Commit | Line | Data |
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75ba64d6 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 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 | |
6922d92f | 182 | finalize_bignum (void *ptr, void *data) |
864e7d42 LC |
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; | |
220 | ||
221 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
222 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
223 | "bignum"); | |
224 | p[0] = scm_tc16_big; | |
225 | ||
75ba64d6 | 226 | scm_i_set_finalizer (p, finalize_bignum, NULL); |
864e7d42 | 227 | |
d017fcdf LC |
228 | return SCM_PACK (p); |
229 | } | |
ac0c002c | 230 | |
864e7d42 | 231 | |
189171c5 | 232 | SCM |
ca46fb90 RB |
233 | scm_i_mkbig () |
234 | { | |
235 | /* Return a newly created bignum. */ | |
d017fcdf | 236 | SCM z = make_bignum (); |
ca46fb90 RB |
237 | mpz_init (SCM_I_BIG_MPZ (z)); |
238 | return z; | |
239 | } | |
240 | ||
e25f3727 AW |
241 | static SCM |
242 | scm_i_inum2big (scm_t_inum x) | |
243 | { | |
244 | /* Return a newly created bignum initialized to X. */ | |
245 | SCM z = make_bignum (); | |
246 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
247 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
248 | #else | |
249 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
250 | mpz_*_si invocations in Guile. */ | |
251 | #error creation of mpz not implemented for this inum size | |
252 | #endif | |
253 | return z; | |
254 | } | |
255 | ||
189171c5 | 256 | SCM |
c71b0706 MV |
257 | scm_i_long2big (long x) |
258 | { | |
259 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 260 | SCM z = make_bignum (); |
c71b0706 MV |
261 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
262 | return z; | |
263 | } | |
264 | ||
189171c5 | 265 | SCM |
c71b0706 MV |
266 | scm_i_ulong2big (unsigned long x) |
267 | { | |
268 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 269 | SCM z = make_bignum (); |
c71b0706 MV |
270 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
271 | return z; | |
272 | } | |
273 | ||
189171c5 | 274 | SCM |
ca46fb90 RB |
275 | scm_i_clonebig (SCM src_big, int same_sign_p) |
276 | { | |
277 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 278 | SCM z = make_bignum (); |
ca46fb90 | 279 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
280 | if (!same_sign_p) |
281 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
282 | return z; |
283 | } | |
284 | ||
189171c5 | 285 | int |
ca46fb90 RB |
286 | scm_i_bigcmp (SCM x, SCM y) |
287 | { | |
288 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
289 | /* presume we already know x and y are bignums */ | |
290 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
291 | scm_remember_upto_here_2 (x, y); | |
292 | return result; | |
293 | } | |
294 | ||
189171c5 | 295 | SCM |
ca46fb90 RB |
296 | scm_i_dbl2big (double d) |
297 | { | |
298 | /* results are only defined if d is an integer */ | |
d017fcdf | 299 | SCM z = make_bignum (); |
ca46fb90 RB |
300 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
301 | return z; | |
302 | } | |
303 | ||
f92e85f7 MV |
304 | /* Convert a integer in double representation to a SCM number. */ |
305 | ||
189171c5 | 306 | SCM |
f92e85f7 MV |
307 | scm_i_dbl2num (double u) |
308 | { | |
309 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
310 | powers of 2, so there's no rounding when making "double" values | |
311 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
312 | get rounded on a 64-bit machine, hence the "+1". | |
313 | ||
314 | The use of floor() to force to an integer value ensures we get a | |
315 | "numerically closest" value without depending on how a | |
316 | double->long cast or how mpz_set_d will round. For reference, | |
317 | double->long probably follows the hardware rounding mode, | |
318 | mpz_set_d truncates towards zero. */ | |
319 | ||
320 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
321 | representable as a double? */ | |
322 | ||
323 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
324 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 325 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
326 | else |
327 | return scm_i_dbl2big (u); | |
328 | } | |
329 | ||
089c9a59 KR |
330 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
331 | with R5RS exact->inexact. | |
332 | ||
333 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
334 | (ie. truncate towards zero), then adjust to get the closest double by |
335 | examining the next lower bit and adding 1 (to the absolute value) if | |
336 | necessary. | |
337 | ||
338 | Bignums exactly half way between representable doubles are rounded to the | |
339 | next higher absolute value (ie. away from zero). This seems like an | |
340 | adequate interpretation of R5RS "numerically closest", and it's easier | |
341 | and faster than a full "nearest-even" style. | |
342 | ||
343 | The bit test must be done on the absolute value of the mpz_t, which means | |
344 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
345 | negatives as twos complement. | |
346 | ||
18d78c5e MW |
347 | In GMP before 4.2, mpz_get_d rounding was unspecified. It ended up |
348 | following the hardware rounding mode, but applied to the absolute | |
349 | value of the mpz_t operand. This is not what we want so we put the | |
350 | high DBL_MANT_DIG bits into a temporary. Starting with GMP 4.2 | |
351 | (released in March 2006) mpz_get_d now always truncates towards zero. | |
f8a8200b | 352 | |
18d78c5e MW |
353 | ENHANCE-ME: The temporary init+clear to force the rounding in GMP |
354 | before 4.2 is a slowdown. It'd be faster to pick out the relevant | |
355 | high bits with mpz_getlimbn. */ | |
089c9a59 KR |
356 | |
357 | double | |
ca46fb90 RB |
358 | scm_i_big2dbl (SCM b) |
359 | { | |
089c9a59 KR |
360 | double result; |
361 | size_t bits; | |
362 | ||
363 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
364 | ||
f8a8200b | 365 | #if 1 |
089c9a59 | 366 | { |
18d78c5e MW |
367 | /* For GMP earlier than 4.2, force truncation towards zero */ |
368 | ||
369 | /* FIXME: DBL_MANT_DIG is the number of base-`FLT_RADIX' digits, | |
370 | _not_ the number of bits, so this code will break badly on a | |
371 | system with non-binary doubles. */ | |
372 | ||
089c9a59 KR |
373 | mpz_t tmp; |
374 | if (bits > DBL_MANT_DIG) | |
375 | { | |
376 | size_t shift = bits - DBL_MANT_DIG; | |
377 | mpz_init2 (tmp, DBL_MANT_DIG); | |
378 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
379 | result = ldexp (mpz_get_d (tmp), shift); | |
380 | mpz_clear (tmp); | |
381 | } | |
382 | else | |
383 | { | |
384 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
385 | } | |
386 | } | |
387 | #else | |
18d78c5e | 388 | /* GMP 4.2 or later */ |
089c9a59 KR |
389 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
390 | #endif | |
391 | ||
392 | if (bits > DBL_MANT_DIG) | |
393 | { | |
394 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
395 | /* test bit number "pos" in absolute value */ | |
396 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
397 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
398 | { | |
399 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
400 | } | |
401 | } | |
402 | ||
ca46fb90 RB |
403 | scm_remember_upto_here_1 (b); |
404 | return result; | |
405 | } | |
406 | ||
189171c5 | 407 | SCM |
ca46fb90 RB |
408 | scm_i_normbig (SCM b) |
409 | { | |
410 | /* convert a big back to a fixnum if it'll fit */ | |
411 | /* presume b is a bignum */ | |
412 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
413 | { | |
e25f3727 | 414 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 415 | if (SCM_FIXABLE (val)) |
d956fa6f | 416 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
417 | } |
418 | return b; | |
419 | } | |
f872b822 | 420 | |
f92e85f7 MV |
421 | static SCM_C_INLINE_KEYWORD SCM |
422 | scm_i_mpz2num (mpz_t b) | |
423 | { | |
424 | /* convert a mpz number to a SCM number. */ | |
425 | if (mpz_fits_slong_p (b)) | |
426 | { | |
e25f3727 | 427 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 428 | if (SCM_FIXABLE (val)) |
d956fa6f | 429 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
430 | } |
431 | ||
432 | { | |
d017fcdf | 433 | SCM z = make_bignum (); |
f92e85f7 MV |
434 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
435 | return z; | |
436 | } | |
437 | } | |
438 | ||
439 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
440 | static SCM scm_divide2real (SCM x, SCM y); | |
441 | ||
cba42c93 MV |
442 | static SCM |
443 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 444 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 445 | { |
c60e130c MV |
446 | /* First make sure the arguments are proper. |
447 | */ | |
e11e83f3 | 448 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 449 | { |
bc36d050 | 450 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 451 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 452 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
453 | return numerator; |
454 | } | |
455 | else | |
456 | { | |
457 | if (!(SCM_BIGP(denominator))) | |
458 | SCM_WRONG_TYPE_ARG (2, denominator); | |
459 | } | |
e11e83f3 | 460 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
461 | SCM_WRONG_TYPE_ARG (1, numerator); |
462 | ||
463 | /* Then flip signs so that the denominator is positive. | |
464 | */ | |
73e4de09 | 465 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
466 | { |
467 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
468 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
469 | } | |
470 | ||
471 | /* Now consider for each of the four fixnum/bignum combinations | |
472 | whether the rational number is really an integer. | |
473 | */ | |
e11e83f3 | 474 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 475 | { |
e25f3727 | 476 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 477 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 478 | return SCM_INUM0; |
e11e83f3 | 479 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 480 | { |
e25f3727 | 481 | scm_t_inum y; |
e11e83f3 | 482 | y = SCM_I_INUM (denominator); |
f92e85f7 | 483 | if (x == y) |
cff5fa33 | 484 | return SCM_INUM1; |
f92e85f7 | 485 | if ((x % y) == 0) |
d956fa6f | 486 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 487 | } |
dd5130ca KR |
488 | else |
489 | { | |
490 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
491 | of that value for the denominator, as a bignum. Apart from |
492 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
493 | integer. */ | |
494 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
495 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
496 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 497 | return SCM_I_MAKINUM(-1); |
dd5130ca | 498 | } |
f92e85f7 | 499 | } |
c60e130c | 500 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 501 | { |
e11e83f3 | 502 | if (SCM_I_INUMP (denominator)) |
c60e130c | 503 | { |
e25f3727 | 504 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
505 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
506 | return scm_divide (numerator, denominator); | |
507 | } | |
508 | else | |
f92e85f7 | 509 | { |
bc36d050 | 510 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 511 | return SCM_INUM1; |
c60e130c MV |
512 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
513 | SCM_I_BIG_MPZ (denominator))) | |
514 | return scm_divide(numerator, denominator); | |
f92e85f7 | 515 | } |
f92e85f7 | 516 | } |
c60e130c MV |
517 | |
518 | /* No, it's a proper fraction. | |
519 | */ | |
e2bf3b19 HWN |
520 | { |
521 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 522 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
523 | { |
524 | numerator = scm_divide (numerator, divisor); | |
525 | denominator = scm_divide (denominator, divisor); | |
526 | } | |
527 | ||
528 | return scm_double_cell (scm_tc16_fraction, | |
529 | SCM_UNPACK (numerator), | |
530 | SCM_UNPACK (denominator), 0); | |
531 | } | |
f92e85f7 | 532 | } |
c60e130c | 533 | #undef FUNC_NAME |
f92e85f7 | 534 | |
f92e85f7 MV |
535 | double |
536 | scm_i_fraction2double (SCM z) | |
537 | { | |
55f26379 MV |
538 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
539 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
540 | } |
541 | ||
2e274311 MW |
542 | static int |
543 | double_is_non_negative_zero (double x) | |
544 | { | |
545 | static double zero = 0.0; | |
546 | ||
547 | return !memcmp (&x, &zero, sizeof(double)); | |
548 | } | |
549 | ||
2519490c MW |
550 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
551 | (SCM x), | |
942e5b91 MG |
552 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
553 | "otherwise.") | |
1bbd0b84 | 554 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 555 | { |
41df63cf MW |
556 | if (SCM_INEXACTP (x)) |
557 | return SCM_BOOL_F; | |
558 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 559 | return SCM_BOOL_T; |
41df63cf | 560 | else |
2519490c | 561 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
562 | } |
563 | #undef FUNC_NAME | |
564 | ||
022dda69 MG |
565 | int |
566 | scm_is_exact (SCM val) | |
567 | { | |
568 | return scm_is_true (scm_exact_p (val)); | |
569 | } | |
41df63cf | 570 | |
2519490c | 571 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
572 | (SCM x), |
573 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
574 | "else.") | |
575 | #define FUNC_NAME s_scm_inexact_p | |
576 | { | |
577 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 578 | return SCM_BOOL_T; |
41df63cf | 579 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 580 | return SCM_BOOL_F; |
41df63cf | 581 | else |
2519490c | 582 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 583 | } |
1bbd0b84 | 584 | #undef FUNC_NAME |
0f2d19dd | 585 | |
022dda69 MG |
586 | int |
587 | scm_is_inexact (SCM val) | |
588 | { | |
589 | return scm_is_true (scm_inexact_p (val)); | |
590 | } | |
4219f20d | 591 | |
2519490c | 592 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 593 | (SCM n), |
942e5b91 MG |
594 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
595 | "otherwise.") | |
1bbd0b84 | 596 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 597 | { |
e11e83f3 | 598 | if (SCM_I_INUMP (n)) |
0aacf84e | 599 | { |
e25f3727 | 600 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 601 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
602 | } |
603 | else if (SCM_BIGP (n)) | |
604 | { | |
605 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
606 | scm_remember_upto_here_1 (n); | |
73e4de09 | 607 | return scm_from_bool (odd_p); |
0aacf84e | 608 | } |
f92e85f7 MV |
609 | else if (SCM_REALP (n)) |
610 | { | |
2519490c MW |
611 | double val = SCM_REAL_VALUE (n); |
612 | if (DOUBLE_IS_FINITE (val)) | |
613 | { | |
614 | double rem = fabs (fmod (val, 2.0)); | |
615 | if (rem == 1.0) | |
616 | return SCM_BOOL_T; | |
617 | else if (rem == 0.0) | |
618 | return SCM_BOOL_F; | |
619 | } | |
f92e85f7 | 620 | } |
2519490c | 621 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 622 | } |
1bbd0b84 | 623 | #undef FUNC_NAME |
0f2d19dd | 624 | |
4219f20d | 625 | |
2519490c | 626 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 627 | (SCM n), |
942e5b91 MG |
628 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
629 | "otherwise.") | |
1bbd0b84 | 630 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 631 | { |
e11e83f3 | 632 | if (SCM_I_INUMP (n)) |
0aacf84e | 633 | { |
e25f3727 | 634 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 635 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
636 | } |
637 | else if (SCM_BIGP (n)) | |
638 | { | |
639 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
640 | scm_remember_upto_here_1 (n); | |
73e4de09 | 641 | return scm_from_bool (even_p); |
0aacf84e | 642 | } |
f92e85f7 MV |
643 | else if (SCM_REALP (n)) |
644 | { | |
2519490c MW |
645 | double val = SCM_REAL_VALUE (n); |
646 | if (DOUBLE_IS_FINITE (val)) | |
647 | { | |
648 | double rem = fabs (fmod (val, 2.0)); | |
649 | if (rem == 1.0) | |
650 | return SCM_BOOL_F; | |
651 | else if (rem == 0.0) | |
652 | return SCM_BOOL_T; | |
653 | } | |
f92e85f7 | 654 | } |
2519490c | 655 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 656 | } |
1bbd0b84 | 657 | #undef FUNC_NAME |
0f2d19dd | 658 | |
2519490c MW |
659 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
660 | (SCM x), | |
10391e06 AW |
661 | "Return @code{#t} if the real number @var{x} is neither\n" |
662 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
663 | #define FUNC_NAME s_scm_finite_p |
664 | { | |
665 | if (SCM_REALP (x)) | |
666 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 667 | else if (scm_is_real (x)) |
7112615f MW |
668 | return SCM_BOOL_T; |
669 | else | |
2519490c | 670 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
671 | } |
672 | #undef FUNC_NAME | |
673 | ||
2519490c MW |
674 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
675 | (SCM x), | |
676 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
677 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
678 | #define FUNC_NAME s_scm_inf_p |
679 | { | |
b1092b3a | 680 | if (SCM_REALP (x)) |
2e65b52f | 681 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 682 | else if (scm_is_real (x)) |
7351e207 | 683 | return SCM_BOOL_F; |
10391e06 | 684 | else |
2519490c | 685 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
686 | } |
687 | #undef FUNC_NAME | |
688 | ||
2519490c MW |
689 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
690 | (SCM x), | |
10391e06 AW |
691 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
692 | "or @code{#f} otherwise.") | |
7351e207 MV |
693 | #define FUNC_NAME s_scm_nan_p |
694 | { | |
10391e06 AW |
695 | if (SCM_REALP (x)) |
696 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
697 | else if (scm_is_real (x)) | |
7351e207 | 698 | return SCM_BOOL_F; |
10391e06 | 699 | else |
2519490c | 700 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
701 | } |
702 | #undef FUNC_NAME | |
703 | ||
704 | /* Guile's idea of infinity. */ | |
705 | static double guile_Inf; | |
706 | ||
707 | /* Guile's idea of not a number. */ | |
708 | static double guile_NaN; | |
709 | ||
710 | static void | |
711 | guile_ieee_init (void) | |
712 | { | |
7351e207 MV |
713 | /* Some version of gcc on some old version of Linux used to crash when |
714 | trying to make Inf and NaN. */ | |
715 | ||
240a27d2 KR |
716 | #ifdef INFINITY |
717 | /* C99 INFINITY, when available. | |
718 | FIXME: The standard allows for INFINITY to be something that overflows | |
719 | at compile time. We ought to have a configure test to check for that | |
720 | before trying to use it. (But in practice we believe this is not a | |
721 | problem on any system guile is likely to target.) */ | |
722 | guile_Inf = INFINITY; | |
56a3dcd4 | 723 | #elif defined HAVE_DINFINITY |
240a27d2 | 724 | /* OSF */ |
7351e207 | 725 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 726 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
727 | #else |
728 | double tmp = 1e+10; | |
729 | guile_Inf = tmp; | |
730 | for (;;) | |
731 | { | |
732 | guile_Inf *= 1e+10; | |
733 | if (guile_Inf == tmp) | |
734 | break; | |
735 | tmp = guile_Inf; | |
736 | } | |
737 | #endif | |
738 | ||
240a27d2 KR |
739 | #ifdef NAN |
740 | /* C99 NAN, when available */ | |
741 | guile_NaN = NAN; | |
56a3dcd4 | 742 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
743 | { |
744 | /* OSF */ | |
745 | extern unsigned int DQNAN[2]; | |
746 | guile_NaN = (*((double *)(DQNAN))); | |
747 | } | |
7351e207 MV |
748 | #else |
749 | guile_NaN = guile_Inf / guile_Inf; | |
750 | #endif | |
7351e207 MV |
751 | } |
752 | ||
753 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
754 | (void), | |
755 | "Return Inf.") | |
756 | #define FUNC_NAME s_scm_inf | |
757 | { | |
758 | static int initialized = 0; | |
759 | if (! initialized) | |
760 | { | |
761 | guile_ieee_init (); | |
762 | initialized = 1; | |
763 | } | |
55f26379 | 764 | return scm_from_double (guile_Inf); |
7351e207 MV |
765 | } |
766 | #undef FUNC_NAME | |
767 | ||
768 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
769 | (void), | |
770 | "Return NaN.") | |
771 | #define FUNC_NAME s_scm_nan | |
772 | { | |
773 | static int initialized = 0; | |
0aacf84e | 774 | if (!initialized) |
7351e207 MV |
775 | { |
776 | guile_ieee_init (); | |
777 | initialized = 1; | |
778 | } | |
55f26379 | 779 | return scm_from_double (guile_NaN); |
7351e207 MV |
780 | } |
781 | #undef FUNC_NAME | |
782 | ||
4219f20d | 783 | |
a48d60b1 MD |
784 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
785 | (SCM x), | |
786 | "Return the absolute value of @var{x}.") | |
2519490c | 787 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 788 | { |
e11e83f3 | 789 | if (SCM_I_INUMP (x)) |
0aacf84e | 790 | { |
e25f3727 | 791 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
792 | if (xx >= 0) |
793 | return x; | |
794 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 795 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 796 | else |
e25f3727 | 797 | return scm_i_inum2big (-xx); |
4219f20d | 798 | } |
9b9ef10c MW |
799 | else if (SCM_LIKELY (SCM_REALP (x))) |
800 | { | |
801 | double xx = SCM_REAL_VALUE (x); | |
802 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
803 | if (xx < 0.0) | |
804 | return scm_from_double (-xx); | |
805 | /* Handle signed zeroes properly */ | |
806 | else if (SCM_UNLIKELY (xx == 0.0)) | |
807 | return flo0; | |
808 | else | |
809 | return x; | |
810 | } | |
0aacf84e MD |
811 | else if (SCM_BIGP (x)) |
812 | { | |
813 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
814 | if (sgn < 0) | |
815 | return scm_i_clonebig (x, 0); | |
816 | else | |
817 | return x; | |
4219f20d | 818 | } |
f92e85f7 MV |
819 | else if (SCM_FRACTIONP (x)) |
820 | { | |
73e4de09 | 821 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 822 | return x; |
cba42c93 | 823 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
824 | SCM_FRACTION_DENOMINATOR (x)); |
825 | } | |
0aacf84e | 826 | else |
a48d60b1 | 827 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 828 | } |
a48d60b1 | 829 | #undef FUNC_NAME |
0f2d19dd | 830 | |
4219f20d | 831 | |
2519490c MW |
832 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
833 | (SCM x, SCM y), | |
834 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
835 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 836 | { |
495a39c4 | 837 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 838 | { |
495a39c4 | 839 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 840 | return scm_truncate_quotient (x, y); |
0aacf84e | 841 | else |
2519490c | 842 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 843 | } |
0aacf84e | 844 | else |
2519490c | 845 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 846 | } |
2519490c | 847 | #undef FUNC_NAME |
0f2d19dd | 848 | |
2519490c MW |
849 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
850 | (SCM x, SCM y), | |
851 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
852 | "@lisp\n" | |
853 | "(remainder 13 4) @result{} 1\n" | |
854 | "(remainder -13 4) @result{} -1\n" | |
855 | "@end lisp") | |
856 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 857 | { |
495a39c4 | 858 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 859 | { |
495a39c4 | 860 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 861 | return scm_truncate_remainder (x, y); |
0aacf84e | 862 | else |
2519490c | 863 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 864 | } |
0aacf84e | 865 | else |
2519490c | 866 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 867 | } |
2519490c | 868 | #undef FUNC_NAME |
0f2d19dd | 869 | |
89a7e495 | 870 | |
2519490c MW |
871 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
872 | (SCM x, SCM y), | |
873 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
874 | "@lisp\n" | |
875 | "(modulo 13 4) @result{} 1\n" | |
876 | "(modulo -13 4) @result{} 3\n" | |
877 | "@end lisp") | |
878 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 879 | { |
495a39c4 | 880 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 881 | { |
495a39c4 | 882 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 883 | return scm_floor_remainder (x, y); |
0aacf84e | 884 | else |
2519490c | 885 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 886 | } |
0aacf84e | 887 | else |
2519490c | 888 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 889 | } |
2519490c | 890 | #undef FUNC_NAME |
0f2d19dd | 891 | |
5fbf680b MW |
892 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
893 | two-valued functions. It is called from primitive generics that take | |
894 | two arguments and return two values, when the core procedure is | |
895 | unable to handle the given argument types. If there are GOOPS | |
896 | methods for this primitive generic, it dispatches to GOOPS and, if | |
897 | successful, expects two values to be returned, which are placed in | |
898 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
899 | wrong-type-arg exception. | |
900 | ||
901 | FIXME: This obviously belongs somewhere else, but until we decide on | |
902 | the right API, it is here as a static function, because it is needed | |
903 | by the *_divide functions below. | |
904 | */ | |
905 | static void | |
906 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
907 | const char *subr, SCM *rp1, SCM *rp2) | |
908 | { | |
909 | if (SCM_UNPACK (gf)) | |
910 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
911 | else | |
912 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
913 | } | |
914 | ||
a8da6d93 MW |
915 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
916 | (SCM x, SCM y), | |
917 | "Return the integer @var{q} such that\n" | |
918 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
919 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
920 | "@lisp\n" | |
921 | "(euclidean-quotient 123 10) @result{} 12\n" | |
922 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
923 | "(euclidean-quotient -123 10) @result{} -13\n" | |
924 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
925 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
926 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
927 | "@end lisp") | |
ff62c168 MW |
928 | #define FUNC_NAME s_scm_euclidean_quotient |
929 | { | |
a8da6d93 MW |
930 | if (scm_is_false (scm_negative_p (y))) |
931 | return scm_floor_quotient (x, y); | |
ff62c168 | 932 | else |
a8da6d93 | 933 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
934 | } |
935 | #undef FUNC_NAME | |
936 | ||
a8da6d93 MW |
937 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
938 | (SCM x, SCM y), | |
939 | "Return the real number @var{r} such that\n" | |
940 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
941 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
942 | "for some integer @var{q}.\n" | |
943 | "@lisp\n" | |
944 | "(euclidean-remainder 123 10) @result{} 3\n" | |
945 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
946 | "(euclidean-remainder -123 10) @result{} 7\n" | |
947 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
948 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
949 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
950 | "@end lisp") | |
ff62c168 MW |
951 | #define FUNC_NAME s_scm_euclidean_remainder |
952 | { | |
a8da6d93 MW |
953 | if (scm_is_false (scm_negative_p (y))) |
954 | return scm_floor_remainder (x, y); | |
ff62c168 | 955 | else |
a8da6d93 | 956 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
957 | } |
958 | #undef FUNC_NAME | |
959 | ||
a8da6d93 MW |
960 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
961 | (SCM x, SCM y), | |
962 | "Return the integer @var{q} and the real number @var{r}\n" | |
963 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
964 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
965 | "@lisp\n" | |
966 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
967 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
968 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
969 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
970 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
971 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
972 | "@end lisp") | |
5fbf680b MW |
973 | #define FUNC_NAME s_scm_i_euclidean_divide |
974 | { | |
a8da6d93 MW |
975 | if (scm_is_false (scm_negative_p (y))) |
976 | return scm_i_floor_divide (x, y); | |
977 | else | |
978 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
979 | } |
980 | #undef FUNC_NAME | |
981 | ||
5fbf680b MW |
982 | void |
983 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 984 | { |
a8da6d93 MW |
985 | if (scm_is_false (scm_negative_p (y))) |
986 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 987 | else |
a8da6d93 | 988 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
989 | } |
990 | ||
8f9da340 MW |
991 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
992 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
993 | ||
994 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
995 | (SCM x, SCM y), | |
996 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
997 | "@lisp\n" | |
998 | "(floor-quotient 123 10) @result{} 12\n" | |
999 | "(floor-quotient 123 -10) @result{} -13\n" | |
1000 | "(floor-quotient -123 10) @result{} -13\n" | |
1001 | "(floor-quotient -123 -10) @result{} 12\n" | |
1002 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1003 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1004 | "@end lisp") | |
1005 | #define FUNC_NAME s_scm_floor_quotient | |
1006 | { | |
1007 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1008 | { | |
1009 | scm_t_inum xx = SCM_I_INUM (x); | |
1010 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1011 | { | |
1012 | scm_t_inum yy = SCM_I_INUM (y); | |
1013 | scm_t_inum xx1 = xx; | |
1014 | scm_t_inum qq; | |
1015 | if (SCM_LIKELY (yy > 0)) | |
1016 | { | |
1017 | if (SCM_UNLIKELY (xx < 0)) | |
1018 | xx1 = xx - yy + 1; | |
1019 | } | |
1020 | else if (SCM_UNLIKELY (yy == 0)) | |
1021 | scm_num_overflow (s_scm_floor_quotient); | |
1022 | else if (xx > 0) | |
1023 | xx1 = xx - yy - 1; | |
1024 | qq = xx1 / yy; | |
1025 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1026 | return SCM_I_MAKINUM (qq); | |
1027 | else | |
1028 | return scm_i_inum2big (qq); | |
1029 | } | |
1030 | else if (SCM_BIGP (y)) | |
1031 | { | |
1032 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1033 | scm_remember_upto_here_1 (y); | |
1034 | if (sign > 0) | |
1035 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1036 | else | |
1037 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1038 | } | |
1039 | else if (SCM_REALP (y)) | |
1040 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1041 | else if (SCM_FRACTIONP (y)) | |
1042 | return scm_i_exact_rational_floor_quotient (x, y); | |
1043 | else | |
1044 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1045 | s_scm_floor_quotient); | |
1046 | } | |
1047 | else if (SCM_BIGP (x)) | |
1048 | { | |
1049 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1050 | { | |
1051 | scm_t_inum yy = SCM_I_INUM (y); | |
1052 | if (SCM_UNLIKELY (yy == 0)) | |
1053 | scm_num_overflow (s_scm_floor_quotient); | |
1054 | else if (SCM_UNLIKELY (yy == 1)) | |
1055 | return x; | |
1056 | else | |
1057 | { | |
1058 | SCM q = scm_i_mkbig (); | |
1059 | if (yy > 0) | |
1060 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1061 | else | |
1062 | { | |
1063 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1064 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1065 | } | |
1066 | scm_remember_upto_here_1 (x); | |
1067 | return scm_i_normbig (q); | |
1068 | } | |
1069 | } | |
1070 | else if (SCM_BIGP (y)) | |
1071 | { | |
1072 | SCM q = scm_i_mkbig (); | |
1073 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1074 | SCM_I_BIG_MPZ (x), | |
1075 | SCM_I_BIG_MPZ (y)); | |
1076 | scm_remember_upto_here_2 (x, y); | |
1077 | return scm_i_normbig (q); | |
1078 | } | |
1079 | else if (SCM_REALP (y)) | |
1080 | return scm_i_inexact_floor_quotient | |
1081 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1082 | else if (SCM_FRACTIONP (y)) | |
1083 | return scm_i_exact_rational_floor_quotient (x, y); | |
1084 | else | |
1085 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1086 | s_scm_floor_quotient); | |
1087 | } | |
1088 | else if (SCM_REALP (x)) | |
1089 | { | |
1090 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1091 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1092 | return scm_i_inexact_floor_quotient | |
1093 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1094 | else | |
1095 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1096 | s_scm_floor_quotient); | |
1097 | } | |
1098 | else if (SCM_FRACTIONP (x)) | |
1099 | { | |
1100 | if (SCM_REALP (y)) | |
1101 | return scm_i_inexact_floor_quotient | |
1102 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1103 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1104 | return scm_i_exact_rational_floor_quotient (x, y); | |
1105 | else | |
1106 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1107 | s_scm_floor_quotient); | |
1108 | } | |
1109 | else | |
1110 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1111 | s_scm_floor_quotient); | |
1112 | } | |
1113 | #undef FUNC_NAME | |
1114 | ||
1115 | static SCM | |
1116 | scm_i_inexact_floor_quotient (double x, double y) | |
1117 | { | |
1118 | if (SCM_UNLIKELY (y == 0)) | |
1119 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1120 | else | |
1121 | return scm_from_double (floor (x / y)); | |
1122 | } | |
1123 | ||
1124 | static SCM | |
1125 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1126 | { | |
1127 | return scm_floor_quotient | |
1128 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1129 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1130 | } | |
1131 | ||
1132 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1133 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1134 | ||
1135 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1136 | (SCM x, SCM y), | |
1137 | "Return the real number @var{r} such that\n" | |
1138 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1139 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1140 | "@lisp\n" | |
1141 | "(floor-remainder 123 10) @result{} 3\n" | |
1142 | "(floor-remainder 123 -10) @result{} -7\n" | |
1143 | "(floor-remainder -123 10) @result{} 7\n" | |
1144 | "(floor-remainder -123 -10) @result{} -3\n" | |
1145 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1146 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1147 | "@end lisp") | |
1148 | #define FUNC_NAME s_scm_floor_remainder | |
1149 | { | |
1150 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1151 | { | |
1152 | scm_t_inum xx = SCM_I_INUM (x); | |
1153 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1154 | { | |
1155 | scm_t_inum yy = SCM_I_INUM (y); | |
1156 | if (SCM_UNLIKELY (yy == 0)) | |
1157 | scm_num_overflow (s_scm_floor_remainder); | |
1158 | else | |
1159 | { | |
1160 | scm_t_inum rr = xx % yy; | |
1161 | int needs_adjustment; | |
1162 | ||
1163 | if (SCM_LIKELY (yy > 0)) | |
1164 | needs_adjustment = (rr < 0); | |
1165 | else | |
1166 | needs_adjustment = (rr > 0); | |
1167 | ||
1168 | if (needs_adjustment) | |
1169 | rr += yy; | |
1170 | return SCM_I_MAKINUM (rr); | |
1171 | } | |
1172 | } | |
1173 | else if (SCM_BIGP (y)) | |
1174 | { | |
1175 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1176 | scm_remember_upto_here_1 (y); | |
1177 | if (sign > 0) | |
1178 | { | |
1179 | if (xx < 0) | |
1180 | { | |
1181 | SCM r = scm_i_mkbig (); | |
1182 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1183 | scm_remember_upto_here_1 (y); | |
1184 | return scm_i_normbig (r); | |
1185 | } | |
1186 | else | |
1187 | return x; | |
1188 | } | |
1189 | else if (xx <= 0) | |
1190 | return x; | |
1191 | else | |
1192 | { | |
1193 | SCM r = scm_i_mkbig (); | |
1194 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1195 | scm_remember_upto_here_1 (y); | |
1196 | return scm_i_normbig (r); | |
1197 | } | |
1198 | } | |
1199 | else if (SCM_REALP (y)) | |
1200 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1201 | else if (SCM_FRACTIONP (y)) | |
1202 | return scm_i_exact_rational_floor_remainder (x, y); | |
1203 | else | |
1204 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1205 | s_scm_floor_remainder); | |
1206 | } | |
1207 | else if (SCM_BIGP (x)) | |
1208 | { | |
1209 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1210 | { | |
1211 | scm_t_inum yy = SCM_I_INUM (y); | |
1212 | if (SCM_UNLIKELY (yy == 0)) | |
1213 | scm_num_overflow (s_scm_floor_remainder); | |
1214 | else | |
1215 | { | |
1216 | scm_t_inum rr; | |
1217 | if (yy > 0) | |
1218 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1219 | else | |
1220 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1221 | scm_remember_upto_here_1 (x); | |
1222 | return SCM_I_MAKINUM (rr); | |
1223 | } | |
1224 | } | |
1225 | else if (SCM_BIGP (y)) | |
1226 | { | |
1227 | SCM r = scm_i_mkbig (); | |
1228 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1229 | SCM_I_BIG_MPZ (x), | |
1230 | SCM_I_BIG_MPZ (y)); | |
1231 | scm_remember_upto_here_2 (x, y); | |
1232 | return scm_i_normbig (r); | |
1233 | } | |
1234 | else if (SCM_REALP (y)) | |
1235 | return scm_i_inexact_floor_remainder | |
1236 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1237 | else if (SCM_FRACTIONP (y)) | |
1238 | return scm_i_exact_rational_floor_remainder (x, y); | |
1239 | else | |
1240 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1241 | s_scm_floor_remainder); | |
1242 | } | |
1243 | else if (SCM_REALP (x)) | |
1244 | { | |
1245 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1246 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1247 | return scm_i_inexact_floor_remainder | |
1248 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1249 | else | |
1250 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1251 | s_scm_floor_remainder); | |
1252 | } | |
1253 | else if (SCM_FRACTIONP (x)) | |
1254 | { | |
1255 | if (SCM_REALP (y)) | |
1256 | return scm_i_inexact_floor_remainder | |
1257 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1258 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1259 | return scm_i_exact_rational_floor_remainder (x, y); | |
1260 | else | |
1261 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1262 | s_scm_floor_remainder); | |
1263 | } | |
1264 | else | |
1265 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1266 | s_scm_floor_remainder); | |
1267 | } | |
1268 | #undef FUNC_NAME | |
1269 | ||
1270 | static SCM | |
1271 | scm_i_inexact_floor_remainder (double x, double y) | |
1272 | { | |
1273 | /* Although it would be more efficient to use fmod here, we can't | |
1274 | because it would in some cases produce results inconsistent with | |
1275 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1276 | close). In particular, when x is very close to a multiple of y, | |
1277 | then r might be either 0.0 or y, but those two cases must | |
1278 | correspond to different choices of q. If r = 0.0 then q must be | |
1279 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1280 | and remainder chooses the other, it would be bad. */ | |
1281 | if (SCM_UNLIKELY (y == 0)) | |
1282 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1283 | else | |
1284 | return scm_from_double (x - y * floor (x / y)); | |
1285 | } | |
1286 | ||
1287 | static SCM | |
1288 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1289 | { | |
1290 | SCM xd = scm_denominator (x); | |
1291 | SCM yd = scm_denominator (y); | |
1292 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1293 | scm_product (scm_numerator (y), xd)); | |
1294 | return scm_divide (r1, scm_product (xd, yd)); | |
1295 | } | |
1296 | ||
1297 | ||
1298 | static void scm_i_inexact_floor_divide (double x, double y, | |
1299 | SCM *qp, SCM *rp); | |
1300 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1301 | SCM *qp, SCM *rp); | |
1302 | ||
1303 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1304 | (SCM x, SCM y), | |
1305 | "Return the integer @var{q} and the real number @var{r}\n" | |
1306 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1307 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1308 | "@lisp\n" | |
1309 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1310 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1311 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1312 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1313 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1314 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1315 | "@end lisp") | |
1316 | #define FUNC_NAME s_scm_i_floor_divide | |
1317 | { | |
1318 | SCM q, r; | |
1319 | ||
1320 | scm_floor_divide(x, y, &q, &r); | |
1321 | return scm_values (scm_list_2 (q, r)); | |
1322 | } | |
1323 | #undef FUNC_NAME | |
1324 | ||
1325 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1326 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1327 | ||
1328 | void | |
1329 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1330 | { | |
1331 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1332 | { | |
1333 | scm_t_inum xx = SCM_I_INUM (x); | |
1334 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1335 | { | |
1336 | scm_t_inum yy = SCM_I_INUM (y); | |
1337 | if (SCM_UNLIKELY (yy == 0)) | |
1338 | scm_num_overflow (s_scm_floor_divide); | |
1339 | else | |
1340 | { | |
1341 | scm_t_inum qq = xx / yy; | |
1342 | scm_t_inum rr = xx % yy; | |
1343 | int needs_adjustment; | |
1344 | ||
1345 | if (SCM_LIKELY (yy > 0)) | |
1346 | needs_adjustment = (rr < 0); | |
1347 | else | |
1348 | needs_adjustment = (rr > 0); | |
1349 | ||
1350 | if (needs_adjustment) | |
1351 | { | |
1352 | rr += yy; | |
1353 | qq--; | |
1354 | } | |
1355 | ||
1356 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1357 | *qp = SCM_I_MAKINUM (qq); | |
1358 | else | |
1359 | *qp = scm_i_inum2big (qq); | |
1360 | *rp = SCM_I_MAKINUM (rr); | |
1361 | } | |
1362 | return; | |
1363 | } | |
1364 | else if (SCM_BIGP (y)) | |
1365 | { | |
1366 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1367 | scm_remember_upto_here_1 (y); | |
1368 | if (sign > 0) | |
1369 | { | |
1370 | if (xx < 0) | |
1371 | { | |
1372 | SCM r = scm_i_mkbig (); | |
1373 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1374 | scm_remember_upto_here_1 (y); | |
1375 | *qp = SCM_I_MAKINUM (-1); | |
1376 | *rp = scm_i_normbig (r); | |
1377 | } | |
1378 | else | |
1379 | { | |
1380 | *qp = SCM_INUM0; | |
1381 | *rp = x; | |
1382 | } | |
1383 | } | |
1384 | else if (xx <= 0) | |
1385 | { | |
1386 | *qp = SCM_INUM0; | |
1387 | *rp = x; | |
1388 | } | |
1389 | else | |
1390 | { | |
1391 | SCM r = scm_i_mkbig (); | |
1392 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1393 | scm_remember_upto_here_1 (y); | |
1394 | *qp = SCM_I_MAKINUM (-1); | |
1395 | *rp = scm_i_normbig (r); | |
1396 | } | |
1397 | return; | |
1398 | } | |
1399 | else if (SCM_REALP (y)) | |
1400 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1401 | else if (SCM_FRACTIONP (y)) | |
1402 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1403 | else | |
1404 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1405 | s_scm_floor_divide, qp, rp); | |
1406 | } | |
1407 | else if (SCM_BIGP (x)) | |
1408 | { | |
1409 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1410 | { | |
1411 | scm_t_inum yy = SCM_I_INUM (y); | |
1412 | if (SCM_UNLIKELY (yy == 0)) | |
