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 LC |
50 | #include <verify.h> |
51 | ||
0f2d19dd | 52 | #include <math.h> |
fc194577 | 53 | #include <string.h> |
3f47e526 MG |
54 | #include <unicase.h> |
55 | #include <unictype.h> | |
f92e85f7 | 56 | |
8ab3d8a0 KR |
57 | #if HAVE_COMPLEX_H |
58 | #include <complex.h> | |
59 | #endif | |
60 | ||
07b390d5 LC |
61 | #include <stdarg.h> |
62 | ||
a0599745 | 63 | #include "libguile/_scm.h" |
a0599745 MD |
64 | #include "libguile/feature.h" |
65 | #include "libguile/ports.h" | |
66 | #include "libguile/root.h" | |
67 | #include "libguile/smob.h" | |
68 | #include "libguile/strings.h" | |
864e7d42 | 69 | #include "libguile/bdw-gc.h" |
a0599745 MD |
70 | |
71 | #include "libguile/validate.h" | |
72 | #include "libguile/numbers.h" | |
1be6b49c | 73 | #include "libguile/deprecation.h" |
f4c627b3 | 74 | |
f92e85f7 MV |
75 | #include "libguile/eq.h" |
76 | ||
8ab3d8a0 KR |
77 | /* values per glibc, if not already defined */ |
78 | #ifndef M_LOG10E | |
79 | #define M_LOG10E 0.43429448190325182765 | |
80 | #endif | |
85bdb6ac MW |
81 | #ifndef M_LN2 |
82 | #define M_LN2 0.69314718055994530942 | |
83 | #endif | |
8ab3d8a0 KR |
84 | #ifndef M_PI |
85 | #define M_PI 3.14159265358979323846 | |
86 | #endif | |
87 | ||
cba521fe MW |
88 | /* FIXME: We assume that FLT_RADIX is 2 */ |
89 | verify (FLT_RADIX == 2); | |
90 | ||
e25f3727 AW |
91 | typedef scm_t_signed_bits scm_t_inum; |
92 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
93 | ||
7112615f MW |
94 | /* Tests to see if a C double is neither infinite nor a NaN. |
95 | TODO: if it's available, use C99's isfinite(x) instead */ | |
96 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
97 | ||
041fccf6 MW |
98 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
99 | of the infinity, but other platforms return a boolean only. */ | |
100 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
101 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
102 | ||
4cc2e41c MW |
103 | /* Test an inum to see if it can be converted to a double without loss |
104 | of precision. Note that this will sometimes return 0 even when 1 | |
105 | could have been returned, e.g. for large powers of 2. It is designed | |
106 | to be a fast check to optimize common cases. */ | |
107 | #define INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE(n) \ | |
108 | (SCM_I_FIXNUM_BIT-1 <= DBL_MANT_DIG \ | |
109 | || ((n) ^ ((n) >> (SCM_I_FIXNUM_BIT-1))) < (1L << DBL_MANT_DIG)) | |
07b390d5 LC |
110 | |
111 | #if ! HAVE_DECL_MPZ_INITS | |
112 | ||
113 | /* GMP < 5.0.0 lacks `mpz_inits' and `mpz_clears'. Provide them. */ | |
114 | ||
115 | #define VARARG_MPZ_ITERATOR(func) \ | |
116 | static void \ | |
117 | func ## s (mpz_t x, ...) \ | |
118 | { \ | |
119 | va_list ap; \ | |
120 | \ | |
121 | va_start (ap, x); \ | |
122 | while (x != NULL) \ | |
123 | { \ | |
124 | func (x); \ | |
125 | x = va_arg (ap, mpz_ptr); \ | |
126 | } \ | |
127 | va_end (ap); \ | |
128 | } | |
129 | ||
130 | VARARG_MPZ_ITERATOR (mpz_init) | |
131 | VARARG_MPZ_ITERATOR (mpz_clear) | |
132 | ||
133 | #endif | |
134 | ||
0f2d19dd | 135 | \f |
f4c627b3 | 136 | |
ca46fb90 RB |
137 | /* |
138 | Wonder if this might be faster for some of our code? A switch on | |
139 | the numtag would jump directly to the right case, and the | |
140 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
141 | ||
142 | #define SCM_I_NUMTAG_NOTNUM 0 | |
143 | #define SCM_I_NUMTAG_INUM 1 | |
144 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
145 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
146 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
147 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 148 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 149 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 150 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
151 | : SCM_I_NUMTAG_NOTNUM))) |
152 | */ | |
f92e85f7 | 153 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
154 | |
155 | ||
b57bf272 AW |
156 | /* Default to 1, because as we used to hard-code `free' as the |
157 | deallocator, we know that overriding these functions with | |
158 | instrumented `malloc' / `free' is OK. */ | |
159 | int scm_install_gmp_memory_functions = 1; | |
e7efe8e7 | 160 | static SCM flo0; |
ff62c168 | 161 | static SCM exactly_one_half; |
a5f6b751 | 162 | static SCM flo_log10e; |
e7efe8e7 | 163 | |
34d19ef6 | 164 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 165 | |
56e55ac7 | 166 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
167 | * printed or scm_string representation of an inexact number. |
168 | */ | |
0b799eea | 169 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 170 | |
b127c712 | 171 | |
ad79736c AW |
172 | #if !defined (HAVE_ASINH) |
173 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
174 | #endif | |
175 | #if !defined (HAVE_ACOSH) | |
176 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
177 | #endif | |
178 | #if !defined (HAVE_ATANH) | |
179 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
180 | #endif | |
181 | ||
18d78c5e MW |
182 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
183 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released | |
184 | in March 2006), mpz_cmp_d now handles infinities properly. */ | |
f8a8200b | 185 | #if 1 |
b127c712 | 186 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 187 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
188 | #else |
189 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
190 | #endif | |
191 | ||
f92e85f7 | 192 | |
4b26c03e | 193 | #if defined (GUILE_I) |
03976fee | 194 | #if defined HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
195 | |
196 | /* For an SCM object Z which is a complex number (ie. satisfies | |
197 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
198 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 199 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 200 | |
7a35784c | 201 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
202 | |
203 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 204 | static inline SCM |
8ab3d8a0 KR |
205 | scm_from_complex_double (complex double z) |
206 | { | |
207 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
208 | } | |
bca69a9f | 209 | |
8ab3d8a0 | 210 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 211 | #endif /* GUILE_I */ |
8ab3d8a0 | 212 | |
0f2d19dd JB |
213 | \f |
214 | ||
713a4259 | 215 | static mpz_t z_negative_one; |
ac0c002c DH |
216 | |
217 | \f | |
b57bf272 | 218 | |
864e7d42 LC |
219 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
220 | static void | |
6922d92f | 221 | finalize_bignum (void *ptr, void *data) |
864e7d42 LC |
222 | { |
223 | SCM bignum; | |
224 | ||
21041372 | 225 | bignum = SCM_PACK_POINTER (ptr); |
864e7d42 LC |
226 | mpz_clear (SCM_I_BIG_MPZ (bignum)); |
227 | } | |
228 | ||
b57bf272 AW |
229 | /* The next three functions (custom_libgmp_*) are passed to |
230 | mp_set_memory_functions (in GMP) so that memory used by the digits | |
231 | themselves is known to the garbage collector. This is needed so | |
232 | that GC will be run at appropriate times. Otherwise, a program which | |
233 | creates many large bignums would malloc a huge amount of memory | |
234 | before the GC runs. */ | |
235 | static void * | |
236 | custom_gmp_malloc (size_t alloc_size) | |
237 | { | |
238 | return scm_malloc (alloc_size); | |
239 | } | |
240 | ||
241 | static void * | |
242 | custom_gmp_realloc (void *old_ptr, size_t old_size, size_t new_size) | |
243 | { | |
244 | return scm_realloc (old_ptr, new_size); | |
245 | } | |
246 | ||
247 | static void | |
248 | custom_gmp_free (void *ptr, size_t size) | |
249 | { | |
250 | free (ptr); | |
251 | } | |
252 | ||
253 | ||
d017fcdf LC |
254 | /* Return a new uninitialized bignum. */ |
255 | static inline SCM | |
256 | make_bignum (void) | |
257 | { | |
258 | scm_t_bits *p; | |
259 | ||
260 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
261 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
262 | "bignum"); | |
263 | p[0] = scm_tc16_big; | |
264 | ||
6978c673 | 265 | scm_i_set_finalizer (p, finalize_bignum, NULL); |
864e7d42 | 266 | |
d017fcdf LC |
267 | return SCM_PACK (p); |
268 | } | |
ac0c002c | 269 | |
864e7d42 | 270 | |
189171c5 | 271 | SCM |
ca46fb90 RB |
272 | scm_i_mkbig () |
273 | { | |
274 | /* Return a newly created bignum. */ | |
d017fcdf | 275 | SCM z = make_bignum (); |
ca46fb90 RB |
276 | mpz_init (SCM_I_BIG_MPZ (z)); |
277 | return z; | |
278 | } | |
279 | ||
e25f3727 AW |
280 | static SCM |
281 | scm_i_inum2big (scm_t_inum x) | |
282 | { | |
283 | /* Return a newly created bignum initialized to X. */ | |
284 | SCM z = make_bignum (); | |
285 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
286 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
287 | #else | |
288 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
289 | mpz_*_si invocations in Guile. */ | |
290 | #error creation of mpz not implemented for this inum size | |
291 | #endif | |
292 | return z; | |
293 | } | |
294 | ||
189171c5 | 295 | SCM |
c71b0706 MV |
296 | scm_i_long2big (long x) |
297 | { | |
298 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 299 | SCM z = make_bignum (); |
c71b0706 MV |
300 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
301 | return z; | |
302 | } | |
303 | ||
189171c5 | 304 | SCM |
c71b0706 MV |
305 | scm_i_ulong2big (unsigned long x) |
306 | { | |
307 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 308 | SCM z = make_bignum (); |
c71b0706 MV |
309 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
310 | return z; | |
311 | } | |
312 | ||
189171c5 | 313 | SCM |
ca46fb90 RB |
314 | scm_i_clonebig (SCM src_big, int same_sign_p) |
315 | { | |
316 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 317 | SCM z = make_bignum (); |
ca46fb90 | 318 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
319 | if (!same_sign_p) |
320 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
321 | return z; |
322 | } | |
323 | ||
189171c5 | 324 | int |
ca46fb90 RB |
325 | scm_i_bigcmp (SCM x, SCM y) |
326 | { | |
327 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
328 | /* presume we already know x and y are bignums */ | |
329 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
330 | scm_remember_upto_here_2 (x, y); | |
331 | return result; | |
332 | } | |
333 | ||
189171c5 | 334 | SCM |
ca46fb90 RB |
335 | scm_i_dbl2big (double d) |
336 | { | |
337 | /* results are only defined if d is an integer */ | |
d017fcdf | 338 | SCM z = make_bignum (); |
ca46fb90 RB |
339 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
340 | return z; | |
341 | } | |
342 | ||
f92e85f7 MV |
343 | /* Convert a integer in double representation to a SCM number. */ |
344 | ||
189171c5 | 345 | SCM |
f92e85f7 MV |
346 | scm_i_dbl2num (double u) |
347 | { | |
348 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
349 | powers of 2, so there's no rounding when making "double" values | |
350 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
351 | get rounded on a 64-bit machine, hence the "+1". | |
352 | ||
353 | The use of floor() to force to an integer value ensures we get a | |
354 | "numerically closest" value without depending on how a | |
355 | double->long cast or how mpz_set_d will round. For reference, | |
356 | double->long probably follows the hardware rounding mode, | |
357 | mpz_set_d truncates towards zero. */ | |
358 | ||
359 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
360 | representable as a double? */ | |
361 | ||
362 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
363 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 364 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
365 | else |
366 | return scm_i_dbl2big (u); | |
367 | } | |
368 | ||
1eb6a33a | 369 | static SCM round_right_shift_exact_integer (SCM n, long count); |
f8a8200b | 370 | |
1eb6a33a MW |
371 | /* scm_i_big2dbl_2exp() is like frexp for bignums: it converts the |
372 | bignum b into a normalized significand and exponent such that | |
373 | b = significand * 2^exponent and 1/2 <= abs(significand) < 1. | |
374 | The return value is the significand rounded to the closest | |
375 | representable double, and the exponent is placed into *expon_p. | |
376 | If b is zero, then the returned exponent and significand are both | |
377 | zero. */ | |
f8a8200b | 378 | |
1eb6a33a MW |
379 | static double |
380 | scm_i_big2dbl_2exp (SCM b, long *expon_p) | |
ca46fb90 | 381 | { |
1eb6a33a MW |
382 | size_t bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); |
383 | size_t shift = 0; | |
089c9a59 KR |
384 | |
385 | if (bits > DBL_MANT_DIG) | |
386 | { | |
1eb6a33a MW |
387 | shift = bits - DBL_MANT_DIG; |
388 | b = round_right_shift_exact_integer (b, shift); | |
389 | if (SCM_I_INUMP (b)) | |
089c9a59 | 390 | { |
1eb6a33a MW |
391 | int expon; |
392 | double signif = frexp (SCM_I_INUM (b), &expon); | |
393 | *expon_p = expon + shift; | |
394 | return signif; | |
089c9a59 KR |
395 | } |
396 | } | |
397 | ||
1eb6a33a MW |
398 | { |
399 | long expon; | |
400 | double signif = mpz_get_d_2exp (&expon, SCM_I_BIG_MPZ (b)); | |
401 | scm_remember_upto_here_1 (b); | |
402 | *expon_p = expon + shift; | |
403 | return signif; | |
404 | } | |
405 | } | |
406 | ||
407 | /* scm_i_big2dbl() rounds to the closest representable double, | |
408 | in accordance with R5RS exact->inexact. */ | |
409 | double | |
410 | scm_i_big2dbl (SCM b) | |
411 | { | |
412 | long expon; | |
413 | double signif = scm_i_big2dbl_2exp (b, &expon); | |
414 | return ldexp (signif, expon); | |
ca46fb90 RB |
415 | } |
416 | ||
189171c5 | 417 | SCM |
ca46fb90 RB |
418 | scm_i_normbig (SCM b) |
419 | { | |
420 | /* convert a big back to a fixnum if it'll fit */ | |
421 | /* presume b is a bignum */ | |
422 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
423 | { | |
e25f3727 | 424 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 425 | if (SCM_FIXABLE (val)) |
d956fa6f | 426 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
427 | } |
428 | return b; | |
429 | } | |
f872b822 | 430 | |
f92e85f7 MV |
431 | static SCM_C_INLINE_KEYWORD SCM |
432 | scm_i_mpz2num (mpz_t b) | |
433 | { | |
434 | /* convert a mpz number to a SCM number. */ | |
435 | if (mpz_fits_slong_p (b)) | |
436 | { | |
e25f3727 | 437 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 438 | if (SCM_FIXABLE (val)) |
d956fa6f | 439 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
440 | } |
441 | ||
442 | { | |
d017fcdf | 443 | SCM z = make_bignum (); |
f92e85f7 MV |
444 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
445 | return z; | |
446 | } | |
447 | } | |
448 | ||
a285b18c MW |
449 | /* Make the ratio NUMERATOR/DENOMINATOR, where: |
450 | 1. NUMERATOR and DENOMINATOR are exact integers | |
451 | 2. NUMERATOR and DENOMINATOR are reduced to lowest terms: gcd(n,d) == 1 */ | |
cba42c93 | 452 | static SCM |
a285b18c | 453 | scm_i_make_ratio_already_reduced (SCM numerator, SCM denominator) |
f92e85f7 | 454 | { |
a285b18c MW |
455 | /* Flip signs so that the denominator is positive. */ |
456 | if (scm_is_false (scm_positive_p (denominator))) | |
f92e85f7 | 457 | { |
a285b18c | 458 | if (SCM_UNLIKELY (scm_is_eq (denominator, SCM_INUM0))) |
f92e85f7 | 459 | scm_num_overflow ("make-ratio"); |
a285b18c | 460 | else |
f92e85f7 | 461 | { |
a285b18c MW |
462 | numerator = scm_difference (numerator, SCM_UNDEFINED); |
463 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
f92e85f7 | 464 | } |
f92e85f7 | 465 | } |
c60e130c | 466 | |
a285b18c MW |
467 | /* Check for the integer case */ |
468 | if (scm_is_eq (denominator, SCM_INUM1)) | |
469 | return numerator; | |
c60e130c | 470 | |
a285b18c MW |
471 | return scm_double_cell (scm_tc16_fraction, |
472 | SCM_UNPACK (numerator), | |
473 | SCM_UNPACK (denominator), 0); | |
474 | } | |
475 | ||
476 | static SCM scm_exact_integer_quotient (SCM x, SCM y); | |
477 | ||
478 | /* Make the ratio NUMERATOR/DENOMINATOR */ | |
479 | static SCM | |
480 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
481 | #define FUNC_NAME "make-ratio" | |
482 | { | |
483 | /* Make sure the arguments are proper */ | |
484 | if (!SCM_LIKELY (SCM_I_INUMP (numerator) || SCM_BIGP (numerator))) | |
485 | SCM_WRONG_TYPE_ARG (1, numerator); | |
486 | else if (!SCM_LIKELY (SCM_I_INUMP (denominator) || SCM_BIGP (denominator))) | |
487 | SCM_WRONG_TYPE_ARG (2, denominator); | |
488 | else | |
f92e85f7 | 489 | { |
a285b18c MW |
490 | SCM the_gcd = scm_gcd (numerator, denominator); |
491 | if (!(scm_is_eq (the_gcd, SCM_INUM1))) | |
f92e85f7 | 492 | { |
a285b18c MW |
493 | /* Reduce to lowest terms */ |
494 | numerator = scm_exact_integer_quotient (numerator, the_gcd); | |
495 | denominator = scm_exact_integer_quotient (denominator, the_gcd); | |
f92e85f7 | 496 | } |
a285b18c | 497 | return scm_i_make_ratio_already_reduced (numerator, denominator); |
f92e85f7 | 498 | } |
f92e85f7 | 499 | } |
c60e130c | 500 | #undef FUNC_NAME |
f92e85f7 | 501 | |
98237784 MW |
502 | static mpz_t scm_i_divide2double_lo2b; |
503 | ||
504 | /* Return the double that is closest to the exact rational N/D, with | |
505 | ties rounded toward even mantissas. N and D must be exact | |
506 | integers. */ | |
507 | static double | |
508 | scm_i_divide2double (SCM n, SCM d) | |
509 | { | |
510 | int neg; | |
511 | mpz_t nn, dd, lo, hi, x; | |
512 | ssize_t e; | |
513 | ||
c8248c8e | 514 | if (SCM_LIKELY (SCM_I_INUMP (d))) |
f92e85f7 | 515 | { |
4cc2e41c MW |
516 | if (SCM_LIKELY |
517 | (SCM_I_INUMP (n) | |
518 | && INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE (SCM_I_INUM (n)) | |
519 | && INUM_LOSSLESSLY_CONVERTIBLE_TO_DOUBLE (SCM_I_INUM (d)))) | |
c8248c8e MW |
520 | /* If both N and D can be losslessly converted to doubles, then |
521 | we can rely on IEEE floating point to do proper rounding much | |
522 | faster than we can. */ | |
523 | return ((double) SCM_I_INUM (n)) / ((double) SCM_I_INUM (d)); | |
524 | ||
98237784 MW |
525 | if (SCM_UNLIKELY (scm_is_eq (d, SCM_INUM0))) |
526 | { | |
527 | if (scm_is_true (scm_positive_p (n))) | |
528 | return 1.0 / 0.0; | |
529 | else if (scm_is_true (scm_negative_p (n))) | |
530 | return -1.0 / 0.0; | |
531 | else | |
532 | return 0.0 / 0.0; | |
533 | } | |
c8248c8e | 534 | |
98237784 | 535 | mpz_init_set_si (dd, SCM_I_INUM (d)); |
f92e85f7 | 536 | } |
98237784 MW |
537 | else |
538 | mpz_init_set (dd, SCM_I_BIG_MPZ (d)); | |
c60e130c | 539 | |
98237784 MW |
540 | if (SCM_I_INUMP (n)) |
541 | mpz_init_set_si (nn, SCM_I_INUM (n)); | |
542 | else | |
543 | mpz_init_set (nn, SCM_I_BIG_MPZ (n)); | |
544 | ||
545 | neg = (mpz_sgn (nn) < 0) ^ (mpz_sgn (dd) < 0); | |
546 | mpz_abs (nn, nn); | |
547 | mpz_abs (dd, dd); | |
548 | ||
549 | /* Now we need to find the value of e such that: | |
550 | ||
551 | For e <= 0: | |
552 | b^{p-1} - 1/2b <= b^-e n / d < b^p - 1/2 [1A] | |
553 | (2 b^p - 1) <= 2 b b^-e n / d < (2 b^p - 1) b [2A] | |
554 | (2 b^p - 1) d <= 2 b b^-e n < (2 b^p - 1) d b [3A] | |
555 | ||
556 | For e >= 0: | |
557 | b^{p-1} - 1/2b <= n / b^e d < b^p - 1/2 [1B] | |
558 | (2 b^p - 1) <= 2 b n / b^e d < (2 b^p - 1) b [2B] | |
559 | (2 b^p - 1) d b^e <= 2 b n < (2 b^p - 1) d b b^e [3B] | |
560 | ||
561 | where: p = DBL_MANT_DIG | |
562 | b = FLT_RADIX (here assumed to be 2) | |
563 | ||
564 | After rounding, the mantissa must be an integer between b^{p-1} and | |
565 | (b^p - 1), except for subnormal numbers. In the inequations [1A] | |
566 | and [1B], the middle expression represents the mantissa *before* | |
567 | rounding, and therefore is bounded by the range of values that will | |
568 | round to a floating-point number with the exponent e. The upper | |
569 | bound is (b^p - 1 + 1/2) = (b^p - 1/2), and is exclusive because | |
570 | ties will round up to the next power of b. The lower bound is | |
571 | (b^{p-1} - 1/2b), and is inclusive because ties will round toward | |
572 | this power of b. Here we subtract 1/2b instead of 1/2 because it | |
573 | is in the range of the next smaller exponent, where the | |
574 | representable numbers are closer together by a factor of b. | |
575 | ||
576 | Inequations [2A] and [2B] are derived from [1A] and [1B] by | |
577 | multiplying by 2b, and in [3A] and [3B] we multiply by the | |
578 | denominator of the middle value to obtain integer expressions. | |
579 | ||
580 | In the code below, we refer to the three expressions in [3A] or | |
581 | [3B] as lo, x, and hi. If the number is normalizable, we will | |
582 | achieve the goal: lo <= x < hi */ | |
583 | ||
584 | /* Make an initial guess for e */ | |
585 | e = mpz_sizeinbase (nn, 2) - mpz_sizeinbase (dd, 2) - (DBL_MANT_DIG-1); | |
586 | if (e < DBL_MIN_EXP - DBL_MANT_DIG) | |
587 | e = DBL_MIN_EXP - DBL_MANT_DIG; | |
588 | ||
589 | /* Compute the initial values of lo, x, and hi | |
590 | based on the initial guess of e */ | |
591 | mpz_inits (lo, hi, x, NULL); | |
592 | mpz_mul_2exp (x, nn, 2 + ((e < 0) ? -e : 0)); | |
593 | mpz_mul (lo, dd, scm_i_divide2double_lo2b); | |
594 | if (e > 0) | |
595 | mpz_mul_2exp (lo, lo, e); | |
596 | mpz_mul_2exp (hi, lo, 1); | |
597 | ||
598 | /* Adjust e as needed to satisfy the inequality lo <= x < hi, | |
599 | (but without making e less then the minimum exponent) */ | |
600 | while (mpz_cmp (x, lo) < 0 && e > DBL_MIN_EXP - DBL_MANT_DIG) | |
601 | { | |
602 | mpz_mul_2exp (x, x, 1); | |
603 | e--; | |
604 | } | |
605 | while (mpz_cmp (x, hi) >= 0) | |
606 | { | |
607 | /* If we ever used lo's value again, | |
608 | we would need to double lo here. */ | |
609 | mpz_mul_2exp (hi, hi, 1); | |
610 | e++; | |
611 | } | |
612 | ||
613 | /* Now compute the rounded mantissa: | |
614 | n / b^e d (if e >= 0) | |
615 | n b^-e / d (if e <= 0) */ | |
e2bf3b19 | 616 | { |
98237784 MW |
617 | int cmp; |
618 | double result; | |
619 | ||
620 | if (e < 0) | |
621 | mpz_mul_2exp (nn, nn, -e); | |
622 | else | |
623 | mpz_mul_2exp (dd, dd, e); | |
624 | ||
625 | /* mpz does not directly support rounded right | |
626 | shifts, so we have to do it the hard way. | |
627 | For efficiency, we reuse lo and hi. | |
628 | hi == quotient, lo == remainder */ | |
629 | mpz_fdiv_qr (hi, lo, nn, dd); | |
630 | ||
631 | /* The fractional part of the unrounded mantissa would be | |
632 | remainder/dividend, i.e. lo/dd. So we have a tie if | |
633 | lo/dd = 1/2. Multiplying both sides by 2*dd yields the | |
634 | integer expression 2*lo = dd. Here we do that comparison | |
635 | to decide whether to round up or down. */ | |
636 | mpz_mul_2exp (lo, lo, 1); | |
637 | cmp = mpz_cmp (lo, dd); | |
638 | if (cmp > 0 || (cmp == 0 && mpz_odd_p (hi))) | |
639 | mpz_add_ui (hi, hi, 1); | |
640 | ||
641 | result = ldexp (mpz_get_d (hi), e); | |
642 | if (neg) | |
643 | result = -result; | |
644 | ||
645 | mpz_clears (nn, dd, lo, hi, x, NULL); | |
646 | return result; | |
e2bf3b19 | 647 | } |
f92e85f7 MV |
648 | } |
649 | ||
f92e85f7 MV |
650 | double |
651 | scm_i_fraction2double (SCM z) | |
652 | { | |
98237784 MW |
653 | return scm_i_divide2double (SCM_FRACTION_NUMERATOR (z), |
654 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 MV |
655 | } |
656 | ||
2e274311 MW |
657 | static int |
658 | double_is_non_negative_zero (double x) | |
659 | { | |
660 | static double zero = 0.0; | |
661 | ||
662 | return !memcmp (&x, &zero, sizeof(double)); | |
663 | } | |
664 | ||
2519490c MW |
665 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
666 | (SCM x), | |
942e5b91 MG |
667 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
668 | "otherwise.") | |
1bbd0b84 | 669 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 670 | { |
41df63cf MW |
671 | if (SCM_INEXACTP (x)) |
672 | return SCM_BOOL_F; | |
673 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 674 | return SCM_BOOL_T; |
41df63cf | 675 | else |
fa075d40 | 676 | return scm_wta_dispatch_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
677 | } |
678 | #undef FUNC_NAME | |
679 | ||
022dda69 MG |
680 | int |
681 | scm_is_exact (SCM val) | |
682 | { | |
683 | return scm_is_true (scm_exact_p (val)); | |
684 | } | |
41df63cf | 685 | |
2519490c | 686 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
687 | (SCM x), |
688 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
689 | "else.") | |
690 | #define FUNC_NAME s_scm_inexact_p | |
691 | { | |
692 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 693 | return SCM_BOOL_T; |
41df63cf | 694 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 695 | return SCM_BOOL_F; |
41df63cf | 696 | else |
fa075d40 | 697 | return scm_wta_dispatch_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 698 | } |
1bbd0b84 | 699 | #undef FUNC_NAME |
0f2d19dd | 700 | |
022dda69 MG |
701 | int |
702 | scm_is_inexact (SCM val) | |
703 | { | |
704 | return scm_is_true (scm_inexact_p (val)); | |
705 | } | |
4219f20d | 706 | |
2519490c | 707 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 708 | (SCM n), |
942e5b91 MG |
709 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
710 | "otherwise.") | |
1bbd0b84 | 711 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 712 | { |
e11e83f3 | 713 | if (SCM_I_INUMP (n)) |
0aacf84e | 714 | { |
e25f3727 | 715 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 716 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
717 | } |
718 | else if (SCM_BIGP (n)) | |
719 | { | |
720 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
721 | scm_remember_upto_here_1 (n); | |
73e4de09 | 722 | return scm_from_bool (odd_p); |
0aacf84e | 723 | } |
f92e85f7 MV |
724 | else if (SCM_REALP (n)) |
725 | { | |
2519490c MW |
726 | double val = SCM_REAL_VALUE (n); |
727 | if (DOUBLE_IS_FINITE (val)) | |
728 | { | |
729 | double rem = fabs (fmod (val, 2.0)); | |
730 | if (rem == 1.0) | |
731 | return SCM_BOOL_T; | |
732 | else if (rem == 0.0) | |
733 | return SCM_BOOL_F; | |
734 | } | |
f92e85f7 | 735 | } |
fa075d40 | 736 | return scm_wta_dispatch_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 737 | } |
1bbd0b84 | 738 | #undef FUNC_NAME |
0f2d19dd | 739 | |
4219f20d | 740 | |
2519490c | 741 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 742 | (SCM n), |
942e5b91 MG |
743 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
744 | "otherwise.") | |
1bbd0b84 | 745 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 746 | { |
e11e83f3 | 747 | if (SCM_I_INUMP (n)) |
0aacf84e | 748 | { |
e25f3727 | 749 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 750 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
751 | } |
752 | else if (SCM_BIGP (n)) | |
753 | { | |
754 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
755 | scm_remember_upto_here_1 (n); | |
73e4de09 | 756 | return scm_from_bool (even_p); |
0aacf84e | 757 | } |
f92e85f7 MV |
758 | else if (SCM_REALP (n)) |
759 | { | |
2519490c MW |
760 | double val = SCM_REAL_VALUE (n); |
761 | if (DOUBLE_IS_FINITE (val)) | |
762 | { | |
763 | double rem = fabs (fmod (val, 2.0)); | |
764 | if (rem == 1.0) | |
765 | return SCM_BOOL_F; | |
766 | else if (rem == 0.0) | |
767 | return SCM_BOOL_T; | |
768 | } | |
f92e85f7 | 769 | } |
fa075d40 | 770 | return scm_wta_dispatch_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 771 | } |
1bbd0b84 | 772 | #undef FUNC_NAME |
0f2d19dd | 773 | |
2519490c MW |
774 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
775 | (SCM x), | |
10391e06 AW |
776 | "Return @code{#t} if the real number @var{x} is neither\n" |
777 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
778 | #define FUNC_NAME s_scm_finite_p |
779 | { | |
780 | if (SCM_REALP (x)) | |
781 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 782 | else if (scm_is_real (x)) |
7112615f MW |
783 | return SCM_BOOL_T; |
784 | else | |
fa075d40 | 785 | return scm_wta_dispatch_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
786 | } |
787 | #undef FUNC_NAME | |
788 | ||
2519490c MW |
789 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
790 | (SCM x), | |
791 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
792 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
793 | #define FUNC_NAME s_scm_inf_p |
794 | { | |
b1092b3a | 795 | if (SCM_REALP (x)) |
2e65b52f | 796 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 797 | else if (scm_is_real (x)) |
7351e207 | 798 | return SCM_BOOL_F; |
10391e06 | 799 | else |
fa075d40 | 800 | return scm_wta_dispatch_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
801 | } |
802 | #undef FUNC_NAME | |
803 | ||
2519490c MW |
804 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
805 | (SCM x), | |
10391e06 AW |
806 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
807 | "or @code{#f} otherwise.") | |
7351e207 MV |
808 | #define FUNC_NAME s_scm_nan_p |
809 | { | |
10391e06 AW |
810 | if (SCM_REALP (x)) |
811 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
812 | else if (scm_is_real (x)) | |
7351e207 | 813 | return SCM_BOOL_F; |
10391e06 | 814 | else |
fa075d40 | 815 | return scm_wta_dispatch_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
816 | } |
817 | #undef FUNC_NAME | |
818 | ||
819 | /* Guile's idea of infinity. */ | |
820 | static double guile_Inf; | |
821 | ||
822 | /* Guile's idea of not a number. */ | |
823 | static double guile_NaN; | |
824 | ||
825 | static void | |
826 | guile_ieee_init (void) | |
827 | { | |
7351e207 MV |
828 | /* Some version of gcc on some old version of Linux used to crash when |
829 | trying to make Inf and NaN. */ | |
830 | ||
240a27d2 KR |
831 | #ifdef INFINITY |
832 | /* C99 INFINITY, when available. | |
833 | FIXME: The standard allows for INFINITY to be something that overflows | |
834 | at compile time. We ought to have a configure test to check for that | |
835 | before trying to use it. (But in practice we believe this is not a | |
836 | problem on any system guile is likely to target.) */ | |
837 | guile_Inf = INFINITY; | |
56a3dcd4 | 838 | #elif defined HAVE_DINFINITY |
240a27d2 | 839 | /* OSF */ |
7351e207 | 840 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 841 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
842 | #else |
843 | double tmp = 1e+10; | |
844 | guile_Inf = tmp; | |
845 | for (;;) | |
846 | { | |
847 | guile_Inf *= 1e+10; | |
848 | if (guile_Inf == tmp) | |
849 | break; | |
850 | tmp = guile_Inf; | |
851 | } | |
852 | #endif | |
853 | ||
240a27d2 KR |
854 | #ifdef NAN |
855 | /* C99 NAN, when available */ | |
856 | guile_NaN = NAN; | |
56a3dcd4 | 857 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
858 | { |
859 | /* OSF */ | |
860 | extern unsigned int DQNAN[2]; | |
861 | guile_NaN = (*((double *)(DQNAN))); | |
862 | } | |
7351e207 MV |
863 | #else |
864 | guile_NaN = guile_Inf / guile_Inf; | |
865 | #endif | |
7351e207 MV |
866 | } |
867 | ||
868 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
869 | (void), | |
870 | "Return Inf.") | |
871 | #define FUNC_NAME s_scm_inf | |
872 | { | |
873 | static int initialized = 0; | |
874 | if (! initialized) | |
875 | { | |
876 | guile_ieee_init (); | |
877 | initialized = 1; | |
878 | } | |
55f26379 | 879 | return scm_from_double (guile_Inf); |
7351e207 MV |
880 | } |
881 | #undef FUNC_NAME | |
882 | ||
883 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
884 | (void), | |
885 | "Return NaN.") | |
886 | #define FUNC_NAME s_scm_nan | |
887 | { | |
888 | static int initialized = 0; | |
0aacf84e | 889 | if (!initialized) |
7351e207 MV |
890 | { |
891 | guile_ieee_init (); | |
892 | initialized = 1; | |
893 | } | |
55f26379 | 894 | return scm_from_double (guile_NaN); |
7351e207 MV |
895 | } |
896 | #undef FUNC_NAME | |
897 | ||
4219f20d | 898 | |
a48d60b1 MD |
899 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
900 | (SCM x), | |
901 | "Return the absolute value of @var{x}.") | |
2519490c | 902 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 903 | { |
e11e83f3 | 904 | if (SCM_I_INUMP (x)) |
0aacf84e | 905 | { |
e25f3727 | 906 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
907 | if (xx >= 0) |
908 | return x; | |
909 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 910 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 911 | else |
e25f3727 | 912 | return scm_i_inum2big (-xx); |
4219f20d | 913 | } |
9b9ef10c MW |
914 | else if (SCM_LIKELY (SCM_REALP (x))) |
915 | { | |
916 | double xx = SCM_REAL_VALUE (x); | |
917 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
918 | if (xx < 0.0) | |
919 | return scm_from_double (-xx); | |
920 | /* Handle signed zeroes properly */ | |
921 | else if (SCM_UNLIKELY (xx == 0.0)) | |
922 | return flo0; | |
923 | else | |
924 | return x; | |
925 | } | |
0aacf84e MD |
926 | else if (SCM_BIGP (x)) |
927 | { | |
928 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
929 | if (sgn < 0) | |
930 | return scm_i_clonebig (x, 0); | |
931 | else | |
932 | return x; | |
4219f20d | 933 | } |
f92e85f7 MV |
934 | else if (SCM_FRACTIONP (x)) |
935 | { | |
73e4de09 | 936 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 937 | return x; |
a285b18c MW |
938 | return scm_i_make_ratio_already_reduced |
939 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
940 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 941 | } |
0aacf84e | 942 | else |
fa075d40 | 943 | return scm_wta_dispatch_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 944 | } |
a48d60b1 | 945 | #undef FUNC_NAME |
0f2d19dd | 946 | |
4219f20d | 947 | |
2519490c MW |
948 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
949 | (SCM x, SCM y), | |
950 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
951 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 952 | { |
495a39c4 | 953 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 954 | { |
495a39c4 | 955 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 956 | return scm_truncate_quotient (x, y); |
0aacf84e | 957 | else |
fa075d40 | 958 | return scm_wta_dispatch_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 959 | } |
0aacf84e | 960 | else |
fa075d40 | 961 | return scm_wta_dispatch_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 962 | } |
2519490c | 963 | #undef FUNC_NAME |
0f2d19dd | 964 | |
2519490c MW |
965 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
966 | (SCM x, SCM y), | |
967 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
968 | "@lisp\n" | |
969 | "(remainder 13 4) @result{} 1\n" | |
970 | "(remainder -13 4) @result{} -1\n" | |
971 | "@end lisp") | |
972 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 973 | { |
495a39c4 | 974 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 975 | { |
495a39c4 | 976 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 977 | return scm_truncate_remainder (x, y); |
0aacf84e | 978 | else |
fa075d40 | 979 | return scm_wta_dispatch_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 980 | } |
0aacf84e | 981 | else |
fa075d40 | 982 | return scm_wta_dispatch_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 983 | } |
2519490c | 984 | #undef FUNC_NAME |
0f2d19dd | 985 | |
89a7e495 | 986 | |
2519490c MW |
987 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
988 | (SCM x, SCM y), | |
989 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
990 | "@lisp\n" | |
991 | "(modulo 13 4) @result{} 1\n" | |
992 | "(modulo -13 4) @result{} 3\n" | |
993 | "@end lisp") | |
994 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 995 | { |
495a39c4 | 996 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 997 | { |
495a39c4 | 998 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 999 | return scm_floor_remainder (x, y); |
0aacf84e | 1000 | else |
fa075d40 | 1001 | return scm_wta_dispatch_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 1002 | } |
0aacf84e | 1003 | else |
fa075d40 | 1004 | return scm_wta_dispatch_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1005 | } |
2519490c | 1006 | #undef FUNC_NAME |
0f2d19dd | 1007 | |
a285b18c MW |
1008 | /* Return the exact integer q such that n = q*d, for exact integers n |
1009 | and d, where d is known in advance to divide n evenly (with zero | |
1010 | remainder). For large integers, this can be computed more | |
1011 | efficiently than when the remainder is unknown. */ | |
1012 | static SCM | |
1013 | scm_exact_integer_quotient (SCM n, SCM d) | |
1014 | #define FUNC_NAME "exact-integer-quotient" | |
1015 | { | |
1016 | if (SCM_LIKELY (SCM_I_INUMP (n))) | |
1017 | { | |
1018 | scm_t_inum nn = SCM_I_INUM (n); | |
1019 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
1020 | { | |
1021 | scm_t_inum dd = SCM_I_INUM (d); | |
1022 | if (SCM_UNLIKELY (dd == 0)) | |
1023 | scm_num_overflow ("exact-integer-quotient"); | |
1024 | else | |
1025 | { | |
1026 | scm_t_inum qq = nn / dd; | |
1027 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1028 | return SCM_I_MAKINUM (qq); | |
1029 | else | |
1030 | return scm_i_inum2big (qq); | |
1031 | } | |
1032 | } | |
1033 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
1034 | { | |
1035 | /* n is an inum and d is a bignum. Given that d is known to | |
1036 | divide n evenly, there are only two possibilities: n is 0, | |
1037 | or else n is fixnum-min and d is abs(fixnum-min). */ | |
1038 | if (nn == 0) | |
1039 | return SCM_INUM0; | |
1040 | else | |
1041 | return SCM_I_MAKINUM (-1); | |
1042 | } | |
1043 | else | |
1044 | SCM_WRONG_TYPE_ARG (2, d); | |
1045 | } | |
1046 | else if (SCM_LIKELY (SCM_BIGP (n))) | |
1047 | { | |
1048 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
1049 | { | |
1050 | scm_t_inum dd = SCM_I_INUM (d); | |
1051 | if (SCM_UNLIKELY (dd == 0)) | |
1052 | scm_num_overflow ("exact-integer-quotient"); | |
1053 | else if (SCM_UNLIKELY (dd == 1)) | |
1054 | return n; | |
1055 | else | |
1056 | { | |
1057 | SCM q = scm_i_mkbig (); | |
1058 | if (dd > 0) | |
1059 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), dd); | |
1060 | else | |
1061 | { | |
1062 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), -dd); | |
1063 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1064 | } | |
1065 | scm_remember_upto_here_1 (n); | |
1066 | return scm_i_normbig (q); | |
1067 | } | |
1068 | } | |
1069 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
1070 | { | |
1071 | SCM q = scm_i_mkbig (); | |
1072 | mpz_divexact (SCM_I_BIG_MPZ (q), | |
1073 | SCM_I_BIG_MPZ (n), | |
1074 | SCM_I_BIG_MPZ (d)); | |
1075 | scm_remember_upto_here_2 (n, d); | |
1076 | return scm_i_normbig (q); | |
1077 | } | |
1078 | else | |
1079 | SCM_WRONG_TYPE_ARG (2, d); | |
1080 | } | |
1081 | else | |
1082 | SCM_WRONG_TYPE_ARG (1, n); | |
1083 | } | |
1084 | #undef FUNC_NAME | |
1085 | ||
5fbf680b MW |
1086 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
1087 | two-valued functions. It is called from primitive generics that take | |
1088 | two arguments and return two values, when the core procedure is | |
1089 | unable to handle the given argument types. If there are GOOPS | |
1090 | methods for this primitive generic, it dispatches to GOOPS and, if | |
1091 | successful, expects two values to be returned, which are placed in | |
1092 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
1093 | wrong-type-arg exception. | |
1094 | ||
1095 | FIXME: This obviously belongs somewhere else, but until we decide on | |
1096 | the right API, it is here as a static function, because it is needed | |
1097 | by the *_divide functions below. | |
1098 | */ | |
1099 | static void | |
1100 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
1101 | const char *subr, SCM *rp1, SCM *rp2) | |
1102 | { | |
fa075d40 AW |
1103 | SCM vals = scm_wta_dispatch_2 (gf, a1, a2, pos, subr); |
1104 | ||
1105 | scm_i_extract_values_2 (vals, rp1, rp2); | |
5fbf680b MW |
1106 | } |
1107 | ||
a8da6d93 MW |
1108 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
1109 | (SCM x, SCM y), | |
1110 | "Return the integer @var{q} such that\n" | |
1111 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1112 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1113 | "@lisp\n" | |
1114 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1115 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1116 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1117 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1118 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1119 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1120 | "@end lisp") | |
ff62c168 MW |
1121 | #define FUNC_NAME s_scm_euclidean_quotient |
1122 | { | |
a8da6d93 MW |
1123 | if (scm_is_false (scm_negative_p (y))) |
1124 | return scm_floor_quotient (x, y); | |
ff62c168 | 1125 | else |
a8da6d93 | 1126 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
1127 | } |
1128 | #undef FUNC_NAME | |
1129 | ||
a8da6d93 MW |
1130 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
1131 | (SCM x, SCM y), | |
1132 | "Return the real number @var{r} such that\n" | |
1133 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1134 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1135 | "for some integer @var{q}.\n" | |
1136 | "@lisp\n" | |
1137 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1138 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1139 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1140 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1141 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1142 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1143 | "@end lisp") | |
ff62c168 MW |
1144 | #define FUNC_NAME s_scm_euclidean_remainder |
1145 | { | |
a8da6d93 MW |
1146 | if (scm_is_false (scm_negative_p (y))) |
1147 | return scm_floor_remainder (x, y); | |
ff62c168 | 1148 | else |
a8da6d93 | 1149 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
1150 | } |
1151 | #undef FUNC_NAME | |
1152 | ||
a8da6d93 MW |
1153 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
1154 | (SCM x, SCM y), | |
1155 | "Return the integer @var{q} and the real number @var{r}\n" | |
1156 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1157 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1158 | "@lisp\n" | |
1159 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1160 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1161 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1162 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1163 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1164 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1165 | "@end lisp") | |
5fbf680b MW |
1166 | #define FUNC_NAME s_scm_i_euclidean_divide |
1167 | { | |
a8da6d93 MW |
1168 | if (scm_is_false (scm_negative_p (y))) |
1169 | return scm_i_floor_divide (x, y); | |
1170 | else | |
1171 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
1172 | } |
1173 | #undef FUNC_NAME | |
1174 | ||
5fbf680b MW |
1175 | void |
1176 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 1177 | { |
a8da6d93 MW |
1178 | if (scm_is_false (scm_negative_p (y))) |
1179 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 1180 | else |
a8da6d93 | 1181 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
1182 | } |
1183 | ||
8f9da340 MW |
1184 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
1185 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
1186 | ||
1187 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
1188 | (SCM x, SCM y), | |
1189 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1190 | "@lisp\n" | |
1191 | "(floor-quotient 123 10) @result{} 12\n" | |
1192 | "(floor-quotient 123 -10) @result{} -13\n" | |
1193 | "(floor-quotient -123 10) @result{} -13\n" | |
1194 | "(floor-quotient -123 -10) @result{} 12\n" | |
1195 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1196 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1197 | "@end lisp") | |
1198 | #define FUNC_NAME s_scm_floor_quotient | |
1199 | { | |
1200 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1201 | { | |
1202 | scm_t_inum xx = SCM_I_INUM (x); | |
1203 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1204 | { | |
