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 | ||
413 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
414 | static SCM scm_divide2real (SCM x, SCM y); | |
415 | ||
a285b18c MW |
416 | /* Make the ratio NUMERATOR/DENOMINATOR, where: |
417 | 1. NUMERATOR and DENOMINATOR are exact integers | |
418 | 2. NUMERATOR and DENOMINATOR are reduced to lowest terms: gcd(n,d) == 1 */ | |
cba42c93 | 419 | static SCM |
a285b18c | 420 | scm_i_make_ratio_already_reduced (SCM numerator, SCM denominator) |
f92e85f7 | 421 | { |
a285b18c MW |
422 | /* Flip signs so that the denominator is positive. */ |
423 | if (scm_is_false (scm_positive_p (denominator))) | |
f92e85f7 | 424 | { |
a285b18c | 425 | if (SCM_UNLIKELY (scm_is_eq (denominator, SCM_INUM0))) |
f92e85f7 | 426 | scm_num_overflow ("make-ratio"); |
a285b18c | 427 | else |
f92e85f7 | 428 | { |
a285b18c MW |
429 | numerator = scm_difference (numerator, SCM_UNDEFINED); |
430 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
f92e85f7 MV |
431 | } |
432 | } | |
a285b18c MW |
433 | |
434 | /* Check for the integer case */ | |
435 | if (scm_is_eq (denominator, SCM_INUM1)) | |
436 | return numerator; | |
437 | ||
438 | return scm_double_cell (scm_tc16_fraction, | |
439 | SCM_UNPACK (numerator), | |
440 | SCM_UNPACK (denominator), 0); | |
441 | } | |
442 | ||
443 | static SCM scm_exact_integer_quotient (SCM x, SCM y); | |
444 | ||
445 | /* Make the ratio NUMERATOR/DENOMINATOR */ | |
446 | static SCM | |
447 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
448 | #define FUNC_NAME "make-ratio" | |
449 | { | |
450 | /* Make sure the arguments are proper */ | |
451 | if (!SCM_LIKELY (SCM_I_INUMP (numerator) || SCM_BIGP (numerator))) | |
452 | SCM_WRONG_TYPE_ARG (1, numerator); | |
453 | else if (!SCM_LIKELY (SCM_I_INUMP (denominator) || SCM_BIGP (denominator))) | |
454 | SCM_WRONG_TYPE_ARG (2, denominator); | |
455 | else | |
f92e85f7 | 456 | { |
a285b18c MW |
457 | SCM the_gcd = scm_gcd (numerator, denominator); |
458 | if (!(scm_is_eq (the_gcd, SCM_INUM1))) | |
c60e130c | 459 | { |
a285b18c MW |
460 | /* Reduce to lowest terms */ |
461 | numerator = scm_exact_integer_quotient (numerator, the_gcd); | |
462 | denominator = scm_exact_integer_quotient (denominator, the_gcd); | |
f92e85f7 | 463 | } |
a285b18c | 464 | return scm_i_make_ratio_already_reduced (numerator, denominator); |
f92e85f7 | 465 | } |
f92e85f7 | 466 | } |
c60e130c | 467 | #undef FUNC_NAME |
f92e85f7 | 468 | |
f92e85f7 MV |
469 | double |
470 | scm_i_fraction2double (SCM z) | |
471 | { | |
55f26379 MV |
472 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
473 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
474 | } |
475 | ||
2e274311 MW |
476 | static int |
477 | double_is_non_negative_zero (double x) | |
478 | { | |
479 | static double zero = 0.0; | |
480 | ||
481 | return !memcmp (&x, &zero, sizeof(double)); | |
482 | } | |
483 | ||
2519490c MW |
484 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
485 | (SCM x), | |
942e5b91 MG |
486 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
487 | "otherwise.") | |
1bbd0b84 | 488 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 489 | { |
41df63cf MW |
490 | if (SCM_INEXACTP (x)) |
491 | return SCM_BOOL_F; | |
492 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 493 | return SCM_BOOL_T; |
41df63cf | 494 | else |
2519490c | 495 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
496 | } |
497 | #undef FUNC_NAME | |
498 | ||
022dda69 MG |
499 | int |
500 | scm_is_exact (SCM val) | |
501 | { | |
502 | return scm_is_true (scm_exact_p (val)); | |
503 | } | |
41df63cf | 504 | |
2519490c | 505 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
506 | (SCM x), |
507 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
508 | "else.") | |
509 | #define FUNC_NAME s_scm_inexact_p | |
510 | { | |
511 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 512 | return SCM_BOOL_T; |
41df63cf | 513 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 514 | return SCM_BOOL_F; |
41df63cf | 515 | else |
2519490c | 516 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 517 | } |
1bbd0b84 | 518 | #undef FUNC_NAME |
0f2d19dd | 519 | |
022dda69 MG |
520 | int |
521 | scm_is_inexact (SCM val) | |
522 | { | |
523 | return scm_is_true (scm_inexact_p (val)); | |
524 | } | |
4219f20d | 525 | |
2519490c | 526 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 527 | (SCM n), |
942e5b91 MG |
528 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
529 | "otherwise.") | |
1bbd0b84 | 530 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 531 | { |
e11e83f3 | 532 | if (SCM_I_INUMP (n)) |
0aacf84e | 533 | { |
e25f3727 | 534 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 535 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
536 | } |
537 | else if (SCM_BIGP (n)) | |
538 | { | |
539 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
540 | scm_remember_upto_here_1 (n); | |
73e4de09 | 541 | return scm_from_bool (odd_p); |
0aacf84e | 542 | } |
f92e85f7 MV |
543 | else if (SCM_REALP (n)) |
544 | { | |
2519490c MW |
545 | double val = SCM_REAL_VALUE (n); |
546 | if (DOUBLE_IS_FINITE (val)) | |
547 | { | |
548 | double rem = fabs (fmod (val, 2.0)); | |
549 | if (rem == 1.0) | |
550 | return SCM_BOOL_T; | |
551 | else if (rem == 0.0) | |
552 | return SCM_BOOL_F; | |
553 | } | |
f92e85f7 | 554 | } |
2519490c | 555 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 556 | } |
1bbd0b84 | 557 | #undef FUNC_NAME |
0f2d19dd | 558 | |
4219f20d | 559 | |
2519490c | 560 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 561 | (SCM n), |
942e5b91 MG |
562 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
563 | "otherwise.") | |
1bbd0b84 | 564 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 565 | { |
e11e83f3 | 566 | if (SCM_I_INUMP (n)) |
0aacf84e | 567 | { |
e25f3727 | 568 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 569 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
570 | } |
571 | else if (SCM_BIGP (n)) | |
572 | { | |
573 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
574 | scm_remember_upto_here_1 (n); | |
73e4de09 | 575 | return scm_from_bool (even_p); |
0aacf84e | 576 | } |
f92e85f7 MV |
577 | else if (SCM_REALP (n)) |
578 | { | |
2519490c MW |
579 | double val = SCM_REAL_VALUE (n); |
580 | if (DOUBLE_IS_FINITE (val)) | |
581 | { | |
582 | double rem = fabs (fmod (val, 2.0)); | |
583 | if (rem == 1.0) | |
584 | return SCM_BOOL_F; | |
585 | else if (rem == 0.0) | |
586 | return SCM_BOOL_T; | |
587 | } | |
f92e85f7 | 588 | } |
2519490c | 589 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 590 | } |
1bbd0b84 | 591 | #undef FUNC_NAME |
0f2d19dd | 592 | |
2519490c MW |
593 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
594 | (SCM x), | |
10391e06 AW |
595 | "Return @code{#t} if the real number @var{x} is neither\n" |
596 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
597 | #define FUNC_NAME s_scm_finite_p |
598 | { | |
599 | if (SCM_REALP (x)) | |
600 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 601 | else if (scm_is_real (x)) |
7112615f MW |
602 | return SCM_BOOL_T; |
603 | else | |
2519490c | 604 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
605 | } |
606 | #undef FUNC_NAME | |
607 | ||
2519490c MW |
608 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
609 | (SCM x), | |
610 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
611 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
612 | #define FUNC_NAME s_scm_inf_p |
613 | { | |
b1092b3a | 614 | if (SCM_REALP (x)) |
2e65b52f | 615 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 616 | else if (scm_is_real (x)) |
7351e207 | 617 | return SCM_BOOL_F; |
10391e06 | 618 | else |
2519490c | 619 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
620 | } |
621 | #undef FUNC_NAME | |
622 | ||
2519490c MW |
623 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
624 | (SCM x), | |
10391e06 AW |
625 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
626 | "or @code{#f} otherwise.") | |
7351e207 MV |
627 | #define FUNC_NAME s_scm_nan_p |
628 | { | |
10391e06 AW |
629 | if (SCM_REALP (x)) |
630 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
631 | else if (scm_is_real (x)) | |
7351e207 | 632 | return SCM_BOOL_F; |
10391e06 | 633 | else |
2519490c | 634 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
635 | } |
636 | #undef FUNC_NAME | |
637 | ||
638 | /* Guile's idea of infinity. */ | |
639 | static double guile_Inf; | |
640 | ||
641 | /* Guile's idea of not a number. */ | |
642 | static double guile_NaN; | |
643 | ||
644 | static void | |
645 | guile_ieee_init (void) | |
646 | { | |
7351e207 MV |
647 | /* Some version of gcc on some old version of Linux used to crash when |
648 | trying to make Inf and NaN. */ | |
649 | ||
240a27d2 KR |
650 | #ifdef INFINITY |
651 | /* C99 INFINITY, when available. | |
652 | FIXME: The standard allows for INFINITY to be something that overflows | |
653 | at compile time. We ought to have a configure test to check for that | |
654 | before trying to use it. (But in practice we believe this is not a | |
655 | problem on any system guile is likely to target.) */ | |
656 | guile_Inf = INFINITY; | |
56a3dcd4 | 657 | #elif defined HAVE_DINFINITY |
240a27d2 | 658 | /* OSF */ |
7351e207 | 659 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 660 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
661 | #else |
662 | double tmp = 1e+10; | |
663 | guile_Inf = tmp; | |
664 | for (;;) | |
665 | { | |
666 | guile_Inf *= 1e+10; | |
667 | if (guile_Inf == tmp) | |
668 | break; | |
669 | tmp = guile_Inf; | |
670 | } | |
671 | #endif | |
672 | ||
240a27d2 KR |
673 | #ifdef NAN |
674 | /* C99 NAN, when available */ | |
675 | guile_NaN = NAN; | |
56a3dcd4 | 676 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
677 | { |
678 | /* OSF */ | |
679 | extern unsigned int DQNAN[2]; | |
680 | guile_NaN = (*((double *)(DQNAN))); | |
681 | } | |
7351e207 MV |
682 | #else |
683 | guile_NaN = guile_Inf / guile_Inf; | |
684 | #endif | |
7351e207 MV |
685 | } |
686 | ||
687 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
688 | (void), | |
689 | "Return Inf.") | |
690 | #define FUNC_NAME s_scm_inf | |
691 | { | |
692 | static int initialized = 0; | |
693 | if (! initialized) | |
694 | { | |
695 | guile_ieee_init (); | |
696 | initialized = 1; | |
697 | } | |
55f26379 | 698 | return scm_from_double (guile_Inf); |
7351e207 MV |
699 | } |
700 | #undef FUNC_NAME | |
701 | ||
702 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
703 | (void), | |
704 | "Return NaN.") | |
705 | #define FUNC_NAME s_scm_nan | |
706 | { | |
707 | static int initialized = 0; | |
0aacf84e | 708 | if (!initialized) |
7351e207 MV |
709 | { |
710 | guile_ieee_init (); | |
711 | initialized = 1; | |
712 | } | |
55f26379 | 713 | return scm_from_double (guile_NaN); |
7351e207 MV |
714 | } |
715 | #undef FUNC_NAME | |
716 | ||
4219f20d | 717 | |
a48d60b1 MD |
718 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
719 | (SCM x), | |
720 | "Return the absolute value of @var{x}.") | |
2519490c | 721 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 722 | { |
e11e83f3 | 723 | if (SCM_I_INUMP (x)) |
0aacf84e | 724 | { |
e25f3727 | 725 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
726 | if (xx >= 0) |
727 | return x; | |
728 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 729 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 730 | else |
e25f3727 | 731 | return scm_i_inum2big (-xx); |
4219f20d | 732 | } |
9b9ef10c MW |
733 | else if (SCM_LIKELY (SCM_REALP (x))) |
734 | { | |
735 | double xx = SCM_REAL_VALUE (x); | |
736 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
737 | if (xx < 0.0) | |
738 | return scm_from_double (-xx); | |
739 | /* Handle signed zeroes properly */ | |
740 | else if (SCM_UNLIKELY (xx == 0.0)) | |
741 | return flo0; | |
742 | else | |
743 | return x; | |
744 | } | |
0aacf84e MD |
745 | else if (SCM_BIGP (x)) |
746 | { | |
747 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
748 | if (sgn < 0) | |
749 | return scm_i_clonebig (x, 0); | |
750 | else | |
751 | return x; | |
4219f20d | 752 | } |
f92e85f7 MV |
753 | else if (SCM_FRACTIONP (x)) |
754 | { | |
73e4de09 | 755 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 756 | return x; |
a285b18c MW |
757 | return scm_i_make_ratio_already_reduced |
758 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
759 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 760 | } |
0aacf84e | 761 | else |
a48d60b1 | 762 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 763 | } |
a48d60b1 | 764 | #undef FUNC_NAME |
0f2d19dd | 765 | |
4219f20d | 766 | |
2519490c MW |
767 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
768 | (SCM x, SCM y), | |
769 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
770 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 771 | { |
495a39c4 | 772 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 773 | { |
495a39c4 | 774 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 775 | return scm_truncate_quotient (x, y); |
0aacf84e | 776 | else |
2519490c | 777 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 778 | } |
0aacf84e | 779 | else |
2519490c | 780 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 781 | } |
2519490c | 782 | #undef FUNC_NAME |
0f2d19dd | 783 | |
2519490c MW |
784 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
785 | (SCM x, SCM y), | |
786 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
787 | "@lisp\n" | |
788 | "(remainder 13 4) @result{} 1\n" | |
789 | "(remainder -13 4) @result{} -1\n" | |
790 | "@end lisp") | |
791 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 792 | { |
495a39c4 | 793 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 794 | { |
495a39c4 | 795 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 796 | return scm_truncate_remainder (x, y); |
0aacf84e | 797 | else |
2519490c | 798 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 799 | } |
0aacf84e | 800 | else |
2519490c | 801 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 802 | } |
2519490c | 803 | #undef FUNC_NAME |
0f2d19dd | 804 | |
89a7e495 | 805 | |
2519490c MW |
806 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
807 | (SCM x, SCM y), | |
808 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
809 | "@lisp\n" | |
810 | "(modulo 13 4) @result{} 1\n" | |
811 | "(modulo -13 4) @result{} 3\n" | |
812 | "@end lisp") | |
813 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 814 | { |
495a39c4 | 815 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 816 | { |
495a39c4 | 817 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 818 | return scm_floor_remainder (x, y); |
0aacf84e | 819 | else |
2519490c | 820 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 821 | } |
0aacf84e | 822 | else |
2519490c | 823 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 824 | } |
2519490c | 825 | #undef FUNC_NAME |
0f2d19dd | 826 | |
a285b18c MW |
827 | /* Return the exact integer q such that n = q*d, for exact integers n |
828 | and d, where d is known in advance to divide n evenly (with zero | |
829 | remainder). For large integers, this can be computed more | |
830 | efficiently than when the remainder is unknown. */ | |
831 | static SCM | |
832 | scm_exact_integer_quotient (SCM n, SCM d) | |
833 | #define FUNC_NAME "exact-integer-quotient" | |
834 | { | |
835 | if (SCM_LIKELY (SCM_I_INUMP (n))) | |
836 | { | |
837 | scm_t_inum nn = SCM_I_INUM (n); | |
838 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
839 | { | |
840 | scm_t_inum dd = SCM_I_INUM (d); | |
841 | if (SCM_UNLIKELY (dd == 0)) | |
842 | scm_num_overflow ("exact-integer-quotient"); | |
843 | else | |
844 | { | |
845 | scm_t_inum qq = nn / dd; | |
846 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
847 | return SCM_I_MAKINUM (qq); | |
848 | else | |
849 | return scm_i_inum2big (qq); | |
850 | } | |
851 | } | |
852 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
853 | { | |
854 | /* n is an inum and d is a bignum. Given that d is known to | |
855 | divide n evenly, there are only two possibilities: n is 0, | |
856 | or else n is fixnum-min and d is abs(fixnum-min). */ | |
857 | if (nn == 0) | |
858 | return SCM_INUM0; | |
859 | else | |
860 | return SCM_I_MAKINUM (-1); | |
861 | } | |
862 | else | |
863 | SCM_WRONG_TYPE_ARG (2, d); | |
864 | } | |
865 | else if (SCM_LIKELY (SCM_BIGP (n))) | |
866 | { | |
867 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
868 | { | |
869 | scm_t_inum dd = SCM_I_INUM (d); | |
870 | if (SCM_UNLIKELY (dd == 0)) | |
871 | scm_num_overflow ("exact-integer-quotient"); | |
872 | else if (SCM_UNLIKELY (dd == 1)) | |
873 | return n; | |
874 | else | |
875 | { | |
876 | SCM q = scm_i_mkbig (); | |
877 | if (dd > 0) | |
878 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), dd); | |
879 | else | |
880 | { | |
881 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), -dd); | |
882 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
883 | } | |
884 | scm_remember_upto_here_1 (n); | |
885 | return scm_i_normbig (q); | |
886 | } | |
887 | } | |
888 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
889 | { | |
890 | SCM q = scm_i_mkbig (); | |
891 | mpz_divexact (SCM_I_BIG_MPZ (q), | |
892 | SCM_I_BIG_MPZ (n), | |
893 | SCM_I_BIG_MPZ (d)); | |
894 | scm_remember_upto_here_2 (n, d); | |
895 | return scm_i_normbig (q); | |
896 | } | |
897 | else | |
898 | SCM_WRONG_TYPE_ARG (2, d); | |
899 | } | |
900 | else | |
901 | SCM_WRONG_TYPE_ARG (1, n); | |
902 | } | |
903 | #undef FUNC_NAME | |
904 | ||
5fbf680b MW |
905 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
906 | two-valued functions. It is called from primitive generics that take | |
907 | two arguments and return two values, when the core procedure is | |
908 | unable to handle the given argument types. If there are GOOPS | |
909 | methods for this primitive generic, it dispatches to GOOPS and, if | |
910 | successful, expects two values to be returned, which are placed in | |
911 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
912 | wrong-type-arg exception. | |
913 | ||
914 | FIXME: This obviously belongs somewhere else, but until we decide on | |
915 | the right API, it is here as a static function, because it is needed | |
916 | by the *_divide functions below. | |
917 | */ | |
918 | static void | |
919 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
920 | const char *subr, SCM *rp1, SCM *rp2) | |
921 | { | |
922 | if (SCM_UNPACK (gf)) | |
923 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
924 | else | |
925 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
926 | } | |
927 | ||
a8da6d93 MW |
928 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
929 | (SCM x, SCM y), | |
930 | "Return the integer @var{q} such that\n" | |
931 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
932 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
933 | "@lisp\n" | |
934 | "(euclidean-quotient 123 10) @result{} 12\n" | |
935 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
936 | "(euclidean-quotient -123 10) @result{} -13\n" | |
937 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
938 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
939 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
940 | "@end lisp") | |
ff62c168 MW |
941 | #define FUNC_NAME s_scm_euclidean_quotient |
942 | { | |
a8da6d93 MW |
943 | if (scm_is_false (scm_negative_p (y))) |
944 | return scm_floor_quotient (x, y); | |
ff62c168 | 945 | else |
a8da6d93 | 946 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
947 | } |
948 | #undef FUNC_NAME | |
949 | ||
a8da6d93 MW |
950 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
951 | (SCM x, SCM y), | |
952 | "Return the real number @var{r} such that\n" | |
953 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
954 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
955 | "for some integer @var{q}.\n" | |
956 | "@lisp\n" | |
957 | "(euclidean-remainder 123 10) @result{} 3\n" | |
958 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
959 | "(euclidean-remainder -123 10) @result{} 7\n" | |
960 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
961 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
962 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
963 | "@end lisp") | |
ff62c168 MW |
964 | #define FUNC_NAME s_scm_euclidean_remainder |
965 | { | |
a8da6d93 MW |
966 | if (scm_is_false (scm_negative_p (y))) |
967 | return scm_floor_remainder (x, y); | |
ff62c168 | 968 | else |
a8da6d93 | 969 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
970 | } |
971 | #undef FUNC_NAME | |
972 | ||
a8da6d93 MW |
973 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
974 | (SCM x, SCM y), | |
975 | "Return the integer @var{q} and the real number @var{r}\n" | |