1413 | scm_num_overflow (s_scm_floor_divide); | |
1414 | else | |
1415 | { | |
1416 | SCM q = scm_i_mkbig (); | |
1417 | SCM r = scm_i_mkbig (); | |
1418 | if (yy > 0) | |
1419 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1420 | SCM_I_BIG_MPZ (x), yy); | |
1421 | else | |
1422 | { | |
1423 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1424 | SCM_I_BIG_MPZ (x), -yy); | |
1425 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1426 | } | |
1427 | scm_remember_upto_here_1 (x); | |
1428 | *qp = scm_i_normbig (q); | |
1429 | *rp = scm_i_normbig (r); | |
1430 | } | |
1431 | return; | |
1432 | } | |
1433 | else if (SCM_BIGP (y)) | |
1434 | { | |
1435 | SCM q = scm_i_mkbig (); | |
1436 | SCM r = scm_i_mkbig (); | |
1437 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1438 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1439 | scm_remember_upto_here_2 (x, y); | |
1440 | *qp = scm_i_normbig (q); | |
1441 | *rp = scm_i_normbig (r); | |
1442 | return; | |
1443 | } | |
1444 | else if (SCM_REALP (y)) | |
1445 | return scm_i_inexact_floor_divide | |
1446 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1447 | else if (SCM_FRACTIONP (y)) | |
1448 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1449 | else | |
1450 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1451 | s_scm_floor_divide, qp, rp); | |
1452 | } | |
1453 | else if (SCM_REALP (x)) | |
1454 | { | |
1455 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1456 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1457 | return scm_i_inexact_floor_divide | |
1458 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1459 | else | |
1460 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1461 | s_scm_floor_divide, qp, rp); | |
1462 | } | |
1463 | else if (SCM_FRACTIONP (x)) | |
1464 | { | |
1465 | if (SCM_REALP (y)) | |
1466 | return scm_i_inexact_floor_divide | |
1467 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1468 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1469 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1470 | else | |
1471 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1472 | s_scm_floor_divide, qp, rp); | |
1473 | } | |
1474 | else | |
1475 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1476 | s_scm_floor_divide, qp, rp); | |
1477 | } | |
1478 | ||
1479 | static void | |
1480 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1481 | { | |
1482 | if (SCM_UNLIKELY (y == 0)) | |
1483 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1484 | else | |
1485 | { | |
1486 | double q = floor (x / y); | |
1487 | double r = x - q * y; | |
1488 | *qp = scm_from_double (q); | |
1489 | *rp = scm_from_double (r); | |
1490 | } | |
1491 | } | |
1492 | ||
1493 | static void | |
1494 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1495 | { | |
1496 | SCM r1; | |
1497 | SCM xd = scm_denominator (x); | |
1498 | SCM yd = scm_denominator (y); | |
1499 | ||
1500 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1501 | scm_product (scm_numerator (y), xd), | |
1502 | qp, &r1); | |
1503 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1504 | } | |
1505 | ||
1506 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1507 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1508 | ||
1509 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1510 | (SCM x, SCM y), | |
1511 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1512 | "@lisp\n" | |
1513 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1514 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1515 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1516 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1517 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1518 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1519 | "@end lisp") | |
1520 | #define FUNC_NAME s_scm_ceiling_quotient | |
1521 | { | |
1522 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1523 | { | |
1524 | scm_t_inum xx = SCM_I_INUM (x); | |
1525 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1526 | { | |
1527 | scm_t_inum yy = SCM_I_INUM (y); | |
1528 | if (SCM_UNLIKELY (yy == 0)) | |
1529 | scm_num_overflow (s_scm_ceiling_quotient); | |
1530 | else | |
1531 | { | |
1532 | scm_t_inum xx1 = xx; | |
1533 | scm_t_inum qq; | |
1534 | if (SCM_LIKELY (yy > 0)) | |
1535 | { | |
1536 | if (SCM_LIKELY (xx >= 0)) | |
1537 | xx1 = xx + yy - 1; | |
1538 | } | |
8f9da340 MW |
1539 | else if (xx < 0) |
1540 | xx1 = xx + yy + 1; | |
1541 | qq = xx1 / yy; | |
1542 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1543 | return SCM_I_MAKINUM (qq); | |
1544 | else | |
1545 | return scm_i_inum2big (qq); | |
1546 | } | |
1547 | } | |
1548 | else if (SCM_BIGP (y)) | |
1549 | { | |
1550 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1551 | scm_remember_upto_here_1 (y); | |
1552 | if (SCM_LIKELY (sign > 0)) | |
1553 | { | |
1554 | if (SCM_LIKELY (xx > 0)) | |
1555 | return SCM_INUM1; | |
1556 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1557 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1558 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1559 | { | |
1560 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1561 | scm_remember_upto_here_1 (y); | |
1562 | return SCM_I_MAKINUM (-1); | |
1563 | } | |
1564 | else | |
1565 | return SCM_INUM0; | |
1566 | } | |
1567 | else if (xx >= 0) | |
1568 | return SCM_INUM0; | |
1569 | else | |
1570 | return SCM_INUM1; | |
1571 | } | |
1572 | else if (SCM_REALP (y)) | |
1573 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1574 | else if (SCM_FRACTIONP (y)) | |
1575 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1576 | else | |
1577 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1578 | s_scm_ceiling_quotient); | |
1579 | } | |
1580 | else if (SCM_BIGP (x)) | |
1581 | { | |
1582 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1583 | { | |
1584 | scm_t_inum yy = SCM_I_INUM (y); | |
1585 | if (SCM_UNLIKELY (yy == 0)) | |
1586 | scm_num_overflow (s_scm_ceiling_quotient); | |
1587 | else if (SCM_UNLIKELY (yy == 1)) | |
1588 | return x; | |
1589 | else | |
1590 | { | |
1591 | SCM q = scm_i_mkbig (); | |
1592 | if (yy > 0) | |
1593 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1594 | else | |
1595 | { | |
1596 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1597 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1598 | } | |
1599 | scm_remember_upto_here_1 (x); | |
1600 | return scm_i_normbig (q); | |
1601 | } | |
1602 | } | |
1603 | else if (SCM_BIGP (y)) | |
1604 | { | |
1605 | SCM q = scm_i_mkbig (); | |
1606 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1607 | SCM_I_BIG_MPZ (x), | |
1608 | SCM_I_BIG_MPZ (y)); | |
1609 | scm_remember_upto_here_2 (x, y); | |
1610 | return scm_i_normbig (q); | |
1611 | } | |
1612 | else if (SCM_REALP (y)) | |
1613 | return scm_i_inexact_ceiling_quotient | |
1614 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1615 | else if (SCM_FRACTIONP (y)) | |
1616 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1617 | else | |
1618 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1619 | s_scm_ceiling_quotient); | |
1620 | } | |
1621 | else if (SCM_REALP (x)) | |
1622 | { | |
1623 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1624 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1625 | return scm_i_inexact_ceiling_quotient | |
1626 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1627 | else | |
1628 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1629 | s_scm_ceiling_quotient); | |
1630 | } | |
1631 | else if (SCM_FRACTIONP (x)) | |
1632 | { | |
1633 | if (SCM_REALP (y)) | |
1634 | return scm_i_inexact_ceiling_quotient | |
1635 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1636 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1637 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1638 | else | |
1639 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1640 | s_scm_ceiling_quotient); | |
1641 | } | |
1642 | else | |
1643 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1644 | s_scm_ceiling_quotient); | |
1645 | } | |
1646 | #undef FUNC_NAME | |
1647 | ||
1648 | static SCM | |
1649 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1650 | { | |
1651 | if (SCM_UNLIKELY (y == 0)) | |
1652 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1653 | else | |
1654 | return scm_from_double (ceil (x / y)); | |
1655 | } | |
1656 | ||
1657 | static SCM | |
1658 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1659 | { | |
1660 | return scm_ceiling_quotient | |
1661 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1662 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1663 | } | |
1664 | ||
1665 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1666 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1667 | ||
1668 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1669 | (SCM x, SCM y), | |
1670 | "Return the real number @var{r} such that\n" | |
1671 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1672 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1673 | "@lisp\n" | |
1674 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1675 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1676 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1677 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1678 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1679 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1680 | "@end lisp") | |
1681 | #define FUNC_NAME s_scm_ceiling_remainder | |
1682 | { | |
1683 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1684 | { | |
1685 | scm_t_inum xx = SCM_I_INUM (x); | |
1686 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1687 | { | |
1688 | scm_t_inum yy = SCM_I_INUM (y); | |
1689 | if (SCM_UNLIKELY (yy == 0)) | |
1690 | scm_num_overflow (s_scm_ceiling_remainder); | |
1691 | else | |
1692 | { | |
1693 | scm_t_inum rr = xx % yy; | |
1694 | int needs_adjustment; | |
1695 | ||
1696 | if (SCM_LIKELY (yy > 0)) | |
1697 | needs_adjustment = (rr > 0); | |
1698 | else | |
1699 | needs_adjustment = (rr < 0); | |
1700 | ||
1701 | if (needs_adjustment) | |
1702 | rr -= yy; | |
1703 | return SCM_I_MAKINUM (rr); | |
1704 | } | |
1705 | } | |
1706 | else if (SCM_BIGP (y)) | |
1707 | { | |
1708 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1709 | scm_remember_upto_here_1 (y); | |
1710 | if (SCM_LIKELY (sign > 0)) | |
1711 | { | |
1712 | if (SCM_LIKELY (xx > 0)) | |
1713 | { | |
1714 | SCM r = scm_i_mkbig (); | |
1715 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1716 | scm_remember_upto_here_1 (y); | |
1717 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1718 | return scm_i_normbig (r); | |
1719 | } | |
1720 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1721 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1722 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1723 | { | |
1724 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1725 | scm_remember_upto_here_1 (y); | |
1726 | return SCM_INUM0; | |
1727 | } | |
1728 | else | |
1729 | return x; | |
1730 | } | |
1731 | else if (xx >= 0) | |
1732 | return x; | |
1733 | else | |
1734 | { | |
1735 | SCM r = scm_i_mkbig (); | |
1736 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1737 | scm_remember_upto_here_1 (y); | |
1738 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1739 | return scm_i_normbig (r); | |
1740 | } | |
1741 | } | |
1742 | else if (SCM_REALP (y)) | |
1743 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1744 | else if (SCM_FRACTIONP (y)) | |
1745 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1746 | else | |
1747 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1748 | s_scm_ceiling_remainder); | |
1749 | } | |
1750 | else if (SCM_BIGP (x)) | |
1751 | { | |
1752 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1753 | { | |
1754 | scm_t_inum yy = SCM_I_INUM (y); | |
1755 | if (SCM_UNLIKELY (yy == 0)) | |
1756 | scm_num_overflow (s_scm_ceiling_remainder); | |
1757 | else | |
1758 | { | |
1759 | scm_t_inum rr; | |
1760 | if (yy > 0) | |
1761 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1762 | else | |
1763 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1764 | scm_remember_upto_here_1 (x); | |
1765 | return SCM_I_MAKINUM (rr); | |
1766 | } | |
1767 | } | |
1768 | else if (SCM_BIGP (y)) | |
1769 | { | |
1770 | SCM r = scm_i_mkbig (); | |
1771 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1772 | SCM_I_BIG_MPZ (x), | |
1773 | SCM_I_BIG_MPZ (y)); | |
1774 | scm_remember_upto_here_2 (x, y); | |
1775 | return scm_i_normbig (r); | |
1776 | } | |
1777 | else if (SCM_REALP (y)) | |
1778 | return scm_i_inexact_ceiling_remainder | |
1779 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1780 | else if (SCM_FRACTIONP (y)) | |
1781 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1782 | else | |
1783 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1784 | s_scm_ceiling_remainder); | |
1785 | } | |
1786 | else if (SCM_REALP (x)) | |
1787 | { | |
1788 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1789 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1790 | return scm_i_inexact_ceiling_remainder | |
1791 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1792 | else | |
1793 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1794 | s_scm_ceiling_remainder); | |
1795 | } | |
1796 | else if (SCM_FRACTIONP (x)) | |
1797 | { | |
1798 | if (SCM_REALP (y)) | |
1799 | return scm_i_inexact_ceiling_remainder | |
1800 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1801 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1802 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1803 | else | |
1804 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1805 | s_scm_ceiling_remainder); | |
1806 | } | |
1807 | else | |
1808 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1809 | s_scm_ceiling_remainder); | |
1810 | } | |
1811 | #undef FUNC_NAME | |
1812 | ||
1813 | static SCM | |
1814 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1815 | { | |
1816 | /* Although it would be more efficient to use fmod here, we can't | |
1817 | because it would in some cases produce results inconsistent with | |
1818 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1819 | close). In particular, when x is very close to a multiple of y, | |
1820 | then r might be either 0.0 or -y, but those two cases must | |
1821 | correspond to different choices of q. If r = 0.0 then q must be | |
1822 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1823 | and remainder chooses the other, it would be bad. */ | |
1824 | if (SCM_UNLIKELY (y == 0)) | |
1825 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1826 | else | |
1827 | return scm_from_double (x - y * ceil (x / y)); | |
1828 | } | |
1829 | ||
1830 | static SCM | |
1831 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1832 | { | |
1833 | SCM xd = scm_denominator (x); | |
1834 | SCM yd = scm_denominator (y); | |
1835 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1836 | scm_product (scm_numerator (y), xd)); | |
1837 | return scm_divide (r1, scm_product (xd, yd)); | |
1838 | } | |
1839 | ||
1840 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1841 | SCM *qp, SCM *rp); | |
1842 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1843 | SCM *qp, SCM *rp); | |
1844 | ||
1845 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1846 | (SCM x, SCM y), | |
1847 | "Return the integer @var{q} and the real number @var{r}\n" | |
1848 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1849 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1850 | "@lisp\n" | |
1851 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
1852 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
1853 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
1854 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
1855 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1856 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1857 | "@end lisp") | |
1858 | #define FUNC_NAME s_scm_i_ceiling_divide | |
1859 | { | |
1860 | SCM q, r; | |
1861 | ||
1862 | scm_ceiling_divide(x, y, &q, &r); | |
1863 | return scm_values (scm_list_2 (q, r)); | |
1864 | } | |
1865 | #undef FUNC_NAME | |
1866 | ||
1867 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
1868 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
1869 | ||
1870 | void | |
1871 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1872 | { | |
1873 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1874 | { | |
1875 | scm_t_inum xx = SCM_I_INUM (x); | |
1876 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1877 | { | |
1878 | scm_t_inum yy = SCM_I_INUM (y); | |
1879 | if (SCM_UNLIKELY (yy == 0)) | |
1880 | scm_num_overflow (s_scm_ceiling_divide); | |
1881 | else | |
1882 | { | |
1883 | scm_t_inum qq = xx / yy; | |
1884 | scm_t_inum rr = xx % yy; | |
1885 | int needs_adjustment; | |
1886 | ||
1887 | if (SCM_LIKELY (yy > 0)) | |
1888 | needs_adjustment = (rr > 0); | |
1889 | else | |
1890 | needs_adjustment = (rr < 0); | |
1891 | ||
1892 | if (needs_adjustment) | |
1893 | { | |
1894 | rr -= yy; | |
1895 | qq++; | |
1896 | } | |
1897 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1898 | *qp = SCM_I_MAKINUM (qq); | |
1899 | else | |
1900 | *qp = scm_i_inum2big (qq); | |
1901 | *rp = SCM_I_MAKINUM (rr); | |
1902 | } | |
1903 | return; | |
1904 | } | |
1905 | else if (SCM_BIGP (y)) | |
1906 | { | |
1907 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1908 | scm_remember_upto_here_1 (y); | |
1909 | if (SCM_LIKELY (sign > 0)) | |
1910 | { | |
1911 | if (SCM_LIKELY (xx > 0)) | |
1912 | { | |
1913 | SCM r = scm_i_mkbig (); | |
1914 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1915 | scm_remember_upto_here_1 (y); | |
1916 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1917 | *qp = SCM_INUM1; | |
1918 | *rp = scm_i_normbig (r); | |
1919 | } | |
1920 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1921 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1922 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1923 | { | |
1924 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1925 | scm_remember_upto_here_1 (y); | |
1926 | *qp = SCM_I_MAKINUM (-1); | |
1927 | *rp = SCM_INUM0; | |
1928 | } | |
1929 | else | |
1930 | { | |
1931 | *qp = SCM_INUM0; | |
1932 | *rp = x; | |
1933 | } | |
1934 | } | |
1935 | else if (xx >= 0) | |
1936 | { | |
1937 | *qp = SCM_INUM0; | |
1938 | *rp = x; | |
1939 | } | |
1940 | else | |
1941 | { | |
1942 | SCM r = scm_i_mkbig (); | |
1943 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1944 | scm_remember_upto_here_1 (y); | |
1945 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1946 | *qp = SCM_INUM1; | |
1947 | *rp = scm_i_normbig (r); | |
1948 | } | |
1949 | return; | |
1950 | } | |
1951 | else if (SCM_REALP (y)) | |
1952 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1953 | else if (SCM_FRACTIONP (y)) | |
1954 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1955 | else | |
1956 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1957 | s_scm_ceiling_divide, qp, rp); | |
1958 | } | |
1959 | else if (SCM_BIGP (x)) | |
1960 | { | |
1961 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1962 | { | |
1963 | scm_t_inum yy = SCM_I_INUM (y); | |
1964 | if (SCM_UNLIKELY (yy == 0)) | |
1965 | scm_num_overflow (s_scm_ceiling_divide); | |
1966 | else | |
1967 | { | |
1968 | SCM q = scm_i_mkbig (); | |
1969 | SCM r = scm_i_mkbig (); | |
1970 | if (yy > 0) | |
1971 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1972 | SCM_I_BIG_MPZ (x), yy); | |
1973 | else | |
1974 | { | |
1975 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1976 | SCM_I_BIG_MPZ (x), -yy); | |
1977 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1978 | } | |
1979 | scm_remember_upto_here_1 (x); | |
1980 | *qp = scm_i_normbig (q); | |
1981 | *rp = scm_i_normbig (r); | |
1982 | } | |
1983 | return; | |
1984 | } | |
1985 | else if (SCM_BIGP (y)) | |
1986 | { | |
1987 | SCM q = scm_i_mkbig (); | |
1988 | SCM r = scm_i_mkbig (); | |
1989 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1990 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1991 | scm_remember_upto_here_2 (x, y); | |
1992 | *qp = scm_i_normbig (q); | |
1993 | *rp = scm_i_normbig (r); | |
1994 | return; | |
1995 | } | |
1996 | else if (SCM_REALP (y)) | |
1997 | return scm_i_inexact_ceiling_divide | |
1998 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1999 | else if (SCM_FRACTIONP (y)) | |
2000 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2001 | else | |
2002 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2003 | s_scm_ceiling_divide, qp, rp); | |
2004 | } | |
2005 | else if (SCM_REALP (x)) | |
2006 | { | |
2007 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2008 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2009 | return scm_i_inexact_ceiling_divide | |
2010 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2011 | else | |
2012 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2013 | s_scm_ceiling_divide, qp, rp); | |
2014 | } | |
2015 | else if (SCM_FRACTIONP (x)) | |
2016 | { | |
2017 | if (SCM_REALP (y)) | |
2018 | return scm_i_inexact_ceiling_divide | |
2019 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2020 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2021 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2022 | else | |
2023 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2024 | s_scm_ceiling_divide, qp, rp); | |
2025 | } | |
2026 | else | |
2027 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2028 | s_scm_ceiling_divide, qp, rp); | |
2029 | } | |
2030 | ||
2031 | static void | |
2032 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2033 | { | |
2034 | if (SCM_UNLIKELY (y == 0)) | |
2035 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2036 | else | |
2037 | { | |
2038 | double q = ceil (x / y); | |
2039 | double r = x - q * y; | |
2040 | *qp = scm_from_double (q); | |
2041 | *rp = scm_from_double (r); | |
2042 | } | |
2043 | } | |
2044 | ||
2045 | static void | |
2046 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2047 | { | |
2048 | SCM r1; | |
2049 | SCM xd = scm_denominator (x); | |
2050 | SCM yd = scm_denominator (y); | |
2051 | ||
2052 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2053 | scm_product (scm_numerator (y), xd), | |
2054 | qp, &r1); | |
2055 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2056 | } | |
2057 | ||
2058 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2059 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2060 | ||
2061 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2062 | (SCM x, SCM y), | |
2063 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2064 | "@lisp\n" | |
2065 | "(truncate-quotient 123 10) @result{} 12\n" | |
2066 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2067 | "(truncate-quotient -123 10) @result{} -12\n" | |
2068 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2069 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2070 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2071 | "@end lisp") | |
2072 | #define FUNC_NAME s_scm_truncate_quotient | |
2073 | { | |
2074 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2075 | { | |
2076 | scm_t_inum xx = SCM_I_INUM (x); | |
2077 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2078 | { | |
2079 | scm_t_inum yy = SCM_I_INUM (y); | |
2080 | if (SCM_UNLIKELY (yy == 0)) | |
2081 | scm_num_overflow (s_scm_truncate_quotient); | |
2082 | else | |
2083 | { | |
2084 | scm_t_inum qq = xx / yy; | |
2085 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2086 | return SCM_I_MAKINUM (qq); | |
2087 | else | |
2088 | return scm_i_inum2big (qq); | |
2089 | } | |
2090 | } | |
2091 | else if (SCM_BIGP (y)) | |
2092 | { | |
2093 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2094 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2095 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2096 | { | |
2097 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2098 | scm_remember_upto_here_1 (y); | |
2099 | return SCM_I_MAKINUM (-1); | |
2100 | } | |
2101 | else | |
2102 | return SCM_INUM0; | |
2103 | } | |
2104 | else if (SCM_REALP (y)) | |
2105 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2106 | else if (SCM_FRACTIONP (y)) | |
2107 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2108 | else | |
2109 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2110 | s_scm_truncate_quotient); | |
2111 | } | |
2112 | else if (SCM_BIGP (x)) | |
2113 | { | |
2114 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2115 | { | |
2116 | scm_t_inum yy = SCM_I_INUM (y); | |
2117 | if (SCM_UNLIKELY (yy == 0)) | |
2118 | scm_num_overflow (s_scm_truncate_quotient); | |
2119 | else if (SCM_UNLIKELY (yy == 1)) | |
2120 | return x; | |
2121 | else | |
2122 | { | |
2123 | SCM q = scm_i_mkbig (); | |
2124 | if (yy > 0) | |
2125 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2126 | else | |
2127 | { | |
2128 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2129 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2130 | } | |
2131 | scm_remember_upto_here_1 (x); | |
2132 | return scm_i_normbig (q); | |
2133 | } | |
2134 | } | |
2135 | else if (SCM_BIGP (y)) | |
2136 | { | |
2137 | SCM q = scm_i_mkbig (); | |
2138 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2139 | SCM_I_BIG_MPZ (x), | |
2140 | SCM_I_BIG_MPZ (y)); | |
2141 | scm_remember_upto_here_2 (x, y); | |
2142 | return scm_i_normbig (q); | |
2143 | } | |
2144 | else if (SCM_REALP (y)) | |
2145 | return scm_i_inexact_truncate_quotient | |
2146 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2147 | else if (SCM_FRACTIONP (y)) | |
2148 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2149 | else | |
2150 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2151 | s_scm_truncate_quotient); | |
2152 | } | |
2153 | else if (SCM_REALP (x)) | |
2154 | { | |
2155 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2156 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2157 | return scm_i_inexact_truncate_quotient | |
2158 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2159 | else | |
2160 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2161 | s_scm_truncate_quotient); | |
2162 | } | |
2163 | else if (SCM_FRACTIONP (x)) | |
2164 | { | |
2165 | if (SCM_REALP (y)) | |
2166 | return scm_i_inexact_truncate_quotient | |
2167 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2168 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2169 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2170 | else | |
2171 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2172 | s_scm_truncate_quotient); | |
2173 | } | |
2174 | else | |
2175 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2176 | s_scm_truncate_quotient); | |
2177 | } | |
2178 | #undef FUNC_NAME | |
2179 | ||
2180 | static SCM | |
2181 | scm_i_inexact_truncate_quotient (double x, double y) | |
2182 | { | |
2183 | if (SCM_UNLIKELY (y == 0)) | |
2184 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2185 | else | |
c251ab63 | 2186 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2187 | } |
2188 | ||
2189 | static SCM | |
2190 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2191 | { | |
2192 | return scm_truncate_quotient | |
2193 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2194 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2195 | } | |
2196 | ||
2197 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2198 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2199 | ||
2200 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2201 | (SCM x, SCM y), | |
2202 | "Return the real number @var{r} such that\n" | |
2203 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2204 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2205 | "@lisp\n" | |
2206 | "(truncate-remainder 123 10) @result{} 3\n" | |
2207 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2208 | "(truncate-remainder -123 10) @result{} -3\n" | |
2209 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2210 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2211 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2212 | "@end lisp") | |
2213 | #define FUNC_NAME s_scm_truncate_remainder | |
2214 | { | |
2215 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2216 | { | |
2217 | scm_t_inum xx = SCM_I_INUM (x); | |
2218 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2219 | { | |
2220 | scm_t_inum yy = SCM_I_INUM (y); | |
2221 | if (SCM_UNLIKELY (yy == 0)) | |
2222 | scm_num_overflow (s_scm_truncate_remainder); | |
2223 | else | |
2224 | return SCM_I_MAKINUM (xx % yy); | |
2225 | } | |
2226 | else if (SCM_BIGP (y)) | |
2227 | { | |
2228 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2229 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2230 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2231 | { | |
2232 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2233 | scm_remember_upto_here_1 (y); | |
2234 | return SCM_INUM0; | |
2235 | } | |
2236 | else | |
2237 | return x; | |
2238 | } | |
2239 | else if (SCM_REALP (y)) | |
2240 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2241 | else if (SCM_FRACTIONP (y)) | |
2242 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2243 | else | |
2244 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2245 | s_scm_truncate_remainder); | |
2246 | } | |
2247 | else if (SCM_BIGP (x)) | |
2248 | { | |
2249 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2250 | { | |
2251 | scm_t_inum yy = SCM_I_INUM (y); | |
2252 | if (SCM_UNLIKELY (yy == 0)) | |
2253 | scm_num_overflow (s_scm_truncate_remainder); | |
2254 | else | |
2255 | { | |
2256 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2257 | (yy > 0) ? yy : -yy) | |
2258 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2259 | scm_remember_upto_here_1 (x); | |
2260 | return SCM_I_MAKINUM (rr); | |
2261 | } | |
2262 | } | |
2263 | else if (SCM_BIGP (y)) | |
2264 | { | |
2265 | SCM r = scm_i_mkbig (); | |
2266 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2267 | SCM_I_BIG_MPZ (x), | |
2268 | SCM_I_BIG_MPZ (y)); | |
2269 | scm_remember_upto_here_2 (x, y); | |
2270 | return scm_i_normbig (r); | |
2271 | } | |
2272 | else if (SCM_REALP (y)) | |
2273 | return scm_i_inexact_truncate_remainder | |
2274 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2275 | else if (SCM_FRACTIONP (y)) | |
2276 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2277 | else | |
2278 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2279 | s_scm_truncate_remainder); | |
2280 | } | |
2281 | else if (SCM_REALP (x)) | |
2282 | { | |
2283 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2284 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2285 | return scm_i_inexact_truncate_remainder | |
2286 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2287 | else | |
2288 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2289 | s_scm_truncate_remainder); | |
2290 | } | |
2291 | else if (SCM_FRACTIONP (x)) | |
2292 | { | |
2293 | if (SCM_REALP (y)) | |
2294 | return scm_i_inexact_truncate_remainder | |
2295 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2296 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2297 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2298 | else | |
2299 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2300 | s_scm_truncate_remainder); | |
2301 | } | |
2302 | else | |
2303 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2304 | s_scm_truncate_remainder); | |
2305 | } | |
2306 | #undef FUNC_NAME | |
2307 | ||
2308 | static SCM | |
2309 | scm_i_inexact_truncate_remainder (double x, double y) | |
2310 | { | |
2311 | /* Although it would be more efficient to use fmod here, we can't | |
2312 | because it would in some cases produce results inconsistent with | |
2313 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2314 | close). In particular, when x is very close to a multiple of y, | |
2315 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2316 | correspond to different choices of q. If quotient chooses one and | |
2317 | remainder chooses the other, it would be bad. */ | |
2318 | if (SCM_UNLIKELY (y == 0)) | |
2319 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2320 | else | |
c251ab63 | 2321 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2322 | } |
2323 | ||
2324 | static SCM | |
2325 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2326 | { | |
2327 | SCM xd = scm_denominator (x); | |
2328 | SCM yd = scm_denominator (y); | |
2329 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2330 | scm_product (scm_numerator (y), xd)); | |
2331 | return scm_divide (r1, scm_product (xd, yd)); | |
2332 | } | |
2333 | ||
2334 | ||
2335 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2336 | SCM *qp, SCM *rp); | |
2337 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2338 | SCM *qp, SCM *rp); | |
2339 | ||
2340 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2341 | (SCM x, SCM y), | |
2342 | "Return the integer @var{q} and the real number @var{r}\n" | |
2343 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2344 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2345 | "@lisp\n" | |
2346 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2347 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2348 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2349 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2350 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2351 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2352 | "@end lisp") | |
2353 | #define FUNC_NAME s_scm_i_truncate_divide | |
2354 | { | |
2355 | SCM q, r; | |
2356 | ||
2357 | scm_truncate_divide(x, y, &q, &r); | |
2358 | return scm_values (scm_list_2 (q, r)); | |
2359 | } | |
2360 | #undef FUNC_NAME | |
2361 | ||
2362 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2363 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2364 | ||
2365 | void | |
2366 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2367 | { | |
2368 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2369 | { | |
2370 | scm_t_inum xx = SCM_I_INUM (x); | |
2371 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2372 | { | |
2373 | scm_t_inum yy = SCM_I_INUM (y); | |
2374 | if (SCM_UNLIKELY (yy == 0)) | |
2375 | scm_num_overflow (s_scm_truncate_divide); | |
2376 | else | |
2377 | { | |
2378 | scm_t_inum qq = xx / yy; | |
2379 | scm_t_inum rr = xx % yy; | |
2380 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2381 | *qp = SCM_I_MAKINUM (qq); | |
2382 | else | |
2383 | *qp = scm_i_inum2big (qq); | |
2384 | *rp = SCM_I_MAKINUM (rr); | |
2385 | } | |
2386 | return; | |
2387 | } | |
2388 | else if (SCM_BIGP (y)) | |
2389 | { | |
2390 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2391 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2392 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2393 | { | |
2394 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2395 | scm_remember_upto_here_1 (y); | |
2396 | *qp = SCM_I_MAKINUM (-1); | |
2397 | *rp = SCM_INUM0; | |
2398 | } | |
2399 | else | |
2400 | { | |
2401 | *qp = SCM_INUM0; | |
2402 | *rp = x; | |
2403 | } | |
2404 | return; | |
2405 | } | |
2406 | else if (SCM_REALP (y)) | |
2407 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2408 | else if (SCM_FRACTIONP (y)) | |
2409 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2410 | else | |
2411 | return two_valued_wta_dispatch_2 | |
2412 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2413 | s_scm_truncate_divide, qp, rp); | |
2414 | } | |
2415 | else if (SCM_BIGP (x)) | |
2416 | { | |
2417 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2418 | { | |
2419 | scm_t_inum yy = SCM_I_INUM (y); | |
2420 | if (SCM_UNLIKELY (yy == 0)) | |
2421 | scm_num_overflow (s_scm_truncate_divide); | |
2422 | else | |
2423 | { | |
2424 | SCM q = scm_i_mkbig (); | |
2425 | scm_t_inum rr; | |
2426 | if (yy > 0) | |
2427 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2428 | SCM_I_BIG_MPZ (x), yy); | |
2429 | else | |
2430 | { | |
2431 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2432 | SCM_I_BIG_MPZ (x), -yy); | |
2433 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2434 | } | |
2435 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2436 | scm_remember_upto_here_1 (x); | |
2437 | *qp = scm_i_normbig (q); | |
2438 | *rp = SCM_I_MAKINUM (rr); | |
2439 | } | |
2440 | return; | |
2441 | } | |
2442 | else if (SCM_BIGP (y)) | |
2443 | { | |
2444 | SCM q = scm_i_mkbig (); | |
2445 | SCM r = scm_i_mkbig (); | |
2446 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2447 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2448 | scm_remember_upto_here_2 (x, y); | |
2449 | *qp = scm_i_normbig (q); | |
2450 | *rp = scm_i_normbig (r); | |
2451 | } | |
2452 | else if (SCM_REALP (y)) | |
2453 | return scm_i_inexact_truncate_divide | |
2454 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2455 | else if (SCM_FRACTIONP (y)) | |
2456 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2457 | else | |
2458 | return two_valued_wta_dispatch_2 | |
2459 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2460 | s_scm_truncate_divide, qp, rp); | |
2461 | } | |
2462 | else if (SCM_REALP (x)) | |
2463 | { | |
2464 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2465 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2466 | return scm_i_inexact_truncate_divide | |
2467 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2468 | else | |
2469 | return two_valued_wta_dispatch_2 | |
2470 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2471 | s_scm_truncate_divide, qp, rp); | |
2472 | } | |
2473 | else if (SCM_FRACTIONP (x)) | |
2474 | { | |
2475 | if (SCM_REALP (y)) | |
2476 | return scm_i_inexact_truncate_divide | |
2477 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2478 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2479 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2480 | else | |
2481 | return two_valued_wta_dispatch_2 | |
2482 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2483 | s_scm_truncate_divide, qp, rp); | |
2484 | } | |
2485 | else | |
2486 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2487 | s_scm_truncate_divide, qp, rp); | |
2488 | } | |
2489 | ||
2490 | static void | |
2491 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2492 | { | |
2493 | if (SCM_UNLIKELY (y == 0)) | |
2494 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2495 | else | |
2496 | { | |
c15fe499 MW |
2497 | double q = trunc (x / y); |
2498 | double r = x - q * y; | |
8f9da340 MW |
2499 | *qp = scm_from_double (q); |
2500 | *rp = scm_from_double (r); | |
2501 | } | |
2502 | } | |
2503 | ||
2504 | static void | |
2505 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2506 | { | |
2507 | SCM r1; | |
2508 | SCM xd = scm_denominator (x); | |
2509 | SCM yd = scm_denominator (y); | |
2510 | ||
2511 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2512 | scm_product (scm_numerator (y), xd), | |
2513 | qp, &r1); | |
2514 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2515 | } | |
2516 | ||
ff62c168 MW |
2517 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2518 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2519 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2520 | |
8f9da340 MW |
2521 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2522 | (SCM x, SCM y), | |
2523 | "Return the integer @var{q} such that\n" | |
2524 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2525 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2526 | "@lisp\n" | |
2527 | "(centered-quotient 123 10) @result{} 12\n" | |
2528 | "(centered-quotient 123 -10) @result{} -12\n" | |
2529 | "(centered-quotient -123 10) @result{} -12\n" | |
2530 | "(centered-quotient -123 -10) @result{} 12\n" | |
2531 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2532 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2533 | "@end lisp") | |
2534 | #define FUNC_NAME s_scm_centered_quotient | |
2535 | { | |
2536 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2537 | { | |
2538 | scm_t_inum xx = SCM_I_INUM (x); | |
2539 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2540 | { | |
2541 | scm_t_inum yy = SCM_I_INUM (y); | |
2542 | if (SCM_UNLIKELY (yy == 0)) | |
2543 | scm_num_overflow (s_scm_centered_quotient); | |
2544 | else | |
2545 | { | |
2546 | scm_t_inum qq = xx / yy; | |
2547 | scm_t_inum rr = xx % yy; | |
2548 | if (SCM_LIKELY (xx > 0)) | |
2549 | { | |
2550 | if (SCM_LIKELY (yy > 0)) | |
2551 | { | |
2552 | if (rr >= (yy + 1) / 2) | |
2553 | qq++; | |
2554 | } | |
2555 | else | |
2556 | { | |
2557 | if (rr >= (1 - yy) / 2) | |
2558 | qq--; | |
2559 | } | |
2560 | } | |
2561 | else | |
2562 | { | |
2563 | if (SCM_LIKELY (yy > 0)) | |
2564 | { | |
2565 | if (rr < -yy / 2) | |
2566 | qq--; | |
2567 | } | |
2568 | else | |
2569 | { | |
2570 | if (rr < yy / 2) | |
2571 | qq++; | |
2572 | } | |
2573 | } | |
2574 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2575 | return SCM_I_MAKINUM (qq); | |
2576 | else | |
2577 | return scm_i_inum2big (qq); | |
2578 | } | |
2579 | } | |
2580 | else if (SCM_BIGP (y)) | |
2581 | { | |
2582 | /* Pass a denormalized bignum version of x (even though it | |
2583 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2584 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2585 | } | |
2586 | else if (SCM_REALP (y)) | |
2587 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2588 | else if (SCM_FRACTIONP (y)) | |
2589 | return scm_i_exact_rational_centered_quotient (x, y); | |
2590 | else | |
2591 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2592 | s_scm_centered_quotient); | |
2593 | } | |
2594 | else if (SCM_BIGP (x)) | |
2595 | { | |
2596 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2597 | { | |
2598 | scm_t_inum yy = SCM_I_INUM (y); | |
2599 | if (SCM_UNLIKELY (yy == 0)) | |
2600 | scm_num_overflow (s_scm_centered_quotient); | |
2601 | else if (SCM_UNLIKELY (yy == 1)) | |
2602 | return x; | |
2603 | else | |
2604 | { | |
2605 | SCM q = scm_i_mkbig (); | |
2606 | scm_t_inum rr; | |
2607 | /* Arrange for rr to initially be non-positive, | |
2608 | because that simplifies the test to see | |
2609 | if it is within the needed bounds. */ | |
2610 | if (yy > 0) | |
2611 | { | |
2612 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2613 | SCM_I_BIG_MPZ (x), yy); | |
2614 | scm_remember_upto_here_1 (x); | |
2615 | if (rr < -yy / 2) | |
2616 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2617 | SCM_I_BIG_MPZ (q), 1); | |
2618 | } | |
2619 | else | |
2620 | { | |
2621 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2622 | SCM_I_BIG_MPZ (x), -yy); | |
2623 | scm_remember_upto_here_1 (x); | |
2624 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2625 | if (rr < yy / 2) | |
2626 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2627 | SCM_I_BIG_MPZ (q), 1); | |
2628 | } | |
2629 | return scm_i_normbig (q); | |
2630 | } | |
2631 | } | |
2632 | else if (SCM_BIGP (y)) | |
2633 | return scm_i_bigint_centered_quotient (x, y); | |
2634 | else if (SCM_REALP (y)) | |
2635 | return scm_i_inexact_centered_quotient | |
2636 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2637 | else if (SCM_FRACTIONP (y)) | |
2638 | return scm_i_exact_rational_centered_quotient (x, y); | |
2639 | else | |
2640 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2641 | s_scm_centered_quotient); | |
2642 | } | |
2643 | else if (SCM_REALP (x)) | |
2644 | { | |
