Commit | Line | Data |
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75ba64d6 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e | 7 | * This library is free software; you can redistribute it and/or |
53befeb7 NJ |
8 | * modify it under the terms of the GNU Lesser General Public License |
9 | * as published by the Free Software Foundation; either version 3 of | |
10 | * the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
53befeb7 NJ |
12 | * This library is distributed in the hope that it will be useful, but |
13 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |
73be1d9e MV |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
53befeb7 NJ |
19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
20 | * 02110-1301 USA | |
73be1d9e | 21 | */ |
1bbd0b84 | 22 | |
0f2d19dd | 23 | \f |
ca46fb90 | 24 | /* General assumptions: |
ca46fb90 RB |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
c7218482 | 28 | * XXX What about infinities? They are equal to their own floor! -mhw |
f92e85f7 | 29 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
30 | */ |
31 | ||
32 | /* TODO: | |
33 | ||
34 | - see if special casing bignums and reals in integer-exponent when | |
35 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
36 | ||
37 | - look in to better short-circuiting of common cases in | |
38 | integer-expt and elsewhere. | |
39 | ||
40 | - see if direct mpz operations can help in ash and elsewhere. | |
41 | ||
42 | */ | |
0f2d19dd | 43 | |
dbb605f5 | 44 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
45 | # include <config.h> |
46 | #endif | |
47 | ||
bbec4602 LC |
48 | #include <verify.h> |
49 | ||
0f2d19dd | 50 | #include <math.h> |
fc194577 | 51 | #include <string.h> |
3f47e526 MG |
52 | #include <unicase.h> |
53 | #include <unictype.h> | |
f92e85f7 | 54 | |
8ab3d8a0 KR |
55 | #if HAVE_COMPLEX_H |
56 | #include <complex.h> | |
57 | #endif | |
58 | ||
a0599745 | 59 | #include "libguile/_scm.h" |
a0599745 MD |
60 | #include "libguile/feature.h" |
61 | #include "libguile/ports.h" | |
62 | #include "libguile/root.h" | |
63 | #include "libguile/smob.h" | |
64 | #include "libguile/strings.h" | |
864e7d42 | 65 | #include "libguile/bdw-gc.h" |
a0599745 MD |
66 | |
67 | #include "libguile/validate.h" | |
68 | #include "libguile/numbers.h" | |
1be6b49c | 69 | #include "libguile/deprecation.h" |
f4c627b3 | 70 | |
f92e85f7 MV |
71 | #include "libguile/eq.h" |
72 | ||
8ab3d8a0 KR |
73 | /* values per glibc, if not already defined */ |
74 | #ifndef M_LOG10E | |
75 | #define M_LOG10E 0.43429448190325182765 | |
76 | #endif | |
85bdb6ac MW |
77 | #ifndef M_LN2 |
78 | #define M_LN2 0.69314718055994530942 | |
79 | #endif | |
8ab3d8a0 KR |
80 | #ifndef M_PI |
81 | #define M_PI 3.14159265358979323846 | |
82 | #endif | |
83 | ||
cba521fe MW |
84 | /* FIXME: We assume that FLT_RADIX is 2 */ |
85 | verify (FLT_RADIX == 2); | |
86 | ||
e25f3727 AW |
87 | typedef scm_t_signed_bits scm_t_inum; |
88 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
89 | ||
7112615f MW |
90 | /* Tests to see if a C double is neither infinite nor a NaN. |
91 | TODO: if it's available, use C99's isfinite(x) instead */ | |
92 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
93 | ||
041fccf6 MW |
94 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
95 | of the infinity, but other platforms return a boolean only. */ | |
96 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
97 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
98 | ||
0f2d19dd | 99 | \f |
f4c627b3 | 100 | |
ca46fb90 RB |
101 | /* |
102 | Wonder if this might be faster for some of our code? A switch on | |
103 | the numtag would jump directly to the right case, and the | |
104 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
105 | ||
106 | #define SCM_I_NUMTAG_NOTNUM 0 | |
107 | #define SCM_I_NUMTAG_INUM 1 | |
108 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
109 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
110 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
111 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 112 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 113 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 114 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
115 | : SCM_I_NUMTAG_NOTNUM))) |
116 | */ | |
f92e85f7 | 117 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
118 | |
119 | ||
b57bf272 AW |
120 | /* Default to 1, because as we used to hard-code `free' as the |
121 | deallocator, we know that overriding these functions with | |
122 | instrumented `malloc' / `free' is OK. */ | |
123 | int scm_install_gmp_memory_functions = 1; | |
e7efe8e7 | 124 | static SCM flo0; |
ff62c168 | 125 | static SCM exactly_one_half; |
a5f6b751 | 126 | static SCM flo_log10e; |
e7efe8e7 | 127 | |
34d19ef6 | 128 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 129 | |
56e55ac7 | 130 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
131 | * printed or scm_string representation of an inexact number. |
132 | */ | |
0b799eea | 133 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 134 | |
b127c712 | 135 | |
ad79736c AW |
136 | #if !defined (HAVE_ASINH) |
137 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
138 | #endif | |
139 | #if !defined (HAVE_ACOSH) | |
140 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
141 | #endif | |
142 | #if !defined (HAVE_ATANH) | |
143 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
144 | #endif | |
145 | ||
18d78c5e MW |
146 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
147 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released | |
148 | in March 2006), mpz_cmp_d now handles infinities properly. */ | |
f8a8200b | 149 | #if 1 |
b127c712 | 150 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 151 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
152 | #else |
153 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
154 | #endif | |
155 | ||
f92e85f7 | 156 | |
4b26c03e | 157 | #if defined (GUILE_I) |
03976fee | 158 | #if defined HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
159 | |
160 | /* For an SCM object Z which is a complex number (ie. satisfies | |
161 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
162 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 163 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 164 | |
7a35784c | 165 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
166 | |
167 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 168 | static inline SCM |
8ab3d8a0 KR |
169 | scm_from_complex_double (complex double z) |
170 | { | |
171 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
172 | } | |
bca69a9f | 173 | |
8ab3d8a0 | 174 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 175 | #endif /* GUILE_I */ |
8ab3d8a0 | 176 | |
0f2d19dd JB |
177 | \f |
178 | ||
713a4259 | 179 | static mpz_t z_negative_one; |
ac0c002c DH |
180 | |
181 | \f | |
b57bf272 | 182 | |
864e7d42 LC |
183 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
184 | static void | |
6922d92f | 185 | finalize_bignum (void *ptr, void *data) |
864e7d42 LC |
186 | { |
187 | SCM bignum; | |
188 | ||
189 | bignum = PTR2SCM (ptr); | |
190 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
191 | } | |
192 | ||
b57bf272 AW |
193 | /* The next three functions (custom_libgmp_*) are passed to |
194 | mp_set_memory_functions (in GMP) so that memory used by the digits | |
195 | themselves is known to the garbage collector. This is needed so | |
196 | that GC will be run at appropriate times. Otherwise, a program which | |
197 | creates many large bignums would malloc a huge amount of memory | |
198 | before the GC runs. */ | |
199 | static void * | |
200 | custom_gmp_malloc (size_t alloc_size) | |
201 | { | |
202 | return scm_malloc (alloc_size); | |
203 | } | |
204 | ||
205 | static void * | |
206 | custom_gmp_realloc (void *old_ptr, size_t old_size, size_t new_size) | |
207 | { | |
208 | return scm_realloc (old_ptr, new_size); | |
209 | } | |
210 | ||
211 | static void | |
212 | custom_gmp_free (void *ptr, size_t size) | |
213 | { | |
214 | free (ptr); | |
215 | } | |
216 | ||
217 | ||
d017fcdf LC |
218 | /* Return a new uninitialized bignum. */ |
219 | static inline SCM | |
220 | make_bignum (void) | |
221 | { | |
222 | scm_t_bits *p; | |
223 | ||
224 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
225 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
226 | "bignum"); | |
227 | p[0] = scm_tc16_big; | |
228 | ||
75ba64d6 | 229 | scm_i_set_finalizer (p, finalize_bignum, NULL); |
864e7d42 | 230 | |
d017fcdf LC |
231 | return SCM_PACK (p); |
232 | } | |
ac0c002c | 233 | |
864e7d42 | 234 | |
189171c5 | 235 | SCM |
ca46fb90 RB |
236 | scm_i_mkbig () |
237 | { | |
238 | /* Return a newly created bignum. */ | |
d017fcdf | 239 | SCM z = make_bignum (); |
ca46fb90 RB |
240 | mpz_init (SCM_I_BIG_MPZ (z)); |
241 | return z; | |
242 | } | |
243 | ||
e25f3727 AW |
244 | static SCM |
245 | scm_i_inum2big (scm_t_inum x) | |
246 | { | |
247 | /* Return a newly created bignum initialized to X. */ | |
248 | SCM z = make_bignum (); | |
249 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
250 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
251 | #else | |
252 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
253 | mpz_*_si invocations in Guile. */ | |
254 | #error creation of mpz not implemented for this inum size | |
255 | #endif | |
256 | return z; | |
257 | } | |
258 | ||
189171c5 | 259 | SCM |
c71b0706 MV |
260 | scm_i_long2big (long x) |
261 | { | |
262 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 263 | SCM z = make_bignum (); |
c71b0706 MV |
264 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
265 | return z; | |
266 | } | |
267 | ||
189171c5 | 268 | SCM |
c71b0706 MV |
269 | scm_i_ulong2big (unsigned long x) |
270 | { | |
271 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 272 | SCM z = make_bignum (); |
c71b0706 MV |
273 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
274 | return z; | |
275 | } | |
276 | ||
189171c5 | 277 | SCM |
ca46fb90 RB |
278 | scm_i_clonebig (SCM src_big, int same_sign_p) |
279 | { | |
280 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 281 | SCM z = make_bignum (); |
ca46fb90 | 282 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
283 | if (!same_sign_p) |
284 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
285 | return z; |
286 | } | |
287 | ||
189171c5 | 288 | int |
ca46fb90 RB |
289 | scm_i_bigcmp (SCM x, SCM y) |
290 | { | |
291 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
292 | /* presume we already know x and y are bignums */ | |
293 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
294 | scm_remember_upto_here_2 (x, y); | |
295 | return result; | |
296 | } | |
297 | ||
189171c5 | 298 | SCM |
ca46fb90 RB |
299 | scm_i_dbl2big (double d) |
300 | { | |
301 | /* results are only defined if d is an integer */ | |
d017fcdf | 302 | SCM z = make_bignum (); |
ca46fb90 RB |
303 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
304 | return z; | |
305 | } | |
306 | ||
f92e85f7 MV |
307 | /* Convert a integer in double representation to a SCM number. */ |
308 | ||
189171c5 | 309 | SCM |
f92e85f7 MV |
310 | scm_i_dbl2num (double u) |
311 | { | |
312 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
313 | powers of 2, so there's no rounding when making "double" values | |
314 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
315 | get rounded on a 64-bit machine, hence the "+1". | |
316 | ||
317 | The use of floor() to force to an integer value ensures we get a | |
318 | "numerically closest" value without depending on how a | |
319 | double->long cast or how mpz_set_d will round. For reference, | |
320 | double->long probably follows the hardware rounding mode, | |
321 | mpz_set_d truncates towards zero. */ | |
322 | ||
323 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
324 | representable as a double? */ | |
325 | ||
326 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
327 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 328 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
329 | else |
330 | return scm_i_dbl2big (u); | |
331 | } | |
332 | ||
1eb6a33a MW |
333 | static SCM round_right_shift_exact_integer (SCM n, long count); |
334 | ||
335 | /* scm_i_big2dbl_2exp() is like frexp for bignums: it converts the | |
336 | bignum b into a normalized significand and exponent such that | |
337 | b = significand * 2^exponent and 1/2 <= abs(significand) < 1. | |
338 | The return value is the significand rounded to the closest | |
339 | representable double, and the exponent is placed into *expon_p. | |
340 | If b is zero, then the returned exponent and significand are both | |
341 | zero. */ | |
342 | ||
343 | static double | |
344 | scm_i_big2dbl_2exp (SCM b, long *expon_p) | |
ca46fb90 | 345 | { |
1eb6a33a MW |
346 | size_t bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); |
347 | size_t shift = 0; | |
089c9a59 KR |
348 | |
349 | if (bits > DBL_MANT_DIG) | |
350 | { | |
1eb6a33a MW |
351 | shift = bits - DBL_MANT_DIG; |
352 | b = round_right_shift_exact_integer (b, shift); | |
353 | if (SCM_I_INUMP (b)) | |
089c9a59 | 354 | { |
1eb6a33a MW |
355 | int expon; |
356 | double signif = frexp (SCM_I_INUM (b), &expon); | |
357 | *expon_p = expon + shift; | |
358 | return signif; | |
089c9a59 KR |
359 | } |
360 | } | |
361 | ||
1eb6a33a MW |
362 | { |
363 | long expon; | |
364 | double signif = mpz_get_d_2exp (&expon, SCM_I_BIG_MPZ (b)); | |
365 | scm_remember_upto_here_1 (b); | |
366 | *expon_p = expon + shift; | |
367 | return signif; | |
368 | } | |
369 | } | |
370 | ||
371 | /* scm_i_big2dbl() rounds to the closest representable double, | |
372 | in accordance with R5RS exact->inexact. */ | |
373 | double | |
374 | scm_i_big2dbl (SCM b) | |
375 | { | |
376 | long expon; | |
377 | double signif = scm_i_big2dbl_2exp (b, &expon); | |
378 | return ldexp (signif, expon); | |
ca46fb90 RB |
379 | } |
380 | ||
189171c5 | 381 | SCM |
ca46fb90 RB |
382 | scm_i_normbig (SCM b) |
383 | { | |
384 | /* convert a big back to a fixnum if it'll fit */ | |
385 | /* presume b is a bignum */ | |
386 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
387 | { | |
e25f3727 | 388 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 389 | if (SCM_FIXABLE (val)) |
d956fa6f | 390 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
391 | } |
392 | return b; | |
393 | } | |
f872b822 | 394 | |
f92e85f7 MV |
395 | static SCM_C_INLINE_KEYWORD SCM |
396 | scm_i_mpz2num (mpz_t b) | |
397 | { | |
398 | /* convert a mpz number to a SCM number. */ | |
399 | if (mpz_fits_slong_p (b)) | |
400 | { | |
e25f3727 | 401 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 402 | if (SCM_FIXABLE (val)) |
d956fa6f | 403 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
404 | } |
405 | ||
406 | { | |
d017fcdf | 407 | SCM z = make_bignum (); |
f92e85f7 MV |
408 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
409 | return z; | |
410 | } | |
411 | } | |
412 | ||
a285b18c MW |
413 | /* Make the ratio NUMERATOR/DENOMINATOR, where: |
414 | 1. NUMERATOR and DENOMINATOR are exact integers | |
415 | 2. NUMERATOR and DENOMINATOR are reduced to lowest terms: gcd(n,d) == 1 */ | |
cba42c93 | 416 | static SCM |
a285b18c | 417 | scm_i_make_ratio_already_reduced (SCM numerator, SCM denominator) |
f92e85f7 | 418 | { |
a285b18c MW |
419 | /* Flip signs so that the denominator is positive. */ |
420 | if (scm_is_false (scm_positive_p (denominator))) | |
f92e85f7 | 421 | { |
a285b18c | 422 | if (SCM_UNLIKELY (scm_is_eq (denominator, SCM_INUM0))) |
f92e85f7 | 423 | scm_num_overflow ("make-ratio"); |
a285b18c | 424 | else |
f92e85f7 | 425 | { |
a285b18c MW |
426 | numerator = scm_difference (numerator, SCM_UNDEFINED); |
427 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
f92e85f7 MV |
428 | } |
429 | } | |
a285b18c MW |
430 | |
431 | /* Check for the integer case */ | |
432 | if (scm_is_eq (denominator, SCM_INUM1)) | |
433 | return numerator; | |
434 | ||
435 | return scm_double_cell (scm_tc16_fraction, | |
436 | SCM_UNPACK (numerator), | |
437 | SCM_UNPACK (denominator), 0); | |
438 | } | |
439 | ||
440 | static SCM scm_exact_integer_quotient (SCM x, SCM y); | |
441 | ||
442 | /* Make the ratio NUMERATOR/DENOMINATOR */ | |
443 | static SCM | |
444 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
445 | #define FUNC_NAME "make-ratio" | |
446 | { | |
447 | /* Make sure the arguments are proper */ | |
448 | if (!SCM_LIKELY (SCM_I_INUMP (numerator) || SCM_BIGP (numerator))) | |
449 | SCM_WRONG_TYPE_ARG (1, numerator); | |
450 | else if (!SCM_LIKELY (SCM_I_INUMP (denominator) || SCM_BIGP (denominator))) | |
451 | SCM_WRONG_TYPE_ARG (2, denominator); | |
452 | else | |
f92e85f7 | 453 | { |
a285b18c MW |
454 | SCM the_gcd = scm_gcd (numerator, denominator); |
455 | if (!(scm_is_eq (the_gcd, SCM_INUM1))) | |
c60e130c | 456 | { |
a285b18c MW |
457 | /* Reduce to lowest terms */ |
458 | numerator = scm_exact_integer_quotient (numerator, the_gcd); | |
459 | denominator = scm_exact_integer_quotient (denominator, the_gcd); | |
f92e85f7 | 460 | } |
a285b18c | 461 | return scm_i_make_ratio_already_reduced (numerator, denominator); |
f92e85f7 | 462 | } |
f92e85f7 | 463 | } |
c60e130c | 464 | #undef FUNC_NAME |
f92e85f7 | 465 | |
98237784 MW |
466 | static mpz_t scm_i_divide2double_lo2b; |
467 | ||
468 | /* Return the double that is closest to the exact rational N/D, with | |
469 | ties rounded toward even mantissas. N and D must be exact | |
470 | integers. */ | |
471 | static double | |
472 | scm_i_divide2double (SCM n, SCM d) | |
473 | { | |
474 | int neg; | |
475 | mpz_t nn, dd, lo, hi, x; | |
476 | ssize_t e; | |
477 | ||
c8248c8e | 478 | if (SCM_LIKELY (SCM_I_INUMP (d))) |
98237784 | 479 | { |
c8248c8e MW |
480 | if (SCM_LIKELY (SCM_I_INUMP (n) |
481 | && (SCM_I_FIXNUM_BIT-1 <= DBL_MANT_DIG | |
482 | || (SCM_I_INUM (n) < (1L << DBL_MANT_DIG) | |
483 | && SCM_I_INUM (d) < (1L << DBL_MANT_DIG))))) | |
484 | /* If both N and D can be losslessly converted to doubles, then | |
485 | we can rely on IEEE floating point to do proper rounding much | |
486 | faster than we can. */ | |
487 | return ((double) SCM_I_INUM (n)) / ((double) SCM_I_INUM (d)); | |
488 | ||
98237784 MW |
489 | if (SCM_UNLIKELY (scm_is_eq (d, SCM_INUM0))) |
490 | { | |
491 | if (scm_is_true (scm_positive_p (n))) | |
492 | return 1.0 / 0.0; | |
493 | else if (scm_is_true (scm_negative_p (n))) | |
494 | return -1.0 / 0.0; | |
495 | else | |
496 | return 0.0 / 0.0; | |
497 | } | |
c8248c8e | 498 | |
98237784 MW |
499 | mpz_init_set_si (dd, SCM_I_INUM (d)); |
500 | } | |
501 | else | |
502 | mpz_init_set (dd, SCM_I_BIG_MPZ (d)); | |
503 | ||
504 | if (SCM_I_INUMP (n)) | |
505 | mpz_init_set_si (nn, SCM_I_INUM (n)); | |
506 | else | |
507 | mpz_init_set (nn, SCM_I_BIG_MPZ (n)); | |
508 | ||
509 | neg = (mpz_sgn (nn) < 0) ^ (mpz_sgn (dd) < 0); | |
510 | mpz_abs (nn, nn); | |
511 | mpz_abs (dd, dd); | |
512 | ||
513 | /* Now we need to find the value of e such that: | |
514 | ||
515 | For e <= 0: | |
516 | b^{p-1} - 1/2b <= b^-e n / d < b^p - 1/2 [1A] | |
517 | (2 b^p - 1) <= 2 b b^-e n / d < (2 b^p - 1) b [2A] | |
518 | (2 b^p - 1) d <= 2 b b^-e n < (2 b^p - 1) d b [3A] | |
519 | ||
520 | For e >= 0: | |
521 | b^{p-1} - 1/2b <= n / b^e d < b^p - 1/2 [1B] | |
522 | (2 b^p - 1) <= 2 b n / b^e d < (2 b^p - 1) b [2B] | |
523 | (2 b^p - 1) d b^e <= 2 b n < (2 b^p - 1) d b b^e [3B] | |
524 | ||
525 | where: p = DBL_MANT_DIG | |
526 | b = FLT_RADIX (here assumed to be 2) | |
527 | ||
528 | After rounding, the mantissa must be an integer between b^{p-1} and | |
529 | (b^p - 1), except for subnormal numbers. In the inequations [1A] | |
530 | and [1B], the middle expression represents the mantissa *before* | |
531 | rounding, and therefore is bounded by the range of values that will | |
532 | round to a floating-point number with the exponent e. The upper | |
533 | bound is (b^p - 1 + 1/2) = (b^p - 1/2), and is exclusive because | |
534 | ties will round up to the next power of b. The lower bound is | |
535 | (b^{p-1} - 1/2b), and is inclusive because ties will round toward | |
536 | this power of b. Here we subtract 1/2b instead of 1/2 because it | |
537 | is in the range of the next smaller exponent, where the | |
538 | representable numbers are closer together by a factor of b. | |
539 | ||
540 | Inequations [2A] and [2B] are derived from [1A] and [1B] by | |
541 | multiplying by 2b, and in [3A] and [3B] we multiply by the | |
542 | denominator of the middle value to obtain integer expressions. | |
543 | ||
544 | In the code below, we refer to the three expressions in [3A] or | |
545 | [3B] as lo, x, and hi. If the number is normalizable, we will | |
546 | achieve the goal: lo <= x < hi */ | |
547 | ||
548 | /* Make an initial guess for e */ | |
549 | e = mpz_sizeinbase (nn, 2) - mpz_sizeinbase (dd, 2) - (DBL_MANT_DIG-1); | |
550 | if (e < DBL_MIN_EXP - DBL_MANT_DIG) | |
551 | e = DBL_MIN_EXP - DBL_MANT_DIG; | |
552 | ||
553 | /* Compute the initial values of lo, x, and hi | |
554 | based on the initial guess of e */ | |
555 | mpz_inits (lo, hi, x, NULL); | |
556 | mpz_mul_2exp (x, nn, 2 + ((e < 0) ? -e : 0)); | |
557 | mpz_mul (lo, dd, scm_i_divide2double_lo2b); | |
558 | if (e > 0) | |
559 | mpz_mul_2exp (lo, lo, e); | |
560 | mpz_mul_2exp (hi, lo, 1); | |
561 | ||
562 | /* Adjust e as needed to satisfy the inequality lo <= x < hi, | |
563 | (but without making e less then the minimum exponent) */ | |
564 | while (mpz_cmp (x, lo) < 0 && e > DBL_MIN_EXP - DBL_MANT_DIG) | |
565 | { | |
566 | mpz_mul_2exp (x, x, 1); | |
567 | e--; | |
568 | } | |
569 | while (mpz_cmp (x, hi) >= 0) | |
570 | { | |
571 | /* If we ever used lo's value again, | |
572 | we would need to double lo here. */ | |
573 | mpz_mul_2exp (hi, hi, 1); | |
574 | e++; | |
575 | } | |
576 | ||
577 | /* Now compute the rounded mantissa: | |
578 | n / b^e d (if e >= 0) | |
579 | n b^-e / d (if e <= 0) */ | |
580 | { | |
581 | int cmp; | |
582 | double result; | |
583 | ||
584 | if (e < 0) | |
585 | mpz_mul_2exp (nn, nn, -e); | |
586 | else | |
587 | mpz_mul_2exp (dd, dd, e); | |
588 | ||
589 | /* mpz does not directly support rounded right | |
590 | shifts, so we have to do it the hard way. | |
591 | For efficiency, we reuse lo and hi. | |
592 | hi == quotient, lo == remainder */ | |
593 | mpz_fdiv_qr (hi, lo, nn, dd); | |
594 | ||
595 | /* The fractional part of the unrounded mantissa would be | |
596 | remainder/dividend, i.e. lo/dd. So we have a tie if | |
597 | lo/dd = 1/2. Multiplying both sides by 2*dd yields the | |
598 | integer expression 2*lo = dd. Here we do that comparison | |
599 | to decide whether to round up or down. */ | |
600 | mpz_mul_2exp (lo, lo, 1); | |
601 | cmp = mpz_cmp (lo, dd); | |
602 | if (cmp > 0 || (cmp == 0 && mpz_odd_p (hi))) | |
603 | mpz_add_ui (hi, hi, 1); | |
604 | ||
605 | result = ldexp (mpz_get_d (hi), e); | |
606 | if (neg) | |
607 | result = -result; | |
608 | ||
609 | mpz_clears (nn, dd, lo, hi, x, NULL); | |
610 | return result; | |
611 | } | |
612 | } | |
613 | ||
f92e85f7 MV |
614 | double |
615 | scm_i_fraction2double (SCM z) | |
616 | { | |
98237784 MW |
617 | return scm_i_divide2double (SCM_FRACTION_NUMERATOR (z), |
618 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 MV |
619 | } |
620 | ||
2e274311 MW |
621 | static int |
622 | double_is_non_negative_zero (double x) | |
623 | { | |
624 | static double zero = 0.0; | |
625 | ||
626 | return !memcmp (&x, &zero, sizeof(double)); | |
627 | } | |
628 | ||
2519490c MW |
629 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
630 | (SCM x), | |
942e5b91 MG |
631 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
632 | "otherwise.") | |
1bbd0b84 | 633 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 634 | { |
41df63cf MW |
635 | if (SCM_INEXACTP (x)) |
636 | return SCM_BOOL_F; | |
637 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 638 | return SCM_BOOL_T; |
41df63cf | 639 | else |
2519490c | 640 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
641 | } |
642 | #undef FUNC_NAME | |
643 | ||
022dda69 MG |
644 | int |
645 | scm_is_exact (SCM val) | |
646 | { | |
647 | return scm_is_true (scm_exact_p (val)); | |
648 | } | |
41df63cf | 649 | |
2519490c | 650 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
651 | (SCM x), |
652 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
653 | "else.") | |
654 | #define FUNC_NAME s_scm_inexact_p | |
655 | { | |
656 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 657 | return SCM_BOOL_T; |
41df63cf | 658 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 659 | return SCM_BOOL_F; |
41df63cf | 660 | else |
2519490c | 661 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 662 | } |
1bbd0b84 | 663 | #undef FUNC_NAME |
0f2d19dd | 664 | |
022dda69 MG |
665 | int |
666 | scm_is_inexact (SCM val) | |
667 | { | |
668 | return scm_is_true (scm_inexact_p (val)); | |
669 | } | |
4219f20d | 670 | |
2519490c | 671 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 672 | (SCM n), |
942e5b91 MG |
673 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
674 | "otherwise.") | |
1bbd0b84 | 675 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 676 | { |
e11e83f3 | 677 | if (SCM_I_INUMP (n)) |
0aacf84e | 678 | { |
e25f3727 | 679 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 680 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
681 | } |
682 | else if (SCM_BIGP (n)) | |
683 | { | |
684 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
685 | scm_remember_upto_here_1 (n); | |
73e4de09 | 686 | return scm_from_bool (odd_p); |
0aacf84e | 687 | } |
f92e85f7 MV |
688 | else if (SCM_REALP (n)) |
689 | { | |
2519490c MW |
690 | double val = SCM_REAL_VALUE (n); |
691 | if (DOUBLE_IS_FINITE (val)) | |
692 | { | |
693 | double rem = fabs (fmod (val, 2.0)); | |
694 | if (rem == 1.0) | |
695 | return SCM_BOOL_T; | |
696 | else if (rem == 0.0) | |
697 | return SCM_BOOL_F; | |
698 | } | |
f92e85f7 | 699 | } |
2519490c | 700 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 701 | } |
1bbd0b84 | 702 | #undef FUNC_NAME |
0f2d19dd | 703 | |
4219f20d | 704 | |
2519490c | 705 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 706 | (SCM n), |
942e5b91 MG |
707 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
708 | "otherwise.") | |
1bbd0b84 | 709 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 710 | { |
e11e83f3 | 711 | if (SCM_I_INUMP (n)) |
0aacf84e | 712 | { |
e25f3727 | 713 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 714 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
715 | } |
716 | else if (SCM_BIGP (n)) | |
717 | { | |
718 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
719 | scm_remember_upto_here_1 (n); | |
73e4de09 | 720 | return scm_from_bool (even_p); |
0aacf84e | 721 | } |
f92e85f7 MV |
722 | else if (SCM_REALP (n)) |
723 | { | |
2519490c MW |
724 | double val = SCM_REAL_VALUE (n); |
725 | if (DOUBLE_IS_FINITE (val)) | |
726 | { | |
727 | double rem = fabs (fmod (val, 2.0)); | |
728 | if (rem == 1.0) | |
729 | return SCM_BOOL_F; | |
730 | else if (rem == 0.0) | |
731 | return SCM_BOOL_T; | |
732 | } | |
f92e85f7 | 733 | } |
2519490c | 734 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 735 | } |
1bbd0b84 | 736 | #undef FUNC_NAME |
0f2d19dd | 737 | |
2519490c MW |
738 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
739 | (SCM x), | |
10391e06 AW |
740 | "Return @code{#t} if the real number @var{x} is neither\n" |
741 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
742 | #define FUNC_NAME s_scm_finite_p |
743 | { | |
744 | if (SCM_REALP (x)) | |
745 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 746 | else if (scm_is_real (x)) |
7112615f MW |
747 | return SCM_BOOL_T; |
748 | else | |
2519490c | 749 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
750 | } |
751 | #undef FUNC_NAME | |
752 | ||
2519490c MW |
753 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
754 | (SCM x), | |
755 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
756 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
757 | #define FUNC_NAME s_scm_inf_p |
758 | { | |
b1092b3a | 759 | if (SCM_REALP (x)) |
2e65b52f | 760 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 761 | else if (scm_is_real (x)) |
7351e207 | 762 | return SCM_BOOL_F; |
10391e06 | 763 | else |
2519490c | 764 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
765 | } |
766 | #undef FUNC_NAME | |
767 | ||
2519490c MW |
768 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
769 | (SCM x), | |
10391e06 AW |
770 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
771 | "or @code{#f} otherwise.") | |
7351e207 MV |
772 | #define FUNC_NAME s_scm_nan_p |
773 | { | |
10391e06 AW |
774 | if (SCM_REALP (x)) |
775 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
776 | else if (scm_is_real (x)) | |
7351e207 | 777 | return SCM_BOOL_F; |
10391e06 | 778 | else |
2519490c | 779 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
780 | } |
781 | #undef FUNC_NAME | |
782 | ||
783 | /* Guile's idea of infinity. */ | |
784 | static double guile_Inf; | |
785 | ||
786 | /* Guile's idea of not a number. */ | |
787 | static double guile_NaN; | |
788 | ||
789 | static void | |
790 | guile_ieee_init (void) | |
791 | { | |
7351e207 MV |
792 | /* Some version of gcc on some old version of Linux used to crash when |
793 | trying to make Inf and NaN. */ | |
794 | ||
240a27d2 KR |
795 | #ifdef INFINITY |
796 | /* C99 INFINITY, when available. | |
797 | FIXME: The standard allows for INFINITY to be something that overflows | |
798 | at compile time. We ought to have a configure test to check for that | |
799 | before trying to use it. (But in practice we believe this is not a | |
800 | problem on any system guile is likely to target.) */ | |
801 | guile_Inf = INFINITY; | |
56a3dcd4 | 802 | #elif defined HAVE_DINFINITY |
240a27d2 | 803 | /* OSF */ |
7351e207 | 804 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 805 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
806 | #else |
807 | double tmp = 1e+10; | |
808 | guile_Inf = tmp; | |
809 | for (;;) | |
810 | { | |
811 | guile_Inf *= 1e+10; | |
812 | if (guile_Inf == tmp) | |
813 | break; | |
814 | tmp = guile_Inf; | |
815 | } | |
816 | #endif | |
817 | ||
240a27d2 KR |
818 | #ifdef NAN |
819 | /* C99 NAN, when available */ | |
820 | guile_NaN = NAN; | |
56a3dcd4 | 821 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
822 | { |
823 | /* OSF */ | |
824 | extern unsigned int DQNAN[2]; | |
825 | guile_NaN = (*((double *)(DQNAN))); | |
826 | } | |
7351e207 MV |
827 | #else |
828 | guile_NaN = guile_Inf / guile_Inf; | |
829 | #endif | |
7351e207 MV |
830 | } |
831 | ||
832 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
833 | (void), | |
834 | "Return Inf.") | |
835 | #define FUNC_NAME s_scm_inf | |
836 | { | |
837 | static int initialized = 0; | |
838 | if (! initialized) | |
839 | { | |
840 | guile_ieee_init (); | |
841 | initialized = 1; | |
842 | } | |
55f26379 | 843 | return scm_from_double (guile_Inf); |
7351e207 MV |
844 | } |
845 | #undef FUNC_NAME | |
846 | ||
847 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
848 | (void), | |
849 | "Return NaN.") | |
850 | #define FUNC_NAME s_scm_nan | |
851 | { | |
852 | static int initialized = 0; | |
0aacf84e | 853 | if (!initialized) |
7351e207 MV |
854 | { |
855 | guile_ieee_init (); | |
856 | initialized = 1; | |
857 | } | |
55f26379 | 858 | return scm_from_double (guile_NaN); |
7351e207 MV |
859 | } |
860 | #undef FUNC_NAME | |
861 | ||
4219f20d | 862 | |
a48d60b1 MD |
863 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
864 | (SCM x), | |
865 | "Return the absolute value of @var{x}.") | |
2519490c | 866 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 867 | { |
e11e83f3 | 868 | if (SCM_I_INUMP (x)) |
0aacf84e | 869 | { |
e25f3727 | 870 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
871 | if (xx >= 0) |
872 | return x; | |
873 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 874 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 875 | else |
e25f3727 | 876 | return scm_i_inum2big (-xx); |
4219f20d | 877 | } |
9b9ef10c MW |
878 | else if (SCM_LIKELY (SCM_REALP (x))) |
879 | { | |
880 | double xx = SCM_REAL_VALUE (x); | |
881 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
882 | if (xx < 0.0) | |
883 | return scm_from_double (-xx); | |
884 | /* Handle signed zeroes properly */ | |
885 | else if (SCM_UNLIKELY (xx == 0.0)) | |
886 | return flo0; | |
887 | else | |
888 | return x; | |
889 | } | |
0aacf84e MD |
890 | else if (SCM_BIGP (x)) |
891 | { | |
892 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
893 | if (sgn < 0) | |
894 | return scm_i_clonebig (x, 0); | |
895 | else | |
896 | return x; | |
4219f20d | 897 | } |
f92e85f7 MV |
898 | else if (SCM_FRACTIONP (x)) |
899 | { | |
73e4de09 | 900 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 901 | return x; |
a285b18c MW |
902 | return scm_i_make_ratio_already_reduced |
903 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
904 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 905 | } |
0aacf84e | 906 | else |
a48d60b1 | 907 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 908 | } |
a48d60b1 | 909 | #undef FUNC_NAME |
0f2d19dd | 910 | |
4219f20d | 911 | |
2519490c MW |
912 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
913 | (SCM x, SCM y), | |
914 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
915 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 916 | { |
495a39c4 | 917 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 918 | { |
495a39c4 | 919 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 920 | return scm_truncate_quotient (x, y); |
0aacf84e | 921 | else |
2519490c | 922 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 923 | } |
0aacf84e | 924 | else |
2519490c | 925 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 926 | } |
2519490c | 927 | #undef FUNC_NAME |
0f2d19dd | 928 | |
2519490c MW |
929 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
930 | (SCM x, SCM y), | |
931 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
932 | "@lisp\n" | |
933 | "(remainder 13 4) @result{} 1\n" | |
934 | "(remainder -13 4) @result{} -1\n" | |
935 | "@end lisp") | |
936 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 937 | { |
495a39c4 | 938 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 939 | { |
495a39c4 | 940 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 941 | return scm_truncate_remainder (x, y); |
0aacf84e | 942 | else |
2519490c | 943 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 944 | } |
0aacf84e | 945 | else |
2519490c | 946 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 947 | } |
2519490c | 948 | #undef FUNC_NAME |
0f2d19dd | 949 | |
89a7e495 | 950 | |
2519490c MW |
951 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
952 | (SCM x, SCM y), | |
953 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
954 | "@lisp\n" | |
955 | "(modulo 13 4) @result{} 1\n" | |
956 | "(modulo -13 4) @result{} 3\n" | |
957 | "@end lisp") | |
958 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 959 | { |
495a39c4 | 960 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 961 | { |
495a39c4 | 962 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 963 | return scm_floor_remainder (x, y); |
0aacf84e | 964 | else |
2519490c | 965 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 966 | } |
0aacf84e | 967 | else |
2519490c | 968 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 969 | } |
2519490c | 970 | #undef FUNC_NAME |
0f2d19dd | 971 | |
a285b18c MW |
972 | /* Return the exact integer q such that n = q*d, for exact integers n |
973 | and d, where d is known in advance to divide n evenly (with zero | |
974 | remainder). For large integers, this can be computed more | |
975 | efficiently than when the remainder is unknown. */ | |
976 | static SCM | |
977 | scm_exact_integer_quotient (SCM n, SCM d) | |
978 | #define FUNC_NAME "exact-integer-quotient" | |
979 | { | |
980 | if (SCM_LIKELY (SCM_I_INUMP (n))) | |
981 | { | |
982 | scm_t_inum nn = SCM_I_INUM (n); | |
983 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
984 | { | |
985 | scm_t_inum dd = SCM_I_INUM (d); | |
986 | if (SCM_UNLIKELY (dd == 0)) | |
987 | scm_num_overflow ("exact-integer-quotient"); | |
988 | else | |
989 | { | |
990 | scm_t_inum qq = nn / dd; | |
991 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
992 | return SCM_I_MAKINUM (qq); | |
993 | else | |
994 | return scm_i_inum2big (qq); | |
995 | } | |
996 | } | |
997 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
998 | { | |
999 | /* n is an inum and d is a bignum. Given that d is known to | |
1000 | divide n evenly, there are only two possibilities: n is 0, | |
1001 | or else n is fixnum-min and d is abs(fixnum-min). */ | |
1002 | if (nn == 0) | |
1003 | return SCM_INUM0; | |
1004 | else | |
1005 | return SCM_I_MAKINUM (-1); | |
1006 | } | |
1007 | else | |
1008 | SCM_WRONG_TYPE_ARG (2, d); | |
1009 | } | |
1010 | else if (SCM_LIKELY (SCM_BIGP (n))) | |
1011 | { | |
1012 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
1013 | { | |
1014 | scm_t_inum dd = SCM_I_INUM (d); | |
1015 | if (SCM_UNLIKELY (dd == 0)) | |
1016 | scm_num_overflow ("exact-integer-quotient"); | |
1017 | else if (SCM_UNLIKELY (dd == 1)) | |
1018 | return n; | |
1019 | else | |
1020 | { | |
1021 | SCM q = scm_i_mkbig (); | |
1022 | if (dd > 0) | |
1023 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), dd); | |
1024 | else | |
1025 | { | |
1026 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), -dd); | |
1027 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1028 | } | |
1029 | scm_remember_upto_here_1 (n); | |
1030 | return scm_i_normbig (q); | |
1031 | } | |
1032 | } | |
1033 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
1034 | { | |
1035 | SCM q = scm_i_mkbig (); | |
1036 | mpz_divexact (SCM_I_BIG_MPZ (q), | |
1037 | SCM_I_BIG_MPZ (n), | |
1038 | SCM_I_BIG_MPZ (d)); | |
1039 | scm_remember_upto_here_2 (n, d); | |
1040 | return scm_i_normbig (q); | |
1041 | } | |
1042 | else | |
1043 | SCM_WRONG_TYPE_ARG (2, d); | |
1044 | } | |
1045 | else | |
1046 | SCM_WRONG_TYPE_ARG (1, n); | |
1047 | } | |
1048 | #undef FUNC_NAME | |
1049 | ||
5fbf680b MW |
1050 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
1051 | two-valued functions. It is called from primitive generics that take | |
1052 | two arguments and return two values, when the core procedure is | |
1053 | unable to handle the given argument types. If there are GOOPS | |
1054 | methods for this primitive generic, it dispatches to GOOPS and, if | |
1055 | successful, expects two values to be returned, which are placed in | |
1056 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
1057 | wrong-type-arg exception. | |
1058 | ||
1059 | FIXME: This obviously belongs somewhere else, but until we decide on | |
1060 | the right API, it is here as a static function, because it is needed | |
1061 | by the *_divide functions below. | |
1062 | */ | |
1063 | static void | |
1064 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
1065 | const char *subr, SCM *rp1, SCM *rp2) | |
1066 | { | |
1067 | if (SCM_UNPACK (gf)) | |
1068 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
1069 | else | |
1070 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
1071 | } | |
1072 | ||
a8da6d93 MW |
1073 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
1074 | (SCM x, SCM y), | |
1075 | "Return the integer @var{q} such that\n" | |
1076 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1077 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1078 | "@lisp\n" | |
1079 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1080 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1081 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1082 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1083 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1084 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1085 | "@end lisp") | |
ff62c168 MW |
1086 | #define FUNC_NAME s_scm_euclidean_quotient |
1087 | { | |
a8da6d93 MW |
1088 | if (scm_is_false (scm_negative_p (y))) |
1089 | return scm_floor_quotient (x, y); | |
ff62c168 | 1090 | else |
a8da6d93 | 1091 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
1092 | } |
1093 | #undef FUNC_NAME | |
1094 | ||
a8da6d93 MW |
1095 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
1096 | (SCM x, SCM y), | |
1097 | "Return the real number @var{r} such that\n" | |
1098 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1099 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1100 | "for some integer @var{q}.\n" | |
1101 | "@lisp\n" | |
1102 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1103 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1104 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1105 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1106 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1107 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1108 | "@end lisp") | |
ff62c168 MW |
1109 | #define FUNC_NAME s_scm_euclidean_remainder |
1110 | { | |
a8da6d93 MW |
1111 | if (scm_is_false (scm_negative_p (y))) |
1112 | return scm_floor_remainder (x, y); | |
ff62c168 | 1113 | else |
a8da6d93 | 1114 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
1115 | } |
1116 | #undef FUNC_NAME | |
1117 | ||
a8da6d93 MW |
1118 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
1119 | (SCM x, SCM y), | |
1120 | "Return the integer @var{q} and the real number @var{r}\n" | |
1121 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1122 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1123 | "@lisp\n" | |
1124 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1125 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1126 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1127 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1128 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1129 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1130 | "@end lisp") | |
5fbf680b MW |
1131 | #define FUNC_NAME s_scm_i_euclidean_divide |
1132 | { | |
a8da6d93 MW |
1133 | if (scm_is_false (scm_negative_p (y))) |
1134 | return scm_i_floor_divide (x, y); | |
1135 | else | |
1136 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
1137 | } |
1138 | #undef FUNC_NAME | |
1139 | ||
5fbf680b MW |
1140 | void |
1141 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 1142 | { |
a8da6d93 MW |
1143 | if (scm_is_false (scm_negative_p (y))) |
1144 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 1145 | else |
a8da6d93 | 1146 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
1147 | } |
1148 | ||
8f9da340 MW |
1149 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
1150 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
1151 | ||
1152 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
1153 | (SCM x, SCM y), | |
1154 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1155 | "@lisp\n" | |
1156 | "(floor-quotient 123 10) @result{} 12\n" | |
1157 | "(floor-quotient 123 -10) @result{} -13\n" | |
1158 | "(floor-quotient -123 10) @result{} -13\n" | |
1159 | "(floor-quotient -123 -10) @result{} 12\n" | |
1160 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1161 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1162 | "@end lisp") | |
1163 | #define FUNC_NAME s_scm_floor_quotient | |
1164 | { | |
1165 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1166 | { | |
1167 | scm_t_inum xx = SCM_I_INUM (x); | |
1168 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1169 | { | |
1170 | scm_t_inum yy = SCM_I_INUM (y); | |
1171 | scm_t_inum xx1 = xx; | |
1172 | scm_t_inum qq; | |
1173 | if (SCM_LIKELY (yy > 0)) | |
1174 | { | |
1175 | if (SCM_UNLIKELY (xx < 0)) | |
1176 | xx1 = xx - yy + 1; | |
1177 | } | |
1178 | else if (SCM_UNLIKELY (yy == 0)) | |
1179 | scm_num_overflow (s_scm_floor_quotient); | |
1180 | else if (xx > 0) | |
1181 | xx1 = xx - yy - 1; | |
1182 | qq = xx1 / yy; | |
1183 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1184 | return SCM_I_MAKINUM (qq); | |
1185 | else | |
1186 | return scm_i_inum2big (qq); | |
1187 | } | |
1188 | else if (SCM_BIGP (y)) | |
1189 | { | |
1190 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1191 | scm_remember_upto_here_1 (y); | |
1192 | if (sign > 0) | |
1193 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1194 | else | |
1195 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1196 | } | |
1197 | else if (SCM_REALP (y)) | |
1198 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1199 | else if (SCM_FRACTIONP (y)) | |
1200 | return scm_i_exact_rational_floor_quotient (x, y); | |
1201 | else | |
1202 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1203 | s_scm_floor_quotient); | |
1204 | } | |
1205 | else if (SCM_BIGP (x)) | |
1206 | { | |
1207 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1208 | { | |
1209 | scm_t_inum yy = SCM_I_INUM (y); | |
1210 | if (SCM_UNLIKELY (yy == 0)) | |
1211 | scm_num_overflow (s_scm_floor_quotient); | |
1212 | else if (SCM_UNLIKELY (yy == 1)) | |
1213 | return x; | |
1214 | else | |
1215 | { | |
1216 | SCM q = scm_i_mkbig (); | |
1217 | if (yy > 0) | |
1218 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1219 | else | |
1220 | { | |
1221 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1222 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1223 | } | |
1224 | scm_remember_upto_here_1 (x); | |
1225 | return scm_i_normbig (q); | |
1226 | } | |
1227 | } | |
1228 | else if (SCM_BIGP (y)) | |
1229 | { | |
1230 | SCM q = scm_i_mkbig (); | |
1231 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1232 | SCM_I_BIG_MPZ (x), | |
1233 | SCM_I_BIG_MPZ (y)); | |
1234 | scm_remember_upto_here_2 (x, y); | |
1235 | return scm_i_normbig (q); | |
1236 | } | |
1237 | else if (SCM_REALP (y)) | |
1238 | return scm_i_inexact_floor_quotient | |
1239 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1240 | else if (SCM_FRACTIONP (y)) | |
1241 | return scm_i_exact_rational_floor_quotient (x, y); | |
1242 | else | |
1243 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1244 | s_scm_floor_quotient); | |
1245 | } | |
1246 | else if (SCM_REALP (x)) | |
1247 | { | |
1248 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1249 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1250 | return scm_i_inexact_floor_quotient | |
1251 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1252 | else | |
1253 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1254 | s_scm_floor_quotient); | |
1255 | } | |
1256 | else if (SCM_FRACTIONP (x)) | |
1257 | { | |
1258 | if (SCM_REALP (y)) | |
