | 4188 | else |
09fb7599 | 4189 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4190 | } |
1bbd0b84 | 4191 | #undef FUNC_NAME |
0f2d19dd | 4192 | |
09fb7599 | 4193 | |
78d3deb1 AW |
4194 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4195 | (SCM x, SCM y, SCM rest), | |
4196 | "Return the bitwise OR of the integer arguments.\n\n" | |
4197 | "@lisp\n" | |
4198 | "(logior) @result{} 0\n" | |
4199 | "(logior 7) @result{} 7\n" | |
4200 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4201 | "@end lisp") | |
4202 | #define FUNC_NAME s_scm_i_logior | |
4203 | { | |
4204 | while (!scm_is_null (rest)) | |
4205 | { x = scm_logior (x, y); | |
4206 | y = scm_car (rest); | |
4207 | rest = scm_cdr (rest); | |
4208 | } | |
4209 | return scm_logior (x, y); | |
4210 | } | |
4211 | #undef FUNC_NAME | |
4212 | ||
4213 | #define s_scm_logior s_scm_i_logior | |
4214 | ||
4215 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4216 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4217 | { |
e25f3727 | 4218 | scm_t_inum nn1; |
9a00c9fc | 4219 | |
0aacf84e MD |
4220 | if (SCM_UNBNDP (n2)) |
4221 | { | |
4222 | if (SCM_UNBNDP (n1)) | |
4223 | return SCM_INUM0; | |
4224 | else if (SCM_NUMBERP (n1)) | |
4225 | return n1; | |
4226 | else | |
4227 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4228 | } |
09fb7599 | 4229 | |
e11e83f3 | 4230 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4231 | { |
e11e83f3 MV |
4232 | nn1 = SCM_I_INUM (n1); |
4233 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4234 | { |
e11e83f3 | 4235 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4236 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4237 | } |
4238 | else if (SCM_BIGP (n2)) | |
4239 | { | |
4240 | intbig: | |
4241 | if (nn1 == 0) | |
4242 | return n2; | |
4243 | { | |
4244 | SCM result_z = scm_i_mkbig (); | |
4245 | mpz_t nn1_z; | |
4246 | mpz_init_set_si (nn1_z, nn1); | |
4247 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4248 | scm_remember_upto_here_1 (n2); | |
4249 | mpz_clear (nn1_z); | |
9806de0d | 4250 | return scm_i_normbig (result_z); |
0aacf84e MD |
4251 | } |
4252 | } | |
4253 | else | |
4254 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4255 | } | |
4256 | else if (SCM_BIGP (n1)) | |
4257 | { | |
e11e83f3 | 4258 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4259 | { |
4260 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4261 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4262 | goto intbig; |
4263 | } | |
4264 | else if (SCM_BIGP (n2)) | |
4265 | { | |
4266 | SCM result_z = scm_i_mkbig (); | |
4267 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4268 | SCM_I_BIG_MPZ (n1), | |
4269 | SCM_I_BIG_MPZ (n2)); | |
4270 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4271 | return scm_i_normbig (result_z); |
0aacf84e MD |
4272 | } |
4273 | else | |
4274 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4275 | } |
0aacf84e | 4276 | else |
09fb7599 | 4277 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4278 | } |
1bbd0b84 | 4279 | #undef FUNC_NAME |
0f2d19dd | 4280 | |
09fb7599 | 4281 | |
78d3deb1 AW |
4282 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4283 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4284 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4285 | "set in the result if it is set in an odd number of arguments.\n" | |
4286 | "@lisp\n" | |
4287 | "(logxor) @result{} 0\n" | |
4288 | "(logxor 7) @result{} 7\n" | |
4289 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4290 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4291 | "@end lisp") |
78d3deb1 AW |
4292 | #define FUNC_NAME s_scm_i_logxor |
4293 | { | |
4294 | while (!scm_is_null (rest)) | |
4295 | { x = scm_logxor (x, y); | |
4296 | y = scm_car (rest); | |
4297 | rest = scm_cdr (rest); | |
4298 | } | |
4299 | return scm_logxor (x, y); | |
4300 | } | |
4301 | #undef FUNC_NAME | |
4302 | ||
4303 | #define s_scm_logxor s_scm_i_logxor | |
4304 | ||
4305 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4306 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4307 | { |
e25f3727 | 4308 | scm_t_inum nn1; |
9a00c9fc | 4309 | |
0aacf84e MD |
4310 | if (SCM_UNBNDP (n2)) |
4311 | { | |
4312 | if (SCM_UNBNDP (n1)) | |
4313 | return SCM_INUM0; | |
4314 | else if (SCM_NUMBERP (n1)) | |
4315 | return n1; | |
4316 | else | |
4317 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4318 | } |
09fb7599 | 4319 | |
e11e83f3 | 4320 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4321 | { |
e11e83f3 MV |
4322 | nn1 = SCM_I_INUM (n1); |
4323 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4324 | { |
e25f3727 | 4325 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4326 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4327 | } |
4328 | else if (SCM_BIGP (n2)) | |
4329 | { | |
4330 | intbig: | |
4331 | { | |
4332 | SCM result_z = scm_i_mkbig (); | |
4333 | mpz_t nn1_z; | |
4334 | mpz_init_set_si (nn1_z, nn1); | |
4335 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4336 | scm_remember_upto_here_1 (n2); | |
4337 | mpz_clear (nn1_z); | |
4338 | return scm_i_normbig (result_z); | |
4339 | } | |
4340 | } | |
4341 | else | |
4342 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4343 | } | |
4344 | else if (SCM_BIGP (n1)) | |
4345 | { | |
e11e83f3 | 4346 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4347 | { |
4348 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4349 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4350 | goto intbig; |
4351 | } | |
4352 | else if (SCM_BIGP (n2)) | |
4353 | { | |
4354 | SCM result_z = scm_i_mkbig (); | |
4355 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4356 | SCM_I_BIG_MPZ (n1), | |
4357 | SCM_I_BIG_MPZ (n2)); | |
4358 | scm_remember_upto_here_2 (n1, n2); | |
4359 | return scm_i_normbig (result_z); | |
4360 | } | |
4361 | else | |
4362 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4363 | } |
0aacf84e | 4364 | else |
09fb7599 | 4365 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4366 | } |
1bbd0b84 | 4367 | #undef FUNC_NAME |
0f2d19dd | 4368 | |
09fb7599 | 4369 | |
a1ec6916 | 4370 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4371 | (SCM j, SCM k), |
ba6e7231 KR |
4372 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4373 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4374 | "without actually calculating the @code{logand}, just testing\n" | |
4375 | "for non-zero.\n" | |
4376 | "\n" | |
1e6808ea | 4377 | "@lisp\n" |
b380b885 MD |
4378 | "(logtest #b0100 #b1011) @result{} #f\n" |
4379 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4380 | "@end lisp") |
1bbd0b84 | 4381 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4382 | { |
e25f3727 | 4383 | scm_t_inum nj; |
9a00c9fc | 4384 | |
e11e83f3 | 4385 | if (SCM_I_INUMP (j)) |
0aacf84e | 4386 | { |
e11e83f3 MV |
4387 | nj = SCM_I_INUM (j); |
4388 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4389 | { |
e25f3727 | 4390 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4391 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4392 | } |
4393 | else if (SCM_BIGP (k)) | |
4394 | { | |
4395 | intbig: | |
4396 | if (nj == 0) | |
4397 | return SCM_BOOL_F; | |
4398 | { | |
4399 | SCM result; | |
4400 | mpz_t nj_z; | |
4401 | mpz_init_set_si (nj_z, nj); | |
4402 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4403 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4404 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4405 | mpz_clear (nj_z); |
4406 | return result; | |
4407 | } | |
4408 | } | |
4409 | else | |
4410 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4411 | } | |
4412 | else if (SCM_BIGP (j)) | |
4413 | { | |
e11e83f3 | 4414 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4415 | { |
4416 | SCM_SWAP (j, k); | |
e11e83f3 | 4417 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4418 | goto intbig; |
4419 | } | |
4420 | else if (SCM_BIGP (k)) | |
4421 | { | |
4422 | SCM result; | |
4423 | mpz_t result_z; | |
4424 | mpz_init (result_z); | |
4425 | mpz_and (result_z, | |
4426 | SCM_I_BIG_MPZ (j), | |
4427 | SCM_I_BIG_MPZ (k)); | |
4428 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4429 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4430 | mpz_clear (result_z); |
4431 | return result; | |
4432 | } | |
4433 | else | |
4434 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4435 | } | |
4436 | else | |
4437 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4438 | } |
1bbd0b84 | 4439 | #undef FUNC_NAME |
0f2d19dd | 4440 | |
c1bfcf60 | 4441 | |
a1ec6916 | 4442 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4443 | (SCM index, SCM j), |
ba6e7231 KR |
4444 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4445 | "@var{index} starts from 0 for the least significant bit.\n" | |
4446 | "\n" | |
1e6808ea | 4447 | "@lisp\n" |
b380b885 MD |
4448 | "(logbit? 0 #b1101) @result{} #t\n" |
4449 | "(logbit? 1 #b1101) @result{} #f\n" | |
4450 | "(logbit? 2 #b1101) @result{} #t\n" | |
4451 | "(logbit? 3 #b1101) @result{} #t\n" | |
4452 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4453 | "@end lisp") |
1bbd0b84 | 4454 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4455 | { |
78166ad5 | 4456 | unsigned long int iindex; |
5efd3c7d | 4457 | iindex = scm_to_ulong (index); |
78166ad5 | 4458 | |
e11e83f3 | 4459 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4460 | { |
4461 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4462 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4463 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4464 | } |
0aacf84e MD |
4465 | else if (SCM_BIGP (j)) |
4466 | { | |
4467 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4468 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4469 | return scm_from_bool (val); |
0aacf84e MD |
4470 | } |
4471 | else | |
78166ad5 | 4472 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4473 | } |
1bbd0b84 | 4474 | #undef FUNC_NAME |
0f2d19dd | 4475 | |
78166ad5 | 4476 | |
a1ec6916 | 4477 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4478 | (SCM n), |
4d814788 | 4479 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4480 | "argument.\n" |
4481 | "\n" | |
b380b885 MD |
4482 | "@lisp\n" |
4483 | "(number->string (lognot #b10000000) 2)\n" | |
4484 | " @result{} \"-10000001\"\n" | |
4485 | "(number->string (lognot #b0) 2)\n" | |
4486 | " @result{} \"-1\"\n" | |
1e6808ea | 4487 | "@end lisp") |
1bbd0b84 | 4488 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4489 | { |
e11e83f3 | 4490 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4491 | /* No overflow here, just need to toggle all the bits making up the inum. |
4492 | Enhancement: No need to strip the tag and add it back, could just xor | |
4493 | a block of 1 bits, if that worked with the various debug versions of | |
4494 | the SCM typedef. */ | |
e11e83f3 | 4495 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4496 | |
4497 | } else if (SCM_BIGP (n)) { | |
4498 | SCM result = scm_i_mkbig (); | |
4499 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4500 | scm_remember_upto_here_1 (n); | |
4501 | return result; | |
4502 | ||
4503 | } else { | |
4504 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4505 | } | |
0f2d19dd | 4506 | } |
1bbd0b84 | 4507 | #undef FUNC_NAME |
0f2d19dd | 4508 | |
518b7508 KR |
4509 | /* returns 0 if IN is not an integer. OUT must already be |
4510 | initialized. */ | |
4511 | static int | |
4512 | coerce_to_big (SCM in, mpz_t out) | |
4513 | { | |
4514 | if (SCM_BIGP (in)) | |
4515 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4516 | else if (SCM_I_INUMP (in)) |
4517 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4518 | else |
4519 | return 0; | |
4520 | ||
4521 | return 1; | |
4522 | } | |
4523 | ||
d885e204 | 4524 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4525 | (SCM n, SCM k, SCM m), |
4526 | "Return @var{n} raised to the integer exponent\n" | |
4527 | "@var{k}, modulo @var{m}.\n" | |
4528 | "\n" | |
4529 | "@lisp\n" | |
4530 | "(modulo-expt 2 3 5)\n" | |
4531 | " @result{} 3\n" | |
4532 | "@end lisp") | |
d885e204 | 4533 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4534 | { |
4535 | mpz_t n_tmp; | |
4536 | mpz_t k_tmp; | |
4537 | mpz_t m_tmp; | |
4538 | ||
4539 | /* There are two classes of error we might encounter -- | |
4540 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4541 | and | |
4542 | 2) wrong-type errors, which of course we'll report by calling | |
4543 | SCM_WRONG_TYPE_ARG. | |
4544 | We don't report those errors immediately, however; instead we do | |
4545 | some cleanup first. These variables tell us which error (if | |
4546 | any) we should report after cleaning up. | |
4547 | */ | |
4548 | int report_overflow = 0; | |
4549 | ||
4550 | int position_of_wrong_type = 0; | |
4551 | SCM value_of_wrong_type = SCM_INUM0; | |
4552 | ||
4553 | SCM result = SCM_UNDEFINED; | |
4554 | ||
4555 | mpz_init (n_tmp); | |
4556 | mpz_init (k_tmp); | |
4557 | mpz_init (m_tmp); | |
4558 | ||
bc36d050 | 4559 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4560 | { |
4561 | report_overflow = 1; | |
4562 | goto cleanup; | |
4563 | } | |
4564 | ||
4565 | if (!coerce_to_big (n, n_tmp)) | |
4566 | { | |
4567 | value_of_wrong_type = n; | |
4568 | position_of_wrong_type = 1; | |
4569 | goto cleanup; | |
4570 | } | |
4571 | ||
4572 | if (!coerce_to_big (k, k_tmp)) | |
4573 | { | |
4574 | value_of_wrong_type = k; | |
4575 | position_of_wrong_type = 2; | |
4576 | goto cleanup; | |
4577 | } | |
4578 | ||
4579 | if (!coerce_to_big (m, m_tmp)) | |
4580 | { | |
4581 | value_of_wrong_type = m; | |
4582 | position_of_wrong_type = 3; | |
4583 | goto cleanup; | |
4584 | } | |
4585 | ||
4586 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4587 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4588 | doesn't exist (or is not unique). Since exceptions are hard to | |
4589 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4590 | a simple failure code, which is easy to handle. */ | |
4591 | ||
4592 | if (-1 == mpz_sgn (k_tmp)) | |
4593 | { | |
4594 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4595 | { | |
4596 | report_overflow = 1; | |
4597 | goto cleanup; | |
4598 | } | |
4599 | mpz_neg (k_tmp, k_tmp); | |
4600 | } | |
4601 | ||
4602 | result = scm_i_mkbig (); | |
4603 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4604 | n_tmp, | |
4605 | k_tmp, | |
4606 | m_tmp); | |
b7b8c575 KR |
4607 | |
4608 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4609 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4610 | ||
518b7508 KR |
4611 | cleanup: |
4612 | mpz_clear (m_tmp); | |
4613 | mpz_clear (k_tmp); | |
4614 | mpz_clear (n_tmp); | |
4615 | ||
4616 | if (report_overflow) | |
4617 | scm_num_overflow (FUNC_NAME); | |
4618 | ||
4619 | if (position_of_wrong_type) | |
4620 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4621 | value_of_wrong_type); | |
4622 | ||
4623 | return scm_i_normbig (result); | |
4624 | } | |
4625 | #undef FUNC_NAME | |
4626 | ||
a1ec6916 | 4627 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4628 | (SCM n, SCM k), |
ba6e7231 KR |
4629 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4630 | "exact integer, @var{n} can be any number.\n" | |
4631 | "\n" | |
2519490c MW |
4632 | "Negative @var{k} is supported, and results in\n" |
4633 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4634 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4635 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4636 | "\n" |
b380b885 | 4637 | "@lisp\n" |
ba6e7231 KR |
4638 | "(integer-expt 2 5) @result{} 32\n" |
4639 | "(integer-expt -3 3) @result{} -27\n" | |
4640 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4641 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4642 | "@end lisp") |
1bbd0b84 | 4643 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4644 | { |
e25f3727 | 4645 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4646 | SCM z_i2 = SCM_BOOL_F; |
4647 | int i2_is_big = 0; | |
d956fa6f | 4648 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4649 | |
bfe1f03a MW |
4650 | /* Specifically refrain from checking the type of the first argument. |
4651 | This allows us to exponentiate any object that can be multiplied. | |
4652 | If we must raise to a negative power, we must also be able to | |
4653 | take its reciprocal. */ | |
4654 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4655 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4656 | |
bfe1f03a MW |
4657 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4658 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4659 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4660 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4661 | /* The next check is necessary only because R6RS specifies different | |
4662 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4663 | we simply skip this case and move on. */ | |
4664 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4665 | { | |
4666 | /* k cannot be 0 at this point, because we | |
4667 | have already checked for that case above */ | |
4668 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4669 | return n; |
4670 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4671 | return scm_nan (); | |
4672 | } | |
ca46fb90 | 4673 | |
e11e83f3 MV |
4674 | if (SCM_I_INUMP (k)) |
4675 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4676 | else if (SCM_BIGP (k)) |
4677 | { | |
4678 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4679 | scm_remember_upto_here_1 (k); |
4680 | i2_is_big = 1; | |
4681 | } | |
2830fd91 | 4682 | else |
ca46fb90 RB |
4683 | SCM_WRONG_TYPE_ARG (2, k); |
4684 | ||
4685 | if (i2_is_big) | |
f872b822 | 4686 | { |
ca46fb90 RB |
4687 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4688 | { | |
4689 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4690 | n = scm_divide (n, SCM_UNDEFINED); | |
4691 | } | |
4692 | while (1) | |
4693 | { | |
4694 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4695 | { | |
ca46fb90 RB |
4696 | return acc; |
4697 | } | |
4698 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4699 | { | |
ca46fb90 RB |
4700 | return scm_product (acc, n); |
4701 | } | |
4702 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4703 | acc = scm_product (acc, n); | |
4704 | n = scm_product (n, n); | |
4705 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4706 | } | |
f872b822 | 4707 | } |
ca46fb90 | 4708 | else |
f872b822 | 4709 | { |
ca46fb90 RB |
4710 | if (i2 < 0) |
4711 | { | |
4712 | i2 = -i2; | |
4713 | n = scm_divide (n, SCM_UNDEFINED); | |
4714 | } | |
4715 | while (1) | |
4716 | { | |
4717 | if (0 == i2) | |
4718 | return acc; | |
4719 | if (1 == i2) | |
4720 | return scm_product (acc, n); | |
4721 | if (i2 & 1) | |
4722 | acc = scm_product (acc, n); | |
4723 | n = scm_product (n, n); | |
4724 | i2 >>= 1; | |
4725 | } | |
f872b822 | 4726 | } |
0f2d19dd | 4727 | } |
1bbd0b84 | 4728 | #undef FUNC_NAME |
0f2d19dd | 4729 | |
a1ec6916 | 4730 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 4731 | (SCM n, SCM cnt), |
32f19569 KR |
4732 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
4733 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 4734 | "\n" |
e7644cb2 | 4735 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
4736 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
4737 | "infinity. (Note that this is not the same rounding as\n" | |
4738 | "@code{quotient} does.)\n" | |
4739 | "\n" | |
4740 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
4741 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
4742 | "shift dropping bits.\n" | |
1e6808ea | 4743 | "\n" |
b380b885 | 4744 | "@lisp\n" |
1e6808ea MG |
4745 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
4746 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
4747 | "\n" |
4748 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
4749 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 4750 | "@end lisp") |
1bbd0b84 | 4751 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 4752 | { |
3ab9f56e | 4753 | long bits_to_shift; |
5efd3c7d | 4754 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 4755 | |
788aca27 KR |
4756 | if (SCM_I_INUMP (n)) |
4757 | { | |
e25f3727 | 4758 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
4759 | |
4760 | if (bits_to_shift > 0) | |
4761 | { | |
4762 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
4763 | overflow a non-zero fixnum. For smaller shifts we check the | |
4764 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4765 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4766 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
4767 | bits_to_shift)". */ | |
4768 | ||
4769 | if (nn == 0) | |
4770 | return n; | |
4771 | ||
4772 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4773 | && ((scm_t_bits) |
788aca27 KR |
4774 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
4775 | <= 1)) | |
4776 | { | |
4777 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
4778 | } | |
4779 | else | |
4780 | { | |
e25f3727 | 4781 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
4782 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4783 | bits_to_shift); | |
4784 | return result; | |
4785 | } | |
4786 | } | |
4787 | else | |
4788 | { | |
4789 | bits_to_shift = -bits_to_shift; | |
4790 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 4791 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
4792 | else |
4793 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
4794 | } | |
4795 | ||
4796 | } | |
4797 | else if (SCM_BIGP (n)) | |
ca46fb90 | 4798 | { |
788aca27 KR |
4799 | SCM result; |
4800 | ||
4801 | if (bits_to_shift == 0) | |
4802 | return n; | |
4803 | ||
4804 | result = scm_i_mkbig (); | |
4805 | if (bits_to_shift >= 0) | |
4806 | { | |
4807 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4808 | bits_to_shift); | |
4809 | return result; | |
4810 | } | |
ca46fb90 | 4811 | else |
788aca27 KR |
4812 | { |
4813 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
4814 | we have to allocate a bignum even if the result is going to be a | |
4815 | fixnum. */ | |
4816 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4817 | -bits_to_shift); | |
4818 | return scm_i_normbig (result); | |
4819 | } | |
4820 | ||
ca46fb90 RB |
4821 | } |
4822 | else | |
788aca27 KR |
4823 | { |
4824 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4825 | } | |
0f2d19dd | 4826 | } |
1bbd0b84 | 4827 | #undef FUNC_NAME |
0f2d19dd | 4828 | |
3c9f20f8 | 4829 | |
a1ec6916 | 4830 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 4831 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
4832 | "Return the integer composed of the @var{start} (inclusive)\n" |
4833 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
4834 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
4835 | "\n" | |
b380b885 MD |
4836 | "@lisp\n" |
4837 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
4838 | " @result{} \"1010\"\n" | |
4839 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
4840 | " @result{} \"10110\"\n" | |
4841 | "@end lisp") | |
1bbd0b84 | 4842 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 4843 | { |
7f848242 | 4844 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
4845 | istart = scm_to_ulong (start); |
4846 | iend = scm_to_ulong (end); | |
c1bfcf60 | 4847 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 4848 | |
7f848242 KR |
4849 | /* how many bits to keep */ |
4850 | bits = iend - istart; | |
4851 | ||
e11e83f3 | 4852 | if (SCM_I_INUMP (n)) |
0aacf84e | 4853 | { |
e25f3727 | 4854 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
4855 | |
4856 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 4857 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 4858 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 4859 | |
0aacf84e MD |
4860 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
4861 | { | |
4862 | /* Since we emulate two's complement encoded numbers, this | |
4863 | * special case requires us to produce a result that has | |
7f848242 | 4864 | * more bits than can be stored in a fixnum. |
0aacf84e | 4865 | */ |
e25f3727 | 4866 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
4867 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4868 | bits); | |
4869 | return result; | |
0aacf84e | 4870 | } |
ac0c002c | 4871 | |
7f848242 | 4872 | /* mask down to requisite bits */ |
857ae6af | 4873 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 4874 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
4875 | } |
4876 | else if (SCM_BIGP (n)) | |
ac0c002c | 4877 | { |
7f848242 KR |
4878 | SCM result; |
4879 | if (bits == 1) | |
4880 | { | |
d956fa6f | 4881 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
4882 | } |
4883 | else | |
4884 | { | |
4885 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
4886 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
4887 | such bits into a ulong. */ | |
4888 | result = scm_i_mkbig (); | |
4889 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
4890 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
4891 | result = scm_i_normbig (result); | |
4892 | } | |
4893 | scm_remember_upto_here_1 (n); | |
4894 | return result; | |
ac0c002c | 4895 | } |
0aacf84e | 4896 | else |
78166ad5 | 4897 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 4898 | } |
1bbd0b84 | 4899 | #undef FUNC_NAME |
0f2d19dd | 4900 | |
7f848242 | 4901 | |
e4755e5c JB |
4902 | static const char scm_logtab[] = { |
4903 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
4904 | }; | |
1cc91f1b | 4905 | |
a1ec6916 | 4906 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 4907 | (SCM n), |