2645 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2646 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2647 | return scm_i_inexact_centered_quotient | |
2648 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2649 | else | |
2650 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2651 | s_scm_centered_quotient); | |
2652 | } | |
2653 | else if (SCM_FRACTIONP (x)) | |
2654 | { | |
2655 | if (SCM_REALP (y)) | |
2656 | return scm_i_inexact_centered_quotient | |
2657 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2658 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2659 | return scm_i_exact_rational_centered_quotient (x, y); | |
2660 | else | |
2661 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2662 | s_scm_centered_quotient); | |
2663 | } | |
2664 | else | |
2665 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2666 | s_scm_centered_quotient); | |
2667 | } | |
2668 | #undef FUNC_NAME | |
2669 | ||
2670 | static SCM | |
2671 | scm_i_inexact_centered_quotient (double x, double y) | |
2672 | { | |
2673 | if (SCM_LIKELY (y > 0)) | |
2674 | return scm_from_double (floor (x/y + 0.5)); | |
2675 | else if (SCM_LIKELY (y < 0)) | |
2676 | return scm_from_double (ceil (x/y - 0.5)); | |
2677 | else if (y == 0) | |
2678 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2679 | else | |
2680 | return scm_nan (); | |
2681 | } | |
2682 | ||
2683 | /* Assumes that both x and y are bigints, though | |
2684 | x might be able to fit into a fixnum. */ | |
2685 | static SCM | |
2686 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2687 | { | |
2688 | SCM q, r, min_r; | |
2689 | ||
2690 | /* Note that x might be small enough to fit into a | |
2691 | fixnum, so we must not let it escape into the wild */ | |
2692 | q = scm_i_mkbig (); | |
2693 | r = scm_i_mkbig (); | |
2694 | ||
2695 | /* min_r will eventually become -abs(y)/2 */ | |
2696 | min_r = scm_i_mkbig (); | |
2697 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2698 | SCM_I_BIG_MPZ (y), 1); | |
2699 | ||
2700 | /* Arrange for rr to initially be non-positive, | |
2701 | because that simplifies the test to see | |
2702 | if it is within the needed bounds. */ | |
2703 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2704 | { | |
2705 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2706 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2707 | scm_remember_upto_here_2 (x, y); | |
2708 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2709 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2710 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2711 | SCM_I_BIG_MPZ (q), 1); | |
2712 | } | |
2713 | else | |
2714 | { | |
2715 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2716 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2717 | scm_remember_upto_here_2 (x, y); | |
2718 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2719 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2720 | SCM_I_BIG_MPZ (q), 1); | |
2721 | } | |
2722 | scm_remember_upto_here_2 (r, min_r); | |
2723 | return scm_i_normbig (q); | |
2724 | } | |
2725 | ||
2726 | static SCM | |
2727 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2728 | { | |
2729 | return scm_centered_quotient | |
2730 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2731 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2732 | } | |
2733 | ||
2734 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2735 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2736 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2737 | ||
2738 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2739 | (SCM x, SCM y), | |
2740 | "Return the real number @var{r} such that\n" | |
2741 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2742 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2743 | "for some integer @var{q}.\n" | |
2744 | "@lisp\n" | |
2745 | "(centered-remainder 123 10) @result{} 3\n" | |
2746 | "(centered-remainder 123 -10) @result{} 3\n" | |
2747 | "(centered-remainder -123 10) @result{} -3\n" | |
2748 | "(centered-remainder -123 -10) @result{} -3\n" | |
2749 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2750 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2751 | "@end lisp") | |
2752 | #define FUNC_NAME s_scm_centered_remainder | |
2753 | { | |
2754 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2755 | { | |
2756 | scm_t_inum xx = SCM_I_INUM (x); | |
2757 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2758 | { | |
2759 | scm_t_inum yy = SCM_I_INUM (y); | |
2760 | if (SCM_UNLIKELY (yy == 0)) | |
2761 | scm_num_overflow (s_scm_centered_remainder); | |
2762 | else | |
2763 | { | |
2764 | scm_t_inum rr = xx % yy; | |
2765 | if (SCM_LIKELY (xx > 0)) | |
2766 | { | |
2767 | if (SCM_LIKELY (yy > 0)) | |
2768 | { | |
2769 | if (rr >= (yy + 1) / 2) | |
2770 | rr -= yy; | |
2771 | } | |
2772 | else | |
2773 | { | |
2774 | if (rr >= (1 - yy) / 2) | |
2775 | rr += yy; | |
2776 | } | |
2777 | } | |
2778 | else | |
2779 | { | |
2780 | if (SCM_LIKELY (yy > 0)) | |
2781 | { | |
2782 | if (rr < -yy / 2) | |
2783 | rr += yy; | |
2784 | } | |
2785 | else | |
2786 | { | |
2787 | if (rr < yy / 2) | |
2788 | rr -= yy; | |
2789 | } | |
2790 | } | |
2791 | return SCM_I_MAKINUM (rr); | |
2792 | } | |
2793 | } | |
2794 | else if (SCM_BIGP (y)) | |
2795 | { | |
2796 | /* Pass a denormalized bignum version of x (even though it | |
2797 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2798 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2799 | } | |
2800 | else if (SCM_REALP (y)) | |
2801 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2802 | else if (SCM_FRACTIONP (y)) | |
2803 | return scm_i_exact_rational_centered_remainder (x, y); | |
2804 | else | |
2805 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2806 | s_scm_centered_remainder); | |
2807 | } | |
2808 | else if (SCM_BIGP (x)) | |
2809 | { | |
2810 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2811 | { | |
2812 | scm_t_inum yy = SCM_I_INUM (y); | |
2813 | if (SCM_UNLIKELY (yy == 0)) | |
2814 | scm_num_overflow (s_scm_centered_remainder); | |
2815 | else | |
2816 | { | |
2817 | scm_t_inum rr; | |
2818 | /* Arrange for rr to initially be non-positive, | |
2819 | because that simplifies the test to see | |
2820 | if it is within the needed bounds. */ | |
2821 | if (yy > 0) | |
2822 | { | |
2823 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2824 | scm_remember_upto_here_1 (x); | |
2825 | if (rr < -yy / 2) | |
2826 | rr += yy; | |
2827 | } | |
2828 | else | |
2829 | { | |
2830 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2831 | scm_remember_upto_here_1 (x); | |
2832 | if (rr < yy / 2) | |
2833 | rr -= yy; | |
2834 | } | |
2835 | return SCM_I_MAKINUM (rr); | |
2836 | } | |
2837 | } | |
2838 | else if (SCM_BIGP (y)) | |
2839 | return scm_i_bigint_centered_remainder (x, y); | |
2840 | else if (SCM_REALP (y)) | |
2841 | return scm_i_inexact_centered_remainder | |
2842 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2843 | else if (SCM_FRACTIONP (y)) | |
2844 | return scm_i_exact_rational_centered_remainder (x, y); | |
2845 | else | |
2846 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2847 | s_scm_centered_remainder); | |
2848 | } | |
2849 | else if (SCM_REALP (x)) | |
2850 | { | |
2851 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2852 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2853 | return scm_i_inexact_centered_remainder | |
2854 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2855 | else | |
2856 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2857 | s_scm_centered_remainder); | |
2858 | } | |
2859 | else if (SCM_FRACTIONP (x)) | |
2860 | { | |
2861 | if (SCM_REALP (y)) | |
2862 | return scm_i_inexact_centered_remainder | |
2863 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2864 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2865 | return scm_i_exact_rational_centered_remainder (x, y); | |
2866 | else | |
2867 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2868 | s_scm_centered_remainder); | |
2869 | } | |
2870 | else | |
2871 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2872 | s_scm_centered_remainder); | |
2873 | } | |
2874 | #undef FUNC_NAME | |
2875 | ||
2876 | static SCM | |
2877 | scm_i_inexact_centered_remainder (double x, double y) | |
2878 | { | |
2879 | double q; | |
2880 | ||
2881 | /* Although it would be more efficient to use fmod here, we can't | |
2882 | because it would in some cases produce results inconsistent with | |
2883 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
2884 | close). In particular, when x-y/2 is very close to a multiple of | |
2885 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
2886 | two cases must correspond to different choices of q. If quotient | |
2887 | chooses one and remainder chooses the other, it would be bad. */ | |
2888 | if (SCM_LIKELY (y > 0)) | |
2889 | q = floor (x/y + 0.5); | |
2890 | else if (SCM_LIKELY (y < 0)) | |
2891 | q = ceil (x/y - 0.5); | |
2892 | else if (y == 0) | |
2893 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
2894 | else | |
2895 | return scm_nan (); | |
2896 | return scm_from_double (x - q * y); | |
2897 | } | |
2898 | ||
2899 | /* Assumes that both x and y are bigints, though | |
2900 | x might be able to fit into a fixnum. */ | |
2901 | static SCM | |
2902 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2903 | { | |
2904 | SCM r, min_r; | |
2905 | ||
2906 | /* Note that x might be small enough to fit into a | |
2907 | fixnum, so we must not let it escape into the wild */ | |
2908 | r = scm_i_mkbig (); | |
2909 | ||
2910 | /* min_r will eventually become -abs(y)/2 */ | |
2911 | min_r = scm_i_mkbig (); | |
2912 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2913 | SCM_I_BIG_MPZ (y), 1); | |
2914 | ||
2915 | /* Arrange for rr to initially be non-positive, | |
2916 | because that simplifies the test to see | |
2917 | if it is within the needed bounds. */ | |
2918 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2919 | { | |
2920 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2921 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2922 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2923 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2924 | mpz_add (SCM_I_BIG_MPZ (r), | |
2925 | SCM_I_BIG_MPZ (r), | |
2926 | SCM_I_BIG_MPZ (y)); | |
2927 | } | |
2928 | else | |
2929 | { | |
2930 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2931 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2932 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2933 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2934 | SCM_I_BIG_MPZ (r), | |
2935 | SCM_I_BIG_MPZ (y)); | |
2936 | } | |
2937 | scm_remember_upto_here_2 (x, y); | |
2938 | return scm_i_normbig (r); | |
2939 | } | |
2940 | ||
2941 | static SCM | |
2942 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
2943 | { | |
2944 | SCM xd = scm_denominator (x); | |
2945 | SCM yd = scm_denominator (y); | |
2946 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2947 | scm_product (scm_numerator (y), xd)); | |
2948 | return scm_divide (r1, scm_product (xd, yd)); | |
2949 | } | |
2950 | ||
2951 | ||
2952 | static void scm_i_inexact_centered_divide (double x, double y, | |
2953 | SCM *qp, SCM *rp); | |
2954 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
2955 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
2956 | SCM *qp, SCM *rp); | |
2957 | ||
2958 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
2959 | (SCM x, SCM y), | |
2960 | "Return the integer @var{q} and the real number @var{r}\n" | |
2961 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2962 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2963 | "@lisp\n" | |
2964 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2965 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2966 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2967 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2968 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2969 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2970 | "@end lisp") | |
2971 | #define FUNC_NAME s_scm_i_centered_divide | |
2972 | { | |
2973 | SCM q, r; | |
2974 | ||
2975 | scm_centered_divide(x, y, &q, &r); | |
2976 | return scm_values (scm_list_2 (q, r)); | |
2977 | } | |
2978 | #undef FUNC_NAME | |
2979 | ||
2980 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2981 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2982 | ||
2983 | void | |
2984 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2985 | { | |
2986 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2987 | { | |
2988 | scm_t_inum xx = SCM_I_INUM (x); | |
2989 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2990 | { | |
2991 | scm_t_inum yy = SCM_I_INUM (y); | |
2992 | if (SCM_UNLIKELY (yy == 0)) | |
2993 | scm_num_overflow (s_scm_centered_divide); | |
2994 | else | |
2995 | { | |
2996 | scm_t_inum qq = xx / yy; | |
2997 | scm_t_inum rr = xx % yy; | |
2998 | if (SCM_LIKELY (xx > 0)) | |
2999 | { | |
3000 | if (SCM_LIKELY (yy > 0)) | |
3001 | { | |
3002 | if (rr >= (yy + 1) / 2) | |
3003 | { qq++; rr -= yy; } | |
3004 | } | |
3005 | else | |
3006 | { | |
3007 | if (rr >= (1 - yy) / 2) | |
3008 | { qq--; rr += yy; } | |
3009 | } | |
3010 | } | |
3011 | else | |
3012 | { | |
3013 | if (SCM_LIKELY (yy > 0)) | |
3014 | { | |
3015 | if (rr < -yy / 2) | |
3016 | { qq--; rr += yy; } | |
3017 | } | |
3018 | else | |
3019 | { | |
3020 | if (rr < yy / 2) | |
3021 | { qq++; rr -= yy; } | |
3022 | } | |
3023 | } | |
3024 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3025 | *qp = SCM_I_MAKINUM (qq); | |
3026 | else | |
3027 | *qp = scm_i_inum2big (qq); | |
3028 | *rp = SCM_I_MAKINUM (rr); | |
3029 | } | |
3030 | return; | |
3031 | } | |
3032 | else if (SCM_BIGP (y)) | |
3033 | { | |
3034 | /* Pass a denormalized bignum version of x (even though it | |
3035 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3036 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3037 | } | |
3038 | else if (SCM_REALP (y)) | |
3039 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3040 | else if (SCM_FRACTIONP (y)) | |
3041 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3042 | else | |
3043 | return two_valued_wta_dispatch_2 | |
3044 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3045 | s_scm_centered_divide, qp, rp); | |
3046 | } | |
3047 | else if (SCM_BIGP (x)) | |
3048 | { | |
3049 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3050 | { | |
3051 | scm_t_inum yy = SCM_I_INUM (y); | |
3052 | if (SCM_UNLIKELY (yy == 0)) | |
3053 | scm_num_overflow (s_scm_centered_divide); | |
3054 | else | |
3055 | { | |
3056 | SCM q = scm_i_mkbig (); | |
3057 | scm_t_inum rr; | |
3058 | /* Arrange for rr to initially be non-positive, | |
3059 | because that simplifies the test to see | |
3060 | if it is within the needed bounds. */ | |
3061 | if (yy > 0) | |
3062 | { | |
3063 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3064 | SCM_I_BIG_MPZ (x), yy); | |
3065 | scm_remember_upto_here_1 (x); | |
3066 | if (rr < -yy / 2) | |
3067 | { | |
3068 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3069 | SCM_I_BIG_MPZ (q), 1); | |
3070 | rr += yy; | |
3071 | } | |
3072 | } | |
3073 | else | |
3074 | { | |
3075 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3076 | SCM_I_BIG_MPZ (x), -yy); | |
3077 | scm_remember_upto_here_1 (x); | |
3078 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3079 | if (rr < yy / 2) | |
3080 | { | |
3081 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3082 | SCM_I_BIG_MPZ (q), 1); | |
3083 | rr -= yy; | |
3084 | } | |
3085 | } | |
3086 | *qp = scm_i_normbig (q); | |
3087 | *rp = SCM_I_MAKINUM (rr); | |
3088 | } | |
3089 | return; | |
3090 | } | |
3091 | else if (SCM_BIGP (y)) | |
3092 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3093 | else if (SCM_REALP (y)) | |
3094 | return scm_i_inexact_centered_divide | |
3095 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3096 | else if (SCM_FRACTIONP (y)) | |
3097 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3098 | else | |
3099 | return two_valued_wta_dispatch_2 | |
3100 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3101 | s_scm_centered_divide, qp, rp); | |
3102 | } | |
3103 | else if (SCM_REALP (x)) | |
3104 | { | |
3105 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3106 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3107 | return scm_i_inexact_centered_divide | |
3108 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3109 | else | |
3110 | return two_valued_wta_dispatch_2 | |
3111 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3112 | s_scm_centered_divide, qp, rp); | |
3113 | } | |
3114 | else if (SCM_FRACTIONP (x)) | |
3115 | { | |
3116 | if (SCM_REALP (y)) | |
3117 | return scm_i_inexact_centered_divide | |
3118 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3119 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3120 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3121 | else | |
3122 | return two_valued_wta_dispatch_2 | |
3123 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3124 | s_scm_centered_divide, qp, rp); | |
3125 | } | |
3126 | else | |
3127 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3128 | s_scm_centered_divide, qp, rp); | |
3129 | } | |
3130 | ||
3131 | static void | |
3132 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3133 | { | |
3134 | double q, r; | |
3135 | ||
3136 | if (SCM_LIKELY (y > 0)) | |
3137 | q = floor (x/y + 0.5); | |
3138 | else if (SCM_LIKELY (y < 0)) | |
3139 | q = ceil (x/y - 0.5); | |
3140 | else if (y == 0) | |
3141 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3142 | else | |
3143 | q = guile_NaN; | |
3144 | r = x - q * y; | |
3145 | *qp = scm_from_double (q); | |
3146 | *rp = scm_from_double (r); | |
3147 | } | |
3148 | ||
3149 | /* Assumes that both x and y are bigints, though | |
3150 | x might be able to fit into a fixnum. */ | |
3151 | static void | |
3152 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3153 | { | |
3154 | SCM q, r, min_r; | |
3155 | ||
3156 | /* Note that x might be small enough to fit into a | |
3157 | fixnum, so we must not let it escape into the wild */ | |
3158 | q = scm_i_mkbig (); | |
3159 | r = scm_i_mkbig (); | |
3160 | ||
3161 | /* min_r will eventually become -abs(y/2) */ | |
3162 | min_r = scm_i_mkbig (); | |
3163 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3164 | SCM_I_BIG_MPZ (y), 1); | |
3165 | ||
3166 | /* Arrange for rr to initially be non-positive, | |
3167 | because that simplifies the test to see | |
3168 | if it is within the needed bounds. */ | |
3169 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3170 | { | |
3171 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3172 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3173 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3174 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3175 | { | |
3176 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3177 | SCM_I_BIG_MPZ (q), 1); | |
3178 | mpz_add (SCM_I_BIG_MPZ (r), | |
3179 | SCM_I_BIG_MPZ (r), | |
3180 | SCM_I_BIG_MPZ (y)); | |
3181 | } | |
3182 | } | |
3183 | else | |
3184 | { | |
3185 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3186 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3187 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3188 | { | |
3189 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3190 | SCM_I_BIG_MPZ (q), 1); | |
3191 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3192 | SCM_I_BIG_MPZ (r), | |
3193 | SCM_I_BIG_MPZ (y)); | |
3194 | } | |
3195 | } | |
3196 | scm_remember_upto_here_2 (x, y); | |
3197 | *qp = scm_i_normbig (q); | |
3198 | *rp = scm_i_normbig (r); | |
3199 | } | |
3200 | ||
3201 | static void | |
3202 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3203 | { | |
3204 | SCM r1; | |
3205 | SCM xd = scm_denominator (x); | |
3206 | SCM yd = scm_denominator (y); | |
3207 | ||
3208 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3209 | scm_product (scm_numerator (y), xd), | |
3210 | qp, &r1); | |
3211 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3212 | } | |
3213 | ||
3214 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3215 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3216 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3217 | ||
3218 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3219 | (SCM x, SCM y), |
8f9da340 MW |
3220 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3221 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3222 | "@lisp\n" |
8f9da340 MW |
3223 | "(round-quotient 123 10) @result{} 12\n" |
3224 | "(round-quotient 123 -10) @result{} -12\n" | |
3225 | "(round-quotient -123 10) @result{} -12\n" | |
3226 | "(round-quotient -123 -10) @result{} 12\n" | |
3227 | "(round-quotient 125 10) @result{} 12\n" | |
3228 | "(round-quotient 127 10) @result{} 13\n" | |
3229 | "(round-quotient 135 10) @result{} 14\n" | |
3230 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3231 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3232 | "@end lisp") |
8f9da340 | 3233 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3234 | { |
3235 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3236 | { | |
4a46bc2a | 3237 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3238 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3239 | { | |
3240 | scm_t_inum yy = SCM_I_INUM (y); | |
3241 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3242 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3243 | else |
3244 | { | |
ff62c168 | 3245 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3246 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3247 | scm_t_inum ay = yy; |
3248 | scm_t_inum r2 = 2 * rr; | |
3249 | ||
3250 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3251 | { |
8f9da340 MW |
3252 | ay = -ay; |
3253 | r2 = -r2; | |
3254 | } | |
3255 | ||
3256 | if (qq & 1L) | |
3257 | { | |
3258 | if (r2 >= ay) | |
3259 | qq++; | |
3260 | else if (r2 <= -ay) | |
3261 | qq--; | |
ff62c168 MW |
3262 | } |
3263 | else | |
3264 | { | |
8f9da340 MW |
3265 | if (r2 > ay) |
3266 | qq++; | |
3267 | else if (r2 < -ay) | |
3268 | qq--; | |
ff62c168 | 3269 | } |
4a46bc2a MW |
3270 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3271 | return SCM_I_MAKINUM (qq); | |
3272 | else | |
3273 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3274 | } |
3275 | } | |
3276 | else if (SCM_BIGP (y)) | |
3277 | { | |
3278 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3279 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3280 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3281 | } |
3282 | else if (SCM_REALP (y)) | |
8f9da340 | 3283 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3284 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3285 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3286 | else |
8f9da340 MW |
3287 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3288 | s_scm_round_quotient); | |
ff62c168 MW |
3289 | } |
3290 | else if (SCM_BIGP (x)) | |
3291 | { | |
3292 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3293 | { | |
3294 | scm_t_inum yy = SCM_I_INUM (y); | |
3295 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3296 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3297 | else if (SCM_UNLIKELY (yy == 1)) |
3298 | return x; | |
ff62c168 MW |
3299 | else |
3300 | { | |
3301 | SCM q = scm_i_mkbig (); | |
3302 | scm_t_inum rr; | |
8f9da340 MW |
3303 | int needs_adjustment; |
3304 | ||
ff62c168 MW |
3305 | if (yy > 0) |
3306 | { | |
8f9da340 MW |
3307 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3308 | SCM_I_BIG_MPZ (x), yy); | |
3309 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3310 | needs_adjustment = (2*rr >= yy); | |
3311 | else | |
3312 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3313 | } |
3314 | else | |
3315 | { | |
3316 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3317 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3318 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3319 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3320 | needs_adjustment = (2*rr <= yy); | |
3321 | else | |
3322 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3323 | } |
8f9da340 MW |
3324 | scm_remember_upto_here_1 (x); |
3325 | if (needs_adjustment) | |
3326 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3327 | return scm_i_normbig (q); |
3328 | } | |
3329 | } | |
3330 | else if (SCM_BIGP (y)) | |
8f9da340 | 3331 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3332 | else if (SCM_REALP (y)) |
8f9da340 | 3333 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3334 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3335 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3336 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3337 | else |
8f9da340 MW |
3338 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3339 | s_scm_round_quotient); | |
ff62c168 MW |
3340 | } |
3341 | else if (SCM_REALP (x)) | |
3342 | { | |
3343 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3344 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3345 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3346 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3347 | else | |
8f9da340 MW |
3348 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3349 | s_scm_round_quotient); | |
ff62c168 MW |
3350 | } |
3351 | else if (SCM_FRACTIONP (x)) | |
3352 | { | |
3353 | if (SCM_REALP (y)) | |
8f9da340 | 3354 | return scm_i_inexact_round_quotient |
ff62c168 | 3355 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3356 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3357 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3358 | else |
8f9da340 MW |
3359 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3360 | s_scm_round_quotient); | |
ff62c168 MW |
3361 | } |
3362 | else | |
8f9da340 MW |
3363 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3364 | s_scm_round_quotient); | |
ff62c168 MW |
3365 | } |
3366 | #undef FUNC_NAME | |
3367 | ||
3368 | static SCM | |
8f9da340 | 3369 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3370 | { |
8f9da340 MW |
3371 | if (SCM_UNLIKELY (y == 0)) |
3372 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3373 | else |
8f9da340 | 3374 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3375 | } |
3376 | ||
3377 | /* Assumes that both x and y are bigints, though | |
3378 | x might be able to fit into a fixnum. */ | |
3379 | static SCM | |
8f9da340 | 3380 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3381 | { |
8f9da340 MW |
3382 | SCM q, r, r2; |
3383 | int cmp, needs_adjustment; | |
ff62c168 MW |
3384 | |
3385 | /* Note that x might be small enough to fit into a | |
3386 | fixnum, so we must not let it escape into the wild */ | |
3387 | q = scm_i_mkbig (); | |
3388 | r = scm_i_mkbig (); | |
8f9da340 | 3389 | r2 = scm_i_mkbig (); |
ff62c168 | 3390 | |
8f9da340 MW |
3391 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3392 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3393 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3394 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3395 | |
8f9da340 MW |
3396 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3397 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3398 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3399 | else |
8f9da340 MW |
3400 | needs_adjustment = (cmp > 0); |
3401 | scm_remember_upto_here_2 (r2, y); | |
3402 | ||
3403 | if (needs_adjustment) | |
3404 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3405 | ||
ff62c168 MW |
3406 | return scm_i_normbig (q); |
3407 | } | |
3408 | ||
ff62c168 | 3409 | static SCM |
8f9da340 | 3410 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3411 | { |
8f9da340 | 3412 | return scm_round_quotient |
03ddd15b MW |
3413 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3414 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3415 | } |
3416 | ||
8f9da340 MW |
3417 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3418 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3419 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3420 | |
8f9da340 | 3421 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3422 | (SCM x, SCM y), |
3423 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3424 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3425 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3426 | "nearest integer, with ties going to the nearest\n" | |
3427 | "even integer.\n" | |
ff62c168 | 3428 | "@lisp\n" |
8f9da340 MW |
3429 | "(round-remainder 123 10) @result{} 3\n" |
3430 | "(round-remainder 123 -10) @result{} 3\n" | |
3431 | "(round-remainder -123 10) @result{} -3\n" | |
3432 | "(round-remainder -123 -10) @result{} -3\n" | |
3433 | "(round-remainder 125 10) @result{} 5\n" | |
3434 | "(round-remainder 127 10) @result{} -3\n" | |
3435 | "(round-remainder 135 10) @result{} -5\n" | |
3436 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3437 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3438 | "@end lisp") |
8f9da340 | 3439 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3440 | { |
3441 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3442 | { | |
4a46bc2a | 3443 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3444 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3445 | { | |
3446 | scm_t_inum yy = SCM_I_INUM (y); | |
3447 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3448 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3449 | else |
3450 | { | |
8f9da340 | 3451 | scm_t_inum qq = xx / yy; |
ff62c168 | 3452 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3453 | scm_t_inum ay = yy; |
3454 | scm_t_inum r2 = 2 * rr; | |
3455 | ||
3456 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3457 | { |
8f9da340 MW |
3458 | ay = -ay; |
3459 | r2 = -r2; | |
3460 | } | |
3461 | ||
3462 | if (qq & 1L) | |
3463 | { | |
3464 | if (r2 >= ay) | |
3465 | rr -= yy; | |
3466 | else if (r2 <= -ay) | |
3467 | rr += yy; | |
ff62c168 MW |
3468 | } |
3469 | else | |
3470 | { | |
8f9da340 MW |
3471 | if (r2 > ay) |
3472 | rr -= yy; | |
3473 | else if (r2 < -ay) | |
3474 | rr += yy; | |
ff62c168 MW |
3475 | } |
3476 | return SCM_I_MAKINUM (rr); | |
3477 | } | |
3478 | } | |
3479 | else if (SCM_BIGP (y)) | |
3480 | { | |
3481 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3482 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3483 | return scm_i_bigint_round_remainder | |
3484 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3485 | } |
3486 | else if (SCM_REALP (y)) | |
8f9da340 | 3487 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3488 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3489 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3490 | else |
8f9da340 MW |
3491 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3492 | s_scm_round_remainder); | |
ff62c168 MW |
3493 | } |
3494 | else if (SCM_BIGP (x)) | |
3495 | { | |
3496 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3497 | { | |
3498 | scm_t_inum yy = SCM_I_INUM (y); | |
3499 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3500 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3501 | else |
3502 | { | |
8f9da340 | 3503 | SCM q = scm_i_mkbig (); |
ff62c168 | 3504 | scm_t_inum rr; |
8f9da340 MW |
3505 | int needs_adjustment; |
3506 | ||
ff62c168 MW |
3507 | if (yy > 0) |
3508 | { | |
8f9da340 MW |
3509 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3510 | SCM_I_BIG_MPZ (x), yy); | |
3511 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3512 | needs_adjustment = (2*rr >= yy); | |
3513 | else | |
3514 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3515 | } |
3516 | else | |
3517 | { | |
8f9da340 MW |
3518 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3519 | SCM_I_BIG_MPZ (x), -yy); | |
3520 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3521 | needs_adjustment = (2*rr <= yy); | |
3522 | else | |
3523 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3524 | } |
8f9da340 MW |
3525 | scm_remember_upto_here_2 (x, q); |
3526 | if (needs_adjustment) | |
3527 | rr -= yy; | |
ff62c168 MW |
3528 | return SCM_I_MAKINUM (rr); |
3529 | } | |
3530 | } | |
3531 | else if (SCM_BIGP (y)) | |
8f9da340 | 3532 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3533 | else if (SCM_REALP (y)) |
8f9da340 | 3534 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3535 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3536 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3537 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3538 | else |
8f9da340 MW |
3539 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3540 | s_scm_round_remainder); | |
ff62c168 MW |
3541 | } |
3542 | else if (SCM_REALP (x)) | |
3543 | { | |
3544 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3545 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3546 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3547 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3548 | else | |
8f9da340 MW |
3549 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3550 | s_scm_round_remainder); | |
ff62c168 MW |
3551 | } |
3552 | else if (SCM_FRACTIONP (x)) | |
3553 | { | |
3554 | if (SCM_REALP (y)) | |
8f9da340 | 3555 | return scm_i_inexact_round_remainder |
ff62c168 | 3556 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3557 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3558 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3559 | else |
8f9da340 MW |
3560 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3561 | s_scm_round_remainder); | |
ff62c168 MW |
3562 | } |
3563 | else | |
8f9da340 MW |
3564 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3565 | s_scm_round_remainder); | |
ff62c168 MW |
3566 | } |
3567 | #undef FUNC_NAME | |
3568 | ||
3569 | static SCM | |
8f9da340 | 3570 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3571 | { |
ff62c168 MW |
3572 | /* Although it would be more efficient to use fmod here, we can't |
3573 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3574 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3575 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3576 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3577 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3578 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3579 | |
3580 | if (SCM_UNLIKELY (y == 0)) | |
3581 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3582 | else |
8f9da340 MW |
3583 | { |
3584 | double q = scm_c_round (x / y); | |
3585 | return scm_from_double (x - q * y); | |
3586 | } | |
ff62c168 MW |
3587 | } |
3588 | ||
3589 | /* Assumes that both x and y are bigints, though | |
3590 | x might be able to fit into a fixnum. */ | |
3591 | static SCM | |
8f9da340 | 3592 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3593 | { |
8f9da340 MW |
3594 | SCM q, r, r2; |
3595 | int cmp, needs_adjustment; | |
ff62c168 MW |
3596 | |
3597 | /* Note that x might be small enough to fit into a | |
3598 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3599 | q = scm_i_mkbig (); |
ff62c168 | 3600 | r = scm_i_mkbig (); |
8f9da340 | 3601 | r2 = scm_i_mkbig (); |
ff62c168 | 3602 | |
8f9da340 MW |
3603 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3604 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3605 | scm_remember_upto_here_1 (x); | |
3606 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3607 | |
8f9da340 MW |
3608 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3609 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3610 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3611 | else |
8f9da340 MW |
3612 | needs_adjustment = (cmp > 0); |
3613 | scm_remember_upto_here_2 (q, r2); | |
3614 | ||
3615 | if (needs_adjustment) | |
3616 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3617 | ||
3618 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3619 | return scm_i_normbig (r); |
3620 | } | |
3621 | ||
ff62c168 | 3622 | static SCM |
8f9da340 | 3623 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3624 | { |
03ddd15b MW |
3625 | SCM xd = scm_denominator (x); |
3626 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3627 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3628 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3629 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3630 | } |
3631 | ||
3632 | ||
8f9da340 MW |
3633 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3634 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3635 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3636 | |
8f9da340 | 3637 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3638 | (SCM x, SCM y), |
3639 | "Return the integer @var{q} and the real number @var{r}\n" | |
3640 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3641 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3642 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3643 | "@lisp\n" |
8f9da340 MW |
3644 | "(round/ 123 10) @result{} 12 and 3\n" |
3645 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3646 | "(round/ -123 10) @result{} -12 and -3\n" | |
3647 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3648 | "(round/ 125 10) @result{} 12 and 5\n" | |
3649 | "(round/ 127 10) @result{} 13 and -3\n" | |
3650 | "(round/ 135 10) @result{} 14 and -5\n" | |
3651 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3652 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3653 | "@end lisp") |
8f9da340 | 3654 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3655 | { |
3656 | SCM q, r; | |
3657 | ||
8f9da340 | 3658 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3659 | return scm_values (scm_list_2 (q, r)); |
3660 | } | |
3661 | #undef FUNC_NAME | |
3662 | ||
8f9da340 MW |
3663 | #define s_scm_round_divide s_scm_i_round_divide |
3664 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3665 | |
3666 | void | |
8f9da340 | 3667 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3668 | { |
3669 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3670 | { | |
4a46bc2a | 3671 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3672 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3673 | { | |
3674 | scm_t_inum yy = SCM_I_INUM (y); | |
3675 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3676 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3677 | else |
3678 | { | |
ff62c168 | 3679 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3680 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3681 | scm_t_inum ay = yy; |
3682 | scm_t_inum r2 = 2 * rr; | |
3683 | ||
3684 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3685 | { |
8f9da340 MW |
3686 | ay = -ay; |
3687 | r2 = -r2; | |
3688 | } | |
3689 | ||
3690 | if (qq & 1L) | |
3691 | { | |
3692 | if (r2 >= ay) | |
3693 | { qq++; rr -= yy; } | |
3694 | else if (r2 <= -ay) | |
3695 | { qq--; rr += yy; } | |
ff62c168 MW |
3696 | } |
3697 | else | |
3698 | { | |
8f9da340 MW |
3699 | if (r2 > ay) |
3700 | { qq++; rr -= yy; } | |
3701 | else if (r2 < -ay) | |
3702 | { qq--; rr += yy; } | |
ff62c168 | 3703 | } |
4a46bc2a | 3704 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3705 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3706 | else |
5fbf680b MW |
3707 | *qp = scm_i_inum2big (qq); |
3708 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3709 | } |
5fbf680b | 3710 | return; |
ff62c168 MW |
3711 | } |
3712 | else if (SCM_BIGP (y)) | |
3713 | { | |
3714 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3715 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3716 | return scm_i_bigint_round_divide | |
3717 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3718 | } |
3719 | else if (SCM_REALP (y)) | |
8f9da340 | 3720 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3721 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3722 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3723 | else |
8f9da340 MW |
3724 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3725 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3726 | } |
3727 | else if (SCM_BIGP (x)) | |
3728 | { | |
3729 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3730 | { | |
3731 | scm_t_inum yy = SCM_I_INUM (y); | |
3732 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3733 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3734 | else |
3735 | { | |
3736 | SCM q = scm_i_mkbig (); | |
3737 | scm_t_inum rr; | |
8f9da340 MW |
3738 | int needs_adjustment; |
3739 | ||
ff62c168 MW |
3740 | if (yy > 0) |
3741 | { | |
8f9da340 MW |
3742 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3743 | SCM_I_BIG_MPZ (x), yy); | |
3744 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3745 | needs_adjustment = (2*rr >= yy); | |
3746 | else | |
3747 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3748 | } |
3749 | else | |
3750 | { | |
3751 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3752 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3753 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3754 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3755 | needs_adjustment = (2*rr <= yy); | |
3756 | else | |
3757 | needs_adjustment = (2*rr < yy); | |
3758 | } | |
3759 | scm_remember_upto_here_1 (x); | |
3760 | if (needs_adjustment) | |
3761 | { | |
3762 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3763 | rr -= yy; | |
ff62c168 | 3764 | } |
5fbf680b MW |
3765 | *qp = scm_i_normbig (q); |
3766 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3767 | } |
5fbf680b | 3768 | return; |
ff62c168 MW |
3769 | } |
3770 | else if (SCM_BIGP (y)) | |
8f9da340 | 3771 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3772 | else if (SCM_REALP (y)) |
8f9da340 | 3773 | return scm_i_inexact_round_divide |
5fbf680b | 3774 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3775 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3776 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3777 | else |
8f9da340 MW |
3778 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3779 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3780 | } |
3781 | else if (SCM_REALP (x)) | |
3782 | { | |
3783 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3784 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3785 | return scm_i_inexact_round_divide |
5fbf680b | 3786 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3787 | else |
8f9da340 MW |
3788 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3789 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3790 | } |
3791 | else if (SCM_FRACTIONP (x)) | |
3792 | { | |
3793 | if (SCM_REALP (y)) | |
8f9da340 | 3794 | return scm_i_inexact_round_divide |
5fbf680b | 3795 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3796 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3797 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3798 | else |
8f9da340 MW |
3799 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3800 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3801 | } |
3802 | else | |
8f9da340 MW |
3803 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3804 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3805 | } |
ff62c168 | 3806 | |
5fbf680b | 3807 | static void |
8f9da340 | 3808 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3809 | { |
8f9da340 MW |
3810 | if (SCM_UNLIKELY (y == 0)) |
3811 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3812 | else |
8f9da340 MW |
3813 | { |
3814 | double q = scm_c_round (x / y); | |
3815 | double r = x - q * y; | |
3816 | *qp = scm_from_double (q); | |
3817 | *rp = scm_from_double (r); | |
3818 | } | |