1205 | scm_t_inum yy = SCM_I_INUM (y); | |
1206 | scm_t_inum xx1 = xx; | |
1207 | scm_t_inum qq; | |
1208 | if (SCM_LIKELY (yy > 0)) | |
1209 | { | |
1210 | if (SCM_UNLIKELY (xx < 0)) | |
1211 | xx1 = xx - yy + 1; | |
1212 | } | |
1213 | else if (SCM_UNLIKELY (yy == 0)) | |
1214 | scm_num_overflow (s_scm_floor_quotient); | |
1215 | else if (xx > 0) | |
1216 | xx1 = xx - yy - 1; | |
1217 | qq = xx1 / yy; | |
1218 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1219 | return SCM_I_MAKINUM (qq); | |
1220 | else | |
1221 | return scm_i_inum2big (qq); | |
1222 | } | |
1223 | else if (SCM_BIGP (y)) | |
1224 | { | |
1225 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1226 | scm_remember_upto_here_1 (y); | |
1227 | if (sign > 0) | |
1228 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1229 | else | |
1230 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1231 | } | |
1232 | else if (SCM_REALP (y)) | |
1233 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1234 | else if (SCM_FRACTIONP (y)) | |
1235 | return scm_i_exact_rational_floor_quotient (x, y); | |
1236 | else | |
fa075d40 AW |
1237 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1238 | s_scm_floor_quotient); | |
8f9da340 MW |
1239 | } |
1240 | else if (SCM_BIGP (x)) | |
1241 | { | |
1242 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1243 | { | |
1244 | scm_t_inum yy = SCM_I_INUM (y); | |
1245 | if (SCM_UNLIKELY (yy == 0)) | |
1246 | scm_num_overflow (s_scm_floor_quotient); | |
1247 | else if (SCM_UNLIKELY (yy == 1)) | |
1248 | return x; | |
1249 | else | |
1250 | { | |
1251 | SCM q = scm_i_mkbig (); | |
1252 | if (yy > 0) | |
1253 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1254 | else | |
1255 | { | |
1256 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1257 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1258 | } | |
1259 | scm_remember_upto_here_1 (x); | |
1260 | return scm_i_normbig (q); | |
1261 | } | |
1262 | } | |
1263 | else if (SCM_BIGP (y)) | |
1264 | { | |
1265 | SCM q = scm_i_mkbig (); | |
1266 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1267 | SCM_I_BIG_MPZ (x), | |
1268 | SCM_I_BIG_MPZ (y)); | |
1269 | scm_remember_upto_here_2 (x, y); | |
1270 | return scm_i_normbig (q); | |
1271 | } | |
1272 | else if (SCM_REALP (y)) | |
1273 | return scm_i_inexact_floor_quotient | |
1274 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1275 | else if (SCM_FRACTIONP (y)) | |
1276 | return scm_i_exact_rational_floor_quotient (x, y); | |
1277 | else | |
fa075d40 AW |
1278 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1279 | s_scm_floor_quotient); | |
8f9da340 MW |
1280 | } |
1281 | else if (SCM_REALP (x)) | |
1282 | { | |
1283 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1284 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1285 | return scm_i_inexact_floor_quotient | |
1286 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1287 | else | |
fa075d40 AW |
1288 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1289 | s_scm_floor_quotient); | |
8f9da340 MW |
1290 | } |
1291 | else if (SCM_FRACTIONP (x)) | |
1292 | { | |
1293 | if (SCM_REALP (y)) | |
1294 | return scm_i_inexact_floor_quotient | |
1295 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1296 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1297 | return scm_i_exact_rational_floor_quotient (x, y); | |
1298 | else | |
fa075d40 AW |
1299 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1300 | s_scm_floor_quotient); | |
8f9da340 MW |
1301 | } |
1302 | else | |
fa075d40 AW |
1303 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG1, |
1304 | s_scm_floor_quotient); | |
8f9da340 MW |
1305 | } |
1306 | #undef FUNC_NAME | |
1307 | ||
1308 | static SCM | |
1309 | scm_i_inexact_floor_quotient (double x, double y) | |
1310 | { | |
1311 | if (SCM_UNLIKELY (y == 0)) | |
1312 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1313 | else | |
1314 | return scm_from_double (floor (x / y)); | |
1315 | } | |
1316 | ||
1317 | static SCM | |
1318 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1319 | { | |
1320 | return scm_floor_quotient | |
1321 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1322 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1323 | } | |
1324 | ||
1325 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1326 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1327 | ||
1328 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1329 | (SCM x, SCM y), | |
1330 | "Return the real number @var{r} such that\n" | |
1331 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1332 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1333 | "@lisp\n" | |
1334 | "(floor-remainder 123 10) @result{} 3\n" | |
1335 | "(floor-remainder 123 -10) @result{} -7\n" | |
1336 | "(floor-remainder -123 10) @result{} 7\n" | |
1337 | "(floor-remainder -123 -10) @result{} -3\n" | |
1338 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1339 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1340 | "@end lisp") | |
1341 | #define FUNC_NAME s_scm_floor_remainder | |
1342 | { | |
1343 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1344 | { | |
1345 | scm_t_inum xx = SCM_I_INUM (x); | |
1346 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1347 | { | |
1348 | scm_t_inum yy = SCM_I_INUM (y); | |
1349 | if (SCM_UNLIKELY (yy == 0)) | |
1350 | scm_num_overflow (s_scm_floor_remainder); | |
1351 | else | |
1352 | { | |
1353 | scm_t_inum rr = xx % yy; | |
1354 | int needs_adjustment; | |
1355 | ||
1356 | if (SCM_LIKELY (yy > 0)) | |
1357 | needs_adjustment = (rr < 0); | |
1358 | else | |
1359 | needs_adjustment = (rr > 0); | |
1360 | ||
1361 | if (needs_adjustment) | |
1362 | rr += yy; | |
1363 | return SCM_I_MAKINUM (rr); | |
1364 | } | |
1365 | } | |
1366 | else if (SCM_BIGP (y)) | |
1367 | { | |
1368 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1369 | scm_remember_upto_here_1 (y); | |
1370 | if (sign > 0) | |
1371 | { | |
1372 | if (xx < 0) | |
1373 | { | |
1374 | SCM r = scm_i_mkbig (); | |
1375 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1376 | scm_remember_upto_here_1 (y); | |
1377 | return scm_i_normbig (r); | |
1378 | } | |
1379 | else | |
1380 | return x; | |
1381 | } | |
1382 | else if (xx <= 0) | |
1383 | return x; | |
1384 | else | |
1385 | { | |
1386 | SCM r = scm_i_mkbig (); | |
1387 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1388 | scm_remember_upto_here_1 (y); | |
1389 | return scm_i_normbig (r); | |
1390 | } | |
1391 | } | |
1392 | else if (SCM_REALP (y)) | |
1393 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1394 | else if (SCM_FRACTIONP (y)) | |
1395 | return scm_i_exact_rational_floor_remainder (x, y); | |
1396 | else | |
fa075d40 AW |
1397 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1398 | s_scm_floor_remainder); | |
8f9da340 MW |
1399 | } |
1400 | else if (SCM_BIGP (x)) | |
1401 | { | |
1402 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1403 | { | |
1404 | scm_t_inum yy = SCM_I_INUM (y); | |
1405 | if (SCM_UNLIKELY (yy == 0)) | |
1406 | scm_num_overflow (s_scm_floor_remainder); | |
1407 | else | |
1408 | { | |
1409 | scm_t_inum rr; | |
1410 | if (yy > 0) | |
1411 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1412 | else | |
1413 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1414 | scm_remember_upto_here_1 (x); | |
1415 | return SCM_I_MAKINUM (rr); | |
1416 | } | |
1417 | } | |
1418 | else if (SCM_BIGP (y)) | |
1419 | { | |
1420 | SCM r = scm_i_mkbig (); | |
1421 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1422 | SCM_I_BIG_MPZ (x), | |
1423 | SCM_I_BIG_MPZ (y)); | |
1424 | scm_remember_upto_here_2 (x, y); | |
1425 | return scm_i_normbig (r); | |
1426 | } | |
1427 | else if (SCM_REALP (y)) | |
1428 | return scm_i_inexact_floor_remainder | |
1429 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1430 | else if (SCM_FRACTIONP (y)) | |
1431 | return scm_i_exact_rational_floor_remainder (x, y); | |
1432 | else | |
fa075d40 AW |
1433 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1434 | s_scm_floor_remainder); | |
8f9da340 MW |
1435 | } |
1436 | else if (SCM_REALP (x)) | |
1437 | { | |
1438 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1439 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1440 | return scm_i_inexact_floor_remainder | |
1441 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1442 | else | |
fa075d40 AW |
1443 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1444 | s_scm_floor_remainder); | |
8f9da340 MW |
1445 | } |
1446 | else if (SCM_FRACTIONP (x)) | |
1447 | { | |
1448 | if (SCM_REALP (y)) | |
1449 | return scm_i_inexact_floor_remainder | |
1450 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1451 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1452 | return scm_i_exact_rational_floor_remainder (x, y); | |
1453 | else | |
fa075d40 AW |
1454 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1455 | s_scm_floor_remainder); | |
8f9da340 MW |
1456 | } |
1457 | else | |
fa075d40 AW |
1458 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG1, |
1459 | s_scm_floor_remainder); | |
8f9da340 MW |
1460 | } |
1461 | #undef FUNC_NAME | |
1462 | ||
1463 | static SCM | |
1464 | scm_i_inexact_floor_remainder (double x, double y) | |
1465 | { | |
1466 | /* Although it would be more efficient to use fmod here, we can't | |
1467 | because it would in some cases produce results inconsistent with | |
1468 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1469 | close). In particular, when x is very close to a multiple of y, | |
1470 | then r might be either 0.0 or y, but those two cases must | |
1471 | correspond to different choices of q. If r = 0.0 then q must be | |
1472 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1473 | and remainder chooses the other, it would be bad. */ | |
1474 | if (SCM_UNLIKELY (y == 0)) | |
1475 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1476 | else | |
1477 | return scm_from_double (x - y * floor (x / y)); | |
1478 | } | |
1479 | ||
1480 | static SCM | |
1481 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1482 | { | |
1483 | SCM xd = scm_denominator (x); | |
1484 | SCM yd = scm_denominator (y); | |
1485 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1486 | scm_product (scm_numerator (y), xd)); | |
1487 | return scm_divide (r1, scm_product (xd, yd)); | |
1488 | } | |
1489 | ||
1490 | ||
1491 | static void scm_i_inexact_floor_divide (double x, double y, | |
1492 | SCM *qp, SCM *rp); | |
1493 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1494 | SCM *qp, SCM *rp); | |
1495 | ||
1496 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1497 | (SCM x, SCM y), | |
1498 | "Return the integer @var{q} and the real number @var{r}\n" | |
1499 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1500 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1501 | "@lisp\n" | |
1502 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1503 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1504 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1505 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1506 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1507 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1508 | "@end lisp") | |
1509 | #define FUNC_NAME s_scm_i_floor_divide | |
1510 | { | |
1511 | SCM q, r; | |
1512 | ||
1513 | scm_floor_divide(x, y, &q, &r); | |
1514 | return scm_values (scm_list_2 (q, r)); | |
1515 | } | |
1516 | #undef FUNC_NAME | |
1517 | ||
1518 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1519 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1520 | ||
1521 | void | |
1522 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1523 | { | |
1524 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1525 | { | |
1526 | scm_t_inum xx = SCM_I_INUM (x); | |
1527 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1528 | { | |
1529 | scm_t_inum yy = SCM_I_INUM (y); | |
1530 | if (SCM_UNLIKELY (yy == 0)) | |
1531 | scm_num_overflow (s_scm_floor_divide); | |
1532 | else | |
1533 | { | |
1534 | scm_t_inum qq = xx / yy; | |
1535 | scm_t_inum rr = xx % yy; | |
1536 | int needs_adjustment; | |
1537 | ||
1538 | if (SCM_LIKELY (yy > 0)) | |
1539 | needs_adjustment = (rr < 0); | |
1540 | else | |
1541 | needs_adjustment = (rr > 0); | |
1542 | ||
1543 | if (needs_adjustment) | |
1544 | { | |
1545 | rr += yy; | |
1546 | qq--; | |
1547 | } | |
1548 | ||
1549 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1550 | *qp = SCM_I_MAKINUM (qq); | |
1551 | else | |
1552 | *qp = scm_i_inum2big (qq); | |
1553 | *rp = SCM_I_MAKINUM (rr); | |
1554 | } | |
1555 | return; | |
1556 | } | |
1557 | else if (SCM_BIGP (y)) | |
1558 | { | |
1559 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1560 | scm_remember_upto_here_1 (y); | |
1561 | if (sign > 0) | |
1562 | { | |
1563 | if (xx < 0) | |
1564 | { | |
1565 | SCM r = scm_i_mkbig (); | |
1566 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1567 | scm_remember_upto_here_1 (y); | |
1568 | *qp = SCM_I_MAKINUM (-1); | |
1569 | *rp = scm_i_normbig (r); | |
1570 | } | |
1571 | else | |
1572 | { | |
1573 | *qp = SCM_INUM0; | |
1574 | *rp = x; | |
1575 | } | |
1576 | } | |
1577 | else if (xx <= 0) | |
1578 | { | |
1579 | *qp = SCM_INUM0; | |
1580 | *rp = x; | |
1581 | } | |
1582 | else | |
1583 | { | |
1584 | SCM r = scm_i_mkbig (); | |
1585 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1586 | scm_remember_upto_here_1 (y); | |
1587 | *qp = SCM_I_MAKINUM (-1); | |
1588 | *rp = scm_i_normbig (r); | |
1589 | } | |
1590 | return; | |
1591 | } | |
1592 | else if (SCM_REALP (y)) | |
1593 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1594 | else if (SCM_FRACTIONP (y)) | |
1595 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1596 | else | |
1597 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1598 | s_scm_floor_divide, qp, rp); | |
1599 | } | |
1600 | else if (SCM_BIGP (x)) | |
1601 | { | |
1602 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1603 | { | |
1604 | scm_t_inum yy = SCM_I_INUM (y); | |
1605 | if (SCM_UNLIKELY (yy == 0)) | |
1606 | scm_num_overflow (s_scm_floor_divide); | |
1607 | else | |
1608 | { | |
1609 | SCM q = scm_i_mkbig (); | |
1610 | SCM r = scm_i_mkbig (); | |
1611 | if (yy > 0) | |
1612 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1613 | SCM_I_BIG_MPZ (x), yy); | |
1614 | else | |
1615 | { | |
1616 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1617 | SCM_I_BIG_MPZ (x), -yy); | |
1618 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1619 | } | |
1620 | scm_remember_upto_here_1 (x); | |
1621 | *qp = scm_i_normbig (q); | |
1622 | *rp = scm_i_normbig (r); | |
1623 | } | |
1624 | return; | |
1625 | } | |
1626 | else if (SCM_BIGP (y)) | |
1627 | { | |
1628 | SCM q = scm_i_mkbig (); | |
1629 | SCM r = scm_i_mkbig (); | |
1630 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1631 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1632 | scm_remember_upto_here_2 (x, y); | |
1633 | *qp = scm_i_normbig (q); | |
1634 | *rp = scm_i_normbig (r); | |
1635 | return; | |
1636 | } | |
1637 | else if (SCM_REALP (y)) | |
1638 | return scm_i_inexact_floor_divide | |
1639 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1640 | else if (SCM_FRACTIONP (y)) | |
1641 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1642 | else | |
1643 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1644 | s_scm_floor_divide, qp, rp); | |
1645 | } | |
1646 | else if (SCM_REALP (x)) | |
1647 | { | |
1648 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1649 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1650 | return scm_i_inexact_floor_divide | |
1651 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1652 | else | |
1653 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1654 | s_scm_floor_divide, qp, rp); | |
1655 | } | |
1656 | else if (SCM_FRACTIONP (x)) | |
1657 | { | |
1658 | if (SCM_REALP (y)) | |
1659 | return scm_i_inexact_floor_divide | |
1660 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1661 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1662 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1663 | else | |
1664 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1665 | s_scm_floor_divide, qp, rp); | |
1666 | } | |
1667 | else | |
1668 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1669 | s_scm_floor_divide, qp, rp); | |
1670 | } | |
1671 | ||
1672 | static void | |
1673 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1674 | { | |
1675 | if (SCM_UNLIKELY (y == 0)) | |
1676 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1677 | else | |
1678 | { | |
1679 | double q = floor (x / y); | |
1680 | double r = x - q * y; | |
1681 | *qp = scm_from_double (q); | |
1682 | *rp = scm_from_double (r); | |
1683 | } | |
1684 | } | |
1685 | ||
1686 | static void | |
1687 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1688 | { | |
1689 | SCM r1; | |
1690 | SCM xd = scm_denominator (x); | |
1691 | SCM yd = scm_denominator (y); | |
1692 | ||
1693 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1694 | scm_product (scm_numerator (y), xd), | |
1695 | qp, &r1); | |
1696 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1697 | } | |
1698 | ||
1699 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1700 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1701 | ||
1702 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1703 | (SCM x, SCM y), | |
1704 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1705 | "@lisp\n" | |
1706 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1707 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1708 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1709 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1710 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1711 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1712 | "@end lisp") | |
1713 | #define FUNC_NAME s_scm_ceiling_quotient | |
1714 | { | |
1715 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1716 | { | |
1717 | scm_t_inum xx = SCM_I_INUM (x); | |
1718 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1719 | { | |
1720 | scm_t_inum yy = SCM_I_INUM (y); | |
1721 | if (SCM_UNLIKELY (yy == 0)) | |
1722 | scm_num_overflow (s_scm_ceiling_quotient); | |
1723 | else | |
1724 | { | |
1725 | scm_t_inum xx1 = xx; | |
1726 | scm_t_inum qq; | |
1727 | if (SCM_LIKELY (yy > 0)) | |
1728 | { | |
1729 | if (SCM_LIKELY (xx >= 0)) | |
1730 | xx1 = xx + yy - 1; | |
1731 | } | |
8f9da340 MW |
1732 | else if (xx < 0) |
1733 | xx1 = xx + yy + 1; | |
1734 | qq = xx1 / yy; | |
1735 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1736 | return SCM_I_MAKINUM (qq); | |
1737 | else | |
1738 | return scm_i_inum2big (qq); | |
1739 | } | |
1740 | } | |
1741 | else if (SCM_BIGP (y)) | |
1742 | { | |
1743 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1744 | scm_remember_upto_here_1 (y); | |
1745 | if (SCM_LIKELY (sign > 0)) | |
1746 | { | |
1747 | if (SCM_LIKELY (xx > 0)) | |
1748 | return SCM_INUM1; | |
1749 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1750 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1751 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1752 | { | |
1753 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1754 | scm_remember_upto_here_1 (y); | |
1755 | return SCM_I_MAKINUM (-1); | |
1756 | } | |
1757 | else | |
1758 | return SCM_INUM0; | |
1759 | } | |
1760 | else if (xx >= 0) | |
1761 | return SCM_INUM0; | |
1762 | else | |
1763 | return SCM_INUM1; | |
1764 | } | |
1765 | else if (SCM_REALP (y)) | |
1766 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1767 | else if (SCM_FRACTIONP (y)) | |
1768 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1769 | else | |
fa075d40 AW |
1770 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1771 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1772 | } |
1773 | else if (SCM_BIGP (x)) | |
1774 | { | |
1775 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1776 | { | |
1777 | scm_t_inum yy = SCM_I_INUM (y); | |
1778 | if (SCM_UNLIKELY (yy == 0)) | |
1779 | scm_num_overflow (s_scm_ceiling_quotient); | |
1780 | else if (SCM_UNLIKELY (yy == 1)) | |
1781 | return x; | |
1782 | else | |
1783 | { | |
1784 | SCM q = scm_i_mkbig (); | |
1785 | if (yy > 0) | |
1786 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1787 | else | |
1788 | { | |
1789 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1790 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1791 | } | |
1792 | scm_remember_upto_here_1 (x); | |
1793 | return scm_i_normbig (q); | |
1794 | } | |
1795 | } | |
1796 | else if (SCM_BIGP (y)) | |
1797 | { | |
1798 | SCM q = scm_i_mkbig (); | |
1799 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1800 | SCM_I_BIG_MPZ (x), | |
1801 | SCM_I_BIG_MPZ (y)); | |
1802 | scm_remember_upto_here_2 (x, y); | |
1803 | return scm_i_normbig (q); | |
1804 | } | |
1805 | else if (SCM_REALP (y)) | |
1806 | return scm_i_inexact_ceiling_quotient | |
1807 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1808 | else if (SCM_FRACTIONP (y)) | |
1809 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1810 | else | |
fa075d40 AW |
1811 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1812 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1813 | } |
1814 | else if (SCM_REALP (x)) | |
1815 | { | |
1816 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1817 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1818 | return scm_i_inexact_ceiling_quotient | |
1819 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1820 | else | |
fa075d40 AW |
1821 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1822 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1823 | } |
1824 | else if (SCM_FRACTIONP (x)) | |
1825 | { | |
1826 | if (SCM_REALP (y)) | |
1827 | return scm_i_inexact_ceiling_quotient | |
1828 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1829 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1830 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1831 | else | |
fa075d40 AW |
1832 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1833 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1834 | } |
1835 | else | |
fa075d40 AW |
1836 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, |
1837 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1838 | } |
1839 | #undef FUNC_NAME | |
1840 | ||
1841 | static SCM | |
1842 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1843 | { | |
1844 | if (SCM_UNLIKELY (y == 0)) | |
1845 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1846 | else | |
1847 | return scm_from_double (ceil (x / y)); | |
1848 | } | |
1849 | ||
1850 | static SCM | |
1851 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1852 | { | |
1853 | return scm_ceiling_quotient | |
1854 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1855 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1856 | } | |
1857 | ||
1858 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1859 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1860 | ||
1861 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1862 | (SCM x, SCM y), | |
1863 | "Return the real number @var{r} such that\n" | |
1864 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1865 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1866 | "@lisp\n" | |
1867 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1868 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1869 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1870 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1871 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1872 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1873 | "@end lisp") | |
1874 | #define FUNC_NAME s_scm_ceiling_remainder | |
1875 | { | |
1876 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1877 | { | |
1878 | scm_t_inum xx = SCM_I_INUM (x); | |
1879 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1880 | { | |
1881 | scm_t_inum yy = SCM_I_INUM (y); | |
1882 | if (SCM_UNLIKELY (yy == 0)) | |
1883 | scm_num_overflow (s_scm_ceiling_remainder); | |
1884 | else | |
1885 | { | |
1886 | scm_t_inum rr = xx % yy; | |
1887 | int needs_adjustment; | |
1888 | ||
1889 | if (SCM_LIKELY (yy > 0)) | |
1890 | needs_adjustment = (rr > 0); | |
1891 | else | |
1892 | needs_adjustment = (rr < 0); | |
1893 | ||
1894 | if (needs_adjustment) | |
1895 | rr -= yy; | |
1896 | return SCM_I_MAKINUM (rr); | |
1897 | } | |
1898 | } | |
1899 | else if (SCM_BIGP (y)) | |
1900 | { | |
1901 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1902 | scm_remember_upto_here_1 (y); | |
1903 | if (SCM_LIKELY (sign > 0)) | |
1904 | { | |
1905 | if (SCM_LIKELY (xx > 0)) | |
1906 | { | |
1907 | SCM r = scm_i_mkbig (); | |
1908 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1909 | scm_remember_upto_here_1 (y); | |
1910 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1911 | return scm_i_normbig (r); | |
1912 | } | |
1913 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1914 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1915 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1916 | { | |
1917 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1918 | scm_remember_upto_here_1 (y); | |
1919 | return SCM_INUM0; | |
1920 | } | |
1921 | else | |
1922 | return x; | |
1923 | } | |
1924 | else if (xx >= 0) | |
1925 | return x; | |
1926 | else | |
1927 | { | |
1928 | SCM r = scm_i_mkbig (); | |
1929 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1930 | scm_remember_upto_here_1 (y); | |
1931 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1932 | return scm_i_normbig (r); | |
1933 | } | |
1934 | } | |
1935 | else if (SCM_REALP (y)) | |
1936 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1937 | else if (SCM_FRACTIONP (y)) | |
1938 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1939 | else | |
fa075d40 AW |
1940 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1941 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1942 | } |
1943 | else if (SCM_BIGP (x)) | |
1944 | { | |
1945 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1946 | { | |
1947 | scm_t_inum yy = SCM_I_INUM (y); | |
1948 | if (SCM_UNLIKELY (yy == 0)) | |
1949 | scm_num_overflow (s_scm_ceiling_remainder); | |
1950 | else | |
1951 | { | |
1952 | scm_t_inum rr; | |
1953 | if (yy > 0) | |
1954 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1955 | else | |
1956 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1957 | scm_remember_upto_here_1 (x); | |
1958 | return SCM_I_MAKINUM (rr); | |
1959 | } | |
1960 | } | |
1961 | else if (SCM_BIGP (y)) | |
1962 | { | |
1963 | SCM r = scm_i_mkbig (); | |
1964 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1965 | SCM_I_BIG_MPZ (x), | |
1966 | SCM_I_BIG_MPZ (y)); | |
1967 | scm_remember_upto_here_2 (x, y); | |
1968 | return scm_i_normbig (r); | |
1969 | } | |
1970 | else if (SCM_REALP (y)) | |
1971 | return scm_i_inexact_ceiling_remainder | |
1972 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1973 | else if (SCM_FRACTIONP (y)) | |
1974 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1975 | else | |
fa075d40 AW |
1976 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1977 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1978 | } |
1979 | else if (SCM_REALP (x)) | |
1980 | { | |
1981 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1982 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1983 | return scm_i_inexact_ceiling_remainder | |
1984 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1985 | else | |
fa075d40 AW |
1986 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1987 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1988 | } |
1989 | else if (SCM_FRACTIONP (x)) | |
1990 | { | |
1991 | if (SCM_REALP (y)) | |
1992 | return scm_i_inexact_ceiling_remainder | |
1993 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1994 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1995 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1996 | else | |
fa075d40 AW |
1997 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1998 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1999 | } |
2000 | else | |
fa075d40 AW |
2001 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, |
2002 | s_scm_ceiling_remainder); | |
8f9da340 MW |
2003 | } |
2004 | #undef FUNC_NAME | |
2005 | ||
2006 | static SCM | |
2007 | scm_i_inexact_ceiling_remainder (double x, double y) | |
2008 | { | |
2009 | /* Although it would be more efficient to use fmod here, we can't | |
2010 | because it would in some cases produce results inconsistent with | |
2011 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
2012 | close). In particular, when x is very close to a multiple of y, | |
2013 | then r might be either 0.0 or -y, but those two cases must | |
2014 | correspond to different choices of q. If r = 0.0 then q must be | |
2015 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
2016 | and remainder chooses the other, it would be bad. */ | |
2017 | if (SCM_UNLIKELY (y == 0)) | |
2018 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
2019 | else | |
2020 | return scm_from_double (x - y * ceil (x / y)); | |
2021 | } | |
2022 | ||
2023 | static SCM | |
2024 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
2025 | { | |
2026 | SCM xd = scm_denominator (x); | |
2027 | SCM yd = scm_denominator (y); | |
2028 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
2029 | scm_product (scm_numerator (y), xd)); | |
2030 | return scm_divide (r1, scm_product (xd, yd)); | |
2031 | } | |
2032 | ||
2033 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
2034 | SCM *qp, SCM *rp); | |
2035 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
2036 | SCM *qp, SCM *rp); | |
2037 | ||
2038 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
2039 | (SCM x, SCM y), | |
2040 | "Return the integer @var{q} and the real number @var{r}\n" | |
2041 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2042 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
2043 | "@lisp\n" | |
2044 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
2045 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
2046 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
2047 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
2048 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2049 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2050 | "@end lisp") | |
2051 | #define FUNC_NAME s_scm_i_ceiling_divide | |
2052 | { | |
2053 | SCM q, r; | |
2054 | ||
2055 | scm_ceiling_divide(x, y, &q, &r); | |
2056 | return scm_values (scm_list_2 (q, r)); | |
2057 | } | |
2058 | #undef FUNC_NAME | |
2059 | ||
2060 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
2061 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
2062 | ||
2063 | void | |
2064 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2065 | { | |
2066 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2067 | { | |
2068 | scm_t_inum xx = SCM_I_INUM (x); | |
2069 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2070 | { | |
2071 | scm_t_inum yy = SCM_I_INUM (y); | |
2072 | if (SCM_UNLIKELY (yy == 0)) | |
2073 | scm_num_overflow (s_scm_ceiling_divide); | |
2074 | else | |
2075 | { | |
2076 | scm_t_inum qq = xx / yy; | |
2077 | scm_t_inum rr = xx % yy; | |
2078 | int needs_adjustment; | |
2079 | ||
2080 | if (SCM_LIKELY (yy > 0)) | |
2081 | needs_adjustment = (rr > 0); | |
2082 | else | |
2083 | needs_adjustment = (rr < 0); | |
2084 | ||
2085 | if (needs_adjustment) | |
2086 | { | |
2087 | rr -= yy; | |
2088 | qq++; | |
2089 | } | |
2090 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2091 | *qp = SCM_I_MAKINUM (qq); | |
2092 | else | |
2093 | *qp = scm_i_inum2big (qq); | |
2094 | *rp = SCM_I_MAKINUM (rr); | |
2095 | } | |
2096 | return; | |
2097 | } | |
2098 | else if (SCM_BIGP (y)) | |
2099 | { | |
2100 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2101 | scm_remember_upto_here_1 (y); | |
2102 | if (SCM_LIKELY (sign > 0)) | |
2103 | { | |
2104 | if (SCM_LIKELY (xx > 0)) | |
2105 | { | |
2106 | SCM r = scm_i_mkbig (); | |
2107 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2108 | scm_remember_upto_here_1 (y); | |
2109 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2110 | *qp = SCM_INUM1; | |
2111 | *rp = scm_i_normbig (r); | |
2112 | } | |
2113 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2114 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2115 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2116 | { | |
2117 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2118 | scm_remember_upto_here_1 (y); | |
2119 | *qp = SCM_I_MAKINUM (-1); | |
2120 | *rp = SCM_INUM0; | |
2121 | } | |
2122 | else | |
2123 | { | |
2124 | *qp = SCM_INUM0; | |
2125 | *rp = x; | |
2126 | } | |
2127 | } | |
2128 | else if (xx >= 0) | |
2129 | { | |
2130 | *qp = SCM_INUM0; | |
2131 | *rp = x; | |
2132 | } | |
2133 | else | |
2134 | { | |
2135 | SCM r = scm_i_mkbig (); | |
2136 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2137 | scm_remember_upto_here_1 (y); | |
2138 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2139 | *qp = SCM_INUM1; | |
2140 | *rp = scm_i_normbig (r); | |
2141 | } | |
2142 | return; | |
2143 | } | |
2144 | else if (SCM_REALP (y)) | |
2145 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2146 | else if (SCM_FRACTIONP (y)) | |
2147 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2148 | else | |
2149 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2150 | s_scm_ceiling_divide, qp, rp); | |
2151 | } | |
2152 | else if (SCM_BIGP (x)) | |
2153 | { | |
2154 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2155 | { | |
2156 | scm_t_inum yy = SCM_I_INUM (y); | |
2157 | if (SCM_UNLIKELY (yy == 0)) | |
2158 | scm_num_overflow (s_scm_ceiling_divide); | |
2159 | else | |
2160 | { | |
2161 | SCM q = scm_i_mkbig (); | |
2162 | SCM r = scm_i_mkbig (); | |
2163 | if (yy > 0) | |
2164 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2165 | SCM_I_BIG_MPZ (x), yy); | |
2166 | else | |
2167 | { | |
2168 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2169 | SCM_I_BIG_MPZ (x), -yy); | |
2170 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2171 | } | |
2172 | scm_remember_upto_here_1 (x); | |
2173 | *qp = scm_i_normbig (q); | |
2174 | *rp = scm_i_normbig (r); | |
2175 | } | |
2176 | return; | |
2177 | } | |
2178 | else if (SCM_BIGP (y)) | |
2179 | { | |
2180 | SCM q = scm_i_mkbig (); | |
2181 | SCM r = scm_i_mkbig (); | |
2182 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2183 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2184 | scm_remember_upto_here_2 (x, y); | |
2185 | *qp = scm_i_normbig (q); | |
2186 | *rp = scm_i_normbig (r); | |
2187 | return; | |
2188 | } | |
2189 | else if (SCM_REALP (y)) | |
2190 | return scm_i_inexact_ceiling_divide | |
2191 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2192 | else if (SCM_FRACTIONP (y)) | |
2193 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2194 | else | |
2195 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2196 | s_scm_ceiling_divide, qp, rp); | |
2197 | } | |
2198 | else if (SCM_REALP (x)) | |
2199 | { | |
2200 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2201 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2202 | return scm_i_inexact_ceiling_divide | |
2203 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2204 | else | |
2205 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2206 | s_scm_ceiling_divide, qp, rp); | |
2207 | } | |
2208 | else if (SCM_FRACTIONP (x)) | |
2209 | { | |
2210 | if (SCM_REALP (y)) | |
2211 | return scm_i_inexact_ceiling_divide | |
2212 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2213 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2214 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2215 | else | |
2216 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2217 | s_scm_ceiling_divide, qp, rp); | |
2218 | } | |
2219 | else | |
2220 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2221 | s_scm_ceiling_divide, qp, rp); | |
2222 | } | |
2223 | ||
2224 | static void | |
2225 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2226 | { | |
2227 | if (SCM_UNLIKELY (y == 0)) | |
2228 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2229 | else | |
2230 | { | |
2231 | double q = ceil (x / y); | |
2232 | double r = x - q * y; | |
2233 | *qp = scm_from_double (q); | |
2234 | *rp = scm_from_double (r); | |
2235 | } | |
2236 | } | |
2237 | ||
2238 | static void | |
2239 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2240 | { | |
2241 | SCM r1; | |
2242 | SCM xd = scm_denominator (x); | |
2243 | SCM yd = scm_denominator (y); | |
2244 | ||
2245 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2246 | scm_product (scm_numerator (y), xd), | |
2247 | qp, &r1); | |
2248 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2249 | } | |
2250 | ||
2251 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2252 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2253 | ||
2254 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2255 | (SCM x, SCM y), | |
2256 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2257 | "@lisp\n" | |
2258 | "(truncate-quotient 123 10) @result{} 12\n" | |
2259 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2260 | "(truncate-quotient -123 10) @result{} -12\n" | |
2261 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2262 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2263 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2264 | "@end lisp") | |
2265 | #define FUNC_NAME s_scm_truncate_quotient | |
2266 | { | |
2267 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2268 | { | |
2269 | scm_t_inum xx = SCM_I_INUM (x); | |
2270 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2271 | { | |
2272 | scm_t_inum yy = SCM_I_INUM (y); | |
2273 | if (SCM_UNLIKELY (yy == 0)) | |
2274 | scm_num_overflow (s_scm_truncate_quotient); | |
2275 | else | |
2276 | { | |
2277 | scm_t_inum qq = xx / yy; | |
2278 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2279 | return SCM_I_MAKINUM (qq); | |
2280 | else | |
2281 | return scm_i_inum2big (qq); | |
2282 | } | |
2283 | } | |
2284 | else if (SCM_BIGP (y)) | |
2285 | { | |
2286 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2287 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2288 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2289 | { | |
2290 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2291 | scm_remember_upto_here_1 (y); | |
2292 | return SCM_I_MAKINUM (-1); | |
2293 | } | |
2294 | else | |
2295 | return SCM_INUM0; | |
2296 | } | |
2297 | else if (SCM_REALP (y)) | |
2298 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2299 | else if (SCM_FRACTIONP (y)) | |
2300 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2301 | else | |
fa075d40 AW |
2302 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2303 | s_scm_truncate_quotient); | |
8f9da340 MW |
2304 | } |
2305 | else if (SCM_BIGP (x)) | |
2306 | { | |
2307 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2308 | { | |
2309 | scm_t_inum yy = SCM_I_INUM (y); | |
2310 | if (SCM_UNLIKELY (yy == 0)) | |
2311 | scm_num_overflow (s_scm_truncate_quotient); | |
2312 | else if (SCM_UNLIKELY (yy == 1)) | |
2313 | return x; | |
2314 | else | |
2315 | { | |
2316 | SCM q = scm_i_mkbig (); | |
2317 | if (yy > 0) | |
2318 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2319 | else | |
2320 | { | |
2321 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2322 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2323 | } | |
2324 | scm_remember_upto_here_1 (x); | |
2325 | return scm_i_normbig (q); | |
2326 | } | |
2327 | } | |
2328 | else if (SCM_BIGP (y)) | |
2329 | { | |
2330 | SCM q = scm_i_mkbig (); | |
2331 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2332 | SCM_I_BIG_MPZ (x), | |
2333 | SCM_I_BIG_MPZ (y)); | |
2334 | scm_remember_upto_here_2 (x, y); | |
2335 | return scm_i_normbig (q); | |
2336 | } | |
2337 | else if (SCM_REALP (y)) | |
2338 | return scm_i_inexact_truncate_quotient | |
2339 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2340 | else if (SCM_FRACTIONP (y)) | |
2341 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2342 | else | |
fa075d40 AW |
2343 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2344 | s_scm_truncate_quotient); | |
8f9da340 MW |
2345 | } |
2346 | else if (SCM_REALP (x)) | |
2347 | { | |
2348 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2349 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2350 | return scm_i_inexact_truncate_quotient | |
2351 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2352 | else | |
fa075d40 AW |
2353 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2354 | s_scm_truncate_quotient); | |
8f9da340 MW |
2355 | } |
2356 | else if (SCM_FRACTIONP (x)) | |
2357 | { | |
2358 | if (SCM_REALP (y)) | |
2359 | return scm_i_inexact_truncate_quotient | |
2360 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2361 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2362 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2363 | else | |
fa075d40 AW |
2364 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2365 | s_scm_truncate_quotient); | |
8f9da340 MW |
2366 | } |
2367 | else | |
fa075d40 AW |
2368 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, |
2369 | s_scm_truncate_quotient); | |
8f9da340 MW |
2370 | } |
2371 | #undef FUNC_NAME | |
2372 | ||
2373 | static SCM | |
2374 | scm_i_inexact_truncate_quotient (double x, double y) | |
2375 | { | |
2376 | if (SCM_UNLIKELY (y == 0)) | |
2377 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2378 | else | |
c251ab63 | 2379 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2380 | } |
2381 | ||
2382 | static SCM | |
2383 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2384 | { | |
2385 | return scm_truncate_quotient | |
2386 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2387 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2388 | } | |
2389 | ||
2390 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2391 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2392 | ||
2393 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2394 | (SCM x, SCM y), | |
2395 | "Return the real number @var{r} such that\n" | |
2396 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2397 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2398 | "@lisp\n" | |
2399 | "(truncate-remainder 123 10) @result{} 3\n" | |
2400 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2401 | "(truncate-remainder -123 10) @result{} -3\n" | |
2402 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2403 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2404 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2405 | "@end lisp") | |
2406 | #define FUNC_NAME s_scm_truncate_remainder | |
2407 | { | |
2408 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2409 | { | |
2410 | scm_t_inum xx = SCM_I_INUM (x); | |
2411 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2412 | { | |
2413 | scm_t_inum yy = SCM_I_INUM (y); | |
2414 | if (SCM_UNLIKELY (yy == 0)) | |
2415 | scm_num_overflow (s_scm_truncate_remainder); | |
2416 | else | |
2417 | return SCM_I_MAKINUM (xx % yy); | |
2418 | } | |
2419 | else if (SCM_BIGP (y)) | |
2420 | { | |
2421 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2422 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2423 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2424 | { | |
2425 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2426 | scm_remember_upto_here_1 (y); | |
2427 | return SCM_INUM0; | |
2428 | } | |
2429 | else | |
2430 | return x; | |
2431 | } | |
2432 | else if (SCM_REALP (y)) | |
2433 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2434 | else if (SCM_FRACTIONP (y)) | |
2435 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2436 | else | |
fa075d40 AW |
