Commit | Line | Data |
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07b390d5 LC |
1 | /* Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, |
2 | * 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, | |
3 | * 2013 Free Software Foundation, Inc. | |
ba74ef4e MV |
4 | * |
5 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
6 | * and Bellcore. See scm_divide. | |
7 | * | |
f81e080b | 8 | * |
73be1d9e | 9 | * This library is free software; you can redistribute it and/or |
53befeb7 NJ |
10 | * modify it under the terms of the GNU Lesser General Public License |
11 | * as published by the Free Software Foundation; either version 3 of | |
12 | * the License, or (at your option) any later version. | |
0f2d19dd | 13 | * |
53befeb7 NJ |
14 | * This library is distributed in the hope that it will be useful, but |
15 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |
73be1d9e MV |
16 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
17 | * Lesser General Public License for more details. | |
0f2d19dd | 18 | * |
73be1d9e MV |
19 | * You should have received a copy of the GNU Lesser General Public |
20 | * License along with this library; if not, write to the Free Software | |
53befeb7 NJ |
21 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
22 | * 02110-1301 USA | |
73be1d9e | 23 | */ |
1bbd0b84 | 24 | |
0f2d19dd | 25 | \f |
ca46fb90 | 26 | /* General assumptions: |
ca46fb90 RB |
27 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. |
28 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
29 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
c7218482 | 30 | * XXX What about infinities? They are equal to their own floor! -mhw |
f92e85f7 | 31 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
32 | */ |
33 | ||
34 | /* TODO: | |
35 | ||
36 | - see if special casing bignums and reals in integer-exponent when | |
37 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
38 | ||
39 | - look in to better short-circuiting of common cases in | |
40 | integer-expt and elsewhere. | |
41 | ||
42 | - see if direct mpz operations can help in ash and elsewhere. | |
43 | ||
44 | */ | |
0f2d19dd | 45 | |
dbb605f5 | 46 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
47 | # include <config.h> |
48 | #endif | |
49 | ||
bbec4602 | 50 | #include <verify.h> |
6f82b8f6 | 51 | #include <assert.h> |
bbec4602 | 52 | |
0f2d19dd | 53 | #include <math.h> |
fc194577 | 54 | #include <string.h> |
3f47e526 MG |
55 | #include <unicase.h> |
56 | #include <unictype.h> | |
f92e85f7 | 57 | |
8ab3d8a0 KR |
58 | #if HAVE_COMPLEX_H |
59 | #include <complex.h> | |
60 | #endif | |
61 | ||
07b390d5 LC |
62 | #include <stdarg.h> |
63 | ||
a0599745 | 64 | #include "libguile/_scm.h" |
a0599745 MD |
65 | #include "libguile/feature.h" |
66 | #include "libguile/ports.h" | |
67 | #include "libguile/root.h" | |
68 | #include "libguile/smob.h" | |
69 | #include "libguile/strings.h" | |
864e7d42 | 70 | #include "libguile/bdw-gc.h" |
a0599745 MD |
71 | |
72 | #include "libguile/validate.h" | |
73 | #include "libguile/numbers.h" | |
1be6b49c | 74 | #include "libguile/deprecation.h" |
f4c627b3 | 75 | |
f92e85f7 MV |
76 | #include "libguile/eq.h" |
77 | ||
8ab3d8a0 KR |
78 | /* values per glibc, if not already defined */ |
79 | #ifndef M_LOG10E | |
80 | #define M_LOG10E 0.43429448190325182765 | |
81 | #endif | |
85bdb6ac MW |
82 | #ifndef M_LN2 |
83 | #define M_LN2 0.69314718055994530942 | |
84 | #endif | |
8ab3d8a0 KR |
85 | #ifndef M_PI |
86 | #define M_PI 3.14159265358979323846 | |
87 | #endif | |
88 | ||
cba521fe MW |
89 | /* FIXME: We assume that FLT_RADIX is 2 */ |
90 | verify (FLT_RADIX == 2); | |
91 | ||
e25f3727 AW |
92 | typedef scm_t_signed_bits scm_t_inum; |
93 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
94 | ||
4cc2e41c MW |
95 | /* Test an inum to see if it can be converted to a double without loss |
96 | of precision. Note that this will sometimes return 0 even when 1 | |
97 | could have been returned, e.g. for large powers of 2. It is designed | |
98 | to be a fast check to optimize common cases. */ | |
99 | #define INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE(n) \ | |
100 | (SCM_I_FIXNUM_BIT-1 <= DBL_MANT_DIG \ | |
101 | || ((n) ^ ((n) >> (SCM_I_FIXNUM_BIT-1))) < (1L << DBL_MANT_DIG)) | |
07b390d5 LC |
102 | |
103 | #if ! HAVE_DECL_MPZ_INITS | |
104 | ||
105 | /* GMP < 5.0.0 lacks `mpz_inits' and `mpz_clears'. Provide them. */ | |
106 | ||
107 | #define VARARG_MPZ_ITERATOR(func) \ | |
108 | static void \ | |
109 | func ## s (mpz_t x, ...) \ | |
110 | { \ | |
111 | va_list ap; \ | |
112 | \ | |
113 | va_start (ap, x); \ | |
114 | while (x != NULL) \ | |
115 | { \ | |
116 | func (x); \ | |
117 | x = va_arg (ap, mpz_ptr); \ | |
118 | } \ | |
119 | va_end (ap); \ | |
120 | } | |
121 | ||
122 | VARARG_MPZ_ITERATOR (mpz_init) | |
123 | VARARG_MPZ_ITERATOR (mpz_clear) | |
124 | ||
125 | #endif | |
126 | ||
0f2d19dd | 127 | \f |
f4c627b3 | 128 | |
ca46fb90 RB |
129 | /* |
130 | Wonder if this might be faster for some of our code? A switch on | |
131 | the numtag would jump directly to the right case, and the | |
132 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
133 | ||
134 | #define SCM_I_NUMTAG_NOTNUM 0 | |
135 | #define SCM_I_NUMTAG_INUM 1 | |
136 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
137 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
138 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
139 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 140 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 141 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 142 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
143 | : SCM_I_NUMTAG_NOTNUM))) |
144 | */ | |
f92e85f7 | 145 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
146 | |
147 | ||
b57bf272 AW |
148 | /* Default to 1, because as we used to hard-code `free' as the |
149 | deallocator, we know that overriding these functions with | |
150 | instrumented `malloc' / `free' is OK. */ | |
151 | int scm_install_gmp_memory_functions = 1; | |
e7efe8e7 | 152 | static SCM flo0; |
ff62c168 | 153 | static SCM exactly_one_half; |
a5f6b751 | 154 | static SCM flo_log10e; |
e7efe8e7 | 155 | |
34d19ef6 | 156 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 157 | |
56e55ac7 | 158 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
159 | * printed or scm_string representation of an inexact number. |
160 | */ | |
0b799eea | 161 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 162 | |
b127c712 | 163 | |
ad79736c AW |
164 | #if !defined (HAVE_ASINH) |
165 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
166 | #endif | |
167 | #if !defined (HAVE_ACOSH) | |
168 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
169 | #endif | |
170 | #if !defined (HAVE_ATANH) | |
171 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
172 | #endif | |
173 | ||
18d78c5e MW |
174 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
175 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released | |
176 | in March 2006), mpz_cmp_d now handles infinities properly. */ | |
f8a8200b | 177 | #if 1 |
b127c712 | 178 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 179 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
180 | #else |
181 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
182 | #endif | |
183 | ||
f92e85f7 | 184 | |
4b26c03e | 185 | #if defined (GUILE_I) |
03976fee | 186 | #if defined HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
187 | |
188 | /* For an SCM object Z which is a complex number (ie. satisfies | |
189 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
190 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 191 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 192 | |
7a35784c | 193 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
194 | |
195 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 196 | static inline SCM |
8ab3d8a0 KR |
197 | scm_from_complex_double (complex double z) |
198 | { | |
199 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
200 | } | |
bca69a9f | 201 | |
8ab3d8a0 | 202 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 203 | #endif /* GUILE_I */ |
8ab3d8a0 | 204 | |
0f2d19dd JB |
205 | \f |
206 | ||
713a4259 | 207 | static mpz_t z_negative_one; |
ac0c002c DH |
208 | |
209 | \f | |
b57bf272 | 210 | |
864e7d42 LC |
211 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
212 | static void | |
6922d92f | 213 | finalize_bignum (void *ptr, void *data) |
864e7d42 LC |
214 | { |
215 | SCM bignum; | |
216 | ||
21041372 | 217 | bignum = SCM_PACK_POINTER (ptr); |
864e7d42 LC |
218 | mpz_clear (SCM_I_BIG_MPZ (bignum)); |
219 | } | |
220 | ||
b57bf272 AW |
221 | /* The next three functions (custom_libgmp_*) are passed to |
222 | mp_set_memory_functions (in GMP) so that memory used by the digits | |
223 | themselves is known to the garbage collector. This is needed so | |
224 | that GC will be run at appropriate times. Otherwise, a program which | |
225 | creates many large bignums would malloc a huge amount of memory | |
226 | before the GC runs. */ | |
227 | static void * | |
228 | custom_gmp_malloc (size_t alloc_size) | |
229 | { | |
230 | return scm_malloc (alloc_size); | |
231 | } | |
232 | ||
233 | static void * | |
234 | custom_gmp_realloc (void *old_ptr, size_t old_size, size_t new_size) | |
235 | { | |
236 | return scm_realloc (old_ptr, new_size); | |
237 | } | |
238 | ||
239 | static void | |
240 | custom_gmp_free (void *ptr, size_t size) | |
241 | { | |
242 | free (ptr); | |
243 | } | |
244 | ||
245 | ||
d017fcdf LC |
246 | /* Return a new uninitialized bignum. */ |
247 | static inline SCM | |
248 | make_bignum (void) | |
249 | { | |
250 | scm_t_bits *p; | |
251 | ||
252 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
253 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
254 | "bignum"); | |
255 | p[0] = scm_tc16_big; | |
256 | ||
6978c673 | 257 | scm_i_set_finalizer (p, finalize_bignum, NULL); |
864e7d42 | 258 | |
d017fcdf LC |
259 | return SCM_PACK (p); |
260 | } | |
ac0c002c | 261 | |
864e7d42 | 262 | |
189171c5 | 263 | SCM |
ca46fb90 RB |
264 | scm_i_mkbig () |
265 | { | |
266 | /* Return a newly created bignum. */ | |
d017fcdf | 267 | SCM z = make_bignum (); |
ca46fb90 RB |
268 | mpz_init (SCM_I_BIG_MPZ (z)); |
269 | return z; | |
270 | } | |
271 | ||
e25f3727 AW |
272 | static SCM |
273 | scm_i_inum2big (scm_t_inum x) | |
274 | { | |
275 | /* Return a newly created bignum initialized to X. */ | |
276 | SCM z = make_bignum (); | |
277 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
278 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
279 | #else | |
280 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
281 | mpz_*_si invocations in Guile. */ | |
282 | #error creation of mpz not implemented for this inum size | |
283 | #endif | |
284 | return z; | |
285 | } | |
286 | ||
189171c5 | 287 | SCM |
c71b0706 MV |
288 | scm_i_long2big (long x) |
289 | { | |
290 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 291 | SCM z = make_bignum (); |
c71b0706 MV |
292 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
293 | return z; | |
294 | } | |
295 | ||
189171c5 | 296 | SCM |
c71b0706 MV |
297 | scm_i_ulong2big (unsigned long x) |
298 | { | |
299 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 300 | SCM z = make_bignum (); |
c71b0706 MV |
301 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
302 | return z; | |
303 | } | |
304 | ||
189171c5 | 305 | SCM |
ca46fb90 RB |
306 | scm_i_clonebig (SCM src_big, int same_sign_p) |
307 | { | |
308 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 309 | SCM z = make_bignum (); |
ca46fb90 | 310 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
311 | if (!same_sign_p) |
312 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
313 | return z; |
314 | } | |
315 | ||
189171c5 | 316 | int |
ca46fb90 RB |
317 | scm_i_bigcmp (SCM x, SCM y) |
318 | { | |
319 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
320 | /* presume we already know x and y are bignums */ | |
321 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
322 | scm_remember_upto_here_2 (x, y); | |
323 | return result; | |
324 | } | |
325 | ||
189171c5 | 326 | SCM |
ca46fb90 RB |
327 | scm_i_dbl2big (double d) |
328 | { | |
329 | /* results are only defined if d is an integer */ | |
d017fcdf | 330 | SCM z = make_bignum (); |
ca46fb90 RB |
331 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
332 | return z; | |
333 | } | |
334 | ||
f92e85f7 MV |
335 | /* Convert a integer in double representation to a SCM number. */ |
336 | ||
189171c5 | 337 | SCM |
f92e85f7 MV |
338 | scm_i_dbl2num (double u) |
339 | { | |
340 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
341 | powers of 2, so there's no rounding when making "double" values | |
342 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
343 | get rounded on a 64-bit machine, hence the "+1". | |
344 | ||
345 | The use of floor() to force to an integer value ensures we get a | |
346 | "numerically closest" value without depending on how a | |
347 | double->long cast or how mpz_set_d will round. For reference, | |
348 | double->long probably follows the hardware rounding mode, | |
349 | mpz_set_d truncates towards zero. */ | |
350 | ||
351 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
352 | representable as a double? */ | |
353 | ||
354 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
355 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 356 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
357 | else |
358 | return scm_i_dbl2big (u); | |
359 | } | |
360 | ||
1eb6a33a | 361 | static SCM round_right_shift_exact_integer (SCM n, long count); |
f8a8200b | 362 | |
1eb6a33a MW |
363 | /* scm_i_big2dbl_2exp() is like frexp for bignums: it converts the |
364 | bignum b into a normalized significand and exponent such that | |
365 | b = significand * 2^exponent and 1/2 <= abs(significand) < 1. | |
366 | The return value is the significand rounded to the closest | |
367 | representable double, and the exponent is placed into *expon_p. | |
368 | If b is zero, then the returned exponent and significand are both | |
369 | zero. */ | |
f8a8200b | 370 | |
1eb6a33a MW |
371 | static double |
372 | scm_i_big2dbl_2exp (SCM b, long *expon_p) | |
ca46fb90 | 373 | { |
1eb6a33a MW |
374 | size_t bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); |
375 | size_t shift = 0; | |
089c9a59 KR |
376 | |
377 | if (bits > DBL_MANT_DIG) | |
378 | { | |
1eb6a33a MW |
379 | shift = bits - DBL_MANT_DIG; |
380 | b = round_right_shift_exact_integer (b, shift); | |
381 | if (SCM_I_INUMP (b)) | |
089c9a59 | 382 | { |
1eb6a33a MW |
383 | int expon; |
384 | double signif = frexp (SCM_I_INUM (b), &expon); | |
385 | *expon_p = expon + shift; | |
386 | return signif; | |
089c9a59 KR |
387 | } |
388 | } | |
389 | ||
1eb6a33a MW |
390 | { |
391 | long expon; | |
392 | double signif = mpz_get_d_2exp (&expon, SCM_I_BIG_MPZ (b)); | |
393 | scm_remember_upto_here_1 (b); | |
394 | *expon_p = expon + shift; | |
395 | return signif; | |
396 | } | |
397 | } | |
398 | ||
399 | /* scm_i_big2dbl() rounds to the closest representable double, | |
400 | in accordance with R5RS exact->inexact. */ | |
401 | double | |
402 | scm_i_big2dbl (SCM b) | |
403 | { | |
404 | long expon; | |
405 | double signif = scm_i_big2dbl_2exp (b, &expon); | |
406 | return ldexp (signif, expon); | |
ca46fb90 RB |
407 | } |
408 | ||
189171c5 | 409 | SCM |
ca46fb90 RB |
410 | scm_i_normbig (SCM b) |
411 | { | |
412 | /* convert a big back to a fixnum if it'll fit */ | |
413 | /* presume b is a bignum */ | |
414 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
415 | { | |
e25f3727 | 416 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 417 | if (SCM_FIXABLE (val)) |
d956fa6f | 418 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
419 | } |
420 | return b; | |
421 | } | |
f872b822 | 422 | |
f92e85f7 MV |
423 | static SCM_C_INLINE_KEYWORD SCM |
424 | scm_i_mpz2num (mpz_t b) | |
425 | { | |
426 | /* convert a mpz number to a SCM number. */ | |
427 | if (mpz_fits_slong_p (b)) | |
428 | { | |
e25f3727 | 429 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 430 | if (SCM_FIXABLE (val)) |
d956fa6f | 431 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
432 | } |
433 | ||
434 | { | |
d017fcdf | 435 | SCM z = make_bignum (); |
f92e85f7 MV |
436 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
437 | return z; | |
438 | } | |
439 | } | |
440 | ||
a285b18c MW |
441 | /* Make the ratio NUMERATOR/DENOMINATOR, where: |
442 | 1. NUMERATOR and DENOMINATOR are exact integers | |
443 | 2. NUMERATOR and DENOMINATOR are reduced to lowest terms: gcd(n,d) == 1 */ | |
cba42c93 | 444 | static SCM |
a285b18c | 445 | scm_i_make_ratio_already_reduced (SCM numerator, SCM denominator) |
f92e85f7 | 446 | { |
a285b18c MW |
447 | /* Flip signs so that the denominator is positive. */ |
448 | if (scm_is_false (scm_positive_p (denominator))) | |
f92e85f7 | 449 | { |
a285b18c | 450 | if (SCM_UNLIKELY (scm_is_eq (denominator, SCM_INUM0))) |
f92e85f7 | 451 | scm_num_overflow ("make-ratio"); |
a285b18c | 452 | else |
f92e85f7 | 453 | { |
a285b18c MW |
454 | numerator = scm_difference (numerator, SCM_UNDEFINED); |
455 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
f92e85f7 | 456 | } |
f92e85f7 | 457 | } |
c60e130c | 458 | |
a285b18c MW |
459 | /* Check for the integer case */ |
460 | if (scm_is_eq (denominator, SCM_INUM1)) | |
461 | return numerator; | |
c60e130c | 462 | |
a285b18c MW |
463 | return scm_double_cell (scm_tc16_fraction, |
464 | SCM_UNPACK (numerator), | |
465 | SCM_UNPACK (denominator), 0); | |
466 | } | |
467 | ||
468 | static SCM scm_exact_integer_quotient (SCM x, SCM y); | |
469 | ||
470 | /* Make the ratio NUMERATOR/DENOMINATOR */ | |
471 | static SCM | |
472 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
473 | #define FUNC_NAME "make-ratio" | |
474 | { | |
475 | /* Make sure the arguments are proper */ | |
476 | if (!SCM_LIKELY (SCM_I_INUMP (numerator) || SCM_BIGP (numerator))) | |
477 | SCM_WRONG_TYPE_ARG (1, numerator); | |
478 | else if (!SCM_LIKELY (SCM_I_INUMP (denominator) || SCM_BIGP (denominator))) | |
479 | SCM_WRONG_TYPE_ARG (2, denominator); | |
480 | else | |
f92e85f7 | 481 | { |
a285b18c MW |
482 | SCM the_gcd = scm_gcd (numerator, denominator); |
483 | if (!(scm_is_eq (the_gcd, SCM_INUM1))) | |
f92e85f7 | 484 | { |
a285b18c MW |
485 | /* Reduce to lowest terms */ |
486 | numerator = scm_exact_integer_quotient (numerator, the_gcd); | |
487 | denominator = scm_exact_integer_quotient (denominator, the_gcd); | |
f92e85f7 | 488 | } |
a285b18c | 489 | return scm_i_make_ratio_already_reduced (numerator, denominator); |
f92e85f7 | 490 | } |
f92e85f7 | 491 | } |
c60e130c | 492 | #undef FUNC_NAME |
f92e85f7 | 493 | |
98237784 MW |
494 | static mpz_t scm_i_divide2double_lo2b; |
495 | ||
496 | /* Return the double that is closest to the exact rational N/D, with | |
497 | ties rounded toward even mantissas. N and D must be exact | |
498 | integers. */ | |
499 | static double | |
500 | scm_i_divide2double (SCM n, SCM d) | |
501 | { | |
502 | int neg; | |
503 | mpz_t nn, dd, lo, hi, x; | |
504 | ssize_t e; | |
505 | ||
c8248c8e | 506 | if (SCM_LIKELY (SCM_I_INUMP (d))) |
f92e85f7 | 507 | { |
4cc2e41c MW |
508 | if (SCM_LIKELY |
509 | (SCM_I_INUMP (n) | |
510 | && INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE (SCM_I_INUM (n)) | |
511 | && INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE (SCM_I_INUM (d)))) | |
c8248c8e MW |
512 | /* If both N and D can be losslessly converted to doubles, then |
513 | we can rely on IEEE floating point to do proper rounding much | |
514 | faster than we can. */ | |
515 | return ((double) SCM_I_INUM (n)) / ((double) SCM_I_INUM (d)); | |
516 | ||
98237784 MW |
517 | if (SCM_UNLIKELY (scm_is_eq (d, SCM_INUM0))) |
518 | { | |
519 | if (scm_is_true (scm_positive_p (n))) | |
520 | return 1.0 / 0.0; | |
521 | else if (scm_is_true (scm_negative_p (n))) | |
522 | return -1.0 / 0.0; | |
523 | else | |
524 | return 0.0 / 0.0; | |
525 | } | |
c8248c8e | 526 | |
98237784 | 527 | mpz_init_set_si (dd, SCM_I_INUM (d)); |
f92e85f7 | 528 | } |
98237784 MW |
529 | else |
530 | mpz_init_set (dd, SCM_I_BIG_MPZ (d)); | |
c60e130c | 531 | |
98237784 MW |
532 | if (SCM_I_INUMP (n)) |
533 | mpz_init_set_si (nn, SCM_I_INUM (n)); | |
534 | else | |
535 | mpz_init_set (nn, SCM_I_BIG_MPZ (n)); | |
536 | ||
537 | neg = (mpz_sgn (nn) < 0) ^ (mpz_sgn (dd) < 0); | |
538 | mpz_abs (nn, nn); | |
539 | mpz_abs (dd, dd); | |
540 | ||
541 | /* Now we need to find the value of e such that: | |
542 | ||
543 | For e <= 0: | |
544 | b^{p-1} - 1/2b <= b^-e n / d < b^p - 1/2 [1A] | |
545 | (2 b^p - 1) <= 2 b b^-e n / d < (2 b^p - 1) b [2A] | |
546 | (2 b^p - 1) d <= 2 b b^-e n < (2 b^p - 1) d b [3A] | |
547 | ||
548 | For e >= 0: | |
549 | b^{p-1} - 1/2b <= n / b^e d < b^p - 1/2 [1B] | |
550 | (2 b^p - 1) <= 2 b n / b^e d < (2 b^p - 1) b [2B] | |
551 | (2 b^p - 1) d b^e <= 2 b n < (2 b^p - 1) d b b^e [3B] | |
552 | ||
553 | where: p = DBL_MANT_DIG | |
554 | b = FLT_RADIX (here assumed to be 2) | |
555 | ||
556 | After rounding, the mantissa must be an integer between b^{p-1} and | |
557 | (b^p - 1), except for subnormal numbers. In the inequations [1A] | |
558 | and [1B], the middle expression represents the mantissa *before* | |
559 | rounding, and therefore is bounded by the range of values that will | |
560 | round to a floating-point number with the exponent e. The upper | |
561 | bound is (b^p - 1 + 1/2) = (b^p - 1/2), and is exclusive because | |
562 | ties will round up to the next power of b. The lower bound is | |
563 | (b^{p-1} - 1/2b), and is inclusive because ties will round toward | |
564 | this power of b. Here we subtract 1/2b instead of 1/2 because it | |
565 | is in the range of the next smaller exponent, where the | |
566 | representable numbers are closer together by a factor of b. | |
567 | ||
568 | Inequations [2A] and [2B] are derived from [1A] and [1B] by | |
569 | multiplying by 2b, and in [3A] and [3B] we multiply by the | |
570 | denominator of the middle value to obtain integer expressions. | |
571 | ||
572 | In the code below, we refer to the three expressions in [3A] or | |
573 | [3B] as lo, x, and hi. If the number is normalizable, we will | |
574 | achieve the goal: lo <= x < hi */ | |
575 | ||
576 | /* Make an initial guess for e */ | |
577 | e = mpz_sizeinbase (nn, 2) - mpz_sizeinbase (dd, 2) - (DBL_MANT_DIG-1); | |
578 | if (e < DBL_MIN_EXP - DBL_MANT_DIG) | |
579 | e = DBL_MIN_EXP - DBL_MANT_DIG; | |
580 | ||
581 | /* Compute the initial values of lo, x, and hi | |
582 | based on the initial guess of e */ | |
583 | mpz_inits (lo, hi, x, NULL); | |
584 | mpz_mul_2exp (x, nn, 2 + ((e < 0) ? -e : 0)); | |
585 | mpz_mul (lo, dd, scm_i_divide2double_lo2b); | |
586 | if (e > 0) | |
587 | mpz_mul_2exp (lo, lo, e); | |
588 | mpz_mul_2exp (hi, lo, 1); | |
589 | ||
590 | /* Adjust e as needed to satisfy the inequality lo <= x < hi, | |
591 | (but without making e less then the minimum exponent) */ | |
592 | while (mpz_cmp (x, lo) < 0 && e > DBL_MIN_EXP - DBL_MANT_DIG) | |
593 | { | |
594 | mpz_mul_2exp (x, x, 1); | |
595 | e--; | |
596 | } | |
597 | while (mpz_cmp (x, hi) >= 0) | |
598 | { | |
599 | /* If we ever used lo's value again, | |
600 | we would need to double lo here. */ | |
601 | mpz_mul_2exp (hi, hi, 1); | |
602 | e++; | |
603 | } | |
604 | ||
605 | /* Now compute the rounded mantissa: | |
606 | n / b^e d (if e >= 0) | |
607 | n b^-e / d (if e <= 0) */ | |
e2bf3b19 | 608 | { |
98237784 MW |
609 | int cmp; |
610 | double result; | |
611 | ||
612 | if (e < 0) | |
613 | mpz_mul_2exp (nn, nn, -e); | |
614 | else | |
615 | mpz_mul_2exp (dd, dd, e); | |
616 | ||
617 | /* mpz does not directly support rounded right | |
618 | shifts, so we have to do it the hard way. | |
619 | For efficiency, we reuse lo and hi. | |
620 | hi == quotient, lo == remainder */ | |
621 | mpz_fdiv_qr (hi, lo, nn, dd); | |
622 | ||
623 | /* The fractional part of the unrounded mantissa would be | |
624 | remainder/dividend, i.e. lo/dd. So we have a tie if | |
625 | lo/dd = 1/2. Multiplying both sides by 2*dd yields the | |
626 | integer expression 2*lo = dd. Here we do that comparison | |
627 | to decide whether to round up or down. */ | |
628 | mpz_mul_2exp (lo, lo, 1); | |
629 | cmp = mpz_cmp (lo, dd); | |
630 | if (cmp > 0 || (cmp == 0 && mpz_odd_p (hi))) | |
631 | mpz_add_ui (hi, hi, 1); | |
632 | ||
633 | result = ldexp (mpz_get_d (hi), e); | |
634 | if (neg) | |
635 | result = -result; | |
636 | ||
637 | mpz_clears (nn, dd, lo, hi, x, NULL); | |
638 | return result; | |
e2bf3b19 | 639 | } |
f92e85f7 MV |
640 | } |
641 | ||
f92e85f7 MV |
642 | double |
643 | scm_i_fraction2double (SCM z) | |
644 | { | |
98237784 MW |
645 | return scm_i_divide2double (SCM_FRACTION_NUMERATOR (z), |
646 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 MV |
647 | } |
648 | ||
00472a22 MW |
649 | static SCM |
650 | scm_i_from_double (double val) | |
2e274311 | 651 | { |
00472a22 MW |
652 | SCM z; |
653 | ||
d8d7c7bf | 654 | z = SCM_PACK_POINTER (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); |
00472a22 MW |
655 | |
656 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
657 | SCM_REAL_VALUE (z) = val; | |
2e274311 | 658 | |
00472a22 | 659 | return z; |
2e274311 MW |
660 | } |
661 | ||
2519490c MW |
662 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
663 | (SCM x), | |
942e5b91 MG |
664 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
665 | "otherwise.") | |
1bbd0b84 | 666 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 667 | { |
41df63cf MW |
668 | if (SCM_INEXACTP (x)) |
669 | return SCM_BOOL_F; | |
670 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 671 | return SCM_BOOL_T; |
41df63cf | 672 | else |
fa075d40 | 673 | return scm_wta_dispatch_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
674 | } |
675 | #undef FUNC_NAME | |
676 | ||
022dda69 MG |
677 | int |
678 | scm_is_exact (SCM val) | |
679 | { | |
680 | return scm_is_true (scm_exact_p (val)); | |
681 | } | |
41df63cf | 682 | |
2519490c | 683 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
684 | (SCM x), |
685 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
686 | "else.") | |
687 | #define FUNC_NAME s_scm_inexact_p | |
688 | { | |
689 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 690 | return SCM_BOOL_T; |
41df63cf | 691 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 692 | return SCM_BOOL_F; |
41df63cf | 693 | else |
fa075d40 | 694 | return scm_wta_dispatch_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 695 | } |
1bbd0b84 | 696 | #undef FUNC_NAME |
0f2d19dd | 697 | |
022dda69 MG |
698 | int |
699 | scm_is_inexact (SCM val) | |
700 | { | |
701 | return scm_is_true (scm_inexact_p (val)); | |
702 | } | |
4219f20d | 703 | |
2519490c | 704 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 705 | (SCM n), |
942e5b91 MG |
706 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
707 | "otherwise.") | |
1bbd0b84 | 708 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 709 | { |
e11e83f3 | 710 | if (SCM_I_INUMP (n)) |
0aacf84e | 711 | { |
e25f3727 | 712 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 713 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
714 | } |
715 | else if (SCM_BIGP (n)) | |
716 | { | |
717 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
718 | scm_remember_upto_here_1 (n); | |
73e4de09 | 719 | return scm_from_bool (odd_p); |
0aacf84e | 720 | } |
f92e85f7 MV |
721 | else if (SCM_REALP (n)) |
722 | { | |
2519490c | 723 | double val = SCM_REAL_VALUE (n); |
19374ad2 | 724 | if (isfinite (val)) |
2519490c MW |
725 | { |
726 | double rem = fabs (fmod (val, 2.0)); | |
727 | if (rem == 1.0) | |
728 | return SCM_BOOL_T; | |
729 | else if (rem == 0.0) | |
730 | return SCM_BOOL_F; | |
731 | } | |
f92e85f7 | 732 | } |
fa075d40 | 733 | return scm_wta_dispatch_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 734 | } |
1bbd0b84 | 735 | #undef FUNC_NAME |
0f2d19dd | 736 | |
4219f20d | 737 | |
2519490c | 738 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 739 | (SCM n), |
942e5b91 MG |
740 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
741 | "otherwise.") | |
1bbd0b84 | 742 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 743 | { |
e11e83f3 | 744 | if (SCM_I_INUMP (n)) |
0aacf84e | 745 | { |
e25f3727 | 746 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 747 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
748 | } |
749 | else if (SCM_BIGP (n)) | |
750 | { | |
751 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
752 | scm_remember_upto_here_1 (n); | |
73e4de09 | 753 | return scm_from_bool (even_p); |
0aacf84e | 754 | } |
f92e85f7 MV |
755 | else if (SCM_REALP (n)) |
756 | { | |
2519490c | 757 | double val = SCM_REAL_VALUE (n); |
19374ad2 | 758 | if (isfinite (val)) |
2519490c MW |
759 | { |
760 | double rem = fabs (fmod (val, 2.0)); | |
761 | if (rem == 1.0) | |
762 | return SCM_BOOL_F; | |
763 | else if (rem == 0.0) | |
764 | return SCM_BOOL_T; | |
765 | } | |
f92e85f7 | 766 | } |
fa075d40 | 767 | return scm_wta_dispatch_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 768 | } |
1bbd0b84 | 769 | #undef FUNC_NAME |
0f2d19dd | 770 | |
2519490c MW |
771 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
772 | (SCM x), | |
10391e06 AW |
773 | "Return @code{#t} if the real number @var{x} is neither\n" |
774 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
775 | #define FUNC_NAME s_scm_finite_p |
776 | { | |
777 | if (SCM_REALP (x)) | |
19374ad2 | 778 | return scm_from_bool (isfinite (SCM_REAL_VALUE (x))); |
10391e06 | 779 | else if (scm_is_real (x)) |
7112615f MW |
780 | return SCM_BOOL_T; |
781 | else | |
fa075d40 | 782 | return scm_wta_dispatch_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
783 | } |
784 | #undef FUNC_NAME | |
785 | ||
2519490c MW |
786 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
787 | (SCM x), | |
788 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
789 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
790 | #define FUNC_NAME s_scm_inf_p |
791 | { | |
b1092b3a | 792 | if (SCM_REALP (x)) |
2e65b52f | 793 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 794 | else if (scm_is_real (x)) |
7351e207 | 795 | return SCM_BOOL_F; |
10391e06 | 796 | else |
fa075d40 | 797 | return scm_wta_dispatch_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
798 | } |
799 | #undef FUNC_NAME | |
800 | ||
2519490c MW |
801 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
802 | (SCM x), | |
10391e06 AW |
803 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
804 | "or @code{#f} otherwise.") | |
7351e207 MV |
805 | #define FUNC_NAME s_scm_nan_p |
806 | { | |
10391e06 AW |
807 | if (SCM_REALP (x)) |
808 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
809 | else if (scm_is_real (x)) | |
7351e207 | 810 | return SCM_BOOL_F; |
10391e06 | 811 | else |
fa075d40 | 812 | return scm_wta_dispatch_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
813 | } |
814 | #undef FUNC_NAME | |
815 | ||
816 | /* Guile's idea of infinity. */ | |
817 | static double guile_Inf; | |
818 | ||
819 | /* Guile's idea of not a number. */ | |
820 | static double guile_NaN; | |
821 | ||
822 | static void | |
823 | guile_ieee_init (void) | |
824 | { | |
7351e207 MV |
825 | /* Some version of gcc on some old version of Linux used to crash when |
826 | trying to make Inf and NaN. */ | |
827 | ||
240a27d2 KR |
828 | #ifdef INFINITY |
829 | /* C99 INFINITY, when available. | |
830 | FIXME: The standard allows for INFINITY to be something that overflows | |
831 | at compile time. We ought to have a configure test to check for that | |
832 | before trying to use it. (But in practice we believe this is not a | |
833 | problem on any system guile is likely to target.) */ | |
834 | guile_Inf = INFINITY; | |
56a3dcd4 | 835 | #elif defined HAVE_DINFINITY |
240a27d2 | 836 | /* OSF */ |
7351e207 | 837 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 838 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
839 | #else |
840 | double tmp = 1e+10; | |
841 | guile_Inf = tmp; | |
842 | for (;;) | |
843 | { | |
844 | guile_Inf *= 1e+10; | |
845 | if (guile_Inf == tmp) | |
846 | break; | |
847 | tmp = guile_Inf; | |
848 | } | |
849 | #endif | |
850 | ||
240a27d2 KR |
851 | #ifdef NAN |
852 | /* C99 NAN, when available */ | |
853 | guile_NaN = NAN; | |
56a3dcd4 | 854 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
855 | { |
856 | /* OSF */ | |
857 | extern unsigned int DQNAN[2]; | |
858 | guile_NaN = (*((double *)(DQNAN))); | |
859 | } | |
7351e207 MV |
860 | #else |
861 | guile_NaN = guile_Inf / guile_Inf; | |
862 | #endif | |
7351e207 MV |
863 | } |
864 | ||
865 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
866 | (void), | |
867 | "Return Inf.") | |
868 | #define FUNC_NAME s_scm_inf | |
869 | { | |
870 | static int initialized = 0; | |
871 | if (! initialized) | |
872 | { | |
873 | guile_ieee_init (); | |
874 | initialized = 1; | |
875 | } | |
00472a22 | 876 | return scm_i_from_double (guile_Inf); |
7351e207 MV |
877 | } |
878 | #undef FUNC_NAME | |
879 | ||
880 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
881 | (void), | |
882 | "Return NaN.") | |
883 | #define FUNC_NAME s_scm_nan | |
884 | { | |
885 | static int initialized = 0; | |
0aacf84e | 886 | if (!initialized) |
7351e207 MV |
887 | { |
888 | guile_ieee_init (); | |
889 | initialized = 1; | |
890 | } | |
00472a22 | 891 | return scm_i_from_double (guile_NaN); |
7351e207 MV |
892 | } |
893 | #undef FUNC_NAME | |
894 | ||
4219f20d | 895 | |
a48d60b1 MD |
896 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
897 | (SCM x), | |
898 | "Return the absolute value of @var{x}.") | |
2519490c | 899 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 900 | { |
e11e83f3 | 901 | if (SCM_I_INUMP (x)) |
0aacf84e | 902 | { |
e25f3727 | 903 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
904 | if (xx >= 0) |
905 | return x; | |
906 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 907 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 908 | else |
e25f3727 | 909 | return scm_i_inum2big (-xx); |
4219f20d | 910 | } |
9b9ef10c MW |
911 | else if (SCM_LIKELY (SCM_REALP (x))) |
912 | { | |
913 | double xx = SCM_REAL_VALUE (x); | |
914 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
915 | if (xx < 0.0) | |
00472a22 | 916 | return scm_i_from_double (-xx); |
9b9ef10c MW |
917 | /* Handle signed zeroes properly */ |
918 | else if (SCM_UNLIKELY (xx == 0.0)) | |
919 | return flo0; | |
920 | else | |
921 | return x; | |
922 | } | |
0aacf84e MD |
923 | else if (SCM_BIGP (x)) |
924 | { | |
925 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
926 | if (sgn < 0) | |
927 | return scm_i_clonebig (x, 0); | |
928 | else | |
929 | return x; | |
4219f20d | 930 | } |
f92e85f7 MV |
931 | else if (SCM_FRACTIONP (x)) |
932 | { | |
73e4de09 | 933 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 934 | return x; |
a285b18c MW |
935 | return scm_i_make_ratio_already_reduced |
936 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
937 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 938 | } |
0aacf84e | 939 | else |
fa075d40 | 940 | return scm_wta_dispatch_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 941 | } |
a48d60b1 | 942 | #undef FUNC_NAME |
0f2d19dd | 943 | |
4219f20d | 944 | |
2519490c MW |
945 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
946 | (SCM x, SCM y), | |
947 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
948 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 949 | { |
495a39c4 | 950 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 951 | { |
495a39c4 | 952 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 953 | return scm_truncate_quotient (x, y); |
0aacf84e | 954 | else |
fa075d40 | 955 | return scm_wta_dispatch_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 956 | } |
0aacf84e | 957 | else |
fa075d40 | 958 | return scm_wta_dispatch_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 959 | } |
2519490c | 960 | #undef FUNC_NAME |
0f2d19dd | 961 | |
2519490c MW |
962 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
963 | (SCM x, SCM y), | |
964 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
965 | "@lisp\n" | |
966 | "(remainder 13 4) @result{} 1\n" | |
967 | "(remainder -13 4) @result{} -1\n" | |
968 | "@end lisp") | |
969 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 970 | { |
495a39c4 | 971 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 972 | { |
495a39c4 | 973 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 974 | return scm_truncate_remainder (x, y); |
0aacf84e | 975 | else |
fa075d40 | 976 | return scm_wta_dispatch_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 977 | } |
0aacf84e | 978 | else |
fa075d40 | 979 | return scm_wta_dispatch_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 980 | } |
2519490c | 981 | #undef FUNC_NAME |
0f2d19dd | 982 | |
89a7e495 | 983 | |
2519490c MW |
984 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
985 | (SCM x, SCM y), | |
986 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
987 | "@lisp\n" | |
988 | "(modulo 13 4) @result{} 1\n" | |
989 | "(modulo -13 4) @result{} 3\n" | |
990 | "@end lisp") | |
991 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 992 | { |
495a39c4 | 993 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 994 | { |
495a39c4 | 995 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 996 | return scm_floor_remainder (x, y); |
0aacf84e | 997 | else |
fa075d40 | 998 | return scm_wta_dispatch_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 999 | } |
0aacf84e | 1000 | else |
fa075d40 | 1001 | return scm_wta_dispatch_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1002 | } |
2519490c | 1003 | #undef FUNC_NAME |
0f2d19dd | 1004 | |
a285b18c MW |
1005 | /* Return the exact integer q such that n = q*d, for exact integers n |
1006 | and d, where d is known in advance to divide n evenly (with zero | |
1007 | remainder). For large integers, this can be computed more | |
1008 | efficiently than when the remainder is unknown. */ | |
1009 | static SCM | |
1010 | scm_exact_integer_quotient (SCM n, SCM d) | |
1011 | #define FUNC_NAME "exact-integer-quotient" | |
1012 | { | |
1013 | if (SCM_LIKELY (SCM_I_INUMP (n))) | |
1014 | { | |
1015 | scm_t_inum nn = SCM_I_INUM (n); | |
1016 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
1017 | { | |
1018 | scm_t_inum dd = SCM_I_INUM (d); | |
1019 | if (SCM_UNLIKELY (dd == 0)) | |
1020 | scm_num_overflow ("exact-integer-quotient"); | |
1021 | else | |
1022 | { | |
1023 | scm_t_inum qq = nn / dd; | |
1024 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1025 | return SCM_I_MAKINUM (qq); | |
1026 | else | |
1027 | return scm_i_inum2big (qq); | |
1028 | } | |
1029 | } | |
1030 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
1031 | { | |
1032 | /* n is an inum and d is a bignum. Given that d is known to | |
1033 | divide n evenly, there are only two possibilities: n is 0, | |
1034 | or else n is fixnum-min and d is abs(fixnum-min). */ | |
1035 | if (nn == 0) | |
1036 | return SCM_INUM0; | |
1037 | else | |
1038 | return SCM_I_MAKINUM (-1); | |
1039 | } | |
1040 | else | |
1041 | SCM_WRONG_TYPE_ARG (2, d); | |
1042 | } | |
1043 | else if (SCM_LIKELY (SCM_BIGP (n))) | |
1044 | { | |
1045 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
1046 | { | |
1047 | scm_t_inum dd = SCM_I_INUM (d); | |
1048 | if (SCM_UNLIKELY (dd == 0)) | |
1049 | scm_num_overflow ("exact-integer-quotient"); | |
1050 | else if (SCM_UNLIKELY (dd == 1)) | |
1051 | return n; | |
1052 | else | |
1053 | { | |
1054 | SCM q = scm_i_mkbig (); | |
1055 | if (dd > 0) | |
1056 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), dd); | |
1057 | else | |
1058 | { | |
1059 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), -dd); | |
1060 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1061 | } | |
1062 | scm_remember_upto_here_1 (n); | |
1063 | return scm_i_normbig (q); | |
1064 | } | |
1065 | } | |
1066 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
1067 | { | |
1068 | SCM q = scm_i_mkbig (); | |
1069 | mpz_divexact (SCM_I_BIG_MPZ (q), | |
1070 | SCM_I_BIG_MPZ (n), | |
1071 | SCM_I_BIG_MPZ (d)); | |
1072 | scm_remember_upto_here_2 (n, d); | |
1073 | return scm_i_normbig (q); | |
1074 | } | |
1075 | else | |
1076 | SCM_WRONG_TYPE_ARG (2, d); | |
1077 | } | |
1078 | else | |
1079 | SCM_WRONG_TYPE_ARG (1, n); | |
1080 | } | |
1081 | #undef FUNC_NAME | |
1082 | ||
5fbf680b MW |
1083 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
1084 | two-valued functions. It is called from primitive generics that take | |
1085 | two arguments and return two values, when the core procedure is | |
1086 | unable to handle the given argument types. If there are GOOPS | |
1087 | methods for this primitive generic, it dispatches to GOOPS and, if | |
1088 | successful, expects two values to be returned, which are placed in | |
1089 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
1090 | wrong-type-arg exception. | |
1091 | ||
1092 | FIXME: This obviously belongs somewhere else, but until we decide on | |
1093 | the right API, it is here as a static function, because it is needed | |
1094 | by the *_divide functions below. | |
1095 | */ | |
1096 | static void | |
1097 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
1098 | const char *subr, SCM *rp1, SCM *rp2) | |
1099 | { | |
fa075d40 AW |
1100 | SCM vals = scm_wta_dispatch_2 (gf, a1, a2, pos, subr); |
1101 | ||
1102 | scm_i_extract_values_2 (vals, rp1, rp2); | |
5fbf680b MW |
1103 | } |
1104 | ||
a8da6d93 MW |
1105 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
1106 | (SCM x, SCM y), | |
1107 | "Return the integer @var{q} such that\n" | |
1108 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1109 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1110 | "@lisp\n" | |
1111 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1112 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1113 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1114 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1115 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1116 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1117 | "@end lisp") | |
ff62c168 MW |
1118 | #define FUNC_NAME s_scm_euclidean_quotient |
1119 | { | |
a8da6d93 MW |
1120 | if (scm_is_false (scm_negative_p (y))) |
1121 | return scm_floor_quotient (x, y); | |
ff62c168 | 1122 | else |
a8da6d93 | 1123 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
1124 | } |
1125 | #undef FUNC_NAME | |
1126 | ||
a8da6d93 MW |
1127 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
1128 | (SCM x, SCM y), | |
1129 | "Return the real number @var{r} such that\n" | |
1130 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1131 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1132 | "for some integer @var{q}.\n" | |
1133 | "@lisp\n" | |
1134 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1135 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1136 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1137 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1138 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1139 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1140 | "@end lisp") | |
ff62c168 MW |
1141 | #define FUNC_NAME s_scm_euclidean_remainder |
1142 | { | |
a8da6d93 MW |
1143 | if (scm_is_false (scm_negative_p (y))) |
1144 | return scm_floor_remainder (x, y); | |
ff62c168 | 1145 | else |
a8da6d93 | 1146 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
1147 | } |
1148 | #undef FUNC_NAME | |
1149 | ||
a8da6d93 MW |
1150 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
1151 | (SCM x, SCM y), | |
1152 | "Return the integer @var{q} and the real number @var{r}\n" | |
1153 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1154 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1155 | "@lisp\n" | |
1156 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1157 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1158 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1159 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1160 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1161 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1162 | "@end lisp") | |
5fbf680b MW |
1163 | #define FUNC_NAME s_scm_i_euclidean_divide |
1164 | { | |
a8da6d93 MW |
1165 | if (scm_is_false (scm_negative_p (y))) |
1166 | return scm_i_floor_divide (x, y); | |
1167 | else | |
1168 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
1169 | } |
1170 | #undef FUNC_NAME | |
1171 | ||
5fbf680b MW |
1172 | void |
1173 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 1174 | { |
a8da6d93 MW |
1175 | if (scm_is_false (scm_negative_p (y))) |
1176 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 1177 | else |
a8da6d93 | 1178 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
1179 | } |
1180 | ||
8f9da340 MW |
1181 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
1182 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
1183 | ||
1184 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
1185 | (SCM x, SCM y), | |
1186 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1187 | "@lisp\n" | |
1188 | "(floor-quotient 123 10) @result{} 12\n" | |
1189 | "(floor-quotient 123 -10) @result{} -13\n" | |
1190 | "(floor-quotient -123 10) @result{} -13\n" | |
1191 | "(floor-quotient -123 -10) @result{} 12\n" | |
1192 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1193 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1194 | "@end lisp") | |
1195 | #define FUNC_NAME s_scm_floor_quotient | |
1196 | { | |
1197 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1198 | { | |
1199 | scm_t_inum xx = SCM_I_INUM (x); | |
1200 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1201 | { | |
1202 | scm_t_inum yy = SCM_I_INUM (y); | |
1203 | scm_t_inum xx1 = xx; | |
1204 | scm_t_inum qq; | |
1205 | if (SCM_LIKELY (yy > 0)) | |
1206 | { | |
1207 | if (SCM_UNLIKELY (xx < 0)) | |
1208 | xx1 = xx - yy + 1; | |
1209 | } | |
1210 | else if (SCM_UNLIKELY (yy == 0)) | |
1211 | scm_num_overflow (s_scm_floor_quotient); | |
1212 | else if (xx > 0) | |
1213 | xx1 = xx - yy - 1; | |
1214 | qq = xx1 / yy; | |
1215 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1216 | return SCM_I_MAKINUM (qq); | |
1217 | else | |
1218 | return scm_i_inum2big (qq); | |
1219 | } | |
1220 | else if (SCM_BIGP (y)) | |
1221 | { | |
1222 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1223 | scm_remember_upto_here_1 (y); | |
1224 | if (sign > 0) | |
1225 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1226 | else | |
1227 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1228 | } | |
1229 | else if (SCM_REALP (y)) | |
1230 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1231 | else if (SCM_FRACTIONP (y)) | |
1232 | return scm_i_exact_rational_floor_quotient (x, y); | |
1233 | else | |
fa075d40 AW |
1234 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1235 | s_scm_floor_quotient); | |
8f9da340 MW |
1236 | } |
1237 | else if (SCM_BIGP (x)) | |
1238 | { | |
1239 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1240 | { | |
1241 | scm_t_inum yy = SCM_I_INUM (y); | |
1242 | if (SCM_UNLIKELY (yy == 0)) | |
1243 | scm_num_overflow (s_scm_floor_quotient); | |
1244 | else if (SCM_UNLIKELY (yy == 1)) | |
1245 | return x; | |
1246 | else | |
1247 | { | |
1248 | SCM q = scm_i_mkbig (); | |
1249 | if (yy > 0) | |
1250 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1251 | else | |
1252 | { | |
1253 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1254 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1255 | } | |
1256 | scm_remember_upto_here_1 (x); | |
1257 | return scm_i_normbig (q); | |
1258 | } | |
1259 | } | |
1260 | else if (SCM_BIGP (y)) | |
1261 | { | |
1262 | SCM q = scm_i_mkbig (); | |
1263 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1264 | SCM_I_BIG_MPZ (x), | |
1265 | SCM_I_BIG_MPZ (y)); | |
1266 | scm_remember_upto_here_2 (x, y); | |
1267 | return scm_i_normbig (q); | |
1268 | } | |
1269 | else if (SCM_REALP (y)) | |
1270 | return scm_i_inexact_floor_quotient | |
1271 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1272 | else if (SCM_FRACTIONP (y)) | |
1273 | return scm_i_exact_rational_floor_quotient (x, y); | |
1274 | else | |
fa075d40 AW |
1275 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1276 | s_scm_floor_quotient); | |
8f9da340 MW |
1277 | } |
1278 | else if (SCM_REALP (x)) | |
1279 | { | |
1280 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1281 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1282 | return scm_i_inexact_floor_quotient | |
1283 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1284 | else | |