1e6808ea MG |
4908 | "Return the number of bits in integer @var{n}. If integer is\n" |
4909 | "positive, the 1-bits in its binary representation are counted.\n" | |
4910 | "If negative, the 0-bits in its two's-complement binary\n" | |
4911 | "representation are counted. If 0, 0 is returned.\n" | |
4912 | "\n" | |
b380b885 MD |
4913 | "@lisp\n" |
4914 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
4915 | " @result{} 4\n" |
4916 | "(logcount 0)\n" | |
4917 | " @result{} 0\n" | |
4918 | "(logcount -2)\n" | |
4919 | " @result{} 1\n" | |
4920 | "@end lisp") | |
4921 | #define FUNC_NAME s_scm_logcount | |
4922 | { | |
e11e83f3 | 4923 | if (SCM_I_INUMP (n)) |
f872b822 | 4924 | { |
e25f3727 AW |
4925 | unsigned long c = 0; |
4926 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
4927 | if (nn < 0) |
4928 | nn = -1 - nn; | |
4929 | while (nn) | |
4930 | { | |
4931 | c += scm_logtab[15 & nn]; | |
4932 | nn >>= 4; | |
4933 | } | |
d956fa6f | 4934 | return SCM_I_MAKINUM (c); |
f872b822 | 4935 | } |
ca46fb90 | 4936 | else if (SCM_BIGP (n)) |
f872b822 | 4937 | { |
ca46fb90 | 4938 | unsigned long count; |
713a4259 KR |
4939 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
4940 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 4941 | else |
713a4259 KR |
4942 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
4943 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4944 | return SCM_I_MAKINUM (count); |
f872b822 | 4945 | } |
ca46fb90 RB |
4946 | else |
4947 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 4948 | } |
ca46fb90 | 4949 | #undef FUNC_NAME |
0f2d19dd JB |
4950 | |
4951 | ||
ca46fb90 RB |
4952 | static const char scm_ilentab[] = { |
4953 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
4954 | }; | |
4955 | ||
0f2d19dd | 4956 | |
ca46fb90 RB |
4957 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
4958 | (SCM n), | |
4959 | "Return the number of bits necessary to represent @var{n}.\n" | |
4960 | "\n" | |
4961 | "@lisp\n" | |
4962 | "(integer-length #b10101010)\n" | |
4963 | " @result{} 8\n" | |
4964 | "(integer-length 0)\n" | |
4965 | " @result{} 0\n" | |
4966 | "(integer-length #b1111)\n" | |
4967 | " @result{} 4\n" | |
4968 | "@end lisp") | |
4969 | #define FUNC_NAME s_scm_integer_length | |
4970 | { | |
e11e83f3 | 4971 | if (SCM_I_INUMP (n)) |
0aacf84e | 4972 | { |
e25f3727 | 4973 | unsigned long c = 0; |
0aacf84e | 4974 | unsigned int l = 4; |
e25f3727 | 4975 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
4976 | if (nn < 0) |
4977 | nn = -1 - nn; | |
4978 | while (nn) | |
4979 | { | |
4980 | c += 4; | |
4981 | l = scm_ilentab [15 & nn]; | |
4982 | nn >>= 4; | |
4983 | } | |
d956fa6f | 4984 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
4985 | } |
4986 | else if (SCM_BIGP (n)) | |
4987 | { | |
4988 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
4989 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
4990 | 1 too big, so check for that and adjust. */ | |
4991 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
4992 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
4993 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
4994 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
4995 | size--; | |
4996 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4997 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
4998 | } |
4999 | else | |
ca46fb90 | 5000 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5001 | } |
5002 | #undef FUNC_NAME | |
0f2d19dd JB |
5003 | |
5004 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5005 | #define SCM_MAX_DBL_PREC 60 |
5006 | #define SCM_MAX_DBL_RADIX 36 | |
5007 | ||
5008 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
5009 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
5010 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
5011 | ||
5012 | static | |
5013 | void init_dblprec(int *prec, int radix) { | |
5014 | /* determine floating point precision by adding successively | |
5015 | smaller increments to 1.0 until it is considered == 1.0 */ | |
5016 | double f = ((double)1.0)/radix; | |
5017 | double fsum = 1.0 + f; | |
5018 | ||
5019 | *prec = 0; | |
5020 | while (fsum != 1.0) | |
5021 | { | |
5022 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
5023 | fsum = 1.0; | |
5024 | else | |
5025 | { | |
5026 | f /= radix; | |
5027 | fsum = f + 1.0; | |
5028 | } | |
5029 | } | |
5030 | (*prec) -= 1; | |
5031 | } | |
5032 | ||
5033 | static | |
5034 | void init_fx_radix(double *fx_list, int radix) | |
5035 | { | |
5036 | /* initialize a per-radix list of tolerances. When added | |
5037 | to a number < 1.0, we can determine if we should raund | |
5038 | up and quit converting a number to a string. */ | |
5039 | int i; | |
5040 | fx_list[0] = 0.0; | |
5041 | fx_list[1] = 0.5; | |
5042 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
5043 | fx_list[i] = (fx_list[i-1] / radix); | |
5044 | } | |
5045 | ||
5046 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5047 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5048 | |
1be6b49c | 5049 | static size_t |
0b799eea | 5050 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5051 | { |
0b799eea MV |
5052 | int efmt, dpt, d, i, wp; |
5053 | double *fx; | |
5054 | #ifdef DBL_MIN_10_EXP | |
5055 | double f_cpy; | |
5056 | int exp_cpy; | |
5057 | #endif /* DBL_MIN_10_EXP */ | |
5058 | size_t ch = 0; | |
5059 | int exp = 0; | |
5060 | ||
5061 | if(radix < 2 || | |
5062 | radix > SCM_MAX_DBL_RADIX) | |
5063 | { | |
5064 | /* revert to existing behavior */ | |
5065 | radix = 10; | |
5066 | } | |
5067 | ||
5068 | wp = scm_dblprec[radix-2]; | |
5069 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5070 | |
f872b822 | 5071 | if (f == 0.0) |
abb7e44d MV |
5072 | { |
5073 | #ifdef HAVE_COPYSIGN | |
5074 | double sgn = copysign (1.0, f); | |
5075 | ||
5076 | if (sgn < 0.0) | |
5077 | a[ch++] = '-'; | |
5078 | #endif | |
abb7e44d MV |
5079 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5080 | } | |
7351e207 | 5081 | |
2e65b52f | 5082 | if (isinf (f)) |
7351e207 MV |
5083 | { |
5084 | if (f < 0) | |
5085 | strcpy (a, "-inf.0"); | |
5086 | else | |
5087 | strcpy (a, "+inf.0"); | |
5088 | return ch+6; | |
5089 | } | |
2e65b52f | 5090 | else if (isnan (f)) |
7351e207 MV |
5091 | { |
5092 | strcpy (a, "+nan.0"); | |
5093 | return ch+6; | |
5094 | } | |
5095 | ||
f872b822 MD |
5096 | if (f < 0.0) |
5097 | { | |
5098 | f = -f; | |
5099 | a[ch++] = '-'; | |
5100 | } | |
7351e207 | 5101 | |
f872b822 MD |
5102 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5103 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5104 | /* just do the checking...if it passes, we do the conversion for our |
5105 | radix again below */ | |
5106 | f_cpy = f; | |
5107 | exp_cpy = exp; | |
5108 | ||
5109 | while (f_cpy < 1.0) | |
f872b822 | 5110 | { |
0b799eea MV |
5111 | f_cpy *= 10.0; |
5112 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5113 | { |
5114 | a[ch++] = '#'; | |
5115 | a[ch++] = '.'; | |
5116 | a[ch++] = '#'; | |
5117 | return ch; | |
5118 | } | |
f872b822 | 5119 | } |
0b799eea | 5120 | while (f_cpy > 10.0) |
f872b822 | 5121 | { |
0b799eea MV |
5122 | f_cpy *= 0.10; |
5123 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5124 | { |
5125 | a[ch++] = '#'; | |
5126 | a[ch++] = '.'; | |
5127 | a[ch++] = '#'; | |
5128 | return ch; | |
5129 | } | |
f872b822 | 5130 | } |
0b799eea MV |
5131 | #endif |
5132 | ||
f872b822 MD |
5133 | while (f < 1.0) |
5134 | { | |
0b799eea | 5135 | f *= radix; |
f872b822 MD |
5136 | exp--; |
5137 | } | |
0b799eea | 5138 | while (f > radix) |
f872b822 | 5139 | { |
0b799eea | 5140 | f /= radix; |
f872b822 MD |
5141 | exp++; |
5142 | } | |
0b799eea MV |
5143 | |
5144 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5145 | { |
5146 | f = 1.0; | |
5147 | exp++; | |
5148 | } | |
0f2d19dd | 5149 | zero: |
0b799eea MV |
5150 | #ifdef ENGNOT |
5151 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 5152 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
5153 | exp -= dpt++; |
5154 | efmt = 1; | |
f872b822 MD |
5155 | #else |
5156 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 5157 | if (!efmt) |
cda139a7 MD |
5158 | { |
5159 | if (exp < 0) | |
5160 | { | |
5161 | a[ch++] = '0'; | |
5162 | a[ch++] = '.'; | |
5163 | dpt = exp; | |
f872b822 MD |
5164 | while (++dpt) |
5165 | a[ch++] = '0'; | |
cda139a7 MD |
5166 | } |
5167 | else | |
f872b822 | 5168 | dpt = exp + 1; |
cda139a7 | 5169 | } |
0f2d19dd JB |
5170 | else |
5171 | dpt = 1; | |
f872b822 MD |
5172 | #endif |
5173 | ||
5174 | do | |
5175 | { | |
5176 | d = f; | |
5177 | f -= d; | |
0b799eea | 5178 | a[ch++] = number_chars[d]; |
f872b822 MD |
5179 | if (f < fx[wp]) |
5180 | break; | |
5181 | if (f + fx[wp] >= 1.0) | |
5182 | { | |
0b799eea | 5183 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5184 | break; |
5185 | } | |
0b799eea | 5186 | f *= radix; |
f872b822 MD |
5187 | if (!(--dpt)) |
5188 | a[ch++] = '.'; | |
0f2d19dd | 5189 | } |
f872b822 | 5190 | while (wp--); |
0f2d19dd JB |
5191 | |
5192 | if (dpt > 0) | |
cda139a7 | 5193 | { |
f872b822 | 5194 | #ifndef ENGNOT |
cda139a7 MD |
5195 | if ((dpt > 4) && (exp > 6)) |
5196 | { | |
f872b822 | 5197 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 5198 | for (i = ch++; i > d; i--) |
f872b822 | 5199 | a[i] = a[i - 1]; |
cda139a7 MD |
5200 | a[d] = '.'; |
5201 | efmt = 1; | |
5202 | } | |
5203 | else | |
f872b822 | 5204 | #endif |
cda139a7 | 5205 | { |
f872b822 MD |
5206 | while (--dpt) |
5207 | a[ch++] = '0'; | |
cda139a7 MD |
5208 | a[ch++] = '.'; |
5209 | } | |
5210 | } | |
f872b822 MD |
5211 | if (a[ch - 1] == '.') |
5212 | a[ch++] = '0'; /* trailing zero */ | |
5213 | if (efmt && exp) | |
5214 | { | |
5215 | a[ch++] = 'e'; | |
5216 | if (exp < 0) | |
5217 | { | |
5218 | exp = -exp; | |
5219 | a[ch++] = '-'; | |
5220 | } | |
0b799eea MV |
5221 | for (i = radix; i <= exp; i *= radix); |
5222 | for (i /= radix; i; i /= radix) | |
f872b822 | 5223 | { |
0b799eea | 5224 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5225 | exp %= i; |
5226 | } | |
0f2d19dd | 5227 | } |
0f2d19dd JB |
5228 | return ch; |
5229 | } | |
5230 | ||
7a1aba42 MV |
5231 | |
5232 | static size_t | |
5233 | icmplx2str (double real, double imag, char *str, int radix) | |
5234 | { | |
5235 | size_t i; | |
c7218482 | 5236 | double sgn; |
7a1aba42 MV |
5237 | |
5238 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5239 | #ifdef HAVE_COPYSIGN |
5240 | sgn = copysign (1.0, imag); | |
5241 | #else | |
5242 | sgn = imag; | |
5243 | #endif | |
5244 | /* Don't output a '+' for negative numbers or for Inf and | |
5245 | NaN. They will provide their own sign. */ | |
5246 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5247 | str[i++] = '+'; | |
5248 | i += idbl2str (imag, &str[i], radix); | |
5249 | str[i++] = 'i'; | |
7a1aba42 MV |
5250 | return i; |
5251 | } | |
5252 | ||
1be6b49c | 5253 | static size_t |
0b799eea | 5254 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5255 | { |
1be6b49c | 5256 | size_t i; |
3c9a524f | 5257 | if (SCM_REALP (flt)) |
0b799eea | 5258 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5259 | else |
7a1aba42 MV |
5260 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5261 | str, radix); | |
0f2d19dd JB |
5262 | return i; |
5263 | } | |
0f2d19dd | 5264 | |
2881e77b | 5265 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5266 | characters in the result. |
5267 | rad is output base | |
5268 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5269 | size_t |
2881e77b MV |
5270 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5271 | { | |
5272 | if (num < 0) | |
5273 | { | |
5274 | *p++ = '-'; | |
5275 | return scm_iuint2str (-num, rad, p) + 1; | |
5276 | } | |
5277 | else | |
5278 | return scm_iuint2str (num, rad, p); | |
5279 | } | |
5280 | ||
5281 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5282 | characters in the result. | |
5283 | rad is output base | |
5284 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5285 | size_t | |
5286 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5287 | { |
1be6b49c ML |
5288 | size_t j = 1; |
5289 | size_t i; | |
2881e77b | 5290 | scm_t_uintmax n = num; |
5c11cc9d | 5291 | |
a6f3af16 AW |
5292 | if (rad < 2 || rad > 36) |
5293 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5294 | ||
f872b822 | 5295 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5296 | j++; |
5297 | ||
5298 | i = j; | |
2881e77b | 5299 | n = num; |
f872b822 MD |
5300 | while (i--) |
5301 | { | |
5c11cc9d GH |
5302 | int d = n % rad; |
5303 | ||
f872b822 | 5304 | n /= rad; |
a6f3af16 | 5305 | p[i] = number_chars[d]; |
f872b822 | 5306 | } |
0f2d19dd JB |
5307 | return j; |
5308 | } | |
5309 | ||
a1ec6916 | 5310 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5311 | (SCM n, SCM radix), |
5312 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5313 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5314 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5315 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5316 | { |
1bbd0b84 | 5317 | int base; |
98cb6e75 | 5318 | |
0aacf84e | 5319 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5320 | base = 10; |
0aacf84e | 5321 | else |
5efd3c7d | 5322 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5323 | |
e11e83f3 | 5324 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5325 | { |
5326 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5327 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5328 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5329 | } |
5330 | else if (SCM_BIGP (n)) | |
5331 | { | |
5332 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
d88f5323 AW |
5333 | size_t len = strlen (str); |
5334 | void (*freefunc) (void *, size_t); | |
5335 | SCM ret; | |
5336 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
0aacf84e | 5337 | scm_remember_upto_here_1 (n); |
d88f5323 AW |
5338 | ret = scm_from_latin1_stringn (str, len); |
5339 | freefunc (str, len + 1); | |
5340 | return ret; | |
0aacf84e | 5341 | } |
f92e85f7 MV |
5342 | else if (SCM_FRACTIONP (n)) |
5343 | { | |
f92e85f7 | 5344 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5345 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5346 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5347 | } | |
0aacf84e MD |
5348 | else if (SCM_INEXACTP (n)) |
5349 | { | |
5350 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5351 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5352 | } |
5353 | else | |
bb628794 | 5354 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5355 | } |
1bbd0b84 | 5356 | #undef FUNC_NAME |
0f2d19dd JB |
5357 | |
5358 | ||
ca46fb90 RB |
5359 | /* These print routines used to be stubbed here so that scm_repl.c |
5360 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5361 | |
0f2d19dd | 5362 | int |
e81d98ec | 5363 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5364 | { |
56e55ac7 | 5365 | char num_buf[FLOBUFLEN]; |
0b799eea | 5366 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5367 | return !0; |
5368 | } | |
5369 | ||
b479fe9a MV |
5370 | void |
5371 | scm_i_print_double (double val, SCM port) | |
5372 | { | |
5373 | char num_buf[FLOBUFLEN]; | |
5374 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5375 | } | |
5376 | ||
f3ae5d60 | 5377 | int |
e81d98ec | 5378 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5379 | |
f3ae5d60 | 5380 | { |
56e55ac7 | 5381 | char num_buf[FLOBUFLEN]; |
0b799eea | 5382 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5383 | return !0; |
5384 | } | |
1cc91f1b | 5385 | |
7a1aba42 MV |
5386 | void |
5387 | scm_i_print_complex (double real, double imag, SCM port) | |
5388 | { | |
5389 | char num_buf[FLOBUFLEN]; | |
5390 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5391 | } | |
5392 | ||
f92e85f7 MV |
5393 | int |
5394 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5395 | { | |
5396 | SCM str; | |
f92e85f7 | 5397 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5398 | scm_display (str, port); |
f92e85f7 MV |
5399 | scm_remember_upto_here_1 (str); |
5400 | return !0; | |
5401 | } | |
5402 | ||
0f2d19dd | 5403 | int |
e81d98ec | 5404 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5405 | { |
ca46fb90 | 5406 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
b57bf272 AW |
5407 | size_t len = strlen (str); |
5408 | void (*freefunc) (void *, size_t); | |
5409 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
ca46fb90 | 5410 | scm_remember_upto_here_1 (exp); |
b57bf272 AW |
5411 | scm_lfwrite (str, len, port); |
5412 | freefunc (str, len + 1); | |
0f2d19dd JB |
5413 | return !0; |
5414 | } | |
5415 | /*** END nums->strs ***/ | |
5416 | ||
3c9a524f | 5417 | |
0f2d19dd | 5418 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5419 | |
3c9a524f DH |
5420 | /* The following functions implement the conversion from strings to numbers. |
5421 | * The implementation somehow follows the grammar for numbers as it is given | |
5422 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5423 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5424 | * points should be noted about the implementation: | |
bc3d34f5 | 5425 | * |
3c9a524f DH |
5426 | * * Each function keeps a local index variable 'idx' that points at the |
5427 | * current position within the parsed string. The global index is only | |
5428 | * updated if the function could parse the corresponding syntactic unit | |
5429 | * successfully. | |
bc3d34f5 | 5430 | * |
3c9a524f | 5431 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5432 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5433 | * | |
3c9a524f DH |
5434 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5435 | * Only if these fixnums would overflow, the result variables are updated | |
5436 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5437 | * the temporary variables holding the fixnums are cleared, and the process | |
5438 | * starts over again. If for example fixnums were able to store five decimal | |
5439 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5440 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5441 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5442 | * |
5443 | * Notes on the handling of exactness specifiers: | |
5444 | * | |
5445 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5446 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5447 | * written in rectangular form, exactness specifiers are applied to the | |
5448 | * real and imaginary parts before calling scm_make_rectangular. For | |
5449 | * complex numbers written in polar form, exactness specifiers are applied | |
5450 | * to the magnitude and angle before calling scm_make_polar. | |
5451 | * | |
5452 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5453 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5454 | * the entire number, and applies to both components of a complex number. | |
5455 | * "#e" causes each component to be made exact, and "#i" causes each | |
5456 | * component to be made inexact. If no forced exactness specifier is | |
5457 | * present, then the exactness of each component is determined | |
5458 | * independently by the presence or absence of a decimal point or hash mark | |
5459 | * within that component. If a decimal point or hash mark is present, the | |
5460 | * component is made inexact, otherwise it is made exact. | |
5461 | * | |
5462 | * After the exactness specifiers have been applied to each component, they | |
5463 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5464 | * the final result. Note that this will result in a real number if the | |
5465 | * imaginary part, magnitude, or angle is an exact 0. | |
5466 | * | |
5467 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5468 | * | |
5469 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5470 | */ |
5471 | ||
5472 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5473 | ||
5474 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5475 | ||
a6f3af16 AW |
5476 | /* Caller is responsible for checking that the return value is in range |
5477 | for the given radix, which should be <= 36. */ | |
5478 | static unsigned int | |
5479 | char_decimal_value (scm_t_uint32 c) | |
5480 | { | |
5481 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5482 | that's certainly above any valid decimal, so we take advantage of | |
5483 | that to elide some tests. */ | |
5484 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5485 | ||
5486 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5487 | hexadecimals. */ | |
5488 | if (d >= 10U) | |
5489 | { | |
5490 | c = uc_tolower (c); | |
5491 | if (c >= (scm_t_uint32) 'a') | |
5492 | d = c - (scm_t_uint32)'a' + 10U; | |
5493 | } | |
5494 | return d; | |
5495 | } | |
3c9a524f | 5496 | |
91db4a37 LC |
5497 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5498 | in base RADIX. Upon success, return the unsigned integer and update | |
5499 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5500 | static SCM |
3f47e526 | 5501 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5502 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5503 | { |
3c9a524f DH |
5504 | unsigned int idx = *p_idx; |
5505 | unsigned int hash_seen = 0; | |
5506 | scm_t_bits shift = 1; | |
5507 | scm_t_bits add = 0; | |
5508 | unsigned int digit_value; | |
5509 | SCM result; | |
5510 | char c; | |
3f47e526 | 5511 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5512 | |
5513 | if (idx == len) | |
5514 | return SCM_BOOL_F; | |
2a8fecee | 5515 | |
3f47e526 | 5516 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5517 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5518 | if (digit_value >= radix) |
5519 | return SCM_BOOL_F; | |
5520 | ||
5521 | idx++; | |
d956fa6f | 5522 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5523 | while (idx != len) |
f872b822 | 5524 | { |
3f47e526 | 5525 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5526 | if (c == '#') |
3c9a524f DH |
5527 | { |
5528 | hash_seen = 1; | |
5529 | digit_value = 0; | |
5530 | } | |
a6f3af16 AW |
5531 | else if (hash_seen) |
5532 | break; | |
3c9a524f | 5533 | else |
a6f3af16 AW |
5534 | { |
5535 | digit_value = char_decimal_value (c); | |
5536 | /* This check catches non-decimals in addition to out-of-range | |
5537 | decimals. */ | |
5538 | if (digit_value >= radix) | |
5539 | break; | |
5540 | } | |
3c9a524f DH |
5541 | |
5542 | idx++; | |
5543 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5544 | { | |
d956fa6f | 5545 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5546 | if (add > 0) |
d956fa6f | 5547 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5548 | |
5549 | shift = radix; | |
5550 | add = digit_value; | |
5551 | } | |
5552 | else | |
5553 | { | |
5554 | shift = shift * radix; | |
5555 | add = add * radix + digit_value; | |
5556 | } | |
5557 | }; | |
5558 | ||
5559 | if (shift > 1) | |
d956fa6f | 5560 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5561 | if (add > 0) |
d956fa6f | 5562 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5563 | |
5564 | *p_idx = idx; | |
5565 | if (hash_seen) | |
5566 | *p_exactness = INEXACT; | |
5567 | ||
5568 | return result; | |
2a8fecee JB |
5569 | } |
5570 | ||
5571 | ||
3c9a524f DH |
5572 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5573 | * covers the parts of the rules that start at a potential point. The value | |
5574 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5575 | * in variable result. The content of *p_exactness indicates, whether a hash |
5576 | * has already been seen in the digits before the point. | |
3c9a524f | 5577 | */ |
1cc91f1b | 5578 | |
3f47e526 | 5579 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5580 | |
5581 | static SCM | |
3f47e526 | 5582 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5583 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5584 | { |
3c9a524f DH |
5585 | unsigned int idx = *p_idx; |
5586 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5587 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5588 | |
5589 | if (idx == len) | |
79d34f68 | 5590 | return result; |
3c9a524f | 5591 | |
3f47e526 | 5592 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5593 | { |
5594 | scm_t_bits shift = 1; | |
5595 | scm_t_bits add = 0; | |
5596 | unsigned int digit_value; | |
cff5fa33 | 5597 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5598 | |
5599 | idx++; | |
5600 | while (idx != len) | |
5601 | { | |
3f47e526 MG |
5602 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5603 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5604 | { |
5605 | if (x == INEXACT) | |
5606 | return SCM_BOOL_F; | |
5607 | else | |
5608 | digit_value = DIGIT2UINT (c); | |
5609 | } | |
5610 | else if (c == '#') | |
5611 | { | |
5612 | x = INEXACT; | |
5613 | digit_value = 0; | |
5614 | } | |
5615 | else | |
5616 | break; | |
5617 | ||
5618 | idx++; | |
5619 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5620 | { | |
d956fa6f MV |
5621 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5622 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5623 | if (add > 0) |
d956fa6f | 5624 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5625 | |
5626 | shift = 10; | |
5627 | add = digit_value; | |
5628 | } | |
5629 | else | |
5630 | { | |
5631 | shift = shift * 10; | |
5632 | add = add * 10 + digit_value; | |
5633 | } | |
5634 | }; | |
5635 | ||
5636 | if (add > 0) | |
5637 | { | |
d956fa6f MV |
5638 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5639 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5640 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5641 | } |