2437 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2438 | s_scm_truncate_remainder); | |
8f9da340 MW |
2439 | } |
2440 | else if (SCM_BIGP (x)) | |
2441 | { | |
2442 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2443 | { | |
2444 | scm_t_inum yy = SCM_I_INUM (y); | |
2445 | if (SCM_UNLIKELY (yy == 0)) | |
2446 | scm_num_overflow (s_scm_truncate_remainder); | |
2447 | else | |
2448 | { | |
2449 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2450 | (yy > 0) ? yy : -yy) | |
2451 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2452 | scm_remember_upto_here_1 (x); | |
2453 | return SCM_I_MAKINUM (rr); | |
2454 | } | |
2455 | } | |
2456 | else if (SCM_BIGP (y)) | |
2457 | { | |
2458 | SCM r = scm_i_mkbig (); | |
2459 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2460 | SCM_I_BIG_MPZ (x), | |
2461 | SCM_I_BIG_MPZ (y)); | |
2462 | scm_remember_upto_here_2 (x, y); | |
2463 | return scm_i_normbig (r); | |
2464 | } | |
2465 | else if (SCM_REALP (y)) | |
2466 | return scm_i_inexact_truncate_remainder | |
2467 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2468 | else if (SCM_FRACTIONP (y)) | |
2469 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2470 | else | |
fa075d40 AW |
2471 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2472 | s_scm_truncate_remainder); | |
8f9da340 MW |
2473 | } |
2474 | else if (SCM_REALP (x)) | |
2475 | { | |
2476 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2477 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2478 | return scm_i_inexact_truncate_remainder | |
2479 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2480 | else | |
fa075d40 AW |
2481 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2482 | s_scm_truncate_remainder); | |
8f9da340 MW |
2483 | } |
2484 | else if (SCM_FRACTIONP (x)) | |
2485 | { | |
2486 | if (SCM_REALP (y)) | |
2487 | return scm_i_inexact_truncate_remainder | |
2488 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2489 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2490 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2491 | else | |
fa075d40 AW |
2492 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2493 | s_scm_truncate_remainder); | |
8f9da340 MW |
2494 | } |
2495 | else | |
fa075d40 AW |
2496 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, |
2497 | s_scm_truncate_remainder); | |
8f9da340 MW |
2498 | } |
2499 | #undef FUNC_NAME | |
2500 | ||
2501 | static SCM | |
2502 | scm_i_inexact_truncate_remainder (double x, double y) | |
2503 | { | |
2504 | /* Although it would be more efficient to use fmod here, we can't | |
2505 | because it would in some cases produce results inconsistent with | |
2506 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2507 | close). In particular, when x is very close to a multiple of y, | |
2508 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2509 | correspond to different choices of q. If quotient chooses one and | |
2510 | remainder chooses the other, it would be bad. */ | |
2511 | if (SCM_UNLIKELY (y == 0)) | |
2512 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2513 | else | |
c251ab63 | 2514 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2515 | } |
2516 | ||
2517 | static SCM | |
2518 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2519 | { | |
2520 | SCM xd = scm_denominator (x); | |
2521 | SCM yd = scm_denominator (y); | |
2522 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2523 | scm_product (scm_numerator (y), xd)); | |
2524 | return scm_divide (r1, scm_product (xd, yd)); | |
2525 | } | |
2526 | ||
2527 | ||
2528 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2529 | SCM *qp, SCM *rp); | |
2530 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2531 | SCM *qp, SCM *rp); | |
2532 | ||
2533 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2534 | (SCM x, SCM y), | |
2535 | "Return the integer @var{q} and the real number @var{r}\n" | |
2536 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2537 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2538 | "@lisp\n" | |
2539 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2540 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2541 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2542 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2543 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2544 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2545 | "@end lisp") | |
2546 | #define FUNC_NAME s_scm_i_truncate_divide | |
2547 | { | |
2548 | SCM q, r; | |
2549 | ||
2550 | scm_truncate_divide(x, y, &q, &r); | |
2551 | return scm_values (scm_list_2 (q, r)); | |
2552 | } | |
2553 | #undef FUNC_NAME | |
2554 | ||
2555 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2556 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2557 | ||
2558 | void | |
2559 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2560 | { | |
2561 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2562 | { | |
2563 | scm_t_inum xx = SCM_I_INUM (x); | |
2564 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2565 | { | |
2566 | scm_t_inum yy = SCM_I_INUM (y); | |
2567 | if (SCM_UNLIKELY (yy == 0)) | |
2568 | scm_num_overflow (s_scm_truncate_divide); | |
2569 | else | |
2570 | { | |
2571 | scm_t_inum qq = xx / yy; | |
2572 | scm_t_inum rr = xx % yy; | |
2573 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2574 | *qp = SCM_I_MAKINUM (qq); | |
2575 | else | |
2576 | *qp = scm_i_inum2big (qq); | |
2577 | *rp = SCM_I_MAKINUM (rr); | |
2578 | } | |
2579 | return; | |
2580 | } | |
2581 | else if (SCM_BIGP (y)) | |
2582 | { | |
2583 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2584 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2585 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2586 | { | |
2587 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2588 | scm_remember_upto_here_1 (y); | |
2589 | *qp = SCM_I_MAKINUM (-1); | |
2590 | *rp = SCM_INUM0; | |
2591 | } | |
2592 | else | |
2593 | { | |
2594 | *qp = SCM_INUM0; | |
2595 | *rp = x; | |
2596 | } | |
2597 | return; | |
2598 | } | |
2599 | else if (SCM_REALP (y)) | |
2600 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2601 | else if (SCM_FRACTIONP (y)) | |
2602 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2603 | else | |
2604 | return two_valued_wta_dispatch_2 | |
2605 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2606 | s_scm_truncate_divide, qp, rp); | |
2607 | } | |
2608 | else if (SCM_BIGP (x)) | |
2609 | { | |
2610 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2611 | { | |
2612 | scm_t_inum yy = SCM_I_INUM (y); | |
2613 | if (SCM_UNLIKELY (yy == 0)) | |
2614 | scm_num_overflow (s_scm_truncate_divide); | |
2615 | else | |
2616 | { | |
2617 | SCM q = scm_i_mkbig (); | |
2618 | scm_t_inum rr; | |
2619 | if (yy > 0) | |
2620 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2621 | SCM_I_BIG_MPZ (x), yy); | |
2622 | else | |
2623 | { | |
2624 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2625 | SCM_I_BIG_MPZ (x), -yy); | |
2626 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2627 | } | |
2628 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2629 | scm_remember_upto_here_1 (x); | |
2630 | *qp = scm_i_normbig (q); | |
2631 | *rp = SCM_I_MAKINUM (rr); | |
2632 | } | |
2633 | return; | |
2634 | } | |
2635 | else if (SCM_BIGP (y)) | |
2636 | { | |
2637 | SCM q = scm_i_mkbig (); | |
2638 | SCM r = scm_i_mkbig (); | |
2639 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2640 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2641 | scm_remember_upto_here_2 (x, y); | |
2642 | *qp = scm_i_normbig (q); | |
2643 | *rp = scm_i_normbig (r); | |
2644 | } | |
2645 | else if (SCM_REALP (y)) | |
2646 | return scm_i_inexact_truncate_divide | |
2647 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2648 | else if (SCM_FRACTIONP (y)) | |
2649 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2650 | else | |
2651 | return two_valued_wta_dispatch_2 | |
2652 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2653 | s_scm_truncate_divide, qp, rp); | |
2654 | } | |
2655 | else if (SCM_REALP (x)) | |
2656 | { | |
2657 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2658 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2659 | return scm_i_inexact_truncate_divide | |
2660 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2661 | else | |
2662 | return two_valued_wta_dispatch_2 | |
2663 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2664 | s_scm_truncate_divide, qp, rp); | |
2665 | } | |
2666 | else if (SCM_FRACTIONP (x)) | |
2667 | { | |
2668 | if (SCM_REALP (y)) | |
2669 | return scm_i_inexact_truncate_divide | |
2670 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2671 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2672 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2673 | else | |
2674 | return two_valued_wta_dispatch_2 | |
2675 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2676 | s_scm_truncate_divide, qp, rp); | |
2677 | } | |
2678 | else | |
2679 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2680 | s_scm_truncate_divide, qp, rp); | |
2681 | } | |
2682 | ||
2683 | static void | |
2684 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2685 | { | |
2686 | if (SCM_UNLIKELY (y == 0)) | |
2687 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2688 | else | |
2689 | { | |
c15fe499 MW |
2690 | double q = trunc (x / y); |
2691 | double r = x - q * y; | |
8f9da340 MW |
2692 | *qp = scm_from_double (q); |
2693 | *rp = scm_from_double (r); | |
2694 | } | |
2695 | } | |
2696 | ||
2697 | static void | |
2698 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2699 | { | |
2700 | SCM r1; | |
2701 | SCM xd = scm_denominator (x); | |
2702 | SCM yd = scm_denominator (y); | |
2703 | ||
2704 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2705 | scm_product (scm_numerator (y), xd), | |
2706 | qp, &r1); | |
2707 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2708 | } | |
2709 | ||
ff62c168 MW |
2710 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2711 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2712 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2713 | |
8f9da340 MW |
2714 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2715 | (SCM x, SCM y), | |
2716 | "Return the integer @var{q} such that\n" | |
2717 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2718 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2719 | "@lisp\n" | |
2720 | "(centered-quotient 123 10) @result{} 12\n" | |
2721 | "(centered-quotient 123 -10) @result{} -12\n" | |
2722 | "(centered-quotient -123 10) @result{} -12\n" | |
2723 | "(centered-quotient -123 -10) @result{} 12\n" | |
2724 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2725 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2726 | "@end lisp") | |
2727 | #define FUNC_NAME s_scm_centered_quotient | |
2728 | { | |
2729 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2730 | { | |
2731 | scm_t_inum xx = SCM_I_INUM (x); | |
2732 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2733 | { | |
2734 | scm_t_inum yy = SCM_I_INUM (y); | |
2735 | if (SCM_UNLIKELY (yy == 0)) | |
2736 | scm_num_overflow (s_scm_centered_quotient); | |
2737 | else | |
2738 | { | |
2739 | scm_t_inum qq = xx / yy; | |
2740 | scm_t_inum rr = xx % yy; | |
2741 | if (SCM_LIKELY (xx > 0)) | |
2742 | { | |
2743 | if (SCM_LIKELY (yy > 0)) | |
2744 | { | |
2745 | if (rr >= (yy + 1) / 2) | |
2746 | qq++; | |
2747 | } | |
2748 | else | |
2749 | { | |
2750 | if (rr >= (1 - yy) / 2) | |
2751 | qq--; | |
2752 | } | |
2753 | } | |
2754 | else | |
2755 | { | |
2756 | if (SCM_LIKELY (yy > 0)) | |
2757 | { | |
2758 | if (rr < -yy / 2) | |
2759 | qq--; | |
2760 | } | |
2761 | else | |
2762 | { | |
2763 | if (rr < yy / 2) | |
2764 | qq++; | |
2765 | } | |
2766 | } | |
2767 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2768 | return SCM_I_MAKINUM (qq); | |
2769 | else | |
2770 | return scm_i_inum2big (qq); | |
2771 | } | |
2772 | } | |
2773 | else if (SCM_BIGP (y)) | |
2774 | { | |
2775 | /* Pass a denormalized bignum version of x (even though it | |
2776 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2777 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2778 | } | |
2779 | else if (SCM_REALP (y)) | |
2780 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2781 | else if (SCM_FRACTIONP (y)) | |
2782 | return scm_i_exact_rational_centered_quotient (x, y); | |
2783 | else | |
fa075d40 AW |
2784 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2785 | s_scm_centered_quotient); | |
8f9da340 MW |
2786 | } |
2787 | else if (SCM_BIGP (x)) | |
2788 | { | |
2789 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2790 | { | |
2791 | scm_t_inum yy = SCM_I_INUM (y); | |
2792 | if (SCM_UNLIKELY (yy == 0)) | |
2793 | scm_num_overflow (s_scm_centered_quotient); | |
2794 | else if (SCM_UNLIKELY (yy == 1)) | |
2795 | return x; | |
2796 | else | |
2797 | { | |
2798 | SCM q = scm_i_mkbig (); | |
2799 | scm_t_inum rr; | |
2800 | /* Arrange for rr to initially be non-positive, | |
2801 | because that simplifies the test to see | |
2802 | if it is within the needed bounds. */ | |
2803 | if (yy > 0) | |
2804 | { | |
2805 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2806 | SCM_I_BIG_MPZ (x), yy); | |
2807 | scm_remember_upto_here_1 (x); | |
2808 | if (rr < -yy / 2) | |
2809 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2810 | SCM_I_BIG_MPZ (q), 1); | |
2811 | } | |
2812 | else | |
2813 | { | |
2814 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2815 | SCM_I_BIG_MPZ (x), -yy); | |
2816 | scm_remember_upto_here_1 (x); | |
2817 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2818 | if (rr < yy / 2) | |
2819 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2820 | SCM_I_BIG_MPZ (q), 1); | |
2821 | } | |
2822 | return scm_i_normbig (q); | |
2823 | } | |
2824 | } | |
2825 | else if (SCM_BIGP (y)) | |
2826 | return scm_i_bigint_centered_quotient (x, y); | |
2827 | else if (SCM_REALP (y)) | |
2828 | return scm_i_inexact_centered_quotient | |
2829 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2830 | else if (SCM_FRACTIONP (y)) | |
2831 | return scm_i_exact_rational_centered_quotient (x, y); | |
2832 | else | |
fa075d40 AW |
2833 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2834 | s_scm_centered_quotient); | |
8f9da340 MW |
2835 | } |
2836 | else if (SCM_REALP (x)) | |
2837 | { | |
2838 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2839 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2840 | return scm_i_inexact_centered_quotient | |
2841 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2842 | else | |
fa075d40 AW |
2843 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2844 | s_scm_centered_quotient); | |
8f9da340 MW |
2845 | } |
2846 | else if (SCM_FRACTIONP (x)) | |
2847 | { | |
2848 | if (SCM_REALP (y)) | |
2849 | return scm_i_inexact_centered_quotient | |
2850 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2851 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2852 | return scm_i_exact_rational_centered_quotient (x, y); | |
2853 | else | |
fa075d40 AW |
2854 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2855 | s_scm_centered_quotient); | |
8f9da340 MW |
2856 | } |
2857 | else | |
fa075d40 AW |
2858 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG1, |
2859 | s_scm_centered_quotient); | |
8f9da340 MW |
2860 | } |
2861 | #undef FUNC_NAME | |
2862 | ||
2863 | static SCM | |
2864 | scm_i_inexact_centered_quotient (double x, double y) | |
2865 | { | |
2866 | if (SCM_LIKELY (y > 0)) | |
2867 | return scm_from_double (floor (x/y + 0.5)); | |
2868 | else if (SCM_LIKELY (y < 0)) | |
2869 | return scm_from_double (ceil (x/y - 0.5)); | |
2870 | else if (y == 0) | |
2871 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2872 | else | |
2873 | return scm_nan (); | |
2874 | } | |
2875 | ||
2876 | /* Assumes that both x and y are bigints, though | |
2877 | x might be able to fit into a fixnum. */ | |
2878 | static SCM | |
2879 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2880 | { | |
2881 | SCM q, r, min_r; | |
2882 | ||
2883 | /* Note that x might be small enough to fit into a | |
2884 | fixnum, so we must not let it escape into the wild */ | |
2885 | q = scm_i_mkbig (); | |
2886 | r = scm_i_mkbig (); | |
2887 | ||
2888 | /* min_r will eventually become -abs(y)/2 */ | |
2889 | min_r = scm_i_mkbig (); | |
2890 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2891 | SCM_I_BIG_MPZ (y), 1); | |
2892 | ||
2893 | /* Arrange for rr to initially be non-positive, | |
2894 | because that simplifies the test to see | |
2895 | if it is within the needed bounds. */ | |
2896 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2897 | { | |
2898 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2899 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2900 | scm_remember_upto_here_2 (x, y); | |
2901 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2902 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2903 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2904 | SCM_I_BIG_MPZ (q), 1); | |
2905 | } | |
2906 | else | |
2907 | { | |
2908 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2909 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2910 | scm_remember_upto_here_2 (x, y); | |
2911 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2912 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2913 | SCM_I_BIG_MPZ (q), 1); | |
2914 | } | |
2915 | scm_remember_upto_here_2 (r, min_r); | |
2916 | return scm_i_normbig (q); | |
2917 | } | |
2918 | ||
2919 | static SCM | |
2920 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2921 | { | |
2922 | return scm_centered_quotient | |
2923 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2924 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2925 | } | |
2926 | ||
2927 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2928 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2929 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2930 | ||
2931 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2932 | (SCM x, SCM y), | |
2933 | "Return the real number @var{r} such that\n" | |
2934 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2935 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2936 | "for some integer @var{q}.\n" | |
2937 | "@lisp\n" | |
2938 | "(centered-remainder 123 10) @result{} 3\n" | |
2939 | "(centered-remainder 123 -10) @result{} 3\n" | |
2940 | "(centered-remainder -123 10) @result{} -3\n" | |
2941 | "(centered-remainder -123 -10) @result{} -3\n" | |
2942 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2943 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2944 | "@end lisp") | |
2945 | #define FUNC_NAME s_scm_centered_remainder | |
2946 | { | |
2947 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2948 | { | |
2949 | scm_t_inum xx = SCM_I_INUM (x); | |
2950 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2951 | { | |
2952 | scm_t_inum yy = SCM_I_INUM (y); | |
2953 | if (SCM_UNLIKELY (yy == 0)) | |
2954 | scm_num_overflow (s_scm_centered_remainder); | |
2955 | else | |
2956 | { | |
2957 | scm_t_inum rr = xx % yy; | |
2958 | if (SCM_LIKELY (xx > 0)) | |
2959 | { | |
2960 | if (SCM_LIKELY (yy > 0)) | |
2961 | { | |
2962 | if (rr >= (yy + 1) / 2) | |
2963 | rr -= yy; | |
2964 | } | |
2965 | else | |
2966 | { | |
2967 | if (rr >= (1 - yy) / 2) | |
2968 | rr += yy; | |
2969 | } | |
2970 | } | |
2971 | else | |
2972 | { | |
2973 | if (SCM_LIKELY (yy > 0)) | |
2974 | { | |
2975 | if (rr < -yy / 2) | |
2976 | rr += yy; | |
2977 | } | |
2978 | else | |
2979 | { | |
2980 | if (rr < yy / 2) | |
2981 | rr -= yy; | |
2982 | } | |
2983 | } | |
2984 | return SCM_I_MAKINUM (rr); | |
2985 | } | |
2986 | } | |
2987 | else if (SCM_BIGP (y)) | |
2988 | { | |
2989 | /* Pass a denormalized bignum version of x (even though it | |
2990 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2991 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2992 | } | |
2993 | else if (SCM_REALP (y)) | |
2994 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2995 | else if (SCM_FRACTIONP (y)) | |
2996 | return scm_i_exact_rational_centered_remainder (x, y); | |
2997 | else | |
fa075d40 AW |
2998 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
2999 | s_scm_centered_remainder); | |
8f9da340 MW |
3000 | } |
3001 | else if (SCM_BIGP (x)) | |
3002 | { | |
3003 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3004 | { | |
3005 | scm_t_inum yy = SCM_I_INUM (y); | |
3006 | if (SCM_UNLIKELY (yy == 0)) | |
3007 | scm_num_overflow (s_scm_centered_remainder); | |
3008 | else | |
3009 | { | |
3010 | scm_t_inum rr; | |
3011 | /* Arrange for rr to initially be non-positive, | |
3012 | because that simplifies the test to see | |
3013 | if it is within the needed bounds. */ | |
3014 | if (yy > 0) | |
3015 | { | |
3016 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
3017 | scm_remember_upto_here_1 (x); | |
3018 | if (rr < -yy / 2) | |
3019 | rr += yy; | |
3020 | } | |
3021 | else | |
3022 | { | |
3023 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
3024 | scm_remember_upto_here_1 (x); | |
3025 | if (rr < yy / 2) | |
3026 | rr -= yy; | |
3027 | } | |
3028 | return SCM_I_MAKINUM (rr); | |
3029 | } | |
3030 | } | |
3031 | else if (SCM_BIGP (y)) | |
3032 | return scm_i_bigint_centered_remainder (x, y); | |
3033 | else if (SCM_REALP (y)) | |
3034 | return scm_i_inexact_centered_remainder | |
3035 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
3036 | else if (SCM_FRACTIONP (y)) | |
3037 | return scm_i_exact_rational_centered_remainder (x, y); | |
3038 | else | |
fa075d40 AW |
3039 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
3040 | s_scm_centered_remainder); | |
8f9da340 MW |
3041 | } |
3042 | else if (SCM_REALP (x)) | |
3043 | { | |
3044 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3045 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3046 | return scm_i_inexact_centered_remainder | |
3047 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
3048 | else | |
fa075d40 AW |
3049 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
3050 | s_scm_centered_remainder); | |
8f9da340 MW |
3051 | } |
3052 | else if (SCM_FRACTIONP (x)) | |
3053 | { | |
3054 | if (SCM_REALP (y)) | |
3055 | return scm_i_inexact_centered_remainder | |
3056 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
3057 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3058 | return scm_i_exact_rational_centered_remainder (x, y); | |
3059 | else | |
fa075d40 AW |
3060 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
3061 | s_scm_centered_remainder); | |
8f9da340 MW |
3062 | } |
3063 | else | |
fa075d40 AW |
3064 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG1, |
3065 | s_scm_centered_remainder); | |
8f9da340 MW |
3066 | } |
3067 | #undef FUNC_NAME | |
3068 | ||
3069 | static SCM | |
3070 | scm_i_inexact_centered_remainder (double x, double y) | |
3071 | { | |
3072 | double q; | |
3073 | ||
3074 | /* Although it would be more efficient to use fmod here, we can't | |
3075 | because it would in some cases produce results inconsistent with | |
3076 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
3077 | close). In particular, when x-y/2 is very close to a multiple of | |
3078 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
3079 | two cases must correspond to different choices of q. If quotient | |
3080 | chooses one and remainder chooses the other, it would be bad. */ | |
3081 | if (SCM_LIKELY (y > 0)) | |
3082 | q = floor (x/y + 0.5); | |
3083 | else if (SCM_LIKELY (y < 0)) | |
3084 | q = ceil (x/y - 0.5); | |
3085 | else if (y == 0) | |
3086 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
3087 | else | |
3088 | return scm_nan (); | |
3089 | return scm_from_double (x - q * y); | |
3090 | } | |
3091 | ||
3092 | /* Assumes that both x and y are bigints, though | |
3093 | x might be able to fit into a fixnum. */ | |
3094 | static SCM | |
3095 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
3096 | { | |
3097 | SCM r, min_r; | |
3098 | ||
3099 | /* Note that x might be small enough to fit into a | |
3100 | fixnum, so we must not let it escape into the wild */ | |
3101 | r = scm_i_mkbig (); | |
3102 | ||
3103 | /* min_r will eventually become -abs(y)/2 */ | |
3104 | min_r = scm_i_mkbig (); | |
3105 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3106 | SCM_I_BIG_MPZ (y), 1); | |
3107 | ||
3108 | /* Arrange for rr to initially be non-positive, | |
3109 | because that simplifies the test to see | |
3110 | if it is within the needed bounds. */ | |
3111 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3112 | { | |
3113 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
3114 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3115 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3116 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3117 | mpz_add (SCM_I_BIG_MPZ (r), | |
3118 | SCM_I_BIG_MPZ (r), | |
3119 | SCM_I_BIG_MPZ (y)); | |
3120 | } | |
3121 | else | |
3122 | { | |
3123 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
3124 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3125 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3126 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3127 | SCM_I_BIG_MPZ (r), | |
3128 | SCM_I_BIG_MPZ (y)); | |
3129 | } | |
3130 | scm_remember_upto_here_2 (x, y); | |
3131 | return scm_i_normbig (r); | |
3132 | } | |
3133 | ||
3134 | static SCM | |
3135 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
3136 | { | |
3137 | SCM xd = scm_denominator (x); | |
3138 | SCM yd = scm_denominator (y); | |
3139 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
3140 | scm_product (scm_numerator (y), xd)); | |
3141 | return scm_divide (r1, scm_product (xd, yd)); | |
3142 | } | |
3143 | ||
3144 | ||
3145 | static void scm_i_inexact_centered_divide (double x, double y, | |
3146 | SCM *qp, SCM *rp); | |
3147 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3148 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
3149 | SCM *qp, SCM *rp); | |
3150 | ||
3151 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
3152 | (SCM x, SCM y), | |
3153 | "Return the integer @var{q} and the real number @var{r}\n" | |
3154 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
3155 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
3156 | "@lisp\n" | |
3157 | "(centered/ 123 10) @result{} 12 and 3\n" | |
3158 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
3159 | "(centered/ -123 10) @result{} -12 and -3\n" | |
3160 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
3161 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3162 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
3163 | "@end lisp") | |
3164 | #define FUNC_NAME s_scm_i_centered_divide | |
3165 | { | |
3166 | SCM q, r; | |
3167 | ||
3168 | scm_centered_divide(x, y, &q, &r); | |
3169 | return scm_values (scm_list_2 (q, r)); | |
3170 | } | |
3171 | #undef FUNC_NAME | |
3172 | ||
3173 | #define s_scm_centered_divide s_scm_i_centered_divide | |
3174 | #define g_scm_centered_divide g_scm_i_centered_divide | |
3175 | ||
3176 | void | |
3177 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3178 | { | |
3179 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3180 | { | |
3181 | scm_t_inum xx = SCM_I_INUM (x); | |
3182 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3183 | { | |
3184 | scm_t_inum yy = SCM_I_INUM (y); | |
3185 | if (SCM_UNLIKELY (yy == 0)) | |
3186 | scm_num_overflow (s_scm_centered_divide); | |
3187 | else | |
3188 | { | |
3189 | scm_t_inum qq = xx / yy; | |
3190 | scm_t_inum rr = xx % yy; | |
3191 | if (SCM_LIKELY (xx > 0)) | |
3192 | { | |
3193 | if (SCM_LIKELY (yy > 0)) | |
3194 | { | |
3195 | if (rr >= (yy + 1) / 2) | |
3196 | { qq++; rr -= yy; } | |
3197 | } | |
3198 | else | |
3199 | { | |
3200 | if (rr >= (1 - yy) / 2) | |
3201 | { qq--; rr += yy; } | |
3202 | } | |
3203 | } | |
3204 | else | |
3205 | { | |
3206 | if (SCM_LIKELY (yy > 0)) | |
3207 | { | |
3208 | if (rr < -yy / 2) | |
3209 | { qq--; rr += yy; } | |
3210 | } | |
3211 | else | |
3212 | { | |
3213 | if (rr < yy / 2) | |
3214 | { qq++; rr -= yy; } | |
3215 | } | |
3216 | } | |
3217 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3218 | *qp = SCM_I_MAKINUM (qq); | |
3219 | else | |
3220 | *qp = scm_i_inum2big (qq); | |
3221 | *rp = SCM_I_MAKINUM (rr); | |
3222 | } | |
3223 | return; | |
3224 | } | |
3225 | else if (SCM_BIGP (y)) | |
3226 | { | |
3227 | /* Pass a denormalized bignum version of x (even though it | |
3228 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3229 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3230 | } | |
3231 | else if (SCM_REALP (y)) | |
3232 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3233 | else if (SCM_FRACTIONP (y)) | |
3234 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3235 | else | |
3236 | return two_valued_wta_dispatch_2 | |
3237 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3238 | s_scm_centered_divide, qp, rp); | |
3239 | } | |
3240 | else if (SCM_BIGP (x)) | |
3241 | { | |
3242 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3243 | { | |
3244 | scm_t_inum yy = SCM_I_INUM (y); | |
3245 | if (SCM_UNLIKELY (yy == 0)) | |
3246 | scm_num_overflow (s_scm_centered_divide); | |
3247 | else | |
3248 | { | |
3249 | SCM q = scm_i_mkbig (); | |
3250 | scm_t_inum rr; | |
3251 | /* Arrange for rr to initially be non-positive, | |
3252 | because that simplifies the test to see | |
3253 | if it is within the needed bounds. */ | |
3254 | if (yy > 0) | |
3255 | { | |
3256 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3257 | SCM_I_BIG_MPZ (x), yy); | |
3258 | scm_remember_upto_here_1 (x); | |
3259 | if (rr < -yy / 2) | |
3260 | { | |
3261 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3262 | SCM_I_BIG_MPZ (q), 1); | |
3263 | rr += yy; | |
3264 | } | |
3265 | } | |
3266 | else | |
3267 | { | |
3268 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3269 | SCM_I_BIG_MPZ (x), -yy); | |
3270 | scm_remember_upto_here_1 (x); | |
3271 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3272 | if (rr < yy / 2) | |
3273 | { | |
3274 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3275 | SCM_I_BIG_MPZ (q), 1); | |
3276 | rr -= yy; | |
3277 | } | |
3278 | } | |
3279 | *qp = scm_i_normbig (q); | |
3280 | *rp = SCM_I_MAKINUM (rr); | |
3281 | } | |
3282 | return; | |
3283 | } | |
3284 | else if (SCM_BIGP (y)) | |
3285 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3286 | else if (SCM_REALP (y)) | |
3287 | return scm_i_inexact_centered_divide | |
3288 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3289 | else if (SCM_FRACTIONP (y)) | |
3290 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3291 | else | |
3292 | return two_valued_wta_dispatch_2 | |
3293 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3294 | s_scm_centered_divide, qp, rp); | |
3295 | } | |
3296 | else if (SCM_REALP (x)) | |
3297 | { | |
3298 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3299 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3300 | return scm_i_inexact_centered_divide | |
3301 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3302 | else | |
3303 | return two_valued_wta_dispatch_2 | |
3304 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3305 | s_scm_centered_divide, qp, rp); | |
3306 | } | |
3307 | else if (SCM_FRACTIONP (x)) | |
3308 | { | |
3309 | if (SCM_REALP (y)) | |
3310 | return scm_i_inexact_centered_divide | |
3311 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3312 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3313 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3314 | else | |
3315 | return two_valued_wta_dispatch_2 | |
3316 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3317 | s_scm_centered_divide, qp, rp); | |
3318 | } | |
3319 | else | |
3320 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3321 | s_scm_centered_divide, qp, rp); | |
3322 | } | |
3323 | ||
3324 | static void | |
3325 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3326 | { | |
3327 | double q, r; | |
3328 | ||
3329 | if (SCM_LIKELY (y > 0)) | |
3330 | q = floor (x/y + 0.5); | |
3331 | else if (SCM_LIKELY (y < 0)) | |
3332 | q = ceil (x/y - 0.5); | |
3333 | else if (y == 0) | |
3334 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3335 | else | |
3336 | q = guile_NaN; | |
3337 | r = x - q * y; | |
3338 | *qp = scm_from_double (q); | |
3339 | *rp = scm_from_double (r); | |
3340 | } | |
3341 | ||
3342 | /* Assumes that both x and y are bigints, though | |
3343 | x might be able to fit into a fixnum. */ | |
3344 | static void | |
3345 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3346 | { | |
3347 | SCM q, r, min_r; | |
3348 | ||
3349 | /* Note that x might be small enough to fit into a | |
3350 | fixnum, so we must not let it escape into the wild */ | |
3351 | q = scm_i_mkbig (); | |
3352 | r = scm_i_mkbig (); | |
3353 | ||
3354 | /* min_r will eventually become -abs(y/2) */ | |
3355 | min_r = scm_i_mkbig (); | |
3356 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3357 | SCM_I_BIG_MPZ (y), 1); | |
3358 | ||
3359 | /* Arrange for rr to initially be non-positive, | |
3360 | because that simplifies the test to see | |
3361 | if it is within the needed bounds. */ | |
3362 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3363 | { | |
3364 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3365 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3366 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3367 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3368 | { | |
3369 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3370 | SCM_I_BIG_MPZ (q), 1); | |
3371 | mpz_add (SCM_I_BIG_MPZ (r), | |
3372 | SCM_I_BIG_MPZ (r), | |
3373 | SCM_I_BIG_MPZ (y)); | |
3374 | } | |
3375 | } | |
3376 | else | |
3377 | { | |
3378 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3379 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3380 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3381 | { | |
3382 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3383 | SCM_I_BIG_MPZ (q), 1); | |
3384 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3385 | SCM_I_BIG_MPZ (r), | |
3386 | SCM_I_BIG_MPZ (y)); | |
3387 | } | |
3388 | } | |
3389 | scm_remember_upto_here_2 (x, y); | |
3390 | *qp = scm_i_normbig (q); | |
3391 | *rp = scm_i_normbig (r); | |
3392 | } | |
3393 | ||
3394 | static void | |
3395 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3396 | { | |
3397 | SCM r1; | |
3398 | SCM xd = scm_denominator (x); | |
3399 | SCM yd = scm_denominator (y); | |
3400 | ||
3401 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3402 | scm_product (scm_numerator (y), xd), | |
3403 | qp, &r1); | |
3404 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3405 | } | |
3406 | ||
3407 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3408 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3409 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3410 | ||
3411 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3412 | (SCM x, SCM y), |
8f9da340 MW |
3413 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3414 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3415 | "@lisp\n" |
8f9da340 MW |
3416 | "(round-quotient 123 10) @result{} 12\n" |
3417 | "(round-quotient 123 -10) @result{} -12\n" | |
3418 | "(round-quotient -123 10) @result{} -12\n" | |
3419 | "(round-quotient -123 -10) @result{} 12\n" | |
3420 | "(round-quotient 125 10) @result{} 12\n" | |
3421 | "(round-quotient 127 10) @result{} 13\n" | |
3422 | "(round-quotient 135 10) @result{} 14\n" | |
3423 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3424 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3425 | "@end lisp") |
8f9da340 | 3426 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3427 | { |
3428 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3429 | { | |
4a46bc2a | 3430 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3431 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3432 | { | |
3433 | scm_t_inum yy = SCM_I_INUM (y); | |
3434 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3435 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3436 | else |
3437 | { | |
ff62c168 | 3438 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3439 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3440 | scm_t_inum ay = yy; |
3441 | scm_t_inum r2 = 2 * rr; | |
3442 | ||
3443 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3444 | { |
8f9da340 MW |
3445 | ay = -ay; |
3446 | r2 = -r2; | |
3447 | } | |
3448 | ||
3449 | if (qq & 1L) | |
3450 | { | |
3451 | if (r2 >= ay) | |
3452 | qq++; | |
3453 | else if (r2 <= -ay) | |
3454 | qq--; | |
ff62c168 MW |
3455 | } |
3456 | else | |
3457 | { | |
8f9da340 MW |
3458 | if (r2 > ay) |
3459 | qq++; | |
3460 | else if (r2 < -ay) | |
3461 | qq--; | |
ff62c168 | 3462 | } |
4a46bc2a MW |
3463 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3464 | return SCM_I_MAKINUM (qq); | |
3465 | else | |
3466 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3467 | } |
3468 | } | |
3469 | else if (SCM_BIGP (y)) | |
3470 | { | |
3471 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3472 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3473 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3474 | } |
3475 | else if (SCM_REALP (y)) | |
8f9da340 | 3476 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3477 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3478 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3479 | else |
fa075d40 AW |
3480 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3481 | s_scm_round_quotient); | |
ff62c168 MW |
3482 | } |
3483 | else if (SCM_BIGP (x)) | |
3484 | { | |
3485 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3486 | { | |
3487 | scm_t_inum yy = SCM_I_INUM (y); | |
3488 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3489 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3490 | else if (SCM_UNLIKELY (yy == 1)) |
3491 | return x; | |
ff62c168 MW |
3492 | else |
3493 | { | |
3494 | SCM q = scm_i_mkbig (); | |
3495 | scm_t_inum rr; | |
8f9da340 MW |
3496 | int needs_adjustment; |
3497 | ||
ff62c168 MW |
3498 | if (yy > 0) |
3499 | { | |
8f9da340 MW |
3500 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3501 | SCM_I_BIG_MPZ (x), yy); | |
3502 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3503 | needs_adjustment = (2*rr >= yy); | |
3504 | else | |
3505 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3506 | } |
3507 | else | |
3508 | { | |
3509 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3510 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3511 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3512 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3513 | needs_adjustment = (2*rr <= yy); | |
3514 | else | |
3515 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3516 | } |
8f9da340 MW |
3517 | scm_remember_upto_here_1 (x); |
3518 | if (needs_adjustment) | |
3519 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3520 | return scm_i_normbig (q); |
3521 | } | |
3522 | } | |
3523 | else if (SCM_BIGP (y)) | |
8f9da340 | 3524 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3525 | else if (SCM_REALP (y)) |
8f9da340 | 3526 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3527 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3528 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3529 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3530 | else |
fa075d40 AW |
3531 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3532 | s_scm_round_quotient); | |
ff62c168 MW |
3533 | } |
3534 | else if (SCM_REALP (x)) | |
3535 | { | |
3536 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3537 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3538 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3539 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3540 | else | |
fa075d40 AW |
3541 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3542 | s_scm_round_quotient); | |
ff62c168 MW |
3543 | } |
3544 | else if (SCM_FRACTIONP (x)) | |
3545 | { | |
3546 | if (SCM_REALP (y)) | |
8f9da340 | 3547 | return scm_i_inexact_round_quotient |
ff62c168 | 3548 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3549 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3550 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3551 | else |
fa075d40 AW |
3552 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3553 | s_scm_round_quotient); | |
ff62c168 MW |
3554 | } |
3555 | else | |
fa075d40 AW |
3556 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3557 | s_scm_round_quotient); | |
ff62c168 MW |
3558 | } |
3559 | #undef FUNC_NAME | |
3560 | ||
3561 | static SCM | |
8f9da340 | 3562 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3563 | { |
8f9da340 MW |
3564 | if (SCM_UNLIKELY (y == 0)) |
3565 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3566 | else |
8f9da340 | 3567 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3568 | } |
3569 | ||
3570 | /* Assumes that both x and y are bigints, though | |
3571 | x might be able to fit into a fixnum. */ | |
3572 | static SCM | |
8f9da340 | 3573 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3574 | { |
8f9da340 MW |
3575 | SCM q, r, r2; |
3576 | int cmp, needs_adjustment; | |
ff62c168 MW |
3577 | |
3578 | /* Note that x might be small enough to fit into a | |
3579 | fixnum, so we must not let it escape into the wild */ | |
3580 | q = scm_i_mkbig (); | |
3581 | r = scm_i_mkbig (); | |
8f9da340 | 3582 | r2 = scm_i_mkbig (); |
ff62c168 | 3583 | |
8f9da340 MW |
3584 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3585 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3586 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3587 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3588 | |
8f9da340 MW |
3589 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3590 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3591 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3592 | else |
8f9da340 MW |
3593 | needs_adjustment = (cmp > 0); |
3594 | scm_remember_upto_here_2 (r2, y); | |
3595 | ||
3596 | if (needs_adjustment) | |
3597 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3598 | ||
ff62c168 MW |
3599 | return scm_i_normbig (q); |
3600 | } | |
3601 | ||
ff62c168 | 3602 | static SCM |
8f9da340 | 3603 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3604 | { |
8f9da340 | 3605 | return scm_round_quotient |
03ddd15b MW |
3606 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3607 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3608 | } |
3609 | ||
8f9da340 MW |
3610 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3611 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3612 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3613 | |
8f9da340 | 3614 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3615 | (SCM x, SCM y), |
3616 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3617 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3618 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3619 | "nearest integer, with ties going to the nearest\n" | |
3620 | "even integer.\n" | |
ff62c168 | 3621 | "@lisp\n" |
8f9da340 MW |
3622 | "(round-remainder 123 10) @result{} 3\n" |
3623 | "(round-remainder 123 -10) @result{} 3\n" | |
3624 | "(round-remainder -123 10) @result{} -3\n" | |
3625 | "(round-remainder -123 -10) @result{} -3\n" | |
3626 | "(round-remainder 125 10) @result{} 5\n" | |
3627 | "(round-remainder 127 10) @result{} -3\n" | |
3628 | "(round-remainder 135 10) @result{} -5\n" | |
3629 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3630 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3631 | "@end lisp") |
8f9da340 | 3632 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3633 | { |
3634 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3635 | { | |