fa075d40 AW |
1285 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1286 | s_scm_floor_quotient); | |
8f9da340 MW |
1287 | } |
1288 | else if (SCM_FRACTIONP (x)) | |
1289 | { | |
1290 | if (SCM_REALP (y)) | |
1291 | return scm_i_inexact_floor_quotient | |
1292 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1293 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1294 | return scm_i_exact_rational_floor_quotient (x, y); | |
1295 | else | |
fa075d40 AW |
1296 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1297 | s_scm_floor_quotient); | |
8f9da340 MW |
1298 | } |
1299 | else | |
fa075d40 AW |
1300 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG1, |
1301 | s_scm_floor_quotient); | |
8f9da340 MW |
1302 | } |
1303 | #undef FUNC_NAME | |
1304 | ||
1305 | static SCM | |
1306 | scm_i_inexact_floor_quotient (double x, double y) | |
1307 | { | |
1308 | if (SCM_UNLIKELY (y == 0)) | |
1309 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1310 | else | |
00472a22 | 1311 | return scm_i_from_double (floor (x / y)); |
8f9da340 MW |
1312 | } |
1313 | ||
1314 | static SCM | |
1315 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1316 | { | |
1317 | return scm_floor_quotient | |
1318 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1319 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1320 | } | |
1321 | ||
1322 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1323 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1324 | ||
1325 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1326 | (SCM x, SCM y), | |
1327 | "Return the real number @var{r} such that\n" | |
1328 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1329 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1330 | "@lisp\n" | |
1331 | "(floor-remainder 123 10) @result{} 3\n" | |
1332 | "(floor-remainder 123 -10) @result{} -7\n" | |
1333 | "(floor-remainder -123 10) @result{} 7\n" | |
1334 | "(floor-remainder -123 -10) @result{} -3\n" | |
1335 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1336 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1337 | "@end lisp") | |
1338 | #define FUNC_NAME s_scm_floor_remainder | |
1339 | { | |
1340 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1341 | { | |
1342 | scm_t_inum xx = SCM_I_INUM (x); | |
1343 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1344 | { | |
1345 | scm_t_inum yy = SCM_I_INUM (y); | |
1346 | if (SCM_UNLIKELY (yy == 0)) | |
1347 | scm_num_overflow (s_scm_floor_remainder); | |
1348 | else | |
1349 | { | |
1350 | scm_t_inum rr = xx % yy; | |
1351 | int needs_adjustment; | |
1352 | ||
1353 | if (SCM_LIKELY (yy > 0)) | |
1354 | needs_adjustment = (rr < 0); | |
1355 | else | |
1356 | needs_adjustment = (rr > 0); | |
1357 | ||
1358 | if (needs_adjustment) | |
1359 | rr += yy; | |
1360 | return SCM_I_MAKINUM (rr); | |
1361 | } | |
1362 | } | |
1363 | else if (SCM_BIGP (y)) | |
1364 | { | |
1365 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1366 | scm_remember_upto_here_1 (y); | |
1367 | if (sign > 0) | |
1368 | { | |
1369 | if (xx < 0) | |
1370 | { | |
1371 | SCM r = scm_i_mkbig (); | |
1372 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1373 | scm_remember_upto_here_1 (y); | |
1374 | return scm_i_normbig (r); | |
1375 | } | |
1376 | else | |
1377 | return x; | |
1378 | } | |
1379 | else if (xx <= 0) | |
1380 | return x; | |
1381 | else | |
1382 | { | |
1383 | SCM r = scm_i_mkbig (); | |
1384 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1385 | scm_remember_upto_here_1 (y); | |
1386 | return scm_i_normbig (r); | |
1387 | } | |
1388 | } | |
1389 | else if (SCM_REALP (y)) | |
1390 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1391 | else if (SCM_FRACTIONP (y)) | |
1392 | return scm_i_exact_rational_floor_remainder (x, y); | |
1393 | else | |
fa075d40 AW |
1394 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1395 | s_scm_floor_remainder); | |
8f9da340 MW |
1396 | } |
1397 | else if (SCM_BIGP (x)) | |
1398 | { | |
1399 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1400 | { | |
1401 | scm_t_inum yy = SCM_I_INUM (y); | |
1402 | if (SCM_UNLIKELY (yy == 0)) | |
1403 | scm_num_overflow (s_scm_floor_remainder); | |
1404 | else | |
1405 | { | |
1406 | scm_t_inum rr; | |
1407 | if (yy > 0) | |
1408 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1409 | else | |
1410 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1411 | scm_remember_upto_here_1 (x); | |
1412 | return SCM_I_MAKINUM (rr); | |
1413 | } | |
1414 | } | |
1415 | else if (SCM_BIGP (y)) | |
1416 | { | |
1417 | SCM r = scm_i_mkbig (); | |
1418 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1419 | SCM_I_BIG_MPZ (x), | |
1420 | SCM_I_BIG_MPZ (y)); | |
1421 | scm_remember_upto_here_2 (x, y); | |
1422 | return scm_i_normbig (r); | |
1423 | } | |
1424 | else if (SCM_REALP (y)) | |
1425 | return scm_i_inexact_floor_remainder | |
1426 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1427 | else if (SCM_FRACTIONP (y)) | |
1428 | return scm_i_exact_rational_floor_remainder (x, y); | |
1429 | else | |
fa075d40 AW |
1430 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1431 | s_scm_floor_remainder); | |
8f9da340 MW |
1432 | } |
1433 | else if (SCM_REALP (x)) | |
1434 | { | |
1435 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1436 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1437 | return scm_i_inexact_floor_remainder | |
1438 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1439 | else | |
fa075d40 AW |
1440 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1441 | s_scm_floor_remainder); | |
8f9da340 MW |
1442 | } |
1443 | else if (SCM_FRACTIONP (x)) | |
1444 | { | |
1445 | if (SCM_REALP (y)) | |
1446 | return scm_i_inexact_floor_remainder | |
1447 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1448 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1449 | return scm_i_exact_rational_floor_remainder (x, y); | |
1450 | else | |
fa075d40 AW |
1451 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1452 | s_scm_floor_remainder); | |
8f9da340 MW |
1453 | } |
1454 | else | |
fa075d40 AW |
1455 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG1, |
1456 | s_scm_floor_remainder); | |
8f9da340 MW |
1457 | } |
1458 | #undef FUNC_NAME | |
1459 | ||
1460 | static SCM | |
1461 | scm_i_inexact_floor_remainder (double x, double y) | |
1462 | { | |
1463 | /* Although it would be more efficient to use fmod here, we can't | |
1464 | because it would in some cases produce results inconsistent with | |
1465 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1466 | close). In particular, when x is very close to a multiple of y, | |
1467 | then r might be either 0.0 or y, but those two cases must | |
1468 | correspond to different choices of q. If r = 0.0 then q must be | |
1469 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1470 | and remainder chooses the other, it would be bad. */ | |
1471 | if (SCM_UNLIKELY (y == 0)) | |
1472 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1473 | else | |
00472a22 | 1474 | return scm_i_from_double (x - y * floor (x / y)); |
8f9da340 MW |
1475 | } |
1476 | ||
1477 | static SCM | |
1478 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1479 | { | |
1480 | SCM xd = scm_denominator (x); | |
1481 | SCM yd = scm_denominator (y); | |
1482 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1483 | scm_product (scm_numerator (y), xd)); | |
1484 | return scm_divide (r1, scm_product (xd, yd)); | |
1485 | } | |
1486 | ||
1487 | ||
1488 | static void scm_i_inexact_floor_divide (double x, double y, | |
1489 | SCM *qp, SCM *rp); | |
1490 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1491 | SCM *qp, SCM *rp); | |
1492 | ||
1493 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1494 | (SCM x, SCM y), | |
1495 | "Return the integer @var{q} and the real number @var{r}\n" | |
1496 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1497 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1498 | "@lisp\n" | |
1499 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1500 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1501 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1502 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1503 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1504 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1505 | "@end lisp") | |
1506 | #define FUNC_NAME s_scm_i_floor_divide | |
1507 | { | |
1508 | SCM q, r; | |
1509 | ||
1510 | scm_floor_divide(x, y, &q, &r); | |
1511 | return scm_values (scm_list_2 (q, r)); | |
1512 | } | |
1513 | #undef FUNC_NAME | |
1514 | ||
1515 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1516 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1517 | ||
1518 | void | |
1519 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1520 | { | |
1521 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1522 | { | |
1523 | scm_t_inum xx = SCM_I_INUM (x); | |
1524 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1525 | { | |
1526 | scm_t_inum yy = SCM_I_INUM (y); | |
1527 | if (SCM_UNLIKELY (yy == 0)) | |
1528 | scm_num_overflow (s_scm_floor_divide); | |
1529 | else | |
1530 | { | |
1531 | scm_t_inum qq = xx / yy; | |
1532 | scm_t_inum rr = xx % yy; | |
1533 | int needs_adjustment; | |
1534 | ||
1535 | if (SCM_LIKELY (yy > 0)) | |
1536 | needs_adjustment = (rr < 0); | |
1537 | else | |
1538 | needs_adjustment = (rr > 0); | |
1539 | ||
1540 | if (needs_adjustment) | |
1541 | { | |
1542 | rr += yy; | |
1543 | qq--; | |
1544 | } | |
1545 | ||
1546 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1547 | *qp = SCM_I_MAKINUM (qq); | |
1548 | else | |
1549 | *qp = scm_i_inum2big (qq); | |
1550 | *rp = SCM_I_MAKINUM (rr); | |
1551 | } | |
1552 | return; | |
1553 | } | |
1554 | else if (SCM_BIGP (y)) | |
1555 | { | |
1556 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1557 | scm_remember_upto_here_1 (y); | |
1558 | if (sign > 0) | |
1559 | { | |
1560 | if (xx < 0) | |
1561 | { | |
1562 | SCM r = scm_i_mkbig (); | |
1563 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1564 | scm_remember_upto_here_1 (y); | |
1565 | *qp = SCM_I_MAKINUM (-1); | |
1566 | *rp = scm_i_normbig (r); | |
1567 | } | |
1568 | else | |
1569 | { | |
1570 | *qp = SCM_INUM0; | |
1571 | *rp = x; | |
1572 | } | |
1573 | } | |
1574 | else if (xx <= 0) | |
1575 | { | |
1576 | *qp = SCM_INUM0; | |
1577 | *rp = x; | |
1578 | } | |
1579 | else | |
1580 | { | |
1581 | SCM r = scm_i_mkbig (); | |
1582 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1583 | scm_remember_upto_here_1 (y); | |
1584 | *qp = SCM_I_MAKINUM (-1); | |
1585 | *rp = scm_i_normbig (r); | |
1586 | } | |
1587 | return; | |
1588 | } | |
1589 | else if (SCM_REALP (y)) | |
1590 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1591 | else if (SCM_FRACTIONP (y)) | |
1592 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1593 | else | |
1594 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1595 | s_scm_floor_divide, qp, rp); | |
1596 | } | |
1597 | else if (SCM_BIGP (x)) | |
1598 | { | |
1599 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1600 | { | |
1601 | scm_t_inum yy = SCM_I_INUM (y); | |
1602 | if (SCM_UNLIKELY (yy == 0)) | |
1603 | scm_num_overflow (s_scm_floor_divide); | |
1604 | else | |
1605 | { | |
1606 | SCM q = scm_i_mkbig (); | |
1607 | SCM r = scm_i_mkbig (); | |
1608 | if (yy > 0) | |
1609 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1610 | SCM_I_BIG_MPZ (x), yy); | |
1611 | else | |
1612 | { | |
1613 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1614 | SCM_I_BIG_MPZ (x), -yy); | |
1615 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1616 | } | |
1617 | scm_remember_upto_here_1 (x); | |
1618 | *qp = scm_i_normbig (q); | |
1619 | *rp = scm_i_normbig (r); | |
1620 | } | |
1621 | return; | |
1622 | } | |
1623 | else if (SCM_BIGP (y)) | |
1624 | { | |
1625 | SCM q = scm_i_mkbig (); | |
1626 | SCM r = scm_i_mkbig (); | |
1627 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1628 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1629 | scm_remember_upto_here_2 (x, y); | |
1630 | *qp = scm_i_normbig (q); | |
1631 | *rp = scm_i_normbig (r); | |
1632 | return; | |
1633 | } | |
1634 | else if (SCM_REALP (y)) | |
1635 | return scm_i_inexact_floor_divide | |
1636 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1637 | else if (SCM_FRACTIONP (y)) | |
1638 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1639 | else | |
1640 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1641 | s_scm_floor_divide, qp, rp); | |
1642 | } | |
1643 | else if (SCM_REALP (x)) | |
1644 | { | |
1645 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1646 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1647 | return scm_i_inexact_floor_divide | |
1648 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1649 | else | |
1650 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1651 | s_scm_floor_divide, qp, rp); | |
1652 | } | |
1653 | else if (SCM_FRACTIONP (x)) | |
1654 | { | |
1655 | if (SCM_REALP (y)) | |
1656 | return scm_i_inexact_floor_divide | |
1657 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1658 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1659 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1660 | else | |
1661 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1662 | s_scm_floor_divide, qp, rp); | |
1663 | } | |
1664 | else | |
1665 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1666 | s_scm_floor_divide, qp, rp); | |
1667 | } | |
1668 | ||
1669 | static void | |
1670 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1671 | { | |
1672 | if (SCM_UNLIKELY (y == 0)) | |
1673 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1674 | else | |
1675 | { | |
1676 | double q = floor (x / y); | |
1677 | double r = x - q * y; | |
00472a22 MW |
1678 | *qp = scm_i_from_double (q); |
1679 | *rp = scm_i_from_double (r); | |
8f9da340 MW |
1680 | } |
1681 | } | |
1682 | ||
1683 | static void | |
1684 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1685 | { | |
1686 | SCM r1; | |
1687 | SCM xd = scm_denominator (x); | |
1688 | SCM yd = scm_denominator (y); | |
1689 | ||
1690 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1691 | scm_product (scm_numerator (y), xd), | |
1692 | qp, &r1); | |
1693 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1694 | } | |
1695 | ||
1696 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1697 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1698 | ||
1699 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1700 | (SCM x, SCM y), | |
1701 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1702 | "@lisp\n" | |
1703 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1704 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1705 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1706 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1707 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1708 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1709 | "@end lisp") | |
1710 | #define FUNC_NAME s_scm_ceiling_quotient | |
1711 | { | |
1712 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1713 | { | |
1714 | scm_t_inum xx = SCM_I_INUM (x); | |
1715 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1716 | { | |
1717 | scm_t_inum yy = SCM_I_INUM (y); | |
1718 | if (SCM_UNLIKELY (yy == 0)) | |
1719 | scm_num_overflow (s_scm_ceiling_quotient); | |
1720 | else | |
1721 | { | |
1722 | scm_t_inum xx1 = xx; | |
1723 | scm_t_inum qq; | |
1724 | if (SCM_LIKELY (yy > 0)) | |
1725 | { | |
1726 | if (SCM_LIKELY (xx >= 0)) | |
1727 | xx1 = xx + yy - 1; | |
1728 | } | |
8f9da340 MW |
1729 | else if (xx < 0) |
1730 | xx1 = xx + yy + 1; | |
1731 | qq = xx1 / yy; | |
1732 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1733 | return SCM_I_MAKINUM (qq); | |
1734 | else | |
1735 | return scm_i_inum2big (qq); | |
1736 | } | |
1737 | } | |
1738 | else if (SCM_BIGP (y)) | |
1739 | { | |
1740 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1741 | scm_remember_upto_here_1 (y); | |
1742 | if (SCM_LIKELY (sign > 0)) | |
1743 | { | |
1744 | if (SCM_LIKELY (xx > 0)) | |
1745 | return SCM_INUM1; | |
1746 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1747 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1748 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1749 | { | |
1750 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1751 | scm_remember_upto_here_1 (y); | |
1752 | return SCM_I_MAKINUM (-1); | |
1753 | } | |
1754 | else | |
1755 | return SCM_INUM0; | |
1756 | } | |
1757 | else if (xx >= 0) | |
1758 | return SCM_INUM0; | |
1759 | else | |
1760 | return SCM_INUM1; | |
1761 | } | |
1762 | else if (SCM_REALP (y)) | |
1763 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1764 | else if (SCM_FRACTIONP (y)) | |
1765 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1766 | else | |
fa075d40 AW |
1767 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1768 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1769 | } |
1770 | else if (SCM_BIGP (x)) | |
1771 | { | |
1772 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1773 | { | |
1774 | scm_t_inum yy = SCM_I_INUM (y); | |
1775 | if (SCM_UNLIKELY (yy == 0)) | |
1776 | scm_num_overflow (s_scm_ceiling_quotient); | |
1777 | else if (SCM_UNLIKELY (yy == 1)) | |
1778 | return x; | |
1779 | else | |
1780 | { | |
1781 | SCM q = scm_i_mkbig (); | |
1782 | if (yy > 0) | |
1783 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1784 | else | |
1785 | { | |
1786 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1787 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1788 | } | |
1789 | scm_remember_upto_here_1 (x); | |
1790 | return scm_i_normbig (q); | |
1791 | } | |
1792 | } | |
1793 | else if (SCM_BIGP (y)) | |
1794 | { | |
1795 | SCM q = scm_i_mkbig (); | |
1796 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1797 | SCM_I_BIG_MPZ (x), | |
1798 | SCM_I_BIG_MPZ (y)); | |
1799 | scm_remember_upto_here_2 (x, y); | |
1800 | return scm_i_normbig (q); | |
1801 | } | |
1802 | else if (SCM_REALP (y)) | |
1803 | return scm_i_inexact_ceiling_quotient | |
1804 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1805 | else if (SCM_FRACTIONP (y)) | |
1806 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1807 | else | |
fa075d40 AW |
1808 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1809 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1810 | } |
1811 | else if (SCM_REALP (x)) | |
1812 | { | |
1813 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1814 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1815 | return scm_i_inexact_ceiling_quotient | |
1816 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1817 | else | |
fa075d40 AW |
1818 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1819 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1820 | } |
1821 | else if (SCM_FRACTIONP (x)) | |
1822 | { | |
1823 | if (SCM_REALP (y)) | |
1824 | return scm_i_inexact_ceiling_quotient | |
1825 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1826 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1827 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1828 | else | |
fa075d40 AW |
1829 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1830 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1831 | } |
1832 | else | |
fa075d40 AW |
1833 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, |
1834 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1835 | } |
1836 | #undef FUNC_NAME | |
1837 | ||
1838 | static SCM | |
1839 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1840 | { | |
1841 | if (SCM_UNLIKELY (y == 0)) | |
1842 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1843 | else | |
00472a22 | 1844 | return scm_i_from_double (ceil (x / y)); |
8f9da340 MW |
1845 | } |
1846 | ||
1847 | static SCM | |
1848 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1849 | { | |
1850 | return scm_ceiling_quotient | |
1851 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1852 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1853 | } | |
1854 | ||
1855 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1856 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1857 | ||
1858 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1859 | (SCM x, SCM y), | |
1860 | "Return the real number @var{r} such that\n" | |
1861 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1862 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1863 | "@lisp\n" | |
1864 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1865 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1866 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1867 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1868 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1869 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1870 | "@end lisp") | |
1871 | #define FUNC_NAME s_scm_ceiling_remainder | |
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_remainder); | |
1881 | else | |
1882 | { | |
1883 | scm_t_inum rr = xx % yy; | |
1884 | int needs_adjustment; | |
1885 | ||
1886 | if (SCM_LIKELY (yy > 0)) | |
1887 | needs_adjustment = (rr > 0); | |
1888 | else | |
1889 | needs_adjustment = (rr < 0); | |
1890 | ||
1891 | if (needs_adjustment) | |
1892 | rr -= yy; | |
1893 | return SCM_I_MAKINUM (rr); | |
1894 | } | |
1895 | } | |
1896 | else if (SCM_BIGP (y)) | |
1897 | { | |
1898 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1899 | scm_remember_upto_here_1 (y); | |
1900 | if (SCM_LIKELY (sign > 0)) | |
1901 | { | |
1902 | if (SCM_LIKELY (xx > 0)) | |
1903 | { | |
1904 | SCM r = scm_i_mkbig (); | |
1905 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1906 | scm_remember_upto_here_1 (y); | |
1907 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1908 | return scm_i_normbig (r); | |
1909 | } | |
1910 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1911 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1912 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1913 | { | |
1914 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1915 | scm_remember_upto_here_1 (y); | |
1916 | return SCM_INUM0; | |
1917 | } | |
1918 | else | |
1919 | return x; | |
1920 | } | |
1921 | else if (xx >= 0) | |
1922 | return x; | |
1923 | else | |
1924 | { | |
1925 | SCM r = scm_i_mkbig (); | |
1926 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1927 | scm_remember_upto_here_1 (y); | |
1928 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1929 | return scm_i_normbig (r); | |
1930 | } | |
1931 | } | |
1932 | else if (SCM_REALP (y)) | |
1933 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1934 | else if (SCM_FRACTIONP (y)) | |
1935 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1936 | else | |
fa075d40 AW |
1937 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1938 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1939 | } |
1940 | else if (SCM_BIGP (x)) | |
1941 | { | |
1942 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1943 | { | |
1944 | scm_t_inum yy = SCM_I_INUM (y); | |
1945 | if (SCM_UNLIKELY (yy == 0)) | |
1946 | scm_num_overflow (s_scm_ceiling_remainder); | |
1947 | else | |
1948 | { | |
1949 | scm_t_inum rr; | |
1950 | if (yy > 0) | |
1951 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1952 | else | |
1953 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1954 | scm_remember_upto_here_1 (x); | |
1955 | return SCM_I_MAKINUM (rr); | |
1956 | } | |
1957 | } | |
1958 | else if (SCM_BIGP (y)) | |
1959 | { | |
1960 | SCM r = scm_i_mkbig (); | |
1961 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1962 | SCM_I_BIG_MPZ (x), | |
1963 | SCM_I_BIG_MPZ (y)); | |
1964 | scm_remember_upto_here_2 (x, y); | |
1965 | return scm_i_normbig (r); | |
1966 | } | |
1967 | else if (SCM_REALP (y)) | |
1968 | return scm_i_inexact_ceiling_remainder | |
1969 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1970 | else if (SCM_FRACTIONP (y)) | |
1971 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1972 | else | |
fa075d40 AW |
1973 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1974 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1975 | } |
1976 | else if (SCM_REALP (x)) | |
1977 | { | |
1978 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1979 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1980 | return scm_i_inexact_ceiling_remainder | |
1981 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1982 | else | |
fa075d40 AW |
1983 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1984 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1985 | } |
1986 | else if (SCM_FRACTIONP (x)) | |
1987 | { | |
1988 | if (SCM_REALP (y)) | |
1989 | return scm_i_inexact_ceiling_remainder | |
1990 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1991 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1992 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1993 | else | |
fa075d40 AW |
1994 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1995 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1996 | } |
1997 | else | |
fa075d40 AW |
1998 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, |
1999 | s_scm_ceiling_remainder); | |
8f9da340 MW |
2000 | } |
2001 | #undef FUNC_NAME | |
2002 | ||
2003 | static SCM | |
2004 | scm_i_inexact_ceiling_remainder (double x, double y) | |
2005 | { | |
2006 | /* Although it would be more efficient to use fmod here, we can't | |
2007 | because it would in some cases produce results inconsistent with | |
2008 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
2009 | close). In particular, when x is very close to a multiple of y, | |
2010 | then r might be either 0.0 or -y, but those two cases must | |
2011 | correspond to different choices of q. If r = 0.0 then q must be | |
2012 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
2013 | and remainder chooses the other, it would be bad. */ | |
2014 | if (SCM_UNLIKELY (y == 0)) | |
2015 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
2016 | else | |
00472a22 | 2017 | return scm_i_from_double (x - y * ceil (x / y)); |
8f9da340 MW |
2018 | } |
2019 | ||
2020 | static SCM | |
2021 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
2022 | { | |
2023 | SCM xd = scm_denominator (x); | |
2024 | SCM yd = scm_denominator (y); | |
2025 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
2026 | scm_product (scm_numerator (y), xd)); | |
2027 | return scm_divide (r1, scm_product (xd, yd)); | |
2028 | } | |
2029 | ||
2030 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
2031 | SCM *qp, SCM *rp); | |
2032 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
2033 | SCM *qp, SCM *rp); | |
2034 | ||
2035 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
2036 | (SCM x, SCM y), | |
2037 | "Return the integer @var{q} and the real number @var{r}\n" | |
2038 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2039 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
2040 | "@lisp\n" | |
2041 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
2042 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
2043 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
2044 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
2045 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2046 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2047 | "@end lisp") | |
2048 | #define FUNC_NAME s_scm_i_ceiling_divide | |
2049 | { | |
2050 | SCM q, r; | |
2051 | ||
2052 | scm_ceiling_divide(x, y, &q, &r); | |
2053 | return scm_values (scm_list_2 (q, r)); | |
2054 | } | |
2055 | #undef FUNC_NAME | |
2056 | ||
2057 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
2058 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
2059 | ||
2060 | void | |
2061 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2062 | { | |
2063 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2064 | { | |
2065 | scm_t_inum xx = SCM_I_INUM (x); | |
2066 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2067 | { | |
2068 | scm_t_inum yy = SCM_I_INUM (y); | |
2069 | if (SCM_UNLIKELY (yy == 0)) | |
2070 | scm_num_overflow (s_scm_ceiling_divide); | |
2071 | else | |
2072 | { | |
2073 | scm_t_inum qq = xx / yy; | |
2074 | scm_t_inum rr = xx % yy; | |
2075 | int needs_adjustment; | |
2076 | ||
2077 | if (SCM_LIKELY (yy > 0)) | |
2078 | needs_adjustment = (rr > 0); | |
2079 | else | |
2080 | needs_adjustment = (rr < 0); | |
2081 | ||
2082 | if (needs_adjustment) | |
2083 | { | |
2084 | rr -= yy; | |
2085 | qq++; | |
2086 | } | |
2087 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2088 | *qp = SCM_I_MAKINUM (qq); | |
2089 | else | |
2090 | *qp = scm_i_inum2big (qq); | |
2091 | *rp = SCM_I_MAKINUM (rr); | |
2092 | } | |
2093 | return; | |
2094 | } | |
2095 | else if (SCM_BIGP (y)) | |
2096 | { | |
2097 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2098 | scm_remember_upto_here_1 (y); | |
2099 | if (SCM_LIKELY (sign > 0)) | |
2100 | { | |
2101 | if (SCM_LIKELY (xx > 0)) | |
2102 | { | |
2103 | SCM r = scm_i_mkbig (); | |
2104 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2105 | scm_remember_upto_here_1 (y); | |
2106 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2107 | *qp = SCM_INUM1; | |
2108 | *rp = scm_i_normbig (r); | |
2109 | } | |
2110 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2111 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2112 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2113 | { | |
2114 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2115 | scm_remember_upto_here_1 (y); | |
2116 | *qp = SCM_I_MAKINUM (-1); | |
2117 | *rp = SCM_INUM0; | |
2118 | } | |
2119 | else | |
2120 | { | |
2121 | *qp = SCM_INUM0; | |
2122 | *rp = x; | |
2123 | } | |
2124 | } | |
2125 | else if (xx >= 0) | |
2126 | { | |
2127 | *qp = SCM_INUM0; | |
2128 | *rp = x; | |
2129 | } | |
2130 | else | |
2131 | { | |
2132 | SCM r = scm_i_mkbig (); | |
2133 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2134 | scm_remember_upto_here_1 (y); | |
2135 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2136 | *qp = SCM_INUM1; | |
2137 | *rp = scm_i_normbig (r); | |
2138 | } | |
2139 | return; | |
2140 | } | |
2141 | else if (SCM_REALP (y)) | |
2142 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2143 | else if (SCM_FRACTIONP (y)) | |
2144 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2145 | else | |
2146 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2147 | s_scm_ceiling_divide, qp, rp); | |
2148 | } | |
2149 | else if (SCM_BIGP (x)) | |
2150 | { | |
2151 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2152 | { | |
2153 | scm_t_inum yy = SCM_I_INUM (y); | |
2154 | if (SCM_UNLIKELY (yy == 0)) | |
2155 | scm_num_overflow (s_scm_ceiling_divide); | |
2156 | else | |
2157 | { | |
2158 | SCM q = scm_i_mkbig (); | |
2159 | SCM r = scm_i_mkbig (); | |
2160 | if (yy > 0) | |
2161 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2162 | SCM_I_BIG_MPZ (x), yy); | |
2163 | else | |
2164 | { | |
2165 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2166 | SCM_I_BIG_MPZ (x), -yy); | |
2167 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2168 | } | |
2169 | scm_remember_upto_here_1 (x); | |
2170 | *qp = scm_i_normbig (q); | |
2171 | *rp = scm_i_normbig (r); | |
2172 | } | |
2173 | return; | |
2174 | } | |
2175 | else if (SCM_BIGP (y)) | |
2176 | { | |
2177 | SCM q = scm_i_mkbig (); | |
2178 | SCM r = scm_i_mkbig (); | |
2179 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2180 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2181 | scm_remember_upto_here_2 (x, y); | |
2182 | *qp = scm_i_normbig (q); | |
2183 | *rp = scm_i_normbig (r); | |
2184 | return; | |
2185 | } | |
2186 | else if (SCM_REALP (y)) | |
2187 | return scm_i_inexact_ceiling_divide | |
2188 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2189 | else if (SCM_FRACTIONP (y)) | |
2190 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2191 | else | |
2192 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2193 | s_scm_ceiling_divide, qp, rp); | |
2194 | } | |
2195 | else if (SCM_REALP (x)) | |
2196 | { | |
2197 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2198 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2199 | return scm_i_inexact_ceiling_divide | |
2200 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2201 | else | |
2202 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2203 | s_scm_ceiling_divide, qp, rp); | |
2204 | } | |
2205 | else if (SCM_FRACTIONP (x)) | |
2206 | { | |
2207 | if (SCM_REALP (y)) | |
2208 | return scm_i_inexact_ceiling_divide | |
2209 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2210 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2211 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2212 | else | |
2213 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2214 | s_scm_ceiling_divide, qp, rp); | |
2215 | } | |
2216 | else | |
2217 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2218 | s_scm_ceiling_divide, qp, rp); | |
2219 | } | |
2220 | ||
2221 | static void | |
2222 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2223 | { | |
2224 | if (SCM_UNLIKELY (y == 0)) | |
2225 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2226 | else | |
2227 | { | |
2228 | double q = ceil (x / y); | |
2229 | double r = x - q * y; | |
00472a22 MW |
2230 | *qp = scm_i_from_double (q); |
2231 | *rp = scm_i_from_double (r); | |
8f9da340 MW |
2232 | } |
2233 | } | |
2234 | ||
2235 | static void | |
2236 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2237 | { | |
2238 | SCM r1; | |
2239 | SCM xd = scm_denominator (x); | |
2240 | SCM yd = scm_denominator (y); | |
2241 | ||
2242 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2243 | scm_product (scm_numerator (y), xd), | |
2244 | qp, &r1); | |
2245 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2246 | } | |
2247 | ||
2248 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2249 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2250 | ||
2251 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2252 | (SCM x, SCM y), | |
2253 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2254 | "@lisp\n" | |
2255 | "(truncate-quotient 123 10) @result{} 12\n" | |
2256 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2257 | "(truncate-quotient -123 10) @result{} -12\n" | |
2258 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2259 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2260 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2261 | "@end lisp") | |
2262 | #define FUNC_NAME s_scm_truncate_quotient | |
2263 | { | |
2264 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2265 | { | |
2266 | scm_t_inum xx = SCM_I_INUM (x); | |
2267 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2268 | { | |
2269 | scm_t_inum yy = SCM_I_INUM (y); | |
2270 | if (SCM_UNLIKELY (yy == 0)) | |
2271 | scm_num_overflow (s_scm_truncate_quotient); | |
2272 | else | |
2273 | { | |
2274 | scm_t_inum qq = xx / yy; | |
2275 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2276 | return SCM_I_MAKINUM (qq); | |
2277 | else | |
2278 | return scm_i_inum2big (qq); | |
2279 | } | |
2280 | } | |
2281 | else if (SCM_BIGP (y)) | |
2282 | { | |
2283 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2284 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2285 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2286 | { | |
2287 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2288 | scm_remember_upto_here_1 (y); | |
2289 | return SCM_I_MAKINUM (-1); | |
2290 | } | |
2291 | else | |
2292 | return SCM_INUM0; | |
2293 | } | |
2294 | else if (SCM_REALP (y)) | |
2295 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2296 | else if (SCM_FRACTIONP (y)) | |
2297 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2298 | else | |
fa075d40 AW |
2299 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2300 | s_scm_truncate_quotient); | |
8f9da340 MW |
2301 | } |
2302 | else if (SCM_BIGP (x)) | |
2303 | { | |
2304 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2305 | { | |
2306 | scm_t_inum yy = SCM_I_INUM (y); | |
2307 | if (SCM_UNLIKELY (yy == 0)) | |
2308 | scm_num_overflow (s_scm_truncate_quotient); | |
2309 | else if (SCM_UNLIKELY (yy == 1)) | |
2310 | return x; | |
2311 | else | |
2312 | { | |
2313 | SCM q = scm_i_mkbig (); | |
2314 | if (yy > 0) | |
2315 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2316 | else | |
2317 | { | |
2318 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2319 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2320 | } | |
2321 | scm_remember_upto_here_1 (x); | |
2322 | return scm_i_normbig (q); | |
2323 | } | |
2324 | } | |
2325 | else if (SCM_BIGP (y)) | |
2326 | { | |
2327 | SCM q = scm_i_mkbig (); | |
2328 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2329 | SCM_I_BIG_MPZ (x), | |
2330 | SCM_I_BIG_MPZ (y)); | |
2331 | scm_remember_upto_here_2 (x, y); | |
2332 | return scm_i_normbig (q); | |
2333 | } | |
2334 | else if (SCM_REALP (y)) | |
2335 | return scm_i_inexact_truncate_quotient | |
2336 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2337 | else if (SCM_FRACTIONP (y)) | |
2338 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2339 | else | |
fa075d40 AW |
2340 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2341 | s_scm_truncate_quotient); | |
8f9da340 MW |
2342 | } |
2343 | else if (SCM_REALP (x)) | |
2344 | { | |
2345 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2346 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2347 | return scm_i_inexact_truncate_quotient | |
2348 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2349 | else | |
fa075d40 AW |
2350 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2351 | s_scm_truncate_quotient); | |
8f9da340 MW |
2352 | } |
2353 | else if (SCM_FRACTIONP (x)) | |
2354 | { | |
2355 | if (SCM_REALP (y)) | |
2356 | return scm_i_inexact_truncate_quotient | |
2357 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2358 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2359 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2360 | else | |
fa075d40 AW |
2361 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2362 | s_scm_truncate_quotient); | |
8f9da340 MW |
2363 | } |
2364 | else | |
fa075d40 AW |
2365 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, |
2366 | s_scm_truncate_quotient); | |
8f9da340 MW |
2367 | } |
2368 | #undef FUNC_NAME | |
2369 | ||
2370 | static SCM | |
2371 | scm_i_inexact_truncate_quotient (double x, double y) | |
2372 | { | |
2373 | if (SCM_UNLIKELY (y == 0)) | |
2374 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2375 | else | |
00472a22 | 2376 | return scm_i_from_double (trunc (x / y)); |
8f9da340 MW |
2377 | } |
2378 | ||
2379 | static SCM | |
2380 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2381 | { | |
2382 | return scm_truncate_quotient | |
2383 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2384 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2385 | } | |
2386 | ||
2387 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2388 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2389 | ||
2390 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2391 | (SCM x, SCM y), | |
2392 | "Return the real number @var{r} such that\n" | |
2393 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2394 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2395 | "@lisp\n" | |
2396 | "(truncate-remainder 123 10) @result{} 3\n" | |
2397 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2398 | "(truncate-remainder -123 10) @result{} -3\n" | |
2399 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2400 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2401 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2402 | "@end lisp") | |
2403 | #define FUNC_NAME s_scm_truncate_remainder | |
2404 | { | |
2405 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2406 | { | |
2407 | scm_t_inum xx = SCM_I_INUM (x); | |
2408 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2409 | { | |
2410 | scm_t_inum yy = SCM_I_INUM (y); | |
2411 | if (SCM_UNLIKELY (yy == 0)) | |
2412 | scm_num_overflow (s_scm_truncate_remainder); | |
2413 | else | |
2414 | return SCM_I_MAKINUM (xx % yy); | |
2415 | } | |
2416 | else if (SCM_BIGP (y)) | |
2417 | { | |
2418 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2419 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2420 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2421 | { | |
2422 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2423 | scm_remember_upto_here_1 (y); | |
2424 | return SCM_INUM0; | |
2425 | } | |
2426 | else | |
2427 | return x; | |
2428 | } | |
2429 | else if (SCM_REALP (y)) | |
2430 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2431 | else if (SCM_FRACTIONP (y)) | |
2432 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2433 | else | |
fa075d40 AW |
2434 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2435 | s_scm_truncate_remainder); | |
8f9da340 MW |
2436 | } |
2437 | else if (SCM_BIGP (x)) | |
2438 | { | |
2439 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2440 | { | |
2441 | scm_t_inum yy = SCM_I_INUM (y); | |
2442 | if (SCM_UNLIKELY (yy == 0)) | |
2443 | scm_num_overflow (s_scm_truncate_remainder); | |
2444 | else | |
2445 | { | |
2446 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2447 | (yy > 0) ? yy : -yy) | |
2448 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2449 | scm_remember_upto_here_1 (x); | |
2450 | return SCM_I_MAKINUM (rr); | |
2451 | } | |
2452 | } | |
2453 | else if (SCM_BIGP (y)) | |
2454 | { | |
2455 | SCM r = scm_i_mkbig (); | |
2456 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2457 | SCM_I_BIG_MPZ (x), | |
2458 | SCM_I_BIG_MPZ (y)); | |
2459 | scm_remember_upto_here_2 (x, y); | |
2460 | return scm_i_normbig (r); | |
2461 | } | |
2462 | else if (SCM_REALP (y)) | |
2463 | return scm_i_inexact_truncate_remainder | |
2464 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2465 | else if (SCM_FRACTIONP (y)) | |
2466 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2467 | else | |
fa075d40 AW |
2468 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2469 | s_scm_truncate_remainder); | |
8f9da340 MW |
2470 | } |
2471 | else if (SCM_REALP (x)) | |
2472 | { | |
2473 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2474 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2475 | return scm_i_inexact_truncate_remainder | |
2476 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2477 | else | |
fa075d40 AW |
2478 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2479 | s_scm_truncate_remainder); | |
8f9da340 MW |
2480 | } |
2481 | else if (SCM_FRACTIONP (x)) | |
2482 | { | |
2483 | if (SCM_REALP (y)) | |
2484 | return scm_i_inexact_truncate_remainder | |
2485 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2486 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2487 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2488 | else | |
fa075d40 AW |
2489 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2490 | s_scm_truncate_remainder); | |
8f9da340 MW |
2491 | } |
2492 | else | |
fa075d40 AW |
2493 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, |
2494 | s_scm_truncate_remainder); | |
8f9da340 MW |
2495 | } |
2496 | #undef FUNC_NAME | |
2497 | ||
2498 | static SCM | |
2499 | scm_i_inexact_truncate_remainder (double x, double y) | |
2500 | { | |
2501 | /* Although it would be more efficient to use fmod here, we can't | |
2502 | because it would in some cases produce results inconsistent with | |
2503 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2504 | close). In particular, when x is very close to a multiple of y, | |
2505 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2506 | correspond to different choices of q. If quotient chooses one and | |
2507 | remainder chooses the other, it would be bad. */ | |
2508 | if (SCM_UNLIKELY (y == 0)) | |
2509 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2510 | else | |
00472a22 | 2511 | return scm_i_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2512 | } |
2513 | ||
2514 | static SCM | |
2515 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2516 | { | |
2517 | SCM xd = scm_denominator (x); | |
2518 | SCM yd = scm_denominator (y); | |
2519 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2520 | scm_product (scm_numerator (y), xd)); | |
2521 | return scm_divide (r1, scm_product (xd, yd)); | |
2522 | } | |
2523 | ||
2524 | ||
2525 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2526 | SCM *qp, SCM *rp); | |
2527 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2528 | SCM *qp, SCM *rp); | |
2529 | ||
2530 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2531 | (SCM x, SCM y), | |
2532 | "Return the integer @var{q} and the real number @var{r}\n" | |
2533 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2534 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2535 | "@lisp\n" | |
2536 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2537 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2538 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2539 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2540 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2541 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2542 | "@end lisp") | |
2543 | #define FUNC_NAME s_scm_i_truncate_divide | |
2544 | { | |
2545 | SCM q, r; | |
2546 | ||
2547 | scm_truncate_divide(x, y, &q, &r); | |
2548 | return scm_values (scm_list_2 (q, r)); | |
2549 | } | |
2550 | #undef FUNC_NAME | |
2551 | ||
2552 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2553 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2554 | ||
2555 | void | |
2556 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2557 | { | |
2558 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2559 | { | |
2560 | scm_t_inum xx = SCM_I_INUM (x); | |
2561 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2562 | { | |
2563 | scm_t_inum yy = SCM_I_INUM (y); | |
2564 | if (SCM_UNLIKELY (yy == 0)) | |
2565 | scm_num_overflow (s_scm_truncate_divide); | |
2566 | else | |
2567 | { | |
2568 | scm_t_inum qq = xx / yy; | |
2569 | scm_t_inum rr = xx % yy; | |
2570 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2571 | *qp = SCM_I_MAKINUM (qq); | |
2572 | else | |
2573 | *qp = scm_i_inum2big (qq); | |
2574 | *rp = SCM_I_MAKINUM (rr); | |
2575 | } | |
2576 | return; | |
2577 | } | |
2578 | else if (SCM_BIGP (y)) | |
2579 | { | |
2580 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2581 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2582 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2583 | { | |
2584 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2585 | scm_remember_upto_here_1 (y); | |
2586 | *qp = SCM_I_MAKINUM (-1); | |
2587 | *rp = SCM_INUM0; | |
2588 | } | |
2589 | else | |
2590 | { | |
2591 | *qp = SCM_INUM0; | |
2592 | *rp = x; | |
2593 | } | |
2594 | return; | |
2595 | } | |
2596 | else if (SCM_REALP (y)) | |
2597 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2598 | else if (SCM_FRACTIONP (y)) | |
2599 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2600 | else | |
2601 | return two_valued_wta_dispatch_2 | |
2602 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2603 | s_scm_truncate_divide, qp, rp); | |
2604 | } | |
2605 | else if (SCM_BIGP (x)) | |
2606 | { | |
2607 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2608 | { | |
2609 | scm_t_inum yy = SCM_I_INUM (y); | |
2610 | if (SCM_UNLIKELY (yy == 0)) | |
2611 | scm_num_overflow (s_scm_truncate_divide); | |
2612 | else | |
2613 | { | |
2614 | SCM q = scm_i_mkbig (); | |
2615 | scm_t_inum rr; | |
2616 | if (yy > 0) | |
2617 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2618 | SCM_I_BIG_MPZ (x), yy); | |
2619 | else | |
2620 | { | |
2621 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2622 | SCM_I_BIG_MPZ (x), -yy); | |
2623 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2624 | } | |
2625 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2626 | scm_remember_upto_here_1 (x); | |
2627 | *qp = scm_i_normbig (q); | |
2628 | *rp = SCM_I_MAKINUM (rr); | |
2629 | } | |
2630 | return; | |
2631 | } | |
2632 | else if (SCM_BIGP (y)) | |
2633 | { | |
2634 | SCM q = scm_i_mkbig (); | |
2635 | SCM r = scm_i_mkbig (); | |
2636 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2637 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2638 | scm_remember_upto_here_2 (x, y); | |
2639 | *qp = scm_i_normbig (q); | |
2640 | *rp = scm_i_normbig (r); | |
2641 | } | |
2642 | else if (SCM_REALP (y)) | |
2643 | return scm_i_inexact_truncate_divide | |
2644 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2645 | else if (SCM_FRACTIONP (y)) | |
2646 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2647 | else | |
2648 | return two_valued_wta_dispatch_2 | |
2649 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2650 | s_scm_truncate_divide, qp, rp); | |