5642 | ||
d8592269 | 5643 | result = scm_divide (result, big_shift); |
79d34f68 | 5644 | |
3c9a524f DH |
5645 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5646 | x = INEXACT; | |
f872b822 | 5647 | } |
3c9a524f | 5648 | |
3c9a524f | 5649 | if (idx != len) |
f872b822 | 5650 | { |
3c9a524f DH |
5651 | int sign = 1; |
5652 | unsigned int start; | |
3f47e526 | 5653 | scm_t_wchar c; |
3c9a524f DH |
5654 | int exponent; |
5655 | SCM e; | |
5656 | ||
5657 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5658 | ||
3f47e526 | 5659 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5660 | { |
3c9a524f DH |
5661 | case 'd': case 'D': |
5662 | case 'e': case 'E': | |
5663 | case 'f': case 'F': | |
5664 | case 'l': case 'L': | |
5665 | case 's': case 'S': | |
5666 | idx++; | |
ee0ddd21 AW |
5667 | if (idx == len) |
5668 | return SCM_BOOL_F; | |
5669 | ||
3c9a524f | 5670 | start = idx; |
3f47e526 | 5671 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5672 | if (c == '-') |
5673 | { | |
5674 | idx++; | |
ee0ddd21 AW |
5675 | if (idx == len) |
5676 | return SCM_BOOL_F; | |
5677 | ||
3c9a524f | 5678 | sign = -1; |
3f47e526 | 5679 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5680 | } |
5681 | else if (c == '+') | |
5682 | { | |
5683 | idx++; | |
ee0ddd21 AW |
5684 | if (idx == len) |
5685 | return SCM_BOOL_F; | |
5686 | ||
3c9a524f | 5687 | sign = 1; |
3f47e526 | 5688 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5689 | } |
5690 | else | |
5691 | sign = 1; | |
5692 | ||
3f47e526 | 5693 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5694 | return SCM_BOOL_F; |
5695 | ||
5696 | idx++; | |
5697 | exponent = DIGIT2UINT (c); | |
5698 | while (idx != len) | |
f872b822 | 5699 | { |
3f47e526 MG |
5700 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5701 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5702 | { |
5703 | idx++; | |
5704 | if (exponent <= SCM_MAXEXP) | |
5705 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5706 | } | |
5707 | else | |
5708 | break; | |
f872b822 | 5709 | } |
3c9a524f DH |
5710 | |
5711 | if (exponent > SCM_MAXEXP) | |
f872b822 | 5712 | { |
3c9a524f | 5713 | size_t exp_len = idx - start; |
3f47e526 | 5714 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5715 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5716 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5717 | } |
3c9a524f | 5718 | |
d956fa6f | 5719 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5720 | if (sign == 1) |
5721 | result = scm_product (result, e); | |
5722 | else | |
6ebecdeb | 5723 | result = scm_divide (result, e); |
3c9a524f DH |
5724 | |
5725 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5726 | x = INEXACT; | |
5727 | ||
f872b822 | 5728 | break; |
3c9a524f | 5729 | |
f872b822 | 5730 | default: |
3c9a524f | 5731 | break; |
f872b822 | 5732 | } |
0f2d19dd | 5733 | } |
3c9a524f DH |
5734 | |
5735 | *p_idx = idx; | |
5736 | if (x == INEXACT) | |
5737 | *p_exactness = x; | |
5738 | ||
5739 | return result; | |
0f2d19dd | 5740 | } |
0f2d19dd | 5741 | |
3c9a524f DH |
5742 | |
5743 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5744 | ||
5745 | static SCM | |
3f47e526 | 5746 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 5747 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 5748 | { |
3c9a524f | 5749 | unsigned int idx = *p_idx; |
164d2481 | 5750 | SCM result; |
3f47e526 | 5751 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5752 | |
40f89215 NJ |
5753 | /* Start off believing that the number will be exact. This changes |
5754 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5755 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5756 | |
3c9a524f DH |
5757 | if (idx == len) |
5758 | return SCM_BOOL_F; | |
5759 | ||
3f47e526 | 5760 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
5761 | { |
5762 | *p_idx = idx+5; | |
5763 | return scm_inf (); | |
5764 | } | |
5765 | ||
3f47e526 | 5766 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 5767 | { |
d8592269 MV |
5768 | /* Cobble up the fractional part. We might want to set the |
5769 | NaN's mantissa from it. */ | |
7351e207 | 5770 | idx += 4; |
91db4a37 | 5771 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), SCM_INUM0)) |
5f237d6e AW |
5772 | { |
5773 | #if SCM_ENABLE_DEPRECATED == 1 | |
5774 | scm_c_issue_deprecation_warning | |
5775 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5776 | #else | |
5777 | return SCM_BOOL_F; | |
5778 | #endif | |
5779 | } | |
5780 | ||
7351e207 MV |
5781 | *p_idx = idx; |
5782 | return scm_nan (); | |
5783 | } | |
5784 | ||
3f47e526 | 5785 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5786 | { |
5787 | if (radix != 10) | |
5788 | return SCM_BOOL_F; | |
5789 | else if (idx + 1 == len) | |
5790 | return SCM_BOOL_F; | |
3f47e526 | 5791 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
5792 | return SCM_BOOL_F; |
5793 | else | |
cff5fa33 | 5794 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 5795 | p_idx, &implicit_x); |
f872b822 | 5796 | } |
3c9a524f DH |
5797 | else |
5798 | { | |
3c9a524f | 5799 | SCM uinteger; |
3c9a524f | 5800 | |
9d427b2c | 5801 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5802 | if (scm_is_false (uinteger)) |
3c9a524f DH |
5803 | return SCM_BOOL_F; |
5804 | ||
5805 | if (idx == len) | |
5806 | result = uinteger; | |
3f47e526 | 5807 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 5808 | { |
3c9a524f DH |
5809 | SCM divisor; |
5810 | ||
5811 | idx++; | |
ee0ddd21 AW |
5812 | if (idx == len) |
5813 | return SCM_BOOL_F; | |
3c9a524f | 5814 | |
9d427b2c | 5815 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5816 | if (scm_is_false (divisor)) |
3c9a524f DH |
5817 | return SCM_BOOL_F; |
5818 | ||
f92e85f7 | 5819 | /* both are int/big here, I assume */ |
cba42c93 | 5820 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 5821 | } |
3c9a524f DH |
5822 | else if (radix == 10) |
5823 | { | |
9d427b2c | 5824 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 5825 | if (scm_is_false (result)) |
3c9a524f DH |
5826 | return SCM_BOOL_F; |
5827 | } | |
5828 | else | |
5829 | result = uinteger; | |
5830 | ||
5831 | *p_idx = idx; | |
f872b822 | 5832 | } |
164d2481 | 5833 | |
9d427b2c MW |
5834 | switch (forced_x) |
5835 | { | |
5836 | case EXACT: | |
5837 | if (SCM_INEXACTP (result)) | |
5838 | return scm_inexact_to_exact (result); | |
5839 | else | |
5840 | return result; | |
5841 | case INEXACT: | |
5842 | if (SCM_INEXACTP (result)) | |
5843 | return result; | |
5844 | else | |
5845 | return scm_exact_to_inexact (result); | |
5846 | case NO_EXACTNESS: | |
5847 | if (implicit_x == INEXACT) | |
5848 | { | |
5849 | if (SCM_INEXACTP (result)) | |
5850 | return result; | |
5851 | else | |
5852 | return scm_exact_to_inexact (result); | |
5853 | } | |
5854 | else | |
5855 | return result; | |
5856 | } | |
164d2481 | 5857 | |
9d427b2c MW |
5858 | /* We should never get here */ |
5859 | scm_syserror ("mem2ureal"); | |
3c9a524f | 5860 | } |
0f2d19dd | 5861 | |
0f2d19dd | 5862 | |
3c9a524f | 5863 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 5864 | |
3c9a524f | 5865 | static SCM |
3f47e526 | 5866 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 5867 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 5868 | { |
3f47e526 | 5869 | scm_t_wchar c; |
3c9a524f DH |
5870 | int sign = 0; |
5871 | SCM ureal; | |
3f47e526 | 5872 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5873 | |
5874 | if (idx == len) | |
5875 | return SCM_BOOL_F; | |
5876 | ||
3f47e526 | 5877 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5878 | if (c == '+') |
5879 | { | |
5880 | idx++; | |
5881 | sign = 1; | |
5882 | } | |
5883 | else if (c == '-') | |
5884 | { | |
5885 | idx++; | |
5886 | sign = -1; | |
0f2d19dd | 5887 | } |
0f2d19dd | 5888 | |
3c9a524f DH |
5889 | if (idx == len) |
5890 | return SCM_BOOL_F; | |
5891 | ||
9d427b2c | 5892 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5893 | if (scm_is_false (ureal)) |
f872b822 | 5894 | { |
3c9a524f DH |
5895 | /* input must be either +i or -i */ |
5896 | ||
5897 | if (sign == 0) | |
5898 | return SCM_BOOL_F; | |
5899 | ||
3f47e526 MG |
5900 | if (scm_i_string_ref (mem, idx) == 'i' |
5901 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 5902 | { |
3c9a524f DH |
5903 | idx++; |
5904 | if (idx != len) | |
5905 | return SCM_BOOL_F; | |
5906 | ||
cff5fa33 | 5907 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 5908 | } |
3c9a524f DH |
5909 | else |
5910 | return SCM_BOOL_F; | |
0f2d19dd | 5911 | } |
3c9a524f DH |
5912 | else |
5913 | { | |
73e4de09 | 5914 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 5915 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 5916 | |
3c9a524f DH |
5917 | if (idx == len) |
5918 | return ureal; | |
5919 | ||
3f47e526 | 5920 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 5921 | switch (c) |
f872b822 | 5922 | { |
3c9a524f DH |
5923 | case 'i': case 'I': |
5924 | /* either +<ureal>i or -<ureal>i */ | |
5925 | ||
5926 | idx++; | |
5927 | if (sign == 0) | |
5928 | return SCM_BOOL_F; | |
5929 | if (idx != len) | |
5930 | return SCM_BOOL_F; | |
cff5fa33 | 5931 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
5932 | |
5933 | case '@': | |
5934 | /* polar input: <real>@<real>. */ | |
5935 | ||
5936 | idx++; | |
5937 | if (idx == len) | |
5938 | return SCM_BOOL_F; | |
5939 | else | |
f872b822 | 5940 | { |
3c9a524f DH |
5941 | int sign; |
5942 | SCM angle; | |
5943 | SCM result; | |
5944 | ||
3f47e526 | 5945 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5946 | if (c == '+') |
5947 | { | |
5948 | idx++; | |
ee0ddd21 AW |
5949 | if (idx == len) |
5950 | return SCM_BOOL_F; | |
3c9a524f DH |
5951 | sign = 1; |
5952 | } | |
5953 | else if (c == '-') | |
5954 | { | |
5955 | idx++; | |
ee0ddd21 AW |
5956 | if (idx == len) |
5957 | return SCM_BOOL_F; | |
3c9a524f DH |
5958 | sign = -1; |
5959 | } | |
5960 | else | |
5961 | sign = 1; | |
5962 | ||
9d427b2c | 5963 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5964 | if (scm_is_false (angle)) |
3c9a524f DH |
5965 | return SCM_BOOL_F; |
5966 | if (idx != len) | |
5967 | return SCM_BOOL_F; | |
5968 | ||
73e4de09 | 5969 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
5970 | angle = scm_difference (angle, SCM_UNDEFINED); |
5971 | ||
5972 | result = scm_make_polar (ureal, angle); | |
5973 | return result; | |
f872b822 | 5974 | } |
3c9a524f DH |
5975 | case '+': |
5976 | case '-': | |
5977 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 5978 | |
3c9a524f DH |
5979 | idx++; |
5980 | if (idx == len) | |
5981 | return SCM_BOOL_F; | |
5982 | else | |
5983 | { | |
5984 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 5985 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 5986 | |
73e4de09 | 5987 | if (scm_is_false (imag)) |
d956fa6f | 5988 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 5989 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 5990 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 5991 | |
3c9a524f DH |
5992 | if (idx == len) |
5993 | return SCM_BOOL_F; | |
3f47e526 MG |
5994 | if (scm_i_string_ref (mem, idx) != 'i' |
5995 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 5996 | return SCM_BOOL_F; |
0f2d19dd | 5997 | |
3c9a524f DH |
5998 | idx++; |
5999 | if (idx != len) | |
6000 | return SCM_BOOL_F; | |
0f2d19dd | 6001 | |
1fe5e088 | 6002 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6003 | } |
6004 | default: | |
6005 | return SCM_BOOL_F; | |
6006 | } | |
6007 | } | |
0f2d19dd | 6008 | } |
0f2d19dd JB |
6009 | |
6010 | ||
3c9a524f DH |
6011 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6012 | ||
6013 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6014 | |
0f2d19dd | 6015 | SCM |
3f47e526 | 6016 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6017 | { |
3c9a524f DH |
6018 | unsigned int idx = 0; |
6019 | unsigned int radix = NO_RADIX; | |
6020 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6021 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6022 | |
6023 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6024 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6025 | { |
3f47e526 | 6026 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6027 | { |
6028 | case 'b': case 'B': | |
6029 | if (radix != NO_RADIX) | |
6030 | return SCM_BOOL_F; | |
6031 | radix = DUAL; | |
6032 | break; | |
6033 | case 'd': case 'D': | |
6034 | if (radix != NO_RADIX) | |
6035 | return SCM_BOOL_F; | |
6036 | radix = DEC; | |
6037 | break; | |
6038 | case 'i': case 'I': | |
6039 | if (forced_x != NO_EXACTNESS) | |
6040 | return SCM_BOOL_F; | |
6041 | forced_x = INEXACT; | |
6042 | break; | |
6043 | case 'e': case 'E': | |
6044 | if (forced_x != NO_EXACTNESS) | |
6045 | return SCM_BOOL_F; | |
6046 | forced_x = EXACT; | |
6047 | break; | |
6048 | case 'o': case 'O': | |
6049 | if (radix != NO_RADIX) | |
6050 | return SCM_BOOL_F; | |
6051 | radix = OCT; | |
6052 | break; | |
6053 | case 'x': case 'X': | |
6054 | if (radix != NO_RADIX) | |
6055 | return SCM_BOOL_F; | |
6056 | radix = HEX; | |
6057 | break; | |
6058 | default: | |
f872b822 | 6059 | return SCM_BOOL_F; |
3c9a524f DH |
6060 | } |
6061 | idx += 2; | |
6062 | } | |
6063 | ||
6064 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6065 | if (radix == NO_RADIX) | |
9d427b2c | 6066 | radix = default_radix; |
f872b822 | 6067 | |
9d427b2c | 6068 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6069 | } |
6070 | ||
3f47e526 MG |
6071 | SCM |
6072 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6073 | unsigned int default_radix) | |
6074 | { | |
6075 | SCM str = scm_from_locale_stringn (mem, len); | |
6076 | ||
6077 | return scm_i_string_to_number (str, default_radix); | |
6078 | } | |
6079 | ||
0f2d19dd | 6080 | |
a1ec6916 | 6081 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6082 | (SCM string, SCM radix), |
1e6808ea | 6083 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6084 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6085 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6086 | "is a default radix that may be overridden by an explicit radix\n" | |
6087 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6088 | "supplied, then the default radix is 10. If string is not a\n" | |
6089 | "syntactically valid notation for a number, then\n" | |
6090 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6091 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6092 | { |
6093 | SCM answer; | |
5efd3c7d | 6094 | unsigned int base; |
a6d9e5ab | 6095 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6096 | |
6097 | if (SCM_UNBNDP (radix)) | |
6098 | base = 10; | |
6099 | else | |
6100 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6101 | ||
3f47e526 | 6102 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6103 | scm_remember_upto_here_1 (string); |
6104 | return answer; | |
0f2d19dd | 6105 | } |
1bbd0b84 | 6106 | #undef FUNC_NAME |
3c9a524f DH |
6107 | |
6108 | ||
0f2d19dd JB |
6109 | /*** END strs->nums ***/ |
6110 | ||
5986c47d | 6111 | |
8507ec80 MV |
6112 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6113 | (SCM x), | |
6114 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6115 | "otherwise.") | |
6116 | #define FUNC_NAME s_scm_number_p | |
6117 | { | |
6118 | return scm_from_bool (SCM_NUMBERP (x)); | |
6119 | } | |
6120 | #undef FUNC_NAME | |
6121 | ||
6122 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6123 | (SCM x), |
942e5b91 | 6124 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6125 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6126 | "values form subsets of the set of complex numbers, i. e. the\n" |
6127 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6128 | "rational or integer number.") | |
8507ec80 | 6129 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6130 | { |
8507ec80 MV |
6131 | /* all numbers are complex. */ |
6132 | return scm_number_p (x); | |
0f2d19dd | 6133 | } |
1bbd0b84 | 6134 | #undef FUNC_NAME |
0f2d19dd | 6135 | |
f92e85f7 MV |
6136 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6137 | (SCM x), | |
6138 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6139 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6140 | "the set of real numbers, i. e. the predicate will also be\n" | |
6141 | "fulfilled if @var{x} is an integer number.") | |
6142 | #define FUNC_NAME s_scm_real_p | |
6143 | { | |
c960e556 MW |
6144 | return scm_from_bool |
6145 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6146 | } |
6147 | #undef FUNC_NAME | |
6148 | ||
6149 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6150 | (SCM x), |
942e5b91 | 6151 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6152 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6153 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6154 | "fulfilled if @var{x} is an integer number.") |
6155 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6156 | { |
c960e556 | 6157 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6158 | return SCM_BOOL_T; |
6159 | else if (SCM_REALP (x)) | |
c960e556 MW |
6160 | /* due to their limited precision, finite floating point numbers are |
6161 | rational as well. (finite means neither infinity nor a NaN) */ | |
6162 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6163 | else |
bb628794 | 6164 | return SCM_BOOL_F; |
0f2d19dd | 6165 | } |
1bbd0b84 | 6166 | #undef FUNC_NAME |
0f2d19dd | 6167 | |
a1ec6916 | 6168 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6169 | (SCM x), |
942e5b91 MG |
6170 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6171 | "else.") | |
1bbd0b84 | 6172 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6173 | { |
c960e556 | 6174 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6175 | return SCM_BOOL_T; |
c960e556 MW |
6176 | else if (SCM_REALP (x)) |
6177 | { | |
6178 | double val = SCM_REAL_VALUE (x); | |
6179 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6180 | } | |
6181 | else | |
8e43ed5d | 6182 | return SCM_BOOL_F; |
0f2d19dd | 6183 | } |
1bbd0b84 | 6184 | #undef FUNC_NAME |
0f2d19dd JB |
6185 | |
6186 | ||
8a1f4f98 AW |
6187 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6188 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6189 | (SCM x, SCM y, SCM rest), | |
6190 | "Return @code{#t} if all parameters are numerically equal.") | |
6191 | #define FUNC_NAME s_scm_i_num_eq_p | |
6192 | { | |
6193 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6194 | return SCM_BOOL_T; | |
6195 | while (!scm_is_null (rest)) | |
6196 | { | |
6197 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6198 | return SCM_BOOL_F; | |
6199 | x = y; | |
6200 | y = scm_car (rest); | |
6201 | rest = scm_cdr (rest); | |
6202 | } | |
6203 | return scm_num_eq_p (x, y); | |
6204 | } | |
6205 | #undef FUNC_NAME | |
0f2d19dd | 6206 | SCM |
6e8d25a6 | 6207 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6208 | { |
d8b95e27 | 6209 | again: |
e11e83f3 | 6210 | if (SCM_I_INUMP (x)) |
0aacf84e | 6211 | { |
e25f3727 | 6212 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6213 | if (SCM_I_INUMP (y)) |
0aacf84e | 6214 | { |
e25f3727 | 6215 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6216 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6217 | } |
6218 | else if (SCM_BIGP (y)) | |
6219 | return SCM_BOOL_F; | |
6220 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6221 | { |
6222 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6223 | to a double and compare. | |
6224 | ||
6225 | But on a 64-bit system an inum is bigger than a double and | |
6226 | casting it to a double (call that dxx) will round. dxx is at | |
6227 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6228 | an integer and fits a long. So we cast yy to a long and | |
6229 | compare with plain xx. | |
6230 | ||
6231 | An alternative (for any size system actually) would be to check | |
6232 | yy is an integer (with floor) and is in range of an inum | |
6233 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6234 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6235 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6236 | |
6237 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6238 | return scm_from_bool ((double) xx == yy |
6239 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6240 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6241 | } |
0aacf84e | 6242 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6243 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6244 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6245 | else if (SCM_FRACTIONP (y)) |
6246 | return SCM_BOOL_F; | |
0aacf84e | 6247 | else |
8a1f4f98 | 6248 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6249 | } |
0aacf84e MD |
6250 | else if (SCM_BIGP (x)) |
6251 | { | |
e11e83f3 | 6252 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6253 | return SCM_BOOL_F; |
6254 | else if (SCM_BIGP (y)) | |
6255 | { | |
6256 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6257 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6258 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6259 | } |
6260 | else if (SCM_REALP (y)) | |
6261 | { | |
6262 | int cmp; | |
2e65b52f | 6263 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6264 | return SCM_BOOL_F; |
6265 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6266 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6267 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6268 | } |
6269 | else if (SCM_COMPLEXP (y)) | |
6270 | { | |
6271 | int cmp; | |
6272 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6273 | return SCM_BOOL_F; | |
2e65b52f | 6274 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6275 | return SCM_BOOL_F; |
6276 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6277 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6278 | return scm_from_bool (0 == cmp); |
0aacf84e | 6279 | } |
f92e85f7 MV |
6280 | else if (SCM_FRACTIONP (y)) |
6281 | return SCM_BOOL_F; | |
0aacf84e | 6282 | else |
8a1f4f98 | 6283 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6284 | } |
0aacf84e MD |
6285 | else if (SCM_REALP (x)) |
6286 | { | |
e8c5b1f2 | 6287 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6288 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6289 | { |
6290 | /* see comments with inum/real above */ | |
e25f3727 | 6291 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6292 | return scm_from_bool (xx == (double) yy |
6293 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6294 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6295 | } |
0aacf84e MD |
6296 | else if (SCM_BIGP (y)) |
6297 | { | |
6298 | int cmp; | |
2e65b52f | 6299 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6300 | return SCM_BOOL_F; |
6301 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6302 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6303 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6304 | } |
6305 | else if (SCM_REALP (y)) | |
73e4de09 | 6306 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6307 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6308 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6309 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6310 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6311 | { |
6312 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6313 | if (isnan (xx)) |
d8b95e27 | 6314 | return SCM_BOOL_F; |
2e65b52f | 6315 | if (isinf (xx)) |
73e4de09 | 6316 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6317 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6318 | goto again; | |
6319 | } | |
0aacf84e | 6320 | else |
8a1f4f98 | 6321 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6322 | } |
0aacf84e MD |
6323 | else if (SCM_COMPLEXP (x)) |
6324 | { | |
e11e83f3 MV |
6325 | if (SCM_I_INUMP (y)) |
6326 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6327 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6328 | else if (SCM_BIGP (y)) | |
6329 | { | |
6330 | int cmp; | |
6331 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6332 | return SCM_BOOL_F; | |
2e65b52f | 6333 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6334 | return SCM_BOOL_F; |
6335 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6336 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6337 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6338 | } |
6339 | else if (SCM_REALP (y)) | |
73e4de09 | 6340 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6341 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6342 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6343 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6344 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6345 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6346 | { |
6347 | double xx; | |
6348 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6349 | return SCM_BOOL_F; | |
6350 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6351 | if (isnan (xx)) |
d8b95e27 | 6352 | return SCM_BOOL_F; |
2e65b52f | 6353 | if (isinf (xx)) |
73e4de09 | 6354 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6355 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6356 | goto again; | |
6357 | } | |
f92e85f7 | 6358 | else |
8a1f4f98 | 6359 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6360 | } |
6361 | else if (SCM_FRACTIONP (x)) | |
6362 | { | |
e11e83f3 | 6363 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6364 | return SCM_BOOL_F; |
6365 | else if (SCM_BIGP (y)) | |
6366 | return SCM_BOOL_F; | |
6367 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6368 | { |