4a46bc2a | 3636 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3637 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3638 | { | |
3639 | scm_t_inum yy = SCM_I_INUM (y); | |
3640 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3641 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3642 | else |
3643 | { | |
8f9da340 | 3644 | scm_t_inum qq = xx / yy; |
ff62c168 | 3645 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3646 | scm_t_inum ay = yy; |
3647 | scm_t_inum r2 = 2 * rr; | |
3648 | ||
3649 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3650 | { |
8f9da340 MW |
3651 | ay = -ay; |
3652 | r2 = -r2; | |
3653 | } | |
3654 | ||
3655 | if (qq & 1L) | |
3656 | { | |
3657 | if (r2 >= ay) | |
3658 | rr -= yy; | |
3659 | else if (r2 <= -ay) | |
3660 | rr += yy; | |
ff62c168 MW |
3661 | } |
3662 | else | |
3663 | { | |
8f9da340 MW |
3664 | if (r2 > ay) |
3665 | rr -= yy; | |
3666 | else if (r2 < -ay) | |
3667 | rr += yy; | |
ff62c168 MW |
3668 | } |
3669 | return SCM_I_MAKINUM (rr); | |
3670 | } | |
3671 | } | |
3672 | else if (SCM_BIGP (y)) | |
3673 | { | |
3674 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3675 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3676 | return scm_i_bigint_round_remainder | |
3677 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3678 | } |
3679 | else if (SCM_REALP (y)) | |
8f9da340 | 3680 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3681 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3682 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3683 | else |
fa075d40 AW |
3684 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3685 | s_scm_round_remainder); | |
ff62c168 MW |
3686 | } |
3687 | else if (SCM_BIGP (x)) | |
3688 | { | |
3689 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3690 | { | |
3691 | scm_t_inum yy = SCM_I_INUM (y); | |
3692 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3693 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3694 | else |
3695 | { | |
8f9da340 | 3696 | SCM q = scm_i_mkbig (); |
ff62c168 | 3697 | scm_t_inum rr; |
8f9da340 MW |
3698 | int needs_adjustment; |
3699 | ||
ff62c168 MW |
3700 | if (yy > 0) |
3701 | { | |
8f9da340 MW |
3702 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3703 | SCM_I_BIG_MPZ (x), yy); | |
3704 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3705 | needs_adjustment = (2*rr >= yy); | |
3706 | else | |
3707 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3708 | } |
3709 | else | |
3710 | { | |
8f9da340 MW |
3711 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3712 | SCM_I_BIG_MPZ (x), -yy); | |
3713 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3714 | needs_adjustment = (2*rr <= yy); | |
3715 | else | |
3716 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3717 | } |
8f9da340 MW |
3718 | scm_remember_upto_here_2 (x, q); |
3719 | if (needs_adjustment) | |
3720 | rr -= yy; | |
ff62c168 MW |
3721 | return SCM_I_MAKINUM (rr); |
3722 | } | |
3723 | } | |
3724 | else if (SCM_BIGP (y)) | |
8f9da340 | 3725 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3726 | else if (SCM_REALP (y)) |
8f9da340 | 3727 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3728 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3729 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3730 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3731 | else |
fa075d40 AW |
3732 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3733 | s_scm_round_remainder); | |
ff62c168 MW |
3734 | } |
3735 | else if (SCM_REALP (x)) | |
3736 | { | |
3737 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3738 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3739 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3740 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3741 | else | |
fa075d40 AW |
3742 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3743 | s_scm_round_remainder); | |
ff62c168 MW |
3744 | } |
3745 | else if (SCM_FRACTIONP (x)) | |
3746 | { | |
3747 | if (SCM_REALP (y)) | |
8f9da340 | 3748 | return scm_i_inexact_round_remainder |
ff62c168 | 3749 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3750 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3751 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3752 | else |
fa075d40 AW |
3753 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3754 | s_scm_round_remainder); | |
ff62c168 MW |
3755 | } |
3756 | else | |
fa075d40 AW |
3757 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3758 | s_scm_round_remainder); | |
ff62c168 MW |
3759 | } |
3760 | #undef FUNC_NAME | |
3761 | ||
3762 | static SCM | |
8f9da340 | 3763 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3764 | { |
ff62c168 MW |
3765 | /* Although it would be more efficient to use fmod here, we can't |
3766 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3767 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3768 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3769 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3770 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3771 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3772 | |
3773 | if (SCM_UNLIKELY (y == 0)) | |
3774 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3775 | else |
8f9da340 MW |
3776 | { |
3777 | double q = scm_c_round (x / y); | |
3778 | return scm_from_double (x - q * y); | |
3779 | } | |
ff62c168 MW |
3780 | } |
3781 | ||
3782 | /* Assumes that both x and y are bigints, though | |
3783 | x might be able to fit into a fixnum. */ | |
3784 | static SCM | |
8f9da340 | 3785 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3786 | { |
8f9da340 MW |
3787 | SCM q, r, r2; |
3788 | int cmp, needs_adjustment; | |
ff62c168 MW |
3789 | |
3790 | /* Note that x might be small enough to fit into a | |
3791 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3792 | q = scm_i_mkbig (); |
ff62c168 | 3793 | r = scm_i_mkbig (); |
8f9da340 | 3794 | r2 = scm_i_mkbig (); |
ff62c168 | 3795 | |
8f9da340 MW |
3796 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3797 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3798 | scm_remember_upto_here_1 (x); | |
3799 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3800 | |
8f9da340 MW |
3801 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3802 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3803 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3804 | else |
8f9da340 MW |
3805 | needs_adjustment = (cmp > 0); |
3806 | scm_remember_upto_here_2 (q, r2); | |
3807 | ||
3808 | if (needs_adjustment) | |
3809 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3810 | ||
3811 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3812 | return scm_i_normbig (r); |
3813 | } | |
3814 | ||
ff62c168 | 3815 | static SCM |
8f9da340 | 3816 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3817 | { |
03ddd15b MW |
3818 | SCM xd = scm_denominator (x); |
3819 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3820 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3821 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3822 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3823 | } |
3824 | ||
3825 | ||
8f9da340 MW |
3826 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3827 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3828 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3829 | |
8f9da340 | 3830 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3831 | (SCM x, SCM y), |
3832 | "Return the integer @var{q} and the real number @var{r}\n" | |
3833 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3834 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3835 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3836 | "@lisp\n" |
8f9da340 MW |
3837 | "(round/ 123 10) @result{} 12 and 3\n" |
3838 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3839 | "(round/ -123 10) @result{} -12 and -3\n" | |
3840 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3841 | "(round/ 125 10) @result{} 12 and 5\n" | |
3842 | "(round/ 127 10) @result{} 13 and -3\n" | |
3843 | "(round/ 135 10) @result{} 14 and -5\n" | |
3844 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3845 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3846 | "@end lisp") |
8f9da340 | 3847 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3848 | { |
3849 | SCM q, r; | |
3850 | ||
8f9da340 | 3851 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3852 | return scm_values (scm_list_2 (q, r)); |
3853 | } | |
3854 | #undef FUNC_NAME | |
3855 | ||
8f9da340 MW |
3856 | #define s_scm_round_divide s_scm_i_round_divide |
3857 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3858 | |
3859 | void | |
8f9da340 | 3860 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3861 | { |
3862 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3863 | { | |
4a46bc2a | 3864 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3865 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3866 | { | |
3867 | scm_t_inum yy = SCM_I_INUM (y); | |
3868 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3869 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3870 | else |
3871 | { | |
ff62c168 | 3872 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3873 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3874 | scm_t_inum ay = yy; |
3875 | scm_t_inum r2 = 2 * rr; | |
3876 | ||
3877 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3878 | { |
8f9da340 MW |
3879 | ay = -ay; |
3880 | r2 = -r2; | |
3881 | } | |
3882 | ||
3883 | if (qq & 1L) | |
3884 | { | |
3885 | if (r2 >= ay) | |
3886 | { qq++; rr -= yy; } | |
3887 | else if (r2 <= -ay) | |
3888 | { qq--; rr += yy; } | |
ff62c168 MW |
3889 | } |
3890 | else | |
3891 | { | |
8f9da340 MW |
3892 | if (r2 > ay) |
3893 | { qq++; rr -= yy; } | |
3894 | else if (r2 < -ay) | |
3895 | { qq--; rr += yy; } | |
ff62c168 | 3896 | } |
4a46bc2a | 3897 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3898 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3899 | else |
5fbf680b MW |
3900 | *qp = scm_i_inum2big (qq); |
3901 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3902 | } |
5fbf680b | 3903 | return; |
ff62c168 MW |
3904 | } |
3905 | else if (SCM_BIGP (y)) | |
3906 | { | |
3907 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3908 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3909 | return scm_i_bigint_round_divide | |
3910 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3911 | } |
3912 | else if (SCM_REALP (y)) | |
8f9da340 | 3913 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3914 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3915 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3916 | else |
8f9da340 MW |
3917 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3918 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3919 | } |
3920 | else if (SCM_BIGP (x)) | |
3921 | { | |
3922 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3923 | { | |
3924 | scm_t_inum yy = SCM_I_INUM (y); | |
3925 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3926 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3927 | else |
3928 | { | |
3929 | SCM q = scm_i_mkbig (); | |
3930 | scm_t_inum rr; | |
8f9da340 MW |
3931 | int needs_adjustment; |
3932 | ||
ff62c168 MW |
3933 | if (yy > 0) |
3934 | { | |
8f9da340 MW |
3935 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3936 | SCM_I_BIG_MPZ (x), yy); | |
3937 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3938 | needs_adjustment = (2*rr >= yy); | |
3939 | else | |
3940 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3941 | } |
3942 | else | |
3943 | { | |
3944 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3945 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3946 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3947 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3948 | needs_adjustment = (2*rr <= yy); | |
3949 | else | |
3950 | needs_adjustment = (2*rr < yy); | |
3951 | } | |
3952 | scm_remember_upto_here_1 (x); | |
3953 | if (needs_adjustment) | |
3954 | { | |
3955 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3956 | rr -= yy; | |
ff62c168 | 3957 | } |
5fbf680b MW |
3958 | *qp = scm_i_normbig (q); |
3959 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3960 | } |
5fbf680b | 3961 | return; |
ff62c168 MW |
3962 | } |
3963 | else if (SCM_BIGP (y)) | |
8f9da340 | 3964 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3965 | else if (SCM_REALP (y)) |
8f9da340 | 3966 | return scm_i_inexact_round_divide |
5fbf680b | 3967 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3968 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3969 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3970 | else |
8f9da340 MW |
3971 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3972 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3973 | } |
3974 | else if (SCM_REALP (x)) | |
3975 | { | |
3976 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3977 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3978 | return scm_i_inexact_round_divide |
5fbf680b | 3979 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3980 | else |
8f9da340 MW |
3981 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3982 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3983 | } |
3984 | else if (SCM_FRACTIONP (x)) | |
3985 | { | |
3986 | if (SCM_REALP (y)) | |
8f9da340 | 3987 | return scm_i_inexact_round_divide |
5fbf680b | 3988 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3989 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3990 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3991 | else |
8f9da340 MW |
3992 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3993 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3994 | } |
3995 | else | |
8f9da340 MW |
3996 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3997 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3998 | } |
ff62c168 | 3999 | |
5fbf680b | 4000 | static void |
8f9da340 | 4001 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 4002 | { |
8f9da340 MW |
4003 | if (SCM_UNLIKELY (y == 0)) |
4004 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 4005 | else |
8f9da340 MW |
4006 | { |
4007 | double q = scm_c_round (x / y); | |
4008 | double r = x - q * y; | |
4009 | *qp = scm_from_double (q); | |
4010 | *rp = scm_from_double (r); | |
4011 | } | |
ff62c168 MW |
4012 | } |
4013 | ||
4014 | /* Assumes that both x and y are bigints, though | |
4015 | x might be able to fit into a fixnum. */ | |
5fbf680b | 4016 | static void |
8f9da340 | 4017 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4018 | { |
8f9da340 MW |
4019 | SCM q, r, r2; |
4020 | int cmp, needs_adjustment; | |
ff62c168 MW |
4021 | |
4022 | /* Note that x might be small enough to fit into a | |
4023 | fixnum, so we must not let it escape into the wild */ | |
4024 | q = scm_i_mkbig (); | |
4025 | r = scm_i_mkbig (); | |
8f9da340 | 4026 | r2 = scm_i_mkbig (); |
ff62c168 | 4027 | |
8f9da340 MW |
4028 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
4029 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4030 | scm_remember_upto_here_1 (x); | |
4031 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 4032 | |
8f9da340 MW |
4033 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
4034 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4035 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 4036 | else |
8f9da340 MW |
4037 | needs_adjustment = (cmp > 0); |
4038 | ||
4039 | if (needs_adjustment) | |
ff62c168 | 4040 | { |
8f9da340 MW |
4041 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
4042 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 4043 | } |
8f9da340 MW |
4044 | |
4045 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
4046 | *qp = scm_i_normbig (q); |
4047 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
4048 | } |
4049 | ||
5fbf680b | 4050 | static void |
8f9da340 | 4051 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4052 | { |
03ddd15b MW |
4053 | SCM r1; |
4054 | SCM xd = scm_denominator (x); | |
4055 | SCM yd = scm_denominator (y); | |
4056 | ||
8f9da340 MW |
4057 | scm_round_divide (scm_product (scm_numerator (x), yd), |
4058 | scm_product (scm_numerator (y), xd), | |
4059 | qp, &r1); | |
03ddd15b | 4060 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
4061 | } |
4062 | ||
4063 | ||
78d3deb1 AW |
4064 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
4065 | (SCM x, SCM y, SCM rest), | |
4066 | "Return the greatest common divisor of all parameter values.\n" | |
4067 | "If called without arguments, 0 is returned.") | |
4068 | #define FUNC_NAME s_scm_i_gcd | |
4069 | { | |
4070 | while (!scm_is_null (rest)) | |
4071 | { x = scm_gcd (x, y); | |
4072 | y = scm_car (rest); | |
4073 | rest = scm_cdr (rest); | |
4074 | } | |
4075 | return scm_gcd (x, y); | |
4076 | } | |
4077 | #undef FUNC_NAME | |
4078 | ||
4079 | #define s_gcd s_scm_i_gcd | |
4080 | #define g_gcd g_scm_i_gcd | |
4081 | ||
0f2d19dd | 4082 | SCM |
6e8d25a6 | 4083 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 4084 | { |
a2dead1b | 4085 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
1dd79792 | 4086 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 4087 | |
a2dead1b | 4088 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4089 | { |
a2dead1b | 4090 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4091 | { |
e25f3727 AW |
4092 | scm_t_inum xx = SCM_I_INUM (x); |
4093 | scm_t_inum yy = SCM_I_INUM (y); | |
4094 | scm_t_inum u = xx < 0 ? -xx : xx; | |
4095 | scm_t_inum v = yy < 0 ? -yy : yy; | |
4096 | scm_t_inum result; | |
a2dead1b | 4097 | if (SCM_UNLIKELY (xx == 0)) |
0aacf84e | 4098 | result = v; |
a2dead1b | 4099 | else if (SCM_UNLIKELY (yy == 0)) |
0aacf84e MD |
4100 | result = u; |
4101 | else | |
4102 | { | |
a2dead1b | 4103 | int k = 0; |
0aacf84e | 4104 | /* Determine a common factor 2^k */ |
a2dead1b | 4105 | while (((u | v) & 1) == 0) |
0aacf84e | 4106 | { |
a2dead1b | 4107 | k++; |
0aacf84e MD |
4108 | u >>= 1; |
4109 | v >>= 1; | |
4110 | } | |
4111 | /* Now, any factor 2^n can be eliminated */ | |
a2dead1b MW |
4112 | if ((u & 1) == 0) |
4113 | while ((u & 1) == 0) | |
4114 | u >>= 1; | |
0aacf84e | 4115 | else |
a2dead1b MW |
4116 | while ((v & 1) == 0) |
4117 | v >>= 1; | |
4118 | /* Both u and v are now odd. Subtract the smaller one | |
4119 | from the larger one to produce an even number, remove | |
4120 | more factors of two, and repeat. */ | |
4121 | while (u != v) | |
0aacf84e | 4122 | { |
a2dead1b MW |
4123 | if (u > v) |
4124 | { | |
4125 | u -= v; | |
4126 | while ((u & 1) == 0) | |
4127 | u >>= 1; | |
4128 | } | |
4129 | else | |
4130 | { | |
4131 | v -= u; | |
4132 | while ((v & 1) == 0) | |
4133 | v >>= 1; | |
4134 | } | |
0aacf84e | 4135 | } |
a2dead1b | 4136 | result = u << k; |
0aacf84e MD |
4137 | } |
4138 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 4139 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4140 | : scm_i_inum2big (result)); |
ca46fb90 RB |
4141 | } |
4142 | else if (SCM_BIGP (y)) | |
4143 | { | |
0bff4dce KR |
4144 | SCM_SWAP (x, y); |
4145 | goto big_inum; | |
ca46fb90 | 4146 | } |
3bbca1f7 MW |
4147 | else if (SCM_REALP (y) && scm_is_integer (y)) |
4148 | goto handle_inexacts; | |
ca46fb90 | 4149 | else |
fa075d40 | 4150 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
f872b822 | 4151 | } |
ca46fb90 RB |
4152 | else if (SCM_BIGP (x)) |
4153 | { | |
e11e83f3 | 4154 | if (SCM_I_INUMP (y)) |
ca46fb90 | 4155 | { |
e25f3727 AW |
4156 | scm_t_bits result; |
4157 | scm_t_inum yy; | |
0bff4dce | 4158 | big_inum: |
e11e83f3 | 4159 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
4160 | if (yy == 0) |
4161 | return scm_abs (x); | |
0aacf84e MD |
4162 | if (yy < 0) |
4163 | yy = -yy; | |
ca46fb90 RB |
4164 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
4165 | scm_remember_upto_here_1 (x); | |
0aacf84e | 4166 | return (SCM_POSFIXABLE (result) |
d956fa6f | 4167 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4168 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
4169 | } |
4170 | else if (SCM_BIGP (y)) | |
4171 | { | |
4172 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
4173 | mpz_gcd (SCM_I_BIG_MPZ (result), |
4174 | SCM_I_BIG_MPZ (x), | |
4175 | SCM_I_BIG_MPZ (y)); | |
4176 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
4177 | return scm_i_normbig (result); |
4178 | } | |
3bbca1f7 MW |
4179 | else if (SCM_REALP (y) && scm_is_integer (y)) |
4180 | goto handle_inexacts; | |
4181 | else | |
4182 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
4183 | } | |
4184 | else if (SCM_REALP (x) && scm_is_integer (x)) | |
4185 | { | |
4186 | if (SCM_I_INUMP (y) || SCM_BIGP (y) | |
4187 | || (SCM_REALP (y) && scm_is_integer (y))) | |
4188 | { | |
4189 | handle_inexacts: | |
4190 | return scm_exact_to_inexact (scm_gcd (scm_inexact_to_exact (x), | |
4191 | scm_inexact_to_exact (y))); | |
4192 | } | |
ca46fb90 | 4193 | else |
fa075d40 | 4194 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
09fb7599 | 4195 | } |
ca46fb90 | 4196 | else |
fa075d40 | 4197 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
4198 | } |
4199 | ||
78d3deb1 AW |
4200 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
4201 | (SCM x, SCM y, SCM rest), | |
4202 | "Return the least common multiple of the arguments.\n" | |
4203 | "If called without arguments, 1 is returned.") | |
4204 | #define FUNC_NAME s_scm_i_lcm | |
4205 | { | |
4206 | while (!scm_is_null (rest)) | |
4207 | { x = scm_lcm (x, y); | |
4208 | y = scm_car (rest); | |
4209 | rest = scm_cdr (rest); | |
4210 | } | |
4211 | return scm_lcm (x, y); | |
4212 | } | |
4213 | #undef FUNC_NAME | |
4214 | ||
4215 | #define s_lcm s_scm_i_lcm | |
4216 | #define g_lcm g_scm_i_lcm | |
4217 | ||
0f2d19dd | 4218 | SCM |
6e8d25a6 | 4219 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4220 | { |
3bbca1f7 MW |
4221 | if (SCM_UNLIKELY (SCM_UNBNDP (n2))) |
4222 | return SCM_UNBNDP (n1) ? SCM_INUM1 : scm_abs (n1); | |
09fb7599 | 4223 | |
3bbca1f7 | 4224 | if (SCM_LIKELY (SCM_I_INUMP (n1))) |
ca46fb90 | 4225 | { |
3bbca1f7 | 4226 | if (SCM_LIKELY (SCM_I_INUMP (n2))) |
ca46fb90 RB |
4227 | { |
4228 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4229 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4230 | return d; |
4231 | else | |
4232 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4233 | } | |
3bbca1f7 | 4234 | else if (SCM_LIKELY (SCM_BIGP (n2))) |
ca46fb90 RB |
4235 | { |
4236 | /* inum n1, big n2 */ | |
4237 | inumbig: | |
4238 | { | |
4239 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4240 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4241 | if (nn1 == 0) return SCM_INUM0; |
4242 | if (nn1 < 0) nn1 = - nn1; | |
4243 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4244 | scm_remember_upto_here_1 (n2); | |
4245 | return result; | |
4246 | } | |
4247 | } | |
3bbca1f7 MW |
4248 | else if (SCM_REALP (n2) && scm_is_integer (n2)) |
4249 | goto handle_inexacts; | |
4250 | else | |
902a4e77 | 4251 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
ca46fb90 | 4252 | } |
3bbca1f7 | 4253 | else if (SCM_LIKELY (SCM_BIGP (n1))) |
ca46fb90 RB |
4254 | { |
4255 | /* big n1 */ | |
e11e83f3 | 4256 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4257 | { |
4258 | SCM_SWAP (n1, n2); | |
4259 | goto inumbig; | |
4260 | } | |
3bbca1f7 | 4261 | else if (SCM_LIKELY (SCM_BIGP (n2))) |
ca46fb90 RB |
4262 | { |
4263 | SCM result = scm_i_mkbig (); | |
4264 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4265 | SCM_I_BIG_MPZ (n1), | |
4266 | SCM_I_BIG_MPZ (n2)); | |
4267 | scm_remember_upto_here_2(n1, n2); | |
4268 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4269 | return result; | |
4270 | } | |
3bbca1f7 MW |
4271 | else if (SCM_REALP (n2) && scm_is_integer (n2)) |
4272 | goto handle_inexacts; | |
4273 | else | |
902a4e77 | 4274 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
f872b822 | 4275 | } |
3bbca1f7 MW |
4276 | else if (SCM_REALP (n1) && scm_is_integer (n1)) |
4277 | { | |
4278 | if (SCM_I_INUMP (n2) || SCM_BIGP (n2) | |
4279 | || (SCM_REALP (n2) && scm_is_integer (n2))) | |
4280 | { | |
4281 | handle_inexacts: | |
4282 | return scm_exact_to_inexact (scm_lcm (scm_inexact_to_exact (n1), | |
4283 | scm_inexact_to_exact (n2))); | |
4284 | } | |
4285 | else | |
902a4e77 | 4286 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); |
f872b822 | 4287 | } |
3bbca1f7 | 4288 | else |
902a4e77 | 4289 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG1, s_lcm); |
0f2d19dd JB |
4290 | } |
4291 | ||
8a525303 GB |
4292 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4293 | ||
4294 | Logand: | |
4295 | X Y Result Method: | |
4296 | (len) | |
4297 | + + + x (map digit:logand X Y) | |
4298 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4299 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4300 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4301 | ||
4302 | Logior: | |
4303 | X Y Result Method: | |
4304 | ||
4305 | + + + (map digit:logior X Y) | |
4306 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4307 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4308 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4309 | ||
4310 | Logxor: | |
4311 | X Y Result Method: | |
4312 | ||
4313 | + + + (map digit:logxor X Y) | |
4314 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4315 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4316 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4317 | ||
4318 | Logtest: | |
4319 | X Y Result | |
4320 | ||
4321 | + + (any digit:logand X Y) | |
4322 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4323 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4324 | - - #t | |
4325 | ||
4326 | */ | |
4327 | ||
78d3deb1 AW |
4328 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4329 | (SCM x, SCM y, SCM rest), | |
4330 | "Return the bitwise AND of the integer arguments.\n\n" | |
4331 | "@lisp\n" | |
4332 | "(logand) @result{} -1\n" | |
4333 | "(logand 7) @result{} 7\n" | |
4334 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4335 | "@end lisp") | |
4336 | #define FUNC_NAME s_scm_i_logand | |
4337 | { | |
4338 | while (!scm_is_null (rest)) | |
4339 | { x = scm_logand (x, y); | |
4340 | y = scm_car (rest); | |
4341 | rest = scm_cdr (rest); | |
4342 | } | |
4343 | return scm_logand (x, y); | |
4344 | } | |
4345 | #undef FUNC_NAME | |
4346 | ||
4347 | #define s_scm_logand s_scm_i_logand | |
4348 | ||
4349 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4350 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4351 | { |
e25f3727 | 4352 | scm_t_inum nn1; |
9a00c9fc | 4353 | |
0aacf84e MD |
4354 | if (SCM_UNBNDP (n2)) |
4355 | { | |
4356 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4357 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4358 | else if (!SCM_NUMBERP (n1)) |
4359 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4360 | else if (SCM_NUMBERP (n1)) | |
4361 | return n1; | |
4362 | else | |
4363 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4364 | } |
09fb7599 | 4365 | |
e11e83f3 | 4366 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4367 | { |
e11e83f3 MV |
4368 | nn1 = SCM_I_INUM (n1); |
4369 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4370 | { |
e25f3727 | 4371 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4372 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4373 | } |
4374 | else if SCM_BIGP (n2) | |
4375 | { | |
4376 | intbig: | |
2e16a342 | 4377 | if (nn1 == 0) |
0aacf84e MD |
4378 | return SCM_INUM0; |
4379 | { | |
4380 | SCM result_z = scm_i_mkbig (); | |
4381 | mpz_t nn1_z; | |
4382 | mpz_init_set_si (nn1_z, nn1); | |
4383 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4384 | scm_remember_upto_here_1 (n2); | |
4385 | mpz_clear (nn1_z); | |
4386 | return scm_i_normbig (result_z); | |
4387 | } | |
4388 | } | |
4389 | else | |
4390 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4391 | } | |
4392 | else if (SCM_BIGP (n1)) | |
4393 | { | |
e11e83f3 | 4394 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4395 | { |
4396 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4397 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4398 | goto intbig; |
4399 | } | |
4400 | else if (SCM_BIGP (n2)) | |
4401 | { | |
4402 | SCM result_z = scm_i_mkbig (); | |
4403 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4404 | SCM_I_BIG_MPZ (n1), | |
4405 | SCM_I_BIG_MPZ (n2)); | |
4406 | scm_remember_upto_here_2 (n1, n2); | |
4407 | return scm_i_normbig (result_z); | |
4408 | } | |
4409 | else | |
4410 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4411 | } |
0aacf84e | 4412 | else |
09fb7599 | 4413 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4414 | } |
1bbd0b84 | 4415 | #undef FUNC_NAME |
0f2d19dd | 4416 | |
09fb7599 | 4417 | |
78d3deb1 AW |
4418 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4419 | (SCM x, SCM y, SCM rest), | |
4420 | "Return the bitwise OR of the integer arguments.\n\n" | |
4421 | "@lisp\n" | |
4422 | "(logior) @result{} 0\n" | |
4423 | "(logior 7) @result{} 7\n" | |
4424 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4425 | "@end lisp") | |
4426 | #define FUNC_NAME s_scm_i_logior | |
4427 | { | |
4428 | while (!scm_is_null (rest)) | |
4429 | { x = scm_logior (x, y); | |
4430 | y = scm_car (rest); | |
4431 | rest = scm_cdr (rest); | |
4432 | } | |
4433 | return scm_logior (x, y); | |
4434 | } | |
4435 | #undef FUNC_NAME | |
4436 | ||
4437 | #define s_scm_logior s_scm_i_logior | |
4438 | ||
4439 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4440 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4441 | { |
e25f3727 | 4442 | scm_t_inum nn1; |
9a00c9fc | 4443 | |
0aacf84e MD |
4444 | if (SCM_UNBNDP (n2)) |
4445 | { | |
4446 | if (SCM_UNBNDP (n1)) | |
4447 | return SCM_INUM0; | |
4448 | else if (SCM_NUMBERP (n1)) | |
4449 | return n1; | |
4450 | else | |
4451 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4452 | } |
09fb7599 | 4453 | |
e11e83f3 | 4454 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4455 | { |
e11e83f3 MV |
4456 | nn1 = SCM_I_INUM (n1); |
4457 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4458 | { |
e11e83f3 | 4459 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4460 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4461 | } |
4462 | else if (SCM_BIGP (n2)) | |
4463 | { | |
4464 | intbig: | |
4465 | if (nn1 == 0) | |
4466 | return n2; | |
4467 | { | |
4468 | SCM result_z = scm_i_mkbig (); | |
4469 | mpz_t nn1_z; | |
4470 | mpz_init_set_si (nn1_z, nn1); | |
4471 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4472 | scm_remember_upto_here_1 (n2); | |
4473 | mpz_clear (nn1_z); | |
9806de0d | 4474 | return scm_i_normbig (result_z); |
0aacf84e MD |
4475 | } |
4476 | } | |
4477 | else | |
4478 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4479 | } | |
4480 | else if (SCM_BIGP (n1)) | |
4481 | { | |
e11e83f3 | 4482 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4483 | { |
4484 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4485 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4486 | goto intbig; |
4487 | } | |
4488 | else if (SCM_BIGP (n2)) | |
4489 | { | |
4490 | SCM result_z = scm_i_mkbig (); | |
4491 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4492 | SCM_I_BIG_MPZ (n1), | |
4493 | SCM_I_BIG_MPZ (n2)); | |
4494 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4495 | return scm_i_normbig (result_z); |
0aacf84e MD |
4496 | } |
4497 | else | |
4498 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4499 | } |
0aacf84e | 4500 | else |
09fb7599 | 4501 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4502 | } |
1bbd0b84 | 4503 | #undef FUNC_NAME |
0f2d19dd | 4504 | |
09fb7599 | 4505 | |
78d3deb1 AW |
4506 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4507 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4508 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4509 | "set in the result if it is set in an odd number of arguments.\n" | |
4510 | "@lisp\n" | |
4511 | "(logxor) @result{} 0\n" | |
4512 | "(logxor 7) @result{} 7\n" | |
4513 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4514 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4515 | "@end lisp") |
78d3deb1 AW |
4516 | #define FUNC_NAME s_scm_i_logxor |
4517 | { | |
4518 | while (!scm_is_null (rest)) | |
4519 | { x = scm_logxor (x, y); | |
4520 | y = scm_car (rest); | |
4521 | rest = scm_cdr (rest); | |
4522 | } | |
4523 | return scm_logxor (x, y); | |
4524 | } | |
4525 | #undef FUNC_NAME | |
4526 | ||
4527 | #define s_scm_logxor s_scm_i_logxor | |
4528 | ||
4529 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4530 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4531 | { |
e25f3727 | 4532 | scm_t_inum nn1; |
9a00c9fc | 4533 | |
0aacf84e MD |
4534 | if (SCM_UNBNDP (n2)) |
4535 | { | |
4536 | if (SCM_UNBNDP (n1)) | |
4537 | return SCM_INUM0; | |
4538 | else if (SCM_NUMBERP (n1)) | |
4539 | return n1; | |
4540 | else | |
4541 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4542 | } |
09fb7599 | 4543 | |
e11e83f3 | 4544 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4545 | { |
e11e83f3 MV |
4546 | nn1 = SCM_I_INUM (n1); |
4547 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4548 | { |
e25f3727 | 4549 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4550 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4551 | } |
4552 | else if (SCM_BIGP (n2)) | |
4553 | { | |
4554 | intbig: | |
4555 | { | |
4556 | SCM result_z = scm_i_mkbig (); | |
4557 | mpz_t nn1_z; | |
4558 | mpz_init_set_si (nn1_z, nn1); | |
4559 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4560 | scm_remember_upto_here_1 (n2); | |
4561 | mpz_clear (nn1_z); | |
4562 | return scm_i_normbig (result_z); | |
4563 | } | |
4564 | } | |
4565 | else | |
4566 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4567 | } | |
4568 | else if (SCM_BIGP (n1)) | |
4569 | { | |
e11e83f3 | 4570 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4571 | { |
4572 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4573 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4574 | goto intbig; |
4575 | } | |
4576 | else if (SCM_BIGP (n2)) | |
4577 | { | |
4578 | SCM result_z = scm_i_mkbig (); | |
4579 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4580 | SCM_I_BIG_MPZ (n1), | |
4581 | SCM_I_BIG_MPZ (n2)); | |
4582 | scm_remember_upto_here_2 (n1, n2); | |
4583 | return scm_i_normbig (result_z); | |
4584 | } | |
4585 | else | |
4586 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4587 | } |
0aacf84e | 4588 | else |
09fb7599 | 4589 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4590 | } |
1bbd0b84 | 4591 | #undef FUNC_NAME |
0f2d19dd | 4592 | |
09fb7599 | 4593 | |
a1ec6916 | 4594 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4595 | (SCM j, SCM k), |
ba6e7231 KR |
4596 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4597 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4598 | "without actually calculating the @code{logand}, just testing\n" | |
4599 | "for non-zero.\n" | |
4600 | "\n" | |
1e6808ea | 4601 | "@lisp\n" |
b380b885 MD |
4602 | "(logtest #b0100 #b1011) @result{} #f\n" |
4603 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4604 | "@end lisp") |
1bbd0b84 | 4605 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4606 | { |
e25f3727 | 4607 | scm_t_inum nj; |
9a00c9fc | 4608 | |
e11e83f3 | 4609 | if (SCM_I_INUMP (j)) |
0aacf84e | 4610 | { |
e11e83f3 MV |
4611 | nj = SCM_I_INUM (j); |
4612 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4613 | { |
e25f3727 | 4614 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4615 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4616 | } |
4617 | else if (SCM_BIGP (k)) | |
4618 | { | |
4619 | intbig: | |
4620 | if (nj == 0) | |
4621 | return SCM_BOOL_F; | |
4622 | { | |
4623 | SCM result; | |
4624 | mpz_t nj_z; | |
4625 | mpz_init_set_si (nj_z, nj); | |
4626 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4627 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4628 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4629 | mpz_clear (nj_z); |
4630 | return result; | |
4631 | } | |
4632 | } | |
4633 | else | |
4634 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4635 | } | |
4636 | else if (SCM_BIGP (j)) | |
4637 | { | |
e11e83f3 | 4638 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4639 | { |
4640 | SCM_SWAP (j, k); | |
e11e83f3 | 4641 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4642 | goto intbig; |
4643 | } | |
4644 | else if (SCM_BIGP (k)) | |
4645 | { | |
4646 | SCM result; | |
4647 | mpz_t result_z; | |
4648 | mpz_init (result_z); | |
4649 | mpz_and (result_z, | |
4650 | SCM_I_BIG_MPZ (j), | |
4651 | SCM_I_BIG_MPZ (k)); | |
4652 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4653 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4654 | mpz_clear (result_z); |
4655 | return result; | |
4656 | } | |
4657 | else | |
4658 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4659 | } | |
4660 | else | |
4661 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4662 | } |
1bbd0b84 | 4663 | #undef FUNC_NAME |
0f2d19dd | 4664 | |
c1bfcf60 | 4665 | |
a1ec6916 | 4666 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4667 | (SCM index, SCM j), |
ba6e7231 KR |
4668 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4669 | "@var{index} starts from 0 for the least significant bit.\n" | |
4670 | "\n" | |
1e6808ea | 4671 | "@lisp\n" |
b380b885 MD |
4672 | "(logbit? 0 #b1101) @result{} #t\n" |
4673 | "(logbit? 1 #b1101) @result{} #f\n" | |
4674 | "(logbit? 2 #b1101) @result{} #t\n" | |
4675 | "(logbit? 3 #b1101) @result{} #t\n" | |
4676 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4677 | "@end lisp") |
1bbd0b84 | 4678 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4679 | { |
78166ad5 | 4680 | unsigned long int iindex; |
5efd3c7d | 4681 | iindex = scm_to_ulong (index); |
78166ad5 | 4682 | |
e11e83f3 | 4683 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4684 | { |
4685 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4686 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4687 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4688 | } |
0aacf84e MD |
4689 | else if (SCM_BIGP (j)) |
4690 | { | |
4691 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4692 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4693 | return scm_from_bool (val); |
0aacf84e MD |
4694 | } |
4695 | else | |
78166ad5 | 4696 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4697 | } |
1bbd0b84 | 4698 | #undef FUNC_NAME |
0f2d19dd | 4699 | |
78166ad5 | 4700 | |
a1ec6916 | 4701 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4702 | (SCM n), |
4d814788 | 4703 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4704 | "argument.\n" |
4705 | "\n" | |
b380b885 MD |
4706 | "@lisp\n" |
4707 | "(number->string (lognot #b10000000) 2)\n" | |
4708 | " @result{} \"-10000001\"\n" | |
4709 | "(number->string (lognot #b0) 2)\n" | |
4710 | " @result{} \"-1\"\n" | |
1e6808ea | 4711 | "@end lisp") |
1bbd0b84 | 4712 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4713 | { |
e11e83f3 | 4714 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4715 | /* No overflow here, just need to toggle all the bits making up the inum. |
4716 | Enhancement: No need to strip the tag and add it back, could just xor | |
4717 | a block of 1 bits, if that worked with the various debug versions of | |
4718 | the SCM typedef. */ | |
e11e83f3 | 4719 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4720 | |
4721 | } else if (SCM_BIGP (n)) { | |
4722 | SCM result = scm_i_mkbig (); | |
4723 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4724 | scm_remember_upto_here_1 (n); | |
4725 | return result; | |
4726 | ||
4727 | } else { | |
4728 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4729 | } | |
0f2d19dd | 4730 | } |
1bbd0b84 | 4731 | #undef FUNC_NAME |
0f2d19dd | 4732 | |
518b7508 KR |
4733 | /* returns 0 if IN is not an integer. OUT must already be |
4734 | initialized. */ | |
4735 | static int | |
4736 | coerce_to_big (SCM in, mpz_t out) | |
4737 | { | |
4738 | if (SCM_BIGP (in)) | |
4739 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4740 | else if (SCM_I_INUMP (in)) |
4741 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4742 | else |
4743 | return 0; | |
4744 | ||
4745 | return 1; | |
4746 | } | |
4747 | ||
d885e204 | 4748 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4749 | (SCM n, SCM k, SCM m), |
4750 | "Return @var{n} raised to the integer exponent\n" | |
4751 | "@var{k}, modulo @var{m}.\n" | |
4752 | "\n" | |
4753 | "@lisp\n" | |
4754 | "(modulo-expt 2 3 5)\n" | |
4755 | " @result{} 3\n" | |
4756 | "@end lisp") | |
d885e204 | 4757 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4758 | { |
4759 | mpz_t n_tmp; | |
4760 | mpz_t k_tmp; | |
4761 | mpz_t m_tmp; | |
4762 | ||
4763 | /* There are two classes of error we might encounter -- | |
4764 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4765 | and | |
4766 | 2) wrong-type errors, which of course we'll report by calling | |
4767 | SCM_WRONG_TYPE_ARG. | |
4768 | We don't report those errors immediately, however; instead we do | |
4769 | some cleanup first. These variables tell us which error (if | |
4770 | any) we should report after cleaning up. | |
4771 | */ | |
4772 | int report_overflow = 0; | |
4773 | ||
4774 | int position_of_wrong_type = 0; | |
4775 | SCM value_of_wrong_type = SCM_INUM0; | |
4776 | ||
4777 | SCM result = SCM_UNDEFINED; | |
4778 | ||
4779 | mpz_init (n_tmp); | |
4780 | mpz_init (k_tmp); | |
4781 | mpz_init (m_tmp); | |
4782 | ||
bc36d050 | 4783 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4784 | { |
4785 | report_overflow = 1; | |
4786 | goto cleanup; | |
4787 | } | |
4788 | ||
4789 | if (!coerce_to_big (n, n_tmp)) | |
4790 | { | |
4791 | value_of_wrong_type = n; | |
4792 | position_of_wrong_type = 1; | |
4793 | goto cleanup; | |
4794 | } | |
4795 | ||
4796 | if (!coerce_to_big (k, k_tmp)) | |
4797 | { | |
4798 | value_of_wrong_type = k; | |
4799 | position_of_wrong_type = 2; | |
4800 | goto cleanup; | |
4801 | } | |
4802 | ||
4803 | if (!coerce_to_big (m, m_tmp)) | |
4804 | { | |
4805 | value_of_wrong_type = m; | |
4806 | position_of_wrong_type = 3; | |
4807 | goto cleanup; | |
4808 | } | |
4809 | ||
4810 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4811 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4812 | doesn't exist (or is not unique). Since exceptions are hard to | |
4813 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4814 | a simple failure code, which is easy to handle. */ | |
4815 | ||
4816 | if (-1 == mpz_sgn (k_tmp)) | |
4817 | { | |
4818 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4819 | { | |
4820 | report_overflow = 1; | |
4821 | goto cleanup; | |
4822 | } | |
4823 | mpz_neg (k_tmp, k_tmp); | |
4824 | } | |
4825 | ||
4826 | result = scm_i_mkbig (); | |
4827 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4828 | n_tmp, | |
4829 | k_tmp, | |
4830 | m_tmp); | |
b7b8c575 KR |
4831 | |
4832 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4833 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4834 | ||
518b7508 KR |
4835 | cleanup: |
4836 | mpz_clear (m_tmp); | |
4837 | mpz_clear (k_tmp); | |
4838 | mpz_clear (n_tmp); | |
4839 | ||
4840 | if (report_overflow) | |
4841 | scm_num_overflow (FUNC_NAME); | |
4842 | ||
4843 | if (position_of_wrong_type) | |
4844 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4845 | value_of_wrong_type); | |
4846 | ||
4847 | return scm_i_normbig (result); | |
4848 | } | |
4849 | #undef FUNC_NAME | |
4850 | ||
a1ec6916 | 4851 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4852 | (SCM n, SCM k), |
ba6e7231 KR |
4853 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4854 | "exact integer, @var{n} can be any number.\n" | |
4855 | "\n" | |