976 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
977 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
978 | "@lisp\n" | |
979 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
980 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
981 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
982 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
983 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
984 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
985 | "@end lisp") | |
5fbf680b MW |
986 | #define FUNC_NAME s_scm_i_euclidean_divide |
987 | { | |
a8da6d93 MW |
988 | if (scm_is_false (scm_negative_p (y))) |
989 | return scm_i_floor_divide (x, y); | |
990 | else | |
991 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
992 | } |
993 | #undef FUNC_NAME | |
994 | ||
5fbf680b MW |
995 | void |
996 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 997 | { |
a8da6d93 MW |
998 | if (scm_is_false (scm_negative_p (y))) |
999 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 1000 | else |
a8da6d93 | 1001 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
1002 | } |
1003 | ||
8f9da340 MW |
1004 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
1005 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
1006 | ||
1007 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
1008 | (SCM x, SCM y), | |
1009 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1010 | "@lisp\n" | |
1011 | "(floor-quotient 123 10) @result{} 12\n" | |
1012 | "(floor-quotient 123 -10) @result{} -13\n" | |
1013 | "(floor-quotient -123 10) @result{} -13\n" | |
1014 | "(floor-quotient -123 -10) @result{} 12\n" | |
1015 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1016 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1017 | "@end lisp") | |
1018 | #define FUNC_NAME s_scm_floor_quotient | |
1019 | { | |
1020 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1021 | { | |
1022 | scm_t_inum xx = SCM_I_INUM (x); | |
1023 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1024 | { | |
1025 | scm_t_inum yy = SCM_I_INUM (y); | |
1026 | scm_t_inum xx1 = xx; | |
1027 | scm_t_inum qq; | |
1028 | if (SCM_LIKELY (yy > 0)) | |
1029 | { | |
1030 | if (SCM_UNLIKELY (xx < 0)) | |
1031 | xx1 = xx - yy + 1; | |
1032 | } | |
1033 | else if (SCM_UNLIKELY (yy == 0)) | |
1034 | scm_num_overflow (s_scm_floor_quotient); | |
1035 | else if (xx > 0) | |
1036 | xx1 = xx - yy - 1; | |
1037 | qq = xx1 / yy; | |
1038 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1039 | return SCM_I_MAKINUM (qq); | |
1040 | else | |
1041 | return scm_i_inum2big (qq); | |
1042 | } | |
1043 | else if (SCM_BIGP (y)) | |
1044 | { | |
1045 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1046 | scm_remember_upto_here_1 (y); | |
1047 | if (sign > 0) | |
1048 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1049 | else | |
1050 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1051 | } | |
1052 | else if (SCM_REALP (y)) | |
1053 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1054 | else if (SCM_FRACTIONP (y)) | |
1055 | return scm_i_exact_rational_floor_quotient (x, y); | |
1056 | else | |
1057 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1058 | s_scm_floor_quotient); | |
1059 | } | |
1060 | else if (SCM_BIGP (x)) | |
1061 | { | |
1062 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1063 | { | |
1064 | scm_t_inum yy = SCM_I_INUM (y); | |
1065 | if (SCM_UNLIKELY (yy == 0)) | |
1066 | scm_num_overflow (s_scm_floor_quotient); | |
1067 | else if (SCM_UNLIKELY (yy == 1)) | |
1068 | return x; | |
1069 | else | |
1070 | { | |
1071 | SCM q = scm_i_mkbig (); | |
1072 | if (yy > 0) | |
1073 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1074 | else | |
1075 | { | |
1076 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1077 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1078 | } | |
1079 | scm_remember_upto_here_1 (x); | |
1080 | return scm_i_normbig (q); | |
1081 | } | |
1082 | } | |
1083 | else if (SCM_BIGP (y)) | |
1084 | { | |
1085 | SCM q = scm_i_mkbig (); | |
1086 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1087 | SCM_I_BIG_MPZ (x), | |
1088 | SCM_I_BIG_MPZ (y)); | |
1089 | scm_remember_upto_here_2 (x, y); | |
1090 | return scm_i_normbig (q); | |
1091 | } | |
1092 | else if (SCM_REALP (y)) | |
1093 | return scm_i_inexact_floor_quotient | |
1094 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1095 | else if (SCM_FRACTIONP (y)) | |
1096 | return scm_i_exact_rational_floor_quotient (x, y); | |
1097 | else | |
1098 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1099 | s_scm_floor_quotient); | |
1100 | } | |
1101 | else if (SCM_REALP (x)) | |
1102 | { | |
1103 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1104 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1105 | return scm_i_inexact_floor_quotient | |
1106 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1107 | else | |
1108 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1109 | s_scm_floor_quotient); | |
1110 | } | |
1111 | else if (SCM_FRACTIONP (x)) | |
1112 | { | |
1113 | if (SCM_REALP (y)) | |
1114 | return scm_i_inexact_floor_quotient | |
1115 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1116 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1117 | return scm_i_exact_rational_floor_quotient (x, y); | |
1118 | else | |
1119 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1120 | s_scm_floor_quotient); | |
1121 | } | |
1122 | else | |
1123 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1124 | s_scm_floor_quotient); | |
1125 | } | |
1126 | #undef FUNC_NAME | |
1127 | ||
1128 | static SCM | |
1129 | scm_i_inexact_floor_quotient (double x, double y) | |
1130 | { | |
1131 | if (SCM_UNLIKELY (y == 0)) | |
1132 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1133 | else | |
1134 | return scm_from_double (floor (x / y)); | |
1135 | } | |
1136 | ||
1137 | static SCM | |
1138 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1139 | { | |
1140 | return scm_floor_quotient | |
1141 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1142 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1143 | } | |
1144 | ||
1145 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1146 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1147 | ||
1148 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1149 | (SCM x, SCM y), | |
1150 | "Return the real number @var{r} such that\n" | |
1151 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1152 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1153 | "@lisp\n" | |
1154 | "(floor-remainder 123 10) @result{} 3\n" | |
1155 | "(floor-remainder 123 -10) @result{} -7\n" | |
1156 | "(floor-remainder -123 10) @result{} 7\n" | |
1157 | "(floor-remainder -123 -10) @result{} -3\n" | |
1158 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1159 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1160 | "@end lisp") | |
1161 | #define FUNC_NAME s_scm_floor_remainder | |
1162 | { | |
1163 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1164 | { | |
1165 | scm_t_inum xx = SCM_I_INUM (x); | |
1166 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1167 | { | |
1168 | scm_t_inum yy = SCM_I_INUM (y); | |
1169 | if (SCM_UNLIKELY (yy == 0)) | |
1170 | scm_num_overflow (s_scm_floor_remainder); | |
1171 | else | |
1172 | { | |
1173 | scm_t_inum rr = xx % yy; | |
1174 | int needs_adjustment; | |
1175 | ||
1176 | if (SCM_LIKELY (yy > 0)) | |
1177 | needs_adjustment = (rr < 0); | |
1178 | else | |
1179 | needs_adjustment = (rr > 0); | |
1180 | ||
1181 | if (needs_adjustment) | |
1182 | rr += yy; | |
1183 | return SCM_I_MAKINUM (rr); | |
1184 | } | |
1185 | } | |
1186 | else if (SCM_BIGP (y)) | |
1187 | { | |
1188 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1189 | scm_remember_upto_here_1 (y); | |
1190 | if (sign > 0) | |
1191 | { | |
1192 | if (xx < 0) | |
1193 | { | |
1194 | SCM r = scm_i_mkbig (); | |
1195 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1196 | scm_remember_upto_here_1 (y); | |
1197 | return scm_i_normbig (r); | |
1198 | } | |
1199 | else | |
1200 | return x; | |
1201 | } | |
1202 | else if (xx <= 0) | |
1203 | return x; | |
1204 | else | |
1205 | { | |
1206 | SCM r = scm_i_mkbig (); | |
1207 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1208 | scm_remember_upto_here_1 (y); | |
1209 | return scm_i_normbig (r); | |
1210 | } | |
1211 | } | |
1212 | else if (SCM_REALP (y)) | |
1213 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1214 | else if (SCM_FRACTIONP (y)) | |
1215 | return scm_i_exact_rational_floor_remainder (x, y); | |
1216 | else | |
1217 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1218 | s_scm_floor_remainder); | |
1219 | } | |
1220 | else if (SCM_BIGP (x)) | |
1221 | { | |
1222 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1223 | { | |
1224 | scm_t_inum yy = SCM_I_INUM (y); | |
1225 | if (SCM_UNLIKELY (yy == 0)) | |
1226 | scm_num_overflow (s_scm_floor_remainder); | |
1227 | else | |
1228 | { | |
1229 | scm_t_inum rr; | |
1230 | if (yy > 0) | |
1231 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1232 | else | |
1233 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1234 | scm_remember_upto_here_1 (x); | |
1235 | return SCM_I_MAKINUM (rr); | |
1236 | } | |
1237 | } | |
1238 | else if (SCM_BIGP (y)) | |
1239 | { | |
1240 | SCM r = scm_i_mkbig (); | |
1241 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1242 | SCM_I_BIG_MPZ (x), | |
1243 | SCM_I_BIG_MPZ (y)); | |
1244 | scm_remember_upto_here_2 (x, y); | |
1245 | return scm_i_normbig (r); | |
1246 | } | |
1247 | else if (SCM_REALP (y)) | |
1248 | return scm_i_inexact_floor_remainder | |
1249 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1250 | else if (SCM_FRACTIONP (y)) | |
1251 | return scm_i_exact_rational_floor_remainder (x, y); | |
1252 | else | |
1253 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1254 | s_scm_floor_remainder); | |
1255 | } | |
1256 | else if (SCM_REALP (x)) | |
1257 | { | |
1258 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1259 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1260 | return scm_i_inexact_floor_remainder | |
1261 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1262 | else | |
1263 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1264 | s_scm_floor_remainder); | |
1265 | } | |
1266 | else if (SCM_FRACTIONP (x)) | |
1267 | { | |
1268 | if (SCM_REALP (y)) | |
1269 | return scm_i_inexact_floor_remainder | |
1270 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1271 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1272 | return scm_i_exact_rational_floor_remainder (x, y); | |
1273 | else | |
1274 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1275 | s_scm_floor_remainder); | |
1276 | } | |
1277 | else | |
1278 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1279 | s_scm_floor_remainder); | |
1280 | } | |
1281 | #undef FUNC_NAME | |
1282 | ||
1283 | static SCM | |
1284 | scm_i_inexact_floor_remainder (double x, double y) | |
1285 | { | |
1286 | /* Although it would be more efficient to use fmod here, we can't | |
1287 | because it would in some cases produce results inconsistent with | |
1288 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1289 | close). In particular, when x is very close to a multiple of y, | |
1290 | then r might be either 0.0 or y, but those two cases must | |
1291 | correspond to different choices of q. If r = 0.0 then q must be | |
1292 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1293 | and remainder chooses the other, it would be bad. */ | |
1294 | if (SCM_UNLIKELY (y == 0)) | |
1295 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1296 | else | |
1297 | return scm_from_double (x - y * floor (x / y)); | |
1298 | } | |
1299 | ||
1300 | static SCM | |
1301 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1302 | { | |
1303 | SCM xd = scm_denominator (x); | |
1304 | SCM yd = scm_denominator (y); | |
1305 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1306 | scm_product (scm_numerator (y), xd)); | |
1307 | return scm_divide (r1, scm_product (xd, yd)); | |
1308 | } | |
1309 | ||
1310 | ||
1311 | static void scm_i_inexact_floor_divide (double x, double y, | |
1312 | SCM *qp, SCM *rp); | |
1313 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1314 | SCM *qp, SCM *rp); | |
1315 | ||
1316 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1317 | (SCM x, SCM y), | |
1318 | "Return the integer @var{q} and the real number @var{r}\n" | |
1319 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1320 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1321 | "@lisp\n" | |
1322 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1323 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1324 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1325 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1326 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1327 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1328 | "@end lisp") | |
1329 | #define FUNC_NAME s_scm_i_floor_divide | |
1330 | { | |
1331 | SCM q, r; | |
1332 | ||
1333 | scm_floor_divide(x, y, &q, &r); | |
1334 | return scm_values (scm_list_2 (q, r)); | |
1335 | } | |
1336 | #undef FUNC_NAME | |
1337 | ||
1338 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1339 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1340 | ||
1341 | void | |
1342 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1343 | { | |
1344 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1345 | { | |
1346 | scm_t_inum xx = SCM_I_INUM (x); | |
1347 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1348 | { | |
1349 | scm_t_inum yy = SCM_I_INUM (y); | |
1350 | if (SCM_UNLIKELY (yy == 0)) | |
1351 | scm_num_overflow (s_scm_floor_divide); | |
1352 | else | |
1353 | { | |
1354 | scm_t_inum qq = xx / yy; | |
1355 | scm_t_inum rr = xx % yy; | |
1356 | int needs_adjustment; | |
1357 | ||
1358 | if (SCM_LIKELY (yy > 0)) | |
1359 | needs_adjustment = (rr < 0); | |
1360 | else | |
1361 | needs_adjustment = (rr > 0); | |
1362 | ||
1363 | if (needs_adjustment) | |
1364 | { | |
1365 | rr += yy; | |
1366 | qq--; | |
1367 | } | |
1368 | ||
1369 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1370 | *qp = SCM_I_MAKINUM (qq); | |
1371 | else | |
1372 | *qp = scm_i_inum2big (qq); | |
1373 | *rp = SCM_I_MAKINUM (rr); | |
1374 | } | |
1375 | return; | |
1376 | } | |
1377 | else if (SCM_BIGP (y)) | |
1378 | { | |
1379 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1380 | scm_remember_upto_here_1 (y); | |
1381 | if (sign > 0) | |
1382 | { | |
1383 | if (xx < 0) | |
1384 | { | |
1385 | SCM r = scm_i_mkbig (); | |
1386 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1387 | scm_remember_upto_here_1 (y); | |
1388 | *qp = SCM_I_MAKINUM (-1); | |
1389 | *rp = scm_i_normbig (r); | |
1390 | } | |
1391 | else | |
1392 | { | |
1393 | *qp = SCM_INUM0; | |
1394 | *rp = x; | |
1395 | } | |
1396 | } | |
1397 | else if (xx <= 0) | |
1398 | { | |
1399 | *qp = SCM_INUM0; | |
1400 | *rp = x; | |
1401 | } | |
1402 | else | |
1403 | { | |
1404 | SCM r = scm_i_mkbig (); | |
1405 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1406 | scm_remember_upto_here_1 (y); | |
1407 | *qp = SCM_I_MAKINUM (-1); | |
1408 | *rp = scm_i_normbig (r); | |
1409 | } | |
1410 | return; | |
1411 | } | |
1412 | else if (SCM_REALP (y)) | |
1413 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1414 | else if (SCM_FRACTIONP (y)) | |
1415 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1416 | else | |
1417 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1418 | s_scm_floor_divide, qp, rp); | |
1419 | } | |
1420 | else if (SCM_BIGP (x)) | |
1421 | { | |
1422 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1423 | { | |
1424 | scm_t_inum yy = SCM_I_INUM (y); | |
1425 | if (SCM_UNLIKELY (yy == 0)) | |
1426 | scm_num_overflow (s_scm_floor_divide); | |
1427 | else | |
1428 | { | |
1429 | SCM q = scm_i_mkbig (); | |
1430 | SCM r = scm_i_mkbig (); | |
1431 | if (yy > 0) | |
1432 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1433 | SCM_I_BIG_MPZ (x), yy); | |
1434 | else | |
1435 | { | |
1436 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1437 | SCM_I_BIG_MPZ (x), -yy); | |
1438 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1439 | } | |
1440 | scm_remember_upto_here_1 (x); | |
1441 | *qp = scm_i_normbig (q); | |
1442 | *rp = scm_i_normbig (r); | |
1443 | } | |
1444 | return; | |
1445 | } | |
1446 | else if (SCM_BIGP (y)) | |
1447 | { | |
1448 | SCM q = scm_i_mkbig (); | |
1449 | SCM r = scm_i_mkbig (); | |
1450 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1451 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1452 | scm_remember_upto_here_2 (x, y); | |
1453 | *qp = scm_i_normbig (q); | |
1454 | *rp = scm_i_normbig (r); | |
1455 | return; | |
1456 | } | |
1457 | else if (SCM_REALP (y)) | |
1458 | return scm_i_inexact_floor_divide | |
1459 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1460 | else if (SCM_FRACTIONP (y)) | |
1461 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1462 | else | |
1463 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1464 | s_scm_floor_divide, qp, rp); | |
1465 | } | |
1466 | else if (SCM_REALP (x)) | |
1467 | { | |
1468 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1469 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1470 | return scm_i_inexact_floor_divide | |
1471 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1472 | else | |
1473 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1474 | s_scm_floor_divide, qp, rp); | |
1475 | } | |
1476 | else if (SCM_FRACTIONP (x)) | |
1477 | { | |
1478 | if (SCM_REALP (y)) | |
1479 | return scm_i_inexact_floor_divide | |
1480 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1481 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1482 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1483 | else | |
1484 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1485 | s_scm_floor_divide, qp, rp); | |
1486 | } | |
1487 | else | |
1488 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1489 | s_scm_floor_divide, qp, rp); | |
1490 | } | |
1491 | ||
1492 | static void | |
1493 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1494 | { | |
1495 | if (SCM_UNLIKELY (y == 0)) | |
1496 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1497 | else | |
1498 | { | |
1499 | double q = floor (x / y); | |
1500 | double r = x - q * y; | |
1501 | *qp = scm_from_double (q); | |
1502 | *rp = scm_from_double (r); | |
1503 | } | |
1504 | } | |
1505 | ||
1506 | static void | |
1507 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1508 | { | |
1509 | SCM r1; | |
1510 | SCM xd = scm_denominator (x); | |
1511 | SCM yd = scm_denominator (y); | |
1512 | ||
1513 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1514 | scm_product (scm_numerator (y), xd), | |
1515 | qp, &r1); | |
1516 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1517 | } | |
1518 | ||
1519 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1520 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1521 | ||
1522 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1523 | (SCM x, SCM y), | |
1524 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1525 | "@lisp\n" | |
1526 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1527 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1528 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1529 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1530 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1531 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1532 | "@end lisp") | |
1533 | #define FUNC_NAME s_scm_ceiling_quotient | |
1534 | { | |
1535 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1536 | { | |
1537 | scm_t_inum xx = SCM_I_INUM (x); | |
1538 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1539 | { | |
1540 | scm_t_inum yy = SCM_I_INUM (y); | |
1541 | if (SCM_UNLIKELY (yy == 0)) | |
1542 | scm_num_overflow (s_scm_ceiling_quotient); | |
1543 | else | |
1544 | { | |
1545 | scm_t_inum xx1 = xx; | |
1546 | scm_t_inum qq; | |
1547 | if (SCM_LIKELY (yy > 0)) | |
1548 | { | |
1549 | if (SCM_LIKELY (xx >= 0)) | |
1550 | xx1 = xx + yy - 1; | |
1551 | } | |
8f9da340 MW |
1552 | else if (xx < 0) |
1553 | xx1 = xx + yy + 1; | |
1554 | qq = xx1 / yy; | |
1555 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1556 | return SCM_I_MAKINUM (qq); | |
1557 | else | |
1558 | return scm_i_inum2big (qq); | |
1559 | } | |
1560 | } | |
1561 | else if (SCM_BIGP (y)) | |
1562 | { | |
1563 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1564 | scm_remember_upto_here_1 (y); | |
1565 | if (SCM_LIKELY (sign > 0)) | |
1566 | { | |
1567 | if (SCM_LIKELY (xx > 0)) | |
1568 | return SCM_INUM1; | |
1569 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1570 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1571 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1572 | { | |