6369 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6370 | if (isnan (yy)) |
d8b95e27 | 6371 | return SCM_BOOL_F; |
2e65b52f | 6372 | if (isinf (yy)) |
73e4de09 | 6373 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6374 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6375 | goto again; | |
6376 | } | |
f92e85f7 | 6377 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6378 | { |
6379 | double yy; | |
6380 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6381 | return SCM_BOOL_F; | |
6382 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6383 | if (isnan (yy)) |
d8b95e27 | 6384 | return SCM_BOOL_F; |
2e65b52f | 6385 | if (isinf (yy)) |
73e4de09 | 6386 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6387 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6388 | goto again; | |
6389 | } | |
f92e85f7 MV |
6390 | else if (SCM_FRACTIONP (y)) |
6391 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6392 | else |
8a1f4f98 | 6393 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6394 | } |
0aacf84e | 6395 | else |
8a1f4f98 | 6396 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6397 | } |
6398 | ||
6399 | ||
a5f0b599 KR |
6400 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6401 | done are good for inums, but for bignums an answer can almost always be | |
6402 | had by just examining a few high bits of the operands, as done by GMP in | |
6403 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6404 | of the float exponent to take into account. */ | |
6405 | ||
8c93b597 | 6406 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6407 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6408 | (SCM x, SCM y, SCM rest), | |
6409 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6410 | "increasing.") | |
6411 | #define FUNC_NAME s_scm_i_num_less_p | |
6412 | { | |
6413 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6414 | return SCM_BOOL_T; | |
6415 | while (!scm_is_null (rest)) | |
6416 | { | |
6417 | if (scm_is_false (scm_less_p (x, y))) | |
6418 | return SCM_BOOL_F; | |
6419 | x = y; | |
6420 | y = scm_car (rest); | |
6421 | rest = scm_cdr (rest); | |
6422 | } | |
6423 | return scm_less_p (x, y); | |
6424 | } | |
6425 | #undef FUNC_NAME | |
0f2d19dd | 6426 | SCM |
6e8d25a6 | 6427 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6428 | { |
a5f0b599 | 6429 | again: |
e11e83f3 | 6430 | if (SCM_I_INUMP (x)) |
0aacf84e | 6431 | { |
e25f3727 | 6432 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6433 | if (SCM_I_INUMP (y)) |
0aacf84e | 6434 | { |
e25f3727 | 6435 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6436 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6437 | } |
6438 | else if (SCM_BIGP (y)) | |
6439 | { | |
6440 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6441 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6442 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6443 | } |
6444 | else if (SCM_REALP (y)) | |
73e4de09 | 6445 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6446 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6447 | { |
6448 | /* "x < a/b" becomes "x*b < a" */ | |
6449 | int_frac: | |
6450 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6451 | y = SCM_FRACTION_NUMERATOR (y); | |
6452 | goto again; | |
6453 | } | |
0aacf84e | 6454 | else |
8a1f4f98 | 6455 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6456 | } |
0aacf84e MD |
6457 | else if (SCM_BIGP (x)) |
6458 | { | |
e11e83f3 | 6459 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6460 | { |
6461 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6462 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6463 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6464 | } |
6465 | else if (SCM_BIGP (y)) | |
6466 | { | |
6467 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6468 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6469 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6470 | } |
6471 | else if (SCM_REALP (y)) | |
6472 | { | |
6473 | int cmp; | |
2e65b52f | 6474 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6475 | return SCM_BOOL_F; |
6476 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6477 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6478 | return scm_from_bool (cmp < 0); |
0aacf84e | 6479 | } |
f92e85f7 | 6480 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6481 | goto int_frac; |
0aacf84e | 6482 | else |
8a1f4f98 | 6483 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6484 | } |
0aacf84e MD |
6485 | else if (SCM_REALP (x)) |
6486 | { | |
e11e83f3 MV |
6487 | if (SCM_I_INUMP (y)) |
6488 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6489 | else if (SCM_BIGP (y)) |
6490 | { | |
6491 | int cmp; | |
2e65b52f | 6492 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6493 | return SCM_BOOL_F; |
6494 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6495 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6496 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6497 | } |
6498 | else if (SCM_REALP (y)) | |
73e4de09 | 6499 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6500 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6501 | { |
6502 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6503 | if (isnan (xx)) |
a5f0b599 | 6504 | return SCM_BOOL_F; |
2e65b52f | 6505 | if (isinf (xx)) |
73e4de09 | 6506 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6507 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6508 | goto again; | |
6509 | } | |
f92e85f7 | 6510 | else |
8a1f4f98 | 6511 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6512 | } |
6513 | else if (SCM_FRACTIONP (x)) | |
6514 | { | |
e11e83f3 | 6515 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6516 | { |
6517 | /* "a/b < y" becomes "a < y*b" */ | |
6518 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6519 | x = SCM_FRACTION_NUMERATOR (x); | |
6520 | goto again; | |
6521 | } | |
f92e85f7 | 6522 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6523 | { |
6524 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6525 | if (isnan (yy)) |
a5f0b599 | 6526 | return SCM_BOOL_F; |
2e65b52f | 6527 | if (isinf (yy)) |
73e4de09 | 6528 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6529 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6530 | goto again; | |
6531 | } | |
f92e85f7 | 6532 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6533 | { |
6534 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6535 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6536 | SCM_FRACTION_DENOMINATOR (y)); | |
6537 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6538 | SCM_FRACTION_DENOMINATOR (x)); | |
6539 | x = new_x; | |
6540 | y = new_y; | |
6541 | goto again; | |
6542 | } | |
0aacf84e | 6543 | else |
8a1f4f98 | 6544 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6545 | } |
0aacf84e | 6546 | else |
8a1f4f98 | 6547 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6548 | } |
6549 | ||
6550 | ||
8a1f4f98 AW |
6551 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6552 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6553 | (SCM x, SCM y, SCM rest), | |
6554 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6555 | "decreasing.") | |
6556 | #define FUNC_NAME s_scm_i_num_gr_p | |
6557 | { | |
6558 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6559 | return SCM_BOOL_T; | |
6560 | while (!scm_is_null (rest)) | |
6561 | { | |
6562 | if (scm_is_false (scm_gr_p (x, y))) | |
6563 | return SCM_BOOL_F; | |
6564 | x = y; | |
6565 | y = scm_car (rest); | |
6566 | rest = scm_cdr (rest); | |
6567 | } | |
6568 | return scm_gr_p (x, y); | |
6569 | } | |
6570 | #undef FUNC_NAME | |
6571 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6572 | SCM |
6573 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6574 | { |
c76b1eaf | 6575 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6576 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6577 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6578 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6579 | else |
6580 | return scm_less_p (y, x); | |
0f2d19dd | 6581 | } |
1bbd0b84 | 6582 | #undef FUNC_NAME |
0f2d19dd JB |
6583 | |
6584 | ||
8a1f4f98 AW |
6585 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6586 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6587 | (SCM x, SCM y, SCM rest), | |
6588 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6589 | "non-decreasing.") | |
6590 | #define FUNC_NAME s_scm_i_num_leq_p | |
6591 | { | |
6592 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6593 | return SCM_BOOL_T; | |
6594 | while (!scm_is_null (rest)) | |
6595 | { | |
6596 | if (scm_is_false (scm_leq_p (x, y))) | |
6597 | return SCM_BOOL_F; | |
6598 | x = y; | |
6599 | y = scm_car (rest); | |
6600 | rest = scm_cdr (rest); | |
6601 | } | |
6602 | return scm_leq_p (x, y); | |
6603 | } | |
6604 | #undef FUNC_NAME | |
6605 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6606 | SCM |
6607 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6608 | { |
c76b1eaf | 6609 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6610 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6611 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6612 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6613 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6614 | return SCM_BOOL_F; |
c76b1eaf | 6615 | else |
73e4de09 | 6616 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6617 | } |
1bbd0b84 | 6618 | #undef FUNC_NAME |
0f2d19dd JB |
6619 | |
6620 | ||
8a1f4f98 AW |
6621 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6622 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6623 | (SCM x, SCM y, SCM rest), | |
6624 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6625 | "non-increasing.") | |
6626 | #define FUNC_NAME s_scm_i_num_geq_p | |
6627 | { | |
6628 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6629 | return SCM_BOOL_T; | |
6630 | while (!scm_is_null (rest)) | |
6631 | { | |
6632 | if (scm_is_false (scm_geq_p (x, y))) | |
6633 | return SCM_BOOL_F; | |
6634 | x = y; | |
6635 | y = scm_car (rest); | |
6636 | rest = scm_cdr (rest); | |
6637 | } | |
6638 | return scm_geq_p (x, y); | |
6639 | } | |
6640 | #undef FUNC_NAME | |
6641 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6642 | SCM |
6643 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6644 | { |
c76b1eaf | 6645 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6646 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6647 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6648 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6649 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6650 | return SCM_BOOL_F; |
c76b1eaf | 6651 | else |
73e4de09 | 6652 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6653 | } |
1bbd0b84 | 6654 | #undef FUNC_NAME |
0f2d19dd JB |
6655 | |
6656 | ||
2519490c MW |
6657 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6658 | (SCM z), | |
6659 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6660 | "zero.") | |
6661 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6662 | { |
e11e83f3 | 6663 | if (SCM_I_INUMP (z)) |
bc36d050 | 6664 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6665 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6666 | return SCM_BOOL_F; |
0aacf84e | 6667 | else if (SCM_REALP (z)) |
73e4de09 | 6668 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6669 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6670 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6671 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6672 | else if (SCM_FRACTIONP (z)) |
6673 | return SCM_BOOL_F; | |
0aacf84e | 6674 | else |
2519490c | 6675 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6676 | } |
2519490c | 6677 | #undef FUNC_NAME |
0f2d19dd JB |
6678 | |
6679 | ||
2519490c MW |
6680 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6681 | (SCM x), | |
6682 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6683 | "zero.") | |
6684 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6685 | { |
e11e83f3 MV |
6686 | if (SCM_I_INUMP (x)) |
6687 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6688 | else if (SCM_BIGP (x)) |
6689 | { | |
6690 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6691 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6692 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6693 | } |
6694 | else if (SCM_REALP (x)) | |
73e4de09 | 6695 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6696 | else if (SCM_FRACTIONP (x)) |
6697 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6698 | else |
2519490c | 6699 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6700 | } |
2519490c | 6701 | #undef FUNC_NAME |
0f2d19dd JB |
6702 | |
6703 | ||
2519490c MW |
6704 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6705 | (SCM x), | |
6706 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6707 | "zero.") | |
6708 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6709 | { |
e11e83f3 MV |
6710 | if (SCM_I_INUMP (x)) |
6711 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6712 | else if (SCM_BIGP (x)) |
6713 | { | |
6714 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6715 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6716 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6717 | } |
6718 | else if (SCM_REALP (x)) | |
73e4de09 | 6719 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6720 | else if (SCM_FRACTIONP (x)) |
6721 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6722 | else |
2519490c | 6723 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6724 | } |
2519490c | 6725 | #undef FUNC_NAME |
0f2d19dd JB |
6726 | |
6727 | ||
2a06f791 KR |
6728 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6729 | required by r5rs. On that basis, for exact/inexact combinations the | |
6730 | exact is converted to inexact to compare and possibly return. This is | |
6731 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6732 | its test, such trouble is not required for min and max. */ | |
6733 | ||
78d3deb1 AW |
6734 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6735 | (SCM x, SCM y, SCM rest), | |
6736 | "Return the maximum of all parameter values.") | |
6737 | #define FUNC_NAME s_scm_i_max | |
6738 | { | |
6739 | while (!scm_is_null (rest)) | |
6740 | { x = scm_max (x, y); | |
6741 | y = scm_car (rest); | |
6742 | rest = scm_cdr (rest); | |
6743 | } | |
6744 | return scm_max (x, y); | |
6745 | } | |
6746 | #undef FUNC_NAME | |
6747 | ||
6748 | #define s_max s_scm_i_max | |
6749 | #define g_max g_scm_i_max | |
6750 | ||
0f2d19dd | 6751 | SCM |
6e8d25a6 | 6752 | scm_max (SCM x, SCM y) |
0f2d19dd | 6753 | { |
0aacf84e MD |
6754 | if (SCM_UNBNDP (y)) |
6755 | { | |
6756 | if (SCM_UNBNDP (x)) | |
6757 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 6758 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6759 | return x; |
6760 | else | |
6761 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 6762 | } |
f4c627b3 | 6763 | |
e11e83f3 | 6764 | if (SCM_I_INUMP (x)) |
0aacf84e | 6765 | { |
e25f3727 | 6766 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6767 | if (SCM_I_INUMP (y)) |
0aacf84e | 6768 | { |
e25f3727 | 6769 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6770 | return (xx < yy) ? y : x; |
6771 | } | |
6772 | else if (SCM_BIGP (y)) | |
6773 | { | |
6774 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6775 | scm_remember_upto_here_1 (y); | |
6776 | return (sgn < 0) ? x : y; | |
6777 | } | |
6778 | else if (SCM_REALP (y)) | |
6779 | { | |
2e274311 MW |
6780 | double xxd = xx; |
6781 | double yyd = SCM_REAL_VALUE (y); | |
6782 | ||
6783 | if (xxd > yyd) | |
6784 | return scm_from_double (xxd); | |
6785 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
6786 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6787 | return y; | |
6788 | /* Handle signed zeroes properly */ | |
6789 | else if (xx == 0) | |
6790 | return flo0; | |
6791 | else | |
6792 | return y; | |
0aacf84e | 6793 | } |
f92e85f7 MV |
6794 | else if (SCM_FRACTIONP (y)) |
6795 | { | |
e4bc5d6c | 6796 | use_less: |
73e4de09 | 6797 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 6798 | } |
0aacf84e MD |
6799 | else |
6800 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6801 | } |
0aacf84e MD |
6802 | else if (SCM_BIGP (x)) |
6803 | { | |
e11e83f3 | 6804 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6805 | { |
6806 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6807 | scm_remember_upto_here_1 (x); | |
6808 | return (sgn < 0) ? y : x; | |
6809 | } | |
6810 | else if (SCM_BIGP (y)) | |
6811 | { | |
6812 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6813 | scm_remember_upto_here_2 (x, y); | |
6814 | return (cmp > 0) ? x : y; | |
6815 | } | |
6816 | else if (SCM_REALP (y)) | |
6817 | { | |
2a06f791 KR |
6818 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
6819 | double xx, yy; | |
6820 | big_real: | |
6821 | xx = scm_i_big2dbl (x); | |
6822 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6823 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 6824 | } |
f92e85f7 MV |
6825 | else if (SCM_FRACTIONP (y)) |
6826 | { | |
e4bc5d6c | 6827 | goto use_less; |
f92e85f7 | 6828 | } |
0aacf84e MD |
6829 | else |
6830 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 6831 | } |
0aacf84e MD |
6832 | else if (SCM_REALP (x)) |
6833 | { | |
e11e83f3 | 6834 | if (SCM_I_INUMP (y)) |
0aacf84e | 6835 | { |
2e274311 MW |
6836 | scm_t_inum yy = SCM_I_INUM (y); |
6837 | double xxd = SCM_REAL_VALUE (x); | |
6838 | double yyd = yy; | |
6839 | ||
6840 | if (yyd > xxd) | |
6841 | return scm_from_double (yyd); | |
6842 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
6843 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6844 | return x; | |
6845 | /* Handle signed zeroes properly */ | |
6846 | else if (yy == 0) | |
6847 | return flo0; | |
6848 | else | |
6849 | return x; | |
0aacf84e MD |
6850 | } |
6851 | else if (SCM_BIGP (y)) | |
6852 | { | |
b6f8f763 | 6853 | SCM_SWAP (x, y); |
2a06f791 | 6854 | goto big_real; |
0aacf84e MD |
6855 | } |
6856 | else if (SCM_REALP (y)) | |
6857 | { | |
0aacf84e | 6858 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6859 | double yy = SCM_REAL_VALUE (y); |
6860 | ||
6861 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
6862 | if (xx > yy) | |
6863 | return x; | |
6864 | else if (SCM_LIKELY (xx < yy)) | |
6865 | return y; | |
6866 | /* If neither (xx > yy) nor (xx < yy), then | |
6867 | either they're equal or one is a NaN */ | |
6868 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6869 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 6870 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6871 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6872 | /* xx == yy, but handle signed zeroes properly */ |
6873 | else if (double_is_non_negative_zero (yy)) | |
6874 | return y; | |
6875 | else | |
6876 | return x; | |
0aacf84e | 6877 | } |
f92e85f7 MV |
6878 | else if (SCM_FRACTIONP (y)) |
6879 | { | |
6880 | double yy = scm_i_fraction2double (y); | |
6881 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6882 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
6883 | } |
6884 | else | |
6885 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
6886 | } | |
6887 | else if (SCM_FRACTIONP (x)) | |
6888 | { | |
e11e83f3 | 6889 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6890 | { |
e4bc5d6c | 6891 | goto use_less; |
f92e85f7 MV |
6892 | } |
6893 | else if (SCM_BIGP (y)) | |
6894 | { | |
e4bc5d6c | 6895 | goto use_less; |
f92e85f7 MV |
6896 | } |
6897 | else if (SCM_REALP (y)) | |
6898 | { | |
6899 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
6900 | /* if y==NaN then ">" is false, so we return the NaN y */ |
6901 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
6902 | } |
6903 | else if (SCM_FRACTIONP (y)) | |
6904 | { | |
e4bc5d6c | 6905 | goto use_less; |
f92e85f7 | 6906 | } |
0aacf84e MD |
6907 | else |
6908 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6909 | } |
0aacf84e | 6910 | else |
f4c627b3 | 6911 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
6912 | } |
6913 | ||
6914 | ||
78d3deb1 AW |
6915 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
6916 | (SCM x, SCM y, SCM rest), | |
6917 | "Return the minimum of all parameter values.") | |
6918 | #define FUNC_NAME s_scm_i_min | |
6919 | { | |
6920 | while (!scm_is_null (rest)) | |
6921 | { x = scm_min (x, y); | |
6922 | y = scm_car (rest); | |
6923 | rest = scm_cdr (rest); | |
6924 | } | |
6925 | return scm_min (x, y); | |
6926 | } | |
6927 | #undef FUNC_NAME | |
6928 | ||
6929 | #define s_min s_scm_i_min | |
6930 | #define g_min g_scm_i_min | |
6931 | ||
0f2d19dd | 6932 | SCM |
6e8d25a6 | 6933 | scm_min (SCM x, SCM y) |
0f2d19dd | 6934 | { |
0aacf84e MD |
6935 | if (SCM_UNBNDP (y)) |
6936 | { | |
6937 | if (SCM_UNBNDP (x)) | |
6938 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 6939 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6940 | return x; |
6941 | else | |
6942 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 6943 | } |
f4c627b3 | 6944 | |
e11e83f3 | 6945 | if (SCM_I_INUMP (x)) |
0aacf84e | 6946 | { |
e25f3727 | 6947 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6948 | if (SCM_I_INUMP (y)) |
0aacf84e | 6949 | { |
e25f3727 | 6950 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6951 | return (xx < yy) ? x : y; |
6952 | } | |
6953 | else if (SCM_BIGP (y)) | |
6954 | { | |
6955 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6956 | scm_remember_upto_here_1 (y); | |
6957 | return (sgn < 0) ? y : x; | |
6958 | } | |
6959 | else if (SCM_REALP (y)) | |
6960 | { | |
6961 | double z = xx; | |
6962 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 6963 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 6964 | } |
f92e85f7 MV |
6965 | else if (SCM_FRACTIONP (y)) |
6966 | { | |
e4bc5d6c | 6967 | use_less: |
73e4de09 | 6968 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 6969 | } |
0aacf84e MD |
6970 | else |
6971 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 6972 | } |
0aacf84e MD |
6973 | else if (SCM_BIGP (x)) |
6974 | { | |
e11e83f3 | 6975 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6976 | { |
6977 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6978 | scm_remember_upto_here_1 (x); | |
6979 | return (sgn < 0) ? x : y; | |
6980 | } | |
6981 | else if (SCM_BIGP (y)) | |
6982 | { | |
6983 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6984 | scm_remember_upto_here_2 (x, y); | |
6985 | return (cmp > 0) ? y : x; | |
6986 | } | |
6987 | else if (SCM_REALP (y)) | |
6988 | { | |
2a06f791 KR |
6989 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
6990 | double xx, yy; | |
6991 | big_real: | |
6992 | xx = scm_i_big2dbl (x); | |
6993 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6994 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 6995 | } |
f92e85f7 MV |
6996 | else if (SCM_FRACTIONP (y)) |
6997 | { | |
e4bc5d6c | 6998 | goto use_less; |
f92e85f7 | 6999 | } |
0aacf84e MD |
7000 | else |
7001 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 7002 | } |
0aacf84e MD |
7003 | else if (SCM_REALP (x)) |
7004 | { | |
e11e83f3 | 7005 | if (SCM_I_INUMP (y)) |
0aacf84e | 7006 | { |
e11e83f3 | 7007 | double z = SCM_I_INUM (y); |
0aacf84e | 7008 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7009 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7010 | } |
7011 | else if (SCM_BIGP (y)) | |
7012 | { | |
b6f8f763 | 7013 | SCM_SWAP (x, y); |
2a06f791 | 7014 | goto big_real; |
0aacf84e MD |
7015 | } |
7016 | else if (SCM_REALP (y)) | |
7017 | { | |
0aacf84e | 7018 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7019 | double yy = SCM_REAL_VALUE (y); |
7020 | ||
7021 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
7022 | if (xx < yy) | |
7023 | return x; | |
7024 | else if (SCM_LIKELY (xx > yy)) | |
7025 | return y; | |
7026 | /* If neither (xx < yy) nor (xx > yy), then | |
7027 | either they're equal or one is a NaN */ | |
7028 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7029 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 7030 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7031 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7032 | /* xx == yy, but handle signed zeroes properly */ |
7033 | else if (double_is_non_negative_zero (xx)) | |
7034 | return y; | |
7035 | else | |
7036 | return x; | |
0aacf84e | 7037 | } |
f92e85f7 MV |
7038 | else if (SCM_FRACTIONP (y)) |
7039 | { | |
7040 | double yy = scm_i_fraction2double (y); | |
7041 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7042 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7043 | } |
0aacf84e MD |
7044 | else |
7045 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7046 | } |
f92e85f7 MV |
7047 | else if (SCM_FRACTIONP (x)) |
7048 | { | |
e11e83f3 | 7049 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7050 | { |
e4bc5d6c | 7051 | goto use_less; |
f92e85f7 MV |
7052 | } |
7053 | else if (SCM_BIGP (y)) | |
7054 | { | |
e4bc5d6c | 7055 | goto use_less; |
f92e85f7 MV |
7056 | } |
7057 | else if (SCM_REALP (y)) | |
7058 | { | |
7059 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7060 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7061 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7062 | } |
7063 | else if (SCM_FRACTIONP (y)) | |
7064 | { | |
e4bc5d6c | 7065 | goto use_less; |
f92e85f7 MV |
7066 | } |
7067 | else | |
78d3deb1 | 7068 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7069 | } |
0aacf84e | 7070 | else |