2519490c MW |
4856 | "Negative @var{k} is supported, and results in\n" |
4857 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4858 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4859 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4860 | "\n" |
b380b885 | 4861 | "@lisp\n" |
ba6e7231 KR |
4862 | "(integer-expt 2 5) @result{} 32\n" |
4863 | "(integer-expt -3 3) @result{} -27\n" | |
4864 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4865 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4866 | "@end lisp") |
1bbd0b84 | 4867 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4868 | { |
e25f3727 | 4869 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4870 | SCM z_i2 = SCM_BOOL_F; |
4871 | int i2_is_big = 0; | |
d956fa6f | 4872 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4873 | |
bfe1f03a MW |
4874 | /* Specifically refrain from checking the type of the first argument. |
4875 | This allows us to exponentiate any object that can be multiplied. | |
4876 | If we must raise to a negative power, we must also be able to | |
4877 | take its reciprocal. */ | |
4878 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4879 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4880 | |
bfe1f03a MW |
4881 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4882 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4883 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4884 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4885 | /* The next check is necessary only because R6RS specifies different | |
4886 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4887 | we simply skip this case and move on. */ | |
4888 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4889 | { | |
4890 | /* k cannot be 0 at this point, because we | |
4891 | have already checked for that case above */ | |
4892 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4893 | return n; |
4894 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4895 | return scm_nan (); | |
4896 | } | |
a285b18c MW |
4897 | else if (SCM_FRACTIONP (n)) |
4898 | { | |
4899 | /* Optimize the fraction case by (a/b)^k ==> (a^k)/(b^k), to avoid | |
4900 | needless reduction of intermediate products to lowest terms. | |
4901 | If a and b have no common factors, then a^k and b^k have no | |
4902 | common factors. Use 'scm_i_make_ratio_already_reduced' to | |
4903 | construct the final result, so that no gcd computations are | |
4904 | needed to exponentiate a fraction. */ | |
4905 | if (scm_is_true (scm_positive_p (k))) | |
4906 | return scm_i_make_ratio_already_reduced | |
4907 | (scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k), | |
4908 | scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k)); | |
4909 | else | |
4910 | { | |
4911 | k = scm_difference (k, SCM_UNDEFINED); | |
4912 | return scm_i_make_ratio_already_reduced | |
4913 | (scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k), | |
4914 | scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k)); | |
4915 | } | |
4916 | } | |
ca46fb90 | 4917 | |
e11e83f3 MV |
4918 | if (SCM_I_INUMP (k)) |
4919 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4920 | else if (SCM_BIGP (k)) |
4921 | { | |
4922 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4923 | scm_remember_upto_here_1 (k); |
4924 | i2_is_big = 1; | |
4925 | } | |
2830fd91 | 4926 | else |
ca46fb90 RB |
4927 | SCM_WRONG_TYPE_ARG (2, k); |
4928 | ||
4929 | if (i2_is_big) | |
f872b822 | 4930 | { |
ca46fb90 RB |
4931 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4932 | { | |
4933 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4934 | n = scm_divide (n, SCM_UNDEFINED); | |
4935 | } | |
4936 | while (1) | |
4937 | { | |
4938 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4939 | { | |
ca46fb90 RB |
4940 | return acc; |
4941 | } | |
4942 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4943 | { | |
ca46fb90 RB |
4944 | return scm_product (acc, n); |
4945 | } | |
4946 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4947 | acc = scm_product (acc, n); | |
4948 | n = scm_product (n, n); | |
4949 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4950 | } | |
f872b822 | 4951 | } |
ca46fb90 | 4952 | else |
f872b822 | 4953 | { |
ca46fb90 RB |
4954 | if (i2 < 0) |
4955 | { | |
4956 | i2 = -i2; | |
4957 | n = scm_divide (n, SCM_UNDEFINED); | |
4958 | } | |
4959 | while (1) | |
4960 | { | |
4961 | if (0 == i2) | |
4962 | return acc; | |
4963 | if (1 == i2) | |
4964 | return scm_product (acc, n); | |
4965 | if (i2 & 1) | |
4966 | acc = scm_product (acc, n); | |
4967 | n = scm_product (n, n); | |
4968 | i2 >>= 1; | |
4969 | } | |
f872b822 | 4970 | } |
0f2d19dd | 4971 | } |
1bbd0b84 | 4972 | #undef FUNC_NAME |
0f2d19dd | 4973 | |
e08a12b5 MW |
4974 | /* Efficiently compute (N * 2^COUNT), |
4975 | where N is an exact integer, and COUNT > 0. */ | |
4976 | static SCM | |
4977 | left_shift_exact_integer (SCM n, long count) | |
4978 | { | |
4979 | if (SCM_I_INUMP (n)) | |
4980 | { | |
4981 | scm_t_inum nn = SCM_I_INUM (n); | |
4982 | ||
4983 | /* Left shift of count >= SCM_I_FIXNUM_BIT-1 will always | |
4984 | overflow a non-zero fixnum. For smaller shifts we check the | |
4985 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4986 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4987 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". */ | |
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); | |
5000 | return result; | |
5001 | } | |
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 | |
5011 | scm_syserror ("left_shift_exact_integer"); | |
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 | |
5037 | scm_syserror ("floor_right_shift_exact_integer"); | |
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 | |
5075 | scm_syserror ("round_right_shift_exact_integer"); | |
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 | { |
1ea37620 MW |
5357 | if (!double_is_non_negative_zero (dbl)) |
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. */ | |
5569 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
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 | { | |
5804 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5805 | that's certainly above any valid decimal, so we take advantage of | |
5806 | that to elide some tests. */ | |
5807 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5808 | ||
5809 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5810 | hexadecimals. */ | |
5811 | if (d >= 10U) | |
5812 | { | |
5813 | c = uc_tolower (c); | |
5814 | if (c >= (scm_t_uint32) 'a') | |
5815 | d = c - (scm_t_uint32)'a' + 10U; | |
5816 | } | |
5817 | return d; | |
5818 | } | |
3c9a524f | 5819 | |
91db4a37 LC |
5820 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5821 | in base RADIX. Upon success, return the unsigned integer and update | |
5822 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5823 | static SCM |
3f47e526 | 5824 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5825 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5826 | { |
3c9a524f DH |
5827 | unsigned int idx = *p_idx; |
5828 | unsigned int hash_seen = 0; | |
5829 | scm_t_bits shift = 1; | |
5830 | scm_t_bits add = 0; | |
5831 | unsigned int digit_value; | |
5832 | SCM result; | |
5833 | char c; | |
3f47e526 | 5834 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5835 | |
5836 | if (idx == len) | |
5837 | return SCM_BOOL_F; | |
2a8fecee | 5838 | |
3f47e526 | 5839 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5840 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5841 | if (digit_value >= radix) |
5842 | return SCM_BOOL_F; | |
5843 | ||
5844 | idx++; | |
d956fa6f | 5845 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5846 | while (idx != len) |
f872b822 | 5847 | { |
3f47e526 | 5848 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5849 | if (c == '#') |
3c9a524f DH |
5850 | { |
5851 | hash_seen = 1; | |
5852 | digit_value = 0; | |
5853 | } | |
a6f3af16 AW |
5854 | else if (hash_seen) |
5855 | break; | |
3c9a524f | 5856 | else |
a6f3af16 AW |
5857 | { |
5858 | digit_value = char_decimal_value (c); | |
5859 | /* This check catches non-decimals in addition to out-of-range | |
5860 | decimals. */ | |
5861 | if (digit_value >= radix) | |
5862 | break; | |
5863 | } | |
3c9a524f DH |
5864 | |
5865 | idx++; | |
5866 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5867 | { | |
d956fa6f | 5868 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5869 | if (add > 0) |
d956fa6f | 5870 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5871 | |
5872 | shift = radix; | |
5873 | add = digit_value; | |
5874 | } | |
5875 | else | |
5876 | { | |
5877 | shift = shift * radix; | |
5878 | add = add * radix + digit_value; | |
5879 | } | |
5880 | }; | |
5881 | ||
5882 | if (shift > 1) | |
d956fa6f | 5883 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5884 | if (add > 0) |
d956fa6f | 5885 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5886 | |
5887 | *p_idx = idx; | |
5888 | if (hash_seen) | |
5889 | *p_exactness = INEXACT; | |
5890 | ||
5891 | return result; | |
2a8fecee JB |
5892 | } |
5893 | ||
5894 | ||
3c9a524f DH |
5895 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5896 | * covers the parts of the rules that start at a potential point. The value | |
5897 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5898 | * in variable result. The content of *p_exactness indicates, whether a hash |
5899 | * has already been seen in the digits before the point. | |
3c9a524f | 5900 | */ |
1cc91f1b | 5901 | |
3f47e526 | 5902 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5903 | |
5904 | static SCM | |
3f47e526 | 5905 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5906 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5907 | { |
3c9a524f DH |
5908 | unsigned int idx = *p_idx; |
5909 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5910 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5911 | |
5912 | if (idx == len) | |
79d34f68 | 5913 | return result; |
3c9a524f | 5914 | |
3f47e526 | 5915 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5916 | { |
5917 | scm_t_bits shift = 1; | |
5918 | scm_t_bits add = 0; | |
5919 | unsigned int digit_value; | |
cff5fa33 | 5920 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5921 | |
5922 | idx++; | |
5923 | while (idx != len) | |
5924 | { | |
3f47e526 MG |
5925 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5926 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5927 | { |
5928 | if (x == INEXACT) | |
5929 | return SCM_BOOL_F; | |
5930 | else | |
5931 | digit_value = DIGIT2UINT (c); | |
5932 | } | |
5933 | else if (c == '#') | |
5934 | { | |
5935 | x = INEXACT; | |
5936 | digit_value = 0; | |
5937 | } | |
5938 | else | |
5939 | break; | |
5940 | ||
5941 | idx++; | |
5942 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5943 | { | |
d956fa6f MV |
5944 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5945 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5946 | if (add > 0) |
d956fa6f | 5947 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5948 | |
5949 | shift = 10; | |
5950 | add = digit_value; | |
5951 | } | |
5952 | else | |
5953 | { | |
5954 | shift = shift * 10; | |
5955 | add = add * 10 + digit_value; | |
5956 | } | |
5957 | }; | |
5958 | ||
5959 | if (add > 0) | |
5960 | { | |
d956fa6f MV |
5961 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5962 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5963 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5964 | } |
5965 | ||
d8592269 | 5966 | result = scm_divide (result, big_shift); |
79d34f68 | 5967 | |
3c9a524f DH |
5968 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5969 | x = INEXACT; | |
f872b822 | 5970 | } |
3c9a524f | 5971 | |
3c9a524f | 5972 | if (idx != len) |
f872b822 | 5973 | { |
3c9a524f DH |
5974 | int sign = 1; |
5975 | unsigned int start; | |
3f47e526 | 5976 | scm_t_wchar c; |
3c9a524f DH |
5977 | int exponent; |
5978 | SCM e; | |
5979 | ||
5980 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5981 | ||
3f47e526 | 5982 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5983 | { |
3c9a524f DH |
5984 | case 'd': case 'D': |
5985 | case 'e': case 'E': | |
5986 | case 'f': case 'F': | |
5987 | case 'l': case 'L': | |
5988 | case 's': case 'S': | |
5989 | idx++; | |
ee0ddd21 AW |
5990 | if (idx == len) |
5991 | return SCM_BOOL_F; | |
5992 | ||
3c9a524f | 5993 | start = idx; |
3f47e526 | 5994 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5995 | if (c == '-') |
5996 | { | |
5997 | idx++; | |
ee0ddd21 AW |
5998 | if (idx == len) |
5999 | return SCM_BOOL_F; | |
6000 | ||
3c9a524f | 6001 | sign = -1; |
3f47e526 | 6002 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6003 | } |
6004 | else if (c == '+') | |
6005 | { | |
6006 | idx++; | |
ee0ddd21 AW |
6007 | if (idx == len) |
6008 | return SCM_BOOL_F; | |
6009 | ||
3c9a524f | 6010 | sign = 1; |
3f47e526 | 6011 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6012 | } |
6013 | else | |
6014 | sign = 1; | |
6015 | ||
3f47e526 | 6016 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
6017 | return SCM_BOOL_F; |
6018 | ||
6019 | idx++; | |
6020 | exponent = DIGIT2UINT (c); | |
6021 | while (idx != len) | |
f872b822 | 6022 | { |
3f47e526 MG |
6023 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
6024 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
6025 | { |
6026 | idx++; | |
6027 | if (exponent <= SCM_MAXEXP) | |
6028 | exponent = exponent * 10 + DIGIT2UINT (c); | |
6029 | } | |
6030 | else | |
6031 | break; | |
f872b822 | 6032 | } |
3c9a524f | 6033 | |
1ea37620 | 6034 | if (exponent > ((sign == 1) ? SCM_MAXEXP : SCM_MAXEXP + DBL_DIG + 1)) |
f872b822 | 6035 | { |
3c9a524f | 6036 | size_t exp_len = idx - start; |
3f47e526 | 6037 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
6038 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
6039 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 6040 | } |
3c9a524f | 6041 | |
d956fa6f | 6042 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
6043 | if (sign == 1) |
6044 | result = scm_product (result, e); | |
6045 | else | |
6ebecdeb | 6046 | result = scm_divide (result, e); |
3c9a524f DH |
6047 | |
6048 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
6049 | x = INEXACT; | |
6050 | ||
f872b822 | 6051 | break; |
3c9a524f | 6052 | |
f872b822 | 6053 | default: |
3c9a524f | 6054 | break; |
f872b822 | 6055 | } |
0f2d19dd | 6056 | } |
3c9a524f DH |
6057 | |
6058 | *p_idx = idx; | |
6059 | if (x == INEXACT) | |
6060 | *p_exactness = x; | |
6061 | ||
6062 | return result; | |
0f2d19dd | 6063 | } |
0f2d19dd | 6064 | |
3c9a524f DH |
6065 | |
6066 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
6067 | ||
6068 | static SCM | |
3f47e526 | 6069 | mem2ureal (SCM mem, unsigned int *p_idx, |
929d11b2 MW |
6070 | unsigned int radix, enum t_exactness forced_x, |
6071 | int allow_inf_or_nan) | |
0f2d19dd | 6072 | { |
3c9a524f | 6073 | unsigned int idx = *p_idx; |
164d2481 | 6074 | SCM result; |
3f47e526 | 6075 | size_t len = scm_i_string_length (mem); |
3c9a524f | 6076 | |
40f89215 NJ |
6077 | /* Start off believing that the number will be exact. This changes |
6078 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 6079 | enum t_exactness implicit_x = EXACT; |
40f89215 | 6080 | |
3c9a524f DH |
6081 | if (idx == len) |
6082 | return SCM_BOOL_F; | |
6083 | ||
929d11b2 MW |
6084 | if (allow_inf_or_nan && forced_x != EXACT && idx+5 <= len) |
6085 | switch (scm_i_string_ref (mem, idx)) | |
6086 | { | |
6087 | case 'i': case 'I': | |
6088 | switch (scm_i_string_ref (mem, idx + 1)) | |
6089 | { | |
6090 | case 'n': case 'N': | |
6091 | switch (scm_i_string_ref (mem, idx + 2)) | |
6092 | { | |
6093 | case 'f': case 'F': | |
6094 | if (scm_i_string_ref (mem, idx + 3) == '.' | |
6095 | && scm_i_string_ref (mem, idx + 4) == '0') | |
6096 | { | |
6097 | *p_idx = idx+5; | |
6098 | return scm_inf (); | |
6099 | } | |
6100 | } | |
6101 | } | |
6102 | case 'n': case 'N': | |
6103 | switch (scm_i_string_ref (mem, idx + 1)) | |
6104 | { | |
6105 | case 'a': case 'A': | |
6106 | switch (scm_i_string_ref (mem, idx + 2)) | |
6107 | { | |
6108 | case 'n': case 'N': | |
6109 | if (scm_i_string_ref (mem, idx + 3) == '.') | |
6110 | { | |
6111 | /* Cobble up the fractional part. We might want to | |
6112 | set the NaN's mantissa from it. */ | |
6113 | idx += 4; | |
6114 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), | |
6115 | SCM_INUM0)) | |
6116 | { | |
5f237d6e | 6117 | #if SCM_ENABLE_DEPRECATED == 1 |
929d11b2 MW |
6118 | scm_c_issue_deprecation_warning |
6119 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5f237d6e | 6120 | #else |
929d11b2 | 6121 | return SCM_BOOL_F; |
5f237d6e | 6122 | #endif |
929d11b2 | 6123 | } |
5f237d6e | 6124 | |
929d11b2 MW |
6125 | *p_idx = idx; |
6126 | return scm_nan (); | |
6127 | } | |
6128 | } | |
6129 | } | |
6130 | } | |
7351e207 | 6131 | |
3f47e526 | 6132 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
6133 | { |
6134 | if (radix != 10) | |
6135 | return SCM_BOOL_F; | |
6136 | else if (idx + 1 == len) | |
6137 | return SCM_BOOL_F; | |
3f47e526 | 6138 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
6139 | return SCM_BOOL_F; |
6140 | else | |
cff5fa33 | 6141 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 6142 | p_idx, &implicit_x); |
f872b822 | 6143 | } |
3c9a524f DH |
6144 | else |
6145 | { | |
3c9a524f | 6146 | SCM uinteger; |
3c9a524f | 6147 | |
9d427b2c | 6148 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 6149 | if (scm_is_false (uinteger)) |
3c9a524f DH |
6150 | return SCM_BOOL_F; |
6151 | ||
6152 | if (idx == len) | |
6153 | result = uinteger; | |
3f47e526 | 6154 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 6155 | { |
3c9a524f DH |
6156 | SCM divisor; |
6157 | ||
6158 | idx++; | |
ee0ddd21 AW |
6159 | if (idx == len) |
6160 | return SCM_BOOL_F; | |
3c9a524f | 6161 | |
9d427b2c | 6162 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
929d11b2 | 6163 | if (scm_is_false (divisor) || scm_is_eq (divisor, SCM_INUM0)) |
3c9a524f DH |
6164 | return SCM_BOOL_F; |
6165 | ||
f92e85f7 | 6166 | /* both are int/big here, I assume */ |
cba42c93 | 6167 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 6168 | } |
3c9a524f DH |
6169 | else if (radix == 10) |
6170 | { | |
9d427b2c | 6171 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 6172 | if (scm_is_false (result)) |
3c9a524f DH |
6173 | return SCM_BOOL_F; |
6174 | } | |
6175 | else | |
6176 | result = uinteger; | |
6177 | ||
6178 | *p_idx = idx; | |
f872b822 | 6179 | } |
164d2481 | 6180 | |
9d427b2c MW |
6181 | switch (forced_x) |
6182 | { | |
6183 | case EXACT: | |
6184 | if (SCM_INEXACTP (result)) | |
6185 | return scm_inexact_to_exact (result); | |
6186 | else | |
6187 | return result; | |
6188 | case INEXACT: | |
6189 | if (SCM_INEXACTP (result)) | |
6190 | return result; | |
6191 | else | |
6192 | return scm_exact_to_inexact (result); | |
6193 | case NO_EXACTNESS: | |
6194 | if (implicit_x == INEXACT) | |
6195 | { | |
6196 | if (SCM_INEXACTP (result)) | |
6197 | return result; | |
6198 | else | |
6199 | return scm_exact_to_inexact (result); | |
6200 | } | |
6201 | else | |
6202 | return result; | |
6203 | } | |
164d2481 | 6204 | |
9d427b2c MW |
6205 | /* We should never get here */ |
6206 | scm_syserror ("mem2ureal"); | |
3c9a524f | 6207 | } |
0f2d19dd | 6208 | |
0f2d19dd | 6209 | |
3c9a524f | 6210 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 6211 | |
3c9a524f | 6212 | static SCM |
3f47e526 | 6213 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 6214 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 6215 | { |
3f47e526 | 6216 | scm_t_wchar c; |
3c9a524f DH |
6217 | int sign = 0; |
6218 | SCM ureal; | |
3f47e526 | 6219 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6220 | |
6221 | if (idx == len) | |
6222 | return SCM_BOOL_F; | |
6223 | ||
3f47e526 | 6224 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6225 | if (c == '+') |
6226 | { | |
6227 | idx++; | |
6228 | sign = 1; | |
6229 | } | |
6230 | else if (c == '-') | |
6231 | { | |
6232 | idx++; | |
6233 | sign = -1; | |
0f2d19dd | 6234 | } |
0f2d19dd | 6235 | |
3c9a524f DH |
6236 | if (idx == len) |
6237 | return SCM_BOOL_F; | |
6238 | ||
929d11b2 | 6239 | ureal = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6240 | if (scm_is_false (ureal)) |
f872b822 | 6241 | { |
3c9a524f DH |
6242 | /* input must be either +i or -i */ |
6243 | ||
6244 | if (sign == 0) | |
6245 | return SCM_BOOL_F; | |
6246 | ||
3f47e526 MG |
6247 | if (scm_i_string_ref (mem, idx) == 'i' |
6248 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 6249 | { |
3c9a524f DH |
6250 | idx++; |
6251 | if (idx != len) | |
6252 | return SCM_BOOL_F; | |
6253 | ||
cff5fa33 | 6254 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 6255 | } |
3c9a524f DH |
6256 | else |
6257 | return SCM_BOOL_F; | |
0f2d19dd | 6258 | } |
3c9a524f DH |
6259 | else |
6260 | { | |
73e4de09 | 6261 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 6262 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 6263 | |
3c9a524f DH |
6264 | if (idx == len) |
6265 | return ureal; | |
6266 | ||
3f47e526 | 6267 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 6268 | switch (c) |
f872b822 | 6269 | { |
3c9a524f DH |
6270 | case 'i': case 'I': |
6271 | /* either +<ureal>i or -<ureal>i */ | |
6272 | ||
6273 | idx++; | |
6274 | if (sign == 0) | |
6275 | return SCM_BOOL_F; | |
6276 | if (idx != len) | |
6277 | return SCM_BOOL_F; | |
cff5fa33 | 6278 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
6279 | |
6280 | case '@': | |
6281 | /* polar input: <real>@<real>. */ | |
6282 | ||
6283 | idx++; | |
6284 | if (idx == len) | |
6285 | return SCM_BOOL_F; | |
6286 | else | |
f872b822 | 6287 | { |
3c9a524f DH |
6288 | int sign; |
6289 | SCM angle; | |
6290 | SCM result; | |
6291 | ||
3f47e526 | 6292 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6293 | if (c == '+') |
6294 | { | |
6295 | idx++; | |
ee0ddd21 AW |
6296 | if (idx == len) |
6297 | return SCM_BOOL_F; | |
3c9a524f DH |
6298 | sign = 1; |
6299 | } | |
6300 | else if (c == '-') | |
6301 | { | |
6302 | idx++; | |
ee0ddd21 AW |
6303 | if (idx == len) |
6304 | return SCM_BOOL_F; | |
3c9a524f DH |
6305 | sign = -1; |
6306 | } | |
6307 | else | |
929d11b2 | 6308 | sign = 0; |
3c9a524f | 6309 | |
929d11b2 | 6310 | angle = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6311 | if (scm_is_false (angle)) |
3c9a524f DH |
6312 | return SCM_BOOL_F; |
6313 | if (idx != len) | |
6314 | return SCM_BOOL_F; | |
6315 | ||
73e4de09 | 6316 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
6317 | angle = scm_difference (angle, SCM_UNDEFINED); |
6318 | ||
6319 | result = scm_make_polar (ureal, angle); | |
6320 | return result; | |
f872b822 | 6321 | } |
3c9a524f DH |
6322 | case '+': |
6323 | case '-': | |
6324 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 6325 | |
3c9a524f DH |
6326 | idx++; |
6327 | if (idx == len) | |
6328 | return SCM_BOOL_F; | |
6329 | else | |
6330 | { | |
6331 | int sign = (c == '+') ? 1 : -1; | |
929d11b2 | 6332 | SCM imag = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
0f2d19dd | 6333 | |
73e4de09 | 6334 | if (scm_is_false (imag)) |
d956fa6f | 6335 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 6336 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 6337 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 6338 | |
3c9a524f DH |
6339 | if (idx == len) |
6340 | return SCM_BOOL_F; | |
3f47e526 MG |
6341 | if (scm_i_string_ref (mem, idx) != 'i' |
6342 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 6343 | return SCM_BOOL_F; |
0f2d19dd | 6344 | |
3c9a524f DH |
6345 | idx++; |
6346 | if (idx != len) | |
6347 | return SCM_BOOL_F; | |
0f2d19dd | 6348 | |
1fe5e088 | 6349 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6350 | } |
6351 | default: | |
6352 | return SCM_BOOL_F; | |
6353 | } | |
6354 | } | |
0f2d19dd | 6355 | } |
0f2d19dd JB |
6356 | |
6357 | ||
3c9a524f DH |
6358 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6359 | ||
6360 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6361 | |
0f2d19dd | 6362 | SCM |
3f47e526 | 6363 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6364 | { |
3c9a524f DH |
6365 | unsigned int idx = 0; |
6366 | unsigned int radix = NO_RADIX; | |
6367 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6368 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6369 | |
6370 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6371 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6372 | { |
3f47e526 | 6373 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6374 | { |
6375 | case 'b': case 'B': | |
6376 | if (radix != NO_RADIX) | |
6377 | return SCM_BOOL_F; | |
6378 | radix = DUAL; | |
6379 | break; | |
6380 | case 'd': case 'D': | |
6381 | if (radix != NO_RADIX) | |
6382 | return SCM_BOOL_F; | |
6383 | radix = DEC; | |
6384 | break; | |
6385 | case 'i': case 'I': | |
6386 | if (forced_x != NO_EXACTNESS) | |
6387 | return SCM_BOOL_F; | |
6388 | forced_x = INEXACT; | |
6389 | break; | |
6390 | case 'e': case 'E': | |
6391 | if (forced_x != NO_EXACTNESS) | |
6392 | return SCM_BOOL_F; | |
6393 | forced_x = EXACT; | |
6394 | break; | |
6395 | case 'o': case 'O': | |
6396 | if (radix != NO_RADIX) | |
6397 | return SCM_BOOL_F; | |
6398 | radix = OCT; | |
6399 | break; | |
6400 | case 'x': case 'X': | |
6401 | if (radix != NO_RADIX) | |
6402 | return SCM_BOOL_F; | |
6403 | radix = HEX; | |
6404 | break; | |
6405 | default: | |
f872b822 | 6406 | return SCM_BOOL_F; |
3c9a524f DH |
6407 | } |
6408 | idx += 2; | |
6409 | } | |
6410 | ||
6411 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6412 | if (radix == NO_RADIX) | |
9d427b2c | 6413 | radix = default_radix; |
f872b822 | 6414 | |
9d427b2c | 6415 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6416 | } |
6417 | ||
3f47e526 MG |
6418 | SCM |
6419 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6420 | unsigned int default_radix) | |
6421 | { | |
6422 | SCM str = scm_from_locale_stringn (mem, len); | |
6423 | ||
6424 | return scm_i_string_to_number (str, default_radix); | |
6425 | } | |
6426 | ||
0f2d19dd | 6427 | |
a1ec6916 | 6428 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6429 | (SCM string, SCM radix), |
1e6808ea | 6430 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6431 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6432 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6433 | "is a default radix that may be overridden by an explicit radix\n" | |
6434 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6435 | "supplied, then the default radix is 10. If string is not a\n" | |
6436 | "syntactically valid notation for a number, then\n" | |
6437 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6438 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6439 | { |
6440 | SCM answer; | |
5efd3c7d | 6441 | unsigned int base; |
a6d9e5ab | 6442 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6443 | |
6444 | if (SCM_UNBNDP (radix)) | |
6445 | base = 10; | |
6446 | else | |
6447 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6448 | ||
3f47e526 | 6449 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6450 | scm_remember_upto_here_1 (string); |
6451 | return answer; | |
0f2d19dd | 6452 | } |
1bbd0b84 | 6453 | #undef FUNC_NAME |
3c9a524f DH |
6454 | |
6455 | ||
0f2d19dd JB |
6456 | /*** END strs->nums ***/ |
6457 | ||
5986c47d | 6458 | |
8507ec80 MV |
6459 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6460 | (SCM x), | |
6461 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6462 | "otherwise.") | |
6463 | #define FUNC_NAME s_scm_number_p | |
6464 | { | |
6465 | return scm_from_bool (SCM_NUMBERP (x)); | |
6466 | } | |
6467 | #undef FUNC_NAME | |
6468 | ||
6469 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6470 | (SCM x), |
942e5b91 | 6471 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6472 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6473 | "values form subsets of the set of complex numbers, i. e. the\n" |
6474 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6475 | "rational or integer number.") | |
8507ec80 | 6476 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6477 | { |
8507ec80 MV |
6478 | /* all numbers are complex. */ |
6479 | return scm_number_p (x); | |
0f2d19dd | 6480 | } |
1bbd0b84 | 6481 | #undef FUNC_NAME |
0f2d19dd | 6482 | |
f92e85f7 MV |
6483 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6484 | (SCM x), | |
6485 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6486 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6487 | "the set of real numbers, i. e. the predicate will also be\n" | |
6488 | "fulfilled if @var{x} is an integer number.") | |
6489 | #define FUNC_NAME s_scm_real_p | |
6490 | { | |
c960e556 MW |
6491 | return scm_from_bool |
6492 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6493 | } |
6494 | #undef FUNC_NAME | |
6495 | ||
6496 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6497 | (SCM x), |
942e5b91 | 6498 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6499 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6500 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6501 | "fulfilled if @var{x} is an integer number.") |
6502 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6503 | { |
c960e556 | 6504 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6505 | return SCM_BOOL_T; |
6506 | else if (SCM_REALP (x)) | |
c960e556 MW |
6507 | /* due to their limited precision, finite floating point numbers are |
6508 | rational as well. (finite means neither infinity nor a NaN) */ | |
6509 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6510 | else |
bb628794 | 6511 | return SCM_BOOL_F; |
0f2d19dd | 6512 | } |
1bbd0b84 | 6513 | #undef FUNC_NAME |
0f2d19dd | 6514 | |
a1ec6916 | 6515 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6516 | (SCM x), |
942e5b91 MG |
6517 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6518 | "else.") | |
1bbd0b84 | 6519 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6520 | { |
c960e556 | 6521 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6522 | return SCM_BOOL_T; |
c960e556 MW |
6523 | else if (SCM_REALP (x)) |
6524 | { | |
6525 | double val = SCM_REAL_VALUE (x); | |
6526 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6527 | } | |
6528 | else | |
8e43ed5d | 6529 | return SCM_BOOL_F; |
0f2d19dd | 6530 | } |
1bbd0b84 | 6531 | #undef FUNC_NAME |
0f2d19dd JB |
6532 | |
6533 | ||
8a1f4f98 AW |
6534 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6535 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6536 | (SCM x, SCM y, SCM rest), | |
6537 | "Return @code{#t} if all parameters are numerically equal.") | |
6538 | #define FUNC_NAME s_scm_i_num_eq_p | |
6539 | { | |
6540 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6541 | return SCM_BOOL_T; | |
6542 | while (!scm_is_null (rest)) | |
6543 | { | |
6544 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6545 | return SCM_BOOL_F; | |
6546 | x = y; | |
6547 | y = scm_car (rest); | |
6548 | rest = scm_cdr (rest); | |
6549 | } | |
6550 | return scm_num_eq_p (x, y); | |
6551 | } | |
6552 | #undef FUNC_NAME | |
0f2d19dd | 6553 | SCM |
6e8d25a6 | 6554 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6555 | { |
d8b95e27 | 6556 | again: |
e11e83f3 | 6557 | if (SCM_I_INUMP (x)) |
0aacf84e | 6558 | { |
e25f3727 | 6559 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6560 | if (SCM_I_INUMP (y)) |
0aacf84e | 6561 | { |
e25f3727 | 6562 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6563 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6564 | } |
6565 | else if (SCM_BIGP (y)) | |
6566 | return SCM_BOOL_F; | |
6567 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6568 | { |
6569 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6570 | to a double and compare. | |
6571 | ||
6572 | But on a 64-bit system an inum is bigger than a double and | |
01329288 MW |
6573 | casting it to a double (call that dxx) will round. |
6574 | Although dxx will not in general be equal to xx, dxx will | |
6575 | always be an integer and within a factor of 2 of xx, so if | |
6576 | dxx==yy, we know that yy is an integer and fits in | |
6577 | scm_t_signed_bits. So we cast yy to scm_t_signed_bits and | |
e8c5b1f2 KR |
6578 | compare with plain xx. |
6579 | ||
6580 | An alternative (for any size system actually) would be to check | |
6581 | yy is an integer (with floor) and is in range of an inum | |
6582 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6583 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6584 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6585 | |
6586 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6587 | return scm_from_bool ((double) xx == yy |
6588 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6589 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6590 | } |
0aacf84e | 6591 | else if (SCM_COMPLEXP (y)) |
01329288 MW |
6592 | { |
6593 | /* see comments with inum/real above */ | |
6594 | double ry = SCM_COMPLEX_REAL (y); | |
6595 | return scm_from_bool ((double) xx == ry | |
6596 | && 0.0 == SCM_COMPLEX_IMAG (y) | |
6597 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
6598 | || xx == (scm_t_signed_bits) ry)); | |
6599 | } | |
f92e85f7 MV |
6600 | else if (SCM_FRACTIONP (y)) |
6601 | return SCM_BOOL_F; | |
0aacf84e | 6602 | else |
fa075d40 AW |
6603 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6604 | s_scm_i_num_eq_p); | |
f872b822 | 6605 | } |
0aacf84e MD |
6606 | else if (SCM_BIGP (x)) |
6607 | { | |
e11e83f3 | 6608 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6609 | return SCM_BOOL_F; |
6610 | else if (SCM_BIGP (y)) | |
6611 | { | |
6612 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6613 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6614 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6615 | } |
6616 | else if (SCM_REALP (y)) | |
6617 | { | |
6618 | int cmp; | |
2e65b52f | 6619 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6620 | return SCM_BOOL_F; |
6621 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6622 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6623 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6624 | } |
6625 | else if (SCM_COMPLEXP (y)) | |
6626 | { | |
6627 | int cmp; | |
6628 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6629 | return SCM_BOOL_F; | |
2e65b52f | 6630 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6631 | return SCM_BOOL_F; |
6632 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6633 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6634 | return scm_from_bool (0 == cmp); |
0aacf84e | 6635 | } |
f92e85f7 MV |
6636 | else if (SCM_FRACTIONP (y)) |
6637 | return SCM_BOOL_F; | |
0aacf84e | 6638 | else |
fa075d40 AW |
6639 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6640 | s_scm_i_num_eq_p); | |
f4c627b3 | 6641 | } |
0aacf84e MD |
6642 | else if (SCM_REALP (x)) |
6643 | { | |
e8c5b1f2 | 6644 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6645 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6646 | { |
6647 | /* see comments with inum/real above */ | |
e25f3727 | 6648 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6649 | return scm_from_bool (xx == (double) yy |
6650 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6651 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6652 | } |
0aacf84e MD |
6653 | else if (SCM_BIGP (y)) |
6654 | { | |
6655 | int cmp; | |
01329288 | 6656 | if (isnan (xx)) |
0aacf84e | 6657 | return SCM_BOOL_F; |
01329288 | 6658 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); |
0aacf84e | 6659 | scm_remember_upto_here_1 (y); |
73e4de09 | 6660 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6661 | } |
6662 | else if (SCM_REALP (y)) | |
01329288 | 6663 | return scm_from_bool (xx == SCM_REAL_VALUE (y)); |
0aacf84e | 6664 | else if (SCM_COMPLEXP (y)) |
01329288 MW |
6665 | return scm_from_bool ((xx == SCM_COMPLEX_REAL (y)) |
6666 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
f92e85f7 | 6667 | else if (SCM_FRACTIONP (y)) |
d8b95e27 | 6668 | { |
01329288 | 6669 | if (isnan (xx) || isinf (xx)) |
d8b95e27 | 6670 | return SCM_BOOL_F; |
d8b95e27 KR |
6671 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6672 | goto again; | |
6673 | } | |
0aacf84e | 6674 | else |
fa075d40 AW |
6675 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6676 | s_scm_i_num_eq_p); | |
f872b822 | 6677 | } |
0aacf84e MD |
6678 | else if (SCM_COMPLEXP (x)) |
6679 | { | |
e11e83f3 | 6680 | if (SCM_I_INUMP (y)) |
01329288 MW |
6681 | { |
6682 | /* see comments with inum/real above */ | |
6683 | double rx = SCM_COMPLEX_REAL (x); | |
6684 | scm_t_signed_bits yy = SCM_I_INUM (y); | |
6685 | return scm_from_bool (rx == (double) yy | |
6686 | && 0.0 == SCM_COMPLEX_IMAG (x) | |
6687 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
6688 | || (scm_t_signed_bits) rx == yy)); | |
6689 | } | |
0aacf84e MD |
6690 | else if (SCM_BIGP (y)) |
6691 | { | |
6692 | int cmp; | |
6693 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6694 | return SCM_BOOL_F; | |
2e65b52f | 6695 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6696 | return SCM_BOOL_F; |
6697 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6698 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6699 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6700 | } |
6701 | else if (SCM_REALP (y)) | |
73e4de09 | 6702 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
01329288 | 6703 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
0aacf84e | 6704 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6705 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
01329288 | 6706 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6707 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6708 | { |
6709 | double xx; | |
6710 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6711 | return SCM_BOOL_F; | |
6712 | xx = SCM_COMPLEX_REAL (x); | |
01329288 | 6713 | if (isnan (xx) || isinf (xx)) |
d8b95e27 | 6714 | return SCM_BOOL_F; |
d8b95e27 KR |
6715 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6716 | goto again; | |
6717 | } | |
f92e85f7 | 6718 | else |
fa075d40 AW |
6719 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6720 | s_scm_i_num_eq_p); | |
f92e85f7 MV |
6721 | } |
6722 | else if (SCM_FRACTIONP (x)) | |
6723 | { | |
e11e83f3 | 6724 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6725 | return SCM_BOOL_F; |
6726 | else if (SCM_BIGP (y)) | |
6727 | return SCM_BOOL_F; | |
6728 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6729 | { |
6730 | double yy = SCM_REAL_VALUE (y); | |
01329288 | 6731 | if (isnan (yy) || isinf (yy)) |
d8b95e27 | 6732 | return SCM_BOOL_F; |
d8b95e27 KR |
6733 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6734 | goto again; | |
6735 | } | |
f92e85f7 | 6736 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6737 | { |
6738 | double yy; | |
6739 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6740 | return SCM_BOOL_F; | |
6741 | yy = SCM_COMPLEX_REAL (y); | |
01329288 | 6742 | if (isnan (yy) || isinf(yy)) |
d8b95e27 | 6743 | return SCM_BOOL_F; |
d8b95e27 KR |
6744 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6745 | goto again; | |
6746 | } | |
f92e85f7 MV |
6747 | else if (SCM_FRACTIONP (y)) |
6748 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6749 | else |
fa075d40 AW |
6750 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6751 | s_scm_i_num_eq_p); | |
f4c627b3 | 6752 | } |
0aacf84e | 6753 | else |
fa075d40 AW |
6754 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, |
6755 | s_scm_i_num_eq_p); | |
0f2d19dd JB |
6756 | } |
6757 | ||
6758 | ||
a5f0b599 KR |
6759 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6760 | done are good for inums, but for bignums an answer can almost always be | |
6761 | had by just examining a few high bits of the operands, as done by GMP in | |
6762 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6763 | of the float exponent to take into account. */ | |
6764 | ||
8c93b597 | 6765 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6766 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6767 | (SCM x, SCM y, SCM rest), | |
6768 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6769 | "increasing.") | |
6770 | #define FUNC_NAME s_scm_i_num_less_p | |
6771 | { | |
6772 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6773 | return SCM_BOOL_T; | |
6774 | while (!scm_is_null (rest)) | |
6775 | { | |
6776 | if (scm_is_false (scm_less_p (x, y))) | |
6777 | return SCM_BOOL_F; | |
6778 | x = y; | |
6779 | y = scm_car (rest); | |
6780 | rest = scm_cdr (rest); | |
6781 | } | |
6782 | return scm_less_p (x, y); | |
6783 | } | |
6784 | #undef FUNC_NAME | |
0f2d19dd | 6785 | SCM |
6e8d25a6 | 6786 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6787 | { |
a5f0b599 | 6788 | again: |
e11e83f3 | 6789 | if (SCM_I_INUMP (x)) |
0aacf84e | 6790 | { |
e25f3727 | 6791 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6792 | if (SCM_I_INUMP (y)) |
0aacf84e | 6793 | { |
e25f3727 | 6794 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6795 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6796 | } |
6797 | else if (SCM_BIGP (y)) | |
6798 | { | |
6799 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6800 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6801 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6802 | } |
6803 | else if (SCM_REALP (y)) | |
95ed2217 MW |
6804 | { |
6805 | /* We can safely take the ceiling of y without changing the | |
6806 | result of x<y, given that x is an integer. */ | |
6807 | double yy = ceil (SCM_REAL_VALUE (y)); | |
6808 | ||
6809 | /* In the following comparisons, it's important that the right | |
6810 | hand side always be a power of 2, so that it can be | |
6811 | losslessly converted to a double even on 64-bit | |
6812 | machines. */ | |
6813 | if (yy >= (double) (SCM_MOST_POSITIVE_FIXNUM+1)) | |
6814 | return SCM_BOOL_T; | |
6815 | else if (!(yy > (double) SCM_MOST_NEGATIVE_FIXNUM)) | |
6816 | /* The condition above is carefully written to include the | |
6817 | case where yy==NaN. */ | |
6818 | return SCM_BOOL_F; | |
6819 | else | |
6820 | /* yy is a finite integer that fits in an inum. */ | |
6821 | return scm_from_bool (xx < (scm_t_inum) yy); | |
6822 | } | |
f92e85f7 | 6823 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6824 | { |
6825 | /* "x < a/b" becomes "x*b < a" */ | |
6826 | int_frac: | |
6827 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6828 | y = SCM_FRACTION_NUMERATOR (y); | |
6829 | goto again; | |
6830 | } | |
0aacf84e | 6831 | else |
fa075d40 AW |
6832 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6833 | s_scm_i_num_less_p); | |
f872b822 | 6834 | } |
0aacf84e MD |
6835 | else if (SCM_BIGP (x)) |
6836 | { | |
e11e83f3 | 6837 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6838 | { |
6839 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6840 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6841 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6842 | } |
6843 | else if (SCM_BIGP (y)) | |
6844 | { | |
6845 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6846 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6847 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6848 | } |
6849 | else if (SCM_REALP (y)) | |
6850 | { | |
6851 | int cmp; | |
2e65b52f | 6852 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6853 | return SCM_BOOL_F; |
6854 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6855 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6856 | return scm_from_bool (cmp < 0); |
0aacf84e | 6857 | } |
f92e85f7 | 6858 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6859 | goto int_frac; |
0aacf84e | 6860 | else |
fa075d40 AW |