1259 | return scm_i_inexact_floor_quotient | |
1260 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1261 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1262 | return scm_i_exact_rational_floor_quotient (x, y); | |
1263 | else | |
1264 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1265 | s_scm_floor_quotient); | |
1266 | } | |
1267 | else | |
1268 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1269 | s_scm_floor_quotient); | |
1270 | } | |
1271 | #undef FUNC_NAME | |
1272 | ||
1273 | static SCM | |
1274 | scm_i_inexact_floor_quotient (double x, double y) | |
1275 | { | |
1276 | if (SCM_UNLIKELY (y == 0)) | |
1277 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1278 | else | |
1279 | return scm_from_double (floor (x / y)); | |
1280 | } | |
1281 | ||
1282 | static SCM | |
1283 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1284 | { | |
1285 | return scm_floor_quotient | |
1286 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1287 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1288 | } | |
1289 | ||
1290 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1291 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1292 | ||
1293 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1294 | (SCM x, SCM y), | |
1295 | "Return the real number @var{r} such that\n" | |
1296 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1297 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1298 | "@lisp\n" | |
1299 | "(floor-remainder 123 10) @result{} 3\n" | |
1300 | "(floor-remainder 123 -10) @result{} -7\n" | |
1301 | "(floor-remainder -123 10) @result{} 7\n" | |
1302 | "(floor-remainder -123 -10) @result{} -3\n" | |
1303 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1304 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1305 | "@end lisp") | |
1306 | #define FUNC_NAME s_scm_floor_remainder | |
1307 | { | |
1308 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1309 | { | |
1310 | scm_t_inum xx = SCM_I_INUM (x); | |
1311 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1312 | { | |
1313 | scm_t_inum yy = SCM_I_INUM (y); | |
1314 | if (SCM_UNLIKELY (yy == 0)) | |
1315 | scm_num_overflow (s_scm_floor_remainder); | |
1316 | else | |
1317 | { | |
1318 | scm_t_inum rr = xx % yy; | |
1319 | int needs_adjustment; | |
1320 | ||
1321 | if (SCM_LIKELY (yy > 0)) | |
1322 | needs_adjustment = (rr < 0); | |
1323 | else | |
1324 | needs_adjustment = (rr > 0); | |
1325 | ||
1326 | if (needs_adjustment) | |
1327 | rr += yy; | |
1328 | return SCM_I_MAKINUM (rr); | |
1329 | } | |
1330 | } | |
1331 | else if (SCM_BIGP (y)) | |
1332 | { | |
1333 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1334 | scm_remember_upto_here_1 (y); | |
1335 | if (sign > 0) | |
1336 | { | |
1337 | if (xx < 0) | |
1338 | { | |
1339 | SCM r = scm_i_mkbig (); | |
1340 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1341 | scm_remember_upto_here_1 (y); | |
1342 | return scm_i_normbig (r); | |
1343 | } | |
1344 | else | |
1345 | return x; | |
1346 | } | |
1347 | else if (xx <= 0) | |
1348 | return x; | |
1349 | else | |
1350 | { | |
1351 | SCM r = scm_i_mkbig (); | |
1352 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1353 | scm_remember_upto_here_1 (y); | |
1354 | return scm_i_normbig (r); | |
1355 | } | |
1356 | } | |
1357 | else if (SCM_REALP (y)) | |
1358 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1359 | else if (SCM_FRACTIONP (y)) | |
1360 | return scm_i_exact_rational_floor_remainder (x, y); | |
1361 | else | |
1362 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1363 | s_scm_floor_remainder); | |
1364 | } | |
1365 | else if (SCM_BIGP (x)) | |
1366 | { | |
1367 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1368 | { | |
1369 | scm_t_inum yy = SCM_I_INUM (y); | |
1370 | if (SCM_UNLIKELY (yy == 0)) | |
1371 | scm_num_overflow (s_scm_floor_remainder); | |
1372 | else | |
1373 | { | |
1374 | scm_t_inum rr; | |
1375 | if (yy > 0) | |
1376 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1377 | else | |
1378 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1379 | scm_remember_upto_here_1 (x); | |
1380 | return SCM_I_MAKINUM (rr); | |
1381 | } | |
1382 | } | |
1383 | else if (SCM_BIGP (y)) | |
1384 | { | |
1385 | SCM r = scm_i_mkbig (); | |
1386 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1387 | SCM_I_BIG_MPZ (x), | |
1388 | SCM_I_BIG_MPZ (y)); | |
1389 | scm_remember_upto_here_2 (x, y); | |
1390 | return scm_i_normbig (r); | |
1391 | } | |
1392 | else if (SCM_REALP (y)) | |
1393 | return scm_i_inexact_floor_remainder | |
1394 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1395 | else if (SCM_FRACTIONP (y)) | |
1396 | return scm_i_exact_rational_floor_remainder (x, y); | |
1397 | else | |
1398 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1399 | s_scm_floor_remainder); | |
1400 | } | |
1401 | else if (SCM_REALP (x)) | |
1402 | { | |
1403 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1404 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1405 | return scm_i_inexact_floor_remainder | |
1406 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1407 | else | |
1408 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1409 | s_scm_floor_remainder); | |
1410 | } | |
1411 | else if (SCM_FRACTIONP (x)) | |
1412 | { | |
1413 | if (SCM_REALP (y)) | |
1414 | return scm_i_inexact_floor_remainder | |
1415 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1416 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1417 | return scm_i_exact_rational_floor_remainder (x, y); | |
1418 | else | |
1419 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1420 | s_scm_floor_remainder); | |
1421 | } | |
1422 | else | |
1423 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1424 | s_scm_floor_remainder); | |
1425 | } | |
1426 | #undef FUNC_NAME | |
1427 | ||
1428 | static SCM | |
1429 | scm_i_inexact_floor_remainder (double x, double y) | |
1430 | { | |
1431 | /* Although it would be more efficient to use fmod here, we can't | |
1432 | because it would in some cases produce results inconsistent with | |
1433 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1434 | close). In particular, when x is very close to a multiple of y, | |
1435 | then r might be either 0.0 or y, but those two cases must | |
1436 | correspond to different choices of q. If r = 0.0 then q must be | |
1437 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1438 | and remainder chooses the other, it would be bad. */ | |
1439 | if (SCM_UNLIKELY (y == 0)) | |
1440 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1441 | else | |
1442 | return scm_from_double (x - y * floor (x / y)); | |
1443 | } | |
1444 | ||
1445 | static SCM | |
1446 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1447 | { | |
1448 | SCM xd = scm_denominator (x); | |
1449 | SCM yd = scm_denominator (y); | |
1450 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1451 | scm_product (scm_numerator (y), xd)); | |
1452 | return scm_divide (r1, scm_product (xd, yd)); | |
1453 | } | |
1454 | ||
1455 | ||
1456 | static void scm_i_inexact_floor_divide (double x, double y, | |
1457 | SCM *qp, SCM *rp); | |
1458 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1459 | SCM *qp, SCM *rp); | |
1460 | ||
1461 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1462 | (SCM x, SCM y), | |
1463 | "Return the integer @var{q} and the real number @var{r}\n" | |
1464 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1465 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1466 | "@lisp\n" | |
1467 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1468 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1469 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1470 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1471 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1472 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1473 | "@end lisp") | |
1474 | #define FUNC_NAME s_scm_i_floor_divide | |
1475 | { | |
1476 | SCM q, r; | |
1477 | ||
1478 | scm_floor_divide(x, y, &q, &r); | |
1479 | return scm_values (scm_list_2 (q, r)); | |
1480 | } | |
1481 | #undef FUNC_NAME | |
1482 | ||
1483 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1484 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1485 | ||
1486 | void | |
1487 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1488 | { | |
1489 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1490 | { | |
1491 | scm_t_inum xx = SCM_I_INUM (x); | |
1492 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1493 | { | |
1494 | scm_t_inum yy = SCM_I_INUM (y); | |
1495 | if (SCM_UNLIKELY (yy == 0)) | |
1496 | scm_num_overflow (s_scm_floor_divide); | |
1497 | else | |
1498 | { | |
1499 | scm_t_inum qq = xx / yy; | |
1500 | scm_t_inum rr = xx % yy; | |
1501 | int needs_adjustment; | |
1502 | ||
1503 | if (SCM_LIKELY (yy > 0)) | |
1504 | needs_adjustment = (rr < 0); | |
1505 | else | |
1506 | needs_adjustment = (rr > 0); | |
1507 | ||
1508 | if (needs_adjustment) | |
1509 | { | |
1510 | rr += yy; | |
1511 | qq--; | |
1512 | } | |
1513 | ||
1514 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1515 | *qp = SCM_I_MAKINUM (qq); | |
1516 | else | |
1517 | *qp = scm_i_inum2big (qq); | |
1518 | *rp = SCM_I_MAKINUM (rr); | |
1519 | } | |
1520 | return; | |
1521 | } | |
1522 | else if (SCM_BIGP (y)) | |
1523 | { | |
1524 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1525 | scm_remember_upto_here_1 (y); | |
1526 | if (sign > 0) | |
1527 | { | |
1528 | if (xx < 0) | |
1529 | { | |
1530 | SCM r = scm_i_mkbig (); | |
1531 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1532 | scm_remember_upto_here_1 (y); | |
1533 | *qp = SCM_I_MAKINUM (-1); | |
1534 | *rp = scm_i_normbig (r); | |
1535 | } | |
1536 | else | |
1537 | { | |
1538 | *qp = SCM_INUM0; | |
1539 | *rp = x; | |
1540 | } | |
1541 | } | |
1542 | else if (xx <= 0) | |
1543 | { | |
1544 | *qp = SCM_INUM0; | |
1545 | *rp = x; | |
1546 | } | |
1547 | else | |
1548 | { | |
1549 | SCM r = scm_i_mkbig (); | |
1550 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1551 | scm_remember_upto_here_1 (y); | |
1552 | *qp = SCM_I_MAKINUM (-1); | |
1553 | *rp = scm_i_normbig (r); | |
1554 | } | |
1555 | return; | |
1556 | } | |
1557 | else if (SCM_REALP (y)) | |
1558 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1559 | else if (SCM_FRACTIONP (y)) | |
1560 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1561 | else | |
1562 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1563 | s_scm_floor_divide, qp, rp); | |
1564 | } | |
1565 | else if (SCM_BIGP (x)) | |
1566 | { | |
1567 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1568 | { | |
1569 | scm_t_inum yy = SCM_I_INUM (y); | |
1570 | if (SCM_UNLIKELY (yy == 0)) | |
1571 | scm_num_overflow (s_scm_floor_divide); | |
1572 | else | |
1573 | { | |
1574 | SCM q = scm_i_mkbig (); | |
1575 | SCM r = scm_i_mkbig (); | |
1576 | if (yy > 0) | |
1577 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1578 | SCM_I_BIG_MPZ (x), yy); | |
1579 | else | |
1580 | { | |
1581 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1582 | SCM_I_BIG_MPZ (x), -yy); | |
1583 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1584 | } | |
1585 | scm_remember_upto_here_1 (x); | |
1586 | *qp = scm_i_normbig (q); | |
1587 | *rp = scm_i_normbig (r); | |
1588 | } | |
1589 | return; | |
1590 | } | |
1591 | else if (SCM_BIGP (y)) | |
1592 | { | |
1593 | SCM q = scm_i_mkbig (); | |
1594 | SCM r = scm_i_mkbig (); | |
1595 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1596 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1597 | scm_remember_upto_here_2 (x, y); | |
1598 | *qp = scm_i_normbig (q); | |
1599 | *rp = scm_i_normbig (r); | |
1600 | return; | |
1601 | } | |
1602 | else if (SCM_REALP (y)) | |
1603 | return scm_i_inexact_floor_divide | |
1604 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1605 | else if (SCM_FRACTIONP (y)) | |
1606 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1607 | else | |
1608 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1609 | s_scm_floor_divide, qp, rp); | |
1610 | } | |
1611 | else if (SCM_REALP (x)) | |
1612 | { | |
1613 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1614 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1615 | return scm_i_inexact_floor_divide | |
1616 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1617 | else | |
1618 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1619 | s_scm_floor_divide, qp, rp); | |
1620 | } | |
1621 | else if (SCM_FRACTIONP (x)) | |
1622 | { | |
1623 | if (SCM_REALP (y)) | |
1624 | return scm_i_inexact_floor_divide | |
1625 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1626 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1627 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1628 | else | |
1629 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1630 | s_scm_floor_divide, qp, rp); | |
1631 | } | |
1632 | else | |
1633 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1634 | s_scm_floor_divide, qp, rp); | |
1635 | } | |
1636 | ||
1637 | static void | |
1638 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1639 | { | |
1640 | if (SCM_UNLIKELY (y == 0)) | |
1641 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1642 | else | |
1643 | { | |
1644 | double q = floor (x / y); | |
1645 | double r = x - q * y; | |
1646 | *qp = scm_from_double (q); | |
1647 | *rp = scm_from_double (r); | |
1648 | } | |
1649 | } | |
1650 | ||
1651 | static void | |
1652 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1653 | { | |
1654 | SCM r1; | |
1655 | SCM xd = scm_denominator (x); | |
1656 | SCM yd = scm_denominator (y); | |
1657 | ||
1658 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1659 | scm_product (scm_numerator (y), xd), | |
1660 | qp, &r1); | |
1661 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1662 | } | |
1663 | ||
1664 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1665 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1666 | ||
1667 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1668 | (SCM x, SCM y), | |
1669 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1670 | "@lisp\n" | |
1671 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1672 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1673 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1674 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1675 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1676 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1677 | "@end lisp") | |
1678 | #define FUNC_NAME s_scm_ceiling_quotient | |
1679 | { | |
1680 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1681 | { | |
1682 | scm_t_inum xx = SCM_I_INUM (x); | |
1683 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1684 | { | |
1685 | scm_t_inum yy = SCM_I_INUM (y); | |
1686 | if (SCM_UNLIKELY (yy == 0)) | |
1687 | scm_num_overflow (s_scm_ceiling_quotient); | |
1688 | else | |
1689 | { | |
1690 | scm_t_inum xx1 = xx; | |
1691 | scm_t_inum qq; | |
1692 | if (SCM_LIKELY (yy > 0)) | |
1693 | { | |
1694 | if (SCM_LIKELY (xx >= 0)) | |
1695 | xx1 = xx + yy - 1; | |
1696 | } | |
8f9da340 MW |
1697 | else if (xx < 0) |
1698 | xx1 = xx + yy + 1; | |
1699 | qq = xx1 / yy; | |
1700 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1701 | return SCM_I_MAKINUM (qq); | |
1702 | else | |
1703 | return scm_i_inum2big (qq); | |
1704 | } | |
1705 | } | |
1706 | else if (SCM_BIGP (y)) | |
1707 | { | |
1708 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1709 | scm_remember_upto_here_1 (y); | |
1710 | if (SCM_LIKELY (sign > 0)) | |
1711 | { | |
1712 | if (SCM_LIKELY (xx > 0)) | |
1713 | return SCM_INUM1; | |
1714 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1715 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1716 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1717 | { | |
1718 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1719 | scm_remember_upto_here_1 (y); | |
1720 | return SCM_I_MAKINUM (-1); | |
1721 | } | |
1722 | else | |
1723 | return SCM_INUM0; | |
1724 | } | |
1725 | else if (xx >= 0) | |
1726 | return SCM_INUM0; | |
1727 | else | |
1728 | return SCM_INUM1; | |
1729 | } | |
1730 | else if (SCM_REALP (y)) | |
1731 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1732 | else if (SCM_FRACTIONP (y)) | |
1733 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1734 | else | |
1735 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1736 | s_scm_ceiling_quotient); | |
1737 | } | |
1738 | else if (SCM_BIGP (x)) | |
1739 | { | |
1740 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1741 | { | |
1742 | scm_t_inum yy = SCM_I_INUM (y); | |
1743 | if (SCM_UNLIKELY (yy == 0)) | |
1744 | scm_num_overflow (s_scm_ceiling_quotient); | |
1745 | else if (SCM_UNLIKELY (yy == 1)) | |
1746 | return x; | |
1747 | else | |
1748 | { | |
1749 | SCM q = scm_i_mkbig (); | |
1750 | if (yy > 0) | |
1751 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1752 | else | |
1753 | { | |
1754 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1755 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1756 | } | |
1757 | scm_remember_upto_here_1 (x); | |
1758 | return scm_i_normbig (q); | |
1759 | } | |
1760 | } | |
1761 | else if (SCM_BIGP (y)) | |
1762 | { | |
1763 | SCM q = scm_i_mkbig (); | |
1764 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1765 | SCM_I_BIG_MPZ (x), | |
1766 | SCM_I_BIG_MPZ (y)); | |
1767 | scm_remember_upto_here_2 (x, y); | |
1768 | return scm_i_normbig (q); | |
1769 | } | |
1770 | else if (SCM_REALP (y)) | |
1771 | return scm_i_inexact_ceiling_quotient | |
1772 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1773 | else if (SCM_FRACTIONP (y)) | |
1774 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1775 | else | |
1776 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1777 | s_scm_ceiling_quotient); | |
1778 | } | |
1779 | else if (SCM_REALP (x)) | |
1780 | { | |
1781 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1782 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1783 | return scm_i_inexact_ceiling_quotient | |
1784 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1785 | else | |
1786 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1787 | s_scm_ceiling_quotient); | |
1788 | } | |
1789 | else if (SCM_FRACTIONP (x)) | |
1790 | { | |
1791 | if (SCM_REALP (y)) | |
1792 | return scm_i_inexact_ceiling_quotient | |
1793 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1794 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1795 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1796 | else | |
1797 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1798 | s_scm_ceiling_quotient); | |
1799 | } | |
1800 | else | |
1801 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1802 | s_scm_ceiling_quotient); | |
1803 | } | |
1804 | #undef FUNC_NAME | |
1805 | ||
1806 | static SCM | |
1807 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1808 | { | |
1809 | if (SCM_UNLIKELY (y == 0)) | |
1810 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1811 | else | |
1812 | return scm_from_double (ceil (x / y)); | |
1813 | } | |
1814 | ||
1815 | static SCM | |
1816 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1817 | { | |
1818 | return scm_ceiling_quotient | |
1819 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1820 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1821 | } | |
1822 | ||
1823 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1824 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1825 | ||
1826 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1827 | (SCM x, SCM y), | |
1828 | "Return the real number @var{r} such that\n" | |
1829 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1830 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1831 | "@lisp\n" | |
1832 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1833 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1834 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1835 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1836 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1837 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1838 | "@end lisp") | |
1839 | #define FUNC_NAME s_scm_ceiling_remainder | |
1840 | { | |
1841 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1842 | { | |
1843 | scm_t_inum xx = SCM_I_INUM (x); | |
1844 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1845 | { | |
1846 | scm_t_inum yy = SCM_I_INUM (y); | |
1847 | if (SCM_UNLIKELY (yy == 0)) | |
1848 | scm_num_overflow (s_scm_ceiling_remainder); | |
1849 | else | |
1850 | { | |
1851 | scm_t_inum rr = xx % yy; | |
1852 | int needs_adjustment; | |
1853 | ||
1854 | if (SCM_LIKELY (yy > 0)) | |
1855 | needs_adjustment = (rr > 0); | |
1856 | else | |
1857 | needs_adjustment = (rr < 0); | |
1858 | ||
1859 | if (needs_adjustment) | |
1860 | rr -= yy; | |
1861 | return SCM_I_MAKINUM (rr); | |
1862 | } | |
1863 | } | |
1864 | else if (SCM_BIGP (y)) | |
1865 | { | |
1866 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1867 | scm_remember_upto_here_1 (y); | |
1868 | if (SCM_LIKELY (sign > 0)) | |
1869 | { | |
1870 | if (SCM_LIKELY (xx > 0)) | |
1871 | { | |
1872 | SCM r = scm_i_mkbig (); | |
1873 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1874 | scm_remember_upto_here_1 (y); | |
1875 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1876 | return scm_i_normbig (r); | |
1877 | } | |
1878 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1879 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1880 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1881 | { | |
1882 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1883 | scm_remember_upto_here_1 (y); | |
1884 | return SCM_INUM0; | |
1885 | } | |
1886 | else | |
1887 | return x; | |
1888 | } | |
1889 | else if (xx >= 0) | |
1890 | return x; | |
1891 | else | |
1892 | { | |
1893 | SCM r = scm_i_mkbig (); | |
1894 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1895 | scm_remember_upto_here_1 (y); | |
1896 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1897 | return scm_i_normbig (r); | |
1898 | } | |
1899 | } | |
1900 | else if (SCM_REALP (y)) | |
1901 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1902 | else if (SCM_FRACTIONP (y)) | |
1903 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1904 | else | |
1905 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1906 | s_scm_ceiling_remainder); | |
1907 | } | |
1908 | else if (SCM_BIGP (x)) | |
1909 | { | |
1910 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1911 | { | |
1912 | scm_t_inum yy = SCM_I_INUM (y); | |
1913 | if (SCM_UNLIKELY (yy == 0)) | |
1914 | scm_num_overflow (s_scm_ceiling_remainder); | |
1915 | else | |
1916 | { | |
1917 | scm_t_inum rr; | |
1918 | if (yy > 0) | |
1919 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1920 | else | |
1921 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1922 | scm_remember_upto_here_1 (x); | |
1923 | return SCM_I_MAKINUM (rr); | |
1924 | } | |
1925 | } | |
1926 | else if (SCM_BIGP (y)) | |
1927 | { | |
1928 | SCM r = scm_i_mkbig (); | |
1929 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1930 | SCM_I_BIG_MPZ (x), | |
1931 | SCM_I_BIG_MPZ (y)); | |
1932 | scm_remember_upto_here_2 (x, y); | |
1933 | return scm_i_normbig (r); | |
1934 | } | |
1935 | else if (SCM_REALP (y)) | |
1936 | return scm_i_inexact_ceiling_remainder | |
1937 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1938 | else if (SCM_FRACTIONP (y)) | |
1939 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1940 | else | |
1941 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1942 | s_scm_ceiling_remainder); | |
1943 | } | |
1944 | else if (SCM_REALP (x)) | |
1945 | { | |
1946 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1947 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1948 | return scm_i_inexact_ceiling_remainder | |
1949 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1950 | else | |
1951 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1952 | s_scm_ceiling_remainder); | |
1953 | } | |
1954 | else if (SCM_FRACTIONP (x)) | |
1955 | { | |
1956 | if (SCM_REALP (y)) | |
1957 | return scm_i_inexact_ceiling_remainder | |
1958 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1959 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1960 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1961 | else | |
1962 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1963 | s_scm_ceiling_remainder); | |
1964 | } | |
1965 | else | |
1966 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1967 | s_scm_ceiling_remainder); | |
1968 | } | |
1969 | #undef FUNC_NAME | |
1970 | ||
1971 | static SCM | |
1972 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1973 | { | |
1974 | /* Although it would be more efficient to use fmod here, we can't | |
1975 | because it would in some cases produce results inconsistent with | |
1976 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1977 | close). In particular, when x is very close to a multiple of y, | |
1978 | then r might be either 0.0 or -y, but those two cases must | |
1979 | correspond to different choices of q. If r = 0.0 then q must be | |
1980 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1981 | and remainder chooses the other, it would be bad. */ | |
1982 | if (SCM_UNLIKELY (y == 0)) | |
1983 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1984 | else | |
1985 | return scm_from_double (x - y * ceil (x / y)); | |
1986 | } | |
1987 | ||
1988 | static SCM | |
1989 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1990 | { | |
1991 | SCM xd = scm_denominator (x); | |
1992 | SCM yd = scm_denominator (y); | |
1993 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1994 | scm_product (scm_numerator (y), xd)); | |
1995 | return scm_divide (r1, scm_product (xd, yd)); | |
1996 | } | |
1997 | ||
1998 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1999 | SCM *qp, SCM *rp); | |
2000 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
2001 | SCM *qp, SCM *rp); | |
2002 | ||
2003 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
2004 | (SCM x, SCM y), | |
2005 | "Return the integer @var{q} and the real number @var{r}\n" | |
2006 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2007 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
2008 | "@lisp\n" | |
2009 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
2010 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
2011 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
2012 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
2013 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2014 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2015 | "@end lisp") | |
2016 | #define FUNC_NAME s_scm_i_ceiling_divide | |
2017 | { | |
2018 | SCM q, r; | |
2019 | ||
2020 | scm_ceiling_divide(x, y, &q, &r); | |
2021 | return scm_values (scm_list_2 (q, r)); | |
2022 | } | |
2023 | #undef FUNC_NAME | |
2024 | ||
2025 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
2026 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
2027 | ||
2028 | void | |
2029 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2030 | { | |
2031 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2032 | { | |
2033 | scm_t_inum xx = SCM_I_INUM (x); | |
2034 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2035 | { | |
2036 | scm_t_inum yy = SCM_I_INUM (y); | |
2037 | if (SCM_UNLIKELY (yy == 0)) | |
2038 | scm_num_overflow (s_scm_ceiling_divide); | |
2039 | else | |
2040 | { | |
2041 | scm_t_inum qq = xx / yy; | |
2042 | scm_t_inum rr = xx % yy; | |
2043 | int needs_adjustment; | |
2044 | ||
2045 | if (SCM_LIKELY (yy > 0)) | |
2046 | needs_adjustment = (rr > 0); | |
2047 | else | |
2048 | needs_adjustment = (rr < 0); | |
2049 | ||
2050 | if (needs_adjustment) | |
2051 | { | |
2052 | rr -= yy; | |
2053 | qq++; | |
2054 | } | |
2055 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2056 | *qp = SCM_I_MAKINUM (qq); | |
2057 | else | |
2058 | *qp = scm_i_inum2big (qq); | |
2059 | *rp = SCM_I_MAKINUM (rr); | |
2060 | } | |
2061 | return; | |
2062 | } | |
2063 | else if (SCM_BIGP (y)) | |
2064 | { | |
2065 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2066 | scm_remember_upto_here_1 (y); | |
2067 | if (SCM_LIKELY (sign > 0)) | |
2068 | { | |
2069 | if (SCM_LIKELY (xx > 0)) | |
2070 | { | |
2071 | SCM r = scm_i_mkbig (); | |
2072 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2073 | scm_remember_upto_here_1 (y); | |
2074 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2075 | *qp = SCM_INUM1; | |
2076 | *rp = scm_i_normbig (r); | |
2077 | } | |
2078 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2079 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2080 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2081 | { | |
2082 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2083 | scm_remember_upto_here_1 (y); | |
2084 | *qp = SCM_I_MAKINUM (-1); | |
2085 | *rp = SCM_INUM0; | |
2086 | } | |
2087 | else | |
2088 | { | |
2089 | *qp = SCM_INUM0; | |
2090 | *rp = x; | |
2091 | } | |
2092 | } | |
2093 | else if (xx >= 0) | |
2094 | { | |
2095 | *qp = SCM_INUM0; | |
2096 | *rp = x; | |
2097 | } | |
2098 | else | |
2099 | { | |
2100 | SCM r = scm_i_mkbig (); | |
2101 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2102 | scm_remember_upto_here_1 (y); | |
2103 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2104 | *qp = SCM_INUM1; | |
2105 | *rp = scm_i_normbig (r); | |
2106 | } | |
2107 | return; | |
2108 | } | |
2109 | else if (SCM_REALP (y)) | |
2110 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2111 | else if (SCM_FRACTIONP (y)) | |
2112 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2113 | else | |
2114 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2115 | s_scm_ceiling_divide, qp, rp); | |
2116 | } | |
2117 | else if (SCM_BIGP (x)) | |
2118 | { | |
2119 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2120 | { | |
2121 | scm_t_inum yy = SCM_I_INUM (y); | |
2122 | if (SCM_UNLIKELY (yy == 0)) | |
2123 | scm_num_overflow (s_scm_ceiling_divide); | |
2124 | else | |
2125 | { | |
2126 | SCM q = scm_i_mkbig (); | |
2127 | SCM r = scm_i_mkbig (); | |
2128 | if (yy > 0) | |
2129 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2130 | SCM_I_BIG_MPZ (x), yy); | |
2131 | else | |
2132 | { | |
2133 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2134 | SCM_I_BIG_MPZ (x), -yy); | |
2135 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2136 | } | |
2137 | scm_remember_upto_here_1 (x); | |
2138 | *qp = scm_i_normbig (q); | |
2139 | *rp = scm_i_normbig (r); | |
2140 | } | |
2141 | return; | |
2142 | } | |
2143 | else if (SCM_BIGP (y)) | |
2144 | { | |
2145 | SCM q = scm_i_mkbig (); | |
2146 | SCM r = scm_i_mkbig (); | |
2147 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2148 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2149 | scm_remember_upto_here_2 (x, y); | |
2150 | *qp = scm_i_normbig (q); | |
2151 | *rp = scm_i_normbig (r); | |
2152 | return; | |
2153 | } | |
2154 | else if (SCM_REALP (y)) | |
2155 | return scm_i_inexact_ceiling_divide | |
2156 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2157 | else if (SCM_FRACTIONP (y)) | |
2158 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2159 | else | |
2160 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2161 | s_scm_ceiling_divide, qp, rp); | |
2162 | } | |
2163 | else if (SCM_REALP (x)) | |
2164 | { | |
2165 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2166 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2167 | return scm_i_inexact_ceiling_divide | |
2168 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2169 | else | |
2170 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2171 | s_scm_ceiling_divide, qp, rp); | |
2172 | } | |
2173 | else if (SCM_FRACTIONP (x)) | |
2174 | { | |
2175 | if (SCM_REALP (y)) | |
2176 | return scm_i_inexact_ceiling_divide | |
2177 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2178 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2179 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2180 | else | |
2181 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2182 | s_scm_ceiling_divide, qp, rp); | |
2183 | } | |
2184 | else | |
2185 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2186 | s_scm_ceiling_divide, qp, rp); | |
2187 | } | |
2188 | ||
2189 | static void | |
2190 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2191 | { | |
2192 | if (SCM_UNLIKELY (y == 0)) | |
2193 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2194 | else | |
2195 | { | |
2196 | double q = ceil (x / y); | |
2197 | double r = x - q * y; | |
2198 | *qp = scm_from_double (q); | |
2199 | *rp = scm_from_double (r); | |
2200 | } | |
2201 | } | |
2202 | ||
2203 | static void | |
2204 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2205 | { | |
2206 | SCM r1; | |
2207 | SCM xd = scm_denominator (x); | |
2208 | SCM yd = scm_denominator (y); | |
2209 | ||
2210 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2211 | scm_product (scm_numerator (y), xd), | |
2212 | qp, &r1); | |
2213 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2214 | } | |
2215 | ||
2216 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2217 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2218 | ||
2219 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2220 | (SCM x, SCM y), | |
2221 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2222 | "@lisp\n" | |
2223 | "(truncate-quotient 123 10) @result{} 12\n" | |
2224 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2225 | "(truncate-quotient -123 10) @result{} -12\n" | |
2226 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2227 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2228 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2229 | "@end lisp") | |
2230 | #define FUNC_NAME s_scm_truncate_quotient | |
2231 | { | |
2232 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2233 | { | |
2234 | scm_t_inum xx = SCM_I_INUM (x); | |
2235 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2236 | { | |
2237 | scm_t_inum yy = SCM_I_INUM (y); | |
2238 | if (SCM_UNLIKELY (yy == 0)) | |
2239 | scm_num_overflow (s_scm_truncate_quotient); | |
2240 | else | |
2241 | { | |
2242 | scm_t_inum qq = xx / yy; | |
2243 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2244 | return SCM_I_MAKINUM (qq); | |
2245 | else | |
2246 | return scm_i_inum2big (qq); | |
2247 | } | |
2248 | } | |
2249 | else if (SCM_BIGP (y)) | |
2250 | { | |
2251 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2252 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2253 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2254 | { | |
2255 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2256 | scm_remember_upto_here_1 (y); | |
2257 | return SCM_I_MAKINUM (-1); | |
2258 | } | |
2259 | else | |
2260 | return SCM_INUM0; | |
2261 | } | |
2262 | else if (SCM_REALP (y)) | |
2263 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2264 | else if (SCM_FRACTIONP (y)) | |
2265 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2266 | else | |
2267 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2268 | s_scm_truncate_quotient); | |
2269 | } | |
2270 | else if (SCM_BIGP (x)) | |
2271 | { | |
2272 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2273 | { | |
2274 | scm_t_inum yy = SCM_I_INUM (y); | |
2275 | if (SCM_UNLIKELY (yy == 0)) | |
2276 | scm_num_overflow (s_scm_truncate_quotient); | |
2277 | else if (SCM_UNLIKELY (yy == 1)) | |
2278 | return x; | |
2279 | else | |
2280 | { | |
2281 | SCM q = scm_i_mkbig (); | |
2282 | if (yy > 0) | |
2283 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2284 | else | |
2285 | { | |
2286 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2287 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2288 | } | |
2289 | scm_remember_upto_here_1 (x); | |
2290 | return scm_i_normbig (q); | |
2291 | } | |
2292 | } | |
2293 | else if (SCM_BIGP (y)) | |
2294 | { | |
2295 | SCM q = scm_i_mkbig (); | |
2296 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2297 | SCM_I_BIG_MPZ (x), | |
2298 | SCM_I_BIG_MPZ (y)); | |
2299 | scm_remember_upto_here_2 (x, y); | |
2300 | return scm_i_normbig (q); | |
2301 | } | |
2302 | else if (SCM_REALP (y)) | |
2303 | return scm_i_inexact_truncate_quotient | |
2304 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2305 | else if (SCM_FRACTIONP (y)) | |
2306 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2307 | else | |
2308 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2309 | s_scm_truncate_quotient); | |
2310 | } | |
2311 | else if (SCM_REALP (x)) | |
2312 | { | |
2313 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2314 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2315 | return scm_i_inexact_truncate_quotient | |
2316 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2317 | else | |
2318 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2319 | s_scm_truncate_quotient); | |
2320 | } | |
2321 | else if (SCM_FRACTIONP (x)) | |
2322 | { | |
2323 | if (SCM_REALP (y)) | |
2324 | return scm_i_inexact_truncate_quotient | |
2325 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2326 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2327 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2328 | else | |
2329 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2330 | s_scm_truncate_quotient); | |
2331 | } | |
2332 | else | |
2333 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2334 | s_scm_truncate_quotient); | |
2335 | } | |
2336 | #undef FUNC_NAME | |
2337 | ||
2338 | static SCM | |
2339 | scm_i_inexact_truncate_quotient (double x, double y) | |
2340 | { | |
2341 | if (SCM_UNLIKELY (y == 0)) | |
2342 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2343 | else | |
c251ab63 | 2344 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2345 | } |
2346 | ||
2347 | static SCM | |
2348 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2349 | { | |
2350 | return scm_truncate_quotient | |
2351 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2352 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2353 | } | |
2354 | ||
2355 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2356 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2357 | ||
2358 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2359 | (SCM x, SCM y), | |
2360 | "Return the real number @var{r} such that\n" | |
2361 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2362 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2363 | "@lisp\n" | |
2364 | "(truncate-remainder 123 10) @result{} 3\n" | |
2365 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2366 | "(truncate-remainder -123 10) @result{} -3\n" | |
2367 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2368 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2369 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2370 | "@end lisp") | |
2371 | #define FUNC_NAME s_scm_truncate_remainder | |
2372 | { | |
2373 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2374 | { | |
2375 | scm_t_inum xx = SCM_I_INUM (x); | |
2376 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2377 | { | |
2378 | scm_t_inum yy = SCM_I_INUM (y); | |
2379 | if (SCM_UNLIKELY (yy == 0)) | |
2380 | scm_num_overflow (s_scm_truncate_remainder); | |
2381 | else | |
2382 | return SCM_I_MAKINUM (xx % yy); | |
2383 | } | |
2384 | else if (SCM_BIGP (y)) | |
2385 | { | |
2386 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2387 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2388 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2389 | { | |
2390 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2391 | scm_remember_upto_here_1 (y); | |
2392 | return SCM_INUM0; | |
2393 | } | |
2394 | else | |
2395 | return x; | |
2396 | } | |
2397 | else if (SCM_REALP (y)) | |
2398 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2399 | else if (SCM_FRACTIONP (y)) | |
2400 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2401 | else | |
2402 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2403 | s_scm_truncate_remainder); | |
2404 | } | |
2405 | else if (SCM_BIGP (x)) | |
2406 | { | |
2407 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2408 | { | |
2409 | scm_t_inum yy = SCM_I_INUM (y); | |
2410 | if (SCM_UNLIKELY (yy == 0)) | |
2411 | scm_num_overflow (s_scm_truncate_remainder); | |
2412 | else | |
2413 | { | |
2414 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2415 | (yy > 0) ? yy : -yy) | |
2416 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2417 | scm_remember_upto_here_1 (x); | |
2418 | return SCM_I_MAKINUM (rr); | |
2419 | } | |
2420 | } | |
2421 | else if (SCM_BIGP (y)) | |
2422 | { | |
2423 | SCM r = scm_i_mkbig (); | |
2424 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2425 | SCM_I_BIG_MPZ (x), | |
2426 | SCM_I_BIG_MPZ (y)); | |
2427 | scm_remember_upto_here_2 (x, y); | |
2428 | return scm_i_normbig (r); | |
2429 | } | |
2430 | else if (SCM_REALP (y)) | |
2431 | return scm_i_inexact_truncate_remainder | |
2432 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2433 | else if (SCM_FRACTIONP (y)) | |
2434 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2435 | else | |
2436 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2437 | s_scm_truncate_remainder); | |
2438 | } | |
2439 | else if (SCM_REALP (x)) | |
2440 | { | |
2441 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2442 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2443 | return scm_i_inexact_truncate_remainder | |
2444 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2445 | else | |
2446 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2447 | s_scm_truncate_remainder); | |
2448 | } | |
2449 | else if (SCM_FRACTIONP (x)) | |
2450 | { | |
2451 | if (SCM_REALP (y)) | |
2452 | return scm_i_inexact_truncate_remainder | |
2453 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2454 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2455 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2456 | else | |
2457 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2458 | s_scm_truncate_remainder); | |
2459 | } | |
2460 | else | |
2461 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2462 | s_scm_truncate_remainder); | |
2463 | } | |
2464 | #undef FUNC_NAME | |
2465 | ||
2466 | static SCM | |
2467 | scm_i_inexact_truncate_remainder (double x, double y) | |
2468 | { | |
2469 | /* Although it would be more efficient to use fmod here, we can't | |
2470 | because it would in some cases produce results inconsistent with | |
2471 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2472 | close). In particular, when x is very close to a multiple of y, | |
2473 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2474 | correspond to different choices of q. If quotient chooses one and | |
2475 | remainder chooses the other, it would be bad. */ | |
2476 | if (SCM_UNLIKELY (y == 0)) | |
2477 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2478 | else | |
c251ab63 | 2479 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2480 | } |
2481 | ||
2482 | static SCM | |
2483 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2484 | { | |
2485 | SCM xd = scm_denominator (x); | |
2486 | SCM yd = scm_denominator (y); | |
2487 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2488 | scm_product (scm_numerator (y), xd)); | |
2489 | return scm_divide (r1, scm_product (xd, yd)); | |
2490 | } | |
2491 | ||
2492 | ||
2493 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2494 | SCM *qp, SCM *rp); | |
2495 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2496 | SCM *qp, SCM *rp); | |
2497 | ||
2498 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2499 | (SCM x, SCM y), | |
2500 | "Return the integer @var{q} and the real number @var{r}\n" | |
2501 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2502 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2503 | "@lisp\n" | |
2504 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2505 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2506 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2507 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2508 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2509 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2510 | "@end lisp") | |
2511 | #define FUNC_NAME s_scm_i_truncate_divide | |
2512 | { | |
2513 | SCM q, r; | |
2514 | ||
2515 | scm_truncate_divide(x, y, &q, &r); | |
2516 | return scm_values (scm_list_2 (q, r)); | |
2517 | } | |
2518 | #undef FUNC_NAME | |
2519 | ||
2520 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2521 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2522 | ||
2523 | void | |
2524 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2525 | { | |
2526 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2527 | { | |
2528 | scm_t_inum xx = SCM_I_INUM (x); | |
2529 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2530 | { | |
2531 | scm_t_inum yy = SCM_I_INUM (y); | |
2532 | if (SCM_UNLIKELY (yy == 0)) | |
2533 | scm_num_overflow (s_scm_truncate_divide); | |
2534 | else | |
2535 | { | |
2536 | scm_t_inum qq = xx / yy; | |
2537 | scm_t_inum rr = xx % yy; | |
2538 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2539 | *qp = SCM_I_MAKINUM (qq); | |
2540 | else | |
2541 | *qp = scm_i_inum2big (qq); | |
2542 | *rp = SCM_I_MAKINUM (rr); | |
2543 | } | |
2544 | return; | |
2545 | } | |
2546 | else if (SCM_BIGP (y)) | |
2547 | { | |
2548 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2549 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2550 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2551 | { | |
2552 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2553 | scm_remember_upto_here_1 (y); | |
2554 | *qp = SCM_I_MAKINUM (-1); | |
2555 | *rp = SCM_INUM0; | |
2556 | } | |
2557 | else | |
2558 | { | |
2559 | *qp = SCM_INUM0; | |
2560 | *rp = x; | |
2561 | } | |
2562 | return; | |
2563 | } | |
2564 | else if (SCM_REALP (y)) | |
2565 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2566 | else if (SCM_FRACTIONP (y)) | |
2567 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2568 | else | |
2569 | return two_valued_wta_dispatch_2 | |
2570 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2571 | s_scm_truncate_divide, qp, rp); | |
2572 | } | |
2573 | else if (SCM_BIGP (x)) | |
2574 | { | |
2575 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2576 | { | |
2577 | scm_t_inum yy = SCM_I_INUM (y); | |
2578 | if (SCM_UNLIKELY (yy == 0)) | |
2579 | scm_num_overflow (s_scm_truncate_divide); | |
2580 | else | |
2581 | { | |
2582 | SCM q = scm_i_mkbig (); | |
2583 | scm_t_inum rr; | |
2584 | if (yy > 0) | |