f4c627b3 | 7071 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7072 | } |
7073 | ||
7074 | ||
8ccd24f7 AW |
7075 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7076 | (SCM x, SCM y, SCM rest), | |
7077 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7078 | "any parameters." ) | |
7079 | #define FUNC_NAME s_scm_i_sum | |
7080 | { | |
7081 | while (!scm_is_null (rest)) | |
7082 | { x = scm_sum (x, y); | |
7083 | y = scm_car (rest); | |
7084 | rest = scm_cdr (rest); | |
7085 | } | |
7086 | return scm_sum (x, y); | |
7087 | } | |
7088 | #undef FUNC_NAME | |
7089 | ||
7090 | #define s_sum s_scm_i_sum | |
7091 | #define g_sum g_scm_i_sum | |
7092 | ||
0f2d19dd | 7093 | SCM |
6e8d25a6 | 7094 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7095 | { |
9cc37597 | 7096 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7097 | { |
7098 | if (SCM_NUMBERP (x)) return x; | |
7099 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7100 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7101 | } |
c209c88e | 7102 | |
9cc37597 | 7103 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7104 | { |
9cc37597 | 7105 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7106 | { |
e25f3727 AW |
7107 | scm_t_inum xx = SCM_I_INUM (x); |
7108 | scm_t_inum yy = SCM_I_INUM (y); | |
7109 | scm_t_inum z = xx + yy; | |
7110 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7111 | } |
7112 | else if (SCM_BIGP (y)) | |
7113 | { | |
7114 | SCM_SWAP (x, y); | |
7115 | goto add_big_inum; | |
7116 | } | |
7117 | else if (SCM_REALP (y)) | |
7118 | { | |
e25f3727 | 7119 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7120 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7121 | } |
7122 | else if (SCM_COMPLEXP (y)) | |
7123 | { | |
e25f3727 | 7124 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7125 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7126 | SCM_COMPLEX_IMAG (y)); |
7127 | } | |
f92e85f7 | 7128 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7129 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7130 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7131 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7132 | else |
7133 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7134 | } else if (SCM_BIGP (x)) |
7135 | { | |
e11e83f3 | 7136 | if (SCM_I_INUMP (y)) |
0aacf84e | 7137 | { |
e25f3727 | 7138 | scm_t_inum inum; |
0aacf84e MD |
7139 | int bigsgn; |
7140 | add_big_inum: | |
e11e83f3 | 7141 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7142 | if (inum == 0) |
7143 | return x; | |
7144 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7145 | if (inum < 0) | |
7146 | { | |
7147 | SCM result = scm_i_mkbig (); | |
7148 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7149 | scm_remember_upto_here_1 (x); | |
7150 | /* we know the result will have to be a bignum */ | |
7151 | if (bigsgn == -1) | |
7152 | return result; | |
7153 | return scm_i_normbig (result); | |
7154 | } | |
7155 | else | |
7156 | { | |
7157 | SCM result = scm_i_mkbig (); | |
7158 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7159 | scm_remember_upto_here_1 (x); | |
7160 | /* we know the result will have to be a bignum */ | |
7161 | if (bigsgn == 1) | |
7162 | return result; | |
7163 | return scm_i_normbig (result); | |
7164 | } | |
7165 | } | |
7166 | else if (SCM_BIGP (y)) | |
7167 | { | |
7168 | SCM result = scm_i_mkbig (); | |
7169 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7170 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7171 | mpz_add (SCM_I_BIG_MPZ (result), | |
7172 | SCM_I_BIG_MPZ (x), | |
7173 | SCM_I_BIG_MPZ (y)); | |
7174 | scm_remember_upto_here_2 (x, y); | |
7175 | /* we know the result will have to be a bignum */ | |
7176 | if (sgn_x == sgn_y) | |
7177 | return result; | |
7178 | return scm_i_normbig (result); | |
7179 | } | |
7180 | else if (SCM_REALP (y)) | |
7181 | { | |
7182 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7183 | scm_remember_upto_here_1 (x); | |
55f26379 | 7184 | return scm_from_double (result); |
0aacf84e MD |
7185 | } |
7186 | else if (SCM_COMPLEXP (y)) | |
7187 | { | |
7188 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7189 | + SCM_COMPLEX_REAL (y)); | |
7190 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7191 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7192 | } |
f92e85f7 | 7193 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7194 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7195 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7196 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7197 | else |
7198 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7199 | } |
0aacf84e MD |
7200 | else if (SCM_REALP (x)) |
7201 | { | |
e11e83f3 | 7202 | if (SCM_I_INUMP (y)) |
55f26379 | 7203 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7204 | else if (SCM_BIGP (y)) |
7205 | { | |
7206 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7207 | scm_remember_upto_here_1 (y); | |
55f26379 | 7208 | return scm_from_double (result); |
0aacf84e MD |
7209 | } |
7210 | else if (SCM_REALP (y)) | |
55f26379 | 7211 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7212 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7213 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7214 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7215 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7216 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7217 | else |
7218 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7219 | } |
0aacf84e MD |
7220 | else if (SCM_COMPLEXP (x)) |
7221 | { | |
e11e83f3 | 7222 | if (SCM_I_INUMP (y)) |
8507ec80 | 7223 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7224 | SCM_COMPLEX_IMAG (x)); |
7225 | else if (SCM_BIGP (y)) | |
7226 | { | |
7227 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7228 | + SCM_COMPLEX_REAL (x)); | |
7229 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7230 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7231 | } |
7232 | else if (SCM_REALP (y)) | |
8507ec80 | 7233 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7234 | SCM_COMPLEX_IMAG (x)); |
7235 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7236 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7237 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7238 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7239 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7240 | SCM_COMPLEX_IMAG (x)); |
7241 | else | |
7242 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7243 | } | |
7244 | else if (SCM_FRACTIONP (x)) | |
7245 | { | |
e11e83f3 | 7246 | if (SCM_I_INUMP (y)) |
cba42c93 | 7247 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7248 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7249 | SCM_FRACTION_DENOMINATOR (x)); | |
7250 | else if (SCM_BIGP (y)) | |
cba42c93 | 7251 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7252 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7253 | SCM_FRACTION_DENOMINATOR (x)); | |
7254 | else if (SCM_REALP (y)) | |
55f26379 | 7255 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7256 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7257 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7258 | SCM_COMPLEX_IMAG (y)); |
7259 | else if (SCM_FRACTIONP (y)) | |
7260 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7261 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7262 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7263 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7264 | else |
7265 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7266 | } |
0aacf84e | 7267 | else |
98cb6e75 | 7268 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7269 | } |
7270 | ||
7271 | ||
40882e3d KR |
7272 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7273 | (SCM x), | |
7274 | "Return @math{@var{x}+1}.") | |
7275 | #define FUNC_NAME s_scm_oneplus | |
7276 | { | |
cff5fa33 | 7277 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7278 | } |
7279 | #undef FUNC_NAME | |
7280 | ||
7281 | ||
78d3deb1 AW |
7282 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7283 | (SCM x, SCM y, SCM rest), | |
7284 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7285 | "the sum of all but the first argument are subtracted from the first\n" | |
7286 | "argument.") | |
7287 | #define FUNC_NAME s_scm_i_difference | |
7288 | { | |
7289 | while (!scm_is_null (rest)) | |
7290 | { x = scm_difference (x, y); | |
7291 | y = scm_car (rest); | |
7292 | rest = scm_cdr (rest); | |
7293 | } | |
7294 | return scm_difference (x, y); | |
7295 | } | |
7296 | #undef FUNC_NAME | |
7297 | ||
7298 | #define s_difference s_scm_i_difference | |
7299 | #define g_difference g_scm_i_difference | |
7300 | ||
0f2d19dd | 7301 | SCM |
6e8d25a6 | 7302 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7303 | #define FUNC_NAME s_difference |
0f2d19dd | 7304 | { |
9cc37597 | 7305 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7306 | { |
7307 | if (SCM_UNBNDP (x)) | |
7308 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7309 | else | |
e11e83f3 | 7310 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7311 | { |
e25f3727 | 7312 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7313 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7314 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7315 | else |
e25f3727 | 7316 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7317 | } |
7318 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7319 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7320 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7321 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7322 | else if (SCM_REALP (x)) | |
55f26379 | 7323 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7324 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7325 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7326 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7327 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7328 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 7329 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
7330 | else |
7331 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7332 | } |
ca46fb90 | 7333 | |
9cc37597 | 7334 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7335 | { |
9cc37597 | 7336 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7337 | { |
e25f3727 AW |
7338 | scm_t_inum xx = SCM_I_INUM (x); |
7339 | scm_t_inum yy = SCM_I_INUM (y); | |
7340 | scm_t_inum z = xx - yy; | |
0aacf84e | 7341 | if (SCM_FIXABLE (z)) |
d956fa6f | 7342 | return SCM_I_MAKINUM (z); |
0aacf84e | 7343 | else |
e25f3727 | 7344 | return scm_i_inum2big (z); |
0aacf84e MD |
7345 | } |
7346 | else if (SCM_BIGP (y)) | |
7347 | { | |
7348 | /* inum-x - big-y */ | |
e25f3727 | 7349 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7350 | |
0aacf84e | 7351 | if (xx == 0) |
b5c40589 MW |
7352 | { |
7353 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7354 | bignum, but negating that gives a fixnum. */ | |
7355 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7356 | } | |
0aacf84e MD |
7357 | else |
7358 | { | |
7359 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7360 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7361 | |
0aacf84e MD |
7362 | if (xx >= 0) |
7363 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7364 | else | |
7365 | { | |
7366 | /* x - y == -(y + -x) */ | |
7367 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7368 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7369 | } | |
7370 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7371 | |
0aacf84e MD |
7372 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7373 | /* we know the result will have to be a bignum */ | |
7374 | return result; | |
7375 | else | |
7376 | return scm_i_normbig (result); | |
7377 | } | |
7378 | } | |
7379 | else if (SCM_REALP (y)) | |
7380 | { | |
e25f3727 | 7381 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7382 | |
7383 | /* | |
7384 | * We need to handle x == exact 0 | |
7385 | * specially because R6RS states that: | |
7386 | * (- 0.0) ==> -0.0 and | |
7387 | * (- 0.0 0.0) ==> 0.0 | |
7388 | * and the scheme compiler changes | |
7389 | * (- 0.0) into (- 0 0.0) | |
7390 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7391 | * At the C level, (-x) is different than (0.0 - x). | |
7392 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7393 | */ | |
7394 | if (xx == 0) | |
7395 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7396 | else | |
7397 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7398 | } |
7399 | else if (SCM_COMPLEXP (y)) | |
7400 | { | |
e25f3727 | 7401 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7402 | |
7403 | /* We need to handle x == exact 0 specially. | |
7404 | See the comment above (for SCM_REALP (y)) */ | |
7405 | if (xx == 0) | |
7406 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7407 | - SCM_COMPLEX_IMAG (y)); | |
7408 | else | |
7409 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7410 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7411 | } |
f92e85f7 MV |
7412 | else if (SCM_FRACTIONP (y)) |
7413 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7414 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7415 | SCM_FRACTION_NUMERATOR (y)), |
7416 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7417 | else |
7418 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7419 | } |
0aacf84e MD |
7420 | else if (SCM_BIGP (x)) |
7421 | { | |
e11e83f3 | 7422 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7423 | { |
7424 | /* big-x - inum-y */ | |
e25f3727 | 7425 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7426 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7427 | |
0aacf84e MD |
7428 | scm_remember_upto_here_1 (x); |
7429 | if (sgn_x == 0) | |
c71b0706 | 7430 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7431 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7432 | else |
7433 | { | |
7434 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7435 | |
708f22c6 KR |
7436 | if (yy >= 0) |
7437 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7438 | else | |
7439 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7440 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7441 | |
0aacf84e MD |
7442 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7443 | /* we know the result will have to be a bignum */ | |
7444 | return result; | |
7445 | else | |
7446 | return scm_i_normbig (result); | |
7447 | } | |
7448 | } | |
7449 | else if (SCM_BIGP (y)) | |
7450 | { | |
7451 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7452 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7453 | SCM result = scm_i_mkbig (); | |
7454 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7455 | SCM_I_BIG_MPZ (x), | |
7456 | SCM_I_BIG_MPZ (y)); | |
7457 | scm_remember_upto_here_2 (x, y); | |
7458 | /* we know the result will have to be a bignum */ | |
7459 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7460 | return result; | |
7461 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7462 | return result; | |
7463 | return scm_i_normbig (result); | |
7464 | } | |
7465 | else if (SCM_REALP (y)) | |
7466 | { | |
7467 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7468 | scm_remember_upto_here_1 (x); | |
55f26379 | 7469 | return scm_from_double (result); |
0aacf84e MD |
7470 | } |
7471 | else if (SCM_COMPLEXP (y)) | |
7472 | { | |
7473 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7474 | - SCM_COMPLEX_REAL (y)); | |
7475 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7476 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7477 | } |
f92e85f7 | 7478 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7479 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7480 | SCM_FRACTION_NUMERATOR (y)), |
7481 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7482 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7483 | } |
0aacf84e MD |
7484 | else if (SCM_REALP (x)) |
7485 | { | |
e11e83f3 | 7486 | if (SCM_I_INUMP (y)) |
55f26379 | 7487 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7488 | else if (SCM_BIGP (y)) |
7489 | { | |
7490 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7491 | scm_remember_upto_here_1 (x); | |
55f26379 | 7492 | return scm_from_double (result); |
0aacf84e MD |
7493 | } |
7494 | else if (SCM_REALP (y)) | |
55f26379 | 7495 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7496 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7497 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7498 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7499 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7500 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7501 | else |
7502 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7503 | } |
0aacf84e MD |
7504 | else if (SCM_COMPLEXP (x)) |
7505 | { | |
e11e83f3 | 7506 | if (SCM_I_INUMP (y)) |
8507ec80 | 7507 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7508 | SCM_COMPLEX_IMAG (x)); |
7509 | else if (SCM_BIGP (y)) | |
7510 | { | |
7511 | double real_part = (SCM_COMPLEX_REAL (x) | |
7512 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7513 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7514 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7515 | } |
7516 | else if (SCM_REALP (y)) | |
8507ec80 | 7517 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7518 | SCM_COMPLEX_IMAG (x)); |
7519 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7520 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7521 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7522 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7523 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7524 | SCM_COMPLEX_IMAG (x)); |
7525 | else | |
7526 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7527 | } | |
7528 | else if (SCM_FRACTIONP (x)) | |
7529 | { | |
e11e83f3 | 7530 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7531 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7532 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7533 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7534 | SCM_FRACTION_DENOMINATOR (x)); | |
7535 | else if (SCM_BIGP (y)) | |
cba42c93 | 7536 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7537 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7538 | SCM_FRACTION_DENOMINATOR (x)); | |
7539 | else if (SCM_REALP (y)) | |
55f26379 | 7540 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7541 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7542 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7543 | -SCM_COMPLEX_IMAG (y)); |
7544 | else if (SCM_FRACTIONP (y)) | |
7545 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7546 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7547 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7548 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7549 | else |
7550 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7551 | } |
0aacf84e | 7552 | else |
98cb6e75 | 7553 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7554 | } |
c05e97b7 | 7555 | #undef FUNC_NAME |
0f2d19dd | 7556 | |
ca46fb90 | 7557 | |
40882e3d KR |
7558 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7559 | (SCM x), | |
7560 | "Return @math{@var{x}-1}.") | |
7561 | #define FUNC_NAME s_scm_oneminus | |
7562 | { | |
cff5fa33 | 7563 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7564 | } |
7565 | #undef FUNC_NAME | |
7566 | ||
7567 | ||
78d3deb1 AW |
7568 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7569 | (SCM x, SCM y, SCM rest), | |
7570 | "Return the product of all arguments. If called without arguments,\n" | |
7571 | "1 is returned.") | |
7572 | #define FUNC_NAME s_scm_i_product | |
7573 | { | |
7574 | while (!scm_is_null (rest)) | |
7575 | { x = scm_product (x, y); | |
7576 | y = scm_car (rest); | |
7577 | rest = scm_cdr (rest); | |
7578 | } | |
7579 | return scm_product (x, y); | |
7580 | } | |
7581 | #undef FUNC_NAME | |
7582 | ||
7583 | #define s_product s_scm_i_product | |
7584 | #define g_product g_scm_i_product | |
7585 | ||
0f2d19dd | 7586 | SCM |
6e8d25a6 | 7587 | scm_product (SCM x, SCM y) |
0f2d19dd | 7588 | { |
9cc37597 | 7589 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7590 | { |
7591 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7592 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7593 | else if (SCM_NUMBERP (x)) |
7594 | return x; | |
7595 | else | |
7596 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7597 | } |
ca46fb90 | 7598 | |
9cc37597 | 7599 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7600 | { |
e25f3727 | 7601 | scm_t_inum xx; |
f4c627b3 | 7602 | |
5e791807 | 7603 | xinum: |
e11e83f3 | 7604 | xx = SCM_I_INUM (x); |
f4c627b3 | 7605 | |
0aacf84e MD |
7606 | switch (xx) |
7607 | { | |
5e791807 MW |
7608 | case 1: |
7609 | /* exact1 is the universal multiplicative identity */ | |
7610 | return y; | |
7611 | break; | |
7612 | case 0: | |
7613 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7614 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7615 | return SCM_INUM0; | |
7616 | /* if the other argument is inexact, the result is inexact, | |
7617 | and we must do the multiplication in order to handle | |
7618 | infinities and NaNs properly. */ | |
7619 | else if (SCM_REALP (y)) | |
7620 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7621 | else if (SCM_COMPLEXP (y)) | |
7622 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7623 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7624 | /* we've already handled inexact numbers, | |
7625 | so y must be exact, and we return exact0 */ | |
7626 | else if (SCM_NUMP (y)) | |
7627 | return SCM_INUM0; | |
7628 | else | |
7629 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7630 | break; | |
7631 | case -1: | |
b5c40589 | 7632 | /* |
5e791807 MW |
7633 | * This case is important for more than just optimization. |
7634 | * It handles the case of negating | |
b5c40589 MW |
7635 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7636 | * which is a bignum that must be changed back into a fixnum. | |
7637 | * Failure to do so will cause the following to return #f: | |
7638 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7639 | */ | |
b5c40589 MW |
7640 | return scm_difference(y, SCM_UNDEFINED); |
7641 | break; | |
0aacf84e | 7642 | } |
f4c627b3 | 7643 | |
9cc37597 | 7644 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7645 | { |
e25f3727 AW |
7646 | scm_t_inum yy = SCM_I_INUM (y); |
7647 | scm_t_inum kk = xx * yy; | |
d956fa6f | 7648 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 7649 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
7650 | return k; |
7651 | else | |
7652 | { | |
e25f3727 | 7653 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7654 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7655 | return scm_i_normbig (result); | |
7656 | } | |
7657 | } | |
7658 | else if (SCM_BIGP (y)) | |
7659 | { | |
7660 | SCM result = scm_i_mkbig (); | |
7661 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7662 | scm_remember_upto_here_1 (y); | |
7663 | return result; | |
7664 | } | |
7665 | else if (SCM_REALP (y)) | |
55f26379 | 7666 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7667 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7668 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7669 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7670 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7671 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7672 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7673 | else |
7674 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7675 | } |
0aacf84e MD |
7676 | else if (SCM_BIGP (x)) |
7677 | { | |
e11e83f3 | 7678 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7679 | { |
7680 | SCM_SWAP (x, y); | |
5e791807 | 7681 | goto xinum; |
0aacf84e MD |
7682 | } |
7683 | else if (SCM_BIGP (y)) | |
7684 | { | |
7685 | SCM result = scm_i_mkbig (); | |
7686 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7687 | SCM_I_BIG_MPZ (x), | |
7688 | SCM_I_BIG_MPZ (y)); | |
7689 | scm_remember_upto_here_2 (x, y); | |
7690 | return result; | |
7691 | } | |
7692 | else if (SCM_REALP (y)) | |
7693 | { | |
7694 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7695 | scm_remember_upto_here_1 (x); | |
55f26379 | 7696 | return scm_from_double (result); |
0aacf84e MD |
7697 | } |
7698 | else if (SCM_COMPLEXP (y)) | |
7699 | { | |
7700 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7701 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7702 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7703 | z * SCM_COMPLEX_IMAG (y)); |
7704 | } | |
f92e85f7 | 7705 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7706 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7707 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7708 | else |
7709 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7710 | } |
0aacf84e MD |
7711 | else if (SCM_REALP (x)) |
7712 | { | |
e11e83f3 | 7713 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7714 | { |
7715 | SCM_SWAP (x, y); | |
7716 | goto xinum; | |
7717 | } | |
0aacf84e MD |
7718 | else if (SCM_BIGP (y)) |
7719 | { | |
7720 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7721 | scm_remember_upto_here_1 (y); | |
55f26379 | 7722 | return scm_from_double (result); |
0aacf84e MD |
7723 | } |
7724 | else if (SCM_REALP (y)) | |