2651 | } | |
2652 | else if (SCM_REALP (x)) | |
2653 | { | |
2654 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2655 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2656 | return scm_i_inexact_truncate_divide | |
2657 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2658 | else | |
2659 | return two_valued_wta_dispatch_2 | |
2660 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2661 | s_scm_truncate_divide, qp, rp); | |
2662 | } | |
2663 | else if (SCM_FRACTIONP (x)) | |
2664 | { | |
2665 | if (SCM_REALP (y)) | |
2666 | return scm_i_inexact_truncate_divide | |
2667 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2668 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2669 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2670 | else | |
2671 | return two_valued_wta_dispatch_2 | |
2672 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2673 | s_scm_truncate_divide, qp, rp); | |
2674 | } | |
2675 | else | |
2676 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2677 | s_scm_truncate_divide, qp, rp); | |
2678 | } | |
2679 | ||
2680 | static void | |
2681 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2682 | { | |
2683 | if (SCM_UNLIKELY (y == 0)) | |
2684 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2685 | else | |
2686 | { | |
c15fe499 MW |
2687 | double q = trunc (x / y); |
2688 | double r = x - q * y; | |
00472a22 MW |
2689 | *qp = scm_i_from_double (q); |
2690 | *rp = scm_i_from_double (r); | |
8f9da340 MW |
2691 | } |
2692 | } | |
2693 | ||
2694 | static void | |
2695 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2696 | { | |
2697 | SCM r1; | |
2698 | SCM xd = scm_denominator (x); | |
2699 | SCM yd = scm_denominator (y); | |
2700 | ||
2701 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2702 | scm_product (scm_numerator (y), xd), | |
2703 | qp, &r1); | |
2704 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2705 | } | |
2706 | ||
ff62c168 MW |
2707 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2708 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2709 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2710 | |
8f9da340 MW |
2711 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2712 | (SCM x, SCM y), | |
2713 | "Return the integer @var{q} such that\n" | |
2714 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2715 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2716 | "@lisp\n" | |
2717 | "(centered-quotient 123 10) @result{} 12\n" | |
2718 | "(centered-quotient 123 -10) @result{} -12\n" | |
2719 | "(centered-quotient -123 10) @result{} -12\n" | |
2720 | "(centered-quotient -123 -10) @result{} 12\n" | |
2721 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2722 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2723 | "@end lisp") | |
2724 | #define FUNC_NAME s_scm_centered_quotient | |
2725 | { | |
2726 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2727 | { | |
2728 | scm_t_inum xx = SCM_I_INUM (x); | |
2729 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2730 | { | |
2731 | scm_t_inum yy = SCM_I_INUM (y); | |
2732 | if (SCM_UNLIKELY (yy == 0)) | |
2733 | scm_num_overflow (s_scm_centered_quotient); | |
2734 | else | |
2735 | { | |
2736 | scm_t_inum qq = xx / yy; | |
2737 | scm_t_inum rr = xx % yy; | |
2738 | if (SCM_LIKELY (xx > 0)) | |
2739 | { | |
2740 | if (SCM_LIKELY (yy > 0)) | |
2741 | { | |
2742 | if (rr >= (yy + 1) / 2) | |
2743 | qq++; | |
2744 | } | |
2745 | else | |
2746 | { | |
2747 | if (rr >= (1 - yy) / 2) | |
2748 | qq--; | |
2749 | } | |
2750 | } | |
2751 | else | |
2752 | { | |
2753 | if (SCM_LIKELY (yy > 0)) | |
2754 | { | |
2755 | if (rr < -yy / 2) | |
2756 | qq--; | |
2757 | } | |
2758 | else | |
2759 | { | |
2760 | if (rr < yy / 2) | |
2761 | qq++; | |
2762 | } | |
2763 | } | |
2764 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2765 | return SCM_I_MAKINUM (qq); | |
2766 | else | |
2767 | return scm_i_inum2big (qq); | |
2768 | } | |
2769 | } | |
2770 | else if (SCM_BIGP (y)) | |
2771 | { | |
2772 | /* Pass a denormalized bignum version of x (even though it | |
2773 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2774 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2775 | } | |
2776 | else if (SCM_REALP (y)) | |
2777 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2778 | else if (SCM_FRACTIONP (y)) | |
2779 | return scm_i_exact_rational_centered_quotient (x, y); | |
2780 | else | |
fa075d40 AW |
2781 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2782 | s_scm_centered_quotient); | |
8f9da340 MW |
2783 | } |
2784 | else if (SCM_BIGP (x)) | |
2785 | { | |
2786 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2787 | { | |
2788 | scm_t_inum yy = SCM_I_INUM (y); | |
2789 | if (SCM_UNLIKELY (yy == 0)) | |
2790 | scm_num_overflow (s_scm_centered_quotient); | |
2791 | else if (SCM_UNLIKELY (yy == 1)) | |
2792 | return x; | |
2793 | else | |
2794 | { | |
2795 | SCM q = scm_i_mkbig (); | |
2796 | scm_t_inum rr; | |
2797 | /* Arrange for rr to initially be non-positive, | |
2798 | because that simplifies the test to see | |
2799 | if it is within the needed bounds. */ | |
2800 | if (yy > 0) | |
2801 | { | |
2802 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2803 | SCM_I_BIG_MPZ (x), yy); | |
2804 | scm_remember_upto_here_1 (x); | |
2805 | if (rr < -yy / 2) | |
2806 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2807 | SCM_I_BIG_MPZ (q), 1); | |
2808 | } | |
2809 | else | |
2810 | { | |
2811 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2812 | SCM_I_BIG_MPZ (x), -yy); | |
2813 | scm_remember_upto_here_1 (x); | |
2814 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2815 | if (rr < yy / 2) | |
2816 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2817 | SCM_I_BIG_MPZ (q), 1); | |
2818 | } | |
2819 | return scm_i_normbig (q); | |
2820 | } | |
2821 | } | |
2822 | else if (SCM_BIGP (y)) | |
2823 | return scm_i_bigint_centered_quotient (x, y); | |
2824 | else if (SCM_REALP (y)) | |
2825 | return scm_i_inexact_centered_quotient | |
2826 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2827 | else if (SCM_FRACTIONP (y)) | |
2828 | return scm_i_exact_rational_centered_quotient (x, y); | |
2829 | else | |
fa075d40 AW |
2830 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2831 | s_scm_centered_quotient); | |
8f9da340 MW |
2832 | } |
2833 | else if (SCM_REALP (x)) | |
2834 | { | |
2835 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2836 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2837 | return scm_i_inexact_centered_quotient | |
2838 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2839 | else | |
fa075d40 AW |
2840 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2841 | s_scm_centered_quotient); | |
8f9da340 MW |
2842 | } |
2843 | else if (SCM_FRACTIONP (x)) | |
2844 | { | |
2845 | if (SCM_REALP (y)) | |
2846 | return scm_i_inexact_centered_quotient | |
2847 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2848 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2849 | return scm_i_exact_rational_centered_quotient (x, y); | |
2850 | else | |
fa075d40 AW |
2851 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2852 | s_scm_centered_quotient); | |
8f9da340 MW |
2853 | } |
2854 | else | |
fa075d40 AW |
2855 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG1, |
2856 | s_scm_centered_quotient); | |
8f9da340 MW |
2857 | } |
2858 | #undef FUNC_NAME | |
2859 | ||
2860 | static SCM | |
2861 | scm_i_inexact_centered_quotient (double x, double y) | |
2862 | { | |
2863 | if (SCM_LIKELY (y > 0)) | |
00472a22 | 2864 | return scm_i_from_double (floor (x/y + 0.5)); |
8f9da340 | 2865 | else if (SCM_LIKELY (y < 0)) |
00472a22 | 2866 | return scm_i_from_double (ceil (x/y - 0.5)); |
8f9da340 MW |
2867 | else if (y == 0) |
2868 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2869 | else | |
2870 | return scm_nan (); | |
2871 | } | |
2872 | ||
2873 | /* Assumes that both x and y are bigints, though | |
2874 | x might be able to fit into a fixnum. */ | |
2875 | static SCM | |
2876 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2877 | { | |
2878 | SCM q, r, min_r; | |
2879 | ||
2880 | /* Note that x might be small enough to fit into a | |
2881 | fixnum, so we must not let it escape into the wild */ | |
2882 | q = scm_i_mkbig (); | |
2883 | r = scm_i_mkbig (); | |
2884 | ||
2885 | /* min_r will eventually become -abs(y)/2 */ | |
2886 | min_r = scm_i_mkbig (); | |
2887 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2888 | SCM_I_BIG_MPZ (y), 1); | |
2889 | ||
2890 | /* Arrange for rr to initially be non-positive, | |
2891 | because that simplifies the test to see | |
2892 | if it is within the needed bounds. */ | |
2893 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2894 | { | |
2895 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2896 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2897 | scm_remember_upto_here_2 (x, y); | |
2898 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2899 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2900 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2901 | SCM_I_BIG_MPZ (q), 1); | |
2902 | } | |
2903 | else | |
2904 | { | |
2905 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2906 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2907 | scm_remember_upto_here_2 (x, y); | |
2908 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2909 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2910 | SCM_I_BIG_MPZ (q), 1); | |
2911 | } | |
2912 | scm_remember_upto_here_2 (r, min_r); | |
2913 | return scm_i_normbig (q); | |
2914 | } | |
2915 | ||
2916 | static SCM | |
2917 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2918 | { | |
2919 | return scm_centered_quotient | |
2920 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2921 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2922 | } | |
2923 | ||
2924 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2925 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2926 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2927 | ||
2928 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2929 | (SCM x, SCM y), | |
2930 | "Return the real number @var{r} such that\n" | |
2931 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2932 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2933 | "for some integer @var{q}.\n" | |
2934 | "@lisp\n" | |
2935 | "(centered-remainder 123 10) @result{} 3\n" | |
2936 | "(centered-remainder 123 -10) @result{} 3\n" | |
2937 | "(centered-remainder -123 10) @result{} -3\n" | |
2938 | "(centered-remainder -123 -10) @result{} -3\n" | |
2939 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2940 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2941 | "@end lisp") | |
2942 | #define FUNC_NAME s_scm_centered_remainder | |
2943 | { | |
2944 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2945 | { | |
2946 | scm_t_inum xx = SCM_I_INUM (x); | |
2947 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2948 | { | |
2949 | scm_t_inum yy = SCM_I_INUM (y); | |
2950 | if (SCM_UNLIKELY (yy == 0)) | |
2951 | scm_num_overflow (s_scm_centered_remainder); | |
2952 | else | |
2953 | { | |
2954 | scm_t_inum rr = xx % yy; | |
2955 | if (SCM_LIKELY (xx > 0)) | |
2956 | { | |
2957 | if (SCM_LIKELY (yy > 0)) | |
2958 | { | |
2959 | if (rr >= (yy + 1) / 2) | |
2960 | rr -= yy; | |
2961 | } | |
2962 | else | |
2963 | { | |
2964 | if (rr >= (1 - yy) / 2) | |
2965 | rr += yy; | |
2966 | } | |
2967 | } | |
2968 | else | |
2969 | { | |
2970 | if (SCM_LIKELY (yy > 0)) | |
2971 | { | |
2972 | if (rr < -yy / 2) | |
2973 | rr += yy; | |
2974 | } | |
2975 | else | |
2976 | { | |
2977 | if (rr < yy / 2) | |
2978 | rr -= yy; | |
2979 | } | |
2980 | } | |
2981 | return SCM_I_MAKINUM (rr); | |
2982 | } | |
2983 | } | |
2984 | else if (SCM_BIGP (y)) | |
2985 | { | |
2986 | /* Pass a denormalized bignum version of x (even though it | |
2987 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2988 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2989 | } | |
2990 | else if (SCM_REALP (y)) | |
2991 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2992 | else if (SCM_FRACTIONP (y)) | |
2993 | return scm_i_exact_rational_centered_remainder (x, y); | |
2994 | else | |
fa075d40 AW |
2995 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
2996 | s_scm_centered_remainder); | |
8f9da340 MW |
2997 | } |
2998 | else if (SCM_BIGP (x)) | |
2999 | { | |
3000 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3001 | { | |
3002 | scm_t_inum yy = SCM_I_INUM (y); | |
3003 | if (SCM_UNLIKELY (yy == 0)) | |
3004 | scm_num_overflow (s_scm_centered_remainder); | |
3005 | else | |
3006 | { | |
3007 | scm_t_inum rr; | |
3008 | /* Arrange for rr to initially be non-positive, | |
3009 | because that simplifies the test to see | |
3010 | if it is within the needed bounds. */ | |
3011 | if (yy > 0) | |
3012 | { | |
3013 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
3014 | scm_remember_upto_here_1 (x); | |
3015 | if (rr < -yy / 2) | |
3016 | rr += yy; | |
3017 | } | |
3018 | else | |
3019 | { | |
3020 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
3021 | scm_remember_upto_here_1 (x); | |
3022 | if (rr < yy / 2) | |
3023 | rr -= yy; | |
3024 | } | |
3025 | return SCM_I_MAKINUM (rr); | |
3026 | } | |
3027 | } | |
3028 | else if (SCM_BIGP (y)) | |
3029 | return scm_i_bigint_centered_remainder (x, y); | |
3030 | else if (SCM_REALP (y)) | |
3031 | return scm_i_inexact_centered_remainder | |
3032 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
3033 | else if (SCM_FRACTIONP (y)) | |
3034 | return scm_i_exact_rational_centered_remainder (x, y); | |
3035 | else | |
fa075d40 AW |
3036 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
3037 | s_scm_centered_remainder); | |
8f9da340 MW |
3038 | } |
3039 | else if (SCM_REALP (x)) | |
3040 | { | |
3041 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3042 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3043 | return scm_i_inexact_centered_remainder | |
3044 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
3045 | else | |
fa075d40 AW |
3046 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
3047 | s_scm_centered_remainder); | |
8f9da340 MW |
3048 | } |
3049 | else if (SCM_FRACTIONP (x)) | |
3050 | { | |
3051 | if (SCM_REALP (y)) | |
3052 | return scm_i_inexact_centered_remainder | |
3053 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
3054 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3055 | return scm_i_exact_rational_centered_remainder (x, y); | |
3056 | else | |
fa075d40 AW |
3057 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
3058 | s_scm_centered_remainder); | |
8f9da340 MW |
3059 | } |
3060 | else | |
fa075d40 AW |
3061 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG1, |
3062 | s_scm_centered_remainder); | |
8f9da340 MW |
3063 | } |
3064 | #undef FUNC_NAME | |
3065 | ||
3066 | static SCM | |
3067 | scm_i_inexact_centered_remainder (double x, double y) | |
3068 | { | |
3069 | double q; | |
3070 | ||
3071 | /* Although it would be more efficient to use fmod here, we can't | |
3072 | because it would in some cases produce results inconsistent with | |
3073 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
3074 | close). In particular, when x-y/2 is very close to a multiple of | |
3075 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
3076 | two cases must correspond to different choices of q. If quotient | |
3077 | chooses one and remainder chooses the other, it would be bad. */ | |
3078 | if (SCM_LIKELY (y > 0)) | |
3079 | q = floor (x/y + 0.5); | |
3080 | else if (SCM_LIKELY (y < 0)) | |
3081 | q = ceil (x/y - 0.5); | |
3082 | else if (y == 0) | |
3083 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
3084 | else | |
3085 | return scm_nan (); | |
00472a22 | 3086 | return scm_i_from_double (x - q * y); |
8f9da340 MW |
3087 | } |
3088 | ||
3089 | /* Assumes that both x and y are bigints, though | |
3090 | x might be able to fit into a fixnum. */ | |
3091 | static SCM | |
3092 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
3093 | { | |
3094 | SCM r, min_r; | |
3095 | ||
3096 | /* Note that x might be small enough to fit into a | |
3097 | fixnum, so we must not let it escape into the wild */ | |
3098 | r = scm_i_mkbig (); | |
3099 | ||
3100 | /* min_r will eventually become -abs(y)/2 */ | |
3101 | min_r = scm_i_mkbig (); | |
3102 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3103 | SCM_I_BIG_MPZ (y), 1); | |
3104 | ||
3105 | /* Arrange for rr to initially be non-positive, | |
3106 | because that simplifies the test to see | |
3107 | if it is within the needed bounds. */ | |
3108 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3109 | { | |
3110 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
3111 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3112 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3113 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3114 | mpz_add (SCM_I_BIG_MPZ (r), | |
3115 | SCM_I_BIG_MPZ (r), | |
3116 | SCM_I_BIG_MPZ (y)); | |
3117 | } | |
3118 | else | |
3119 | { | |
3120 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
3121 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3122 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3123 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3124 | SCM_I_BIG_MPZ (r), | |
3125 | SCM_I_BIG_MPZ (y)); | |
3126 | } | |
3127 | scm_remember_upto_here_2 (x, y); | |
3128 | return scm_i_normbig (r); | |
3129 | } | |
3130 | ||
3131 | static SCM | |
3132 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
3133 | { | |
3134 | SCM xd = scm_denominator (x); | |
3135 | SCM yd = scm_denominator (y); | |
3136 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
3137 | scm_product (scm_numerator (y), xd)); | |
3138 | return scm_divide (r1, scm_product (xd, yd)); | |
3139 | } | |
3140 | ||
3141 | ||
3142 | static void scm_i_inexact_centered_divide (double x, double y, | |
3143 | SCM *qp, SCM *rp); | |
3144 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3145 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
3146 | SCM *qp, SCM *rp); | |
3147 | ||
3148 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
3149 | (SCM x, SCM y), | |
3150 | "Return the integer @var{q} and the real number @var{r}\n" | |
3151 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
3152 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
3153 | "@lisp\n" | |
3154 | "(centered/ 123 10) @result{} 12 and 3\n" | |
3155 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
3156 | "(centered/ -123 10) @result{} -12 and -3\n" | |
3157 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
3158 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3159 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
3160 | "@end lisp") | |
3161 | #define FUNC_NAME s_scm_i_centered_divide | |
3162 | { | |
3163 | SCM q, r; | |
3164 | ||
3165 | scm_centered_divide(x, y, &q, &r); | |
3166 | return scm_values (scm_list_2 (q, r)); | |
3167 | } | |
3168 | #undef FUNC_NAME | |
3169 | ||
3170 | #define s_scm_centered_divide s_scm_i_centered_divide | |
3171 | #define g_scm_centered_divide g_scm_i_centered_divide | |
3172 | ||
3173 | void | |
3174 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3175 | { | |
3176 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3177 | { | |
3178 | scm_t_inum xx = SCM_I_INUM (x); | |
3179 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3180 | { | |
3181 | scm_t_inum yy = SCM_I_INUM (y); | |
3182 | if (SCM_UNLIKELY (yy == 0)) | |
3183 | scm_num_overflow (s_scm_centered_divide); | |
3184 | else | |
3185 | { | |
3186 | scm_t_inum qq = xx / yy; | |
3187 | scm_t_inum rr = xx % yy; | |
3188 | if (SCM_LIKELY (xx > 0)) | |
3189 | { | |
3190 | if (SCM_LIKELY (yy > 0)) | |
3191 | { | |
3192 | if (rr >= (yy + 1) / 2) | |
3193 | { qq++; rr -= yy; } | |
3194 | } | |
3195 | else | |
3196 | { | |
3197 | if (rr >= (1 - yy) / 2) | |
3198 | { qq--; rr += yy; } | |
3199 | } | |
3200 | } | |
3201 | else | |
3202 | { | |
3203 | if (SCM_LIKELY (yy > 0)) | |
3204 | { | |
3205 | if (rr < -yy / 2) | |
3206 | { qq--; rr += yy; } | |
3207 | } | |
3208 | else | |
3209 | { | |
3210 | if (rr < yy / 2) | |
3211 | { qq++; rr -= yy; } | |
3212 | } | |
3213 | } | |
3214 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3215 | *qp = SCM_I_MAKINUM (qq); | |
3216 | else | |
3217 | *qp = scm_i_inum2big (qq); | |
3218 | *rp = SCM_I_MAKINUM (rr); | |
3219 | } | |
3220 | return; | |
3221 | } | |
3222 | else if (SCM_BIGP (y)) | |
3223 | { | |
3224 | /* Pass a denormalized bignum version of x (even though it | |
3225 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3226 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3227 | } | |
3228 | else if (SCM_REALP (y)) | |
3229 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3230 | else if (SCM_FRACTIONP (y)) | |
3231 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3232 | else | |
3233 | return two_valued_wta_dispatch_2 | |
3234 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3235 | s_scm_centered_divide, qp, rp); | |
3236 | } | |
3237 | else if (SCM_BIGP (x)) | |
3238 | { | |
3239 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3240 | { | |
3241 | scm_t_inum yy = SCM_I_INUM (y); | |
3242 | if (SCM_UNLIKELY (yy == 0)) | |
3243 | scm_num_overflow (s_scm_centered_divide); | |
3244 | else | |
3245 | { | |
3246 | SCM q = scm_i_mkbig (); | |
3247 | scm_t_inum rr; | |
3248 | /* Arrange for rr to initially be non-positive, | |
3249 | because that simplifies the test to see | |
3250 | if it is within the needed bounds. */ | |
3251 | if (yy > 0) | |
3252 | { | |
3253 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3254 | SCM_I_BIG_MPZ (x), yy); | |
3255 | scm_remember_upto_here_1 (x); | |
3256 | if (rr < -yy / 2) | |
3257 | { | |
3258 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3259 | SCM_I_BIG_MPZ (q), 1); | |
3260 | rr += yy; | |
3261 | } | |
3262 | } | |
3263 | else | |
3264 | { | |
3265 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3266 | SCM_I_BIG_MPZ (x), -yy); | |
3267 | scm_remember_upto_here_1 (x); | |
3268 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3269 | if (rr < yy / 2) | |
3270 | { | |
3271 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3272 | SCM_I_BIG_MPZ (q), 1); | |
3273 | rr -= yy; | |
3274 | } | |
3275 | } | |
3276 | *qp = scm_i_normbig (q); | |
3277 | *rp = SCM_I_MAKINUM (rr); | |
3278 | } | |
3279 | return; | |
3280 | } | |
3281 | else if (SCM_BIGP (y)) | |
3282 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3283 | else if (SCM_REALP (y)) | |
3284 | return scm_i_inexact_centered_divide | |
3285 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3286 | else if (SCM_FRACTIONP (y)) | |
3287 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3288 | else | |
3289 | return two_valued_wta_dispatch_2 | |
3290 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3291 | s_scm_centered_divide, qp, rp); | |
3292 | } | |
3293 | else if (SCM_REALP (x)) | |
3294 | { | |
3295 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3296 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3297 | return scm_i_inexact_centered_divide | |
3298 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3299 | else | |
3300 | return two_valued_wta_dispatch_2 | |
3301 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3302 | s_scm_centered_divide, qp, rp); | |
3303 | } | |
3304 | else if (SCM_FRACTIONP (x)) | |
3305 | { | |
3306 | if (SCM_REALP (y)) | |
3307 | return scm_i_inexact_centered_divide | |
3308 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3309 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3310 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3311 | else | |
3312 | return two_valued_wta_dispatch_2 | |
3313 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3314 | s_scm_centered_divide, qp, rp); | |
3315 | } | |
3316 | else | |
3317 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3318 | s_scm_centered_divide, qp, rp); | |
3319 | } | |
3320 | ||
3321 | static void | |
3322 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3323 | { | |
3324 | double q, r; | |
3325 | ||
3326 | if (SCM_LIKELY (y > 0)) | |
3327 | q = floor (x/y + 0.5); | |
3328 | else if (SCM_LIKELY (y < 0)) | |
3329 | q = ceil (x/y - 0.5); | |
3330 | else if (y == 0) | |
3331 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3332 | else | |
3333 | q = guile_NaN; | |
3334 | r = x - q * y; | |
00472a22 MW |
3335 | *qp = scm_i_from_double (q); |
3336 | *rp = scm_i_from_double (r); | |
8f9da340 MW |
3337 | } |
3338 | ||
3339 | /* Assumes that both x and y are bigints, though | |
3340 | x might be able to fit into a fixnum. */ | |
3341 | static void | |
3342 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3343 | { | |
3344 | SCM q, r, min_r; | |
3345 | ||
3346 | /* Note that x might be small enough to fit into a | |
3347 | fixnum, so we must not let it escape into the wild */ | |
3348 | q = scm_i_mkbig (); | |
3349 | r = scm_i_mkbig (); | |
3350 | ||
3351 | /* min_r will eventually become -abs(y/2) */ | |
3352 | min_r = scm_i_mkbig (); | |
3353 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3354 | SCM_I_BIG_MPZ (y), 1); | |
3355 | ||
3356 | /* Arrange for rr to initially be non-positive, | |
3357 | because that simplifies the test to see | |
3358 | if it is within the needed bounds. */ | |
3359 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3360 | { | |
3361 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3362 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3363 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3364 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3365 | { | |
3366 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3367 | SCM_I_BIG_MPZ (q), 1); | |
3368 | mpz_add (SCM_I_BIG_MPZ (r), | |
3369 | SCM_I_BIG_MPZ (r), | |
3370 | SCM_I_BIG_MPZ (y)); | |
3371 | } | |
3372 | } | |
3373 | else | |
3374 | { | |
3375 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3376 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3377 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3378 | { | |
3379 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3380 | SCM_I_BIG_MPZ (q), 1); | |
3381 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3382 | SCM_I_BIG_MPZ (r), | |
3383 | SCM_I_BIG_MPZ (y)); | |
3384 | } | |
3385 | } | |
3386 | scm_remember_upto_here_2 (x, y); | |
3387 | *qp = scm_i_normbig (q); | |
3388 | *rp = scm_i_normbig (r); | |
3389 | } | |
3390 | ||
3391 | static void | |
3392 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3393 | { | |
3394 | SCM r1; | |
3395 | SCM xd = scm_denominator (x); | |
3396 | SCM yd = scm_denominator (y); | |
3397 | ||
3398 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3399 | scm_product (scm_numerator (y), xd), | |
3400 | qp, &r1); | |
3401 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3402 | } | |
3403 | ||
3404 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3405 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3406 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3407 | ||
3408 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3409 | (SCM x, SCM y), |
8f9da340 MW |
3410 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3411 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3412 | "@lisp\n" |
8f9da340 MW |
3413 | "(round-quotient 123 10) @result{} 12\n" |
3414 | "(round-quotient 123 -10) @result{} -12\n" | |
3415 | "(round-quotient -123 10) @result{} -12\n" | |
3416 | "(round-quotient -123 -10) @result{} 12\n" | |
3417 | "(round-quotient 125 10) @result{} 12\n" | |
3418 | "(round-quotient 127 10) @result{} 13\n" | |
3419 | "(round-quotient 135 10) @result{} 14\n" | |
3420 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3421 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3422 | "@end lisp") |
8f9da340 | 3423 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3424 | { |
3425 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3426 | { | |
4a46bc2a | 3427 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3428 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3429 | { | |
3430 | scm_t_inum yy = SCM_I_INUM (y); | |
3431 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3432 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3433 | else |
3434 | { | |
ff62c168 | 3435 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3436 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3437 | scm_t_inum ay = yy; |
3438 | scm_t_inum r2 = 2 * rr; | |
3439 | ||
3440 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3441 | { |
8f9da340 MW |
3442 | ay = -ay; |
3443 | r2 = -r2; | |
3444 | } | |
3445 | ||
3446 | if (qq & 1L) | |
3447 | { | |
3448 | if (r2 >= ay) | |
3449 | qq++; | |
3450 | else if (r2 <= -ay) | |
3451 | qq--; | |
ff62c168 MW |
3452 | } |
3453 | else | |
3454 | { | |
8f9da340 MW |
3455 | if (r2 > ay) |
3456 | qq++; | |
3457 | else if (r2 < -ay) | |
3458 | qq--; | |
ff62c168 | 3459 | } |
4a46bc2a MW |
3460 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3461 | return SCM_I_MAKINUM (qq); | |
3462 | else | |
3463 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3464 | } |
3465 | } | |
3466 | else if (SCM_BIGP (y)) | |
3467 | { | |
3468 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3469 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3470 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3471 | } |
3472 | else if (SCM_REALP (y)) | |
8f9da340 | 3473 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3474 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3475 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3476 | else |
fa075d40 AW |
3477 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3478 | s_scm_round_quotient); | |
ff62c168 MW |
3479 | } |
3480 | else if (SCM_BIGP (x)) | |
3481 | { | |
3482 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3483 | { | |
3484 | scm_t_inum yy = SCM_I_INUM (y); | |
3485 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3486 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3487 | else if (SCM_UNLIKELY (yy == 1)) |
3488 | return x; | |
ff62c168 MW |
3489 | else |
3490 | { | |
3491 | SCM q = scm_i_mkbig (); | |
3492 | scm_t_inum rr; | |
8f9da340 MW |
3493 | int needs_adjustment; |
3494 | ||
ff62c168 MW |
3495 | if (yy > 0) |
3496 | { | |
8f9da340 MW |
3497 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3498 | SCM_I_BIG_MPZ (x), yy); | |
3499 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3500 | needs_adjustment = (2*rr >= yy); | |
3501 | else | |
3502 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3503 | } |
3504 | else | |
3505 | { | |
3506 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3507 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3508 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3509 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3510 | needs_adjustment = (2*rr <= yy); | |
3511 | else | |
3512 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3513 | } |
8f9da340 MW |
3514 | scm_remember_upto_here_1 (x); |
3515 | if (needs_adjustment) | |
3516 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3517 | return scm_i_normbig (q); |
3518 | } | |
3519 | } | |
3520 | else if (SCM_BIGP (y)) | |
8f9da340 | 3521 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3522 | else if (SCM_REALP (y)) |
8f9da340 | 3523 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3524 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3525 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3526 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3527 | else |
fa075d40 AW |
3528 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3529 | s_scm_round_quotient); | |
ff62c168 MW |
3530 | } |
3531 | else if (SCM_REALP (x)) | |
3532 | { | |
3533 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3534 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3535 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3536 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3537 | else | |
fa075d40 AW |
3538 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3539 | s_scm_round_quotient); | |
ff62c168 MW |
3540 | } |
3541 | else if (SCM_FRACTIONP (x)) | |
3542 | { | |
3543 | if (SCM_REALP (y)) | |
8f9da340 | 3544 | return scm_i_inexact_round_quotient |
ff62c168 | 3545 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3546 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3547 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3548 | else |
fa075d40 AW |
3549 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3550 | s_scm_round_quotient); | |
ff62c168 MW |
3551 | } |
3552 | else | |
fa075d40 AW |
3553 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3554 | s_scm_round_quotient); | |
ff62c168 MW |
3555 | } |
3556 | #undef FUNC_NAME | |
3557 | ||
3558 | static SCM | |
8f9da340 | 3559 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3560 | { |
8f9da340 MW |
3561 | if (SCM_UNLIKELY (y == 0)) |
3562 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3563 | else |
00472a22 | 3564 | return scm_i_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3565 | } |
3566 | ||
3567 | /* Assumes that both x and y are bigints, though | |
3568 | x might be able to fit into a fixnum. */ | |
3569 | static SCM | |
8f9da340 | 3570 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3571 | { |
8f9da340 MW |
3572 | SCM q, r, r2; |
3573 | int cmp, needs_adjustment; | |
ff62c168 MW |
3574 | |
3575 | /* Note that x might be small enough to fit into a | |
3576 | fixnum, so we must not let it escape into the wild */ | |
3577 | q = scm_i_mkbig (); | |
3578 | r = scm_i_mkbig (); | |
8f9da340 | 3579 | r2 = scm_i_mkbig (); |
ff62c168 | 3580 | |
8f9da340 MW |
3581 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3582 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3583 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3584 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3585 | |
8f9da340 MW |
3586 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3587 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3588 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3589 | else |
8f9da340 MW |
3590 | needs_adjustment = (cmp > 0); |
3591 | scm_remember_upto_here_2 (r2, y); | |
3592 | ||
3593 | if (needs_adjustment) | |
3594 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3595 | ||
ff62c168 MW |
3596 | return scm_i_normbig (q); |
3597 | } | |
3598 | ||
ff62c168 | 3599 | static SCM |
8f9da340 | 3600 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3601 | { |
8f9da340 | 3602 | return scm_round_quotient |
03ddd15b MW |
3603 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3604 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3605 | } |
3606 | ||
8f9da340 MW |
3607 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3608 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3609 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3610 | |
8f9da340 | 3611 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3612 | (SCM x, SCM y), |
3613 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3614 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3615 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3616 | "nearest integer, with ties going to the nearest\n" | |
3617 | "even integer.\n" | |
ff62c168 | 3618 | "@lisp\n" |
8f9da340 MW |
3619 | "(round-remainder 123 10) @result{} 3\n" |
3620 | "(round-remainder 123 -10) @result{} 3\n" | |
3621 | "(round-remainder -123 10) @result{} -3\n" | |
3622 | "(round-remainder -123 -10) @result{} -3\n" | |
3623 | "(round-remainder 125 10) @result{} 5\n" | |
3624 | "(round-remainder 127 10) @result{} -3\n" | |
3625 | "(round-remainder 135 10) @result{} -5\n" | |
3626 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3627 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3628 | "@end lisp") |
8f9da340 | 3629 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3630 | { |
3631 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3632 | { | |
4a46bc2a | 3633 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3634 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3635 | { | |
3636 | scm_t_inum yy = SCM_I_INUM (y); | |
3637 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3638 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3639 | else |
3640 | { | |
8f9da340 | 3641 | scm_t_inum qq = xx / yy; |
ff62c168 | 3642 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3643 | scm_t_inum ay = yy; |
3644 | scm_t_inum r2 = 2 * rr; | |
3645 | ||
3646 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3647 | { |
8f9da340 MW |
3648 | ay = -ay; |
3649 | r2 = -r2; | |
3650 | } | |
3651 | ||
3652 | if (qq & 1L) | |
3653 | { | |
3654 | if (r2 >= ay) | |
3655 | rr -= yy; | |
3656 | else if (r2 <= -ay) | |
3657 | rr += yy; | |
ff62c168 MW |
3658 | } |
3659 | else | |
3660 | { | |
8f9da340 MW |
3661 | if (r2 > ay) |
3662 | rr -= yy; | |
3663 | else if (r2 < -ay) | |
3664 | rr += yy; | |
ff62c168 MW |
3665 | } |
3666 | return SCM_I_MAKINUM (rr); | |
3667 | } | |
3668 | } | |
3669 | else if (SCM_BIGP (y)) | |
3670 | { | |
3671 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3672 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3673 | return scm_i_bigint_round_remainder | |
3674 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3675 | } |
3676 | else if (SCM_REALP (y)) | |
8f9da340 | 3677 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3678 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3679 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3680 | else |
fa075d40 AW |
3681 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3682 | s_scm_round_remainder); | |
ff62c168 MW |
3683 | } |
3684 | else if (SCM_BIGP (x)) | |
3685 | { | |
3686 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3687 | { | |
3688 | scm_t_inum yy = SCM_I_INUM (y); | |
3689 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3690 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3691 | else |
3692 | { | |
8f9da340 | 3693 | SCM q = scm_i_mkbig (); |
ff62c168 | 3694 | scm_t_inum rr; |
8f9da340 MW |
3695 | int needs_adjustment; |
3696 | ||
ff62c168 MW |
3697 | if (yy > 0) |
3698 | { | |
8f9da340 MW |
3699 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3700 | SCM_I_BIG_MPZ (x), yy); | |
3701 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3702 | needs_adjustment = (2*rr >= yy); | |
3703 | else | |
3704 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3705 | } |
3706 | else | |
3707 | { | |
8f9da340 MW |
3708 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3709 | SCM_I_BIG_MPZ (x), -yy); | |
3710 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3711 | needs_adjustment = (2*rr <= yy); | |
3712 | else | |
3713 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3714 | } |
8f9da340 MW |
3715 | scm_remember_upto_here_2 (x, q); |
3716 | if (needs_adjustment) | |
3717 | rr -= yy; | |
ff62c168 MW |
3718 | return SCM_I_MAKINUM (rr); |
3719 | } | |
3720 | } | |
3721 | else if (SCM_BIGP (y)) | |
8f9da340 | 3722 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3723 | else if (SCM_REALP (y)) |
8f9da340 | 3724 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3725 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3726 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3727 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3728 | else |
fa075d40 AW |
3729 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3730 | s_scm_round_remainder); | |
ff62c168 MW |
3731 | } |
3732 | else if (SCM_REALP (x)) | |
3733 | { | |
3734 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3735 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3736 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3737 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3738 | else | |
fa075d40 AW |
3739 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3740 | s_scm_round_remainder); | |
ff62c168 MW |
3741 | } |
3742 | else if (SCM_FRACTIONP (x)) | |
3743 | { | |
3744 | if (SCM_REALP (y)) | |
8f9da340 | 3745 | return scm_i_inexact_round_remainder |
ff62c168 | 3746 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3747 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3748 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3749 | else |
fa075d40 AW |
3750 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3751 | s_scm_round_remainder); | |
ff62c168 MW |
3752 | } |
3753 | else | |
fa075d40 AW |
3754 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3755 | s_scm_round_remainder); | |
ff62c168 MW |
3756 | } |
3757 | #undef FUNC_NAME | |
3758 | ||
3759 | static SCM | |
8f9da340 | 3760 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3761 | { |
ff62c168 MW |
3762 | /* Although it would be more efficient to use fmod here, we can't |
3763 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3764 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3765 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3766 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3767 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3768 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3769 | |
3770 | if (SCM_UNLIKELY (y == 0)) | |
3771 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3772 | else |
8f9da340 MW |
3773 | { |
3774 | double q = scm_c_round (x / y); | |
00472a22 | 3775 | return scm_i_from_double (x - q * y); |
8f9da340 | 3776 | } |
ff62c168 MW |
3777 | } |
3778 | ||
3779 | /* Assumes that both x and y are bigints, though | |
3780 | x might be able to fit into a fixnum. */ | |
3781 | static SCM | |
8f9da340 | 3782 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3783 | { |
8f9da340 MW |
3784 | SCM q, r, r2; |
3785 | int cmp, needs_adjustment; | |
ff62c168 MW |
3786 | |
3787 | /* Note that x might be small enough to fit into a | |
3788 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3789 | q = scm_i_mkbig (); |
ff62c168 | 3790 | r = scm_i_mkbig (); |
8f9da340 | 3791 | r2 = scm_i_mkbig (); |
ff62c168 | 3792 | |
8f9da340 MW |
3793 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3794 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3795 | scm_remember_upto_here_1 (x); | |
3796 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3797 | |
8f9da340 MW |
3798 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3799 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3800 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3801 | else |
8f9da340 MW |
3802 | needs_adjustment = (cmp > 0); |
3803 | scm_remember_upto_here_2 (q, r2); | |
3804 | ||
3805 | if (needs_adjustment) | |
3806 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3807 | ||
3808 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3809 | return scm_i_normbig (r); |
3810 | } | |
3811 | ||
ff62c168 | 3812 | static SCM |
8f9da340 | 3813 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3814 | { |
03ddd15b MW |
3815 | SCM xd = scm_denominator (x); |
3816 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3817 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3818 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3819 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3820 | } |
3821 | ||
3822 | ||
8f9da340 MW |
3823 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3824 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3825 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3826 | |
8f9da340 | 3827 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3828 | (SCM x, SCM y), |
3829 | "Return the integer @var{q} and the real number @var{r}\n" | |
3830 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3831 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3832 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3833 | "@lisp\n" |
8f9da340 MW |
3834 | "(round/ 123 10) @result{} 12 and 3\n" |
3835 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3836 | "(round/ -123 10) @result{} -12 and -3\n" | |
3837 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3838 | "(round/ 125 10) @result{} 12 and 5\n" | |
3839 | "(round/ 127 10) @result{} 13 and -3\n" | |
3840 | "(round/ 135 10) @result{} 14 and -5\n" | |
3841 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3842 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3843 | "@end lisp") |
8f9da340 | 3844 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3845 | { |
3846 | SCM q, r; | |
3847 | ||
8f9da340 | 3848 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3849 | return scm_values (scm_list_2 (q, r)); |
3850 | } | |
3851 | #undef FUNC_NAME | |
3852 | ||
8f9da340 MW |
3853 | #define s_scm_round_divide s_scm_i_round_divide |
3854 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3855 | |
3856 | void | |
8f9da340 | 3857 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3858 | { |
3859 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3860 | { | |
4a46bc2a | 3861 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3862 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3863 | { | |
3864 | scm_t_inum yy = SCM_I_INUM (y); | |
3865 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3866 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3867 | else |
3868 | { | |
ff62c168 | 3869 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3870 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3871 | scm_t_inum ay = yy; |
3872 | scm_t_inum r2 = 2 * rr; | |
3873 | ||
3874 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3875 | { |
8f9da340 MW |
3876 | ay = -ay; |
3877 | r2 = -r2; | |
3878 | } | |
3879 | ||
3880 | if (qq & 1L) | |
3881 | { | |
3882 | if (r2 >= ay) | |
3883 | { qq++; rr -= yy; } | |
3884 | else if (r2 <= -ay) | |
3885 | { qq--; rr += yy; } | |
ff62c168 MW |
3886 | } |
3887 | else | |
3888 | { | |
8f9da340 MW |
3889 | if (r2 > ay) |
3890 | { qq++; rr -= yy; } | |
3891 | else if (r2 < -ay) | |
3892 | { qq--; rr += yy; } | |
ff62c168 | 3893 | } |
4a46bc2a | 3894 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3895 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3896 | else |
5fbf680b MW |
3897 | *qp = scm_i_inum2big (qq); |
3898 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3899 | } |
5fbf680b | 3900 | return; |
ff62c168 MW |
3901 | } |
3902 | else if (SCM_BIGP (y)) | |
3903 | { | |
3904 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3905 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3906 | return scm_i_bigint_round_divide | |
3907 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3908 | } |
3909 | else if (SCM_REALP (y)) | |
8f9da340 | 3910 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3911 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3912 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3913 | else |
8f9da340 MW |
3914 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3915 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3916 | } |
3917 | else if (SCM_BIGP (x)) | |
3918 | { | |
3919 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3920 | { | |
3921 | scm_t_inum yy = SCM_I_INUM (y); | |
3922 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3923 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3924 | else |
3925 | { | |
3926 | SCM q = scm_i_mkbig (); | |
3927 | scm_t_inum rr; | |
8f9da340 MW |
3928 | int needs_adjustment; |
3929 | ||
ff62c168 MW |
3930 | if (yy > 0) |
3931 | { | |
8f9da340 MW |
3932 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3933 | SCM_I_BIG_MPZ (x), yy); | |
3934 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3935 | needs_adjustment = (2*rr >= yy); | |
3936 | else | |
3937 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3938 | } |
3939 | else | |
3940 | { | |
3941 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3942 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3943 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3944 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3945 | needs_adjustment = (2*rr <= yy); | |
3946 | else | |
3947 | needs_adjustment = (2*rr < yy); | |
3948 | } | |
3949 | scm_remember_upto_here_1 (x); | |
3950 | if (needs_adjustment) | |
3951 | { | |
3952 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3953 | rr -= yy; | |
ff62c168 | 3954 | } |
5fbf680b MW |
3955 | *qp = scm_i_normbig (q); |
3956 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3957 | } |
5fbf680b | 3958 | return; |
ff62c168 MW |
3959 | } |
3960 | else if (SCM_BIGP (y)) | |
8f9da340 | 3961 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3962 | else if (SCM_REALP (y)) |
8f9da340 | 3963 | return scm_i_inexact_round_divide |
5fbf680b | 3964 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3965 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3966 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3967 | else |
8f9da340 MW |
3968 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3969 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3970 | } |