1573 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1574 | scm_remember_upto_here_1 (y); | |
1575 | return SCM_I_MAKINUM (-1); | |
1576 | } | |
1577 | else | |
1578 | return SCM_INUM0; | |
1579 | } | |
1580 | else if (xx >= 0) | |
1581 | return SCM_INUM0; | |
1582 | else | |
1583 | return SCM_INUM1; | |
1584 | } | |
1585 | else if (SCM_REALP (y)) | |
1586 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1587 | else if (SCM_FRACTIONP (y)) | |
1588 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1589 | else | |
1590 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1591 | s_scm_ceiling_quotient); | |
1592 | } | |
1593 | else if (SCM_BIGP (x)) | |
1594 | { | |
1595 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1596 | { | |
1597 | scm_t_inum yy = SCM_I_INUM (y); | |
1598 | if (SCM_UNLIKELY (yy == 0)) | |
1599 | scm_num_overflow (s_scm_ceiling_quotient); | |
1600 | else if (SCM_UNLIKELY (yy == 1)) | |
1601 | return x; | |
1602 | else | |
1603 | { | |
1604 | SCM q = scm_i_mkbig (); | |
1605 | if (yy > 0) | |
1606 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1607 | else | |
1608 | { | |
1609 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1610 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1611 | } | |
1612 | scm_remember_upto_here_1 (x); | |
1613 | return scm_i_normbig (q); | |
1614 | } | |
1615 | } | |
1616 | else if (SCM_BIGP (y)) | |
1617 | { | |
1618 | SCM q = scm_i_mkbig (); | |
1619 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1620 | SCM_I_BIG_MPZ (x), | |
1621 | SCM_I_BIG_MPZ (y)); | |
1622 | scm_remember_upto_here_2 (x, y); | |
1623 | return scm_i_normbig (q); | |
1624 | } | |
1625 | else if (SCM_REALP (y)) | |
1626 | return scm_i_inexact_ceiling_quotient | |
1627 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1628 | else if (SCM_FRACTIONP (y)) | |
1629 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1630 | else | |
1631 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1632 | s_scm_ceiling_quotient); | |
1633 | } | |
1634 | else if (SCM_REALP (x)) | |
1635 | { | |
1636 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1637 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1638 | return scm_i_inexact_ceiling_quotient | |
1639 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1640 | else | |
1641 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1642 | s_scm_ceiling_quotient); | |
1643 | } | |
1644 | else if (SCM_FRACTIONP (x)) | |
1645 | { | |
1646 | if (SCM_REALP (y)) | |
1647 | return scm_i_inexact_ceiling_quotient | |
1648 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1649 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1650 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1651 | else | |
1652 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1653 | s_scm_ceiling_quotient); | |
1654 | } | |
1655 | else | |
1656 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1657 | s_scm_ceiling_quotient); | |
1658 | } | |
1659 | #undef FUNC_NAME | |
1660 | ||
1661 | static SCM | |
1662 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1663 | { | |
1664 | if (SCM_UNLIKELY (y == 0)) | |
1665 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1666 | else | |
1667 | return scm_from_double (ceil (x / y)); | |
1668 | } | |
1669 | ||
1670 | static SCM | |
1671 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1672 | { | |
1673 | return scm_ceiling_quotient | |
1674 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1675 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1676 | } | |
1677 | ||
1678 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1679 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1680 | ||
1681 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1682 | (SCM x, SCM y), | |
1683 | "Return the real number @var{r} such that\n" | |
1684 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1685 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1686 | "@lisp\n" | |
1687 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1688 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1689 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1690 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1691 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1692 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1693 | "@end lisp") | |
1694 | #define FUNC_NAME s_scm_ceiling_remainder | |
1695 | { | |
1696 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1697 | { | |
1698 | scm_t_inum xx = SCM_I_INUM (x); | |
1699 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1700 | { | |
1701 | scm_t_inum yy = SCM_I_INUM (y); | |
1702 | if (SCM_UNLIKELY (yy == 0)) | |
1703 | scm_num_overflow (s_scm_ceiling_remainder); | |
1704 | else | |
1705 | { | |
1706 | scm_t_inum rr = xx % yy; | |
1707 | int needs_adjustment; | |
1708 | ||
1709 | if (SCM_LIKELY (yy > 0)) | |
1710 | needs_adjustment = (rr > 0); | |
1711 | else | |
1712 | needs_adjustment = (rr < 0); | |
1713 | ||
1714 | if (needs_adjustment) | |
1715 | rr -= yy; | |
1716 | return SCM_I_MAKINUM (rr); | |
1717 | } | |
1718 | } | |
1719 | else if (SCM_BIGP (y)) | |
1720 | { | |
1721 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1722 | scm_remember_upto_here_1 (y); | |
1723 | if (SCM_LIKELY (sign > 0)) | |
1724 | { | |
1725 | if (SCM_LIKELY (xx > 0)) | |
1726 | { | |
1727 | SCM r = scm_i_mkbig (); | |
1728 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1729 | scm_remember_upto_here_1 (y); | |
1730 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1731 | return scm_i_normbig (r); | |
1732 | } | |
1733 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1734 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1735 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1736 | { | |
1737 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1738 | scm_remember_upto_here_1 (y); | |
1739 | return SCM_INUM0; | |
1740 | } | |
1741 | else | |
1742 | return x; | |
1743 | } | |
1744 | else if (xx >= 0) | |
1745 | return x; | |
1746 | else | |
1747 | { | |
1748 | SCM r = scm_i_mkbig (); | |
1749 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1750 | scm_remember_upto_here_1 (y); | |
1751 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1752 | return scm_i_normbig (r); | |
1753 | } | |
1754 | } | |
1755 | else if (SCM_REALP (y)) | |
1756 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1757 | else if (SCM_FRACTIONP (y)) | |
1758 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1759 | else | |
1760 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1761 | s_scm_ceiling_remainder); | |
1762 | } | |
1763 | else if (SCM_BIGP (x)) | |
1764 | { | |
1765 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1766 | { | |
1767 | scm_t_inum yy = SCM_I_INUM (y); | |
1768 | if (SCM_UNLIKELY (yy == 0)) | |
1769 | scm_num_overflow (s_scm_ceiling_remainder); | |
1770 | else | |
1771 | { | |
1772 | scm_t_inum rr; | |
1773 | if (yy > 0) | |
1774 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1775 | else | |
1776 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1777 | scm_remember_upto_here_1 (x); | |
1778 | return SCM_I_MAKINUM (rr); | |
1779 | } | |
1780 | } | |
1781 | else if (SCM_BIGP (y)) | |
1782 | { | |
1783 | SCM r = scm_i_mkbig (); | |
1784 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1785 | SCM_I_BIG_MPZ (x), | |
1786 | SCM_I_BIG_MPZ (y)); | |
1787 | scm_remember_upto_here_2 (x, y); | |
1788 | return scm_i_normbig (r); | |
1789 | } | |
1790 | else if (SCM_REALP (y)) | |
1791 | return scm_i_inexact_ceiling_remainder | |
1792 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1793 | else if (SCM_FRACTIONP (y)) | |
1794 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1795 | else | |
1796 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1797 | s_scm_ceiling_remainder); | |
1798 | } | |
1799 | else if (SCM_REALP (x)) | |
1800 | { | |
1801 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1802 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1803 | return scm_i_inexact_ceiling_remainder | |
1804 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1805 | else | |
1806 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1807 | s_scm_ceiling_remainder); | |
1808 | } | |
1809 | else if (SCM_FRACTIONP (x)) | |
1810 | { | |
1811 | if (SCM_REALP (y)) | |
1812 | return scm_i_inexact_ceiling_remainder | |
1813 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1814 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1815 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1816 | else | |
1817 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1818 | s_scm_ceiling_remainder); | |
1819 | } | |
1820 | else | |
1821 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1822 | s_scm_ceiling_remainder); | |
1823 | } | |
1824 | #undef FUNC_NAME | |
1825 | ||
1826 | static SCM | |
1827 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1828 | { | |
1829 | /* Although it would be more efficient to use fmod here, we can't | |
1830 | because it would in some cases produce results inconsistent with | |
1831 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1832 | close). In particular, when x is very close to a multiple of y, | |
1833 | then r might be either 0.0 or -y, but those two cases must | |
1834 | correspond to different choices of q. If r = 0.0 then q must be | |
1835 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1836 | and remainder chooses the other, it would be bad. */ | |
1837 | if (SCM_UNLIKELY (y == 0)) | |
1838 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1839 | else | |
1840 | return scm_from_double (x - y * ceil (x / y)); | |
1841 | } | |
1842 | ||
1843 | static SCM | |
1844 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1845 | { | |
1846 | SCM xd = scm_denominator (x); | |
1847 | SCM yd = scm_denominator (y); | |
1848 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1849 | scm_product (scm_numerator (y), xd)); | |
1850 | return scm_divide (r1, scm_product (xd, yd)); | |
1851 | } | |
1852 | ||
1853 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1854 | SCM *qp, SCM *rp); | |
1855 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1856 | SCM *qp, SCM *rp); | |
1857 | ||
1858 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1859 | (SCM x, SCM y), | |
1860 | "Return the integer @var{q} and the real number @var{r}\n" | |
1861 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1862 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1863 | "@lisp\n" | |
1864 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
1865 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
1866 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
1867 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
1868 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1869 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1870 | "@end lisp") | |
1871 | #define FUNC_NAME s_scm_i_ceiling_divide | |
1872 | { | |
1873 | SCM q, r; | |
1874 | ||
1875 | scm_ceiling_divide(x, y, &q, &r); | |
1876 | return scm_values (scm_list_2 (q, r)); | |
1877 | } | |
1878 | #undef FUNC_NAME | |
1879 | ||
1880 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
1881 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
1882 | ||
1883 | void | |
1884 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1885 | { | |
1886 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1887 | { | |
1888 | scm_t_inum xx = SCM_I_INUM (x); | |
1889 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1890 | { | |
1891 | scm_t_inum yy = SCM_I_INUM (y); | |
1892 | if (SCM_UNLIKELY (yy == 0)) | |
1893 | scm_num_overflow (s_scm_ceiling_divide); | |
1894 | else | |
1895 | { | |
1896 | scm_t_inum qq = xx / yy; | |
1897 | scm_t_inum rr = xx % yy; | |
1898 | int needs_adjustment; | |
1899 | ||
1900 | if (SCM_LIKELY (yy > 0)) | |
1901 | needs_adjustment = (rr > 0); | |
1902 | else | |
1903 | needs_adjustment = (rr < 0); | |
1904 | ||
1905 | if (needs_adjustment) | |
1906 | { | |
1907 | rr -= yy; | |
1908 | qq++; | |
1909 | } | |
1910 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1911 | *qp = SCM_I_MAKINUM (qq); | |
1912 | else | |
1913 | *qp = scm_i_inum2big (qq); | |
1914 | *rp = SCM_I_MAKINUM (rr); | |
1915 | } | |
1916 | return; | |
1917 | } | |
1918 | else if (SCM_BIGP (y)) | |
1919 | { | |
1920 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1921 | scm_remember_upto_here_1 (y); | |
1922 | if (SCM_LIKELY (sign > 0)) | |
1923 | { | |
1924 | if (SCM_LIKELY (xx > 0)) | |
1925 | { | |
1926 | SCM r = scm_i_mkbig (); | |
1927 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1928 | scm_remember_upto_here_1 (y); | |
1929 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1930 | *qp = SCM_INUM1; | |
1931 | *rp = scm_i_normbig (r); | |
1932 | } | |
1933 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1934 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1935 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1936 | { | |
1937 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1938 | scm_remember_upto_here_1 (y); | |
1939 | *qp = SCM_I_MAKINUM (-1); | |
1940 | *rp = SCM_INUM0; | |
1941 | } | |
1942 | else | |
1943 | { | |
1944 | *qp = SCM_INUM0; | |
1945 | *rp = x; | |
1946 | } | |
1947 | } | |
1948 | else if (xx >= 0) | |
1949 | { | |
1950 | *qp = SCM_INUM0; | |
1951 | *rp = x; | |
1952 | } | |
1953 | else | |
1954 | { | |
1955 | SCM r = scm_i_mkbig (); | |
1956 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1957 | scm_remember_upto_here_1 (y); | |
1958 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1959 | *qp = SCM_INUM1; | |
1960 | *rp = scm_i_normbig (r); | |
1961 | } | |
1962 | return; | |
1963 | } | |
1964 | else if (SCM_REALP (y)) | |
1965 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1966 | else if (SCM_FRACTIONP (y)) | |
1967 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1968 | else | |
1969 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1970 | s_scm_ceiling_divide, qp, rp); | |
1971 | } | |
1972 | else if (SCM_BIGP (x)) | |
1973 | { | |
1974 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1975 | { | |
1976 | scm_t_inum yy = SCM_I_INUM (y); | |
1977 | if (SCM_UNLIKELY (yy == 0)) | |
1978 | scm_num_overflow (s_scm_ceiling_divide); | |
1979 | else | |
1980 | { | |
1981 | SCM q = scm_i_mkbig (); | |
1982 | SCM r = scm_i_mkbig (); | |
1983 | if (yy > 0) | |
1984 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1985 | SCM_I_BIG_MPZ (x), yy); | |
1986 | else | |
1987 | { | |
1988 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1989 | SCM_I_BIG_MPZ (x), -yy); | |
1990 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1991 | } | |
1992 | scm_remember_upto_here_1 (x); | |
1993 | *qp = scm_i_normbig (q); | |
1994 | *rp = scm_i_normbig (r); | |
1995 | } | |
1996 | return; | |
1997 | } | |
1998 | else if (SCM_BIGP (y)) | |
1999 | { | |
2000 | SCM q = scm_i_mkbig (); | |
2001 | SCM r = scm_i_mkbig (); | |
2002 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2003 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2004 | scm_remember_upto_here_2 (x, y); | |
2005 | *qp = scm_i_normbig (q); | |
2006 | *rp = scm_i_normbig (r); | |
2007 | return; | |
2008 | } | |
2009 | else if (SCM_REALP (y)) | |
2010 | return scm_i_inexact_ceiling_divide | |
2011 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2012 | else if (SCM_FRACTIONP (y)) | |
2013 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2014 | else | |
2015 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2016 | s_scm_ceiling_divide, qp, rp); | |
2017 | } | |
2018 | else if (SCM_REALP (x)) | |
2019 | { | |
2020 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2021 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2022 | return scm_i_inexact_ceiling_divide | |
2023 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2024 | else | |
2025 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2026 | s_scm_ceiling_divide, qp, rp); | |
2027 | } | |
2028 | else if (SCM_FRACTIONP (x)) | |
2029 | { | |
2030 | if (SCM_REALP (y)) | |
2031 | return scm_i_inexact_ceiling_divide | |
2032 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2033 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2034 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2035 | else | |
2036 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2037 | s_scm_ceiling_divide, qp, rp); | |
2038 | } | |
2039 | else | |
2040 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2041 | s_scm_ceiling_divide, qp, rp); | |
2042 | } | |
2043 | ||
2044 | static void | |
2045 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2046 | { | |
2047 | if (SCM_UNLIKELY (y == 0)) | |
2048 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2049 | else | |
2050 | { | |
2051 | double q = ceil (x / y); | |
2052 | double r = x - q * y; | |
2053 | *qp = scm_from_double (q); | |
2054 | *rp = scm_from_double (r); | |
2055 | } | |
2056 | } | |
2057 | ||
2058 | static void | |
2059 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2060 | { | |
2061 | SCM r1; | |
2062 | SCM xd = scm_denominator (x); | |
2063 | SCM yd = scm_denominator (y); | |
2064 | ||
2065 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2066 | scm_product (scm_numerator (y), xd), | |
2067 | qp, &r1); | |
2068 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2069 | } | |
2070 | ||
2071 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2072 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2073 | ||
2074 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2075 | (SCM x, SCM y), | |
2076 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2077 | "@lisp\n" | |
2078 | "(truncate-quotient 123 10) @result{} 12\n" | |
2079 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2080 | "(truncate-quotient -123 10) @result{} -12\n" | |
2081 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2082 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2083 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2084 | "@end lisp") | |
2085 | #define FUNC_NAME s_scm_truncate_quotient | |
2086 | { | |
2087 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2088 | { | |
2089 | scm_t_inum xx = SCM_I_INUM (x); | |
2090 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2091 | { | |
2092 | scm_t_inum yy = SCM_I_INUM (y); | |
2093 | if (SCM_UNLIKELY (yy == 0)) | |
2094 | scm_num_overflow (s_scm_truncate_quotient); | |
2095 | else | |
2096 | { | |
2097 | scm_t_inum qq = xx / yy; | |
2098 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2099 | return SCM_I_MAKINUM (qq); | |
2100 | else | |
2101 | return scm_i_inum2big (qq); | |
2102 | } | |
2103 | } | |
2104 | else if (SCM_BIGP (y)) | |
2105 | { | |
2106 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2107 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2108 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2109 | { | |
2110 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2111 | scm_remember_upto_here_1 (y); | |
2112 | return SCM_I_MAKINUM (-1); | |
2113 | } | |
2114 | else | |
2115 | return SCM_INUM0; | |
2116 | } | |
2117 | else if (SCM_REALP (y)) | |
2118 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2119 | else if (SCM_FRACTIONP (y)) | |
2120 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2121 | else | |
2122 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2123 | s_scm_truncate_quotient); | |
2124 | } | |
2125 | else if (SCM_BIGP (x)) | |
2126 | { | |
2127 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2128 | { | |
2129 | scm_t_inum yy = SCM_I_INUM (y); | |
2130 | if (SCM_UNLIKELY (yy == 0)) | |
2131 | scm_num_overflow (s_scm_truncate_quotient); | |
2132 | else if (SCM_UNLIKELY (yy == 1)) | |
2133 | return x; | |
2134 | else | |
2135 | { | |
2136 | SCM q = scm_i_mkbig (); | |
2137 | if (yy > 0) | |
2138 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2139 | else | |
2140 | { | |
2141 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2142 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2143 | } | |
2144 | scm_remember_upto_here_1 (x); | |
2145 | return scm_i_normbig (q); | |
2146 | } | |
2147 | } | |
2148 | else if (SCM_BIGP (y)) | |
2149 | { | |
2150 | SCM q = scm_i_mkbig (); | |
2151 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2152 | SCM_I_BIG_MPZ (x), | |
2153 | SCM_I_BIG_MPZ (y)); | |
2154 | scm_remember_upto_here_2 (x, y); | |
2155 | return scm_i_normbig (q); | |
2156 | } | |
2157 | else if (SCM_REALP (y)) | |
2158 | return scm_i_inexact_truncate_quotient | |
2159 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2160 | else if (SCM_FRACTIONP (y)) | |
2161 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2162 | else | |
2163 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2164 | s_scm_truncate_quotient); | |
2165 | } | |
2166 | else if (SCM_REALP (x)) | |
2167 | { | |