ff62c168 MW |
3819 | } |
3820 | ||
3821 | /* Assumes that both x and y are bigints, though | |
3822 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3823 | static void |
8f9da340 | 3824 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3825 | { |
8f9da340 MW |
3826 | SCM q, r, r2; |
3827 | int cmp, needs_adjustment; | |
ff62c168 MW |
3828 | |
3829 | /* Note that x might be small enough to fit into a | |
3830 | fixnum, so we must not let it escape into the wild */ | |
3831 | q = scm_i_mkbig (); | |
3832 | r = scm_i_mkbig (); | |
8f9da340 | 3833 | r2 = scm_i_mkbig (); |
ff62c168 | 3834 | |
8f9da340 MW |
3835 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3836 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3837 | scm_remember_upto_here_1 (x); | |
3838 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3839 | |
8f9da340 MW |
3840 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3841 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3842 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3843 | else |
8f9da340 MW |
3844 | needs_adjustment = (cmp > 0); |
3845 | ||
3846 | if (needs_adjustment) | |
ff62c168 | 3847 | { |
8f9da340 MW |
3848 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3849 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3850 | } |
8f9da340 MW |
3851 | |
3852 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
3853 | *qp = scm_i_normbig (q); |
3854 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
3855 | } |
3856 | ||
5fbf680b | 3857 | static void |
8f9da340 | 3858 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3859 | { |
03ddd15b MW |
3860 | SCM r1; |
3861 | SCM xd = scm_denominator (x); | |
3862 | SCM yd = scm_denominator (y); | |
3863 | ||
8f9da340 MW |
3864 | scm_round_divide (scm_product (scm_numerator (x), yd), |
3865 | scm_product (scm_numerator (y), xd), | |
3866 | qp, &r1); | |
03ddd15b | 3867 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3868 | } |
3869 | ||
3870 | ||
78d3deb1 AW |
3871 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
3872 | (SCM x, SCM y, SCM rest), | |
3873 | "Return the greatest common divisor of all parameter values.\n" | |
3874 | "If called without arguments, 0 is returned.") | |
3875 | #define FUNC_NAME s_scm_i_gcd | |
3876 | { | |
3877 | while (!scm_is_null (rest)) | |
3878 | { x = scm_gcd (x, y); | |
3879 | y = scm_car (rest); | |
3880 | rest = scm_cdr (rest); | |
3881 | } | |
3882 | return scm_gcd (x, y); | |
3883 | } | |
3884 | #undef FUNC_NAME | |
3885 | ||
3886 | #define s_gcd s_scm_i_gcd | |
3887 | #define g_gcd g_scm_i_gcd | |
3888 | ||
0f2d19dd | 3889 | SCM |
6e8d25a6 | 3890 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 3891 | { |
a2dead1b | 3892 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
1dd79792 | 3893 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 3894 | |
a2dead1b | 3895 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 3896 | { |
a2dead1b | 3897 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 3898 | { |
e25f3727 AW |
3899 | scm_t_inum xx = SCM_I_INUM (x); |
3900 | scm_t_inum yy = SCM_I_INUM (y); | |
3901 | scm_t_inum u = xx < 0 ? -xx : xx; | |
3902 | scm_t_inum v = yy < 0 ? -yy : yy; | |
3903 | scm_t_inum result; | |
a2dead1b | 3904 | if (SCM_UNLIKELY (xx == 0)) |
0aacf84e | 3905 | result = v; |
a2dead1b | 3906 | else if (SCM_UNLIKELY (yy == 0)) |
0aacf84e MD |
3907 | result = u; |
3908 | else | |
3909 | { | |
a2dead1b | 3910 | int k = 0; |
0aacf84e | 3911 | /* Determine a common factor 2^k */ |
a2dead1b | 3912 | while (((u | v) & 1) == 0) |
0aacf84e | 3913 | { |
a2dead1b | 3914 | k++; |
0aacf84e MD |
3915 | u >>= 1; |
3916 | v >>= 1; | |
3917 | } | |
3918 | /* Now, any factor 2^n can be eliminated */ | |
a2dead1b MW |
3919 | if ((u & 1) == 0) |
3920 | while ((u & 1) == 0) | |
3921 | u >>= 1; | |
0aacf84e | 3922 | else |
a2dead1b MW |
3923 | while ((v & 1) == 0) |
3924 | v >>= 1; | |
3925 | /* Both u and v are now odd. Subtract the smaller one | |
3926 | from the larger one to produce an even number, remove | |
3927 | more factors of two, and repeat. */ | |
3928 | while (u != v) | |
0aacf84e | 3929 | { |
a2dead1b MW |
3930 | if (u > v) |
3931 | { | |
3932 | u -= v; | |
3933 | while ((u & 1) == 0) | |
3934 | u >>= 1; | |
3935 | } | |
3936 | else | |
3937 | { | |
3938 | v -= u; | |
3939 | while ((v & 1) == 0) | |
3940 | v >>= 1; | |
3941 | } | |
0aacf84e | 3942 | } |
a2dead1b | 3943 | result = u << k; |
0aacf84e MD |
3944 | } |
3945 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 3946 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3947 | : scm_i_inum2big (result)); |
ca46fb90 RB |
3948 | } |
3949 | else if (SCM_BIGP (y)) | |
3950 | { | |
0bff4dce KR |
3951 | SCM_SWAP (x, y); |
3952 | goto big_inum; | |
ca46fb90 RB |
3953 | } |
3954 | else | |
3955 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 3956 | } |
ca46fb90 RB |
3957 | else if (SCM_BIGP (x)) |
3958 | { | |
e11e83f3 | 3959 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3960 | { |
e25f3727 AW |
3961 | scm_t_bits result; |
3962 | scm_t_inum yy; | |
0bff4dce | 3963 | big_inum: |
e11e83f3 | 3964 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
3965 | if (yy == 0) |
3966 | return scm_abs (x); | |
0aacf84e MD |
3967 | if (yy < 0) |
3968 | yy = -yy; | |
ca46fb90 RB |
3969 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
3970 | scm_remember_upto_here_1 (x); | |
0aacf84e | 3971 | return (SCM_POSFIXABLE (result) |
d956fa6f | 3972 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3973 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
3974 | } |
3975 | else if (SCM_BIGP (y)) | |
3976 | { | |
3977 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
3978 | mpz_gcd (SCM_I_BIG_MPZ (result), |
3979 | SCM_I_BIG_MPZ (x), | |
3980 | SCM_I_BIG_MPZ (y)); | |
3981 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
3982 | return scm_i_normbig (result); |
3983 | } | |
3984 | else | |
3985 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 3986 | } |
ca46fb90 | 3987 | else |
09fb7599 | 3988 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
3989 | } |
3990 | ||
78d3deb1 AW |
3991 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
3992 | (SCM x, SCM y, SCM rest), | |
3993 | "Return the least common multiple of the arguments.\n" | |
3994 | "If called without arguments, 1 is returned.") | |
3995 | #define FUNC_NAME s_scm_i_lcm | |
3996 | { | |
3997 | while (!scm_is_null (rest)) | |
3998 | { x = scm_lcm (x, y); | |
3999 | y = scm_car (rest); | |
4000 | rest = scm_cdr (rest); | |
4001 | } | |
4002 | return scm_lcm (x, y); | |
4003 | } | |
4004 | #undef FUNC_NAME | |
4005 | ||
4006 | #define s_lcm s_scm_i_lcm | |
4007 | #define g_lcm g_scm_i_lcm | |
4008 | ||
0f2d19dd | 4009 | SCM |
6e8d25a6 | 4010 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4011 | { |
ca46fb90 RB |
4012 | if (SCM_UNBNDP (n2)) |
4013 | { | |
4014 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
4015 | return SCM_I_MAKINUM (1L); |
4016 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 4017 | } |
09fb7599 | 4018 | |
e11e83f3 | 4019 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 4020 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 4021 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 4022 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 4023 | |
e11e83f3 | 4024 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 4025 | { |
e11e83f3 | 4026 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4027 | { |
4028 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4029 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4030 | return d; |
4031 | else | |
4032 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4033 | } | |
4034 | else | |
4035 | { | |
4036 | /* inum n1, big n2 */ | |
4037 | inumbig: | |
4038 | { | |
4039 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4040 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4041 | if (nn1 == 0) return SCM_INUM0; |
4042 | if (nn1 < 0) nn1 = - nn1; | |
4043 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4044 | scm_remember_upto_here_1 (n2); | |
4045 | return result; | |
4046 | } | |
4047 | } | |
4048 | } | |
4049 | else | |
4050 | { | |
4051 | /* big n1 */ | |
e11e83f3 | 4052 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4053 | { |
4054 | SCM_SWAP (n1, n2); | |
4055 | goto inumbig; | |
4056 | } | |
4057 | else | |
4058 | { | |
4059 | SCM result = scm_i_mkbig (); | |
4060 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4061 | SCM_I_BIG_MPZ (n1), | |
4062 | SCM_I_BIG_MPZ (n2)); | |
4063 | scm_remember_upto_here_2(n1, n2); | |
4064 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4065 | return result; | |
4066 | } | |
f872b822 | 4067 | } |
0f2d19dd JB |
4068 | } |
4069 | ||
8a525303 GB |
4070 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4071 | ||
4072 | Logand: | |
4073 | X Y Result Method: | |
4074 | (len) | |
4075 | + + + x (map digit:logand X Y) | |
4076 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4077 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4078 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4079 | ||
4080 | Logior: | |
4081 | X Y Result Method: | |
4082 | ||
4083 | + + + (map digit:logior X Y) | |
4084 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4085 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4086 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4087 | ||
4088 | Logxor: | |
4089 | X Y Result Method: | |
4090 | ||
4091 | + + + (map digit:logxor X Y) | |
4092 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4093 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4094 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4095 | ||
4096 | Logtest: | |
4097 | X Y Result | |
4098 | ||
4099 | + + (any digit:logand X Y) | |
4100 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4101 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4102 | - - #t | |
4103 | ||
4104 | */ | |
4105 | ||
78d3deb1 AW |
4106 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4107 | (SCM x, SCM y, SCM rest), | |
4108 | "Return the bitwise AND of the integer arguments.\n\n" | |
4109 | "@lisp\n" | |
4110 | "(logand) @result{} -1\n" | |
4111 | "(logand 7) @result{} 7\n" | |
4112 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4113 | "@end lisp") | |
4114 | #define FUNC_NAME s_scm_i_logand | |
4115 | { | |
4116 | while (!scm_is_null (rest)) | |
4117 | { x = scm_logand (x, y); | |
4118 | y = scm_car (rest); | |
4119 | rest = scm_cdr (rest); | |
4120 | } | |
4121 | return scm_logand (x, y); | |
4122 | } | |
4123 | #undef FUNC_NAME | |
4124 | ||
4125 | #define s_scm_logand s_scm_i_logand | |
4126 | ||
4127 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4128 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4129 | { |
e25f3727 | 4130 | scm_t_inum nn1; |
9a00c9fc | 4131 | |
0aacf84e MD |
4132 | if (SCM_UNBNDP (n2)) |
4133 | { | |
4134 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4135 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4136 | else if (!SCM_NUMBERP (n1)) |
4137 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4138 | else if (SCM_NUMBERP (n1)) | |
4139 | return n1; | |
4140 | else | |
4141 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4142 | } |
09fb7599 | 4143 | |
e11e83f3 | 4144 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4145 | { |
e11e83f3 MV |
4146 | nn1 = SCM_I_INUM (n1); |
4147 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4148 | { |
e25f3727 | 4149 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4150 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4151 | } |
4152 | else if SCM_BIGP (n2) | |
4153 | { | |
4154 | intbig: | |
2e16a342 | 4155 | if (nn1 == 0) |
0aacf84e MD |
4156 | return SCM_INUM0; |
4157 | { | |
4158 | SCM result_z = scm_i_mkbig (); | |
4159 | mpz_t nn1_z; | |
4160 | mpz_init_set_si (nn1_z, nn1); | |
4161 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4162 | scm_remember_upto_here_1 (n2); | |
4163 | mpz_clear (nn1_z); | |
4164 | return scm_i_normbig (result_z); | |
4165 | } | |
4166 | } | |
4167 | else | |
4168 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4169 | } | |
4170 | else if (SCM_BIGP (n1)) | |
4171 | { | |
e11e83f3 | 4172 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4173 | { |
4174 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4175 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4176 | goto intbig; |
4177 | } | |
4178 | else if (SCM_BIGP (n2)) | |
4179 | { | |
4180 | SCM result_z = scm_i_mkbig (); | |
4181 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4182 | SCM_I_BIG_MPZ (n1), | |
4183 | SCM_I_BIG_MPZ (n2)); | |
4184 | scm_remember_upto_here_2 (n1, n2); | |
4185 | return scm_i_normbig (result_z); | |
4186 | } | |
4187 | else | |
4188 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4189 | } |
0aacf84e | 4190 | else |
09fb7599 | 4191 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4192 | } |
1bbd0b84 | 4193 | #undef FUNC_NAME |
0f2d19dd | 4194 | |
09fb7599 | 4195 | |
78d3deb1 AW |
4196 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4197 | (SCM x, SCM y, SCM rest), | |
4198 | "Return the bitwise OR of the integer arguments.\n\n" | |
4199 | "@lisp\n" | |
4200 | "(logior) @result{} 0\n" | |
4201 | "(logior 7) @result{} 7\n" | |
4202 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4203 | "@end lisp") | |
4204 | #define FUNC_NAME s_scm_i_logior | |
4205 | { | |
4206 | while (!scm_is_null (rest)) | |
4207 | { x = scm_logior (x, y); | |
4208 | y = scm_car (rest); | |
4209 | rest = scm_cdr (rest); | |
4210 | } | |
4211 | return scm_logior (x, y); | |
4212 | } | |
4213 | #undef FUNC_NAME | |
4214 | ||
4215 | #define s_scm_logior s_scm_i_logior | |
4216 | ||
4217 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4218 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4219 | { |
e25f3727 | 4220 | scm_t_inum nn1; |
9a00c9fc | 4221 | |
0aacf84e MD |
4222 | if (SCM_UNBNDP (n2)) |
4223 | { | |
4224 | if (SCM_UNBNDP (n1)) | |
4225 | return SCM_INUM0; | |
4226 | else if (SCM_NUMBERP (n1)) | |
4227 | return n1; | |
4228 | else | |
4229 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4230 | } |
09fb7599 | 4231 | |
e11e83f3 | 4232 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4233 | { |
e11e83f3 MV |
4234 | nn1 = SCM_I_INUM (n1); |
4235 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4236 | { |
e11e83f3 | 4237 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4238 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4239 | } |
4240 | else if (SCM_BIGP (n2)) | |
4241 | { | |
4242 | intbig: | |
4243 | if (nn1 == 0) | |
4244 | return n2; | |
4245 | { | |
4246 | SCM result_z = scm_i_mkbig (); | |
4247 | mpz_t nn1_z; | |
4248 | mpz_init_set_si (nn1_z, nn1); | |
4249 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4250 | scm_remember_upto_here_1 (n2); | |
4251 | mpz_clear (nn1_z); | |
9806de0d | 4252 | return scm_i_normbig (result_z); |
0aacf84e MD |
4253 | } |
4254 | } | |
4255 | else | |
4256 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4257 | } | |
4258 | else if (SCM_BIGP (n1)) | |
4259 | { | |
e11e83f3 | 4260 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4261 | { |
4262 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4263 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4264 | goto intbig; |
4265 | } | |
4266 | else if (SCM_BIGP (n2)) | |
4267 | { | |
4268 | SCM result_z = scm_i_mkbig (); | |
4269 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4270 | SCM_I_BIG_MPZ (n1), | |
4271 | SCM_I_BIG_MPZ (n2)); | |
4272 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4273 | return scm_i_normbig (result_z); |
0aacf84e MD |
4274 | } |
4275 | else | |
4276 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4277 | } |
0aacf84e | 4278 | else |
09fb7599 | 4279 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4280 | } |
1bbd0b84 | 4281 | #undef FUNC_NAME |
0f2d19dd | 4282 | |
09fb7599 | 4283 | |
78d3deb1 AW |
4284 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4285 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4286 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4287 | "set in the result if it is set in an odd number of arguments.\n" | |
4288 | "@lisp\n" | |
4289 | "(logxor) @result{} 0\n" | |
4290 | "(logxor 7) @result{} 7\n" | |
4291 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4292 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4293 | "@end lisp") |
78d3deb1 AW |
4294 | #define FUNC_NAME s_scm_i_logxor |
4295 | { | |
4296 | while (!scm_is_null (rest)) | |
4297 | { x = scm_logxor (x, y); | |
4298 | y = scm_car (rest); | |
4299 | rest = scm_cdr (rest); | |
4300 | } | |
4301 | return scm_logxor (x, y); | |
4302 | } | |
4303 | #undef FUNC_NAME | |
4304 | ||
4305 | #define s_scm_logxor s_scm_i_logxor | |
4306 | ||
4307 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4308 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4309 | { |
e25f3727 | 4310 | scm_t_inum nn1; |
9a00c9fc | 4311 | |
0aacf84e MD |
4312 | if (SCM_UNBNDP (n2)) |
4313 | { | |
4314 | if (SCM_UNBNDP (n1)) | |
4315 | return SCM_INUM0; | |
4316 | else if (SCM_NUMBERP (n1)) | |
4317 | return n1; | |
4318 | else | |
4319 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4320 | } |
09fb7599 | 4321 | |
e11e83f3 | 4322 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4323 | { |
e11e83f3 MV |
4324 | nn1 = SCM_I_INUM (n1); |
4325 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4326 | { |
e25f3727 | 4327 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4328 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4329 | } |
4330 | else if (SCM_BIGP (n2)) | |
4331 | { | |
4332 | intbig: | |
4333 | { | |
4334 | SCM result_z = scm_i_mkbig (); | |
4335 | mpz_t nn1_z; | |
4336 | mpz_init_set_si (nn1_z, nn1); | |
4337 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4338 | scm_remember_upto_here_1 (n2); | |
4339 | mpz_clear (nn1_z); | |
4340 | return scm_i_normbig (result_z); | |
4341 | } | |
4342 | } | |
4343 | else | |
4344 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4345 | } | |
4346 | else if (SCM_BIGP (n1)) | |
4347 | { | |
e11e83f3 | 4348 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4349 | { |
4350 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4351 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4352 | goto intbig; |
4353 | } | |
4354 | else if (SCM_BIGP (n2)) | |
4355 | { | |
4356 | SCM result_z = scm_i_mkbig (); | |
4357 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4358 | SCM_I_BIG_MPZ (n1), | |
4359 | SCM_I_BIG_MPZ (n2)); | |
4360 | scm_remember_upto_here_2 (n1, n2); | |
4361 | return scm_i_normbig (result_z); | |
4362 | } | |
4363 | else | |
4364 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4365 | } |
0aacf84e | 4366 | else |
09fb7599 | 4367 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4368 | } |
1bbd0b84 | 4369 | #undef FUNC_NAME |
0f2d19dd | 4370 | |
09fb7599 | 4371 | |
a1ec6916 | 4372 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4373 | (SCM j, SCM k), |
ba6e7231 KR |
4374 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4375 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4376 | "without actually calculating the @code{logand}, just testing\n" | |
4377 | "for non-zero.\n" | |
4378 | "\n" | |
1e6808ea | 4379 | "@lisp\n" |
b380b885 MD |
4380 | "(logtest #b0100 #b1011) @result{} #f\n" |
4381 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4382 | "@end lisp") |
1bbd0b84 | 4383 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4384 | { |
e25f3727 | 4385 | scm_t_inum nj; |
9a00c9fc | 4386 | |
e11e83f3 | 4387 | if (SCM_I_INUMP (j)) |
0aacf84e | 4388 | { |
e11e83f3 MV |
4389 | nj = SCM_I_INUM (j); |
4390 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4391 | { |
e25f3727 | 4392 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4393 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4394 | } |
4395 | else if (SCM_BIGP (k)) | |
4396 | { | |
4397 | intbig: | |
4398 | if (nj == 0) | |
4399 | return SCM_BOOL_F; | |
4400 | { | |
4401 | SCM result; | |
4402 | mpz_t nj_z; | |
4403 | mpz_init_set_si (nj_z, nj); | |
4404 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4405 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4406 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4407 | mpz_clear (nj_z); |
4408 | return result; | |
4409 | } | |
4410 | } | |
4411 | else | |
4412 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4413 | } | |
4414 | else if (SCM_BIGP (j)) | |
4415 | { | |
e11e83f3 | 4416 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4417 | { |
4418 | SCM_SWAP (j, k); | |
e11e83f3 | 4419 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4420 | goto intbig; |
4421 | } | |
4422 | else if (SCM_BIGP (k)) | |
4423 | { | |
4424 | SCM result; | |
4425 | mpz_t result_z; | |
4426 | mpz_init (result_z); | |
4427 | mpz_and (result_z, | |
4428 | SCM_I_BIG_MPZ (j), | |
4429 | SCM_I_BIG_MPZ (k)); | |
4430 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4431 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4432 | mpz_clear (result_z); |
4433 | return result; | |
4434 | } | |
4435 | else | |
4436 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4437 | } | |
4438 | else | |
4439 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4440 | } |
1bbd0b84 | 4441 | #undef FUNC_NAME |
0f2d19dd | 4442 | |
c1bfcf60 | 4443 | |
a1ec6916 | 4444 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4445 | (SCM index, SCM j), |
ba6e7231 KR |
4446 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4447 | "@var{index} starts from 0 for the least significant bit.\n" | |
4448 | "\n" | |
1e6808ea | 4449 | "@lisp\n" |
b380b885 MD |
4450 | "(logbit? 0 #b1101) @result{} #t\n" |
4451 | "(logbit? 1 #b1101) @result{} #f\n" | |
4452 | "(logbit? 2 #b1101) @result{} #t\n" | |
4453 | "(logbit? 3 #b1101) @result{} #t\n" | |
4454 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4455 | "@end lisp") |
1bbd0b84 | 4456 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4457 | { |
78166ad5 | 4458 | unsigned long int iindex; |
5efd3c7d | 4459 | iindex = scm_to_ulong (index); |
78166ad5 | 4460 | |
e11e83f3 | 4461 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4462 | { |
4463 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4464 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4465 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4466 | } |
0aacf84e MD |
4467 | else if (SCM_BIGP (j)) |
4468 | { | |
4469 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4470 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4471 | return scm_from_bool (val); |
0aacf84e MD |
4472 | } |
4473 | else | |
78166ad5 | 4474 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4475 | } |
1bbd0b84 | 4476 | #undef FUNC_NAME |
0f2d19dd | 4477 | |
78166ad5 | 4478 | |
a1ec6916 | 4479 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4480 | (SCM n), |
4d814788 | 4481 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4482 | "argument.\n" |
4483 | "\n" | |
b380b885 MD |
4484 | "@lisp\n" |
4485 | "(number->string (lognot #b10000000) 2)\n" | |
4486 | " @result{} \"-10000001\"\n" | |
4487 | "(number->string (lognot #b0) 2)\n" | |
4488 | " @result{} \"-1\"\n" | |
1e6808ea | 4489 | "@end lisp") |
1bbd0b84 | 4490 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4491 | { |
e11e83f3 | 4492 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4493 | /* No overflow here, just need to toggle all the bits making up the inum. |
4494 | Enhancement: No need to strip the tag and add it back, could just xor | |
4495 | a block of 1 bits, if that worked with the various debug versions of | |
4496 | the SCM typedef. */ | |
e11e83f3 | 4497 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4498 | |
4499 | } else if (SCM_BIGP (n)) { | |
4500 | SCM result = scm_i_mkbig (); | |
4501 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4502 | scm_remember_upto_here_1 (n); | |
4503 | return result; | |
4504 | ||
4505 | } else { | |
4506 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4507 | } | |
0f2d19dd | 4508 | } |
1bbd0b84 | 4509 | #undef FUNC_NAME |
0f2d19dd | 4510 | |
518b7508 KR |
4511 | /* returns 0 if IN is not an integer. OUT must already be |
4512 | initialized. */ | |
4513 | static int | |
4514 | coerce_to_big (SCM in, mpz_t out) | |
4515 | { | |
4516 | if (SCM_BIGP (in)) | |
4517 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4518 | else if (SCM_I_INUMP (in)) |
4519 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4520 | else |
4521 | return 0; | |
4522 | ||
4523 | return 1; | |
4524 | } | |
4525 | ||
d885e204 | 4526 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4527 | (SCM n, SCM k, SCM m), |
4528 | "Return @var{n} raised to the integer exponent\n" | |
4529 | "@var{k}, modulo @var{m}.\n" | |
4530 | "\n" | |
4531 | "@lisp\n" | |
4532 | "(modulo-expt 2 3 5)\n" | |
4533 | " @result{} 3\n" | |
4534 | "@end lisp") | |
d885e204 | 4535 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4536 | { |
4537 | mpz_t n_tmp; | |
4538 | mpz_t k_tmp; | |
4539 | mpz_t m_tmp; | |
4540 | ||
4541 | /* There are two classes of error we might encounter -- | |
4542 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4543 | and | |
4544 | 2) wrong-type errors, which of course we'll report by calling | |
4545 | SCM_WRONG_TYPE_ARG. | |
4546 | We don't report those errors immediately, however; instead we do | |
4547 | some cleanup first. These variables tell us which error (if | |
4548 | any) we should report after cleaning up. | |
4549 | */ | |
4550 | int report_overflow = 0; | |
4551 | ||
4552 | int position_of_wrong_type = 0; | |
4553 | SCM value_of_wrong_type = SCM_INUM0; | |
4554 | ||
4555 | SCM result = SCM_UNDEFINED; | |
4556 | ||
4557 | mpz_init (n_tmp); | |
4558 | mpz_init (k_tmp); | |
4559 | mpz_init (m_tmp); | |
4560 | ||
bc36d050 | 4561 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4562 | { |
4563 | report_overflow = 1; | |
4564 | goto cleanup; | |
4565 | } | |
4566 | ||
4567 | if (!coerce_to_big (n, n_tmp)) | |
4568 | { | |
4569 | value_of_wrong_type = n; | |
4570 | position_of_wrong_type = 1; | |
4571 | goto cleanup; | |
4572 | } | |
4573 | ||
4574 | if (!coerce_to_big (k, k_tmp)) | |
4575 | { | |
4576 | value_of_wrong_type = k; | |
4577 | position_of_wrong_type = 2; | |
4578 | goto cleanup; | |
4579 | } | |
4580 | ||
4581 | if (!coerce_to_big (m, m_tmp)) | |
4582 | { | |
4583 | value_of_wrong_type = m; | |
4584 | position_of_wrong_type = 3; | |
4585 | goto cleanup; | |
4586 | } | |
4587 | ||
4588 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4589 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4590 | doesn't exist (or is not unique). Since exceptions are hard to | |
4591 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4592 | a simple failure code, which is easy to handle. */ | |
4593 | ||
4594 | if (-1 == mpz_sgn (k_tmp)) | |
4595 | { | |
4596 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4597 | { | |
4598 | report_overflow = 1; | |
4599 | goto cleanup; | |
4600 | } | |
4601 | mpz_neg (k_tmp, k_tmp); | |
4602 | } | |
4603 | ||
4604 | result = scm_i_mkbig (); | |
4605 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4606 | n_tmp, | |
4607 | k_tmp, | |
4608 | m_tmp); | |
b7b8c575 KR |
4609 | |
4610 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4611 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4612 | ||
518b7508 KR |
4613 | cleanup: |
4614 | mpz_clear (m_tmp); | |
4615 | mpz_clear (k_tmp); | |
4616 | mpz_clear (n_tmp); | |
4617 | ||
4618 | if (report_overflow) | |
4619 | scm_num_overflow (FUNC_NAME); | |
4620 | ||
4621 | if (position_of_wrong_type) | |
4622 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4623 | value_of_wrong_type); | |
4624 | ||
4625 | return scm_i_normbig (result); | |
4626 | } | |
4627 | #undef FUNC_NAME | |
4628 | ||
a1ec6916 | 4629 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4630 | (SCM n, SCM k), |
ba6e7231 KR |
4631 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4632 | "exact integer, @var{n} can be any number.\n" | |
4633 | "\n" | |
2519490c MW |
4634 | "Negative @var{k} is supported, and results in\n" |
4635 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4636 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4637 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4638 | "\n" |
b380b885 | 4639 | "@lisp\n" |
ba6e7231 KR |
4640 | "(integer-expt 2 5) @result{} 32\n" |
4641 | "(integer-expt -3 3) @result{} -27\n" | |
4642 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4643 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4644 | "@end lisp") |
1bbd0b84 | 4645 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4646 | { |
e25f3727 | 4647 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4648 | SCM z_i2 = SCM_BOOL_F; |
4649 | int i2_is_big = 0; | |
d956fa6f | 4650 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4651 | |
bfe1f03a MW |
4652 | /* Specifically refrain from checking the type of the first argument. |
4653 | This allows us to exponentiate any object that can be multiplied. | |
4654 | If we must raise to a negative power, we must also be able to | |
4655 | take its reciprocal. */ | |
4656 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4657 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4658 | |
bfe1f03a MW |
4659 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4660 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4661 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4662 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4663 | /* The next check is necessary only because R6RS specifies different | |
4664 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4665 | we simply skip this case and move on. */ | |
4666 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4667 | { | |
4668 | /* k cannot be 0 at this point, because we | |
4669 | have already checked for that case above */ | |
4670 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4671 | return n; |
4672 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4673 | return scm_nan (); | |
4674 | } | |
ca46fb90 | 4675 | |
e11e83f3 MV |
4676 | if (SCM_I_INUMP (k)) |
4677 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4678 | else if (SCM_BIGP (k)) |
4679 | { | |
4680 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4681 | scm_remember_upto_here_1 (k); |
4682 | i2_is_big = 1; | |
4683 | } | |
2830fd91 | 4684 | else |
ca46fb90 RB |
4685 | SCM_WRONG_TYPE_ARG (2, k); |
4686 | ||
4687 | if (i2_is_big) | |
f872b822 | 4688 | { |
ca46fb90 RB |
4689 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4690 | { | |
4691 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4692 | n = scm_divide (n, SCM_UNDEFINED); | |
4693 | } | |
4694 | while (1) | |
4695 | { | |
4696 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4697 | { | |
ca46fb90 RB |
4698 | return acc; |
4699 | } | |
4700 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4701 | { | |
ca46fb90 RB |
4702 | return scm_product (acc, n); |
4703 | } | |
4704 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4705 | acc = scm_product (acc, n); | |
4706 | n = scm_product (n, n); | |
4707 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4708 | } | |
f872b822 | 4709 | } |
ca46fb90 | 4710 | else |
f872b822 | 4711 | { |
ca46fb90 RB |
4712 | if (i2 < 0) |
4713 | { | |
4714 | i2 = -i2; | |
4715 | n = scm_divide (n, SCM_UNDEFINED); | |
4716 | } | |
4717 | while (1) | |
4718 | { | |
4719 | if (0 == i2) | |
4720 | return acc; | |
4721 | if (1 == i2) | |
4722 | return scm_product (acc, n); | |
4723 | if (i2 & 1) | |
4724 | acc = scm_product (acc, n); | |
4725 | n = scm_product (n, n); | |
4726 | i2 >>= 1; | |
4727 | } | |
f872b822 | 4728 | } |
0f2d19dd | 4729 | } |
1bbd0b84 | 4730 | #undef FUNC_NAME |
0f2d19dd | 4731 | |
a1ec6916 | 4732 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 4733 | (SCM n, SCM cnt), |
32f19569 KR |
4734 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
4735 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 4736 | "\n" |
e7644cb2 | 4737 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
4738 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
4739 | "infinity. (Note that this is not the same rounding as\n" | |
4740 | "@code{quotient} does.)\n" | |
4741 | "\n" | |
4742 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
4743 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
4744 | "shift dropping bits.\n" | |
1e6808ea | 4745 | "\n" |
b380b885 | 4746 | "@lisp\n" |
1e6808ea MG |
4747 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
4748 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
4749 | "\n" |
4750 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
4751 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 4752 | "@end lisp") |
1bbd0b84 | 4753 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 4754 | { |
3ab9f56e | 4755 | long bits_to_shift; |
5efd3c7d | 4756 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 4757 | |
788aca27 KR |
4758 | if (SCM_I_INUMP (n)) |
4759 | { | |
e25f3727 | 4760 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
4761 | |
4762 | if (bits_to_shift > 0) | |
4763 | { | |
4764 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
4765 | overflow a non-zero fixnum. For smaller shifts we check the | |
4766 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4767 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4768 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
4769 | bits_to_shift)". */ | |
4770 | ||
4771 | if (nn == 0) | |
4772 | return n; | |
4773 | ||
4774 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4775 | && ((scm_t_bits) |
788aca27 KR |
4776 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
4777 | <= 1)) | |
4778 | { | |
4779 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
4780 | } | |
4781 | else | |
4782 | { | |
e25f3727 | 4783 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
4784 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4785 | bits_to_shift); | |
4786 | return result; | |
4787 | } | |
4788 | } | |
4789 | else | |
4790 | { | |
4791 | bits_to_shift = -bits_to_shift; | |
4792 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 4793 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
4794 | else |
4795 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
4796 | } | |
4797 | ||
4798 | } | |
4799 | else if (SCM_BIGP (n)) | |
ca46fb90 | 4800 | { |
788aca27 KR |
4801 | SCM result; |
4802 | ||
4803 | if (bits_to_shift == 0) | |
4804 | return n; | |
4805 | ||
4806 | result = scm_i_mkbig (); | |
4807 | if (bits_to_shift >= 0) | |
4808 | { | |
4809 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4810 | bits_to_shift); | |
4811 | return result; | |
4812 | } | |
ca46fb90 | 4813 | else |
788aca27 KR |
4814 | { |
4815 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
4816 | we have to allocate a bignum even if the result is going to be a | |
4817 | fixnum. */ | |
4818 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4819 | -bits_to_shift); | |
4820 | return scm_i_normbig (result); | |
4821 | } | |
4822 | ||
ca46fb90 RB |
4823 | } |
4824 | else | |
788aca27 KR |
4825 | { |
4826 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4827 | } | |
0f2d19dd | 4828 | } |
1bbd0b84 | 4829 | #undef FUNC_NAME |
0f2d19dd | 4830 | |
3c9f20f8 | 4831 | |
a1ec6916 | 4832 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 4833 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
4834 | "Return the integer composed of the @var{start} (inclusive)\n" |
4835 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
4836 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
4837 | "\n" | |
b380b885 MD |
4838 | "@lisp\n" |
4839 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
4840 | " @result{} \"1010\"\n" | |
4841 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
4842 | " @result{} \"10110\"\n" | |
4843 | "@end lisp") | |
1bbd0b84 | 4844 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 4845 | { |
7f848242 | 4846 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
4847 | istart = scm_to_ulong (start); |
4848 | iend = scm_to_ulong (end); | |
c1bfcf60 | 4849 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 4850 | |
7f848242 KR |
4851 | /* how many bits to keep */ |
4852 | bits = iend - istart; | |
4853 | ||
e11e83f3 | 4854 | if (SCM_I_INUMP (n)) |
0aacf84e | 4855 | { |
e25f3727 | 4856 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
4857 | |
4858 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 4859 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 4860 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 4861 | |
0aacf84e MD |
4862 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
4863 | { | |
4864 | /* Since we emulate two's complement encoded numbers, this | |
4865 | * special case requires us to produce a result that has | |
7f848242 | 4866 | * more bits than can be stored in a fixnum. |
0aacf84e | 4867 | */ |
e25f3727 | 4868 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
4869 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4870 | bits); | |
4871 | return result; | |
0aacf84e | 4872 | } |
ac0c002c | 4873 | |
7f848242 | 4874 | /* mask down to requisite bits */ |
857ae6af | 4875 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 4876 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
4877 | } |
4878 | else if (SCM_BIGP (n)) | |
ac0c002c | 4879 | { |
7f848242 KR |
4880 | SCM result; |
4881 | if (bits == 1) | |
4882 | { | |
d956fa6f | 4883 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
4884 | } |
4885 | else | |
4886 | { | |
4887 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
4888 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
4889 | such bits into a ulong. */ | |
4890 | result = scm_i_mkbig (); | |
4891 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
4892 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
4893 | result = scm_i_normbig (result); | |
4894 | } | |
4895 | scm_remember_upto_here_1 (n); | |
4896 | return result; | |
ac0c002c | 4897 | } |
0aacf84e | 4898 | else |
78166ad5 | 4899 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 4900 | } |
1bbd0b84 | 4901 | #undef FUNC_NAME |
0f2d19dd | 4902 | |
7f848242 | 4903 | |
e4755e5c JB |
4904 | static const char scm_logtab[] = { |
4905 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
4906 | }; | |
1cc91f1b | 4907 | |
a1ec6916 | 4908 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 4909 | (SCM n), |
1e6808ea MG |
4910 | "Return the number of bits in integer @var{n}. If integer is\n" |
4911 | "positive, the 1-bits in its binary representation are counted.\n" | |
4912 | "If negative, the 0-bits in its two's-complement binary\n" | |
4913 | "representation are counted. If 0, 0 is returned.\n" | |
4914 | "\n" | |
b380b885 MD |
4915 | "@lisp\n" |
4916 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
4917 | " @result{} 4\n" |
4918 | "(logcount 0)\n" | |
4919 | " @result{} 0\n" | |
4920 | "(logcount -2)\n" | |
4921 | " @result{} 1\n" | |
4922 | "@end lisp") | |
4923 | #define FUNC_NAME s_scm_logcount | |
4924 | { | |
e11e83f3 | 4925 | if (SCM_I_INUMP (n)) |
f872b822 | 4926 | { |
e25f3727 AW |
4927 | unsigned long c = 0; |
4928 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
4929 | if (nn < 0) |
4930 | nn = -1 - nn; | |
4931 | while (nn) | |
4932 | { | |
4933 | c += scm_logtab[15 & nn]; | |
4934 | nn >>= 4; | |
4935 | } | |
d956fa6f | 4936 | return SCM_I_MAKINUM (c); |
f872b822 | 4937 | } |
ca46fb90 | 4938 | else if (SCM_BIGP (n)) |
f872b822 | 4939 | { |
ca46fb90 | 4940 | unsigned long count; |
713a4259 KR |
4941 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
4942 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 4943 | else |
713a4259 KR |
4944 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
4945 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4946 | return SCM_I_MAKINUM (count); |
f872b822 | 4947 | } |
ca46fb90 RB |
4948 | else |
4949 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 4950 | } |
ca46fb90 | 4951 | #undef FUNC_NAME |
0f2d19dd JB |
4952 | |
4953 | ||
ca46fb90 RB |
4954 | static const char scm_ilentab[] = { |
4955 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
4956 | }; | |
4957 | ||
0f2d19dd | 4958 | |
ca46fb90 RB |
4959 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
4960 | (SCM n), | |
4961 | "Return the number of bits necessary to represent @var{n}.\n" | |
4962 | "\n" | |
4963 | "@lisp\n" | |
4964 | "(integer-length #b10101010)\n" | |
4965 | " @result{} 8\n" | |
4966 | "(integer-length 0)\n" | |
4967 | " @result{} 0\n" | |
4968 | "(integer-length #b1111)\n" | |
4969 | " @result{} 4\n" | |
4970 | "@end lisp") | |
4971 | #define FUNC_NAME s_scm_integer_length | |
4972 | { | |
e11e83f3 | 4973 | if (SCM_I_INUMP (n)) |
0aacf84e | 4974 | { |
e25f3727 | 4975 | unsigned long c = 0; |
0aacf84e | 4976 | unsigned int l = 4; |
e25f3727 | 4977 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
4978 | if (nn < 0) |
4979 | nn = -1 - nn; | |
4980 | while (nn) | |
4981 | { | |
4982 | c += 4; | |
4983 | l = scm_ilentab [15 & nn]; | |
4984 | nn >>= 4; | |
4985 | } | |
d956fa6f | 4986 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
4987 | } |
4988 | else if (SCM_BIGP (n)) | |
4989 | { | |
4990 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
4991 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
4992 | 1 too big, so check for that and adjust. */ | |
4993 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
4994 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
4995 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
4996 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
4997 | size--; | |
4998 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4999 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
5000 | } |
5001 | else | |
ca46fb90 | 5002 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5003 | } |
5004 | #undef FUNC_NAME | |
0f2d19dd JB |
5005 | |
5006 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5007 | #define SCM_MAX_DBL_PREC 60 |
5008 | #define SCM_MAX_DBL_RADIX 36 | |
5009 | ||
5010 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
5011 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
5012 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
5013 | ||
5014 | static | |
5015 | void init_dblprec(int *prec, int radix) { | |
5016 | /* determine floating point precision by adding successively | |
5017 | smaller increments to 1.0 until it is considered == 1.0 */ | |
5018 | double f = ((double)1.0)/radix; | |
5019 | double fsum = 1.0 + f; | |
5020 | ||
5021 | *prec = 0; | |
5022 | while (fsum != 1.0) | |
5023 | { | |
5024 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
5025 | fsum = 1.0; | |
5026 | else | |
5027 | { | |
5028 | f /= radix; | |
5029 | fsum = f + 1.0; | |
5030 | } | |
5031 | } | |
5032 | (*prec) -= 1; | |
5033 | } | |
5034 | ||
5035 | static | |
5036 | void init_fx_radix(double *fx_list, int radix) | |
5037 | { | |
5038 | /* initialize a per-radix list of tolerances. When added | |
5039 | to a number < 1.0, we can determine if we should raund | |
5040 | up and quit converting a number to a string. */ | |
5041 | int i; | |
5042 | fx_list[0] = 0.0; | |
5043 | fx_list[1] = 0.5; | |
5044 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
5045 | fx_list[i] = (fx_list[i-1] / radix); | |
5046 | } | |
5047 | ||
5048 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5049 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5050 | |
1be6b49c | 5051 | static size_t |