2585 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2586 | SCM_I_BIG_MPZ (x), yy); | |
2587 | else | |
2588 | { | |
2589 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2590 | SCM_I_BIG_MPZ (x), -yy); | |
2591 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2592 | } | |
2593 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2594 | scm_remember_upto_here_1 (x); | |
2595 | *qp = scm_i_normbig (q); | |
2596 | *rp = SCM_I_MAKINUM (rr); | |
2597 | } | |
2598 | return; | |
2599 | } | |
2600 | else if (SCM_BIGP (y)) | |
2601 | { | |
2602 | SCM q = scm_i_mkbig (); | |
2603 | SCM r = scm_i_mkbig (); | |
2604 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2605 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2606 | scm_remember_upto_here_2 (x, y); | |
2607 | *qp = scm_i_normbig (q); | |
2608 | *rp = scm_i_normbig (r); | |
2609 | } | |
2610 | else if (SCM_REALP (y)) | |
2611 | return scm_i_inexact_truncate_divide | |
2612 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2613 | else if (SCM_FRACTIONP (y)) | |
2614 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2615 | else | |
2616 | return two_valued_wta_dispatch_2 | |
2617 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2618 | s_scm_truncate_divide, qp, rp); | |
2619 | } | |
2620 | else if (SCM_REALP (x)) | |
2621 | { | |
2622 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2623 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2624 | return scm_i_inexact_truncate_divide | |
2625 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2626 | else | |
2627 | return two_valued_wta_dispatch_2 | |
2628 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2629 | s_scm_truncate_divide, qp, rp); | |
2630 | } | |
2631 | else if (SCM_FRACTIONP (x)) | |
2632 | { | |
2633 | if (SCM_REALP (y)) | |
2634 | return scm_i_inexact_truncate_divide | |
2635 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2636 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2637 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2638 | else | |
2639 | return two_valued_wta_dispatch_2 | |
2640 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2641 | s_scm_truncate_divide, qp, rp); | |
2642 | } | |
2643 | else | |
2644 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2645 | s_scm_truncate_divide, qp, rp); | |
2646 | } | |
2647 | ||
2648 | static void | |
2649 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2650 | { | |
2651 | if (SCM_UNLIKELY (y == 0)) | |
2652 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2653 | else | |
2654 | { | |
c15fe499 MW |
2655 | double q = trunc (x / y); |
2656 | double r = x - q * y; | |
8f9da340 MW |
2657 | *qp = scm_from_double (q); |
2658 | *rp = scm_from_double (r); | |
2659 | } | |
2660 | } | |
2661 | ||
2662 | static void | |
2663 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2664 | { | |
2665 | SCM r1; | |
2666 | SCM xd = scm_denominator (x); | |
2667 | SCM yd = scm_denominator (y); | |
2668 | ||
2669 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2670 | scm_product (scm_numerator (y), xd), | |
2671 | qp, &r1); | |
2672 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2673 | } | |
2674 | ||
ff62c168 MW |
2675 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2676 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2677 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2678 | |
8f9da340 MW |
2679 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2680 | (SCM x, SCM y), | |
2681 | "Return the integer @var{q} such that\n" | |
2682 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2683 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2684 | "@lisp\n" | |
2685 | "(centered-quotient 123 10) @result{} 12\n" | |
2686 | "(centered-quotient 123 -10) @result{} -12\n" | |
2687 | "(centered-quotient -123 10) @result{} -12\n" | |
2688 | "(centered-quotient -123 -10) @result{} 12\n" | |
2689 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2690 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2691 | "@end lisp") | |
2692 | #define FUNC_NAME s_scm_centered_quotient | |
2693 | { | |
2694 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2695 | { | |
2696 | scm_t_inum xx = SCM_I_INUM (x); | |
2697 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2698 | { | |
2699 | scm_t_inum yy = SCM_I_INUM (y); | |
2700 | if (SCM_UNLIKELY (yy == 0)) | |
2701 | scm_num_overflow (s_scm_centered_quotient); | |
2702 | else | |
2703 | { | |
2704 | scm_t_inum qq = xx / yy; | |
2705 | scm_t_inum rr = xx % yy; | |
2706 | if (SCM_LIKELY (xx > 0)) | |
2707 | { | |
2708 | if (SCM_LIKELY (yy > 0)) | |
2709 | { | |
2710 | if (rr >= (yy + 1) / 2) | |
2711 | qq++; | |
2712 | } | |
2713 | else | |
2714 | { | |
2715 | if (rr >= (1 - yy) / 2) | |
2716 | qq--; | |
2717 | } | |
2718 | } | |
2719 | else | |
2720 | { | |
2721 | if (SCM_LIKELY (yy > 0)) | |
2722 | { | |
2723 | if (rr < -yy / 2) | |
2724 | qq--; | |
2725 | } | |
2726 | else | |
2727 | { | |
2728 | if (rr < yy / 2) | |
2729 | qq++; | |
2730 | } | |
2731 | } | |
2732 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2733 | return SCM_I_MAKINUM (qq); | |
2734 | else | |
2735 | return scm_i_inum2big (qq); | |
2736 | } | |
2737 | } | |
2738 | else if (SCM_BIGP (y)) | |
2739 | { | |
2740 | /* Pass a denormalized bignum version of x (even though it | |
2741 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2742 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2743 | } | |
2744 | else if (SCM_REALP (y)) | |
2745 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2746 | else if (SCM_FRACTIONP (y)) | |
2747 | return scm_i_exact_rational_centered_quotient (x, y); | |
2748 | else | |
2749 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2750 | s_scm_centered_quotient); | |
2751 | } | |
2752 | else if (SCM_BIGP (x)) | |
2753 | { | |
2754 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2755 | { | |
2756 | scm_t_inum yy = SCM_I_INUM (y); | |
2757 | if (SCM_UNLIKELY (yy == 0)) | |
2758 | scm_num_overflow (s_scm_centered_quotient); | |
2759 | else if (SCM_UNLIKELY (yy == 1)) | |
2760 | return x; | |
2761 | else | |
2762 | { | |
2763 | SCM q = scm_i_mkbig (); | |
2764 | scm_t_inum rr; | |
2765 | /* Arrange for rr to initially be non-positive, | |
2766 | because that simplifies the test to see | |
2767 | if it is within the needed bounds. */ | |
2768 | if (yy > 0) | |
2769 | { | |
2770 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2771 | SCM_I_BIG_MPZ (x), yy); | |
2772 | scm_remember_upto_here_1 (x); | |
2773 | if (rr < -yy / 2) | |
2774 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2775 | SCM_I_BIG_MPZ (q), 1); | |
2776 | } | |
2777 | else | |
2778 | { | |
2779 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2780 | SCM_I_BIG_MPZ (x), -yy); | |
2781 | scm_remember_upto_here_1 (x); | |
2782 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2783 | if (rr < yy / 2) | |
2784 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2785 | SCM_I_BIG_MPZ (q), 1); | |
2786 | } | |
2787 | return scm_i_normbig (q); | |
2788 | } | |
2789 | } | |
2790 | else if (SCM_BIGP (y)) | |
2791 | return scm_i_bigint_centered_quotient (x, y); | |
2792 | else if (SCM_REALP (y)) | |
2793 | return scm_i_inexact_centered_quotient | |
2794 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2795 | else if (SCM_FRACTIONP (y)) | |
2796 | return scm_i_exact_rational_centered_quotient (x, y); | |
2797 | else | |
2798 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2799 | s_scm_centered_quotient); | |
2800 | } | |
2801 | else if (SCM_REALP (x)) | |
2802 | { | |
2803 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2804 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2805 | return scm_i_inexact_centered_quotient | |
2806 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2807 | else | |
2808 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2809 | s_scm_centered_quotient); | |
2810 | } | |
2811 | else if (SCM_FRACTIONP (x)) | |
2812 | { | |
2813 | if (SCM_REALP (y)) | |
2814 | return scm_i_inexact_centered_quotient | |
2815 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2816 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2817 | return scm_i_exact_rational_centered_quotient (x, y); | |
2818 | else | |
2819 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2820 | s_scm_centered_quotient); | |
2821 | } | |
2822 | else | |
2823 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2824 | s_scm_centered_quotient); | |
2825 | } | |
2826 | #undef FUNC_NAME | |
2827 | ||
2828 | static SCM | |
2829 | scm_i_inexact_centered_quotient (double x, double y) | |
2830 | { | |
2831 | if (SCM_LIKELY (y > 0)) | |
2832 | return scm_from_double (floor (x/y + 0.5)); | |
2833 | else if (SCM_LIKELY (y < 0)) | |
2834 | return scm_from_double (ceil (x/y - 0.5)); | |
2835 | else if (y == 0) | |
2836 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2837 | else | |
2838 | return scm_nan (); | |
2839 | } | |
2840 | ||
2841 | /* Assumes that both x and y are bigints, though | |
2842 | x might be able to fit into a fixnum. */ | |
2843 | static SCM | |
2844 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2845 | { | |
2846 | SCM q, r, min_r; | |
2847 | ||
2848 | /* Note that x might be small enough to fit into a | |
2849 | fixnum, so we must not let it escape into the wild */ | |
2850 | q = scm_i_mkbig (); | |
2851 | r = scm_i_mkbig (); | |
2852 | ||
2853 | /* min_r will eventually become -abs(y)/2 */ | |
2854 | min_r = scm_i_mkbig (); | |
2855 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2856 | SCM_I_BIG_MPZ (y), 1); | |
2857 | ||
2858 | /* Arrange for rr to initially be non-positive, | |
2859 | because that simplifies the test to see | |
2860 | if it is within the needed bounds. */ | |
2861 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2862 | { | |
2863 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2864 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2865 | scm_remember_upto_here_2 (x, y); | |
2866 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2867 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2868 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2869 | SCM_I_BIG_MPZ (q), 1); | |
2870 | } | |
2871 | else | |
2872 | { | |
2873 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2874 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2875 | scm_remember_upto_here_2 (x, y); | |
2876 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2877 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2878 | SCM_I_BIG_MPZ (q), 1); | |
2879 | } | |
2880 | scm_remember_upto_here_2 (r, min_r); | |
2881 | return scm_i_normbig (q); | |
2882 | } | |
2883 | ||
2884 | static SCM | |
2885 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2886 | { | |
2887 | return scm_centered_quotient | |
2888 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2889 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2890 | } | |
2891 | ||
2892 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2893 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2894 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2895 | ||
2896 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2897 | (SCM x, SCM y), | |
2898 | "Return the real number @var{r} such that\n" | |
2899 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2900 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2901 | "for some integer @var{q}.\n" | |
2902 | "@lisp\n" | |
2903 | "(centered-remainder 123 10) @result{} 3\n" | |
2904 | "(centered-remainder 123 -10) @result{} 3\n" | |
2905 | "(centered-remainder -123 10) @result{} -3\n" | |
2906 | "(centered-remainder -123 -10) @result{} -3\n" | |
2907 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2908 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2909 | "@end lisp") | |
2910 | #define FUNC_NAME s_scm_centered_remainder | |
2911 | { | |
2912 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2913 | { | |
2914 | scm_t_inum xx = SCM_I_INUM (x); | |
2915 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2916 | { | |
2917 | scm_t_inum yy = SCM_I_INUM (y); | |
2918 | if (SCM_UNLIKELY (yy == 0)) | |
2919 | scm_num_overflow (s_scm_centered_remainder); | |
2920 | else | |
2921 | { | |
2922 | scm_t_inum rr = xx % yy; | |
2923 | if (SCM_LIKELY (xx > 0)) | |
2924 | { | |
2925 | if (SCM_LIKELY (yy > 0)) | |
2926 | { | |
2927 | if (rr >= (yy + 1) / 2) | |
2928 | rr -= yy; | |
2929 | } | |
2930 | else | |
2931 | { | |
2932 | if (rr >= (1 - yy) / 2) | |
2933 | rr += yy; | |
2934 | } | |
2935 | } | |
2936 | else | |
2937 | { | |
2938 | if (SCM_LIKELY (yy > 0)) | |
2939 | { | |
2940 | if (rr < -yy / 2) | |
2941 | rr += yy; | |
2942 | } | |
2943 | else | |
2944 | { | |
2945 | if (rr < yy / 2) | |
2946 | rr -= yy; | |
2947 | } | |
2948 | } | |
2949 | return SCM_I_MAKINUM (rr); | |
2950 | } | |
2951 | } | |
2952 | else if (SCM_BIGP (y)) | |
2953 | { | |
2954 | /* Pass a denormalized bignum version of x (even though it | |
2955 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2956 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2957 | } | |
2958 | else if (SCM_REALP (y)) | |
2959 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2960 | else if (SCM_FRACTIONP (y)) | |
2961 | return scm_i_exact_rational_centered_remainder (x, y); | |
2962 | else | |
2963 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2964 | s_scm_centered_remainder); | |
2965 | } | |
2966 | else if (SCM_BIGP (x)) | |
2967 | { | |
2968 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2969 | { | |
2970 | scm_t_inum yy = SCM_I_INUM (y); | |
2971 | if (SCM_UNLIKELY (yy == 0)) | |
2972 | scm_num_overflow (s_scm_centered_remainder); | |
2973 | else | |
2974 | { | |
2975 | scm_t_inum rr; | |
2976 | /* Arrange for rr to initially be non-positive, | |
2977 | because that simplifies the test to see | |
2978 | if it is within the needed bounds. */ | |
2979 | if (yy > 0) | |
2980 | { | |
2981 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2982 | scm_remember_upto_here_1 (x); | |
2983 | if (rr < -yy / 2) | |
2984 | rr += yy; | |
2985 | } | |
2986 | else | |
2987 | { | |
2988 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2989 | scm_remember_upto_here_1 (x); | |
2990 | if (rr < yy / 2) | |
2991 | rr -= yy; | |
2992 | } | |
2993 | return SCM_I_MAKINUM (rr); | |
2994 | } | |
2995 | } | |
2996 | else if (SCM_BIGP (y)) | |
2997 | return scm_i_bigint_centered_remainder (x, y); | |
2998 | else if (SCM_REALP (y)) | |
2999 | return scm_i_inexact_centered_remainder | |
3000 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
3001 | else if (SCM_FRACTIONP (y)) | |
3002 | return scm_i_exact_rational_centered_remainder (x, y); | |
3003 | else | |
3004 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3005 | s_scm_centered_remainder); | |
3006 | } | |
3007 | else if (SCM_REALP (x)) | |
3008 | { | |
3009 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3010 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3011 | return scm_i_inexact_centered_remainder | |
3012 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
3013 | else | |
3014 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3015 | s_scm_centered_remainder); | |
3016 | } | |
3017 | else if (SCM_FRACTIONP (x)) | |
3018 | { | |
3019 | if (SCM_REALP (y)) | |
3020 | return scm_i_inexact_centered_remainder | |
3021 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
3022 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3023 | return scm_i_exact_rational_centered_remainder (x, y); | |
3024 | else | |
3025 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3026 | s_scm_centered_remainder); | |
3027 | } | |
3028 | else | |
3029 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
3030 | s_scm_centered_remainder); | |
3031 | } | |
3032 | #undef FUNC_NAME | |
3033 | ||
3034 | static SCM | |
3035 | scm_i_inexact_centered_remainder (double x, double y) | |
3036 | { | |
3037 | double q; | |
3038 | ||
3039 | /* Although it would be more efficient to use fmod here, we can't | |
3040 | because it would in some cases produce results inconsistent with | |
3041 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
3042 | close). In particular, when x-y/2 is very close to a multiple of | |
3043 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
3044 | two cases must correspond to different choices of q. If quotient | |
3045 | chooses one and remainder chooses the other, it would be bad. */ | |
3046 | if (SCM_LIKELY (y > 0)) | |
3047 | q = floor (x/y + 0.5); | |
3048 | else if (SCM_LIKELY (y < 0)) | |
3049 | q = ceil (x/y - 0.5); | |
3050 | else if (y == 0) | |
3051 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
3052 | else | |
3053 | return scm_nan (); | |
3054 | return scm_from_double (x - q * y); | |
3055 | } | |
3056 | ||
3057 | /* Assumes that both x and y are bigints, though | |
3058 | x might be able to fit into a fixnum. */ | |
3059 | static SCM | |
3060 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
3061 | { | |
3062 | SCM r, min_r; | |
3063 | ||
3064 | /* Note that x might be small enough to fit into a | |
3065 | fixnum, so we must not let it escape into the wild */ | |
3066 | r = scm_i_mkbig (); | |
3067 | ||
3068 | /* min_r will eventually become -abs(y)/2 */ | |
3069 | min_r = scm_i_mkbig (); | |
3070 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3071 | SCM_I_BIG_MPZ (y), 1); | |
3072 | ||
3073 | /* Arrange for rr to initially be non-positive, | |
3074 | because that simplifies the test to see | |
3075 | if it is within the needed bounds. */ | |
3076 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3077 | { | |
3078 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
3079 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3080 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3081 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3082 | mpz_add (SCM_I_BIG_MPZ (r), | |
3083 | SCM_I_BIG_MPZ (r), | |
3084 | SCM_I_BIG_MPZ (y)); | |
3085 | } | |
3086 | else | |
3087 | { | |
3088 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
3089 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3090 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3091 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3092 | SCM_I_BIG_MPZ (r), | |
3093 | SCM_I_BIG_MPZ (y)); | |
3094 | } | |
3095 | scm_remember_upto_here_2 (x, y); | |
3096 | return scm_i_normbig (r); | |
3097 | } | |
3098 | ||
3099 | static SCM | |
3100 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
3101 | { | |
3102 | SCM xd = scm_denominator (x); | |
3103 | SCM yd = scm_denominator (y); | |
3104 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
3105 | scm_product (scm_numerator (y), xd)); | |
3106 | return scm_divide (r1, scm_product (xd, yd)); | |
3107 | } | |
3108 | ||
3109 | ||
3110 | static void scm_i_inexact_centered_divide (double x, double y, | |
3111 | SCM *qp, SCM *rp); | |
3112 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3113 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
3114 | SCM *qp, SCM *rp); | |
3115 | ||
3116 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
3117 | (SCM x, SCM y), | |
3118 | "Return the integer @var{q} and the real number @var{r}\n" | |
3119 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
3120 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
3121 | "@lisp\n" | |
3122 | "(centered/ 123 10) @result{} 12 and 3\n" | |
3123 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
3124 | "(centered/ -123 10) @result{} -12 and -3\n" | |
3125 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
3126 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3127 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
3128 | "@end lisp") | |
3129 | #define FUNC_NAME s_scm_i_centered_divide | |
3130 | { | |
3131 | SCM q, r; | |
3132 | ||
3133 | scm_centered_divide(x, y, &q, &r); | |
3134 | return scm_values (scm_list_2 (q, r)); | |
3135 | } | |
3136 | #undef FUNC_NAME | |
3137 | ||
3138 | #define s_scm_centered_divide s_scm_i_centered_divide | |
3139 | #define g_scm_centered_divide g_scm_i_centered_divide | |
3140 | ||
3141 | void | |
3142 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3143 | { | |
3144 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3145 | { | |
3146 | scm_t_inum xx = SCM_I_INUM (x); | |
3147 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3148 | { | |
3149 | scm_t_inum yy = SCM_I_INUM (y); | |
3150 | if (SCM_UNLIKELY (yy == 0)) | |
3151 | scm_num_overflow (s_scm_centered_divide); | |
3152 | else | |
3153 | { | |
3154 | scm_t_inum qq = xx / yy; | |
3155 | scm_t_inum rr = xx % yy; | |
3156 | if (SCM_LIKELY (xx > 0)) | |
3157 | { | |
3158 | if (SCM_LIKELY (yy > 0)) | |
3159 | { | |
3160 | if (rr >= (yy + 1) / 2) | |
3161 | { qq++; rr -= yy; } | |
3162 | } | |
3163 | else | |
3164 | { | |
3165 | if (rr >= (1 - yy) / 2) | |
3166 | { qq--; rr += yy; } | |
3167 | } | |
3168 | } | |
3169 | else | |
3170 | { | |
3171 | if (SCM_LIKELY (yy > 0)) | |
3172 | { | |
3173 | if (rr < -yy / 2) | |
3174 | { qq--; rr += yy; } | |
3175 | } | |
3176 | else | |
3177 | { | |
3178 | if (rr < yy / 2) | |
3179 | { qq++; rr -= yy; } | |
3180 | } | |
3181 | } | |
3182 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3183 | *qp = SCM_I_MAKINUM (qq); | |
3184 | else | |
3185 | *qp = scm_i_inum2big (qq); | |
3186 | *rp = SCM_I_MAKINUM (rr); | |
3187 | } | |
3188 | return; | |
3189 | } | |
3190 | else if (SCM_BIGP (y)) | |
3191 | { | |
3192 | /* Pass a denormalized bignum version of x (even though it | |
3193 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3194 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3195 | } | |
3196 | else if (SCM_REALP (y)) | |
3197 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3198 | else if (SCM_FRACTIONP (y)) | |
3199 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3200 | else | |
3201 | return two_valued_wta_dispatch_2 | |
3202 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3203 | s_scm_centered_divide, qp, rp); | |
3204 | } | |
3205 | else if (SCM_BIGP (x)) | |
3206 | { | |
3207 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3208 | { | |
3209 | scm_t_inum yy = SCM_I_INUM (y); | |
3210 | if (SCM_UNLIKELY (yy == 0)) | |
3211 | scm_num_overflow (s_scm_centered_divide); | |
3212 | else | |
3213 | { | |
3214 | SCM q = scm_i_mkbig (); | |
3215 | scm_t_inum rr; | |
3216 | /* Arrange for rr to initially be non-positive, | |
3217 | because that simplifies the test to see | |
3218 | if it is within the needed bounds. */ | |
3219 | if (yy > 0) | |
3220 | { | |
3221 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3222 | SCM_I_BIG_MPZ (x), yy); | |
3223 | scm_remember_upto_here_1 (x); | |
3224 | if (rr < -yy / 2) | |
3225 | { | |
3226 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3227 | SCM_I_BIG_MPZ (q), 1); | |
3228 | rr += yy; | |
3229 | } | |
3230 | } | |
3231 | else | |
3232 | { | |
3233 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3234 | SCM_I_BIG_MPZ (x), -yy); | |
3235 | scm_remember_upto_here_1 (x); | |
3236 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3237 | if (rr < yy / 2) | |
3238 | { | |
3239 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3240 | SCM_I_BIG_MPZ (q), 1); | |
3241 | rr -= yy; | |
3242 | } | |
3243 | } | |
3244 | *qp = scm_i_normbig (q); | |
3245 | *rp = SCM_I_MAKINUM (rr); | |
3246 | } | |
3247 | return; | |
3248 | } | |
3249 | else if (SCM_BIGP (y)) | |
3250 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3251 | else if (SCM_REALP (y)) | |
3252 | return scm_i_inexact_centered_divide | |
3253 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3254 | else if (SCM_FRACTIONP (y)) | |
3255 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3256 | else | |
3257 | return two_valued_wta_dispatch_2 | |
3258 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3259 | s_scm_centered_divide, qp, rp); | |
3260 | } | |
3261 | else if (SCM_REALP (x)) | |
3262 | { | |
3263 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3264 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3265 | return scm_i_inexact_centered_divide | |
3266 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3267 | else | |
3268 | return two_valued_wta_dispatch_2 | |
3269 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3270 | s_scm_centered_divide, qp, rp); | |
3271 | } | |
3272 | else if (SCM_FRACTIONP (x)) | |
3273 | { | |
3274 | if (SCM_REALP (y)) | |
3275 | return scm_i_inexact_centered_divide | |
3276 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3277 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3278 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3279 | else | |
3280 | return two_valued_wta_dispatch_2 | |
3281 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3282 | s_scm_centered_divide, qp, rp); | |
3283 | } | |
3284 | else | |
3285 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3286 | s_scm_centered_divide, qp, rp); | |
3287 | } | |
3288 | ||
3289 | static void | |
3290 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3291 | { | |
3292 | double q, r; | |
3293 | ||
3294 | if (SCM_LIKELY (y > 0)) | |
3295 | q = floor (x/y + 0.5); | |
3296 | else if (SCM_LIKELY (y < 0)) | |
3297 | q = ceil (x/y - 0.5); | |
3298 | else if (y == 0) | |
3299 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3300 | else | |
3301 | q = guile_NaN; | |
3302 | r = x - q * y; | |
3303 | *qp = scm_from_double (q); | |
3304 | *rp = scm_from_double (r); | |
3305 | } | |
3306 | ||
3307 | /* Assumes that both x and y are bigints, though | |
3308 | x might be able to fit into a fixnum. */ | |
3309 | static void | |
3310 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3311 | { | |
3312 | SCM q, r, min_r; | |
3313 | ||
3314 | /* Note that x might be small enough to fit into a | |
3315 | fixnum, so we must not let it escape into the wild */ | |
3316 | q = scm_i_mkbig (); | |
3317 | r = scm_i_mkbig (); | |
3318 | ||
3319 | /* min_r will eventually become -abs(y/2) */ | |
3320 | min_r = scm_i_mkbig (); | |
3321 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3322 | SCM_I_BIG_MPZ (y), 1); | |
3323 | ||
3324 | /* Arrange for rr to initially be non-positive, | |
3325 | because that simplifies the test to see | |
3326 | if it is within the needed bounds. */ | |
3327 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3328 | { | |
3329 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3330 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3331 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3332 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3333 | { | |
3334 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3335 | SCM_I_BIG_MPZ (q), 1); | |
3336 | mpz_add (SCM_I_BIG_MPZ (r), | |
3337 | SCM_I_BIG_MPZ (r), | |
3338 | SCM_I_BIG_MPZ (y)); | |
3339 | } | |
3340 | } | |
3341 | else | |
3342 | { | |
3343 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3344 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3345 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3346 | { | |
3347 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3348 | SCM_I_BIG_MPZ (q), 1); | |
3349 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3350 | SCM_I_BIG_MPZ (r), | |
3351 | SCM_I_BIG_MPZ (y)); | |
3352 | } | |
3353 | } | |
3354 | scm_remember_upto_here_2 (x, y); | |
3355 | *qp = scm_i_normbig (q); | |
3356 | *rp = scm_i_normbig (r); | |
3357 | } | |
3358 | ||
3359 | static void | |
3360 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3361 | { | |
3362 | SCM r1; | |
3363 | SCM xd = scm_denominator (x); | |
3364 | SCM yd = scm_denominator (y); | |
3365 | ||
3366 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3367 | scm_product (scm_numerator (y), xd), | |
3368 | qp, &r1); | |
3369 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3370 | } | |
3371 | ||
3372 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3373 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3374 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3375 | ||
3376 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3377 | (SCM x, SCM y), |
8f9da340 MW |
3378 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3379 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3380 | "@lisp\n" |
8f9da340 MW |
3381 | "(round-quotient 123 10) @result{} 12\n" |
3382 | "(round-quotient 123 -10) @result{} -12\n" | |
3383 | "(round-quotient -123 10) @result{} -12\n" | |
3384 | "(round-quotient -123 -10) @result{} 12\n" | |
3385 | "(round-quotient 125 10) @result{} 12\n" | |
3386 | "(round-quotient 127 10) @result{} 13\n" | |
3387 | "(round-quotient 135 10) @result{} 14\n" | |
3388 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3389 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3390 | "@end lisp") |
8f9da340 | 3391 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3392 | { |
3393 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3394 | { | |
4a46bc2a | 3395 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3396 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3397 | { | |
3398 | scm_t_inum yy = SCM_I_INUM (y); | |
3399 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3400 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3401 | else |
3402 | { | |
ff62c168 | 3403 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3404 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3405 | scm_t_inum ay = yy; |
3406 | scm_t_inum r2 = 2 * rr; | |
3407 | ||
3408 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3409 | { |
8f9da340 MW |
3410 | ay = -ay; |
3411 | r2 = -r2; | |
3412 | } | |
3413 | ||
3414 | if (qq & 1L) | |
3415 | { | |
3416 | if (r2 >= ay) | |
3417 | qq++; | |
3418 | else if (r2 <= -ay) | |
3419 | qq--; | |
ff62c168 MW |
3420 | } |
3421 | else | |
3422 | { | |
8f9da340 MW |
3423 | if (r2 > ay) |
3424 | qq++; | |
3425 | else if (r2 < -ay) | |
3426 | qq--; | |
ff62c168 | 3427 | } |
4a46bc2a MW |
3428 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3429 | return SCM_I_MAKINUM (qq); | |
3430 | else | |
3431 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3432 | } |
3433 | } | |
3434 | else if (SCM_BIGP (y)) | |
3435 | { | |
3436 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3437 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3438 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3439 | } |
3440 | else if (SCM_REALP (y)) | |
8f9da340 | 3441 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3442 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3443 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3444 | else |
8f9da340 MW |
3445 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3446 | s_scm_round_quotient); | |
ff62c168 MW |
3447 | } |
3448 | else if (SCM_BIGP (x)) | |
3449 | { | |
3450 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3451 | { | |
3452 | scm_t_inum yy = SCM_I_INUM (y); | |
3453 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3454 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3455 | else if (SCM_UNLIKELY (yy == 1)) |
3456 | return x; | |
ff62c168 MW |
3457 | else |
3458 | { | |
3459 | SCM q = scm_i_mkbig (); | |
3460 | scm_t_inum rr; | |
8f9da340 MW |
3461 | int needs_adjustment; |
3462 | ||
ff62c168 MW |
3463 | if (yy > 0) |
3464 | { | |
8f9da340 MW |
3465 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3466 | SCM_I_BIG_MPZ (x), yy); | |
3467 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3468 | needs_adjustment = (2*rr >= yy); | |
3469 | else | |
3470 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3471 | } |
3472 | else | |
3473 | { | |
3474 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3475 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3476 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3477 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3478 | needs_adjustment = (2*rr <= yy); | |
3479 | else | |
3480 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3481 | } |
8f9da340 MW |
3482 | scm_remember_upto_here_1 (x); |
3483 | if (needs_adjustment) | |
3484 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3485 | return scm_i_normbig (q); |
3486 | } | |
3487 | } | |
3488 | else if (SCM_BIGP (y)) | |
8f9da340 | 3489 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3490 | else if (SCM_REALP (y)) |
8f9da340 | 3491 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3492 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3493 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3494 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3495 | else |
8f9da340 MW |
3496 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3497 | s_scm_round_quotient); | |
ff62c168 MW |
3498 | } |
3499 | else if (SCM_REALP (x)) | |
3500 | { | |
3501 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3502 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3503 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3504 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3505 | else | |
8f9da340 MW |
3506 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3507 | s_scm_round_quotient); | |
ff62c168 MW |
3508 | } |
3509 | else if (SCM_FRACTIONP (x)) | |
3510 | { | |
3511 | if (SCM_REALP (y)) | |
8f9da340 | 3512 | return scm_i_inexact_round_quotient |
ff62c168 | 3513 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3514 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3515 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3516 | else |
8f9da340 MW |
3517 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3518 | s_scm_round_quotient); | |
ff62c168 MW |
3519 | } |
3520 | else | |
8f9da340 MW |
3521 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3522 | s_scm_round_quotient); | |
ff62c168 MW |
3523 | } |
3524 | #undef FUNC_NAME | |
3525 | ||
3526 | static SCM | |
8f9da340 | 3527 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3528 | { |
8f9da340 MW |
3529 | if (SCM_UNLIKELY (y == 0)) |
3530 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3531 | else |
8f9da340 | 3532 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3533 | } |
3534 | ||
3535 | /* Assumes that both x and y are bigints, though | |
3536 | x might be able to fit into a fixnum. */ | |
3537 | static SCM | |
8f9da340 | 3538 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3539 | { |
8f9da340 MW |
3540 | SCM q, r, r2; |
3541 | int cmp, needs_adjustment; | |
ff62c168 MW |
3542 | |
3543 | /* Note that x might be small enough to fit into a | |
3544 | fixnum, so we must not let it escape into the wild */ | |
3545 | q = scm_i_mkbig (); | |
3546 | r = scm_i_mkbig (); | |
8f9da340 | 3547 | r2 = scm_i_mkbig (); |
ff62c168 | 3548 | |
8f9da340 MW |
3549 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3550 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3551 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3552 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3553 | |
8f9da340 MW |
3554 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3555 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3556 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3557 | else |
8f9da340 MW |
3558 | needs_adjustment = (cmp > 0); |
3559 | scm_remember_upto_here_2 (r2, y); | |
3560 | ||
3561 | if (needs_adjustment) | |
3562 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3563 | ||
ff62c168 MW |
3564 | return scm_i_normbig (q); |
3565 | } | |
3566 | ||
ff62c168 | 3567 | static SCM |
8f9da340 | 3568 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3569 | { |
8f9da340 | 3570 | return scm_round_quotient |
03ddd15b MW |
3571 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3572 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3573 | } |
3574 | ||
8f9da340 MW |
3575 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3576 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3577 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3578 | |
8f9da340 | 3579 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3580 | (SCM x, SCM y), |
3581 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3582 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3583 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3584 | "nearest integer, with ties going to the nearest\n" | |
3585 | "even integer.\n" | |
ff62c168 | 3586 | "@lisp\n" |
8f9da340 MW |
3587 | "(round-remainder 123 10) @result{} 3\n" |
3588 | "(round-remainder 123 -10) @result{} 3\n" | |
3589 | "(round-remainder -123 10) @result{} -3\n" | |
3590 | "(round-remainder -123 -10) @result{} -3\n" | |
3591 | "(round-remainder 125 10) @result{} 5\n" | |
3592 | "(round-remainder 127 10) @result{} -3\n" | |
3593 | "(round-remainder 135 10) @result{} -5\n" | |
3594 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3595 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3596 | "@end lisp") |
8f9da340 | 3597 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3598 | { |
3599 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3600 | { | |
4a46bc2a | 3601 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3602 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3603 | { | |
3604 | scm_t_inum yy = SCM_I_INUM (y); | |
3605 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3606 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3607 | else |
3608 | { | |
8f9da340 | 3609 | scm_t_inum qq = xx / yy; |
ff62c168 | 3610 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3611 | scm_t_inum ay = yy; |
3612 | scm_t_inum r2 = 2 * rr; | |
3613 | ||
3614 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3615 | { |
8f9da340 MW |
3616 | ay = -ay; |
3617 | r2 = -r2; | |
3618 | } | |
3619 | ||
3620 | if (qq & 1L) | |
3621 | { | |
3622 | if (r2 >= ay) | |
3623 | rr -= yy; | |
3624 | else if (r2 <= -ay) | |
3625 | rr += yy; | |
ff62c168 MW |
3626 | } |
3627 | else | |
3628 | { | |
8f9da340 MW |
3629 | if (r2 > ay) |
3630 | rr -= yy; | |
3631 | else if (r2 < -ay) | |
3632 | rr += yy; | |
ff62c168 MW |
3633 | } |
3634 | return SCM_I_MAKINUM (rr); | |
3635 | } | |
3636 | } | |
3637 | else if (SCM_BIGP (y)) | |
3638 | { | |
3639 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3640 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3641 | return scm_i_bigint_round_remainder | |
3642 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3643 | } |
3644 | else if (SCM_REALP (y)) | |
8f9da340 | 3645 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3646 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3647 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3648 | else |
8f9da340 MW |
3649 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3650 | s_scm_round_remainder); | |
ff62c168 MW |
3651 | } |
3652 | else if (SCM_BIGP (x)) | |
3653 | { | |
3654 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3655 | { | |
3656 | scm_t_inum yy = SCM_I_INUM (y); | |
3657 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3658 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3659 | else |
3660 | { | |
8f9da340 | 3661 | SCM q = scm_i_mkbig (); |
ff62c168 | 3662 | scm_t_inum rr; |
8f9da340 MW |
3663 | int needs_adjustment; |
3664 | ||
ff62c168 MW |
3665 | if (yy > 0) |
3666 | { | |
8f9da340 MW |
3667 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3668 | SCM_I_BIG_MPZ (x), yy); | |
3669 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3670 | needs_adjustment = (2*rr >= yy); | |
3671 | else | |
3672 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3673 | } |
3674 | else | |
3675 | { | |
8f9da340 MW |
3676 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3677 | SCM_I_BIG_MPZ (x), -yy); | |
3678 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3679 | needs_adjustment = (2*rr <= yy); | |
3680 | else | |
3681 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3682 | } |
8f9da340 MW |
3683 | scm_remember_upto_here_2 (x, q); |
3684 | if (needs_adjustment) | |
3685 | rr -= yy; | |
ff62c168 MW |
3686 | return SCM_I_MAKINUM (rr); |
3687 | } | |
3688 | } | |
3689 | else if (SCM_BIGP (y)) | |
8f9da340 | 3690 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3691 | else if (SCM_REALP (y)) |
8f9da340 | 3692 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3693 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3694 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3695 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3696 | else |
8f9da340 MW |
3697 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3698 | s_scm_round_remainder); | |
ff62c168 MW |
3699 | } |
3700 | else if (SCM_REALP (x)) | |
3701 | { | |
3702 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3703 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3704 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3705 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3706 | else | |
8f9da340 MW |
3707 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3708 | s_scm_round_remainder); | |
ff62c168 MW |
3709 | } |
3710 | else if (SCM_FRACTIONP (x)) | |
3711 | { | |
3712 | if (SCM_REALP (y)) | |
8f9da340 | 3713 | return scm_i_inexact_round_remainder |
ff62c168 | 3714 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3715 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3716 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3717 | else |
8f9da340 MW |
3718 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3719 | s_scm_round_remainder); | |
ff62c168 MW |
3720 | } |
3721 | else | |
8f9da340 MW |
3722 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3723 | s_scm_round_remainder); | |
ff62c168 MW |
3724 | } |
3725 | #undef FUNC_NAME | |
3726 | ||
3727 | static SCM | |
8f9da340 | 3728 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3729 | { |
ff62c168 MW |
3730 | /* Although it would be more efficient to use fmod here, we can't |
3731 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3732 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3733 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3734 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3735 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3736 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3737 | |
3738 | if (SCM_UNLIKELY (y == 0)) | |
3739 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3740 | else |
8f9da340 MW |
3741 | { |
3742 | double q = scm_c_round (x / y); | |
3743 | return scm_from_double (x - q * y); | |
3744 | } | |
ff62c168 MW |
3745 | } |
3746 | ||
3747 | /* Assumes that both x and y are bigints, though | |
3748 | x might be able to fit into a fixnum. */ | |
3749 | static SCM | |
8f9da340 | 3750 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3751 | { |
8f9da340 MW |
3752 | SCM q, r, r2; |
3753 | int cmp, needs_adjustment; | |
ff62c168 MW |
3754 | |
3755 | /* Note that x might be small enough to fit into a | |
3756 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3757 | q = scm_i_mkbig (); |
ff62c168 | 3758 | r = scm_i_mkbig (); |
8f9da340 | 3759 | r2 = scm_i_mkbig (); |
ff62c168 | 3760 | |
8f9da340 MW |
3761 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3762 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3763 | scm_remember_upto_here_1 (x); | |
3764 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3765 | |
8f9da340 MW |
3766 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3767 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3768 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3769 | else |
8f9da340 MW |
3770 | needs_adjustment = (cmp > 0); |
3771 | scm_remember_upto_here_2 (q, r2); | |
3772 | ||
3773 | if (needs_adjustment) | |
3774 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3775 | ||
3776 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3777 | return scm_i_normbig (r); |
3778 | } | |
3779 | ||
ff62c168 | 3780 | static SCM |
8f9da340 | 3781 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3782 | { |
03ddd15b MW |
3783 | SCM xd = scm_denominator (x); |
3784 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3785 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3786 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3787 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3788 | } |
3789 | ||
3790 | ||
8f9da340 MW |
3791 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3792 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3793 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3794 | |
8f9da340 | 3795 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3796 | (SCM x, SCM y), |
3797 | "Return the integer @var{q} and the real number @var{r}\n" | |
3798 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3799 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3800 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3801 | "@lisp\n" |
8f9da340 MW |
3802 | "(round/ 123 10) @result{} 12 and 3\n" |
3803 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3804 | "(round/ -123 10) @result{} -12 and -3\n" | |
3805 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3806 | "(round/ 125 10) @result{} 12 and 5\n" | |
3807 | "(round/ 127 10) @result{} 13 and -3\n" | |
3808 | "(round/ 135 10) @result{} 14 and -5\n" | |
3809 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3810 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3811 | "@end lisp") |
8f9da340 | 3812 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3813 | { |
3814 | SCM q, r; | |
3815 | ||
8f9da340 | 3816 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3817 | return scm_values (scm_list_2 (q, r)); |
3818 | } | |
3819 | #undef FUNC_NAME | |
3820 | ||
8f9da340 MW |
3821 | #define s_scm_round_divide s_scm_i_round_divide |
3822 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3823 | |
3824 | void | |
8f9da340 | 3825 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3826 | { |
3827 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3828 | { | |
4a46bc2a | 3829 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3830 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3831 | { | |
3832 | scm_t_inum yy = SCM_I_INUM (y); | |
3833 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3834 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3835 | else |
3836 | { | |
ff62c168 | 3837 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3838 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3839 | scm_t_inum ay = yy; |
3840 | scm_t_inum r2 = 2 * rr; | |
3841 | ||
3842 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3843 | { |
8f9da340 MW |
3844 | ay = -ay; |
3845 | r2 = -r2; | |
3846 | } | |
3847 | ||
3848 | if (qq & 1L) | |
3849 | { | |
3850 | if (r2 >= ay) | |
3851 | { qq++; rr -= yy; } | |
3852 | else if (r2 <= -ay) | |
3853 | { qq--; rr += yy; } | |
ff62c168 MW |
3854 | } |
3855 | else | |
3856 | { | |
8f9da340 MW |
3857 | if (r2 > ay) |
3858 | { qq++; rr -= yy; } | |
3859 | else if (r2 < -ay) | |
3860 | { qq--; rr += yy; } | |
ff62c168 | 3861 | } |