2168 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2169 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2170 | return scm_i_inexact_truncate_quotient | |
2171 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2172 | else | |
2173 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2174 | s_scm_truncate_quotient); | |
2175 | } | |
2176 | else if (SCM_FRACTIONP (x)) | |
2177 | { | |
2178 | if (SCM_REALP (y)) | |
2179 | return scm_i_inexact_truncate_quotient | |
2180 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2181 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2182 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2183 | else | |
2184 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2185 | s_scm_truncate_quotient); | |
2186 | } | |
2187 | else | |
2188 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2189 | s_scm_truncate_quotient); | |
2190 | } | |
2191 | #undef FUNC_NAME | |
2192 | ||
2193 | static SCM | |
2194 | scm_i_inexact_truncate_quotient (double x, double y) | |
2195 | { | |
2196 | if (SCM_UNLIKELY (y == 0)) | |
2197 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2198 | else | |
c251ab63 | 2199 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2200 | } |
2201 | ||
2202 | static SCM | |
2203 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2204 | { | |
2205 | return scm_truncate_quotient | |
2206 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2207 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2208 | } | |
2209 | ||
2210 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2211 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2212 | ||
2213 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2214 | (SCM x, SCM y), | |
2215 | "Return the real number @var{r} such that\n" | |
2216 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2217 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2218 | "@lisp\n" | |
2219 | "(truncate-remainder 123 10) @result{} 3\n" | |
2220 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2221 | "(truncate-remainder -123 10) @result{} -3\n" | |
2222 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2223 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2224 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2225 | "@end lisp") | |
2226 | #define FUNC_NAME s_scm_truncate_remainder | |
2227 | { | |
2228 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2229 | { | |
2230 | scm_t_inum xx = SCM_I_INUM (x); | |
2231 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2232 | { | |
2233 | scm_t_inum yy = SCM_I_INUM (y); | |
2234 | if (SCM_UNLIKELY (yy == 0)) | |
2235 | scm_num_overflow (s_scm_truncate_remainder); | |
2236 | else | |
2237 | return SCM_I_MAKINUM (xx % yy); | |
2238 | } | |
2239 | else if (SCM_BIGP (y)) | |
2240 | { | |
2241 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2242 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2243 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2244 | { | |
2245 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2246 | scm_remember_upto_here_1 (y); | |
2247 | return SCM_INUM0; | |
2248 | } | |
2249 | else | |
2250 | return x; | |
2251 | } | |
2252 | else if (SCM_REALP (y)) | |
2253 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2254 | else if (SCM_FRACTIONP (y)) | |
2255 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2256 | else | |
2257 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2258 | s_scm_truncate_remainder); | |
2259 | } | |
2260 | else if (SCM_BIGP (x)) | |
2261 | { | |
2262 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2263 | { | |
2264 | scm_t_inum yy = SCM_I_INUM (y); | |
2265 | if (SCM_UNLIKELY (yy == 0)) | |
2266 | scm_num_overflow (s_scm_truncate_remainder); | |
2267 | else | |
2268 | { | |
2269 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2270 | (yy > 0) ? yy : -yy) | |
2271 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2272 | scm_remember_upto_here_1 (x); | |
2273 | return SCM_I_MAKINUM (rr); | |
2274 | } | |
2275 | } | |
2276 | else if (SCM_BIGP (y)) | |
2277 | { | |
2278 | SCM r = scm_i_mkbig (); | |
2279 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2280 | SCM_I_BIG_MPZ (x), | |
2281 | SCM_I_BIG_MPZ (y)); | |
2282 | scm_remember_upto_here_2 (x, y); | |
2283 | return scm_i_normbig (r); | |
2284 | } | |
2285 | else if (SCM_REALP (y)) | |
2286 | return scm_i_inexact_truncate_remainder | |
2287 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2288 | else if (SCM_FRACTIONP (y)) | |
2289 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2290 | else | |
2291 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2292 | s_scm_truncate_remainder); | |
2293 | } | |
2294 | else if (SCM_REALP (x)) | |
2295 | { | |
2296 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2297 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2298 | return scm_i_inexact_truncate_remainder | |
2299 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2300 | else | |
2301 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2302 | s_scm_truncate_remainder); | |
2303 | } | |
2304 | else if (SCM_FRACTIONP (x)) | |
2305 | { | |
2306 | if (SCM_REALP (y)) | |
2307 | return scm_i_inexact_truncate_remainder | |
2308 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2309 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2310 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2311 | else | |
2312 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2313 | s_scm_truncate_remainder); | |
2314 | } | |
2315 | else | |
2316 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2317 | s_scm_truncate_remainder); | |
2318 | } | |
2319 | #undef FUNC_NAME | |
2320 | ||
2321 | static SCM | |
2322 | scm_i_inexact_truncate_remainder (double x, double y) | |
2323 | { | |
2324 | /* Although it would be more efficient to use fmod here, we can't | |
2325 | because it would in some cases produce results inconsistent with | |
2326 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2327 | close). In particular, when x is very close to a multiple of y, | |
2328 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2329 | correspond to different choices of q. If quotient chooses one and | |
2330 | remainder chooses the other, it would be bad. */ | |
2331 | if (SCM_UNLIKELY (y == 0)) | |
2332 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2333 | else | |
c251ab63 | 2334 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2335 | } |
2336 | ||
2337 | static SCM | |
2338 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2339 | { | |
2340 | SCM xd = scm_denominator (x); | |
2341 | SCM yd = scm_denominator (y); | |
2342 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2343 | scm_product (scm_numerator (y), xd)); | |
2344 | return scm_divide (r1, scm_product (xd, yd)); | |
2345 | } | |
2346 | ||
2347 | ||
2348 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2349 | SCM *qp, SCM *rp); | |
2350 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2351 | SCM *qp, SCM *rp); | |
2352 | ||
2353 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2354 | (SCM x, SCM y), | |
2355 | "Return the integer @var{q} and the real number @var{r}\n" | |
2356 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2357 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2358 | "@lisp\n" | |
2359 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2360 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2361 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2362 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2363 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2364 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2365 | "@end lisp") | |
2366 | #define FUNC_NAME s_scm_i_truncate_divide | |
2367 | { | |
2368 | SCM q, r; | |
2369 | ||
2370 | scm_truncate_divide(x, y, &q, &r); | |
2371 | return scm_values (scm_list_2 (q, r)); | |
2372 | } | |
2373 | #undef FUNC_NAME | |
2374 | ||
2375 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2376 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2377 | ||
2378 | void | |
2379 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2380 | { | |
2381 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2382 | { | |
2383 | scm_t_inum xx = SCM_I_INUM (x); | |
2384 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2385 | { | |
2386 | scm_t_inum yy = SCM_I_INUM (y); | |
2387 | if (SCM_UNLIKELY (yy == 0)) | |
2388 | scm_num_overflow (s_scm_truncate_divide); | |
2389 | else | |
2390 | { | |
2391 | scm_t_inum qq = xx / yy; | |
2392 | scm_t_inum rr = xx % yy; | |
2393 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2394 | *qp = SCM_I_MAKINUM (qq); | |
2395 | else | |
2396 | *qp = scm_i_inum2big (qq); | |
2397 | *rp = SCM_I_MAKINUM (rr); | |
2398 | } | |
2399 | return; | |
2400 | } | |
2401 | else if (SCM_BIGP (y)) | |
2402 | { | |
2403 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2404 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2405 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2406 | { | |
2407 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2408 | scm_remember_upto_here_1 (y); | |
2409 | *qp = SCM_I_MAKINUM (-1); | |
2410 | *rp = SCM_INUM0; | |
2411 | } | |
2412 | else | |
2413 | { | |
2414 | *qp = SCM_INUM0; | |
2415 | *rp = x; | |
2416 | } | |
2417 | return; | |
2418 | } | |
2419 | else if (SCM_REALP (y)) | |
2420 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2421 | else if (SCM_FRACTIONP (y)) | |
2422 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2423 | else | |
2424 | return two_valued_wta_dispatch_2 | |
2425 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2426 | s_scm_truncate_divide, qp, rp); | |
2427 | } | |
2428 | else if (SCM_BIGP (x)) | |
2429 | { | |
2430 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2431 | { | |
2432 | scm_t_inum yy = SCM_I_INUM (y); | |
2433 | if (SCM_UNLIKELY (yy == 0)) | |
2434 | scm_num_overflow (s_scm_truncate_divide); | |
2435 | else | |
2436 | { | |
2437 | SCM q = scm_i_mkbig (); | |
2438 | scm_t_inum rr; | |
2439 | if (yy > 0) | |
2440 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2441 | SCM_I_BIG_MPZ (x), yy); | |
2442 | else | |
2443 | { | |
2444 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2445 | SCM_I_BIG_MPZ (x), -yy); | |
2446 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2447 | } | |
2448 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2449 | scm_remember_upto_here_1 (x); | |
2450 | *qp = scm_i_normbig (q); | |
2451 | *rp = SCM_I_MAKINUM (rr); | |
2452 | } | |
2453 | return; | |
2454 | } | |
2455 | else if (SCM_BIGP (y)) | |
2456 | { | |
2457 | SCM q = scm_i_mkbig (); | |
2458 | SCM r = scm_i_mkbig (); | |
2459 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2460 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2461 | scm_remember_upto_here_2 (x, y); | |
2462 | *qp = scm_i_normbig (q); | |
2463 | *rp = scm_i_normbig (r); | |
2464 | } | |
2465 | else if (SCM_REALP (y)) | |
2466 | return scm_i_inexact_truncate_divide | |
2467 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2468 | else if (SCM_FRACTIONP (y)) | |
2469 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2470 | else | |
2471 | return two_valued_wta_dispatch_2 | |
2472 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2473 | s_scm_truncate_divide, qp, rp); | |
2474 | } | |
2475 | else if (SCM_REALP (x)) | |
2476 | { | |
2477 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2478 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2479 | return scm_i_inexact_truncate_divide | |
2480 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2481 | else | |
2482 | return two_valued_wta_dispatch_2 | |
2483 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2484 | s_scm_truncate_divide, qp, rp); | |
2485 | } | |
2486 | else if (SCM_FRACTIONP (x)) | |
2487 | { | |
2488 | if (SCM_REALP (y)) | |
2489 | return scm_i_inexact_truncate_divide | |
2490 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2491 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2492 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2493 | else | |
2494 | return two_valued_wta_dispatch_2 | |
2495 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2496 | s_scm_truncate_divide, qp, rp); | |
2497 | } | |
2498 | else | |
2499 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2500 | s_scm_truncate_divide, qp, rp); | |
2501 | } | |
2502 | ||
2503 | static void | |
2504 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2505 | { | |
2506 | if (SCM_UNLIKELY (y == 0)) | |
2507 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2508 | else | |
2509 | { | |
c15fe499 MW |
2510 | double q = trunc (x / y); |
2511 | double r = x - q * y; | |
8f9da340 MW |
2512 | *qp = scm_from_double (q); |
2513 | *rp = scm_from_double (r); | |
2514 | } | |
2515 | } | |
2516 | ||
2517 | static void | |
2518 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2519 | { | |
2520 | SCM r1; | |
2521 | SCM xd = scm_denominator (x); | |
2522 | SCM yd = scm_denominator (y); | |
2523 | ||
2524 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2525 | scm_product (scm_numerator (y), xd), | |
2526 | qp, &r1); | |
2527 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2528 | } | |
2529 | ||
ff62c168 MW |
2530 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2531 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2532 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2533 | |
8f9da340 MW |
2534 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2535 | (SCM x, SCM y), | |
2536 | "Return the integer @var{q} such that\n" | |
2537 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2538 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2539 | "@lisp\n" | |
2540 | "(centered-quotient 123 10) @result{} 12\n" | |
2541 | "(centered-quotient 123 -10) @result{} -12\n" | |
2542 | "(centered-quotient -123 10) @result{} -12\n" | |
2543 | "(centered-quotient -123 -10) @result{} 12\n" | |
2544 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2545 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2546 | "@end lisp") | |
2547 | #define FUNC_NAME s_scm_centered_quotient | |
2548 | { | |
2549 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2550 | { | |
2551 | scm_t_inum xx = SCM_I_INUM (x); | |
2552 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2553 | { | |
2554 | scm_t_inum yy = SCM_I_INUM (y); | |
2555 | if (SCM_UNLIKELY (yy == 0)) | |
2556 | scm_num_overflow (s_scm_centered_quotient); | |
2557 | else | |
2558 | { | |
2559 | scm_t_inum qq = xx / yy; | |
2560 | scm_t_inum rr = xx % yy; | |
2561 | if (SCM_LIKELY (xx > 0)) | |
2562 | { | |
2563 | if (SCM_LIKELY (yy > 0)) | |
2564 | { | |
2565 | if (rr >= (yy + 1) / 2) | |
2566 | qq++; | |
2567 | } | |
2568 | else | |
2569 | { | |
2570 | if (rr >= (1 - yy) / 2) | |
2571 | qq--; | |
2572 | } | |
2573 | } | |
2574 | else | |
2575 | { | |
2576 | if (SCM_LIKELY (yy > 0)) | |
2577 | { | |
2578 | if (rr < -yy / 2) | |
2579 | qq--; | |
2580 | } | |
2581 | else | |
2582 | { | |
2583 | if (rr < yy / 2) | |
2584 | qq++; | |
2585 | } | |
2586 | } | |
2587 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2588 | return SCM_I_MAKINUM (qq); | |
2589 | else | |
2590 | return scm_i_inum2big (qq); | |
2591 | } | |
2592 | } | |
2593 | else if (SCM_BIGP (y)) | |
2594 | { | |
2595 | /* Pass a denormalized bignum version of x (even though it | |
2596 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2597 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2598 | } | |
2599 | else if (SCM_REALP (y)) | |
2600 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2601 | else if (SCM_FRACTIONP (y)) | |
2602 | return scm_i_exact_rational_centered_quotient (x, y); | |
2603 | else | |
2604 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2605 | s_scm_centered_quotient); | |
2606 | } | |
2607 | else if (SCM_BIGP (x)) | |
2608 | { | |
2609 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2610 | { | |
2611 | scm_t_inum yy = SCM_I_INUM (y); | |
2612 | if (SCM_UNLIKELY (yy == 0)) | |
2613 | scm_num_overflow (s_scm_centered_quotient); | |
2614 | else if (SCM_UNLIKELY (yy == 1)) | |
2615 | return x; | |
2616 | else | |
2617 | { | |
2618 | SCM q = scm_i_mkbig (); | |
2619 | scm_t_inum rr; | |
2620 | /* Arrange for rr to initially be non-positive, | |
2621 | because that simplifies the test to see | |
2622 | if it is within the needed bounds. */ | |
2623 | if (yy > 0) | |
2624 | { | |
2625 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2626 | SCM_I_BIG_MPZ (x), yy); | |
2627 | scm_remember_upto_here_1 (x); | |
2628 | if (rr < -yy / 2) | |
2629 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2630 | SCM_I_BIG_MPZ (q), 1); | |
2631 | } | |
2632 | else | |
2633 | { | |
2634 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2635 | SCM_I_BIG_MPZ (x), -yy); | |
2636 | scm_remember_upto_here_1 (x); | |
2637 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2638 | if (rr < yy / 2) | |
2639 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2640 | SCM_I_BIG_MPZ (q), 1); | |
2641 | } | |
2642 | return scm_i_normbig (q); | |
2643 | } | |
2644 | } | |
2645 | else if (SCM_BIGP (y)) | |
2646 | return scm_i_bigint_centered_quotient (x, y); | |
2647 | else if (SCM_REALP (y)) | |
2648 | return scm_i_inexact_centered_quotient | |
2649 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2650 | else if (SCM_FRACTIONP (y)) | |
2651 | return scm_i_exact_rational_centered_quotient (x, y); | |
2652 | else | |
2653 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2654 | s_scm_centered_quotient); | |
2655 | } | |
2656 | else if (SCM_REALP (x)) | |
2657 | { | |
2658 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2659 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2660 | return scm_i_inexact_centered_quotient | |
2661 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2662 | else | |
2663 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2664 | s_scm_centered_quotient); | |
2665 | } | |
2666 | else if (SCM_FRACTIONP (x)) | |
2667 | { | |
2668 | if (SCM_REALP (y)) | |
2669 | return scm_i_inexact_centered_quotient | |
2670 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2671 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2672 | return scm_i_exact_rational_centered_quotient (x, y); | |
2673 | else | |
2674 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2675 | s_scm_centered_quotient); | |
2676 | } | |
2677 | else | |
2678 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2679 | s_scm_centered_quotient); | |
2680 | } | |
2681 | #undef FUNC_NAME | |
2682 | ||
2683 | static SCM | |
2684 | scm_i_inexact_centered_quotient (double x, double y) | |
2685 | { | |
2686 | if (SCM_LIKELY (y > 0)) | |
2687 | return scm_from_double (floor (x/y + 0.5)); | |
2688 | else if (SCM_LIKELY (y < 0)) | |
2689 | return scm_from_double (ceil (x/y - 0.5)); | |
2690 | else if (y == 0) | |
2691 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2692 | else | |
2693 | return scm_nan (); | |
2694 | } | |
2695 | ||
2696 | /* Assumes that both x and y are bigints, though | |
2697 | x might be able to fit into a fixnum. */ | |
2698 | static SCM | |
2699 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2700 | { | |
2701 | SCM q, r, min_r; | |
2702 | ||
2703 | /* Note that x might be small enough to fit into a | |
2704 | fixnum, so we must not let it escape into the wild */ | |
2705 | q = scm_i_mkbig (); | |
2706 | r = scm_i_mkbig (); | |
2707 | ||
2708 | /* min_r will eventually become -abs(y)/2 */ | |
2709 | min_r = scm_i_mkbig (); | |
2710 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2711 | SCM_I_BIG_MPZ (y), 1); | |
2712 | ||
2713 | /* Arrange for rr to initially be non-positive, | |
2714 | because that simplifies the test to see | |
2715 | if it is within the needed bounds. */ | |
2716 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2717 | { | |
2718 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2719 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2720 | scm_remember_upto_here_2 (x, y); | |
2721 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2722 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2723 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2724 | SCM_I_BIG_MPZ (q), 1); | |
2725 | } | |
2726 | else | |
2727 | { | |
2728 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2729 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2730 | scm_remember_upto_here_2 (x, y); | |
2731 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2732 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2733 | SCM_I_BIG_MPZ (q), 1); | |
2734 | } | |
2735 | scm_remember_upto_here_2 (r, min_r); | |
2736 | return scm_i_normbig (q); | |
2737 | } | |
2738 | ||
2739 | static SCM | |
2740 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2741 | { | |
2742 | return scm_centered_quotient | |