55f26379 | 7725 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7726 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7727 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7728 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7729 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7730 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
7731 | else |
7732 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7733 | } |
0aacf84e MD |
7734 | else if (SCM_COMPLEXP (x)) |
7735 | { | |
e11e83f3 | 7736 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7737 | { |
7738 | SCM_SWAP (x, y); | |
7739 | goto xinum; | |
7740 | } | |
0aacf84e MD |
7741 | else if (SCM_BIGP (y)) |
7742 | { | |
7743 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7744 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7745 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7746 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7747 | } |
7748 | else if (SCM_REALP (y)) | |
8507ec80 | 7749 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
7750 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
7751 | else if (SCM_COMPLEXP (y)) | |
7752 | { | |
8507ec80 | 7753 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
7754 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
7755 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
7756 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
7757 | } | |
f92e85f7 MV |
7758 | else if (SCM_FRACTIONP (y)) |
7759 | { | |
7760 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 7761 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
7762 | yy * SCM_COMPLEX_IMAG (x)); |
7763 | } | |
7764 | else | |
7765 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7766 | } | |
7767 | else if (SCM_FRACTIONP (x)) | |
7768 | { | |
e11e83f3 | 7769 | if (SCM_I_INUMP (y)) |
cba42c93 | 7770 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7771 | SCM_FRACTION_DENOMINATOR (x)); |
7772 | else if (SCM_BIGP (y)) | |
cba42c93 | 7773 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7774 | SCM_FRACTION_DENOMINATOR (x)); |
7775 | else if (SCM_REALP (y)) | |
55f26379 | 7776 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
7777 | else if (SCM_COMPLEXP (y)) |
7778 | { | |
7779 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 7780 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7781 | xx * SCM_COMPLEX_IMAG (y)); |
7782 | } | |
7783 | else if (SCM_FRACTIONP (y)) | |
7784 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 7785 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7786 | SCM_FRACTION_NUMERATOR (y)), |
7787 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
7788 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7789 | else |
7790 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7791 | } |
0aacf84e | 7792 | else |
f4c627b3 | 7793 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
7794 | } |
7795 | ||
7351e207 MV |
7796 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
7797 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
7798 | #define ALLOW_DIVIDE_BY_ZERO | |
7799 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
7800 | #endif | |
0f2d19dd | 7801 | |
ba74ef4e MV |
7802 | /* The code below for complex division is adapted from the GNU |
7803 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
7804 | this copyright: */ | |
7805 | ||
7806 | /**************************************************************** | |
7807 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
7808 | ||
7809 | Permission to use, copy, modify, and distribute this software | |
7810 | and its documentation for any purpose and without fee is hereby | |
7811 | granted, provided that the above copyright notice appear in all | |
7812 | copies and that both that the copyright notice and this | |
7813 | permission notice and warranty disclaimer appear in supporting | |
7814 | documentation, and that the names of AT&T Bell Laboratories or | |
7815 | Bellcore or any of their entities not be used in advertising or | |
7816 | publicity pertaining to distribution of the software without | |
7817 | specific, written prior permission. | |
7818 | ||
7819 | AT&T and Bellcore disclaim all warranties with regard to this | |
7820 | software, including all implied warranties of merchantability | |
7821 | and fitness. In no event shall AT&T or Bellcore be liable for | |
7822 | any special, indirect or consequential damages or any damages | |
7823 | whatsoever resulting from loss of use, data or profits, whether | |
7824 | in an action of contract, negligence or other tortious action, | |
7825 | arising out of or in connection with the use or performance of | |
7826 | this software. | |
7827 | ****************************************************************/ | |
7828 | ||
78d3deb1 AW |
7829 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
7830 | (SCM x, SCM y, SCM rest), | |
7831 | "Divide the first argument by the product of the remaining\n" | |
7832 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
7833 | "returned.") | |
7834 | #define FUNC_NAME s_scm_i_divide | |
7835 | { | |
7836 | while (!scm_is_null (rest)) | |
7837 | { x = scm_divide (x, y); | |
7838 | y = scm_car (rest); | |
7839 | rest = scm_cdr (rest); | |
7840 | } | |
7841 | return scm_divide (x, y); | |
7842 | } | |
7843 | #undef FUNC_NAME | |
7844 | ||
7845 | #define s_divide s_scm_i_divide | |
7846 | #define g_divide g_scm_i_divide | |
7847 | ||
f92e85f7 | 7848 | static SCM |
78d3deb1 AW |
7849 | do_divide (SCM x, SCM y, int inexact) |
7850 | #define FUNC_NAME s_divide | |
0f2d19dd | 7851 | { |
f8de44c1 DH |
7852 | double a; |
7853 | ||
9cc37597 | 7854 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7855 | { |
7856 | if (SCM_UNBNDP (x)) | |
7857 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 7858 | else if (SCM_I_INUMP (x)) |
0aacf84e | 7859 | { |
e25f3727 | 7860 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
7861 | if (xx == 1 || xx == -1) |
7862 | return x; | |
7351e207 | 7863 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
7864 | else if (xx == 0) |
7865 | scm_num_overflow (s_divide); | |
7351e207 | 7866 | #endif |
0aacf84e | 7867 | else |
f92e85f7 MV |
7868 | { |
7869 | if (inexact) | |
55f26379 | 7870 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 7871 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7872 | } |
0aacf84e MD |
7873 | } |
7874 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
7875 | { |
7876 | if (inexact) | |
55f26379 | 7877 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 7878 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7879 | } |
0aacf84e MD |
7880 | else if (SCM_REALP (x)) |
7881 | { | |
7882 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 7883 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7884 | if (xx == 0.0) |
7885 | scm_num_overflow (s_divide); | |
7886 | else | |
7351e207 | 7887 | #endif |
55f26379 | 7888 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
7889 | } |
7890 | else if (SCM_COMPLEXP (x)) | |
7891 | { | |
7892 | double r = SCM_COMPLEX_REAL (x); | |
7893 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 7894 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7895 | { |
7896 | double t = r / i; | |
7897 | double d = i * (1.0 + t * t); | |
8507ec80 | 7898 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
7899 | } |
7900 | else | |
7901 | { | |
7902 | double t = i / r; | |
7903 | double d = r * (1.0 + t * t); | |
8507ec80 | 7904 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
7905 | } |
7906 | } | |
f92e85f7 | 7907 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7908 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 7909 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
7910 | else |
7911 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 7912 | } |
f8de44c1 | 7913 | |
9cc37597 | 7914 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7915 | { |
e25f3727 | 7916 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 7917 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7918 | { |
e25f3727 | 7919 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7920 | if (yy == 0) |
7921 | { | |
7351e207 | 7922 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7923 | scm_num_overflow (s_divide); |
7351e207 | 7924 | #else |
55f26379 | 7925 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 7926 | #endif |
0aacf84e MD |
7927 | } |
7928 | else if (xx % yy != 0) | |
f92e85f7 MV |
7929 | { |
7930 | if (inexact) | |
55f26379 | 7931 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 7932 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7933 | } |
0aacf84e MD |
7934 | else |
7935 | { | |
e25f3727 | 7936 | scm_t_inum z = xx / yy; |
0aacf84e | 7937 | if (SCM_FIXABLE (z)) |
d956fa6f | 7938 | return SCM_I_MAKINUM (z); |
0aacf84e | 7939 | else |
e25f3727 | 7940 | return scm_i_inum2big (z); |
0aacf84e | 7941 | } |
f872b822 | 7942 | } |
0aacf84e | 7943 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
7944 | { |
7945 | if (inexact) | |
55f26379 | 7946 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 7947 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7948 | } |
0aacf84e MD |
7949 | else if (SCM_REALP (y)) |
7950 | { | |
7951 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 7952 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7953 | if (yy == 0.0) |
7954 | scm_num_overflow (s_divide); | |
7955 | else | |
7351e207 | 7956 | #endif |
55f26379 | 7957 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 7958 | } |
0aacf84e MD |
7959 | else if (SCM_COMPLEXP (y)) |
7960 | { | |
7961 | a = xx; | |
7962 | complex_div: /* y _must_ be a complex number */ | |
7963 | { | |
7964 | double r = SCM_COMPLEX_REAL (y); | |
7965 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 7966 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7967 | { |
7968 | double t = r / i; | |
7969 | double d = i * (1.0 + t * t); | |
8507ec80 | 7970 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
7971 | } |
7972 | else | |
7973 | { | |
7974 | double t = i / r; | |
7975 | double d = r * (1.0 + t * t); | |
8507ec80 | 7976 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
7977 | } |
7978 | } | |
7979 | } | |
f92e85f7 MV |
7980 | else if (SCM_FRACTIONP (y)) |
7981 | /* a / b/c = ac / b */ | |
cba42c93 | 7982 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 7983 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
7984 | else |
7985 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 7986 | } |
0aacf84e MD |
7987 | else if (SCM_BIGP (x)) |
7988 | { | |
e11e83f3 | 7989 | if (SCM_I_INUMP (y)) |
0aacf84e | 7990 | { |
e25f3727 | 7991 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7992 | if (yy == 0) |
7993 | { | |
7351e207 | 7994 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7995 | scm_num_overflow (s_divide); |
7351e207 | 7996 | #else |
0aacf84e MD |
7997 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
7998 | scm_remember_upto_here_1 (x); | |
7999 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8000 | #endif |
0aacf84e MD |
8001 | } |
8002 | else if (yy == 1) | |
8003 | return x; | |
8004 | else | |
8005 | { | |
8006 | /* FIXME: HMM, what are the relative performance issues here? | |
8007 | We need to test. Is it faster on average to test | |
8008 | divisible_p, then perform whichever operation, or is it | |
8009 | faster to perform the integer div opportunistically and | |
8010 | switch to real if there's a remainder? For now we take the | |
8011 | middle ground: test, then if divisible, use the faster div | |
8012 | func. */ | |
8013 | ||
e25f3727 | 8014 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8015 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8016 | ||
8017 | if (divisible_p) | |
8018 | { | |
8019 | SCM result = scm_i_mkbig (); | |
8020 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8021 | scm_remember_upto_here_1 (x); | |
8022 | if (yy < 0) | |
8023 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8024 | return scm_i_normbig (result); | |
8025 | } | |
8026 | else | |
f92e85f7 MV |
8027 | { |
8028 | if (inexact) | |
55f26379 | 8029 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 8030 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8031 | } |
0aacf84e MD |
8032 | } |
8033 | } | |
8034 | else if (SCM_BIGP (y)) | |
8035 | { | |
a4955a04 MW |
8036 | /* big_x / big_y */ |
8037 | if (inexact) | |
0aacf84e | 8038 | { |
a4955a04 MW |
8039 | /* It's easily possible for the ratio x/y to fit a double |
8040 | but one or both x and y be too big to fit a double, | |
8041 | hence the use of mpq_get_d rather than converting and | |
8042 | dividing. */ | |
8043 | mpq_t q; | |
8044 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
8045 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
8046 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
8047 | } |
8048 | else | |
8049 | { | |
a4955a04 MW |
8050 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8051 | SCM_I_BIG_MPZ (y)); | |
8052 | if (divisible_p) | |
8053 | { | |
8054 | SCM result = scm_i_mkbig (); | |
8055 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8056 | SCM_I_BIG_MPZ (x), | |
8057 | SCM_I_BIG_MPZ (y)); | |
8058 | scm_remember_upto_here_2 (x, y); | |
8059 | return scm_i_normbig (result); | |
8060 | } | |
8061 | else | |
8062 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8063 | } |
8064 | } | |
8065 | else if (SCM_REALP (y)) | |
8066 | { | |
8067 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8068 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8069 | if (yy == 0.0) |
8070 | scm_num_overflow (s_divide); | |
8071 | else | |
7351e207 | 8072 | #endif |
55f26379 | 8073 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8074 | } |
8075 | else if (SCM_COMPLEXP (y)) | |
8076 | { | |
8077 | a = scm_i_big2dbl (x); | |
8078 | goto complex_div; | |
8079 | } | |
f92e85f7 | 8080 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8081 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8082 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8083 | else |
8084 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8085 | } |
0aacf84e MD |
8086 | else if (SCM_REALP (x)) |
8087 | { | |
8088 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8089 | if (SCM_I_INUMP (y)) |
0aacf84e | 8090 | { |
e25f3727 | 8091 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8092 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8093 | if (yy == 0) |
8094 | scm_num_overflow (s_divide); | |
8095 | else | |
7351e207 | 8096 | #endif |
55f26379 | 8097 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8098 | } |
8099 | else if (SCM_BIGP (y)) | |
8100 | { | |
8101 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8102 | scm_remember_upto_here_1 (y); | |
55f26379 | 8103 | return scm_from_double (rx / dby); |
0aacf84e MD |
8104 | } |
8105 | else if (SCM_REALP (y)) | |
8106 | { | |
8107 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8108 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8109 | if (yy == 0.0) |
8110 | scm_num_overflow (s_divide); | |
8111 | else | |
7351e207 | 8112 | #endif |
55f26379 | 8113 | return scm_from_double (rx / yy); |
0aacf84e MD |
8114 | } |
8115 | else if (SCM_COMPLEXP (y)) | |
8116 | { | |
8117 | a = rx; | |
8118 | goto complex_div; | |
8119 | } | |
f92e85f7 | 8120 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8121 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8122 | else |
8123 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8124 | } |
0aacf84e MD |
8125 | else if (SCM_COMPLEXP (x)) |
8126 | { | |
8127 | double rx = SCM_COMPLEX_REAL (x); | |
8128 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8129 | if (SCM_I_INUMP (y)) |
0aacf84e | 8130 | { |
e25f3727 | 8131 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8132 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8133 | if (yy == 0) |
8134 | scm_num_overflow (s_divide); | |
8135 | else | |
7351e207 | 8136 | #endif |
0aacf84e MD |
8137 | { |
8138 | double d = yy; | |
8507ec80 | 8139 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8140 | } |
8141 | } | |
8142 | else if (SCM_BIGP (y)) | |
8143 | { | |
8144 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8145 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8146 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8147 | } |
8148 | else if (SCM_REALP (y)) | |
8149 | { | |
8150 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8151 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8152 | if (yy == 0.0) |
8153 | scm_num_overflow (s_divide); | |
8154 | else | |
7351e207 | 8155 | #endif |
8507ec80 | 8156 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8157 | } |
8158 | else if (SCM_COMPLEXP (y)) | |
8159 | { | |
8160 | double ry = SCM_COMPLEX_REAL (y); | |
8161 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8162 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8163 | { |
8164 | double t = ry / iy; | |
8165 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8166 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8167 | } |
8168 | else | |
8169 | { | |
8170 | double t = iy / ry; | |
8171 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8172 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8173 | } |
8174 | } | |
f92e85f7 MV |
8175 | else if (SCM_FRACTIONP (y)) |
8176 | { | |
8177 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8178 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8179 | } |
0aacf84e MD |
8180 | else |
8181 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8182 | } |
f92e85f7 MV |
8183 | else if (SCM_FRACTIONP (x)) |
8184 | { | |
e11e83f3 | 8185 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8186 | { |
e25f3727 | 8187 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8188 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8189 | if (yy == 0) | |
8190 | scm_num_overflow (s_divide); | |
8191 | else | |
8192 | #endif | |
cba42c93 | 8193 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8194 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8195 | } | |
8196 | else if (SCM_BIGP (y)) | |
8197 | { | |
cba42c93 | 8198 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8199 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8200 | } | |
8201 | else if (SCM_REALP (y)) | |
8202 | { | |
8203 | double yy = SCM_REAL_VALUE (y); | |
8204 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8205 | if (yy == 0.0) | |
8206 | scm_num_overflow (s_divide); | |
8207 | else | |
8208 | #endif | |
55f26379 | 8209 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8210 | } |
8211 | else if (SCM_COMPLEXP (y)) | |
8212 | { | |
8213 | a = scm_i_fraction2double (x); | |
8214 | goto complex_div; | |
8215 | } | |
8216 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8217 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8218 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8219 | else | |
8220 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8221 | } | |
0aacf84e | 8222 | else |
f8de44c1 | 8223 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8224 | } |
f92e85f7 MV |
8225 | |
8226 | SCM | |
8227 | scm_divide (SCM x, SCM y) | |
8228 | { | |
78d3deb1 | 8229 | return do_divide (x, y, 0); |
f92e85f7 MV |
8230 | } |
8231 | ||
8232 | static SCM scm_divide2real (SCM x, SCM y) | |
8233 | { | |
78d3deb1 | 8234 | return do_divide (x, y, 1); |
f92e85f7 | 8235 | } |
c05e97b7 | 8236 | #undef FUNC_NAME |
0f2d19dd | 8237 | |
fa605590 | 8238 | |
0f2d19dd | 8239 | double |
3101f40f | 8240 | scm_c_truncate (double x) |
0f2d19dd | 8241 | { |
fa605590 | 8242 | return trunc (x); |
0f2d19dd | 8243 | } |
0f2d19dd | 8244 | |
3101f40f MV |
8245 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8246 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8247 | Then half-way cases are identified and adjusted down if the | |
8248 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8249 | |
8250 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8251 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8252 | ||
8253 | An odd "result" value is identified with result/2 != floor(result/2). | |
8254 | This is done with plus_half, since that value is ready for use sooner in | |
8255 | a pipelined cpu, and we're already requiring plus_half == result. | |
8256 | ||
8257 | Note however that we need to be careful when x is big and already an | |
8258 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8259 | us to return such a value, incorrectly. For instance if the hardware is | |
8260 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8261 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8262 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8263 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8264 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8265 | ||
8266 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8267 | x is already an integer. If it is then clearly that's the desired result | |
8268 | already. And if it's not then the exponent must be small enough to allow | |
8269 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8270 | ||
0f2d19dd | 8271 | double |
3101f40f | 8272 | scm_c_round (double x) |
0f2d19dd | 8273 | { |
6187f48b KR |
8274 | double plus_half, result; |
8275 | ||
8276 | if (x == floor (x)) | |
8277 | return x; | |
8278 | ||
8279 | plus_half = x + 0.5; | |
8280 | result = floor (plus_half); | |
3101f40f | 8281 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8282 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8283 | ? result - 1 | |
8284 | : result); | |
0f2d19dd JB |
8285 | } |
8286 | ||
8b56bcec MW |
8287 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8288 | (SCM x), | |
8289 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8290 | #define FUNC_NAME s_scm_truncate_number |
8291 | { | |
8b56bcec MW |
8292 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8293 | return x; | |
8294 | else if (SCM_REALP (x)) | |
c251ab63 | 8295 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8296 | else if (SCM_FRACTIONP (x)) |
8297 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8298 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8299 | else |
8b56bcec MW |
8300 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8301 | s_scm_truncate_number); | |
f92e85f7 MV |
8302 | } |
8303 | #undef FUNC_NAME | |
8304 | ||
8b56bcec MW |
8305 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8306 | (SCM x), | |
8307 | "Round the number @var{x} towards the nearest integer. " | |
8308 | "When it is exactly halfway between two integers, " | |
8309 | "round towards the even one.") | |
f92e85f7 MV |
8310 | #define FUNC_NAME s_scm_round_number |
8311 | { | |
e11e83f3 | 8312 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8313 | return x; |
8314 | else if (SCM_REALP (x)) | |
3101f40f | 8315 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8316 | else if (SCM_FRACTIONP (x)) |
8317 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8318 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8319 | else |
8b56bcec MW |
8320 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8321 | s_scm_round_number); | |
f92e85f7 MV |
8322 | } |
8323 | #undef FUNC_NAME | |
8324 | ||
8325 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8326 | (SCM x), | |
8327 | "Round the number @var{x} towards minus infinity.") | |
8328 | #define FUNC_NAME s_scm_floor | |
8329 | { | |
e11e83f3 | 8330 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8331 | return x; |
8332 | else if (SCM_REALP (x)) | |
55f26379 | 8333 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8334 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8335 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8336 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8337 | else |
8338 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8339 | } | |
8340 | #undef FUNC_NAME | |
8341 | ||
8342 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8343 | (SCM x), | |
8344 | "Round the number @var{x} towards infinity.") | |
8345 | #define FUNC_NAME s_scm_ceiling | |
8346 | { | |
e11e83f3 | 8347 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8348 | return x; |
8349 | else if (SCM_REALP (x)) | |
55f26379 | 8350 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8351 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8352 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8353 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8354 | else |
8355 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8356 | } | |
8357 | #undef FUNC_NAME | |
0f2d19dd | 8358 | |
2519490c MW |
8359 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8360 | (SCM x, SCM y), | |
8361 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8362 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8363 | { |
01c7284a MW |
8364 | if (scm_is_integer (y)) |
8365 | { | |
8366 | if (scm_is_true (scm_exact_p (y))) | |
8367 | return scm_integer_expt (x, y); | |
8368 | else | |
8369 | { | |
8370 | /* Here we handle the case where the exponent is an inexact | |
8371 | integer. We make the exponent exact in order to use | |
8372 | scm_integer_expt, and thus avoid the spurious imaginary | |
8373 | parts that may result from round-off errors in the general | |
8374 | e^(y log x) method below (for example when squaring a large | |
8375 | negative number). In this case, we must return an inexact | |
8376 | result for correctness. We also make the base inexact so | |
8377 | that scm_integer_expt will use fast inexact arithmetic | |
8378 | internally. Note that making the base inexact is not | |
8379 | sufficient to guarantee an inexact result, because | |
8380 | scm_integer_expt will return an exact 1 when the exponent | |