4a46bc2a | 3862 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3863 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3864 | else |
5fbf680b MW |
3865 | *qp = scm_i_inum2big (qq); |
3866 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3867 | } |
5fbf680b | 3868 | return; |
ff62c168 MW |
3869 | } |
3870 | else if (SCM_BIGP (y)) | |
3871 | { | |
3872 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3873 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3874 | return scm_i_bigint_round_divide | |
3875 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3876 | } |
3877 | else if (SCM_REALP (y)) | |
8f9da340 | 3878 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3879 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3880 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3881 | else |
8f9da340 MW |
3882 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3883 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3884 | } |
3885 | else if (SCM_BIGP (x)) | |
3886 | { | |
3887 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3888 | { | |
3889 | scm_t_inum yy = SCM_I_INUM (y); | |
3890 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3891 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3892 | else |
3893 | { | |
3894 | SCM q = scm_i_mkbig (); | |
3895 | scm_t_inum rr; | |
8f9da340 MW |
3896 | int needs_adjustment; |
3897 | ||
ff62c168 MW |
3898 | if (yy > 0) |
3899 | { | |
8f9da340 MW |
3900 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3901 | SCM_I_BIG_MPZ (x), yy); | |
3902 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3903 | needs_adjustment = (2*rr >= yy); | |
3904 | else | |
3905 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3906 | } |
3907 | else | |
3908 | { | |
3909 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3910 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3911 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3912 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3913 | needs_adjustment = (2*rr <= yy); | |
3914 | else | |
3915 | needs_adjustment = (2*rr < yy); | |
3916 | } | |
3917 | scm_remember_upto_here_1 (x); | |
3918 | if (needs_adjustment) | |
3919 | { | |
3920 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3921 | rr -= yy; | |
ff62c168 | 3922 | } |
5fbf680b MW |
3923 | *qp = scm_i_normbig (q); |
3924 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3925 | } |
5fbf680b | 3926 | return; |
ff62c168 MW |
3927 | } |
3928 | else if (SCM_BIGP (y)) | |
8f9da340 | 3929 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3930 | else if (SCM_REALP (y)) |
8f9da340 | 3931 | return scm_i_inexact_round_divide |
5fbf680b | 3932 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3933 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3934 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3935 | else |
8f9da340 MW |
3936 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3937 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3938 | } |
3939 | else if (SCM_REALP (x)) | |
3940 | { | |
3941 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3942 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3943 | return scm_i_inexact_round_divide |
5fbf680b | 3944 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3945 | else |
8f9da340 MW |
3946 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3947 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3948 | } |
3949 | else if (SCM_FRACTIONP (x)) | |
3950 | { | |
3951 | if (SCM_REALP (y)) | |
8f9da340 | 3952 | return scm_i_inexact_round_divide |
5fbf680b | 3953 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3954 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3955 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3956 | else |
8f9da340 MW |
3957 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3958 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3959 | } |
3960 | else | |
8f9da340 MW |
3961 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3962 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3963 | } |
ff62c168 | 3964 | |
5fbf680b | 3965 | static void |
8f9da340 | 3966 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3967 | { |
8f9da340 MW |
3968 | if (SCM_UNLIKELY (y == 0)) |
3969 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3970 | else |
8f9da340 MW |
3971 | { |
3972 | double q = scm_c_round (x / y); | |
3973 | double r = x - q * y; | |
3974 | *qp = scm_from_double (q); | |
3975 | *rp = scm_from_double (r); | |
3976 | } | |
ff62c168 MW |
3977 | } |
3978 | ||
3979 | /* Assumes that both x and y are bigints, though | |
3980 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3981 | static void |
8f9da340 | 3982 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3983 | { |
8f9da340 MW |
3984 | SCM q, r, r2; |
3985 | int cmp, needs_adjustment; | |
ff62c168 MW |
3986 | |
3987 | /* Note that x might be small enough to fit into a | |
3988 | fixnum, so we must not let it escape into the wild */ | |
3989 | q = scm_i_mkbig (); | |
3990 | r = scm_i_mkbig (); | |
8f9da340 | 3991 | r2 = scm_i_mkbig (); |
ff62c168 | 3992 | |
8f9da340 MW |
3993 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3994 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3995 | scm_remember_upto_here_1 (x); | |
3996 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3997 | |
8f9da340 MW |
3998 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3999 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4000 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 4001 | else |
8f9da340 MW |
4002 | needs_adjustment = (cmp > 0); |
4003 | ||
4004 | if (needs_adjustment) | |
ff62c168 | 4005 | { |
8f9da340 MW |
4006 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
4007 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 4008 | } |
8f9da340 MW |
4009 | |
4010 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
4011 | *qp = scm_i_normbig (q); |
4012 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
4013 | } |
4014 | ||
5fbf680b | 4015 | static void |
8f9da340 | 4016 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4017 | { |
03ddd15b MW |
4018 | SCM r1; |
4019 | SCM xd = scm_denominator (x); | |
4020 | SCM yd = scm_denominator (y); | |
4021 | ||
8f9da340 MW |
4022 | scm_round_divide (scm_product (scm_numerator (x), yd), |
4023 | scm_product (scm_numerator (y), xd), | |
4024 | qp, &r1); | |
03ddd15b | 4025 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
4026 | } |
4027 | ||
4028 | ||
78d3deb1 AW |
4029 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
4030 | (SCM x, SCM y, SCM rest), | |
4031 | "Return the greatest common divisor of all parameter values.\n" | |
4032 | "If called without arguments, 0 is returned.") | |
4033 | #define FUNC_NAME s_scm_i_gcd | |
4034 | { | |
4035 | while (!scm_is_null (rest)) | |
4036 | { x = scm_gcd (x, y); | |
4037 | y = scm_car (rest); | |
4038 | rest = scm_cdr (rest); | |
4039 | } | |
4040 | return scm_gcd (x, y); | |
4041 | } | |
4042 | #undef FUNC_NAME | |
4043 | ||
4044 | #define s_gcd s_scm_i_gcd | |
4045 | #define g_gcd g_scm_i_gcd | |
4046 | ||
0f2d19dd | 4047 | SCM |
6e8d25a6 | 4048 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 4049 | { |
a2dead1b | 4050 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
1dd79792 | 4051 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 4052 | |
a2dead1b | 4053 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4054 | { |
a2dead1b | 4055 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4056 | { |
e25f3727 AW |
4057 | scm_t_inum xx = SCM_I_INUM (x); |
4058 | scm_t_inum yy = SCM_I_INUM (y); | |
4059 | scm_t_inum u = xx < 0 ? -xx : xx; | |
4060 | scm_t_inum v = yy < 0 ? -yy : yy; | |
4061 | scm_t_inum result; | |
a2dead1b | 4062 | if (SCM_UNLIKELY (xx == 0)) |
0aacf84e | 4063 | result = v; |
a2dead1b | 4064 | else if (SCM_UNLIKELY (yy == 0)) |
0aacf84e MD |
4065 | result = u; |
4066 | else | |
4067 | { | |
a2dead1b | 4068 | int k = 0; |
0aacf84e | 4069 | /* Determine a common factor 2^k */ |
a2dead1b | 4070 | while (((u | v) & 1) == 0) |
0aacf84e | 4071 | { |
a2dead1b | 4072 | k++; |
0aacf84e MD |
4073 | u >>= 1; |
4074 | v >>= 1; | |
4075 | } | |
4076 | /* Now, any factor 2^n can be eliminated */ | |
a2dead1b MW |
4077 | if ((u & 1) == 0) |
4078 | while ((u & 1) == 0) | |
4079 | u >>= 1; | |
0aacf84e | 4080 | else |
a2dead1b MW |
4081 | while ((v & 1) == 0) |
4082 | v >>= 1; | |
4083 | /* Both u and v are now odd. Subtract the smaller one | |
4084 | from the larger one to produce an even number, remove | |
4085 | more factors of two, and repeat. */ | |
4086 | while (u != v) | |
0aacf84e | 4087 | { |
a2dead1b MW |
4088 | if (u > v) |
4089 | { | |
4090 | u -= v; | |
4091 | while ((u & 1) == 0) | |
4092 | u >>= 1; | |
4093 | } | |
4094 | else | |
4095 | { | |
4096 | v -= u; | |
4097 | while ((v & 1) == 0) | |
4098 | v >>= 1; | |
4099 | } | |
0aacf84e | 4100 | } |
a2dead1b | 4101 | result = u << k; |
0aacf84e MD |
4102 | } |
4103 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 4104 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4105 | : scm_i_inum2big (result)); |
ca46fb90 RB |
4106 | } |
4107 | else if (SCM_BIGP (y)) | |
4108 | { | |
0bff4dce KR |
4109 | SCM_SWAP (x, y); |
4110 | goto big_inum; | |
ca46fb90 RB |
4111 | } |
4112 | else | |
4113 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 4114 | } |
ca46fb90 RB |
4115 | else if (SCM_BIGP (x)) |
4116 | { | |
e11e83f3 | 4117 | if (SCM_I_INUMP (y)) |
ca46fb90 | 4118 | { |
e25f3727 AW |
4119 | scm_t_bits result; |
4120 | scm_t_inum yy; | |
0bff4dce | 4121 | big_inum: |
e11e83f3 | 4122 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
4123 | if (yy == 0) |
4124 | return scm_abs (x); | |
0aacf84e MD |
4125 | if (yy < 0) |
4126 | yy = -yy; | |
ca46fb90 RB |
4127 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
4128 | scm_remember_upto_here_1 (x); | |
0aacf84e | 4129 | return (SCM_POSFIXABLE (result) |
d956fa6f | 4130 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4131 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
4132 | } |
4133 | else if (SCM_BIGP (y)) | |
4134 | { | |
4135 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
4136 | mpz_gcd (SCM_I_BIG_MPZ (result), |
4137 | SCM_I_BIG_MPZ (x), | |
4138 | SCM_I_BIG_MPZ (y)); | |
4139 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
4140 | return scm_i_normbig (result); |
4141 | } | |
4142 | else | |
4143 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 4144 | } |
ca46fb90 | 4145 | else |
09fb7599 | 4146 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
4147 | } |
4148 | ||
78d3deb1 AW |
4149 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
4150 | (SCM x, SCM y, SCM rest), | |
4151 | "Return the least common multiple of the arguments.\n" | |
4152 | "If called without arguments, 1 is returned.") | |
4153 | #define FUNC_NAME s_scm_i_lcm | |
4154 | { | |
4155 | while (!scm_is_null (rest)) | |
4156 | { x = scm_lcm (x, y); | |
4157 | y = scm_car (rest); | |
4158 | rest = scm_cdr (rest); | |
4159 | } | |
4160 | return scm_lcm (x, y); | |
4161 | } | |
4162 | #undef FUNC_NAME | |
4163 | ||
4164 | #define s_lcm s_scm_i_lcm | |
4165 | #define g_lcm g_scm_i_lcm | |
4166 | ||
0f2d19dd | 4167 | SCM |
6e8d25a6 | 4168 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4169 | { |
ca46fb90 RB |
4170 | if (SCM_UNBNDP (n2)) |
4171 | { | |
4172 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
4173 | return SCM_I_MAKINUM (1L); |
4174 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 4175 | } |
09fb7599 | 4176 | |
e11e83f3 | 4177 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 4178 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 4179 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 4180 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 4181 | |
e11e83f3 | 4182 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 4183 | { |
e11e83f3 | 4184 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4185 | { |
4186 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4187 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4188 | return d; |
4189 | else | |
4190 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4191 | } | |
4192 | else | |
4193 | { | |
4194 | /* inum n1, big n2 */ | |
4195 | inumbig: | |
4196 | { | |
4197 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4198 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4199 | if (nn1 == 0) return SCM_INUM0; |
4200 | if (nn1 < 0) nn1 = - nn1; | |
4201 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4202 | scm_remember_upto_here_1 (n2); | |
4203 | return result; | |
4204 | } | |
4205 | } | |
4206 | } | |
4207 | else | |
4208 | { | |
4209 | /* big n1 */ | |
e11e83f3 | 4210 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4211 | { |
4212 | SCM_SWAP (n1, n2); | |
4213 | goto inumbig; | |
4214 | } | |
4215 | else | |
4216 | { | |
4217 | SCM result = scm_i_mkbig (); | |
4218 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4219 | SCM_I_BIG_MPZ (n1), | |
4220 | SCM_I_BIG_MPZ (n2)); | |
4221 | scm_remember_upto_here_2(n1, n2); | |
4222 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4223 | return result; | |
4224 | } | |
f872b822 | 4225 | } |
0f2d19dd JB |
4226 | } |
4227 | ||
8a525303 GB |
4228 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4229 | ||
4230 | Logand: | |
4231 | X Y Result Method: | |
4232 | (len) | |
4233 | + + + x (map digit:logand X Y) | |
4234 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4235 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4236 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4237 | ||
4238 | Logior: | |
4239 | X Y Result Method: | |
4240 | ||
4241 | + + + (map digit:logior X Y) | |
4242 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4243 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4244 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4245 | ||
4246 | Logxor: | |
4247 | X Y Result Method: | |
4248 | ||
4249 | + + + (map digit:logxor X Y) | |
4250 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4251 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4252 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4253 | ||
4254 | Logtest: | |
4255 | X Y Result | |
4256 | ||
4257 | + + (any digit:logand X Y) | |
4258 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4259 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4260 | - - #t | |
4261 | ||
4262 | */ | |
4263 | ||
78d3deb1 AW |
4264 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4265 | (SCM x, SCM y, SCM rest), | |
4266 | "Return the bitwise AND of the integer arguments.\n\n" | |
4267 | "@lisp\n" | |
4268 | "(logand) @result{} -1\n" | |
4269 | "(logand 7) @result{} 7\n" | |
4270 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4271 | "@end lisp") | |
4272 | #define FUNC_NAME s_scm_i_logand | |
4273 | { | |
4274 | while (!scm_is_null (rest)) | |
4275 | { x = scm_logand (x, y); | |
4276 | y = scm_car (rest); | |
4277 | rest = scm_cdr (rest); | |
4278 | } | |
4279 | return scm_logand (x, y); | |
4280 | } | |
4281 | #undef FUNC_NAME | |
4282 | ||
4283 | #define s_scm_logand s_scm_i_logand | |
4284 | ||
4285 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4286 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4287 | { |
e25f3727 | 4288 | scm_t_inum nn1; |
9a00c9fc | 4289 | |
0aacf84e MD |
4290 | if (SCM_UNBNDP (n2)) |
4291 | { | |
4292 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4293 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4294 | else if (!SCM_NUMBERP (n1)) |
4295 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4296 | else if (SCM_NUMBERP (n1)) | |
4297 | return n1; | |
4298 | else | |
4299 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4300 | } |
09fb7599 | 4301 | |
e11e83f3 | 4302 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4303 | { |
e11e83f3 MV |
4304 | nn1 = SCM_I_INUM (n1); |
4305 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4306 | { |
e25f3727 | 4307 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4308 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4309 | } |
4310 | else if SCM_BIGP (n2) | |
4311 | { | |
4312 | intbig: | |
2e16a342 | 4313 | if (nn1 == 0) |
0aacf84e MD |
4314 | return SCM_INUM0; |
4315 | { | |
4316 | SCM result_z = scm_i_mkbig (); | |
4317 | mpz_t nn1_z; | |
4318 | mpz_init_set_si (nn1_z, nn1); | |
4319 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4320 | scm_remember_upto_here_1 (n2); | |
4321 | mpz_clear (nn1_z); | |
4322 | return scm_i_normbig (result_z); | |
4323 | } | |
4324 | } | |
4325 | else | |
4326 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4327 | } | |
4328 | else if (SCM_BIGP (n1)) | |
4329 | { | |
e11e83f3 | 4330 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4331 | { |
4332 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4333 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4334 | goto intbig; |
4335 | } | |
4336 | else if (SCM_BIGP (n2)) | |
4337 | { | |
4338 | SCM result_z = scm_i_mkbig (); | |
4339 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4340 | SCM_I_BIG_MPZ (n1), | |
4341 | SCM_I_BIG_MPZ (n2)); | |
4342 | scm_remember_upto_here_2 (n1, n2); | |
4343 | return scm_i_normbig (result_z); | |
4344 | } | |
4345 | else | |
4346 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4347 | } |
0aacf84e | 4348 | else |
09fb7599 | 4349 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4350 | } |
1bbd0b84 | 4351 | #undef FUNC_NAME |
0f2d19dd | 4352 | |
09fb7599 | 4353 | |
78d3deb1 AW |
4354 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4355 | (SCM x, SCM y, SCM rest), | |
4356 | "Return the bitwise OR of the integer arguments.\n\n" | |
4357 | "@lisp\n" | |
4358 | "(logior) @result{} 0\n" | |
4359 | "(logior 7) @result{} 7\n" | |
4360 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4361 | "@end lisp") | |
4362 | #define FUNC_NAME s_scm_i_logior | |
4363 | { | |
4364 | while (!scm_is_null (rest)) | |
4365 | { x = scm_logior (x, y); | |
4366 | y = scm_car (rest); | |
4367 | rest = scm_cdr (rest); | |
4368 | } | |
4369 | return scm_logior (x, y); | |
4370 | } | |
4371 | #undef FUNC_NAME | |
4372 | ||
4373 | #define s_scm_logior s_scm_i_logior | |
4374 | ||
4375 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4376 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4377 | { |
e25f3727 | 4378 | scm_t_inum nn1; |
9a00c9fc | 4379 | |
0aacf84e MD |
4380 | if (SCM_UNBNDP (n2)) |
4381 | { | |
4382 | if (SCM_UNBNDP (n1)) | |
4383 | return SCM_INUM0; | |
4384 | else if (SCM_NUMBERP (n1)) | |
4385 | return n1; | |
4386 | else | |
4387 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4388 | } |
09fb7599 | 4389 | |
e11e83f3 | 4390 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4391 | { |
e11e83f3 MV |
4392 | nn1 = SCM_I_INUM (n1); |
4393 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4394 | { |
e11e83f3 | 4395 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4396 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4397 | } |
4398 | else if (SCM_BIGP (n2)) | |
4399 | { | |
4400 | intbig: | |
4401 | if (nn1 == 0) | |
4402 | return n2; | |
4403 | { | |
4404 | SCM result_z = scm_i_mkbig (); | |
4405 | mpz_t nn1_z; | |
4406 | mpz_init_set_si (nn1_z, nn1); | |
4407 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4408 | scm_remember_upto_here_1 (n2); | |
4409 | mpz_clear (nn1_z); | |
9806de0d | 4410 | return scm_i_normbig (result_z); |
0aacf84e MD |
4411 | } |
4412 | } | |
4413 | else | |
4414 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4415 | } | |
4416 | else if (SCM_BIGP (n1)) | |
4417 | { | |
e11e83f3 | 4418 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4419 | { |
4420 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4421 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4422 | goto intbig; |
4423 | } | |
4424 | else if (SCM_BIGP (n2)) | |
4425 | { | |
4426 | SCM result_z = scm_i_mkbig (); | |
4427 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4428 | SCM_I_BIG_MPZ (n1), | |
4429 | SCM_I_BIG_MPZ (n2)); | |
4430 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4431 | return scm_i_normbig (result_z); |
0aacf84e MD |
4432 | } |
4433 | else | |
4434 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4435 | } |
0aacf84e | 4436 | else |
09fb7599 | 4437 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4438 | } |
1bbd0b84 | 4439 | #undef FUNC_NAME |
0f2d19dd | 4440 | |
09fb7599 | 4441 | |
78d3deb1 AW |
4442 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4443 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4444 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4445 | "set in the result if it is set in an odd number of arguments.\n" | |
4446 | "@lisp\n" | |
4447 | "(logxor) @result{} 0\n" | |
4448 | "(logxor 7) @result{} 7\n" | |
4449 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4450 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4451 | "@end lisp") |
78d3deb1 AW |
4452 | #define FUNC_NAME s_scm_i_logxor |
4453 | { | |
4454 | while (!scm_is_null (rest)) | |
4455 | { x = scm_logxor (x, y); | |
4456 | y = scm_car (rest); | |
4457 | rest = scm_cdr (rest); | |
4458 | } | |
4459 | return scm_logxor (x, y); | |
4460 | } | |
4461 | #undef FUNC_NAME | |
4462 | ||
4463 | #define s_scm_logxor s_scm_i_logxor | |
4464 | ||
4465 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4466 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4467 | { |
e25f3727 | 4468 | scm_t_inum nn1; |
9a00c9fc | 4469 | |
0aacf84e MD |
4470 | if (SCM_UNBNDP (n2)) |
4471 | { | |
4472 | if (SCM_UNBNDP (n1)) | |
4473 | return SCM_INUM0; | |
4474 | else if (SCM_NUMBERP (n1)) | |
4475 | return n1; | |
4476 | else | |
4477 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4478 | } |
09fb7599 | 4479 | |
e11e83f3 | 4480 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4481 | { |
e11e83f3 MV |
4482 | nn1 = SCM_I_INUM (n1); |
4483 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4484 | { |
e25f3727 | 4485 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4486 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4487 | } |
4488 | else if (SCM_BIGP (n2)) | |
4489 | { | |
4490 | intbig: | |
4491 | { | |
4492 | SCM result_z = scm_i_mkbig (); | |
4493 | mpz_t nn1_z; | |
4494 | mpz_init_set_si (nn1_z, nn1); | |
4495 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4496 | scm_remember_upto_here_1 (n2); | |
4497 | mpz_clear (nn1_z); | |
4498 | return scm_i_normbig (result_z); | |
4499 | } | |
4500 | } | |
4501 | else | |
4502 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4503 | } | |
4504 | else if (SCM_BIGP (n1)) | |
4505 | { | |
e11e83f3 | 4506 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4507 | { |
4508 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4509 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4510 | goto intbig; |
4511 | } | |
4512 | else if (SCM_BIGP (n2)) | |
4513 | { | |
4514 | SCM result_z = scm_i_mkbig (); | |
4515 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4516 | SCM_I_BIG_MPZ (n1), | |
4517 | SCM_I_BIG_MPZ (n2)); | |
4518 | scm_remember_upto_here_2 (n1, n2); | |
4519 | return scm_i_normbig (result_z); | |
4520 | } | |
4521 | else | |
4522 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4523 | } |
0aacf84e | 4524 | else |
09fb7599 | 4525 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4526 | } |
1bbd0b84 | 4527 | #undef FUNC_NAME |
0f2d19dd | 4528 | |
09fb7599 | 4529 | |
a1ec6916 | 4530 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4531 | (SCM j, SCM k), |
ba6e7231 KR |
4532 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4533 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4534 | "without actually calculating the @code{logand}, just testing\n" | |
4535 | "for non-zero.\n" | |
4536 | "\n" | |
1e6808ea | 4537 | "@lisp\n" |
b380b885 MD |
4538 | "(logtest #b0100 #b1011) @result{} #f\n" |
4539 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4540 | "@end lisp") |
1bbd0b84 | 4541 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4542 | { |
e25f3727 | 4543 | scm_t_inum nj; |
9a00c9fc | 4544 | |
e11e83f3 | 4545 | if (SCM_I_INUMP (j)) |
0aacf84e | 4546 | { |
e11e83f3 MV |
4547 | nj = SCM_I_INUM (j); |
4548 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4549 | { |
e25f3727 | 4550 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4551 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4552 | } |
4553 | else if (SCM_BIGP (k)) | |
4554 | { | |
4555 | intbig: | |
4556 | if (nj == 0) | |
4557 | return SCM_BOOL_F; | |
4558 | { | |
4559 | SCM result; | |
4560 | mpz_t nj_z; | |
4561 | mpz_init_set_si (nj_z, nj); | |
4562 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4563 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4564 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4565 | mpz_clear (nj_z); |
4566 | return result; | |
4567 | } | |
4568 | } | |
4569 | else | |
4570 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4571 | } | |
4572 | else if (SCM_BIGP (j)) | |
4573 | { | |
e11e83f3 | 4574 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4575 | { |
4576 | SCM_SWAP (j, k); | |
e11e83f3 | 4577 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4578 | goto intbig; |
4579 | } | |
4580 | else if (SCM_BIGP (k)) | |
4581 | { | |
4582 | SCM result; | |
4583 | mpz_t result_z; | |
4584 | mpz_init (result_z); | |
4585 | mpz_and (result_z, | |
4586 | SCM_I_BIG_MPZ (j), | |
4587 | SCM_I_BIG_MPZ (k)); | |
4588 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4589 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4590 | mpz_clear (result_z); |
4591 | return result; | |
4592 | } | |
4593 | else | |
4594 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4595 | } | |
4596 | else | |
4597 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4598 | } |
1bbd0b84 | 4599 | #undef FUNC_NAME |
0f2d19dd | 4600 | |
c1bfcf60 | 4601 | |
a1ec6916 | 4602 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4603 | (SCM index, SCM j), |
ba6e7231 KR |
4604 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4605 | "@var{index} starts from 0 for the least significant bit.\n" | |
4606 | "\n" | |
1e6808ea | 4607 | "@lisp\n" |
b380b885 MD |
4608 | "(logbit? 0 #b1101) @result{} #t\n" |
4609 | "(logbit? 1 #b1101) @result{} #f\n" | |
4610 | "(logbit? 2 #b1101) @result{} #t\n" | |
4611 | "(logbit? 3 #b1101) @result{} #t\n" | |
4612 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4613 | "@end lisp") |
1bbd0b84 | 4614 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4615 | { |
78166ad5 | 4616 | unsigned long int iindex; |
5efd3c7d | 4617 | iindex = scm_to_ulong (index); |
78166ad5 | 4618 | |
e11e83f3 | 4619 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4620 | { |
4621 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4622 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4623 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4624 | } |
0aacf84e MD |
4625 | else if (SCM_BIGP (j)) |
4626 | { | |
4627 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4628 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4629 | return scm_from_bool (val); |
0aacf84e MD |
4630 | } |
4631 | else | |
78166ad5 | 4632 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4633 | } |
1bbd0b84 | 4634 | #undef FUNC_NAME |
0f2d19dd | 4635 | |
78166ad5 | 4636 | |
a1ec6916 | 4637 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4638 | (SCM n), |
4d814788 | 4639 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4640 | "argument.\n" |
4641 | "\n" | |
b380b885 MD |
4642 | "@lisp\n" |
4643 | "(number->string (lognot #b10000000) 2)\n" | |
4644 | " @result{} \"-10000001\"\n" | |
4645 | "(number->string (lognot #b0) 2)\n" | |
4646 | " @result{} \"-1\"\n" | |
1e6808ea | 4647 | "@end lisp") |
1bbd0b84 | 4648 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4649 | { |
e11e83f3 | 4650 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4651 | /* No overflow here, just need to toggle all the bits making up the inum. |
4652 | Enhancement: No need to strip the tag and add it back, could just xor | |
4653 | a block of 1 bits, if that worked with the various debug versions of | |
4654 | the SCM typedef. */ | |
e11e83f3 | 4655 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4656 | |
4657 | } else if (SCM_BIGP (n)) { | |
4658 | SCM result = scm_i_mkbig (); | |
4659 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4660 | scm_remember_upto_here_1 (n); | |
4661 | return result; | |
4662 | ||
4663 | } else { | |
4664 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4665 | } | |
0f2d19dd | 4666 | } |
1bbd0b84 | 4667 | #undef FUNC_NAME |
0f2d19dd | 4668 | |
518b7508 KR |
4669 | /* returns 0 if IN is not an integer. OUT must already be |
4670 | initialized. */ | |
4671 | static int | |
4672 | coerce_to_big (SCM in, mpz_t out) | |
4673 | { | |
4674 | if (SCM_BIGP (in)) | |
4675 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4676 | else if (SCM_I_INUMP (in)) |
4677 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4678 | else |
4679 | return 0; | |
4680 | ||
4681 | return 1; | |
4682 | } | |
4683 | ||
d885e204 | 4684 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4685 | (SCM n, SCM k, SCM m), |
4686 | "Return @var{n} raised to the integer exponent\n" | |
4687 | "@var{k}, modulo @var{m}.\n" | |
4688 | "\n" | |
4689 | "@lisp\n" | |
4690 | "(modulo-expt 2 3 5)\n" | |
4691 | " @result{} 3\n" | |
4692 | "@end lisp") | |
d885e204 | 4693 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4694 | { |
4695 | mpz_t n_tmp; | |
4696 | mpz_t k_tmp; | |
4697 | mpz_t m_tmp; | |
4698 | ||
4699 | /* There are two classes of error we might encounter -- | |
4700 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4701 | and | |
4702 | 2) wrong-type errors, which of course we'll report by calling | |
4703 | SCM_WRONG_TYPE_ARG. | |
4704 | We don't report those errors immediately, however; instead we do | |
4705 | some cleanup first. These variables tell us which error (if | |
4706 | any) we should report after cleaning up. | |
4707 | */ | |
4708 | int report_overflow = 0; | |
4709 | ||
4710 | int position_of_wrong_type = 0; | |
4711 | SCM value_of_wrong_type = SCM_INUM0; | |
4712 | ||
4713 | SCM result = SCM_UNDEFINED; | |
4714 | ||
4715 | mpz_init (n_tmp); | |
4716 | mpz_init (k_tmp); | |
4717 | mpz_init (m_tmp); | |
4718 | ||
bc36d050 | 4719 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4720 | { |
4721 | report_overflow = 1; | |
4722 | goto cleanup; | |
4723 | } | |
4724 | ||
4725 | if (!coerce_to_big (n, n_tmp)) | |
4726 | { | |
4727 | value_of_wrong_type = n; | |
4728 | position_of_wrong_type = 1; | |
4729 | goto cleanup; | |
4730 | } | |
4731 | ||
4732 | if (!coerce_to_big (k, k_tmp)) | |
4733 | { | |
4734 | value_of_wrong_type = k; | |
4735 | position_of_wrong_type = 2; | |
4736 | goto cleanup; | |
4737 | } | |
4738 | ||
4739 | if (!coerce_to_big (m, m_tmp)) | |
4740 | { | |
4741 | value_of_wrong_type = m; | |
4742 | position_of_wrong_type = 3; | |
4743 | goto cleanup; | |
4744 | } | |
4745 | ||
4746 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4747 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4748 | doesn't exist (or is not unique). Since exceptions are hard to | |
4749 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4750 | a simple failure code, which is easy to handle. */ | |
4751 | ||
4752 | if (-1 == mpz_sgn (k_tmp)) | |
4753 | { | |
4754 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4755 | { | |
4756 | report_overflow = 1; | |
4757 | goto cleanup; | |
4758 | } | |
4759 | mpz_neg (k_tmp, k_tmp); | |
4760 | } | |
4761 | ||
4762 | result = scm_i_mkbig (); | |
4763 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4764 | n_tmp, | |
4765 | k_tmp, | |
4766 | m_tmp); | |
b7b8c575 KR |
4767 | |
4768 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4769 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4770 | ||
518b7508 KR |
4771 | cleanup: |
4772 | mpz_clear (m_tmp); | |
4773 | mpz_clear (k_tmp); | |
4774 | mpz_clear (n_tmp); | |
4775 | ||
4776 | if (report_overflow) | |
4777 | scm_num_overflow (FUNC_NAME); | |
4778 | ||
4779 | if (position_of_wrong_type) | |
4780 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4781 | value_of_wrong_type); | |
4782 | ||
4783 | return scm_i_normbig (result); | |
4784 | } | |
4785 | #undef FUNC_NAME | |
4786 | ||
a1ec6916 | 4787 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4788 | (SCM n, SCM k), |
ba6e7231 KR |
4789 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4790 | "exact integer, @var{n} can be any number.\n" | |
4791 | "\n" | |
2519490c MW |
4792 | "Negative @var{k} is supported, and results in\n" |
4793 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4794 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4795 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4796 | "\n" |
b380b885 | 4797 | "@lisp\n" |
ba6e7231 KR |
4798 | "(integer-expt 2 5) @result{} 32\n" |
4799 | "(integer-expt -3 3) @result{} -27\n" | |
4800 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4801 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4802 | "@end lisp") |
1bbd0b84 | 4803 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4804 | { |
e25f3727 | 4805 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4806 | SCM z_i2 = SCM_BOOL_F; |
4807 | int i2_is_big = 0; | |
d956fa6f | 4808 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4809 | |
bfe1f03a MW |
4810 | /* Specifically refrain from checking the type of the first argument. |
4811 | This allows us to exponentiate any object that can be multiplied. | |
4812 | If we must raise to a negative power, we must also be able to | |
4813 | take its reciprocal. */ | |
4814 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4815 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4816 | |
bfe1f03a MW |
4817 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4818 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4819 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4820 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4821 | /* The next check is necessary only because R6RS specifies different | |
4822 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4823 | we simply skip this case and move on. */ | |
4824 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4825 | { | |
4826 | /* k cannot be 0 at this point, because we | |
4827 | have already checked for that case above */ | |
4828 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4829 | return n; |
4830 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4831 | return scm_nan (); | |
4832 | } | |
a285b18c MW |
4833 | else if (SCM_FRACTIONP (n)) |
4834 | { | |
4835 | /* Optimize the fraction case by (a/b)^k ==> (a^k)/(b^k), to avoid | |
4836 | needless reduction of intermediate products to lowest terms. | |
4837 | If a and b have no common factors, then a^k and b^k have no | |
4838 | common factors. Use 'scm_i_make_ratio_already_reduced' to | |
4839 | construct the final result, so that no gcd computations are | |
4840 | needed to exponentiate a fraction. */ | |
4841 | if (scm_is_true (scm_positive_p (k))) | |
4842 | return scm_i_make_ratio_already_reduced | |
4843 | (scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k), | |
4844 | scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k)); | |
4845 | else | |
4846 | { | |
4847 | k = scm_difference (k, SCM_UNDEFINED); | |
4848 | return scm_i_make_ratio_already_reduced | |
4849 | (scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k), | |
4850 | scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k)); | |
4851 | } | |
4852 | } | |
ca46fb90 | 4853 | |
e11e83f3 MV |
4854 | if (SCM_I_INUMP (k)) |
4855 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4856 | else if (SCM_BIGP (k)) |
4857 | { | |
4858 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4859 | scm_remember_upto_here_1 (k); |
4860 | i2_is_big = 1; | |
4861 | } | |
2830fd91 | 4862 | else |
ca46fb90 RB |
4863 | SCM_WRONG_TYPE_ARG (2, k); |
4864 | ||
4865 | if (i2_is_big) | |
f872b822 | 4866 | { |
ca46fb90 RB |
4867 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4868 | { | |
4869 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4870 | n = scm_divide (n, SCM_UNDEFINED); | |
4871 | } | |
4872 | while (1) | |
4873 | { | |
4874 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4875 | { | |
ca46fb90 RB |
4876 | return acc; |
4877 | } | |
4878 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4879 | { | |
ca46fb90 RB |
4880 | return scm_product (acc, n); |
4881 | } | |
4882 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4883 | acc = scm_product (acc, n); | |
4884 | n = scm_product (n, n); | |
4885 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4886 | } | |
f872b822 | 4887 | } |
ca46fb90 | 4888 | else |
f872b822 | 4889 | { |
ca46fb90 RB |
4890 | if (i2 < 0) |
4891 | { | |
4892 | i2 = -i2; | |
4893 | n = scm_divide (n, SCM_UNDEFINED); | |
4894 | } | |
4895 | while (1) | |
4896 | { | |
4897 | if (0 == i2) | |
4898 | return acc; | |
4899 | if (1 == i2) | |
4900 | return scm_product (acc, n); | |
4901 | if (i2 & 1) | |
4902 | acc = scm_product (acc, n); | |
4903 | n = scm_product (n, n); | |
4904 | i2 >>= 1; | |
4905 | } | |
f872b822 | 4906 | } |
0f2d19dd | 4907 | } |
1bbd0b84 | 4908 | #undef FUNC_NAME |
0f2d19dd | 4909 | |
e08a12b5 MW |
4910 | /* Efficiently compute (N * 2^COUNT), |
4911 | where N is an exact integer, and COUNT > 0. */ | |
4912 | static SCM | |
4913 | left_shift_exact_integer (SCM n, long count) | |
4914 | { | |
4915 | if (SCM_I_INUMP (n)) | |
4916 | { | |
4917 | scm_t_inum nn = SCM_I_INUM (n); | |
4918 | ||
4919 | /* Left shift of count >= SCM_I_FIXNUM_BIT-1 will always | |
4920 | overflow a non-zero fixnum. For smaller shifts we check the | |
4921 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4922 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4923 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". */ | |
4924 | ||
4925 | if (nn == 0) | |
4926 | return n; | |
4927 | else if (count < SCM_I_FIXNUM_BIT-1 && | |
4928 | ((scm_t_bits) (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - count)) + 1) | |
4929 | <= 1)) | |
4930 | return SCM_I_MAKINUM (nn << count); | |
4931 | else | |
4932 | { | |
4933 | SCM result = scm_i_inum2big (nn); | |
4934 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
4935 | count); | |
4936 | return result; | |
4937 | } | |
4938 | } | |
4939 | else if (SCM_BIGP (n)) | |
4940 | { | |
4941 | SCM result = scm_i_mkbig (); | |
4942 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), count); | |
4943 | scm_remember_upto_here_1 (n); | |
4944 | return result; | |
4945 | } | |
4946 | else | |
4947 | scm_syserror ("left_shift_exact_integer"); | |
4948 | } | |
4949 | ||
4950 | /* Efficiently compute floor (N / 2^COUNT), | |
4951 | where N is an exact integer and COUNT > 0. */ | |
4952 | static SCM | |
4953 | floor_right_shift_exact_integer (SCM n, long count) | |
4954 | { | |
4955 | if (SCM_I_INUMP (n)) | |
4956 | { | |
4957 | scm_t_inum nn = SCM_I_INUM (n); | |
4958 | ||
4959 | if (count >= SCM_I_FIXNUM_BIT) | |
4960 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM (-1)); | |
4961 | else | |
4962 | return SCM_I_MAKINUM (SCM_SRS (nn, count)); | |
4963 | } | |
4964 | else if (SCM_BIGP (n)) | |
4965 | { | |
4966 | SCM result = scm_i_mkbig (); | |
4967 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4968 | count); | |
4969 | scm_remember_upto_here_1 (n); | |
4970 | return scm_i_normbig (result); | |
4971 | } | |
4972 | else | |
4973 | scm_syserror ("floor_right_shift_exact_integer"); | |
4974 | } | |
4975 | ||
4976 | /* Efficiently compute round (N / 2^COUNT), | |
4977 | where N is an exact integer and COUNT > 0. */ | |
4978 | static SCM | |
4979 | round_right_shift_exact_integer (SCM n, long count) | |
4980 | { | |
4981 | if (SCM_I_INUMP (n)) | |
4982 | { | |
4983 | if (count >= SCM_I_FIXNUM_BIT) | |
4984 | return SCM_INUM0; | |
4985 | else | |
4986 | { | |
4987 | scm_t_inum nn = SCM_I_INUM (n); | |
4988 | scm_t_inum qq = SCM_SRS (nn, count); | |
4989 | ||
4990 | if (0 == (nn & (1L << (count-1)))) | |
4991 | return SCM_I_MAKINUM (qq); /* round down */ | |
4992 | else if (nn & ((1L << (count-1)) - 1)) | |
4993 | return SCM_I_MAKINUM (qq + 1); /* round up */ | |
4994 | else | |
4995 | return SCM_I_MAKINUM ((~1L) & (qq + 1)); /* round to even */ | |
4996 | } | |
4997 | } | |
4998 | else if (SCM_BIGP (n)) | |
4999 | { | |
5000 | SCM q = scm_i_mkbig (); | |
5001 | ||
5002 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), count); | |
5003 | if (mpz_tstbit (SCM_I_BIG_MPZ (n), count-1) | |
5004 | && (mpz_odd_p (SCM_I_BIG_MPZ (q)) | |
5005 | || (mpz_scan1 (SCM_I_BIG_MPZ (n), 0) < count-1))) | |
5006 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
5007 | scm_remember_upto_here_1 (n); | |
5008 | return scm_i_normbig (q); | |
5009 | } | |
5010 | else | |
5011 | scm_syserror ("round_right_shift_exact_integer"); | |
5012 | } | |
5013 | ||
a1ec6916 | 5014 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
e08a12b5 MW |
5015 | (SCM n, SCM count), |
5016 | "Return @math{floor(@var{n} * 2^@var{count})}.\n" | |
5017 | "@var{n} and @var{count} must be exact integers.\n" | |
1e6808ea | 5018 | "\n" |
e08a12b5 MW |
5019 | "With @var{n} viewed as an infinite-precision twos-complement\n" |
5020 | "integer, @code{ash} means a left shift introducing zero bits\n" | |
5021 | "when @var{count} is positive, or a right shift dropping bits\n" | |
5022 | "when @var{count} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 5023 | "\n" |
b380b885 | 5024 | "@lisp\n" |
1e6808ea MG |
5025 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
5026 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
5027 | "\n" |
5028 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
5029 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 5030 | "@end lisp") |
1bbd0b84 | 5031 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 5032 | { |
e08a12b5 | 5033 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) |
788aca27 | 5034 | { |
e08a12b5 | 5035 | long bits_to_shift = scm_to_long (count); |
788aca27 KR |
5036 | |
5037 | if (bits_to_shift > 0) | |
e08a12b5 MW |
5038 | return left_shift_exact_integer (n, bits_to_shift); |
5039 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
5040 | return floor_right_shift_exact_integer (n, -bits_to_shift); | |
788aca27 | 5041 | else |
e08a12b5 | 5042 | return n; |
788aca27 | 5043 | } |
e08a12b5 MW |
5044 | else |
5045 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
5046 | } | |
5047 | #undef FUNC_NAME | |
788aca27 | 5048 | |
e08a12b5 MW |
5049 | SCM_DEFINE (scm_round_ash, "round-ash", 2, 0, 0, |
5050 | (SCM n, SCM count), | |
5051 | "Return @math{round(@var{n} * 2^@var{count})}.\n" | |
5052 | "@var{n} and @var{count} must be exact integers.\n" | |
5053 | "\n" | |
5054 | "With @var{n} viewed as an infinite-precision twos-complement\n" | |
5055 | "integer, @code{round-ash} means a left shift introducing zero\n" | |
5056 | "bits when @var{count} is positive, or a right shift rounding\n" | |
5057 | "to the nearest integer (with ties going to the nearest even\n" | |
5058 | "integer) when @var{count} is negative. This is a rounded\n" | |
5059 | "``arithmetic'' shift.\n" | |
5060 | "\n" | |
5061 | "@lisp\n" | |
5062 | "(number->string (round-ash #b1 3) 2) @result{} \"1000\"\n" | |
5063 | "(number->string (round-ash #b1010 -1) 2) @result{} \"101\"\n" | |
5064 | "(number->string (round-ash #b1010 -2) 2) @result{} \"10\"\n" | |
5065 | "(number->string (round-ash #b1011 -2) 2) @result{} \"11\"\n" | |
5066 | "(number->string (round-ash #b1101 -2) 2) @result{} \"11\"\n" | |
5067 | "(number->string (round-ash #b1110 -2) 2) @result{} \"100\"\n" | |
5068 | "@end lisp") | |
5069 | #define FUNC_NAME s_scm_round_ash | |
5070 | { | |
5071 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) | |
5072 | { | |
5073 | long bits_to_shift = scm_to_long (count); | |
788aca27 | 5074 | |
e08a12b5 MW |
5075 | if (bits_to_shift > 0) |
5076 | return left_shift_exact_integer (n, bits_to_shift); | |
5077 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
5078 | return round_right_shift_exact_integer (n, -bits_to_shift); | |
ca46fb90 | 5079 | else |
e08a12b5 | 5080 | return n; |
ca46fb90 RB |
5081 | } |
5082 | else | |
e08a12b5 | 5083 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5084 | } |
1bbd0b84 | 5085 | #undef FUNC_NAME |
0f2d19dd | 5086 | |
3c9f20f8 | 5087 | |
a1ec6916 | 5088 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 5089 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
5090 | "Return the integer composed of the @var{start} (inclusive)\n" |
5091 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
5092 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
5093 | "\n" | |
b380b885 MD |
5094 | "@lisp\n" |
5095 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
5096 | " @result{} \"1010\"\n" | |
5097 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
5098 | " @result{} \"10110\"\n" | |
5099 | "@end lisp") | |
1bbd0b84 | 5100 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 5101 | { |
7f848242 | 5102 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
5103 | istart = scm_to_ulong (start); |
5104 | iend = scm_to_ulong (end); | |
c1bfcf60 | 5105 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 5106 | |
7f848242 KR |
5107 | /* how many bits to keep */ |
5108 | bits = iend - istart; | |
5109 | ||
e11e83f3 | 5110 | if (SCM_I_INUMP (n)) |
0aacf84e | 5111 | { |
e25f3727 | 5112 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
5113 | |
5114 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 5115 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 5116 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 5117 | |
0aacf84e MD |
5118 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
5119 | { | |
5120 | /* Since we emulate two's complement encoded numbers, this | |
5121 | * special case requires us to produce a result that has | |
7f848242 | 5122 | * more bits than can be stored in a fixnum. |
0aacf84e | 5123 | */ |
e25f3727 | 5124 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
5125 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
5126 | bits); | |
5127 | return result; | |
0aacf84e | 5128 | } |
ac0c002c | 5129 | |
7f848242 | 5130 | /* mask down to requisite bits */ |
857ae6af | 5131 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 5132 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
5133 | } |
5134 | else if (SCM_BIGP (n)) | |
ac0c002c | 5135 | { |
7f848242 KR |
5136 | SCM result; |
5137 | if (bits == 1) | |
5138 | { | |
d956fa6f | 5139 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
5140 | } |
5141 | else | |
5142 | { | |
5143 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
5144 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