3971 | else if (SCM_REALP (x)) | |
3972 | { | |
3973 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3974 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3975 | return scm_i_inexact_round_divide |
5fbf680b | 3976 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3977 | else |
8f9da340 MW |
3978 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3979 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3980 | } |
3981 | else if (SCM_FRACTIONP (x)) | |
3982 | { | |
3983 | if (SCM_REALP (y)) | |
8f9da340 | 3984 | return scm_i_inexact_round_divide |
5fbf680b | 3985 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3986 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3987 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3988 | else |
8f9da340 MW |
3989 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3990 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3991 | } |
3992 | else | |
8f9da340 MW |
3993 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3994 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3995 | } |
ff62c168 | 3996 | |
5fbf680b | 3997 | static void |
8f9da340 | 3998 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3999 | { |
8f9da340 MW |
4000 | if (SCM_UNLIKELY (y == 0)) |
4001 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 4002 | else |
8f9da340 MW |
4003 | { |
4004 | double q = scm_c_round (x / y); | |
4005 | double r = x - q * y; | |
00472a22 MW |
4006 | *qp = scm_i_from_double (q); |
4007 | *rp = scm_i_from_double (r); | |
8f9da340 | 4008 | } |
ff62c168 MW |
4009 | } |
4010 | ||
4011 | /* Assumes that both x and y are bigints, though | |
4012 | x might be able to fit into a fixnum. */ | |
5fbf680b | 4013 | static void |
8f9da340 | 4014 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4015 | { |
8f9da340 MW |
4016 | SCM q, r, r2; |
4017 | int cmp, needs_adjustment; | |
ff62c168 MW |
4018 | |
4019 | /* Note that x might be small enough to fit into a | |
4020 | fixnum, so we must not let it escape into the wild */ | |
4021 | q = scm_i_mkbig (); | |
4022 | r = scm_i_mkbig (); | |
8f9da340 | 4023 | r2 = scm_i_mkbig (); |
ff62c168 | 4024 | |
8f9da340 MW |
4025 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
4026 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4027 | scm_remember_upto_here_1 (x); | |
4028 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 4029 | |
8f9da340 MW |
4030 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
4031 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4032 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 4033 | else |
8f9da340 MW |
4034 | needs_adjustment = (cmp > 0); |
4035 | ||
4036 | if (needs_adjustment) | |
ff62c168 | 4037 | { |
8f9da340 MW |
4038 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
4039 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 4040 | } |
8f9da340 MW |
4041 | |
4042 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
4043 | *qp = scm_i_normbig (q); |
4044 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
4045 | } |
4046 | ||
5fbf680b | 4047 | static void |
8f9da340 | 4048 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4049 | { |
03ddd15b MW |
4050 | SCM r1; |
4051 | SCM xd = scm_denominator (x); | |
4052 | SCM yd = scm_denominator (y); | |
4053 | ||
8f9da340 MW |
4054 | scm_round_divide (scm_product (scm_numerator (x), yd), |
4055 | scm_product (scm_numerator (y), xd), | |
4056 | qp, &r1); | |
03ddd15b | 4057 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
4058 | } |
4059 | ||
4060 | ||
78d3deb1 AW |
4061 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
4062 | (SCM x, SCM y, SCM rest), | |
4063 | "Return the greatest common divisor of all parameter values.\n" | |
4064 | "If called without arguments, 0 is returned.") | |
4065 | #define FUNC_NAME s_scm_i_gcd | |
4066 | { | |
4067 | while (!scm_is_null (rest)) | |
4068 | { x = scm_gcd (x, y); | |
4069 | y = scm_car (rest); | |
4070 | rest = scm_cdr (rest); | |
4071 | } | |
4072 | return scm_gcd (x, y); | |
4073 | } | |
4074 | #undef FUNC_NAME | |
4075 | ||
4076 | #define s_gcd s_scm_i_gcd | |
4077 | #define g_gcd g_scm_i_gcd | |
4078 | ||
0f2d19dd | 4079 | SCM |
6e8d25a6 | 4080 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 4081 | { |
a2dead1b | 4082 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
1dd79792 | 4083 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 4084 | |
a2dead1b | 4085 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4086 | { |
a2dead1b | 4087 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4088 | { |
e25f3727 AW |
4089 | scm_t_inum xx = SCM_I_INUM (x); |
4090 | scm_t_inum yy = SCM_I_INUM (y); | |
4091 | scm_t_inum u = xx < 0 ? -xx : xx; | |
4092 | scm_t_inum v = yy < 0 ? -yy : yy; | |
4093 | scm_t_inum result; | |
a2dead1b | 4094 | if (SCM_UNLIKELY (xx == 0)) |
0aacf84e | 4095 | result = v; |
a2dead1b | 4096 | else if (SCM_UNLIKELY (yy == 0)) |
0aacf84e MD |
4097 | result = u; |
4098 | else | |
4099 | { | |
a2dead1b | 4100 | int k = 0; |
0aacf84e | 4101 | /* Determine a common factor 2^k */ |
a2dead1b | 4102 | while (((u | v) & 1) == 0) |
0aacf84e | 4103 | { |
a2dead1b | 4104 | k++; |
0aacf84e MD |
4105 | u >>= 1; |
4106 | v >>= 1; | |
4107 | } | |
4108 | /* Now, any factor 2^n can be eliminated */ | |
a2dead1b MW |
4109 | if ((u & 1) == 0) |
4110 | while ((u & 1) == 0) | |
4111 | u >>= 1; | |
0aacf84e | 4112 | else |
a2dead1b MW |
4113 | while ((v & 1) == 0) |
4114 | v >>= 1; | |
4115 | /* Both u and v are now odd. Subtract the smaller one | |
4116 | from the larger one to produce an even number, remove | |
4117 | more factors of two, and repeat. */ | |
4118 | while (u != v) | |
0aacf84e | 4119 | { |
a2dead1b MW |
4120 | if (u > v) |
4121 | { | |
4122 | u -= v; | |
4123 | while ((u & 1) == 0) | |
4124 | u >>= 1; | |
4125 | } | |
4126 | else | |
4127 | { | |
4128 | v -= u; | |
4129 | while ((v & 1) == 0) | |
4130 | v >>= 1; | |
4131 | } | |
0aacf84e | 4132 | } |
a2dead1b | 4133 | result = u << k; |
0aacf84e MD |
4134 | } |
4135 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 4136 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4137 | : scm_i_inum2big (result)); |
ca46fb90 RB |
4138 | } |
4139 | else if (SCM_BIGP (y)) | |
4140 | { | |
0bff4dce KR |
4141 | SCM_SWAP (x, y); |
4142 | goto big_inum; | |
ca46fb90 | 4143 | } |
3bbca1f7 MW |
4144 | else if (SCM_REALP (y) && scm_is_integer (y)) |
4145 | goto handle_inexacts; | |
ca46fb90 | 4146 | else |
fa075d40 | 4147 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
f872b822 | 4148 | } |
ca46fb90 RB |
4149 | else if (SCM_BIGP (x)) |
4150 | { | |
e11e83f3 | 4151 | if (SCM_I_INUMP (y)) |
ca46fb90 | 4152 | { |
e25f3727 AW |
4153 | scm_t_bits result; |
4154 | scm_t_inum yy; | |
0bff4dce | 4155 | big_inum: |
e11e83f3 | 4156 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
4157 | if (yy == 0) |
4158 | return scm_abs (x); | |
0aacf84e MD |
4159 | if (yy < 0) |
4160 | yy = -yy; | |
ca46fb90 RB |
4161 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
4162 | scm_remember_upto_here_1 (x); | |
0aacf84e | 4163 | return (SCM_POSFIXABLE (result) |
d956fa6f | 4164 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4165 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
4166 | } |
4167 | else if (SCM_BIGP (y)) | |
4168 | { | |
4169 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
4170 | mpz_gcd (SCM_I_BIG_MPZ (result), |
4171 | SCM_I_BIG_MPZ (x), | |
4172 | SCM_I_BIG_MPZ (y)); | |
4173 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
4174 | return scm_i_normbig (result); |
4175 | } | |
3bbca1f7 MW |
4176 | else if (SCM_REALP (y) && scm_is_integer (y)) |
4177 | goto handle_inexacts; | |
4178 | else | |
056e3470 | 4179 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
3bbca1f7 MW |
4180 | } |
4181 | else if (SCM_REALP (x) && scm_is_integer (x)) | |
4182 | { | |
4183 | if (SCM_I_INUMP (y) || SCM_BIGP (y) | |
4184 | || (SCM_REALP (y) && scm_is_integer (y))) | |
4185 | { | |
4186 | handle_inexacts: | |
4187 | return scm_exact_to_inexact (scm_gcd (scm_inexact_to_exact (x), | |
4188 | scm_inexact_to_exact (y))); | |
4189 | } | |
ca46fb90 | 4190 | else |
fa075d40 | 4191 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
09fb7599 | 4192 | } |
ca46fb90 | 4193 | else |
fa075d40 | 4194 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
4195 | } |
4196 | ||
78d3deb1 AW |
4197 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
4198 | (SCM x, SCM y, SCM rest), | |
4199 | "Return the least common multiple of the arguments.\n" | |
4200 | "If called without arguments, 1 is returned.") | |
4201 | #define FUNC_NAME s_scm_i_lcm | |
4202 | { | |
4203 | while (!scm_is_null (rest)) | |
4204 | { x = scm_lcm (x, y); | |
4205 | y = scm_car (rest); | |
4206 | rest = scm_cdr (rest); | |
4207 | } | |
4208 | return scm_lcm (x, y); | |
4209 | } | |
4210 | #undef FUNC_NAME | |
4211 | ||
4212 | #define s_lcm s_scm_i_lcm | |
4213 | #define g_lcm g_scm_i_lcm | |
4214 | ||
0f2d19dd | 4215 | SCM |
6e8d25a6 | 4216 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4217 | { |
3bbca1f7 MW |
4218 | if (SCM_UNLIKELY (SCM_UNBNDP (n2))) |
4219 | return SCM_UNBNDP (n1) ? SCM_INUM1 : scm_abs (n1); | |
09fb7599 | 4220 | |
3bbca1f7 | 4221 | if (SCM_LIKELY (SCM_I_INUMP (n1))) |
ca46fb90 | 4222 | { |
3bbca1f7 | 4223 | if (SCM_LIKELY (SCM_I_INUMP (n2))) |
ca46fb90 RB |
4224 | { |
4225 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4226 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4227 | return d; |
4228 | else | |
4229 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4230 | } | |
3bbca1f7 | 4231 | else if (SCM_LIKELY (SCM_BIGP (n2))) |
ca46fb90 RB |
4232 | { |
4233 | /* inum n1, big n2 */ | |
4234 | inumbig: | |
4235 | { | |
4236 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4237 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4238 | if (nn1 == 0) return SCM_INUM0; |
4239 | if (nn1 < 0) nn1 = - nn1; | |
4240 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4241 | scm_remember_upto_here_1 (n2); | |
4242 | return result; | |
4243 | } | |
4244 | } | |
3bbca1f7 MW |
4245 | else if (SCM_REALP (n2) && scm_is_integer (n2)) |
4246 | goto handle_inexacts; | |
4247 | else | |
902a4e77 | 4248 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
ca46fb90 | 4249 | } |
3bbca1f7 | 4250 | else if (SCM_LIKELY (SCM_BIGP (n1))) |
ca46fb90 RB |
4251 | { |
4252 | /* big n1 */ | |
e11e83f3 | 4253 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4254 | { |
4255 | SCM_SWAP (n1, n2); | |
4256 | goto inumbig; | |
4257 | } | |
3bbca1f7 | 4258 | else if (SCM_LIKELY (SCM_BIGP (n2))) |
ca46fb90 RB |
4259 | { |
4260 | SCM result = scm_i_mkbig (); | |
4261 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4262 | SCM_I_BIG_MPZ (n1), | |
4263 | SCM_I_BIG_MPZ (n2)); | |
4264 | scm_remember_upto_here_2(n1, n2); | |
4265 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4266 | return result; | |
4267 | } | |
3bbca1f7 MW |
4268 | else if (SCM_REALP (n2) && scm_is_integer (n2)) |
4269 | goto handle_inexacts; | |
4270 | else | |
902a4e77 | 4271 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
f872b822 | 4272 | } |
3bbca1f7 MW |
4273 | else if (SCM_REALP (n1) && scm_is_integer (n1)) |
4274 | { | |
4275 | if (SCM_I_INUMP (n2) || SCM_BIGP (n2) | |
4276 | || (SCM_REALP (n2) && scm_is_integer (n2))) | |
4277 | { | |
4278 | handle_inexacts: | |
4279 | return scm_exact_to_inexact (scm_lcm (scm_inexact_to_exact (n1), | |
4280 | scm_inexact_to_exact (n2))); | |
4281 | } | |
4282 | else | |
902a4e77 | 4283 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
f872b822 | 4284 | } |
3bbca1f7 | 4285 | else |
902a4e77 | 4286 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG1, s_lcm); |
0f2d19dd JB |
4287 | } |
4288 | ||
8a525303 GB |
4289 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4290 | ||
4291 | Logand: | |
4292 | X Y Result Method: | |
4293 | (len) | |
4294 | + + + x (map digit:logand X Y) | |
4295 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4296 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4297 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4298 | ||
4299 | Logior: | |
4300 | X Y Result Method: | |
4301 | ||
4302 | + + + (map digit:logior X Y) | |
4303 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4304 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4305 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4306 | ||
4307 | Logxor: | |
4308 | X Y Result Method: | |
4309 | ||
4310 | + + + (map digit:logxor X Y) | |
4311 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4312 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4313 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4314 | ||
4315 | Logtest: | |
4316 | X Y Result | |
4317 | ||
4318 | + + (any digit:logand X Y) | |
4319 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4320 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4321 | - - #t | |
4322 | ||
4323 | */ | |
4324 | ||
78d3deb1 AW |
4325 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4326 | (SCM x, SCM y, SCM rest), | |
4327 | "Return the bitwise AND of the integer arguments.\n\n" | |
4328 | "@lisp\n" | |
4329 | "(logand) @result{} -1\n" | |
4330 | "(logand 7) @result{} 7\n" | |
4331 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4332 | "@end lisp") | |
4333 | #define FUNC_NAME s_scm_i_logand | |
4334 | { | |
4335 | while (!scm_is_null (rest)) | |
4336 | { x = scm_logand (x, y); | |
4337 | y = scm_car (rest); | |
4338 | rest = scm_cdr (rest); | |
4339 | } | |
4340 | return scm_logand (x, y); | |
4341 | } | |
4342 | #undef FUNC_NAME | |
4343 | ||
4344 | #define s_scm_logand s_scm_i_logand | |
4345 | ||
4346 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4347 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4348 | { |
e25f3727 | 4349 | scm_t_inum nn1; |
9a00c9fc | 4350 | |
0aacf84e MD |
4351 | if (SCM_UNBNDP (n2)) |
4352 | { | |
4353 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4354 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4355 | else if (!SCM_NUMBERP (n1)) |
4356 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4357 | else if (SCM_NUMBERP (n1)) | |
4358 | return n1; | |
4359 | else | |
4360 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4361 | } |
09fb7599 | 4362 | |
e11e83f3 | 4363 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4364 | { |
e11e83f3 MV |
4365 | nn1 = SCM_I_INUM (n1); |
4366 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4367 | { |
e25f3727 | 4368 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4369 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4370 | } |
4371 | else if SCM_BIGP (n2) | |
4372 | { | |
4373 | intbig: | |
2e16a342 | 4374 | if (nn1 == 0) |
0aacf84e MD |
4375 | return SCM_INUM0; |
4376 | { | |
4377 | SCM result_z = scm_i_mkbig (); | |
4378 | mpz_t nn1_z; | |
4379 | mpz_init_set_si (nn1_z, nn1); | |
4380 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4381 | scm_remember_upto_here_1 (n2); | |
4382 | mpz_clear (nn1_z); | |
4383 | return scm_i_normbig (result_z); | |
4384 | } | |
4385 | } | |
4386 | else | |
4387 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4388 | } | |
4389 | else if (SCM_BIGP (n1)) | |
4390 | { | |
e11e83f3 | 4391 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4392 | { |
4393 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4394 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4395 | goto intbig; |
4396 | } | |
4397 | else if (SCM_BIGP (n2)) | |
4398 | { | |
4399 | SCM result_z = scm_i_mkbig (); | |
4400 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4401 | SCM_I_BIG_MPZ (n1), | |
4402 | SCM_I_BIG_MPZ (n2)); | |
4403 | scm_remember_upto_here_2 (n1, n2); | |
4404 | return scm_i_normbig (result_z); | |
4405 | } | |
4406 | else | |
4407 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4408 | } |
0aacf84e | 4409 | else |
09fb7599 | 4410 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4411 | } |
1bbd0b84 | 4412 | #undef FUNC_NAME |
0f2d19dd | 4413 | |
09fb7599 | 4414 | |
78d3deb1 AW |
4415 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4416 | (SCM x, SCM y, SCM rest), | |
4417 | "Return the bitwise OR of the integer arguments.\n\n" | |
4418 | "@lisp\n" | |
4419 | "(logior) @result{} 0\n" | |
4420 | "(logior 7) @result{} 7\n" | |
4421 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4422 | "@end lisp") | |
4423 | #define FUNC_NAME s_scm_i_logior | |
4424 | { | |
4425 | while (!scm_is_null (rest)) | |
4426 | { x = scm_logior (x, y); | |
4427 | y = scm_car (rest); | |
4428 | rest = scm_cdr (rest); | |
4429 | } | |
4430 | return scm_logior (x, y); | |
4431 | } | |
4432 | #undef FUNC_NAME | |
4433 | ||
4434 | #define s_scm_logior s_scm_i_logior | |
4435 | ||
4436 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4437 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4438 | { |
e25f3727 | 4439 | scm_t_inum nn1; |
9a00c9fc | 4440 | |
0aacf84e MD |
4441 | if (SCM_UNBNDP (n2)) |
4442 | { | |
4443 | if (SCM_UNBNDP (n1)) | |
4444 | return SCM_INUM0; | |
4445 | else if (SCM_NUMBERP (n1)) | |
4446 | return n1; | |
4447 | else | |
4448 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4449 | } |
09fb7599 | 4450 | |
e11e83f3 | 4451 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4452 | { |
e11e83f3 MV |
4453 | nn1 = SCM_I_INUM (n1); |
4454 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4455 | { |
e11e83f3 | 4456 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4457 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4458 | } |
4459 | else if (SCM_BIGP (n2)) | |
4460 | { | |
4461 | intbig: | |
4462 | if (nn1 == 0) | |
4463 | return n2; | |
4464 | { | |
4465 | SCM result_z = scm_i_mkbig (); | |
4466 | mpz_t nn1_z; | |
4467 | mpz_init_set_si (nn1_z, nn1); | |
4468 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4469 | scm_remember_upto_here_1 (n2); | |
4470 | mpz_clear (nn1_z); | |
9806de0d | 4471 | return scm_i_normbig (result_z); |
0aacf84e MD |
4472 | } |
4473 | } | |
4474 | else | |
4475 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4476 | } | |
4477 | else if (SCM_BIGP (n1)) | |
4478 | { | |
e11e83f3 | 4479 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4480 | { |
4481 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4482 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4483 | goto intbig; |
4484 | } | |
4485 | else if (SCM_BIGP (n2)) | |
4486 | { | |
4487 | SCM result_z = scm_i_mkbig (); | |
4488 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4489 | SCM_I_BIG_MPZ (n1), | |
4490 | SCM_I_BIG_MPZ (n2)); | |
4491 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4492 | return scm_i_normbig (result_z); |
0aacf84e MD |
4493 | } |
4494 | else | |
4495 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4496 | } |
0aacf84e | 4497 | else |
09fb7599 | 4498 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4499 | } |
1bbd0b84 | 4500 | #undef FUNC_NAME |
0f2d19dd | 4501 | |
09fb7599 | 4502 | |
78d3deb1 AW |
4503 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4504 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4505 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4506 | "set in the result if it is set in an odd number of arguments.\n" | |
4507 | "@lisp\n" | |
4508 | "(logxor) @result{} 0\n" | |
4509 | "(logxor 7) @result{} 7\n" | |
4510 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4511 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4512 | "@end lisp") |
78d3deb1 AW |
4513 | #define FUNC_NAME s_scm_i_logxor |
4514 | { | |
4515 | while (!scm_is_null (rest)) | |
4516 | { x = scm_logxor (x, y); | |
4517 | y = scm_car (rest); | |
4518 | rest = scm_cdr (rest); | |
4519 | } | |
4520 | return scm_logxor (x, y); | |
4521 | } | |
4522 | #undef FUNC_NAME | |
4523 | ||
4524 | #define s_scm_logxor s_scm_i_logxor | |
4525 | ||
4526 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4527 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4528 | { |
e25f3727 | 4529 | scm_t_inum nn1; |
9a00c9fc | 4530 | |
0aacf84e MD |
4531 | if (SCM_UNBNDP (n2)) |
4532 | { | |
4533 | if (SCM_UNBNDP (n1)) | |
4534 | return SCM_INUM0; | |
4535 | else if (SCM_NUMBERP (n1)) | |
4536 | return n1; | |
4537 | else | |
4538 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4539 | } |
09fb7599 | 4540 | |
e11e83f3 | 4541 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4542 | { |
e11e83f3 MV |
4543 | nn1 = SCM_I_INUM (n1); |
4544 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4545 | { |
e25f3727 | 4546 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4547 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4548 | } |
4549 | else if (SCM_BIGP (n2)) | |
4550 | { | |
4551 | intbig: | |
4552 | { | |
4553 | SCM result_z = scm_i_mkbig (); | |
4554 | mpz_t nn1_z; | |
4555 | mpz_init_set_si (nn1_z, nn1); | |
4556 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4557 | scm_remember_upto_here_1 (n2); | |
4558 | mpz_clear (nn1_z); | |
4559 | return scm_i_normbig (result_z); | |
4560 | } | |
4561 | } | |
4562 | else | |
4563 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4564 | } | |
4565 | else if (SCM_BIGP (n1)) | |
4566 | { | |
e11e83f3 | 4567 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4568 | { |
4569 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4570 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4571 | goto intbig; |
4572 | } | |
4573 | else if (SCM_BIGP (n2)) | |
4574 | { | |
4575 | SCM result_z = scm_i_mkbig (); | |
4576 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4577 | SCM_I_BIG_MPZ (n1), | |
4578 | SCM_I_BIG_MPZ (n2)); | |
4579 | scm_remember_upto_here_2 (n1, n2); | |
4580 | return scm_i_normbig (result_z); | |
4581 | } | |
4582 | else | |
4583 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4584 | } |
0aacf84e | 4585 | else |
09fb7599 | 4586 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4587 | } |
1bbd0b84 | 4588 | #undef FUNC_NAME |
0f2d19dd | 4589 | |
09fb7599 | 4590 | |
a1ec6916 | 4591 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4592 | (SCM j, SCM k), |
ba6e7231 KR |
4593 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4594 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4595 | "without actually calculating the @code{logand}, just testing\n" | |
4596 | "for non-zero.\n" | |
4597 | "\n" | |
1e6808ea | 4598 | "@lisp\n" |
b380b885 MD |
4599 | "(logtest #b0100 #b1011) @result{} #f\n" |
4600 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4601 | "@end lisp") |
1bbd0b84 | 4602 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4603 | { |
e25f3727 | 4604 | scm_t_inum nj; |
9a00c9fc | 4605 | |
e11e83f3 | 4606 | if (SCM_I_INUMP (j)) |
0aacf84e | 4607 | { |
e11e83f3 MV |
4608 | nj = SCM_I_INUM (j); |
4609 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4610 | { |
e25f3727 | 4611 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4612 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4613 | } |
4614 | else if (SCM_BIGP (k)) | |
4615 | { | |
4616 | intbig: | |
4617 | if (nj == 0) | |
4618 | return SCM_BOOL_F; | |
4619 | { | |
4620 | SCM result; | |
4621 | mpz_t nj_z; | |
4622 | mpz_init_set_si (nj_z, nj); | |
4623 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4624 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4625 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4626 | mpz_clear (nj_z); |
4627 | return result; | |
4628 | } | |
4629 | } | |
4630 | else | |
4631 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4632 | } | |
4633 | else if (SCM_BIGP (j)) | |
4634 | { | |
e11e83f3 | 4635 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4636 | { |
4637 | SCM_SWAP (j, k); | |
e11e83f3 | 4638 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4639 | goto intbig; |
4640 | } | |
4641 | else if (SCM_BIGP (k)) | |
4642 | { | |
4643 | SCM result; | |
4644 | mpz_t result_z; | |
4645 | mpz_init (result_z); | |
4646 | mpz_and (result_z, | |
4647 | SCM_I_BIG_MPZ (j), | |
4648 | SCM_I_BIG_MPZ (k)); | |
4649 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4650 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4651 | mpz_clear (result_z); |
4652 | return result; | |
4653 | } | |
4654 | else | |
4655 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4656 | } | |
4657 | else | |
4658 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4659 | } |
1bbd0b84 | 4660 | #undef FUNC_NAME |
0f2d19dd | 4661 | |
c1bfcf60 | 4662 | |
a1ec6916 | 4663 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4664 | (SCM index, SCM j), |
ba6e7231 KR |
4665 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4666 | "@var{index} starts from 0 for the least significant bit.\n" | |
4667 | "\n" | |
1e6808ea | 4668 | "@lisp\n" |
b380b885 MD |
4669 | "(logbit? 0 #b1101) @result{} #t\n" |
4670 | "(logbit? 1 #b1101) @result{} #f\n" | |
4671 | "(logbit? 2 #b1101) @result{} #t\n" | |
4672 | "(logbit? 3 #b1101) @result{} #t\n" | |
4673 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4674 | "@end lisp") |
1bbd0b84 | 4675 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4676 | { |
78166ad5 | 4677 | unsigned long int iindex; |
5efd3c7d | 4678 | iindex = scm_to_ulong (index); |
78166ad5 | 4679 | |
e11e83f3 | 4680 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4681 | { |
4682 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4683 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4684 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4685 | } |
0aacf84e MD |
4686 | else if (SCM_BIGP (j)) |
4687 | { | |
4688 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4689 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4690 | return scm_from_bool (val); |
0aacf84e MD |
4691 | } |
4692 | else | |
78166ad5 | 4693 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4694 | } |
1bbd0b84 | 4695 | #undef FUNC_NAME |
0f2d19dd | 4696 | |
78166ad5 | 4697 | |
a1ec6916 | 4698 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4699 | (SCM n), |
4d814788 | 4700 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4701 | "argument.\n" |
4702 | "\n" | |
b380b885 MD |
4703 | "@lisp\n" |
4704 | "(number->string (lognot #b10000000) 2)\n" | |
4705 | " @result{} \"-10000001\"\n" | |
4706 | "(number->string (lognot #b0) 2)\n" | |
4707 | " @result{} \"-1\"\n" | |
1e6808ea | 4708 | "@end lisp") |
1bbd0b84 | 4709 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4710 | { |
e11e83f3 | 4711 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4712 | /* No overflow here, just need to toggle all the bits making up the inum. |
4713 | Enhancement: No need to strip the tag and add it back, could just xor | |
4714 | a block of 1 bits, if that worked with the various debug versions of | |
4715 | the SCM typedef. */ | |
e11e83f3 | 4716 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4717 | |
4718 | } else if (SCM_BIGP (n)) { | |
4719 | SCM result = scm_i_mkbig (); | |
4720 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4721 | scm_remember_upto_here_1 (n); | |
4722 | return result; | |
4723 | ||
4724 | } else { | |
4725 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4726 | } | |
0f2d19dd | 4727 | } |
1bbd0b84 | 4728 | #undef FUNC_NAME |
0f2d19dd | 4729 | |
518b7508 KR |
4730 | /* returns 0 if IN is not an integer. OUT must already be |
4731 | initialized. */ | |
4732 | static int | |
4733 | coerce_to_big (SCM in, mpz_t out) | |
4734 | { | |
4735 | if (SCM_BIGP (in)) | |
4736 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4737 | else if (SCM_I_INUMP (in)) |
4738 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4739 | else |
4740 | return 0; | |
4741 | ||
4742 | return 1; | |
4743 | } | |
4744 | ||
d885e204 | 4745 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4746 | (SCM n, SCM k, SCM m), |
4747 | "Return @var{n} raised to the integer exponent\n" | |
4748 | "@var{k}, modulo @var{m}.\n" | |
4749 | "\n" | |
4750 | "@lisp\n" | |
4751 | "(modulo-expt 2 3 5)\n" | |
4752 | " @result{} 3\n" | |
4753 | "@end lisp") | |
d885e204 | 4754 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4755 | { |
4756 | mpz_t n_tmp; | |
4757 | mpz_t k_tmp; | |
4758 | mpz_t m_tmp; | |
4759 | ||
4760 | /* There are two classes of error we might encounter -- | |
4761 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4762 | and | |
4763 | 2) wrong-type errors, which of course we'll report by calling | |
4764 | SCM_WRONG_TYPE_ARG. | |
4765 | We don't report those errors immediately, however; instead we do | |
4766 | some cleanup first. These variables tell us which error (if | |
4767 | any) we should report after cleaning up. | |
4768 | */ | |
4769 | int report_overflow = 0; | |
4770 | ||
4771 | int position_of_wrong_type = 0; | |
4772 | SCM value_of_wrong_type = SCM_INUM0; | |
4773 | ||
4774 | SCM result = SCM_UNDEFINED; | |
4775 | ||
4776 | mpz_init (n_tmp); | |
4777 | mpz_init (k_tmp); | |
4778 | mpz_init (m_tmp); | |
4779 | ||
bc36d050 | 4780 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4781 | { |
4782 | report_overflow = 1; | |
4783 | goto cleanup; | |
4784 | } | |
4785 | ||
4786 | if (!coerce_to_big (n, n_tmp)) | |
4787 | { | |
4788 | value_of_wrong_type = n; | |
4789 | position_of_wrong_type = 1; | |
4790 | goto cleanup; | |
4791 | } | |
4792 | ||
4793 | if (!coerce_to_big (k, k_tmp)) | |
4794 | { | |
4795 | value_of_wrong_type = k; | |
4796 | position_of_wrong_type = 2; | |
4797 | goto cleanup; | |
4798 | } | |
4799 | ||
4800 | if (!coerce_to_big (m, m_tmp)) | |
4801 | { | |
4802 | value_of_wrong_type = m; | |
4803 | position_of_wrong_type = 3; | |
4804 | goto cleanup; | |
4805 | } | |
4806 | ||
4807 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4808 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4809 | doesn't exist (or is not unique). Since exceptions are hard to | |
4810 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4811 | a simple failure code, which is easy to handle. */ | |
4812 | ||
4813 | if (-1 == mpz_sgn (k_tmp)) | |
4814 | { | |
4815 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4816 | { | |
4817 | report_overflow = 1; | |
4818 | goto cleanup; | |
4819 | } | |
4820 | mpz_neg (k_tmp, k_tmp); | |
4821 | } | |
4822 | ||
4823 | result = scm_i_mkbig (); | |
4824 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4825 | n_tmp, | |
4826 | k_tmp, | |
4827 | m_tmp); | |
b7b8c575 KR |
4828 | |
4829 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4830 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4831 | ||
518b7508 KR |
4832 | cleanup: |
4833 | mpz_clear (m_tmp); | |
4834 | mpz_clear (k_tmp); | |
4835 | mpz_clear (n_tmp); | |
4836 | ||
4837 | if (report_overflow) | |
4838 | scm_num_overflow (FUNC_NAME); | |
4839 | ||
4840 | if (position_of_wrong_type) | |
4841 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4842 | value_of_wrong_type); | |
4843 | ||
4844 | return scm_i_normbig (result); | |
4845 | } | |
4846 | #undef FUNC_NAME | |
4847 | ||
a1ec6916 | 4848 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4849 | (SCM n, SCM k), |
ba6e7231 KR |
4850 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4851 | "exact integer, @var{n} can be any number.\n" | |
4852 | "\n" | |
2519490c MW |
4853 | "Negative @var{k} is supported, and results in\n" |
4854 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4855 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4856 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4857 | "\n" |
b380b885 | 4858 | "@lisp\n" |
ba6e7231 KR |
4859 | "(integer-expt 2 5) @result{} 32\n" |
4860 | "(integer-expt -3 3) @result{} -27\n" | |
4861 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4862 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4863 | "@end lisp") |
1bbd0b84 | 4864 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4865 | { |
e25f3727 | 4866 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4867 | SCM z_i2 = SCM_BOOL_F; |
4868 | int i2_is_big = 0; | |
d956fa6f | 4869 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4870 | |
bfe1f03a MW |
4871 | /* Specifically refrain from checking the type of the first argument. |
4872 | This allows us to exponentiate any object that can be multiplied. | |
4873 | If we must raise to a negative power, we must also be able to | |
4874 | take its reciprocal. */ | |
4875 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4876 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4877 | |
bfe1f03a MW |
4878 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4879 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4880 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4881 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4882 | /* The next check is necessary only because R6RS specifies different | |
4883 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4884 | we simply skip this case and move on. */ | |
4885 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4886 | { | |
4887 | /* k cannot be 0 at this point, because we | |
4888 | have already checked for that case above */ | |
4889 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4890 | return n; |
4891 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4892 | return scm_nan (); | |
4893 | } | |
a285b18c MW |
4894 | else if (SCM_FRACTIONP (n)) |
4895 | { | |
4896 | /* Optimize the fraction case by (a/b)^k ==> (a^k)/(b^k), to avoid | |
4897 | needless reduction of intermediate products to lowest terms. | |
4898 | If a and b have no common factors, then a^k and b^k have no | |
4899 | common factors. Use 'scm_i_make_ratio_already_reduced' to | |
4900 | construct the final result, so that no gcd computations are | |
4901 | needed to exponentiate a fraction. */ | |
4902 | if (scm_is_true (scm_positive_p (k))) | |
4903 | return scm_i_make_ratio_already_reduced | |
4904 | (scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k), | |
4905 | scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k)); | |
4906 | else | |
4907 | { | |
4908 | k = scm_difference (k, SCM_UNDEFINED); | |
4909 | return scm_i_make_ratio_already_reduced | |
4910 | (scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k), | |
4911 | scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k)); | |
4912 | } | |
4913 | } | |
ca46fb90 | 4914 | |
e11e83f3 MV |
4915 | if (SCM_I_INUMP (k)) |
4916 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4917 | else if (SCM_BIGP (k)) |
4918 | { | |
4919 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4920 | scm_remember_upto_here_1 (k); |
4921 | i2_is_big = 1; | |
4922 | } | |
2830fd91 | 4923 | else |
ca46fb90 RB |
4924 | SCM_WRONG_TYPE_ARG (2, k); |
4925 | ||
4926 | if (i2_is_big) | |
f872b822 | 4927 | { |
ca46fb90 RB |
4928 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4929 | { | |
4930 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4931 | n = scm_divide (n, SCM_UNDEFINED); | |
4932 | } | |
4933 | while (1) | |
4934 | { | |
4935 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4936 | { | |
ca46fb90 RB |
4937 | return acc; |
4938 | } | |
4939 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4940 | { | |
ca46fb90 RB |
4941 | return scm_product (acc, n); |
4942 | } | |
4943 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4944 | acc = scm_product (acc, n); | |
4945 | n = scm_product (n, n); | |
4946 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4947 | } | |
f872b822 | 4948 | } |
ca46fb90 | 4949 | else |
f872b822 | 4950 | { |
ca46fb90 RB |
4951 | if (i2 < 0) |
4952 | { | |
4953 | i2 = -i2; | |
4954 | n = scm_divide (n, SCM_UNDEFINED); | |
4955 | } | |
4956 | while (1) | |
4957 | { | |
4958 | if (0 == i2) | |
4959 | return acc; | |
4960 | if (1 == i2) | |
4961 | return scm_product (acc, n); | |
4962 | if (i2 & 1) | |
4963 | acc = scm_product (acc, n); | |
4964 | n = scm_product (n, n); | |
4965 | i2 >>= 1; | |
4966 | } | |
f872b822 | 4967 | } |
0f2d19dd | 4968 | } |
1bbd0b84 | 4969 | #undef FUNC_NAME |
0f2d19dd | 4970 | |
e08a12b5 MW |
4971 | /* Efficiently compute (N * 2^COUNT), |
4972 | where N is an exact integer, and COUNT > 0. */ | |
4973 | static SCM | |
4974 | left_shift_exact_integer (SCM n, long count) | |
4975 | { | |
4976 | if (SCM_I_INUMP (n)) | |
4977 | { | |
4978 | scm_t_inum nn = SCM_I_INUM (n); | |
4979 | ||
8df68898 | 4980 | /* Left shift of count >= SCM_I_FIXNUM_BIT-1 will almost[*] always |
e08a12b5 MW |
4981 | overflow a non-zero fixnum. For smaller shifts we check the |
4982 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4983 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
8df68898 MW |
4984 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". |
4985 | ||
4986 | [*] There's one exception: | |
4987 | (-1) << SCM_I_FIXNUM_BIT-1 == SCM_MOST_NEGATIVE_FIXNUM */ | |
e08a12b5 MW |
4988 | |
4989 | if (nn == 0) | |
4990 | return n; | |
4991 | else if (count < SCM_I_FIXNUM_BIT-1 && | |
4992 | ((scm_t_bits) (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - count)) + 1) | |
4993 | <= 1)) | |
4994 | return SCM_I_MAKINUM (nn << count); | |
4995 | else | |
4996 | { | |
4997 | SCM result = scm_i_inum2big (nn); | |
4998 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
4999 | count); | |
8df68898 | 5000 | return scm_i_normbig (result); |
1ea0803e | 5001 | } |
e08a12b5 MW |
5002 | } |
5003 | else if (SCM_BIGP (n)) | |
5004 | { | |
5005 | SCM result = scm_i_mkbig (); | |
5006 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), count); | |
5007 | scm_remember_upto_here_1 (n); | |
5008 | return result; | |
5009 | } | |
5010 | else | |
6f82b8f6 | 5011 | assert (0); |
e08a12b5 MW |
5012 | } |
5013 | ||
5014 | /* Efficiently compute floor (N / 2^COUNT), | |
5015 | where N is an exact integer and COUNT > 0. */ | |
5016 | static SCM | |
5017 | floor_right_shift_exact_integer (SCM n, long count) | |
5018 | { | |
5019 | if (SCM_I_INUMP (n)) | |
5020 | { | |
5021 | scm_t_inum nn = SCM_I_INUM (n); | |
5022 | ||
5023 | if (count >= SCM_I_FIXNUM_BIT) | |
5024 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM (-1)); | |
5025 | else | |
5026 | return SCM_I_MAKINUM (SCM_SRS (nn, count)); | |
5027 | } | |
5028 | else if (SCM_BIGP (n)) | |
5029 | { | |
5030 | SCM result = scm_i_mkbig (); | |
5031 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
5032 | count); | |
5033 | scm_remember_upto_here_1 (n); | |
5034 | return scm_i_normbig (result); | |
5035 | } | |
5036 | else | |
6f82b8f6 | 5037 | assert (0); |
e08a12b5 MW |
5038 | } |
5039 | ||
5040 | /* Efficiently compute round (N / 2^COUNT), | |
5041 | where N is an exact integer and COUNT > 0. */ | |
5042 | static SCM | |
5043 | round_right_shift_exact_integer (SCM n, long count) | |
5044 | { | |
5045 | if (SCM_I_INUMP (n)) | |
5046 | { | |
5047 | if (count >= SCM_I_FIXNUM_BIT) | |
5048 | return SCM_INUM0; | |
5049 | else | |
5050 | { | |
5051 | scm_t_inum nn = SCM_I_INUM (n); | |
5052 | scm_t_inum qq = SCM_SRS (nn, count); | |
5053 | ||
5054 | if (0 == (nn & (1L << (count-1)))) | |
5055 | return SCM_I_MAKINUM (qq); /* round down */ | |
5056 | else if (nn & ((1L << (count-1)) - 1)) | |
5057 | return SCM_I_MAKINUM (qq + 1); /* round up */ | |
5058 | else | |
5059 | return SCM_I_MAKINUM ((~1L) & (qq + 1)); /* round to even */ | |
5060 | } | |
5061 | } | |
5062 | else if (SCM_BIGP (n)) | |
5063 | { | |
5064 | SCM q = scm_i_mkbig (); | |
5065 | ||
5066 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), count); | |
5067 | if (mpz_tstbit (SCM_I_BIG_MPZ (n), count-1) | |
5068 | && (mpz_odd_p (SCM_I_BIG_MPZ (q)) | |
5069 | || (mpz_scan1 (SCM_I_BIG_MPZ (n), 0) < count-1))) | |
5070 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
5071 | scm_remember_upto_here_1 (n); | |
5072 | return scm_i_normbig (q); | |
5073 | } | |
5074 | else | |
6f82b8f6 | 5075 | assert (0); |
e08a12b5 MW |
5076 | } |
5077 | ||
a1ec6916 | 5078 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
e08a12b5 MW |
5079 | (SCM n, SCM count), |
5080 | "Return @math{floor(@var{n} * 2^@var{count})}.\n" | |
5081 | "@var{n} and @var{count} must be exact integers.\n" | |
1e6808ea | 5082 | "\n" |
e08a12b5 MW |
5083 | "With @var{n} viewed as an infinite-precision twos-complement\n" |
5084 | "integer, @code{ash} means a left shift introducing zero bits\n" | |
5085 | "when @var{count} is positive, or a right shift dropping bits\n" | |
5086 | "when @var{count} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 5087 | "\n" |
b380b885 | 5088 | "@lisp\n" |
1e6808ea MG |
5089 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
5090 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
5091 | "\n" |
5092 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
5093 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 5094 | "@end lisp") |
1bbd0b84 | 5095 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 5096 | { |
e08a12b5 | 5097 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) |
788aca27 | 5098 | { |
e08a12b5 | 5099 | long bits_to_shift = scm_to_long (count); |
788aca27 KR |
5100 | |
5101 | if (bits_to_shift > 0) | |
e08a12b5 MW |
5102 | return left_shift_exact_integer (n, bits_to_shift); |
5103 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
5104 | return floor_right_shift_exact_integer (n, -bits_to_shift); | |
788aca27 | 5105 | else |
e08a12b5 | 5106 | return n; |
788aca27 | 5107 | } |
e08a12b5 MW |
5108 | else |
5109 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
5110 | } | |
5111 | #undef FUNC_NAME | |
788aca27 | 5112 | |
e08a12b5 MW |
5113 | SCM_DEFINE (scm_round_ash, "round-ash", 2, 0, 0, |
5114 | (SCM n, SCM count), | |
5115 | "Return @math{round(@var{n} * 2^@var{count})}.\n" | |
5116 | "@var{n} and @var{count} must be exact integers.\n" | |
5117 | "\n" | |
5118 | "With @var{n} viewed as an infinite-precision twos-complement\n" | |
5119 | "integer, @code{round-ash} means a left shift introducing zero\n" | |
5120 | "bits when @var{count} is positive, or a right shift rounding\n" | |
5121 | "to the nearest integer (with ties going to the nearest even\n" | |
5122 | "integer) when @var{count} is negative. This is a rounded\n" | |
5123 | "``arithmetic'' shift.\n" | |
5124 | "\n" | |
5125 | "@lisp\n" | |
5126 | "(number->string (round-ash #b1 3) 2) @result{} \"1000\"\n" | |
5127 | "(number->string (round-ash #b1010 -1) 2) @result{} \"101\"\n" | |
5128 | "(number->string (round-ash #b1010 -2) 2) @result{} \"10\"\n" | |
5129 | "(number->string (round-ash #b1011 -2) 2) @result{} \"11\"\n" | |
5130 | "(number->string (round-ash #b1101 -2) 2) @result{} \"11\"\n" | |
5131 | "(number->string (round-ash #b1110 -2) 2) @result{} \"100\"\n" | |
5132 | "@end lisp") | |
5133 | #define FUNC_NAME s_scm_round_ash | |
5134 | { | |
5135 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) | |
5136 | { | |
5137 | long bits_to_shift = scm_to_long (count); | |
788aca27 | 5138 | |
e08a12b5 MW |
5139 | if (bits_to_shift > 0) |
5140 | return left_shift_exact_integer (n, bits_to_shift); | |
5141 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
5142 | return round_right_shift_exact_integer (n, -bits_to_shift); | |
ca46fb90 | 5143 | else |
e08a12b5 | 5144 | return n; |
ca46fb90 RB |
5145 | } |
5146 | else | |
e08a12b5 | 5147 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5148 | } |
1bbd0b84 | 5149 | #undef FUNC_NAME |
0f2d19dd | 5150 | |
3c9f20f8 | 5151 | |
a1ec6916 | 5152 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 5153 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
5154 | "Return the integer composed of the @var{start} (inclusive)\n" |
5155 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
5156 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
5157 | "\n" | |
b380b885 MD |
5158 | "@lisp\n" |
5159 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
5160 | " @result{} \"1010\"\n" | |
5161 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
5162 | " @result{} \"10110\"\n" | |
5163 | "@end lisp") | |
1bbd0b84 | 5164 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 5165 | { |
7f848242 | 5166 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
5167 | istart = scm_to_ulong (start); |
5168 | iend = scm_to_ulong (end); | |
c1bfcf60 | 5169 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 5170 | |
7f848242 KR |
5171 | /* how many bits to keep */ |
5172 | bits = iend - istart; | |
5173 | ||
e11e83f3 | 5174 | if (SCM_I_INUMP (n)) |
0aacf84e | 5175 | { |
e25f3727 | 5176 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
5177 | |
5178 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 5179 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 5180 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 5181 | |
0aacf84e MD |
5182 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
5183 | { | |
5184 | /* Since we emulate two's complement encoded numbers, this | |
5185 | * special case requires us to produce a result that has | |
7f848242 | 5186 | * more bits than can be stored in a fixnum. |
0aacf84e | 5187 | */ |
e25f3727 | 5188 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
5189 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
5190 | bits); | |
5191 | return result; | |
0aacf84e | 5192 | } |
ac0c002c | 5193 | |
7f848242 | 5194 | /* mask down to requisite bits */ |
857ae6af | 5195 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 5196 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
5197 | } |
5198 | else if (SCM_BIGP (n)) | |
ac0c002c | 5199 | { |
7f848242 KR |
5200 | SCM result; |
5201 | if (bits == 1) | |
5202 | { | |
d956fa6f | 5203 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
5204 | } |
5205 | else | |
5206 | { | |
5207 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
5208 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
5209 | such bits into a ulong. */ | |
5210 | result = scm_i_mkbig (); | |
5211 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
5212 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
5213 | result = scm_i_normbig (result); | |
5214 | } | |
5215 | scm_remember_upto_here_1 (n); | |
5216 | return result; | |
ac0c002c | 5217 | } |
0aacf84e | 5218 | else |
78166ad5 | 5219 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5220 | } |
1bbd0b84 | 5221 | #undef FUNC_NAME |
0f2d19dd | 5222 | |
7f848242 | 5223 | |
e4755e5c JB |
5224 | static const char scm_logtab[] = { |
5225 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
5226 | }; | |
1cc91f1b | 5227 | |
a1ec6916 | 5228 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 5229 | (SCM n), |
1e6808ea MG |
5230 | "Return the number of bits in integer @var{n}. If integer is\n" |
5231 | "positive, the 1-bits in its binary representation are counted.\n" | |
5232 | "If negative, the 0-bits in its two's-complement binary\n" | |
5233 | "representation are counted. If 0, 0 is returned.\n" | |
5234 | "\n" | |
b380b885 MD |
5235 | "@lisp\n" |
5236 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
5237 | " @result{} 4\n" |
5238 | "(logcount 0)\n" | |
5239 | " @result{} 0\n" | |
5240 | "(logcount -2)\n" | |
5241 | " @result{} 1\n" | |
5242 | "@end lisp") | |
5243 | #define FUNC_NAME s_scm_logcount | |
5244 | { | |
e11e83f3 | 5245 | if (SCM_I_INUMP (n)) |
f872b822 | 5246 | { |
e25f3727 AW |
5247 | unsigned long c = 0; |
5248 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
5249 | if (nn < 0) |
5250 | nn = -1 - nn; | |
5251 | while (nn) | |
5252 | { | |
5253 | c += scm_logtab[15 & nn]; | |
5254 | nn >>= 4; | |
5255 | } | |
d956fa6f | 5256 | return SCM_I_MAKINUM (c); |
f872b822 | 5257 | } |
ca46fb90 | 5258 | else if (SCM_BIGP (n)) |
f872b822 | 5259 | { |
ca46fb90 | 5260 | unsigned long count; |
713a4259 KR |
5261 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
5262 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 5263 | else |
713a4259 KR |
5264 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
5265 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5266 | return SCM_I_MAKINUM (count); |
f872b822 | 5267 | } |
ca46fb90 RB |
5268 | else |
5269 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 5270 | } |
ca46fb90 | 5271 | #undef FUNC_NAME |
0f2d19dd JB |
5272 | |
5273 | ||
ca46fb90 RB |
5274 | static const char scm_ilentab[] = { |
5275 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
5276 | }; | |
5277 | ||
0f2d19dd | 5278 | |
ca46fb90 RB |
5279 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
5280 | (SCM n), | |
5281 | "Return the number of bits necessary to represent @var{n}.\n" | |
5282 | "\n" | |
5283 | "@lisp\n" | |
5284 | "(integer-length #b10101010)\n" | |
5285 | " @result{} 8\n" | |
5286 | "(integer-length 0)\n" | |
5287 | " @result{} 0\n" | |
5288 | "(integer-length #b1111)\n" | |
5289 | " @result{} 4\n" | |
5290 | "@end lisp") | |
5291 | #define FUNC_NAME s_scm_integer_length | |
5292 | { | |
e11e83f3 | 5293 | if (SCM_I_INUMP (n)) |
0aacf84e | 5294 | { |
e25f3727 | 5295 | unsigned long c = 0; |
0aacf84e | 5296 | unsigned int l = 4; |
e25f3727 | 5297 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
5298 | if (nn < 0) |
5299 | nn = -1 - nn; | |
5300 | while (nn) | |
5301 | { | |
5302 | c += 4; | |