6861 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6862 | s_scm_i_num_less_p); | |
f4c627b3 | 6863 | } |
0aacf84e MD |
6864 | else if (SCM_REALP (x)) |
6865 | { | |
e11e83f3 | 6866 | if (SCM_I_INUMP (y)) |
95ed2217 MW |
6867 | { |
6868 | /* We can safely take the floor of x without changing the | |
6869 | result of x<y, given that y is an integer. */ | |
6870 | double xx = floor (SCM_REAL_VALUE (x)); | |
6871 | ||
6872 | /* In the following comparisons, it's important that the right | |
6873 | hand side always be a power of 2, so that it can be | |
6874 | losslessly converted to a double even on 64-bit | |
6875 | machines. */ | |
6876 | if (xx < (double) SCM_MOST_NEGATIVE_FIXNUM) | |
6877 | return SCM_BOOL_T; | |
6878 | else if (!(xx < (double) (SCM_MOST_POSITIVE_FIXNUM+1))) | |
6879 | /* The condition above is carefully written to include the | |
6880 | case where xx==NaN. */ | |
6881 | return SCM_BOOL_F; | |
6882 | else | |
6883 | /* xx is a finite integer that fits in an inum. */ | |
6884 | return scm_from_bool ((scm_t_inum) xx < SCM_I_INUM (y)); | |
6885 | } | |
0aacf84e MD |
6886 | else if (SCM_BIGP (y)) |
6887 | { | |
6888 | int cmp; | |
2e65b52f | 6889 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6890 | return SCM_BOOL_F; |
6891 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6892 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6893 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6894 | } |
6895 | else if (SCM_REALP (y)) | |
73e4de09 | 6896 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6897 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6898 | { |
6899 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6900 | if (isnan (xx)) |
a5f0b599 | 6901 | return SCM_BOOL_F; |
2e65b52f | 6902 | if (isinf (xx)) |
73e4de09 | 6903 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6904 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6905 | goto again; | |
6906 | } | |
f92e85f7 | 6907 | else |
fa075d40 AW |
6908 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6909 | s_scm_i_num_less_p); | |
f92e85f7 MV |
6910 | } |
6911 | else if (SCM_FRACTIONP (x)) | |
6912 | { | |
e11e83f3 | 6913 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6914 | { |
6915 | /* "a/b < y" becomes "a < y*b" */ | |
6916 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6917 | x = SCM_FRACTION_NUMERATOR (x); | |
6918 | goto again; | |
6919 | } | |
f92e85f7 | 6920 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6921 | { |
6922 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6923 | if (isnan (yy)) |
a5f0b599 | 6924 | return SCM_BOOL_F; |
2e65b52f | 6925 | if (isinf (yy)) |
73e4de09 | 6926 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6927 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6928 | goto again; | |
6929 | } | |
f92e85f7 | 6930 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6931 | { |
6932 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6933 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6934 | SCM_FRACTION_DENOMINATOR (y)); | |
6935 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6936 | SCM_FRACTION_DENOMINATOR (x)); | |
6937 | x = new_x; | |
6938 | y = new_y; | |
6939 | goto again; | |
6940 | } | |
0aacf84e | 6941 | else |
fa075d40 AW |
6942 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6943 | s_scm_i_num_less_p); | |
f872b822 | 6944 | } |
0aacf84e | 6945 | else |
fa075d40 AW |
6946 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, |
6947 | s_scm_i_num_less_p); | |
0f2d19dd JB |
6948 | } |
6949 | ||
6950 | ||
8a1f4f98 AW |
6951 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6952 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6953 | (SCM x, SCM y, SCM rest), | |
6954 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6955 | "decreasing.") | |
6956 | #define FUNC_NAME s_scm_i_num_gr_p | |
6957 | { | |
6958 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6959 | return SCM_BOOL_T; | |
6960 | while (!scm_is_null (rest)) | |
6961 | { | |
6962 | if (scm_is_false (scm_gr_p (x, y))) | |
6963 | return SCM_BOOL_F; | |
6964 | x = y; | |
6965 | y = scm_car (rest); | |
6966 | rest = scm_cdr (rest); | |
6967 | } | |
6968 | return scm_gr_p (x, y); | |
6969 | } | |
6970 | #undef FUNC_NAME | |
6971 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6972 | SCM |
6973 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6974 | { |
c76b1eaf | 6975 | if (!SCM_NUMBERP (x)) |
fa075d40 | 6976 | return scm_wta_dispatch_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6977 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 6978 | return scm_wta_dispatch_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6979 | else |
6980 | return scm_less_p (y, x); | |
0f2d19dd | 6981 | } |
1bbd0b84 | 6982 | #undef FUNC_NAME |
0f2d19dd JB |
6983 | |
6984 | ||
8a1f4f98 AW |
6985 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6986 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6987 | (SCM x, SCM y, SCM rest), | |
6988 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6989 | "non-decreasing.") | |
6990 | #define FUNC_NAME s_scm_i_num_leq_p | |
6991 | { | |
6992 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6993 | return SCM_BOOL_T; | |
6994 | while (!scm_is_null (rest)) | |
6995 | { | |
6996 | if (scm_is_false (scm_leq_p (x, y))) | |
6997 | return SCM_BOOL_F; | |
6998 | x = y; | |
6999 | y = scm_car (rest); | |
7000 | rest = scm_cdr (rest); | |
7001 | } | |
7002 | return scm_leq_p (x, y); | |
7003 | } | |
7004 | #undef FUNC_NAME | |
7005 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
7006 | SCM |
7007 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 7008 | { |
c76b1eaf | 7009 | if (!SCM_NUMBERP (x)) |
fa075d40 | 7010 | return scm_wta_dispatch_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7011 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 7012 | return scm_wta_dispatch_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 7013 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 7014 | return SCM_BOOL_F; |
c76b1eaf | 7015 | else |
73e4de09 | 7016 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 7017 | } |
1bbd0b84 | 7018 | #undef FUNC_NAME |
0f2d19dd JB |
7019 | |
7020 | ||
8a1f4f98 AW |
7021 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
7022 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
7023 | (SCM x, SCM y, SCM rest), | |
7024 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7025 | "non-increasing.") | |
7026 | #define FUNC_NAME s_scm_i_num_geq_p | |
7027 | { | |
7028 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7029 | return SCM_BOOL_T; | |
7030 | while (!scm_is_null (rest)) | |
7031 | { | |
7032 | if (scm_is_false (scm_geq_p (x, y))) | |
7033 | return SCM_BOOL_F; | |
7034 | x = y; | |
7035 | y = scm_car (rest); | |
7036 | rest = scm_cdr (rest); | |
7037 | } | |
7038 | return scm_geq_p (x, y); | |
7039 | } | |
7040 | #undef FUNC_NAME | |
7041 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
7042 | SCM |
7043 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 7044 | { |
c76b1eaf | 7045 | if (!SCM_NUMBERP (x)) |
fa075d40 | 7046 | return scm_wta_dispatch_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7047 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 7048 | return scm_wta_dispatch_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 7049 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 7050 | return SCM_BOOL_F; |
c76b1eaf | 7051 | else |
73e4de09 | 7052 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 7053 | } |
1bbd0b84 | 7054 | #undef FUNC_NAME |
0f2d19dd JB |
7055 | |
7056 | ||
2519490c MW |
7057 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
7058 | (SCM z), | |
7059 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
7060 | "zero.") | |
7061 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 7062 | { |
e11e83f3 | 7063 | if (SCM_I_INUMP (z)) |
bc36d050 | 7064 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 7065 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 7066 | return SCM_BOOL_F; |
0aacf84e | 7067 | else if (SCM_REALP (z)) |
73e4de09 | 7068 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 7069 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 7070 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 7071 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
7072 | else if (SCM_FRACTIONP (z)) |
7073 | return SCM_BOOL_F; | |
0aacf84e | 7074 | else |
fa075d40 | 7075 | return scm_wta_dispatch_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 7076 | } |
2519490c | 7077 | #undef FUNC_NAME |
0f2d19dd JB |
7078 | |
7079 | ||
2519490c MW |
7080 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
7081 | (SCM x), | |
7082 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
7083 | "zero.") | |
7084 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 7085 | { |
e11e83f3 MV |
7086 | if (SCM_I_INUMP (x)) |
7087 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
7088 | else if (SCM_BIGP (x)) |
7089 | { | |
7090 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7091 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7092 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
7093 | } |
7094 | else if (SCM_REALP (x)) | |
73e4de09 | 7095 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
7096 | else if (SCM_FRACTIONP (x)) |
7097 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7098 | else |
fa075d40 | 7099 | return scm_wta_dispatch_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 7100 | } |
2519490c | 7101 | #undef FUNC_NAME |
0f2d19dd JB |
7102 | |
7103 | ||
2519490c MW |
7104 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
7105 | (SCM x), | |
7106 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
7107 | "zero.") | |
7108 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 7109 | { |
e11e83f3 MV |
7110 | if (SCM_I_INUMP (x)) |
7111 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
7112 | else if (SCM_BIGP (x)) |
7113 | { | |
7114 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7115 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7116 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
7117 | } |
7118 | else if (SCM_REALP (x)) | |
73e4de09 | 7119 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
7120 | else if (SCM_FRACTIONP (x)) |
7121 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7122 | else |
fa075d40 | 7123 | return scm_wta_dispatch_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 7124 | } |
2519490c | 7125 | #undef FUNC_NAME |
0f2d19dd JB |
7126 | |
7127 | ||
2a06f791 KR |
7128 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
7129 | required by r5rs. On that basis, for exact/inexact combinations the | |
7130 | exact is converted to inexact to compare and possibly return. This is | |
7131 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
7132 | its test, such trouble is not required for min and max. */ | |
7133 | ||
78d3deb1 AW |
7134 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
7135 | (SCM x, SCM y, SCM rest), | |
7136 | "Return the maximum of all parameter values.") | |
7137 | #define FUNC_NAME s_scm_i_max | |
7138 | { | |
7139 | while (!scm_is_null (rest)) | |
7140 | { x = scm_max (x, y); | |
7141 | y = scm_car (rest); | |
7142 | rest = scm_cdr (rest); | |
7143 | } | |
7144 | return scm_max (x, y); | |
7145 | } | |
7146 | #undef FUNC_NAME | |
7147 | ||
7148 | #define s_max s_scm_i_max | |
7149 | #define g_max g_scm_i_max | |
7150 | ||
0f2d19dd | 7151 | SCM |
6e8d25a6 | 7152 | scm_max (SCM x, SCM y) |
0f2d19dd | 7153 | { |
0aacf84e MD |
7154 | if (SCM_UNBNDP (y)) |
7155 | { | |
7156 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7157 | return scm_wta_dispatch_0 (g_max, s_max); |
e11e83f3 | 7158 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7159 | return x; |
7160 | else | |
fa075d40 | 7161 | return scm_wta_dispatch_1 (g_max, x, SCM_ARG1, s_max); |
f872b822 | 7162 | } |
f4c627b3 | 7163 | |
e11e83f3 | 7164 | if (SCM_I_INUMP (x)) |
0aacf84e | 7165 | { |
e25f3727 | 7166 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7167 | if (SCM_I_INUMP (y)) |
0aacf84e | 7168 | { |
e25f3727 | 7169 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7170 | return (xx < yy) ? y : x; |
7171 | } | |
7172 | else if (SCM_BIGP (y)) | |
7173 | { | |
7174 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7175 | scm_remember_upto_here_1 (y); | |
7176 | return (sgn < 0) ? x : y; | |
7177 | } | |
7178 | else if (SCM_REALP (y)) | |
7179 | { | |
2e274311 MW |
7180 | double xxd = xx; |
7181 | double yyd = SCM_REAL_VALUE (y); | |
7182 | ||
7183 | if (xxd > yyd) | |
7184 | return scm_from_double (xxd); | |
7185 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
7186 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7187 | return y; | |
7188 | /* Handle signed zeroes properly */ | |
7189 | else if (xx == 0) | |
7190 | return flo0; | |
7191 | else | |
7192 | return y; | |
0aacf84e | 7193 | } |
f92e85f7 MV |
7194 | else if (SCM_FRACTIONP (y)) |
7195 | { | |
e4bc5d6c | 7196 | use_less: |
73e4de09 | 7197 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 7198 | } |
0aacf84e | 7199 | else |
fa075d40 | 7200 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f872b822 | 7201 | } |
0aacf84e MD |
7202 | else if (SCM_BIGP (x)) |
7203 | { | |
e11e83f3 | 7204 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7205 | { |
7206 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7207 | scm_remember_upto_here_1 (x); | |
7208 | return (sgn < 0) ? y : x; | |
7209 | } | |
7210 | else if (SCM_BIGP (y)) | |
7211 | { | |
7212 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7213 | scm_remember_upto_here_2 (x, y); | |
7214 | return (cmp > 0) ? x : y; | |
7215 | } | |
7216 | else if (SCM_REALP (y)) | |
7217 | { | |
2a06f791 KR |
7218 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
7219 | double xx, yy; | |
7220 | big_real: | |
7221 | xx = scm_i_big2dbl (x); | |
7222 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7223 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 7224 | } |
f92e85f7 MV |
7225 | else if (SCM_FRACTIONP (y)) |
7226 | { | |
e4bc5d6c | 7227 | goto use_less; |
f92e85f7 | 7228 | } |
0aacf84e | 7229 | else |
fa075d40 | 7230 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f4c627b3 | 7231 | } |
0aacf84e MD |
7232 | else if (SCM_REALP (x)) |
7233 | { | |
e11e83f3 | 7234 | if (SCM_I_INUMP (y)) |
0aacf84e | 7235 | { |
2e274311 MW |
7236 | scm_t_inum yy = SCM_I_INUM (y); |
7237 | double xxd = SCM_REAL_VALUE (x); | |
7238 | double yyd = yy; | |
7239 | ||
7240 | if (yyd > xxd) | |
7241 | return scm_from_double (yyd); | |
7242 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
7243 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7244 | return x; | |
7245 | /* Handle signed zeroes properly */ | |
7246 | else if (yy == 0) | |
7247 | return flo0; | |
7248 | else | |
7249 | return x; | |
0aacf84e MD |
7250 | } |
7251 | else if (SCM_BIGP (y)) | |
7252 | { | |
b6f8f763 | 7253 | SCM_SWAP (x, y); |
2a06f791 | 7254 | goto big_real; |
0aacf84e MD |
7255 | } |
7256 | else if (SCM_REALP (y)) | |
7257 | { | |
0aacf84e | 7258 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7259 | double yy = SCM_REAL_VALUE (y); |
7260 | ||
b4c55c9c MW |
7261 | /* For purposes of max: nan > +inf.0 > everything else, |
7262 | per the R6RS errata */ | |
2e274311 MW |
7263 | if (xx > yy) |
7264 | return x; | |
7265 | else if (SCM_LIKELY (xx < yy)) | |
7266 | return y; | |
7267 | /* If neither (xx > yy) nor (xx < yy), then | |
7268 | either they're equal or one is a NaN */ | |
b4c55c9c MW |
7269 | else if (SCM_UNLIKELY (xx != yy)) |
7270 | return (xx != xx) ? x : y; /* Return the NaN */ | |
2e274311 MW |
7271 | /* xx == yy, but handle signed zeroes properly */ |
7272 | else if (double_is_non_negative_zero (yy)) | |
7273 | return y; | |
7274 | else | |
7275 | return x; | |
0aacf84e | 7276 | } |
f92e85f7 MV |
7277 | else if (SCM_FRACTIONP (y)) |
7278 | { | |
7279 | double yy = scm_i_fraction2double (y); | |
7280 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7281 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
7282 | } |
7283 | else | |
fa075d40 | 7284 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f92e85f7 MV |
7285 | } |
7286 | else if (SCM_FRACTIONP (x)) | |
7287 | { | |
e11e83f3 | 7288 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7289 | { |
e4bc5d6c | 7290 | goto use_less; |
f92e85f7 MV |
7291 | } |
7292 | else if (SCM_BIGP (y)) | |
7293 | { | |
e4bc5d6c | 7294 | goto use_less; |
f92e85f7 MV |
7295 | } |
7296 | else if (SCM_REALP (y)) | |
7297 | { | |
7298 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7299 | /* if y==NaN then ">" is false, so we return the NaN y */ |
7300 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7301 | } |
7302 | else if (SCM_FRACTIONP (y)) | |
7303 | { | |
e4bc5d6c | 7304 | goto use_less; |
f92e85f7 | 7305 | } |
0aacf84e | 7306 | else |
fa075d40 | 7307 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f872b822 | 7308 | } |
0aacf84e | 7309 | else |
fa075d40 | 7310 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
7311 | } |
7312 | ||
7313 | ||
78d3deb1 AW |
7314 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
7315 | (SCM x, SCM y, SCM rest), | |
7316 | "Return the minimum of all parameter values.") | |
7317 | #define FUNC_NAME s_scm_i_min | |
7318 | { | |
7319 | while (!scm_is_null (rest)) | |
7320 | { x = scm_min (x, y); | |
7321 | y = scm_car (rest); | |
7322 | rest = scm_cdr (rest); | |
7323 | } | |
7324 | return scm_min (x, y); | |
7325 | } | |
7326 | #undef FUNC_NAME | |
7327 | ||
7328 | #define s_min s_scm_i_min | |
7329 | #define g_min g_scm_i_min | |
7330 | ||
0f2d19dd | 7331 | SCM |
6e8d25a6 | 7332 | scm_min (SCM x, SCM y) |
0f2d19dd | 7333 | { |
0aacf84e MD |
7334 | if (SCM_UNBNDP (y)) |
7335 | { | |
7336 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7337 | return scm_wta_dispatch_0 (g_min, s_min); |
e11e83f3 | 7338 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7339 | return x; |
7340 | else | |
fa075d40 | 7341 | return scm_wta_dispatch_1 (g_min, x, SCM_ARG1, s_min); |
f872b822 | 7342 | } |
f4c627b3 | 7343 | |
e11e83f3 | 7344 | if (SCM_I_INUMP (x)) |
0aacf84e | 7345 | { |
e25f3727 | 7346 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7347 | if (SCM_I_INUMP (y)) |
0aacf84e | 7348 | { |
e25f3727 | 7349 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7350 | return (xx < yy) ? x : y; |
7351 | } | |
7352 | else if (SCM_BIGP (y)) | |
7353 | { | |
7354 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7355 | scm_remember_upto_here_1 (y); | |
7356 | return (sgn < 0) ? y : x; | |
7357 | } | |
7358 | else if (SCM_REALP (y)) | |
7359 | { | |
7360 | double z = xx; | |
7361 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 7362 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 7363 | } |
f92e85f7 MV |
7364 | else if (SCM_FRACTIONP (y)) |
7365 | { | |
e4bc5d6c | 7366 | use_less: |
73e4de09 | 7367 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 7368 | } |
0aacf84e | 7369 | else |
fa075d40 | 7370 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f872b822 | 7371 | } |
0aacf84e MD |
7372 | else if (SCM_BIGP (x)) |
7373 | { | |
e11e83f3 | 7374 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7375 | { |
7376 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7377 | scm_remember_upto_here_1 (x); | |
7378 | return (sgn < 0) ? x : y; | |
7379 | } | |
7380 | else if (SCM_BIGP (y)) | |
7381 | { | |
7382 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7383 | scm_remember_upto_here_2 (x, y); | |
7384 | return (cmp > 0) ? y : x; | |
7385 | } | |
7386 | else if (SCM_REALP (y)) | |
7387 | { | |
2a06f791 KR |
7388 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
7389 | double xx, yy; | |
7390 | big_real: | |
7391 | xx = scm_i_big2dbl (x); | |
7392 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7393 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 7394 | } |
f92e85f7 MV |
7395 | else if (SCM_FRACTIONP (y)) |
7396 | { | |
e4bc5d6c | 7397 | goto use_less; |
f92e85f7 | 7398 | } |
0aacf84e | 7399 | else |
fa075d40 | 7400 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f4c627b3 | 7401 | } |
0aacf84e MD |
7402 | else if (SCM_REALP (x)) |
7403 | { | |
e11e83f3 | 7404 | if (SCM_I_INUMP (y)) |
0aacf84e | 7405 | { |
e11e83f3 | 7406 | double z = SCM_I_INUM (y); |
0aacf84e | 7407 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7408 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7409 | } |
7410 | else if (SCM_BIGP (y)) | |
7411 | { | |
b6f8f763 | 7412 | SCM_SWAP (x, y); |
2a06f791 | 7413 | goto big_real; |
0aacf84e MD |
7414 | } |
7415 | else if (SCM_REALP (y)) | |
7416 | { | |
0aacf84e | 7417 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7418 | double yy = SCM_REAL_VALUE (y); |
7419 | ||
b4c55c9c MW |
7420 | /* For purposes of min: nan < -inf.0 < everything else, |
7421 | per the R6RS errata */ | |
2e274311 MW |
7422 | if (xx < yy) |
7423 | return x; | |
7424 | else if (SCM_LIKELY (xx > yy)) | |
7425 | return y; | |
7426 | /* If neither (xx < yy) nor (xx > yy), then | |
7427 | either they're equal or one is a NaN */ | |
b4c55c9c MW |
7428 | else if (SCM_UNLIKELY (xx != yy)) |
7429 | return (xx != xx) ? x : y; /* Return the NaN */ | |
2e274311 MW |
7430 | /* xx == yy, but handle signed zeroes properly */ |
7431 | else if (double_is_non_negative_zero (xx)) | |
7432 | return y; | |
7433 | else | |
7434 | return x; | |
0aacf84e | 7435 | } |
f92e85f7 MV |
7436 | else if (SCM_FRACTIONP (y)) |
7437 | { | |
7438 | double yy = scm_i_fraction2double (y); | |
7439 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7440 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7441 | } |
0aacf84e | 7442 | else |
fa075d40 | 7443 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f872b822 | 7444 | } |
f92e85f7 MV |
7445 | else if (SCM_FRACTIONP (x)) |
7446 | { | |
e11e83f3 | 7447 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7448 | { |
e4bc5d6c | 7449 | goto use_less; |
f92e85f7 MV |
7450 | } |
7451 | else if (SCM_BIGP (y)) | |
7452 | { | |
e4bc5d6c | 7453 | goto use_less; |
f92e85f7 MV |
7454 | } |
7455 | else if (SCM_REALP (y)) | |
7456 | { | |
7457 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7458 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7459 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7460 | } |
7461 | else if (SCM_FRACTIONP (y)) | |
7462 | { | |
e4bc5d6c | 7463 | goto use_less; |
f92e85f7 MV |
7464 | } |
7465 | else | |
fa075d40 | 7466 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7467 | } |
0aacf84e | 7468 | else |
fa075d40 | 7469 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7470 | } |
7471 | ||
7472 | ||
8ccd24f7 AW |
7473 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7474 | (SCM x, SCM y, SCM rest), | |
7475 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7476 | "any parameters." ) | |
7477 | #define FUNC_NAME s_scm_i_sum | |
7478 | { | |
7479 | while (!scm_is_null (rest)) | |
7480 | { x = scm_sum (x, y); | |
7481 | y = scm_car (rest); | |
7482 | rest = scm_cdr (rest); | |
7483 | } | |
7484 | return scm_sum (x, y); | |
7485 | } | |
7486 | #undef FUNC_NAME | |
7487 | ||
7488 | #define s_sum s_scm_i_sum | |
7489 | #define g_sum g_scm_i_sum | |
7490 | ||
0f2d19dd | 7491 | SCM |
6e8d25a6 | 7492 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7493 | { |
9cc37597 | 7494 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7495 | { |
7496 | if (SCM_NUMBERP (x)) return x; | |
7497 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
fa075d40 | 7498 | return scm_wta_dispatch_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7499 | } |
c209c88e | 7500 | |
9cc37597 | 7501 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7502 | { |
9cc37597 | 7503 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7504 | { |
e25f3727 AW |
7505 | scm_t_inum xx = SCM_I_INUM (x); |
7506 | scm_t_inum yy = SCM_I_INUM (y); | |
7507 | scm_t_inum z = xx + yy; | |
7508 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7509 | } |
7510 | else if (SCM_BIGP (y)) | |
7511 | { | |
7512 | SCM_SWAP (x, y); | |
7513 | goto add_big_inum; | |
7514 | } | |
7515 | else if (SCM_REALP (y)) | |
7516 | { | |
e25f3727 | 7517 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7518 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7519 | } |
7520 | else if (SCM_COMPLEXP (y)) | |
7521 | { | |
e25f3727 | 7522 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7523 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7524 | SCM_COMPLEX_IMAG (y)); |
7525 | } | |
f92e85f7 | 7526 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7527 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7528 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7529 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 | 7530 | else |
fa075d40 | 7531 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
0aacf84e MD |
7532 | } else if (SCM_BIGP (x)) |
7533 | { | |
e11e83f3 | 7534 | if (SCM_I_INUMP (y)) |
0aacf84e | 7535 | { |
e25f3727 | 7536 | scm_t_inum inum; |
0aacf84e MD |
7537 | int bigsgn; |
7538 | add_big_inum: | |
e11e83f3 | 7539 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7540 | if (inum == 0) |
7541 | return x; | |
7542 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7543 | if (inum < 0) | |
7544 | { | |
7545 | SCM result = scm_i_mkbig (); | |
7546 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7547 | scm_remember_upto_here_1 (x); | |
7548 | /* we know the result will have to be a bignum */ | |
7549 | if (bigsgn == -1) | |
7550 | return result; | |
7551 | return scm_i_normbig (result); | |
7552 | } | |
7553 | else | |
7554 | { | |
7555 | SCM result = scm_i_mkbig (); | |
7556 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7557 | scm_remember_upto_here_1 (x); | |
7558 | /* we know the result will have to be a bignum */ | |
7559 | if (bigsgn == 1) | |
7560 | return result; | |
7561 | return scm_i_normbig (result); | |
7562 | } | |
7563 | } | |
7564 | else if (SCM_BIGP (y)) | |
7565 | { | |
7566 | SCM result = scm_i_mkbig (); | |
7567 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7568 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7569 | mpz_add (SCM_I_BIG_MPZ (result), | |
7570 | SCM_I_BIG_MPZ (x), | |
7571 | SCM_I_BIG_MPZ (y)); | |
7572 | scm_remember_upto_here_2 (x, y); | |
7573 | /* we know the result will have to be a bignum */ | |
7574 | if (sgn_x == sgn_y) | |
7575 | return result; | |
7576 | return scm_i_normbig (result); | |
7577 | } | |
7578 | else if (SCM_REALP (y)) | |
7579 | { | |
7580 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7581 | scm_remember_upto_here_1 (x); | |
55f26379 | 7582 | return scm_from_double (result); |
0aacf84e MD |
7583 | } |
7584 | else if (SCM_COMPLEXP (y)) | |
7585 | { | |
7586 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7587 | + SCM_COMPLEX_REAL (y)); | |
7588 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7589 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7590 | } |
f92e85f7 | 7591 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7592 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7593 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7594 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7595 | else |
fa075d40 | 7596 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
0f2d19dd | 7597 | } |
0aacf84e MD |
7598 | else if (SCM_REALP (x)) |
7599 | { | |
e11e83f3 | 7600 | if (SCM_I_INUMP (y)) |
55f26379 | 7601 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7602 | else if (SCM_BIGP (y)) |
7603 | { | |
7604 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7605 | scm_remember_upto_here_1 (y); | |
55f26379 | 7606 | return scm_from_double (result); |
0aacf84e MD |
7607 | } |
7608 | else if (SCM_REALP (y)) | |
55f26379 | 7609 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7610 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7611 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7612 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7613 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7614 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e | 7615 | else |
fa075d40 | 7616 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
f872b822 | 7617 | } |
0aacf84e MD |
7618 | else if (SCM_COMPLEXP (x)) |
7619 | { | |
e11e83f3 | 7620 | if (SCM_I_INUMP (y)) |
8507ec80 | 7621 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7622 | SCM_COMPLEX_IMAG (x)); |
7623 | else if (SCM_BIGP (y)) | |
7624 | { | |
7625 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7626 | + SCM_COMPLEX_REAL (x)); | |
7627 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7628 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7629 | } |
7630 | else if (SCM_REALP (y)) | |
8507ec80 | 7631 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7632 | SCM_COMPLEX_IMAG (x)); |
7633 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7634 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7635 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7636 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7637 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7638 | SCM_COMPLEX_IMAG (x)); |
7639 | else | |
fa075d40 | 7640 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
f92e85f7 MV |
7641 | } |
7642 | else if (SCM_FRACTIONP (x)) | |
7643 | { | |
e11e83f3 | 7644 | if (SCM_I_INUMP (y)) |
cba42c93 | 7645 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7646 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7647 | SCM_FRACTION_DENOMINATOR (x)); | |
7648 | else if (SCM_BIGP (y)) | |
cba42c93 | 7649 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7650 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7651 | SCM_FRACTION_DENOMINATOR (x)); | |
7652 | else if (SCM_REALP (y)) | |
55f26379 | 7653 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7654 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7655 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7656 | SCM_COMPLEX_IMAG (y)); |
7657 | else if (SCM_FRACTIONP (y)) | |
7658 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7659 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7660 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7661 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7662 | else |
fa075d40 | 7663 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
98cb6e75 | 7664 | } |
0aacf84e | 7665 | else |
fa075d40 | 7666 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7667 | } |
7668 | ||
7669 | ||
40882e3d KR |
7670 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7671 | (SCM x), | |
7672 | "Return @math{@var{x}+1}.") | |
7673 | #define FUNC_NAME s_scm_oneplus | |
7674 | { | |
cff5fa33 | 7675 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7676 | } |
7677 | #undef FUNC_NAME | |
7678 | ||
7679 | ||
78d3deb1 AW |
7680 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7681 | (SCM x, SCM y, SCM rest), | |
7682 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7683 | "the sum of all but the first argument are subtracted from the first\n" | |
7684 | "argument.") | |
7685 | #define FUNC_NAME s_scm_i_difference | |
7686 | { | |
7687 | while (!scm_is_null (rest)) | |
7688 | { x = scm_difference (x, y); | |
7689 | y = scm_car (rest); | |
7690 | rest = scm_cdr (rest); | |
7691 | } | |
7692 | return scm_difference (x, y); | |
7693 | } | |
7694 | #undef FUNC_NAME | |
7695 | ||
7696 | #define s_difference s_scm_i_difference | |
7697 | #define g_difference g_scm_i_difference | |
7698 | ||
0f2d19dd | 7699 | SCM |
6e8d25a6 | 7700 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7701 | #define FUNC_NAME s_difference |
0f2d19dd | 7702 | { |
9cc37597 | 7703 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7704 | { |
7705 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7706 | return scm_wta_dispatch_0 (g_difference, s_difference); |
ca46fb90 | 7707 | else |
e11e83f3 | 7708 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7709 | { |
e25f3727 | 7710 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7711 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7712 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7713 | else |
e25f3727 | 7714 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7715 | } |
7716 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7717 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7718 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7719 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7720 | else if (SCM_REALP (x)) | |
55f26379 | 7721 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7722 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7723 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7724 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7725 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
7726 | return scm_i_make_ratio_already_reduced |
7727 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
7728 | SCM_FRACTION_DENOMINATOR (x)); | |
ca46fb90 | 7729 | else |
fa075d40 | 7730 | return scm_wta_dispatch_1 (g_difference, x, SCM_ARG1, s_difference); |
f872b822 | 7731 | } |
ca46fb90 | 7732 | |
9cc37597 | 7733 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7734 | { |
9cc37597 | 7735 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7736 | { |
e25f3727 AW |
7737 | scm_t_inum xx = SCM_I_INUM (x); |
7738 | scm_t_inum yy = SCM_I_INUM (y); | |
7739 | scm_t_inum z = xx - yy; | |
0aacf84e | 7740 | if (SCM_FIXABLE (z)) |
d956fa6f | 7741 | return SCM_I_MAKINUM (z); |
0aacf84e | 7742 | else |
e25f3727 | 7743 | return scm_i_inum2big (z); |
0aacf84e MD |
7744 | } |
7745 | else if (SCM_BIGP (y)) | |
7746 | { | |
7747 | /* inum-x - big-y */ | |
e25f3727 | 7748 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7749 | |
0aacf84e | 7750 | if (xx == 0) |
b5c40589 MW |
7751 | { |
7752 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7753 | bignum, but negating that gives a fixnum. */ | |
7754 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7755 | } | |
0aacf84e MD |
7756 | else |
7757 | { | |
7758 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7759 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7760 | |
0aacf84e MD |
7761 | if (xx >= 0) |
7762 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7763 | else | |
7764 | { | |
7765 | /* x - y == -(y + -x) */ | |
7766 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7767 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7768 | } | |
7769 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7770 | |
0aacf84e MD |
7771 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7772 | /* we know the result will have to be a bignum */ | |
7773 | return result; | |
7774 | else | |
7775 | return scm_i_normbig (result); | |
7776 | } | |
7777 | } | |
7778 | else if (SCM_REALP (y)) | |
7779 | { | |
e25f3727 | 7780 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7781 | |
7782 | /* | |
7783 | * We need to handle x == exact 0 | |
7784 | * specially because R6RS states that: | |
7785 | * (- 0.0) ==> -0.0 and | |
7786 | * (- 0.0 0.0) ==> 0.0 | |
7787 | * and the scheme compiler changes | |
7788 | * (- 0.0) into (- 0 0.0) | |
7789 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7790 | * At the C level, (-x) is different than (0.0 - x). | |
7791 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7792 | */ | |
7793 | if (xx == 0) | |
7794 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7795 | else | |
7796 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7797 | } |
7798 | else if (SCM_COMPLEXP (y)) | |
7799 | { | |
e25f3727 | 7800 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7801 | |
7802 | /* We need to handle x == exact 0 specially. | |
7803 | See the comment above (for SCM_REALP (y)) */ | |
7804 | if (xx == 0) | |
7805 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7806 | - SCM_COMPLEX_IMAG (y)); | |
7807 | else | |
7808 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7809 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7810 | } |
f92e85f7 MV |
7811 | else if (SCM_FRACTIONP (y)) |
7812 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7813 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7814 | SCM_FRACTION_NUMERATOR (y)), |
7815 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7816 | else |
fa075d40 | 7817 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
f872b822 | 7818 | } |
0aacf84e MD |
7819 | else if (SCM_BIGP (x)) |
7820 | { | |
e11e83f3 | 7821 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7822 | { |
7823 | /* big-x - inum-y */ | |
e25f3727 | 7824 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7825 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7826 | |
0aacf84e MD |
7827 | scm_remember_upto_here_1 (x); |
7828 | if (sgn_x == 0) | |
c71b0706 | 7829 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7830 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7831 | else |
7832 | { | |
7833 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7834 | |
708f22c6 KR |
7835 | if (yy >= 0) |
7836 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7837 | else | |
7838 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7839 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7840 | |
0aacf84e MD |
7841 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7842 | /* we know the result will have to be a bignum */ | |
7843 | return result; | |
7844 | else | |
7845 | return scm_i_normbig (result); | |
7846 | } | |
7847 | } | |
7848 | else if (SCM_BIGP (y)) | |
7849 | { | |
7850 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7851 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7852 | SCM result = scm_i_mkbig (); | |
7853 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7854 | SCM_I_BIG_MPZ (x), | |
7855 | SCM_I_BIG_MPZ (y)); | |
7856 | scm_remember_upto_here_2 (x, y); | |
7857 | /* we know the result will have to be a bignum */ | |
7858 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7859 | return result; | |
7860 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7861 | return result; | |
7862 | return scm_i_normbig (result); | |
7863 | } | |
7864 | else if (SCM_REALP (y)) | |
7865 | { | |
7866 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7867 | scm_remember_upto_here_1 (x); | |
55f26379 | 7868 | return scm_from_double (result); |
0aacf84e MD |
7869 | } |
7870 | else if (SCM_COMPLEXP (y)) | |
7871 | { | |
7872 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7873 | - SCM_COMPLEX_REAL (y)); | |
7874 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7875 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7876 | } |
f92e85f7 | 7877 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7878 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7879 | SCM_FRACTION_NUMERATOR (y)), |
7880 | SCM_FRACTION_DENOMINATOR (y)); | |
fa075d40 AW |
7881 | else |
7882 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
ca46fb90 | 7883 | } |
0aacf84e MD |
7884 | else if (SCM_REALP (x)) |
7885 | { | |
e11e83f3 | 7886 | if (SCM_I_INUMP (y)) |
55f26379 | 7887 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7888 | else if (SCM_BIGP (y)) |
7889 | { | |
7890 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7891 | scm_remember_upto_here_1 (x); | |
55f26379 | 7892 | return scm_from_double (result); |
0aacf84e MD |
7893 | } |
7894 | else if (SCM_REALP (y)) | |
55f26379 | 7895 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7896 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7897 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7898 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7899 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7900 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e | 7901 | else |
fa075d40 | 7902 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
98cb6e75 | 7903 | } |
0aacf84e MD |
7904 | else if (SCM_COMPLEXP (x)) |
7905 | { | |
e11e83f3 | 7906 | if (SCM_I_INUMP (y)) |
8507ec80 | 7907 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7908 | SCM_COMPLEX_IMAG (x)); |
7909 | else if (SCM_BIGP (y)) | |
7910 | { | |
7911 | double real_part = (SCM_COMPLEX_REAL (x) | |
7912 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7913 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7914 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7915 | } |
7916 | else if (SCM_REALP (y)) | |
8507ec80 | 7917 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7918 | SCM_COMPLEX_IMAG (x)); |
7919 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7920 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7921 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7922 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7923 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7924 | SCM_COMPLEX_IMAG (x)); |
7925 | else | |
fa075d40 | 7926 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
f92e85f7 MV |
7927 | } |
7928 | else if (SCM_FRACTIONP (x)) | |
7929 | { | |
e11e83f3 | 7930 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7931 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7932 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7933 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7934 | SCM_FRACTION_DENOMINATOR (x)); | |
7935 | else if (SCM_BIGP (y)) | |
cba42c93 | 7936 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7937 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7938 | SCM_FRACTION_DENOMINATOR (x)); | |
7939 | else if (SCM_REALP (y)) | |
55f26379 | 7940 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7941 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7942 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7943 | -SCM_COMPLEX_IMAG (y)); |
7944 | else if (SCM_FRACTIONP (y)) | |
7945 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7946 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7947 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7948 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7949 | else |
fa075d40 | 7950 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
98cb6e75 | 7951 | } |
0aacf84e | 7952 | else |
fa075d40 | 7953 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7954 | } |
c05e97b7 | 7955 | #undef FUNC_NAME |
0f2d19dd | 7956 | |
ca46fb90 | 7957 | |
40882e3d KR |
7958 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7959 | (SCM x), | |
7960 | "Return @math{@var{x}-1}.") | |
7961 | #define FUNC_NAME s_scm_oneminus | |
7962 | { | |
cff5fa33 | 7963 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7964 | } |
7965 | #undef FUNC_NAME | |
7966 | ||
7967 | ||
78d3deb1 AW |
7968 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7969 | (SCM x, SCM y, SCM rest), | |
7970 | "Return the product of all arguments. If called without arguments,\n" | |
7971 | "1 is returned.") | |
7972 | #define FUNC_NAME s_scm_i_product | |
7973 | { | |
7974 | while (!scm_is_null (rest)) | |
7975 | { x = scm_product (x, y); | |
7976 | y = scm_car (rest); | |
7977 | rest = scm_cdr (rest); | |
7978 | } | |
7979 | return scm_product (x, y); | |
7980 | } | |
7981 | #undef FUNC_NAME | |
7982 | ||
7983 | #define s_product s_scm_i_product | |
7984 | #define g_product g_scm_i_product | |
7985 | ||
0f2d19dd | 7986 | SCM |
6e8d25a6 | 7987 | scm_product (SCM x, SCM y) |
0f2d19dd | 7988 | { |
9cc37597 | 7989 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7990 | { |
7991 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7992 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7993 | else if (SCM_NUMBERP (x)) |
7994 | return x; | |
7995 | else | |
fa075d40 | 7996 | return scm_wta_dispatch_1 (g_product, x, SCM_ARG1, s_product); |
f872b822 | 7997 | } |
ca46fb90 | 7998 | |
9cc37597 | 7999 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8000 | { |
e25f3727 | 8001 | scm_t_inum xx; |
f4c627b3 | 8002 | |
5e791807 | 8003 | xinum: |
e11e83f3 | 8004 | xx = SCM_I_INUM (x); |
f4c627b3 | 8005 | |
0aacf84e MD |