5145 | such bits into a ulong. */ | |
5146 | result = scm_i_mkbig (); | |
5147 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
5148 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
5149 | result = scm_i_normbig (result); | |
5150 | } | |
5151 | scm_remember_upto_here_1 (n); | |
5152 | return result; | |
ac0c002c | 5153 | } |
0aacf84e | 5154 | else |
78166ad5 | 5155 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5156 | } |
1bbd0b84 | 5157 | #undef FUNC_NAME |
0f2d19dd | 5158 | |
7f848242 | 5159 | |
e4755e5c JB |
5160 | static const char scm_logtab[] = { |
5161 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
5162 | }; | |
1cc91f1b | 5163 | |
a1ec6916 | 5164 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 5165 | (SCM n), |
1e6808ea MG |
5166 | "Return the number of bits in integer @var{n}. If integer is\n" |
5167 | "positive, the 1-bits in its binary representation are counted.\n" | |
5168 | "If negative, the 0-bits in its two's-complement binary\n" | |
5169 | "representation are counted. If 0, 0 is returned.\n" | |
5170 | "\n" | |
b380b885 MD |
5171 | "@lisp\n" |
5172 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
5173 | " @result{} 4\n" |
5174 | "(logcount 0)\n" | |
5175 | " @result{} 0\n" | |
5176 | "(logcount -2)\n" | |
5177 | " @result{} 1\n" | |
5178 | "@end lisp") | |
5179 | #define FUNC_NAME s_scm_logcount | |
5180 | { | |
e11e83f3 | 5181 | if (SCM_I_INUMP (n)) |
f872b822 | 5182 | { |
e25f3727 AW |
5183 | unsigned long c = 0; |
5184 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
5185 | if (nn < 0) |
5186 | nn = -1 - nn; | |
5187 | while (nn) | |
5188 | { | |
5189 | c += scm_logtab[15 & nn]; | |
5190 | nn >>= 4; | |
5191 | } | |
d956fa6f | 5192 | return SCM_I_MAKINUM (c); |
f872b822 | 5193 | } |
ca46fb90 | 5194 | else if (SCM_BIGP (n)) |
f872b822 | 5195 | { |
ca46fb90 | 5196 | unsigned long count; |
713a4259 KR |
5197 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
5198 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 5199 | else |
713a4259 KR |
5200 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
5201 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5202 | return SCM_I_MAKINUM (count); |
f872b822 | 5203 | } |
ca46fb90 RB |
5204 | else |
5205 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 5206 | } |
ca46fb90 | 5207 | #undef FUNC_NAME |
0f2d19dd JB |
5208 | |
5209 | ||
ca46fb90 RB |
5210 | static const char scm_ilentab[] = { |
5211 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
5212 | }; | |
5213 | ||
0f2d19dd | 5214 | |
ca46fb90 RB |
5215 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
5216 | (SCM n), | |
5217 | "Return the number of bits necessary to represent @var{n}.\n" | |
5218 | "\n" | |
5219 | "@lisp\n" | |
5220 | "(integer-length #b10101010)\n" | |
5221 | " @result{} 8\n" | |
5222 | "(integer-length 0)\n" | |
5223 | " @result{} 0\n" | |
5224 | "(integer-length #b1111)\n" | |
5225 | " @result{} 4\n" | |
5226 | "@end lisp") | |
5227 | #define FUNC_NAME s_scm_integer_length | |
5228 | { | |
e11e83f3 | 5229 | if (SCM_I_INUMP (n)) |
0aacf84e | 5230 | { |
e25f3727 | 5231 | unsigned long c = 0; |
0aacf84e | 5232 | unsigned int l = 4; |
e25f3727 | 5233 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
5234 | if (nn < 0) |
5235 | nn = -1 - nn; | |
5236 | while (nn) | |
5237 | { | |
5238 | c += 4; | |
5239 | l = scm_ilentab [15 & nn]; | |
5240 | nn >>= 4; | |
5241 | } | |
d956fa6f | 5242 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
5243 | } |
5244 | else if (SCM_BIGP (n)) | |
5245 | { | |
5246 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
5247 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
5248 | 1 too big, so check for that and adjust. */ | |
5249 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
5250 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
5251 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
5252 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
5253 | size--; | |
5254 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5255 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
5256 | } |
5257 | else | |
ca46fb90 | 5258 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5259 | } |
5260 | #undef FUNC_NAME | |
0f2d19dd JB |
5261 | |
5262 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5263 | #define SCM_MAX_DBL_RADIX 36 |
5264 | ||
0b799eea | 5265 | /* use this array as a way to generate a single digit */ |
9b5fcde6 | 5266 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5267 | |
1ea37620 MW |
5268 | static mpz_t dbl_minimum_normal_mantissa; |
5269 | ||
1be6b49c | 5270 | static size_t |
1ea37620 | 5271 | idbl2str (double dbl, char *a, int radix) |
0f2d19dd | 5272 | { |
1ea37620 | 5273 | int ch = 0; |
0b799eea | 5274 | |
1ea37620 MW |
5275 | if (radix < 2 || radix > SCM_MAX_DBL_RADIX) |
5276 | /* revert to existing behavior */ | |
5277 | radix = 10; | |
0f2d19dd | 5278 | |
1ea37620 | 5279 | if (isinf (dbl)) |
abb7e44d | 5280 | { |
1ea37620 MW |
5281 | strcpy (a, (dbl > 0.0) ? "+inf.0" : "-inf.0"); |
5282 | return 6; | |
abb7e44d | 5283 | } |
1ea37620 MW |
5284 | else if (dbl > 0.0) |
5285 | ; | |
5286 | else if (dbl < 0.0) | |
7351e207 | 5287 | { |
1ea37620 MW |
5288 | dbl = -dbl; |
5289 | a[ch++] = '-'; | |
7351e207 | 5290 | } |
1ea37620 | 5291 | else if (dbl == 0.0) |
7351e207 | 5292 | { |
1ea37620 MW |
5293 | if (!double_is_non_negative_zero (dbl)) |
5294 | a[ch++] = '-'; | |
5295 | strcpy (a + ch, "0.0"); | |
5296 | return ch + 3; | |
7351e207 | 5297 | } |
1ea37620 | 5298 | else if (isnan (dbl)) |
f872b822 | 5299 | { |
1ea37620 MW |
5300 | strcpy (a, "+nan.0"); |
5301 | return 6; | |
f872b822 | 5302 | } |
7351e207 | 5303 | |
1ea37620 MW |
5304 | /* Algorithm taken from "Printing Floating-Point Numbers Quickly and |
5305 | Accurately" by Robert G. Burger and R. Kent Dybvig */ | |
5306 | { | |
5307 | int e, k; | |
5308 | mpz_t f, r, s, mplus, mminus, hi, digit; | |
5309 | int f_is_even, f_is_odd; | |
8150dfa1 | 5310 | int expon; |
1ea37620 MW |
5311 | int show_exp = 0; |
5312 | ||
5313 | mpz_inits (f, r, s, mplus, mminus, hi, digit, NULL); | |
5314 | mpz_set_d (f, ldexp (frexp (dbl, &e), DBL_MANT_DIG)); | |
5315 | if (e < DBL_MIN_EXP) | |
5316 | { | |
5317 | mpz_tdiv_q_2exp (f, f, DBL_MIN_EXP - e); | |
5318 | e = DBL_MIN_EXP; | |
5319 | } | |
5320 | e -= DBL_MANT_DIG; | |
0b799eea | 5321 | |
1ea37620 MW |
5322 | f_is_even = !mpz_odd_p (f); |
5323 | f_is_odd = !f_is_even; | |
0b799eea | 5324 | |
1ea37620 MW |
5325 | /* Initialize r, s, mplus, and mminus according |
5326 | to Table 1 from the paper. */ | |
5327 | if (e < 0) | |
5328 | { | |
5329 | mpz_set_ui (mminus, 1); | |
5330 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0 | |
5331 | || e == DBL_MIN_EXP - DBL_MANT_DIG) | |
5332 | { | |
5333 | mpz_set_ui (mplus, 1); | |
5334 | mpz_mul_2exp (r, f, 1); | |
5335 | mpz_mul_2exp (s, mminus, 1 - e); | |
5336 | } | |
5337 | else | |
5338 | { | |
5339 | mpz_set_ui (mplus, 2); | |
5340 | mpz_mul_2exp (r, f, 2); | |
5341 | mpz_mul_2exp (s, mminus, 2 - e); | |
5342 | } | |
5343 | } | |
5344 | else | |
5345 | { | |
5346 | mpz_set_ui (mminus, 1); | |
5347 | mpz_mul_2exp (mminus, mminus, e); | |
5348 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0) | |
5349 | { | |
5350 | mpz_set (mplus, mminus); | |
5351 | mpz_mul_2exp (r, f, 1 + e); | |
5352 | mpz_set_ui (s, 2); | |
5353 | } | |
5354 | else | |
5355 | { | |
5356 | mpz_mul_2exp (mplus, mminus, 1); | |
5357 | mpz_mul_2exp (r, f, 2 + e); | |
5358 | mpz_set_ui (s, 4); | |
5359 | } | |
5360 | } | |
0b799eea | 5361 | |
1ea37620 MW |
5362 | /* Find the smallest k such that: |
5363 | (r + mplus) / s < radix^k (if f is even) | |
5364 | (r + mplus) / s <= radix^k (if f is odd) */ | |
f872b822 | 5365 | { |
1ea37620 MW |
5366 | /* IMPROVE-ME: Make an initial guess to speed this up */ |
5367 | mpz_add (hi, r, mplus); | |
5368 | k = 0; | |
5369 | while (mpz_cmp (hi, s) >= f_is_odd) | |
5370 | { | |
5371 | mpz_mul_ui (s, s, radix); | |
5372 | k++; | |
5373 | } | |
5374 | if (k == 0) | |
5375 | { | |
5376 | mpz_mul_ui (hi, hi, radix); | |
5377 | while (mpz_cmp (hi, s) < f_is_odd) | |
5378 | { | |
5379 | mpz_mul_ui (r, r, radix); | |
5380 | mpz_mul_ui (mplus, mplus, radix); | |
5381 | mpz_mul_ui (mminus, mminus, radix); | |
5382 | mpz_mul_ui (hi, hi, radix); | |
5383 | k--; | |
5384 | } | |
5385 | } | |
cda139a7 | 5386 | } |
f872b822 | 5387 | |
8150dfa1 MW |
5388 | expon = k - 1; |
5389 | if (k <= 0) | |
1ea37620 | 5390 | { |
8150dfa1 MW |
5391 | if (k <= -3) |
5392 | { | |
5393 | /* Use scientific notation */ | |
5394 | show_exp = 1; | |
5395 | k = 1; | |
5396 | } | |
5397 | else | |
5398 | { | |
5399 | int i; | |
0f2d19dd | 5400 | |
8150dfa1 MW |
5401 | /* Print leading zeroes */ |
5402 | a[ch++] = '0'; | |
5403 | a[ch++] = '.'; | |
5404 | for (i = 0; i > k; i--) | |
5405 | a[ch++] = '0'; | |
5406 | } | |
1ea37620 MW |
5407 | } |
5408 | ||
5409 | for (;;) | |
5410 | { | |
5411 | int end_1_p, end_2_p; | |
5412 | int d; | |
5413 | ||
5414 | mpz_mul_ui (mplus, mplus, radix); | |
5415 | mpz_mul_ui (mminus, mminus, radix); | |
5416 | mpz_mul_ui (r, r, radix); | |
5417 | mpz_fdiv_qr (digit, r, r, s); | |
5418 | d = mpz_get_ui (digit); | |
5419 | ||
5420 | mpz_add (hi, r, mplus); | |
5421 | end_1_p = (mpz_cmp (r, mminus) < f_is_even); | |
5422 | end_2_p = (mpz_cmp (s, hi) < f_is_even); | |
5423 | if (end_1_p || end_2_p) | |
5424 | { | |
5425 | mpz_mul_2exp (r, r, 1); | |
5426 | if (!end_2_p) | |
5427 | ; | |
5428 | else if (!end_1_p) | |
5429 | d++; | |
5430 | else if (mpz_cmp (r, s) >= !(d & 1)) | |
5431 | d++; | |
5432 | a[ch++] = number_chars[d]; | |
5433 | if (--k == 0) | |
5434 | a[ch++] = '.'; | |
5435 | break; | |
5436 | } | |
5437 | else | |
5438 | { | |
5439 | a[ch++] = number_chars[d]; | |
5440 | if (--k == 0) | |
5441 | a[ch++] = '.'; | |
5442 | } | |
5443 | } | |
5444 | ||
5445 | if (k > 0) | |
5446 | { | |
8150dfa1 MW |
5447 | if (expon >= 7 && k >= 4 && expon >= k) |
5448 | { | |
5449 | /* Here we would have to print more than three zeroes | |
5450 | followed by a decimal point and another zero. It | |
5451 | makes more sense to use scientific notation. */ | |
5452 | ||
5453 | /* Adjust k to what it would have been if we had chosen | |
5454 | scientific notation from the beginning. */ | |
5455 | k -= expon; | |
5456 | ||
5457 | /* k will now be <= 0, with magnitude equal to the number of | |
5458 | digits that we printed which should now be put after the | |
5459 | decimal point. */ | |
5460 | ||
5461 | /* Insert a decimal point */ | |
5462 | memmove (a + ch + k + 1, a + ch + k, -k); | |
5463 | a[ch + k] = '.'; | |
5464 | ch++; | |
5465 | ||
5466 | show_exp = 1; | |
5467 | } | |
5468 | else | |
5469 | { | |
5470 | for (; k > 0; k--) | |
5471 | a[ch++] = '0'; | |
5472 | a[ch++] = '.'; | |
5473 | } | |
1ea37620 MW |
5474 | } |
5475 | ||
5476 | if (k == 0) | |
5477 | a[ch++] = '0'; | |
5478 | ||
5479 | if (show_exp) | |
5480 | { | |
5481 | a[ch++] = 'e'; | |
8150dfa1 | 5482 | ch += scm_iint2str (expon, radix, a + ch); |
1ea37620 MW |
5483 | } |
5484 | ||
5485 | mpz_clears (f, r, s, mplus, mminus, hi, digit, NULL); | |
5486 | } | |
0f2d19dd JB |
5487 | return ch; |
5488 | } | |
5489 | ||
7a1aba42 MV |
5490 | |
5491 | static size_t | |
5492 | icmplx2str (double real, double imag, char *str, int radix) | |
5493 | { | |
5494 | size_t i; | |
c7218482 | 5495 | double sgn; |
7a1aba42 MV |
5496 | |
5497 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5498 | #ifdef HAVE_COPYSIGN |
5499 | sgn = copysign (1.0, imag); | |
5500 | #else | |
5501 | sgn = imag; | |
5502 | #endif | |
5503 | /* Don't output a '+' for negative numbers or for Inf and | |
5504 | NaN. They will provide their own sign. */ | |
5505 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5506 | str[i++] = '+'; | |
5507 | i += idbl2str (imag, &str[i], radix); | |
5508 | str[i++] = 'i'; | |
7a1aba42 MV |
5509 | return i; |
5510 | } | |
5511 | ||
1be6b49c | 5512 | static size_t |
0b799eea | 5513 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5514 | { |
1be6b49c | 5515 | size_t i; |
3c9a524f | 5516 | if (SCM_REALP (flt)) |
0b799eea | 5517 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5518 | else |
7a1aba42 MV |
5519 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5520 | str, radix); | |
0f2d19dd JB |
5521 | return i; |
5522 | } | |
0f2d19dd | 5523 | |
2881e77b | 5524 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5525 | characters in the result. |
5526 | rad is output base | |
5527 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5528 | size_t |
2881e77b MV |
5529 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5530 | { | |
5531 | if (num < 0) | |
5532 | { | |
5533 | *p++ = '-'; | |
5534 | return scm_iuint2str (-num, rad, p) + 1; | |
5535 | } | |
5536 | else | |
5537 | return scm_iuint2str (num, rad, p); | |
5538 | } | |
5539 | ||
5540 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5541 | characters in the result. | |
5542 | rad is output base | |
5543 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5544 | size_t | |
5545 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5546 | { |
1be6b49c ML |
5547 | size_t j = 1; |
5548 | size_t i; | |
2881e77b | 5549 | scm_t_uintmax n = num; |
5c11cc9d | 5550 | |
a6f3af16 AW |
5551 | if (rad < 2 || rad > 36) |
5552 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5553 | ||
f872b822 | 5554 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5555 | j++; |
5556 | ||
5557 | i = j; | |
2881e77b | 5558 | n = num; |
f872b822 MD |
5559 | while (i--) |
5560 | { | |
5c11cc9d GH |
5561 | int d = n % rad; |
5562 | ||
f872b822 | 5563 | n /= rad; |
a6f3af16 | 5564 | p[i] = number_chars[d]; |
f872b822 | 5565 | } |
0f2d19dd JB |
5566 | return j; |
5567 | } | |
5568 | ||
a1ec6916 | 5569 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5570 | (SCM n, SCM radix), |
5571 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5572 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5573 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5574 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5575 | { |
1bbd0b84 | 5576 | int base; |
98cb6e75 | 5577 | |
0aacf84e | 5578 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5579 | base = 10; |
0aacf84e | 5580 | else |
5efd3c7d | 5581 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5582 | |
e11e83f3 | 5583 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5584 | { |
5585 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5586 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5587 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5588 | } |
5589 | else if (SCM_BIGP (n)) | |
5590 | { | |
5591 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
d88f5323 AW |
5592 | size_t len = strlen (str); |
5593 | void (*freefunc) (void *, size_t); | |
5594 | SCM ret; | |
5595 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
0aacf84e | 5596 | scm_remember_upto_here_1 (n); |
d88f5323 AW |
5597 | ret = scm_from_latin1_stringn (str, len); |
5598 | freefunc (str, len + 1); | |
5599 | return ret; | |
0aacf84e | 5600 | } |
f92e85f7 MV |
5601 | else if (SCM_FRACTIONP (n)) |
5602 | { | |
f92e85f7 | 5603 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5604 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5605 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5606 | } | |
0aacf84e MD |
5607 | else if (SCM_INEXACTP (n)) |
5608 | { | |
5609 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5610 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5611 | } |
5612 | else | |
bb628794 | 5613 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5614 | } |
1bbd0b84 | 5615 | #undef FUNC_NAME |
0f2d19dd JB |
5616 | |
5617 | ||
ca46fb90 RB |
5618 | /* These print routines used to be stubbed here so that scm_repl.c |
5619 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5620 | |
0f2d19dd | 5621 | int |
e81d98ec | 5622 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5623 | { |
56e55ac7 | 5624 | char num_buf[FLOBUFLEN]; |
0b799eea | 5625 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5626 | return !0; |
5627 | } | |
5628 | ||
b479fe9a MV |
5629 | void |
5630 | scm_i_print_double (double val, SCM port) | |
5631 | { | |
5632 | char num_buf[FLOBUFLEN]; | |
5633 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5634 | } | |
5635 | ||
f3ae5d60 | 5636 | int |
e81d98ec | 5637 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5638 | |
f3ae5d60 | 5639 | { |
56e55ac7 | 5640 | char num_buf[FLOBUFLEN]; |
0b799eea | 5641 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5642 | return !0; |
5643 | } | |
1cc91f1b | 5644 | |
7a1aba42 MV |
5645 | void |
5646 | scm_i_print_complex (double real, double imag, SCM port) | |
5647 | { | |
5648 | char num_buf[FLOBUFLEN]; | |
5649 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5650 | } | |
5651 | ||
f92e85f7 MV |
5652 | int |
5653 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5654 | { | |
5655 | SCM str; | |
f92e85f7 | 5656 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5657 | scm_display (str, port); |
f92e85f7 MV |
5658 | scm_remember_upto_here_1 (str); |
5659 | return !0; | |
5660 | } | |
5661 | ||
0f2d19dd | 5662 | int |
e81d98ec | 5663 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5664 | { |
ca46fb90 | 5665 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
b57bf272 AW |
5666 | size_t len = strlen (str); |
5667 | void (*freefunc) (void *, size_t); | |
5668 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
ca46fb90 | 5669 | scm_remember_upto_here_1 (exp); |
b57bf272 AW |
5670 | scm_lfwrite (str, len, port); |
5671 | freefunc (str, len + 1); | |
0f2d19dd JB |
5672 | return !0; |
5673 | } | |
5674 | /*** END nums->strs ***/ | |
5675 | ||
3c9a524f | 5676 | |
0f2d19dd | 5677 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5678 | |
3c9a524f DH |
5679 | /* The following functions implement the conversion from strings to numbers. |
5680 | * The implementation somehow follows the grammar for numbers as it is given | |
5681 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5682 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5683 | * points should be noted about the implementation: | |
bc3d34f5 | 5684 | * |
3c9a524f DH |
5685 | * * Each function keeps a local index variable 'idx' that points at the |
5686 | * current position within the parsed string. The global index is only | |
5687 | * updated if the function could parse the corresponding syntactic unit | |
5688 | * successfully. | |
bc3d34f5 | 5689 | * |
3c9a524f | 5690 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5691 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5692 | * | |
3c9a524f DH |
5693 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5694 | * Only if these fixnums would overflow, the result variables are updated | |
5695 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5696 | * the temporary variables holding the fixnums are cleared, and the process | |
5697 | * starts over again. If for example fixnums were able to store five decimal | |
5698 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5699 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5700 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5701 | * |
5702 | * Notes on the handling of exactness specifiers: | |
5703 | * | |
5704 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5705 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5706 | * written in rectangular form, exactness specifiers are applied to the | |
5707 | * real and imaginary parts before calling scm_make_rectangular. For | |
5708 | * complex numbers written in polar form, exactness specifiers are applied | |
5709 | * to the magnitude and angle before calling scm_make_polar. | |
5710 | * | |
5711 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5712 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5713 | * the entire number, and applies to both components of a complex number. | |
5714 | * "#e" causes each component to be made exact, and "#i" causes each | |
5715 | * component to be made inexact. If no forced exactness specifier is | |
5716 | * present, then the exactness of each component is determined | |
5717 | * independently by the presence or absence of a decimal point or hash mark | |
5718 | * within that component. If a decimal point or hash mark is present, the | |
5719 | * component is made inexact, otherwise it is made exact. | |
5720 | * | |
5721 | * After the exactness specifiers have been applied to each component, they | |
5722 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5723 | * the final result. Note that this will result in a real number if the | |
5724 | * imaginary part, magnitude, or angle is an exact 0. | |
5725 | * | |
5726 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5727 | * | |
5728 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5729 | */ |
5730 | ||
5731 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5732 | ||
5733 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5734 | ||
a6f3af16 AW |
5735 | /* Caller is responsible for checking that the return value is in range |
5736 | for the given radix, which should be <= 36. */ | |
5737 | static unsigned int | |
5738 | char_decimal_value (scm_t_uint32 c) | |
5739 | { | |
5740 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5741 | that's certainly above any valid decimal, so we take advantage of | |
5742 | that to elide some tests. */ | |
5743 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5744 | ||
5745 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5746 | hexadecimals. */ | |
5747 | if (d >= 10U) | |
5748 | { | |
5749 | c = uc_tolower (c); | |
5750 | if (c >= (scm_t_uint32) 'a') | |
5751 | d = c - (scm_t_uint32)'a' + 10U; | |
5752 | } | |
5753 | return d; | |
5754 | } | |
3c9a524f | 5755 | |
91db4a37 LC |
5756 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5757 | in base RADIX. Upon success, return the unsigned integer and update | |
5758 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5759 | static SCM |
3f47e526 | 5760 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5761 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5762 | { |
3c9a524f DH |
5763 | unsigned int idx = *p_idx; |
5764 | unsigned int hash_seen = 0; | |
5765 | scm_t_bits shift = 1; | |
5766 | scm_t_bits add = 0; | |
5767 | unsigned int digit_value; | |
5768 | SCM result; | |
5769 | char c; | |
3f47e526 | 5770 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5771 | |
5772 | if (idx == len) | |
5773 | return SCM_BOOL_F; | |
2a8fecee | 5774 | |
3f47e526 | 5775 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5776 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5777 | if (digit_value >= radix) |
5778 | return SCM_BOOL_F; | |
5779 | ||
5780 | idx++; | |
d956fa6f | 5781 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5782 | while (idx != len) |
f872b822 | 5783 | { |
3f47e526 | 5784 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5785 | if (c == '#') |
3c9a524f DH |
5786 | { |
5787 | hash_seen = 1; | |
5788 | digit_value = 0; | |
5789 | } | |
a6f3af16 AW |
5790 | else if (hash_seen) |
5791 | break; | |
3c9a524f | 5792 | else |
a6f3af16 AW |
5793 | { |
5794 | digit_value = char_decimal_value (c); | |
5795 | /* This check catches non-decimals in addition to out-of-range | |
5796 | decimals. */ | |
5797 | if (digit_value >= radix) | |
5798 | break; | |
5799 | } | |
3c9a524f DH |
5800 | |
5801 | idx++; | |
5802 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5803 | { | |
d956fa6f | 5804 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5805 | if (add > 0) |
d956fa6f | 5806 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5807 | |
5808 | shift = radix; | |
5809 | add = digit_value; | |
5810 | } | |
5811 | else | |
5812 | { | |
5813 | shift = shift * radix; | |
5814 | add = add * radix + digit_value; | |
5815 | } | |
5816 | }; | |
5817 | ||
5818 | if (shift > 1) | |
d956fa6f | 5819 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5820 | if (add > 0) |
d956fa6f | 5821 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5822 | |
5823 | *p_idx = idx; | |
5824 | if (hash_seen) | |
5825 | *p_exactness = INEXACT; | |
5826 | ||
5827 | return result; | |
2a8fecee JB |
5828 | } |
5829 | ||
5830 | ||
3c9a524f DH |
5831 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5832 | * covers the parts of the rules that start at a potential point. The value | |
5833 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5834 | * in variable result. The content of *p_exactness indicates, whether a hash |
5835 | * has already been seen in the digits before the point. | |
3c9a524f | 5836 | */ |
1cc91f1b | 5837 | |
3f47e526 | 5838 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5839 | |
5840 | static SCM | |
3f47e526 | 5841 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5842 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5843 | { |
3c9a524f DH |
5844 | unsigned int idx = *p_idx; |
5845 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5846 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5847 | |
5848 | if (idx == len) | |
79d34f68 | 5849 | return result; |
3c9a524f | 5850 | |
3f47e526 | 5851 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5852 | { |
5853 | scm_t_bits shift = 1; | |
5854 | scm_t_bits add = 0; | |
5855 | unsigned int digit_value; | |
cff5fa33 | 5856 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5857 | |
5858 | idx++; | |
5859 | while (idx != len) | |
5860 | { | |
3f47e526 MG |
5861 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5862 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5863 | { |
5864 | if (x == INEXACT) | |
5865 | return SCM_BOOL_F; | |
5866 | else | |
5867 | digit_value = DIGIT2UINT (c); | |
5868 | } | |
5869 | else if (c == '#') | |
5870 | { | |
5871 | x = INEXACT; | |
5872 | digit_value = 0; | |
5873 | } | |
5874 | else | |
5875 | break; | |
5876 | ||
5877 | idx++; | |
5878 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5879 | { | |
d956fa6f MV |
5880 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5881 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5882 | if (add > 0) |
d956fa6f | 5883 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5884 | |
5885 | shift = 10; | |
5886 | add = digit_value; | |
5887 | } | |
5888 | else | |
5889 | { | |
5890 | shift = shift * 10; | |
5891 | add = add * 10 + digit_value; | |
5892 | } | |
5893 | }; | |
5894 | ||
5895 | if (add > 0) | |
5896 | { | |
d956fa6f MV |
5897 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5898 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5899 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5900 | } |
5901 | ||
d8592269 | 5902 | result = scm_divide (result, big_shift); |
79d34f68 | 5903 | |
3c9a524f DH |
5904 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5905 | x = INEXACT; | |
f872b822 | 5906 | } |
3c9a524f | 5907 | |
3c9a524f | 5908 | if (idx != len) |
f872b822 | 5909 | { |
3c9a524f DH |
5910 | int sign = 1; |
5911 | unsigned int start; | |
3f47e526 | 5912 | scm_t_wchar c; |
3c9a524f DH |
5913 | int exponent; |
5914 | SCM e; | |
5915 | ||
5916 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5917 | ||
3f47e526 | 5918 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5919 | { |
3c9a524f DH |
5920 | case 'd': case 'D': |
5921 | case 'e': case 'E': | |
5922 | case 'f': case 'F': | |
5923 | case 'l': case 'L': | |
5924 | case 's': case 'S': | |
5925 | idx++; | |
ee0ddd21 AW |
5926 | if (idx == len) |
5927 | return SCM_BOOL_F; | |
5928 | ||
3c9a524f | 5929 | start = idx; |
3f47e526 | 5930 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5931 | if (c == '-') |
5932 | { | |
5933 | idx++; | |
ee0ddd21 AW |
5934 | if (idx == len) |
5935 | return SCM_BOOL_F; | |
5936 | ||
3c9a524f | 5937 | sign = -1; |
3f47e526 | 5938 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5939 | } |
5940 | else if (c == '+') | |
5941 | { | |
5942 | idx++; | |
ee0ddd21 AW |
5943 | if (idx == len) |
5944 | return SCM_BOOL_F; | |
5945 | ||
3c9a524f | 5946 | sign = 1; |
3f47e526 | 5947 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5948 | } |
5949 | else | |
5950 | sign = 1; | |
5951 | ||
3f47e526 | 5952 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5953 | return SCM_BOOL_F; |
5954 | ||
5955 | idx++; | |
5956 | exponent = DIGIT2UINT (c); | |
5957 | while (idx != len) | |
f872b822 | 5958 | { |
3f47e526 MG |
5959 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5960 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5961 | { |
5962 | idx++; | |
5963 | if (exponent <= SCM_MAXEXP) | |
5964 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5965 | } | |
5966 | else | |
5967 | break; | |
f872b822 | 5968 | } |
3c9a524f | 5969 | |
1ea37620 | 5970 | if (exponent > ((sign == 1) ? SCM_MAXEXP : SCM_MAXEXP + DBL_DIG + 1)) |
f872b822 | 5971 | { |
3c9a524f | 5972 | size_t exp_len = idx - start; |
3f47e526 | 5973 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5974 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5975 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5976 | } |
3c9a524f | 5977 | |
d956fa6f | 5978 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5979 | if (sign == 1) |
5980 | result = scm_product (result, e); | |
5981 | else | |
6ebecdeb | 5982 | result = scm_divide (result, e); |
3c9a524f DH |
5983 | |
5984 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5985 | x = INEXACT; | |
5986 | ||
f872b822 | 5987 | break; |
3c9a524f | 5988 | |
f872b822 | 5989 | default: |
3c9a524f | 5990 | break; |
f872b822 | 5991 | } |
0f2d19dd | 5992 | } |
3c9a524f DH |
5993 | |
5994 | *p_idx = idx; | |
5995 | if (x == INEXACT) | |
5996 | *p_exactness = x; | |
5997 | ||
5998 | return result; | |
0f2d19dd | 5999 | } |
0f2d19dd | 6000 | |
3c9a524f DH |
6001 | |
6002 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
6003 | ||
6004 | static SCM | |
3f47e526 | 6005 | mem2ureal (SCM mem, unsigned int *p_idx, |
929d11b2 MW |
6006 | unsigned int radix, enum t_exactness forced_x, |
6007 | int allow_inf_or_nan) | |
0f2d19dd | 6008 | { |
3c9a524f | 6009 | unsigned int idx = *p_idx; |
164d2481 | 6010 | SCM result; |
3f47e526 | 6011 | size_t len = scm_i_string_length (mem); |
3c9a524f | 6012 | |
40f89215 NJ |
6013 | /* Start off believing that the number will be exact. This changes |
6014 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 6015 | enum t_exactness implicit_x = EXACT; |
40f89215 | 6016 | |
3c9a524f DH |
6017 | if (idx == len) |
6018 | return SCM_BOOL_F; | |
6019 | ||
929d11b2 MW |
6020 | if (allow_inf_or_nan && forced_x != EXACT && idx+5 <= len) |
6021 | switch (scm_i_string_ref (mem, idx)) | |
6022 | { | |
6023 | case 'i': case 'I': | |
6024 | switch (scm_i_string_ref (mem, idx + 1)) | |
6025 | { | |
6026 | case 'n': case 'N': | |
6027 | switch (scm_i_string_ref (mem, idx + 2)) | |
6028 | { | |
6029 | case 'f': case 'F': | |
6030 | if (scm_i_string_ref (mem, idx + 3) == '.' | |
6031 | && scm_i_string_ref (mem, idx + 4) == '0') | |
6032 | { | |
6033 | *p_idx = idx+5; | |
6034 | return scm_inf (); | |
6035 | } | |
6036 | } | |
6037 | } | |
6038 | case 'n': case 'N': | |
6039 | switch (scm_i_string_ref (mem, idx + 1)) | |
6040 | { | |
6041 | case 'a': case 'A': | |
6042 | switch (scm_i_string_ref (mem, idx + 2)) | |
6043 | { | |
6044 | case 'n': case 'N': | |
6045 | if (scm_i_string_ref (mem, idx + 3) == '.') | |
6046 | { | |
6047 | /* Cobble up the fractional part. We might want to | |
6048 | set the NaN's mantissa from it. */ | |
6049 | idx += 4; | |
6050 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), | |
6051 | SCM_INUM0)) | |
6052 | { | |
5f237d6e | 6053 | #if SCM_ENABLE_DEPRECATED == 1 |
929d11b2 MW |
6054 | scm_c_issue_deprecation_warning |
6055 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5f237d6e | 6056 | #else |
929d11b2 | 6057 | return SCM_BOOL_F; |
5f237d6e | 6058 | #endif |
929d11b2 | 6059 | } |
5f237d6e | 6060 | |
929d11b2 MW |
6061 | *p_idx = idx; |
6062 | return scm_nan (); | |
6063 | } | |
6064 | } | |
6065 | } | |
6066 | } | |
7351e207 | 6067 | |
3f47e526 | 6068 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
6069 | { |
6070 | if (radix != 10) | |
6071 | return SCM_BOOL_F; | |
6072 | else if (idx + 1 == len) | |
6073 | return SCM_BOOL_F; | |
3f47e526 | 6074 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
6075 | return SCM_BOOL_F; |
6076 | else | |
cff5fa33 | 6077 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 6078 | p_idx, &implicit_x); |
f872b822 | 6079 | } |
3c9a524f DH |
6080 | else |
6081 | { | |
3c9a524f | 6082 | SCM uinteger; |
3c9a524f | 6083 | |
9d427b2c | 6084 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 6085 | if (scm_is_false (uinteger)) |
3c9a524f DH |
6086 | return SCM_BOOL_F; |
6087 | ||
6088 | if (idx == len) | |
6089 | result = uinteger; | |
3f47e526 | 6090 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 6091 | { |
3c9a524f DH |
6092 | SCM divisor; |
6093 | ||
6094 | idx++; | |
ee0ddd21 AW |
6095 | if (idx == len) |
6096 | return SCM_BOOL_F; | |
3c9a524f | 6097 | |
9d427b2c | 6098 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
929d11b2 | 6099 | if (scm_is_false (divisor) || scm_is_eq (divisor, SCM_INUM0)) |
3c9a524f DH |
6100 | return SCM_BOOL_F; |
6101 | ||
f92e85f7 | 6102 | /* both are int/big here, I assume */ |
cba42c93 | 6103 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 6104 | } |
3c9a524f DH |
6105 | else if (radix == 10) |
6106 | { | |
9d427b2c | 6107 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 6108 | if (scm_is_false (result)) |
3c9a524f DH |
6109 | return SCM_BOOL_F; |
6110 | } | |
6111 | else | |
6112 | result = uinteger; | |
6113 | ||
6114 | *p_idx = idx; | |
f872b822 | 6115 | } |
164d2481 | 6116 | |
9d427b2c MW |
6117 | switch (forced_x) |
6118 | { | |
6119 | case EXACT: | |
6120 | if (SCM_INEXACTP (result)) | |
6121 | return scm_inexact_to_exact (result); | |
6122 | else | |
6123 | return result; | |
6124 | case INEXACT: | |
6125 | if (SCM_INEXACTP (result)) | |
6126 | return result; | |
6127 | else | |
6128 | return scm_exact_to_inexact (result); | |
6129 | case NO_EXACTNESS: | |
6130 | if (implicit_x == INEXACT) | |
6131 | { | |
6132 | if (SCM_INEXACTP (result)) | |
6133 | return result; | |
6134 | else | |
6135 | return scm_exact_to_inexact (result); | |
6136 | } | |
6137 | else | |
6138 | return result; | |
6139 | } | |
164d2481 | 6140 | |
9d427b2c MW |
6141 | /* We should never get here */ |
6142 | scm_syserror ("mem2ureal"); | |
3c9a524f | 6143 | } |
0f2d19dd | 6144 | |
0f2d19dd | 6145 | |
3c9a524f | 6146 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 6147 | |
3c9a524f | 6148 | static SCM |
3f47e526 | 6149 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 6150 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 6151 | { |
3f47e526 | 6152 | scm_t_wchar c; |
3c9a524f DH |
6153 | int sign = 0; |
6154 | SCM ureal; | |
3f47e526 | 6155 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6156 | |
6157 | if (idx == len) | |
6158 | return SCM_BOOL_F; | |
6159 | ||
3f47e526 | 6160 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6161 | if (c == '+') |
6162 | { | |
6163 | idx++; | |
6164 | sign = 1; | |
6165 | } | |
6166 | else if (c == '-') | |
6167 | { | |
6168 | idx++; | |
6169 | sign = -1; | |
0f2d19dd | 6170 | } |
0f2d19dd | 6171 | |
3c9a524f DH |
6172 | if (idx == len) |
6173 | return SCM_BOOL_F; | |
6174 | ||
929d11b2 | 6175 | ureal = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6176 | if (scm_is_false (ureal)) |
f872b822 | 6177 | { |
3c9a524f DH |
6178 | /* input must be either +i or -i */ |
6179 | ||
6180 | if (sign == 0) | |
6181 | return SCM_BOOL_F; | |
6182 | ||
3f47e526 MG |
6183 | if (scm_i_string_ref (mem, idx) == 'i' |
6184 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 6185 | { |
3c9a524f DH |
6186 | idx++; |
6187 | if (idx != len) | |
6188 | return SCM_BOOL_F; | |
6189 | ||
cff5fa33 | 6190 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 6191 | } |
3c9a524f DH |
6192 | else |
6193 | return SCM_BOOL_F; | |
0f2d19dd | 6194 | } |
3c9a524f DH |
6195 | else |
6196 | { | |
73e4de09 | 6197 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 6198 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 6199 | |
3c9a524f DH |
6200 | if (idx == len) |
6201 | return ureal; | |
6202 | ||
3f47e526 | 6203 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 6204 | switch (c) |
f872b822 | 6205 | { |
3c9a524f DH |
6206 | case 'i': case 'I': |
6207 | /* either +<ureal>i or -<ureal>i */ | |
6208 | ||
6209 | idx++; | |
6210 | if (sign == 0) | |
6211 | return SCM_BOOL_F; | |
6212 | if (idx != len) | |
6213 | return SCM_BOOL_F; | |
cff5fa33 | 6214 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
6215 | |
6216 | case '@': | |
6217 | /* polar input: <real>@<real>. */ | |
6218 | ||
6219 | idx++; | |
6220 | if (idx == len) | |
6221 | return SCM_BOOL_F; | |
6222 | else | |
f872b822 | 6223 | { |
3c9a524f DH |
6224 | int sign; |
6225 | SCM angle; | |
6226 | SCM result; | |
6227 | ||
3f47e526 | 6228 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6229 | if (c == '+') |
6230 | { | |
6231 | idx++; | |
ee0ddd21 AW |
6232 | if (idx == len) |
6233 | return SCM_BOOL_F; | |
3c9a524f DH |
6234 | sign = 1; |
6235 | } | |
6236 | else if (c == '-') | |
6237 | { | |
6238 | idx++; | |
ee0ddd21 AW |
6239 | if (idx == len) |
6240 | return SCM_BOOL_F; | |
3c9a524f DH |
6241 | sign = -1; |
6242 | } | |
6243 | else | |
929d11b2 | 6244 | sign = 0; |
3c9a524f | 6245 | |
929d11b2 | 6246 | angle = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6247 | if (scm_is_false (angle)) |
3c9a524f DH |
6248 | return SCM_BOOL_F; |
6249 | if (idx != len) | |
6250 | return SCM_BOOL_F; | |
6251 | ||
73e4de09 | 6252 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
6253 | angle = scm_difference (angle, SCM_UNDEFINED); |
6254 | ||
6255 | result = scm_make_polar (ureal, angle); | |
6256 | return result; | |
f872b822 | 6257 | } |
3c9a524f DH |
6258 | case '+': |
6259 | case '-': | |
6260 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 6261 | |
3c9a524f DH |
6262 | idx++; |
6263 | if (idx == len) | |
6264 | return SCM_BOOL_F; | |
6265 | else | |
6266 | { | |
6267 | int sign = (c == '+') ? 1 : -1; | |
929d11b2 | 6268 | SCM imag = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
0f2d19dd | 6269 | |
73e4de09 | 6270 | if (scm_is_false (imag)) |
d956fa6f | 6271 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 6272 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 6273 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 6274 | |
3c9a524f DH |
6275 | if (idx == len) |
6276 | return SCM_BOOL_F; | |
3f47e526 MG |
6277 | if (scm_i_string_ref (mem, idx) != 'i' |
6278 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 6279 | return SCM_BOOL_F; |
0f2d19dd | 6280 | |
3c9a524f DH |
6281 | idx++; |
6282 | if (idx != len) | |
6283 | return SCM_BOOL_F; | |
0f2d19dd | 6284 | |
1fe5e088 | 6285 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6286 | } |
6287 | default: | |
6288 | return SCM_BOOL_F; | |
6289 | } | |
6290 | } | |
0f2d19dd | 6291 | } |
0f2d19dd JB |
6292 | |
6293 | ||
3c9a524f DH |
6294 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6295 | ||
6296 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6297 | |
0f2d19dd | 6298 | SCM |
3f47e526 | 6299 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6300 | { |
3c9a524f DH |
6301 | unsigned int idx = 0; |
6302 | unsigned int radix = NO_RADIX; | |
6303 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6304 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6305 | |
6306 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6307 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6308 | { |
3f47e526 | 6309 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6310 | { |
6311 | case 'b': case 'B': | |
6312 | if (radix != NO_RADIX) | |
6313 | return SCM_BOOL_F; | |
6314 | radix = DUAL; | |
6315 | break; | |
6316 | case 'd': case 'D': | |
6317 | if (radix != NO_RADIX) | |
6318 | return SCM_BOOL_F; | |
6319 | radix = DEC; | |
6320 | break; | |
6321 | case 'i': case 'I': | |
6322 | if (forced_x != NO_EXACTNESS) | |
6323 | return SCM_BOOL_F; | |
6324 | forced_x = INEXACT; | |
6325 | break; | |
6326 | case 'e': case 'E': | |
6327 | if (forced_x != NO_EXACTNESS) | |
6328 | return SCM_BOOL_F; | |
6329 | forced_x = EXACT; | |
6330 | break; | |
6331 | case 'o': case 'O': | |
6332 | if (radix != NO_RADIX) | |
6333 | return SCM_BOOL_F; | |
6334 | radix = OCT; | |
6335 | break; | |
6336 | case 'x': case 'X': | |
6337 | if (radix != NO_RADIX) | |
6338 | return SCM_BOOL_F; | |
6339 | radix = HEX; | |
6340 | break; | |
6341 | default: | |
f872b822 | 6342 | return SCM_BOOL_F; |
3c9a524f DH |
6343 | } |
6344 | idx += 2; | |
6345 | } | |
6346 | ||
6347 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6348 | if (radix == NO_RADIX) | |
9d427b2c | 6349 | radix = default_radix; |
f872b822 | 6350 | |
9d427b2c | 6351 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6352 | } |
6353 | ||
3f47e526 MG |
6354 | SCM |
6355 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6356 | unsigned int default_radix) | |
6357 | { | |
6358 | SCM str = scm_from_locale_stringn (mem, len); | |
6359 | ||
6360 | return scm_i_string_to_number (str, default_radix); | |
6361 | } | |
6362 | ||
0f2d19dd | 6363 | |
a1ec6916 | 6364 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6365 | (SCM string, SCM radix), |
1e6808ea | 6366 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6367 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6368 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6369 | "is a default radix that may be overridden by an explicit radix\n" | |
6370 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6371 | "supplied, then the default radix is 10. If string is not a\n" | |
6372 | "syntactically valid notation for a number, then\n" | |
6373 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6374 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6375 | { |
6376 | SCM answer; | |
5efd3c7d | 6377 | unsigned int base; |
a6d9e5ab | 6378 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6379 | |
6380 | if (SCM_UNBNDP (radix)) | |
6381 | base = 10; | |
6382 | else | |
6383 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6384 | ||
3f47e526 | 6385 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6386 | scm_remember_upto_here_1 (string); |
6387 | return answer; | |
0f2d19dd | 6388 | } |
1bbd0b84 | 6389 | #undef FUNC_NAME |
3c9a524f DH |
6390 | |
6391 | ||
0f2d19dd JB |
6392 | /*** END strs->nums ***/ |
6393 | ||
5986c47d | 6394 | |
8507ec80 MV |
6395 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6396 | (SCM x), | |
6397 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6398 | "otherwise.") | |
6399 | #define FUNC_NAME s_scm_number_p | |
6400 | { | |
6401 | return scm_from_bool (SCM_NUMBERP (x)); | |
6402 | } | |
6403 | #undef FUNC_NAME | |
6404 | ||
6405 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6406 | (SCM x), |
942e5b91 | 6407 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6408 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6409 | "values form subsets of the set of complex numbers, i. e. the\n" |
6410 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6411 | "rational or integer number.") | |
8507ec80 | 6412 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6413 | { |
8507ec80 MV |
6414 | /* all numbers are complex. */ |
6415 | return scm_number_p (x); | |
0f2d19dd | 6416 | } |
1bbd0b84 | 6417 | #undef FUNC_NAME |
0f2d19dd | 6418 | |
f92e85f7 MV |
6419 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6420 | (SCM x), | |
6421 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6422 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6423 | "the set of real numbers, i. e. the predicate will also be\n" | |
6424 | "fulfilled if @var{x} is an integer number.") | |
6425 | #define FUNC_NAME s_scm_real_p | |
6426 | { | |
c960e556 MW |
6427 | return scm_from_bool |
6428 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6429 | } |
6430 | #undef FUNC_NAME | |
6431 | ||
6432 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6433 | (SCM x), |
942e5b91 | 6434 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6435 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6436 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6437 | "fulfilled if @var{x} is an integer number.") |
6438 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6439 | { |
c960e556 | 6440 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6441 | return SCM_BOOL_T; |
6442 | else if (SCM_REALP (x)) | |
c960e556 MW |
6443 | /* due to their limited precision, finite floating point numbers are |
6444 | rational as well. (finite means neither infinity nor a NaN) */ | |
6445 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6446 | else |
bb628794 | 6447 | return SCM_BOOL_F; |
0f2d19dd | 6448 | } |
1bbd0b84 | 6449 | #undef FUNC_NAME |
0f2d19dd | 6450 | |
a1ec6916 | 6451 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6452 | (SCM x), |
942e5b91 MG |
6453 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6454 | "else.") | |
1bbd0b84 | 6455 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6456 | { |
c960e556 | 6457 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6458 | return SCM_BOOL_T; |
c960e556 MW |
6459 | else if (SCM_REALP (x)) |
6460 | { | |
6461 | double val = SCM_REAL_VALUE (x); | |
6462 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6463 | } | |
6464 | else | |
8e43ed5d | 6465 | return SCM_BOOL_F; |
0f2d19dd | 6466 | } |
1bbd0b84 | 6467 | #undef FUNC_NAME |
0f2d19dd JB |
6468 | |
6469 | ||
8a1f4f98 AW |
6470 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6471 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6472 | (SCM x, SCM y, SCM rest), | |
6473 | "Return @code{#t} if all parameters are numerically equal.") | |
6474 | #define FUNC_NAME s_scm_i_num_eq_p | |
6475 | { | |
6476 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6477 | return SCM_BOOL_T; | |
6478 | while (!scm_is_null (rest)) | |
6479 | { | |
6480 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6481 | return SCM_BOOL_F; | |
6482 | x = y; | |
6483 | y = scm_car (rest); | |
6484 | rest = scm_cdr (rest); | |
6485 | } | |
6486 | return scm_num_eq_p (x, y); | |
6487 | } | |
6488 | #undef FUNC_NAME | |
0f2d19dd | 6489 | SCM |
6e8d25a6 | 6490 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6491 | { |
d8b95e27 | 6492 | again: |
e11e83f3 | 6493 | if (SCM_I_INUMP (x)) |
0aacf84e | 6494 | { |
e25f3727 | 6495 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6496 | if (SCM_I_INUMP (y)) |
0aacf84e | 6497 | { |