5303 | l = scm_ilentab [15 & nn]; | |
5304 | nn >>= 4; | |
5305 | } | |
d956fa6f | 5306 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
5307 | } |
5308 | else if (SCM_BIGP (n)) | |
5309 | { | |
5310 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
5311 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
5312 | 1 too big, so check for that and adjust. */ | |
5313 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
5314 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
5315 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
5316 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
5317 | size--; | |
5318 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5319 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
5320 | } |
5321 | else | |
ca46fb90 | 5322 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5323 | } |
5324 | #undef FUNC_NAME | |
0f2d19dd JB |
5325 | |
5326 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5327 | #define SCM_MAX_DBL_RADIX 36 |
5328 | ||
0b799eea | 5329 | /* use this array as a way to generate a single digit */ |
9b5fcde6 | 5330 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5331 | |
1ea37620 MW |
5332 | static mpz_t dbl_minimum_normal_mantissa; |
5333 | ||
1be6b49c | 5334 | static size_t |
1ea37620 | 5335 | idbl2str (double dbl, char *a, int radix) |
0f2d19dd | 5336 | { |
1ea37620 | 5337 | int ch = 0; |
0b799eea | 5338 | |
1ea37620 MW |
5339 | if (radix < 2 || radix > SCM_MAX_DBL_RADIX) |
5340 | /* revert to existing behavior */ | |
5341 | radix = 10; | |
0f2d19dd | 5342 | |
1ea37620 | 5343 | if (isinf (dbl)) |
abb7e44d | 5344 | { |
1ea37620 MW |
5345 | strcpy (a, (dbl > 0.0) ? "+inf.0" : "-inf.0"); |
5346 | return 6; | |
abb7e44d | 5347 | } |
1ea37620 MW |
5348 | else if (dbl > 0.0) |
5349 | ; | |
5350 | else if (dbl < 0.0) | |
7351e207 | 5351 | { |
1ea37620 MW |
5352 | dbl = -dbl; |
5353 | a[ch++] = '-'; | |
7351e207 | 5354 | } |
1ea37620 | 5355 | else if (dbl == 0.0) |
7351e207 | 5356 | { |
e1592f8a | 5357 | if (copysign (1.0, dbl) < 0.0) |
1ea37620 MW |
5358 | a[ch++] = '-'; |
5359 | strcpy (a + ch, "0.0"); | |
5360 | return ch + 3; | |
7351e207 | 5361 | } |
1ea37620 | 5362 | else if (isnan (dbl)) |
f872b822 | 5363 | { |
1ea37620 MW |
5364 | strcpy (a, "+nan.0"); |
5365 | return 6; | |
f872b822 | 5366 | } |
7351e207 | 5367 | |
1ea37620 MW |
5368 | /* Algorithm taken from "Printing Floating-Point Numbers Quickly and |
5369 | Accurately" by Robert G. Burger and R. Kent Dybvig */ | |
5370 | { | |
5371 | int e, k; | |
5372 | mpz_t f, r, s, mplus, mminus, hi, digit; | |
5373 | int f_is_even, f_is_odd; | |
8150dfa1 | 5374 | int expon; |
1ea37620 MW |
5375 | int show_exp = 0; |
5376 | ||
5377 | mpz_inits (f, r, s, mplus, mminus, hi, digit, NULL); | |
5378 | mpz_set_d (f, ldexp (frexp (dbl, &e), DBL_MANT_DIG)); | |
5379 | if (e < DBL_MIN_EXP) | |
5380 | { | |
5381 | mpz_tdiv_q_2exp (f, f, DBL_MIN_EXP - e); | |
5382 | e = DBL_MIN_EXP; | |
5383 | } | |
5384 | e -= DBL_MANT_DIG; | |
0b799eea | 5385 | |
1ea37620 MW |
5386 | f_is_even = !mpz_odd_p (f); |
5387 | f_is_odd = !f_is_even; | |
0b799eea | 5388 | |
1ea37620 MW |
5389 | /* Initialize r, s, mplus, and mminus according |
5390 | to Table 1 from the paper. */ | |
5391 | if (e < 0) | |
5392 | { | |
5393 | mpz_set_ui (mminus, 1); | |
5394 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0 | |
5395 | || e == DBL_MIN_EXP - DBL_MANT_DIG) | |
5396 | { | |
5397 | mpz_set_ui (mplus, 1); | |
5398 | mpz_mul_2exp (r, f, 1); | |
5399 | mpz_mul_2exp (s, mminus, 1 - e); | |
5400 | } | |
5401 | else | |
5402 | { | |
5403 | mpz_set_ui (mplus, 2); | |
5404 | mpz_mul_2exp (r, f, 2); | |
5405 | mpz_mul_2exp (s, mminus, 2 - e); | |
5406 | } | |
5407 | } | |
5408 | else | |
5409 | { | |
5410 | mpz_set_ui (mminus, 1); | |
5411 | mpz_mul_2exp (mminus, mminus, e); | |
5412 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0) | |
5413 | { | |
5414 | mpz_set (mplus, mminus); | |
5415 | mpz_mul_2exp (r, f, 1 + e); | |
5416 | mpz_set_ui (s, 2); | |
5417 | } | |
5418 | else | |
5419 | { | |
5420 | mpz_mul_2exp (mplus, mminus, 1); | |
5421 | mpz_mul_2exp (r, f, 2 + e); | |
5422 | mpz_set_ui (s, 4); | |
5423 | } | |
5424 | } | |
0b799eea | 5425 | |
1ea37620 MW |
5426 | /* Find the smallest k such that: |
5427 | (r + mplus) / s < radix^k (if f is even) | |
5428 | (r + mplus) / s <= radix^k (if f is odd) */ | |
f872b822 | 5429 | { |
1ea37620 MW |
5430 | /* IMPROVE-ME: Make an initial guess to speed this up */ |
5431 | mpz_add (hi, r, mplus); | |
5432 | k = 0; | |
5433 | while (mpz_cmp (hi, s) >= f_is_odd) | |
5434 | { | |
5435 | mpz_mul_ui (s, s, radix); | |
5436 | k++; | |
5437 | } | |
5438 | if (k == 0) | |
5439 | { | |
5440 | mpz_mul_ui (hi, hi, radix); | |
5441 | while (mpz_cmp (hi, s) < f_is_odd) | |
5442 | { | |
5443 | mpz_mul_ui (r, r, radix); | |
5444 | mpz_mul_ui (mplus, mplus, radix); | |
5445 | mpz_mul_ui (mminus, mminus, radix); | |
5446 | mpz_mul_ui (hi, hi, radix); | |
5447 | k--; | |
5448 | } | |
5449 | } | |
cda139a7 | 5450 | } |
f872b822 | 5451 | |
8150dfa1 MW |
5452 | expon = k - 1; |
5453 | if (k <= 0) | |
1ea37620 | 5454 | { |
8150dfa1 MW |
5455 | if (k <= -3) |
5456 | { | |
5457 | /* Use scientific notation */ | |
5458 | show_exp = 1; | |
5459 | k = 1; | |
5460 | } | |
5461 | else | |
5462 | { | |
5463 | int i; | |
0f2d19dd | 5464 | |
8150dfa1 MW |
5465 | /* Print leading zeroes */ |
5466 | a[ch++] = '0'; | |
5467 | a[ch++] = '.'; | |
5468 | for (i = 0; i > k; i--) | |
5469 | a[ch++] = '0'; | |
5470 | } | |
1ea37620 MW |
5471 | } |
5472 | ||
5473 | for (;;) | |
5474 | { | |
5475 | int end_1_p, end_2_p; | |
5476 | int d; | |
5477 | ||
5478 | mpz_mul_ui (mplus, mplus, radix); | |
5479 | mpz_mul_ui (mminus, mminus, radix); | |
5480 | mpz_mul_ui (r, r, radix); | |
5481 | mpz_fdiv_qr (digit, r, r, s); | |
5482 | d = mpz_get_ui (digit); | |
5483 | ||
5484 | mpz_add (hi, r, mplus); | |
5485 | end_1_p = (mpz_cmp (r, mminus) < f_is_even); | |
5486 | end_2_p = (mpz_cmp (s, hi) < f_is_even); | |
5487 | if (end_1_p || end_2_p) | |
5488 | { | |
5489 | mpz_mul_2exp (r, r, 1); | |
5490 | if (!end_2_p) | |
5491 | ; | |
5492 | else if (!end_1_p) | |
5493 | d++; | |
5494 | else if (mpz_cmp (r, s) >= !(d & 1)) | |
5495 | d++; | |
5496 | a[ch++] = number_chars[d]; | |
5497 | if (--k == 0) | |
5498 | a[ch++] = '.'; | |
5499 | break; | |
5500 | } | |
5501 | else | |
5502 | { | |
5503 | a[ch++] = number_chars[d]; | |
5504 | if (--k == 0) | |
5505 | a[ch++] = '.'; | |
5506 | } | |
5507 | } | |
5508 | ||
5509 | if (k > 0) | |
5510 | { | |
8150dfa1 MW |
5511 | if (expon >= 7 && k >= 4 && expon >= k) |
5512 | { | |
5513 | /* Here we would have to print more than three zeroes | |
5514 | followed by a decimal point and another zero. It | |
5515 | makes more sense to use scientific notation. */ | |
5516 | ||
5517 | /* Adjust k to what it would have been if we had chosen | |
5518 | scientific notation from the beginning. */ | |
5519 | k -= expon; | |
5520 | ||
5521 | /* k will now be <= 0, with magnitude equal to the number of | |
5522 | digits that we printed which should now be put after the | |
5523 | decimal point. */ | |
5524 | ||
5525 | /* Insert a decimal point */ | |
5526 | memmove (a + ch + k + 1, a + ch + k, -k); | |
5527 | a[ch + k] = '.'; | |
5528 | ch++; | |
5529 | ||
5530 | show_exp = 1; | |
5531 | } | |
5532 | else | |
5533 | { | |
5534 | for (; k > 0; k--) | |
5535 | a[ch++] = '0'; | |
5536 | a[ch++] = '.'; | |
5537 | } | |
1ea37620 MW |
5538 | } |
5539 | ||
5540 | if (k == 0) | |
5541 | a[ch++] = '0'; | |
5542 | ||
5543 | if (show_exp) | |
5544 | { | |
5545 | a[ch++] = 'e'; | |
8150dfa1 | 5546 | ch += scm_iint2str (expon, radix, a + ch); |
1ea37620 MW |
5547 | } |
5548 | ||
5549 | mpz_clears (f, r, s, mplus, mminus, hi, digit, NULL); | |
5550 | } | |
0f2d19dd JB |
5551 | return ch; |
5552 | } | |
5553 | ||
7a1aba42 MV |
5554 | |
5555 | static size_t | |
5556 | icmplx2str (double real, double imag, char *str, int radix) | |
5557 | { | |
5558 | size_t i; | |
c7218482 | 5559 | double sgn; |
7a1aba42 MV |
5560 | |
5561 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5562 | #ifdef HAVE_COPYSIGN |
5563 | sgn = copysign (1.0, imag); | |
5564 | #else | |
5565 | sgn = imag; | |
5566 | #endif | |
5567 | /* Don't output a '+' for negative numbers or for Inf and | |
5568 | NaN. They will provide their own sign. */ | |
19374ad2 | 5569 | if (sgn >= 0 && isfinite (imag)) |
c7218482 MW |
5570 | str[i++] = '+'; |
5571 | i += idbl2str (imag, &str[i], radix); | |
5572 | str[i++] = 'i'; | |
7a1aba42 MV |
5573 | return i; |
5574 | } | |
5575 | ||
1be6b49c | 5576 | static size_t |
0b799eea | 5577 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5578 | { |
1be6b49c | 5579 | size_t i; |
3c9a524f | 5580 | if (SCM_REALP (flt)) |
0b799eea | 5581 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5582 | else |
7a1aba42 MV |
5583 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5584 | str, radix); | |
0f2d19dd JB |
5585 | return i; |
5586 | } | |
0f2d19dd | 5587 | |
2881e77b | 5588 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5589 | characters in the result. |
5590 | rad is output base | |
5591 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5592 | size_t |
2881e77b MV |
5593 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5594 | { | |
5595 | if (num < 0) | |
5596 | { | |
5597 | *p++ = '-'; | |
5598 | return scm_iuint2str (-num, rad, p) + 1; | |
5599 | } | |
5600 | else | |
5601 | return scm_iuint2str (num, rad, p); | |
5602 | } | |
5603 | ||
5604 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5605 | characters in the result. | |
5606 | rad is output base | |
5607 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5608 | size_t | |
5609 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5610 | { |
1be6b49c ML |
5611 | size_t j = 1; |
5612 | size_t i; | |
2881e77b | 5613 | scm_t_uintmax n = num; |
5c11cc9d | 5614 | |
a6f3af16 AW |
5615 | if (rad < 2 || rad > 36) |
5616 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5617 | ||
f872b822 | 5618 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5619 | j++; |
5620 | ||
5621 | i = j; | |
2881e77b | 5622 | n = num; |
f872b822 MD |
5623 | while (i--) |
5624 | { | |
5c11cc9d GH |
5625 | int d = n % rad; |
5626 | ||
f872b822 | 5627 | n /= rad; |
a6f3af16 | 5628 | p[i] = number_chars[d]; |
f872b822 | 5629 | } |
0f2d19dd JB |
5630 | return j; |
5631 | } | |
5632 | ||
a1ec6916 | 5633 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5634 | (SCM n, SCM radix), |
5635 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5636 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5637 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5638 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5639 | { |
1bbd0b84 | 5640 | int base; |
98cb6e75 | 5641 | |
0aacf84e | 5642 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5643 | base = 10; |
0aacf84e | 5644 | else |
5efd3c7d | 5645 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5646 | |
e11e83f3 | 5647 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5648 | { |
5649 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5650 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5651 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5652 | } |
5653 | else if (SCM_BIGP (n)) | |
5654 | { | |
5655 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
d88f5323 AW |
5656 | size_t len = strlen (str); |
5657 | void (*freefunc) (void *, size_t); | |
5658 | SCM ret; | |
5659 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
0aacf84e | 5660 | scm_remember_upto_here_1 (n); |
d88f5323 AW |
5661 | ret = scm_from_latin1_stringn (str, len); |
5662 | freefunc (str, len + 1); | |
5663 | return ret; | |
0aacf84e | 5664 | } |
f92e85f7 MV |
5665 | else if (SCM_FRACTIONP (n)) |
5666 | { | |
f92e85f7 | 5667 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5668 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5669 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5670 | } | |
0aacf84e MD |
5671 | else if (SCM_INEXACTP (n)) |
5672 | { | |
5673 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5674 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5675 | } |
5676 | else | |
bb628794 | 5677 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5678 | } |
1bbd0b84 | 5679 | #undef FUNC_NAME |
0f2d19dd JB |
5680 | |
5681 | ||
ca46fb90 RB |
5682 | /* These print routines used to be stubbed here so that scm_repl.c |
5683 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5684 | |
0f2d19dd | 5685 | int |
e81d98ec | 5686 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5687 | { |
56e55ac7 | 5688 | char num_buf[FLOBUFLEN]; |
f209aeee | 5689 | scm_lfwrite_unlocked (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5690 | return !0; |
5691 | } | |
5692 | ||
b479fe9a MV |
5693 | void |
5694 | scm_i_print_double (double val, SCM port) | |
5695 | { | |
5696 | char num_buf[FLOBUFLEN]; | |
f209aeee | 5697 | scm_lfwrite_unlocked (num_buf, idbl2str (val, num_buf, 10), port); |
b479fe9a MV |
5698 | } |
5699 | ||
f3ae5d60 | 5700 | int |
e81d98ec | 5701 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5702 | |
f3ae5d60 | 5703 | { |
56e55ac7 | 5704 | char num_buf[FLOBUFLEN]; |
f209aeee | 5705 | scm_lfwrite_unlocked (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5706 | return !0; |
5707 | } | |
1cc91f1b | 5708 | |
7a1aba42 MV |
5709 | void |
5710 | scm_i_print_complex (double real, double imag, SCM port) | |
5711 | { | |
5712 | char num_buf[FLOBUFLEN]; | |
f209aeee | 5713 | scm_lfwrite_unlocked (num_buf, icmplx2str (real, imag, num_buf, 10), port); |
7a1aba42 MV |
5714 | } |
5715 | ||
f92e85f7 MV |
5716 | int |
5717 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5718 | { | |
5719 | SCM str; | |
f92e85f7 | 5720 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5721 | scm_display (str, port); |
f92e85f7 MV |
5722 | scm_remember_upto_here_1 (str); |
5723 | return !0; | |
5724 | } | |
5725 | ||
0f2d19dd | 5726 | int |
e81d98ec | 5727 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5728 | { |
ca46fb90 | 5729 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
b57bf272 AW |
5730 | size_t len = strlen (str); |
5731 | void (*freefunc) (void *, size_t); | |
5732 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
ca46fb90 | 5733 | scm_remember_upto_here_1 (exp); |
ea0582c2 | 5734 | scm_lfwrite_unlocked (str, len, port); |
b57bf272 | 5735 | freefunc (str, len + 1); |
0f2d19dd JB |
5736 | return !0; |
5737 | } | |
5738 | /*** END nums->strs ***/ | |
5739 | ||
3c9a524f | 5740 | |
0f2d19dd | 5741 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5742 | |
3c9a524f DH |
5743 | /* The following functions implement the conversion from strings to numbers. |
5744 | * The implementation somehow follows the grammar for numbers as it is given | |
5745 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5746 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5747 | * points should be noted about the implementation: | |
bc3d34f5 | 5748 | * |
3c9a524f DH |
5749 | * * Each function keeps a local index variable 'idx' that points at the |
5750 | * current position within the parsed string. The global index is only | |
5751 | * updated if the function could parse the corresponding syntactic unit | |
5752 | * successfully. | |
bc3d34f5 | 5753 | * |
3c9a524f | 5754 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5755 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5756 | * | |
3c9a524f DH |
5757 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5758 | * Only if these fixnums would overflow, the result variables are updated | |
5759 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5760 | * the temporary variables holding the fixnums are cleared, and the process | |
5761 | * starts over again. If for example fixnums were able to store five decimal | |
5762 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5763 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5764 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5765 | * |
5766 | * Notes on the handling of exactness specifiers: | |
5767 | * | |
5768 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5769 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5770 | * written in rectangular form, exactness specifiers are applied to the | |
5771 | * real and imaginary parts before calling scm_make_rectangular. For | |
5772 | * complex numbers written in polar form, exactness specifiers are applied | |
5773 | * to the magnitude and angle before calling scm_make_polar. | |
5774 | * | |
5775 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5776 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5777 | * the entire number, and applies to both components of a complex number. | |
5778 | * "#e" causes each component to be made exact, and "#i" causes each | |
5779 | * component to be made inexact. If no forced exactness specifier is | |
5780 | * present, then the exactness of each component is determined | |
5781 | * independently by the presence or absence of a decimal point or hash mark | |
5782 | * within that component. If a decimal point or hash mark is present, the | |
5783 | * component is made inexact, otherwise it is made exact. | |
5784 | * | |
5785 | * After the exactness specifiers have been applied to each component, they | |
5786 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5787 | * the final result. Note that this will result in a real number if the | |
5788 | * imaginary part, magnitude, or angle is an exact 0. | |
5789 | * | |
5790 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5791 | * | |
5792 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5793 | */ |
5794 | ||
5795 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5796 | ||
5797 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5798 | ||
a6f3af16 AW |
5799 | /* Caller is responsible for checking that the return value is in range |
5800 | for the given radix, which should be <= 36. */ | |
5801 | static unsigned int | |
5802 | char_decimal_value (scm_t_uint32 c) | |
5803 | { | |
68713277 AW |
5804 | if (c >= (scm_t_uint32) '0' && c <= (scm_t_uint32) '9') |
5805 | return c - (scm_t_uint32) '0'; | |
5806 | else | |
a6f3af16 | 5807 | { |
68713277 AW |
5808 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, |
5809 | that's certainly above any valid decimal, so we take advantage of | |
5810 | that to elide some tests. */ | |
5811 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5812 | ||
5813 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5814 | hexadecimals. */ | |
5815 | if (d >= 10U) | |
5816 | { | |
5817 | c = uc_tolower (c); | |
5818 | if (c >= (scm_t_uint32) 'a') | |
5819 | d = c - (scm_t_uint32)'a' + 10U; | |
5820 | } | |
5821 | return d; | |
a6f3af16 | 5822 | } |
a6f3af16 | 5823 | } |
3c9a524f | 5824 | |
91db4a37 LC |
5825 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5826 | in base RADIX. Upon success, return the unsigned integer and update | |
5827 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5828 | static SCM |
3f47e526 | 5829 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5830 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5831 | { |
3c9a524f DH |
5832 | unsigned int idx = *p_idx; |
5833 | unsigned int hash_seen = 0; | |
5834 | scm_t_bits shift = 1; | |
5835 | scm_t_bits add = 0; | |
5836 | unsigned int digit_value; | |
5837 | SCM result; | |
5838 | char c; | |
3f47e526 | 5839 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5840 | |
5841 | if (idx == len) | |
5842 | return SCM_BOOL_F; | |
2a8fecee | 5843 | |
3f47e526 | 5844 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5845 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5846 | if (digit_value >= radix) |
5847 | return SCM_BOOL_F; | |
5848 | ||
5849 | idx++; | |
d956fa6f | 5850 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5851 | while (idx != len) |
f872b822 | 5852 | { |
3f47e526 | 5853 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5854 | if (c == '#') |
3c9a524f DH |
5855 | { |
5856 | hash_seen = 1; | |
5857 | digit_value = 0; | |
5858 | } | |
a6f3af16 AW |
5859 | else if (hash_seen) |
5860 | break; | |
3c9a524f | 5861 | else |
a6f3af16 AW |
5862 | { |
5863 | digit_value = char_decimal_value (c); | |
5864 | /* This check catches non-decimals in addition to out-of-range | |
5865 | decimals. */ | |
5866 | if (digit_value >= radix) | |
5867 | break; | |
5868 | } | |
3c9a524f DH |
5869 | |
5870 | idx++; | |
5871 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5872 | { | |
d956fa6f | 5873 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5874 | if (add > 0) |
d956fa6f | 5875 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5876 | |
5877 | shift = radix; | |
5878 | add = digit_value; | |
5879 | } | |
5880 | else | |
5881 | { | |
5882 | shift = shift * radix; | |
5883 | add = add * radix + digit_value; | |
5884 | } | |
5885 | }; | |
5886 | ||
5887 | if (shift > 1) | |
d956fa6f | 5888 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5889 | if (add > 0) |
d956fa6f | 5890 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5891 | |
5892 | *p_idx = idx; | |
5893 | if (hash_seen) | |
5894 | *p_exactness = INEXACT; | |
5895 | ||
5896 | return result; | |
2a8fecee JB |
5897 | } |
5898 | ||
5899 | ||
3c9a524f DH |
5900 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5901 | * covers the parts of the rules that start at a potential point. The value | |
5902 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5903 | * in variable result. The content of *p_exactness indicates, whether a hash |
5904 | * has already been seen in the digits before the point. | |
3c9a524f | 5905 | */ |
1cc91f1b | 5906 | |
3f47e526 | 5907 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5908 | |
5909 | static SCM | |
3f47e526 | 5910 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5911 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5912 | { |
3c9a524f DH |
5913 | unsigned int idx = *p_idx; |
5914 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5915 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5916 | |
5917 | if (idx == len) | |
79d34f68 | 5918 | return result; |
3c9a524f | 5919 | |
3f47e526 | 5920 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5921 | { |
5922 | scm_t_bits shift = 1; | |
5923 | scm_t_bits add = 0; | |
5924 | unsigned int digit_value; | |
cff5fa33 | 5925 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5926 | |
5927 | idx++; | |
5928 | while (idx != len) | |
5929 | { | |
3f47e526 MG |
5930 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5931 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5932 | { |
5933 | if (x == INEXACT) | |
5934 | return SCM_BOOL_F; | |
5935 | else | |
5936 | digit_value = DIGIT2UINT (c); | |
5937 | } | |
5938 | else if (c == '#') | |
5939 | { | |
5940 | x = INEXACT; | |
5941 | digit_value = 0; | |
5942 | } | |
5943 | else | |
5944 | break; | |
5945 | ||
5946 | idx++; | |
5947 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5948 | { | |
d956fa6f MV |
5949 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5950 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5951 | if (add > 0) |
d956fa6f | 5952 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5953 | |
5954 | shift = 10; | |
5955 | add = digit_value; | |
5956 | } | |
5957 | else | |
5958 | { | |
5959 | shift = shift * 10; | |
5960 | add = add * 10 + digit_value; | |
5961 | } | |
5962 | }; | |
5963 | ||
5964 | if (add > 0) | |
5965 | { | |
d956fa6f MV |
5966 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5967 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5968 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5969 | } |
5970 | ||
d8592269 | 5971 | result = scm_divide (result, big_shift); |
79d34f68 | 5972 | |
3c9a524f DH |
5973 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5974 | x = INEXACT; | |
f872b822 | 5975 | } |
3c9a524f | 5976 | |
3c9a524f | 5977 | if (idx != len) |
f872b822 | 5978 | { |
3c9a524f DH |
5979 | int sign = 1; |
5980 | unsigned int start; | |
3f47e526 | 5981 | scm_t_wchar c; |
3c9a524f DH |
5982 | int exponent; |
5983 | SCM e; | |
5984 | ||
5985 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5986 | ||
3f47e526 | 5987 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5988 | { |
3c9a524f DH |
5989 | case 'd': case 'D': |
5990 | case 'e': case 'E': | |
5991 | case 'f': case 'F': | |
5992 | case 'l': case 'L': | |
5993 | case 's': case 'S': | |
5994 | idx++; | |
ee0ddd21 AW |
5995 | if (idx == len) |
5996 | return SCM_BOOL_F; | |
5997 | ||
3c9a524f | 5998 | start = idx; |
3f47e526 | 5999 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6000 | if (c == '-') |
6001 | { | |
6002 | idx++; | |
ee0ddd21 AW |
6003 | if (idx == len) |
6004 | return SCM_BOOL_F; | |
6005 | ||
3c9a524f | 6006 | sign = -1; |
3f47e526 | 6007 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6008 | } |
6009 | else if (c == '+') | |
6010 | { | |
6011 | idx++; | |
ee0ddd21 AW |
6012 | if (idx == len) |
6013 | return SCM_BOOL_F; | |
6014 | ||
3c9a524f | 6015 | sign = 1; |
3f47e526 | 6016 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6017 | } |
6018 | else | |
6019 | sign = 1; | |
6020 | ||
3f47e526 | 6021 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
6022 | return SCM_BOOL_F; |
6023 | ||
6024 | idx++; | |
6025 | exponent = DIGIT2UINT (c); | |
6026 | while (idx != len) | |
f872b822 | 6027 | { |
3f47e526 MG |
6028 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
6029 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
6030 | { |
6031 | idx++; | |
6032 | if (exponent <= SCM_MAXEXP) | |
6033 | exponent = exponent * 10 + DIGIT2UINT (c); | |
6034 | } | |
6035 | else | |
6036 | break; | |
f872b822 | 6037 | } |
3c9a524f | 6038 | |
1ea37620 | 6039 | if (exponent > ((sign == 1) ? SCM_MAXEXP : SCM_MAXEXP + DBL_DIG + 1)) |
f872b822 | 6040 | { |
3c9a524f | 6041 | size_t exp_len = idx - start; |
3f47e526 | 6042 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
6043 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
6044 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 6045 | } |
3c9a524f | 6046 | |
d956fa6f | 6047 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
6048 | if (sign == 1) |
6049 | result = scm_product (result, e); | |
6050 | else | |
6ebecdeb | 6051 | result = scm_divide (result, e); |
3c9a524f DH |
6052 | |
6053 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
6054 | x = INEXACT; | |
6055 | ||
f872b822 | 6056 | break; |
3c9a524f | 6057 | |
f872b822 | 6058 | default: |
3c9a524f | 6059 | break; |
f872b822 | 6060 | } |
0f2d19dd | 6061 | } |
3c9a524f DH |
6062 | |
6063 | *p_idx = idx; | |
6064 | if (x == INEXACT) | |
6065 | *p_exactness = x; | |
6066 | ||
6067 | return result; | |
0f2d19dd | 6068 | } |
0f2d19dd | 6069 | |
3c9a524f DH |
6070 | |
6071 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
6072 | ||
6073 | static SCM | |
3f47e526 | 6074 | mem2ureal (SCM mem, unsigned int *p_idx, |
929d11b2 MW |
6075 | unsigned int radix, enum t_exactness forced_x, |
6076 | int allow_inf_or_nan) | |
0f2d19dd | 6077 | { |
3c9a524f | 6078 | unsigned int idx = *p_idx; |
164d2481 | 6079 | SCM result; |
3f47e526 | 6080 | size_t len = scm_i_string_length (mem); |
3c9a524f | 6081 | |
40f89215 NJ |
6082 | /* Start off believing that the number will be exact. This changes |
6083 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 6084 | enum t_exactness implicit_x = EXACT; |
40f89215 | 6085 | |
3c9a524f DH |
6086 | if (idx == len) |
6087 | return SCM_BOOL_F; | |
6088 | ||
929d11b2 MW |
6089 | if (allow_inf_or_nan && forced_x != EXACT && idx+5 <= len) |
6090 | switch (scm_i_string_ref (mem, idx)) | |
6091 | { | |
6092 | case 'i': case 'I': | |
6093 | switch (scm_i_string_ref (mem, idx + 1)) | |
6094 | { | |
6095 | case 'n': case 'N': | |
6096 | switch (scm_i_string_ref (mem, idx + 2)) | |
6097 | { | |
6098 | case 'f': case 'F': | |
6099 | if (scm_i_string_ref (mem, idx + 3) == '.' | |
6100 | && scm_i_string_ref (mem, idx + 4) == '0') | |
6101 | { | |
6102 | *p_idx = idx+5; | |
6103 | return scm_inf (); | |
6104 | } | |
6105 | } | |
6106 | } | |
6107 | case 'n': case 'N': | |
6108 | switch (scm_i_string_ref (mem, idx + 1)) | |
6109 | { | |
6110 | case 'a': case 'A': | |
6111 | switch (scm_i_string_ref (mem, idx + 2)) | |
6112 | { | |
6113 | case 'n': case 'N': | |
6114 | if (scm_i_string_ref (mem, idx + 3) == '.') | |
6115 | { | |
6116 | /* Cobble up the fractional part. We might want to | |
6117 | set the NaN's mantissa from it. */ | |
6118 | idx += 4; | |
6119 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), | |
6120 | SCM_INUM0)) | |
6121 | { | |
5f237d6e | 6122 | #if SCM_ENABLE_DEPRECATED == 1 |
929d11b2 MW |
6123 | scm_c_issue_deprecation_warning |
6124 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5f237d6e | 6125 | #else |
929d11b2 | 6126 | return SCM_BOOL_F; |
5f237d6e | 6127 | #endif |
929d11b2 | 6128 | } |
5f237d6e | 6129 | |
929d11b2 MW |
6130 | *p_idx = idx; |
6131 | return scm_nan (); | |
6132 | } | |
6133 | } | |
6134 | } | |
6135 | } | |
7351e207 | 6136 | |
3f47e526 | 6137 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
6138 | { |
6139 | if (radix != 10) | |
6140 | return SCM_BOOL_F; | |
6141 | else if (idx + 1 == len) | |
6142 | return SCM_BOOL_F; | |
3f47e526 | 6143 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
6144 | return SCM_BOOL_F; |
6145 | else | |
cff5fa33 | 6146 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 6147 | p_idx, &implicit_x); |
f872b822 | 6148 | } |
3c9a524f DH |
6149 | else |
6150 | { | |
3c9a524f | 6151 | SCM uinteger; |
3c9a524f | 6152 | |
9d427b2c | 6153 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 6154 | if (scm_is_false (uinteger)) |
3c9a524f DH |
6155 | return SCM_BOOL_F; |
6156 | ||
6157 | if (idx == len) | |
6158 | result = uinteger; | |
3f47e526 | 6159 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 6160 | { |
3c9a524f DH |
6161 | SCM divisor; |
6162 | ||
6163 | idx++; | |
ee0ddd21 AW |
6164 | if (idx == len) |
6165 | return SCM_BOOL_F; | |
3c9a524f | 6166 | |
9d427b2c | 6167 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
929d11b2 | 6168 | if (scm_is_false (divisor) || scm_is_eq (divisor, SCM_INUM0)) |
3c9a524f DH |
6169 | return SCM_BOOL_F; |
6170 | ||
f92e85f7 | 6171 | /* both are int/big here, I assume */ |
cba42c93 | 6172 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 6173 | } |
3c9a524f DH |
6174 | else if (radix == 10) |
6175 | { | |
9d427b2c | 6176 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 6177 | if (scm_is_false (result)) |
3c9a524f DH |
6178 | return SCM_BOOL_F; |
6179 | } | |
6180 | else | |
6181 | result = uinteger; | |
6182 | ||
6183 | *p_idx = idx; | |
f872b822 | 6184 | } |
164d2481 | 6185 | |
9d427b2c MW |
6186 | switch (forced_x) |
6187 | { | |
6188 | case EXACT: | |
6189 | if (SCM_INEXACTP (result)) | |
6190 | return scm_inexact_to_exact (result); | |
6191 | else | |
6192 | return result; | |
6193 | case INEXACT: | |
6194 | if (SCM_INEXACTP (result)) | |
6195 | return result; | |
6196 | else | |
6197 | return scm_exact_to_inexact (result); | |
6198 | case NO_EXACTNESS: | |
6199 | if (implicit_x == INEXACT) | |
6200 | { | |
6201 | if (SCM_INEXACTP (result)) | |
6202 | return result; | |
6203 | else | |
6204 | return scm_exact_to_inexact (result); | |
6205 | } | |
6206 | else | |
6207 | return result; | |
6208 | } | |
164d2481 | 6209 | |
9d427b2c | 6210 | /* We should never get here */ |
6f82b8f6 | 6211 | assert (0); |
3c9a524f | 6212 | } |
0f2d19dd | 6213 | |
0f2d19dd | 6214 | |
3c9a524f | 6215 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 6216 | |
3c9a524f | 6217 | static SCM |
3f47e526 | 6218 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 6219 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 6220 | { |
3f47e526 | 6221 | scm_t_wchar c; |
3c9a524f DH |
6222 | int sign = 0; |
6223 | SCM ureal; | |
3f47e526 | 6224 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6225 | |
6226 | if (idx == len) | |
6227 | return SCM_BOOL_F; | |
6228 | ||
3f47e526 | 6229 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6230 | if (c == '+') |
6231 | { | |
6232 | idx++; | |
6233 | sign = 1; | |
6234 | } | |
6235 | else if (c == '-') | |
6236 | { | |
6237 | idx++; | |
6238 | sign = -1; | |
0f2d19dd | 6239 | } |
0f2d19dd | 6240 | |
3c9a524f DH |
6241 | if (idx == len) |
6242 | return SCM_BOOL_F; | |
6243 | ||
929d11b2 | 6244 | ureal = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6245 | if (scm_is_false (ureal)) |
f872b822 | 6246 | { |
3c9a524f DH |
6247 | /* input must be either +i or -i */ |
6248 | ||
6249 | if (sign == 0) | |
6250 | return SCM_BOOL_F; | |
6251 | ||
3f47e526 MG |
6252 | if (scm_i_string_ref (mem, idx) == 'i' |
6253 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 6254 | { |
3c9a524f DH |
6255 | idx++; |
6256 | if (idx != len) | |
6257 | return SCM_BOOL_F; | |
6258 | ||
cff5fa33 | 6259 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 6260 | } |
3c9a524f DH |
6261 | else |
6262 | return SCM_BOOL_F; | |
0f2d19dd | 6263 | } |
3c9a524f DH |
6264 | else |
6265 | { | |
73e4de09 | 6266 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 6267 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 6268 | |
3c9a524f DH |
6269 | if (idx == len) |
6270 | return ureal; | |
6271 | ||
3f47e526 | 6272 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 6273 | switch (c) |
f872b822 | 6274 | { |
3c9a524f DH |
6275 | case 'i': case 'I': |
6276 | /* either +<ureal>i or -<ureal>i */ | |
6277 | ||
6278 | idx++; | |
6279 | if (sign == 0) | |
6280 | return SCM_BOOL_F; | |
6281 | if (idx != len) | |
6282 | return SCM_BOOL_F; | |
cff5fa33 | 6283 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
6284 | |
6285 | case '@': | |
6286 | /* polar input: <real>@<real>. */ | |
6287 | ||
6288 | idx++; | |
6289 | if (idx == len) | |
6290 | return SCM_BOOL_F; | |
6291 | else | |
f872b822 | 6292 | { |
3c9a524f DH |
6293 | int sign; |
6294 | SCM angle; | |
6295 | SCM result; | |
6296 | ||
3f47e526 | 6297 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6298 | if (c == '+') |
6299 | { | |
6300 | idx++; | |
ee0ddd21 AW |
6301 | if (idx == len) |
6302 | return SCM_BOOL_F; | |
3c9a524f DH |
6303 | sign = 1; |
6304 | } | |
6305 | else if (c == '-') | |
6306 | { | |
6307 | idx++; | |
ee0ddd21 AW |
6308 | if (idx == len) |
6309 | return SCM_BOOL_F; | |
3c9a524f DH |
6310 | sign = -1; |
6311 | } | |
6312 | else | |
929d11b2 | 6313 | sign = 0; |
3c9a524f | 6314 | |
929d11b2 | 6315 | angle = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6316 | if (scm_is_false (angle)) |
3c9a524f DH |
6317 | return SCM_BOOL_F; |
6318 | if (idx != len) | |
6319 | return SCM_BOOL_F; | |
6320 | ||
73e4de09 | 6321 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
6322 | angle = scm_difference (angle, SCM_UNDEFINED); |
6323 | ||
6324 | result = scm_make_polar (ureal, angle); | |
6325 | return result; | |
f872b822 | 6326 | } |
3c9a524f DH |
6327 | case '+': |
6328 | case '-': | |
6329 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 6330 | |
3c9a524f DH |
6331 | idx++; |
6332 | if (idx == len) | |
6333 | return SCM_BOOL_F; | |
6334 | else | |
6335 | { | |
6336 | int sign = (c == '+') ? 1 : -1; | |
929d11b2 | 6337 | SCM imag = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
0f2d19dd | 6338 | |
73e4de09 | 6339 | if (scm_is_false (imag)) |
d956fa6f | 6340 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 6341 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 6342 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 6343 | |
3c9a524f DH |
6344 | if (idx == len) |
6345 | return SCM_BOOL_F; | |
3f47e526 MG |
6346 | if (scm_i_string_ref (mem, idx) != 'i' |
6347 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 6348 | return SCM_BOOL_F; |
0f2d19dd | 6349 | |
3c9a524f DH |
6350 | idx++; |
6351 | if (idx != len) | |
6352 | return SCM_BOOL_F; | |
0f2d19dd | 6353 | |
1fe5e088 | 6354 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6355 | } |
6356 | default: | |
6357 | return SCM_BOOL_F; | |
6358 | } | |
6359 | } | |
0f2d19dd | 6360 | } |
0f2d19dd JB |
6361 | |
6362 | ||
3c9a524f DH |
6363 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6364 | ||
6365 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6366 | |
0f2d19dd | 6367 | SCM |
3f47e526 | 6368 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6369 | { |
3c9a524f DH |
6370 | unsigned int idx = 0; |
6371 | unsigned int radix = NO_RADIX; | |
6372 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6373 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6374 | |
6375 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6376 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6377 | { |
3f47e526 | 6378 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6379 | { |
6380 | case 'b': case 'B': | |
6381 | if (radix != NO_RADIX) | |
6382 | return SCM_BOOL_F; | |
6383 | radix = DUAL; | |
6384 | break; | |
6385 | case 'd': case 'D': | |
6386 | if (radix != NO_RADIX) | |
6387 | return SCM_BOOL_F; | |
6388 | radix = DEC; | |
6389 | break; | |
6390 | case 'i': case 'I': | |
6391 | if (forced_x != NO_EXACTNESS) | |
6392 | return SCM_BOOL_F; | |
6393 | forced_x = INEXACT; | |
6394 | break; | |
6395 | case 'e': case 'E': | |
6396 | if (forced_x != NO_EXACTNESS) | |
6397 | return SCM_BOOL_F; | |
6398 | forced_x = EXACT; | |
6399 | break; | |
6400 | case 'o': case 'O': | |
6401 | if (radix != NO_RADIX) | |
6402 | return SCM_BOOL_F; | |
6403 | radix = OCT; | |
6404 | break; | |
6405 | case 'x': case 'X': | |
6406 | if (radix != NO_RADIX) | |
6407 | return SCM_BOOL_F; | |
6408 | radix = HEX; | |
6409 | break; | |
6410 | default: | |
f872b822 | 6411 | return SCM_BOOL_F; |
3c9a524f DH |
6412 | } |
6413 | idx += 2; | |
6414 | } | |
6415 | ||
6416 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6417 | if (radix == NO_RADIX) | |
9d427b2c | 6418 | radix = default_radix; |
f872b822 | 6419 | |
9d427b2c | 6420 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6421 | } |
6422 | ||
3f47e526 MG |
6423 | SCM |
6424 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6425 | unsigned int default_radix) | |
6426 | { | |
6427 | SCM str = scm_from_locale_stringn (mem, len); | |
6428 | ||
6429 | return scm_i_string_to_number (str, default_radix); | |
6430 | } | |
6431 | ||
0f2d19dd | 6432 | |
a1ec6916 | 6433 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6434 | (SCM string, SCM radix), |
1e6808ea | 6435 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6436 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6437 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6438 | "is a default radix that may be overridden by an explicit radix\n" | |
6439 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6440 | "supplied, then the default radix is 10. If string is not a\n" | |
6441 | "syntactically valid notation for a number, then\n" | |
6442 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6443 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6444 | { |
6445 | SCM answer; | |
5efd3c7d | 6446 | unsigned int base; |
a6d9e5ab | 6447 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6448 | |
6449 | if (SCM_UNBNDP (radix)) | |
6450 | base = 10; | |
6451 | else | |
6452 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6453 | ||
3f47e526 | 6454 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6455 | scm_remember_upto_here_1 (string); |
6456 | return answer; | |
0f2d19dd | 6457 | } |
1bbd0b84 | 6458 | #undef FUNC_NAME |
3c9a524f DH |
6459 | |
6460 | ||
0f2d19dd JB |
6461 | /*** END strs->nums ***/ |
6462 | ||
5986c47d | 6463 | |
8507ec80 MV |
6464 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6465 | (SCM x), | |
6466 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6467 | "otherwise.") | |
6468 | #define FUNC_NAME s_scm_number_p | |
6469 | { | |
6470 | return scm_from_bool (SCM_NUMBERP (x)); | |
6471 | } | |
6472 | #undef FUNC_NAME | |
6473 | ||
6474 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6475 | (SCM x), |
942e5b91 | 6476 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6477 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6478 | "values form subsets of the set of complex numbers, i. e. the\n" |
6479 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6480 | "rational or integer number.") | |
8507ec80 | 6481 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6482 | { |
8507ec80 MV |
6483 | /* all numbers are complex. */ |
6484 | return scm_number_p (x); | |
0f2d19dd | 6485 | } |
1bbd0b84 | 6486 | #undef FUNC_NAME |
0f2d19dd | 6487 | |
f92e85f7 MV |
6488 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6489 | (SCM x), | |
6490 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6491 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6492 | "the set of real numbers, i. e. the predicate will also be\n" | |
6493 | "fulfilled if @var{x} is an integer number.") | |
6494 | #define FUNC_NAME s_scm_real_p | |
6495 | { | |
c960e556 MW |
6496 | return scm_from_bool |
6497 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6498 | } |
6499 | #undef FUNC_NAME | |
6500 | ||
6501 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6502 | (SCM x), |
942e5b91 | 6503 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6504 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6505 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6506 | "fulfilled if @var{x} is an integer number.") |
6507 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6508 | { |
c960e556 | 6509 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6510 | return SCM_BOOL_T; |
6511 | else if (SCM_REALP (x)) | |
c960e556 MW |
6512 | /* due to their limited precision, finite floating point numbers are |
6513 | rational as well. (finite means neither infinity nor a NaN) */ | |
19374ad2 | 6514 | return scm_from_bool (isfinite (SCM_REAL_VALUE (x))); |
0aacf84e | 6515 | else |
bb628794 | 6516 | return SCM_BOOL_F; |
0f2d19dd | 6517 | } |
1bbd0b84 | 6518 | #undef FUNC_NAME |
0f2d19dd | 6519 | |
a1ec6916 | 6520 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6521 | (SCM x), |
900a897c MW |
6522 | "Return @code{#t} if @var{x} is an integer number,\n" |
6523 | "else return @code{#f}.") | |
1bbd0b84 | 6524 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6525 | { |
c960e556 | 6526 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6527 | return SCM_BOOL_T; |
c960e556 MW |
6528 | else if (SCM_REALP (x)) |
6529 | { | |
6530 | double val = SCM_REAL_VALUE (x); | |
6531 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6532 | } | |
6533 | else | |
8e43ed5d | 6534 | return SCM_BOOL_F; |
0f2d19dd | 6535 | } |
1bbd0b84 | 6536 | #undef FUNC_NAME |
0f2d19dd | 6537 | |
900a897c MW |
6538 | SCM_DEFINE (scm_exact_integer_p, "exact-integer?", 1, 0, 0, |
6539 | (SCM x), | |
6540 | "Return @code{#t} if @var{x} is an exact integer number,\n" | |
6541 | "else return @code{#f}.") | |
6542 | #define FUNC_NAME s_scm_exact_integer_p | |
6543 | { | |
6544 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) | |
6545 | return SCM_BOOL_T; | |
6546 | else | |
6547 | return SCM_BOOL_F; | |
6548 | } | |
6549 | #undef FUNC_NAME | |
6550 | ||
0f2d19dd | 6551 | |
8a1f4f98 AW |
6552 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6553 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6554 | (SCM x, SCM y, SCM rest), | |
6555 | "Return @code{#t} if all parameters are numerically equal.") | |
6556 | #define FUNC_NAME s_scm_i_num_eq_p | |
6557 | { | |
6558 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6559 | return SCM_BOOL_T; | |
6560 | while (!scm_is_null (rest)) | |
6561 | { | |
6562 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6563 | return SCM_BOOL_F; | |
6564 | x = y; | |
6565 | y = scm_car (rest); | |
6566 | rest = scm_cdr (rest); | |
6567 | } | |
6568 | return scm_num_eq_p (x, y); | |
6569 | } | |
6570 | #undef FUNC_NAME | |
0f2d19dd | 6571 | SCM |
6e8d25a6 | 6572 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6573 | { |
d8b95e27 | 6574 | again: |
e11e83f3 | 6575 | if (SCM_I_INUMP (x)) |
0aacf84e | 6576 | { |
e25f3727 | 6577 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6578 | if (SCM_I_INUMP (y)) |
0aacf84e | 6579 | { |
e25f3727 | 6580 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6581 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6582 | } |
6583 | else if (SCM_BIGP (y)) | |
6584 | return SCM_BOOL_F; | |
6585 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6586 | { |
6587 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6588 | to a double and compare. | |
6589 | ||
6590 | But on a 64-bit system an inum is bigger than a double and | |
01329288 MW |
6591 | casting it to a double (call that dxx) will round. |
6592 | Although dxx will not in general be equal to xx, dxx will | |
6593 | always be an integer and within a factor of 2 of xx, so if | |
6594 | dxx==yy, we know that yy is an integer and fits in | |
6595 | scm_t_signed_bits. So we cast yy to scm_t_signed_bits and | |
e8c5b1f2 KR |
6596 | compare with plain xx. |
6597 | ||
6598 | An alternative (for any size system actually) would be to check | |
6599 | yy is an integer (with floor) and is in range of an inum | |
6600 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6601 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6602 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6603 | |
6604 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6605 | return scm_from_bool ((double) xx == yy |
6606 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6607 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6608 | } |
0aacf84e | 6609 | else if (SCM_COMPLEXP (y)) |
01329288 MW |
6610 | { |
6611 | /* see comments with inum/real above */ | |
6612 | double ry = SCM_COMPLEX_REAL (y); | |
6613 | return scm_from_bool ((double) xx == ry | |
6614 | && 0.0 == SCM_COMPLEX_IMAG (y) | |
6615 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
6616 | || xx == (scm_t_signed_bits) ry)); | |
6617 | } | |
f92e85f7 MV |
6618 | else if (SCM_FRACTIONP (y)) |
6619 | return SCM_BOOL_F; | |
0aacf84e | 6620 | else |
fa075d40 AW |
6621 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6622 | s_scm_i_num_eq_p); | |
f872b822 | 6623 | } |
0aacf84e MD |
6624 | else if (SCM_BIGP (x)) |
6625 | { | |
e11e83f3 | 6626 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6627 | return SCM_BOOL_F; |
6628 | else if (SCM_BIGP (y)) | |
6629 | { | |
6630 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6631 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6632 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6633 | } |
6634 | else if (SCM_REALP (y)) | |
6635 | { | |
6636 | int cmp; | |
2e65b52f | 6637 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6638 | return SCM_BOOL_F; |
6639 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6640 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6641 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6642 | } |
6643 | else if (SCM_COMPLEXP (y)) | |
6644 | { | |
6645 | int cmp; | |
6646 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6647 | return SCM_BOOL_F; | |
2e65b52f | 6648 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6649 | return SCM_BOOL_F; |
6650 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6651 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6652 | return scm_from_bool (0 == cmp); |
0aacf84e | 6653 | } |
f92e85f7 MV |
6654 | else if (SCM_FRACTIONP (y)) |
6655 | return SCM_BOOL_F; | |
0aacf84e | 6656 | else |
fa075d40 AW |
6657 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6658 | s_scm_i_num_eq_p); | |
f4c627b3 | 6659 | } |
0aacf84e MD |
6660 | else if (SCM_REALP (x)) |
6661 | { | |
e8c5b1f2 | 6662 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6663 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6664 | { |
6665 | /* see comments with inum/real above */ | |
e25f3727 | 6666 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6667 | return scm_from_bool (xx == (double) yy |
6668 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6669 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6670 | } |
0aacf84e MD |
6671 | else if (SCM_BIGP (y)) |
6672 | { | |
6673 | int cmp; | |
01329288 | 6674 | if (isnan (xx)) |
0aacf84e | 6675 | return SCM_BOOL_F; |
01329288 | 6676 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); |
0aacf84e | 6677 | scm_remember_upto_here_1 (y); |
73e4de09 | 6678 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6679 | } |
6680 | else if (SCM_REALP (y)) | |
01329288 | 6681 | return scm_from_bool (xx == SCM_REAL_VALUE (y)); |
0aacf84e | 6682 | else if (SCM_COMPLEXP (y)) |
01329288 MW |
6683 | return scm_from_bool ((xx == SCM_COMPLEX_REAL (y)) |
6684 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
f92e85f7 | 6685 | else if (SCM_FRACTIONP (y)) |
d8b95e27 | 6686 | { |
01329288 | 6687 | if (isnan (xx) || isinf (xx)) |