0b799eea | 5052 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5053 | { |
0b799eea MV |
5054 | int efmt, dpt, d, i, wp; |
5055 | double *fx; | |
5056 | #ifdef DBL_MIN_10_EXP | |
5057 | double f_cpy; | |
5058 | int exp_cpy; | |
5059 | #endif /* DBL_MIN_10_EXP */ | |
5060 | size_t ch = 0; | |
5061 | int exp = 0; | |
5062 | ||
5063 | if(radix < 2 || | |
5064 | radix > SCM_MAX_DBL_RADIX) | |
5065 | { | |
5066 | /* revert to existing behavior */ | |
5067 | radix = 10; | |
5068 | } | |
5069 | ||
5070 | wp = scm_dblprec[radix-2]; | |
5071 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5072 | |
f872b822 | 5073 | if (f == 0.0) |
abb7e44d MV |
5074 | { |
5075 | #ifdef HAVE_COPYSIGN | |
5076 | double sgn = copysign (1.0, f); | |
5077 | ||
5078 | if (sgn < 0.0) | |
5079 | a[ch++] = '-'; | |
5080 | #endif | |
abb7e44d MV |
5081 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5082 | } | |
7351e207 | 5083 | |
2e65b52f | 5084 | if (isinf (f)) |
7351e207 MV |
5085 | { |
5086 | if (f < 0) | |
5087 | strcpy (a, "-inf.0"); | |
5088 | else | |
5089 | strcpy (a, "+inf.0"); | |
5090 | return ch+6; | |
5091 | } | |
2e65b52f | 5092 | else if (isnan (f)) |
7351e207 MV |
5093 | { |
5094 | strcpy (a, "+nan.0"); | |
5095 | return ch+6; | |
5096 | } | |
5097 | ||
f872b822 MD |
5098 | if (f < 0.0) |
5099 | { | |
5100 | f = -f; | |
5101 | a[ch++] = '-'; | |
5102 | } | |
7351e207 | 5103 | |
f872b822 MD |
5104 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5105 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5106 | /* just do the checking...if it passes, we do the conversion for our |
5107 | radix again below */ | |
5108 | f_cpy = f; | |
5109 | exp_cpy = exp; | |
5110 | ||
5111 | while (f_cpy < 1.0) | |
f872b822 | 5112 | { |
0b799eea MV |
5113 | f_cpy *= 10.0; |
5114 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5115 | { |
5116 | a[ch++] = '#'; | |
5117 | a[ch++] = '.'; | |
5118 | a[ch++] = '#'; | |
5119 | return ch; | |
5120 | } | |
f872b822 | 5121 | } |
0b799eea | 5122 | while (f_cpy > 10.0) |
f872b822 | 5123 | { |
0b799eea MV |
5124 | f_cpy *= 0.10; |
5125 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5126 | { |
5127 | a[ch++] = '#'; | |
5128 | a[ch++] = '.'; | |
5129 | a[ch++] = '#'; | |
5130 | return ch; | |
5131 | } | |
f872b822 | 5132 | } |
0b799eea MV |
5133 | #endif |
5134 | ||
f872b822 MD |
5135 | while (f < 1.0) |
5136 | { | |
0b799eea | 5137 | f *= radix; |
f872b822 MD |
5138 | exp--; |
5139 | } | |
0b799eea | 5140 | while (f > radix) |
f872b822 | 5141 | { |
0b799eea | 5142 | f /= radix; |
f872b822 MD |
5143 | exp++; |
5144 | } | |
0b799eea MV |
5145 | |
5146 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5147 | { |
5148 | f = 1.0; | |
5149 | exp++; | |
5150 | } | |
0f2d19dd | 5151 | zero: |
0b799eea MV |
5152 | #ifdef ENGNOT |
5153 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 5154 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
5155 | exp -= dpt++; |
5156 | efmt = 1; | |
f872b822 MD |
5157 | #else |
5158 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 5159 | if (!efmt) |
cda139a7 MD |
5160 | { |
5161 | if (exp < 0) | |
5162 | { | |
5163 | a[ch++] = '0'; | |
5164 | a[ch++] = '.'; | |
5165 | dpt = exp; | |
f872b822 MD |
5166 | while (++dpt) |
5167 | a[ch++] = '0'; | |
cda139a7 MD |
5168 | } |
5169 | else | |
f872b822 | 5170 | dpt = exp + 1; |
cda139a7 | 5171 | } |
0f2d19dd JB |
5172 | else |
5173 | dpt = 1; | |
f872b822 MD |
5174 | #endif |
5175 | ||
5176 | do | |
5177 | { | |
5178 | d = f; | |
5179 | f -= d; | |
0b799eea | 5180 | a[ch++] = number_chars[d]; |
f872b822 MD |
5181 | if (f < fx[wp]) |
5182 | break; | |
5183 | if (f + fx[wp] >= 1.0) | |
5184 | { | |
0b799eea | 5185 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5186 | break; |
5187 | } | |
0b799eea | 5188 | f *= radix; |
f872b822 MD |
5189 | if (!(--dpt)) |
5190 | a[ch++] = '.'; | |
0f2d19dd | 5191 | } |
f872b822 | 5192 | while (wp--); |
0f2d19dd JB |
5193 | |
5194 | if (dpt > 0) | |
cda139a7 | 5195 | { |
f872b822 | 5196 | #ifndef ENGNOT |
cda139a7 MD |
5197 | if ((dpt > 4) && (exp > 6)) |
5198 | { | |
f872b822 | 5199 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 5200 | for (i = ch++; i > d; i--) |
f872b822 | 5201 | a[i] = a[i - 1]; |
cda139a7 MD |
5202 | a[d] = '.'; |
5203 | efmt = 1; | |
5204 | } | |
5205 | else | |
f872b822 | 5206 | #endif |
cda139a7 | 5207 | { |
f872b822 MD |
5208 | while (--dpt) |
5209 | a[ch++] = '0'; | |
cda139a7 MD |
5210 | a[ch++] = '.'; |
5211 | } | |
5212 | } | |
f872b822 MD |
5213 | if (a[ch - 1] == '.') |
5214 | a[ch++] = '0'; /* trailing zero */ | |
5215 | if (efmt && exp) | |
5216 | { | |
5217 | a[ch++] = 'e'; | |
5218 | if (exp < 0) | |
5219 | { | |
5220 | exp = -exp; | |
5221 | a[ch++] = '-'; | |
5222 | } | |
0b799eea MV |
5223 | for (i = radix; i <= exp; i *= radix); |
5224 | for (i /= radix; i; i /= radix) | |
f872b822 | 5225 | { |
0b799eea | 5226 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5227 | exp %= i; |
5228 | } | |
0f2d19dd | 5229 | } |
0f2d19dd JB |
5230 | return ch; |
5231 | } | |
5232 | ||
7a1aba42 MV |
5233 | |
5234 | static size_t | |
5235 | icmplx2str (double real, double imag, char *str, int radix) | |
5236 | { | |
5237 | size_t i; | |
c7218482 | 5238 | double sgn; |
7a1aba42 MV |
5239 | |
5240 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5241 | #ifdef HAVE_COPYSIGN |
5242 | sgn = copysign (1.0, imag); | |
5243 | #else | |
5244 | sgn = imag; | |
5245 | #endif | |
5246 | /* Don't output a '+' for negative numbers or for Inf and | |
5247 | NaN. They will provide their own sign. */ | |
5248 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5249 | str[i++] = '+'; | |
5250 | i += idbl2str (imag, &str[i], radix); | |
5251 | str[i++] = 'i'; | |
7a1aba42 MV |
5252 | return i; |
5253 | } | |
5254 | ||
1be6b49c | 5255 | static size_t |
0b799eea | 5256 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5257 | { |
1be6b49c | 5258 | size_t i; |
3c9a524f | 5259 | if (SCM_REALP (flt)) |
0b799eea | 5260 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5261 | else |
7a1aba42 MV |
5262 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5263 | str, radix); | |
0f2d19dd JB |
5264 | return i; |
5265 | } | |
0f2d19dd | 5266 | |
2881e77b | 5267 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5268 | characters in the result. |
5269 | rad is output base | |
5270 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5271 | size_t |
2881e77b MV |
5272 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5273 | { | |
5274 | if (num < 0) | |
5275 | { | |
5276 | *p++ = '-'; | |
5277 | return scm_iuint2str (-num, rad, p) + 1; | |
5278 | } | |
5279 | else | |
5280 | return scm_iuint2str (num, rad, p); | |
5281 | } | |
5282 | ||
5283 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5284 | characters in the result. | |
5285 | rad is output base | |
5286 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5287 | size_t | |
5288 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5289 | { |
1be6b49c ML |
5290 | size_t j = 1; |
5291 | size_t i; | |
2881e77b | 5292 | scm_t_uintmax n = num; |
5c11cc9d | 5293 | |
a6f3af16 AW |
5294 | if (rad < 2 || rad > 36) |
5295 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5296 | ||
f872b822 | 5297 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5298 | j++; |
5299 | ||
5300 | i = j; | |
2881e77b | 5301 | n = num; |
f872b822 MD |
5302 | while (i--) |
5303 | { | |
5c11cc9d GH |
5304 | int d = n % rad; |
5305 | ||
f872b822 | 5306 | n /= rad; |
a6f3af16 | 5307 | p[i] = number_chars[d]; |
f872b822 | 5308 | } |
0f2d19dd JB |
5309 | return j; |
5310 | } | |
5311 | ||
a1ec6916 | 5312 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5313 | (SCM n, SCM radix), |
5314 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5315 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5316 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5317 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5318 | { |
1bbd0b84 | 5319 | int base; |
98cb6e75 | 5320 | |
0aacf84e | 5321 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5322 | base = 10; |
0aacf84e | 5323 | else |
5efd3c7d | 5324 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5325 | |
e11e83f3 | 5326 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5327 | { |
5328 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5329 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5330 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5331 | } |
5332 | else if (SCM_BIGP (n)) | |
5333 | { | |
5334 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
d88f5323 AW |
5335 | size_t len = strlen (str); |
5336 | void (*freefunc) (void *, size_t); | |
5337 | SCM ret; | |
5338 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
0aacf84e | 5339 | scm_remember_upto_here_1 (n); |
d88f5323 AW |
5340 | ret = scm_from_latin1_stringn (str, len); |
5341 | freefunc (str, len + 1); | |
5342 | return ret; | |
0aacf84e | 5343 | } |
f92e85f7 MV |
5344 | else if (SCM_FRACTIONP (n)) |
5345 | { | |
f92e85f7 | 5346 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5347 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5348 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5349 | } | |
0aacf84e MD |
5350 | else if (SCM_INEXACTP (n)) |
5351 | { | |
5352 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5353 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5354 | } |
5355 | else | |
bb628794 | 5356 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5357 | } |
1bbd0b84 | 5358 | #undef FUNC_NAME |
0f2d19dd JB |
5359 | |
5360 | ||
ca46fb90 RB |
5361 | /* These print routines used to be stubbed here so that scm_repl.c |
5362 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5363 | |
0f2d19dd | 5364 | int |
e81d98ec | 5365 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5366 | { |
56e55ac7 | 5367 | char num_buf[FLOBUFLEN]; |
0b799eea | 5368 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5369 | return !0; |
5370 | } | |
5371 | ||
b479fe9a MV |
5372 | void |
5373 | scm_i_print_double (double val, SCM port) | |
5374 | { | |
5375 | char num_buf[FLOBUFLEN]; | |
5376 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5377 | } | |
5378 | ||
f3ae5d60 | 5379 | int |
e81d98ec | 5380 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5381 | |
f3ae5d60 | 5382 | { |
56e55ac7 | 5383 | char num_buf[FLOBUFLEN]; |
0b799eea | 5384 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5385 | return !0; |
5386 | } | |
1cc91f1b | 5387 | |
7a1aba42 MV |
5388 | void |
5389 | scm_i_print_complex (double real, double imag, SCM port) | |
5390 | { | |
5391 | char num_buf[FLOBUFLEN]; | |
5392 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5393 | } | |
5394 | ||
f92e85f7 MV |
5395 | int |
5396 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5397 | { | |
5398 | SCM str; | |
f92e85f7 | 5399 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5400 | scm_display (str, port); |
f92e85f7 MV |
5401 | scm_remember_upto_here_1 (str); |
5402 | return !0; | |
5403 | } | |
5404 | ||
0f2d19dd | 5405 | int |
e81d98ec | 5406 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5407 | { |
ca46fb90 | 5408 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
b57bf272 AW |
5409 | size_t len = strlen (str); |
5410 | void (*freefunc) (void *, size_t); | |
5411 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
ca46fb90 | 5412 | scm_remember_upto_here_1 (exp); |
b57bf272 AW |
5413 | scm_lfwrite (str, len, port); |
5414 | freefunc (str, len + 1); | |
0f2d19dd JB |
5415 | return !0; |
5416 | } | |
5417 | /*** END nums->strs ***/ | |
5418 | ||
3c9a524f | 5419 | |
0f2d19dd | 5420 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5421 | |
3c9a524f DH |
5422 | /* The following functions implement the conversion from strings to numbers. |
5423 | * The implementation somehow follows the grammar for numbers as it is given | |
5424 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5425 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5426 | * points should be noted about the implementation: | |
bc3d34f5 | 5427 | * |
3c9a524f DH |
5428 | * * Each function keeps a local index variable 'idx' that points at the |
5429 | * current position within the parsed string. The global index is only | |
5430 | * updated if the function could parse the corresponding syntactic unit | |
5431 | * successfully. | |
bc3d34f5 | 5432 | * |
3c9a524f | 5433 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5434 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5435 | * | |
3c9a524f DH |
5436 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5437 | * Only if these fixnums would overflow, the result variables are updated | |
5438 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5439 | * the temporary variables holding the fixnums are cleared, and the process | |
5440 | * starts over again. If for example fixnums were able to store five decimal | |
5441 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5442 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5443 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5444 | * |
5445 | * Notes on the handling of exactness specifiers: | |
5446 | * | |
5447 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5448 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5449 | * written in rectangular form, exactness specifiers are applied to the | |
5450 | * real and imaginary parts before calling scm_make_rectangular. For | |
5451 | * complex numbers written in polar form, exactness specifiers are applied | |
5452 | * to the magnitude and angle before calling scm_make_polar. | |
5453 | * | |
5454 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5455 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5456 | * the entire number, and applies to both components of a complex number. | |
5457 | * "#e" causes each component to be made exact, and "#i" causes each | |
5458 | * component to be made inexact. If no forced exactness specifier is | |
5459 | * present, then the exactness of each component is determined | |
5460 | * independently by the presence or absence of a decimal point or hash mark | |
5461 | * within that component. If a decimal point or hash mark is present, the | |
5462 | * component is made inexact, otherwise it is made exact. | |
5463 | * | |
5464 | * After the exactness specifiers have been applied to each component, they | |
5465 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5466 | * the final result. Note that this will result in a real number if the | |
5467 | * imaginary part, magnitude, or angle is an exact 0. | |
5468 | * | |
5469 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5470 | * | |
5471 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5472 | */ |
5473 | ||
5474 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5475 | ||
5476 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5477 | ||
a6f3af16 AW |
5478 | /* Caller is responsible for checking that the return value is in range |
5479 | for the given radix, which should be <= 36. */ | |
5480 | static unsigned int | |
5481 | char_decimal_value (scm_t_uint32 c) | |
5482 | { | |
5483 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5484 | that's certainly above any valid decimal, so we take advantage of | |
5485 | that to elide some tests. */ | |
5486 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5487 | ||
5488 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5489 | hexadecimals. */ | |
5490 | if (d >= 10U) | |
5491 | { | |
5492 | c = uc_tolower (c); | |
5493 | if (c >= (scm_t_uint32) 'a') | |
5494 | d = c - (scm_t_uint32)'a' + 10U; | |
5495 | } | |
5496 | return d; | |
5497 | } | |
3c9a524f | 5498 | |
91db4a37 LC |
5499 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5500 | in base RADIX. Upon success, return the unsigned integer and update | |
5501 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5502 | static SCM |
3f47e526 | 5503 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5504 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5505 | { |
3c9a524f DH |
5506 | unsigned int idx = *p_idx; |
5507 | unsigned int hash_seen = 0; | |
5508 | scm_t_bits shift = 1; | |
5509 | scm_t_bits add = 0; | |
5510 | unsigned int digit_value; | |
5511 | SCM result; | |
5512 | char c; | |
3f47e526 | 5513 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5514 | |
5515 | if (idx == len) | |
5516 | return SCM_BOOL_F; | |
2a8fecee | 5517 | |
3f47e526 | 5518 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5519 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5520 | if (digit_value >= radix) |
5521 | return SCM_BOOL_F; | |
5522 | ||
5523 | idx++; | |
d956fa6f | 5524 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5525 | while (idx != len) |
f872b822 | 5526 | { |
3f47e526 | 5527 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5528 | if (c == '#') |
3c9a524f DH |
5529 | { |
5530 | hash_seen = 1; | |
5531 | digit_value = 0; | |
5532 | } | |
a6f3af16 AW |
5533 | else if (hash_seen) |
5534 | break; | |
3c9a524f | 5535 | else |
a6f3af16 AW |
5536 | { |
5537 | digit_value = char_decimal_value (c); | |
5538 | /* This check catches non-decimals in addition to out-of-range | |
5539 | decimals. */ | |
5540 | if (digit_value >= radix) | |
5541 | break; | |
5542 | } | |
3c9a524f DH |
5543 | |
5544 | idx++; | |
5545 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5546 | { | |
d956fa6f | 5547 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5548 | if (add > 0) |
d956fa6f | 5549 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5550 | |
5551 | shift = radix; | |
5552 | add = digit_value; | |
5553 | } | |
5554 | else | |
5555 | { | |
5556 | shift = shift * radix; | |
5557 | add = add * radix + digit_value; | |
5558 | } | |
5559 | }; | |
5560 | ||
5561 | if (shift > 1) | |
d956fa6f | 5562 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5563 | if (add > 0) |
d956fa6f | 5564 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5565 | |
5566 | *p_idx = idx; | |
5567 | if (hash_seen) | |
5568 | *p_exactness = INEXACT; | |
5569 | ||
5570 | return result; | |
2a8fecee JB |
5571 | } |
5572 | ||
5573 | ||
3c9a524f DH |
5574 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5575 | * covers the parts of the rules that start at a potential point. The value | |
5576 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5577 | * in variable result. The content of *p_exactness indicates, whether a hash |
5578 | * has already been seen in the digits before the point. | |
3c9a524f | 5579 | */ |
1cc91f1b | 5580 | |
3f47e526 | 5581 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5582 | |
5583 | static SCM | |
3f47e526 | 5584 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5585 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5586 | { |
3c9a524f DH |
5587 | unsigned int idx = *p_idx; |
5588 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5589 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5590 | |
5591 | if (idx == len) | |
79d34f68 | 5592 | return result; |
3c9a524f | 5593 | |
3f47e526 | 5594 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5595 | { |
5596 | scm_t_bits shift = 1; | |
5597 | scm_t_bits add = 0; | |
5598 | unsigned int digit_value; | |
cff5fa33 | 5599 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5600 | |
5601 | idx++; | |
5602 | while (idx != len) | |
5603 | { | |
3f47e526 MG |
5604 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5605 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5606 | { |
5607 | if (x == INEXACT) | |
5608 | return SCM_BOOL_F; | |
5609 | else | |
5610 | digit_value = DIGIT2UINT (c); | |
5611 | } | |
5612 | else if (c == '#') | |
5613 | { | |
5614 | x = INEXACT; | |
5615 | digit_value = 0; | |
5616 | } | |
5617 | else | |
5618 | break; | |
5619 | ||
5620 | idx++; | |
5621 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5622 | { | |
d956fa6f MV |
5623 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5624 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5625 | if (add > 0) |
d956fa6f | 5626 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5627 | |
5628 | shift = 10; | |
5629 | add = digit_value; | |
5630 | } | |
5631 | else | |
5632 | { | |
5633 | shift = shift * 10; | |
5634 | add = add * 10 + digit_value; | |
5635 | } | |
5636 | }; | |
5637 | ||
5638 | if (add > 0) | |
5639 | { | |
d956fa6f MV |
5640 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5641 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5642 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5643 | } |
5644 | ||
d8592269 | 5645 | result = scm_divide (result, big_shift); |
79d34f68 | 5646 | |
3c9a524f DH |
5647 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5648 | x = INEXACT; | |
f872b822 | 5649 | } |
3c9a524f | 5650 | |
3c9a524f | 5651 | if (idx != len) |
f872b822 | 5652 | { |
3c9a524f DH |
5653 | int sign = 1; |
5654 | unsigned int start; | |
3f47e526 | 5655 | scm_t_wchar c; |
3c9a524f DH |
5656 | int exponent; |
5657 | SCM e; | |
5658 | ||
5659 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5660 | ||
3f47e526 | 5661 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5662 | { |
3c9a524f DH |
5663 | case 'd': case 'D': |
5664 | case 'e': case 'E': | |
5665 | case 'f': case 'F': | |
5666 | case 'l': case 'L': | |
5667 | case 's': case 'S': | |
5668 | idx++; | |
ee0ddd21 AW |
5669 | if (idx == len) |
5670 | return SCM_BOOL_F; | |
5671 | ||
3c9a524f | 5672 | start = idx; |
3f47e526 | 5673 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5674 | if (c == '-') |
5675 | { | |
5676 | idx++; | |
ee0ddd21 AW |
5677 | if (idx == len) |
5678 | return SCM_BOOL_F; | |
5679 | ||
3c9a524f | 5680 | sign = -1; |
3f47e526 | 5681 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5682 | } |
5683 | else if (c == '+') | |
5684 | { | |
5685 | idx++; | |
ee0ddd21 AW |
5686 | if (idx == len) |
5687 | return SCM_BOOL_F; | |
5688 | ||
3c9a524f | 5689 | sign = 1; |
3f47e526 | 5690 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5691 | } |
5692 | else | |
5693 | sign = 1; | |
5694 | ||
3f47e526 | 5695 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5696 | return SCM_BOOL_F; |
5697 | ||
5698 | idx++; | |
5699 | exponent = DIGIT2UINT (c); | |
5700 | while (idx != len) | |
f872b822 | 5701 | { |
3f47e526 MG |
5702 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5703 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5704 | { |
5705 | idx++; | |
5706 | if (exponent <= SCM_MAXEXP) | |
5707 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5708 | } | |
5709 | else | |
5710 | break; | |
f872b822 | 5711 | } |
3c9a524f DH |
5712 | |
5713 | if (exponent > SCM_MAXEXP) | |
f872b822 | 5714 | { |
3c9a524f | 5715 | size_t exp_len = idx - start; |
3f47e526 | 5716 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5717 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5718 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5719 | } |
3c9a524f | 5720 | |
d956fa6f | 5721 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5722 | if (sign == 1) |
5723 | result = scm_product (result, e); | |
5724 | else | |
6ebecdeb | 5725 | result = scm_divide (result, e); |
3c9a524f DH |
5726 | |
5727 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5728 | x = INEXACT; | |
5729 | ||
f872b822 | 5730 | break; |
3c9a524f | 5731 | |
f872b822 | 5732 | default: |
3c9a524f | 5733 | break; |
f872b822 | 5734 | } |
0f2d19dd | 5735 | } |
3c9a524f DH |
5736 | |
5737 | *p_idx = idx; | |
5738 | if (x == INEXACT) | |
5739 | *p_exactness = x; | |
5740 | ||
5741 | return result; | |
0f2d19dd | 5742 | } |
0f2d19dd | 5743 | |
3c9a524f DH |
5744 | |
5745 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5746 | ||
5747 | static SCM | |
3f47e526 | 5748 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 5749 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 5750 | { |
3c9a524f | 5751 | unsigned int idx = *p_idx; |
164d2481 | 5752 | SCM result; |
3f47e526 | 5753 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5754 | |
40f89215 NJ |
5755 | /* Start off believing that the number will be exact. This changes |
5756 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5757 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5758 | |
3c9a524f DH |
5759 | if (idx == len) |
5760 | return SCM_BOOL_F; | |
5761 | ||
3f47e526 | 5762 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
5763 | { |
5764 | *p_idx = idx+5; | |
5765 | return scm_inf (); | |
5766 | } | |
5767 | ||
3f47e526 | 5768 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 5769 | { |
d8592269 MV |
5770 | /* Cobble up the fractional part. We might want to set the |
5771 | NaN's mantissa from it. */ | |
7351e207 | 5772 | idx += 4; |
91db4a37 | 5773 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), SCM_INUM0)) |
5f237d6e AW |
5774 | { |
5775 | #if SCM_ENABLE_DEPRECATED == 1 | |
5776 | scm_c_issue_deprecation_warning | |
5777 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5778 | #else | |
5779 | return SCM_BOOL_F; | |
5780 | #endif | |
5781 | } | |
5782 | ||
7351e207 MV |
5783 | *p_idx = idx; |
5784 | return scm_nan (); | |
5785 | } | |
5786 | ||
3f47e526 | 5787 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5788 | { |
5789 | if (radix != 10) | |
5790 | return SCM_BOOL_F; | |
5791 | else if (idx + 1 == len) | |
5792 | return SCM_BOOL_F; | |
3f47e526 | 5793 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
5794 | return SCM_BOOL_F; |
5795 | else | |
cff5fa33 | 5796 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 5797 | p_idx, &implicit_x); |
f872b822 | 5798 | } |
3c9a524f DH |
5799 | else |
5800 | { | |
3c9a524f | 5801 | SCM uinteger; |
3c9a524f | 5802 | |
9d427b2c | 5803 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5804 | if (scm_is_false (uinteger)) |
3c9a524f DH |
5805 | return SCM_BOOL_F; |
5806 | ||
5807 | if (idx == len) | |
5808 | result = uinteger; | |
3f47e526 | 5809 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 5810 | { |
3c9a524f DH |
5811 | SCM divisor; |
5812 | ||
5813 | idx++; | |
ee0ddd21 AW |
5814 | if (idx == len) |
5815 | return SCM_BOOL_F; | |
3c9a524f | 5816 | |
9d427b2c | 5817 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5818 | if (scm_is_false (divisor)) |
3c9a524f DH |
5819 | return SCM_BOOL_F; |
5820 | ||
f92e85f7 | 5821 | /* both are int/big here, I assume */ |
cba42c93 | 5822 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 5823 | } |
3c9a524f DH |
5824 | else if (radix == 10) |
5825 | { | |
9d427b2c | 5826 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 5827 | if (scm_is_false (result)) |
3c9a524f DH |
5828 | return SCM_BOOL_F; |
5829 | } | |
5830 | else | |
5831 | result = uinteger; | |
5832 | ||
5833 | *p_idx = idx; | |
f872b822 | 5834 | } |
164d2481 | 5835 | |
9d427b2c MW |
5836 | switch (forced_x) |
5837 | { | |
5838 | case EXACT: | |
5839 | if (SCM_INEXACTP (result)) | |
5840 | return scm_inexact_to_exact (result); | |
5841 | else | |
5842 | return result; | |
5843 | case INEXACT: | |
5844 | if (SCM_INEXACTP (result)) | |
5845 | return result; | |
5846 | else | |
5847 | return scm_exact_to_inexact (result); | |
5848 | case NO_EXACTNESS: | |
5849 | if (implicit_x == INEXACT) | |
5850 | { | |
5851 | if (SCM_INEXACTP (result)) | |
5852 | return result; | |
5853 | else | |
5854 | return scm_exact_to_inexact (result); | |
5855 | } | |
5856 | else | |
5857 | return result; | |
5858 | } | |
164d2481 | 5859 | |
9d427b2c MW |
5860 | /* We should never get here */ |
5861 | scm_syserror ("mem2ureal"); | |
3c9a524f | 5862 | } |
0f2d19dd | 5863 | |
0f2d19dd | 5864 | |
3c9a524f | 5865 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 5866 | |
3c9a524f | 5867 | static SCM |
3f47e526 | 5868 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 5869 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 5870 | { |
3f47e526 | 5871 | scm_t_wchar c; |
3c9a524f DH |
5872 | int sign = 0; |
5873 | SCM ureal; | |
3f47e526 | 5874 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5875 | |
5876 | if (idx == len) | |
5877 | return SCM_BOOL_F; | |
5878 | ||
3f47e526 | 5879 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5880 | if (c == '+') |
5881 | { | |
5882 | idx++; | |
5883 | sign = 1; | |
5884 | } | |
5885 | else if (c == '-') | |
5886 | { | |
5887 | idx++; | |
5888 | sign = -1; | |
0f2d19dd | 5889 | } |
0f2d19dd | 5890 | |
3c9a524f DH |
5891 | if (idx == len) |
5892 | return SCM_BOOL_F; | |
5893 | ||
9d427b2c | 5894 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5895 | if (scm_is_false (ureal)) |
f872b822 | 5896 | { |
3c9a524f DH |
5897 | /* input must be either +i or -i */ |
5898 | ||
5899 | if (sign == 0) | |
5900 | return SCM_BOOL_F; | |
5901 | ||
3f47e526 MG |
5902 | if (scm_i_string_ref (mem, idx) == 'i' |
5903 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 5904 | { |
3c9a524f DH |
5905 | idx++; |
5906 | if (idx != len) | |
5907 | return SCM_BOOL_F; | |
5908 | ||
cff5fa33 | 5909 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 5910 | } |
3c9a524f DH |
5911 | else |
5912 | return SCM_BOOL_F; | |
0f2d19dd | 5913 | } |
3c9a524f DH |
5914 | else |
5915 | { | |
73e4de09 | 5916 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 5917 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 5918 | |
3c9a524f DH |
5919 | if (idx == len) |
5920 | return ureal; | |
5921 | ||
3f47e526 | 5922 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 5923 | switch (c) |
f872b822 | 5924 | { |
3c9a524f DH |
5925 | case 'i': case 'I': |
5926 | /* either +<ureal>i or -<ureal>i */ | |
5927 | ||
5928 | idx++; | |
5929 | if (sign == 0) | |
5930 | return SCM_BOOL_F; | |
5931 | if (idx != len) | |
5932 | return SCM_BOOL_F; | |
cff5fa33 | 5933 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
5934 | |
5935 | case '@': | |
5936 | /* polar input: <real>@<real>. */ | |
5937 | ||
5938 | idx++; | |
5939 | if (idx == len) | |
5940 | return SCM_BOOL_F; | |
5941 | else | |
f872b822 | 5942 | { |
3c9a524f DH |
5943 | int sign; |
5944 | SCM angle; | |
5945 | SCM result; | |
5946 | ||
3f47e526 | 5947 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5948 | if (c == '+') |
5949 | { | |
5950 | idx++; | |
ee0ddd21 AW |
5951 | if (idx == len) |
5952 | return SCM_BOOL_F; | |
3c9a524f DH |
5953 | sign = 1; |
5954 | } | |
5955 | else if (c == '-') | |
5956 | { | |
5957 | idx++; | |
ee0ddd21 AW |
5958 | if (idx == len) |
5959 | return SCM_BOOL_F; | |
3c9a524f DH |
5960 | sign = -1; |
5961 | } | |
5962 | else | |
5963 | sign = 1; | |
5964 | ||
9d427b2c | 5965 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5966 | if (scm_is_false (angle)) |
3c9a524f DH |
5967 | return SCM_BOOL_F; |
5968 | if (idx != len) | |
5969 | return SCM_BOOL_F; | |
5970 | ||
73e4de09 | 5971 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
5972 | angle = scm_difference (angle, SCM_UNDEFINED); |
5973 | ||
5974 | result = scm_make_polar (ureal, angle); | |
5975 | return result; | |
f872b822 | 5976 | } |
3c9a524f DH |
5977 | case '+': |
5978 | case '-': | |
5979 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 5980 | |
3c9a524f DH |
5981 | idx++; |
5982 | if (idx == len) | |
5983 | return SCM_BOOL_F; | |
5984 | else | |
5985 | { | |
5986 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 5987 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 5988 | |
73e4de09 | 5989 | if (scm_is_false (imag)) |
d956fa6f | 5990 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 5991 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 5992 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 5993 | |
3c9a524f DH |
5994 | if (idx == len) |
5995 | return SCM_BOOL_F; | |
3f47e526 MG |
5996 | if (scm_i_string_ref (mem, idx) != 'i' |
5997 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 5998 | return SCM_BOOL_F; |
0f2d19dd | 5999 | |
3c9a524f DH |
6000 | idx++; |
6001 | if (idx != len) | |
6002 | return SCM_BOOL_F; | |
0f2d19dd | 6003 | |
1fe5e088 | 6004 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6005 | } |
6006 | default: | |
6007 | return SCM_BOOL_F; | |
6008 | } | |
6009 | } | |
0f2d19dd | 6010 | } |
0f2d19dd JB |
6011 | |
6012 | ||
3c9a524f DH |
6013 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6014 | ||
6015 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6016 | |
0f2d19dd | 6017 | SCM |
3f47e526 | 6018 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6019 | { |
3c9a524f DH |
6020 | unsigned int idx = 0; |
6021 | unsigned int radix = NO_RADIX; | |
6022 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6023 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6024 | |
6025 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6026 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6027 | { |
3f47e526 | 6028 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6029 | { |
6030 | case 'b': case 'B': | |
6031 | if (radix != NO_RADIX) | |
6032 | return SCM_BOOL_F; | |
6033 | radix = DUAL; | |
6034 | break; | |
6035 | case 'd': case 'D': | |
6036 | if (radix != NO_RADIX) | |
6037 | return SCM_BOOL_F; | |
6038 | radix = DEC; | |
6039 | break; | |
6040 | case 'i': case 'I': | |
6041 | if (forced_x != NO_EXACTNESS) | |
6042 | return SCM_BOOL_F; | |
6043 | forced_x = INEXACT; | |
6044 | break; | |
6045 | case 'e': case 'E': | |
6046 | if (forced_x != NO_EXACTNESS) | |
6047 | return SCM_BOOL_F; | |
6048 | forced_x = EXACT; | |
6049 | break; | |
6050 | case 'o': case 'O': | |
6051 | if (radix != NO_RADIX) | |
6052 | return SCM_BOOL_F; | |
6053 | radix = OCT; | |
6054 | break; | |
6055 | case 'x': case 'X': | |
6056 | if (radix != NO_RADIX) | |
6057 | return SCM_BOOL_F; | |
6058 | radix = HEX; | |
6059 | break; | |
6060 | default: | |
f872b822 | 6061 | return SCM_BOOL_F; |
3c9a524f DH |
6062 | } |
6063 | idx += 2; | |
6064 | } | |
6065 | ||
6066 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6067 | if (radix == NO_RADIX) | |
9d427b2c | 6068 | radix = default_radix; |
f872b822 | 6069 | |
9d427b2c | 6070 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6071 | } |
6072 | ||
3f47e526 MG |
6073 | SCM |
6074 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6075 | unsigned int default_radix) | |
6076 | { | |
6077 | SCM str = scm_from_locale_stringn (mem, len); | |
6078 | ||
6079 | return scm_i_string_to_number (str, default_radix); | |
6080 | } | |
6081 | ||
0f2d19dd | 6082 | |
a1ec6916 | 6083 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6084 | (SCM string, SCM radix), |
1e6808ea | 6085 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6086 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6087 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6088 | "is a default radix that may be overridden by an explicit radix\n" | |
6089 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6090 | "supplied, then the default radix is 10. If string is not a\n" | |
6091 | "syntactically valid notation for a number, then\n" | |
6092 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6093 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6094 | { |
6095 | SCM answer; | |
5efd3c7d | 6096 | unsigned int base; |
a6d9e5ab | 6097 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6098 | |
6099 | if (SCM_UNBNDP (radix)) | |
6100 | base = 10; | |
6101 | else | |
6102 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6103 | ||
3f47e526 | 6104 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6105 | scm_remember_upto_here_1 (string); |
6106 | return answer; | |
0f2d19dd | 6107 | } |
1bbd0b84 | 6108 | #undef FUNC_NAME |
3c9a524f DH |
6109 | |
6110 | ||
0f2d19dd JB |
6111 | /*** END strs->nums ***/ |
6112 | ||
5986c47d | 6113 | |
8507ec80 MV |
6114 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6115 | (SCM x), | |
6116 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6117 | "otherwise.") | |
6118 | #define FUNC_NAME s_scm_number_p | |
6119 | { | |
6120 | return scm_from_bool (SCM_NUMBERP (x)); | |
6121 | } | |
6122 | #undef FUNC_NAME | |
6123 | ||
6124 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6125 | (SCM x), |
942e5b91 | 6126 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6127 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6128 | "values form subsets of the set of complex numbers, i. e. the\n" |
6129 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6130 | "rational or integer number.") | |
8507ec80 | 6131 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6132 | { |
8507ec80 MV |
6133 | /* all numbers are complex. */ |
6134 | return scm_number_p (x); | |
0f2d19dd | 6135 | } |
1bbd0b84 | 6136 | #undef FUNC_NAME |
0f2d19dd | 6137 | |
f92e85f7 MV |
6138 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6139 | (SCM x), | |
6140 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6141 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6142 | "the set of real numbers, i. e. the predicate will also be\n" | |
6143 | "fulfilled if @var{x} is an integer number.") | |
6144 | #define FUNC_NAME s_scm_real_p | |
6145 | { | |
c960e556 MW |
6146 | return scm_from_bool |
6147 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6148 | } |
6149 | #undef FUNC_NAME | |
6150 | ||
6151 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6152 | (SCM x), |
942e5b91 | 6153 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6154 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6155 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6156 | "fulfilled if @var{x} is an integer number.") |
6157 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6158 | { |
c960e556 | 6159 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6160 | return SCM_BOOL_T; |
6161 | else if (SCM_REALP (x)) | |
c960e556 MW |
6162 | /* due to their limited precision, finite floating point numbers are |
6163 | rational as well. (finite means neither infinity nor a NaN) */ | |
6164 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6165 | else |
bb628794 | 6166 | return SCM_BOOL_F; |
0f2d19dd | 6167 | } |
1bbd0b84 | 6168 | #undef FUNC_NAME |
0f2d19dd | 6169 | |
a1ec6916 | 6170 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6171 | (SCM x), |
942e5b91 MG |
6172 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6173 | "else.") | |
1bbd0b84 | 6174 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6175 | { |
c960e556 | 6176 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6177 | return SCM_BOOL_T; |
c960e556 MW |
6178 | else if (SCM_REALP (x)) |
6179 | { | |
6180 | double val = SCM_REAL_VALUE (x); | |
6181 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6182 | } | |
6183 | else | |
8e43ed5d | 6184 | return SCM_BOOL_F; |
0f2d19dd | 6185 | } |
1bbd0b84 | 6186 | #undef FUNC_NAME |
0f2d19dd JB |
6187 | |
6188 | ||
8a1f4f98 AW |
6189 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6190 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6191 | (SCM x, SCM y, SCM rest), | |
6192 | "Return @code{#t} if all parameters are numerically equal.") | |
6193 | #define FUNC_NAME s_scm_i_num_eq_p | |
6194 | { | |
6195 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6196 | return SCM_BOOL_T; | |
6197 | while (!scm_is_null (rest)) | |
6198 | { | |
6199 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6200 | return SCM_BOOL_F; | |
6201 | x = y; | |
6202 | y = scm_car (rest); | |
6203 | rest = scm_cdr (rest); | |
6204 | } | |
6205 | return scm_num_eq_p (x, y); | |
6206 | } | |
6207 | #undef FUNC_NAME | |
0f2d19dd | 6208 | SCM |
6e8d25a6 | 6209 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6210 | { |
d8b95e27 | 6211 | again: |
e11e83f3 | 6212 | if (SCM_I_INUMP (x)) |
0aacf84e | 6213 | { |
e25f3727 | 6214 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6215 | if (SCM_I_INUMP (y)) |
0aacf84e | 6216 | { |
e25f3727 | 6217 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6218 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6219 | } |
6220 | else if (SCM_BIGP (y)) | |
6221 | return SCM_BOOL_F; | |
6222 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6223 | { |
6224 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6225 | to a double and compare. | |
6226 | ||
6227 | But on a 64-bit system an inum is bigger than a double and | |
6228 | casting it to a double (call that dxx) will round. dxx is at | |
6229 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6230 | an integer and fits a long. So we cast yy to a long and | |
6231 | compare with plain xx. | |
6232 | ||
6233 | An alternative (for any size system actually) would be to check | |
6234 | yy is an integer (with floor) and is in range of an inum | |
6235 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6236 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6237 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6238 | |
6239 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6240 | return scm_from_bool ((double) xx == yy |
6241 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6242 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6243 | } |
0aacf84e | 6244 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6245 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6246 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6247 | else if (SCM_FRACTIONP (y)) |
6248 | return SCM_BOOL_F; | |
0aacf84e | 6249 | else |
8a1f4f98 | 6250 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6251 | } |
0aacf84e MD |
6252 | else if (SCM_BIGP (x)) |
6253 | { | |
e11e83f3 | 6254 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6255 | return SCM_BOOL_F; |
6256 | else if (SCM_BIGP (y)) | |
6257 | { | |
6258 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6259 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6260 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6261 | } |
6262 | else if (SCM_REALP (y)) | |
6263 | { | |
6264 | int cmp; | |
2e65b52f | 6265 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6266 | return SCM_BOOL_F; |
6267 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6268 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6269 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6270 | } |
6271 | else if (SCM_COMPLEXP (y)) | |
6272 | { | |
6273 | int cmp; | |
6274 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6275 | return SCM_BOOL_F; | |
2e65b52f | 6276 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6277 | return SCM_BOOL_F; |
6278 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6279 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6280 | return scm_from_bool (0 == cmp); |
0aacf84e | 6281 | } |
f92e85f7 MV |
6282 | else if (SCM_FRACTIONP (y)) |
6283 | return SCM_BOOL_F; | |
0aacf84e | 6284 | else |
8a1f4f98 | 6285 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6286 | } |
0aacf84e MD |
6287 | else if (SCM_REALP (x)) |
6288 | { | |
e8c5b1f2 | 6289 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6290 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6291 | { |
6292 | /* see comments with inum/real above */ | |
e25f3727 | 6293 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6294 | return scm_from_bool (xx == (double) yy |
6295 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6296 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6297 | } |
0aacf84e MD |
6298 | else if (SCM_BIGP (y)) |
6299 | { | |
6300 | int cmp; | |
2e65b52f | 6301 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6302 | return SCM_BOOL_F; |
6303 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6304 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6305 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6306 | } |
6307 | else if (SCM_REALP (y)) | |