e25f3727 | 6498 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6499 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6500 | } |
6501 | else if (SCM_BIGP (y)) | |
6502 | return SCM_BOOL_F; | |
6503 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6504 | { |
6505 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6506 | to a double and compare. | |
6507 | ||
6508 | But on a 64-bit system an inum is bigger than a double and | |
6509 | casting it to a double (call that dxx) will round. dxx is at | |
6510 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6511 | an integer and fits a long. So we cast yy to a long and | |
6512 | compare with plain xx. | |
6513 | ||
6514 | An alternative (for any size system actually) would be to check | |
6515 | yy is an integer (with floor) and is in range of an inum | |
6516 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6517 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6518 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6519 | |
6520 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6521 | return scm_from_bool ((double) xx == yy |
6522 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6523 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6524 | } |
0aacf84e | 6525 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6526 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6527 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6528 | else if (SCM_FRACTIONP (y)) |
6529 | return SCM_BOOL_F; | |
0aacf84e | 6530 | else |
8a1f4f98 | 6531 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6532 | } |
0aacf84e MD |
6533 | else if (SCM_BIGP (x)) |
6534 | { | |
e11e83f3 | 6535 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6536 | return SCM_BOOL_F; |
6537 | else if (SCM_BIGP (y)) | |
6538 | { | |
6539 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6540 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6541 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6542 | } |
6543 | else if (SCM_REALP (y)) | |
6544 | { | |
6545 | int cmp; | |
2e65b52f | 6546 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6547 | return SCM_BOOL_F; |
6548 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6549 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6550 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6551 | } |
6552 | else if (SCM_COMPLEXP (y)) | |
6553 | { | |
6554 | int cmp; | |
6555 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6556 | return SCM_BOOL_F; | |
2e65b52f | 6557 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6558 | return SCM_BOOL_F; |
6559 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6560 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6561 | return scm_from_bool (0 == cmp); |
0aacf84e | 6562 | } |
f92e85f7 MV |
6563 | else if (SCM_FRACTIONP (y)) |
6564 | return SCM_BOOL_F; | |
0aacf84e | 6565 | else |
8a1f4f98 | 6566 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6567 | } |
0aacf84e MD |
6568 | else if (SCM_REALP (x)) |
6569 | { | |
e8c5b1f2 | 6570 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6571 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6572 | { |
6573 | /* see comments with inum/real above */ | |
e25f3727 | 6574 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6575 | return scm_from_bool (xx == (double) yy |
6576 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6577 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6578 | } |
0aacf84e MD |
6579 | else if (SCM_BIGP (y)) |
6580 | { | |
6581 | int cmp; | |
2e65b52f | 6582 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6583 | return SCM_BOOL_F; |
6584 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6585 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6586 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6587 | } |
6588 | else if (SCM_REALP (y)) | |
73e4de09 | 6589 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6590 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6591 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6592 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6593 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6594 | { |
6595 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6596 | if (isnan (xx)) |
d8b95e27 | 6597 | return SCM_BOOL_F; |
2e65b52f | 6598 | if (isinf (xx)) |
73e4de09 | 6599 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6600 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6601 | goto again; | |
6602 | } | |
0aacf84e | 6603 | else |
8a1f4f98 | 6604 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6605 | } |
0aacf84e MD |
6606 | else if (SCM_COMPLEXP (x)) |
6607 | { | |
e11e83f3 MV |
6608 | if (SCM_I_INUMP (y)) |
6609 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6610 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6611 | else if (SCM_BIGP (y)) | |
6612 | { | |
6613 | int cmp; | |
6614 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6615 | return SCM_BOOL_F; | |
2e65b52f | 6616 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6617 | return SCM_BOOL_F; |
6618 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6619 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6620 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6621 | } |
6622 | else if (SCM_REALP (y)) | |
73e4de09 | 6623 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6624 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6625 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6626 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6627 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6628 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6629 | { |
6630 | double xx; | |
6631 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6632 | return SCM_BOOL_F; | |
6633 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6634 | if (isnan (xx)) |
d8b95e27 | 6635 | return SCM_BOOL_F; |
2e65b52f | 6636 | if (isinf (xx)) |
73e4de09 | 6637 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6638 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6639 | goto again; | |
6640 | } | |
f92e85f7 | 6641 | else |
8a1f4f98 | 6642 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6643 | } |
6644 | else if (SCM_FRACTIONP (x)) | |
6645 | { | |
e11e83f3 | 6646 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6647 | return SCM_BOOL_F; |
6648 | else if (SCM_BIGP (y)) | |
6649 | return SCM_BOOL_F; | |
6650 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6651 | { |
6652 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6653 | if (isnan (yy)) |
d8b95e27 | 6654 | return SCM_BOOL_F; |
2e65b52f | 6655 | if (isinf (yy)) |
73e4de09 | 6656 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6657 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6658 | goto again; | |
6659 | } | |
f92e85f7 | 6660 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6661 | { |
6662 | double yy; | |
6663 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6664 | return SCM_BOOL_F; | |
6665 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6666 | if (isnan (yy)) |
d8b95e27 | 6667 | return SCM_BOOL_F; |
2e65b52f | 6668 | if (isinf (yy)) |
73e4de09 | 6669 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6670 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6671 | goto again; | |
6672 | } | |
f92e85f7 MV |
6673 | else if (SCM_FRACTIONP (y)) |
6674 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6675 | else |
8a1f4f98 | 6676 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6677 | } |
0aacf84e | 6678 | else |
8a1f4f98 | 6679 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6680 | } |
6681 | ||
6682 | ||
a5f0b599 KR |
6683 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6684 | done are good for inums, but for bignums an answer can almost always be | |
6685 | had by just examining a few high bits of the operands, as done by GMP in | |
6686 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6687 | of the float exponent to take into account. */ | |
6688 | ||
8c93b597 | 6689 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6690 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6691 | (SCM x, SCM y, SCM rest), | |
6692 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6693 | "increasing.") | |
6694 | #define FUNC_NAME s_scm_i_num_less_p | |
6695 | { | |
6696 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6697 | return SCM_BOOL_T; | |
6698 | while (!scm_is_null (rest)) | |
6699 | { | |
6700 | if (scm_is_false (scm_less_p (x, y))) | |
6701 | return SCM_BOOL_F; | |
6702 | x = y; | |
6703 | y = scm_car (rest); | |
6704 | rest = scm_cdr (rest); | |
6705 | } | |
6706 | return scm_less_p (x, y); | |
6707 | } | |
6708 | #undef FUNC_NAME | |
0f2d19dd | 6709 | SCM |
6e8d25a6 | 6710 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6711 | { |
a5f0b599 | 6712 | again: |
e11e83f3 | 6713 | if (SCM_I_INUMP (x)) |
0aacf84e | 6714 | { |
e25f3727 | 6715 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6716 | if (SCM_I_INUMP (y)) |
0aacf84e | 6717 | { |
e25f3727 | 6718 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6719 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6720 | } |
6721 | else if (SCM_BIGP (y)) | |
6722 | { | |
6723 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6724 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6725 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6726 | } |
6727 | else if (SCM_REALP (y)) | |
73e4de09 | 6728 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6729 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6730 | { |
6731 | /* "x < a/b" becomes "x*b < a" */ | |
6732 | int_frac: | |
6733 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6734 | y = SCM_FRACTION_NUMERATOR (y); | |
6735 | goto again; | |
6736 | } | |
0aacf84e | 6737 | else |
8a1f4f98 | 6738 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6739 | } |
0aacf84e MD |
6740 | else if (SCM_BIGP (x)) |
6741 | { | |
e11e83f3 | 6742 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6743 | { |
6744 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6745 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6746 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6747 | } |
6748 | else if (SCM_BIGP (y)) | |
6749 | { | |
6750 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6751 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6752 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6753 | } |
6754 | else if (SCM_REALP (y)) | |
6755 | { | |
6756 | int cmp; | |
2e65b52f | 6757 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6758 | return SCM_BOOL_F; |
6759 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6760 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6761 | return scm_from_bool (cmp < 0); |
0aacf84e | 6762 | } |
f92e85f7 | 6763 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6764 | goto int_frac; |
0aacf84e | 6765 | else |
8a1f4f98 | 6766 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6767 | } |
0aacf84e MD |
6768 | else if (SCM_REALP (x)) |
6769 | { | |
e11e83f3 MV |
6770 | if (SCM_I_INUMP (y)) |
6771 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6772 | else if (SCM_BIGP (y)) |
6773 | { | |
6774 | int cmp; | |
2e65b52f | 6775 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6776 | return SCM_BOOL_F; |
6777 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6778 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6779 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6780 | } |
6781 | else if (SCM_REALP (y)) | |
73e4de09 | 6782 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6783 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6784 | { |
6785 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6786 | if (isnan (xx)) |
a5f0b599 | 6787 | return SCM_BOOL_F; |
2e65b52f | 6788 | if (isinf (xx)) |
73e4de09 | 6789 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6790 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6791 | goto again; | |
6792 | } | |
f92e85f7 | 6793 | else |
8a1f4f98 | 6794 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6795 | } |
6796 | else if (SCM_FRACTIONP (x)) | |
6797 | { | |
e11e83f3 | 6798 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6799 | { |
6800 | /* "a/b < y" becomes "a < y*b" */ | |
6801 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6802 | x = SCM_FRACTION_NUMERATOR (x); | |
6803 | goto again; | |
6804 | } | |
f92e85f7 | 6805 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6806 | { |
6807 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6808 | if (isnan (yy)) |
a5f0b599 | 6809 | return SCM_BOOL_F; |
2e65b52f | 6810 | if (isinf (yy)) |
73e4de09 | 6811 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6812 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6813 | goto again; | |
6814 | } | |
f92e85f7 | 6815 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6816 | { |
6817 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6818 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6819 | SCM_FRACTION_DENOMINATOR (y)); | |
6820 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6821 | SCM_FRACTION_DENOMINATOR (x)); | |
6822 | x = new_x; | |
6823 | y = new_y; | |
6824 | goto again; | |
6825 | } | |
0aacf84e | 6826 | else |
8a1f4f98 | 6827 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6828 | } |
0aacf84e | 6829 | else |
8a1f4f98 | 6830 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6831 | } |
6832 | ||
6833 | ||
8a1f4f98 AW |
6834 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6835 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6836 | (SCM x, SCM y, SCM rest), | |
6837 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6838 | "decreasing.") | |
6839 | #define FUNC_NAME s_scm_i_num_gr_p | |
6840 | { | |
6841 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6842 | return SCM_BOOL_T; | |
6843 | while (!scm_is_null (rest)) | |
6844 | { | |
6845 | if (scm_is_false (scm_gr_p (x, y))) | |
6846 | return SCM_BOOL_F; | |
6847 | x = y; | |
6848 | y = scm_car (rest); | |
6849 | rest = scm_cdr (rest); | |
6850 | } | |
6851 | return scm_gr_p (x, y); | |
6852 | } | |
6853 | #undef FUNC_NAME | |
6854 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6855 | SCM |
6856 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6857 | { |
c76b1eaf | 6858 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6859 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6860 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6861 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6862 | else |
6863 | return scm_less_p (y, x); | |
0f2d19dd | 6864 | } |
1bbd0b84 | 6865 | #undef FUNC_NAME |
0f2d19dd JB |
6866 | |
6867 | ||
8a1f4f98 AW |
6868 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6869 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6870 | (SCM x, SCM y, SCM rest), | |
6871 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6872 | "non-decreasing.") | |
6873 | #define FUNC_NAME s_scm_i_num_leq_p | |
6874 | { | |
6875 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6876 | return SCM_BOOL_T; | |
6877 | while (!scm_is_null (rest)) | |
6878 | { | |
6879 | if (scm_is_false (scm_leq_p (x, y))) | |
6880 | return SCM_BOOL_F; | |
6881 | x = y; | |
6882 | y = scm_car (rest); | |
6883 | rest = scm_cdr (rest); | |
6884 | } | |
6885 | return scm_leq_p (x, y); | |
6886 | } | |
6887 | #undef FUNC_NAME | |
6888 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6889 | SCM |
6890 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6891 | { |
c76b1eaf | 6892 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6893 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6894 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6895 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6896 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6897 | return SCM_BOOL_F; |
c76b1eaf | 6898 | else |
73e4de09 | 6899 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6900 | } |
1bbd0b84 | 6901 | #undef FUNC_NAME |
0f2d19dd JB |
6902 | |
6903 | ||
8a1f4f98 AW |
6904 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6905 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6906 | (SCM x, SCM y, SCM rest), | |
6907 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6908 | "non-increasing.") | |
6909 | #define FUNC_NAME s_scm_i_num_geq_p | |
6910 | { | |
6911 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6912 | return SCM_BOOL_T; | |
6913 | while (!scm_is_null (rest)) | |
6914 | { | |
6915 | if (scm_is_false (scm_geq_p (x, y))) | |
6916 | return SCM_BOOL_F; | |
6917 | x = y; | |
6918 | y = scm_car (rest); | |
6919 | rest = scm_cdr (rest); | |
6920 | } | |
6921 | return scm_geq_p (x, y); | |
6922 | } | |
6923 | #undef FUNC_NAME | |
6924 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6925 | SCM |
6926 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6927 | { |
c76b1eaf | 6928 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6929 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6930 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6931 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6932 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6933 | return SCM_BOOL_F; |
c76b1eaf | 6934 | else |
73e4de09 | 6935 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6936 | } |
1bbd0b84 | 6937 | #undef FUNC_NAME |
0f2d19dd JB |
6938 | |
6939 | ||
2519490c MW |
6940 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6941 | (SCM z), | |
6942 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6943 | "zero.") | |
6944 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6945 | { |
e11e83f3 | 6946 | if (SCM_I_INUMP (z)) |
bc36d050 | 6947 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6948 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6949 | return SCM_BOOL_F; |
0aacf84e | 6950 | else if (SCM_REALP (z)) |
73e4de09 | 6951 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6952 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6953 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6954 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6955 | else if (SCM_FRACTIONP (z)) |
6956 | return SCM_BOOL_F; | |
0aacf84e | 6957 | else |
2519490c | 6958 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6959 | } |
2519490c | 6960 | #undef FUNC_NAME |
0f2d19dd JB |
6961 | |
6962 | ||
2519490c MW |
6963 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6964 | (SCM x), | |
6965 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6966 | "zero.") | |
6967 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6968 | { |
e11e83f3 MV |
6969 | if (SCM_I_INUMP (x)) |
6970 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6971 | else if (SCM_BIGP (x)) |
6972 | { | |
6973 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6974 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6975 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6976 | } |
6977 | else if (SCM_REALP (x)) | |
73e4de09 | 6978 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6979 | else if (SCM_FRACTIONP (x)) |
6980 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6981 | else |
2519490c | 6982 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6983 | } |
2519490c | 6984 | #undef FUNC_NAME |
0f2d19dd JB |
6985 | |
6986 | ||
2519490c MW |
6987 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6988 | (SCM x), | |
6989 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6990 | "zero.") | |
6991 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6992 | { |
e11e83f3 MV |
6993 | if (SCM_I_INUMP (x)) |
6994 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6995 | else if (SCM_BIGP (x)) |
6996 | { | |
6997 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6998 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6999 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
7000 | } |
7001 | else if (SCM_REALP (x)) | |
73e4de09 | 7002 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
7003 | else if (SCM_FRACTIONP (x)) |
7004 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7005 | else |
2519490c | 7006 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 7007 | } |
2519490c | 7008 | #undef FUNC_NAME |
0f2d19dd JB |
7009 | |
7010 | ||
2a06f791 KR |
7011 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
7012 | required by r5rs. On that basis, for exact/inexact combinations the | |
7013 | exact is converted to inexact to compare and possibly return. This is | |
7014 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
7015 | its test, such trouble is not required for min and max. */ | |
7016 | ||
78d3deb1 AW |
7017 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
7018 | (SCM x, SCM y, SCM rest), | |
7019 | "Return the maximum of all parameter values.") | |
7020 | #define FUNC_NAME s_scm_i_max | |
7021 | { | |
7022 | while (!scm_is_null (rest)) | |
7023 | { x = scm_max (x, y); | |
7024 | y = scm_car (rest); | |
7025 | rest = scm_cdr (rest); | |
7026 | } | |
7027 | return scm_max (x, y); | |
7028 | } | |
7029 | #undef FUNC_NAME | |
7030 | ||
7031 | #define s_max s_scm_i_max | |
7032 | #define g_max g_scm_i_max | |
7033 | ||
0f2d19dd | 7034 | SCM |
6e8d25a6 | 7035 | scm_max (SCM x, SCM y) |
0f2d19dd | 7036 | { |
0aacf84e MD |
7037 | if (SCM_UNBNDP (y)) |
7038 | { | |
7039 | if (SCM_UNBNDP (x)) | |
7040 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 7041 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7042 | return x; |
7043 | else | |
7044 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 7045 | } |
f4c627b3 | 7046 | |
e11e83f3 | 7047 | if (SCM_I_INUMP (x)) |
0aacf84e | 7048 | { |
e25f3727 | 7049 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7050 | if (SCM_I_INUMP (y)) |
0aacf84e | 7051 | { |
e25f3727 | 7052 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7053 | return (xx < yy) ? y : x; |
7054 | } | |
7055 | else if (SCM_BIGP (y)) | |
7056 | { | |
7057 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7058 | scm_remember_upto_here_1 (y); | |
7059 | return (sgn < 0) ? x : y; | |
7060 | } | |
7061 | else if (SCM_REALP (y)) | |
7062 | { | |
2e274311 MW |
7063 | double xxd = xx; |
7064 | double yyd = SCM_REAL_VALUE (y); | |
7065 | ||
7066 | if (xxd > yyd) | |
7067 | return scm_from_double (xxd); | |
7068 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
7069 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7070 | return y; | |
7071 | /* Handle signed zeroes properly */ | |
7072 | else if (xx == 0) | |
7073 | return flo0; | |
7074 | else | |
7075 | return y; | |
0aacf84e | 7076 | } |
f92e85f7 MV |
7077 | else if (SCM_FRACTIONP (y)) |
7078 | { | |
e4bc5d6c | 7079 | use_less: |
73e4de09 | 7080 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 7081 | } |
0aacf84e MD |
7082 | else |
7083 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7084 | } |
0aacf84e MD |
7085 | else if (SCM_BIGP (x)) |
7086 | { | |
e11e83f3 | 7087 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7088 | { |
7089 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7090 | scm_remember_upto_here_1 (x); | |
7091 | return (sgn < 0) ? y : x; | |
7092 | } | |
7093 | else if (SCM_BIGP (y)) | |
7094 | { | |
7095 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7096 | scm_remember_upto_here_2 (x, y); | |
7097 | return (cmp > 0) ? x : y; | |
7098 | } | |
7099 | else if (SCM_REALP (y)) | |
7100 | { | |
2a06f791 KR |
7101 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
7102 | double xx, yy; | |
7103 | big_real: | |
7104 | xx = scm_i_big2dbl (x); | |
7105 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7106 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 7107 | } |
f92e85f7 MV |
7108 | else if (SCM_FRACTIONP (y)) |
7109 | { | |
e4bc5d6c | 7110 | goto use_less; |
f92e85f7 | 7111 | } |
0aacf84e MD |
7112 | else |
7113 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 7114 | } |
0aacf84e MD |
7115 | else if (SCM_REALP (x)) |
7116 | { | |
e11e83f3 | 7117 | if (SCM_I_INUMP (y)) |
0aacf84e | 7118 | { |
2e274311 MW |
7119 | scm_t_inum yy = SCM_I_INUM (y); |
7120 | double xxd = SCM_REAL_VALUE (x); | |
7121 | double yyd = yy; | |
7122 | ||
7123 | if (yyd > xxd) | |
7124 | return scm_from_double (yyd); | |
7125 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
7126 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7127 | return x; | |
7128 | /* Handle signed zeroes properly */ | |
7129 | else if (yy == 0) | |
7130 | return flo0; | |
7131 | else | |
7132 | return x; | |
0aacf84e MD |
7133 | } |
7134 | else if (SCM_BIGP (y)) | |
7135 | { | |
b6f8f763 | 7136 | SCM_SWAP (x, y); |
2a06f791 | 7137 | goto big_real; |
0aacf84e MD |
7138 | } |
7139 | else if (SCM_REALP (y)) | |
7140 | { | |
0aacf84e | 7141 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7142 | double yy = SCM_REAL_VALUE (y); |
7143 | ||
7144 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
7145 | if (xx > yy) | |
7146 | return x; | |
7147 | else if (SCM_LIKELY (xx < yy)) | |
7148 | return y; | |
7149 | /* If neither (xx > yy) nor (xx < yy), then | |
7150 | either they're equal or one is a NaN */ | |
7151 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7152 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 7153 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7154 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7155 | /* xx == yy, but handle signed zeroes properly */ |
7156 | else if (double_is_non_negative_zero (yy)) | |
7157 | return y; | |
7158 | else | |
7159 | return x; | |
0aacf84e | 7160 | } |
f92e85f7 MV |
7161 | else if (SCM_FRACTIONP (y)) |
7162 | { | |
7163 | double yy = scm_i_fraction2double (y); | |
7164 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7165 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
7166 | } |
7167 | else | |
7168 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
7169 | } | |
7170 | else if (SCM_FRACTIONP (x)) | |
7171 | { | |
e11e83f3 | 7172 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7173 | { |
e4bc5d6c | 7174 | goto use_less; |
f92e85f7 MV |
7175 | } |
7176 | else if (SCM_BIGP (y)) | |
7177 | { | |
e4bc5d6c | 7178 | goto use_less; |
f92e85f7 MV |
7179 | } |
7180 | else if (SCM_REALP (y)) | |
7181 | { | |
7182 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7183 | /* if y==NaN then ">" is false, so we return the NaN y */ |
7184 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7185 | } |
7186 | else if (SCM_FRACTIONP (y)) | |
7187 | { | |
e4bc5d6c | 7188 | goto use_less; |
f92e85f7 | 7189 | } |
0aacf84e MD |
7190 | else |
7191 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7192 | } |
0aacf84e | 7193 | else |
f4c627b3 | 7194 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
7195 | } |
7196 | ||
7197 | ||
78d3deb1 AW |
7198 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
7199 | (SCM x, SCM y, SCM rest), | |
7200 | "Return the minimum of all parameter values.") | |
7201 | #define FUNC_NAME s_scm_i_min | |
7202 | { | |
7203 | while (!scm_is_null (rest)) | |
7204 | { x = scm_min (x, y); | |
7205 | y = scm_car (rest); | |
7206 | rest = scm_cdr (rest); | |
7207 | } | |
7208 | return scm_min (x, y); | |
7209 | } | |
7210 | #undef FUNC_NAME | |
7211 | ||
7212 | #define s_min s_scm_i_min | |
7213 | #define g_min g_scm_i_min | |
7214 | ||
0f2d19dd | 7215 | SCM |
6e8d25a6 | 7216 | scm_min (SCM x, SCM y) |
0f2d19dd | 7217 | { |
0aacf84e MD |
7218 | if (SCM_UNBNDP (y)) |
7219 | { | |
7220 | if (SCM_UNBNDP (x)) | |
7221 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 7222 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7223 | return x; |
7224 | else | |
7225 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 7226 | } |
f4c627b3 | 7227 | |
e11e83f3 | 7228 | if (SCM_I_INUMP (x)) |
0aacf84e | 7229 | { |
e25f3727 | 7230 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7231 | if (SCM_I_INUMP (y)) |
0aacf84e | 7232 | { |
e25f3727 | 7233 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7234 | return (xx < yy) ? x : y; |
7235 | } | |
7236 | else if (SCM_BIGP (y)) | |
7237 | { | |
7238 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7239 | scm_remember_upto_here_1 (y); | |
7240 | return (sgn < 0) ? y : x; | |
7241 | } | |
7242 | else if (SCM_REALP (y)) | |
7243 | { | |
7244 | double z = xx; | |
7245 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 7246 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 7247 | } |
f92e85f7 MV |
7248 | else if (SCM_FRACTIONP (y)) |
7249 | { | |
e4bc5d6c | 7250 | use_less: |
73e4de09 | 7251 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 7252 | } |
0aacf84e MD |
7253 | else |
7254 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7255 | } |
0aacf84e MD |
7256 | else if (SCM_BIGP (x)) |
7257 | { | |
e11e83f3 | 7258 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7259 | { |
7260 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7261 | scm_remember_upto_here_1 (x); | |
7262 | return (sgn < 0) ? x : y; | |
7263 | } | |
7264 | else if (SCM_BIGP (y)) | |
7265 | { | |
7266 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7267 | scm_remember_upto_here_2 (x, y); | |
7268 | return (cmp > 0) ? y : x; | |
7269 | } | |
7270 | else if (SCM_REALP (y)) | |
7271 | { | |
2a06f791 KR |
7272 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
7273 | double xx, yy; | |
7274 | big_real: | |
7275 | xx = scm_i_big2dbl (x); | |
7276 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7277 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 7278 | } |
f92e85f7 MV |
7279 | else if (SCM_FRACTIONP (y)) |
7280 | { | |
e4bc5d6c | 7281 | goto use_less; |
f92e85f7 | 7282 | } |
0aacf84e MD |
7283 | else |
7284 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 7285 | } |
0aacf84e MD |
7286 | else if (SCM_REALP (x)) |
7287 | { | |
e11e83f3 | 7288 | if (SCM_I_INUMP (y)) |
0aacf84e | 7289 | { |
e11e83f3 | 7290 | double z = SCM_I_INUM (y); |
0aacf84e | 7291 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7292 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7293 | } |
7294 | else if (SCM_BIGP (y)) | |
7295 | { | |
b6f8f763 | 7296 | SCM_SWAP (x, y); |
2a06f791 | 7297 | goto big_real; |
0aacf84e MD |
7298 | } |
7299 | else if (SCM_REALP (y)) | |
7300 | { | |
0aacf84e | 7301 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7302 | double yy = SCM_REAL_VALUE (y); |
7303 | ||
7304 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
7305 | if (xx < yy) | |
7306 | return x; | |
7307 | else if (SCM_LIKELY (xx > yy)) | |
7308 | return y; | |
7309 | /* If neither (xx < yy) nor (xx > yy), then | |
7310 | either they're equal or one is a NaN */ | |
7311 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7312 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 7313 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7314 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7315 | /* xx == yy, but handle signed zeroes properly */ |
7316 | else if (double_is_non_negative_zero (xx)) | |
7317 | return y; | |
7318 | else | |
7319 | return x; | |
0aacf84e | 7320 | } |
f92e85f7 MV |
7321 | else if (SCM_FRACTIONP (y)) |
7322 | { | |
7323 | double yy = scm_i_fraction2double (y); | |
7324 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7325 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7326 | } |
0aacf84e MD |
7327 | else |
7328 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7329 | } |
f92e85f7 MV |
7330 | else if (SCM_FRACTIONP (x)) |
7331 | { | |
e11e83f3 | 7332 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7333 | { |
e4bc5d6c | 7334 | goto use_less; |
f92e85f7 MV |
7335 | } |
7336 | else if (SCM_BIGP (y)) | |
7337 | { | |
e4bc5d6c | 7338 | goto use_less; |
f92e85f7 MV |
7339 | } |
7340 | else if (SCM_REALP (y)) | |
7341 | { | |
7342 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7343 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7344 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7345 | } |
7346 | else if (SCM_FRACTIONP (y)) | |
7347 | { | |
e4bc5d6c | 7348 | goto use_less; |
f92e85f7 MV |
7349 | } |
7350 | else | |
78d3deb1 | 7351 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7352 | } |
0aacf84e | 7353 | else |
f4c627b3 | 7354 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7355 | } |
7356 | ||
7357 | ||
8ccd24f7 AW |
7358 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7359 | (SCM x, SCM y, SCM rest), | |
7360 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7361 | "any parameters." ) | |
7362 | #define FUNC_NAME s_scm_i_sum | |
7363 | { | |
7364 | while (!scm_is_null (rest)) | |
7365 | { x = scm_sum (x, y); | |
7366 | y = scm_car (rest); | |
7367 | rest = scm_cdr (rest); | |
7368 | } | |
7369 | return scm_sum (x, y); | |
7370 | } | |
7371 | #undef FUNC_NAME | |
7372 | ||
7373 | #define s_sum s_scm_i_sum | |
7374 | #define g_sum g_scm_i_sum | |
7375 | ||
0f2d19dd | 7376 | SCM |
6e8d25a6 | 7377 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7378 | { |
9cc37597 | 7379 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7380 | { |
7381 | if (SCM_NUMBERP (x)) return x; | |
7382 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7383 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7384 | } |
c209c88e | 7385 | |
9cc37597 | 7386 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7387 | { |
9cc37597 | 7388 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7389 | { |
e25f3727 AW |
7390 | scm_t_inum xx = SCM_I_INUM (x); |
7391 | scm_t_inum yy = SCM_I_INUM (y); | |
7392 | scm_t_inum z = xx + yy; | |
7393 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7394 | } |
7395 | else if (SCM_BIGP (y)) | |
7396 | { | |
7397 | SCM_SWAP (x, y); | |
7398 | goto add_big_inum; | |
7399 | } | |
7400 | else if (SCM_REALP (y)) | |
7401 | { | |
e25f3727 | 7402 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7403 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7404 | } |
7405 | else if (SCM_COMPLEXP (y)) | |
7406 | { | |
e25f3727 | 7407 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7408 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7409 | SCM_COMPLEX_IMAG (y)); |
7410 | } | |
f92e85f7 | 7411 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7412 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7413 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7414 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7415 | else |
7416 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7417 | } else if (SCM_BIGP (x)) |
7418 | { | |
e11e83f3 | 7419 | if (SCM_I_INUMP (y)) |
0aacf84e | 7420 | { |
e25f3727 | 7421 | scm_t_inum inum; |
0aacf84e MD |
7422 | int bigsgn; |
7423 | add_big_inum: | |
e11e83f3 | 7424 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7425 | if (inum == 0) |
7426 | return x; | |
7427 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7428 | if (inum < 0) | |
7429 | { | |
7430 | SCM result = scm_i_mkbig (); | |
7431 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7432 | scm_remember_upto_here_1 (x); | |
7433 | /* we know the result will have to be a bignum */ | |
7434 | if (bigsgn == -1) | |
7435 | return result; | |
7436 | return scm_i_normbig (result); | |
7437 | } | |
7438 | else | |
7439 | { | |
7440 | SCM result = scm_i_mkbig (); | |
7441 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7442 | scm_remember_upto_here_1 (x); | |
7443 | /* we know the result will have to be a bignum */ | |
7444 | if (bigsgn == 1) | |
7445 | return result; | |
7446 | return scm_i_normbig (result); | |
7447 | } | |
7448 | } | |
7449 | else if (SCM_BIGP (y)) | |
7450 | { | |
7451 | SCM result = scm_i_mkbig (); | |
7452 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7453 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7454 | mpz_add (SCM_I_BIG_MPZ (result), | |
7455 | SCM_I_BIG_MPZ (x), | |
7456 | SCM_I_BIG_MPZ (y)); | |
7457 | scm_remember_upto_here_2 (x, y); | |
7458 | /* we know the result will have to be a bignum */ | |
7459 | if (sgn_x == sgn_y) | |
7460 | return result; | |
7461 | return scm_i_normbig (result); | |
7462 | } | |
7463 | else if (SCM_REALP (y)) | |
7464 | { | |
7465 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7466 | scm_remember_upto_here_1 (x); | |
55f26379 | 7467 | return scm_from_double (result); |
0aacf84e MD |
7468 | } |
7469 | else if (SCM_COMPLEXP (y)) | |
7470 | { | |
7471 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7472 | + SCM_COMPLEX_REAL (y)); | |
7473 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7474 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7475 | } |
f92e85f7 | 7476 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7477 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7478 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7479 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7480 | else |
7481 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7482 | } |
0aacf84e MD |
7483 | else if (SCM_REALP (x)) |
7484 | { | |
e11e83f3 | 7485 | if (SCM_I_INUMP (y)) |
55f26379 | 7486 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7487 | else if (SCM_BIGP (y)) |
7488 | { | |
7489 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7490 | scm_remember_upto_here_1 (y); | |
55f26379 | 7491 | return scm_from_double (result); |
0aacf84e MD |
7492 | } |
7493 | else if (SCM_REALP (y)) | |
55f26379 | 7494 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7495 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7496 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7497 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7498 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7499 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7500 | else |
7501 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7502 | } |
0aacf84e MD |
7503 | else if (SCM_COMPLEXP (x)) |
7504 | { | |
e11e83f3 | 7505 | if (SCM_I_INUMP (y)) |
8507ec80 | 7506 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7507 | SCM_COMPLEX_IMAG (x)); |
7508 | else if (SCM_BIGP (y)) | |
7509 | { | |
7510 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7511 | + SCM_COMPLEX_REAL (x)); | |
7512 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7513 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7514 | } |
7515 | else if (SCM_REALP (y)) | |
8507ec80 | 7516 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7517 | SCM_COMPLEX_IMAG (x)); |
7518 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7519 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7520 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7521 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7522 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7523 | SCM_COMPLEX_IMAG (x)); |
7524 | else | |
7525 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7526 | } | |
7527 | else if (SCM_FRACTIONP (x)) | |
7528 | { | |
e11e83f3 | 7529 | if (SCM_I_INUMP (y)) |
cba42c93 | 7530 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7531 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7532 | SCM_FRACTION_DENOMINATOR (x)); | |
7533 | else if (SCM_BIGP (y)) | |
cba42c93 | 7534 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7535 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7536 | SCM_FRACTION_DENOMINATOR (x)); | |
7537 | else if (SCM_REALP (y)) | |
55f26379 | 7538 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7539 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7540 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7541 | SCM_COMPLEX_IMAG (y)); |
7542 | else if (SCM_FRACTIONP (y)) | |
7543 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7544 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7545 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7546 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7547 | else |
7548 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7549 | } |
0aacf84e | 7550 | else |
98cb6e75 | 7551 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7552 | } |
7553 | ||
7554 | ||
40882e3d KR |
7555 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7556 | (SCM x), | |
7557 | "Return @math{@var{x}+1}.") | |
7558 | #define FUNC_NAME s_scm_oneplus | |
7559 | { | |
cff5fa33 | 7560 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7561 | } |
7562 | #undef FUNC_NAME | |
7563 | ||
7564 | ||
78d3deb1 AW |
7565 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7566 | (SCM x, SCM y, SCM rest), | |
7567 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7568 | "the sum of all but the first argument are subtracted from the first\n" | |
7569 | "argument.") | |
7570 | #define FUNC_NAME s_scm_i_difference | |
7571 | { | |
7572 | while (!scm_is_null (rest)) | |
7573 | { x = scm_difference (x, y); | |
7574 | y = scm_car (rest); | |
7575 | rest = scm_cdr (rest); | |
7576 | } | |
7577 | return scm_difference (x, y); | |
7578 | } | |
7579 | #undef FUNC_NAME | |
7580 | ||
7581 | #define s_difference s_scm_i_difference | |
7582 | #define g_difference g_scm_i_difference | |
7583 | ||
0f2d19dd | 7584 | SCM |
6e8d25a6 | 7585 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7586 | #define FUNC_NAME s_difference |
0f2d19dd | 7587 | { |
9cc37597 | 7588 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7589 | { |
7590 | if (SCM_UNBNDP (x)) | |
7591 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7592 | else | |
e11e83f3 | 7593 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7594 | { |
e25f3727 | 7595 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7596 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7597 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7598 | else |
e25f3727 | 7599 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7600 | } |
7601 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7602 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7603 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7604 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7605 | else if (SCM_REALP (x)) | |
55f26379 | 7606 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7607 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7608 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7609 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7610 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
7611 | return scm_i_make_ratio_already_reduced |
7612 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
7613 | SCM_FRACTION_DENOMINATOR (x)); | |
ca46fb90 RB |
7614 | else |
7615 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7616 | } |
ca46fb90 | 7617 | |
9cc37597 | 7618 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7619 | { |
9cc37597 | 7620 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7621 | { |
e25f3727 AW |
7622 | scm_t_inum xx = SCM_I_INUM (x); |
7623 | scm_t_inum yy = SCM_I_INUM (y); | |
7624 | scm_t_inum z = xx - yy; | |
0aacf84e | 7625 | if (SCM_FIXABLE (z)) |
d956fa6f | 7626 | return SCM_I_MAKINUM (z); |
0aacf84e | 7627 | else |
e25f3727 | 7628 | return scm_i_inum2big (z); |
0aacf84e MD |
7629 | } |
7630 | else if (SCM_BIGP (y)) | |
7631 | { | |
7632 | /* inum-x - big-y */ | |
e25f3727 | 7633 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7634 | |
0aacf84e | 7635 | if (xx == 0) |
b5c40589 MW |
7636 | { |
7637 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7638 | bignum, but negating that gives a fixnum. */ | |
7639 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7640 | } | |
0aacf84e MD |
7641 | else |
7642 | { | |
7643 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7644 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7645 | |
0aacf84e MD |
7646 | if (xx >= 0) |
7647 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7648 | else | |
7649 | { | |
7650 | /* x - y == -(y + -x) */ | |
7651 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7652 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7653 | } | |
7654 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7655 | |
0aacf84e MD |
7656 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7657 | /* we know the result will have to be a bignum */ | |
7658 | return result; | |
7659 | else | |
7660 | return scm_i_normbig (result); | |
7661 | } | |
7662 | } | |
7663 | else if (SCM_REALP (y)) | |
7664 | { | |
e25f3727 | 7665 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7666 | |
7667 | /* | |
7668 | * We need to handle x == exact 0 | |
7669 | * specially because R6RS states that: | |
7670 | * (- 0.0) ==> -0.0 and | |
7671 | * (- 0.0 0.0) ==> 0.0 | |
7672 | * and the scheme compiler changes | |
7673 | * (- 0.0) into (- 0 0.0) | |
7674 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7675 | * At the C level, (-x) is different than (0.0 - x). | |
7676 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7677 | */ | |
7678 | if (xx == 0) | |
7679 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7680 | else | |
7681 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7682 | } |
7683 | else if (SCM_COMPLEXP (y)) | |
7684 | { | |
e25f3727 | 7685 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7686 | |
7687 | /* We need to handle x == exact 0 specially. | |
7688 | See the comment above (for SCM_REALP (y)) */ | |
7689 | if (xx == 0) | |
7690 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7691 | - SCM_COMPLEX_IMAG (y)); | |
7692 | else | |
7693 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7694 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7695 | } |
f92e85f7 MV |
7696 | else if (SCM_FRACTIONP (y)) |
7697 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7698 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7699 | SCM_FRACTION_NUMERATOR (y)), |
7700 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7701 | else |
7702 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7703 | } |
0aacf84e MD |
7704 | else if (SCM_BIGP (x)) |
7705 | { | |
e11e83f3 | 7706 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7707 | { |
7708 | /* big-x - inum-y */ | |
e25f3727 | 7709 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7710 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7711 | |
0aacf84e MD |
7712 | scm_remember_upto_here_1 (x); |
7713 | if (sgn_x == 0) | |
c71b0706 | 7714 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7715 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7716 | else |
7717 | { | |
7718 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7719 | |
708f22c6 KR |
7720 | if (yy >= 0) |
7721 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7722 | else | |
7723 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7724 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7725 | |
0aacf84e MD |
7726 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7727 | /* we know the result will have to be a bignum */ | |
7728 | return result; | |
7729 | else | |
7730 | return scm_i_normbig (result); | |
7731 | } | |
7732 | } | |
7733 | else if (SCM_BIGP (y)) | |
7734 | { | |