8006 | switch (xx) |
8007 | { | |
5e791807 MW |
8008 | case 1: |
8009 | /* exact1 is the universal multiplicative identity */ | |
8010 | return y; | |
8011 | break; | |
8012 | case 0: | |
8013 | /* exact0 times a fixnum is exact0: optimize this case */ | |
8014 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
8015 | return SCM_INUM0; | |
8016 | /* if the other argument is inexact, the result is inexact, | |
8017 | and we must do the multiplication in order to handle | |
8018 | infinities and NaNs properly. */ | |
8019 | else if (SCM_REALP (y)) | |
8020 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
8021 | else if (SCM_COMPLEXP (y)) | |
8022 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
8023 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
8024 | /* we've already handled inexact numbers, | |
8025 | so y must be exact, and we return exact0 */ | |
8026 | else if (SCM_NUMP (y)) | |
8027 | return SCM_INUM0; | |
8028 | else | |
fa075d40 | 8029 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
5e791807 MW |
8030 | break; |
8031 | case -1: | |
b5c40589 | 8032 | /* |
5e791807 MW |
8033 | * This case is important for more than just optimization. |
8034 | * It handles the case of negating | |
b5c40589 MW |
8035 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
8036 | * which is a bignum that must be changed back into a fixnum. | |
8037 | * Failure to do so will cause the following to return #f: | |
8038 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
8039 | */ | |
b5c40589 MW |
8040 | return scm_difference(y, SCM_UNDEFINED); |
8041 | break; | |
0aacf84e | 8042 | } |
f4c627b3 | 8043 | |
9cc37597 | 8044 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8045 | { |
e25f3727 | 8046 | scm_t_inum yy = SCM_I_INUM (y); |
2355f017 MW |
8047 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
8048 | scm_t_int64 kk = xx * (scm_t_int64) yy; | |
8049 | if (SCM_FIXABLE (kk)) | |
8050 | return SCM_I_MAKINUM (kk); | |
8051 | #else | |
8052 | scm_t_inum axx = (xx > 0) ? xx : -xx; | |
8053 | scm_t_inum ayy = (yy > 0) ? yy : -yy; | |
8054 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) | |
8055 | return SCM_I_MAKINUM (xx * yy); | |
8056 | #endif | |
0aacf84e MD |
8057 | else |
8058 | { | |
e25f3727 | 8059 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
8060 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
8061 | return scm_i_normbig (result); | |
8062 | } | |
8063 | } | |
8064 | else if (SCM_BIGP (y)) | |
8065 | { | |
8066 | SCM result = scm_i_mkbig (); | |
8067 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
8068 | scm_remember_upto_here_1 (y); | |
8069 | return result; | |
8070 | } | |
8071 | else if (SCM_REALP (y)) | |
55f26379 | 8072 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 8073 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8074 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 8075 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8076 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8077 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 8078 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e | 8079 | else |
fa075d40 | 8080 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8081 | } |
0aacf84e MD |
8082 | else if (SCM_BIGP (x)) |
8083 | { | |
e11e83f3 | 8084 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
8085 | { |
8086 | SCM_SWAP (x, y); | |
5e791807 | 8087 | goto xinum; |
0aacf84e MD |
8088 | } |
8089 | else if (SCM_BIGP (y)) | |
8090 | { | |
8091 | SCM result = scm_i_mkbig (); | |
8092 | mpz_mul (SCM_I_BIG_MPZ (result), | |
8093 | SCM_I_BIG_MPZ (x), | |
8094 | SCM_I_BIG_MPZ (y)); | |
8095 | scm_remember_upto_here_2 (x, y); | |
8096 | return result; | |
8097 | } | |
8098 | else if (SCM_REALP (y)) | |
8099 | { | |
8100 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
8101 | scm_remember_upto_here_1 (x); | |
55f26379 | 8102 | return scm_from_double (result); |
0aacf84e MD |
8103 | } |
8104 | else if (SCM_COMPLEXP (y)) | |
8105 | { | |
8106 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
8107 | scm_remember_upto_here_1 (x); | |
8507ec80 | 8108 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
8109 | z * SCM_COMPLEX_IMAG (y)); |
8110 | } | |
f92e85f7 | 8111 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8112 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 8113 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e | 8114 | else |
fa075d40 | 8115 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8116 | } |
0aacf84e MD |
8117 | else if (SCM_REALP (x)) |
8118 | { | |
e11e83f3 | 8119 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8120 | { |
8121 | SCM_SWAP (x, y); | |
8122 | goto xinum; | |
8123 | } | |
0aacf84e MD |
8124 | else if (SCM_BIGP (y)) |
8125 | { | |
8126 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
8127 | scm_remember_upto_here_1 (y); | |
55f26379 | 8128 | return scm_from_double (result); |
0aacf84e MD |
8129 | } |
8130 | else if (SCM_REALP (y)) | |
55f26379 | 8131 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 8132 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8133 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 8134 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8135 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8136 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e | 8137 | else |
fa075d40 | 8138 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8139 | } |
0aacf84e MD |
8140 | else if (SCM_COMPLEXP (x)) |
8141 | { | |
e11e83f3 | 8142 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8143 | { |
8144 | SCM_SWAP (x, y); | |
8145 | goto xinum; | |
8146 | } | |
0aacf84e MD |
8147 | else if (SCM_BIGP (y)) |
8148 | { | |
8149 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8150 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8151 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 8152 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
8153 | } |
8154 | else if (SCM_REALP (y)) | |
8507ec80 | 8155 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
8156 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
8157 | else if (SCM_COMPLEXP (y)) | |
8158 | { | |
8507ec80 | 8159 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
8160 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
8161 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
8162 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
8163 | } | |
f92e85f7 MV |
8164 | else if (SCM_FRACTIONP (y)) |
8165 | { | |
8166 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8167 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
8168 | yy * SCM_COMPLEX_IMAG (x)); |
8169 | } | |
8170 | else | |
fa075d40 | 8171 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f92e85f7 MV |
8172 | } |
8173 | else if (SCM_FRACTIONP (x)) | |
8174 | { | |
e11e83f3 | 8175 | if (SCM_I_INUMP (y)) |
cba42c93 | 8176 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8177 | SCM_FRACTION_DENOMINATOR (x)); |
8178 | else if (SCM_BIGP (y)) | |
cba42c93 | 8179 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8180 | SCM_FRACTION_DENOMINATOR (x)); |
8181 | else if (SCM_REALP (y)) | |
55f26379 | 8182 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
8183 | else if (SCM_COMPLEXP (y)) |
8184 | { | |
8185 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 8186 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
8187 | xx * SCM_COMPLEX_IMAG (y)); |
8188 | } | |
8189 | else if (SCM_FRACTIONP (y)) | |
8190 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 8191 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8192 | SCM_FRACTION_NUMERATOR (y)), |
8193 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
8194 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 8195 | else |
fa075d40 | 8196 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 8197 | } |
0aacf84e | 8198 | else |
fa075d40 | 8199 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
8200 | } |
8201 | ||
7351e207 MV |
8202 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
8203 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
8204 | #define ALLOW_DIVIDE_BY_ZERO | |
8205 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
8206 | #endif | |
0f2d19dd | 8207 | |
ba74ef4e MV |
8208 | /* The code below for complex division is adapted from the GNU |
8209 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
8210 | this copyright: */ | |
8211 | ||
8212 | /**************************************************************** | |
8213 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
8214 | ||
8215 | Permission to use, copy, modify, and distribute this software | |
8216 | and its documentation for any purpose and without fee is hereby | |
8217 | granted, provided that the above copyright notice appear in all | |
8218 | copies and that both that the copyright notice and this | |
8219 | permission notice and warranty disclaimer appear in supporting | |
8220 | documentation, and that the names of AT&T Bell Laboratories or | |
8221 | Bellcore or any of their entities not be used in advertising or | |
8222 | publicity pertaining to distribution of the software without | |
8223 | specific, written prior permission. | |
8224 | ||
8225 | AT&T and Bellcore disclaim all warranties with regard to this | |
8226 | software, including all implied warranties of merchantability | |
8227 | and fitness. In no event shall AT&T or Bellcore be liable for | |
8228 | any special, indirect or consequential damages or any damages | |
8229 | whatsoever resulting from loss of use, data or profits, whether | |
8230 | in an action of contract, negligence or other tortious action, | |
8231 | arising out of or in connection with the use or performance of | |
8232 | this software. | |
8233 | ****************************************************************/ | |
8234 | ||
78d3deb1 AW |
8235 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
8236 | (SCM x, SCM y, SCM rest), | |
8237 | "Divide the first argument by the product of the remaining\n" | |
8238 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
8239 | "returned.") | |
8240 | #define FUNC_NAME s_scm_i_divide | |
8241 | { | |
8242 | while (!scm_is_null (rest)) | |
8243 | { x = scm_divide (x, y); | |
8244 | y = scm_car (rest); | |
8245 | rest = scm_cdr (rest); | |
8246 | } | |
8247 | return scm_divide (x, y); | |
8248 | } | |
8249 | #undef FUNC_NAME | |
8250 | ||
8251 | #define s_divide s_scm_i_divide | |
8252 | #define g_divide g_scm_i_divide | |
8253 | ||
98237784 MW |
8254 | SCM |
8255 | scm_divide (SCM x, SCM y) | |
78d3deb1 | 8256 | #define FUNC_NAME s_divide |
0f2d19dd | 8257 | { |
f8de44c1 DH |
8258 | double a; |
8259 | ||
9cc37597 | 8260 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8261 | { |
8262 | if (SCM_UNBNDP (x)) | |
fa075d40 | 8263 | return scm_wta_dispatch_0 (g_divide, s_divide); |
e11e83f3 | 8264 | else if (SCM_I_INUMP (x)) |
0aacf84e | 8265 | { |
e25f3727 | 8266 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
8267 | if (xx == 1 || xx == -1) |
8268 | return x; | |
7351e207 | 8269 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8270 | else if (xx == 0) |
8271 | scm_num_overflow (s_divide); | |
7351e207 | 8272 | #endif |
0aacf84e | 8273 | else |
98237784 | 8274 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8275 | } |
8276 | else if (SCM_BIGP (x)) | |
98237784 | 8277 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8278 | else if (SCM_REALP (x)) |
8279 | { | |
8280 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 8281 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8282 | if (xx == 0.0) |
8283 | scm_num_overflow (s_divide); | |
8284 | else | |
7351e207 | 8285 | #endif |
55f26379 | 8286 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
8287 | } |
8288 | else if (SCM_COMPLEXP (x)) | |
8289 | { | |
8290 | double r = SCM_COMPLEX_REAL (x); | |
8291 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 8292 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8293 | { |
8294 | double t = r / i; | |
8295 | double d = i * (1.0 + t * t); | |
8507ec80 | 8296 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
8297 | } |
8298 | else | |
8299 | { | |
8300 | double t = i / r; | |
8301 | double d = r * (1.0 + t * t); | |
8507ec80 | 8302 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
8303 | } |
8304 | } | |
f92e85f7 | 8305 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
8306 | return scm_i_make_ratio_already_reduced (SCM_FRACTION_DENOMINATOR (x), |
8307 | SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 8308 | else |
fa075d40 | 8309 | return scm_wta_dispatch_1 (g_divide, x, SCM_ARG1, s_divide); |
f8de44c1 | 8310 | } |
f8de44c1 | 8311 | |
9cc37597 | 8312 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8313 | { |
e25f3727 | 8314 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 8315 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8316 | { |
e25f3727 | 8317 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8318 | if (yy == 0) |
8319 | { | |
7351e207 | 8320 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8321 | scm_num_overflow (s_divide); |
7351e207 | 8322 | #else |
55f26379 | 8323 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 8324 | #endif |
0aacf84e MD |
8325 | } |
8326 | else if (xx % yy != 0) | |
98237784 | 8327 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8328 | else |
8329 | { | |
e25f3727 | 8330 | scm_t_inum z = xx / yy; |
0aacf84e | 8331 | if (SCM_FIXABLE (z)) |
d956fa6f | 8332 | return SCM_I_MAKINUM (z); |
0aacf84e | 8333 | else |
e25f3727 | 8334 | return scm_i_inum2big (z); |
0aacf84e | 8335 | } |
f872b822 | 8336 | } |
0aacf84e | 8337 | else if (SCM_BIGP (y)) |
98237784 | 8338 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8339 | else if (SCM_REALP (y)) |
8340 | { | |
8341 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8342 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8343 | if (yy == 0.0) |
8344 | scm_num_overflow (s_divide); | |
8345 | else | |
7351e207 | 8346 | #endif |
98237784 MW |
8347 | /* FIXME: Precision may be lost here due to: |
8348 | (1) The cast from 'scm_t_inum' to 'double' | |
8349 | (2) Double rounding */ | |
55f26379 | 8350 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 8351 | } |
0aacf84e MD |
8352 | else if (SCM_COMPLEXP (y)) |
8353 | { | |
8354 | a = xx; | |
8355 | complex_div: /* y _must_ be a complex number */ | |
8356 | { | |
8357 | double r = SCM_COMPLEX_REAL (y); | |
8358 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8359 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8360 | { |
8361 | double t = r / i; | |
8362 | double d = i * (1.0 + t * t); | |
8507ec80 | 8363 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
8364 | } |
8365 | else | |
8366 | { | |
8367 | double t = i / r; | |
8368 | double d = r * (1.0 + t * t); | |
8507ec80 | 8369 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
8370 | } |
8371 | } | |
8372 | } | |
f92e85f7 MV |
8373 | else if (SCM_FRACTIONP (y)) |
8374 | /* a / b/c = ac / b */ | |
cba42c93 | 8375 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8376 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e | 8377 | else |
fa075d40 | 8378 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f8de44c1 | 8379 | } |
0aacf84e MD |
8380 | else if (SCM_BIGP (x)) |
8381 | { | |
e11e83f3 | 8382 | if (SCM_I_INUMP (y)) |
0aacf84e | 8383 | { |
e25f3727 | 8384 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8385 | if (yy == 0) |
8386 | { | |
7351e207 | 8387 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8388 | scm_num_overflow (s_divide); |
7351e207 | 8389 | #else |
0aacf84e MD |
8390 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8391 | scm_remember_upto_here_1 (x); | |
8392 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8393 | #endif |
0aacf84e MD |
8394 | } |
8395 | else if (yy == 1) | |
8396 | return x; | |
8397 | else | |
8398 | { | |
8399 | /* FIXME: HMM, what are the relative performance issues here? | |
8400 | We need to test. Is it faster on average to test | |
8401 | divisible_p, then perform whichever operation, or is it | |
8402 | faster to perform the integer div opportunistically and | |
8403 | switch to real if there's a remainder? For now we take the | |
8404 | middle ground: test, then if divisible, use the faster div | |
8405 | func. */ | |
8406 | ||
e25f3727 | 8407 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8408 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8409 | ||
8410 | if (divisible_p) | |
8411 | { | |
8412 | SCM result = scm_i_mkbig (); | |
8413 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8414 | scm_remember_upto_here_1 (x); | |
8415 | if (yy < 0) | |
8416 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8417 | return scm_i_normbig (result); | |
8418 | } | |
8419 | else | |
98237784 | 8420 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8421 | } |
8422 | } | |
8423 | else if (SCM_BIGP (y)) | |
8424 | { | |
98237784 MW |
8425 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8426 | SCM_I_BIG_MPZ (y)); | |
8427 | if (divisible_p) | |
8428 | { | |
8429 | SCM result = scm_i_mkbig (); | |
8430 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8431 | SCM_I_BIG_MPZ (x), | |
8432 | SCM_I_BIG_MPZ (y)); | |
8433 | scm_remember_upto_here_2 (x, y); | |
8434 | return scm_i_normbig (result); | |
8435 | } | |
8436 | else | |
8437 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8438 | } |
8439 | else if (SCM_REALP (y)) | |
8440 | { | |
8441 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8442 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8443 | if (yy == 0.0) |
8444 | scm_num_overflow (s_divide); | |
8445 | else | |
7351e207 | 8446 | #endif |
98237784 MW |
8447 | /* FIXME: Precision may be lost here due to: |
8448 | (1) scm_i_big2dbl (2) Double rounding */ | |
55f26379 | 8449 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8450 | } |
8451 | else if (SCM_COMPLEXP (y)) | |
8452 | { | |
8453 | a = scm_i_big2dbl (x); | |
8454 | goto complex_div; | |
8455 | } | |
f92e85f7 | 8456 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8457 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8458 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e | 8459 | else |
fa075d40 | 8460 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f872b822 | 8461 | } |
0aacf84e MD |
8462 | else if (SCM_REALP (x)) |
8463 | { | |
8464 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8465 | if (SCM_I_INUMP (y)) |
0aacf84e | 8466 | { |
e25f3727 | 8467 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8468 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8469 | if (yy == 0) |
8470 | scm_num_overflow (s_divide); | |
8471 | else | |
7351e207 | 8472 | #endif |
98237784 MW |
8473 | /* FIXME: Precision may be lost here due to: |
8474 | (1) The cast from 'scm_t_inum' to 'double' | |
8475 | (2) Double rounding */ | |
55f26379 | 8476 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8477 | } |
8478 | else if (SCM_BIGP (y)) | |
8479 | { | |
98237784 MW |
8480 | /* FIXME: Precision may be lost here due to: |
8481 | (1) The conversion from bignum to double | |
8482 | (2) Double rounding */ | |
0aacf84e MD |
8483 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8484 | scm_remember_upto_here_1 (y); | |
55f26379 | 8485 | return scm_from_double (rx / dby); |
0aacf84e MD |
8486 | } |
8487 | else if (SCM_REALP (y)) | |
8488 | { | |
8489 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8490 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8491 | if (yy == 0.0) |
8492 | scm_num_overflow (s_divide); | |
8493 | else | |
7351e207 | 8494 | #endif |
55f26379 | 8495 | return scm_from_double (rx / yy); |
0aacf84e MD |
8496 | } |
8497 | else if (SCM_COMPLEXP (y)) | |
8498 | { | |
8499 | a = rx; | |
8500 | goto complex_div; | |
8501 | } | |
f92e85f7 | 8502 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8503 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e | 8504 | else |
fa075d40 | 8505 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f872b822 | 8506 | } |
0aacf84e MD |
8507 | else if (SCM_COMPLEXP (x)) |
8508 | { | |
8509 | double rx = SCM_COMPLEX_REAL (x); | |
8510 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8511 | if (SCM_I_INUMP (y)) |
0aacf84e | 8512 | { |
e25f3727 | 8513 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8514 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8515 | if (yy == 0) |
8516 | scm_num_overflow (s_divide); | |
8517 | else | |
7351e207 | 8518 | #endif |
0aacf84e | 8519 | { |
98237784 MW |
8520 | /* FIXME: Precision may be lost here due to: |
8521 | (1) The conversion from 'scm_t_inum' to double | |
8522 | (2) Double rounding */ | |
0aacf84e | 8523 | double d = yy; |
8507ec80 | 8524 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8525 | } |
8526 | } | |
8527 | else if (SCM_BIGP (y)) | |
8528 | { | |
98237784 MW |
8529 | /* FIXME: Precision may be lost here due to: |
8530 | (1) The conversion from bignum to double | |
8531 | (2) Double rounding */ | |
0aacf84e MD |
8532 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8533 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8534 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8535 | } |
8536 | else if (SCM_REALP (y)) | |
8537 | { | |
8538 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8539 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8540 | if (yy == 0.0) |
8541 | scm_num_overflow (s_divide); | |
8542 | else | |
7351e207 | 8543 | #endif |
8507ec80 | 8544 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8545 | } |
8546 | else if (SCM_COMPLEXP (y)) | |
8547 | { | |
8548 | double ry = SCM_COMPLEX_REAL (y); | |
8549 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8550 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8551 | { |
8552 | double t = ry / iy; | |
8553 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8554 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8555 | } |
8556 | else | |
8557 | { | |
8558 | double t = iy / ry; | |
8559 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8560 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8561 | } |
8562 | } | |
f92e85f7 MV |
8563 | else if (SCM_FRACTIONP (y)) |
8564 | { | |
98237784 MW |
8565 | /* FIXME: Precision may be lost here due to: |
8566 | (1) The conversion from fraction to double | |
8567 | (2) Double rounding */ | |
f92e85f7 | 8568 | double yy = scm_i_fraction2double (y); |
8507ec80 | 8569 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8570 | } |
0aacf84e | 8571 | else |
fa075d40 | 8572 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f8de44c1 | 8573 | } |
f92e85f7 MV |
8574 | else if (SCM_FRACTIONP (x)) |
8575 | { | |
e11e83f3 | 8576 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8577 | { |
e25f3727 | 8578 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8579 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8580 | if (yy == 0) | |
8581 | scm_num_overflow (s_divide); | |
8582 | else | |
8583 | #endif | |
cba42c93 | 8584 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8585 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8586 | } |
8587 | else if (SCM_BIGP (y)) | |
8588 | { | |
cba42c93 | 8589 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8590 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8591 | } |
8592 | else if (SCM_REALP (y)) | |
8593 | { | |
8594 | double yy = SCM_REAL_VALUE (y); | |
8595 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8596 | if (yy == 0.0) | |
8597 | scm_num_overflow (s_divide); | |
8598 | else | |
8599 | #endif | |
98237784 MW |
8600 | /* FIXME: Precision may be lost here due to: |
8601 | (1) The conversion from fraction to double | |
8602 | (2) Double rounding */ | |
55f26379 | 8603 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8604 | } |
8605 | else if (SCM_COMPLEXP (y)) | |
8606 | { | |
98237784 MW |
8607 | /* FIXME: Precision may be lost here due to: |
8608 | (1) The conversion from fraction to double | |
8609 | (2) Double rounding */ | |
f92e85f7 MV |
8610 | a = scm_i_fraction2double (x); |
8611 | goto complex_div; | |
8612 | } | |
8613 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8614 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8615 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
f92e85f7 | 8616 | else |
fa075d40 | 8617 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f92e85f7 | 8618 | } |
0aacf84e | 8619 | else |
fa075d40 | 8620 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8621 | } |
c05e97b7 | 8622 | #undef FUNC_NAME |
0f2d19dd | 8623 | |
fa605590 | 8624 | |
0f2d19dd | 8625 | double |
3101f40f | 8626 | scm_c_truncate (double x) |
0f2d19dd | 8627 | { |
fa605590 | 8628 | return trunc (x); |
0f2d19dd | 8629 | } |
0f2d19dd | 8630 | |
3101f40f MV |
8631 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8632 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8633 | Then half-way cases are identified and adjusted down if the | |
8634 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8635 | |
8636 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8637 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8638 | ||
8639 | An odd "result" value is identified with result/2 != floor(result/2). | |
8640 | This is done with plus_half, since that value is ready for use sooner in | |
8641 | a pipelined cpu, and we're already requiring plus_half == result. | |
8642 | ||
8643 | Note however that we need to be careful when x is big and already an | |
8644 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8645 | us to return such a value, incorrectly. For instance if the hardware is | |
8646 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8647 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8648 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8649 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8650 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8651 | ||
8652 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8653 | x is already an integer. If it is then clearly that's the desired result | |
8654 | already. And if it's not then the exponent must be small enough to allow | |
8655 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8656 | ||
0f2d19dd | 8657 | double |
3101f40f | 8658 | scm_c_round (double x) |
0f2d19dd | 8659 | { |
6187f48b KR |
8660 | double plus_half, result; |
8661 | ||
8662 | if (x == floor (x)) | |
8663 | return x; | |
8664 | ||
8665 | plus_half = x + 0.5; | |
8666 | result = floor (plus_half); | |
3101f40f | 8667 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8668 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8669 | ? result - 1 | |
8670 | : result); | |
0f2d19dd JB |
8671 | } |
8672 | ||
8b56bcec MW |
8673 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8674 | (SCM x), | |
8675 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8676 | #define FUNC_NAME s_scm_truncate_number |
8677 | { | |
8b56bcec MW |
8678 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8679 | return x; | |
8680 | else if (SCM_REALP (x)) | |
c251ab63 | 8681 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8682 | else if (SCM_FRACTIONP (x)) |
8683 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8684 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8685 | else |
fa075d40 | 8686 | return scm_wta_dispatch_1 (g_scm_truncate_number, x, SCM_ARG1, |
8b56bcec | 8687 | s_scm_truncate_number); |
f92e85f7 MV |
8688 | } |
8689 | #undef FUNC_NAME | |
8690 | ||
8b56bcec MW |
8691 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8692 | (SCM x), | |
8693 | "Round the number @var{x} towards the nearest integer. " | |
8694 | "When it is exactly halfway between two integers, " | |
8695 | "round towards the even one.") | |
f92e85f7 MV |
8696 | #define FUNC_NAME s_scm_round_number |
8697 | { | |
e11e83f3 | 8698 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8699 | return x; |
8700 | else if (SCM_REALP (x)) | |
3101f40f | 8701 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8702 | else if (SCM_FRACTIONP (x)) |
8703 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8704 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8705 | else |
fa075d40 AW |
8706 | return scm_wta_dispatch_1 (g_scm_round_number, x, SCM_ARG1, |
8707 | s_scm_round_number); | |
f92e85f7 MV |
8708 | } |
8709 | #undef FUNC_NAME | |
8710 | ||
8711 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8712 | (SCM x), | |
8713 | "Round the number @var{x} towards minus infinity.") | |
8714 | #define FUNC_NAME s_scm_floor | |
8715 | { | |
e11e83f3 | 8716 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8717 | return x; |
8718 | else if (SCM_REALP (x)) | |
55f26379 | 8719 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8720 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8721 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8722 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8723 | else |
fa075d40 | 8724 | return scm_wta_dispatch_1 (g_scm_floor, x, 1, s_scm_floor); |
f92e85f7 MV |
8725 | } |
8726 | #undef FUNC_NAME | |
8727 | ||
8728 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8729 | (SCM x), | |
8730 | "Round the number @var{x} towards infinity.") | |
8731 | #define FUNC_NAME s_scm_ceiling | |
8732 | { | |
e11e83f3 | 8733 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8734 | return x; |
8735 | else if (SCM_REALP (x)) | |
55f26379 | 8736 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8737 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8738 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8739 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8740 | else |
fa075d40 | 8741 | return scm_wta_dispatch_1 (g_scm_ceiling, x, 1, s_scm_ceiling); |
f92e85f7 MV |
8742 | } |
8743 | #undef FUNC_NAME | |
0f2d19dd | 8744 | |
2519490c MW |
8745 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8746 | (SCM x, SCM y), | |
8747 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8748 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8749 | { |
01c7284a MW |
8750 | if (scm_is_integer (y)) |
8751 | { | |
8752 | if (scm_is_true (scm_exact_p (y))) | |
8753 | return scm_integer_expt (x, y); | |
8754 | else | |
8755 | { | |
8756 | /* Here we handle the case where the exponent is an inexact | |
8757 | integer. We make the exponent exact in order to use | |
8758 | scm_integer_expt, and thus avoid the spurious imaginary | |
8759 | parts that may result from round-off errors in the general | |
8760 | e^(y log x) method below (for example when squaring a large | |
8761 | negative number). In this case, we must return an inexact | |
8762 | result for correctness. We also make the base inexact so | |
8763 | that scm_integer_expt will use fast inexact arithmetic | |
8764 | internally. Note that making the base inexact is not | |
8765 | sufficient to guarantee an inexact result, because | |
8766 | scm_integer_expt will return an exact 1 when the exponent | |
8767 | is 0, even if the base is inexact. */ | |
8768 | return scm_exact_to_inexact | |
8769 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8770 | scm_inexact_to_exact (y))); | |
8771 | } | |
8772 | } | |
6fc4d012 AW |
8773 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8774 | { | |
8775 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8776 | } | |
2519490c | 8777 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8778 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c | 8779 | else if (scm_is_complex (x)) |
fa075d40 | 8780 | return scm_wta_dispatch_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); |
2519490c | 8781 | else |
fa075d40 | 8782 | return scm_wta_dispatch_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); |
0f2d19dd | 8783 | } |
1bbd0b84 | 8784 | #undef FUNC_NAME |
0f2d19dd | 8785 | |
7f41099e MW |
8786 | /* sin/cos/tan/asin/acos/atan |
8787 | sinh/cosh/tanh/asinh/acosh/atanh | |
8788 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8789 | Written by Jerry D. Hedden, (C) FSF. | |
8790 | See the file `COPYING' for terms applying to this program. */ | |
8791 | ||
ad79736c AW |
8792 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8793 | (SCM z), | |
8794 | "Compute the sine of @var{z}.") | |
8795 | #define FUNC_NAME s_scm_sin | |
8796 | { | |
8deddc94 MW |
8797 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8798 | return z; /* sin(exact0) = exact0 */ | |
8799 | else if (scm_is_real (z)) | |
ad79736c AW |
8800 | return scm_from_double (sin (scm_to_double (z))); |
8801 | else if (SCM_COMPLEXP (z)) | |
8802 | { double x, y; | |
8803 | x = SCM_COMPLEX_REAL (z); | |
8804 | y = SCM_COMPLEX_IMAG (z); | |
8805 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8806 | cos (x) * sinh (y)); | |
8807 | } | |
8808 | else | |
fa075d40 | 8809 | return scm_wta_dispatch_1 (g_scm_sin, z, 1, s_scm_sin); |
ad79736c AW |
8810 | } |
8811 | #undef FUNC_NAME | |
0f2d19dd | 8812 | |
ad79736c AW |
8813 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8814 | (SCM z), | |
8815 | "Compute the cosine of @var{z}.") | |
8816 | #define FUNC_NAME s_scm_cos | |
8817 | { | |
8deddc94 MW |
8818 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8819 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8820 | else if (scm_is_real (z)) | |
ad79736c AW |
8821 | return scm_from_double (cos (scm_to_double (z))); |
8822 | else if (SCM_COMPLEXP (z)) | |
8823 | { double x, y; | |
8824 | x = SCM_COMPLEX_REAL (z); | |
8825 | y = SCM_COMPLEX_IMAG (z); | |
8826 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8827 | -sin (x) * sinh (y)); | |
8828 | } | |
8829 | else | |
fa075d40 | 8830 | return scm_wta_dispatch_1 (g_scm_cos, z, 1, s_scm_cos); |
ad79736c AW |
8831 | } |
8832 | #undef FUNC_NAME | |
8833 | ||
8834 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8835 | (SCM z), | |
8836 | "Compute the tangent of @var{z}.") | |
8837 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8838 | { |
8deddc94 MW |
8839 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8840 | return z; /* tan(exact0) = exact0 */ | |
8841 | else if (scm_is_real (z)) | |
ad79736c AW |
8842 | return scm_from_double (tan (scm_to_double (z))); |
8843 | else if (SCM_COMPLEXP (z)) | |
8844 | { double x, y, w; | |
8845 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8846 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8847 | w = cos (x) + cosh (y); | |
8848 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8849 | if (w == 0.0) | |
8850 | scm_num_overflow (s_scm_tan); | |
8851 | #endif | |
8852 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8853 | } | |
8854 | else | |
fa075d40 | 8855 | return scm_wta_dispatch_1 (g_scm_tan, z, 1, s_scm_tan); |
ad79736c AW |
8856 | } |
8857 | #undef FUNC_NAME | |
8858 | ||
8859 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8860 | (SCM z), | |
8861 | "Compute the hyperbolic sine of @var{z}.") | |
8862 | #define FUNC_NAME s_scm_sinh | |
8863 | { | |
8deddc94 MW |
8864 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8865 | return z; /* sinh(exact0) = exact0 */ | |
8866 | else if (scm_is_real (z)) | |
ad79736c AW |
8867 | return scm_from_double (sinh (scm_to_double (z))); |
8868 | else if (SCM_COMPLEXP (z)) | |
8869 | { double x, y; | |
8870 | x = SCM_COMPLEX_REAL (z); | |
8871 | y = SCM_COMPLEX_IMAG (z); | |
8872 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8873 | cosh (x) * sin (y)); | |
8874 | } | |
8875 | else | |
fa075d40 | 8876 | return scm_wta_dispatch_1 (g_scm_sinh, z, 1, s_scm_sinh); |
ad79736c AW |
8877 | } |
8878 | #undef FUNC_NAME | |
8879 | ||
8880 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8881 | (SCM z), | |
8882 | "Compute the hyperbolic cosine of @var{z}.") | |
8883 | #define FUNC_NAME s_scm_cosh | |
8884 | { | |
8deddc94 MW |
8885 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8886 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8887 | else if (scm_is_real (z)) | |
ad79736c AW |
8888 | return scm_from_double (cosh (scm_to_double (z))); |
8889 | else if (SCM_COMPLEXP (z)) | |
8890 | { double x, y; | |
8891 | x = SCM_COMPLEX_REAL (z); | |
8892 | y = SCM_COMPLEX_IMAG (z); | |
8893 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8894 | sinh (x) * sin (y)); | |
8895 | } | |
8896 | else | |
fa075d40 | 8897 | return scm_wta_dispatch_1 (g_scm_cosh, z, 1, s_scm_cosh); |
ad79736c AW |
8898 | } |
8899 | #undef FUNC_NAME | |
8900 | ||
8901 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8902 | (SCM z), | |
8903 | "Compute the hyperbolic tangent of @var{z}.") | |
8904 | #define FUNC_NAME s_scm_tanh | |
8905 | { | |
8deddc94 MW |
8906 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8907 | return z; /* tanh(exact0) = exact0 */ | |
8908 | else if (scm_is_real (z)) | |
ad79736c AW |
8909 | return scm_from_double (tanh (scm_to_double (z))); |
8910 | else if (SCM_COMPLEXP (z)) | |
8911 | { double x, y, w; | |
8912 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8913 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8914 | w = cosh (x) + cos (y); | |
8915 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8916 | if (w == 0.0) | |
8917 | scm_num_overflow (s_scm_tanh); | |
8918 | #endif | |
8919 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8920 | } | |
8921 | else | |
fa075d40 | 8922 | return scm_wta_dispatch_1 (g_scm_tanh, z, 1, s_scm_tanh); |
ad79736c AW |
8923 | } |
8924 | #undef FUNC_NAME | |
8925 | ||
8926 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8927 | (SCM z), | |
8928 | "Compute the arc sine of @var{z}.") | |
8929 | #define FUNC_NAME s_scm_asin | |
8930 | { | |
8deddc94 MW |
8931 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8932 | return z; /* asin(exact0) = exact0 */ | |
8933 | else if (scm_is_real (z)) | |
ad79736c AW |
8934 | { |
8935 | double w = scm_to_double (z); | |
8936 | if (w >= -1.0 && w <= 1.0) | |
8937 | return scm_from_double (asin (w)); | |
8938 | else | |
8939 | return scm_product (scm_c_make_rectangular (0, -1), | |
8940 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8941 | } | |
8942 | else if (SCM_COMPLEXP (z)) | |
8943 | { double x, y; | |
8944 | x = SCM_COMPLEX_REAL (z); | |
8945 | y = SCM_COMPLEX_IMAG (z); | |
8946 | return scm_product (scm_c_make_rectangular (0, -1), | |
8947 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8948 | } | |
8949 | else | |
fa075d40 | 8950 | return scm_wta_dispatch_1 (g_scm_asin, z, 1, s_scm_asin); |
ad79736c AW |
8951 | } |
8952 | #undef FUNC_NAME | |
8953 | ||
8954 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8955 | (SCM z), | |
8956 | "Compute the arc cosine of @var{z}.") | |
8957 | #define FUNC_NAME s_scm_acos | |
8958 | { | |
8deddc94 MW |
8959 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8960 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8961 | else if (scm_is_real (z)) | |
ad79736c AW |
8962 | { |
8963 | double w = scm_to_double (z); | |
8964 | if (w >= -1.0 && w <= 1.0) | |
8965 | return scm_from_double (acos (w)); | |
8966 | else | |
8967 | return scm_sum (scm_from_double (acos (0.0)), | |
8968 | scm_product (scm_c_make_rectangular (0, 1), | |
8969 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8970 | } | |
8971 | else if (SCM_COMPLEXP (z)) | |
8972 | { double x, y; | |
8973 | x = SCM_COMPLEX_REAL (z); | |
8974 | y = SCM_COMPLEX_IMAG (z); | |
8975 | return scm_sum (scm_from_double (acos (0.0)), | |
8976 | scm_product (scm_c_make_rectangular (0, 1), | |
8977 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8978 | } | |
8979 | else | |
fa075d40 | 8980 | return scm_wta_dispatch_1 (g_scm_acos, z, 1, s_scm_acos); |
ad79736c AW |
8981 | } |
8982 | #undef FUNC_NAME | |
8983 | ||
8984 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8985 | (SCM z, SCM y), | |
8986 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8987 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8988 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8989 | #define FUNC_NAME s_scm_atan | |
8990 | { | |
8991 | if (SCM_UNBNDP (y)) | |
8992 | { | |
8deddc94 MW |
8993 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8994 | return z; /* atan(exact0) = exact0 */ | |
8995 | else if (scm_is_real (z)) | |
ad79736c AW |
8996 | return scm_from_double (atan (scm_to_double (z))); |
8997 | else if (SCM_COMPLEXP (z)) | |
8998 | { | |
8999 | double v, w; | |
9000 | v = SCM_COMPLEX_REAL (z); | |
9001 | w = SCM_COMPLEX_IMAG (z); | |
9002 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
9003 | scm_c_make_rectangular (v, w + 1.0))), | |
9004 | scm_c_make_rectangular (0, 2)); | |
9005 | } | |
9006 | else | |
fa075d40 | 9007 | return scm_wta_dispatch_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
9008 | } |
9009 | else if (scm_is_real (z)) | |
9010 | { | |
9011 | if (scm_is_real (y)) | |
9012 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
9013 | else | |
fa075d40 | 9014 | return scm_wta_dispatch_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); |
ad79736c AW |
9015 | } |
9016 | else | |
fa075d40 | 9017 | return scm_wta_dispatch_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); |
ad79736c AW |
9018 | } |
9019 | #undef FUNC_NAME | |
9020 | ||
9021 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
9022 | (SCM z), | |
9023 | "Compute the inverse hyperbolic sine of @var{z}.") | |
9024 | #define FUNC_NAME s_scm_sys_asinh | |
9025 | { | |
8deddc94 MW |
9026 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9027 | return z; /* asinh(exact0) = exact0 */ | |
9028 | else if (scm_is_real (z)) | |
ad79736c AW |
9029 | return scm_from_double (asinh (scm_to_double (z))); |
9030 | else if (scm_is_number (z)) | |
9031 | return scm_log (scm_sum (z, | |
9032 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 9033 | SCM_INUM1)))); |
ad79736c | 9034 | else |
fa075d40 | 9035 | return scm_wta_dispatch_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); |
ad79736c AW |
9036 | } |
9037 | #undef FUNC_NAME | |
9038 | ||
9039 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
9040 | (SCM z), | |
9041 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
9042 | #define FUNC_NAME s_scm_sys_acosh | |
9043 | { | |
8deddc94 MW |
9044 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
9045 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
9046 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
9047 | return scm_from_double (acosh (scm_to_double (z))); |
9048 | else if (scm_is_number (z)) | |
9049 | return scm_log (scm_sum (z, | |
9050 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 9051 | SCM_INUM1)))); |
ad79736c | 9052 | else |
fa075d40 | 9053 | return scm_wta_dispatch_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); |
ad79736c AW |
9054 | } |
9055 | #undef FUNC_NAME | |
9056 | ||
9057 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
9058 | (SCM z), | |
9059 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
9060 | #define FUNC_NAME s_scm_sys_atanh | |
9061 | { | |
8deddc94 MW |
9062 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9063 | return z; /* atanh(exact0) = exact0 */ | |
9064 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
9065 | return scm_from_double (atanh (scm_to_double (z))); |
9066 | else if (scm_is_number (z)) | |
cff5fa33 MW |
9067 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
9068 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
9069 | SCM_I_MAKINUM (2)); |
9070 | else | |
fa075d40 | 9071 | return scm_wta_dispatch_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); |
0f2d19dd | 9072 | } |
1bbd0b84 | 9073 | #undef FUNC_NAME |
0f2d19dd | 9074 | |
8507ec80 MV |
9075 | SCM |
9076 | scm_c_make_rectangular (double re, double im) | |
9077 | { | |
c7218482 | 9078 | SCM z; |
03604fcf | 9079 | |
21041372 | 9080 | z = SCM_PACK_POINTER (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
c7218482 MW |
9081 | "complex")); |
9082 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
9083 | SCM_COMPLEX_REAL (z) = re; | |
9084 | SCM_COMPLEX_IMAG (z) = im; | |
9085 | return z; | |