d8b95e27 | 6688 | return SCM_BOOL_F; |
d8b95e27 KR |
6689 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6690 | goto again; | |
6691 | } | |
0aacf84e | 6692 | else |
fa075d40 AW |
6693 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6694 | s_scm_i_num_eq_p); | |
f872b822 | 6695 | } |
0aacf84e MD |
6696 | else if (SCM_COMPLEXP (x)) |
6697 | { | |
e11e83f3 | 6698 | if (SCM_I_INUMP (y)) |
01329288 MW |
6699 | { |
6700 | /* see comments with inum/real above */ | |
6701 | double rx = SCM_COMPLEX_REAL (x); | |
6702 | scm_t_signed_bits yy = SCM_I_INUM (y); | |
6703 | return scm_from_bool (rx == (double) yy | |
6704 | && 0.0 == SCM_COMPLEX_IMAG (x) | |
6705 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
6706 | || (scm_t_signed_bits) rx == yy)); | |
6707 | } | |
0aacf84e MD |
6708 | else if (SCM_BIGP (y)) |
6709 | { | |
6710 | int cmp; | |
6711 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6712 | return SCM_BOOL_F; | |
2e65b52f | 6713 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6714 | return SCM_BOOL_F; |
6715 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6716 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6717 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6718 | } |
6719 | else if (SCM_REALP (y)) | |
73e4de09 | 6720 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
01329288 | 6721 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
0aacf84e | 6722 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6723 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
01329288 | 6724 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6725 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6726 | { |
6727 | double xx; | |
6728 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6729 | return SCM_BOOL_F; | |
6730 | xx = SCM_COMPLEX_REAL (x); | |
01329288 | 6731 | if (isnan (xx) || isinf (xx)) |
d8b95e27 | 6732 | return SCM_BOOL_F; |
d8b95e27 KR |
6733 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6734 | goto again; | |
6735 | } | |
f92e85f7 | 6736 | else |
fa075d40 AW |
6737 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6738 | s_scm_i_num_eq_p); | |
f92e85f7 MV |
6739 | } |
6740 | else if (SCM_FRACTIONP (x)) | |
6741 | { | |
e11e83f3 | 6742 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6743 | return SCM_BOOL_F; |
6744 | else if (SCM_BIGP (y)) | |
6745 | return SCM_BOOL_F; | |
6746 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6747 | { |
6748 | double yy = SCM_REAL_VALUE (y); | |
01329288 | 6749 | if (isnan (yy) || isinf (yy)) |
d8b95e27 | 6750 | return SCM_BOOL_F; |
d8b95e27 KR |
6751 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6752 | goto again; | |
6753 | } | |
f92e85f7 | 6754 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6755 | { |
6756 | double yy; | |
6757 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6758 | return SCM_BOOL_F; | |
6759 | yy = SCM_COMPLEX_REAL (y); | |
01329288 | 6760 | if (isnan (yy) || isinf(yy)) |
d8b95e27 | 6761 | return SCM_BOOL_F; |
d8b95e27 KR |
6762 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6763 | goto again; | |
6764 | } | |
f92e85f7 MV |
6765 | else if (SCM_FRACTIONP (y)) |
6766 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6767 | else |
fa075d40 AW |
6768 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6769 | s_scm_i_num_eq_p); | |
f4c627b3 | 6770 | } |
0aacf84e | 6771 | else |
fa075d40 AW |
6772 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, |
6773 | s_scm_i_num_eq_p); | |
0f2d19dd JB |
6774 | } |
6775 | ||
6776 | ||
a5f0b599 KR |
6777 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6778 | done are good for inums, but for bignums an answer can almost always be | |
6779 | had by just examining a few high bits of the operands, as done by GMP in | |
6780 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6781 | of the float exponent to take into account. */ | |
6782 | ||
8c93b597 | 6783 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6784 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6785 | (SCM x, SCM y, SCM rest), | |
6786 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6787 | "increasing.") | |
6788 | #define FUNC_NAME s_scm_i_num_less_p | |
6789 | { | |
6790 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6791 | return SCM_BOOL_T; | |
6792 | while (!scm_is_null (rest)) | |
6793 | { | |
6794 | if (scm_is_false (scm_less_p (x, y))) | |
6795 | return SCM_BOOL_F; | |
6796 | x = y; | |
6797 | y = scm_car (rest); | |
6798 | rest = scm_cdr (rest); | |
6799 | } | |
6800 | return scm_less_p (x, y); | |
6801 | } | |
6802 | #undef FUNC_NAME | |
0f2d19dd | 6803 | SCM |
6e8d25a6 | 6804 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6805 | { |
a5f0b599 | 6806 | again: |
e11e83f3 | 6807 | if (SCM_I_INUMP (x)) |
0aacf84e | 6808 | { |
e25f3727 | 6809 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6810 | if (SCM_I_INUMP (y)) |
0aacf84e | 6811 | { |
e25f3727 | 6812 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6813 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6814 | } |
6815 | else if (SCM_BIGP (y)) | |
6816 | { | |
6817 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6818 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6819 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6820 | } |
6821 | else if (SCM_REALP (y)) | |
95ed2217 MW |
6822 | { |
6823 | /* We can safely take the ceiling of y without changing the | |
6824 | result of x<y, given that x is an integer. */ | |
6825 | double yy = ceil (SCM_REAL_VALUE (y)); | |
6826 | ||
6827 | /* In the following comparisons, it's important that the right | |
6828 | hand side always be a power of 2, so that it can be | |
6829 | losslessly converted to a double even on 64-bit | |
6830 | machines. */ | |
6831 | if (yy >= (double) (SCM_MOST_POSITIVE_FIXNUM+1)) | |
6832 | return SCM_BOOL_T; | |
6833 | else if (!(yy > (double) SCM_MOST_NEGATIVE_FIXNUM)) | |
6834 | /* The condition above is carefully written to include the | |
6835 | case where yy==NaN. */ | |
6836 | return SCM_BOOL_F; | |
6837 | else | |
6838 | /* yy is a finite integer that fits in an inum. */ | |
6839 | return scm_from_bool (xx < (scm_t_inum) yy); | |
6840 | } | |
f92e85f7 | 6841 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6842 | { |
6843 | /* "x < a/b" becomes "x*b < a" */ | |
6844 | int_frac: | |
6845 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6846 | y = SCM_FRACTION_NUMERATOR (y); | |
6847 | goto again; | |
6848 | } | |
0aacf84e | 6849 | else |
fa075d40 AW |
6850 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6851 | s_scm_i_num_less_p); | |
f872b822 | 6852 | } |
0aacf84e MD |
6853 | else if (SCM_BIGP (x)) |
6854 | { | |
e11e83f3 | 6855 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6856 | { |
6857 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6858 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6859 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6860 | } |
6861 | else if (SCM_BIGP (y)) | |
6862 | { | |
6863 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6864 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6865 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6866 | } |
6867 | else if (SCM_REALP (y)) | |
6868 | { | |
6869 | int cmp; | |
2e65b52f | 6870 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6871 | return SCM_BOOL_F; |
6872 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6873 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6874 | return scm_from_bool (cmp < 0); |
0aacf84e | 6875 | } |
f92e85f7 | 6876 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6877 | goto int_frac; |
0aacf84e | 6878 | else |
fa075d40 AW |
6879 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6880 | s_scm_i_num_less_p); | |
f4c627b3 | 6881 | } |
0aacf84e MD |
6882 | else if (SCM_REALP (x)) |
6883 | { | |
e11e83f3 | 6884 | if (SCM_I_INUMP (y)) |
95ed2217 MW |
6885 | { |
6886 | /* We can safely take the floor of x without changing the | |
6887 | result of x<y, given that y is an integer. */ | |
6888 | double xx = floor (SCM_REAL_VALUE (x)); | |
6889 | ||
6890 | /* In the following comparisons, it's important that the right | |
6891 | hand side always be a power of 2, so that it can be | |
6892 | losslessly converted to a double even on 64-bit | |
6893 | machines. */ | |
6894 | if (xx < (double) SCM_MOST_NEGATIVE_FIXNUM) | |
6895 | return SCM_BOOL_T; | |
6896 | else if (!(xx < (double) (SCM_MOST_POSITIVE_FIXNUM+1))) | |
6897 | /* The condition above is carefully written to include the | |
6898 | case where xx==NaN. */ | |
6899 | return SCM_BOOL_F; | |
6900 | else | |
6901 | /* xx is a finite integer that fits in an inum. */ | |
6902 | return scm_from_bool ((scm_t_inum) xx < SCM_I_INUM (y)); | |
6903 | } | |
0aacf84e MD |
6904 | else if (SCM_BIGP (y)) |
6905 | { | |
6906 | int cmp; | |
2e65b52f | 6907 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6908 | return SCM_BOOL_F; |
6909 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6910 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6911 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6912 | } |
6913 | else if (SCM_REALP (y)) | |
73e4de09 | 6914 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6915 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6916 | { |
6917 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6918 | if (isnan (xx)) |
a5f0b599 | 6919 | return SCM_BOOL_F; |
2e65b52f | 6920 | if (isinf (xx)) |
73e4de09 | 6921 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6922 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6923 | goto again; | |
6924 | } | |
f92e85f7 | 6925 | else |
fa075d40 AW |
6926 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6927 | s_scm_i_num_less_p); | |
f92e85f7 MV |
6928 | } |
6929 | else if (SCM_FRACTIONP (x)) | |
6930 | { | |
e11e83f3 | 6931 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6932 | { |
6933 | /* "a/b < y" becomes "a < y*b" */ | |
6934 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6935 | x = SCM_FRACTION_NUMERATOR (x); | |
6936 | goto again; | |
6937 | } | |
f92e85f7 | 6938 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6939 | { |
6940 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6941 | if (isnan (yy)) |
a5f0b599 | 6942 | return SCM_BOOL_F; |
2e65b52f | 6943 | if (isinf (yy)) |
73e4de09 | 6944 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6945 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6946 | goto again; | |
6947 | } | |
f92e85f7 | 6948 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6949 | { |
6950 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6951 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6952 | SCM_FRACTION_DENOMINATOR (y)); | |
6953 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6954 | SCM_FRACTION_DENOMINATOR (x)); | |
6955 | x = new_x; | |
6956 | y = new_y; | |
6957 | goto again; | |
6958 | } | |
0aacf84e | 6959 | else |
fa075d40 AW |
6960 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6961 | s_scm_i_num_less_p); | |
f872b822 | 6962 | } |
0aacf84e | 6963 | else |
fa075d40 AW |
6964 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, |
6965 | s_scm_i_num_less_p); | |
0f2d19dd JB |
6966 | } |
6967 | ||
6968 | ||
8a1f4f98 AW |
6969 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6970 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6971 | (SCM x, SCM y, SCM rest), | |
6972 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6973 | "decreasing.") | |
6974 | #define FUNC_NAME s_scm_i_num_gr_p | |
6975 | { | |
6976 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6977 | return SCM_BOOL_T; | |
6978 | while (!scm_is_null (rest)) | |
6979 | { | |
6980 | if (scm_is_false (scm_gr_p (x, y))) | |
6981 | return SCM_BOOL_F; | |
6982 | x = y; | |
6983 | y = scm_car (rest); | |
6984 | rest = scm_cdr (rest); | |
6985 | } | |
6986 | return scm_gr_p (x, y); | |
6987 | } | |
6988 | #undef FUNC_NAME | |
6989 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6990 | SCM |
6991 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6992 | { |
c76b1eaf | 6993 | if (!SCM_NUMBERP (x)) |
fa075d40 | 6994 | return scm_wta_dispatch_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6995 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 6996 | return scm_wta_dispatch_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6997 | else |
6998 | return scm_less_p (y, x); | |
0f2d19dd | 6999 | } |
1bbd0b84 | 7000 | #undef FUNC_NAME |
0f2d19dd JB |
7001 | |
7002 | ||
8a1f4f98 AW |
7003 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
7004 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
7005 | (SCM x, SCM y, SCM rest), | |
7006 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7007 | "non-decreasing.") | |
7008 | #define FUNC_NAME s_scm_i_num_leq_p | |
7009 | { | |
7010 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7011 | return SCM_BOOL_T; | |
7012 | while (!scm_is_null (rest)) | |
7013 | { | |
7014 | if (scm_is_false (scm_leq_p (x, y))) | |
7015 | return SCM_BOOL_F; | |
7016 | x = y; | |
7017 | y = scm_car (rest); | |
7018 | rest = scm_cdr (rest); | |
7019 | } | |
7020 | return scm_leq_p (x, y); | |
7021 | } | |
7022 | #undef FUNC_NAME | |
7023 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
7024 | SCM |
7025 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 7026 | { |
c76b1eaf | 7027 | if (!SCM_NUMBERP (x)) |
fa075d40 | 7028 | return scm_wta_dispatch_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7029 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 7030 | return scm_wta_dispatch_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 7031 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 7032 | return SCM_BOOL_F; |
c76b1eaf | 7033 | else |
73e4de09 | 7034 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 7035 | } |
1bbd0b84 | 7036 | #undef FUNC_NAME |
0f2d19dd JB |
7037 | |
7038 | ||
8a1f4f98 AW |
7039 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
7040 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
7041 | (SCM x, SCM y, SCM rest), | |
7042 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7043 | "non-increasing.") | |
7044 | #define FUNC_NAME s_scm_i_num_geq_p | |
7045 | { | |
7046 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7047 | return SCM_BOOL_T; | |
7048 | while (!scm_is_null (rest)) | |
7049 | { | |
7050 | if (scm_is_false (scm_geq_p (x, y))) | |
7051 | return SCM_BOOL_F; | |
7052 | x = y; | |
7053 | y = scm_car (rest); | |
7054 | rest = scm_cdr (rest); | |
7055 | } | |
7056 | return scm_geq_p (x, y); | |
7057 | } | |
7058 | #undef FUNC_NAME | |
7059 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
7060 | SCM |
7061 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 7062 | { |
c76b1eaf | 7063 | if (!SCM_NUMBERP (x)) |
fa075d40 | 7064 | return scm_wta_dispatch_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7065 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 7066 | return scm_wta_dispatch_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 7067 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 7068 | return SCM_BOOL_F; |
c76b1eaf | 7069 | else |
73e4de09 | 7070 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 7071 | } |
1bbd0b84 | 7072 | #undef FUNC_NAME |
0f2d19dd JB |
7073 | |
7074 | ||
2519490c MW |
7075 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
7076 | (SCM z), | |
7077 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
7078 | "zero.") | |
7079 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 7080 | { |
e11e83f3 | 7081 | if (SCM_I_INUMP (z)) |
bc36d050 | 7082 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 7083 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 7084 | return SCM_BOOL_F; |
0aacf84e | 7085 | else if (SCM_REALP (z)) |
73e4de09 | 7086 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 7087 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 7088 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 7089 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
7090 | else if (SCM_FRACTIONP (z)) |
7091 | return SCM_BOOL_F; | |
0aacf84e | 7092 | else |
fa075d40 | 7093 | return scm_wta_dispatch_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 7094 | } |
2519490c | 7095 | #undef FUNC_NAME |
0f2d19dd JB |
7096 | |
7097 | ||
2519490c MW |
7098 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
7099 | (SCM x), | |
7100 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
7101 | "zero.") | |
7102 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 7103 | { |
e11e83f3 MV |
7104 | if (SCM_I_INUMP (x)) |
7105 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
7106 | else if (SCM_BIGP (x)) |
7107 | { | |
7108 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7109 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7110 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
7111 | } |
7112 | else if (SCM_REALP (x)) | |
73e4de09 | 7113 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
7114 | else if (SCM_FRACTIONP (x)) |
7115 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7116 | else |
fa075d40 | 7117 | return scm_wta_dispatch_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 7118 | } |
2519490c | 7119 | #undef FUNC_NAME |
0f2d19dd JB |
7120 | |
7121 | ||
2519490c MW |
7122 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
7123 | (SCM x), | |
7124 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
7125 | "zero.") | |
7126 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 7127 | { |
e11e83f3 MV |
7128 | if (SCM_I_INUMP (x)) |
7129 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
7130 | else if (SCM_BIGP (x)) |
7131 | { | |
7132 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7133 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7134 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
7135 | } |
7136 | else if (SCM_REALP (x)) | |
73e4de09 | 7137 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
7138 | else if (SCM_FRACTIONP (x)) |
7139 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7140 | else |
fa075d40 | 7141 | return scm_wta_dispatch_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 7142 | } |
2519490c | 7143 | #undef FUNC_NAME |
0f2d19dd JB |
7144 | |
7145 | ||
2a06f791 KR |
7146 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
7147 | required by r5rs. On that basis, for exact/inexact combinations the | |
7148 | exact is converted to inexact to compare and possibly return. This is | |
7149 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
7150 | its test, such trouble is not required for min and max. */ | |
7151 | ||
78d3deb1 AW |
7152 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
7153 | (SCM x, SCM y, SCM rest), | |
7154 | "Return the maximum of all parameter values.") | |
7155 | #define FUNC_NAME s_scm_i_max | |
7156 | { | |
7157 | while (!scm_is_null (rest)) | |
7158 | { x = scm_max (x, y); | |
7159 | y = scm_car (rest); | |
7160 | rest = scm_cdr (rest); | |
7161 | } | |
7162 | return scm_max (x, y); | |
7163 | } | |
7164 | #undef FUNC_NAME | |
7165 | ||
7166 | #define s_max s_scm_i_max | |
7167 | #define g_max g_scm_i_max | |
7168 | ||
0f2d19dd | 7169 | SCM |
6e8d25a6 | 7170 | scm_max (SCM x, SCM y) |
0f2d19dd | 7171 | { |
0aacf84e MD |
7172 | if (SCM_UNBNDP (y)) |
7173 | { | |
7174 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7175 | return scm_wta_dispatch_0 (g_max, s_max); |
e11e83f3 | 7176 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7177 | return x; |
7178 | else | |
fa075d40 | 7179 | return scm_wta_dispatch_1 (g_max, x, SCM_ARG1, s_max); |
f872b822 | 7180 | } |
f4c627b3 | 7181 | |
e11e83f3 | 7182 | if (SCM_I_INUMP (x)) |
0aacf84e | 7183 | { |
e25f3727 | 7184 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7185 | if (SCM_I_INUMP (y)) |
0aacf84e | 7186 | { |
e25f3727 | 7187 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7188 | return (xx < yy) ? y : x; |
7189 | } | |
7190 | else if (SCM_BIGP (y)) | |
7191 | { | |
7192 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7193 | scm_remember_upto_here_1 (y); | |
7194 | return (sgn < 0) ? x : y; | |
7195 | } | |
7196 | else if (SCM_REALP (y)) | |
7197 | { | |
2e274311 MW |
7198 | double xxd = xx; |
7199 | double yyd = SCM_REAL_VALUE (y); | |
7200 | ||
7201 | if (xxd > yyd) | |
00472a22 | 7202 | return scm_i_from_double (xxd); |
2e274311 MW |
7203 | /* If y is a NaN, then "==" is false and we return the NaN */ |
7204 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7205 | return y; | |
7206 | /* Handle signed zeroes properly */ | |
7207 | else if (xx == 0) | |
7208 | return flo0; | |
7209 | else | |
7210 | return y; | |
0aacf84e | 7211 | } |
f92e85f7 MV |
7212 | else if (SCM_FRACTIONP (y)) |
7213 | { | |
e4bc5d6c | 7214 | use_less: |
73e4de09 | 7215 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 7216 | } |
0aacf84e | 7217 | else |
fa075d40 | 7218 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f872b822 | 7219 | } |
0aacf84e MD |
7220 | else if (SCM_BIGP (x)) |
7221 | { | |
e11e83f3 | 7222 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7223 | { |
7224 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7225 | scm_remember_upto_here_1 (x); | |
7226 | return (sgn < 0) ? y : x; | |
7227 | } | |
7228 | else if (SCM_BIGP (y)) | |
7229 | { | |
7230 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7231 | scm_remember_upto_here_2 (x, y); | |
7232 | return (cmp > 0) ? x : y; | |
7233 | } | |
7234 | else if (SCM_REALP (y)) | |
7235 | { | |
2a06f791 KR |
7236 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
7237 | double xx, yy; | |
7238 | big_real: | |
7239 | xx = scm_i_big2dbl (x); | |
7240 | yy = SCM_REAL_VALUE (y); | |
00472a22 | 7241 | return (xx > yy ? scm_i_from_double (xx) : y); |
0aacf84e | 7242 | } |
f92e85f7 MV |
7243 | else if (SCM_FRACTIONP (y)) |
7244 | { | |
e4bc5d6c | 7245 | goto use_less; |
f92e85f7 | 7246 | } |
0aacf84e | 7247 | else |
fa075d40 | 7248 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f4c627b3 | 7249 | } |
0aacf84e MD |
7250 | else if (SCM_REALP (x)) |
7251 | { | |
e11e83f3 | 7252 | if (SCM_I_INUMP (y)) |
0aacf84e | 7253 | { |
2e274311 MW |
7254 | scm_t_inum yy = SCM_I_INUM (y); |
7255 | double xxd = SCM_REAL_VALUE (x); | |
7256 | double yyd = yy; | |
7257 | ||
7258 | if (yyd > xxd) | |
00472a22 | 7259 | return scm_i_from_double (yyd); |
2e274311 MW |
7260 | /* If x is a NaN, then "==" is false and we return the NaN */ |
7261 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7262 | return x; | |
7263 | /* Handle signed zeroes properly */ | |
7264 | else if (yy == 0) | |
7265 | return flo0; | |
7266 | else | |
7267 | return x; | |
0aacf84e MD |
7268 | } |
7269 | else if (SCM_BIGP (y)) | |
7270 | { | |
b6f8f763 | 7271 | SCM_SWAP (x, y); |
2a06f791 | 7272 | goto big_real; |
0aacf84e MD |
7273 | } |
7274 | else if (SCM_REALP (y)) | |
7275 | { | |
0aacf84e | 7276 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7277 | double yy = SCM_REAL_VALUE (y); |
7278 | ||
b4c55c9c MW |
7279 | /* For purposes of max: nan > +inf.0 > everything else, |
7280 | per the R6RS errata */ | |
2e274311 MW |
7281 | if (xx > yy) |
7282 | return x; | |
7283 | else if (SCM_LIKELY (xx < yy)) | |
7284 | return y; | |
7285 | /* If neither (xx > yy) nor (xx < yy), then | |
7286 | either they're equal or one is a NaN */ | |
b4c55c9c MW |
7287 | else if (SCM_UNLIKELY (xx != yy)) |
7288 | return (xx != xx) ? x : y; /* Return the NaN */ | |
2e274311 | 7289 | /* xx == yy, but handle signed zeroes properly */ |
e1592f8a | 7290 | else if (copysign (1.0, yy) < 0.0) |
2e274311 | 7291 | return x; |
e1592f8a MW |
7292 | else |
7293 | return y; | |
0aacf84e | 7294 | } |
f92e85f7 MV |
7295 | else if (SCM_FRACTIONP (y)) |
7296 | { | |
7297 | double yy = scm_i_fraction2double (y); | |
7298 | double xx = SCM_REAL_VALUE (x); | |
00472a22 | 7299 | return (xx < yy) ? scm_i_from_double (yy) : x; |
f92e85f7 MV |
7300 | } |
7301 | else | |
fa075d40 | 7302 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f92e85f7 MV |
7303 | } |
7304 | else if (SCM_FRACTIONP (x)) | |
7305 | { | |
e11e83f3 | 7306 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7307 | { |
e4bc5d6c | 7308 | goto use_less; |
f92e85f7 MV |
7309 | } |
7310 | else if (SCM_BIGP (y)) | |
7311 | { | |
e4bc5d6c | 7312 | goto use_less; |
f92e85f7 MV |
7313 | } |
7314 | else if (SCM_REALP (y)) | |
7315 | { | |
7316 | double xx = scm_i_fraction2double (x); | |
2e274311 | 7317 | /* if y==NaN then ">" is false, so we return the NaN y */ |
00472a22 | 7318 | return (xx > SCM_REAL_VALUE (y)) ? scm_i_from_double (xx) : y; |
f92e85f7 MV |
7319 | } |
7320 | else if (SCM_FRACTIONP (y)) | |
7321 | { | |
e4bc5d6c | 7322 | goto use_less; |
f92e85f7 | 7323 | } |
0aacf84e | 7324 | else |
fa075d40 | 7325 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f872b822 | 7326 | } |
0aacf84e | 7327 | else |
fa075d40 | 7328 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
7329 | } |
7330 | ||
7331 | ||
78d3deb1 AW |
7332 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
7333 | (SCM x, SCM y, SCM rest), | |
7334 | "Return the minimum of all parameter values.") | |
7335 | #define FUNC_NAME s_scm_i_min | |
7336 | { | |
7337 | while (!scm_is_null (rest)) | |
7338 | { x = scm_min (x, y); | |
7339 | y = scm_car (rest); | |
7340 | rest = scm_cdr (rest); | |
7341 | } | |
7342 | return scm_min (x, y); | |
7343 | } | |
7344 | #undef FUNC_NAME | |
7345 | ||
7346 | #define s_min s_scm_i_min | |
7347 | #define g_min g_scm_i_min | |
7348 | ||
0f2d19dd | 7349 | SCM |
6e8d25a6 | 7350 | scm_min (SCM x, SCM y) |
0f2d19dd | 7351 | { |
0aacf84e MD |
7352 | if (SCM_UNBNDP (y)) |
7353 | { | |
7354 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7355 | return scm_wta_dispatch_0 (g_min, s_min); |
e11e83f3 | 7356 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7357 | return x; |
7358 | else | |
fa075d40 | 7359 | return scm_wta_dispatch_1 (g_min, x, SCM_ARG1, s_min); |
f872b822 | 7360 | } |
f4c627b3 | 7361 | |
e11e83f3 | 7362 | if (SCM_I_INUMP (x)) |
0aacf84e | 7363 | { |
e25f3727 | 7364 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7365 | if (SCM_I_INUMP (y)) |
0aacf84e | 7366 | { |
e25f3727 | 7367 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7368 | return (xx < yy) ? x : y; |
7369 | } | |
7370 | else if (SCM_BIGP (y)) | |
7371 | { | |
7372 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7373 | scm_remember_upto_here_1 (y); | |
7374 | return (sgn < 0) ? y : x; | |
7375 | } | |
7376 | else if (SCM_REALP (y)) | |
7377 | { | |
7378 | double z = xx; | |
7379 | /* if y==NaN then "<" is false and we return NaN */ | |
00472a22 | 7380 | return (z < SCM_REAL_VALUE (y)) ? scm_i_from_double (z) : y; |
0aacf84e | 7381 | } |
f92e85f7 MV |
7382 | else if (SCM_FRACTIONP (y)) |
7383 | { | |
e4bc5d6c | 7384 | use_less: |
73e4de09 | 7385 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 7386 | } |
0aacf84e | 7387 | else |
fa075d40 | 7388 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f872b822 | 7389 | } |
0aacf84e MD |
7390 | else if (SCM_BIGP (x)) |
7391 | { | |
e11e83f3 | 7392 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7393 | { |
7394 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7395 | scm_remember_upto_here_1 (x); | |
7396 | return (sgn < 0) ? x : y; | |
7397 | } | |
7398 | else if (SCM_BIGP (y)) | |
7399 | { | |
7400 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7401 | scm_remember_upto_here_2 (x, y); | |
7402 | return (cmp > 0) ? y : x; | |
7403 | } | |
7404 | else if (SCM_REALP (y)) | |
7405 | { | |
2a06f791 KR |
7406 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
7407 | double xx, yy; | |
7408 | big_real: | |
7409 | xx = scm_i_big2dbl (x); | |
7410 | yy = SCM_REAL_VALUE (y); | |
00472a22 | 7411 | return (xx < yy ? scm_i_from_double (xx) : y); |
0aacf84e | 7412 | } |
f92e85f7 MV |
7413 | else if (SCM_FRACTIONP (y)) |
7414 | { | |
e4bc5d6c | 7415 | goto use_less; |
f92e85f7 | 7416 | } |
0aacf84e | 7417 | else |
fa075d40 | 7418 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f4c627b3 | 7419 | } |
0aacf84e MD |
7420 | else if (SCM_REALP (x)) |
7421 | { | |
e11e83f3 | 7422 | if (SCM_I_INUMP (y)) |
0aacf84e | 7423 | { |
e11e83f3 | 7424 | double z = SCM_I_INUM (y); |
0aacf84e | 7425 | /* if x==NaN then "<" is false and we return NaN */ |
00472a22 | 7426 | return (z < SCM_REAL_VALUE (x)) ? scm_i_from_double (z) : x; |
0aacf84e MD |
7427 | } |
7428 | else if (SCM_BIGP (y)) | |
7429 | { | |
b6f8f763 | 7430 | SCM_SWAP (x, y); |
2a06f791 | 7431 | goto big_real; |
0aacf84e MD |
7432 | } |
7433 | else if (SCM_REALP (y)) | |
7434 | { | |
0aacf84e | 7435 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7436 | double yy = SCM_REAL_VALUE (y); |
7437 | ||
b4c55c9c MW |
7438 | /* For purposes of min: nan < -inf.0 < everything else, |
7439 | per the R6RS errata */ | |
2e274311 MW |
7440 | if (xx < yy) |
7441 | return x; | |
7442 | else if (SCM_LIKELY (xx > yy)) | |
7443 | return y; | |
7444 | /* If neither (xx < yy) nor (xx > yy), then | |
7445 | either they're equal or one is a NaN */ | |
b4c55c9c MW |
7446 | else if (SCM_UNLIKELY (xx != yy)) |
7447 | return (xx != xx) ? x : y; /* Return the NaN */ | |
2e274311 | 7448 | /* xx == yy, but handle signed zeroes properly */ |
e1592f8a | 7449 | else if (copysign (1.0, xx) < 0.0) |
2e274311 | 7450 | return x; |
e1592f8a MW |
7451 | else |
7452 | return y; | |
0aacf84e | 7453 | } |
f92e85f7 MV |
7454 | else if (SCM_FRACTIONP (y)) |
7455 | { | |
7456 | double yy = scm_i_fraction2double (y); | |
7457 | double xx = SCM_REAL_VALUE (x); | |
00472a22 | 7458 | return (yy < xx) ? scm_i_from_double (yy) : x; |
f92e85f7 | 7459 | } |
0aacf84e | 7460 | else |
fa075d40 | 7461 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f872b822 | 7462 | } |
f92e85f7 MV |
7463 | else if (SCM_FRACTIONP (x)) |
7464 | { | |
e11e83f3 | 7465 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7466 | { |
e4bc5d6c | 7467 | goto use_less; |
f92e85f7 MV |
7468 | } |
7469 | else if (SCM_BIGP (y)) | |
7470 | { | |
e4bc5d6c | 7471 | goto use_less; |
f92e85f7 MV |
7472 | } |
7473 | else if (SCM_REALP (y)) | |
7474 | { | |
7475 | double xx = scm_i_fraction2double (x); | |
2e274311 | 7476 | /* if y==NaN then "<" is false, so we return the NaN y */ |
00472a22 | 7477 | return (xx < SCM_REAL_VALUE (y)) ? scm_i_from_double (xx) : y; |
f92e85f7 MV |
7478 | } |
7479 | else if (SCM_FRACTIONP (y)) | |
7480 | { | |
e4bc5d6c | 7481 | goto use_less; |
f92e85f7 MV |
7482 | } |
7483 | else | |
fa075d40 | 7484 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7485 | } |
0aacf84e | 7486 | else |
fa075d40 | 7487 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7488 | } |
7489 | ||
7490 | ||
8ccd24f7 AW |
7491 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7492 | (SCM x, SCM y, SCM rest), | |
7493 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7494 | "any parameters." ) | |
7495 | #define FUNC_NAME s_scm_i_sum | |
7496 | { | |
7497 | while (!scm_is_null (rest)) | |
7498 | { x = scm_sum (x, y); | |
7499 | y = scm_car (rest); | |
7500 | rest = scm_cdr (rest); | |
7501 | } | |
7502 | return scm_sum (x, y); | |
7503 | } | |
7504 | #undef FUNC_NAME | |
7505 | ||
7506 | #define s_sum s_scm_i_sum | |
7507 | #define g_sum g_scm_i_sum | |
7508 | ||
0f2d19dd | 7509 | SCM |
6e8d25a6 | 7510 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7511 | { |
9cc37597 | 7512 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7513 | { |
7514 | if (SCM_NUMBERP (x)) return x; | |
7515 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
fa075d40 | 7516 | return scm_wta_dispatch_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7517 | } |
c209c88e | 7518 | |
9cc37597 | 7519 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7520 | { |
9cc37597 | 7521 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7522 | { |
e25f3727 AW |
7523 | scm_t_inum xx = SCM_I_INUM (x); |
7524 | scm_t_inum yy = SCM_I_INUM (y); | |
7525 | scm_t_inum z = xx + yy; | |
7526 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7527 | } |
7528 | else if (SCM_BIGP (y)) | |
7529 | { | |
7530 | SCM_SWAP (x, y); | |
7531 | goto add_big_inum; | |
7532 | } | |
7533 | else if (SCM_REALP (y)) | |
7534 | { | |
e25f3727 | 7535 | scm_t_inum xx = SCM_I_INUM (x); |
00472a22 | 7536 | return scm_i_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7537 | } |
7538 | else if (SCM_COMPLEXP (y)) | |
7539 | { | |
e25f3727 | 7540 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7541 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7542 | SCM_COMPLEX_IMAG (y)); |
7543 | } | |
f92e85f7 | 7544 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7545 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7546 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7547 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 | 7548 | else |
fa075d40 | 7549 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
0aacf84e MD |
7550 | } else if (SCM_BIGP (x)) |
7551 | { | |
e11e83f3 | 7552 | if (SCM_I_INUMP (y)) |
0aacf84e | 7553 | { |
e25f3727 | 7554 | scm_t_inum inum; |
0aacf84e MD |
7555 | int bigsgn; |
7556 | add_big_inum: | |
e11e83f3 | 7557 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7558 | if (inum == 0) |
7559 | return x; | |
7560 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7561 | if (inum < 0) | |
7562 | { | |
7563 | SCM result = scm_i_mkbig (); | |
7564 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7565 | scm_remember_upto_here_1 (x); | |
7566 | /* we know the result will have to be a bignum */ | |
7567 | if (bigsgn == -1) | |
7568 | return result; | |
7569 | return scm_i_normbig (result); | |
7570 | } | |
7571 | else | |
7572 | { | |
7573 | SCM result = scm_i_mkbig (); | |
7574 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7575 | scm_remember_upto_here_1 (x); | |
7576 | /* we know the result will have to be a bignum */ | |
7577 | if (bigsgn == 1) | |
7578 | return result; | |
7579 | return scm_i_normbig (result); | |
7580 | } | |
7581 | } | |
7582 | else if (SCM_BIGP (y)) | |
7583 | { | |
7584 | SCM result = scm_i_mkbig (); | |
7585 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7586 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7587 | mpz_add (SCM_I_BIG_MPZ (result), | |
7588 | SCM_I_BIG_MPZ (x), | |
7589 | SCM_I_BIG_MPZ (y)); | |
7590 | scm_remember_upto_here_2 (x, y); | |
7591 | /* we know the result will have to be a bignum */ | |
7592 | if (sgn_x == sgn_y) | |
7593 | return result; | |
7594 | return scm_i_normbig (result); | |
7595 | } | |
7596 | else if (SCM_REALP (y)) | |
7597 | { | |
7598 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7599 | scm_remember_upto_here_1 (x); | |
00472a22 | 7600 | return scm_i_from_double (result); |
0aacf84e MD |
7601 | } |
7602 | else if (SCM_COMPLEXP (y)) | |
7603 | { | |
7604 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7605 | + SCM_COMPLEX_REAL (y)); | |
7606 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7607 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7608 | } |
f92e85f7 | 7609 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7610 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7611 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7612 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7613 | else |
fa075d40 | 7614 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
0f2d19dd | 7615 | } |
0aacf84e MD |
7616 | else if (SCM_REALP (x)) |
7617 | { | |
e11e83f3 | 7618 | if (SCM_I_INUMP (y)) |
00472a22 | 7619 | return scm_i_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7620 | else if (SCM_BIGP (y)) |
7621 | { | |
7622 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7623 | scm_remember_upto_here_1 (y); | |
00472a22 | 7624 | return scm_i_from_double (result); |
0aacf84e MD |
7625 | } |
7626 | else if (SCM_REALP (y)) | |
00472a22 | 7627 | return scm_i_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7628 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7629 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7630 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7631 | else if (SCM_FRACTIONP (y)) |
00472a22 | 7632 | return scm_i_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e | 7633 | else |
fa075d40 | 7634 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
f872b822 | 7635 | } |
0aacf84e MD |
7636 | else if (SCM_COMPLEXP (x)) |
7637 | { | |
e11e83f3 | 7638 | if (SCM_I_INUMP (y)) |
8507ec80 | 7639 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7640 | SCM_COMPLEX_IMAG (x)); |
7641 | else if (SCM_BIGP (y)) | |
7642 | { | |
7643 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7644 | + SCM_COMPLEX_REAL (x)); | |
7645 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7646 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7647 | } |
7648 | else if (SCM_REALP (y)) | |
8507ec80 | 7649 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7650 | SCM_COMPLEX_IMAG (x)); |
7651 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7652 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7653 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7654 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7655 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7656 | SCM_COMPLEX_IMAG (x)); |
7657 | else | |
fa075d40 | 7658 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
f92e85f7 MV |
7659 | } |
7660 | else if (SCM_FRACTIONP (x)) | |
7661 | { | |
e11e83f3 | 7662 | if (SCM_I_INUMP (y)) |
cba42c93 | 7663 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7664 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7665 | SCM_FRACTION_DENOMINATOR (x)); | |
7666 | else if (SCM_BIGP (y)) | |
cba42c93 | 7667 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7668 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7669 | SCM_FRACTION_DENOMINATOR (x)); | |
7670 | else if (SCM_REALP (y)) | |
00472a22 | 7671 | return scm_i_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7672 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7673 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7674 | SCM_COMPLEX_IMAG (y)); |
7675 | else if (SCM_FRACTIONP (y)) | |
7676 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7677 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7678 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7679 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7680 | else |
fa075d40 | 7681 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
98cb6e75 | 7682 | } |
0aacf84e | 7683 | else |
fa075d40 | 7684 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7685 | } |
7686 | ||
7687 | ||
40882e3d KR |
7688 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7689 | (SCM x), | |
7690 | "Return @math{@var{x}+1}.") | |
7691 | #define FUNC_NAME s_scm_oneplus | |
7692 | { | |
cff5fa33 | 7693 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7694 | } |
7695 | #undef FUNC_NAME | |
7696 | ||
7697 | ||
78d3deb1 AW |
7698 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7699 | (SCM x, SCM y, SCM rest), | |
7700 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7701 | "the sum of all but the first argument are subtracted from the first\n" | |
7702 | "argument.") | |
7703 | #define FUNC_NAME s_scm_i_difference | |
7704 | { | |
7705 | while (!scm_is_null (rest)) | |
7706 | { x = scm_difference (x, y); | |
7707 | y = scm_car (rest); | |
7708 | rest = scm_cdr (rest); | |
7709 | } | |
7710 | return scm_difference (x, y); | |
7711 | } | |
7712 | #undef FUNC_NAME | |
7713 | ||
7714 | #define s_difference s_scm_i_difference | |
7715 | #define g_difference g_scm_i_difference | |
7716 | ||
0f2d19dd | 7717 | SCM |
6e8d25a6 | 7718 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7719 | #define FUNC_NAME s_difference |
0f2d19dd | 7720 | { |
9cc37597 | 7721 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7722 | { |
7723 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7724 | return scm_wta_dispatch_0 (g_difference, s_difference); |
ca46fb90 | 7725 | else |
e11e83f3 | 7726 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7727 | { |
e25f3727 | 7728 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7729 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7730 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7731 | else |
e25f3727 | 7732 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7733 | } |
7734 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7735 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7736 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7737 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7738 | else if (SCM_REALP (x)) | |
00472a22 | 7739 | return scm_i_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7740 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7741 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7742 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7743 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
7744 | return scm_i_make_ratio_already_reduced |
7745 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
7746 | SCM_FRACTION_DENOMINATOR (x)); | |
ca46fb90 | 7747 | else |
fa075d40 | 7748 | return scm_wta_dispatch_1 (g_difference, x, SCM_ARG1, s_difference); |
f872b822 | 7749 | } |
ca46fb90 | 7750 | |
9cc37597 | 7751 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7752 | { |
9cc37597 | 7753 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7754 | { |
e25f3727 AW |
7755 | scm_t_inum xx = SCM_I_INUM (x); |
7756 | scm_t_inum yy = SCM_I_INUM (y); | |
7757 | scm_t_inum z = xx - yy; | |
0aacf84e | 7758 | if (SCM_FIXABLE (z)) |
d956fa6f | 7759 | return SCM_I_MAKINUM (z); |
0aacf84e | 7760 | else |
e25f3727 | 7761 | return scm_i_inum2big (z); |
0aacf84e MD |
7762 | } |
7763 | else if (SCM_BIGP (y)) | |
7764 | { | |
7765 | /* inum-x - big-y */ | |
e25f3727 | 7766 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7767 | |
0aacf84e | 7768 | if (xx == 0) |
b5c40589 MW |
7769 | { |
7770 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7771 | bignum, but negating that gives a fixnum. */ | |
7772 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7773 | } | |
0aacf84e MD |
7774 | else |
7775 | { | |
7776 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7777 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7778 | |
0aacf84e MD |
7779 | if (xx >= 0) |
7780 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7781 | else | |
7782 | { | |
7783 | /* x - y == -(y + -x) */ | |
7784 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7785 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7786 | } | |
7787 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7788 | |
0aacf84e MD |
7789 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7790 | /* we know the result will have to be a bignum */ | |
7791 | return result; | |
7792 | else | |
7793 | return scm_i_normbig (result); | |
7794 | } | |
7795 | } | |
7796 | else if (SCM_REALP (y)) | |
7797 | { | |
e25f3727 | 7798 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7799 | |
7800 | /* | |
7801 | * We need to handle x == exact 0 | |
7802 | * specially because R6RS states that: | |
7803 | * (- 0.0) ==> -0.0 and | |
7804 | * (- 0.0 0.0) ==> 0.0 | |
7805 | * and the scheme compiler changes | |
7806 | * (- 0.0) into (- 0 0.0) | |
7807 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7808 | * At the C level, (-x) is different than (0.0 - x). | |
7809 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7810 | */ | |
7811 | if (xx == 0) | |
00472a22 | 7812 | return scm_i_from_double (- SCM_REAL_VALUE (y)); |
9b9ef10c | 7813 | else |
00472a22 | 7814 | return scm_i_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
7815 | } |
7816 | else if (SCM_COMPLEXP (y)) | |
7817 | { | |
e25f3727 | 7818 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7819 | |
7820 | /* We need to handle x == exact 0 specially. | |
7821 | See the comment above (for SCM_REALP (y)) */ | |
7822 | if (xx == 0) | |
7823 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7824 | - SCM_COMPLEX_IMAG (y)); | |
7825 | else | |
7826 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7827 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7828 | } |
f92e85f7 MV |
7829 | else if (SCM_FRACTIONP (y)) |
7830 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7831 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7832 | SCM_FRACTION_NUMERATOR (y)), |
7833 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7834 | else |
fa075d40 | 7835 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
f872b822 | 7836 | } |
0aacf84e MD |
7837 | else if (SCM_BIGP (x)) |
7838 | { | |
e11e83f3 | 7839 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7840 | { |
7841 | /* big-x - inum-y */ | |
e25f3727 | 7842 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7843 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7844 | |
0aacf84e MD |
7845 | scm_remember_upto_here_1 (x); |
7846 | if (sgn_x == 0) | |
c71b0706 | 7847 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7848 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7849 | else |
7850 | { | |
7851 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7852 | |
708f22c6 KR |
7853 | if (yy >= 0) |
7854 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7855 | else | |
7856 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7857 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7858 | |
0aacf84e MD |
7859 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7860 | /* we know the result will have to be a bignum */ | |
7861 | return result; | |
7862 | else | |
7863 | return scm_i_normbig (result); | |
7864 | } | |
7865 | } | |
7866 | else if (SCM_BIGP (y)) | |
7867 | { | |
7868 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7869 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7870 | SCM result = scm_i_mkbig (); | |
7871 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7872 | SCM_I_BIG_MPZ (x), | |
7873 | SCM_I_BIG_MPZ (y)); | |
7874 | scm_remember_upto_here_2 (x, y); | |
7875 | /* we know the result will have to be a bignum */ | |
7876 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7877 | return result; | |
7878 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7879 | return result; | |
7880 | return scm_i_normbig (result); | |
7881 | } | |
7882 | else if (SCM_REALP (y)) | |
7883 | { | |
7884 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7885 | scm_remember_upto_here_1 (x); | |
00472a22 | 7886 | return scm_i_from_double (result); |
0aacf84e MD |
7887 | } |
7888 | else if (SCM_COMPLEXP (y)) | |
7889 | { | |
7890 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7891 | - SCM_COMPLEX_REAL (y)); | |
7892 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7893 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7894 | } |
f92e85f7 | 7895 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7896 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7897 | SCM_FRACTION_NUMERATOR (y)), |
7898 | SCM_FRACTION_DENOMINATOR (y)); | |
fa075d40 AW |
7899 | else |
7900 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
ca46fb90 | 7901 | } |
0aacf84e MD |
7902 | else if (SCM_REALP (x)) |
7903 | { | |
e11e83f3 | 7904 | if (SCM_I_INUMP (y)) |
00472a22 | 7905 | return scm_i_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7906 | else if (SCM_BIGP (y)) |
7907 | { | |
7908 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7909 | scm_remember_upto_here_1 (x); | |
00472a22 | 7910 | return scm_i_from_double (result); |
0aacf84e MD |
7911 | } |
7912 | else if (SCM_REALP (y)) | |
00472a22 | 7913 | return scm_i_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7914 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7915 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7916 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7917 | else if (SCM_FRACTIONP (y)) |
00472a22 | 7918 | return scm_i_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e | 7919 | else |
fa075d40 | 7920 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
98cb6e75 | 7921 | } |
0aacf84e MD |
7922 | else if (SCM_COMPLEXP (x)) |
7923 | { | |
e11e83f3 | 7924 | if (SCM_I_INUMP (y)) |
8507ec80 | 7925 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7926 | SCM_COMPLEX_IMAG (x)); |
7927 | else if (SCM_BIGP (y)) | |
7928 | { | |
7929 | double real_part = (SCM_COMPLEX_REAL (x) | |
7930 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7931 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7932 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7933 | } |
7934 | else if (SCM_REALP (y)) | |
8507ec80 | 7935 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7936 | SCM_COMPLEX_IMAG (x)); |
7937 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7938 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7939 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7940 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7941 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7942 | SCM_COMPLEX_IMAG (x)); |