2743 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2744 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2745 | } | |
2746 | ||
2747 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2748 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2749 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2750 | ||
2751 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2752 | (SCM x, SCM y), | |
2753 | "Return the real number @var{r} such that\n" | |
2754 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2755 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2756 | "for some integer @var{q}.\n" | |
2757 | "@lisp\n" | |
2758 | "(centered-remainder 123 10) @result{} 3\n" | |
2759 | "(centered-remainder 123 -10) @result{} 3\n" | |
2760 | "(centered-remainder -123 10) @result{} -3\n" | |
2761 | "(centered-remainder -123 -10) @result{} -3\n" | |
2762 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2763 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2764 | "@end lisp") | |
2765 | #define FUNC_NAME s_scm_centered_remainder | |
2766 | { | |
2767 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2768 | { | |
2769 | scm_t_inum xx = SCM_I_INUM (x); | |
2770 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2771 | { | |
2772 | scm_t_inum yy = SCM_I_INUM (y); | |
2773 | if (SCM_UNLIKELY (yy == 0)) | |
2774 | scm_num_overflow (s_scm_centered_remainder); | |
2775 | else | |
2776 | { | |
2777 | scm_t_inum rr = xx % yy; | |
2778 | if (SCM_LIKELY (xx > 0)) | |
2779 | { | |
2780 | if (SCM_LIKELY (yy > 0)) | |
2781 | { | |
2782 | if (rr >= (yy + 1) / 2) | |
2783 | rr -= yy; | |
2784 | } | |
2785 | else | |
2786 | { | |
2787 | if (rr >= (1 - yy) / 2) | |
2788 | rr += yy; | |
2789 | } | |
2790 | } | |
2791 | else | |
2792 | { | |
2793 | if (SCM_LIKELY (yy > 0)) | |
2794 | { | |
2795 | if (rr < -yy / 2) | |
2796 | rr += yy; | |
2797 | } | |
2798 | else | |
2799 | { | |
2800 | if (rr < yy / 2) | |
2801 | rr -= yy; | |
2802 | } | |
2803 | } | |
2804 | return SCM_I_MAKINUM (rr); | |
2805 | } | |
2806 | } | |
2807 | else if (SCM_BIGP (y)) | |
2808 | { | |
2809 | /* Pass a denormalized bignum version of x (even though it | |
2810 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2811 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2812 | } | |
2813 | else if (SCM_REALP (y)) | |
2814 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2815 | else if (SCM_FRACTIONP (y)) | |
2816 | return scm_i_exact_rational_centered_remainder (x, y); | |
2817 | else | |
2818 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2819 | s_scm_centered_remainder); | |
2820 | } | |
2821 | else if (SCM_BIGP (x)) | |
2822 | { | |
2823 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2824 | { | |
2825 | scm_t_inum yy = SCM_I_INUM (y); | |
2826 | if (SCM_UNLIKELY (yy == 0)) | |
2827 | scm_num_overflow (s_scm_centered_remainder); | |
2828 | else | |
2829 | { | |
2830 | scm_t_inum rr; | |
2831 | /* Arrange for rr to initially be non-positive, | |
2832 | because that simplifies the test to see | |
2833 | if it is within the needed bounds. */ | |
2834 | if (yy > 0) | |
2835 | { | |
2836 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2837 | scm_remember_upto_here_1 (x); | |
2838 | if (rr < -yy / 2) | |
2839 | rr += yy; | |
2840 | } | |
2841 | else | |
2842 | { | |
2843 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2844 | scm_remember_upto_here_1 (x); | |
2845 | if (rr < yy / 2) | |
2846 | rr -= yy; | |
2847 | } | |
2848 | return SCM_I_MAKINUM (rr); | |
2849 | } | |
2850 | } | |
2851 | else if (SCM_BIGP (y)) | |
2852 | return scm_i_bigint_centered_remainder (x, y); | |
2853 | else if (SCM_REALP (y)) | |
2854 | return scm_i_inexact_centered_remainder | |
2855 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2856 | else if (SCM_FRACTIONP (y)) | |
2857 | return scm_i_exact_rational_centered_remainder (x, y); | |
2858 | else | |
2859 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2860 | s_scm_centered_remainder); | |
2861 | } | |
2862 | else if (SCM_REALP (x)) | |
2863 | { | |
2864 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2865 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2866 | return scm_i_inexact_centered_remainder | |
2867 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2868 | else | |
2869 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2870 | s_scm_centered_remainder); | |
2871 | } | |
2872 | else if (SCM_FRACTIONP (x)) | |
2873 | { | |
2874 | if (SCM_REALP (y)) | |
2875 | return scm_i_inexact_centered_remainder | |
2876 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2877 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2878 | return scm_i_exact_rational_centered_remainder (x, y); | |
2879 | else | |
2880 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2881 | s_scm_centered_remainder); | |
2882 | } | |
2883 | else | |
2884 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2885 | s_scm_centered_remainder); | |
2886 | } | |
2887 | #undef FUNC_NAME | |
2888 | ||
2889 | static SCM | |
2890 | scm_i_inexact_centered_remainder (double x, double y) | |
2891 | { | |
2892 | double q; | |
2893 | ||
2894 | /* Although it would be more efficient to use fmod here, we can't | |
2895 | because it would in some cases produce results inconsistent with | |
2896 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
2897 | close). In particular, when x-y/2 is very close to a multiple of | |
2898 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
2899 | two cases must correspond to different choices of q. If quotient | |
2900 | chooses one and remainder chooses the other, it would be bad. */ | |
2901 | if (SCM_LIKELY (y > 0)) | |
2902 | q = floor (x/y + 0.5); | |
2903 | else if (SCM_LIKELY (y < 0)) | |
2904 | q = ceil (x/y - 0.5); | |
2905 | else if (y == 0) | |
2906 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
2907 | else | |
2908 | return scm_nan (); | |
2909 | return scm_from_double (x - q * y); | |
2910 | } | |
2911 | ||
2912 | /* Assumes that both x and y are bigints, though | |
2913 | x might be able to fit into a fixnum. */ | |
2914 | static SCM | |
2915 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2916 | { | |
2917 | SCM r, min_r; | |
2918 | ||
2919 | /* Note that x might be small enough to fit into a | |
2920 | fixnum, so we must not let it escape into the wild */ | |
2921 | r = scm_i_mkbig (); | |
2922 | ||
2923 | /* min_r will eventually become -abs(y)/2 */ | |
2924 | min_r = scm_i_mkbig (); | |
2925 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2926 | SCM_I_BIG_MPZ (y), 1); | |
2927 | ||
2928 | /* Arrange for rr to initially be non-positive, | |
2929 | because that simplifies the test to see | |
2930 | if it is within the needed bounds. */ | |
2931 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2932 | { | |
2933 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2934 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2935 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2936 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2937 | mpz_add (SCM_I_BIG_MPZ (r), | |
2938 | SCM_I_BIG_MPZ (r), | |
2939 | SCM_I_BIG_MPZ (y)); | |
2940 | } | |
2941 | else | |
2942 | { | |
2943 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2944 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2945 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2946 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2947 | SCM_I_BIG_MPZ (r), | |
2948 | SCM_I_BIG_MPZ (y)); | |
2949 | } | |
2950 | scm_remember_upto_here_2 (x, y); | |
2951 | return scm_i_normbig (r); | |
2952 | } | |
2953 | ||
2954 | static SCM | |
2955 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
2956 | { | |
2957 | SCM xd = scm_denominator (x); | |
2958 | SCM yd = scm_denominator (y); | |
2959 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2960 | scm_product (scm_numerator (y), xd)); | |
2961 | return scm_divide (r1, scm_product (xd, yd)); | |
2962 | } | |
2963 | ||
2964 | ||
2965 | static void scm_i_inexact_centered_divide (double x, double y, | |
2966 | SCM *qp, SCM *rp); | |
2967 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
2968 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
2969 | SCM *qp, SCM *rp); | |
2970 | ||
2971 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
2972 | (SCM x, SCM y), | |
2973 | "Return the integer @var{q} and the real number @var{r}\n" | |
2974 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2975 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2976 | "@lisp\n" | |
2977 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2978 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2979 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2980 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2981 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2982 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2983 | "@end lisp") | |
2984 | #define FUNC_NAME s_scm_i_centered_divide | |
2985 | { | |
2986 | SCM q, r; | |
2987 | ||
2988 | scm_centered_divide(x, y, &q, &r); | |
2989 | return scm_values (scm_list_2 (q, r)); | |
2990 | } | |
2991 | #undef FUNC_NAME | |
2992 | ||
2993 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2994 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2995 | ||
2996 | void | |
2997 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2998 | { | |
2999 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3000 | { | |
3001 | scm_t_inum xx = SCM_I_INUM (x); | |
3002 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3003 | { | |
3004 | scm_t_inum yy = SCM_I_INUM (y); | |
3005 | if (SCM_UNLIKELY (yy == 0)) | |
3006 | scm_num_overflow (s_scm_centered_divide); | |
3007 | else | |
3008 | { | |
3009 | scm_t_inum qq = xx / yy; | |
3010 | scm_t_inum rr = xx % yy; | |
3011 | if (SCM_LIKELY (xx > 0)) | |
3012 | { | |
3013 | if (SCM_LIKELY (yy > 0)) | |
3014 | { | |
3015 | if (rr >= (yy + 1) / 2) | |
3016 | { qq++; rr -= yy; } | |
3017 | } | |
3018 | else | |
3019 | { | |
3020 | if (rr >= (1 - yy) / 2) | |
3021 | { qq--; rr += yy; } | |
3022 | } | |
3023 | } | |
3024 | else | |
3025 | { | |
3026 | if (SCM_LIKELY (yy > 0)) | |
3027 | { | |
3028 | if (rr < -yy / 2) | |
3029 | { qq--; rr += yy; } | |
3030 | } | |
3031 | else | |
3032 | { | |
3033 | if (rr < yy / 2) | |
3034 | { qq++; rr -= yy; } | |
3035 | } | |
3036 | } | |
3037 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3038 | *qp = SCM_I_MAKINUM (qq); | |
3039 | else | |
3040 | *qp = scm_i_inum2big (qq); | |
3041 | *rp = SCM_I_MAKINUM (rr); | |
3042 | } | |
3043 | return; | |
3044 | } | |
3045 | else if (SCM_BIGP (y)) | |
3046 | { | |
3047 | /* Pass a denormalized bignum version of x (even though it | |
3048 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3049 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3050 | } | |
3051 | else if (SCM_REALP (y)) | |
3052 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3053 | else if (SCM_FRACTIONP (y)) | |
3054 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3055 | else | |
3056 | return two_valued_wta_dispatch_2 | |
3057 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3058 | s_scm_centered_divide, qp, rp); | |
3059 | } | |
3060 | else if (SCM_BIGP (x)) | |
3061 | { | |
3062 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3063 | { | |
3064 | scm_t_inum yy = SCM_I_INUM (y); | |
3065 | if (SCM_UNLIKELY (yy == 0)) | |
3066 | scm_num_overflow (s_scm_centered_divide); | |
3067 | else | |
3068 | { | |
3069 | SCM q = scm_i_mkbig (); | |
3070 | scm_t_inum rr; | |
3071 | /* Arrange for rr to initially be non-positive, | |
3072 | because that simplifies the test to see | |
3073 | if it is within the needed bounds. */ | |
3074 | if (yy > 0) | |
3075 | { | |
3076 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3077 | SCM_I_BIG_MPZ (x), yy); | |
3078 | scm_remember_upto_here_1 (x); | |
3079 | if (rr < -yy / 2) | |
3080 | { | |
3081 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3082 | SCM_I_BIG_MPZ (q), 1); | |
3083 | rr += yy; | |
3084 | } | |
3085 | } | |
3086 | else | |
3087 | { | |
3088 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3089 | SCM_I_BIG_MPZ (x), -yy); | |
3090 | scm_remember_upto_here_1 (x); | |
3091 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3092 | if (rr < yy / 2) | |
3093 | { | |
3094 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3095 | SCM_I_BIG_MPZ (q), 1); | |
3096 | rr -= yy; | |
3097 | } | |
3098 | } | |
3099 | *qp = scm_i_normbig (q); | |
3100 | *rp = SCM_I_MAKINUM (rr); | |
3101 | } | |
3102 | return; | |
3103 | } | |
3104 | else if (SCM_BIGP (y)) | |
3105 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3106 | else if (SCM_REALP (y)) | |
3107 | return scm_i_inexact_centered_divide | |
3108 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3109 | else if (SCM_FRACTIONP (y)) | |
3110 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3111 | else | |
3112 | return two_valued_wta_dispatch_2 | |
3113 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3114 | s_scm_centered_divide, qp, rp); | |
3115 | } | |
3116 | else if (SCM_REALP (x)) | |
3117 | { | |
3118 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3119 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3120 | return scm_i_inexact_centered_divide | |
3121 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3122 | else | |
3123 | return two_valued_wta_dispatch_2 | |
3124 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3125 | s_scm_centered_divide, qp, rp); | |
3126 | } | |
3127 | else if (SCM_FRACTIONP (x)) | |
3128 | { | |
3129 | if (SCM_REALP (y)) | |
3130 | return scm_i_inexact_centered_divide | |
3131 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3132 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3133 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3134 | else | |
3135 | return two_valued_wta_dispatch_2 | |
3136 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3137 | s_scm_centered_divide, qp, rp); | |
3138 | } | |
3139 | else | |
3140 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3141 | s_scm_centered_divide, qp, rp); | |
3142 | } | |
3143 | ||
3144 | static void | |
3145 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3146 | { | |
3147 | double q, r; | |
3148 | ||
3149 | if (SCM_LIKELY (y > 0)) | |
3150 | q = floor (x/y + 0.5); | |
3151 | else if (SCM_LIKELY (y < 0)) | |
3152 | q = ceil (x/y - 0.5); | |
3153 | else if (y == 0) | |
3154 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3155 | else | |
3156 | q = guile_NaN; | |
3157 | r = x - q * y; | |
3158 | *qp = scm_from_double (q); | |
3159 | *rp = scm_from_double (r); | |
3160 | } | |
3161 | ||
3162 | /* Assumes that both x and y are bigints, though | |
3163 | x might be able to fit into a fixnum. */ | |
3164 | static void | |
3165 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3166 | { | |
3167 | SCM q, r, min_r; | |
3168 | ||
3169 | /* Note that x might be small enough to fit into a | |
3170 | fixnum, so we must not let it escape into the wild */ | |
3171 | q = scm_i_mkbig (); | |
3172 | r = scm_i_mkbig (); | |
3173 | ||
3174 | /* min_r will eventually become -abs(y/2) */ | |
3175 | min_r = scm_i_mkbig (); | |
3176 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3177 | SCM_I_BIG_MPZ (y), 1); | |
3178 | ||
3179 | /* Arrange for rr to initially be non-positive, | |
3180 | because that simplifies the test to see | |
3181 | if it is within the needed bounds. */ | |
3182 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3183 | { | |
3184 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3185 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3186 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3187 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3188 | { | |
3189 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3190 | SCM_I_BIG_MPZ (q), 1); | |
3191 | mpz_add (SCM_I_BIG_MPZ (r), | |
3192 | SCM_I_BIG_MPZ (r), | |
3193 | SCM_I_BIG_MPZ (y)); | |
3194 | } | |
3195 | } | |
3196 | else | |
3197 | { | |
3198 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3199 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3200 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3201 | { | |
3202 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3203 | SCM_I_BIG_MPZ (q), 1); | |
3204 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3205 | SCM_I_BIG_MPZ (r), | |
3206 | SCM_I_BIG_MPZ (y)); | |
3207 | } | |
3208 | } | |
3209 | scm_remember_upto_here_2 (x, y); | |
3210 | *qp = scm_i_normbig (q); | |
3211 | *rp = scm_i_normbig (r); | |
3212 | } | |
3213 | ||
3214 | static void | |
3215 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3216 | { | |
3217 | SCM r1; | |
3218 | SCM xd = scm_denominator (x); | |
3219 | SCM yd = scm_denominator (y); | |
3220 | ||
3221 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3222 | scm_product (scm_numerator (y), xd), | |
3223 | qp, &r1); | |
3224 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3225 | } | |
3226 | ||
3227 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3228 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3229 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3230 | ||
3231 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3232 | (SCM x, SCM y), |
8f9da340 MW |
3233 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3234 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3235 | "@lisp\n" |
8f9da340 MW |
3236 | "(round-quotient 123 10) @result{} 12\n" |
3237 | "(round-quotient 123 -10) @result{} -12\n" | |
3238 | "(round-quotient -123 10) @result{} -12\n" | |
3239 | "(round-quotient -123 -10) @result{} 12\n" | |
3240 | "(round-quotient 125 10) @result{} 12\n" | |
3241 | "(round-quotient 127 10) @result{} 13\n" | |
3242 | "(round-quotient 135 10) @result{} 14\n" | |
3243 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3244 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3245 | "@end lisp") |
8f9da340 | 3246 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3247 | { |
3248 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3249 | { | |
4a46bc2a | 3250 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3251 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3252 | { | |
3253 | scm_t_inum yy = SCM_I_INUM (y); | |
3254 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3255 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3256 | else |
3257 | { | |
ff62c168 | 3258 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3259 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3260 | scm_t_inum ay = yy; |
3261 | scm_t_inum r2 = 2 * rr; | |
3262 | ||
3263 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3264 | { |
8f9da340 MW |
3265 | ay = -ay; |
3266 | r2 = -r2; | |
3267 | } | |
3268 | ||
3269 | if (qq & 1L) | |
3270 | { | |
3271 | if (r2 >= ay) | |
3272 | qq++; | |
3273 | else if (r2 <= -ay) | |
3274 | qq--; | |
ff62c168 MW |
3275 | } |
3276 | else | |
3277 | { | |
8f9da340 MW |
3278 | if (r2 > ay) |
3279 | qq++; | |
3280 | else if (r2 < -ay) | |
3281 | qq--; | |
ff62c168 | 3282 | } |
4a46bc2a MW |
3283 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3284 | return SCM_I_MAKINUM (qq); | |
3285 | else | |
3286 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3287 | } |
3288 | } | |
3289 | else if (SCM_BIGP (y)) | |
3290 | { | |
3291 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3292 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3293 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3294 | } |
3295 | else if (SCM_REALP (y)) | |
8f9da340 | 3296 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3297 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3298 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3299 | else |
8f9da340 MW |
3300 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3301 | s_scm_round_quotient); | |
ff62c168 MW |
3302 | } |
3303 | else if (SCM_BIGP (x)) | |
3304 | { | |
3305 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3306 | { | |
3307 | scm_t_inum yy = SCM_I_INUM (y); | |
3308 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3309 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3310 | else if (SCM_UNLIKELY (yy == 1)) |
3311 | return x; | |
ff62c168 MW |
3312 | else |
3313 | { | |
3314 | SCM q = scm_i_mkbig (); | |
3315 | scm_t_inum rr; | |
8f9da340 MW |
3316 | int needs_adjustment; |
3317 | ||
ff62c168 MW |
3318 | if (yy > 0) |
3319 | { | |
8f9da340 MW |
3320 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3321 | SCM_I_BIG_MPZ (x), yy); | |
3322 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3323 | needs_adjustment = (2*rr >= yy); | |
3324 | else | |
3325 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3326 | } |
3327 | else | |
3328 | { | |
3329 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3330 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3331 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3332 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3333 | needs_adjustment = (2*rr <= yy); | |