8381 | is 0, even if the base is inexact. */ | |
8382 | return scm_exact_to_inexact | |
8383 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8384 | scm_inexact_to_exact (y))); | |
8385 | } | |
8386 | } | |
6fc4d012 AW |
8387 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8388 | { | |
8389 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8390 | } | |
2519490c | 8391 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8392 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8393 | else if (scm_is_complex (x)) |
8394 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8395 | else | |
8396 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8397 | } |
1bbd0b84 | 8398 | #undef FUNC_NAME |
0f2d19dd | 8399 | |
7f41099e MW |
8400 | /* sin/cos/tan/asin/acos/atan |
8401 | sinh/cosh/tanh/asinh/acosh/atanh | |
8402 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8403 | Written by Jerry D. Hedden, (C) FSF. | |
8404 | See the file `COPYING' for terms applying to this program. */ | |
8405 | ||
ad79736c AW |
8406 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8407 | (SCM z), | |
8408 | "Compute the sine of @var{z}.") | |
8409 | #define FUNC_NAME s_scm_sin | |
8410 | { | |
8deddc94 MW |
8411 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8412 | return z; /* sin(exact0) = exact0 */ | |
8413 | else if (scm_is_real (z)) | |
ad79736c AW |
8414 | return scm_from_double (sin (scm_to_double (z))); |
8415 | else if (SCM_COMPLEXP (z)) | |
8416 | { double x, y; | |
8417 | x = SCM_COMPLEX_REAL (z); | |
8418 | y = SCM_COMPLEX_IMAG (z); | |
8419 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8420 | cos (x) * sinh (y)); | |
8421 | } | |
8422 | else | |
8423 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8424 | } | |
8425 | #undef FUNC_NAME | |
0f2d19dd | 8426 | |
ad79736c AW |
8427 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8428 | (SCM z), | |
8429 | "Compute the cosine of @var{z}.") | |
8430 | #define FUNC_NAME s_scm_cos | |
8431 | { | |
8deddc94 MW |
8432 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8433 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8434 | else if (scm_is_real (z)) | |
ad79736c AW |
8435 | return scm_from_double (cos (scm_to_double (z))); |
8436 | else if (SCM_COMPLEXP (z)) | |
8437 | { double x, y; | |
8438 | x = SCM_COMPLEX_REAL (z); | |
8439 | y = SCM_COMPLEX_IMAG (z); | |
8440 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8441 | -sin (x) * sinh (y)); | |
8442 | } | |
8443 | else | |
8444 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8445 | } | |
8446 | #undef FUNC_NAME | |
8447 | ||
8448 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8449 | (SCM z), | |
8450 | "Compute the tangent of @var{z}.") | |
8451 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8452 | { |
8deddc94 MW |
8453 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8454 | return z; /* tan(exact0) = exact0 */ | |
8455 | else if (scm_is_real (z)) | |
ad79736c AW |
8456 | return scm_from_double (tan (scm_to_double (z))); |
8457 | else if (SCM_COMPLEXP (z)) | |
8458 | { double x, y, w; | |
8459 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8460 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8461 | w = cos (x) + cosh (y); | |
8462 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8463 | if (w == 0.0) | |
8464 | scm_num_overflow (s_scm_tan); | |
8465 | #endif | |
8466 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8467 | } | |
8468 | else | |
8469 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8470 | } | |
8471 | #undef FUNC_NAME | |
8472 | ||
8473 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8474 | (SCM z), | |
8475 | "Compute the hyperbolic sine of @var{z}.") | |
8476 | #define FUNC_NAME s_scm_sinh | |
8477 | { | |
8deddc94 MW |
8478 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8479 | return z; /* sinh(exact0) = exact0 */ | |
8480 | else if (scm_is_real (z)) | |
ad79736c AW |
8481 | return scm_from_double (sinh (scm_to_double (z))); |
8482 | else if (SCM_COMPLEXP (z)) | |
8483 | { double x, y; | |
8484 | x = SCM_COMPLEX_REAL (z); | |
8485 | y = SCM_COMPLEX_IMAG (z); | |
8486 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8487 | cosh (x) * sin (y)); | |
8488 | } | |
8489 | else | |
8490 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8491 | } | |
8492 | #undef FUNC_NAME | |
8493 | ||
8494 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8495 | (SCM z), | |
8496 | "Compute the hyperbolic cosine of @var{z}.") | |
8497 | #define FUNC_NAME s_scm_cosh | |
8498 | { | |
8deddc94 MW |
8499 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8500 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8501 | else if (scm_is_real (z)) | |
ad79736c AW |
8502 | return scm_from_double (cosh (scm_to_double (z))); |
8503 | else if (SCM_COMPLEXP (z)) | |
8504 | { double x, y; | |
8505 | x = SCM_COMPLEX_REAL (z); | |
8506 | y = SCM_COMPLEX_IMAG (z); | |
8507 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8508 | sinh (x) * sin (y)); | |
8509 | } | |
8510 | else | |
8511 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8512 | } | |
8513 | #undef FUNC_NAME | |
8514 | ||
8515 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8516 | (SCM z), | |
8517 | "Compute the hyperbolic tangent of @var{z}.") | |
8518 | #define FUNC_NAME s_scm_tanh | |
8519 | { | |
8deddc94 MW |
8520 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8521 | return z; /* tanh(exact0) = exact0 */ | |
8522 | else if (scm_is_real (z)) | |
ad79736c AW |
8523 | return scm_from_double (tanh (scm_to_double (z))); |
8524 | else if (SCM_COMPLEXP (z)) | |
8525 | { double x, y, w; | |
8526 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8527 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8528 | w = cosh (x) + cos (y); | |
8529 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8530 | if (w == 0.0) | |
8531 | scm_num_overflow (s_scm_tanh); | |
8532 | #endif | |
8533 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8534 | } | |
8535 | else | |
8536 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8537 | } | |
8538 | #undef FUNC_NAME | |
8539 | ||
8540 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8541 | (SCM z), | |
8542 | "Compute the arc sine of @var{z}.") | |
8543 | #define FUNC_NAME s_scm_asin | |
8544 | { | |
8deddc94 MW |
8545 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8546 | return z; /* asin(exact0) = exact0 */ | |
8547 | else if (scm_is_real (z)) | |
ad79736c AW |
8548 | { |
8549 | double w = scm_to_double (z); | |
8550 | if (w >= -1.0 && w <= 1.0) | |
8551 | return scm_from_double (asin (w)); | |
8552 | else | |
8553 | return scm_product (scm_c_make_rectangular (0, -1), | |
8554 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8555 | } | |
8556 | else if (SCM_COMPLEXP (z)) | |
8557 | { double x, y; | |
8558 | x = SCM_COMPLEX_REAL (z); | |
8559 | y = SCM_COMPLEX_IMAG (z); | |
8560 | return scm_product (scm_c_make_rectangular (0, -1), | |
8561 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8562 | } | |
8563 | else | |
8564 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8565 | } | |
8566 | #undef FUNC_NAME | |
8567 | ||
8568 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8569 | (SCM z), | |
8570 | "Compute the arc cosine of @var{z}.") | |
8571 | #define FUNC_NAME s_scm_acos | |
8572 | { | |
8deddc94 MW |
8573 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8574 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8575 | else if (scm_is_real (z)) | |
ad79736c AW |
8576 | { |
8577 | double w = scm_to_double (z); | |
8578 | if (w >= -1.0 && w <= 1.0) | |
8579 | return scm_from_double (acos (w)); | |
8580 | else | |
8581 | return scm_sum (scm_from_double (acos (0.0)), | |
8582 | scm_product (scm_c_make_rectangular (0, 1), | |
8583 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8584 | } | |
8585 | else if (SCM_COMPLEXP (z)) | |
8586 | { double x, y; | |
8587 | x = SCM_COMPLEX_REAL (z); | |
8588 | y = SCM_COMPLEX_IMAG (z); | |
8589 | return scm_sum (scm_from_double (acos (0.0)), | |
8590 | scm_product (scm_c_make_rectangular (0, 1), | |
8591 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8592 | } | |
8593 | else | |
8594 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8595 | } | |
8596 | #undef FUNC_NAME | |
8597 | ||
8598 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8599 | (SCM z, SCM y), | |
8600 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8601 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8602 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8603 | #define FUNC_NAME s_scm_atan | |
8604 | { | |
8605 | if (SCM_UNBNDP (y)) | |
8606 | { | |
8deddc94 MW |
8607 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8608 | return z; /* atan(exact0) = exact0 */ | |
8609 | else if (scm_is_real (z)) | |
ad79736c AW |
8610 | return scm_from_double (atan (scm_to_double (z))); |
8611 | else if (SCM_COMPLEXP (z)) | |
8612 | { | |
8613 | double v, w; | |
8614 | v = SCM_COMPLEX_REAL (z); | |
8615 | w = SCM_COMPLEX_IMAG (z); | |
8616 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8617 | scm_c_make_rectangular (v, w + 1.0))), | |
8618 | scm_c_make_rectangular (0, 2)); | |
8619 | } | |
8620 | else | |
18104cac | 8621 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8622 | } |
8623 | else if (scm_is_real (z)) | |
8624 | { | |
8625 | if (scm_is_real (y)) | |
8626 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8627 | else | |
8628 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8629 | } | |
8630 | else | |
8631 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8632 | } | |
8633 | #undef FUNC_NAME | |
8634 | ||
8635 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8636 | (SCM z), | |
8637 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8638 | #define FUNC_NAME s_scm_sys_asinh | |
8639 | { | |
8deddc94 MW |
8640 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8641 | return z; /* asinh(exact0) = exact0 */ | |
8642 | else if (scm_is_real (z)) | |
ad79736c AW |
8643 | return scm_from_double (asinh (scm_to_double (z))); |
8644 | else if (scm_is_number (z)) | |
8645 | return scm_log (scm_sum (z, | |
8646 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8647 | SCM_INUM1)))); |
ad79736c AW |
8648 | else |
8649 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8650 | } | |
8651 | #undef FUNC_NAME | |
8652 | ||
8653 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8654 | (SCM z), | |
8655 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8656 | #define FUNC_NAME s_scm_sys_acosh | |
8657 | { | |
8deddc94 MW |
8658 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8659 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8660 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8661 | return scm_from_double (acosh (scm_to_double (z))); |
8662 | else if (scm_is_number (z)) | |
8663 | return scm_log (scm_sum (z, | |
8664 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8665 | SCM_INUM1)))); |
ad79736c AW |
8666 | else |
8667 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8668 | } | |
8669 | #undef FUNC_NAME | |
8670 | ||
8671 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8672 | (SCM z), | |
8673 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8674 | #define FUNC_NAME s_scm_sys_atanh | |
8675 | { | |
8deddc94 MW |
8676 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8677 | return z; /* atanh(exact0) = exact0 */ | |
8678 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8679 | return scm_from_double (atanh (scm_to_double (z))); |
8680 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8681 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8682 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8683 | SCM_I_MAKINUM (2)); |
8684 | else | |
8685 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8686 | } |
1bbd0b84 | 8687 | #undef FUNC_NAME |
0f2d19dd | 8688 | |
8507ec80 MV |
8689 | SCM |
8690 | scm_c_make_rectangular (double re, double im) | |
8691 | { | |
c7218482 | 8692 | SCM z; |
03604fcf | 8693 | |
c7218482 MW |
8694 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8695 | "complex")); | |
8696 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8697 | SCM_COMPLEX_REAL (z) = re; | |
8698 | SCM_COMPLEX_IMAG (z) = im; | |
8699 | return z; | |
8507ec80 | 8700 | } |
0f2d19dd | 8701 | |
a1ec6916 | 8702 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 8703 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
8704 | "Return a complex number constructed of the given @var{real_part} " |
8705 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 8706 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8707 | { |
ad79736c AW |
8708 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8709 | SCM_ARG1, FUNC_NAME, "real"); | |
8710 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8711 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8712 | |
8713 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8714 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8715 | return real_part; | |
8716 | else | |
8717 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8718 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8719 | } |
1bbd0b84 | 8720 | #undef FUNC_NAME |
0f2d19dd | 8721 | |
8507ec80 MV |
8722 | SCM |
8723 | scm_c_make_polar (double mag, double ang) | |
8724 | { | |
8725 | double s, c; | |
5e647d08 LC |
8726 | |
8727 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8728 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8729 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8730 | details. */ | |
8731 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8732 | sincos (ang, &s, &c); |
8733 | #else | |
8734 | s = sin (ang); | |
8735 | c = cos (ang); | |
8736 | #endif | |
9d427b2c MW |
8737 | |
8738 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8739 | infinite, or perhaps simply too large to determine its value | |
8740 | mod 2*pi. However, we know something that the floating-point | |
8741 | implementation doesn't know: We know that s and c are finite. | |
8742 | Therefore, if the magnitude is zero, return a complex zero. | |
8743 | ||
8744 | The reason we check for the NaNs instead of using this case | |
8745 | whenever mag == 0.0 is because when the angle is known, we'd | |
8746 | like to return the correct kind of non-real complex zero: | |
8747 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8748 | on which quadrant the angle is in. | |
8749 | */ | |
8750 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8751 | return scm_c_make_rectangular (0.0, 0.0); | |
8752 | else | |
8753 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8754 | } |
0f2d19dd | 8755 | |
a1ec6916 | 8756 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8757 | (SCM mag, SCM ang), |
8758 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8759 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8760 | { |
c7218482 MW |
8761 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8762 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8763 | ||
8764 | /* If mag is exact0, return exact0 */ | |
8765 | if (scm_is_eq (mag, SCM_INUM0)) | |
8766 | return SCM_INUM0; | |
8767 | /* Return a real if ang is exact0 */ | |
8768 | else if (scm_is_eq (ang, SCM_INUM0)) | |
8769 | return mag; | |
8770 | else | |
8771 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 8772 | } |
1bbd0b84 | 8773 | #undef FUNC_NAME |
0f2d19dd JB |
8774 | |
8775 | ||
2519490c MW |
8776 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
8777 | (SCM z), | |
8778 | "Return the real part of the number @var{z}.") | |
8779 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 8780 | { |
2519490c | 8781 | if (SCM_COMPLEXP (z)) |
55f26379 | 8782 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 8783 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 8784 | return z; |
0aacf84e | 8785 | else |
2519490c | 8786 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 8787 | } |
2519490c | 8788 | #undef FUNC_NAME |
0f2d19dd JB |
8789 | |
8790 | ||
2519490c MW |
8791 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
8792 | (SCM z), | |
8793 | "Return the imaginary part of the number @var{z}.") | |
8794 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 8795 | { |
2519490c MW |
8796 | if (SCM_COMPLEXP (z)) |
8797 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 8798 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 8799 | return SCM_INUM0; |
0aacf84e | 8800 | else |
2519490c | 8801 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 8802 | } |
2519490c | 8803 | #undef FUNC_NAME |
0f2d19dd | 8804 | |
2519490c MW |
8805 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
8806 | (SCM z), | |
8807 | "Return the numerator of the number @var{z}.") | |
8808 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 8809 | { |
2519490c | 8810 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
8811 | return z; |
8812 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 8813 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
8814 | else if (SCM_REALP (z)) |
8815 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
8816 | else | |
2519490c | 8817 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 8818 | } |
2519490c | 8819 | #undef FUNC_NAME |
f92e85f7 MV |
8820 | |
8821 | ||
2519490c MW |
8822 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
8823 | (SCM z), | |
8824 | "Return the denominator of the number @var{z}.") | |
8825 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 8826 | { |
2519490c | 8827 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 8828 | return SCM_INUM1; |
f92e85f7 | 8829 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 8830 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
8831 | else if (SCM_REALP (z)) |
8832 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
8833 | else | |
2519490c | 8834 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 8835 | } |
2519490c | 8836 | #undef FUNC_NAME |
0f2d19dd | 8837 | |
2519490c MW |
8838 | |
8839 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
8840 | (SCM z), | |
8841 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
8842 | "@code{abs} for real arguments, but also allows complex numbers.") | |
8843 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 8844 | { |
e11e83f3 | 8845 | if (SCM_I_INUMP (z)) |
0aacf84e | 8846 | { |
e25f3727 | 8847 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
8848 | if (zz >= 0) |
8849 | return z; | |
8850 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 8851 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 8852 | else |
e25f3727 | 8853 | return scm_i_inum2big (-zz); |
5986c47d | 8854 | } |
0aacf84e MD |
8855 | else if (SCM_BIGP (z)) |
8856 | { | |
8857 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8858 | scm_remember_upto_here_1 (z); | |
8859 | if (sgn < 0) | |
8860 | return scm_i_clonebig (z, 0); | |
8861 | else | |
8862 | return z; | |
5986c47d | 8863 | } |
0aacf84e | 8864 | else if (SCM_REALP (z)) |
55f26379 | 8865 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 8866 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8867 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
8868 | else if (SCM_FRACTIONP (z)) |
8869 | { | |
73e4de09 | 8870 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 8871 | return z; |
cba42c93 | 8872 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
8873 | SCM_FRACTION_DENOMINATOR (z)); |
8874 | } | |
0aacf84e | 8875 | else |
2519490c | 8876 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 8877 | } |
2519490c | 8878 | #undef FUNC_NAME |
0f2d19dd JB |
8879 | |
8880 | ||
2519490c MW |
8881 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
8882 | (SCM z), | |
8883 | "Return the angle of the complex number @var{z}.") | |
8884 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 8885 | { |
c8ae173e | 8886 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 8887 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
8888 | But if atan2 follows the floating point rounding mode, then the value |
8889 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 8890 | if (SCM_I_INUMP (z)) |
0aacf84e | 8891 | { |
e11e83f3 | 8892 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 8893 | return flo0; |
0aacf84e | 8894 | else |
55f26379 | 8895 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 8896 | } |
0aacf84e MD |
8897 | else if (SCM_BIGP (z)) |
8898 | { | |
8899 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8900 | scm_remember_upto_here_1 (z); | |
8901 | if (sgn < 0) | |
55f26379 | 8902 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 8903 | else |
e7efe8e7 | 8904 | return flo0; |
0f2d19dd | 8905 | } |
0aacf84e | 8906 | else if (SCM_REALP (z)) |
c8ae173e KR |
8907 | { |
8908 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 8909 | return flo0; |
c8ae173e | 8910 | else |
55f26379 | 8911 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 8912 | } |
0aacf84e | 8913 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8914 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
8915 | else if (SCM_FRACTIONP (z)) |
8916 | { | |
73e4de09 | 8917 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 8918 | return flo0; |
55f26379 | 8919 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 8920 | } |
0aacf84e | 8921 | else |
2519490c | 8922 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 8923 | } |
2519490c | 8924 | #undef FUNC_NAME |
0f2d19dd JB |
8925 | |
8926 | ||
2519490c MW |
8927 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
8928 | (SCM z), | |
8929 | "Convert the number @var{z} to its inexact representation.\n") | |
8930 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 8931 | { |
e11e83f3 | 8932 | if (SCM_I_INUMP (z)) |
55f26379 | 8933 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 8934 | else if (SCM_BIGP (z)) |
55f26379 | 8935 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 8936 | else if (SCM_FRACTIONP (z)) |
55f26379 | 8937 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
8938 | else if (SCM_INEXACTP (z)) |
8939 | return z; | |
8940 | else | |
2519490c | 8941 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 8942 | } |
2519490c | 8943 | #undef FUNC_NAME |
3c9a524f DH |
8944 | |
8945 | ||
2519490c MW |
8946 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
8947 | (SCM z), | |
8948 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 8949 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 8950 | { |
c7218482 | 8951 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 8952 | return z; |
c7218482 | 8953 | else |
0aacf84e | 8954 | { |
c7218482 MW |
8955 | double val; |
8956 | ||
8957 | if (SCM_REALP (z)) | |
8958 | val = SCM_REAL_VALUE (z); | |
8959 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
8960 | val = SCM_COMPLEX_REAL (z); | |
8961 | else | |
8962 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
8963 | ||
8964 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 8965 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 8966 | else |
f92e85f7 MV |
8967 | { |
8968 | mpq_t frac; | |
8969 | SCM q; | |
8970 | ||
8971 | mpq_init (frac); | |
c7218482 | 8972 | mpq_set_d (frac, val); |
cba42c93 | 8973 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 8974 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 8975 | |
cba42c93 | 8976 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
8977 | for frac... |
8978 | */ | |
8979 | mpq_clear (frac); | |
8980 | return q; | |
8981 | } | |
c2ff8ab0 | 8982 | } |
0f2d19dd | 8983 | } |
1bbd0b84 | 8984 | #undef FUNC_NAME |
0f2d19dd | 8985 | |
f92e85f7 | 8986 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
8987 | (SCM x, SCM eps), |
8988 | "Returns the @emph{simplest} rational number differing\n" | |
8989 | "from @var{x} by no more than @var{eps}.\n" | |
8990 | "\n" | |
8991 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
8992 | "exact result when both its arguments are exact. Thus, you might need\n" | |
8993 | "to use @code{inexact->exact} on the arguments.\n" | |
8994 | "\n" | |
8995 | "@lisp\n" | |
8996 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
8997 | "@result{} 6/5\n" | |
8998 | "@end lisp") | |
f92e85f7 MV |
8999 | #define FUNC_NAME s_scm_rationalize |
9000 | { | |
605f6980 MW |
9001 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9002 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9003 | eps = scm_abs (eps); | |
9004 | if (scm_is_false (scm_positive_p (eps))) | |
9005 | { | |
9006 | /* eps is either zero or a NaN */ | |
9007 | if (scm_is_true (scm_nan_p (eps))) | |
9008 | return scm_nan (); | |
9009 | else if (SCM_INEXACTP (eps)) | |
9010 | return scm_exact_to_inexact (x); | |
9011 | else | |
9012 | return x; | |
9013 | } | |
9014 | else if (scm_is_false (scm_finite_p (eps))) | |
9015 | { | |
9016 | if (scm_is_true (scm_finite_p (x))) | |
9017 | return flo0; | |
9018 | else | |
9019 | return scm_nan (); | |
9020 | } | |
9021 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9022 | return x; |
605f6980 MW |
9023 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9024 | scm_ceiling (scm_difference (x, eps))))) | |
9025 | { | |
9026 | /* There's an integer within range; we want the one closest to zero */ | |
9027 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9028 | { | |
9029 | /* zero is within range */ | |
9030 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9031 | return flo0; | |
9032 | else | |
9033 | return SCM_INUM0; | |
9034 | } | |
9035 | else if (scm_is_true (scm_positive_p (x))) | |
9036 | return scm_ceiling (scm_difference (x, eps)); | |