7735 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7736 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7737 | SCM result = scm_i_mkbig (); | |
7738 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7739 | SCM_I_BIG_MPZ (x), | |
7740 | SCM_I_BIG_MPZ (y)); | |
7741 | scm_remember_upto_here_2 (x, y); | |
7742 | /* we know the result will have to be a bignum */ | |
7743 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7744 | return result; | |
7745 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7746 | return result; | |
7747 | return scm_i_normbig (result); | |
7748 | } | |
7749 | else if (SCM_REALP (y)) | |
7750 | { | |
7751 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7752 | scm_remember_upto_here_1 (x); | |
55f26379 | 7753 | return scm_from_double (result); |
0aacf84e MD |
7754 | } |
7755 | else if (SCM_COMPLEXP (y)) | |
7756 | { | |
7757 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7758 | - SCM_COMPLEX_REAL (y)); | |
7759 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7760 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7761 | } |
f92e85f7 | 7762 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7763 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7764 | SCM_FRACTION_NUMERATOR (y)), |
7765 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7766 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7767 | } |
0aacf84e MD |
7768 | else if (SCM_REALP (x)) |
7769 | { | |
e11e83f3 | 7770 | if (SCM_I_INUMP (y)) |
55f26379 | 7771 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7772 | else if (SCM_BIGP (y)) |
7773 | { | |
7774 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7775 | scm_remember_upto_here_1 (x); | |
55f26379 | 7776 | return scm_from_double (result); |
0aacf84e MD |
7777 | } |
7778 | else if (SCM_REALP (y)) | |
55f26379 | 7779 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7780 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7781 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7782 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7783 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7784 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7785 | else |
7786 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7787 | } |
0aacf84e MD |
7788 | else if (SCM_COMPLEXP (x)) |
7789 | { | |
e11e83f3 | 7790 | if (SCM_I_INUMP (y)) |
8507ec80 | 7791 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7792 | SCM_COMPLEX_IMAG (x)); |
7793 | else if (SCM_BIGP (y)) | |
7794 | { | |
7795 | double real_part = (SCM_COMPLEX_REAL (x) | |
7796 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7797 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7798 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7799 | } |
7800 | else if (SCM_REALP (y)) | |
8507ec80 | 7801 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7802 | SCM_COMPLEX_IMAG (x)); |
7803 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7804 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7805 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7806 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7807 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7808 | SCM_COMPLEX_IMAG (x)); |
7809 | else | |
7810 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7811 | } | |
7812 | else if (SCM_FRACTIONP (x)) | |
7813 | { | |
e11e83f3 | 7814 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7815 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7816 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7817 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7818 | SCM_FRACTION_DENOMINATOR (x)); | |
7819 | else if (SCM_BIGP (y)) | |
cba42c93 | 7820 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7821 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7822 | SCM_FRACTION_DENOMINATOR (x)); | |
7823 | else if (SCM_REALP (y)) | |
55f26379 | 7824 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7825 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7826 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7827 | -SCM_COMPLEX_IMAG (y)); |
7828 | else if (SCM_FRACTIONP (y)) | |
7829 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7830 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7831 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7832 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7833 | else |
7834 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7835 | } |
0aacf84e | 7836 | else |
98cb6e75 | 7837 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7838 | } |
c05e97b7 | 7839 | #undef FUNC_NAME |
0f2d19dd | 7840 | |
ca46fb90 | 7841 | |
40882e3d KR |
7842 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7843 | (SCM x), | |
7844 | "Return @math{@var{x}-1}.") | |
7845 | #define FUNC_NAME s_scm_oneminus | |
7846 | { | |
cff5fa33 | 7847 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7848 | } |
7849 | #undef FUNC_NAME | |
7850 | ||
7851 | ||
78d3deb1 AW |
7852 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7853 | (SCM x, SCM y, SCM rest), | |
7854 | "Return the product of all arguments. If called without arguments,\n" | |
7855 | "1 is returned.") | |
7856 | #define FUNC_NAME s_scm_i_product | |
7857 | { | |
7858 | while (!scm_is_null (rest)) | |
7859 | { x = scm_product (x, y); | |
7860 | y = scm_car (rest); | |
7861 | rest = scm_cdr (rest); | |
7862 | } | |
7863 | return scm_product (x, y); | |
7864 | } | |
7865 | #undef FUNC_NAME | |
7866 | ||
7867 | #define s_product s_scm_i_product | |
7868 | #define g_product g_scm_i_product | |
7869 | ||
0f2d19dd | 7870 | SCM |
6e8d25a6 | 7871 | scm_product (SCM x, SCM y) |
0f2d19dd | 7872 | { |
9cc37597 | 7873 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7874 | { |
7875 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7876 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7877 | else if (SCM_NUMBERP (x)) |
7878 | return x; | |
7879 | else | |
7880 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7881 | } |
ca46fb90 | 7882 | |
9cc37597 | 7883 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7884 | { |
e25f3727 | 7885 | scm_t_inum xx; |
f4c627b3 | 7886 | |
5e791807 | 7887 | xinum: |
e11e83f3 | 7888 | xx = SCM_I_INUM (x); |
f4c627b3 | 7889 | |
0aacf84e MD |
7890 | switch (xx) |
7891 | { | |
5e791807 MW |
7892 | case 1: |
7893 | /* exact1 is the universal multiplicative identity */ | |
7894 | return y; | |
7895 | break; | |
7896 | case 0: | |
7897 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7898 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7899 | return SCM_INUM0; | |
7900 | /* if the other argument is inexact, the result is inexact, | |
7901 | and we must do the multiplication in order to handle | |
7902 | infinities and NaNs properly. */ | |
7903 | else if (SCM_REALP (y)) | |
7904 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7905 | else if (SCM_COMPLEXP (y)) | |
7906 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7907 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7908 | /* we've already handled inexact numbers, | |
7909 | so y must be exact, and we return exact0 */ | |
7910 | else if (SCM_NUMP (y)) | |
7911 | return SCM_INUM0; | |
7912 | else | |
7913 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7914 | break; | |
7915 | case -1: | |
b5c40589 | 7916 | /* |
5e791807 MW |
7917 | * This case is important for more than just optimization. |
7918 | * It handles the case of negating | |
b5c40589 MW |
7919 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7920 | * which is a bignum that must be changed back into a fixnum. | |
7921 | * Failure to do so will cause the following to return #f: | |
7922 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7923 | */ | |
b5c40589 MW |
7924 | return scm_difference(y, SCM_UNDEFINED); |
7925 | break; | |
0aacf84e | 7926 | } |
f4c627b3 | 7927 | |
9cc37597 | 7928 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7929 | { |
e25f3727 | 7930 | scm_t_inum yy = SCM_I_INUM (y); |
2355f017 MW |
7931 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
7932 | scm_t_int64 kk = xx * (scm_t_int64) yy; | |
7933 | if (SCM_FIXABLE (kk)) | |
7934 | return SCM_I_MAKINUM (kk); | |
7935 | #else | |
7936 | scm_t_inum axx = (xx > 0) ? xx : -xx; | |
7937 | scm_t_inum ayy = (yy > 0) ? yy : -yy; | |
7938 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) | |
7939 | return SCM_I_MAKINUM (xx * yy); | |
7940 | #endif | |
0aacf84e MD |
7941 | else |
7942 | { | |
e25f3727 | 7943 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7944 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7945 | return scm_i_normbig (result); | |
7946 | } | |
7947 | } | |
7948 | else if (SCM_BIGP (y)) | |
7949 | { | |
7950 | SCM result = scm_i_mkbig (); | |
7951 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7952 | scm_remember_upto_here_1 (y); | |
7953 | return result; | |
7954 | } | |
7955 | else if (SCM_REALP (y)) | |
55f26379 | 7956 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7957 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7958 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7959 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7960 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7961 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7962 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7963 | else |
7964 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7965 | } |
0aacf84e MD |
7966 | else if (SCM_BIGP (x)) |
7967 | { | |
e11e83f3 | 7968 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7969 | { |
7970 | SCM_SWAP (x, y); | |
5e791807 | 7971 | goto xinum; |
0aacf84e MD |
7972 | } |
7973 | else if (SCM_BIGP (y)) | |
7974 | { | |
7975 | SCM result = scm_i_mkbig (); | |
7976 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7977 | SCM_I_BIG_MPZ (x), | |
7978 | SCM_I_BIG_MPZ (y)); | |
7979 | scm_remember_upto_here_2 (x, y); | |
7980 | return result; | |
7981 | } | |
7982 | else if (SCM_REALP (y)) | |
7983 | { | |
7984 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7985 | scm_remember_upto_here_1 (x); | |
55f26379 | 7986 | return scm_from_double (result); |
0aacf84e MD |
7987 | } |
7988 | else if (SCM_COMPLEXP (y)) | |
7989 | { | |
7990 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7991 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7992 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7993 | z * SCM_COMPLEX_IMAG (y)); |
7994 | } | |
f92e85f7 | 7995 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7996 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7997 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7998 | else |
7999 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8000 | } |
0aacf84e MD |
8001 | else if (SCM_REALP (x)) |
8002 | { | |
e11e83f3 | 8003 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8004 | { |
8005 | SCM_SWAP (x, y); | |
8006 | goto xinum; | |
8007 | } | |
0aacf84e MD |
8008 | else if (SCM_BIGP (y)) |
8009 | { | |
8010 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
8011 | scm_remember_upto_here_1 (y); | |
55f26379 | 8012 | return scm_from_double (result); |
0aacf84e MD |
8013 | } |
8014 | else if (SCM_REALP (y)) | |
55f26379 | 8015 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 8016 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8017 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 8018 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8019 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8020 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
8021 | else |
8022 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8023 | } |
0aacf84e MD |
8024 | else if (SCM_COMPLEXP (x)) |
8025 | { | |
e11e83f3 | 8026 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8027 | { |
8028 | SCM_SWAP (x, y); | |
8029 | goto xinum; | |
8030 | } | |
0aacf84e MD |
8031 | else if (SCM_BIGP (y)) |
8032 | { | |
8033 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8034 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8035 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 8036 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
8037 | } |
8038 | else if (SCM_REALP (y)) | |
8507ec80 | 8039 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
8040 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
8041 | else if (SCM_COMPLEXP (y)) | |
8042 | { | |
8507ec80 | 8043 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
8044 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
8045 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
8046 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
8047 | } | |
f92e85f7 MV |
8048 | else if (SCM_FRACTIONP (y)) |
8049 | { | |
8050 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8051 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
8052 | yy * SCM_COMPLEX_IMAG (x)); |
8053 | } | |
8054 | else | |
8055 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
8056 | } | |
8057 | else if (SCM_FRACTIONP (x)) | |
8058 | { | |
e11e83f3 | 8059 | if (SCM_I_INUMP (y)) |
cba42c93 | 8060 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8061 | SCM_FRACTION_DENOMINATOR (x)); |
8062 | else if (SCM_BIGP (y)) | |
cba42c93 | 8063 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8064 | SCM_FRACTION_DENOMINATOR (x)); |
8065 | else if (SCM_REALP (y)) | |
55f26379 | 8066 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
8067 | else if (SCM_COMPLEXP (y)) |
8068 | { | |
8069 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 8070 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
8071 | xx * SCM_COMPLEX_IMAG (y)); |
8072 | } | |
8073 | else if (SCM_FRACTIONP (y)) | |
8074 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 8075 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8076 | SCM_FRACTION_NUMERATOR (y)), |
8077 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
8078 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
8079 | else |
8080 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8081 | } |
0aacf84e | 8082 | else |
f4c627b3 | 8083 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
8084 | } |
8085 | ||
7351e207 MV |
8086 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
8087 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
8088 | #define ALLOW_DIVIDE_BY_ZERO | |
8089 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
8090 | #endif | |
0f2d19dd | 8091 | |
ba74ef4e MV |
8092 | /* The code below for complex division is adapted from the GNU |
8093 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
8094 | this copyright: */ | |
8095 | ||
8096 | /**************************************************************** | |
8097 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
8098 | ||
8099 | Permission to use, copy, modify, and distribute this software | |
8100 | and its documentation for any purpose and without fee is hereby | |
8101 | granted, provided that the above copyright notice appear in all | |
8102 | copies and that both that the copyright notice and this | |
8103 | permission notice and warranty disclaimer appear in supporting | |
8104 | documentation, and that the names of AT&T Bell Laboratories or | |
8105 | Bellcore or any of their entities not be used in advertising or | |
8106 | publicity pertaining to distribution of the software without | |
8107 | specific, written prior permission. | |
8108 | ||
8109 | AT&T and Bellcore disclaim all warranties with regard to this | |
8110 | software, including all implied warranties of merchantability | |
8111 | and fitness. In no event shall AT&T or Bellcore be liable for | |
8112 | any special, indirect or consequential damages or any damages | |
8113 | whatsoever resulting from loss of use, data or profits, whether | |
8114 | in an action of contract, negligence or other tortious action, | |
8115 | arising out of or in connection with the use or performance of | |
8116 | this software. | |
8117 | ****************************************************************/ | |
8118 | ||
78d3deb1 AW |
8119 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
8120 | (SCM x, SCM y, SCM rest), | |
8121 | "Divide the first argument by the product of the remaining\n" | |
8122 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
8123 | "returned.") | |
8124 | #define FUNC_NAME s_scm_i_divide | |
8125 | { | |
8126 | while (!scm_is_null (rest)) | |
8127 | { x = scm_divide (x, y); | |
8128 | y = scm_car (rest); | |
8129 | rest = scm_cdr (rest); | |
8130 | } | |
8131 | return scm_divide (x, y); | |
8132 | } | |
8133 | #undef FUNC_NAME | |
8134 | ||
8135 | #define s_divide s_scm_i_divide | |
8136 | #define g_divide g_scm_i_divide | |
8137 | ||
98237784 MW |
8138 | SCM |
8139 | scm_divide (SCM x, SCM y) | |
78d3deb1 | 8140 | #define FUNC_NAME s_divide |
0f2d19dd | 8141 | { |
f8de44c1 DH |
8142 | double a; |
8143 | ||
9cc37597 | 8144 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8145 | { |
8146 | if (SCM_UNBNDP (x)) | |
8147 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 8148 | else if (SCM_I_INUMP (x)) |
0aacf84e | 8149 | { |
e25f3727 | 8150 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
8151 | if (xx == 1 || xx == -1) |
8152 | return x; | |
7351e207 | 8153 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8154 | else if (xx == 0) |
8155 | scm_num_overflow (s_divide); | |
7351e207 | 8156 | #endif |
0aacf84e | 8157 | else |
98237784 | 8158 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8159 | } |
8160 | else if (SCM_BIGP (x)) | |
98237784 | 8161 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8162 | else if (SCM_REALP (x)) |
8163 | { | |
8164 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 8165 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8166 | if (xx == 0.0) |
8167 | scm_num_overflow (s_divide); | |
8168 | else | |
7351e207 | 8169 | #endif |
55f26379 | 8170 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
8171 | } |
8172 | else if (SCM_COMPLEXP (x)) | |
8173 | { | |
8174 | double r = SCM_COMPLEX_REAL (x); | |
8175 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 8176 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8177 | { |
8178 | double t = r / i; | |
8179 | double d = i * (1.0 + t * t); | |
8507ec80 | 8180 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
8181 | } |
8182 | else | |
8183 | { | |
8184 | double t = i / r; | |
8185 | double d = r * (1.0 + t * t); | |
8507ec80 | 8186 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
8187 | } |
8188 | } | |
f92e85f7 | 8189 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
8190 | return scm_i_make_ratio_already_reduced (SCM_FRACTION_DENOMINATOR (x), |
8191 | SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e MD |
8192 | else |
8193 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 8194 | } |
f8de44c1 | 8195 | |
9cc37597 | 8196 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8197 | { |
e25f3727 | 8198 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 8199 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8200 | { |
e25f3727 | 8201 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8202 | if (yy == 0) |
8203 | { | |
7351e207 | 8204 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8205 | scm_num_overflow (s_divide); |
7351e207 | 8206 | #else |
55f26379 | 8207 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 8208 | #endif |
0aacf84e MD |
8209 | } |
8210 | else if (xx % yy != 0) | |
98237784 | 8211 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8212 | else |
8213 | { | |
e25f3727 | 8214 | scm_t_inum z = xx / yy; |
0aacf84e | 8215 | if (SCM_FIXABLE (z)) |
d956fa6f | 8216 | return SCM_I_MAKINUM (z); |
0aacf84e | 8217 | else |
e25f3727 | 8218 | return scm_i_inum2big (z); |
0aacf84e | 8219 | } |
f872b822 | 8220 | } |
0aacf84e | 8221 | else if (SCM_BIGP (y)) |
98237784 | 8222 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8223 | else if (SCM_REALP (y)) |
8224 | { | |
8225 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8226 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8227 | if (yy == 0.0) |
8228 | scm_num_overflow (s_divide); | |
8229 | else | |
7351e207 | 8230 | #endif |
98237784 MW |
8231 | /* FIXME: Precision may be lost here due to: |
8232 | (1) The cast from 'scm_t_inum' to 'double' | |
8233 | (2) Double rounding */ | |
55f26379 | 8234 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 8235 | } |
0aacf84e MD |
8236 | else if (SCM_COMPLEXP (y)) |
8237 | { | |
8238 | a = xx; | |
8239 | complex_div: /* y _must_ be a complex number */ | |
8240 | { | |
8241 | double r = SCM_COMPLEX_REAL (y); | |
8242 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8243 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8244 | { |
8245 | double t = r / i; | |
8246 | double d = i * (1.0 + t * t); | |
8507ec80 | 8247 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
8248 | } |
8249 | else | |
8250 | { | |
8251 | double t = i / r; | |
8252 | double d = r * (1.0 + t * t); | |
8507ec80 | 8253 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
8254 | } |
8255 | } | |
8256 | } | |
f92e85f7 MV |
8257 | else if (SCM_FRACTIONP (y)) |
8258 | /* a / b/c = ac / b */ | |
cba42c93 | 8259 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8260 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8261 | else |
8262 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8263 | } |
0aacf84e MD |
8264 | else if (SCM_BIGP (x)) |
8265 | { | |
e11e83f3 | 8266 | if (SCM_I_INUMP (y)) |
0aacf84e | 8267 | { |
e25f3727 | 8268 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8269 | if (yy == 0) |
8270 | { | |
7351e207 | 8271 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8272 | scm_num_overflow (s_divide); |
7351e207 | 8273 | #else |
0aacf84e MD |
8274 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8275 | scm_remember_upto_here_1 (x); | |
8276 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8277 | #endif |
0aacf84e MD |
8278 | } |
8279 | else if (yy == 1) | |
8280 | return x; | |
8281 | else | |
8282 | { | |
8283 | /* FIXME: HMM, what are the relative performance issues here? | |
8284 | We need to test. Is it faster on average to test | |
8285 | divisible_p, then perform whichever operation, or is it | |
8286 | faster to perform the integer div opportunistically and | |
8287 | switch to real if there's a remainder? For now we take the | |
8288 | middle ground: test, then if divisible, use the faster div | |
8289 | func. */ | |
8290 | ||
e25f3727 | 8291 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8292 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8293 | ||
8294 | if (divisible_p) | |
8295 | { | |
8296 | SCM result = scm_i_mkbig (); | |
8297 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8298 | scm_remember_upto_here_1 (x); | |
8299 | if (yy < 0) | |
8300 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8301 | return scm_i_normbig (result); | |
8302 | } | |
8303 | else | |
98237784 | 8304 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8305 | } |
8306 | } | |
8307 | else if (SCM_BIGP (y)) | |
8308 | { | |
98237784 MW |
8309 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8310 | SCM_I_BIG_MPZ (y)); | |
8311 | if (divisible_p) | |
8312 | { | |
8313 | SCM result = scm_i_mkbig (); | |
8314 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8315 | SCM_I_BIG_MPZ (x), | |
8316 | SCM_I_BIG_MPZ (y)); | |
8317 | scm_remember_upto_here_2 (x, y); | |
8318 | return scm_i_normbig (result); | |
8319 | } | |
8320 | else | |
8321 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8322 | } |
8323 | else if (SCM_REALP (y)) | |
8324 | { | |
8325 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8326 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8327 | if (yy == 0.0) |
8328 | scm_num_overflow (s_divide); | |
8329 | else | |
7351e207 | 8330 | #endif |
98237784 MW |
8331 | /* FIXME: Precision may be lost here due to: |
8332 | (1) scm_i_big2dbl (2) Double rounding */ | |
55f26379 | 8333 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8334 | } |
8335 | else if (SCM_COMPLEXP (y)) | |
8336 | { | |
8337 | a = scm_i_big2dbl (x); | |
8338 | goto complex_div; | |
8339 | } | |
f92e85f7 | 8340 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8341 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8342 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8343 | else |
8344 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8345 | } |
0aacf84e MD |
8346 | else if (SCM_REALP (x)) |
8347 | { | |
8348 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8349 | if (SCM_I_INUMP (y)) |
0aacf84e | 8350 | { |
e25f3727 | 8351 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8352 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8353 | if (yy == 0) |
8354 | scm_num_overflow (s_divide); | |
8355 | else | |
7351e207 | 8356 | #endif |
98237784 MW |
8357 | /* FIXME: Precision may be lost here due to: |
8358 | (1) The cast from 'scm_t_inum' to 'double' | |
8359 | (2) Double rounding */ | |
55f26379 | 8360 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8361 | } |
8362 | else if (SCM_BIGP (y)) | |
8363 | { | |
98237784 MW |
8364 | /* FIXME: Precision may be lost here due to: |
8365 | (1) The conversion from bignum to double | |
8366 | (2) Double rounding */ | |
0aacf84e MD |
8367 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8368 | scm_remember_upto_here_1 (y); | |
55f26379 | 8369 | return scm_from_double (rx / dby); |
0aacf84e MD |
8370 | } |
8371 | else if (SCM_REALP (y)) | |
8372 | { | |
8373 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8374 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8375 | if (yy == 0.0) |
8376 | scm_num_overflow (s_divide); | |
8377 | else | |
7351e207 | 8378 | #endif |
55f26379 | 8379 | return scm_from_double (rx / yy); |
0aacf84e MD |
8380 | } |
8381 | else if (SCM_COMPLEXP (y)) | |
8382 | { | |
8383 | a = rx; | |
8384 | goto complex_div; | |
8385 | } | |
f92e85f7 | 8386 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8387 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8388 | else |
8389 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8390 | } |
0aacf84e MD |
8391 | else if (SCM_COMPLEXP (x)) |
8392 | { | |
8393 | double rx = SCM_COMPLEX_REAL (x); | |
8394 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8395 | if (SCM_I_INUMP (y)) |
0aacf84e | 8396 | { |
e25f3727 | 8397 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8398 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8399 | if (yy == 0) |
8400 | scm_num_overflow (s_divide); | |
8401 | else | |
7351e207 | 8402 | #endif |
0aacf84e | 8403 | { |
98237784 MW |
8404 | /* FIXME: Precision may be lost here due to: |
8405 | (1) The conversion from 'scm_t_inum' to double | |
8406 | (2) Double rounding */ | |
0aacf84e | 8407 | double d = yy; |
8507ec80 | 8408 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8409 | } |
8410 | } | |
8411 | else if (SCM_BIGP (y)) | |
8412 | { | |
98237784 MW |
8413 | /* FIXME: Precision may be lost here due to: |
8414 | (1) The conversion from bignum to double | |
8415 | (2) Double rounding */ | |
0aacf84e MD |
8416 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8417 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8418 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8419 | } |
8420 | else if (SCM_REALP (y)) | |
8421 | { | |
8422 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8423 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8424 | if (yy == 0.0) |
8425 | scm_num_overflow (s_divide); | |
8426 | else | |
7351e207 | 8427 | #endif |
8507ec80 | 8428 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8429 | } |
8430 | else if (SCM_COMPLEXP (y)) | |
8431 | { | |
8432 | double ry = SCM_COMPLEX_REAL (y); | |
8433 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8434 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8435 | { |
8436 | double t = ry / iy; | |
8437 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8438 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8439 | } |
8440 | else | |
8441 | { | |
8442 | double t = iy / ry; | |
8443 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8444 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8445 | } |
8446 | } | |
f92e85f7 MV |
8447 | else if (SCM_FRACTIONP (y)) |
8448 | { | |
98237784 MW |
8449 | /* FIXME: Precision may be lost here due to: |
8450 | (1) The conversion from fraction to double | |
8451 | (2) Double rounding */ | |
f92e85f7 | 8452 | double yy = scm_i_fraction2double (y); |
8507ec80 | 8453 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8454 | } |
0aacf84e MD |
8455 | else |
8456 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8457 | } |
f92e85f7 MV |
8458 | else if (SCM_FRACTIONP (x)) |
8459 | { | |
e11e83f3 | 8460 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8461 | { |
e25f3727 | 8462 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8463 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8464 | if (yy == 0) | |
8465 | scm_num_overflow (s_divide); | |
8466 | else | |
8467 | #endif | |
cba42c93 | 8468 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8469 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8470 | } |
8471 | else if (SCM_BIGP (y)) | |
8472 | { | |
cba42c93 | 8473 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8474 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8475 | } |
8476 | else if (SCM_REALP (y)) | |
8477 | { | |
8478 | double yy = SCM_REAL_VALUE (y); | |
8479 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8480 | if (yy == 0.0) | |
8481 | scm_num_overflow (s_divide); | |
8482 | else | |
8483 | #endif | |
98237784 MW |
8484 | /* FIXME: Precision may be lost here due to: |
8485 | (1) The conversion from fraction to double | |
8486 | (2) Double rounding */ | |
55f26379 | 8487 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8488 | } |
8489 | else if (SCM_COMPLEXP (y)) | |
8490 | { | |
98237784 MW |
8491 | /* FIXME: Precision may be lost here due to: |
8492 | (1) The conversion from fraction to double | |
8493 | (2) Double rounding */ | |
f92e85f7 MV |
8494 | a = scm_i_fraction2double (x); |
8495 | goto complex_div; | |
8496 | } | |
8497 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8498 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8499 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
f92e85f7 MV |
8500 | else |
8501 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8502 | } | |
0aacf84e | 8503 | else |
f8de44c1 | 8504 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8505 | } |
c05e97b7 | 8506 | #undef FUNC_NAME |
0f2d19dd | 8507 | |
fa605590 | 8508 | |
0f2d19dd | 8509 | double |
3101f40f | 8510 | scm_c_truncate (double x) |
0f2d19dd | 8511 | { |
fa605590 | 8512 | return trunc (x); |
0f2d19dd | 8513 | } |
0f2d19dd | 8514 | |
3101f40f MV |
8515 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8516 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8517 | Then half-way cases are identified and adjusted down if the | |
8518 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8519 | |
8520 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8521 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8522 | ||
8523 | An odd "result" value is identified with result/2 != floor(result/2). | |
8524 | This is done with plus_half, since that value is ready for use sooner in | |
8525 | a pipelined cpu, and we're already requiring plus_half == result. | |
8526 | ||
8527 | Note however that we need to be careful when x is big and already an | |
8528 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8529 | us to return such a value, incorrectly. For instance if the hardware is | |
8530 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8531 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8532 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8533 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8534 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8535 | ||
8536 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8537 | x is already an integer. If it is then clearly that's the desired result | |
8538 | already. And if it's not then the exponent must be small enough to allow | |
8539 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8540 | ||
0f2d19dd | 8541 | double |
3101f40f | 8542 | scm_c_round (double x) |
0f2d19dd | 8543 | { |
6187f48b KR |
8544 | double plus_half, result; |
8545 | ||
8546 | if (x == floor (x)) | |
8547 | return x; | |
8548 | ||
8549 | plus_half = x + 0.5; | |
8550 | result = floor (plus_half); | |
3101f40f | 8551 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8552 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8553 | ? result - 1 | |
8554 | : result); | |
0f2d19dd JB |
8555 | } |
8556 | ||
8b56bcec MW |
8557 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8558 | (SCM x), | |
8559 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8560 | #define FUNC_NAME s_scm_truncate_number |
8561 | { | |
8b56bcec MW |
8562 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8563 | return x; | |
8564 | else if (SCM_REALP (x)) | |
c251ab63 | 8565 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8566 | else if (SCM_FRACTIONP (x)) |
8567 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8568 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8569 | else |
8b56bcec MW |
8570 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8571 | s_scm_truncate_number); | |
f92e85f7 MV |
8572 | } |
8573 | #undef FUNC_NAME | |
8574 | ||
8b56bcec MW |
8575 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8576 | (SCM x), | |
8577 | "Round the number @var{x} towards the nearest integer. " | |
8578 | "When it is exactly halfway between two integers, " | |
8579 | "round towards the even one.") | |
f92e85f7 MV |
8580 | #define FUNC_NAME s_scm_round_number |
8581 | { | |
e11e83f3 | 8582 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8583 | return x; |
8584 | else if (SCM_REALP (x)) | |
3101f40f | 8585 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8586 | else if (SCM_FRACTIONP (x)) |
8587 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8588 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8589 | else |
8b56bcec MW |
8590 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8591 | s_scm_round_number); | |
f92e85f7 MV |
8592 | } |
8593 | #undef FUNC_NAME | |
8594 | ||
8595 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8596 | (SCM x), | |
8597 | "Round the number @var{x} towards minus infinity.") | |
8598 | #define FUNC_NAME s_scm_floor | |
8599 | { | |
e11e83f3 | 8600 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8601 | return x; |
8602 | else if (SCM_REALP (x)) | |
55f26379 | 8603 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8604 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8605 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8606 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8607 | else |
8608 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8609 | } | |
8610 | #undef FUNC_NAME | |
8611 | ||
8612 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8613 | (SCM x), | |
8614 | "Round the number @var{x} towards infinity.") | |
8615 | #define FUNC_NAME s_scm_ceiling | |
8616 | { | |
e11e83f3 | 8617 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8618 | return x; |
8619 | else if (SCM_REALP (x)) | |
55f26379 | 8620 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8621 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8622 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8623 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8624 | else |
8625 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8626 | } | |
8627 | #undef FUNC_NAME | |
0f2d19dd | 8628 | |
2519490c MW |
8629 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8630 | (SCM x, SCM y), | |
8631 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8632 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8633 | { |
01c7284a MW |
8634 | if (scm_is_integer (y)) |
8635 | { | |
8636 | if (scm_is_true (scm_exact_p (y))) | |
8637 | return scm_integer_expt (x, y); | |
8638 | else | |
8639 | { | |
8640 | /* Here we handle the case where the exponent is an inexact | |
8641 | integer. We make the exponent exact in order to use | |
8642 | scm_integer_expt, and thus avoid the spurious imaginary | |
8643 | parts that may result from round-off errors in the general | |
8644 | e^(y log x) method below (for example when squaring a large | |
8645 | negative number). In this case, we must return an inexact | |
8646 | result for correctness. We also make the base inexact so | |
8647 | that scm_integer_expt will use fast inexact arithmetic | |
8648 | internally. Note that making the base inexact is not | |
8649 | sufficient to guarantee an inexact result, because | |
8650 | scm_integer_expt will return an exact 1 when the exponent | |
8651 | is 0, even if the base is inexact. */ | |
8652 | return scm_exact_to_inexact | |
8653 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8654 | scm_inexact_to_exact (y))); | |
8655 | } | |
8656 | } | |
6fc4d012 AW |
8657 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8658 | { | |
8659 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8660 | } | |
2519490c | 8661 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8662 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8663 | else if (scm_is_complex (x)) |
8664 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8665 | else | |
8666 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8667 | } |
1bbd0b84 | 8668 | #undef FUNC_NAME |
0f2d19dd | 8669 | |
7f41099e MW |
8670 | /* sin/cos/tan/asin/acos/atan |
8671 | sinh/cosh/tanh/asinh/acosh/atanh | |
8672 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8673 | Written by Jerry D. Hedden, (C) FSF. | |
8674 | See the file `COPYING' for terms applying to this program. */ | |
8675 | ||
ad79736c AW |
8676 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8677 | (SCM z), | |
8678 | "Compute the sine of @var{z}.") | |
8679 | #define FUNC_NAME s_scm_sin | |
8680 | { | |
8deddc94 MW |
8681 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8682 | return z; /* sin(exact0) = exact0 */ | |
8683 | else if (scm_is_real (z)) | |
ad79736c AW |
8684 | return scm_from_double (sin (scm_to_double (z))); |
8685 | else if (SCM_COMPLEXP (z)) | |
8686 | { double x, y; | |
8687 | x = SCM_COMPLEX_REAL (z); | |
8688 | y = SCM_COMPLEX_IMAG (z); | |
8689 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8690 | cos (x) * sinh (y)); | |
8691 | } | |
8692 | else | |
8693 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8694 | } | |
8695 | #undef FUNC_NAME | |
0f2d19dd | 8696 | |
ad79736c AW |
8697 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8698 | (SCM z), | |
8699 | "Compute the cosine of @var{z}.") | |
8700 | #define FUNC_NAME s_scm_cos | |
8701 | { | |
8deddc94 MW |
8702 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8703 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8704 | else if (scm_is_real (z)) | |
ad79736c AW |
8705 | return scm_from_double (cos (scm_to_double (z))); |
8706 | else if (SCM_COMPLEXP (z)) | |
8707 | { double x, y; | |
8708 | x = SCM_COMPLEX_REAL (z); | |
8709 | y = SCM_COMPLEX_IMAG (z); | |
8710 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8711 | -sin (x) * sinh (y)); | |
8712 | } | |
8713 | else | |
8714 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8715 | } | |
8716 | #undef FUNC_NAME | |
8717 | ||
8718 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8719 | (SCM z), | |
8720 | "Compute the tangent of @var{z}.") | |
8721 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8722 | { |
8deddc94 MW |
8723 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8724 | return z; /* tan(exact0) = exact0 */ | |
8725 | else if (scm_is_real (z)) | |
ad79736c AW |
8726 | return scm_from_double (tan (scm_to_double (z))); |
8727 | else if (SCM_COMPLEXP (z)) | |
8728 | { double x, y, w; | |
8729 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8730 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8731 | w = cos (x) + cosh (y); | |
8732 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8733 | if (w == 0.0) | |
8734 | scm_num_overflow (s_scm_tan); | |
8735 | #endif | |
8736 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8737 | } | |
8738 | else | |
8739 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8740 | } | |
8741 | #undef FUNC_NAME | |
8742 | ||
8743 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8744 | (SCM z), | |
8745 | "Compute the hyperbolic sine of @var{z}.") | |
8746 | #define FUNC_NAME s_scm_sinh | |
8747 | { | |
8deddc94 MW |
8748 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8749 | return z; /* sinh(exact0) = exact0 */ | |
8750 | else if (scm_is_real (z)) | |
ad79736c AW |
8751 | return scm_from_double (sinh (scm_to_double (z))); |
8752 | else if (SCM_COMPLEXP (z)) | |
8753 | { double x, y; | |
8754 | x = SCM_COMPLEX_REAL (z); | |
8755 | y = SCM_COMPLEX_IMAG (z); | |
8756 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8757 | cosh (x) * sin (y)); | |
8758 | } | |
8759 | else | |
8760 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8761 | } | |
8762 | #undef FUNC_NAME | |
8763 | ||
8764 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8765 | (SCM z), | |
8766 | "Compute the hyperbolic cosine of @var{z}.") | |
8767 | #define FUNC_NAME s_scm_cosh | |
8768 | { | |
8deddc94 MW |
8769 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8770 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8771 | else if (scm_is_real (z)) | |
ad79736c AW |
8772 | return scm_from_double (cosh (scm_to_double (z))); |
8773 | else if (SCM_COMPLEXP (z)) | |
8774 | { double x, y; | |
8775 | x = SCM_COMPLEX_REAL (z); | |
8776 | y = SCM_COMPLEX_IMAG (z); | |
8777 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8778 | sinh (x) * sin (y)); | |
8779 | } | |
8780 | else | |
8781 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8782 | } | |
8783 | #undef FUNC_NAME | |
8784 | ||
8785 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8786 | (SCM z), | |
8787 | "Compute the hyperbolic tangent of @var{z}.") | |
8788 | #define FUNC_NAME s_scm_tanh | |
8789 | { | |
8deddc94 MW |
8790 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8791 | return z; /* tanh(exact0) = exact0 */ | |
8792 | else if (scm_is_real (z)) | |
ad79736c AW |
8793 | return scm_from_double (tanh (scm_to_double (z))); |
8794 | else if (SCM_COMPLEXP (z)) | |
8795 | { double x, y, w; | |
8796 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8797 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8798 | w = cosh (x) + cos (y); | |
8799 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8800 | if (w == 0.0) | |
8801 | scm_num_overflow (s_scm_tanh); | |
8802 | #endif | |
8803 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8804 | } | |
8805 | else | |
8806 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8807 | } | |
8808 | #undef FUNC_NAME | |
8809 | ||
8810 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8811 | (SCM z), | |
8812 | "Compute the arc sine of @var{z}.") | |
8813 | #define FUNC_NAME s_scm_asin | |
8814 | { | |
8deddc94 MW |
8815 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8816 | return z; /* asin(exact0) = exact0 */ | |
8817 | else if (scm_is_real (z)) | |
ad79736c AW |
8818 | { |
8819 | double w = scm_to_double (z); | |
8820 | if (w >= -1.0 && w <= 1.0) | |
8821 | return scm_from_double (asin (w)); | |
8822 | else | |
8823 | return scm_product (scm_c_make_rectangular (0, -1), | |
8824 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8825 | } | |
8826 | else if (SCM_COMPLEXP (z)) | |
8827 | { double x, y; | |
8828 | x = SCM_COMPLEX_REAL (z); | |
8829 | y = SCM_COMPLEX_IMAG (z); | |
8830 | return scm_product (scm_c_make_rectangular (0, -1), | |
8831 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8832 | } | |
8833 | else | |
8834 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8835 | } | |
8836 | #undef FUNC_NAME | |
8837 | ||
8838 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8839 | (SCM z), | |
8840 | "Compute the arc cosine of @var{z}.") | |
8841 | #define FUNC_NAME s_scm_acos | |
8842 | { | |
8deddc94 MW |
8843 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8844 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8845 | else if (scm_is_real (z)) | |
ad79736c AW |
8846 | { |
8847 | double w = scm_to_double (z); | |
8848 | if (w >= -1.0 && w <= 1.0) | |
8849 | return scm_from_double (acos (w)); | |
8850 | else | |
8851 | return scm_sum (scm_from_double (acos (0.0)), | |
8852 | scm_product (scm_c_make_rectangular (0, 1), | |
8853 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8854 | } | |
8855 | else if (SCM_COMPLEXP (z)) | |
8856 | { double x, y; | |
8857 | x = SCM_COMPLEX_REAL (z); | |
8858 | y = SCM_COMPLEX_IMAG (z); | |
8859 | return scm_sum (scm_from_double (acos (0.0)), | |
8860 | scm_product (scm_c_make_rectangular (0, 1), | |
8861 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8862 | } | |
8863 | else | |
8864 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8865 | } | |
8866 | #undef FUNC_NAME | |
8867 | ||
8868 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8869 | (SCM z, SCM y), | |
8870 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8871 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8872 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8873 | #define FUNC_NAME s_scm_atan | |
8874 | { | |
8875 | if (SCM_UNBNDP (y)) | |
8876 | { | |
8deddc94 MW |
8877 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8878 | return z; /* atan(exact0) = exact0 */ | |
8879 | else if (scm_is_real (z)) | |
ad79736c AW |
8880 | return scm_from_double (atan (scm_to_double (z))); |
8881 | else if (SCM_COMPLEXP (z)) | |
8882 | { | |
8883 | double v, w; | |
8884 | v = SCM_COMPLEX_REAL (z); | |
8885 | w = SCM_COMPLEX_IMAG (z); | |
8886 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8887 | scm_c_make_rectangular (v, w + 1.0))), | |
8888 | scm_c_make_rectangular (0, 2)); | |
8889 | } | |
8890 | else | |
18104cac | 8891 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8892 | } |
8893 | else if (scm_is_real (z)) | |
8894 | { | |
8895 | if (scm_is_real (y)) | |
8896 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8897 | else | |
8898 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8899 | } | |
8900 | else | |
8901 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8902 | } | |
8903 | #undef FUNC_NAME | |
8904 | ||
8905 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8906 | (SCM z), | |
8907 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8908 | #define FUNC_NAME s_scm_sys_asinh | |
8909 | { | |
8deddc94 MW |
8910 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8911 | return z; /* asinh(exact0) = exact0 */ | |
8912 | else if (scm_is_real (z)) | |