3334 | else | |
3335 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3336 | } |
8f9da340 MW |
3337 | scm_remember_upto_here_1 (x); |
3338 | if (needs_adjustment) | |
3339 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3340 | return scm_i_normbig (q); |
3341 | } | |
3342 | } | |
3343 | else if (SCM_BIGP (y)) | |
8f9da340 | 3344 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3345 | else if (SCM_REALP (y)) |
8f9da340 | 3346 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3347 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3348 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3349 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3350 | else |
8f9da340 MW |
3351 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3352 | s_scm_round_quotient); | |
ff62c168 MW |
3353 | } |
3354 | else if (SCM_REALP (x)) | |
3355 | { | |
3356 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3357 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3358 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3359 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3360 | else | |
8f9da340 MW |
3361 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3362 | s_scm_round_quotient); | |
ff62c168 MW |
3363 | } |
3364 | else if (SCM_FRACTIONP (x)) | |
3365 | { | |
3366 | if (SCM_REALP (y)) | |
8f9da340 | 3367 | return scm_i_inexact_round_quotient |
ff62c168 | 3368 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3369 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3370 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3371 | else |
8f9da340 MW |
3372 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3373 | s_scm_round_quotient); | |
ff62c168 MW |
3374 | } |
3375 | else | |
8f9da340 MW |
3376 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3377 | s_scm_round_quotient); | |
ff62c168 MW |
3378 | } |
3379 | #undef FUNC_NAME | |
3380 | ||
3381 | static SCM | |
8f9da340 | 3382 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3383 | { |
8f9da340 MW |
3384 | if (SCM_UNLIKELY (y == 0)) |
3385 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3386 | else |
8f9da340 | 3387 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3388 | } |
3389 | ||
3390 | /* Assumes that both x and y are bigints, though | |
3391 | x might be able to fit into a fixnum. */ | |
3392 | static SCM | |
8f9da340 | 3393 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3394 | { |
8f9da340 MW |
3395 | SCM q, r, r2; |
3396 | int cmp, needs_adjustment; | |
ff62c168 MW |
3397 | |
3398 | /* Note that x might be small enough to fit into a | |
3399 | fixnum, so we must not let it escape into the wild */ | |
3400 | q = scm_i_mkbig (); | |
3401 | r = scm_i_mkbig (); | |
8f9da340 | 3402 | r2 = scm_i_mkbig (); |
ff62c168 | 3403 | |
8f9da340 MW |
3404 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3405 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3406 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3407 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3408 | |
8f9da340 MW |
3409 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3410 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3411 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3412 | else |
8f9da340 MW |
3413 | needs_adjustment = (cmp > 0); |
3414 | scm_remember_upto_here_2 (r2, y); | |
3415 | ||
3416 | if (needs_adjustment) | |
3417 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3418 | ||
ff62c168 MW |
3419 | return scm_i_normbig (q); |
3420 | } | |
3421 | ||
ff62c168 | 3422 | static SCM |
8f9da340 | 3423 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3424 | { |
8f9da340 | 3425 | return scm_round_quotient |
03ddd15b MW |
3426 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3427 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3428 | } |
3429 | ||
8f9da340 MW |
3430 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3431 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3432 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3433 | |
8f9da340 | 3434 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3435 | (SCM x, SCM y), |
3436 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3437 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3438 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3439 | "nearest integer, with ties going to the nearest\n" | |
3440 | "even integer.\n" | |
ff62c168 | 3441 | "@lisp\n" |
8f9da340 MW |
3442 | "(round-remainder 123 10) @result{} 3\n" |
3443 | "(round-remainder 123 -10) @result{} 3\n" | |
3444 | "(round-remainder -123 10) @result{} -3\n" | |
3445 | "(round-remainder -123 -10) @result{} -3\n" | |
3446 | "(round-remainder 125 10) @result{} 5\n" | |
3447 | "(round-remainder 127 10) @result{} -3\n" | |
3448 | "(round-remainder 135 10) @result{} -5\n" | |
3449 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3450 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3451 | "@end lisp") |
8f9da340 | 3452 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3453 | { |
3454 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3455 | { | |
4a46bc2a | 3456 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3457 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3458 | { | |
3459 | scm_t_inum yy = SCM_I_INUM (y); | |
3460 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3461 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3462 | else |
3463 | { | |
8f9da340 | 3464 | scm_t_inum qq = xx / yy; |
ff62c168 | 3465 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3466 | scm_t_inum ay = yy; |
3467 | scm_t_inum r2 = 2 * rr; | |
3468 | ||
3469 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3470 | { |
8f9da340 MW |
3471 | ay = -ay; |
3472 | r2 = -r2; | |
3473 | } | |
3474 | ||
3475 | if (qq & 1L) | |
3476 | { | |
3477 | if (r2 >= ay) | |
3478 | rr -= yy; | |
3479 | else if (r2 <= -ay) | |
3480 | rr += yy; | |
ff62c168 MW |
3481 | } |
3482 | else | |
3483 | { | |
8f9da340 MW |
3484 | if (r2 > ay) |
3485 | rr -= yy; | |
3486 | else if (r2 < -ay) | |
3487 | rr += yy; | |
ff62c168 MW |
3488 | } |
3489 | return SCM_I_MAKINUM (rr); | |
3490 | } | |
3491 | } | |
3492 | else if (SCM_BIGP (y)) | |
3493 | { | |
3494 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3495 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3496 | return scm_i_bigint_round_remainder | |
3497 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3498 | } |
3499 | else if (SCM_REALP (y)) | |
8f9da340 | 3500 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3501 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3502 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3503 | else |
8f9da340 MW |
3504 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3505 | s_scm_round_remainder); | |
ff62c168 MW |
3506 | } |
3507 | else if (SCM_BIGP (x)) | |
3508 | { | |
3509 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3510 | { | |
3511 | scm_t_inum yy = SCM_I_INUM (y); | |
3512 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3513 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3514 | else |
3515 | { | |
8f9da340 | 3516 | SCM q = scm_i_mkbig (); |
ff62c168 | 3517 | scm_t_inum rr; |
8f9da340 MW |
3518 | int needs_adjustment; |
3519 | ||
ff62c168 MW |
3520 | if (yy > 0) |
3521 | { | |
8f9da340 MW |
3522 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3523 | SCM_I_BIG_MPZ (x), yy); | |
3524 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3525 | needs_adjustment = (2*rr >= yy); | |
3526 | else | |
3527 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3528 | } |
3529 | else | |
3530 | { | |
8f9da340 MW |
3531 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3532 | SCM_I_BIG_MPZ (x), -yy); | |
3533 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3534 | needs_adjustment = (2*rr <= yy); | |
3535 | else | |
3536 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3537 | } |
8f9da340 MW |
3538 | scm_remember_upto_here_2 (x, q); |
3539 | if (needs_adjustment) | |
3540 | rr -= yy; | |
ff62c168 MW |
3541 | return SCM_I_MAKINUM (rr); |
3542 | } | |
3543 | } | |
3544 | else if (SCM_BIGP (y)) | |
8f9da340 | 3545 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3546 | else if (SCM_REALP (y)) |
8f9da340 | 3547 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3548 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3549 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3550 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3551 | else |
8f9da340 MW |
3552 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3553 | s_scm_round_remainder); | |
ff62c168 MW |
3554 | } |
3555 | else if (SCM_REALP (x)) | |
3556 | { | |
3557 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3558 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3559 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3560 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3561 | else | |
8f9da340 MW |
3562 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3563 | s_scm_round_remainder); | |
ff62c168 MW |
3564 | } |
3565 | else if (SCM_FRACTIONP (x)) | |
3566 | { | |
3567 | if (SCM_REALP (y)) | |
8f9da340 | 3568 | return scm_i_inexact_round_remainder |
ff62c168 | 3569 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3570 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3571 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3572 | else |
8f9da340 MW |
3573 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3574 | s_scm_round_remainder); | |
ff62c168 MW |
3575 | } |
3576 | else | |
8f9da340 MW |
3577 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3578 | s_scm_round_remainder); | |
ff62c168 MW |
3579 | } |
3580 | #undef FUNC_NAME | |
3581 | ||
3582 | static SCM | |
8f9da340 | 3583 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3584 | { |
ff62c168 MW |
3585 | /* Although it would be more efficient to use fmod here, we can't |
3586 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3587 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3588 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3589 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3590 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3591 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3592 | |
3593 | if (SCM_UNLIKELY (y == 0)) | |
3594 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3595 | else |
8f9da340 MW |
3596 | { |
3597 | double q = scm_c_round (x / y); | |
3598 | return scm_from_double (x - q * y); | |
3599 | } | |
ff62c168 MW |
3600 | } |
3601 | ||
3602 | /* Assumes that both x and y are bigints, though | |
3603 | x might be able to fit into a fixnum. */ | |
3604 | static SCM | |
8f9da340 | 3605 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3606 | { |
8f9da340 MW |
3607 | SCM q, r, r2; |
3608 | int cmp, needs_adjustment; | |
ff62c168 MW |
3609 | |
3610 | /* Note that x might be small enough to fit into a | |
3611 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3612 | q = scm_i_mkbig (); |
ff62c168 | 3613 | r = scm_i_mkbig (); |
8f9da340 | 3614 | r2 = scm_i_mkbig (); |
ff62c168 | 3615 | |
8f9da340 MW |
3616 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3617 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3618 | scm_remember_upto_here_1 (x); | |
3619 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3620 | |
8f9da340 MW |
3621 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3622 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3623 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3624 | else |
8f9da340 MW |
3625 | needs_adjustment = (cmp > 0); |
3626 | scm_remember_upto_here_2 (q, r2); | |
3627 | ||
3628 | if (needs_adjustment) | |
3629 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3630 | ||
3631 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3632 | return scm_i_normbig (r); |
3633 | } | |
3634 | ||
ff62c168 | 3635 | static SCM |
8f9da340 | 3636 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3637 | { |
03ddd15b MW |
3638 | SCM xd = scm_denominator (x); |
3639 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3640 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3641 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3642 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3643 | } |
3644 | ||
3645 | ||
8f9da340 MW |
3646 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3647 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3648 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3649 | |
8f9da340 | 3650 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3651 | (SCM x, SCM y), |
3652 | "Return the integer @var{q} and the real number @var{r}\n" | |
3653 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3654 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3655 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3656 | "@lisp\n" |
8f9da340 MW |
3657 | "(round/ 123 10) @result{} 12 and 3\n" |
3658 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3659 | "(round/ -123 10) @result{} -12 and -3\n" | |
3660 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3661 | "(round/ 125 10) @result{} 12 and 5\n" | |
3662 | "(round/ 127 10) @result{} 13 and -3\n" | |
3663 | "(round/ 135 10) @result{} 14 and -5\n" | |
3664 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3665 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3666 | "@end lisp") |
8f9da340 | 3667 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3668 | { |
3669 | SCM q, r; | |
3670 | ||
8f9da340 | 3671 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3672 | return scm_values (scm_list_2 (q, r)); |
3673 | } | |
3674 | #undef FUNC_NAME | |
3675 | ||
8f9da340 MW |
3676 | #define s_scm_round_divide s_scm_i_round_divide |
3677 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3678 | |
3679 | void | |
8f9da340 | 3680 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3681 | { |
3682 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3683 | { | |
4a46bc2a | 3684 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3685 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3686 | { | |
3687 | scm_t_inum yy = SCM_I_INUM (y); | |
3688 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3689 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3690 | else |
3691 | { | |
ff62c168 | 3692 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3693 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3694 | scm_t_inum ay = yy; |
3695 | scm_t_inum r2 = 2 * rr; | |
3696 | ||
3697 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3698 | { |
8f9da340 MW |
3699 | ay = -ay; |
3700 | r2 = -r2; | |
3701 | } | |
3702 | ||
3703 | if (qq & 1L) | |
3704 | { | |
3705 | if (r2 >= ay) | |
3706 | { qq++; rr -= yy; } | |
3707 | else if (r2 <= -ay) | |
3708 | { qq--; rr += yy; } | |
ff62c168 MW |
3709 | } |
3710 | else | |
3711 | { | |
8f9da340 MW |
3712 | if (r2 > ay) |
3713 | { qq++; rr -= yy; } | |
3714 | else if (r2 < -ay) | |
3715 | { qq--; rr += yy; } | |
ff62c168 | 3716 | } |
4a46bc2a | 3717 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3718 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3719 | else |
5fbf680b MW |
3720 | *qp = scm_i_inum2big (qq); |
3721 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3722 | } |
5fbf680b | 3723 | return; |
ff62c168 MW |
3724 | } |
3725 | else if (SCM_BIGP (y)) | |
3726 | { | |
3727 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3728 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3729 | return scm_i_bigint_round_divide | |
3730 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3731 | } |
3732 | else if (SCM_REALP (y)) | |
8f9da340 | 3733 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3734 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3735 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3736 | else |
8f9da340 MW |
3737 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3738 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3739 | } |
3740 | else if (SCM_BIGP (x)) | |
3741 | { | |
3742 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3743 | { | |
3744 | scm_t_inum yy = SCM_I_INUM (y); | |
3745 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3746 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3747 | else |
3748 | { | |
3749 | SCM q = scm_i_mkbig (); | |
3750 | scm_t_inum rr; | |
8f9da340 MW |
3751 | int needs_adjustment; |
3752 | ||
ff62c168 MW |
3753 | if (yy > 0) |
3754 | { | |
8f9da340 MW |
3755 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3756 | SCM_I_BIG_MPZ (x), yy); | |
3757 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3758 | needs_adjustment = (2*rr >= yy); | |
3759 | else | |
3760 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3761 | } |
3762 | else | |
3763 | { | |
3764 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3765 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3766 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3767 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3768 | needs_adjustment = (2*rr <= yy); | |
3769 | else | |
3770 | needs_adjustment = (2*rr < yy); | |
3771 | } | |
3772 | scm_remember_upto_here_1 (x); | |
3773 | if (needs_adjustment) | |
3774 | { | |
3775 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3776 | rr -= yy; | |
ff62c168 | 3777 | } |
5fbf680b MW |
3778 | *qp = scm_i_normbig (q); |
3779 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3780 | } |
5fbf680b | 3781 | return; |
ff62c168 MW |
3782 | } |
3783 | else if (SCM_BIGP (y)) | |
8f9da340 | 3784 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3785 | else if (SCM_REALP (y)) |
8f9da340 | 3786 | return scm_i_inexact_round_divide |
5fbf680b | 3787 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3788 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3789 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3790 | else |
8f9da340 MW |
3791 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3792 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3793 | } |
3794 | else if (SCM_REALP (x)) | |
3795 | { | |
3796 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3797 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3798 | return scm_i_inexact_round_divide |
5fbf680b | 3799 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3800 | else |
8f9da340 MW |
3801 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3802 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3803 | } |
3804 | else if (SCM_FRACTIONP (x)) | |
3805 | { | |
3806 | if (SCM_REALP (y)) | |
8f9da340 | 3807 | return scm_i_inexact_round_divide |
5fbf680b | 3808 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3809 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3810 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3811 | else |
8f9da340 MW |
3812 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3813 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3814 | } |
3815 | else | |
8f9da340 MW |
3816 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3817 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3818 | } |
ff62c168 | 3819 | |
5fbf680b | 3820 | static void |
8f9da340 | 3821 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3822 | { |
8f9da340 MW |
3823 | if (SCM_UNLIKELY (y == 0)) |
3824 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3825 | else |
8f9da340 MW |
3826 | { |
3827 | double q = scm_c_round (x / y); | |
3828 | double r = x - q * y; | |
3829 | *qp = scm_from_double (q); | |
3830 | *rp = scm_from_double (r); | |
3831 | } | |
ff62c168 MW |
3832 | } |
3833 | ||
3834 | /* Assumes that both x and y are bigints, though | |
3835 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3836 | static void |
8f9da340 | 3837 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3838 | { |
8f9da340 MW |
3839 | SCM q, r, r2; |
3840 | int cmp, needs_adjustment; | |
ff62c168 MW |
3841 | |
3842 | /* Note that x might be small enough to fit into a | |
3843 | fixnum, so we must not let it escape into the wild */ | |
3844 | q = scm_i_mkbig (); | |
3845 | r = scm_i_mkbig (); | |
8f9da340 | 3846 | r2 = scm_i_mkbig (); |
ff62c168 | 3847 | |
8f9da340 MW |
3848 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3849 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3850 | scm_remember_upto_here_1 (x); | |
3851 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3852 | |
8f9da340 MW |
3853 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3854 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3855 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3856 | else |
8f9da340 MW |
3857 | needs_adjustment = (cmp > 0); |
3858 | ||
3859 | if (needs_adjustment) | |
ff62c168 | 3860 | { |
8f9da340 MW |
3861 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3862 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3863 | } |
8f9da340 MW |
3864 | |
3865 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