9037 | else | |
9038 | return scm_floor (scm_sum (x, eps)); | |
9039 | } | |
9040 | else | |
f92e85f7 MV |
9041 | { |
9042 | /* Use continued fractions to find closest ratio. All | |
9043 | arithmetic is done with exact numbers. | |
9044 | */ | |
9045 | ||
9046 | SCM ex = scm_inexact_to_exact (x); | |
9047 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9048 | SCM tt = SCM_INUM1; |
9049 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9050 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9051 | SCM rx; |
9052 | int i = 0; | |
9053 | ||
f92e85f7 MV |
9054 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9055 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9056 | ||
9057 | /* We stop after a million iterations just to be absolutely sure | |
9058 | that we don't go into an infinite loop. The process normally | |
9059 | converges after less than a dozen iterations. | |
9060 | */ | |
9061 | ||
f92e85f7 MV |
9062 | while (++i < 1000000) |
9063 | { | |
9064 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9065 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9066 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9067 | scm_is_false | |
f92e85f7 | 9068 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9069 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9070 | { |
9071 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9072 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9073 | return scm_exact_to_inexact (res); |
9074 | else | |
9075 | return res; | |
9076 | } | |
f92e85f7 MV |
9077 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9078 | SCM_UNDEFINED); | |
9079 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9080 | a2 = a1; | |
9081 | b2 = b1; | |
9082 | a1 = a; | |
9083 | b1 = b; | |
9084 | } | |
9085 | scm_num_overflow (s_scm_rationalize); | |
9086 | } | |
f92e85f7 MV |
9087 | } |
9088 | #undef FUNC_NAME | |
9089 | ||
73e4de09 MV |
9090 | /* conversion functions */ |
9091 | ||
9092 | int | |
9093 | scm_is_integer (SCM val) | |
9094 | { | |
9095 | return scm_is_true (scm_integer_p (val)); | |
9096 | } | |
9097 | ||
9098 | int | |
9099 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9100 | { | |
e11e83f3 | 9101 | if (SCM_I_INUMP (val)) |
73e4de09 | 9102 | { |
e11e83f3 | 9103 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9104 | return n >= min && n <= max; |
9105 | } | |
9106 | else if (SCM_BIGP (val)) | |
9107 | { | |
9108 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9109 | return 0; | |
9110 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9111 | { |
9112 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9113 | { | |
9114 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9115 | return n >= min && n <= max; | |
9116 | } | |
9117 | else | |
9118 | return 0; | |
9119 | } | |
73e4de09 MV |
9120 | else |
9121 | { | |
d956fa6f MV |
9122 | scm_t_intmax n; |
9123 | size_t count; | |
73e4de09 | 9124 | |
d956fa6f MV |
9125 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9126 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9127 | return 0; | |
9128 | ||
9129 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9130 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9131 | |
d956fa6f | 9132 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9133 | { |
d956fa6f MV |
9134 | if (n < 0) |
9135 | return 0; | |
73e4de09 | 9136 | } |
73e4de09 MV |
9137 | else |
9138 | { | |
d956fa6f MV |
9139 | n = -n; |
9140 | if (n >= 0) | |
9141 | return 0; | |
73e4de09 | 9142 | } |
d956fa6f MV |
9143 | |
9144 | return n >= min && n <= max; | |
73e4de09 MV |
9145 | } |
9146 | } | |
73e4de09 MV |
9147 | else |
9148 | return 0; | |
9149 | } | |
9150 | ||
9151 | int | |
9152 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9153 | { | |
e11e83f3 | 9154 | if (SCM_I_INUMP (val)) |
73e4de09 | 9155 | { |
e11e83f3 | 9156 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9157 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9158 | } | |
9159 | else if (SCM_BIGP (val)) | |
9160 | { | |
9161 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9162 | return 0; | |
9163 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9164 | { |
9165 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9166 | { | |
9167 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9168 | return n >= min && n <= max; | |
9169 | } | |
9170 | else | |
9171 | return 0; | |
9172 | } | |
73e4de09 MV |
9173 | else |
9174 | { | |
d956fa6f MV |
9175 | scm_t_uintmax n; |
9176 | size_t count; | |
73e4de09 | 9177 | |
d956fa6f MV |
9178 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9179 | return 0; | |
73e4de09 | 9180 | |
d956fa6f MV |
9181 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9182 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9183 | return 0; |
d956fa6f MV |
9184 | |
9185 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9186 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9187 | |
d956fa6f | 9188 | return n >= min && n <= max; |
73e4de09 MV |
9189 | } |
9190 | } | |
73e4de09 MV |
9191 | else |
9192 | return 0; | |
9193 | } | |
9194 | ||
1713d319 MV |
9195 | static void |
9196 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9197 | { | |
9198 | scm_error (scm_out_of_range_key, | |
9199 | NULL, | |
9200 | "Value out of range ~S to ~S: ~S", | |
9201 | scm_list_3 (min, max, bad_val), | |
9202 | scm_list_1 (bad_val)); | |
9203 | } | |
9204 | ||
bfd7932e MV |
9205 | #define TYPE scm_t_intmax |
9206 | #define TYPE_MIN min | |
9207 | #define TYPE_MAX max | |
9208 | #define SIZEOF_TYPE 0 | |
9209 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9210 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9211 | #include "libguile/conv-integer.i.c" | |
9212 | ||
9213 | #define TYPE scm_t_uintmax | |
9214 | #define TYPE_MIN min | |
9215 | #define TYPE_MAX max | |
9216 | #define SIZEOF_TYPE 0 | |
9217 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9218 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9219 | #include "libguile/conv-uinteger.i.c" | |
9220 | ||
9221 | #define TYPE scm_t_int8 | |
9222 | #define TYPE_MIN SCM_T_INT8_MIN | |
9223 | #define TYPE_MAX SCM_T_INT8_MAX | |
9224 | #define SIZEOF_TYPE 1 | |
9225 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9226 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9227 | #include "libguile/conv-integer.i.c" | |
9228 | ||
9229 | #define TYPE scm_t_uint8 | |
9230 | #define TYPE_MIN 0 | |
9231 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9232 | #define SIZEOF_TYPE 1 | |
9233 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9234 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9235 | #include "libguile/conv-uinteger.i.c" | |
9236 | ||
9237 | #define TYPE scm_t_int16 | |
9238 | #define TYPE_MIN SCM_T_INT16_MIN | |
9239 | #define TYPE_MAX SCM_T_INT16_MAX | |
9240 | #define SIZEOF_TYPE 2 | |
9241 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9242 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9243 | #include "libguile/conv-integer.i.c" | |
9244 | ||
9245 | #define TYPE scm_t_uint16 | |
9246 | #define TYPE_MIN 0 | |
9247 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9248 | #define SIZEOF_TYPE 2 | |
9249 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9250 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9251 | #include "libguile/conv-uinteger.i.c" | |
9252 | ||
9253 | #define TYPE scm_t_int32 | |
9254 | #define TYPE_MIN SCM_T_INT32_MIN | |
9255 | #define TYPE_MAX SCM_T_INT32_MAX | |
9256 | #define SIZEOF_TYPE 4 | |
9257 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9258 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9259 | #include "libguile/conv-integer.i.c" | |
9260 | ||
9261 | #define TYPE scm_t_uint32 | |
9262 | #define TYPE_MIN 0 | |
9263 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9264 | #define SIZEOF_TYPE 4 | |
9265 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9266 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9267 | #include "libguile/conv-uinteger.i.c" | |
9268 | ||
904a78f1 MG |
9269 | #define TYPE scm_t_wchar |
9270 | #define TYPE_MIN (scm_t_int32)-1 | |
9271 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9272 | #define SIZEOF_TYPE 4 | |
9273 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9274 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9275 | #include "libguile/conv-integer.i.c" | |
9276 | ||
bfd7932e MV |
9277 | #define TYPE scm_t_int64 |
9278 | #define TYPE_MIN SCM_T_INT64_MIN | |
9279 | #define TYPE_MAX SCM_T_INT64_MAX | |
9280 | #define SIZEOF_TYPE 8 | |
9281 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9282 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9283 | #include "libguile/conv-integer.i.c" | |
9284 | ||
9285 | #define TYPE scm_t_uint64 | |
9286 | #define TYPE_MIN 0 | |
9287 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9288 | #define SIZEOF_TYPE 8 | |
9289 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9290 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9291 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9292 | |
cd036260 MV |
9293 | void |
9294 | scm_to_mpz (SCM val, mpz_t rop) | |
9295 | { | |
9296 | if (SCM_I_INUMP (val)) | |
9297 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9298 | else if (SCM_BIGP (val)) | |
9299 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9300 | else | |
9301 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9302 | } | |
9303 | ||
9304 | SCM | |
9305 | scm_from_mpz (mpz_t val) | |
9306 | { | |
9307 | return scm_i_mpz2num (val); | |
9308 | } | |
9309 | ||
73e4de09 MV |
9310 | int |
9311 | scm_is_real (SCM val) | |
9312 | { | |
9313 | return scm_is_true (scm_real_p (val)); | |
9314 | } | |
9315 | ||
55f26379 MV |
9316 | int |
9317 | scm_is_rational (SCM val) | |
9318 | { | |
9319 | return scm_is_true (scm_rational_p (val)); | |
9320 | } | |
9321 | ||
73e4de09 MV |
9322 | double |
9323 | scm_to_double (SCM val) | |
9324 | { | |
55f26379 MV |
9325 | if (SCM_I_INUMP (val)) |
9326 | return SCM_I_INUM (val); | |
9327 | else if (SCM_BIGP (val)) | |
9328 | return scm_i_big2dbl (val); | |
9329 | else if (SCM_FRACTIONP (val)) | |
9330 | return scm_i_fraction2double (val); | |
9331 | else if (SCM_REALP (val)) | |
9332 | return SCM_REAL_VALUE (val); | |
9333 | else | |
7a1aba42 | 9334 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9335 | } |
9336 | ||
9337 | SCM | |
9338 | scm_from_double (double val) | |
9339 | { | |
978c52d1 LC |
9340 | SCM z; |
9341 | ||
9342 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9343 | ||
9344 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9345 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9346 | |
55f26379 | 9347 | return z; |
73e4de09 MV |
9348 | } |
9349 | ||
220058a8 | 9350 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9351 | |
9352 | float | |
e25f3727 | 9353 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9354 | { |
220058a8 AW |
9355 | scm_c_issue_deprecation_warning |
9356 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9357 | ||
55f26379 MV |
9358 | if (SCM_BIGP (num)) |
9359 | { | |
9360 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9361 | if (!isinf (res)) |
55f26379 MV |
9362 | return res; |
9363 | else | |
9364 | scm_out_of_range (NULL, num); | |
9365 | } | |
9366 | else | |
9367 | return scm_to_double (num); | |
9368 | } | |
9369 | ||
9370 | double | |
e25f3727 | 9371 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9372 | { |
220058a8 AW |
9373 | scm_c_issue_deprecation_warning |
9374 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9375 | ||
55f26379 MV |
9376 | if (SCM_BIGP (num)) |
9377 | { | |
9378 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9379 | if (!isinf (res)) |
55f26379 MV |
9380 | return res; |
9381 | else | |
9382 | scm_out_of_range (NULL, num); | |
9383 | } | |
9384 | else | |
9385 | return scm_to_double (num); | |
9386 | } | |
9387 | ||
9388 | #endif | |
9389 | ||
8507ec80 MV |
9390 | int |
9391 | scm_is_complex (SCM val) | |
9392 | { | |
9393 | return scm_is_true (scm_complex_p (val)); | |
9394 | } | |
9395 | ||
9396 | double | |
9397 | scm_c_real_part (SCM z) | |
9398 | { | |
9399 | if (SCM_COMPLEXP (z)) | |
9400 | return SCM_COMPLEX_REAL (z); | |
9401 | else | |
9402 | { | |
9403 | /* Use the scm_real_part to get proper error checking and | |
9404 | dispatching. | |
9405 | */ | |
9406 | return scm_to_double (scm_real_part (z)); | |
9407 | } | |
9408 | } | |
9409 | ||
9410 | double | |
9411 | scm_c_imag_part (SCM z) | |
9412 | { | |
9413 | if (SCM_COMPLEXP (z)) | |
9414 | return SCM_COMPLEX_IMAG (z); | |
9415 | else | |
9416 | { | |
9417 | /* Use the scm_imag_part to get proper error checking and | |
9418 | dispatching. The result will almost always be 0.0, but not | |
9419 | always. | |
9420 | */ | |
9421 | return scm_to_double (scm_imag_part (z)); | |
9422 | } | |
9423 | } | |
9424 | ||
9425 | double | |
9426 | scm_c_magnitude (SCM z) | |
9427 | { | |
9428 | return scm_to_double (scm_magnitude (z)); | |
9429 | } | |
9430 | ||
9431 | double | |
9432 | scm_c_angle (SCM z) | |
9433 | { | |
9434 | return scm_to_double (scm_angle (z)); | |
9435 | } | |
9436 | ||
9437 | int | |
9438 | scm_is_number (SCM z) | |
9439 | { | |
9440 | return scm_is_true (scm_number_p (z)); | |
9441 | } | |
9442 | ||
8ab3d8a0 | 9443 | |
a5f6b751 MW |
9444 | /* Returns log(x * 2^shift) */ |
9445 | static SCM | |
9446 | log_of_shifted_double (double x, long shift) | |
9447 | { | |
9448 | double ans = log (fabs (x)) + shift * M_LN2; | |
9449 | ||
9450 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9451 | return scm_from_double (ans); | |
9452 | else | |
9453 | return scm_c_make_rectangular (ans, M_PI); | |
9454 | } | |
9455 | ||
9456 | /* Returns log(n), for exact integer n of integer-length size */ | |
9457 | static SCM | |
9458 | log_of_exact_integer_with_size (SCM n, long size) | |
9459 | { | |
9460 | long shift = size - 2 * scm_dblprec[0]; | |
9461 | ||
9462 | if (shift > 0) | |
9463 | return log_of_shifted_double | |
9464 | (scm_to_double (scm_ash (n, scm_from_long(-shift))), | |
9465 | shift); | |
9466 | else | |
9467 | return log_of_shifted_double (scm_to_double (n), 0); | |
9468 | } | |
9469 | ||
85bdb6ac | 9470 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9471 | static SCM |
9472 | log_of_exact_integer (SCM n) | |
9473 | { | |
9474 | return log_of_exact_integer_with_size | |
9475 | (n, scm_to_long (scm_integer_length (n))); | |
9476 | } | |
9477 | ||
9478 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9479 | static SCM | |
9480 | log_of_fraction (SCM n, SCM d) | |
9481 | { | |
9482 | long n_size = scm_to_long (scm_integer_length (n)); | |
9483 | long d_size = scm_to_long (scm_integer_length (d)); | |
9484 | ||
9485 | if (abs (n_size - d_size) > 1) | |
9486 | return (scm_difference (log_of_exact_integer_with_size (n, n_size), | |
9487 | log_of_exact_integer_with_size (d, d_size))); | |
9488 | else if (scm_is_false (scm_negative_p (n))) | |
9489 | return scm_from_double | |
9490 | (log1p (scm_to_double (scm_divide2real (scm_difference (n, d), d)))); | |
9491 | else | |
9492 | return scm_c_make_rectangular | |
9493 | (log1p (scm_to_double (scm_divide2real | |
9494 | (scm_difference (scm_abs (n), d), | |
9495 | d))), | |
9496 | M_PI); | |
9497 | } | |
9498 | ||
9499 | ||
8ab3d8a0 KR |
9500 | /* In the following functions we dispatch to the real-arg funcs like log() |
9501 | when we know the arg is real, instead of just handing everything to | |
9502 | clog() for instance. This is in case clog() doesn't optimize for a | |
9503 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9504 | well use it to go straight to the applicable C func. */ | |
9505 | ||
2519490c MW |
9506 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9507 | (SCM z), | |
9508 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9509 | #define FUNC_NAME s_scm_log |
9510 | { | |
9511 | if (SCM_COMPLEXP (z)) | |
9512 | { | |
03976fee AW |
9513 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9514 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9515 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9516 | #else | |
9517 | double re = SCM_COMPLEX_REAL (z); | |
9518 | double im = SCM_COMPLEX_IMAG (z); | |
9519 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9520 | atan2 (im, re)); | |
9521 | #endif | |
9522 | } | |
a5f6b751 MW |
9523 | else if (SCM_REALP (z)) |
9524 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9525 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9526 | { |
a5f6b751 MW |
9527 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9528 | if (scm_is_eq (z, SCM_INUM0)) | |
9529 | scm_num_overflow (s_scm_log); | |
9530 | #endif | |
9531 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9532 | } |
a5f6b751 MW |
9533 | else if (SCM_BIGP (z)) |
9534 | return log_of_exact_integer (z); | |
9535 | else if (SCM_FRACTIONP (z)) | |
9536 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9537 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9538 | else |
9539 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9540 | } |
9541 | #undef FUNC_NAME | |
9542 | ||
9543 | ||
2519490c MW |
9544 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9545 | (SCM z), | |
9546 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9547 | #define FUNC_NAME s_scm_log10 |
9548 | { | |
9549 | if (SCM_COMPLEXP (z)) | |
9550 | { | |
9551 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9552 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9553 | log10+hypot+atan2.) */ | |
f328f862 LC |
9554 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9555 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9556 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9557 | #else | |
9558 | double re = SCM_COMPLEX_REAL (z); | |
9559 | double im = SCM_COMPLEX_IMAG (z); | |
9560 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9561 | M_LOG10E * atan2 (im, re)); | |
9562 | #endif | |
9563 | } | |
a5f6b751 | 9564 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9565 | { |
a5f6b751 MW |
9566 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9567 | if (scm_is_eq (z, SCM_INUM0)) | |
9568 | scm_num_overflow (s_scm_log10); | |
9569 | #endif | |
9570 | { | |
9571 | double re = scm_to_double (z); | |
9572 | double l = log10 (fabs (re)); | |
9573 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9574 | return scm_from_double (l); | |
9575 | else | |
9576 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9577 | } | |
8ab3d8a0 | 9578 | } |
a5f6b751 MW |
9579 | else if (SCM_BIGP (z)) |
9580 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9581 | else if (SCM_FRACTIONP (z)) | |
9582 | return scm_product (flo_log10e, | |
9583 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9584 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9585 | else |
9586 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9587 | } |
9588 | #undef FUNC_NAME | |
9589 | ||
9590 | ||
2519490c MW |
9591 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9592 | (SCM z), | |
9593 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9594 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9595 | #define FUNC_NAME s_scm_exp |
9596 | { | |
9597 | if (SCM_COMPLEXP (z)) | |
9598 | { | |
03976fee AW |
9599 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9600 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9601 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
9602 | #else | |
9603 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
9604 | SCM_COMPLEX_IMAG (z)); | |
9605 | #endif | |
9606 | } | |
2519490c | 9607 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9608 | { |
9609 | /* When z is a negative bignum the conversion to double overflows, | |
9610 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9611 | return scm_from_double (exp (scm_to_double (z))); | |
9612 | } | |
2519490c MW |
9613 | else |
9614 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9615 | } |
9616 | #undef FUNC_NAME | |
9617 | ||
9618 | ||
882c8963 MW |
9619 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9620 | (SCM k), | |
9621 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9622 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9623 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9624 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9625 | "\n" | |
9626 | "@lisp\n" | |
9627 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9628 | "@end lisp") | |
9629 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9630 | { | |
9631 | SCM s, r; | |
9632 | ||
9633 | scm_exact_integer_sqrt (k, &s, &r); | |
9634 | return scm_values (scm_list_2 (s, r)); | |
9635 | } | |
9636 | #undef FUNC_NAME | |
9637 | ||
9638 | void | |
9639 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9640 | { | |
9641 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9642 | { | |
9643 | scm_t_inum kk = SCM_I_INUM (k); | |
9644 | scm_t_inum uu = kk; | |
9645 | scm_t_inum ss; | |
9646 | ||
9647 | if (SCM_LIKELY (kk > 0)) | |
9648 | { | |
9649 | do | |
9650 | { | |
9651 | ss = uu; | |
9652 | uu = (ss + kk/ss) / 2; | |
9653 | } while (uu < ss); | |
9654 | *sp = SCM_I_MAKINUM (ss); | |
9655 | *rp = SCM_I_MAKINUM (kk - ss*ss); | |
9656 | } | |
9657 | else if (SCM_LIKELY (kk == 0)) | |
9658 | *sp = *rp = SCM_INUM0; | |
9659 | else | |
9660 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9661 | "exact non-negative integer"); | |
9662 | } | |
9663 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9664 | { | |
9665 | SCM s, r; | |
9666 | ||
9667 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9668 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9669 | "exact non-negative integer"); | |
9670 | s = scm_i_mkbig (); | |
9671 | r = scm_i_mkbig (); | |
9672 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9673 | scm_remember_upto_here_1 (k); | |
9674 | *sp = scm_i_normbig (s); | |
9675 | *rp = scm_i_normbig (r); | |
9676 | } | |
9677 | else | |
9678 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9679 | "exact non-negative integer"); | |
9680 | } | |
9681 | ||
9682 | ||
2519490c MW |
9683 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9684 | (SCM z), | |
9685 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9686 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9687 | "is returned, or if that's zero then a positive imaginary part.\n" |
9688 | "Thus,\n" | |
9689 | "\n" | |
9690 | "@example\n" | |
9691 | "(sqrt 9.0) @result{} 3.0\n" | |
9692 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9693 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9694 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9695 | "@end example") | |
8ab3d8a0 KR |
9696 | #define FUNC_NAME s_scm_sqrt |
9697 | { | |
2519490c | 9698 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9699 | { |
f328f862 LC |
9700 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9701 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9702 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9703 | #else |
2519490c MW |
9704 | double re = SCM_COMPLEX_REAL (z); |
9705 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9706 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9707 | 0.5 * atan2 (im, re)); | |
9708 | #endif | |
9709 | } | |
2519490c | 9710 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9711 | { |
2519490c | 9712 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9713 | if (xx < 0) |
9714 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9715 | else | |
9716 | return scm_from_double (sqrt (xx)); | |
9717 | } | |
2519490c MW |
9718 | else |
9719 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
9720 | } |
9721 | #undef FUNC_NAME | |
9722 | ||
9723 | ||
9724 | ||
0f2d19dd JB |
9725 | void |
9726 | scm_init_numbers () | |
0f2d19dd | 9727 | { |
0b799eea MV |
9728 | int i; |
9729 | ||
b57bf272 AW |
9730 | if (scm_install_gmp_memory_functions) |
9731 | mp_set_memory_functions (custom_gmp_malloc, | |
9732 | custom_gmp_realloc, | |
9733 | custom_gmp_free); | |
9734 | ||
713a4259 KR |
9735 | mpz_init_set_si (z_negative_one, -1); |
9736 | ||
a261c0e9 DH |
9737 | /* It may be possible to tune the performance of some algorithms by using |
9738 | * the following constants to avoid the creation of bignums. Please, before | |
9739 | * using these values, remember the two rules of program optimization: | |
9740 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9741 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9742 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9743 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9744 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9745 | |
f3ae5d60 MD |
9746 | scm_add_feature ("complex"); |
9747 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9748 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9749 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea MV |
9750 | |
9751 | /* determine floating point precision */ | |
55f26379 | 9752 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
9753 | { |
9754 | init_dblprec(&scm_dblprec[i-2],i); | |
9755 | init_fx_radix(fx_per_radix[i-2],i); | |
9756 | } | |
f872b822 | 9757 | #ifdef DBL_DIG |
0b799eea | 9758 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 9759 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 9760 | #endif |
1be6b49c | 9761 | |
cff5fa33 | 9762 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 9763 | #include "libguile/numbers.x" |
0f2d19dd | 9764 | } |
89e00824 ML |
9765 | |
9766 | /* | |
9767 | Local Variables: | |
9768 | c-file-style: "gnu" | |
9769 | End: | |
9770 | */ |