73e4de09 | 6308 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6309 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6310 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6311 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6312 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6313 | { |
6314 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6315 | if (isnan (xx)) |
d8b95e27 | 6316 | return SCM_BOOL_F; |
2e65b52f | 6317 | if (isinf (xx)) |
73e4de09 | 6318 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6319 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6320 | goto again; | |
6321 | } | |
0aacf84e | 6322 | else |
8a1f4f98 | 6323 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6324 | } |
0aacf84e MD |
6325 | else if (SCM_COMPLEXP (x)) |
6326 | { | |
e11e83f3 MV |
6327 | if (SCM_I_INUMP (y)) |
6328 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6329 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6330 | else if (SCM_BIGP (y)) | |
6331 | { | |
6332 | int cmp; | |
6333 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6334 | return SCM_BOOL_F; | |
2e65b52f | 6335 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6336 | return SCM_BOOL_F; |
6337 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6338 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6339 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6340 | } |
6341 | else if (SCM_REALP (y)) | |
73e4de09 | 6342 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6343 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6344 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6345 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6346 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6347 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6348 | { |
6349 | double xx; | |
6350 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6351 | return SCM_BOOL_F; | |
6352 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6353 | if (isnan (xx)) |
d8b95e27 | 6354 | return SCM_BOOL_F; |
2e65b52f | 6355 | if (isinf (xx)) |
73e4de09 | 6356 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6357 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6358 | goto again; | |
6359 | } | |
f92e85f7 | 6360 | else |
8a1f4f98 | 6361 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6362 | } |
6363 | else if (SCM_FRACTIONP (x)) | |
6364 | { | |
e11e83f3 | 6365 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6366 | return SCM_BOOL_F; |
6367 | else if (SCM_BIGP (y)) | |
6368 | return SCM_BOOL_F; | |
6369 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6370 | { |
6371 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6372 | if (isnan (yy)) |
d8b95e27 | 6373 | return SCM_BOOL_F; |
2e65b52f | 6374 | if (isinf (yy)) |
73e4de09 | 6375 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6376 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6377 | goto again; | |
6378 | } | |
f92e85f7 | 6379 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6380 | { |
6381 | double yy; | |
6382 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6383 | return SCM_BOOL_F; | |
6384 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6385 | if (isnan (yy)) |
d8b95e27 | 6386 | return SCM_BOOL_F; |
2e65b52f | 6387 | if (isinf (yy)) |
73e4de09 | 6388 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6389 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6390 | goto again; | |
6391 | } | |
f92e85f7 MV |
6392 | else if (SCM_FRACTIONP (y)) |
6393 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6394 | else |
8a1f4f98 | 6395 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6396 | } |
0aacf84e | 6397 | else |
8a1f4f98 | 6398 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6399 | } |
6400 | ||
6401 | ||
a5f0b599 KR |
6402 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6403 | done are good for inums, but for bignums an answer can almost always be | |
6404 | had by just examining a few high bits of the operands, as done by GMP in | |
6405 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6406 | of the float exponent to take into account. */ | |
6407 | ||
8c93b597 | 6408 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6409 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6410 | (SCM x, SCM y, SCM rest), | |
6411 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6412 | "increasing.") | |
6413 | #define FUNC_NAME s_scm_i_num_less_p | |
6414 | { | |
6415 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6416 | return SCM_BOOL_T; | |
6417 | while (!scm_is_null (rest)) | |
6418 | { | |
6419 | if (scm_is_false (scm_less_p (x, y))) | |
6420 | return SCM_BOOL_F; | |
6421 | x = y; | |
6422 | y = scm_car (rest); | |
6423 | rest = scm_cdr (rest); | |
6424 | } | |
6425 | return scm_less_p (x, y); | |
6426 | } | |
6427 | #undef FUNC_NAME | |
0f2d19dd | 6428 | SCM |
6e8d25a6 | 6429 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6430 | { |
a5f0b599 | 6431 | again: |
e11e83f3 | 6432 | if (SCM_I_INUMP (x)) |
0aacf84e | 6433 | { |
e25f3727 | 6434 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6435 | if (SCM_I_INUMP (y)) |
0aacf84e | 6436 | { |
e25f3727 | 6437 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6438 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6439 | } |
6440 | else if (SCM_BIGP (y)) | |
6441 | { | |
6442 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6443 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6444 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6445 | } |
6446 | else if (SCM_REALP (y)) | |
73e4de09 | 6447 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6448 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6449 | { |
6450 | /* "x < a/b" becomes "x*b < a" */ | |
6451 | int_frac: | |
6452 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6453 | y = SCM_FRACTION_NUMERATOR (y); | |
6454 | goto again; | |
6455 | } | |
0aacf84e | 6456 | else |
8a1f4f98 | 6457 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6458 | } |
0aacf84e MD |
6459 | else if (SCM_BIGP (x)) |
6460 | { | |
e11e83f3 | 6461 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6462 | { |
6463 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6464 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6465 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6466 | } |
6467 | else if (SCM_BIGP (y)) | |
6468 | { | |
6469 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6470 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6471 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6472 | } |
6473 | else if (SCM_REALP (y)) | |
6474 | { | |
6475 | int cmp; | |
2e65b52f | 6476 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6477 | return SCM_BOOL_F; |
6478 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6479 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6480 | return scm_from_bool (cmp < 0); |
0aacf84e | 6481 | } |
f92e85f7 | 6482 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6483 | goto int_frac; |
0aacf84e | 6484 | else |
8a1f4f98 | 6485 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6486 | } |
0aacf84e MD |
6487 | else if (SCM_REALP (x)) |
6488 | { | |
e11e83f3 MV |
6489 | if (SCM_I_INUMP (y)) |
6490 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6491 | else if (SCM_BIGP (y)) |
6492 | { | |
6493 | int cmp; | |
2e65b52f | 6494 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6495 | return SCM_BOOL_F; |
6496 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6497 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6498 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6499 | } |
6500 | else if (SCM_REALP (y)) | |
73e4de09 | 6501 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6502 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6503 | { |
6504 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6505 | if (isnan (xx)) |
a5f0b599 | 6506 | return SCM_BOOL_F; |
2e65b52f | 6507 | if (isinf (xx)) |
73e4de09 | 6508 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6509 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6510 | goto again; | |
6511 | } | |
f92e85f7 | 6512 | else |
8a1f4f98 | 6513 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6514 | } |
6515 | else if (SCM_FRACTIONP (x)) | |
6516 | { | |
e11e83f3 | 6517 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6518 | { |
6519 | /* "a/b < y" becomes "a < y*b" */ | |
6520 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6521 | x = SCM_FRACTION_NUMERATOR (x); | |
6522 | goto again; | |
6523 | } | |
f92e85f7 | 6524 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6525 | { |
6526 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6527 | if (isnan (yy)) |
a5f0b599 | 6528 | return SCM_BOOL_F; |
2e65b52f | 6529 | if (isinf (yy)) |
73e4de09 | 6530 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6531 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6532 | goto again; | |
6533 | } | |
f92e85f7 | 6534 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6535 | { |
6536 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6537 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6538 | SCM_FRACTION_DENOMINATOR (y)); | |
6539 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6540 | SCM_FRACTION_DENOMINATOR (x)); | |
6541 | x = new_x; | |
6542 | y = new_y; | |
6543 | goto again; | |
6544 | } | |
0aacf84e | 6545 | else |
8a1f4f98 | 6546 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6547 | } |
0aacf84e | 6548 | else |
8a1f4f98 | 6549 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6550 | } |
6551 | ||
6552 | ||
8a1f4f98 AW |
6553 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6554 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6555 | (SCM x, SCM y, SCM rest), | |
6556 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6557 | "decreasing.") | |
6558 | #define FUNC_NAME s_scm_i_num_gr_p | |
6559 | { | |
6560 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6561 | return SCM_BOOL_T; | |
6562 | while (!scm_is_null (rest)) | |
6563 | { | |
6564 | if (scm_is_false (scm_gr_p (x, y))) | |
6565 | return SCM_BOOL_F; | |
6566 | x = y; | |
6567 | y = scm_car (rest); | |
6568 | rest = scm_cdr (rest); | |
6569 | } | |
6570 | return scm_gr_p (x, y); | |
6571 | } | |
6572 | #undef FUNC_NAME | |
6573 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6574 | SCM |
6575 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6576 | { |
c76b1eaf | 6577 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6578 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6579 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6580 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6581 | else |
6582 | return scm_less_p (y, x); | |
0f2d19dd | 6583 | } |
1bbd0b84 | 6584 | #undef FUNC_NAME |
0f2d19dd JB |
6585 | |
6586 | ||
8a1f4f98 AW |
6587 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6588 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6589 | (SCM x, SCM y, SCM rest), | |
6590 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6591 | "non-decreasing.") | |
6592 | #define FUNC_NAME s_scm_i_num_leq_p | |
6593 | { | |
6594 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6595 | return SCM_BOOL_T; | |
6596 | while (!scm_is_null (rest)) | |
6597 | { | |
6598 | if (scm_is_false (scm_leq_p (x, y))) | |
6599 | return SCM_BOOL_F; | |
6600 | x = y; | |
6601 | y = scm_car (rest); | |
6602 | rest = scm_cdr (rest); | |
6603 | } | |
6604 | return scm_leq_p (x, y); | |
6605 | } | |
6606 | #undef FUNC_NAME | |
6607 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6608 | SCM |
6609 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6610 | { |
c76b1eaf | 6611 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6612 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6613 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6614 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6615 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6616 | return SCM_BOOL_F; |
c76b1eaf | 6617 | else |
73e4de09 | 6618 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6619 | } |
1bbd0b84 | 6620 | #undef FUNC_NAME |
0f2d19dd JB |
6621 | |
6622 | ||
8a1f4f98 AW |
6623 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6624 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6625 | (SCM x, SCM y, SCM rest), | |
6626 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6627 | "non-increasing.") | |
6628 | #define FUNC_NAME s_scm_i_num_geq_p | |
6629 | { | |
6630 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6631 | return SCM_BOOL_T; | |
6632 | while (!scm_is_null (rest)) | |
6633 | { | |
6634 | if (scm_is_false (scm_geq_p (x, y))) | |
6635 | return SCM_BOOL_F; | |
6636 | x = y; | |
6637 | y = scm_car (rest); | |
6638 | rest = scm_cdr (rest); | |
6639 | } | |
6640 | return scm_geq_p (x, y); | |
6641 | } | |
6642 | #undef FUNC_NAME | |
6643 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6644 | SCM |
6645 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6646 | { |
c76b1eaf | 6647 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6648 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6649 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6650 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6651 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6652 | return SCM_BOOL_F; |
c76b1eaf | 6653 | else |
73e4de09 | 6654 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6655 | } |
1bbd0b84 | 6656 | #undef FUNC_NAME |
0f2d19dd JB |
6657 | |
6658 | ||
2519490c MW |
6659 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6660 | (SCM z), | |
6661 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6662 | "zero.") | |
6663 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6664 | { |
e11e83f3 | 6665 | if (SCM_I_INUMP (z)) |
bc36d050 | 6666 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6667 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6668 | return SCM_BOOL_F; |
0aacf84e | 6669 | else if (SCM_REALP (z)) |
73e4de09 | 6670 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6671 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6672 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6673 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6674 | else if (SCM_FRACTIONP (z)) |
6675 | return SCM_BOOL_F; | |
0aacf84e | 6676 | else |
2519490c | 6677 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6678 | } |
2519490c | 6679 | #undef FUNC_NAME |
0f2d19dd JB |
6680 | |
6681 | ||
2519490c MW |
6682 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6683 | (SCM x), | |
6684 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6685 | "zero.") | |
6686 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6687 | { |
e11e83f3 MV |
6688 | if (SCM_I_INUMP (x)) |
6689 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6690 | else if (SCM_BIGP (x)) |
6691 | { | |
6692 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6693 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6694 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6695 | } |
6696 | else if (SCM_REALP (x)) | |
73e4de09 | 6697 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6698 | else if (SCM_FRACTIONP (x)) |
6699 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6700 | else |
2519490c | 6701 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6702 | } |
2519490c | 6703 | #undef FUNC_NAME |
0f2d19dd JB |
6704 | |
6705 | ||
2519490c MW |
6706 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6707 | (SCM x), | |
6708 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6709 | "zero.") | |
6710 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6711 | { |
e11e83f3 MV |
6712 | if (SCM_I_INUMP (x)) |
6713 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6714 | else if (SCM_BIGP (x)) |
6715 | { | |
6716 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6717 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6718 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6719 | } |
6720 | else if (SCM_REALP (x)) | |
73e4de09 | 6721 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6722 | else if (SCM_FRACTIONP (x)) |
6723 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6724 | else |
2519490c | 6725 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6726 | } |
2519490c | 6727 | #undef FUNC_NAME |
0f2d19dd JB |
6728 | |
6729 | ||
2a06f791 KR |
6730 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6731 | required by r5rs. On that basis, for exact/inexact combinations the | |
6732 | exact is converted to inexact to compare and possibly return. This is | |
6733 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6734 | its test, such trouble is not required for min and max. */ | |
6735 | ||
78d3deb1 AW |
6736 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6737 | (SCM x, SCM y, SCM rest), | |
6738 | "Return the maximum of all parameter values.") | |
6739 | #define FUNC_NAME s_scm_i_max | |
6740 | { | |
6741 | while (!scm_is_null (rest)) | |
6742 | { x = scm_max (x, y); | |
6743 | y = scm_car (rest); | |
6744 | rest = scm_cdr (rest); | |
6745 | } | |
6746 | return scm_max (x, y); | |
6747 | } | |
6748 | #undef FUNC_NAME | |
6749 | ||
6750 | #define s_max s_scm_i_max | |
6751 | #define g_max g_scm_i_max | |
6752 | ||
0f2d19dd | 6753 | SCM |
6e8d25a6 | 6754 | scm_max (SCM x, SCM y) |
0f2d19dd | 6755 | { |
0aacf84e MD |
6756 | if (SCM_UNBNDP (y)) |
6757 | { | |
6758 | if (SCM_UNBNDP (x)) | |
6759 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 6760 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6761 | return x; |
6762 | else | |
6763 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 6764 | } |
f4c627b3 | 6765 | |
e11e83f3 | 6766 | if (SCM_I_INUMP (x)) |
0aacf84e | 6767 | { |
e25f3727 | 6768 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6769 | if (SCM_I_INUMP (y)) |
0aacf84e | 6770 | { |
e25f3727 | 6771 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6772 | return (xx < yy) ? y : x; |
6773 | } | |
6774 | else if (SCM_BIGP (y)) | |
6775 | { | |
6776 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6777 | scm_remember_upto_here_1 (y); | |
6778 | return (sgn < 0) ? x : y; | |
6779 | } | |
6780 | else if (SCM_REALP (y)) | |
6781 | { | |
2e274311 MW |
6782 | double xxd = xx; |
6783 | double yyd = SCM_REAL_VALUE (y); | |
6784 | ||
6785 | if (xxd > yyd) | |
6786 | return scm_from_double (xxd); | |
6787 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
6788 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6789 | return y; | |
6790 | /* Handle signed zeroes properly */ | |
6791 | else if (xx == 0) | |
6792 | return flo0; | |
6793 | else | |
6794 | return y; | |
0aacf84e | 6795 | } |
f92e85f7 MV |
6796 | else if (SCM_FRACTIONP (y)) |
6797 | { | |
e4bc5d6c | 6798 | use_less: |
73e4de09 | 6799 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 6800 | } |
0aacf84e MD |
6801 | else |
6802 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6803 | } |
0aacf84e MD |
6804 | else if (SCM_BIGP (x)) |
6805 | { | |
e11e83f3 | 6806 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6807 | { |
6808 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6809 | scm_remember_upto_here_1 (x); | |
6810 | return (sgn < 0) ? y : x; | |
6811 | } | |
6812 | else if (SCM_BIGP (y)) | |
6813 | { | |
6814 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6815 | scm_remember_upto_here_2 (x, y); | |
6816 | return (cmp > 0) ? x : y; | |
6817 | } | |
6818 | else if (SCM_REALP (y)) | |
6819 | { | |
2a06f791 KR |
6820 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
6821 | double xx, yy; | |
6822 | big_real: | |
6823 | xx = scm_i_big2dbl (x); | |
6824 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6825 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 6826 | } |
f92e85f7 MV |
6827 | else if (SCM_FRACTIONP (y)) |
6828 | { | |
e4bc5d6c | 6829 | goto use_less; |
f92e85f7 | 6830 | } |
0aacf84e MD |
6831 | else |
6832 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 6833 | } |
0aacf84e MD |
6834 | else if (SCM_REALP (x)) |
6835 | { | |
e11e83f3 | 6836 | if (SCM_I_INUMP (y)) |
0aacf84e | 6837 | { |
2e274311 MW |
6838 | scm_t_inum yy = SCM_I_INUM (y); |
6839 | double xxd = SCM_REAL_VALUE (x); | |
6840 | double yyd = yy; | |
6841 | ||
6842 | if (yyd > xxd) | |
6843 | return scm_from_double (yyd); | |
6844 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
6845 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6846 | return x; | |
6847 | /* Handle signed zeroes properly */ | |
6848 | else if (yy == 0) | |
6849 | return flo0; | |
6850 | else | |
6851 | return x; | |
0aacf84e MD |
6852 | } |
6853 | else if (SCM_BIGP (y)) | |
6854 | { | |
b6f8f763 | 6855 | SCM_SWAP (x, y); |
2a06f791 | 6856 | goto big_real; |
0aacf84e MD |
6857 | } |
6858 | else if (SCM_REALP (y)) | |
6859 | { | |
0aacf84e | 6860 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6861 | double yy = SCM_REAL_VALUE (y); |
6862 | ||
6863 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
6864 | if (xx > yy) | |
6865 | return x; | |
6866 | else if (SCM_LIKELY (xx < yy)) | |
6867 | return y; | |
6868 | /* If neither (xx > yy) nor (xx < yy), then | |
6869 | either they're equal or one is a NaN */ | |
6870 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6871 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 6872 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6873 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6874 | /* xx == yy, but handle signed zeroes properly */ |
6875 | else if (double_is_non_negative_zero (yy)) | |
6876 | return y; | |
6877 | else | |
6878 | return x; | |
0aacf84e | 6879 | } |
f92e85f7 MV |
6880 | else if (SCM_FRACTIONP (y)) |
6881 | { | |
6882 | double yy = scm_i_fraction2double (y); | |
6883 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6884 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
6885 | } |
6886 | else | |
6887 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
6888 | } | |
6889 | else if (SCM_FRACTIONP (x)) | |
6890 | { | |
e11e83f3 | 6891 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6892 | { |
e4bc5d6c | 6893 | goto use_less; |
f92e85f7 MV |
6894 | } |
6895 | else if (SCM_BIGP (y)) | |
6896 | { | |
e4bc5d6c | 6897 | goto use_less; |
f92e85f7 MV |
6898 | } |
6899 | else if (SCM_REALP (y)) | |
6900 | { | |
6901 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
6902 | /* if y==NaN then ">" is false, so we return the NaN y */ |
6903 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
6904 | } |
6905 | else if (SCM_FRACTIONP (y)) | |
6906 | { | |
e4bc5d6c | 6907 | goto use_less; |
f92e85f7 | 6908 | } |
0aacf84e MD |
6909 | else |
6910 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6911 | } |
0aacf84e | 6912 | else |
f4c627b3 | 6913 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
6914 | } |
6915 | ||
6916 | ||
78d3deb1 AW |
6917 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
6918 | (SCM x, SCM y, SCM rest), | |
6919 | "Return the minimum of all parameter values.") | |
6920 | #define FUNC_NAME s_scm_i_min | |
6921 | { | |
6922 | while (!scm_is_null (rest)) | |
6923 | { x = scm_min (x, y); | |
6924 | y = scm_car (rest); | |
6925 | rest = scm_cdr (rest); | |
6926 | } | |
6927 | return scm_min (x, y); | |
6928 | } | |
6929 | #undef FUNC_NAME | |
6930 | ||
6931 | #define s_min s_scm_i_min | |
6932 | #define g_min g_scm_i_min | |
6933 | ||
0f2d19dd | 6934 | SCM |
6e8d25a6 | 6935 | scm_min (SCM x, SCM y) |
0f2d19dd | 6936 | { |
0aacf84e MD |
6937 | if (SCM_UNBNDP (y)) |
6938 | { | |
6939 | if (SCM_UNBNDP (x)) | |
6940 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 6941 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6942 | return x; |
6943 | else | |
6944 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 6945 | } |
f4c627b3 | 6946 | |
e11e83f3 | 6947 | if (SCM_I_INUMP (x)) |
0aacf84e | 6948 | { |
e25f3727 | 6949 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6950 | if (SCM_I_INUMP (y)) |
0aacf84e | 6951 | { |
e25f3727 | 6952 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6953 | return (xx < yy) ? x : y; |
6954 | } | |
6955 | else if (SCM_BIGP (y)) | |
6956 | { | |
6957 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6958 | scm_remember_upto_here_1 (y); | |
6959 | return (sgn < 0) ? y : x; | |
6960 | } | |
6961 | else if (SCM_REALP (y)) | |
6962 | { | |
6963 | double z = xx; | |
6964 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 6965 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 6966 | } |
f92e85f7 MV |
6967 | else if (SCM_FRACTIONP (y)) |
6968 | { | |
e4bc5d6c | 6969 | use_less: |
73e4de09 | 6970 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 6971 | } |
0aacf84e MD |
6972 | else |
6973 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 6974 | } |
0aacf84e MD |
6975 | else if (SCM_BIGP (x)) |
6976 | { | |
e11e83f3 | 6977 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6978 | { |
6979 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6980 | scm_remember_upto_here_1 (x); | |
6981 | return (sgn < 0) ? x : y; | |
6982 | } | |
6983 | else if (SCM_BIGP (y)) | |
6984 | { | |
6985 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6986 | scm_remember_upto_here_2 (x, y); | |
6987 | return (cmp > 0) ? y : x; | |
6988 | } | |
6989 | else if (SCM_REALP (y)) | |
6990 | { | |
2a06f791 KR |
6991 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
6992 | double xx, yy; | |
6993 | big_real: | |
6994 | xx = scm_i_big2dbl (x); | |
6995 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6996 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 6997 | } |
f92e85f7 MV |
6998 | else if (SCM_FRACTIONP (y)) |
6999 | { | |
e4bc5d6c | 7000 | goto use_less; |
f92e85f7 | 7001 | } |
0aacf84e MD |
7002 | else |
7003 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 7004 | } |
0aacf84e MD |
7005 | else if (SCM_REALP (x)) |
7006 | { | |
e11e83f3 | 7007 | if (SCM_I_INUMP (y)) |
0aacf84e | 7008 | { |
e11e83f3 | 7009 | double z = SCM_I_INUM (y); |
0aacf84e | 7010 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7011 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7012 | } |
7013 | else if (SCM_BIGP (y)) | |
7014 | { | |
b6f8f763 | 7015 | SCM_SWAP (x, y); |
2a06f791 | 7016 | goto big_real; |
0aacf84e MD |
7017 | } |
7018 | else if (SCM_REALP (y)) | |
7019 | { | |
0aacf84e | 7020 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7021 | double yy = SCM_REAL_VALUE (y); |
7022 | ||
7023 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
7024 | if (xx < yy) | |
7025 | return x; | |
7026 | else if (SCM_LIKELY (xx > yy)) | |
7027 | return y; | |
7028 | /* If neither (xx < yy) nor (xx > yy), then | |
7029 | either they're equal or one is a NaN */ | |
7030 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7031 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 7032 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7033 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7034 | /* xx == yy, but handle signed zeroes properly */ |
7035 | else if (double_is_non_negative_zero (xx)) | |
7036 | return y; | |
7037 | else | |
7038 | return x; | |
0aacf84e | 7039 | } |
f92e85f7 MV |
7040 | else if (SCM_FRACTIONP (y)) |
7041 | { | |
7042 | double yy = scm_i_fraction2double (y); | |
7043 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7044 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7045 | } |
0aacf84e MD |
7046 | else |
7047 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7048 | } |
f92e85f7 MV |
7049 | else if (SCM_FRACTIONP (x)) |
7050 | { | |
e11e83f3 | 7051 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7052 | { |
e4bc5d6c | 7053 | goto use_less; |
f92e85f7 MV |
7054 | } |
7055 | else if (SCM_BIGP (y)) | |
7056 | { | |
e4bc5d6c | 7057 | goto use_less; |
f92e85f7 MV |
7058 | } |
7059 | else if (SCM_REALP (y)) | |
7060 | { | |
7061 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7062 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7063 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7064 | } |
7065 | else if (SCM_FRACTIONP (y)) | |
7066 | { | |
e4bc5d6c | 7067 | goto use_less; |
f92e85f7 MV |
7068 | } |
7069 | else | |
78d3deb1 | 7070 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7071 | } |
0aacf84e | 7072 | else |
f4c627b3 | 7073 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7074 | } |
7075 | ||
7076 | ||
8ccd24f7 AW |
7077 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7078 | (SCM x, SCM y, SCM rest), | |
7079 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7080 | "any parameters." ) | |
7081 | #define FUNC_NAME s_scm_i_sum | |
7082 | { | |
7083 | while (!scm_is_null (rest)) | |
7084 | { x = scm_sum (x, y); | |
7085 | y = scm_car (rest); | |
7086 | rest = scm_cdr (rest); | |
7087 | } | |
7088 | return scm_sum (x, y); | |
7089 | } | |
7090 | #undef FUNC_NAME | |
7091 | ||
7092 | #define s_sum s_scm_i_sum | |
7093 | #define g_sum g_scm_i_sum | |
7094 | ||
0f2d19dd | 7095 | SCM |
6e8d25a6 | 7096 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7097 | { |
9cc37597 | 7098 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7099 | { |
7100 | if (SCM_NUMBERP (x)) return x; | |
7101 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7102 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7103 | } |
c209c88e | 7104 | |
9cc37597 | 7105 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7106 | { |
9cc37597 | 7107 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7108 | { |
e25f3727 AW |
7109 | scm_t_inum xx = SCM_I_INUM (x); |
7110 | scm_t_inum yy = SCM_I_INUM (y); | |
7111 | scm_t_inum z = xx + yy; | |
7112 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7113 | } |
7114 | else if (SCM_BIGP (y)) | |
7115 | { | |
7116 | SCM_SWAP (x, y); | |
7117 | goto add_big_inum; | |
7118 | } | |
7119 | else if (SCM_REALP (y)) | |
7120 | { | |
e25f3727 | 7121 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7122 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7123 | } |
7124 | else if (SCM_COMPLEXP (y)) | |
7125 | { | |
e25f3727 | 7126 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7127 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7128 | SCM_COMPLEX_IMAG (y)); |
7129 | } | |
f92e85f7 | 7130 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7131 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7132 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7133 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7134 | else |
7135 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7136 | } else if (SCM_BIGP (x)) |
7137 | { | |
e11e83f3 | 7138 | if (SCM_I_INUMP (y)) |
0aacf84e | 7139 | { |
e25f3727 | 7140 | scm_t_inum inum; |
0aacf84e MD |
7141 | int bigsgn; |
7142 | add_big_inum: | |
e11e83f3 | 7143 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7144 | if (inum == 0) |
7145 | return x; | |
7146 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7147 | if (inum < 0) | |
7148 | { | |
7149 | SCM result = scm_i_mkbig (); | |
7150 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7151 | scm_remember_upto_here_1 (x); | |
7152 | /* we know the result will have to be a bignum */ | |
7153 | if (bigsgn == -1) | |
7154 | return result; | |
7155 | return scm_i_normbig (result); | |
7156 | } | |
7157 | else | |
7158 | { | |
7159 | SCM result = scm_i_mkbig (); | |
7160 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7161 | scm_remember_upto_here_1 (x); | |
7162 | /* we know the result will have to be a bignum */ | |
7163 | if (bigsgn == 1) | |
7164 | return result; | |
7165 | return scm_i_normbig (result); | |
7166 | } | |
7167 | } | |
7168 | else if (SCM_BIGP (y)) | |
7169 | { | |
7170 | SCM result = scm_i_mkbig (); | |
7171 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7172 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7173 | mpz_add (SCM_I_BIG_MPZ (result), | |
7174 | SCM_I_BIG_MPZ (x), | |
7175 | SCM_I_BIG_MPZ (y)); | |
7176 | scm_remember_upto_here_2 (x, y); | |
7177 | /* we know the result will have to be a bignum */ | |
7178 | if (sgn_x == sgn_y) | |
7179 | return result; | |
7180 | return scm_i_normbig (result); | |
7181 | } | |
7182 | else if (SCM_REALP (y)) | |
7183 | { | |
7184 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7185 | scm_remember_upto_here_1 (x); | |
55f26379 | 7186 | return scm_from_double (result); |
0aacf84e MD |
7187 | } |
7188 | else if (SCM_COMPLEXP (y)) | |
7189 | { | |
7190 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7191 | + SCM_COMPLEX_REAL (y)); | |
7192 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7193 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7194 | } |
f92e85f7 | 7195 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7196 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7197 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7198 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7199 | else |
7200 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7201 | } |
0aacf84e MD |
7202 | else if (SCM_REALP (x)) |
7203 | { | |
e11e83f3 | 7204 | if (SCM_I_INUMP (y)) |
55f26379 | 7205 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7206 | else if (SCM_BIGP (y)) |
7207 | { | |
7208 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7209 | scm_remember_upto_here_1 (y); | |
55f26379 | 7210 | return scm_from_double (result); |
0aacf84e MD |
7211 | } |
7212 | else if (SCM_REALP (y)) | |
55f26379 | 7213 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7214 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7215 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7216 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7217 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7218 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7219 | else |
7220 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7221 | } |
0aacf84e MD |
7222 | else if (SCM_COMPLEXP (x)) |
7223 | { | |
e11e83f3 | 7224 | if (SCM_I_INUMP (y)) |
8507ec80 | 7225 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7226 | SCM_COMPLEX_IMAG (x)); |
7227 | else if (SCM_BIGP (y)) | |
7228 | { | |
7229 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7230 | + SCM_COMPLEX_REAL (x)); | |
7231 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7232 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7233 | } |
7234 | else if (SCM_REALP (y)) | |
8507ec80 | 7235 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7236 | SCM_COMPLEX_IMAG (x)); |
7237 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7238 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7239 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7240 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7241 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7242 | SCM_COMPLEX_IMAG (x)); |
7243 | else | |
7244 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7245 | } | |
7246 | else if (SCM_FRACTIONP (x)) | |
7247 | { | |
e11e83f3 | 7248 | if (SCM_I_INUMP (y)) |
cba42c93 | 7249 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7250 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7251 | SCM_FRACTION_DENOMINATOR (x)); | |
7252 | else if (SCM_BIGP (y)) | |
cba42c93 | 7253 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7254 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7255 | SCM_FRACTION_DENOMINATOR (x)); | |
7256 | else if (SCM_REALP (y)) | |
55f26379 | 7257 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7258 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7259 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7260 | SCM_COMPLEX_IMAG (y)); |
7261 | else if (SCM_FRACTIONP (y)) | |
7262 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7263 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7264 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7265 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7266 | else |
7267 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7268 | } |
0aacf84e | 7269 | else |
98cb6e75 | 7270 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7271 | } |
7272 | ||
7273 | ||
40882e3d KR |
7274 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7275 | (SCM x), | |
7276 | "Return @math{@var{x}+1}.") | |
7277 | #define FUNC_NAME s_scm_oneplus | |
7278 | { | |
cff5fa33 | 7279 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7280 | } |
7281 | #undef FUNC_NAME | |
7282 | ||
7283 | ||
78d3deb1 AW |
7284 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7285 | (SCM x, SCM y, SCM rest), | |
7286 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7287 | "the sum of all but the first argument are subtracted from the first\n" | |
7288 | "argument.") | |
7289 | #define FUNC_NAME s_scm_i_difference | |
7290 | { | |
7291 | while (!scm_is_null (rest)) | |
7292 | { x = scm_difference (x, y); | |
7293 | y = scm_car (rest); | |
7294 | rest = scm_cdr (rest); | |
7295 | } | |
7296 | return scm_difference (x, y); | |
7297 | } | |
7298 | #undef FUNC_NAME | |
7299 | ||
7300 | #define s_difference s_scm_i_difference | |
7301 | #define g_difference g_scm_i_difference | |
7302 | ||
0f2d19dd | 7303 | SCM |
6e8d25a6 | 7304 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7305 | #define FUNC_NAME s_difference |
0f2d19dd | 7306 | { |
9cc37597 | 7307 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7308 | { |
7309 | if (SCM_UNBNDP (x)) | |
7310 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7311 | else | |
e11e83f3 | 7312 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7313 | { |
e25f3727 | 7314 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7315 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7316 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7317 | else |
e25f3727 | 7318 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7319 | } |
7320 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7321 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7322 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7323 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7324 | else if (SCM_REALP (x)) | |
55f26379 | 7325 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7326 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7327 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7328 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7329 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7330 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 7331 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
7332 | else |
7333 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7334 | } |
ca46fb90 | 7335 | |
9cc37597 | 7336 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7337 | { |
9cc37597 | 7338 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7339 | { |
e25f3727 AW |
7340 | scm_t_inum xx = SCM_I_INUM (x); |
7341 | scm_t_inum yy = SCM_I_INUM (y); | |
7342 | scm_t_inum z = xx - yy; | |
0aacf84e | 7343 | if (SCM_FIXABLE (z)) |
d956fa6f | 7344 | return SCM_I_MAKINUM (z); |
0aacf84e | 7345 | else |
e25f3727 | 7346 | return scm_i_inum2big (z); |
0aacf84e MD |
7347 | } |
7348 | else if (SCM_BIGP (y)) | |
7349 | { | |
7350 | /* inum-x - big-y */ | |
e25f3727 | 7351 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7352 | |
0aacf84e | 7353 | if (xx == 0) |
b5c40589 MW |
7354 | { |
7355 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7356 | bignum, but negating that gives a fixnum. */ | |
7357 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7358 | } | |
0aacf84e MD |
7359 | else |
7360 | { | |
7361 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7362 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7363 | |
0aacf84e MD |
7364 | if (xx >= 0) |
7365 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7366 | else | |
7367 | { | |
7368 | /* x - y == -(y + -x) */ | |
7369 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7370 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7371 | } | |
7372 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7373 | |
0aacf84e MD |
7374 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7375 | /* we know the result will have to be a bignum */ | |
7376 | return result; | |
7377 | else | |
7378 | return scm_i_normbig (result); | |
7379 | } | |
7380 | } | |
7381 | else if (SCM_REALP (y)) | |
7382 | { | |
e25f3727 | 7383 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7384 | |
7385 | /* | |
7386 | * We need to handle x == exact 0 | |
7387 | * specially because R6RS states that: | |
7388 | * (- 0.0) ==> -0.0 and | |
7389 | * (- 0.0 0.0) ==> 0.0 | |
7390 | * and the scheme compiler changes | |
7391 | * (- 0.0) into (- 0 0.0) | |
7392 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7393 | * At the C level, (-x) is different than (0.0 - x). | |
7394 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7395 | */ | |
7396 | if (xx == 0) | |
7397 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7398 | else | |
7399 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7400 | } |
7401 | else if (SCM_COMPLEXP (y)) | |
7402 | { | |
e25f3727 | 7403 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7404 | |
7405 | /* We need to handle x == exact 0 specially. | |
7406 | See the comment above (for SCM_REALP (y)) */ | |
7407 | if (xx == 0) | |
7408 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7409 | - SCM_COMPLEX_IMAG (y)); | |
7410 | else | |
7411 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7412 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7413 | } |
f92e85f7 MV |
7414 | else if (SCM_FRACTIONP (y)) |
7415 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7416 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7417 | SCM_FRACTION_NUMERATOR (y)), |
7418 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7419 | else |
7420 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7421 | } |
0aacf84e MD |
7422 | else if (SCM_BIGP (x)) |
7423 | { | |
e11e83f3 | 7424 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7425 | { |
7426 | /* big-x - inum-y */ | |
e25f3727 | 7427 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7428 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7429 | |
0aacf84e MD |
7430 | scm_remember_upto_here_1 (x); |
7431 | if (sgn_x == 0) | |
c71b0706 | 7432 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7433 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7434 | else |
7435 | { | |
7436 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7437 | |
708f22c6 KR |
7438 | if (yy >= 0) |
7439 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7440 | else | |
7441 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7442 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7443 | |
0aacf84e MD |
7444 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7445 | /* we know the result will have to be a bignum */ | |
7446 | return result; | |
7447 | else | |
7448 | return scm_i_normbig (result); | |
7449 | } | |
7450 | } | |
7451 | else if (SCM_BIGP (y)) | |
7452 | { | |
7453 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7454 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7455 | SCM result = scm_i_mkbig (); | |
7456 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7457 | SCM_I_BIG_MPZ (x), | |
7458 | SCM_I_BIG_MPZ (y)); | |
7459 | scm_remember_upto_here_2 (x, y); | |
7460 | /* we know the result will have to be a bignum */ | |
7461 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7462 | return result; | |
7463 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7464 | return result; | |
7465 | return scm_i_normbig (result); | |
7466 | } | |
7467 | else if (SCM_REALP (y)) | |
7468 | { | |
7469 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7470 | scm_remember_upto_here_1 (x); | |
55f26379 | 7471 | return scm_from_double (result); |
0aacf84e MD |
7472 | } |
7473 | else if (SCM_COMPLEXP (y)) | |
7474 | { | |