3866 | *qp = scm_i_normbig (q); |
3867 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
3868 | } |
3869 | ||
5fbf680b | 3870 | static void |
8f9da340 | 3871 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3872 | { |
03ddd15b MW |
3873 | SCM r1; |
3874 | SCM xd = scm_denominator (x); | |
3875 | SCM yd = scm_denominator (y); | |
3876 | ||
8f9da340 MW |
3877 | scm_round_divide (scm_product (scm_numerator (x), yd), |
3878 | scm_product (scm_numerator (y), xd), | |
3879 | qp, &r1); | |
03ddd15b | 3880 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3881 | } |
3882 | ||
3883 | ||
78d3deb1 AW |
3884 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
3885 | (SCM x, SCM y, SCM rest), | |
3886 | "Return the greatest common divisor of all parameter values.\n" | |
3887 | "If called without arguments, 0 is returned.") | |
3888 | #define FUNC_NAME s_scm_i_gcd | |
3889 | { | |
3890 | while (!scm_is_null (rest)) | |
3891 | { x = scm_gcd (x, y); | |
3892 | y = scm_car (rest); | |
3893 | rest = scm_cdr (rest); | |
3894 | } | |
3895 | return scm_gcd (x, y); | |
3896 | } | |
3897 | #undef FUNC_NAME | |
3898 | ||
3899 | #define s_gcd s_scm_i_gcd | |
3900 | #define g_gcd g_scm_i_gcd | |
3901 | ||
0f2d19dd | 3902 | SCM |
6e8d25a6 | 3903 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 3904 | { |
a2dead1b | 3905 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
1dd79792 | 3906 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 3907 | |
a2dead1b | 3908 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 3909 | { |
a2dead1b | 3910 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 3911 | { |
e25f3727 AW |
3912 | scm_t_inum xx = SCM_I_INUM (x); |
3913 | scm_t_inum yy = SCM_I_INUM (y); | |
3914 | scm_t_inum u = xx < 0 ? -xx : xx; | |
3915 | scm_t_inum v = yy < 0 ? -yy : yy; | |
3916 | scm_t_inum result; | |
a2dead1b | 3917 | if (SCM_UNLIKELY (xx == 0)) |
0aacf84e | 3918 | result = v; |
a2dead1b | 3919 | else if (SCM_UNLIKELY (yy == 0)) |
0aacf84e MD |
3920 | result = u; |
3921 | else | |
3922 | { | |
a2dead1b | 3923 | int k = 0; |
0aacf84e | 3924 | /* Determine a common factor 2^k */ |
a2dead1b | 3925 | while (((u | v) & 1) == 0) |
0aacf84e | 3926 | { |
a2dead1b | 3927 | k++; |
0aacf84e MD |
3928 | u >>= 1; |
3929 | v >>= 1; | |
3930 | } | |
3931 | /* Now, any factor 2^n can be eliminated */ | |
a2dead1b MW |
3932 | if ((u & 1) == 0) |
3933 | while ((u & 1) == 0) | |
3934 | u >>= 1; | |
0aacf84e | 3935 | else |
a2dead1b MW |
3936 | while ((v & 1) == 0) |
3937 | v >>= 1; | |
3938 | /* Both u and v are now odd. Subtract the smaller one | |
3939 | from the larger one to produce an even number, remove | |
3940 | more factors of two, and repeat. */ | |
3941 | while (u != v) | |
0aacf84e | 3942 | { |
a2dead1b MW |
3943 | if (u > v) |
3944 | { | |
3945 | u -= v; | |
3946 | while ((u & 1) == 0) | |
3947 | u >>= 1; | |
3948 | } | |
3949 | else | |
3950 | { | |
3951 | v -= u; | |
3952 | while ((v & 1) == 0) | |
3953 | v >>= 1; | |
3954 | } | |
0aacf84e | 3955 | } |
a2dead1b | 3956 | result = u << k; |
0aacf84e MD |
3957 | } |
3958 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 3959 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3960 | : scm_i_inum2big (result)); |
ca46fb90 RB |
3961 | } |
3962 | else if (SCM_BIGP (y)) | |
3963 | { | |
0bff4dce KR |
3964 | SCM_SWAP (x, y); |
3965 | goto big_inum; | |
ca46fb90 RB |
3966 | } |
3967 | else | |
3968 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 3969 | } |
ca46fb90 RB |
3970 | else if (SCM_BIGP (x)) |
3971 | { | |
e11e83f3 | 3972 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3973 | { |
e25f3727 AW |
3974 | scm_t_bits result; |
3975 | scm_t_inum yy; | |
0bff4dce | 3976 | big_inum: |
e11e83f3 | 3977 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
3978 | if (yy == 0) |
3979 | return scm_abs (x); | |
0aacf84e MD |
3980 | if (yy < 0) |
3981 | yy = -yy; | |
ca46fb90 RB |
3982 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
3983 | scm_remember_upto_here_1 (x); | |
0aacf84e | 3984 | return (SCM_POSFIXABLE (result) |
d956fa6f | 3985 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3986 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
3987 | } |
3988 | else if (SCM_BIGP (y)) | |
3989 | { | |
3990 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
3991 | mpz_gcd (SCM_I_BIG_MPZ (result), |
3992 | SCM_I_BIG_MPZ (x), | |
3993 | SCM_I_BIG_MPZ (y)); | |
3994 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
3995 | return scm_i_normbig (result); |
3996 | } | |
3997 | else | |
3998 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 3999 | } |
ca46fb90 | 4000 | else |
09fb7599 | 4001 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
4002 | } |
4003 | ||
78d3deb1 AW |
4004 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
4005 | (SCM x, SCM y, SCM rest), | |
4006 | "Return the least common multiple of the arguments.\n" | |
4007 | "If called without arguments, 1 is returned.") | |
4008 | #define FUNC_NAME s_scm_i_lcm | |
4009 | { | |
4010 | while (!scm_is_null (rest)) | |
4011 | { x = scm_lcm (x, y); | |
4012 | y = scm_car (rest); | |
4013 | rest = scm_cdr (rest); | |
4014 | } | |
4015 | return scm_lcm (x, y); | |
4016 | } | |
4017 | #undef FUNC_NAME | |
4018 | ||
4019 | #define s_lcm s_scm_i_lcm | |
4020 | #define g_lcm g_scm_i_lcm | |
4021 | ||
0f2d19dd | 4022 | SCM |
6e8d25a6 | 4023 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4024 | { |
ca46fb90 RB |
4025 | if (SCM_UNBNDP (n2)) |
4026 | { | |
4027 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
4028 | return SCM_I_MAKINUM (1L); |
4029 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 4030 | } |
09fb7599 | 4031 | |
e11e83f3 | 4032 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 4033 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 4034 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 4035 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 4036 | |
e11e83f3 | 4037 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 4038 | { |
e11e83f3 | 4039 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4040 | { |
4041 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4042 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4043 | return d; |
4044 | else | |
4045 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4046 | } | |
4047 | else | |
4048 | { | |
4049 | /* inum n1, big n2 */ | |
4050 | inumbig: | |
4051 | { | |
4052 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4053 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4054 | if (nn1 == 0) return SCM_INUM0; |
4055 | if (nn1 < 0) nn1 = - nn1; | |
4056 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4057 | scm_remember_upto_here_1 (n2); | |
4058 | return result; | |
4059 | } | |
4060 | } | |
4061 | } | |
4062 | else | |
4063 | { | |
4064 | /* big n1 */ | |
e11e83f3 | 4065 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4066 | { |
4067 | SCM_SWAP (n1, n2); | |
4068 | goto inumbig; | |
4069 | } | |
4070 | else | |
4071 | { | |
4072 | SCM result = scm_i_mkbig (); | |
4073 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4074 | SCM_I_BIG_MPZ (n1), | |
4075 | SCM_I_BIG_MPZ (n2)); | |
4076 | scm_remember_upto_here_2(n1, n2); | |
4077 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4078 | return result; | |
4079 | } | |
f872b822 | 4080 | } |
0f2d19dd JB |
4081 | } |
4082 | ||
8a525303 GB |
4083 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4084 | ||
4085 | Logand: | |
4086 | X Y Result Method: | |
4087 | (len) | |
4088 | + + + x (map digit:logand X Y) | |
4089 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4090 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4091 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4092 | ||
4093 | Logior: | |
4094 | X Y Result Method: | |
4095 | ||
4096 | + + + (map digit:logior X Y) | |
4097 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4098 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4099 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4100 | ||
4101 | Logxor: | |
4102 | X Y Result Method: | |
4103 | ||
4104 | + + + (map digit:logxor X Y) | |
4105 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4106 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4107 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4108 | ||
4109 | Logtest: | |
4110 | X Y Result | |
4111 | ||
4112 | + + (any digit:logand X Y) | |
4113 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4114 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4115 | - - #t | |
4116 | ||
4117 | */ | |
4118 | ||
78d3deb1 AW |
4119 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4120 | (SCM x, SCM y, SCM rest), | |
4121 | "Return the bitwise AND of the integer arguments.\n\n" | |
4122 | "@lisp\n" | |
4123 | "(logand) @result{} -1\n" | |
4124 | "(logand 7) @result{} 7\n" | |
4125 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4126 | "@end lisp") | |
4127 | #define FUNC_NAME s_scm_i_logand | |
4128 | { | |
4129 | while (!scm_is_null (rest)) | |
4130 | { x = scm_logand (x, y); | |
4131 | y = scm_car (rest); | |
4132 | rest = scm_cdr (rest); | |
4133 | } | |
4134 | return scm_logand (x, y); | |
4135 | } | |
4136 | #undef FUNC_NAME | |
4137 | ||
4138 | #define s_scm_logand s_scm_i_logand | |
4139 | ||
4140 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4141 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4142 | { |
e25f3727 | 4143 | scm_t_inum nn1; |
9a00c9fc | 4144 | |
0aacf84e MD |
4145 | if (SCM_UNBNDP (n2)) |
4146 | { | |
4147 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4148 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4149 | else if (!SCM_NUMBERP (n1)) |
4150 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4151 | else if (SCM_NUMBERP (n1)) | |
4152 | return n1; | |
4153 | else | |
4154 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4155 | } |
09fb7599 | 4156 | |
e11e83f3 | 4157 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4158 | { |
e11e83f3 MV |
4159 | nn1 = SCM_I_INUM (n1); |
4160 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4161 | { |
e25f3727 | 4162 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4163 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4164 | } |
4165 | else if SCM_BIGP (n2) | |
4166 | { | |
4167 | intbig: | |
2e16a342 | 4168 | if (nn1 == 0) |
0aacf84e MD |
4169 | return SCM_INUM0; |
4170 | { | |
4171 | SCM result_z = scm_i_mkbig (); | |
4172 | mpz_t nn1_z; | |
4173 | mpz_init_set_si (nn1_z, nn1); | |
4174 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4175 | scm_remember_upto_here_1 (n2); | |
4176 | mpz_clear (nn1_z); | |
4177 | return scm_i_normbig (result_z); | |
4178 | } | |
4179 | } | |
4180 | else | |
4181 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4182 | } | |
4183 | else if (SCM_BIGP (n1)) | |
4184 | { | |
e11e83f3 | 4185 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4186 | { |
4187 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4188 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4189 | goto intbig; |
4190 | } | |
4191 | else if (SCM_BIGP (n2)) | |
4192 | { | |
4193 | SCM result_z = scm_i_mkbig (); | |
4194 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4195 | SCM_I_BIG_MPZ (n1), | |
4196 | SCM_I_BIG_MPZ (n2)); | |
4197 | scm_remember_upto_here_2 (n1, n2); | |
4198 | return scm_i_normbig (result_z); | |
4199 | } | |
4200 | else | |
4201 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4202 | } |
0aacf84e | 4203 | else |
09fb7599 | 4204 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4205 | } |
1bbd0b84 | 4206 | #undef FUNC_NAME |
0f2d19dd | 4207 | |
09fb7599 | 4208 | |
78d3deb1 AW |
4209 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4210 | (SCM x, SCM y, SCM rest), | |
4211 | "Return the bitwise OR of the integer arguments.\n\n" | |
4212 | "@lisp\n" | |
4213 | "(logior) @result{} 0\n" | |
4214 | "(logior 7) @result{} 7\n" | |
4215 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4216 | "@end lisp") | |
4217 | #define FUNC_NAME s_scm_i_logior | |
4218 | { | |
4219 | while (!scm_is_null (rest)) | |
4220 | { x = scm_logior (x, y); | |
4221 | y = scm_car (rest); | |
4222 | rest = scm_cdr (rest); | |
4223 | } | |
4224 | return scm_logior (x, y); | |
4225 | } | |
4226 | #undef FUNC_NAME | |
4227 | ||
4228 | #define s_scm_logior s_scm_i_logior | |
4229 | ||
4230 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4231 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4232 | { |
e25f3727 | 4233 | scm_t_inum nn1; |
9a00c9fc | 4234 | |
0aacf84e MD |
4235 | if (SCM_UNBNDP (n2)) |
4236 | { | |
4237 | if (SCM_UNBNDP (n1)) | |
4238 | return SCM_INUM0; | |
4239 | else if (SCM_NUMBERP (n1)) | |
4240 | return n1; | |
4241 | else | |
4242 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4243 | } |
09fb7599 | 4244 | |
e11e83f3 | 4245 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4246 | { |
e11e83f3 MV |
4247 | nn1 = SCM_I_INUM (n1); |
4248 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4249 | { |
e11e83f3 | 4250 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4251 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4252 | } |
4253 | else if (SCM_BIGP (n2)) | |
4254 | { | |
4255 | intbig: | |
4256 | if (nn1 == 0) | |
4257 | return n2; | |
4258 | { | |
4259 | SCM result_z = scm_i_mkbig (); | |
4260 | mpz_t nn1_z; | |
4261 | mpz_init_set_si (nn1_z, nn1); | |
4262 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4263 | scm_remember_upto_here_1 (n2); | |
4264 | mpz_clear (nn1_z); | |
9806de0d | 4265 | return scm_i_normbig (result_z); |
0aacf84e MD |
4266 | } |
4267 | } | |
4268 | else | |
4269 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4270 | } | |
4271 | else if (SCM_BIGP (n1)) | |
4272 | { | |
e11e83f3 | 4273 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4274 | { |
4275 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4276 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4277 | goto intbig; |
4278 | } | |
4279 | else if (SCM_BIGP (n2)) | |
4280 | { | |
4281 | SCM result_z = scm_i_mkbig (); | |
4282 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4283 | SCM_I_BIG_MPZ (n1), | |
4284 | SCM_I_BIG_MPZ (n2)); | |
4285 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4286 | return scm_i_normbig (result_z); |
0aacf84e MD |
4287 | } |
4288 | else | |
4289 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4290 | } |
0aacf84e | 4291 | else |
09fb7599 | 4292 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4293 | } |
1bbd0b84 | 4294 | #undef FUNC_NAME |
0f2d19dd | 4295 | |
09fb7599 | 4296 | |
78d3deb1 AW |
4297 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4298 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4299 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4300 | "set in the result if it is set in an odd number of arguments.\n" | |
4301 | "@lisp\n" | |
4302 | "(logxor) @result{} 0\n" | |
4303 | "(logxor 7) @result{} 7\n" | |
4304 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4305 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4306 | "@end lisp") |
78d3deb1 AW |
4307 | #define FUNC_NAME s_scm_i_logxor |
4308 | { | |
4309 | while (!scm_is_null (rest)) | |
4310 | { x = scm_logxor (x, y); | |
4311 | y = scm_car (rest); | |
4312 | rest = scm_cdr (rest); | |
4313 | } | |
4314 | return scm_logxor (x, y); | |
4315 | } | |
4316 | #undef FUNC_NAME | |
4317 | ||
4318 | #define s_scm_logxor s_scm_i_logxor | |
4319 | ||
4320 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4321 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4322 | { |
e25f3727 | 4323 | scm_t_inum nn1; |
9a00c9fc | 4324 | |
0aacf84e MD |
4325 | if (SCM_UNBNDP (n2)) |
4326 | { | |
4327 | if (SCM_UNBNDP (n1)) | |
4328 | return SCM_INUM0; | |
4329 | else if (SCM_NUMBERP (n1)) | |
4330 | return n1; | |
4331 | else | |
4332 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4333 | } |
09fb7599 | 4334 | |
e11e83f3 | 4335 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4336 | { |
e11e83f3 MV |
4337 | nn1 = SCM_I_INUM (n1); |
4338 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4339 | { |
e25f3727 | 4340 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4341 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4342 | } |
4343 | else if (SCM_BIGP (n2)) | |
4344 | { | |
4345 | intbig: | |
4346 | { | |
4347 | SCM result_z = scm_i_mkbig (); | |
4348 | mpz_t nn1_z; | |
4349 | mpz_init_set_si (nn1_z, nn1); | |
4350 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4351 | scm_remember_upto_here_1 (n2); | |
4352 | mpz_clear (nn1_z); | |
4353 | return scm_i_normbig (result_z); | |
4354 | } | |
4355 | } | |
4356 | else | |
4357 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4358 | } | |
4359 | else if (SCM_BIGP (n1)) | |
4360 | { | |
e11e83f3 | 4361 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4362 | { |
4363 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4364 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4365 | goto intbig; |
4366 | } | |
4367 | else if (SCM_BIGP (n2)) | |
4368 | { | |
4369 | SCM result_z = scm_i_mkbig (); | |
4370 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4371 | SCM_I_BIG_MPZ (n1), | |
4372 | SCM_I_BIG_MPZ (n2)); | |
4373 | scm_remember_upto_here_2 (n1, n2); | |
4374 | return scm_i_normbig (result_z); | |
4375 | } | |
4376 | else | |
4377 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4378 | } |
0aacf84e | 4379 | else |
09fb7599 | 4380 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4381 | } |
1bbd0b84 | 4382 | #undef FUNC_NAME |
0f2d19dd | 4383 | |
09fb7599 | 4384 | |
a1ec6916 | 4385 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4386 | (SCM j, SCM k), |
ba6e7231 KR |
4387 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4388 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4389 | "without actually calculating the @code{logand}, just testing\n" | |
4390 | "for non-zero.\n" | |
4391 | "\n" | |
1e6808ea | 4392 | "@lisp\n" |
b380b885 MD |
4393 | "(logtest #b0100 #b1011) @result{} #f\n" |
4394 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4395 | "@end lisp") |
1bbd0b84 | 4396 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4397 | { |
e25f3727 | 4398 | scm_t_inum nj; |
9a00c9fc | 4399 | |
e11e83f3 | 4400 | if (SCM_I_INUMP (j)) |
0aacf84e | 4401 | { |
e11e83f3 MV |
4402 | nj = SCM_I_INUM (j); |
4403 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4404 | { |
e25f3727 | 4405 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4406 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4407 | } |
4408 | else if (SCM_BIGP (k)) | |
4409 | { | |
4410 | intbig: | |
4411 | if (nj == 0) | |
4412 | return SCM_BOOL_F; | |
4413 | { | |
4414 | SCM result; | |
4415 | mpz_t nj_z; | |
4416 | mpz_init_set_si (nj_z, nj); | |
4417 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4418 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4419 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4420 | mpz_clear (nj_z); |
4421 | return result; | |
4422 | } | |
4423 | } | |
4424 | else | |
4425 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4426 | } | |
4427 | else if (SCM_BIGP (j)) | |
4428 | { | |
e11e83f3 | 4429 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4430 | { |
4431 | SCM_SWAP (j, k); | |
e11e83f3 | 4432 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4433 | goto intbig; |
4434 | } | |
4435 | else if (SCM_BIGP (k)) | |
4436 | { | |
4437 | SCM result; | |
4438 | mpz_t result_z; | |
4439 | mpz_init (result_z); | |
4440 | mpz_and (result_z, | |
4441 | SCM_I_BIG_MPZ (j), | |
4442 | SCM_I_BIG_MPZ (k)); | |
4443 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4444 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4445 | mpz_clear (result_z); |
4446 | return result; | |
4447 | } | |
4448 | else | |
4449 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4450 | } | |
4451 | else | |
4452 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4453 | } |
1bbd0b84 | 4454 | #undef FUNC_NAME |
0f2d19dd | 4455 | |
c1bfcf60 | 4456 | |
a1ec6916 | 4457 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4458 | (SCM index, SCM j), |
ba6e7231 KR |
4459 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4460 | "@var{index} starts from 0 for the least significant bit.\n" | |
4461 | "\n" | |
1e6808ea | 4462 | "@lisp\n" |
b380b885 MD |
4463 | "(logbit? 0 #b1101) @result{} #t\n" |
4464 | "(logbit? 1 #b1101) @result{} #f\n" | |
4465 | "(logbit? 2 #b1101) @result{} #t\n" | |
4466 | "(logbit? 3 #b1101) @result{} #t\n" | |
4467 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4468 | "@end lisp") |
1bbd0b84 | 4469 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4470 | { |
78166ad5 | 4471 | unsigned long int iindex; |
5efd3c7d | 4472 | iindex = scm_to_ulong (index); |
78166ad5 | 4473 | |
e11e83f3 | 4474 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4475 | { |