7943 | else | |
fa075d40 | 7944 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
f92e85f7 MV |
7945 | } |
7946 | else if (SCM_FRACTIONP (x)) | |
7947 | { | |
e11e83f3 | 7948 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7949 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7950 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7951 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7952 | SCM_FRACTION_DENOMINATOR (x)); | |
7953 | else if (SCM_BIGP (y)) | |
cba42c93 | 7954 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7955 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7956 | SCM_FRACTION_DENOMINATOR (x)); | |
7957 | else if (SCM_REALP (y)) | |
00472a22 | 7958 | return scm_i_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7959 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7960 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7961 | -SCM_COMPLEX_IMAG (y)); |
7962 | else if (SCM_FRACTIONP (y)) | |
7963 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7964 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7965 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7966 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7967 | else |
fa075d40 | 7968 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
98cb6e75 | 7969 | } |
0aacf84e | 7970 | else |
fa075d40 | 7971 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7972 | } |
c05e97b7 | 7973 | #undef FUNC_NAME |
0f2d19dd | 7974 | |
ca46fb90 | 7975 | |
40882e3d KR |
7976 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7977 | (SCM x), | |
7978 | "Return @math{@var{x}-1}.") | |
7979 | #define FUNC_NAME s_scm_oneminus | |
7980 | { | |
cff5fa33 | 7981 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7982 | } |
7983 | #undef FUNC_NAME | |
7984 | ||
7985 | ||
78d3deb1 AW |
7986 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7987 | (SCM x, SCM y, SCM rest), | |
7988 | "Return the product of all arguments. If called without arguments,\n" | |
7989 | "1 is returned.") | |
7990 | #define FUNC_NAME s_scm_i_product | |
7991 | { | |
7992 | while (!scm_is_null (rest)) | |
7993 | { x = scm_product (x, y); | |
7994 | y = scm_car (rest); | |
7995 | rest = scm_cdr (rest); | |
7996 | } | |
7997 | return scm_product (x, y); | |
7998 | } | |
7999 | #undef FUNC_NAME | |
8000 | ||
8001 | #define s_product s_scm_i_product | |
8002 | #define g_product g_scm_i_product | |
8003 | ||
0f2d19dd | 8004 | SCM |
6e8d25a6 | 8005 | scm_product (SCM x, SCM y) |
0f2d19dd | 8006 | { |
9cc37597 | 8007 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8008 | { |
8009 | if (SCM_UNBNDP (x)) | |
d956fa6f | 8010 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
8011 | else if (SCM_NUMBERP (x)) |
8012 | return x; | |
8013 | else | |
fa075d40 | 8014 | return scm_wta_dispatch_1 (g_product, x, SCM_ARG1, s_product); |
f872b822 | 8015 | } |
ca46fb90 | 8016 | |
9cc37597 | 8017 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8018 | { |
e25f3727 | 8019 | scm_t_inum xx; |
f4c627b3 | 8020 | |
5e791807 | 8021 | xinum: |
e11e83f3 | 8022 | xx = SCM_I_INUM (x); |
f4c627b3 | 8023 | |
0aacf84e MD |
8024 | switch (xx) |
8025 | { | |
5e791807 MW |
8026 | case 1: |
8027 | /* exact1 is the universal multiplicative identity */ | |
8028 | return y; | |
8029 | break; | |
8030 | case 0: | |
8031 | /* exact0 times a fixnum is exact0: optimize this case */ | |
8032 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
8033 | return SCM_INUM0; | |
8034 | /* if the other argument is inexact, the result is inexact, | |
8035 | and we must do the multiplication in order to handle | |
8036 | infinities and NaNs properly. */ | |
8037 | else if (SCM_REALP (y)) | |
00472a22 | 8038 | return scm_i_from_double (0.0 * SCM_REAL_VALUE (y)); |
5e791807 MW |
8039 | else if (SCM_COMPLEXP (y)) |
8040 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
8041 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
8042 | /* we've already handled inexact numbers, | |
8043 | so y must be exact, and we return exact0 */ | |
8044 | else if (SCM_NUMP (y)) | |
8045 | return SCM_INUM0; | |
8046 | else | |
fa075d40 | 8047 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
5e791807 MW |
8048 | break; |
8049 | case -1: | |
b5c40589 | 8050 | /* |
5e791807 MW |
8051 | * This case is important for more than just optimization. |
8052 | * It handles the case of negating | |
b5c40589 MW |
8053 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
8054 | * which is a bignum that must be changed back into a fixnum. | |
8055 | * Failure to do so will cause the following to return #f: | |
8056 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
8057 | */ | |
b5c40589 MW |
8058 | return scm_difference(y, SCM_UNDEFINED); |
8059 | break; | |
0aacf84e | 8060 | } |
f4c627b3 | 8061 | |
9cc37597 | 8062 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8063 | { |
e25f3727 | 8064 | scm_t_inum yy = SCM_I_INUM (y); |
2355f017 MW |
8065 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
8066 | scm_t_int64 kk = xx * (scm_t_int64) yy; | |
8067 | if (SCM_FIXABLE (kk)) | |
8068 | return SCM_I_MAKINUM (kk); | |
8069 | #else | |
8070 | scm_t_inum axx = (xx > 0) ? xx : -xx; | |
8071 | scm_t_inum ayy = (yy > 0) ? yy : -yy; | |
8072 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) | |
8073 | return SCM_I_MAKINUM (xx * yy); | |
8074 | #endif | |
0aacf84e MD |
8075 | else |
8076 | { | |
e25f3727 | 8077 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
8078 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
8079 | return scm_i_normbig (result); | |
8080 | } | |
8081 | } | |
8082 | else if (SCM_BIGP (y)) | |
8083 | { | |
8084 | SCM result = scm_i_mkbig (); | |
8085 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
8086 | scm_remember_upto_here_1 (y); | |
8087 | return result; | |
8088 | } | |
8089 | else if (SCM_REALP (y)) | |
00472a22 | 8090 | return scm_i_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 8091 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8092 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 8093 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8094 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8095 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 8096 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e | 8097 | else |
fa075d40 | 8098 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8099 | } |
0aacf84e MD |
8100 | else if (SCM_BIGP (x)) |
8101 | { | |
e11e83f3 | 8102 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
8103 | { |
8104 | SCM_SWAP (x, y); | |
5e791807 | 8105 | goto xinum; |
0aacf84e MD |
8106 | } |
8107 | else if (SCM_BIGP (y)) | |
8108 | { | |
8109 | SCM result = scm_i_mkbig (); | |
8110 | mpz_mul (SCM_I_BIG_MPZ (result), | |
8111 | SCM_I_BIG_MPZ (x), | |
8112 | SCM_I_BIG_MPZ (y)); | |
8113 | scm_remember_upto_here_2 (x, y); | |
8114 | return result; | |
8115 | } | |
8116 | else if (SCM_REALP (y)) | |
8117 | { | |
8118 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
8119 | scm_remember_upto_here_1 (x); | |
00472a22 | 8120 | return scm_i_from_double (result); |
0aacf84e MD |
8121 | } |
8122 | else if (SCM_COMPLEXP (y)) | |
8123 | { | |
8124 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
8125 | scm_remember_upto_here_1 (x); | |
8507ec80 | 8126 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
8127 | z * SCM_COMPLEX_IMAG (y)); |
8128 | } | |
f92e85f7 | 8129 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8130 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 8131 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e | 8132 | else |
fa075d40 | 8133 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8134 | } |
0aacf84e MD |
8135 | else if (SCM_REALP (x)) |
8136 | { | |
e11e83f3 | 8137 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8138 | { |
8139 | SCM_SWAP (x, y); | |
8140 | goto xinum; | |
8141 | } | |
0aacf84e MD |
8142 | else if (SCM_BIGP (y)) |
8143 | { | |
8144 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
8145 | scm_remember_upto_here_1 (y); | |
00472a22 | 8146 | return scm_i_from_double (result); |
0aacf84e MD |
8147 | } |
8148 | else if (SCM_REALP (y)) | |
00472a22 | 8149 | return scm_i_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 8150 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8151 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 8152 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8153 | else if (SCM_FRACTIONP (y)) |
00472a22 | 8154 | return scm_i_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e | 8155 | else |
fa075d40 | 8156 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8157 | } |
0aacf84e MD |
8158 | else if (SCM_COMPLEXP (x)) |
8159 | { | |
e11e83f3 | 8160 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8161 | { |
8162 | SCM_SWAP (x, y); | |
8163 | goto xinum; | |
8164 | } | |
0aacf84e MD |
8165 | else if (SCM_BIGP (y)) |
8166 | { | |
8167 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8168 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8169 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 8170 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
8171 | } |
8172 | else if (SCM_REALP (y)) | |
8507ec80 | 8173 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
8174 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
8175 | else if (SCM_COMPLEXP (y)) | |
8176 | { | |
8507ec80 | 8177 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
8178 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
8179 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
8180 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
8181 | } | |
f92e85f7 MV |
8182 | else if (SCM_FRACTIONP (y)) |
8183 | { | |
8184 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8185 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
8186 | yy * SCM_COMPLEX_IMAG (x)); |
8187 | } | |
8188 | else | |
fa075d40 | 8189 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f92e85f7 MV |
8190 | } |
8191 | else if (SCM_FRACTIONP (x)) | |
8192 | { | |
e11e83f3 | 8193 | if (SCM_I_INUMP (y)) |
cba42c93 | 8194 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8195 | SCM_FRACTION_DENOMINATOR (x)); |
8196 | else if (SCM_BIGP (y)) | |
cba42c93 | 8197 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8198 | SCM_FRACTION_DENOMINATOR (x)); |
8199 | else if (SCM_REALP (y)) | |
00472a22 | 8200 | return scm_i_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
8201 | else if (SCM_COMPLEXP (y)) |
8202 | { | |
8203 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 8204 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
8205 | xx * SCM_COMPLEX_IMAG (y)); |
8206 | } | |
8207 | else if (SCM_FRACTIONP (y)) | |
8208 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 8209 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8210 | SCM_FRACTION_NUMERATOR (y)), |
8211 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
8212 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 8213 | else |
fa075d40 | 8214 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8215 | } |
0aacf84e | 8216 | else |
fa075d40 | 8217 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
8218 | } |
8219 | ||
7351e207 MV |
8220 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
8221 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
8222 | #define ALLOW_DIVIDE_BY_ZERO | |
8223 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
8224 | #endif | |
0f2d19dd | 8225 | |
ba74ef4e MV |
8226 | /* The code below for complex division is adapted from the GNU |
8227 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
8228 | this copyright: */ | |
8229 | ||
8230 | /**************************************************************** | |
8231 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
8232 | ||
8233 | Permission to use, copy, modify, and distribute this software | |
8234 | and its documentation for any purpose and without fee is hereby | |
8235 | granted, provided that the above copyright notice appear in all | |
8236 | copies and that both that the copyright notice and this | |
8237 | permission notice and warranty disclaimer appear in supporting | |
8238 | documentation, and that the names of AT&T Bell Laboratories or | |
8239 | Bellcore or any of their entities not be used in advertising or | |
8240 | publicity pertaining to distribution of the software without | |
8241 | specific, written prior permission. | |
8242 | ||
8243 | AT&T and Bellcore disclaim all warranties with regard to this | |
8244 | software, including all implied warranties of merchantability | |
8245 | and fitness. In no event shall AT&T or Bellcore be liable for | |
8246 | any special, indirect or consequential damages or any damages | |
8247 | whatsoever resulting from loss of use, data or profits, whether | |
8248 | in an action of contract, negligence or other tortious action, | |
8249 | arising out of or in connection with the use or performance of | |
8250 | this software. | |
8251 | ****************************************************************/ | |
8252 | ||
78d3deb1 AW |
8253 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
8254 | (SCM x, SCM y, SCM rest), | |
8255 | "Divide the first argument by the product of the remaining\n" | |
8256 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
8257 | "returned.") | |
8258 | #define FUNC_NAME s_scm_i_divide | |
8259 | { | |
8260 | while (!scm_is_null (rest)) | |
8261 | { x = scm_divide (x, y); | |
8262 | y = scm_car (rest); | |
8263 | rest = scm_cdr (rest); | |
8264 | } | |
8265 | return scm_divide (x, y); | |
8266 | } | |
8267 | #undef FUNC_NAME | |
8268 | ||
8269 | #define s_divide s_scm_i_divide | |
8270 | #define g_divide g_scm_i_divide | |
8271 | ||
98237784 MW |
8272 | SCM |
8273 | scm_divide (SCM x, SCM y) | |
78d3deb1 | 8274 | #define FUNC_NAME s_divide |
0f2d19dd | 8275 | { |
f8de44c1 DH |
8276 | double a; |
8277 | ||
9cc37597 | 8278 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8279 | { |
8280 | if (SCM_UNBNDP (x)) | |
fa075d40 | 8281 | return scm_wta_dispatch_0 (g_divide, s_divide); |
e11e83f3 | 8282 | else if (SCM_I_INUMP (x)) |
0aacf84e | 8283 | { |
e25f3727 | 8284 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
8285 | if (xx == 1 || xx == -1) |
8286 | return x; | |
7351e207 | 8287 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8288 | else if (xx == 0) |
8289 | scm_num_overflow (s_divide); | |
7351e207 | 8290 | #endif |
0aacf84e | 8291 | else |
98237784 | 8292 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8293 | } |
8294 | else if (SCM_BIGP (x)) | |
98237784 | 8295 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8296 | else if (SCM_REALP (x)) |
8297 | { | |
8298 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 8299 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8300 | if (xx == 0.0) |
8301 | scm_num_overflow (s_divide); | |
8302 | else | |
7351e207 | 8303 | #endif |
00472a22 | 8304 | return scm_i_from_double (1.0 / xx); |
0aacf84e MD |
8305 | } |
8306 | else if (SCM_COMPLEXP (x)) | |
8307 | { | |
8308 | double r = SCM_COMPLEX_REAL (x); | |
8309 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 8310 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8311 | { |
8312 | double t = r / i; | |
8313 | double d = i * (1.0 + t * t); | |
8507ec80 | 8314 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
8315 | } |
8316 | else | |
8317 | { | |
8318 | double t = i / r; | |
8319 | double d = r * (1.0 + t * t); | |
8507ec80 | 8320 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
8321 | } |
8322 | } | |
f92e85f7 | 8323 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
8324 | return scm_i_make_ratio_already_reduced (SCM_FRACTION_DENOMINATOR (x), |
8325 | SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 8326 | else |
fa075d40 | 8327 | return scm_wta_dispatch_1 (g_divide, x, SCM_ARG1, s_divide); |
f8de44c1 | 8328 | } |
f8de44c1 | 8329 | |
9cc37597 | 8330 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8331 | { |
e25f3727 | 8332 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 8333 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8334 | { |
e25f3727 | 8335 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8336 | if (yy == 0) |
8337 | { | |
7351e207 | 8338 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8339 | scm_num_overflow (s_divide); |
7351e207 | 8340 | #else |
00472a22 | 8341 | return scm_i_from_double ((double) xx / (double) yy); |
7351e207 | 8342 | #endif |
0aacf84e MD |
8343 | } |
8344 | else if (xx % yy != 0) | |
98237784 | 8345 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8346 | else |
8347 | { | |
e25f3727 | 8348 | scm_t_inum z = xx / yy; |
0aacf84e | 8349 | if (SCM_FIXABLE (z)) |
d956fa6f | 8350 | return SCM_I_MAKINUM (z); |
0aacf84e | 8351 | else |
e25f3727 | 8352 | return scm_i_inum2big (z); |
0aacf84e | 8353 | } |
f872b822 | 8354 | } |
0aacf84e | 8355 | else if (SCM_BIGP (y)) |
98237784 | 8356 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8357 | else if (SCM_REALP (y)) |
8358 | { | |
8359 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8360 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8361 | if (yy == 0.0) |
8362 | scm_num_overflow (s_divide); | |
8363 | else | |
7351e207 | 8364 | #endif |
98237784 MW |
8365 | /* FIXME: Precision may be lost here due to: |
8366 | (1) The cast from 'scm_t_inum' to 'double' | |
8367 | (2) Double rounding */ | |
00472a22 | 8368 | return scm_i_from_double ((double) xx / yy); |
ba74ef4e | 8369 | } |
0aacf84e MD |
8370 | else if (SCM_COMPLEXP (y)) |
8371 | { | |
8372 | a = xx; | |
8373 | complex_div: /* y _must_ be a complex number */ | |
8374 | { | |
8375 | double r = SCM_COMPLEX_REAL (y); | |
8376 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8377 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8378 | { |
8379 | double t = r / i; | |
8380 | double d = i * (1.0 + t * t); | |
8507ec80 | 8381 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
8382 | } |
8383 | else | |
8384 | { | |
8385 | double t = i / r; | |
8386 | double d = r * (1.0 + t * t); | |
8507ec80 | 8387 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
8388 | } |
8389 | } | |
8390 | } | |
f92e85f7 MV |
8391 | else if (SCM_FRACTIONP (y)) |
8392 | /* a / b/c = ac / b */ | |
cba42c93 | 8393 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8394 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e | 8395 | else |
fa075d40 | 8396 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f8de44c1 | 8397 | } |
0aacf84e MD |
8398 | else if (SCM_BIGP (x)) |
8399 | { | |
e11e83f3 | 8400 | if (SCM_I_INUMP (y)) |
0aacf84e | 8401 | { |
e25f3727 | 8402 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8403 | if (yy == 0) |
8404 | { | |
7351e207 | 8405 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8406 | scm_num_overflow (s_divide); |
7351e207 | 8407 | #else |
0aacf84e MD |
8408 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8409 | scm_remember_upto_here_1 (x); | |
8410 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8411 | #endif |
0aacf84e MD |
8412 | } |
8413 | else if (yy == 1) | |
8414 | return x; | |
8415 | else | |
8416 | { | |
8417 | /* FIXME: HMM, what are the relative performance issues here? | |
8418 | We need to test. Is it faster on average to test | |
8419 | divisible_p, then perform whichever operation, or is it | |
8420 | faster to perform the integer div opportunistically and | |
8421 | switch to real if there's a remainder? For now we take the | |
8422 | middle ground: test, then if divisible, use the faster div | |
8423 | func. */ | |
8424 | ||
e25f3727 | 8425 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8426 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8427 | ||
8428 | if (divisible_p) | |
8429 | { | |
8430 | SCM result = scm_i_mkbig (); | |
8431 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8432 | scm_remember_upto_here_1 (x); | |
8433 | if (yy < 0) | |
8434 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8435 | return scm_i_normbig (result); | |
8436 | } | |
8437 | else | |
98237784 | 8438 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8439 | } |
8440 | } | |
8441 | else if (SCM_BIGP (y)) | |
8442 | { | |
98237784 MW |
8443 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8444 | SCM_I_BIG_MPZ (y)); | |
8445 | if (divisible_p) | |
8446 | { | |
8447 | SCM result = scm_i_mkbig (); | |
8448 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8449 | SCM_I_BIG_MPZ (x), | |
8450 | SCM_I_BIG_MPZ (y)); | |
8451 | scm_remember_upto_here_2 (x, y); | |
8452 | return scm_i_normbig (result); | |
8453 | } | |
8454 | else | |
8455 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8456 | } |
8457 | else if (SCM_REALP (y)) | |
8458 | { | |
8459 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8460 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8461 | if (yy == 0.0) |
8462 | scm_num_overflow (s_divide); | |
8463 | else | |
7351e207 | 8464 | #endif |
98237784 MW |
8465 | /* FIXME: Precision may be lost here due to: |
8466 | (1) scm_i_big2dbl (2) Double rounding */ | |
00472a22 | 8467 | return scm_i_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8468 | } |
8469 | else if (SCM_COMPLEXP (y)) | |
8470 | { | |
8471 | a = scm_i_big2dbl (x); | |
8472 | goto complex_div; | |
8473 | } | |
f92e85f7 | 8474 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8475 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8476 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e | 8477 | else |
fa075d40 | 8478 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f872b822 | 8479 | } |
0aacf84e MD |
8480 | else if (SCM_REALP (x)) |
8481 | { | |
8482 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8483 | if (SCM_I_INUMP (y)) |
0aacf84e | 8484 | { |
e25f3727 | 8485 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8486 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8487 | if (yy == 0) |
8488 | scm_num_overflow (s_divide); | |
8489 | else | |
7351e207 | 8490 | #endif |
98237784 MW |
8491 | /* FIXME: Precision may be lost here due to: |
8492 | (1) The cast from 'scm_t_inum' to 'double' | |
8493 | (2) Double rounding */ | |
00472a22 | 8494 | return scm_i_from_double (rx / (double) yy); |
0aacf84e MD |
8495 | } |
8496 | else if (SCM_BIGP (y)) | |
8497 | { | |
98237784 MW |
8498 | /* FIXME: Precision may be lost here due to: |
8499 | (1) The conversion from bignum to double | |
8500 | (2) Double rounding */ | |
0aacf84e MD |
8501 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8502 | scm_remember_upto_here_1 (y); | |
00472a22 | 8503 | return scm_i_from_double (rx / dby); |
0aacf84e MD |
8504 | } |
8505 | else if (SCM_REALP (y)) | |
8506 | { | |
8507 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8508 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8509 | if (yy == 0.0) |
8510 | scm_num_overflow (s_divide); | |
8511 | else | |
7351e207 | 8512 | #endif |
00472a22 | 8513 | return scm_i_from_double (rx / yy); |
0aacf84e MD |
8514 | } |
8515 | else if (SCM_COMPLEXP (y)) | |
8516 | { | |
8517 | a = rx; | |
8518 | goto complex_div; | |
8519 | } | |
f92e85f7 | 8520 | else if (SCM_FRACTIONP (y)) |
00472a22 | 8521 | return scm_i_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e | 8522 | else |
fa075d40 | 8523 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f872b822 | 8524 | } |
0aacf84e MD |
8525 | else if (SCM_COMPLEXP (x)) |
8526 | { | |
8527 | double rx = SCM_COMPLEX_REAL (x); | |
8528 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8529 | if (SCM_I_INUMP (y)) |
0aacf84e | 8530 | { |
e25f3727 | 8531 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8532 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8533 | if (yy == 0) |
8534 | scm_num_overflow (s_divide); | |
8535 | else | |
7351e207 | 8536 | #endif |
0aacf84e | 8537 | { |
98237784 MW |
8538 | /* FIXME: Precision may be lost here due to: |
8539 | (1) The conversion from 'scm_t_inum' to double | |
8540 | (2) Double rounding */ | |
0aacf84e | 8541 | double d = yy; |
8507ec80 | 8542 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8543 | } |
8544 | } | |
8545 | else if (SCM_BIGP (y)) | |
8546 | { | |
98237784 MW |
8547 | /* FIXME: Precision may be lost here due to: |
8548 | (1) The conversion from bignum to double | |
8549 | (2) Double rounding */ | |
0aacf84e MD |
8550 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8551 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8552 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8553 | } |
8554 | else if (SCM_REALP (y)) | |
8555 | { | |
8556 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8557 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8558 | if (yy == 0.0) |
8559 | scm_num_overflow (s_divide); | |
8560 | else | |
7351e207 | 8561 | #endif |
8507ec80 | 8562 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8563 | } |
8564 | else if (SCM_COMPLEXP (y)) | |
8565 | { | |
8566 | double ry = SCM_COMPLEX_REAL (y); | |
8567 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8568 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8569 | { |
8570 | double t = ry / iy; | |
8571 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8572 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8573 | } |
8574 | else | |
8575 | { | |
8576 | double t = iy / ry; | |
8577 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8578 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8579 | } |
8580 | } | |
f92e85f7 MV |
8581 | else if (SCM_FRACTIONP (y)) |
8582 | { | |
98237784 MW |
8583 | /* FIXME: Precision may be lost here due to: |
8584 | (1) The conversion from fraction to double | |
8585 | (2) Double rounding */ | |
f92e85f7 | 8586 | double yy = scm_i_fraction2double (y); |
8507ec80 | 8587 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8588 | } |
0aacf84e | 8589 | else |
fa075d40 | 8590 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f8de44c1 | 8591 | } |
f92e85f7 MV |
8592 | else if (SCM_FRACTIONP (x)) |
8593 | { | |
e11e83f3 | 8594 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8595 | { |
e25f3727 | 8596 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8597 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8598 | if (yy == 0) | |
8599 | scm_num_overflow (s_divide); | |
8600 | else | |
8601 | #endif | |
cba42c93 | 8602 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8603 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8604 | } |
8605 | else if (SCM_BIGP (y)) | |
8606 | { | |
cba42c93 | 8607 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8608 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8609 | } |
8610 | else if (SCM_REALP (y)) | |
8611 | { | |
8612 | double yy = SCM_REAL_VALUE (y); | |
8613 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8614 | if (yy == 0.0) | |
8615 | scm_num_overflow (s_divide); | |
8616 | else | |
8617 | #endif | |
98237784 MW |
8618 | /* FIXME: Precision may be lost here due to: |
8619 | (1) The conversion from fraction to double | |
8620 | (2) Double rounding */ | |
00472a22 | 8621 | return scm_i_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8622 | } |
8623 | else if (SCM_COMPLEXP (y)) | |
8624 | { | |
98237784 MW |
8625 | /* FIXME: Precision may be lost here due to: |
8626 | (1) The conversion from fraction to double | |
8627 | (2) Double rounding */ | |
f92e85f7 MV |
8628 | a = scm_i_fraction2double (x); |
8629 | goto complex_div; | |
8630 | } | |
8631 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8632 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8633 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
f92e85f7 | 8634 | else |
fa075d40 | 8635 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f92e85f7 | 8636 | } |
0aacf84e | 8637 | else |
fa075d40 | 8638 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8639 | } |
c05e97b7 | 8640 | #undef FUNC_NAME |
0f2d19dd | 8641 | |
fa605590 | 8642 | |
0f2d19dd | 8643 | double |
3101f40f | 8644 | scm_c_truncate (double x) |
0f2d19dd | 8645 | { |
fa605590 | 8646 | return trunc (x); |
0f2d19dd | 8647 | } |
0f2d19dd | 8648 | |
3101f40f MV |
8649 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8650 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8651 | Then half-way cases are identified and adjusted down if the | |
8652 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8653 | |
8654 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8655 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8656 | ||
8657 | An odd "result" value is identified with result/2 != floor(result/2). | |
8658 | This is done with plus_half, since that value is ready for use sooner in | |
8659 | a pipelined cpu, and we're already requiring plus_half == result. | |
8660 | ||
8661 | Note however that we need to be careful when x is big and already an | |
8662 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8663 | us to return such a value, incorrectly. For instance if the hardware is | |
8664 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8665 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8666 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8667 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8668 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8669 | ||
8670 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8671 | x is already an integer. If it is then clearly that's the desired result | |
8672 | already. And if it's not then the exponent must be small enough to allow | |
8673 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8674 | ||
0f2d19dd | 8675 | double |
3101f40f | 8676 | scm_c_round (double x) |
0f2d19dd | 8677 | { |
6187f48b KR |
8678 | double plus_half, result; |
8679 | ||
8680 | if (x == floor (x)) | |
8681 | return x; | |
8682 | ||
8683 | plus_half = x + 0.5; | |
8684 | result = floor (plus_half); | |
3101f40f | 8685 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8686 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8687 | ? result - 1 | |
8688 | : result); | |
0f2d19dd JB |
8689 | } |
8690 | ||
8b56bcec MW |
8691 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8692 | (SCM x), | |
8693 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8694 | #define FUNC_NAME s_scm_truncate_number |
8695 | { | |
8b56bcec MW |
8696 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8697 | return x; | |
8698 | else if (SCM_REALP (x)) | |
00472a22 | 8699 | return scm_i_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8700 | else if (SCM_FRACTIONP (x)) |
8701 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8702 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8703 | else |
fa075d40 | 8704 | return scm_wta_dispatch_1 (g_scm_truncate_number, x, SCM_ARG1, |
8b56bcec | 8705 | s_scm_truncate_number); |
f92e85f7 MV |
8706 | } |
8707 | #undef FUNC_NAME | |
8708 | ||
8b56bcec MW |
8709 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8710 | (SCM x), | |
8711 | "Round the number @var{x} towards the nearest integer. " | |
8712 | "When it is exactly halfway between two integers, " | |
8713 | "round towards the even one.") | |
f92e85f7 MV |
8714 | #define FUNC_NAME s_scm_round_number |
8715 | { | |
e11e83f3 | 8716 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8717 | return x; |
8718 | else if (SCM_REALP (x)) | |
00472a22 | 8719 | return scm_i_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8720 | else if (SCM_FRACTIONP (x)) |
8721 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8722 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8723 | else |
fa075d40 AW |
8724 | return scm_wta_dispatch_1 (g_scm_round_number, x, SCM_ARG1, |
8725 | s_scm_round_number); | |
f92e85f7 MV |
8726 | } |
8727 | #undef FUNC_NAME | |
8728 | ||
8729 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8730 | (SCM x), | |
8731 | "Round the number @var{x} towards minus infinity.") | |
8732 | #define FUNC_NAME s_scm_floor | |
8733 | { | |
e11e83f3 | 8734 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8735 | return x; |
8736 | else if (SCM_REALP (x)) | |
00472a22 | 8737 | return scm_i_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8738 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8739 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8740 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8741 | else |
fa075d40 | 8742 | return scm_wta_dispatch_1 (g_scm_floor, x, 1, s_scm_floor); |
f92e85f7 MV |
8743 | } |
8744 | #undef FUNC_NAME | |
8745 | ||
8746 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8747 | (SCM x), | |
8748 | "Round the number @var{x} towards infinity.") | |
8749 | #define FUNC_NAME s_scm_ceiling | |
8750 | { | |
e11e83f3 | 8751 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8752 | return x; |
8753 | else if (SCM_REALP (x)) | |
00472a22 | 8754 | return scm_i_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8755 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8756 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8757 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8758 | else |
fa075d40 | 8759 | return scm_wta_dispatch_1 (g_scm_ceiling, x, 1, s_scm_ceiling); |
f92e85f7 MV |
8760 | } |
8761 | #undef FUNC_NAME | |
0f2d19dd | 8762 | |
2519490c MW |
8763 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8764 | (SCM x, SCM y), | |
8765 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8766 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8767 | { |
01c7284a MW |
8768 | if (scm_is_integer (y)) |
8769 | { | |
8770 | if (scm_is_true (scm_exact_p (y))) | |
8771 | return scm_integer_expt (x, y); | |
8772 | else | |
8773 | { | |
8774 | /* Here we handle the case where the exponent is an inexact | |
8775 | integer. We make the exponent exact in order to use | |
8776 | scm_integer_expt, and thus avoid the spurious imaginary | |
8777 | parts that may result from round-off errors in the general | |
8778 | e^(y log x) method below (for example when squaring a large | |
8779 | negative number). In this case, we must return an inexact | |
8780 | result for correctness. We also make the base inexact so | |
8781 | that scm_integer_expt will use fast inexact arithmetic | |
8782 | internally. Note that making the base inexact is not | |
8783 | sufficient to guarantee an inexact result, because | |
8784 | scm_integer_expt will return an exact 1 when the exponent | |
8785 | is 0, even if the base is inexact. */ | |
8786 | return scm_exact_to_inexact | |
8787 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8788 | scm_inexact_to_exact (y))); | |
8789 | } | |
8790 | } | |
6fc4d012 AW |
8791 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8792 | { | |
00472a22 | 8793 | return scm_i_from_double (pow (scm_to_double (x), scm_to_double (y))); |
6fc4d012 | 8794 | } |
2519490c | 8795 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8796 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c | 8797 | else if (scm_is_complex (x)) |
fa075d40 | 8798 | return scm_wta_dispatch_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); |
2519490c | 8799 | else |
fa075d40 | 8800 | return scm_wta_dispatch_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); |
0f2d19dd | 8801 | } |
1bbd0b84 | 8802 | #undef FUNC_NAME |
0f2d19dd | 8803 | |
7f41099e MW |
8804 | /* sin/cos/tan/asin/acos/atan |
8805 | sinh/cosh/tanh/asinh/acosh/atanh | |
8806 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8807 | Written by Jerry D. Hedden, (C) FSF. | |
8808 | See the file `COPYING' for terms applying to this program. */ | |
8809 | ||
ad79736c AW |
8810 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8811 | (SCM z), | |
8812 | "Compute the sine of @var{z}.") | |
8813 | #define FUNC_NAME s_scm_sin | |
8814 | { | |
8deddc94 MW |
8815 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8816 | return z; /* sin(exact0) = exact0 */ | |
8817 | else if (scm_is_real (z)) | |
00472a22 | 8818 | return scm_i_from_double (sin (scm_to_double (z))); |
ad79736c AW |
8819 | else if (SCM_COMPLEXP (z)) |
8820 | { double x, y; | |
8821 | x = SCM_COMPLEX_REAL (z); | |
8822 | y = SCM_COMPLEX_IMAG (z); | |
8823 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8824 | cos (x) * sinh (y)); | |
8825 | } | |
8826 | else | |
fa075d40 | 8827 | return scm_wta_dispatch_1 (g_scm_sin, z, 1, s_scm_sin); |
ad79736c AW |
8828 | } |
8829 | #undef FUNC_NAME | |
0f2d19dd | 8830 | |
ad79736c AW |
8831 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8832 | (SCM z), | |
8833 | "Compute the cosine of @var{z}.") | |
8834 | #define FUNC_NAME s_scm_cos | |
8835 | { | |
8deddc94 MW |
8836 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8837 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8838 | else if (scm_is_real (z)) | |
00472a22 | 8839 | return scm_i_from_double (cos (scm_to_double (z))); |
ad79736c AW |
8840 | else if (SCM_COMPLEXP (z)) |
8841 | { double x, y; | |
8842 | x = SCM_COMPLEX_REAL (z); | |
8843 | y = SCM_COMPLEX_IMAG (z); | |
8844 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8845 | -sin (x) * sinh (y)); | |
8846 | } | |
8847 | else | |
fa075d40 | 8848 | return scm_wta_dispatch_1 (g_scm_cos, z, 1, s_scm_cos); |
ad79736c AW |
8849 | } |
8850 | #undef FUNC_NAME | |
8851 | ||
8852 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8853 | (SCM z), | |
8854 | "Compute the tangent of @var{z}.") | |
8855 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8856 | { |
8deddc94 MW |
8857 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8858 | return z; /* tan(exact0) = exact0 */ | |
8859 | else if (scm_is_real (z)) | |
00472a22 | 8860 | return scm_i_from_double (tan (scm_to_double (z))); |
ad79736c AW |
8861 | else if (SCM_COMPLEXP (z)) |
8862 | { double x, y, w; | |
8863 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8864 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8865 | w = cos (x) + cosh (y); | |
8866 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8867 | if (w == 0.0) | |
8868 | scm_num_overflow (s_scm_tan); | |
8869 | #endif | |
8870 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8871 | } | |
8872 | else | |
fa075d40 | 8873 | return scm_wta_dispatch_1 (g_scm_tan, z, 1, s_scm_tan); |
ad79736c AW |
8874 | } |
8875 | #undef FUNC_NAME | |
8876 | ||
8877 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8878 | (SCM z), | |
8879 | "Compute the hyperbolic sine of @var{z}.") | |
8880 | #define FUNC_NAME s_scm_sinh | |
8881 | { | |
8deddc94 MW |
8882 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8883 | return z; /* sinh(exact0) = exact0 */ | |
8884 | else if (scm_is_real (z)) | |
00472a22 | 8885 | return scm_i_from_double (sinh (scm_to_double (z))); |
ad79736c AW |
8886 | else if (SCM_COMPLEXP (z)) |
8887 | { double x, y; | |
8888 | x = SCM_COMPLEX_REAL (z); | |
8889 | y = SCM_COMPLEX_IMAG (z); | |
8890 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8891 | cosh (x) * sin (y)); | |
8892 | } | |
8893 | else | |
fa075d40 | 8894 | return scm_wta_dispatch_1 (g_scm_sinh, z, 1, s_scm_sinh); |
ad79736c AW |
8895 | } |
8896 | #undef FUNC_NAME | |
8897 | ||
8898 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8899 | (SCM z), | |
8900 | "Compute the hyperbolic cosine of @var{z}.") | |
8901 | #define FUNC_NAME s_scm_cosh | |
8902 | { | |
8deddc94 MW |
8903 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8904 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8905 | else if (scm_is_real (z)) | |
00472a22 | 8906 | return scm_i_from_double (cosh (scm_to_double (z))); |
ad79736c AW |
8907 | else if (SCM_COMPLEXP (z)) |
8908 | { double x, y; | |
8909 | x = SCM_COMPLEX_REAL (z); | |
8910 | y = SCM_COMPLEX_IMAG (z); | |
8911 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8912 | sinh (x) * sin (y)); | |
8913 | } | |
8914 | else | |
fa075d40 | 8915 | return scm_wta_dispatch_1 (g_scm_cosh, z, 1, s_scm_cosh); |
ad79736c AW |
8916 | } |
8917 | #undef FUNC_NAME | |
8918 | ||
8919 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8920 | (SCM z), | |
8921 | "Compute the hyperbolic tangent of @var{z}.") | |
8922 | #define FUNC_NAME s_scm_tanh | |
8923 | { | |
8deddc94 MW |
8924 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8925 | return z; /* tanh(exact0) = exact0 */ | |
8926 | else if (scm_is_real (z)) | |
00472a22 | 8927 | return scm_i_from_double (tanh (scm_to_double (z))); |
ad79736c AW |
8928 | else if (SCM_COMPLEXP (z)) |
8929 | { double x, y, w; | |
8930 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8931 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8932 | w = cosh (x) + cos (y); | |
8933 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8934 | if (w == 0.0) | |
8935 | scm_num_overflow (s_scm_tanh); | |
8936 | #endif | |
8937 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8938 | } | |
8939 | else | |
fa075d40 | 8940 | return scm_wta_dispatch_1 (g_scm_tanh, z, 1, s_scm_tanh); |
ad79736c AW |
8941 | } |
8942 | #undef FUNC_NAME | |
8943 | ||
8944 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8945 | (SCM z), | |
8946 | "Compute the arc sine of @var{z}.") | |
8947 | #define FUNC_NAME s_scm_asin | |
8948 | { | |
8deddc94 MW |
8949 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8950 | return z; /* asin(exact0) = exact0 */ | |
8951 | else if (scm_is_real (z)) | |
ad79736c AW |
8952 | { |
8953 | double w = scm_to_double (z); | |
8954 | if (w >= -1.0 && w <= 1.0) | |
00472a22 | 8955 | return scm_i_from_double (asin (w)); |
ad79736c AW |
8956 | else |
8957 | return scm_product (scm_c_make_rectangular (0, -1), | |
8958 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8959 | } | |
8960 | else if (SCM_COMPLEXP (z)) | |
8961 | { double x, y; | |
8962 | x = SCM_COMPLEX_REAL (z); | |
8963 | y = SCM_COMPLEX_IMAG (z); | |
8964 | return scm_product (scm_c_make_rectangular (0, -1), | |
8965 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8966 | } | |
8967 | else | |
fa075d40 | 8968 | return scm_wta_dispatch_1 (g_scm_asin, z, 1, s_scm_asin); |
ad79736c AW |
8969 | } |
8970 | #undef FUNC_NAME | |
8971 | ||
8972 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8973 | (SCM z), | |
8974 | "Compute the arc cosine of @var{z}.") | |
8975 | #define FUNC_NAME s_scm_acos | |
8976 | { | |
8deddc94 MW |
8977 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8978 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8979 | else if (scm_is_real (z)) | |
ad79736c AW |
8980 | { |
8981 | double w = scm_to_double (z); | |
8982 | if (w >= -1.0 && w <= 1.0) | |
00472a22 | 8983 | return scm_i_from_double (acos (w)); |
ad79736c | 8984 | else |
00472a22 | 8985 | return scm_sum (scm_i_from_double (acos (0.0)), |
ad79736c AW |
8986 | scm_product (scm_c_make_rectangular (0, 1), |
8987 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8988 | } | |
8989 | else if (SCM_COMPLEXP (z)) | |
8990 | { double x, y; | |
8991 | x = SCM_COMPLEX_REAL (z); | |
8992 | y = SCM_COMPLEX_IMAG (z); | |
00472a22 | 8993 | return scm_sum (scm_i_from_double (acos (0.0)), |
ad79736c AW |
8994 | scm_product (scm_c_make_rectangular (0, 1), |
8995 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8996 | } | |
8997 | else | |
fa075d40 | 8998 | return scm_wta_dispatch_1 (g_scm_acos, z, 1, s_scm_acos); |
ad79736c AW |
8999 | } |
9000 | #undef FUNC_NAME | |
9001 | ||
9002 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
9003 | (SCM z, SCM y), | |
9004 | "With one argument, compute the arc tangent of @var{z}.\n" | |
9005 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
9006 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
9007 | #define FUNC_NAME s_scm_atan | |
9008 | { | |
9009 | if (SCM_UNBNDP (y)) | |
9010 | { | |
8deddc94 MW |
9011 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9012 | return z; /* atan(exact0) = exact0 */ | |
9013 | else if (scm_is_real (z)) | |
00472a22 | 9014 | return scm_i_from_double (atan (scm_to_double (z))); |
ad79736c AW |
9015 | else if (SCM_COMPLEXP (z)) |
9016 | { | |
9017 | double v, w; | |
9018 | v = SCM_COMPLEX_REAL (z); | |
9019 | w = SCM_COMPLEX_IMAG (z); | |
9020 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
9021 | scm_c_make_rectangular (v, w + 1.0))), | |
9022 | scm_c_make_rectangular (0, 2)); | |
9023 | } | |
9024 | else | |
fa075d40 | 9025 | return scm_wta_dispatch_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
9026 | } |
9027 | else if (scm_is_real (z)) | |
9028 | { | |
9029 | if (scm_is_real (y)) | |
00472a22 | 9030 | return scm_i_from_double (atan2 (scm_to_double (z), scm_to_double (y))); |
ad79736c | 9031 | else |
fa075d40 | 9032 | return scm_wta_dispatch_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); |
ad79736c AW |
9033 | } |
9034 | else | |
fa075d40 | 9035 | return scm_wta_dispatch_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); |
ad79736c AW |
9036 | } |
9037 | #undef FUNC_NAME | |
9038 | ||
9039 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
9040 | (SCM z), | |
9041 | "Compute the inverse hyperbolic sine of @var{z}.") | |
9042 | #define FUNC_NAME s_scm_sys_asinh | |
9043 | { | |
8deddc94 MW |
9044 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9045 | return z; /* asinh(exact0) = exact0 */ | |
9046 | else if (scm_is_real (z)) | |
00472a22 | 9047 | return scm_i_from_double (asinh (scm_to_double (z))); |
ad79736c AW |
9048 | else if (scm_is_number (z)) |
9049 | return scm_log (scm_sum (z, | |
9050 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 9051 | SCM_INUM1)))); |
ad79736c | 9052 | else |
fa075d40 | 9053 | return scm_wta_dispatch_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); |
ad79736c AW |
9054 | } |
9055 | #undef FUNC_NAME | |
9056 | ||
9057 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
9058 | (SCM z), | |
9059 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
9060 | #define FUNC_NAME s_scm_sys_acosh | |
9061 | { | |
8deddc94 MW |
9062 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
9063 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
9064 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
00472a22 | 9065 | return scm_i_from_double (acosh (scm_to_double (z))); |
ad79736c AW |
9066 | else if (scm_is_number (z)) |
9067 | return scm_log (scm_sum (z, | |
9068 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 9069 | SCM_INUM1)))); |
ad79736c | 9070 | else |
fa075d40 | 9071 | return scm_wta_dispatch_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); |
ad79736c AW |
9072 | } |
9073 | #undef FUNC_NAME | |
9074 | ||
9075 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
9076 | (SCM z), | |
9077 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
9078 | #define FUNC_NAME s_scm_sys_atanh | |
9079 | { | |
8deddc94 MW |
9080 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9081 | return z; /* atanh(exact0) = exact0 */ | |
9082 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
00472a22 | 9083 | return scm_i_from_double (atanh (scm_to_double (z))); |
ad79736c | 9084 | else if (scm_is_number (z)) |
cff5fa33 MW |
9085 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
9086 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
9087 | SCM_I_MAKINUM (2)); |
9088 | else | |
fa075d40 | 9089 | return scm_wta_dispatch_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); |
0f2d19dd | 9090 | } |
1bbd0b84 | 9091 | #undef FUNC_NAME |
0f2d19dd | 9092 | |
8507ec80 MV |
9093 | SCM |
9094 | scm_c_make_rectangular (double re, double im) | |
9095 | { | |
c7218482 | 9096 | SCM z; |
03604fcf | 9097 | |
21041372 | 9098 | z = SCM_PACK_POINTER (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
c7218482 MW |
9099 | "complex")); |
9100 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
9101 | SCM_COMPLEX_REAL (z) = re; | |
9102 | SCM_COMPLEX_IMAG (z) = im; | |
9103 | return z; | |
8507ec80 | 9104 | } |
0f2d19dd | 9105 | |
a1ec6916 | 9106 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 9107 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
9108 | "Return a complex number constructed of the given @var{real_part} " |
9109 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 9110 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 9111 | { |
ad79736c AW |
9112 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
9113 | SCM_ARG1, FUNC_NAME, "real"); | |
9114 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
9115 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
9116 | |
9117 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
9118 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
9119 | return real_part; | |
9120 | else | |
9121 | return scm_c_make_rectangular (scm_to_double (real_part), | |
9122 | scm_to_double (imaginary_part)); | |
0f2d19dd | 9123 | } |
1bbd0b84 | 9124 | #undef FUNC_NAME |
0f2d19dd | 9125 | |
8507ec80 MV |
9126 | SCM |
9127 | scm_c_make_polar (double mag, double ang) | |
9128 | { | |
9129 | double s, c; | |
5e647d08 LC |
9130 | |
9131 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
9132 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
9133 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
9134 | details. */ | |