ad79736c AW |
8913 | return scm_from_double (asinh (scm_to_double (z))); |
8914 | else if (scm_is_number (z)) | |
8915 | return scm_log (scm_sum (z, | |
8916 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8917 | SCM_INUM1)))); |
ad79736c AW |
8918 | else |
8919 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8920 | } | |
8921 | #undef FUNC_NAME | |
8922 | ||
8923 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8924 | (SCM z), | |
8925 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8926 | #define FUNC_NAME s_scm_sys_acosh | |
8927 | { | |
8deddc94 MW |
8928 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8929 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8930 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8931 | return scm_from_double (acosh (scm_to_double (z))); |
8932 | else if (scm_is_number (z)) | |
8933 | return scm_log (scm_sum (z, | |
8934 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8935 | SCM_INUM1)))); |
ad79736c AW |
8936 | else |
8937 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8938 | } | |
8939 | #undef FUNC_NAME | |
8940 | ||
8941 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8942 | (SCM z), | |
8943 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8944 | #define FUNC_NAME s_scm_sys_atanh | |
8945 | { | |
8deddc94 MW |
8946 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8947 | return z; /* atanh(exact0) = exact0 */ | |
8948 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8949 | return scm_from_double (atanh (scm_to_double (z))); |
8950 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8951 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8952 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8953 | SCM_I_MAKINUM (2)); |
8954 | else | |
8955 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8956 | } |
1bbd0b84 | 8957 | #undef FUNC_NAME |
0f2d19dd | 8958 | |
8507ec80 MV |
8959 | SCM |
8960 | scm_c_make_rectangular (double re, double im) | |
8961 | { | |
c7218482 | 8962 | SCM z; |
03604fcf | 8963 | |
c7218482 MW |
8964 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8965 | "complex")); | |
8966 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8967 | SCM_COMPLEX_REAL (z) = re; | |
8968 | SCM_COMPLEX_IMAG (z) = im; | |
8969 | return z; | |
8507ec80 | 8970 | } |
0f2d19dd | 8971 | |
a1ec6916 | 8972 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 8973 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
8974 | "Return a complex number constructed of the given @var{real_part} " |
8975 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 8976 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8977 | { |
ad79736c AW |
8978 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8979 | SCM_ARG1, FUNC_NAME, "real"); | |
8980 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8981 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8982 | |
8983 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8984 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8985 | return real_part; | |
8986 | else | |
8987 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8988 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8989 | } |
1bbd0b84 | 8990 | #undef FUNC_NAME |
0f2d19dd | 8991 | |
8507ec80 MV |
8992 | SCM |
8993 | scm_c_make_polar (double mag, double ang) | |
8994 | { | |
8995 | double s, c; | |
5e647d08 LC |
8996 | |
8997 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8998 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8999 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
9000 | details. */ | |
9001 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
9002 | sincos (ang, &s, &c); |
9003 | #else | |
9004 | s = sin (ang); | |
9005 | c = cos (ang); | |
9006 | #endif | |
9d427b2c MW |
9007 | |
9008 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
9009 | infinite, or perhaps simply too large to determine its value | |
9010 | mod 2*pi. However, we know something that the floating-point | |
9011 | implementation doesn't know: We know that s and c are finite. | |
9012 | Therefore, if the magnitude is zero, return a complex zero. | |
9013 | ||
9014 | The reason we check for the NaNs instead of using this case | |
9015 | whenever mag == 0.0 is because when the angle is known, we'd | |
9016 | like to return the correct kind of non-real complex zero: | |
9017 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
9018 | on which quadrant the angle is in. | |
9019 | */ | |
9020 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
9021 | return scm_c_make_rectangular (0.0, 0.0); | |
9022 | else | |
9023 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 9024 | } |
0f2d19dd | 9025 | |
a1ec6916 | 9026 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
9027 | (SCM mag, SCM ang), |
9028 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 9029 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 9030 | { |
c7218482 MW |
9031 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
9032 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
9033 | ||
9034 | /* If mag is exact0, return exact0 */ | |
9035 | if (scm_is_eq (mag, SCM_INUM0)) | |
9036 | return SCM_INUM0; | |
9037 | /* Return a real if ang is exact0 */ | |
9038 | else if (scm_is_eq (ang, SCM_INUM0)) | |
9039 | return mag; | |
9040 | else | |
9041 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 9042 | } |
1bbd0b84 | 9043 | #undef FUNC_NAME |
0f2d19dd JB |
9044 | |
9045 | ||
2519490c MW |
9046 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
9047 | (SCM z), | |
9048 | "Return the real part of the number @var{z}.") | |
9049 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 9050 | { |
2519490c | 9051 | if (SCM_COMPLEXP (z)) |
55f26379 | 9052 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 9053 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 9054 | return z; |
0aacf84e | 9055 | else |
2519490c | 9056 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 9057 | } |
2519490c | 9058 | #undef FUNC_NAME |
0f2d19dd JB |
9059 | |
9060 | ||
2519490c MW |
9061 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
9062 | (SCM z), | |
9063 | "Return the imaginary part of the number @var{z}.") | |
9064 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 9065 | { |
2519490c MW |
9066 | if (SCM_COMPLEXP (z)) |
9067 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 9068 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 9069 | return SCM_INUM0; |
0aacf84e | 9070 | else |
2519490c | 9071 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 9072 | } |
2519490c | 9073 | #undef FUNC_NAME |
0f2d19dd | 9074 | |
2519490c MW |
9075 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
9076 | (SCM z), | |
9077 | "Return the numerator of the number @var{z}.") | |
9078 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 9079 | { |
2519490c | 9080 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
9081 | return z; |
9082 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 9083 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
9084 | else if (SCM_REALP (z)) |
9085 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
9086 | else | |
2519490c | 9087 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 9088 | } |
2519490c | 9089 | #undef FUNC_NAME |
f92e85f7 MV |
9090 | |
9091 | ||
2519490c MW |
9092 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
9093 | (SCM z), | |
9094 | "Return the denominator of the number @var{z}.") | |
9095 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 9096 | { |
2519490c | 9097 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 9098 | return SCM_INUM1; |
f92e85f7 | 9099 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 9100 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
9101 | else if (SCM_REALP (z)) |
9102 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
9103 | else | |
2519490c | 9104 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 9105 | } |
2519490c | 9106 | #undef FUNC_NAME |
0f2d19dd | 9107 | |
2519490c MW |
9108 | |
9109 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
9110 | (SCM z), | |
9111 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
9112 | "@code{abs} for real arguments, but also allows complex numbers.") | |
9113 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 9114 | { |
e11e83f3 | 9115 | if (SCM_I_INUMP (z)) |
0aacf84e | 9116 | { |
e25f3727 | 9117 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
9118 | if (zz >= 0) |
9119 | return z; | |
9120 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 9121 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 9122 | else |
e25f3727 | 9123 | return scm_i_inum2big (-zz); |
5986c47d | 9124 | } |
0aacf84e MD |
9125 | else if (SCM_BIGP (z)) |
9126 | { | |
9127 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9128 | scm_remember_upto_here_1 (z); | |
9129 | if (sgn < 0) | |
9130 | return scm_i_clonebig (z, 0); | |
9131 | else | |
9132 | return z; | |
5986c47d | 9133 | } |
0aacf84e | 9134 | else if (SCM_REALP (z)) |
55f26379 | 9135 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 9136 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9137 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
9138 | else if (SCM_FRACTIONP (z)) |
9139 | { | |
73e4de09 | 9140 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 9141 | return z; |
a285b18c MW |
9142 | return scm_i_make_ratio_already_reduced |
9143 | (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), | |
9144 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 | 9145 | } |
0aacf84e | 9146 | else |
2519490c | 9147 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 9148 | } |
2519490c | 9149 | #undef FUNC_NAME |
0f2d19dd JB |
9150 | |
9151 | ||
2519490c MW |
9152 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
9153 | (SCM z), | |
9154 | "Return the angle of the complex number @var{z}.") | |
9155 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 9156 | { |
c8ae173e | 9157 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 9158 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
9159 | But if atan2 follows the floating point rounding mode, then the value |
9160 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 9161 | if (SCM_I_INUMP (z)) |
0aacf84e | 9162 | { |
e11e83f3 | 9163 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 9164 | return flo0; |
0aacf84e | 9165 | else |
55f26379 | 9166 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 9167 | } |
0aacf84e MD |
9168 | else if (SCM_BIGP (z)) |
9169 | { | |
9170 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9171 | scm_remember_upto_here_1 (z); | |
9172 | if (sgn < 0) | |
55f26379 | 9173 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 9174 | else |
e7efe8e7 | 9175 | return flo0; |
0f2d19dd | 9176 | } |
0aacf84e | 9177 | else if (SCM_REALP (z)) |
c8ae173e | 9178 | { |
10a97755 MW |
9179 | double x = SCM_REAL_VALUE (z); |
9180 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
e7efe8e7 | 9181 | return flo0; |
c8ae173e | 9182 | else |
55f26379 | 9183 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 9184 | } |
0aacf84e | 9185 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9186 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
9187 | else if (SCM_FRACTIONP (z)) |
9188 | { | |
73e4de09 | 9189 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 9190 | return flo0; |
55f26379 | 9191 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 9192 | } |
0aacf84e | 9193 | else |
2519490c | 9194 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 9195 | } |
2519490c | 9196 | #undef FUNC_NAME |
0f2d19dd JB |
9197 | |
9198 | ||
2519490c MW |
9199 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
9200 | (SCM z), | |
9201 | "Convert the number @var{z} to its inexact representation.\n") | |
9202 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 9203 | { |
e11e83f3 | 9204 | if (SCM_I_INUMP (z)) |
55f26379 | 9205 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 9206 | else if (SCM_BIGP (z)) |
55f26379 | 9207 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 9208 | else if (SCM_FRACTIONP (z)) |
55f26379 | 9209 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
9210 | else if (SCM_INEXACTP (z)) |
9211 | return z; | |
9212 | else | |
2519490c | 9213 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 9214 | } |
2519490c | 9215 | #undef FUNC_NAME |
3c9a524f DH |
9216 | |
9217 | ||
2519490c MW |
9218 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
9219 | (SCM z), | |
9220 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 9221 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 9222 | { |
c7218482 | 9223 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 9224 | return z; |
c7218482 | 9225 | else |
0aacf84e | 9226 | { |
c7218482 MW |
9227 | double val; |
9228 | ||
9229 | if (SCM_REALP (z)) | |
9230 | val = SCM_REAL_VALUE (z); | |
9231 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
9232 | val = SCM_COMPLEX_REAL (z); | |
9233 | else | |
9234 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
9235 | ||
9236 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 9237 | SCM_OUT_OF_RANGE (1, z); |
24475b86 MW |
9238 | else if (val == 0.0) |
9239 | return SCM_INUM0; | |
2be24db4 | 9240 | else |
f92e85f7 | 9241 | { |
24475b86 MW |
9242 | int expon; |
9243 | SCM numerator; | |
9244 | ||
9245 | numerator = scm_i_dbl2big (ldexp (frexp (val, &expon), | |
9246 | DBL_MANT_DIG)); | |
9247 | expon -= DBL_MANT_DIG; | |
9248 | if (expon < 0) | |
9249 | { | |
9250 | int shift = mpz_scan1 (SCM_I_BIG_MPZ (numerator), 0); | |
9251 | ||
9252 | if (shift > -expon) | |
9253 | shift = -expon; | |
9254 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (numerator), | |
9255 | SCM_I_BIG_MPZ (numerator), | |
9256 | shift); | |
9257 | expon += shift; | |
9258 | } | |
9259 | numerator = scm_i_normbig (numerator); | |
9260 | if (expon < 0) | |
9261 | return scm_i_make_ratio_already_reduced | |
9262 | (numerator, left_shift_exact_integer (SCM_INUM1, -expon)); | |
9263 | else if (expon > 0) | |
9264 | return left_shift_exact_integer (numerator, expon); | |
9265 | else | |
9266 | return numerator; | |
f92e85f7 | 9267 | } |
c2ff8ab0 | 9268 | } |
0f2d19dd | 9269 | } |
1bbd0b84 | 9270 | #undef FUNC_NAME |
0f2d19dd | 9271 | |
f92e85f7 | 9272 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
9273 | (SCM x, SCM eps), |
9274 | "Returns the @emph{simplest} rational number differing\n" | |
9275 | "from @var{x} by no more than @var{eps}.\n" | |
9276 | "\n" | |
9277 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9278 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9279 | "to use @code{inexact->exact} on the arguments.\n" | |
9280 | "\n" | |
9281 | "@lisp\n" | |
9282 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9283 | "@result{} 6/5\n" | |
9284 | "@end lisp") | |
f92e85f7 MV |
9285 | #define FUNC_NAME s_scm_rationalize |
9286 | { | |
605f6980 MW |
9287 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9288 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9289 | eps = scm_abs (eps); | |
9290 | if (scm_is_false (scm_positive_p (eps))) | |
9291 | { | |
9292 | /* eps is either zero or a NaN */ | |
9293 | if (scm_is_true (scm_nan_p (eps))) | |
9294 | return scm_nan (); | |
9295 | else if (SCM_INEXACTP (eps)) | |
9296 | return scm_exact_to_inexact (x); | |
9297 | else | |
9298 | return x; | |
9299 | } | |
9300 | else if (scm_is_false (scm_finite_p (eps))) | |
9301 | { | |
9302 | if (scm_is_true (scm_finite_p (x))) | |
9303 | return flo0; | |
9304 | else | |
9305 | return scm_nan (); | |
9306 | } | |
9307 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9308 | return x; |
605f6980 MW |
9309 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9310 | scm_ceiling (scm_difference (x, eps))))) | |
9311 | { | |
9312 | /* There's an integer within range; we want the one closest to zero */ | |
9313 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9314 | { | |
9315 | /* zero is within range */ | |
9316 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9317 | return flo0; | |
9318 | else | |
9319 | return SCM_INUM0; | |
9320 | } | |
9321 | else if (scm_is_true (scm_positive_p (x))) | |
9322 | return scm_ceiling (scm_difference (x, eps)); | |
9323 | else | |
9324 | return scm_floor (scm_sum (x, eps)); | |
9325 | } | |
9326 | else | |
f92e85f7 MV |
9327 | { |
9328 | /* Use continued fractions to find closest ratio. All | |
9329 | arithmetic is done with exact numbers. | |
9330 | */ | |
9331 | ||
9332 | SCM ex = scm_inexact_to_exact (x); | |
9333 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9334 | SCM tt = SCM_INUM1; |
9335 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9336 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9337 | SCM rx; |
9338 | int i = 0; | |
9339 | ||
f92e85f7 MV |
9340 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9341 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9342 | ||
9343 | /* We stop after a million iterations just to be absolutely sure | |
9344 | that we don't go into an infinite loop. The process normally | |
9345 | converges after less than a dozen iterations. | |
9346 | */ | |
9347 | ||
f92e85f7 MV |
9348 | while (++i < 1000000) |
9349 | { | |
9350 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9351 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9352 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9353 | scm_is_false | |
f92e85f7 | 9354 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9355 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9356 | { |
9357 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9358 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9359 | return scm_exact_to_inexact (res); |
9360 | else | |
9361 | return res; | |
9362 | } | |
f92e85f7 MV |
9363 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9364 | SCM_UNDEFINED); | |
9365 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9366 | a2 = a1; | |
9367 | b2 = b1; | |
9368 | a1 = a; | |
9369 | b1 = b; | |
9370 | } | |
9371 | scm_num_overflow (s_scm_rationalize); | |
9372 | } | |
f92e85f7 MV |
9373 | } |
9374 | #undef FUNC_NAME | |
9375 | ||
73e4de09 MV |
9376 | /* conversion functions */ |
9377 | ||
9378 | int | |
9379 | scm_is_integer (SCM val) | |
9380 | { | |
9381 | return scm_is_true (scm_integer_p (val)); | |
9382 | } | |
9383 | ||
9384 | int | |
9385 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9386 | { | |
e11e83f3 | 9387 | if (SCM_I_INUMP (val)) |
73e4de09 | 9388 | { |
e11e83f3 | 9389 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9390 | return n >= min && n <= max; |
9391 | } | |
9392 | else if (SCM_BIGP (val)) | |
9393 | { | |
9394 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9395 | return 0; | |
9396 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9397 | { |
9398 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9399 | { | |
9400 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9401 | return n >= min && n <= max; | |
9402 | } | |
9403 | else | |
9404 | return 0; | |
9405 | } | |
73e4de09 MV |
9406 | else |
9407 | { | |
d956fa6f MV |
9408 | scm_t_intmax n; |
9409 | size_t count; | |
73e4de09 | 9410 | |
d956fa6f MV |
9411 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9412 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9413 | return 0; | |
9414 | ||
9415 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9416 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9417 | |
d956fa6f | 9418 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9419 | { |
d956fa6f MV |
9420 | if (n < 0) |
9421 | return 0; | |
73e4de09 | 9422 | } |
73e4de09 MV |
9423 | else |
9424 | { | |
d956fa6f MV |
9425 | n = -n; |
9426 | if (n >= 0) | |
9427 | return 0; | |
73e4de09 | 9428 | } |
d956fa6f MV |
9429 | |
9430 | return n >= min && n <= max; | |
73e4de09 MV |
9431 | } |
9432 | } | |
73e4de09 MV |
9433 | else |
9434 | return 0; | |
9435 | } | |
9436 | ||
9437 | int | |
9438 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9439 | { | |
e11e83f3 | 9440 | if (SCM_I_INUMP (val)) |
73e4de09 | 9441 | { |
e11e83f3 | 9442 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9443 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9444 | } | |
9445 | else if (SCM_BIGP (val)) | |
9446 | { | |
9447 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9448 | return 0; | |
9449 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9450 | { |
9451 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9452 | { | |
9453 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9454 | return n >= min && n <= max; | |
9455 | } | |
9456 | else | |
9457 | return 0; | |
9458 | } | |
73e4de09 MV |
9459 | else |
9460 | { | |
d956fa6f MV |
9461 | scm_t_uintmax n; |
9462 | size_t count; | |
73e4de09 | 9463 | |
d956fa6f MV |
9464 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9465 | return 0; | |
73e4de09 | 9466 | |
d956fa6f MV |
9467 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9468 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9469 | return 0; |
d956fa6f MV |
9470 | |
9471 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9472 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9473 | |
d956fa6f | 9474 | return n >= min && n <= max; |
73e4de09 MV |
9475 | } |
9476 | } | |
73e4de09 MV |
9477 | else |
9478 | return 0; | |
9479 | } | |
9480 | ||
1713d319 MV |
9481 | static void |
9482 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9483 | { | |
9484 | scm_error (scm_out_of_range_key, | |
9485 | NULL, | |
9486 | "Value out of range ~S to ~S: ~S", | |
9487 | scm_list_3 (min, max, bad_val), | |
9488 | scm_list_1 (bad_val)); | |
9489 | } | |
9490 | ||
bfd7932e MV |
9491 | #define TYPE scm_t_intmax |
9492 | #define TYPE_MIN min | |
9493 | #define TYPE_MAX max | |
9494 | #define SIZEOF_TYPE 0 | |
9495 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9496 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9497 | #include "libguile/conv-integer.i.c" | |
9498 | ||
9499 | #define TYPE scm_t_uintmax | |
9500 | #define TYPE_MIN min | |
9501 | #define TYPE_MAX max | |
9502 | #define SIZEOF_TYPE 0 | |
9503 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9504 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9505 | #include "libguile/conv-uinteger.i.c" | |
9506 | ||
9507 | #define TYPE scm_t_int8 | |
9508 | #define TYPE_MIN SCM_T_INT8_MIN | |
9509 | #define TYPE_MAX SCM_T_INT8_MAX | |
9510 | #define SIZEOF_TYPE 1 | |
9511 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9512 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9513 | #include "libguile/conv-integer.i.c" | |
9514 | ||
9515 | #define TYPE scm_t_uint8 | |
9516 | #define TYPE_MIN 0 | |
9517 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9518 | #define SIZEOF_TYPE 1 | |
9519 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9520 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9521 | #include "libguile/conv-uinteger.i.c" | |
9522 | ||
9523 | #define TYPE scm_t_int16 | |
9524 | #define TYPE_MIN SCM_T_INT16_MIN | |
9525 | #define TYPE_MAX SCM_T_INT16_MAX | |
9526 | #define SIZEOF_TYPE 2 | |
9527 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9528 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9529 | #include "libguile/conv-integer.i.c" | |
9530 | ||
9531 | #define TYPE scm_t_uint16 | |
9532 | #define TYPE_MIN 0 | |
9533 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9534 | #define SIZEOF_TYPE 2 | |
9535 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9536 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9537 | #include "libguile/conv-uinteger.i.c" | |
9538 | ||
9539 | #define TYPE scm_t_int32 | |
9540 | #define TYPE_MIN SCM_T_INT32_MIN | |
9541 | #define TYPE_MAX SCM_T_INT32_MAX | |
9542 | #define SIZEOF_TYPE 4 | |
9543 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9544 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9545 | #include "libguile/conv-integer.i.c" | |
9546 | ||
9547 | #define TYPE scm_t_uint32 | |
9548 | #define TYPE_MIN 0 | |
9549 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9550 | #define SIZEOF_TYPE 4 | |
9551 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9552 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9553 | #include "libguile/conv-uinteger.i.c" | |
9554 | ||
904a78f1 MG |
9555 | #define TYPE scm_t_wchar |
9556 | #define TYPE_MIN (scm_t_int32)-1 | |
9557 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9558 | #define SIZEOF_TYPE 4 | |
9559 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9560 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9561 | #include "libguile/conv-integer.i.c" | |
9562 | ||
bfd7932e MV |
9563 | #define TYPE scm_t_int64 |
9564 | #define TYPE_MIN SCM_T_INT64_MIN | |
9565 | #define TYPE_MAX SCM_T_INT64_MAX | |
9566 | #define SIZEOF_TYPE 8 | |
9567 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9568 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9569 | #include "libguile/conv-integer.i.c" | |
9570 | ||
9571 | #define TYPE scm_t_uint64 | |
9572 | #define TYPE_MIN 0 | |
9573 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9574 | #define SIZEOF_TYPE 8 | |
9575 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9576 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9577 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9578 | |
cd036260 MV |
9579 | void |
9580 | scm_to_mpz (SCM val, mpz_t rop) | |
9581 | { | |
9582 | if (SCM_I_INUMP (val)) | |
9583 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9584 | else if (SCM_BIGP (val)) | |
9585 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9586 | else | |
9587 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9588 | } | |
9589 | ||
9590 | SCM | |
9591 | scm_from_mpz (mpz_t val) | |
9592 | { | |
9593 | return scm_i_mpz2num (val); | |
9594 | } | |
9595 | ||
73e4de09 MV |
9596 | int |
9597 | scm_is_real (SCM val) | |
9598 | { | |
9599 | return scm_is_true (scm_real_p (val)); | |
9600 | } | |
9601 | ||
55f26379 MV |
9602 | int |
9603 | scm_is_rational (SCM val) | |
9604 | { | |
9605 | return scm_is_true (scm_rational_p (val)); | |
9606 | } | |
9607 | ||
73e4de09 MV |
9608 | double |
9609 | scm_to_double (SCM val) | |
9610 | { | |
55f26379 MV |
9611 | if (SCM_I_INUMP (val)) |
9612 | return SCM_I_INUM (val); | |
9613 | else if (SCM_BIGP (val)) | |
9614 | return scm_i_big2dbl (val); | |
9615 | else if (SCM_FRACTIONP (val)) | |
9616 | return scm_i_fraction2double (val); | |
9617 | else if (SCM_REALP (val)) | |
9618 | return SCM_REAL_VALUE (val); | |
9619 | else | |
7a1aba42 | 9620 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9621 | } |
9622 | ||
9623 | SCM | |
9624 | scm_from_double (double val) | |
9625 | { | |
978c52d1 LC |
9626 | SCM z; |
9627 | ||
9628 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9629 | ||
9630 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9631 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9632 | |
55f26379 | 9633 | return z; |
73e4de09 MV |
9634 | } |
9635 | ||
220058a8 | 9636 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9637 | |
9638 | float | |
e25f3727 | 9639 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9640 | { |
220058a8 AW |
9641 | scm_c_issue_deprecation_warning |
9642 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9643 | ||
55f26379 MV |
9644 | if (SCM_BIGP (num)) |
9645 | { | |
9646 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9647 | if (!isinf (res)) |
55f26379 MV |
9648 | return res; |
9649 | else | |
9650 | scm_out_of_range (NULL, num); | |
9651 | } | |
9652 | else | |
9653 | return scm_to_double (num); | |
9654 | } | |
9655 | ||
9656 | double | |
e25f3727 | 9657 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9658 | { |
220058a8 AW |
9659 | scm_c_issue_deprecation_warning |
9660 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9661 | ||
55f26379 MV |
9662 | if (SCM_BIGP (num)) |
9663 | { | |
9664 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9665 | if (!isinf (res)) |
55f26379 MV |
9666 | return res; |
9667 | else | |
9668 | scm_out_of_range (NULL, num); | |
9669 | } | |
9670 | else | |
9671 | return scm_to_double (num); | |
9672 | } | |
9673 | ||
9674 | #endif | |
9675 | ||
8507ec80 MV |
9676 | int |
9677 | scm_is_complex (SCM val) | |
9678 | { | |
9679 | return scm_is_true (scm_complex_p (val)); | |
9680 | } | |
9681 | ||
9682 | double | |
9683 | scm_c_real_part (SCM z) | |
9684 | { | |
9685 | if (SCM_COMPLEXP (z)) | |
9686 | return SCM_COMPLEX_REAL (z); | |
9687 | else | |
9688 | { | |
9689 | /* Use the scm_real_part to get proper error checking and | |
9690 | dispatching. | |
9691 | */ | |
9692 | return scm_to_double (scm_real_part (z)); | |
9693 | } | |
9694 | } | |
9695 | ||
9696 | double | |
9697 | scm_c_imag_part (SCM z) | |
9698 | { | |
9699 | if (SCM_COMPLEXP (z)) | |
9700 | return SCM_COMPLEX_IMAG (z); | |
9701 | else | |
9702 | { | |
9703 | /* Use the scm_imag_part to get proper error checking and | |
9704 | dispatching. The result will almost always be 0.0, but not | |
9705 | always. | |
9706 | */ | |
9707 | return scm_to_double (scm_imag_part (z)); | |
9708 | } | |
9709 | } | |
9710 | ||
9711 | double | |
9712 | scm_c_magnitude (SCM z) | |
9713 | { | |
9714 | return scm_to_double (scm_magnitude (z)); | |
9715 | } | |
9716 | ||
9717 | double | |
9718 | scm_c_angle (SCM z) | |
9719 | { | |
9720 | return scm_to_double (scm_angle (z)); | |
9721 | } | |
9722 | ||
9723 | int | |
9724 | scm_is_number (SCM z) | |
9725 | { | |
9726 | return scm_is_true (scm_number_p (z)); | |
9727 | } | |
9728 | ||
8ab3d8a0 | 9729 | |
a5f6b751 MW |
9730 | /* Returns log(x * 2^shift) */ |
9731 | static SCM | |
9732 | log_of_shifted_double (double x, long shift) | |
9733 | { | |
9734 | double ans = log (fabs (x)) + shift * M_LN2; | |
9735 | ||
9736 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9737 | return scm_from_double (ans); | |
9738 | else | |
9739 | return scm_c_make_rectangular (ans, M_PI); | |
9740 | } | |
9741 | ||
85bdb6ac | 9742 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9743 | static SCM |
9744 | log_of_exact_integer (SCM n) | |
9745 | { | |
7f34acd8 MW |
9746 | if (SCM_I_INUMP (n)) |
9747 | return log_of_shifted_double (SCM_I_INUM (n), 0); | |
9748 | else if (SCM_BIGP (n)) | |
9749 | { | |
9750 | long expon; | |
9751 | double signif = scm_i_big2dbl_2exp (n, &expon); | |
9752 | return log_of_shifted_double (signif, expon); | |
9753 | } | |
9754 | else | |
9755 | scm_wrong_type_arg ("log_of_exact_integer", SCM_ARG1, n); | |
a5f6b751 MW |
9756 | } |
9757 | ||
9758 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9759 | static SCM | |
9760 | log_of_fraction (SCM n, SCM d) | |
9761 | { | |
9762 | long n_size = scm_to_long (scm_integer_length (n)); | |
9763 | long d_size = scm_to_long (scm_integer_length (d)); | |
9764 | ||
9765 | if (abs (n_size - d_size) > 1) | |
7f34acd8 MW |
9766 | return (scm_difference (log_of_exact_integer (n), |
9767 | log_of_exact_integer (d))); | |
a5f6b751 MW |
9768 | else if (scm_is_false (scm_negative_p (n))) |
9769 | return scm_from_double | |
98237784 | 9770 | (log1p (scm_i_divide2double (scm_difference (n, d), d))); |
a5f6b751 MW |
9771 | else |
9772 | return scm_c_make_rectangular | |
98237784 MW |
9773 | (log1p (scm_i_divide2double (scm_difference (scm_abs (n), d), |
9774 | d)), | |
a5f6b751 MW |
9775 | M_PI); |
9776 | } | |
9777 | ||
9778 | ||
8ab3d8a0 KR |
9779 | /* In the following functions we dispatch to the real-arg funcs like log() |
9780 | when we know the arg is real, instead of just handing everything to | |
9781 | clog() for instance. This is in case clog() doesn't optimize for a | |
9782 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9783 | well use it to go straight to the applicable C func. */ | |
9784 | ||
2519490c MW |
9785 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9786 | (SCM z), | |
9787 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9788 | #define FUNC_NAME s_scm_log |
9789 | { | |
9790 | if (SCM_COMPLEXP (z)) | |
9791 | { | |
03976fee AW |
9792 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9793 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9794 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9795 | #else | |
9796 | double re = SCM_COMPLEX_REAL (z); | |
9797 | double im = SCM_COMPLEX_IMAG (z); | |
9798 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9799 | atan2 (im, re)); | |
9800 | #endif | |
9801 | } | |
a5f6b751 MW |
9802 | else if (SCM_REALP (z)) |
9803 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9804 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9805 | { |
a5f6b751 MW |
9806 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9807 | if (scm_is_eq (z, SCM_INUM0)) | |
9808 | scm_num_overflow (s_scm_log); | |
9809 | #endif | |
9810 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9811 | } |
a5f6b751 MW |
9812 | else if (SCM_BIGP (z)) |
9813 | return log_of_exact_integer (z); | |
9814 | else if (SCM_FRACTIONP (z)) | |
9815 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9816 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9817 | else |
9818 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9819 | } |
9820 | #undef FUNC_NAME | |
9821 | ||
9822 | ||
2519490c MW |
9823 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9824 | (SCM z), | |
9825 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9826 | #define FUNC_NAME s_scm_log10 |
9827 | { | |
9828 | if (SCM_COMPLEXP (z)) | |
9829 | { | |
9830 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9831 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9832 | log10+hypot+atan2.) */ | |
f328f862 LC |
9833 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9834 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9835 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9836 | #else | |
9837 | double re = SCM_COMPLEX_REAL (z); | |
9838 | double im = SCM_COMPLEX_IMAG (z); | |
9839 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9840 | M_LOG10E * atan2 (im, re)); | |
9841 | #endif | |
9842 | } | |
a5f6b751 | 9843 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9844 | { |
a5f6b751 MW |
9845 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9846 | if (scm_is_eq (z, SCM_INUM0)) | |
9847 | scm_num_overflow (s_scm_log10); | |
9848 | #endif | |
9849 | { | |
9850 | double re = scm_to_double (z); | |
9851 | double l = log10 (fabs (re)); | |
9852 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9853 | return scm_from_double (l); | |
9854 | else | |
9855 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9856 | } | |
8ab3d8a0 | 9857 | } |
a5f6b751 MW |
9858 | else if (SCM_BIGP (z)) |
9859 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9860 | else if (SCM_FRACTIONP (z)) | |
9861 | return scm_product (flo_log10e, | |
9862 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9863 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9864 | else |
9865 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9866 | } |
9867 | #undef FUNC_NAME | |
9868 | ||
9869 | ||
2519490c MW |
9870 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9871 | (SCM z), | |
9872 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9873 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9874 | #define FUNC_NAME s_scm_exp |
9875 | { | |
9876 | if (SCM_COMPLEXP (z)) | |
9877 | { | |
93723f3d MW |
9878 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9879 | && defined (SCM_COMPLEX_VALUE) | |
9880 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); | |
9881 | #else | |
8ab3d8a0 KR |
9882 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), |
9883 | SCM_COMPLEX_IMAG (z)); | |
93723f3d | 9884 | #endif |
8ab3d8a0 | 9885 | } |
2519490c | 9886 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9887 | { |
9888 | /* When z is a negative bignum the conversion to double overflows, | |
9889 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9890 | return scm_from_double (exp (scm_to_double (z))); | |
9891 | } | |
2519490c MW |
9892 | else |
9893 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9894 | } |
9895 | #undef FUNC_NAME | |
9896 | ||
9897 | ||
882c8963 MW |
9898 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9899 | (SCM k), | |
9900 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9901 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9902 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9903 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9904 | "\n" | |
9905 | "@lisp\n" | |
9906 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9907 | "@end lisp") | |
9908 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9909 | { | |
9910 | SCM s, r; | |
9911 | ||
9912 | scm_exact_integer_sqrt (k, &s, &r); | |
9913 | return scm_values (scm_list_2 (s, r)); | |
9914 | } | |
9915 | #undef FUNC_NAME | |
9916 | ||
9917 | void | |
9918 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9919 | { | |
9920 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9921 | { | |
687a87bf | 9922 | mpz_t kk, ss, rr; |
882c8963 | 9923 | |
687a87bf | 9924 | if (SCM_I_INUM (k) < 0) |
882c8963 MW |
9925 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, |
9926 | "exact non-negative integer"); | |
687a87bf MW |
9927 | mpz_init_set_ui (kk, SCM_I_INUM (k)); |
9928 | mpz_inits (ss, rr, NULL); | |
9929 | mpz_sqrtrem (ss, rr, kk); | |
9930 | *sp = SCM_I_MAKINUM (mpz_get_ui (ss)); | |
9931 | *rp = SCM_I_MAKINUM (mpz_get_ui (rr)); | |
9932 | mpz_clears (kk, ss, rr, NULL); | |
882c8963 MW |
9933 | } |
9934 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9935 | { | |
9936 | SCM s, r; | |
9937 | ||
9938 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9939 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9940 | "exact non-negative integer"); | |
9941 | s = scm_i_mkbig (); | |
9942 | r = scm_i_mkbig (); | |
9943 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9944 | scm_remember_upto_here_1 (k); | |
9945 | *sp = scm_i_normbig (s); | |
9946 | *rp = scm_i_normbig (r); | |
9947 | } | |
9948 | else | |
9949 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9950 | "exact non-negative integer"); | |
9951 | } | |
9952 | ||
ddb71742 MW |
9953 | /* Return true iff K is a perfect square. |
9954 | K must be an exact integer. */ | |
9955 | static int | |
9956 | exact_integer_is_perfect_square (SCM k) | |
9957 | { | |
9958 | int result; | |
9959 | ||
9960 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9961 | { | |
9962 | mpz_t kk; | |
9963 | ||
9964 | mpz_init_set_si (kk, SCM_I_INUM (k)); | |
9965 | result = mpz_perfect_square_p (kk); | |
9966 | mpz_clear (kk); | |
9967 | } | |
9968 | else | |
9969 | { | |
9970 | result = mpz_perfect_square_p (SCM_I_BIG_MPZ (k)); | |
9971 | scm_remember_upto_here_1 (k); | |
9972 | } | |
9973 | return result; | |
9974 | } | |
9975 | ||
9976 | /* Return the floor of the square root of K. | |
9977 | K must be an exact integer. */ | |
9978 | static SCM | |
9979 | exact_integer_floor_square_root (SCM k) | |
9980 | { | |
9981 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9982 | { | |
9983 | mpz_t kk; | |
9984 | scm_t_inum ss; | |
9985 | ||
9986 | mpz_init_set_ui (kk, SCM_I_INUM (k)); | |
9987 | mpz_sqrt (kk, kk); | |
9988 | ss = mpz_get_ui (kk); | |
9989 | mpz_clear (kk); | |
9990 | return SCM_I_MAKINUM (ss); | |
9991 | } | |
9992 | else | |
9993 | { | |
9994 | SCM s; | |
9995 | ||
9996 | s = scm_i_mkbig (); | |
9997 | mpz_sqrt (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (k)); | |
9998 | scm_remember_upto_here_1 (k); | |
9999 | return scm_i_normbig (s); | |
10000 | } | |
10001 | } | |
10002 | ||
882c8963 | 10003 | |
2519490c MW |
10004 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
10005 | (SCM z), | |
10006 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 10007 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
10008 | "is returned, or if that's zero then a positive imaginary part.\n" |
10009 | "Thus,\n" | |
10010 | "\n" | |
10011 | "@example\n" | |
10012 | "(sqrt 9.0) @result{} 3.0\n" | |
10013 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
10014 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
10015 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
10016 | "@end example") | |
8ab3d8a0 KR |
10017 | #define FUNC_NAME s_scm_sqrt |
10018 | { | |
2519490c | 10019 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 10020 | { |
f328f862 LC |
10021 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
10022 | && defined SCM_COMPLEX_VALUE | |
2519490c | 10023 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 10024 | #else |
2519490c MW |
10025 | double re = SCM_COMPLEX_REAL (z); |
10026 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
10027 | return scm_c_make_polar (sqrt (hypot (re, im)), |
10028 | 0.5 * atan2 (im, re)); | |
10029 | #endif | |
10030 | } | |
2519490c | 10031 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 10032 | { |
44002664 MW |
10033 | if (SCM_I_INUMP (z)) |
10034 | { | |
ddb71742 MW |
10035 | scm_t_inum x = SCM_I_INUM (z); |
10036 | ||
10037 | if (SCM_LIKELY (x >= 0)) | |
44002664 | 10038 | { |
ddb71742 MW |
10039 | if (SCM_LIKELY (SCM_I_FIXNUM_BIT < DBL_MANT_DIG |
10040 | || x < (1L << (DBL_MANT_DIG - 1)))) | |
44002664 | 10041 | { |
ddb71742 | 10042 | double root = sqrt (x); |
44002664 MW |
10043 | |
10044 | /* If 0 <= x < 2^(DBL_MANT_DIG-1) and sqrt(x) is an | |
10045 | integer, then the result is exact. */ | |
10046 | if (root == floor (root)) | |
10047 | return SCM_I_MAKINUM ((scm_t_inum) root); | |
10048 | else | |
10049 | return scm_from_double (root); | |
10050 | } | |
10051 | else | |
10052 | { | |
ddb71742 | 10053 | mpz_t xx; |
44002664 MW |
10054 | scm_t_inum root; |
10055 | ||
ddb71742 MW |
10056 | mpz_init_set_ui (xx, x); |
10057 | if (mpz_perfect_square_p (xx)) | |
44002664 | 10058 | { |
ddb71742 MW |
10059 | mpz_sqrt (xx, xx); |
10060 | root = mpz_get_ui (xx); | |
10061 | mpz_clear (xx); | |
44002664 MW |
10062 | return SCM_I_MAKINUM (root); |
10063 | } | |
10064 | else | |
ddb71742 | 10065 | mpz_clear (xx); |
44002664 MW |
10066 | } |
10067 | } | |
10068 | } | |
10069 | else if (SCM_BIGP (z)) | |
10070 | { | |
ddb71742 | 10071 | if (mpz_perfect_square_p (SCM_I_BIG_MPZ (z))) |
44002664 MW |
10072 | { |
10073 | SCM root = scm_i_mkbig (); | |
10074 | ||
10075 | mpz_sqrt (SCM_I_BIG_MPZ (root), SCM_I_BIG_MPZ (z)); | |
10076 | scm_remember_upto_here_1 (z); | |
10077 | return scm_i_normbig (root); | |
10078 | } | |
ddb71742 MW |
10079 | else |
10080 | { | |
10081 | long expon; | |
10082 | double signif = scm_i_big2dbl_2exp (z, &expon); | |
10083 | ||
10084 | if (expon & 1) | |
10085 | { | |
10086 | signif *= 2; | |
10087 | expon--; | |
10088 | } | |
10089 | if (signif < 0) | |
10090 | return scm_c_make_rectangular | |
10091 | (0.0, ldexp (sqrt (-signif), expon / 2)); | |
10092 | else | |
10093 | return scm_from_double (ldexp (sqrt (signif), expon / 2)); | |
10094 | } | |
44002664 MW |
10095 | } |
10096 | else if (SCM_FRACTIONP (z)) | |
ddb71742 MW |
10097 | { |
10098 | SCM n = SCM_FRACTION_NUMERATOR (z); | |
10099 | SCM d = SCM_FRACTION_DENOMINATOR (z); | |
10100 | ||
10101 | if (exact_integer_is_perfect_square (n) | |
10102 | && exact_integer_is_perfect_square (d)) | |
10103 | return scm_i_make_ratio_already_reduced | |
10104 | (exact_integer_floor_square_root (n), | |
10105 | exact_integer_floor_square_root (d)); | |
10106 | else | |
10107 | { | |
10108 | double xx = scm_i_divide2double (n, d); | |
10109 | double abs_xx = fabs (xx); | |
10110 | long shift = 0; | |
10111 | ||
10112 | if (SCM_UNLIKELY (abs_xx > DBL_MAX || abs_xx < DBL_MIN)) | |
10113 | { | |
10114 | shift = (scm_to_long (scm_integer_length (n)) | |
10115 | - scm_to_long (scm_integer_length (d))) / 2; | |
10116 | if (shift > 0) | |
10117 | d = left_shift_exact_integer (d, 2 * shift); | |
10118 | else | |
10119 | n = left_shift_exact_integer (n, -2 * shift); | |
10120 | xx = scm_i_divide2double (n, d); | |
10121 | } | |
10122 | ||
10123 | if (xx < 0) | |
10124 | return scm_c_make_rectangular (0.0, ldexp (sqrt (-xx), shift)); | |
10125 | else | |
10126 | return scm_from_double (ldexp (sqrt (xx), shift)); | |
10127 | } | |
10128 | } | |
44002664 MW |
10129 | |
10130 | /* Fallback method, when the cases above do not apply. */ | |
10131 | { | |
10132 | double xx = scm_to_double (z); | |
10133 | if (xx < 0) | |
10134 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
10135 | else | |
10136 | return scm_from_double (sqrt (xx)); | |
10137 | } | |
8ab3d8a0 | 10138 | } |
2519490c MW |
10139 | else |
10140 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
10141 | } |
10142 | #undef FUNC_NAME | |
10143 | ||
10144 | ||
10145 | ||
0f2d19dd JB |
10146 | void |
10147 | scm_init_numbers () | |
0f2d19dd | 10148 | { |
b57bf272 AW |
10149 | if (scm_install_gmp_memory_functions) |
10150 | mp_set_memory_functions (custom_gmp_malloc, | |
10151 | custom_gmp_realloc, | |
10152 | custom_gmp_free); | |
10153 | ||
713a4259 KR |
10154 | mpz_init_set_si (z_negative_one, -1); |
10155 | ||
a261c0e9 DH |
10156 | /* It may be possible to tune the performance of some algorithms by using |
10157 | * the following constants to avoid the creation of bignums. Please, before | |
10158 | * using these values, remember the two rules of program optimization: | |
10159 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 10160 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 10161 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 10162 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 10163 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 10164 | |
f3ae5d60 MD |
10165 | scm_add_feature ("complex"); |
10166 | scm_add_feature ("inexact"); | |
e7efe8e7 | 10167 | flo0 = scm_from_double (0.0); |
a5f6b751 | 10168 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea | 10169 | |
cff5fa33 | 10170 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
98237784 MW |
10171 | |
10172 | { | |
10173 | /* Set scm_i_divide2double_lo2b to (2 b^p - 1) */ | |
10174 | mpz_init_set_ui (scm_i_divide2double_lo2b, 1); | |
10175 | mpz_mul_2exp (scm_i_divide2double_lo2b, | |
10176 | scm_i_divide2double_lo2b, | |
10177 | DBL_MANT_DIG + 1); /* 2 b^p */ | |
10178 | mpz_sub_ui (scm_i_divide2double_lo2b, scm_i_divide2double_lo2b, 1); | |
10179 | } | |
10180 | ||
1ea37620 MW |
10181 | { |
10182 | /* Set dbl_minimum_normal_mantissa to b^{p-1} */ | |
10183 | mpz_init_set_ui (dbl_minimum_normal_mantissa, 1); | |
10184 | mpz_mul_2exp (dbl_minimum_normal_mantissa, | |
10185 | dbl_minimum_normal_mantissa, | |
10186 | DBL_MANT_DIG - 1); | |
10187 | } | |
10188 | ||
a0599745 | 10189 | #include "libguile/numbers.x" |
0f2d19dd | 10190 | } |
89e00824 ML |
10191 | |
10192 | /* | |
10193 | Local Variables: | |
10194 | c-file-style: "gnu" | |
10195 | End: | |
10196 | */ |