7475 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7476 | - SCM_COMPLEX_REAL (y)); | |
7477 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7478 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7479 | } |
f92e85f7 | 7480 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7481 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7482 | SCM_FRACTION_NUMERATOR (y)), |
7483 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7484 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7485 | } |
0aacf84e MD |
7486 | else if (SCM_REALP (x)) |
7487 | { | |
e11e83f3 | 7488 | if (SCM_I_INUMP (y)) |
55f26379 | 7489 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7490 | else if (SCM_BIGP (y)) |
7491 | { | |
7492 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7493 | scm_remember_upto_here_1 (x); | |
55f26379 | 7494 | return scm_from_double (result); |
0aacf84e MD |
7495 | } |
7496 | else if (SCM_REALP (y)) | |
55f26379 | 7497 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7498 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7499 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7500 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7501 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7502 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7503 | else |
7504 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7505 | } |
0aacf84e MD |
7506 | else if (SCM_COMPLEXP (x)) |
7507 | { | |
e11e83f3 | 7508 | if (SCM_I_INUMP (y)) |
8507ec80 | 7509 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7510 | SCM_COMPLEX_IMAG (x)); |
7511 | else if (SCM_BIGP (y)) | |
7512 | { | |
7513 | double real_part = (SCM_COMPLEX_REAL (x) | |
7514 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7515 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7516 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7517 | } |
7518 | else if (SCM_REALP (y)) | |
8507ec80 | 7519 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7520 | SCM_COMPLEX_IMAG (x)); |
7521 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7522 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7523 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7524 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7525 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7526 | SCM_COMPLEX_IMAG (x)); |
7527 | else | |
7528 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7529 | } | |
7530 | else if (SCM_FRACTIONP (x)) | |
7531 | { | |
e11e83f3 | 7532 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7533 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7534 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7535 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7536 | SCM_FRACTION_DENOMINATOR (x)); | |
7537 | else if (SCM_BIGP (y)) | |
cba42c93 | 7538 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7539 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7540 | SCM_FRACTION_DENOMINATOR (x)); | |
7541 | else if (SCM_REALP (y)) | |
55f26379 | 7542 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7543 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7544 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7545 | -SCM_COMPLEX_IMAG (y)); |
7546 | else if (SCM_FRACTIONP (y)) | |
7547 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7548 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7549 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7550 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7551 | else |
7552 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7553 | } |
0aacf84e | 7554 | else |
98cb6e75 | 7555 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7556 | } |
c05e97b7 | 7557 | #undef FUNC_NAME |
0f2d19dd | 7558 | |
ca46fb90 | 7559 | |
40882e3d KR |
7560 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7561 | (SCM x), | |
7562 | "Return @math{@var{x}-1}.") | |
7563 | #define FUNC_NAME s_scm_oneminus | |
7564 | { | |
cff5fa33 | 7565 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7566 | } |
7567 | #undef FUNC_NAME | |
7568 | ||
7569 | ||
78d3deb1 AW |
7570 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7571 | (SCM x, SCM y, SCM rest), | |
7572 | "Return the product of all arguments. If called without arguments,\n" | |
7573 | "1 is returned.") | |
7574 | #define FUNC_NAME s_scm_i_product | |
7575 | { | |
7576 | while (!scm_is_null (rest)) | |
7577 | { x = scm_product (x, y); | |
7578 | y = scm_car (rest); | |
7579 | rest = scm_cdr (rest); | |
7580 | } | |
7581 | return scm_product (x, y); | |
7582 | } | |
7583 | #undef FUNC_NAME | |
7584 | ||
7585 | #define s_product s_scm_i_product | |
7586 | #define g_product g_scm_i_product | |
7587 | ||
0f2d19dd | 7588 | SCM |
6e8d25a6 | 7589 | scm_product (SCM x, SCM y) |
0f2d19dd | 7590 | { |
9cc37597 | 7591 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7592 | { |
7593 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7594 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7595 | else if (SCM_NUMBERP (x)) |
7596 | return x; | |
7597 | else | |
7598 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7599 | } |
ca46fb90 | 7600 | |
9cc37597 | 7601 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7602 | { |
e25f3727 | 7603 | scm_t_inum xx; |
f4c627b3 | 7604 | |
5e791807 | 7605 | xinum: |
e11e83f3 | 7606 | xx = SCM_I_INUM (x); |
f4c627b3 | 7607 | |
0aacf84e MD |
7608 | switch (xx) |
7609 | { | |
5e791807 MW |
7610 | case 1: |
7611 | /* exact1 is the universal multiplicative identity */ | |
7612 | return y; | |
7613 | break; | |
7614 | case 0: | |
7615 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7616 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7617 | return SCM_INUM0; | |
7618 | /* if the other argument is inexact, the result is inexact, | |
7619 | and we must do the multiplication in order to handle | |
7620 | infinities and NaNs properly. */ | |
7621 | else if (SCM_REALP (y)) | |
7622 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7623 | else if (SCM_COMPLEXP (y)) | |
7624 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7625 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7626 | /* we've already handled inexact numbers, | |
7627 | so y must be exact, and we return exact0 */ | |
7628 | else if (SCM_NUMP (y)) | |
7629 | return SCM_INUM0; | |
7630 | else | |
7631 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7632 | break; | |
7633 | case -1: | |
b5c40589 | 7634 | /* |
5e791807 MW |
7635 | * This case is important for more than just optimization. |
7636 | * It handles the case of negating | |
b5c40589 MW |
7637 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7638 | * which is a bignum that must be changed back into a fixnum. | |
7639 | * Failure to do so will cause the following to return #f: | |
7640 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7641 | */ | |
b5c40589 MW |
7642 | return scm_difference(y, SCM_UNDEFINED); |
7643 | break; | |
0aacf84e | 7644 | } |
f4c627b3 | 7645 | |
9cc37597 | 7646 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7647 | { |
e25f3727 | 7648 | scm_t_inum yy = SCM_I_INUM (y); |
2355f017 MW |
7649 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
7650 | scm_t_int64 kk = xx * (scm_t_int64) yy; | |
7651 | if (SCM_FIXABLE (kk)) | |
7652 | return SCM_I_MAKINUM (kk); | |
7653 | #else | |
7654 | scm_t_inum axx = (xx > 0) ? xx : -xx; | |
7655 | scm_t_inum ayy = (yy > 0) ? yy : -yy; | |
7656 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) | |
7657 | return SCM_I_MAKINUM (xx * yy); | |
7658 | #endif | |
0aacf84e MD |
7659 | else |
7660 | { | |
e25f3727 | 7661 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7662 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7663 | return scm_i_normbig (result); | |
7664 | } | |
7665 | } | |
7666 | else if (SCM_BIGP (y)) | |
7667 | { | |
7668 | SCM result = scm_i_mkbig (); | |
7669 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7670 | scm_remember_upto_here_1 (y); | |
7671 | return result; | |
7672 | } | |
7673 | else if (SCM_REALP (y)) | |
55f26379 | 7674 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7675 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7676 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7677 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7678 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7679 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7680 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7681 | else |
7682 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7683 | } |
0aacf84e MD |
7684 | else if (SCM_BIGP (x)) |
7685 | { | |
e11e83f3 | 7686 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7687 | { |
7688 | SCM_SWAP (x, y); | |
5e791807 | 7689 | goto xinum; |
0aacf84e MD |
7690 | } |
7691 | else if (SCM_BIGP (y)) | |
7692 | { | |
7693 | SCM result = scm_i_mkbig (); | |
7694 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7695 | SCM_I_BIG_MPZ (x), | |
7696 | SCM_I_BIG_MPZ (y)); | |
7697 | scm_remember_upto_here_2 (x, y); | |
7698 | return result; | |
7699 | } | |
7700 | else if (SCM_REALP (y)) | |
7701 | { | |
7702 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7703 | scm_remember_upto_here_1 (x); | |
55f26379 | 7704 | return scm_from_double (result); |
0aacf84e MD |
7705 | } |
7706 | else if (SCM_COMPLEXP (y)) | |
7707 | { | |
7708 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7709 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7710 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7711 | z * SCM_COMPLEX_IMAG (y)); |
7712 | } | |
f92e85f7 | 7713 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7714 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7715 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7716 | else |
7717 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7718 | } |
0aacf84e MD |
7719 | else if (SCM_REALP (x)) |
7720 | { | |
e11e83f3 | 7721 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7722 | { |
7723 | SCM_SWAP (x, y); | |
7724 | goto xinum; | |
7725 | } | |
0aacf84e MD |
7726 | else if (SCM_BIGP (y)) |
7727 | { | |
7728 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7729 | scm_remember_upto_here_1 (y); | |
55f26379 | 7730 | return scm_from_double (result); |
0aacf84e MD |
7731 | } |
7732 | else if (SCM_REALP (y)) | |
55f26379 | 7733 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7734 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7735 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7736 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7737 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7738 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
7739 | else |
7740 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7741 | } |
0aacf84e MD |
7742 | else if (SCM_COMPLEXP (x)) |
7743 | { | |
e11e83f3 | 7744 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7745 | { |
7746 | SCM_SWAP (x, y); | |
7747 | goto xinum; | |
7748 | } | |
0aacf84e MD |
7749 | else if (SCM_BIGP (y)) |
7750 | { | |
7751 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7752 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7753 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7754 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7755 | } |
7756 | else if (SCM_REALP (y)) | |
8507ec80 | 7757 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
7758 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
7759 | else if (SCM_COMPLEXP (y)) | |
7760 | { | |
8507ec80 | 7761 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
7762 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
7763 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
7764 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
7765 | } | |
f92e85f7 MV |
7766 | else if (SCM_FRACTIONP (y)) |
7767 | { | |
7768 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 7769 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
7770 | yy * SCM_COMPLEX_IMAG (x)); |
7771 | } | |
7772 | else | |
7773 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7774 | } | |
7775 | else if (SCM_FRACTIONP (x)) | |
7776 | { | |
e11e83f3 | 7777 | if (SCM_I_INUMP (y)) |
cba42c93 | 7778 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7779 | SCM_FRACTION_DENOMINATOR (x)); |
7780 | else if (SCM_BIGP (y)) | |
cba42c93 | 7781 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7782 | SCM_FRACTION_DENOMINATOR (x)); |
7783 | else if (SCM_REALP (y)) | |
55f26379 | 7784 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
7785 | else if (SCM_COMPLEXP (y)) |
7786 | { | |
7787 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 7788 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7789 | xx * SCM_COMPLEX_IMAG (y)); |
7790 | } | |
7791 | else if (SCM_FRACTIONP (y)) | |
7792 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 7793 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7794 | SCM_FRACTION_NUMERATOR (y)), |
7795 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
7796 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7797 | else |
7798 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7799 | } |
0aacf84e | 7800 | else |
f4c627b3 | 7801 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
7802 | } |
7803 | ||
7351e207 MV |
7804 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
7805 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
7806 | #define ALLOW_DIVIDE_BY_ZERO | |
7807 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
7808 | #endif | |
0f2d19dd | 7809 | |
ba74ef4e MV |
7810 | /* The code below for complex division is adapted from the GNU |
7811 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
7812 | this copyright: */ | |
7813 | ||
7814 | /**************************************************************** | |
7815 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
7816 | ||
7817 | Permission to use, copy, modify, and distribute this software | |
7818 | and its documentation for any purpose and without fee is hereby | |
7819 | granted, provided that the above copyright notice appear in all | |
7820 | copies and that both that the copyright notice and this | |
7821 | permission notice and warranty disclaimer appear in supporting | |
7822 | documentation, and that the names of AT&T Bell Laboratories or | |
7823 | Bellcore or any of their entities not be used in advertising or | |
7824 | publicity pertaining to distribution of the software without | |
7825 | specific, written prior permission. | |
7826 | ||
7827 | AT&T and Bellcore disclaim all warranties with regard to this | |
7828 | software, including all implied warranties of merchantability | |
7829 | and fitness. In no event shall AT&T or Bellcore be liable for | |
7830 | any special, indirect or consequential damages or any damages | |
7831 | whatsoever resulting from loss of use, data or profits, whether | |
7832 | in an action of contract, negligence or other tortious action, | |
7833 | arising out of or in connection with the use or performance of | |
7834 | this software. | |
7835 | ****************************************************************/ | |
7836 | ||
78d3deb1 AW |
7837 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
7838 | (SCM x, SCM y, SCM rest), | |
7839 | "Divide the first argument by the product of the remaining\n" | |
7840 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
7841 | "returned.") | |
7842 | #define FUNC_NAME s_scm_i_divide | |
7843 | { | |
7844 | while (!scm_is_null (rest)) | |
7845 | { x = scm_divide (x, y); | |
7846 | y = scm_car (rest); | |
7847 | rest = scm_cdr (rest); | |
7848 | } | |
7849 | return scm_divide (x, y); | |
7850 | } | |
7851 | #undef FUNC_NAME | |
7852 | ||
7853 | #define s_divide s_scm_i_divide | |
7854 | #define g_divide g_scm_i_divide | |
7855 | ||
f92e85f7 | 7856 | static SCM |
78d3deb1 AW |
7857 | do_divide (SCM x, SCM y, int inexact) |
7858 | #define FUNC_NAME s_divide | |
0f2d19dd | 7859 | { |
f8de44c1 DH |
7860 | double a; |
7861 | ||
9cc37597 | 7862 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7863 | { |
7864 | if (SCM_UNBNDP (x)) | |
7865 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 7866 | else if (SCM_I_INUMP (x)) |
0aacf84e | 7867 | { |
e25f3727 | 7868 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
7869 | if (xx == 1 || xx == -1) |
7870 | return x; | |
7351e207 | 7871 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
7872 | else if (xx == 0) |
7873 | scm_num_overflow (s_divide); | |
7351e207 | 7874 | #endif |
0aacf84e | 7875 | else |
f92e85f7 MV |
7876 | { |
7877 | if (inexact) | |
55f26379 | 7878 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 7879 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7880 | } |
0aacf84e MD |
7881 | } |
7882 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
7883 | { |
7884 | if (inexact) | |
55f26379 | 7885 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 7886 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7887 | } |
0aacf84e MD |
7888 | else if (SCM_REALP (x)) |
7889 | { | |
7890 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 7891 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7892 | if (xx == 0.0) |
7893 | scm_num_overflow (s_divide); | |
7894 | else | |
7351e207 | 7895 | #endif |
55f26379 | 7896 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
7897 | } |
7898 | else if (SCM_COMPLEXP (x)) | |
7899 | { | |
7900 | double r = SCM_COMPLEX_REAL (x); | |
7901 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 7902 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7903 | { |
7904 | double t = r / i; | |
7905 | double d = i * (1.0 + t * t); | |
8507ec80 | 7906 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
7907 | } |
7908 | else | |
7909 | { | |
7910 | double t = i / r; | |
7911 | double d = r * (1.0 + t * t); | |
8507ec80 | 7912 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
7913 | } |
7914 | } | |
f92e85f7 | 7915 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7916 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 7917 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
7918 | else |
7919 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 7920 | } |
f8de44c1 | 7921 | |
9cc37597 | 7922 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7923 | { |
e25f3727 | 7924 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 7925 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7926 | { |
e25f3727 | 7927 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7928 | if (yy == 0) |
7929 | { | |
7351e207 | 7930 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7931 | scm_num_overflow (s_divide); |
7351e207 | 7932 | #else |
55f26379 | 7933 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 7934 | #endif |
0aacf84e MD |
7935 | } |
7936 | else if (xx % yy != 0) | |
f92e85f7 MV |
7937 | { |
7938 | if (inexact) | |
55f26379 | 7939 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 7940 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7941 | } |
0aacf84e MD |
7942 | else |
7943 | { | |
e25f3727 | 7944 | scm_t_inum z = xx / yy; |
0aacf84e | 7945 | if (SCM_FIXABLE (z)) |
d956fa6f | 7946 | return SCM_I_MAKINUM (z); |
0aacf84e | 7947 | else |
e25f3727 | 7948 | return scm_i_inum2big (z); |
0aacf84e | 7949 | } |
f872b822 | 7950 | } |
0aacf84e | 7951 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
7952 | { |
7953 | if (inexact) | |
55f26379 | 7954 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 7955 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7956 | } |
0aacf84e MD |
7957 | else if (SCM_REALP (y)) |
7958 | { | |
7959 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 7960 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7961 | if (yy == 0.0) |
7962 | scm_num_overflow (s_divide); | |
7963 | else | |
7351e207 | 7964 | #endif |
55f26379 | 7965 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 7966 | } |
0aacf84e MD |
7967 | else if (SCM_COMPLEXP (y)) |
7968 | { | |
7969 | a = xx; | |
7970 | complex_div: /* y _must_ be a complex number */ | |
7971 | { | |
7972 | double r = SCM_COMPLEX_REAL (y); | |
7973 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 7974 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7975 | { |
7976 | double t = r / i; | |
7977 | double d = i * (1.0 + t * t); | |
8507ec80 | 7978 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
7979 | } |
7980 | else | |
7981 | { | |
7982 | double t = i / r; | |
7983 | double d = r * (1.0 + t * t); | |
8507ec80 | 7984 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
7985 | } |
7986 | } | |
7987 | } | |
f92e85f7 MV |
7988 | else if (SCM_FRACTIONP (y)) |
7989 | /* a / b/c = ac / b */ | |
cba42c93 | 7990 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 7991 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
7992 | else |
7993 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 7994 | } |
0aacf84e MD |
7995 | else if (SCM_BIGP (x)) |
7996 | { | |
e11e83f3 | 7997 | if (SCM_I_INUMP (y)) |
0aacf84e | 7998 | { |
e25f3727 | 7999 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8000 | if (yy == 0) |
8001 | { | |
7351e207 | 8002 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8003 | scm_num_overflow (s_divide); |
7351e207 | 8004 | #else |
0aacf84e MD |
8005 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8006 | scm_remember_upto_here_1 (x); | |
8007 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8008 | #endif |
0aacf84e MD |
8009 | } |
8010 | else if (yy == 1) | |
8011 | return x; | |
8012 | else | |
8013 | { | |
8014 | /* FIXME: HMM, what are the relative performance issues here? | |
8015 | We need to test. Is it faster on average to test | |
8016 | divisible_p, then perform whichever operation, or is it | |
8017 | faster to perform the integer div opportunistically and | |
8018 | switch to real if there's a remainder? For now we take the | |
8019 | middle ground: test, then if divisible, use the faster div | |
8020 | func. */ | |
8021 | ||
e25f3727 | 8022 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8023 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8024 | ||
8025 | if (divisible_p) | |
8026 | { | |
8027 | SCM result = scm_i_mkbig (); | |
8028 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8029 | scm_remember_upto_here_1 (x); | |
8030 | if (yy < 0) | |
8031 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8032 | return scm_i_normbig (result); | |
8033 | } | |
8034 | else | |
f92e85f7 MV |
8035 | { |
8036 | if (inexact) | |
55f26379 | 8037 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 8038 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8039 | } |
0aacf84e MD |
8040 | } |
8041 | } | |
8042 | else if (SCM_BIGP (y)) | |
8043 | { | |
a4955a04 MW |
8044 | /* big_x / big_y */ |
8045 | if (inexact) | |
0aacf84e | 8046 | { |
a4955a04 MW |
8047 | /* It's easily possible for the ratio x/y to fit a double |
8048 | but one or both x and y be too big to fit a double, | |
8049 | hence the use of mpq_get_d rather than converting and | |
8050 | dividing. */ | |
8051 | mpq_t q; | |
8052 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
8053 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
8054 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
8055 | } |
8056 | else | |
8057 | { | |
a4955a04 MW |
8058 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8059 | SCM_I_BIG_MPZ (y)); | |
8060 | if (divisible_p) | |
8061 | { | |
8062 | SCM result = scm_i_mkbig (); | |
8063 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8064 | SCM_I_BIG_MPZ (x), | |
8065 | SCM_I_BIG_MPZ (y)); | |
8066 | scm_remember_upto_here_2 (x, y); | |
8067 | return scm_i_normbig (result); | |
8068 | } | |
8069 | else | |
8070 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8071 | } |
8072 | } | |
8073 | else if (SCM_REALP (y)) | |
8074 | { | |
8075 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8076 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8077 | if (yy == 0.0) |
8078 | scm_num_overflow (s_divide); | |
8079 | else | |
7351e207 | 8080 | #endif |
55f26379 | 8081 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8082 | } |
8083 | else if (SCM_COMPLEXP (y)) | |
8084 | { | |
8085 | a = scm_i_big2dbl (x); | |
8086 | goto complex_div; | |
8087 | } | |
f92e85f7 | 8088 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8089 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8090 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8091 | else |
8092 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8093 | } |
0aacf84e MD |
8094 | else if (SCM_REALP (x)) |
8095 | { | |
8096 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8097 | if (SCM_I_INUMP (y)) |
0aacf84e | 8098 | { |
e25f3727 | 8099 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8100 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8101 | if (yy == 0) |
8102 | scm_num_overflow (s_divide); | |
8103 | else | |
7351e207 | 8104 | #endif |
55f26379 | 8105 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8106 | } |
8107 | else if (SCM_BIGP (y)) | |
8108 | { | |
8109 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8110 | scm_remember_upto_here_1 (y); | |
55f26379 | 8111 | return scm_from_double (rx / dby); |
0aacf84e MD |
8112 | } |
8113 | else if (SCM_REALP (y)) | |
8114 | { | |
8115 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8116 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8117 | if (yy == 0.0) |
8118 | scm_num_overflow (s_divide); | |
8119 | else | |
7351e207 | 8120 | #endif |
55f26379 | 8121 | return scm_from_double (rx / yy); |
0aacf84e MD |
8122 | } |
8123 | else if (SCM_COMPLEXP (y)) | |
8124 | { | |
8125 | a = rx; | |
8126 | goto complex_div; | |
8127 | } | |
f92e85f7 | 8128 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8129 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8130 | else |
8131 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8132 | } |
0aacf84e MD |
8133 | else if (SCM_COMPLEXP (x)) |
8134 | { | |
8135 | double rx = SCM_COMPLEX_REAL (x); | |
8136 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8137 | if (SCM_I_INUMP (y)) |
0aacf84e | 8138 | { |
e25f3727 | 8139 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8140 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8141 | if (yy == 0) |
8142 | scm_num_overflow (s_divide); | |
8143 | else | |
7351e207 | 8144 | #endif |
0aacf84e MD |
8145 | { |
8146 | double d = yy; | |
8507ec80 | 8147 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8148 | } |
8149 | } | |
8150 | else if (SCM_BIGP (y)) | |
8151 | { | |
8152 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8153 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8154 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8155 | } |
8156 | else if (SCM_REALP (y)) | |
8157 | { | |
8158 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8159 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8160 | if (yy == 0.0) |
8161 | scm_num_overflow (s_divide); | |
8162 | else | |
7351e207 | 8163 | #endif |
8507ec80 | 8164 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8165 | } |
8166 | else if (SCM_COMPLEXP (y)) | |
8167 | { | |
8168 | double ry = SCM_COMPLEX_REAL (y); | |
8169 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8170 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8171 | { |
8172 | double t = ry / iy; | |
8173 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8174 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8175 | } |
8176 | else | |
8177 | { | |
8178 | double t = iy / ry; | |
8179 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8180 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8181 | } |
8182 | } | |
f92e85f7 MV |
8183 | else if (SCM_FRACTIONP (y)) |
8184 | { | |
8185 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8186 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8187 | } |
0aacf84e MD |
8188 | else |
8189 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8190 | } |
f92e85f7 MV |
8191 | else if (SCM_FRACTIONP (x)) |
8192 | { | |
e11e83f3 | 8193 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8194 | { |
e25f3727 | 8195 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8196 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8197 | if (yy == 0) | |
8198 | scm_num_overflow (s_divide); | |
8199 | else | |
8200 | #endif | |
cba42c93 | 8201 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8202 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8203 | } | |
8204 | else if (SCM_BIGP (y)) | |
8205 | { | |
cba42c93 | 8206 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8207 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8208 | } | |
8209 | else if (SCM_REALP (y)) | |
8210 | { | |
8211 | double yy = SCM_REAL_VALUE (y); | |
8212 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8213 | if (yy == 0.0) | |
8214 | scm_num_overflow (s_divide); | |
8215 | else | |
8216 | #endif | |
55f26379 | 8217 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8218 | } |
8219 | else if (SCM_COMPLEXP (y)) | |
8220 | { | |
8221 | a = scm_i_fraction2double (x); | |
8222 | goto complex_div; | |
8223 | } | |
8224 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8225 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8226 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8227 | else | |
8228 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8229 | } | |
0aacf84e | 8230 | else |
f8de44c1 | 8231 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8232 | } |
f92e85f7 MV |
8233 | |
8234 | SCM | |
8235 | scm_divide (SCM x, SCM y) | |
8236 | { | |
78d3deb1 | 8237 | return do_divide (x, y, 0); |
f92e85f7 MV |
8238 | } |
8239 | ||
8240 | static SCM scm_divide2real (SCM x, SCM y) | |
8241 | { | |
78d3deb1 | 8242 | return do_divide (x, y, 1); |
f92e85f7 | 8243 | } |
c05e97b7 | 8244 | #undef FUNC_NAME |
0f2d19dd | 8245 | |
fa605590 | 8246 | |
0f2d19dd | 8247 | double |
3101f40f | 8248 | scm_c_truncate (double x) |
0f2d19dd | 8249 | { |
fa605590 | 8250 | return trunc (x); |
0f2d19dd | 8251 | } |
0f2d19dd | 8252 | |
3101f40f MV |
8253 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8254 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8255 | Then half-way cases are identified and adjusted down if the | |
8256 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8257 | |
8258 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8259 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8260 | ||
8261 | An odd "result" value is identified with result/2 != floor(result/2). | |
8262 | This is done with plus_half, since that value is ready for use sooner in | |
8263 | a pipelined cpu, and we're already requiring plus_half == result. | |
8264 | ||
8265 | Note however that we need to be careful when x is big and already an | |
8266 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8267 | us to return such a value, incorrectly. For instance if the hardware is | |
8268 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8269 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8270 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8271 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8272 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8273 | ||
8274 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8275 | x is already an integer. If it is then clearly that's the desired result | |
8276 | already. And if it's not then the exponent must be small enough to allow | |
8277 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8278 | ||
0f2d19dd | 8279 | double |
3101f40f | 8280 | scm_c_round (double x) |
0f2d19dd | 8281 | { |
6187f48b KR |
8282 | double plus_half, result; |
8283 | ||
8284 | if (x == floor (x)) | |
8285 | return x; | |
8286 | ||
8287 | plus_half = x + 0.5; | |
8288 | result = floor (plus_half); | |
3101f40f | 8289 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8290 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8291 | ? result - 1 | |
8292 | : result); | |
0f2d19dd JB |
8293 | } |
8294 | ||
8b56bcec MW |
8295 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8296 | (SCM x), | |
8297 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8298 | #define FUNC_NAME s_scm_truncate_number |
8299 | { | |
8b56bcec MW |
8300 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8301 | return x; | |
8302 | else if (SCM_REALP (x)) | |
c251ab63 | 8303 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8304 | else if (SCM_FRACTIONP (x)) |
8305 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8306 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8307 | else |
8b56bcec MW |
8308 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8309 | s_scm_truncate_number); | |
f92e85f7 MV |
8310 | } |
8311 | #undef FUNC_NAME | |
8312 | ||
8b56bcec MW |
8313 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8314 | (SCM x), | |
8315 | "Round the number @var{x} towards the nearest integer. " | |
8316 | "When it is exactly halfway between two integers, " | |
8317 | "round towards the even one.") | |
f92e85f7 MV |
8318 | #define FUNC_NAME s_scm_round_number |
8319 | { | |
e11e83f3 | 8320 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8321 | return x; |
8322 | else if (SCM_REALP (x)) | |
3101f40f | 8323 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8324 | else if (SCM_FRACTIONP (x)) |
8325 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8326 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8327 | else |
8b56bcec MW |
8328 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8329 | s_scm_round_number); | |
f92e85f7 MV |
8330 | } |
8331 | #undef FUNC_NAME | |
8332 | ||
8333 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8334 | (SCM x), | |
8335 | "Round the number @var{x} towards minus infinity.") | |
8336 | #define FUNC_NAME s_scm_floor | |
8337 | { | |
e11e83f3 | 8338 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8339 | return x; |
8340 | else if (SCM_REALP (x)) | |
55f26379 | 8341 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8342 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8343 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8344 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8345 | else |
8346 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8347 | } | |
8348 | #undef FUNC_NAME | |
8349 | ||
8350 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8351 | (SCM x), | |
8352 | "Round the number @var{x} towards infinity.") | |
8353 | #define FUNC_NAME s_scm_ceiling | |
8354 | { | |
e11e83f3 | 8355 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8356 | return x; |
8357 | else if (SCM_REALP (x)) | |
55f26379 | 8358 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8359 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8360 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8361 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8362 | else |
8363 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8364 | } | |
8365 | #undef FUNC_NAME | |
0f2d19dd | 8366 | |
2519490c MW |
8367 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8368 | (SCM x, SCM y), | |
8369 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8370 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8371 | { |
01c7284a MW |
8372 | if (scm_is_integer (y)) |
8373 | { | |
8374 | if (scm_is_true (scm_exact_p (y))) | |
8375 | return scm_integer_expt (x, y); | |
8376 | else | |
8377 | { | |
8378 | /* Here we handle the case where the exponent is an inexact | |
8379 | integer. We make the exponent exact in order to use | |
8380 | scm_integer_expt, and thus avoid the spurious imaginary | |
8381 | parts that may result from round-off errors in the general | |
8382 | e^(y log x) method below (for example when squaring a large | |
8383 | negative number). In this case, we must return an inexact | |
8384 | result for correctness. We also make the base inexact so | |
8385 | that scm_integer_expt will use fast inexact arithmetic | |
8386 | internally. Note that making the base inexact is not | |
8387 | sufficient to guarantee an inexact result, because | |
8388 | scm_integer_expt will return an exact 1 when the exponent | |
8389 | is 0, even if the base is inexact. */ | |
8390 | return scm_exact_to_inexact | |
8391 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8392 | scm_inexact_to_exact (y))); | |
8393 | } | |
8394 | } | |
6fc4d012 AW |
8395 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8396 | { | |
8397 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8398 | } | |
2519490c | 8399 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8400 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8401 | else if (scm_is_complex (x)) |
8402 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8403 | else | |
8404 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8405 | } |
1bbd0b84 | 8406 | #undef FUNC_NAME |
0f2d19dd | 8407 | |
7f41099e MW |
8408 | /* sin/cos/tan/asin/acos/atan |
8409 | sinh/cosh/tanh/asinh/acosh/atanh | |
8410 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8411 | Written by Jerry D. Hedden, (C) FSF. | |
8412 | See the file `COPYING' for terms applying to this program. */ | |
8413 | ||
ad79736c AW |
8414 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8415 | (SCM z), | |
8416 | "Compute the sine of @var{z}.") | |
8417 | #define FUNC_NAME s_scm_sin | |
8418 | { | |
8deddc94 MW |
8419 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8420 | return z; /* sin(exact0) = exact0 */ | |
8421 | else if (scm_is_real (z)) | |
ad79736c AW |
8422 | return scm_from_double (sin (scm_to_double (z))); |
8423 | else if (SCM_COMPLEXP (z)) | |
8424 | { double x, y; | |
8425 | x = SCM_COMPLEX_REAL (z); | |
8426 | y = SCM_COMPLEX_IMAG (z); | |
8427 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8428 | cos (x) * sinh (y)); | |
8429 | } | |
8430 | else | |
8431 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8432 | } | |
8433 | #undef FUNC_NAME | |
0f2d19dd | 8434 | |
ad79736c AW |
8435 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8436 | (SCM z), | |
8437 | "Compute the cosine of @var{z}.") | |
8438 | #define FUNC_NAME s_scm_cos | |
8439 | { | |
8deddc94 MW |
8440 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8441 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8442 | else if (scm_is_real (z)) | |
ad79736c AW |
8443 | return scm_from_double (cos (scm_to_double (z))); |
8444 | else if (SCM_COMPLEXP (z)) | |
8445 | { double x, y; | |
8446 | x = SCM_COMPLEX_REAL (z); | |
8447 | y = SCM_COMPLEX_IMAG (z); | |
8448 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8449 | -sin (x) * sinh (y)); | |
8450 | } | |
8451 | else | |
8452 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8453 | } | |
8454 | #undef FUNC_NAME | |
8455 | ||
8456 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8457 | (SCM z), | |
8458 | "Compute the tangent of @var{z}.") | |
8459 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8460 | { |
8deddc94 MW |
8461 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8462 | return z; /* tan(exact0) = exact0 */ | |
8463 | else if (scm_is_real (z)) | |
ad79736c AW |
8464 | return scm_from_double (tan (scm_to_double (z))); |
8465 | else if (SCM_COMPLEXP (z)) | |
8466 | { double x, y, w; | |
8467 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8468 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8469 | w = cos (x) + cosh (y); | |
8470 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8471 | if (w == 0.0) | |
8472 | scm_num_overflow (s_scm_tan); | |
8473 | #endif | |
8474 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8475 | } | |
8476 | else | |
8477 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8478 | } | |
8479 | #undef FUNC_NAME | |
8480 | ||
8481 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8482 | (SCM z), | |
8483 | "Compute the hyperbolic sine of @var{z}.") | |
8484 | #define FUNC_NAME s_scm_sinh | |
8485 | { | |
8deddc94 MW |
8486 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8487 | return z; /* sinh(exact0) = exact0 */ | |
8488 | else if (scm_is_real (z)) | |
ad79736c AW |
8489 | return scm_from_double (sinh (scm_to_double (z))); |
8490 | else if (SCM_COMPLEXP (z)) | |
8491 | { double x, y; | |
8492 | x = SCM_COMPLEX_REAL (z); | |
8493 | y = SCM_COMPLEX_IMAG (z); | |
8494 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8495 | cosh (x) * sin (y)); | |
8496 | } | |
8497 | else | |
8498 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8499 | } | |
8500 | #undef FUNC_NAME | |
8501 | ||
8502 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8503 | (SCM z), | |
8504 | "Compute the hyperbolic cosine of @var{z}.") | |
8505 | #define FUNC_NAME s_scm_cosh | |
8506 | { | |
8deddc94 MW |
8507 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8508 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8509 | else if (scm_is_real (z)) | |
ad79736c AW |
8510 | return scm_from_double (cosh (scm_to_double (z))); |
8511 | else if (SCM_COMPLEXP (z)) | |
8512 | { double x, y; | |
8513 | x = SCM_COMPLEX_REAL (z); | |
8514 | y = SCM_COMPLEX_IMAG (z); | |
8515 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8516 | sinh (x) * sin (y)); | |
8517 | } | |
8518 | else | |
8519 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8520 | } | |
8521 | #undef FUNC_NAME | |
8522 | ||
8523 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8524 | (SCM z), | |
8525 | "Compute the hyperbolic tangent of @var{z}.") | |
8526 | #define FUNC_NAME s_scm_tanh | |
8527 | { | |
8deddc94 MW |
8528 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8529 | return z; /* tanh(exact0) = exact0 */ | |
8530 | else if (scm_is_real (z)) | |
ad79736c AW |
8531 | return scm_from_double (tanh (scm_to_double (z))); |
8532 | else if (SCM_COMPLEXP (z)) | |
8533 | { double x, y, w; | |
8534 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8535 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8536 | w = cosh (x) + cos (y); | |
8537 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8538 | if (w == 0.0) | |
8539 | scm_num_overflow (s_scm_tanh); | |
8540 | #endif | |
8541 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8542 | } | |
8543 | else | |
8544 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8545 | } | |
8546 | #undef FUNC_NAME | |
8547 | ||
8548 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8549 | (SCM z), | |
8550 | "Compute the arc sine of @var{z}.") | |
8551 | #define FUNC_NAME s_scm_asin | |
8552 | { | |
8deddc94 MW |
8553 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8554 | return z; /* asin(exact0) = exact0 */ | |
8555 | else if (scm_is_real (z)) | |
ad79736c AW |
8556 | { |
8557 | double w = scm_to_double (z); | |
8558 | if (w >= -1.0 && w <= 1.0) | |
8559 | return scm_from_double (asin (w)); | |
8560 | else | |
8561 | return scm_product (scm_c_make_rectangular (0, -1), | |
8562 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8563 | } | |
8564 | else if (SCM_COMPLEXP (z)) | |
8565 | { double x, y; | |
8566 | x = SCM_COMPLEX_REAL (z); | |
8567 | y = SCM_COMPLEX_IMAG (z); | |
8568 | return scm_product (scm_c_make_rectangular (0, -1), | |
8569 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8570 | } | |
8571 | else | |
8572 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8573 | } | |
8574 | #undef FUNC_NAME | |
8575 | ||
8576 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8577 | (SCM z), | |
8578 | "Compute the arc cosine of @var{z}.") | |
8579 | #define FUNC_NAME s_scm_acos | |
8580 | { | |
8deddc94 MW |
8581 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8582 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8583 | else if (scm_is_real (z)) | |
ad79736c AW |
8584 | { |
8585 | double w = scm_to_double (z); | |