9135 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
9136 | sincos (ang, &s, &c); |
9137 | #else | |
9138 | s = sin (ang); | |
9139 | c = cos (ang); | |
9140 | #endif | |
9d427b2c MW |
9141 | |
9142 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
9143 | infinite, or perhaps simply too large to determine its value | |
9144 | mod 2*pi. However, we know something that the floating-point | |
9145 | implementation doesn't know: We know that s and c are finite. | |
9146 | Therefore, if the magnitude is zero, return a complex zero. | |
9147 | ||
9148 | The reason we check for the NaNs instead of using this case | |
9149 | whenever mag == 0.0 is because when the angle is known, we'd | |
9150 | like to return the correct kind of non-real complex zero: | |
9151 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
9152 | on which quadrant the angle is in. | |
9153 | */ | |
9154 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
9155 | return scm_c_make_rectangular (0.0, 0.0); | |
9156 | else | |
9157 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 9158 | } |
0f2d19dd | 9159 | |
a1ec6916 | 9160 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
9161 | (SCM mag, SCM ang), |
9162 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 9163 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 9164 | { |
c7218482 MW |
9165 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
9166 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
9167 | ||
9168 | /* If mag is exact0, return exact0 */ | |
9169 | if (scm_is_eq (mag, SCM_INUM0)) | |
9170 | return SCM_INUM0; | |
9171 | /* Return a real if ang is exact0 */ | |
9172 | else if (scm_is_eq (ang, SCM_INUM0)) | |
9173 | return mag; | |
9174 | else | |
9175 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 9176 | } |
1bbd0b84 | 9177 | #undef FUNC_NAME |
0f2d19dd JB |
9178 | |
9179 | ||
2519490c MW |
9180 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
9181 | (SCM z), | |
9182 | "Return the real part of the number @var{z}.") | |
9183 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 9184 | { |
2519490c | 9185 | if (SCM_COMPLEXP (z)) |
00472a22 | 9186 | return scm_i_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 9187 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 9188 | return z; |
0aacf84e | 9189 | else |
fa075d40 | 9190 | return scm_wta_dispatch_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 9191 | } |
2519490c | 9192 | #undef FUNC_NAME |
0f2d19dd JB |
9193 | |
9194 | ||
2519490c MW |
9195 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
9196 | (SCM z), | |
9197 | "Return the imaginary part of the number @var{z}.") | |
9198 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 9199 | { |
2519490c | 9200 | if (SCM_COMPLEXP (z)) |
00472a22 | 9201 | return scm_i_from_double (SCM_COMPLEX_IMAG (z)); |
c7218482 | 9202 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 9203 | return SCM_INUM0; |
0aacf84e | 9204 | else |
fa075d40 | 9205 | return scm_wta_dispatch_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 9206 | } |
2519490c | 9207 | #undef FUNC_NAME |
0f2d19dd | 9208 | |
2519490c MW |
9209 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
9210 | (SCM z), | |
9211 | "Return the numerator of the number @var{z}.") | |
9212 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 9213 | { |
2519490c | 9214 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
9215 | return z; |
9216 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 9217 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 | 9218 | else if (SCM_REALP (z)) |
fa102e73 MW |
9219 | { |
9220 | double zz = SCM_REAL_VALUE (z); | |
9221 | if (zz == floor (zz)) | |
9222 | /* Handle -0.0 and infinities in accordance with R6RS | |
9223 | flnumerator, and optimize handling of integers. */ | |
9224 | return z; | |
9225 | else | |
9226 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
9227 | } | |
f92e85f7 | 9228 | else |
fa075d40 | 9229 | return scm_wta_dispatch_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 9230 | } |
2519490c | 9231 | #undef FUNC_NAME |
f92e85f7 MV |
9232 | |
9233 | ||
2519490c MW |
9234 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
9235 | (SCM z), | |
9236 | "Return the denominator of the number @var{z}.") | |
9237 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 9238 | { |
2519490c | 9239 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 9240 | return SCM_INUM1; |
f92e85f7 | 9241 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 9242 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 | 9243 | else if (SCM_REALP (z)) |
fa102e73 MW |
9244 | { |
9245 | double zz = SCM_REAL_VALUE (z); | |
9246 | if (zz == floor (zz)) | |
9247 | /* Handle infinities in accordance with R6RS fldenominator, and | |
9248 | optimize handling of integers. */ | |
9249 | return scm_i_from_double (1.0); | |
9250 | else | |
9251 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
9252 | } | |
f92e85f7 | 9253 | else |
fa075d40 AW |
9254 | return scm_wta_dispatch_1 (g_scm_denominator, z, SCM_ARG1, |
9255 | s_scm_denominator); | |
f92e85f7 | 9256 | } |
2519490c | 9257 | #undef FUNC_NAME |
0f2d19dd | 9258 | |
2519490c MW |
9259 | |
9260 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
9261 | (SCM z), | |
9262 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
9263 | "@code{abs} for real arguments, but also allows complex numbers.") | |
9264 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 9265 | { |
e11e83f3 | 9266 | if (SCM_I_INUMP (z)) |
0aacf84e | 9267 | { |
e25f3727 | 9268 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
9269 | if (zz >= 0) |
9270 | return z; | |
9271 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 9272 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 9273 | else |
e25f3727 | 9274 | return scm_i_inum2big (-zz); |
5986c47d | 9275 | } |
0aacf84e MD |
9276 | else if (SCM_BIGP (z)) |
9277 | { | |
9278 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9279 | scm_remember_upto_here_1 (z); | |
9280 | if (sgn < 0) | |
9281 | return scm_i_clonebig (z, 0); | |
9282 | else | |
9283 | return z; | |
5986c47d | 9284 | } |
0aacf84e | 9285 | else if (SCM_REALP (z)) |
00472a22 | 9286 | return scm_i_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 9287 | else if (SCM_COMPLEXP (z)) |
00472a22 | 9288 | return scm_i_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
9289 | else if (SCM_FRACTIONP (z)) |
9290 | { | |
73e4de09 | 9291 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 9292 | return z; |
a285b18c MW |
9293 | return scm_i_make_ratio_already_reduced |
9294 | (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), | |
9295 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 | 9296 | } |
0aacf84e | 9297 | else |
fa075d40 AW |
9298 | return scm_wta_dispatch_1 (g_scm_magnitude, z, SCM_ARG1, |
9299 | s_scm_magnitude); | |
0f2d19dd | 9300 | } |
2519490c | 9301 | #undef FUNC_NAME |
0f2d19dd JB |
9302 | |
9303 | ||
2519490c MW |
9304 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
9305 | (SCM z), | |
9306 | "Return the angle of the complex number @var{z}.") | |
9307 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 9308 | { |
c8ae173e | 9309 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
00472a22 | 9310 | flo0 to save allocating a new flonum with scm_i_from_double each time. |
c8ae173e KR |
9311 | But if atan2 follows the floating point rounding mode, then the value |
9312 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 9313 | if (SCM_I_INUMP (z)) |
0aacf84e | 9314 | { |
e11e83f3 | 9315 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 9316 | return flo0; |
0aacf84e | 9317 | else |
00472a22 | 9318 | return scm_i_from_double (atan2 (0.0, -1.0)); |
f872b822 | 9319 | } |
0aacf84e MD |
9320 | else if (SCM_BIGP (z)) |
9321 | { | |
9322 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9323 | scm_remember_upto_here_1 (z); | |
9324 | if (sgn < 0) | |
00472a22 | 9325 | return scm_i_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 9326 | else |
e7efe8e7 | 9327 | return flo0; |
0f2d19dd | 9328 | } |
0aacf84e | 9329 | else if (SCM_REALP (z)) |
c8ae173e | 9330 | { |
10a97755 | 9331 | double x = SCM_REAL_VALUE (z); |
e1592f8a | 9332 | if (copysign (1.0, x) > 0.0) |
e7efe8e7 | 9333 | return flo0; |
c8ae173e | 9334 | else |
00472a22 | 9335 | return scm_i_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 9336 | } |
0aacf84e | 9337 | else if (SCM_COMPLEXP (z)) |
00472a22 | 9338 | return scm_i_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
9339 | else if (SCM_FRACTIONP (z)) |
9340 | { | |
73e4de09 | 9341 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 9342 | return flo0; |
00472a22 | 9343 | else return scm_i_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 9344 | } |
0aacf84e | 9345 | else |
fa075d40 | 9346 | return scm_wta_dispatch_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 9347 | } |
2519490c | 9348 | #undef FUNC_NAME |
0f2d19dd JB |
9349 | |
9350 | ||
2519490c MW |
9351 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
9352 | (SCM z), | |
9353 | "Convert the number @var{z} to its inexact representation.\n") | |
9354 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 9355 | { |
e11e83f3 | 9356 | if (SCM_I_INUMP (z)) |
00472a22 | 9357 | return scm_i_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 9358 | else if (SCM_BIGP (z)) |
00472a22 | 9359 | return scm_i_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 9360 | else if (SCM_FRACTIONP (z)) |
00472a22 | 9361 | return scm_i_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
9362 | else if (SCM_INEXACTP (z)) |
9363 | return z; | |
9364 | else | |
fa075d40 AW |
9365 | return scm_wta_dispatch_1 (g_scm_exact_to_inexact, z, 1, |
9366 | s_scm_exact_to_inexact); | |
3c9a524f | 9367 | } |
2519490c | 9368 | #undef FUNC_NAME |
3c9a524f DH |
9369 | |
9370 | ||
2519490c MW |
9371 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
9372 | (SCM z), | |
9373 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 9374 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 9375 | { |
c7218482 | 9376 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 9377 | return z; |
c7218482 | 9378 | else |
0aacf84e | 9379 | { |
c7218482 MW |
9380 | double val; |
9381 | ||
9382 | if (SCM_REALP (z)) | |
9383 | val = SCM_REAL_VALUE (z); | |
9384 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
9385 | val = SCM_COMPLEX_REAL (z); | |
9386 | else | |
fa075d40 AW |
9387 | return scm_wta_dispatch_1 (g_scm_inexact_to_exact, z, 1, |
9388 | s_scm_inexact_to_exact); | |
c7218482 | 9389 | |
19374ad2 | 9390 | if (!SCM_LIKELY (isfinite (val))) |
f92e85f7 | 9391 | SCM_OUT_OF_RANGE (1, z); |
24475b86 MW |
9392 | else if (val == 0.0) |
9393 | return SCM_INUM0; | |
2be24db4 | 9394 | else |
f92e85f7 | 9395 | { |
24475b86 MW |
9396 | int expon; |
9397 | SCM numerator; | |
f92e85f7 | 9398 | |
24475b86 MW |
9399 | numerator = scm_i_dbl2big (ldexp (frexp (val, &expon), |
9400 | DBL_MANT_DIG)); | |
9401 | expon -= DBL_MANT_DIG; | |
9402 | if (expon < 0) | |
9403 | { | |
9404 | int shift = mpz_scan1 (SCM_I_BIG_MPZ (numerator), 0); | |
9405 | ||
9406 | if (shift > -expon) | |
9407 | shift = -expon; | |
9408 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (numerator), | |
9409 | SCM_I_BIG_MPZ (numerator), | |
9410 | shift); | |
9411 | expon += shift; | |
9412 | } | |
9413 | numerator = scm_i_normbig (numerator); | |
9414 | if (expon < 0) | |
9415 | return scm_i_make_ratio_already_reduced | |
9416 | (numerator, left_shift_exact_integer (SCM_INUM1, -expon)); | |
9417 | else if (expon > 0) | |
9418 | return left_shift_exact_integer (numerator, expon); | |
9419 | else | |
9420 | return numerator; | |
f92e85f7 | 9421 | } |
c2ff8ab0 | 9422 | } |
0f2d19dd | 9423 | } |
1bbd0b84 | 9424 | #undef FUNC_NAME |
0f2d19dd | 9425 | |
f92e85f7 | 9426 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
9427 | (SCM x, SCM eps), |
9428 | "Returns the @emph{simplest} rational number differing\n" | |
9429 | "from @var{x} by no more than @var{eps}.\n" | |
9430 | "\n" | |
9431 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9432 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9433 | "to use @code{inexact->exact} on the arguments.\n" | |
9434 | "\n" | |
9435 | "@lisp\n" | |
9436 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9437 | "@result{} 6/5\n" | |
9438 | "@end lisp") | |
f92e85f7 MV |
9439 | #define FUNC_NAME s_scm_rationalize |
9440 | { | |
605f6980 MW |
9441 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9442 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
620c13e8 MW |
9443 | |
9444 | if (SCM_UNLIKELY (!scm_is_exact (eps) || !scm_is_exact (x))) | |
605f6980 | 9445 | { |
620c13e8 MW |
9446 | if (SCM_UNLIKELY (scm_is_false (scm_finite_p (eps)))) |
9447 | { | |
9448 | if (scm_is_false (scm_nan_p (eps)) && scm_is_true (scm_finite_p (x))) | |
9449 | return flo0; | |
9450 | else | |
9451 | return scm_nan (); | |
9452 | } | |
9453 | else if (SCM_UNLIKELY (scm_is_false (scm_finite_p (x)))) | |
9454 | return x; | |
605f6980 | 9455 | else |
620c13e8 MW |
9456 | return scm_exact_to_inexact |
9457 | (scm_rationalize (scm_inexact_to_exact (x), | |
9458 | scm_inexact_to_exact (eps))); | |
605f6980 MW |
9459 | } |
9460 | else | |
f92e85f7 | 9461 | { |
620c13e8 MW |
9462 | /* X and EPS are exact rationals. |
9463 | ||
9464 | The code that follows is equivalent to the following Scheme code: | |
9465 | ||
9466 | (define (exact-rationalize x eps) | |
9467 | (let ((n1 (if (negative? x) -1 1)) | |
9468 | (x (abs x)) | |
9469 | (eps (abs eps))) | |
9470 | (let ((lo (- x eps)) | |
9471 | (hi (+ x eps))) | |
9472 | (if (<= lo 0) | |
9473 | 0 | |
9474 | (let loop ((nlo (numerator lo)) (dlo (denominator lo)) | |
9475 | (nhi (numerator hi)) (dhi (denominator hi)) | |
9476 | (n1 n1) (d1 0) (n2 0) (d2 1)) | |
9477 | (let-values (((qlo rlo) (floor/ nlo dlo)) | |
9478 | ((qhi rhi) (floor/ nhi dhi))) | |
9479 | (let ((n0 (+ n2 (* n1 qlo))) | |
9480 | (d0 (+ d2 (* d1 qlo)))) | |
9481 | (cond ((zero? rlo) (/ n0 d0)) | |
9482 | ((< qlo qhi) (/ (+ n0 n1) (+ d0 d1))) | |
9483 | (else (loop dhi rhi dlo rlo n0 d0 n1 d1)))))))))) | |
f92e85f7 MV |
9484 | */ |
9485 | ||
620c13e8 MW |
9486 | int n1_init = 1; |
9487 | SCM lo, hi; | |
f92e85f7 | 9488 | |
620c13e8 MW |
9489 | eps = scm_abs (eps); |
9490 | if (scm_is_true (scm_negative_p (x))) | |
9491 | { | |
9492 | n1_init = -1; | |
9493 | x = scm_difference (x, SCM_UNDEFINED); | |
9494 | } | |
f92e85f7 | 9495 | |
620c13e8 | 9496 | /* X and EPS are non-negative exact rationals. */ |
f92e85f7 | 9497 | |
620c13e8 MW |
9498 | lo = scm_difference (x, eps); |
9499 | hi = scm_sum (x, eps); | |
f92e85f7 | 9500 | |
620c13e8 MW |
9501 | if (scm_is_false (scm_positive_p (lo))) |
9502 | /* If zero is included in the interval, return it. | |
9503 | It is the simplest rational of all. */ | |
9504 | return SCM_INUM0; | |
9505 | else | |
9506 | { | |
9507 | SCM result; | |
9508 | mpz_t n0, d0, n1, d1, n2, d2; | |
9509 | mpz_t nlo, dlo, nhi, dhi; | |
9510 | mpz_t qlo, rlo, qhi, rhi; | |
9511 | ||
9512 | /* LO and HI are positive exact rationals. */ | |
9513 | ||
9514 | /* Our approach here follows the method described by Alan | |
9515 | Bawden in a message entitled "(rationalize x y)" on the | |
9516 | rrrs-authors mailing list, dated 16 Feb 1988 14:08:28 EST: | |
9517 | ||
9518 | http://groups.csail.mit.edu/mac/ftpdir/scheme-mail/HTML/rrrs-1988/msg00063.html | |
9519 | ||
9520 | In brief, we compute the continued fractions of the two | |
9521 | endpoints of the interval (LO and HI). The continued | |
9522 | fraction of the result consists of the common prefix of the | |
9523 | continued fractions of LO and HI, plus one final term. The | |
9524 | final term of the result is the smallest integer contained | |
9525 | in the interval between the remainders of LO and HI after | |
9526 | the common prefix has been removed. | |
9527 | ||
9528 | The following code lazily computes the continued fraction | |
9529 | representations of LO and HI, and simultaneously converts | |
9530 | the continued fraction of the result into a rational | |
9531 | number. We use MPZ functions directly to avoid type | |
9532 | dispatch and GC allocation during the loop. */ | |
9533 | ||
9534 | mpz_inits (n0, d0, n1, d1, n2, d2, | |
9535 | nlo, dlo, nhi, dhi, | |
9536 | qlo, rlo, qhi, rhi, | |
9537 | NULL); | |
9538 | ||
9539 | /* The variables N1, D1, N2 and D2 are used to compute the | |
9540 | resulting rational from its continued fraction. At each | |
9541 | step, N2/D2 and N1/D1 are the last two convergents. They | |
9542 | are normally initialized to 0/1 and 1/0, respectively. | |
9543 | However, if we negated X then we must negate the result as | |
9544 | well, and we do that by initializing N1/D1 to -1/0. */ | |
9545 | mpz_set_si (n1, n1_init); | |
9546 | mpz_set_ui (d1, 0); | |
9547 | mpz_set_ui (n2, 0); | |
9548 | mpz_set_ui (d2, 1); | |
9549 | ||
9550 | /* The variables NLO, DLO, NHI, and DHI are used to lazily | |
9551 | compute the continued fraction representations of LO and HI | |
9552 | using Euclid's algorithm. Initially, NLO/DLO == LO and | |
9553 | NHI/DHI == HI. */ | |
9554 | scm_to_mpz (scm_numerator (lo), nlo); | |
9555 | scm_to_mpz (scm_denominator (lo), dlo); | |
9556 | scm_to_mpz (scm_numerator (hi), nhi); | |
9557 | scm_to_mpz (scm_denominator (hi), dhi); | |
9558 | ||
9559 | /* As long as we're using exact arithmetic, the following loop | |
9560 | is guaranteed to terminate. */ | |
9561 | for (;;) | |
9562 | { | |
9563 | /* Compute the next terms (QLO and QHI) of the continued | |
9564 | fractions of LO and HI. */ | |
9565 | mpz_fdiv_qr (qlo, rlo, nlo, dlo); /* QLO <-- floor (NLO/DLO), RLO <-- NLO - QLO * DLO */ | |
9566 | mpz_fdiv_qr (qhi, rhi, nhi, dhi); /* QHI <-- floor (NHI/DHI), RHI <-- NHI - QHI * DHI */ | |
9567 | ||
9568 | /* The next term of the result will be either QLO or | |
9569 | QLO+1. Here we compute the next convergent of the | |
9570 | result based on the assumption that QLO is the next | |
9571 | term. If that turns out to be wrong, we'll adjust | |
9572 | these later by adding N1 to N0 and D1 to D0. */ | |
9573 | mpz_set (n0, n2); mpz_addmul (n0, n1, qlo); /* N0 <-- N2 + (QLO * N1) */ | |
9574 | mpz_set (d0, d2); mpz_addmul (d0, d1, qlo); /* D0 <-- D2 + (QLO * D1) */ | |
9575 | ||
9576 | /* We stop iterating when an integer is contained in the | |
9577 | interval between the remainders NLO/DLO and NHI/DHI. | |
9578 | There are two cases to consider: either NLO/DLO == QLO | |
9579 | is an integer (indicated by RLO == 0), or QLO < QHI. */ | |
d9e7774f MW |
9580 | if (mpz_sgn (rlo) == 0 || mpz_cmp (qlo, qhi) != 0) |
9581 | break; | |
620c13e8 MW |
9582 | |
9583 | /* Efficiently shuffle variables around for the next | |
9584 | iteration. First we shift the recent convergents. */ | |
9585 | mpz_swap (n2, n1); mpz_swap (n1, n0); /* N2 <-- N1 <-- N0 */ | |
9586 | mpz_swap (d2, d1); mpz_swap (d1, d0); /* D2 <-- D1 <-- D0 */ | |
9587 | ||
9588 | /* The following shuffling is a bit confusing, so some | |
9589 | explanation is in order. Conceptually, we're doing a | |
9590 | couple of things here. After substracting the floor of | |
9591 | NLO/DLO, the remainder is RLO/DLO. The rest of the | |
9592 | continued fraction will represent the remainder's | |
9593 | reciprocal DLO/RLO. Similarly for the HI endpoint. | |
9594 | So in the next iteration, the new endpoints will be | |
9595 | DLO/RLO and DHI/RHI. However, when we take the | |
9596 | reciprocals of these endpoints, their order is | |
9597 | switched. So in summary, we want NLO/DLO <-- DHI/RHI | |
9598 | and NHI/DHI <-- DLO/RLO. */ | |
9599 | mpz_swap (nlo, dhi); mpz_swap (dhi, rlo); /* NLO <-- DHI <-- RLO */ | |
9600 | mpz_swap (nhi, dlo); mpz_swap (dlo, rhi); /* NHI <-- DLO <-- RHI */ | |
9601 | } | |
9602 | ||
9603 | /* There is now an integer in the interval [NLO/DLO NHI/DHI]. | |
9604 | The last term of the result will be the smallest integer in | |
9605 | that interval, which is ceiling(NLO/DLO). We have already | |
9606 | computed floor(NLO/DLO) in QLO, so now we adjust QLO to be | |
9607 | equal to the ceiling. */ | |
9608 | if (mpz_sgn (rlo) != 0) | |
9609 | { | |
9610 | /* If RLO is non-zero, then NLO/DLO is not an integer and | |
9611 | the next term will be QLO+1. QLO was used in the | |
9612 | computation of N0 and D0 above. Here we adjust N0 and | |
9613 | D0 to be based on QLO+1 instead of QLO. */ | |
9614 | mpz_add (n0, n0, n1); /* N0 <-- N0 + N1 */ | |
9615 | mpz_add (d0, d0, d1); /* D0 <-- D0 + D1 */ | |
9616 | } | |
9617 | ||
9618 | /* The simplest rational in the interval is N0/D0 */ | |
9619 | result = scm_i_make_ratio_already_reduced (scm_from_mpz (n0), | |
9620 | scm_from_mpz (d0)); | |
9621 | mpz_clears (n0, d0, n1, d1, n2, d2, | |
9622 | nlo, dlo, nhi, dhi, | |
9623 | qlo, rlo, qhi, rhi, | |
9624 | NULL); | |
9625 | return result; | |
9626 | } | |
f92e85f7 | 9627 | } |
f92e85f7 MV |
9628 | } |
9629 | #undef FUNC_NAME | |
9630 | ||
73e4de09 MV |
9631 | /* conversion functions */ |
9632 | ||
9633 | int | |
9634 | scm_is_integer (SCM val) | |
9635 | { | |
9636 | return scm_is_true (scm_integer_p (val)); | |
9637 | } | |
9638 | ||
900a897c MW |
9639 | int |
9640 | scm_is_exact_integer (SCM val) | |
9641 | { | |
9642 | return scm_is_true (scm_exact_integer_p (val)); | |
9643 | } | |
9644 | ||
73e4de09 MV |
9645 | int |
9646 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9647 | { | |
e11e83f3 | 9648 | if (SCM_I_INUMP (val)) |
73e4de09 | 9649 | { |
e11e83f3 | 9650 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9651 | return n >= min && n <= max; |
9652 | } | |
9653 | else if (SCM_BIGP (val)) | |
9654 | { | |
9655 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9656 | return 0; | |
9657 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9658 | { |
9659 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9660 | { | |
9661 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9662 | return n >= min && n <= max; | |
9663 | } | |
9664 | else | |
9665 | return 0; | |
9666 | } | |
73e4de09 MV |
9667 | else |
9668 | { | |
d956fa6f MV |
9669 | scm_t_intmax n; |
9670 | size_t count; | |
73e4de09 | 9671 | |
d956fa6f MV |
9672 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9673 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9674 | return 0; | |
9675 | ||
9676 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9677 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9678 | |
d956fa6f | 9679 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9680 | { |
d956fa6f MV |
9681 | if (n < 0) |
9682 | return 0; | |
73e4de09 | 9683 | } |
73e4de09 MV |
9684 | else |
9685 | { | |
d956fa6f MV |
9686 | n = -n; |
9687 | if (n >= 0) | |
9688 | return 0; | |
73e4de09 | 9689 | } |
d956fa6f MV |
9690 | |
9691 | return n >= min && n <= max; | |
73e4de09 MV |
9692 | } |
9693 | } | |
73e4de09 MV |
9694 | else |
9695 | return 0; | |
9696 | } | |
9697 | ||
9698 | int | |
9699 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9700 | { | |
e11e83f3 | 9701 | if (SCM_I_INUMP (val)) |
73e4de09 | 9702 | { |
e11e83f3 | 9703 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9704 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9705 | } | |
9706 | else if (SCM_BIGP (val)) | |
9707 | { | |
9708 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9709 | return 0; | |
9710 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9711 | { |
9712 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9713 | { | |
9714 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9715 | return n >= min && n <= max; | |
9716 | } | |
9717 | else | |
9718 | return 0; | |
9719 | } | |
73e4de09 MV |
9720 | else |
9721 | { | |
d956fa6f MV |
9722 | scm_t_uintmax n; |
9723 | size_t count; | |
73e4de09 | 9724 | |
d956fa6f MV |
9725 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9726 | return 0; | |
73e4de09 | 9727 | |
d956fa6f MV |
9728 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9729 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9730 | return 0; |
d956fa6f MV |
9731 | |
9732 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9733 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9734 | |
d956fa6f | 9735 | return n >= min && n <= max; |
73e4de09 MV |
9736 | } |
9737 | } | |
73e4de09 MV |
9738 | else |
9739 | return 0; | |
9740 | } | |
9741 | ||
1713d319 MV |
9742 | static void |
9743 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9744 | { | |
9745 | scm_error (scm_out_of_range_key, | |
9746 | NULL, | |
9747 | "Value out of range ~S to ~S: ~S", | |
9748 | scm_list_3 (min, max, bad_val), | |
9749 | scm_list_1 (bad_val)); | |
9750 | } | |
9751 | ||
bfd7932e MV |
9752 | #define TYPE scm_t_intmax |
9753 | #define TYPE_MIN min | |
9754 | #define TYPE_MAX max | |
9755 | #define SIZEOF_TYPE 0 | |
9756 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9757 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9758 | #include "libguile/conv-integer.i.c" | |
9759 | ||
9760 | #define TYPE scm_t_uintmax | |
9761 | #define TYPE_MIN min | |
9762 | #define TYPE_MAX max | |
9763 | #define SIZEOF_TYPE 0 | |
9764 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9765 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9766 | #include "libguile/conv-uinteger.i.c" | |
9767 | ||
9768 | #define TYPE scm_t_int8 | |
9769 | #define TYPE_MIN SCM_T_INT8_MIN | |
9770 | #define TYPE_MAX SCM_T_INT8_MAX | |
9771 | #define SIZEOF_TYPE 1 | |
9772 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9773 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9774 | #include "libguile/conv-integer.i.c" | |
9775 | ||
9776 | #define TYPE scm_t_uint8 | |
9777 | #define TYPE_MIN 0 | |
9778 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9779 | #define SIZEOF_TYPE 1 | |
9780 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9781 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9782 | #include "libguile/conv-uinteger.i.c" | |
9783 | ||
9784 | #define TYPE scm_t_int16 | |
9785 | #define TYPE_MIN SCM_T_INT16_MIN | |
9786 | #define TYPE_MAX SCM_T_INT16_MAX | |
9787 | #define SIZEOF_TYPE 2 | |
9788 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9789 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9790 | #include "libguile/conv-integer.i.c" | |
9791 | ||
9792 | #define TYPE scm_t_uint16 | |
9793 | #define TYPE_MIN 0 | |
9794 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9795 | #define SIZEOF_TYPE 2 | |
9796 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9797 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9798 | #include "libguile/conv-uinteger.i.c" | |
9799 | ||
9800 | #define TYPE scm_t_int32 | |
9801 | #define TYPE_MIN SCM_T_INT32_MIN | |
9802 | #define TYPE_MAX SCM_T_INT32_MAX | |
9803 | #define SIZEOF_TYPE 4 | |
9804 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9805 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9806 | #include "libguile/conv-integer.i.c" | |
9807 | ||
9808 | #define TYPE scm_t_uint32 | |
9809 | #define TYPE_MIN 0 | |
9810 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9811 | #define SIZEOF_TYPE 4 | |
9812 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9813 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9814 | #include "libguile/conv-uinteger.i.c" | |
9815 | ||
904a78f1 MG |
9816 | #define TYPE scm_t_wchar |
9817 | #define TYPE_MIN (scm_t_int32)-1 | |
9818 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9819 | #define SIZEOF_TYPE 4 | |
9820 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9821 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9822 | #include "libguile/conv-integer.i.c" | |
9823 | ||
bfd7932e MV |
9824 | #define TYPE scm_t_int64 |
9825 | #define TYPE_MIN SCM_T_INT64_MIN | |
9826 | #define TYPE_MAX SCM_T_INT64_MAX | |
9827 | #define SIZEOF_TYPE 8 | |
9828 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9829 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9830 | #include "libguile/conv-integer.i.c" | |
9831 | ||
9832 | #define TYPE scm_t_uint64 | |
9833 | #define TYPE_MIN 0 | |
9834 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9835 | #define SIZEOF_TYPE 8 | |
9836 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9837 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9838 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9839 | |
cd036260 MV |
9840 | void |
9841 | scm_to_mpz (SCM val, mpz_t rop) | |
9842 | { | |
9843 | if (SCM_I_INUMP (val)) | |
9844 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9845 | else if (SCM_BIGP (val)) | |
9846 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9847 | else | |
9848 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9849 | } | |
9850 | ||
9851 | SCM | |
9852 | scm_from_mpz (mpz_t val) | |
9853 | { | |
9854 | return scm_i_mpz2num (val); | |
9855 | } | |
9856 | ||
73e4de09 MV |
9857 | int |
9858 | scm_is_real (SCM val) | |
9859 | { | |
9860 | return scm_is_true (scm_real_p (val)); | |
9861 | } | |
9862 | ||
55f26379 MV |
9863 | int |
9864 | scm_is_rational (SCM val) | |
9865 | { | |
9866 | return scm_is_true (scm_rational_p (val)); | |
9867 | } | |
9868 | ||
73e4de09 MV |
9869 | double |
9870 | scm_to_double (SCM val) | |
9871 | { | |
55f26379 MV |
9872 | if (SCM_I_INUMP (val)) |
9873 | return SCM_I_INUM (val); | |
9874 | else if (SCM_BIGP (val)) | |
9875 | return scm_i_big2dbl (val); | |
9876 | else if (SCM_FRACTIONP (val)) | |
9877 | return scm_i_fraction2double (val); | |
9878 | else if (SCM_REALP (val)) | |
9879 | return SCM_REAL_VALUE (val); | |
9880 | else | |
7a1aba42 | 9881 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9882 | } |
9883 | ||
9884 | SCM | |
9885 | scm_from_double (double val) | |
9886 | { | |
00472a22 | 9887 | return scm_i_from_double (val); |
73e4de09 MV |
9888 | } |
9889 | ||
8507ec80 MV |
9890 | int |
9891 | scm_is_complex (SCM val) | |
9892 | { | |
9893 | return scm_is_true (scm_complex_p (val)); | |
9894 | } | |
9895 | ||
9896 | double | |
9897 | scm_c_real_part (SCM z) | |
9898 | { | |
9899 | if (SCM_COMPLEXP (z)) | |
9900 | return SCM_COMPLEX_REAL (z); | |
9901 | else | |
9902 | { | |
9903 | /* Use the scm_real_part to get proper error checking and | |
9904 | dispatching. | |
9905 | */ | |
9906 | return scm_to_double (scm_real_part (z)); | |
9907 | } | |
9908 | } | |
9909 | ||
9910 | double | |
9911 | scm_c_imag_part (SCM z) | |
9912 | { | |
9913 | if (SCM_COMPLEXP (z)) | |
9914 | return SCM_COMPLEX_IMAG (z); | |
9915 | else | |
9916 | { | |
9917 | /* Use the scm_imag_part to get proper error checking and | |
9918 | dispatching. The result will almost always be 0.0, but not | |
9919 | always. | |
9920 | */ | |
9921 | return scm_to_double (scm_imag_part (z)); | |
9922 | } | |
9923 | } | |
9924 | ||
9925 | double | |
9926 | scm_c_magnitude (SCM z) | |
9927 | { | |
9928 | return scm_to_double (scm_magnitude (z)); | |
9929 | } | |
9930 | ||
9931 | double | |
9932 | scm_c_angle (SCM z) | |
9933 | { | |
9934 | return scm_to_double (scm_angle (z)); | |
9935 | } | |
9936 | ||
9937 | int | |
9938 | scm_is_number (SCM z) | |
9939 | { | |
9940 | return scm_is_true (scm_number_p (z)); | |
9941 | } | |
9942 | ||
8ab3d8a0 | 9943 | |
a5f6b751 MW |
9944 | /* Returns log(x * 2^shift) */ |
9945 | static SCM | |
9946 | log_of_shifted_double (double x, long shift) | |
9947 | { | |
9948 | double ans = log (fabs (x)) + shift * M_LN2; | |
9949 | ||
e1592f8a | 9950 | if (copysign (1.0, x) > 0.0) |
00472a22 | 9951 | return scm_i_from_double (ans); |
a5f6b751 MW |
9952 | else |
9953 | return scm_c_make_rectangular (ans, M_PI); | |
9954 | } | |
9955 | ||
85bdb6ac | 9956 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9957 | static SCM |
9958 | log_of_exact_integer (SCM n) | |
9959 | { | |
7f34acd8 MW |
9960 | if (SCM_I_INUMP (n)) |
9961 | return log_of_shifted_double (SCM_I_INUM (n), 0); | |
9962 | else if (SCM_BIGP (n)) | |
9963 | { | |
9964 | long expon; | |
9965 | double signif = scm_i_big2dbl_2exp (n, &expon); | |
9966 | return log_of_shifted_double (signif, expon); | |
9967 | } | |
9968 | else | |
9969 | scm_wrong_type_arg ("log_of_exact_integer", SCM_ARG1, n); | |
a5f6b751 MW |
9970 | } |
9971 | ||
9972 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9973 | static SCM | |
9974 | log_of_fraction (SCM n, SCM d) | |
9975 | { | |
9976 | long n_size = scm_to_long (scm_integer_length (n)); | |
9977 | long d_size = scm_to_long (scm_integer_length (d)); | |
9978 | ||
9979 | if (abs (n_size - d_size) > 1) | |
7f34acd8 MW |
9980 | return (scm_difference (log_of_exact_integer (n), |
9981 | log_of_exact_integer (d))); | |
a5f6b751 | 9982 | else if (scm_is_false (scm_negative_p (n))) |
00472a22 | 9983 | return scm_i_from_double |
98237784 | 9984 | (log1p (scm_i_divide2double (scm_difference (n, d), d))); |
a5f6b751 MW |
9985 | else |
9986 | return scm_c_make_rectangular | |
98237784 MW |
9987 | (log1p (scm_i_divide2double (scm_difference (scm_abs (n), d), |
9988 | d)), | |
a5f6b751 MW |
9989 | M_PI); |
9990 | } | |
9991 | ||
9992 | ||
8ab3d8a0 KR |
9993 | /* In the following functions we dispatch to the real-arg funcs like log() |
9994 | when we know the arg is real, instead of just handing everything to | |
9995 | clog() for instance. This is in case clog() doesn't optimize for a | |
9996 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9997 | well use it to go straight to the applicable C func. */ | |
9998 | ||
2519490c MW |
9999 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
10000 | (SCM z), | |
10001 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
10002 | #define FUNC_NAME s_scm_log |
10003 | { | |
10004 | if (SCM_COMPLEXP (z)) | |
10005 | { | |
03976fee AW |
10006 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
10007 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
10008 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
10009 | #else | |
10010 | double re = SCM_COMPLEX_REAL (z); | |
10011 | double im = SCM_COMPLEX_IMAG (z); | |
10012 | return scm_c_make_rectangular (log (hypot (re, im)), | |
10013 | atan2 (im, re)); | |
10014 | #endif | |
10015 | } | |
a5f6b751 MW |
10016 | else if (SCM_REALP (z)) |
10017 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
10018 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 10019 | { |
a5f6b751 MW |
10020 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
10021 | if (scm_is_eq (z, SCM_INUM0)) | |
10022 | scm_num_overflow (s_scm_log); | |
10023 | #endif | |
10024 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 10025 | } |
a5f6b751 MW |
10026 | else if (SCM_BIGP (z)) |
10027 | return log_of_exact_integer (z); | |
10028 | else if (SCM_FRACTIONP (z)) | |
10029 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
10030 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c | 10031 | else |
fa075d40 | 10032 | return scm_wta_dispatch_1 (g_scm_log, z, 1, s_scm_log); |
8ab3d8a0 KR |
10033 | } |
10034 | #undef FUNC_NAME | |
10035 | ||
10036 | ||
2519490c MW |
10037 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
10038 | (SCM z), | |
10039 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
10040 | #define FUNC_NAME s_scm_log10 |
10041 | { | |
10042 | if (SCM_COMPLEXP (z)) | |
10043 | { | |
10044 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
10045 | clog() and a multiply by M_LOG10E, rather than the fallback | |
10046 | log10+hypot+atan2.) */ | |
f328f862 LC |
10047 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
10048 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
10049 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
10050 | #else | |
10051 | double re = SCM_COMPLEX_REAL (z); | |
10052 | double im = SCM_COMPLEX_IMAG (z); | |
10053 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
10054 | M_LOG10E * atan2 (im, re)); | |
10055 | #endif | |
10056 | } | |
a5f6b751 | 10057 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 10058 | { |
a5f6b751 MW |
10059 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
10060 | if (scm_is_eq (z, SCM_INUM0)) | |
10061 | scm_num_overflow (s_scm_log10); | |
10062 | #endif | |
10063 | { | |
10064 | double re = scm_to_double (z); | |
10065 | double l = log10 (fabs (re)); | |
e1592f8a | 10066 | if (copysign (1.0, re) > 0.0) |
00472a22 | 10067 | return scm_i_from_double (l); |
a5f6b751 MW |
10068 | else |
10069 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
10070 | } | |
8ab3d8a0 | 10071 | } |
a5f6b751 MW |
10072 | else if (SCM_BIGP (z)) |
10073 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
10074 | else if (SCM_FRACTIONP (z)) | |
10075 | return scm_product (flo_log10e, | |
10076 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
10077 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c | 10078 | else |
fa075d40 | 10079 | return scm_wta_dispatch_1 (g_scm_log10, z, 1, s_scm_log10); |
8ab3d8a0 KR |
10080 | } |
10081 | #undef FUNC_NAME | |
10082 | ||
10083 | ||
2519490c MW |
10084 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
10085 | (SCM z), | |
10086 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
10087 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
10088 | #define FUNC_NAME s_scm_exp |
10089 | { | |
10090 | if (SCM_COMPLEXP (z)) | |
10091 | { | |
03976fee AW |
10092 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
10093 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
10094 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
10095 | #else | |
10096 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
10097 | SCM_COMPLEX_IMAG (z)); | |
10098 | #endif | |
10099 | } | |
2519490c | 10100 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
10101 | { |
10102 | /* When z is a negative bignum the conversion to double overflows, | |
10103 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
00472a22 | 10104 | return scm_i_from_double (exp (scm_to_double (z))); |
8ab3d8a0 | 10105 | } |
2519490c | 10106 | else |
fa075d40 | 10107 | return scm_wta_dispatch_1 (g_scm_exp, z, 1, s_scm_exp); |
8ab3d8a0 KR |
10108 | } |
10109 | #undef FUNC_NAME | |
10110 | ||
10111 | ||
882c8963 MW |
10112 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
10113 | (SCM k), | |
10114 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
10115 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
10116 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
10117 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
10118 | "\n" | |
10119 | "@lisp\n" | |
10120 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
10121 | "@end lisp") | |
10122 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
10123 | { | |
10124 | SCM s, r; | |
10125 | ||
10126 | scm_exact_integer_sqrt (k, &s, &r); | |
10127 | return scm_values (scm_list_2 (s, r)); | |
10128 | } | |
10129 | #undef FUNC_NAME | |
10130 | ||
10131 | void | |
10132 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
10133 | { | |
10134 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
10135 | { | |
687a87bf | 10136 | mpz_t kk, ss, rr; |
882c8963 | 10137 | |
687a87bf | 10138 | if (SCM_I_INUM (k) < 0) |
882c8963 MW |
10139 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, |
10140 | "exact non-negative integer"); | |
687a87bf MW |
10141 | mpz_init_set_ui (kk, SCM_I_INUM (k)); |
10142 | mpz_inits (ss, rr, NULL); | |
10143 | mpz_sqrtrem (ss, rr, kk); | |
10144 | *sp = SCM_I_MAKINUM (mpz_get_ui (ss)); | |
10145 | *rp = SCM_I_MAKINUM (mpz_get_ui (rr)); | |
10146 | mpz_clears (kk, ss, rr, NULL); | |
882c8963 MW |
10147 | } |
10148 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
10149 | { | |
10150 | SCM s, r; | |
10151 | ||
10152 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
10153 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
10154 | "exact non-negative integer"); | |
10155 | s = scm_i_mkbig (); | |
10156 | r = scm_i_mkbig (); | |
10157 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
10158 | scm_remember_upto_here_1 (k); | |
10159 | *sp = scm_i_normbig (s); | |
10160 | *rp = scm_i_normbig (r); | |
10161 | } | |
10162 | else | |
10163 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
10164 | "exact non-negative integer"); | |
10165 | } | |
10166 | ||
ddb71742 MW |
10167 | /* Return true iff K is a perfect square. |
10168 | K must be an exact integer. */ | |
10169 | static int | |
10170 | exact_integer_is_perfect_square (SCM k) | |
10171 | { | |
10172 | int result; | |
10173 | ||
10174 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
10175 | { | |
10176 | mpz_t kk; | |
10177 | ||
10178 | mpz_init_set_si (kk, SCM_I_INUM (k)); | |
10179 | result = mpz_perfect_square_p (kk); | |
10180 | mpz_clear (kk); | |
10181 | } | |
10182 | else | |
10183 | { | |
10184 | result = mpz_perfect_square_p (SCM_I_BIG_MPZ (k)); | |
10185 | scm_remember_upto_here_1 (k); | |
10186 | } | |
10187 | return result; | |
10188 | } | |
10189 | ||
10190 | /* Return the floor of the square root of K. | |
10191 | K must be an exact integer. */ | |
10192 | static SCM | |
10193 | exact_integer_floor_square_root (SCM k) | |
10194 | { | |
10195 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
10196 | { | |
10197 | mpz_t kk; | |
10198 | scm_t_inum ss; | |
10199 | ||
10200 | mpz_init_set_ui (kk, SCM_I_INUM (k)); | |
10201 | mpz_sqrt (kk, kk); | |
10202 | ss = mpz_get_ui (kk); | |
10203 | mpz_clear (kk); | |
10204 | return SCM_I_MAKINUM (ss); | |
10205 | } | |
10206 | else | |
10207 | { | |
10208 | SCM s; | |
10209 | ||
10210 | s = scm_i_mkbig (); | |
10211 | mpz_sqrt (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (k)); | |
10212 | scm_remember_upto_here_1 (k); | |
10213 | return scm_i_normbig (s); | |
10214 | } | |
10215 | } | |
10216 | ||
882c8963 | 10217 | |
2519490c MW |
10218 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
10219 | (SCM z), | |
10220 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 10221 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
10222 | "is returned, or if that's zero then a positive imaginary part.\n" |
10223 | "Thus,\n" | |
10224 | "\n" | |
10225 | "@example\n" | |
10226 | "(sqrt 9.0) @result{} 3.0\n" | |
10227 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
10228 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
10229 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
10230 | "@end example") | |
8ab3d8a0 KR |
10231 | #define FUNC_NAME s_scm_sqrt |
10232 | { | |
2519490c | 10233 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 10234 | { |
f328f862 LC |
10235 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
10236 | && defined SCM_COMPLEX_VALUE | |
2519490c | 10237 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 10238 | #else |
2519490c MW |
10239 | double re = SCM_COMPLEX_REAL (z); |
10240 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
10241 | return scm_c_make_polar (sqrt (hypot (re, im)), |
10242 | 0.5 * atan2 (im, re)); | |
10243 | #endif | |
10244 | } | |
2519490c | 10245 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 10246 | { |
44002664 MW |
10247 | if (SCM_I_INUMP (z)) |
10248 | { | |
ddb71742 MW |
10249 | scm_t_inum x = SCM_I_INUM (z); |
10250 | ||
10251 | if (SCM_LIKELY (x >= 0)) | |
44002664 | 10252 | { |
ddb71742 MW |
10253 | if (SCM_LIKELY (SCM_I_FIXNUM_BIT < DBL_MANT_DIG |
10254 | || x < (1L << (DBL_MANT_DIG - 1)))) | |
44002664 | 10255 | { |
ddb71742 | 10256 | double root = sqrt (x); |
44002664 MW |
10257 | |
10258 | /* If 0 <= x < 2^(DBL_MANT_DIG-1) and sqrt(x) is an | |
10259 | integer, then the result is exact. */ | |
10260 | if (root == floor (root)) | |
10261 | return SCM_I_MAKINUM ((scm_t_inum) root); | |
10262 | else | |
00472a22 | 10263 | return scm_i_from_double (root); |
44002664 MW |
10264 | } |
10265 | else | |
10266 | { | |
ddb71742 | 10267 | mpz_t xx; |
44002664 MW |
10268 | scm_t_inum root; |
10269 | ||
ddb71742 MW |
10270 | mpz_init_set_ui (xx, x); |
10271 | if (mpz_perfect_square_p (xx)) | |
44002664 | 10272 | { |
ddb71742 MW |
10273 | mpz_sqrt (xx, xx); |
10274 | root = mpz_get_ui (xx); | |
10275 | mpz_clear (xx); | |
44002664 MW |
10276 | return SCM_I_MAKINUM (root); |
10277 | } | |
10278 | else | |
ddb71742 | 10279 | mpz_clear (xx); |
44002664 MW |
10280 | } |
10281 | } | |
10282 | } | |
10283 | else if (SCM_BIGP (z)) | |
10284 | { | |
ddb71742 | 10285 | if (mpz_perfect_square_p (SCM_I_BIG_MPZ (z))) |
44002664 MW |
10286 | { |
10287 | SCM root = scm_i_mkbig (); | |
10288 | ||
10289 | mpz_sqrt (SCM_I_BIG_MPZ (root), SCM_I_BIG_MPZ (z)); | |
10290 | scm_remember_upto_here_1 (z); | |
10291 | return scm_i_normbig (root); | |
10292 | } | |
ddb71742 MW |
10293 | else |
10294 | { | |
10295 | long expon; | |
10296 | double signif = scm_i_big2dbl_2exp (z, &expon); | |
10297 | ||
10298 | if (expon & 1) | |
10299 | { | |
10300 | signif *= 2; | |
10301 | expon--; | |
10302 | } | |
10303 | if (signif < 0) | |
10304 | return scm_c_make_rectangular | |
10305 | (0.0, ldexp (sqrt (-signif), expon / 2)); | |
10306 | else | |
00472a22 | 10307 | return scm_i_from_double (ldexp (sqrt (signif), expon / 2)); |
ddb71742 | 10308 | } |
44002664 MW |
10309 | } |
10310 | else if (SCM_FRACTIONP (z)) | |
ddb71742 MW |
10311 | { |
10312 | SCM n = SCM_FRACTION_NUMERATOR (z); | |
10313 | SCM d = SCM_FRACTION_DENOMINATOR (z); | |
10314 | ||
10315 | if (exact_integer_is_perfect_square (n) | |
10316 | && exact_integer_is_perfect_square (d)) | |
10317 | return scm_i_make_ratio_already_reduced | |
10318 | (exact_integer_floor_square_root (n), | |
10319 | exact_integer_floor_square_root (d)); | |
10320 | else | |
10321 | { | |
10322 | double xx = scm_i_divide2double (n, d); | |
10323 | double abs_xx = fabs (xx); | |
10324 | long shift = 0; | |
10325 | ||
10326 | if (SCM_UNLIKELY (abs_xx > DBL_MAX || abs_xx < DBL_MIN)) | |
10327 | { | |
10328 | shift = (scm_to_long (scm_integer_length (n)) | |
10329 | - scm_to_long (scm_integer_length (d))) / 2; | |
10330 | if (shift > 0) | |
10331 | d = left_shift_exact_integer (d, 2 * shift); | |
10332 | else | |
10333 | n = left_shift_exact_integer (n, -2 * shift); | |
10334 | xx = scm_i_divide2double (n, d); | |
10335 | } | |
10336 | ||
10337 | if (xx < 0) | |
10338 | return scm_c_make_rectangular (0.0, ldexp (sqrt (-xx), shift)); | |
10339 | else | |
00472a22 | 10340 | return scm_i_from_double (ldexp (sqrt (xx), shift)); |
ddb71742 MW |
10341 | } |
10342 | } | |
44002664 MW |
10343 | |
10344 | /* Fallback method, when the cases above do not apply. */ | |
10345 | { | |
10346 | double xx = scm_to_double (z); | |
10347 | if (xx < 0) | |
10348 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
10349 | else | |
00472a22 | 10350 | return scm_i_from_double (sqrt (xx)); |
44002664 | 10351 | } |
8ab3d8a0 | 10352 | } |
2519490c | 10353 | else |
fa075d40 | 10354 | return scm_wta_dispatch_1 (g_scm_sqrt, z, 1, s_scm_sqrt); |
8ab3d8a0 KR |
10355 | } |
10356 | #undef FUNC_NAME | |
10357 | ||
10358 | ||
10359 | ||
0f2d19dd JB |
10360 | void |
10361 | scm_init_numbers () | |
0f2d19dd | 10362 | { |
b57bf272 AW |
10363 | if (scm_install_gmp_memory_functions) |
10364 | mp_set_memory_functions (custom_gmp_malloc, | |
10365 | custom_gmp_realloc, | |
10366 | custom_gmp_free); | |
10367 | ||
713a4259 KR |
10368 | mpz_init_set_si (z_negative_one, -1); |
10369 | ||
a261c0e9 DH |
10370 | /* It may be possible to tune the performance of some algorithms by using |
10371 | * the following constants to avoid the creation of bignums. Please, before | |
10372 | * using these values, remember the two rules of program optimization: | |
10373 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 10374 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 10375 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 10376 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 10377 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 10378 | |
f3ae5d60 MD |
10379 | scm_add_feature ("complex"); |
10380 | scm_add_feature ("inexact"); | |
00472a22 MW |
10381 | flo0 = scm_i_from_double (0.0); |
10382 | flo_log10e = scm_i_from_double (M_LOG10E); | |
0b799eea | 10383 | |
cff5fa33 | 10384 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
98237784 MW |
10385 | |
10386 | { | |
10387 | /* Set scm_i_divide2double_lo2b to (2 b^p - 1) */ | |
10388 | mpz_init_set_ui (scm_i_divide2double_lo2b, 1); | |
10389 | mpz_mul_2exp (scm_i_divide2double_lo2b, | |
10390 | scm_i_divide2double_lo2b, | |
10391 | DBL_MANT_DIG + 1); /* 2 b^p */ | |
10392 | mpz_sub_ui (scm_i_divide2double_lo2b, scm_i_divide2double_lo2b, 1); | |
10393 | } | |
10394 | ||
1ea37620 MW |
10395 | { |
10396 | /* Set dbl_minimum_normal_mantissa to b^{p-1} */ | |
10397 | mpz_init_set_ui (dbl_minimum_normal_mantissa, 1); | |
10398 | mpz_mul_2exp (dbl_minimum_normal_mantissa, | |
10399 | dbl_minimum_normal_mantissa, | |
10400 | DBL_MANT_DIG - 1); | |
10401 | } | |
10402 | ||
a0599745 | 10403 | #include "libguile/numbers.x" |
0f2d19dd | 10404 | } |
89e00824 ML |
10405 | |
10406 | /* | |
10407 | Local Variables: | |
10408 | c-file-style: "gnu" | |
10409 | End: | |
10410 | */ |