8507ec80 | 9086 | } |
0f2d19dd | 9087 | |
a1ec6916 | 9088 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 9089 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
9090 | "Return a complex number constructed of the given @var{real_part} " |
9091 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 9092 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 9093 | { |
ad79736c AW |
9094 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
9095 | SCM_ARG1, FUNC_NAME, "real"); | |
9096 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
9097 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
9098 | |
9099 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
9100 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
9101 | return real_part; | |
9102 | else | |
9103 | return scm_c_make_rectangular (scm_to_double (real_part), | |
9104 | scm_to_double (imaginary_part)); | |
0f2d19dd | 9105 | } |
1bbd0b84 | 9106 | #undef FUNC_NAME |
0f2d19dd | 9107 | |
8507ec80 MV |
9108 | SCM |
9109 | scm_c_make_polar (double mag, double ang) | |
9110 | { | |
9111 | double s, c; | |
5e647d08 LC |
9112 | |
9113 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
9114 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
9115 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
9116 | details. */ | |
9117 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
9118 | sincos (ang, &s, &c); |
9119 | #else | |
9120 | s = sin (ang); | |
9121 | c = cos (ang); | |
9122 | #endif | |
9d427b2c MW |
9123 | |
9124 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
9125 | infinite, or perhaps simply too large to determine its value | |
9126 | mod 2*pi. However, we know something that the floating-point | |
9127 | implementation doesn't know: We know that s and c are finite. | |
9128 | Therefore, if the magnitude is zero, return a complex zero. | |
9129 | ||
9130 | The reason we check for the NaNs instead of using this case | |
9131 | whenever mag == 0.0 is because when the angle is known, we'd | |
9132 | like to return the correct kind of non-real complex zero: | |
9133 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
9134 | on which quadrant the angle is in. | |
9135 | */ | |
9136 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
9137 | return scm_c_make_rectangular (0.0, 0.0); | |
9138 | else | |
9139 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 9140 | } |
0f2d19dd | 9141 | |
a1ec6916 | 9142 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
9143 | (SCM mag, SCM ang), |
9144 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 9145 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 9146 | { |
c7218482 MW |
9147 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
9148 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
9149 | ||
9150 | /* If mag is exact0, return exact0 */ | |
9151 | if (scm_is_eq (mag, SCM_INUM0)) | |
9152 | return SCM_INUM0; | |
9153 | /* Return a real if ang is exact0 */ | |
9154 | else if (scm_is_eq (ang, SCM_INUM0)) | |
9155 | return mag; | |
9156 | else | |
9157 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 9158 | } |
1bbd0b84 | 9159 | #undef FUNC_NAME |
0f2d19dd JB |
9160 | |
9161 | ||
2519490c MW |
9162 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
9163 | (SCM z), | |
9164 | "Return the real part of the number @var{z}.") | |
9165 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 9166 | { |
2519490c | 9167 | if (SCM_COMPLEXP (z)) |
55f26379 | 9168 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 9169 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 9170 | return z; |
0aacf84e | 9171 | else |
fa075d40 | 9172 | return scm_wta_dispatch_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 9173 | } |
2519490c | 9174 | #undef FUNC_NAME |
0f2d19dd JB |
9175 | |
9176 | ||
2519490c MW |
9177 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
9178 | (SCM z), | |
9179 | "Return the imaginary part of the number @var{z}.") | |
9180 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 9181 | { |
2519490c MW |
9182 | if (SCM_COMPLEXP (z)) |
9183 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 9184 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 9185 | return SCM_INUM0; |
0aacf84e | 9186 | else |
fa075d40 | 9187 | return scm_wta_dispatch_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 9188 | } |
2519490c | 9189 | #undef FUNC_NAME |
0f2d19dd | 9190 | |
2519490c MW |
9191 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
9192 | (SCM z), | |
9193 | "Return the numerator of the number @var{z}.") | |
9194 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 9195 | { |
2519490c | 9196 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
9197 | return z; |
9198 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 9199 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
9200 | else if (SCM_REALP (z)) |
9201 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
9202 | else | |
fa075d40 | 9203 | return scm_wta_dispatch_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 9204 | } |
2519490c | 9205 | #undef FUNC_NAME |
f92e85f7 MV |
9206 | |
9207 | ||
2519490c MW |
9208 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
9209 | (SCM z), | |
9210 | "Return the denominator of the number @var{z}.") | |
9211 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 9212 | { |
2519490c | 9213 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 9214 | return SCM_INUM1; |
f92e85f7 | 9215 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 9216 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
9217 | else if (SCM_REALP (z)) |
9218 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
9219 | else | |
fa075d40 AW |
9220 | return scm_wta_dispatch_1 (g_scm_denominator, z, SCM_ARG1, |
9221 | s_scm_denominator); | |
f92e85f7 | 9222 | } |
2519490c | 9223 | #undef FUNC_NAME |
0f2d19dd | 9224 | |
2519490c MW |
9225 | |
9226 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
9227 | (SCM z), | |
9228 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
9229 | "@code{abs} for real arguments, but also allows complex numbers.") | |
9230 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 9231 | { |
e11e83f3 | 9232 | if (SCM_I_INUMP (z)) |
0aacf84e | 9233 | { |
e25f3727 | 9234 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
9235 | if (zz >= 0) |
9236 | return z; | |
9237 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 9238 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 9239 | else |
e25f3727 | 9240 | return scm_i_inum2big (-zz); |
5986c47d | 9241 | } |
0aacf84e MD |
9242 | else if (SCM_BIGP (z)) |
9243 | { | |
9244 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9245 | scm_remember_upto_here_1 (z); | |
9246 | if (sgn < 0) | |
9247 | return scm_i_clonebig (z, 0); | |
9248 | else | |
9249 | return z; | |
5986c47d | 9250 | } |
0aacf84e | 9251 | else if (SCM_REALP (z)) |
55f26379 | 9252 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 9253 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9254 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
9255 | else if (SCM_FRACTIONP (z)) |
9256 | { | |
73e4de09 | 9257 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 9258 | return z; |
a285b18c MW |
9259 | return scm_i_make_ratio_already_reduced |
9260 | (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), | |
9261 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 | 9262 | } |
0aacf84e | 9263 | else |
fa075d40 AW |
9264 | return scm_wta_dispatch_1 (g_scm_magnitude, z, SCM_ARG1, |
9265 | s_scm_magnitude); | |
0f2d19dd | 9266 | } |
2519490c | 9267 | #undef FUNC_NAME |
0f2d19dd JB |
9268 | |
9269 | ||
2519490c MW |
9270 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
9271 | (SCM z), | |
9272 | "Return the angle of the complex number @var{z}.") | |
9273 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 9274 | { |
c8ae173e | 9275 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 9276 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
9277 | But if atan2 follows the floating point rounding mode, then the value |
9278 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 9279 | if (SCM_I_INUMP (z)) |
0aacf84e | 9280 | { |
e11e83f3 | 9281 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 9282 | return flo0; |
0aacf84e | 9283 | else |
55f26379 | 9284 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 9285 | } |
0aacf84e MD |
9286 | else if (SCM_BIGP (z)) |
9287 | { | |
9288 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9289 | scm_remember_upto_here_1 (z); | |
9290 | if (sgn < 0) | |
55f26379 | 9291 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 9292 | else |
e7efe8e7 | 9293 | return flo0; |
0f2d19dd | 9294 | } |
0aacf84e | 9295 | else if (SCM_REALP (z)) |
c8ae173e | 9296 | { |
10a97755 MW |
9297 | double x = SCM_REAL_VALUE (z); |
9298 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
e7efe8e7 | 9299 | return flo0; |
c8ae173e | 9300 | else |
55f26379 | 9301 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 9302 | } |
0aacf84e | 9303 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9304 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
9305 | else if (SCM_FRACTIONP (z)) |
9306 | { | |
73e4de09 | 9307 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 9308 | return flo0; |
55f26379 | 9309 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 9310 | } |
0aacf84e | 9311 | else |
fa075d40 | 9312 | return scm_wta_dispatch_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 9313 | } |
2519490c | 9314 | #undef FUNC_NAME |
0f2d19dd JB |
9315 | |
9316 | ||
2519490c MW |
9317 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
9318 | (SCM z), | |
9319 | "Convert the number @var{z} to its inexact representation.\n") | |
9320 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 9321 | { |
e11e83f3 | 9322 | if (SCM_I_INUMP (z)) |
55f26379 | 9323 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 9324 | else if (SCM_BIGP (z)) |
55f26379 | 9325 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 9326 | else if (SCM_FRACTIONP (z)) |
55f26379 | 9327 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
9328 | else if (SCM_INEXACTP (z)) |
9329 | return z; | |
9330 | else | |
fa075d40 AW |
9331 | return scm_wta_dispatch_1 (g_scm_exact_to_inexact, z, 1, |
9332 | s_scm_exact_to_inexact); | |
3c9a524f | 9333 | } |
2519490c | 9334 | #undef FUNC_NAME |
3c9a524f DH |
9335 | |
9336 | ||
2519490c MW |
9337 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
9338 | (SCM z), | |
9339 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 9340 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 9341 | { |
c7218482 | 9342 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 9343 | return z; |
c7218482 | 9344 | else |
0aacf84e | 9345 | { |
c7218482 MW |
9346 | double val; |
9347 | ||
9348 | if (SCM_REALP (z)) | |
9349 | val = SCM_REAL_VALUE (z); | |
9350 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
9351 | val = SCM_COMPLEX_REAL (z); | |
9352 | else | |
fa075d40 AW |
9353 | return scm_wta_dispatch_1 (g_scm_inexact_to_exact, z, 1, |
9354 | s_scm_inexact_to_exact); | |
c7218482 MW |
9355 | |
9356 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 9357 | SCM_OUT_OF_RANGE (1, z); |
24475b86 MW |
9358 | else if (val == 0.0) |
9359 | return SCM_INUM0; | |
2be24db4 | 9360 | else |
f92e85f7 | 9361 | { |
24475b86 MW |
9362 | int expon; |
9363 | SCM numerator; | |
f92e85f7 | 9364 | |
24475b86 MW |
9365 | numerator = scm_i_dbl2big (ldexp (frexp (val, &expon), |
9366 | DBL_MANT_DIG)); | |
9367 | expon -= DBL_MANT_DIG; | |
9368 | if (expon < 0) | |
9369 | { | |
9370 | int shift = mpz_scan1 (SCM_I_BIG_MPZ (numerator), 0); | |
9371 | ||
9372 | if (shift > -expon) | |
9373 | shift = -expon; | |
9374 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (numerator), | |
9375 | SCM_I_BIG_MPZ (numerator), | |
9376 | shift); | |
9377 | expon += shift; | |
9378 | } | |
9379 | numerator = scm_i_normbig (numerator); | |
9380 | if (expon < 0) | |
9381 | return scm_i_make_ratio_already_reduced | |
9382 | (numerator, left_shift_exact_integer (SCM_INUM1, -expon)); | |
9383 | else if (expon > 0) | |
9384 | return left_shift_exact_integer (numerator, expon); | |
9385 | else | |
9386 | return numerator; | |
f92e85f7 | 9387 | } |
c2ff8ab0 | 9388 | } |
0f2d19dd | 9389 | } |
1bbd0b84 | 9390 | #undef FUNC_NAME |
0f2d19dd | 9391 | |
f92e85f7 | 9392 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
9393 | (SCM x, SCM eps), |
9394 | "Returns the @emph{simplest} rational number differing\n" | |
9395 | "from @var{x} by no more than @var{eps}.\n" | |
9396 | "\n" | |
9397 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9398 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9399 | "to use @code{inexact->exact} on the arguments.\n" | |
9400 | "\n" | |
9401 | "@lisp\n" | |
9402 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9403 | "@result{} 6/5\n" | |
9404 | "@end lisp") | |
f92e85f7 MV |
9405 | #define FUNC_NAME s_scm_rationalize |
9406 | { | |
605f6980 MW |
9407 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9408 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9409 | eps = scm_abs (eps); | |
9410 | if (scm_is_false (scm_positive_p (eps))) | |
9411 | { | |
9412 | /* eps is either zero or a NaN */ | |
9413 | if (scm_is_true (scm_nan_p (eps))) | |
9414 | return scm_nan (); | |
9415 | else if (SCM_INEXACTP (eps)) | |
9416 | return scm_exact_to_inexact (x); | |
9417 | else | |
9418 | return x; | |
9419 | } | |
9420 | else if (scm_is_false (scm_finite_p (eps))) | |
9421 | { | |
9422 | if (scm_is_true (scm_finite_p (x))) | |
9423 | return flo0; | |
9424 | else | |
9425 | return scm_nan (); | |
9426 | } | |
9427 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9428 | return x; |
605f6980 MW |
9429 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9430 | scm_ceiling (scm_difference (x, eps))))) | |
9431 | { | |
9432 | /* There's an integer within range; we want the one closest to zero */ | |
9433 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9434 | { | |
9435 | /* zero is within range */ | |
9436 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9437 | return flo0; | |
9438 | else | |
9439 | return SCM_INUM0; | |
9440 | } | |
9441 | else if (scm_is_true (scm_positive_p (x))) | |
9442 | return scm_ceiling (scm_difference (x, eps)); | |
9443 | else | |
9444 | return scm_floor (scm_sum (x, eps)); | |
9445 | } | |
9446 | else | |
f92e85f7 MV |
9447 | { |
9448 | /* Use continued fractions to find closest ratio. All | |
9449 | arithmetic is done with exact numbers. | |
9450 | */ | |
9451 | ||
9452 | SCM ex = scm_inexact_to_exact (x); | |
9453 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9454 | SCM tt = SCM_INUM1; |
9455 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9456 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9457 | SCM rx; |
9458 | int i = 0; | |
9459 | ||
f92e85f7 MV |
9460 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9461 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9462 | ||
9463 | /* We stop after a million iterations just to be absolutely sure | |
9464 | that we don't go into an infinite loop. The process normally | |
9465 | converges after less than a dozen iterations. | |
9466 | */ | |
9467 | ||
f92e85f7 MV |
9468 | while (++i < 1000000) |
9469 | { | |
9470 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9471 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9472 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9473 | scm_is_false | |
f92e85f7 | 9474 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9475 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9476 | { |
9477 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9478 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9479 | return scm_exact_to_inexact (res); |
9480 | else | |
9481 | return res; | |
9482 | } | |
f92e85f7 MV |
9483 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9484 | SCM_UNDEFINED); | |
9485 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9486 | a2 = a1; | |
9487 | b2 = b1; | |
9488 | a1 = a; | |
9489 | b1 = b; | |
9490 | } | |
9491 | scm_num_overflow (s_scm_rationalize); | |
9492 | } | |
f92e85f7 MV |
9493 | } |
9494 | #undef FUNC_NAME | |
9495 | ||
73e4de09 MV |
9496 | /* conversion functions */ |
9497 | ||
9498 | int | |
9499 | scm_is_integer (SCM val) | |
9500 | { | |
9501 | return scm_is_true (scm_integer_p (val)); | |
9502 | } | |
9503 | ||
9504 | int | |
9505 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9506 | { | |
e11e83f3 | 9507 | if (SCM_I_INUMP (val)) |
73e4de09 | 9508 | { |
e11e83f3 | 9509 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9510 | return n >= min && n <= max; |
9511 | } | |
9512 | else if (SCM_BIGP (val)) | |
9513 | { | |
9514 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9515 | return 0; | |
9516 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9517 | { |
9518 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9519 | { | |
9520 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9521 | return n >= min && n <= max; | |
9522 | } | |
9523 | else | |
9524 | return 0; | |
9525 | } | |
73e4de09 MV |
9526 | else |
9527 | { | |
d956fa6f MV |
9528 | scm_t_intmax n; |
9529 | size_t count; | |
73e4de09 | 9530 | |
d956fa6f MV |
9531 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9532 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9533 | return 0; | |
9534 | ||
9535 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9536 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9537 | |
d956fa6f | 9538 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9539 | { |
d956fa6f MV |
9540 | if (n < 0) |
9541 | return 0; | |
73e4de09 | 9542 | } |
73e4de09 MV |
9543 | else |
9544 | { | |
d956fa6f MV |
9545 | n = -n; |
9546 | if (n >= 0) | |
9547 | return 0; | |
73e4de09 | 9548 | } |
d956fa6f MV |
9549 | |
9550 | return n >= min && n <= max; | |
73e4de09 MV |
9551 | } |
9552 | } | |
73e4de09 MV |
9553 | else |
9554 | return 0; | |
9555 | } | |
9556 | ||
9557 | int | |
9558 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9559 | { | |
e11e83f3 | 9560 | if (SCM_I_INUMP (val)) |
73e4de09 | 9561 | { |
e11e83f3 | 9562 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9563 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9564 | } | |
9565 | else if (SCM_BIGP (val)) | |
9566 | { | |
9567 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9568 | return 0; | |
9569 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9570 | { |
9571 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9572 | { | |
9573 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9574 | return n >= min && n <= max; | |
9575 | } | |
9576 | else | |
9577 | return 0; | |
9578 | } | |
73e4de09 MV |
9579 | else |
9580 | { | |
d956fa6f MV |
9581 | scm_t_uintmax n; |
9582 | size_t count; | |
73e4de09 | 9583 | |
d956fa6f MV |
9584 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9585 | return 0; | |
73e4de09 | 9586 | |
d956fa6f MV |
9587 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9588 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9589 | return 0; |
d956fa6f MV |
9590 | |
9591 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9592 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9593 | |
d956fa6f | 9594 | return n >= min && n <= max; |
73e4de09 MV |
9595 | } |
9596 | } | |
73e4de09 MV |
9597 | else |
9598 | return 0; | |
9599 | } | |
9600 | ||
1713d319 MV |
9601 | static void |
9602 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9603 | { | |
9604 | scm_error (scm_out_of_range_key, | |
9605 | NULL, | |
9606 | "Value out of range ~S to ~S: ~S", | |
9607 | scm_list_3 (min, max, bad_val), | |
9608 | scm_list_1 (bad_val)); | |
9609 | } | |
9610 | ||
bfd7932e MV |
9611 | #define TYPE scm_t_intmax |
9612 | #define TYPE_MIN min | |
9613 | #define TYPE_MAX max | |
9614 | #define SIZEOF_TYPE 0 | |
9615 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9616 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9617 | #include "libguile/conv-integer.i.c" | |
9618 | ||
9619 | #define TYPE scm_t_uintmax | |
9620 | #define TYPE_MIN min | |
9621 | #define TYPE_MAX max | |
9622 | #define SIZEOF_TYPE 0 | |
9623 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9624 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9625 | #include "libguile/conv-uinteger.i.c" | |
9626 | ||
9627 | #define TYPE scm_t_int8 | |
9628 | #define TYPE_MIN SCM_T_INT8_MIN | |
9629 | #define TYPE_MAX SCM_T_INT8_MAX | |
9630 | #define SIZEOF_TYPE 1 | |
9631 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9632 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9633 | #include "libguile/conv-integer.i.c" | |
9634 | ||
9635 | #define TYPE scm_t_uint8 | |
9636 | #define TYPE_MIN 0 | |
9637 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9638 | #define SIZEOF_TYPE 1 | |
9639 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9640 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9641 | #include "libguile/conv-uinteger.i.c" | |
9642 | ||
9643 | #define TYPE scm_t_int16 | |
9644 | #define TYPE_MIN SCM_T_INT16_MIN | |
9645 | #define TYPE_MAX SCM_T_INT16_MAX | |
9646 | #define SIZEOF_TYPE 2 | |
9647 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9648 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9649 | #include "libguile/conv-integer.i.c" | |
9650 | ||
9651 | #define TYPE scm_t_uint16 | |
9652 | #define TYPE_MIN 0 | |
9653 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9654 | #define SIZEOF_TYPE 2 | |
9655 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9656 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9657 | #include "libguile/conv-uinteger.i.c" | |
9658 | ||
9659 | #define TYPE scm_t_int32 | |
9660 | #define TYPE_MIN SCM_T_INT32_MIN | |
9661 | #define TYPE_MAX SCM_T_INT32_MAX | |
9662 | #define SIZEOF_TYPE 4 | |
9663 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9664 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9665 | #include "libguile/conv-integer.i.c" | |
9666 | ||
9667 | #define TYPE scm_t_uint32 | |
9668 | #define TYPE_MIN 0 | |
9669 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9670 | #define SIZEOF_TYPE 4 | |
9671 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9672 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9673 | #include "libguile/conv-uinteger.i.c" | |
9674 | ||
904a78f1 MG |
9675 | #define TYPE scm_t_wchar |
9676 | #define TYPE_MIN (scm_t_int32)-1 | |
9677 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9678 | #define SIZEOF_TYPE 4 | |
9679 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9680 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9681 | #include "libguile/conv-integer.i.c" | |
9682 | ||
bfd7932e MV |
9683 | #define TYPE scm_t_int64 |
9684 | #define TYPE_MIN SCM_T_INT64_MIN | |
9685 | #define TYPE_MAX SCM_T_INT64_MAX | |
9686 | #define SIZEOF_TYPE 8 | |
9687 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9688 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9689 | #include "libguile/conv-integer.i.c" | |
9690 | ||
9691 | #define TYPE scm_t_uint64 | |
9692 | #define TYPE_MIN 0 | |
9693 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9694 | #define SIZEOF_TYPE 8 | |
9695 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9696 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9697 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9698 | |
cd036260 MV |
9699 | void |
9700 | scm_to_mpz (SCM val, mpz_t rop) | |
9701 | { | |
9702 | if (SCM_I_INUMP (val)) | |
9703 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9704 | else if (SCM_BIGP (val)) | |
9705 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9706 | else | |
9707 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9708 | } | |
9709 | ||
9710 | SCM | |
9711 | scm_from_mpz (mpz_t val) | |
9712 | { | |
9713 | return scm_i_mpz2num (val); | |
9714 | } | |
9715 | ||
73e4de09 MV |
9716 | int |
9717 | scm_is_real (SCM val) | |
9718 | { | |
9719 | return scm_is_true (scm_real_p (val)); | |
9720 | } | |
9721 | ||
55f26379 MV |
9722 | int |
9723 | scm_is_rational (SCM val) | |
9724 | { | |
9725 | return scm_is_true (scm_rational_p (val)); | |
9726 | } | |
9727 | ||
73e4de09 MV |
9728 | double |
9729 | scm_to_double (SCM val) | |
9730 | { | |
55f26379 MV |
9731 | if (SCM_I_INUMP (val)) |
9732 | return SCM_I_INUM (val); | |
9733 | else if (SCM_BIGP (val)) | |
9734 | return scm_i_big2dbl (val); | |
9735 | else if (SCM_FRACTIONP (val)) | |
9736 | return scm_i_fraction2double (val); | |
9737 | else if (SCM_REALP (val)) | |
9738 | return SCM_REAL_VALUE (val); | |
9739 | else | |
7a1aba42 | 9740 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9741 | } |
9742 | ||
9743 | SCM | |
9744 | scm_from_double (double val) | |
9745 | { | |
978c52d1 LC |
9746 | SCM z; |
9747 | ||
21041372 | 9748 | z = SCM_PACK_POINTER (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); |
978c52d1 LC |
9749 | |
9750 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9751 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9752 | |
55f26379 | 9753 | return z; |
73e4de09 MV |
9754 | } |
9755 | ||
8507ec80 MV |
9756 | int |
9757 | scm_is_complex (SCM val) | |
9758 | { | |
9759 | return scm_is_true (scm_complex_p (val)); | |
9760 | } | |
9761 | ||
9762 | double | |
9763 | scm_c_real_part (SCM z) | |
9764 | { | |
9765 | if (SCM_COMPLEXP (z)) | |
9766 | return SCM_COMPLEX_REAL (z); | |
9767 | else | |
9768 | { | |
9769 | /* Use the scm_real_part to get proper error checking and | |
9770 | dispatching. | |
9771 | */ | |
9772 | return scm_to_double (scm_real_part (z)); | |
9773 | } | |
9774 | } | |
9775 | ||
9776 | double | |
9777 | scm_c_imag_part (SCM z) | |
9778 | { | |
9779 | if (SCM_COMPLEXP (z)) | |
9780 | return SCM_COMPLEX_IMAG (z); | |
9781 | else | |
9782 | { | |
9783 | /* Use the scm_imag_part to get proper error checking and | |
9784 | dispatching. The result will almost always be 0.0, but not | |
9785 | always. | |
9786 | */ | |
9787 | return scm_to_double (scm_imag_part (z)); | |
9788 | } | |
9789 | } | |
9790 | ||
9791 | double | |
9792 | scm_c_magnitude (SCM z) | |
9793 | { | |
9794 | return scm_to_double (scm_magnitude (z)); | |
9795 | } | |
9796 | ||
9797 | double | |
9798 | scm_c_angle (SCM z) | |
9799 | { | |
9800 | return scm_to_double (scm_angle (z)); | |
9801 | } | |
9802 | ||
9803 | int | |
9804 | scm_is_number (SCM z) | |
9805 | { | |
9806 | return scm_is_true (scm_number_p (z)); | |
9807 | } | |
9808 | ||
8ab3d8a0 | 9809 | |
a5f6b751 MW |
9810 | /* Returns log(x * 2^shift) */ |
9811 | static SCM | |
9812 | log_of_shifted_double (double x, long shift) | |
9813 | { | |
9814 | double ans = log (fabs (x)) + shift * M_LN2; | |
9815 | ||
9816 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9817 | return scm_from_double (ans); | |
9818 | else | |
9819 | return scm_c_make_rectangular (ans, M_PI); | |
9820 | } | |
9821 | ||
85bdb6ac | 9822 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9823 | static SCM |
9824 | log_of_exact_integer (SCM n) | |
9825 | { | |
7f34acd8 MW |
9826 | if (SCM_I_INUMP (n)) |
9827 | return log_of_shifted_double (SCM_I_INUM (n), 0); | |
9828 | else if (SCM_BIGP (n)) | |
9829 | { | |
9830 | long expon; | |
9831 | double signif = scm_i_big2dbl_2exp (n, &expon); | |
9832 | return log_of_shifted_double (signif, expon); | |
9833 | } | |
9834 | else | |
9835 | scm_wrong_type_arg ("log_of_exact_integer", SCM_ARG1, n); | |
a5f6b751 MW |
9836 | } |
9837 | ||
9838 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9839 | static SCM | |
9840 | log_of_fraction (SCM n, SCM d) | |
9841 | { | |
9842 | long n_size = scm_to_long (scm_integer_length (n)); | |
9843 | long d_size = scm_to_long (scm_integer_length (d)); | |
9844 | ||
9845 | if (abs (n_size - d_size) > 1) | |
7f34acd8 MW |
9846 | return (scm_difference (log_of_exact_integer (n), |
9847 | log_of_exact_integer (d))); | |
a5f6b751 MW |
9848 | else if (scm_is_false (scm_negative_p (n))) |
9849 | return scm_from_double | |
98237784 | 9850 | (log1p (scm_i_divide2double (scm_difference (n, d), d))); |
a5f6b751 MW |
9851 | else |
9852 | return scm_c_make_rectangular | |
98237784 MW |
9853 | (log1p (scm_i_divide2double (scm_difference (scm_abs (n), d), |
9854 | d)), | |
a5f6b751 MW |
9855 | M_PI); |
9856 | } | |
9857 | ||
9858 | ||
8ab3d8a0 KR |
9859 | /* In the following functions we dispatch to the real-arg funcs like log() |
9860 | when we know the arg is real, instead of just handing everything to | |
9861 | clog() for instance. This is in case clog() doesn't optimize for a | |
9862 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9863 | well use it to go straight to the applicable C func. */ | |
9864 | ||
2519490c MW |
9865 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9866 | (SCM z), | |
9867 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9868 | #define FUNC_NAME s_scm_log |
9869 | { | |
9870 | if (SCM_COMPLEXP (z)) | |
9871 | { | |
03976fee AW |
9872 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9873 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9874 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9875 | #else | |
9876 | double re = SCM_COMPLEX_REAL (z); | |
9877 | double im = SCM_COMPLEX_IMAG (z); | |
9878 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9879 | atan2 (im, re)); | |
9880 | #endif | |
9881 | } | |
a5f6b751 MW |
9882 | else if (SCM_REALP (z)) |
9883 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9884 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9885 | { |
a5f6b751 MW |
9886 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9887 | if (scm_is_eq (z, SCM_INUM0)) | |
9888 | scm_num_overflow (s_scm_log); | |
9889 | #endif | |
9890 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9891 | } |
a5f6b751 MW |
9892 | else if (SCM_BIGP (z)) |
9893 | return log_of_exact_integer (z); | |
9894 | else if (SCM_FRACTIONP (z)) | |
9895 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9896 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c | 9897 | else |
fa075d40 | 9898 | return scm_wta_dispatch_1 (g_scm_log, z, 1, s_scm_log); |
8ab3d8a0 KR |
9899 | } |
9900 | #undef FUNC_NAME | |
9901 | ||
9902 | ||
2519490c MW |
9903 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9904 | (SCM z), | |
9905 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9906 | #define FUNC_NAME s_scm_log10 |
9907 | { | |
9908 | if (SCM_COMPLEXP (z)) | |
9909 | { | |
9910 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9911 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9912 | log10+hypot+atan2.) */ | |
f328f862 LC |
9913 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9914 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9915 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9916 | #else | |
9917 | double re = SCM_COMPLEX_REAL (z); | |
9918 | double im = SCM_COMPLEX_IMAG (z); | |
9919 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9920 | M_LOG10E * atan2 (im, re)); | |
9921 | #endif | |
9922 | } | |
a5f6b751 | 9923 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9924 | { |
a5f6b751 MW |
9925 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9926 | if (scm_is_eq (z, SCM_INUM0)) | |
9927 | scm_num_overflow (s_scm_log10); | |
9928 | #endif | |
9929 | { | |
9930 | double re = scm_to_double (z); | |
9931 | double l = log10 (fabs (re)); | |
9932 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9933 | return scm_from_double (l); | |
9934 | else | |
9935 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9936 | } | |
8ab3d8a0 | 9937 | } |
a5f6b751 MW |
9938 | else if (SCM_BIGP (z)) |
9939 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9940 | else if (SCM_FRACTIONP (z)) | |
9941 | return scm_product (flo_log10e, | |
9942 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9943 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c | 9944 | else |
fa075d40 | 9945 | return scm_wta_dispatch_1 (g_scm_log10, z, 1, s_scm_log10); |
8ab3d8a0 KR |
9946 | } |
9947 | #undef FUNC_NAME | |
9948 | ||
9949 | ||
2519490c MW |
9950 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9951 | (SCM z), | |
9952 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9953 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9954 | #define FUNC_NAME s_scm_exp |
9955 | { | |
9956 | if (SCM_COMPLEXP (z)) | |
9957 | { | |
03976fee AW |
9958 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9959 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9960 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
9961 | #else | |
9962 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
9963 | SCM_COMPLEX_IMAG (z)); | |
9964 | #endif | |
9965 | } | |
2519490c | 9966 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9967 | { |
9968 | /* When z is a negative bignum the conversion to double overflows, | |
9969 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9970 | return scm_from_double (exp (scm_to_double (z))); | |
9971 | } | |
2519490c | 9972 | else |
fa075d40 | 9973 | return scm_wta_dispatch_1 (g_scm_exp, z, 1, s_scm_exp); |
8ab3d8a0 KR |
9974 | } |
9975 | #undef FUNC_NAME | |
9976 | ||
9977 | ||
882c8963 MW |
9978 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9979 | (SCM k), | |
9980 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9981 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9982 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9983 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9984 | "\n" | |
9985 | "@lisp\n" | |
9986 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9987 | "@end lisp") | |
9988 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9989 | { | |
9990 | SCM s, r; | |
9991 | ||
9992 | scm_exact_integer_sqrt (k, &s, &r); | |
9993 | return scm_values (scm_list_2 (s, r)); | |
9994 | } | |
9995 | #undef FUNC_NAME | |
9996 | ||
9997 | void | |
9998 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9999 | { | |
10000 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
10001 | { | |
687a87bf | 10002 | mpz_t kk, ss, rr; |
882c8963 | 10003 | |
687a87bf | 10004 | if (SCM_I_INUM (k) < 0) |
882c8963 MW |
10005 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, |
10006 | "exact non-negative integer"); | |
687a87bf MW |
10007 | mpz_init_set_ui (kk, SCM_I_INUM (k)); |
10008 | mpz_inits (ss, rr, NULL); | |
10009 | mpz_sqrtrem (ss, rr, kk); | |
10010 | *sp = SCM_I_MAKINUM (mpz_get_ui (ss)); | |
10011 | *rp = SCM_I_MAKINUM (mpz_get_ui (rr)); | |
10012 | mpz_clears (kk, ss, rr, NULL); | |
882c8963 MW |
10013 | } |
10014 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
10015 | { | |
10016 | SCM s, r; | |
10017 | ||
10018 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
10019 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
10020 | "exact non-negative integer"); | |
10021 | s = scm_i_mkbig (); | |
10022 | r = scm_i_mkbig (); | |
10023 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
10024 | scm_remember_upto_here_1 (k); | |
10025 | *sp = scm_i_normbig (s); | |
10026 | *rp = scm_i_normbig (r); | |
10027 | } | |
10028 | else | |
10029 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
10030 | "exact non-negative integer"); | |
10031 | } | |
10032 | ||
ddb71742 MW |
10033 | /* Return true iff K is a perfect square. |
10034 | K must be an exact integer. */ | |
10035 | static int | |
10036 | exact_integer_is_perfect_square (SCM k) | |
10037 | { | |
10038 | int result; | |
10039 | ||
10040 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
10041 | { | |
10042 | mpz_t kk; | |
10043 | ||
10044 | mpz_init_set_si (kk, SCM_I_INUM (k)); | |
10045 | result = mpz_perfect_square_p (kk); | |
10046 | mpz_clear (kk); | |
10047 | } | |
10048 | else | |
10049 | { | |
10050 | result = mpz_perfect_square_p (SCM_I_BIG_MPZ (k)); | |
10051 | scm_remember_upto_here_1 (k); | |
10052 | } | |
10053 | return result; | |
10054 | } | |
10055 | ||
10056 | /* Return the floor of the square root of K. | |
10057 | K must be an exact integer. */ | |
10058 | static SCM | |
10059 | exact_integer_floor_square_root (SCM k) | |
10060 | { | |
10061 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
10062 | { | |
10063 | mpz_t kk; | |
10064 | scm_t_inum ss; | |
10065 | ||
10066 | mpz_init_set_ui (kk, SCM_I_INUM (k)); | |
10067 | mpz_sqrt (kk, kk); | |
10068 | ss = mpz_get_ui (kk); | |
10069 | mpz_clear (kk); | |
10070 | return SCM_I_MAKINUM (ss); | |
10071 | } | |
10072 | else | |
10073 | { | |
10074 | SCM s; | |
10075 | ||
10076 | s = scm_i_mkbig (); | |
10077 | mpz_sqrt (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (k)); | |
10078 | scm_remember_upto_here_1 (k); | |
10079 | return scm_i_normbig (s); | |
10080 | } | |
10081 | } | |
10082 | ||
882c8963 | 10083 | |
2519490c MW |
10084 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
10085 | (SCM z), | |
10086 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 10087 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
10088 | "is returned, or if that's zero then a positive imaginary part.\n" |
10089 | "Thus,\n" | |
10090 | "\n" | |
10091 | "@example\n" | |
10092 | "(sqrt 9.0) @result{} 3.0\n" | |
10093 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
10094 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
10095 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
10096 | "@end example") | |
8ab3d8a0 KR |
10097 | #define FUNC_NAME s_scm_sqrt |
10098 | { | |
2519490c | 10099 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 10100 | { |
f328f862 LC |
10101 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
10102 | && defined SCM_COMPLEX_VALUE | |
2519490c | 10103 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 10104 | #else |
2519490c MW |
10105 | double re = SCM_COMPLEX_REAL (z); |
10106 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
10107 | return scm_c_make_polar (sqrt (hypot (re, im)), |
10108 | 0.5 * atan2 (im, re)); | |
10109 | #endif | |
10110 | } | |
2519490c | 10111 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 10112 | { |
44002664 MW |
10113 | if (SCM_I_INUMP (z)) |
10114 | { | |
ddb71742 MW |
10115 | scm_t_inum x = SCM_I_INUM (z); |
10116 | ||
10117 | if (SCM_LIKELY (x >= 0)) | |
44002664 | 10118 | { |
ddb71742 MW |
10119 | if (SCM_LIKELY (SCM_I_FIXNUM_BIT < DBL_MANT_DIG |
10120 | || x < (1L << (DBL_MANT_DIG - 1)))) | |
44002664 | 10121 | { |
ddb71742 | 10122 | double root = sqrt (x); |
44002664 MW |
10123 | |
10124 | /* If 0 <= x < 2^(DBL_MANT_DIG-1) and sqrt(x) is an | |
10125 | integer, then the result is exact. */ | |
10126 | if (root == floor (root)) | |
10127 | return SCM_I_MAKINUM ((scm_t_inum) root); | |
10128 | else | |
10129 | return scm_from_double (root); | |
10130 | } | |
10131 | else | |
10132 | { | |
ddb71742 | 10133 | mpz_t xx; |
44002664 MW |
10134 | scm_t_inum root; |
10135 | ||
ddb71742 MW |
10136 | mpz_init_set_ui (xx, x); |
10137 | if (mpz_perfect_square_p (xx)) | |
44002664 | 10138 | { |
ddb71742 MW |
10139 | mpz_sqrt (xx, xx); |
10140 | root = mpz_get_ui (xx); | |
10141 | mpz_clear (xx); | |
44002664 MW |
10142 | return SCM_I_MAKINUM (root); |
10143 | } | |
10144 | else | |
ddb71742 | 10145 | mpz_clear (xx); |
44002664 MW |
10146 | } |
10147 | } | |
10148 | } | |
10149 | else if (SCM_BIGP (z)) | |
10150 | { | |
ddb71742 | 10151 | if (mpz_perfect_square_p (SCM_I_BIG_MPZ (z))) |
44002664 MW |
10152 | { |
10153 | SCM root = scm_i_mkbig (); | |
10154 | ||
10155 | mpz_sqrt (SCM_I_BIG_MPZ (root), SCM_I_BIG_MPZ (z)); | |
10156 | scm_remember_upto_here_1 (z); | |
10157 | return scm_i_normbig (root); | |
10158 | } | |
ddb71742 MW |
10159 | else |
10160 | { | |
10161 | long expon; | |
10162 | double signif = scm_i_big2dbl_2exp (z, &expon); | |
10163 | ||
10164 | if (expon & 1) | |
10165 | { | |
10166 | signif *= 2; | |
10167 | expon--; | |
10168 | } | |
10169 | if (signif < 0) | |
10170 | return scm_c_make_rectangular | |
10171 | (0.0, ldexp (sqrt (-signif), expon / 2)); | |
10172 | else | |
10173 | return scm_from_double (ldexp (sqrt (signif), expon / 2)); | |
10174 | } | |
44002664 MW |
10175 | } |
10176 | else if (SCM_FRACTIONP (z)) | |
ddb71742 MW |
10177 | { |
10178 | SCM n = SCM_FRACTION_NUMERATOR (z); | |
10179 | SCM d = SCM_FRACTION_DENOMINATOR (z); | |
10180 | ||
10181 | if (exact_integer_is_perfect_square (n) | |
10182 | && exact_integer_is_perfect_square (d)) | |
10183 | return scm_i_make_ratio_already_reduced | |
10184 | (exact_integer_floor_square_root (n), | |
10185 | exact_integer_floor_square_root (d)); | |
10186 | else | |
10187 | { | |
10188 | double xx = scm_i_divide2double (n, d); | |
10189 | double abs_xx = fabs (xx); | |
10190 | long shift = 0; | |
10191 | ||
10192 | if (SCM_UNLIKELY (abs_xx > DBL_MAX || abs_xx < DBL_MIN)) | |
10193 | { | |
10194 | shift = (scm_to_long (scm_integer_length (n)) | |
10195 | - scm_to_long (scm_integer_length (d))) / 2; | |
10196 | if (shift > 0) | |
10197 | d = left_shift_exact_integer (d, 2 * shift); | |
10198 | else | |
10199 | n = left_shift_exact_integer (n, -2 * shift); | |
10200 | xx = scm_i_divide2double (n, d); | |
10201 | } | |
10202 | ||
10203 | if (xx < 0) | |
10204 | return scm_c_make_rectangular (0.0, ldexp (sqrt (-xx), shift)); | |
10205 | else | |
10206 | return scm_from_double (ldexp (sqrt (xx), shift)); | |
10207 | } | |
10208 | } | |
44002664 MW |
10209 | |
10210 | /* Fallback method, when the cases above do not apply. */ | |
10211 | { | |
10212 | double xx = scm_to_double (z); | |
10213 | if (xx < 0) | |
10214 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
10215 | else | |
10216 | return scm_from_double (sqrt (xx)); | |
10217 | } | |
8ab3d8a0 | 10218 | } |
2519490c | 10219 | else |
fa075d40 | 10220 | return scm_wta_dispatch_1 (g_scm_sqrt, z, 1, s_scm_sqrt); |
8ab3d8a0 KR |
10221 | } |
10222 | #undef FUNC_NAME | |
10223 | ||
10224 | ||
10225 | ||
0f2d19dd JB |
10226 | void |
10227 | scm_init_numbers () | |
0f2d19dd | 10228 | { |
b57bf272 AW |
10229 | if (scm_install_gmp_memory_functions) |
10230 | mp_set_memory_functions (custom_gmp_malloc, | |
10231 | custom_gmp_realloc, | |
10232 | custom_gmp_free); | |
10233 | ||
713a4259 KR |
10234 | mpz_init_set_si (z_negative_one, -1); |
10235 | ||
a261c0e9 DH |
10236 | /* It may be possible to tune the performance of some algorithms by using |
10237 | * the following constants to avoid the creation of bignums. Please, before | |
10238 | * using these values, remember the two rules of program optimization: | |
10239 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 10240 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 10241 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 10242 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 10243 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 10244 | |
f3ae5d60 MD |
10245 | scm_add_feature ("complex"); |
10246 | scm_add_feature ("inexact"); | |
e7efe8e7 | 10247 | flo0 = scm_from_double (0.0); |
a5f6b751 | 10248 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea | 10249 | |
cff5fa33 | 10250 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
98237784 MW |
10251 | |
10252 | { | |
10253 | /* Set scm_i_divide2double_lo2b to (2 b^p - 1) */ | |
10254 | mpz_init_set_ui (scm_i_divide2double_lo2b, 1); | |
10255 | mpz_mul_2exp (scm_i_divide2double_lo2b, | |
10256 | scm_i_divide2double_lo2b, | |
10257 | DBL_MANT_DIG + 1); /* 2 b^p */ | |
10258 | mpz_sub_ui (scm_i_divide2double_lo2b, scm_i_divide2double_lo2b, 1); | |
10259 | } | |
10260 | ||
1ea37620 MW |
10261 | { |
10262 | /* Set dbl_minimum_normal_mantissa to b^{p-1} */ | |
10263 | mpz_init_set_ui (dbl_minimum_normal_mantissa, 1); | |
10264 | mpz_mul_2exp (dbl_minimum_normal_mantissa, | |
10265 | dbl_minimum_normal_mantissa, | |
10266 | DBL_MANT_DIG - 1); | |
10267 | } | |
10268 | ||
a0599745 | 10269 | #include "libguile/numbers.x" |
0f2d19dd | 10270 | } |
89e00824 ML |
10271 | |
10272 | /* | |
10273 | Local Variables: | |
10274 | c-file-style: "gnu" | |
10275 | End: | |
10276 | */ |