8586 | if (w >= -1.0 && w <= 1.0) | |
8587 | return scm_from_double (acos (w)); | |
8588 | else | |
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 (0, w)))); | |
8592 | } | |
8593 | else if (SCM_COMPLEXP (z)) | |
8594 | { double x, y; | |
8595 | x = SCM_COMPLEX_REAL (z); | |
8596 | y = SCM_COMPLEX_IMAG (z); | |
8597 | return scm_sum (scm_from_double (acos (0.0)), | |
8598 | scm_product (scm_c_make_rectangular (0, 1), | |
8599 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8600 | } | |
8601 | else | |
8602 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8603 | } | |
8604 | #undef FUNC_NAME | |
8605 | ||
8606 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8607 | (SCM z, SCM y), | |
8608 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8609 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8610 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8611 | #define FUNC_NAME s_scm_atan | |
8612 | { | |
8613 | if (SCM_UNBNDP (y)) | |
8614 | { | |
8deddc94 MW |
8615 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8616 | return z; /* atan(exact0) = exact0 */ | |
8617 | else if (scm_is_real (z)) | |
ad79736c AW |
8618 | return scm_from_double (atan (scm_to_double (z))); |
8619 | else if (SCM_COMPLEXP (z)) | |
8620 | { | |
8621 | double v, w; | |
8622 | v = SCM_COMPLEX_REAL (z); | |
8623 | w = SCM_COMPLEX_IMAG (z); | |
8624 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8625 | scm_c_make_rectangular (v, w + 1.0))), | |
8626 | scm_c_make_rectangular (0, 2)); | |
8627 | } | |
8628 | else | |
18104cac | 8629 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8630 | } |
8631 | else if (scm_is_real (z)) | |
8632 | { | |
8633 | if (scm_is_real (y)) | |
8634 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8635 | else | |
8636 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8637 | } | |
8638 | else | |
8639 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8640 | } | |
8641 | #undef FUNC_NAME | |
8642 | ||
8643 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8644 | (SCM z), | |
8645 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8646 | #define FUNC_NAME s_scm_sys_asinh | |
8647 | { | |
8deddc94 MW |
8648 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8649 | return z; /* asinh(exact0) = exact0 */ | |
8650 | else if (scm_is_real (z)) | |
ad79736c AW |
8651 | return scm_from_double (asinh (scm_to_double (z))); |
8652 | else if (scm_is_number (z)) | |
8653 | return scm_log (scm_sum (z, | |
8654 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8655 | SCM_INUM1)))); |
ad79736c AW |
8656 | else |
8657 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8658 | } | |
8659 | #undef FUNC_NAME | |
8660 | ||
8661 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8662 | (SCM z), | |
8663 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8664 | #define FUNC_NAME s_scm_sys_acosh | |
8665 | { | |
8deddc94 MW |
8666 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8667 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8668 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8669 | return scm_from_double (acosh (scm_to_double (z))); |
8670 | else if (scm_is_number (z)) | |
8671 | return scm_log (scm_sum (z, | |
8672 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8673 | SCM_INUM1)))); |
ad79736c AW |
8674 | else |
8675 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8676 | } | |
8677 | #undef FUNC_NAME | |
8678 | ||
8679 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8680 | (SCM z), | |
8681 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8682 | #define FUNC_NAME s_scm_sys_atanh | |
8683 | { | |
8deddc94 MW |
8684 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8685 | return z; /* atanh(exact0) = exact0 */ | |
8686 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8687 | return scm_from_double (atanh (scm_to_double (z))); |
8688 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8689 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8690 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8691 | SCM_I_MAKINUM (2)); |
8692 | else | |
8693 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8694 | } |
1bbd0b84 | 8695 | #undef FUNC_NAME |
0f2d19dd | 8696 | |
8507ec80 MV |
8697 | SCM |
8698 | scm_c_make_rectangular (double re, double im) | |
8699 | { | |
c7218482 | 8700 | SCM z; |
03604fcf | 8701 | |
c7218482 MW |
8702 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8703 | "complex")); | |
8704 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8705 | SCM_COMPLEX_REAL (z) = re; | |
8706 | SCM_COMPLEX_IMAG (z) = im; | |
8707 | return z; | |
8507ec80 | 8708 | } |
0f2d19dd | 8709 | |
a1ec6916 | 8710 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 8711 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
8712 | "Return a complex number constructed of the given @var{real_part} " |
8713 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 8714 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8715 | { |
ad79736c AW |
8716 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8717 | SCM_ARG1, FUNC_NAME, "real"); | |
8718 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8719 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8720 | |
8721 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8722 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8723 | return real_part; | |
8724 | else | |
8725 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8726 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8727 | } |
1bbd0b84 | 8728 | #undef FUNC_NAME |
0f2d19dd | 8729 | |
8507ec80 MV |
8730 | SCM |
8731 | scm_c_make_polar (double mag, double ang) | |
8732 | { | |
8733 | double s, c; | |
5e647d08 LC |
8734 | |
8735 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8736 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8737 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8738 | details. */ | |
8739 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8740 | sincos (ang, &s, &c); |
8741 | #else | |
8742 | s = sin (ang); | |
8743 | c = cos (ang); | |
8744 | #endif | |
9d427b2c MW |
8745 | |
8746 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8747 | infinite, or perhaps simply too large to determine its value | |
8748 | mod 2*pi. However, we know something that the floating-point | |
8749 | implementation doesn't know: We know that s and c are finite. | |
8750 | Therefore, if the magnitude is zero, return a complex zero. | |
8751 | ||
8752 | The reason we check for the NaNs instead of using this case | |
8753 | whenever mag == 0.0 is because when the angle is known, we'd | |
8754 | like to return the correct kind of non-real complex zero: | |
8755 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8756 | on which quadrant the angle is in. | |
8757 | */ | |
8758 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8759 | return scm_c_make_rectangular (0.0, 0.0); | |
8760 | else | |
8761 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8762 | } |
0f2d19dd | 8763 | |
a1ec6916 | 8764 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8765 | (SCM mag, SCM ang), |
8766 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8767 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8768 | { |
c7218482 MW |
8769 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8770 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8771 | ||
8772 | /* If mag is exact0, return exact0 */ | |
8773 | if (scm_is_eq (mag, SCM_INUM0)) | |
8774 | return SCM_INUM0; | |
8775 | /* Return a real if ang is exact0 */ | |
8776 | else if (scm_is_eq (ang, SCM_INUM0)) | |
8777 | return mag; | |
8778 | else | |
8779 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 8780 | } |
1bbd0b84 | 8781 | #undef FUNC_NAME |
0f2d19dd JB |
8782 | |
8783 | ||
2519490c MW |
8784 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
8785 | (SCM z), | |
8786 | "Return the real part of the number @var{z}.") | |
8787 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 8788 | { |
2519490c | 8789 | if (SCM_COMPLEXP (z)) |
55f26379 | 8790 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 8791 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 8792 | return z; |
0aacf84e | 8793 | else |
2519490c | 8794 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 8795 | } |
2519490c | 8796 | #undef FUNC_NAME |
0f2d19dd JB |
8797 | |
8798 | ||
2519490c MW |
8799 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
8800 | (SCM z), | |
8801 | "Return the imaginary part of the number @var{z}.") | |
8802 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 8803 | { |
2519490c MW |
8804 | if (SCM_COMPLEXP (z)) |
8805 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 8806 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 8807 | return SCM_INUM0; |
0aacf84e | 8808 | else |
2519490c | 8809 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 8810 | } |
2519490c | 8811 | #undef FUNC_NAME |
0f2d19dd | 8812 | |
2519490c MW |
8813 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
8814 | (SCM z), | |
8815 | "Return the numerator of the number @var{z}.") | |
8816 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 8817 | { |
2519490c | 8818 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
8819 | return z; |
8820 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 8821 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
8822 | else if (SCM_REALP (z)) |
8823 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
8824 | else | |
2519490c | 8825 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 8826 | } |
2519490c | 8827 | #undef FUNC_NAME |
f92e85f7 MV |
8828 | |
8829 | ||
2519490c MW |
8830 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
8831 | (SCM z), | |
8832 | "Return the denominator of the number @var{z}.") | |
8833 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 8834 | { |
2519490c | 8835 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 8836 | return SCM_INUM1; |
f92e85f7 | 8837 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 8838 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
8839 | else if (SCM_REALP (z)) |
8840 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
8841 | else | |
2519490c | 8842 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 8843 | } |
2519490c | 8844 | #undef FUNC_NAME |
0f2d19dd | 8845 | |
2519490c MW |
8846 | |
8847 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
8848 | (SCM z), | |
8849 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
8850 | "@code{abs} for real arguments, but also allows complex numbers.") | |
8851 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 8852 | { |
e11e83f3 | 8853 | if (SCM_I_INUMP (z)) |
0aacf84e | 8854 | { |
e25f3727 | 8855 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
8856 | if (zz >= 0) |
8857 | return z; | |
8858 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 8859 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 8860 | else |
e25f3727 | 8861 | return scm_i_inum2big (-zz); |
5986c47d | 8862 | } |
0aacf84e MD |
8863 | else if (SCM_BIGP (z)) |
8864 | { | |
8865 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8866 | scm_remember_upto_here_1 (z); | |
8867 | if (sgn < 0) | |
8868 | return scm_i_clonebig (z, 0); | |
8869 | else | |
8870 | return z; | |
5986c47d | 8871 | } |
0aacf84e | 8872 | else if (SCM_REALP (z)) |
55f26379 | 8873 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 8874 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8875 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
8876 | else if (SCM_FRACTIONP (z)) |
8877 | { | |
73e4de09 | 8878 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 8879 | return z; |
cba42c93 | 8880 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
8881 | SCM_FRACTION_DENOMINATOR (z)); |
8882 | } | |
0aacf84e | 8883 | else |
2519490c | 8884 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 8885 | } |
2519490c | 8886 | #undef FUNC_NAME |
0f2d19dd JB |
8887 | |
8888 | ||
2519490c MW |
8889 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
8890 | (SCM z), | |
8891 | "Return the angle of the complex number @var{z}.") | |
8892 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 8893 | { |
c8ae173e | 8894 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 8895 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
8896 | But if atan2 follows the floating point rounding mode, then the value |
8897 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 8898 | if (SCM_I_INUMP (z)) |
0aacf84e | 8899 | { |
e11e83f3 | 8900 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 8901 | return flo0; |
0aacf84e | 8902 | else |
55f26379 | 8903 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 8904 | } |
0aacf84e MD |
8905 | else if (SCM_BIGP (z)) |
8906 | { | |
8907 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8908 | scm_remember_upto_here_1 (z); | |
8909 | if (sgn < 0) | |
55f26379 | 8910 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 8911 | else |
e7efe8e7 | 8912 | return flo0; |
0f2d19dd | 8913 | } |
0aacf84e | 8914 | else if (SCM_REALP (z)) |
c8ae173e | 8915 | { |
10a97755 MW |
8916 | double x = SCM_REAL_VALUE (z); |
8917 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
e7efe8e7 | 8918 | return flo0; |
c8ae173e | 8919 | else |
55f26379 | 8920 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 8921 | } |
0aacf84e | 8922 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8923 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
8924 | else if (SCM_FRACTIONP (z)) |
8925 | { | |
73e4de09 | 8926 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 8927 | return flo0; |
55f26379 | 8928 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 8929 | } |
0aacf84e | 8930 | else |
2519490c | 8931 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 8932 | } |
2519490c | 8933 | #undef FUNC_NAME |
0f2d19dd JB |
8934 | |
8935 | ||
2519490c MW |
8936 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
8937 | (SCM z), | |
8938 | "Convert the number @var{z} to its inexact representation.\n") | |
8939 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 8940 | { |
e11e83f3 | 8941 | if (SCM_I_INUMP (z)) |
55f26379 | 8942 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 8943 | else if (SCM_BIGP (z)) |
55f26379 | 8944 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 8945 | else if (SCM_FRACTIONP (z)) |
55f26379 | 8946 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
8947 | else if (SCM_INEXACTP (z)) |
8948 | return z; | |
8949 | else | |
2519490c | 8950 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 8951 | } |
2519490c | 8952 | #undef FUNC_NAME |
3c9a524f DH |
8953 | |
8954 | ||
2519490c MW |
8955 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
8956 | (SCM z), | |
8957 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 8958 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 8959 | { |
c7218482 | 8960 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 8961 | return z; |
c7218482 | 8962 | else |
0aacf84e | 8963 | { |
c7218482 MW |
8964 | double val; |
8965 | ||
8966 | if (SCM_REALP (z)) | |
8967 | val = SCM_REAL_VALUE (z); | |
8968 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
8969 | val = SCM_COMPLEX_REAL (z); | |
8970 | else | |
8971 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
8972 | ||
8973 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 8974 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 8975 | else |
f92e85f7 MV |
8976 | { |
8977 | mpq_t frac; | |
8978 | SCM q; | |
8979 | ||
8980 | mpq_init (frac); | |
c7218482 | 8981 | mpq_set_d (frac, val); |
cba42c93 | 8982 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 8983 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 8984 | |
cba42c93 | 8985 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
8986 | for frac... |
8987 | */ | |
8988 | mpq_clear (frac); | |
8989 | return q; | |
8990 | } | |
c2ff8ab0 | 8991 | } |
0f2d19dd | 8992 | } |
1bbd0b84 | 8993 | #undef FUNC_NAME |
0f2d19dd | 8994 | |
f92e85f7 | 8995 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
8996 | (SCM x, SCM eps), |
8997 | "Returns the @emph{simplest} rational number differing\n" | |
8998 | "from @var{x} by no more than @var{eps}.\n" | |
8999 | "\n" | |
9000 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9001 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9002 | "to use @code{inexact->exact} on the arguments.\n" | |
9003 | "\n" | |
9004 | "@lisp\n" | |
9005 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9006 | "@result{} 6/5\n" | |
9007 | "@end lisp") | |
f92e85f7 MV |
9008 | #define FUNC_NAME s_scm_rationalize |
9009 | { | |
605f6980 MW |
9010 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9011 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9012 | eps = scm_abs (eps); | |
9013 | if (scm_is_false (scm_positive_p (eps))) | |
9014 | { | |
9015 | /* eps is either zero or a NaN */ | |
9016 | if (scm_is_true (scm_nan_p (eps))) | |
9017 | return scm_nan (); | |
9018 | else if (SCM_INEXACTP (eps)) | |
9019 | return scm_exact_to_inexact (x); | |
9020 | else | |
9021 | return x; | |
9022 | } | |
9023 | else if (scm_is_false (scm_finite_p (eps))) | |
9024 | { | |
9025 | if (scm_is_true (scm_finite_p (x))) | |
9026 | return flo0; | |
9027 | else | |
9028 | return scm_nan (); | |
9029 | } | |
9030 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9031 | return x; |
605f6980 MW |
9032 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9033 | scm_ceiling (scm_difference (x, eps))))) | |
9034 | { | |
9035 | /* There's an integer within range; we want the one closest to zero */ | |
9036 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9037 | { | |
9038 | /* zero is within range */ | |
9039 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9040 | return flo0; | |
9041 | else | |
9042 | return SCM_INUM0; | |
9043 | } | |
9044 | else if (scm_is_true (scm_positive_p (x))) | |
9045 | return scm_ceiling (scm_difference (x, eps)); | |
9046 | else | |
9047 | return scm_floor (scm_sum (x, eps)); | |
9048 | } | |
9049 | else | |
f92e85f7 MV |
9050 | { |
9051 | /* Use continued fractions to find closest ratio. All | |
9052 | arithmetic is done with exact numbers. | |
9053 | */ | |
9054 | ||
9055 | SCM ex = scm_inexact_to_exact (x); | |
9056 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9057 | SCM tt = SCM_INUM1; |
9058 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9059 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9060 | SCM rx; |
9061 | int i = 0; | |
9062 | ||
f92e85f7 MV |
9063 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9064 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9065 | ||
9066 | /* We stop after a million iterations just to be absolutely sure | |
9067 | that we don't go into an infinite loop. The process normally | |
9068 | converges after less than a dozen iterations. | |
9069 | */ | |
9070 | ||
f92e85f7 MV |
9071 | while (++i < 1000000) |
9072 | { | |
9073 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9074 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9075 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9076 | scm_is_false | |
f92e85f7 | 9077 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9078 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9079 | { |
9080 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9081 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9082 | return scm_exact_to_inexact (res); |
9083 | else | |
9084 | return res; | |
9085 | } | |
f92e85f7 MV |
9086 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9087 | SCM_UNDEFINED); | |
9088 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9089 | a2 = a1; | |
9090 | b2 = b1; | |
9091 | a1 = a; | |
9092 | b1 = b; | |
9093 | } | |
9094 | scm_num_overflow (s_scm_rationalize); | |
9095 | } | |
f92e85f7 MV |
9096 | } |
9097 | #undef FUNC_NAME | |
9098 | ||
73e4de09 MV |
9099 | /* conversion functions */ |
9100 | ||
9101 | int | |
9102 | scm_is_integer (SCM val) | |
9103 | { | |
9104 | return scm_is_true (scm_integer_p (val)); | |
9105 | } | |
9106 | ||
9107 | int | |
9108 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9109 | { | |
e11e83f3 | 9110 | if (SCM_I_INUMP (val)) |
73e4de09 | 9111 | { |
e11e83f3 | 9112 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9113 | return n >= min && n <= max; |
9114 | } | |
9115 | else if (SCM_BIGP (val)) | |
9116 | { | |
9117 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9118 | return 0; | |
9119 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9120 | { |
9121 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9122 | { | |
9123 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9124 | return n >= min && n <= max; | |
9125 | } | |
9126 | else | |
9127 | return 0; | |
9128 | } | |
73e4de09 MV |
9129 | else |
9130 | { | |
d956fa6f MV |
9131 | scm_t_intmax n; |
9132 | size_t count; | |
73e4de09 | 9133 | |
d956fa6f MV |
9134 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9135 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9136 | return 0; | |
9137 | ||
9138 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9139 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9140 | |
d956fa6f | 9141 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9142 | { |
d956fa6f MV |
9143 | if (n < 0) |
9144 | return 0; | |
73e4de09 | 9145 | } |
73e4de09 MV |
9146 | else |
9147 | { | |
d956fa6f MV |
9148 | n = -n; |
9149 | if (n >= 0) | |
9150 | return 0; | |
73e4de09 | 9151 | } |
d956fa6f MV |
9152 | |
9153 | return n >= min && n <= max; | |
73e4de09 MV |
9154 | } |
9155 | } | |
73e4de09 MV |
9156 | else |
9157 | return 0; | |
9158 | } | |
9159 | ||
9160 | int | |
9161 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9162 | { | |
e11e83f3 | 9163 | if (SCM_I_INUMP (val)) |
73e4de09 | 9164 | { |
e11e83f3 | 9165 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9166 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9167 | } | |
9168 | else if (SCM_BIGP (val)) | |
9169 | { | |
9170 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9171 | return 0; | |
9172 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9173 | { |
9174 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9175 | { | |
9176 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9177 | return n >= min && n <= max; | |
9178 | } | |
9179 | else | |
9180 | return 0; | |
9181 | } | |
73e4de09 MV |
9182 | else |
9183 | { | |
d956fa6f MV |
9184 | scm_t_uintmax n; |
9185 | size_t count; | |
73e4de09 | 9186 | |
d956fa6f MV |
9187 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9188 | return 0; | |
73e4de09 | 9189 | |
d956fa6f MV |
9190 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9191 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9192 | return 0; |
d956fa6f MV |
9193 | |
9194 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9195 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9196 | |
d956fa6f | 9197 | return n >= min && n <= max; |
73e4de09 MV |
9198 | } |
9199 | } | |
73e4de09 MV |
9200 | else |
9201 | return 0; | |
9202 | } | |
9203 | ||
1713d319 MV |
9204 | static void |
9205 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9206 | { | |
9207 | scm_error (scm_out_of_range_key, | |
9208 | NULL, | |
9209 | "Value out of range ~S to ~S: ~S", | |
9210 | scm_list_3 (min, max, bad_val), | |
9211 | scm_list_1 (bad_val)); | |
9212 | } | |
9213 | ||
bfd7932e MV |
9214 | #define TYPE scm_t_intmax |
9215 | #define TYPE_MIN min | |
9216 | #define TYPE_MAX max | |
9217 | #define SIZEOF_TYPE 0 | |
9218 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9219 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9220 | #include "libguile/conv-integer.i.c" | |
9221 | ||
9222 | #define TYPE scm_t_uintmax | |
9223 | #define TYPE_MIN min | |
9224 | #define TYPE_MAX max | |
9225 | #define SIZEOF_TYPE 0 | |
9226 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9227 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9228 | #include "libguile/conv-uinteger.i.c" | |
9229 | ||
9230 | #define TYPE scm_t_int8 | |
9231 | #define TYPE_MIN SCM_T_INT8_MIN | |
9232 | #define TYPE_MAX SCM_T_INT8_MAX | |
9233 | #define SIZEOF_TYPE 1 | |
9234 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9235 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9236 | #include "libguile/conv-integer.i.c" | |
9237 | ||
9238 | #define TYPE scm_t_uint8 | |
9239 | #define TYPE_MIN 0 | |
9240 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9241 | #define SIZEOF_TYPE 1 | |
9242 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9243 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9244 | #include "libguile/conv-uinteger.i.c" | |
9245 | ||
9246 | #define TYPE scm_t_int16 | |
9247 | #define TYPE_MIN SCM_T_INT16_MIN | |
9248 | #define TYPE_MAX SCM_T_INT16_MAX | |
9249 | #define SIZEOF_TYPE 2 | |
9250 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9251 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9252 | #include "libguile/conv-integer.i.c" | |
9253 | ||
9254 | #define TYPE scm_t_uint16 | |
9255 | #define TYPE_MIN 0 | |
9256 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9257 | #define SIZEOF_TYPE 2 | |
9258 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9259 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9260 | #include "libguile/conv-uinteger.i.c" | |
9261 | ||
9262 | #define TYPE scm_t_int32 | |
9263 | #define TYPE_MIN SCM_T_INT32_MIN | |
9264 | #define TYPE_MAX SCM_T_INT32_MAX | |
9265 | #define SIZEOF_TYPE 4 | |
9266 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9267 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9268 | #include "libguile/conv-integer.i.c" | |
9269 | ||
9270 | #define TYPE scm_t_uint32 | |
9271 | #define TYPE_MIN 0 | |
9272 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9273 | #define SIZEOF_TYPE 4 | |
9274 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9275 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9276 | #include "libguile/conv-uinteger.i.c" | |
9277 | ||
904a78f1 MG |
9278 | #define TYPE scm_t_wchar |
9279 | #define TYPE_MIN (scm_t_int32)-1 | |
9280 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9281 | #define SIZEOF_TYPE 4 | |
9282 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9283 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9284 | #include "libguile/conv-integer.i.c" | |
9285 | ||
bfd7932e MV |
9286 | #define TYPE scm_t_int64 |
9287 | #define TYPE_MIN SCM_T_INT64_MIN | |
9288 | #define TYPE_MAX SCM_T_INT64_MAX | |
9289 | #define SIZEOF_TYPE 8 | |
9290 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9291 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9292 | #include "libguile/conv-integer.i.c" | |
9293 | ||
9294 | #define TYPE scm_t_uint64 | |
9295 | #define TYPE_MIN 0 | |
9296 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9297 | #define SIZEOF_TYPE 8 | |
9298 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9299 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9300 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9301 | |
cd036260 MV |
9302 | void |
9303 | scm_to_mpz (SCM val, mpz_t rop) | |
9304 | { | |
9305 | if (SCM_I_INUMP (val)) | |
9306 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9307 | else if (SCM_BIGP (val)) | |
9308 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9309 | else | |
9310 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9311 | } | |
9312 | ||
9313 | SCM | |
9314 | scm_from_mpz (mpz_t val) | |
9315 | { | |
9316 | return scm_i_mpz2num (val); | |
9317 | } | |
9318 | ||
73e4de09 MV |
9319 | int |
9320 | scm_is_real (SCM val) | |
9321 | { | |
9322 | return scm_is_true (scm_real_p (val)); | |
9323 | } | |
9324 | ||
55f26379 MV |
9325 | int |
9326 | scm_is_rational (SCM val) | |
9327 | { | |
9328 | return scm_is_true (scm_rational_p (val)); | |
9329 | } | |
9330 | ||
73e4de09 MV |
9331 | double |
9332 | scm_to_double (SCM val) | |
9333 | { | |
55f26379 MV |
9334 | if (SCM_I_INUMP (val)) |
9335 | return SCM_I_INUM (val); | |
9336 | else if (SCM_BIGP (val)) | |
9337 | return scm_i_big2dbl (val); | |
9338 | else if (SCM_FRACTIONP (val)) | |
9339 | return scm_i_fraction2double (val); | |
9340 | else if (SCM_REALP (val)) | |
9341 | return SCM_REAL_VALUE (val); | |
9342 | else | |
7a1aba42 | 9343 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9344 | } |
9345 | ||
9346 | SCM | |
9347 | scm_from_double (double val) | |
9348 | { | |
978c52d1 LC |
9349 | SCM z; |
9350 | ||
9351 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9352 | ||
9353 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9354 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9355 | |
55f26379 | 9356 | return z; |
73e4de09 MV |
9357 | } |
9358 | ||
220058a8 | 9359 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9360 | |
9361 | float | |
e25f3727 | 9362 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9363 | { |
220058a8 AW |
9364 | scm_c_issue_deprecation_warning |
9365 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9366 | ||
55f26379 MV |
9367 | if (SCM_BIGP (num)) |
9368 | { | |
9369 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9370 | if (!isinf (res)) |
55f26379 MV |
9371 | return res; |
9372 | else | |
9373 | scm_out_of_range (NULL, num); | |
9374 | } | |
9375 | else | |
9376 | return scm_to_double (num); | |
9377 | } | |
9378 | ||
9379 | double | |
e25f3727 | 9380 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9381 | { |
220058a8 AW |
9382 | scm_c_issue_deprecation_warning |
9383 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9384 | ||
55f26379 MV |
9385 | if (SCM_BIGP (num)) |
9386 | { | |
9387 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9388 | if (!isinf (res)) |
55f26379 MV |
9389 | return res; |
9390 | else | |
9391 | scm_out_of_range (NULL, num); | |
9392 | } | |
9393 | else | |
9394 | return scm_to_double (num); | |
9395 | } | |
9396 | ||
9397 | #endif | |
9398 | ||
8507ec80 MV |
9399 | int |
9400 | scm_is_complex (SCM val) | |
9401 | { | |
9402 | return scm_is_true (scm_complex_p (val)); | |
9403 | } | |
9404 | ||
9405 | double | |
9406 | scm_c_real_part (SCM z) | |
9407 | { | |
9408 | if (SCM_COMPLEXP (z)) | |
9409 | return SCM_COMPLEX_REAL (z); | |
9410 | else | |
9411 | { | |
9412 | /* Use the scm_real_part to get proper error checking and | |
9413 | dispatching. | |
9414 | */ | |
9415 | return scm_to_double (scm_real_part (z)); | |
9416 | } | |
9417 | } | |
9418 | ||
9419 | double | |
9420 | scm_c_imag_part (SCM z) | |
9421 | { | |
9422 | if (SCM_COMPLEXP (z)) | |
9423 | return SCM_COMPLEX_IMAG (z); | |
9424 | else | |
9425 | { | |
9426 | /* Use the scm_imag_part to get proper error checking and | |
9427 | dispatching. The result will almost always be 0.0, but not | |
9428 | always. | |
9429 | */ | |
9430 | return scm_to_double (scm_imag_part (z)); | |
9431 | } | |
9432 | } | |
9433 | ||
9434 | double | |
9435 | scm_c_magnitude (SCM z) | |
9436 | { | |
9437 | return scm_to_double (scm_magnitude (z)); | |
9438 | } | |
9439 | ||
9440 | double | |
9441 | scm_c_angle (SCM z) | |
9442 | { | |
9443 | return scm_to_double (scm_angle (z)); | |
9444 | } | |
9445 | ||
9446 | int | |
9447 | scm_is_number (SCM z) | |
9448 | { | |
9449 | return scm_is_true (scm_number_p (z)); | |
9450 | } | |
9451 | ||
8ab3d8a0 | 9452 | |
a5f6b751 MW |
9453 | /* Returns log(x * 2^shift) */ |
9454 | static SCM | |
9455 | log_of_shifted_double (double x, long shift) | |
9456 | { | |
9457 | double ans = log (fabs (x)) + shift * M_LN2; | |
9458 | ||
9459 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9460 | return scm_from_double (ans); | |
9461 | else | |
9462 | return scm_c_make_rectangular (ans, M_PI); | |
9463 | } | |
9464 | ||
9465 | /* Returns log(n), for exact integer n of integer-length size */ | |
9466 | static SCM | |
9467 | log_of_exact_integer_with_size (SCM n, long size) | |
9468 | { | |
9469 | long shift = size - 2 * scm_dblprec[0]; | |
9470 | ||
9471 | if (shift > 0) | |
9472 | return log_of_shifted_double | |
9473 | (scm_to_double (scm_ash (n, scm_from_long(-shift))), | |
9474 | shift); | |
9475 | else | |
9476 | return log_of_shifted_double (scm_to_double (n), 0); | |
9477 | } | |
9478 | ||
85bdb6ac | 9479 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9480 | static SCM |
9481 | log_of_exact_integer (SCM n) | |
9482 | { | |
9483 | return log_of_exact_integer_with_size | |
9484 | (n, scm_to_long (scm_integer_length (n))); | |
9485 | } | |
9486 | ||
9487 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9488 | static SCM | |
9489 | log_of_fraction (SCM n, SCM d) | |
9490 | { | |
9491 | long n_size = scm_to_long (scm_integer_length (n)); | |
9492 | long d_size = scm_to_long (scm_integer_length (d)); | |
9493 | ||
9494 | if (abs (n_size - d_size) > 1) | |
9495 | return (scm_difference (log_of_exact_integer_with_size (n, n_size), | |
9496 | log_of_exact_integer_with_size (d, d_size))); | |
9497 | else if (scm_is_false (scm_negative_p (n))) | |
9498 | return scm_from_double | |
9499 | (log1p (scm_to_double (scm_divide2real (scm_difference (n, d), d)))); | |
9500 | else | |
9501 | return scm_c_make_rectangular | |
9502 | (log1p (scm_to_double (scm_divide2real | |
9503 | (scm_difference (scm_abs (n), d), | |
9504 | d))), | |
9505 | M_PI); | |
9506 | } | |
9507 | ||
9508 | ||
8ab3d8a0 KR |
9509 | /* In the following functions we dispatch to the real-arg funcs like log() |
9510 | when we know the arg is real, instead of just handing everything to | |
9511 | clog() for instance. This is in case clog() doesn't optimize for a | |
9512 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9513 | well use it to go straight to the applicable C func. */ | |
9514 | ||
2519490c MW |
9515 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9516 | (SCM z), | |
9517 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9518 | #define FUNC_NAME s_scm_log |
9519 | { | |
9520 | if (SCM_COMPLEXP (z)) | |
9521 | { | |
03976fee AW |
9522 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9523 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9524 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9525 | #else | |
9526 | double re = SCM_COMPLEX_REAL (z); | |
9527 | double im = SCM_COMPLEX_IMAG (z); | |
9528 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9529 | atan2 (im, re)); | |
9530 | #endif | |
9531 | } | |
a5f6b751 MW |
9532 | else if (SCM_REALP (z)) |
9533 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9534 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9535 | { |
a5f6b751 MW |
9536 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9537 | if (scm_is_eq (z, SCM_INUM0)) | |
9538 | scm_num_overflow (s_scm_log); | |
9539 | #endif | |
9540 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9541 | } |
a5f6b751 MW |
9542 | else if (SCM_BIGP (z)) |
9543 | return log_of_exact_integer (z); | |
9544 | else if (SCM_FRACTIONP (z)) | |
9545 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9546 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9547 | else |
9548 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9549 | } |
9550 | #undef FUNC_NAME | |
9551 | ||
9552 | ||
2519490c MW |
9553 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9554 | (SCM z), | |
9555 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9556 | #define FUNC_NAME s_scm_log10 |
9557 | { | |
9558 | if (SCM_COMPLEXP (z)) | |
9559 | { | |
9560 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9561 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9562 | log10+hypot+atan2.) */ | |
f328f862 LC |
9563 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9564 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9565 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9566 | #else | |
9567 | double re = SCM_COMPLEX_REAL (z); | |
9568 | double im = SCM_COMPLEX_IMAG (z); | |
9569 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9570 | M_LOG10E * atan2 (im, re)); | |
9571 | #endif | |
9572 | } | |
a5f6b751 | 9573 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9574 | { |
a5f6b751 MW |
9575 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9576 | if (scm_is_eq (z, SCM_INUM0)) | |
9577 | scm_num_overflow (s_scm_log10); | |
9578 | #endif | |
9579 | { | |
9580 | double re = scm_to_double (z); | |
9581 | double l = log10 (fabs (re)); | |
9582 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9583 | return scm_from_double (l); | |
9584 | else | |
9585 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9586 | } | |
8ab3d8a0 | 9587 | } |
a5f6b751 MW |
9588 | else if (SCM_BIGP (z)) |
9589 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9590 | else if (SCM_FRACTIONP (z)) | |
9591 | return scm_product (flo_log10e, | |
9592 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9593 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9594 | else |
9595 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9596 | } |
9597 | #undef FUNC_NAME | |
9598 | ||
9599 | ||
2519490c MW |
9600 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9601 | (SCM z), | |
9602 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9603 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9604 | #define FUNC_NAME s_scm_exp |
9605 | { | |
9606 | if (SCM_COMPLEXP (z)) | |
9607 | { | |
93723f3d MW |
9608 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9609 | && defined (SCM_COMPLEX_VALUE) | |
9610 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); | |
9611 | #else | |
8ab3d8a0 KR |
9612 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), |
9613 | SCM_COMPLEX_IMAG (z)); | |
93723f3d | 9614 | #endif |
8ab3d8a0 | 9615 | } |
2519490c | 9616 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9617 | { |
9618 | /* When z is a negative bignum the conversion to double overflows, | |
9619 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9620 | return scm_from_double (exp (scm_to_double (z))); | |
9621 | } | |
2519490c MW |
9622 | else |
9623 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9624 | } |
9625 | #undef FUNC_NAME | |
9626 | ||
9627 | ||
882c8963 MW |
9628 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9629 | (SCM k), | |
9630 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9631 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9632 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9633 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9634 | "\n" | |
9635 | "@lisp\n" | |
9636 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9637 | "@end lisp") | |
9638 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9639 | { | |
9640 | SCM s, r; | |
9641 | ||
9642 | scm_exact_integer_sqrt (k, &s, &r); | |
9643 | return scm_values (scm_list_2 (s, r)); | |
9644 | } | |
9645 | #undef FUNC_NAME | |
9646 | ||
9647 | void | |
9648 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9649 | { | |
9650 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9651 | { | |
9652 | scm_t_inum kk = SCM_I_INUM (k); | |
9653 | scm_t_inum uu = kk; | |
9654 | scm_t_inum ss; | |
9655 | ||
9656 | if (SCM_LIKELY (kk > 0)) | |
9657 | { | |
9658 | do | |
9659 | { | |
9660 | ss = uu; | |
9661 | uu = (ss + kk/ss) / 2; | |
9662 | } while (uu < ss); | |
9663 | *sp = SCM_I_MAKINUM (ss); | |
9664 | *rp = SCM_I_MAKINUM (kk - ss*ss); | |
9665 | } | |
9666 | else if (SCM_LIKELY (kk == 0)) | |
9667 | *sp = *rp = SCM_INUM0; | |
9668 | else | |
9669 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9670 | "exact non-negative integer"); | |
9671 | } | |
9672 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9673 | { | |
9674 | SCM s, r; | |
9675 | ||
9676 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9677 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9678 | "exact non-negative integer"); | |
9679 | s = scm_i_mkbig (); | |
9680 | r = scm_i_mkbig (); | |
9681 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9682 | scm_remember_upto_here_1 (k); | |
9683 | *sp = scm_i_normbig (s); | |
9684 | *rp = scm_i_normbig (r); | |
9685 | } | |
9686 | else | |
9687 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9688 | "exact non-negative integer"); | |
9689 | } | |
9690 | ||
9691 | ||
2519490c MW |
9692 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9693 | (SCM z), | |
9694 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9695 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9696 | "is returned, or if that's zero then a positive imaginary part.\n" |
9697 | "Thus,\n" | |
9698 | "\n" | |
9699 | "@example\n" | |
9700 | "(sqrt 9.0) @result{} 3.0\n" | |
9701 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9702 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9703 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9704 | "@end example") | |
8ab3d8a0 KR |
9705 | #define FUNC_NAME s_scm_sqrt |
9706 | { | |
2519490c | 9707 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9708 | { |
f328f862 LC |
9709 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9710 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9711 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9712 | #else |
2519490c MW |
9713 | double re = SCM_COMPLEX_REAL (z); |
9714 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9715 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9716 | 0.5 * atan2 (im, re)); | |
9717 | #endif | |
9718 | } | |
2519490c | 9719 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9720 | { |
2519490c | 9721 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9722 | if (xx < 0) |
9723 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9724 | else | |
9725 | return scm_from_double (sqrt (xx)); | |
9726 | } | |
2519490c MW |
9727 | else |
9728 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
9729 | } |
9730 | #undef FUNC_NAME | |
9731 | ||
9732 | ||
9733 | ||
0f2d19dd JB |
9734 | void |
9735 | scm_init_numbers () | |
0f2d19dd | 9736 | { |
0b799eea MV |
9737 | int i; |
9738 | ||
b57bf272 AW |
9739 | if (scm_install_gmp_memory_functions) |
9740 | mp_set_memory_functions (custom_gmp_malloc, | |
9741 | custom_gmp_realloc, | |
9742 | custom_gmp_free); | |
9743 | ||
713a4259 KR |
9744 | mpz_init_set_si (z_negative_one, -1); |
9745 | ||
a261c0e9 DH |
9746 | /* It may be possible to tune the performance of some algorithms by using |
9747 | * the following constants to avoid the creation of bignums. Please, before | |
9748 | * using these values, remember the two rules of program optimization: | |
9749 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9750 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9751 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9752 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9753 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9754 | |
f3ae5d60 MD |
9755 | scm_add_feature ("complex"); |
9756 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9757 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9758 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea MV |
9759 | |
9760 | /* determine floating point precision */ | |
55f26379 | 9761 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
9762 | { |
9763 | init_dblprec(&scm_dblprec[i-2],i); | |
9764 | init_fx_radix(fx_per_radix[i-2],i); | |
9765 | } | |
f872b822 | 9766 | #ifdef DBL_DIG |
0b799eea | 9767 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 9768 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 9769 | #endif |
1be6b49c | 9770 | |
cff5fa33 | 9771 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 9772 | #include "libguile/numbers.x" |
0f2d19dd | 9773 | } |
89e00824 ML |
9774 | |
9775 | /* | |
9776 | Local Variables: | |
9777 | c-file-style: "gnu" | |
9778 | End: | |
9779 | */ |