4476 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4477 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4478 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4479 | } |
0aacf84e MD |
4480 | else if (SCM_BIGP (j)) |
4481 | { | |
4482 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4483 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4484 | return scm_from_bool (val); |
0aacf84e MD |
4485 | } |
4486 | else | |
78166ad5 | 4487 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4488 | } |
1bbd0b84 | 4489 | #undef FUNC_NAME |
0f2d19dd | 4490 | |
78166ad5 | 4491 | |
a1ec6916 | 4492 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4493 | (SCM n), |
4d814788 | 4494 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4495 | "argument.\n" |
4496 | "\n" | |
b380b885 MD |
4497 | "@lisp\n" |
4498 | "(number->string (lognot #b10000000) 2)\n" | |
4499 | " @result{} \"-10000001\"\n" | |
4500 | "(number->string (lognot #b0) 2)\n" | |
4501 | " @result{} \"-1\"\n" | |
1e6808ea | 4502 | "@end lisp") |
1bbd0b84 | 4503 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4504 | { |
e11e83f3 | 4505 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4506 | /* No overflow here, just need to toggle all the bits making up the inum. |
4507 | Enhancement: No need to strip the tag and add it back, could just xor | |
4508 | a block of 1 bits, if that worked with the various debug versions of | |
4509 | the SCM typedef. */ | |
e11e83f3 | 4510 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4511 | |
4512 | } else if (SCM_BIGP (n)) { | |
4513 | SCM result = scm_i_mkbig (); | |
4514 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4515 | scm_remember_upto_here_1 (n); | |
4516 | return result; | |
4517 | ||
4518 | } else { | |
4519 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4520 | } | |
0f2d19dd | 4521 | } |
1bbd0b84 | 4522 | #undef FUNC_NAME |
0f2d19dd | 4523 | |
518b7508 KR |
4524 | /* returns 0 if IN is not an integer. OUT must already be |
4525 | initialized. */ | |
4526 | static int | |
4527 | coerce_to_big (SCM in, mpz_t out) | |
4528 | { | |
4529 | if (SCM_BIGP (in)) | |
4530 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4531 | else if (SCM_I_INUMP (in)) |
4532 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4533 | else |
4534 | return 0; | |
4535 | ||
4536 | return 1; | |
4537 | } | |
4538 | ||
d885e204 | 4539 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4540 | (SCM n, SCM k, SCM m), |
4541 | "Return @var{n} raised to the integer exponent\n" | |
4542 | "@var{k}, modulo @var{m}.\n" | |
4543 | "\n" | |
4544 | "@lisp\n" | |
4545 | "(modulo-expt 2 3 5)\n" | |
4546 | " @result{} 3\n" | |
4547 | "@end lisp") | |
d885e204 | 4548 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4549 | { |
4550 | mpz_t n_tmp; | |
4551 | mpz_t k_tmp; | |
4552 | mpz_t m_tmp; | |
4553 | ||
4554 | /* There are two classes of error we might encounter -- | |
4555 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4556 | and | |
4557 | 2) wrong-type errors, which of course we'll report by calling | |
4558 | SCM_WRONG_TYPE_ARG. | |
4559 | We don't report those errors immediately, however; instead we do | |
4560 | some cleanup first. These variables tell us which error (if | |
4561 | any) we should report after cleaning up. | |
4562 | */ | |
4563 | int report_overflow = 0; | |
4564 | ||
4565 | int position_of_wrong_type = 0; | |
4566 | SCM value_of_wrong_type = SCM_INUM0; | |
4567 | ||
4568 | SCM result = SCM_UNDEFINED; | |
4569 | ||
4570 | mpz_init (n_tmp); | |
4571 | mpz_init (k_tmp); | |
4572 | mpz_init (m_tmp); | |
4573 | ||
bc36d050 | 4574 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4575 | { |
4576 | report_overflow = 1; | |
4577 | goto cleanup; | |
4578 | } | |
4579 | ||
4580 | if (!coerce_to_big (n, n_tmp)) | |
4581 | { | |
4582 | value_of_wrong_type = n; | |
4583 | position_of_wrong_type = 1; | |
4584 | goto cleanup; | |
4585 | } | |
4586 | ||
4587 | if (!coerce_to_big (k, k_tmp)) | |
4588 | { | |
4589 | value_of_wrong_type = k; | |
4590 | position_of_wrong_type = 2; | |
4591 | goto cleanup; | |
4592 | } | |
4593 | ||
4594 | if (!coerce_to_big (m, m_tmp)) | |
4595 | { | |
4596 | value_of_wrong_type = m; | |
4597 | position_of_wrong_type = 3; | |
4598 | goto cleanup; | |
4599 | } | |
4600 | ||
4601 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4602 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4603 | doesn't exist (or is not unique). Since exceptions are hard to | |
4604 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4605 | a simple failure code, which is easy to handle. */ | |
4606 | ||
4607 | if (-1 == mpz_sgn (k_tmp)) | |
4608 | { | |
4609 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4610 | { | |
4611 | report_overflow = 1; | |
4612 | goto cleanup; | |
4613 | } | |
4614 | mpz_neg (k_tmp, k_tmp); | |
4615 | } | |
4616 | ||
4617 | result = scm_i_mkbig (); | |
4618 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4619 | n_tmp, | |
4620 | k_tmp, | |
4621 | m_tmp); | |
b7b8c575 KR |
4622 | |
4623 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4624 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4625 | ||
518b7508 KR |
4626 | cleanup: |
4627 | mpz_clear (m_tmp); | |
4628 | mpz_clear (k_tmp); | |
4629 | mpz_clear (n_tmp); | |
4630 | ||
4631 | if (report_overflow) | |
4632 | scm_num_overflow (FUNC_NAME); | |
4633 | ||
4634 | if (position_of_wrong_type) | |
4635 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4636 | value_of_wrong_type); | |
4637 | ||
4638 | return scm_i_normbig (result); | |
4639 | } | |
4640 | #undef FUNC_NAME | |
4641 | ||
a1ec6916 | 4642 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4643 | (SCM n, SCM k), |
ba6e7231 KR |
4644 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4645 | "exact integer, @var{n} can be any number.\n" | |
4646 | "\n" | |
2519490c MW |
4647 | "Negative @var{k} is supported, and results in\n" |
4648 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4649 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4650 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4651 | "\n" |
b380b885 | 4652 | "@lisp\n" |
ba6e7231 KR |
4653 | "(integer-expt 2 5) @result{} 32\n" |
4654 | "(integer-expt -3 3) @result{} -27\n" | |
4655 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4656 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4657 | "@end lisp") |
1bbd0b84 | 4658 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4659 | { |
e25f3727 | 4660 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4661 | SCM z_i2 = SCM_BOOL_F; |
4662 | int i2_is_big = 0; | |
d956fa6f | 4663 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4664 | |
bfe1f03a MW |
4665 | /* Specifically refrain from checking the type of the first argument. |
4666 | This allows us to exponentiate any object that can be multiplied. | |
4667 | If we must raise to a negative power, we must also be able to | |
4668 | take its reciprocal. */ | |
4669 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4670 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4671 | |
bfe1f03a MW |
4672 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4673 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4674 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4675 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4676 | /* The next check is necessary only because R6RS specifies different | |
4677 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4678 | we simply skip this case and move on. */ | |
4679 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4680 | { | |
4681 | /* k cannot be 0 at this point, because we | |
4682 | have already checked for that case above */ | |
4683 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4684 | return n; |
4685 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4686 | return scm_nan (); | |
4687 | } | |
a285b18c MW |
4688 | else if (SCM_FRACTIONP (n)) |
4689 | { | |
4690 | /* Optimize the fraction case by (a/b)^k ==> (a^k)/(b^k), to avoid | |
4691 | needless reduction of intermediate products to lowest terms. | |
4692 | If a and b have no common factors, then a^k and b^k have no | |
4693 | common factors. Use 'scm_i_make_ratio_already_reduced' to | |
4694 | construct the final result, so that no gcd computations are | |
4695 | needed to exponentiate a fraction. */ | |
4696 | if (scm_is_true (scm_positive_p (k))) | |
4697 | return scm_i_make_ratio_already_reduced | |
4698 | (scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k), | |
4699 | scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k)); | |
4700 | else | |
4701 | { | |
4702 | k = scm_difference (k, SCM_UNDEFINED); | |
4703 | return scm_i_make_ratio_already_reduced | |
4704 | (scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k), | |
4705 | scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k)); | |
4706 | } | |
4707 | } | |
ca46fb90 | 4708 | |
e11e83f3 MV |
4709 | if (SCM_I_INUMP (k)) |
4710 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4711 | else if (SCM_BIGP (k)) |
4712 | { | |
4713 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4714 | scm_remember_upto_here_1 (k); |
4715 | i2_is_big = 1; | |
4716 | } | |
2830fd91 | 4717 | else |
ca46fb90 RB |
4718 | SCM_WRONG_TYPE_ARG (2, k); |
4719 | ||
4720 | if (i2_is_big) | |
f872b822 | 4721 | { |
ca46fb90 RB |
4722 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4723 | { | |
4724 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4725 | n = scm_divide (n, SCM_UNDEFINED); | |
4726 | } | |
4727 | while (1) | |
4728 | { | |
4729 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4730 | { | |
ca46fb90 RB |
4731 | return acc; |
4732 | } | |
4733 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4734 | { | |
ca46fb90 RB |
4735 | return scm_product (acc, n); |
4736 | } | |
4737 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4738 | acc = scm_product (acc, n); | |
4739 | n = scm_product (n, n); | |
4740 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4741 | } | |
f872b822 | 4742 | } |
ca46fb90 | 4743 | else |
f872b822 | 4744 | { |
ca46fb90 RB |
4745 | if (i2 < 0) |
4746 | { | |
4747 | i2 = -i2; | |
4748 | n = scm_divide (n, SCM_UNDEFINED); | |
4749 | } | |
4750 | while (1) | |
4751 | { | |
4752 | if (0 == i2) | |
4753 | return acc; | |
4754 | if (1 == i2) | |
4755 | return scm_product (acc, n); | |
4756 | if (i2 & 1) | |
4757 | acc = scm_product (acc, n); | |
4758 | n = scm_product (n, n); | |
4759 | i2 >>= 1; | |
4760 | } | |
f872b822 | 4761 | } |
0f2d19dd | 4762 | } |
1bbd0b84 | 4763 | #undef FUNC_NAME |
0f2d19dd | 4764 | |
e08a12b5 MW |
4765 | /* Efficiently compute (N * 2^COUNT), |
4766 | where N is an exact integer, and COUNT > 0. */ | |
4767 | static SCM | |
4768 | left_shift_exact_integer (SCM n, long count) | |
4769 | { | |
4770 | if (SCM_I_INUMP (n)) | |
4771 | { | |
4772 | scm_t_inum nn = SCM_I_INUM (n); | |
4773 | ||
4774 | /* Left shift of count >= SCM_I_FIXNUM_BIT-1 will always | |
4775 | overflow a non-zero fixnum. For smaller shifts we check the | |
4776 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4777 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4778 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". */ | |
4779 | ||
4780 | if (nn == 0) | |
4781 | return n; | |
4782 | else if (count < SCM_I_FIXNUM_BIT-1 && | |
4783 | ((scm_t_bits) (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - count)) + 1) | |
4784 | <= 1)) | |
4785 | return SCM_I_MAKINUM (nn << count); | |
4786 | else | |
4787 | { | |
4788 | SCM result = scm_i_inum2big (nn); | |
4789 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
4790 | count); | |
4791 | return result; | |
4792 | } | |
4793 | } | |
4794 | else if (SCM_BIGP (n)) | |
4795 | { | |
4796 | SCM result = scm_i_mkbig (); | |
4797 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), count); | |
4798 | scm_remember_upto_here_1 (n); | |
4799 | return result; | |
4800 | } | |
4801 | else | |
4802 | scm_syserror ("left_shift_exact_integer"); | |
4803 | } | |
4804 | ||
4805 | /* Efficiently compute floor (N / 2^COUNT), | |
4806 | where N is an exact integer and COUNT > 0. */ | |
4807 | static SCM | |
4808 | floor_right_shift_exact_integer (SCM n, long count) | |
4809 | { | |
4810 | if (SCM_I_INUMP (n)) | |
4811 | { | |
4812 | scm_t_inum nn = SCM_I_INUM (n); | |
4813 | ||
4814 | if (count >= SCM_I_FIXNUM_BIT) | |
4815 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM (-1)); | |
4816 | else | |
4817 | return SCM_I_MAKINUM (SCM_SRS (nn, count)); | |
4818 | } | |
4819 | else if (SCM_BIGP (n)) | |
4820 | { | |
4821 | SCM result = scm_i_mkbig (); | |
4822 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4823 | count); | |
4824 | scm_remember_upto_here_1 (n); | |
4825 | return scm_i_normbig (result); | |
4826 | } | |
4827 | else | |
4828 | scm_syserror ("floor_right_shift_exact_integer"); | |
4829 | } | |
4830 | ||
4831 | /* Efficiently compute round (N / 2^COUNT), | |
4832 | where N is an exact integer and COUNT > 0. */ | |
4833 | static SCM | |
4834 | round_right_shift_exact_integer (SCM n, long count) | |
4835 | { | |
4836 | if (SCM_I_INUMP (n)) | |
4837 | { | |
4838 | if (count >= SCM_I_FIXNUM_BIT) | |
4839 | return SCM_INUM0; | |
4840 | else | |
4841 | { | |
4842 | scm_t_inum nn = SCM_I_INUM (n); | |
4843 | scm_t_inum qq = SCM_SRS (nn, count); | |
4844 | ||
4845 | if (0 == (nn & (1L << (count-1)))) | |
4846 | return SCM_I_MAKINUM (qq); /* round down */ | |
4847 | else if (nn & ((1L << (count-1)) - 1)) | |
4848 | return SCM_I_MAKINUM (qq + 1); /* round up */ | |
4849 | else | |
4850 | return SCM_I_MAKINUM ((~1L) & (qq + 1)); /* round to even */ | |
4851 | } | |
4852 | } | |
4853 | else if (SCM_BIGP (n)) | |
4854 | { | |
4855 | SCM q = scm_i_mkbig (); | |
4856 | ||
4857 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), count); | |
4858 | if (mpz_tstbit (SCM_I_BIG_MPZ (n), count-1) | |
4859 | && (mpz_odd_p (SCM_I_BIG_MPZ (q)) | |
4860 | || (mpz_scan1 (SCM_I_BIG_MPZ (n), 0) < count-1))) | |
4861 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
4862 | scm_remember_upto_here_1 (n); | |
4863 | return scm_i_normbig (q); | |
4864 | } | |
4865 | else | |
4866 | scm_syserror ("round_right_shift_exact_integer"); | |
4867 | } | |
4868 | ||
a1ec6916 | 4869 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
e08a12b5 MW |
4870 | (SCM n, SCM count), |
4871 | "Return @math{floor(@var{n} * 2^@var{count})}.\n" | |
4872 | "@var{n} and @var{count} must be exact integers.\n" | |
1e6808ea | 4873 | "\n" |
e08a12b5 MW |
4874 | "With @var{n} viewed as an infinite-precision twos-complement\n" |
4875 | "integer, @code{ash} means a left shift introducing zero bits\n" | |
4876 | "when @var{count} is positive, or a right shift dropping bits\n" | |
4877 | "when @var{count} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 4878 | "\n" |
b380b885 | 4879 | "@lisp\n" |
1e6808ea MG |
4880 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
4881 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
4882 | "\n" |
4883 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
4884 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 4885 | "@end lisp") |
1bbd0b84 | 4886 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 4887 | { |
e08a12b5 | 4888 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) |
788aca27 | 4889 | { |
e08a12b5 | 4890 | long bits_to_shift = scm_to_long (count); |
788aca27 KR |
4891 | |
4892 | if (bits_to_shift > 0) | |
e08a12b5 MW |
4893 | return left_shift_exact_integer (n, bits_to_shift); |
4894 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
4895 | return floor_right_shift_exact_integer (n, -bits_to_shift); | |
788aca27 | 4896 | else |
e08a12b5 | 4897 | return n; |
788aca27 | 4898 | } |
e08a12b5 MW |
4899 | else |
4900 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4901 | } | |
4902 | #undef FUNC_NAME | |
788aca27 | 4903 | |
e08a12b5 MW |
4904 | SCM_DEFINE (scm_round_ash, "round-ash", 2, 0, 0, |
4905 | (SCM n, SCM count), | |
4906 | "Return @math{round(@var{n} * 2^@var{count})}.\n" | |
4907 | "@var{n} and @var{count} must be exact integers.\n" | |
4908 | "\n" | |
4909 | "With @var{n} viewed as an infinite-precision twos-complement\n" | |
4910 | "integer, @code{round-ash} means a left shift introducing zero\n" | |
4911 | "bits when @var{count} is positive, or a right shift rounding\n" | |
4912 | "to the nearest integer (with ties going to the nearest even\n" | |
4913 | "integer) when @var{count} is negative. This is a rounded\n" | |
4914 | "``arithmetic'' shift.\n" | |
4915 | "\n" | |
4916 | "@lisp\n" | |
4917 | "(number->string (round-ash #b1 3) 2) @result{} \"1000\"\n" | |
4918 | "(number->string (round-ash #b1010 -1) 2) @result{} \"101\"\n" | |
4919 | "(number->string (round-ash #b1010 -2) 2) @result{} \"10\"\n" | |
4920 | "(number->string (round-ash #b1011 -2) 2) @result{} \"11\"\n" | |
4921 | "(number->string (round-ash #b1101 -2) 2) @result{} \"11\"\n" | |
4922 | "(number->string (round-ash #b1110 -2) 2) @result{} \"100\"\n" | |
4923 | "@end lisp") | |
4924 | #define FUNC_NAME s_scm_round_ash | |
4925 | { | |
4926 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) | |
4927 | { | |
4928 | long bits_to_shift = scm_to_long (count); | |
788aca27 | 4929 | |
e08a12b5 MW |
4930 | if (bits_to_shift > 0) |
4931 | return left_shift_exact_integer (n, bits_to_shift); | |
4932 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
4933 | return round_right_shift_exact_integer (n, -bits_to_shift); | |
ca46fb90 | 4934 | else |
e08a12b5 | 4935 | return n; |
ca46fb90 RB |
4936 | } |
4937 | else | |
e08a12b5 | 4938 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 4939 | } |
1bbd0b84 | 4940 | #undef FUNC_NAME |
0f2d19dd | 4941 | |
3c9f20f8 | 4942 | |
a1ec6916 | 4943 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 4944 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
4945 | "Return the integer composed of the @var{start} (inclusive)\n" |
4946 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
4947 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
4948 | "\n" | |
b380b885 MD |
4949 | "@lisp\n" |
4950 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
4951 | " @result{} \"1010\"\n" | |
4952 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
4953 | " @result{} \"10110\"\n" | |
4954 | "@end lisp") | |
1bbd0b84 | 4955 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 4956 | { |
7f848242 | 4957 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
4958 | istart = scm_to_ulong (start); |
4959 | iend = scm_to_ulong (end); | |
c1bfcf60 | 4960 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 4961 | |
7f848242 KR |
4962 | /* how many bits to keep */ |
4963 | bits = iend - istart; | |
4964 | ||
e11e83f3 | 4965 | if (SCM_I_INUMP (n)) |
0aacf84e | 4966 | { |
e25f3727 | 4967 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
4968 | |
4969 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 4970 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 4971 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 4972 | |
0aacf84e MD |
4973 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
4974 | { | |
4975 | /* Since we emulate two's complement encoded numbers, this | |
4976 | * special case requires us to produce a result that has | |
7f848242 | 4977 | * more bits than can be stored in a fixnum. |
0aacf84e | 4978 | */ |
e25f3727 | 4979 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
4980 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4981 | bits); | |
4982 | return result; | |
0aacf84e | 4983 | } |
ac0c002c | 4984 | |
7f848242 | 4985 | /* mask down to requisite bits */ |
857ae6af | 4986 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 4987 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
4988 | } |
4989 | else if (SCM_BIGP (n)) | |
ac0c002c | 4990 | { |
7f848242 KR |
4991 | SCM result; |
4992 | if (bits == 1) | |
4993 | { | |
d956fa6f | 4994 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
4995 | } |
4996 | else | |
4997 | { | |
4998 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
4999 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
5000 | such bits into a ulong. */ | |
5001 | result = scm_i_mkbig (); | |
5002 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
5003 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
5004 | result = scm_i_normbig (result); | |
5005 | } | |
5006 | scm_remember_upto_here_1 (n); | |
5007 | return result; | |
ac0c002c | 5008 | } |
0aacf84e | 5009 | else |
78166ad5 | 5010 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5011 | } |
1bbd0b84 | 5012 | #undef FUNC_NAME |
0f2d19dd | 5013 | |
7f848242 | 5014 | |
e4755e5c JB |
5015 | static const char scm_logtab[] = { |
5016 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
5017 | }; | |
1cc91f1b | 5018 | |
a1ec6916 | 5019 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 5020 | (SCM n), |
1e6808ea MG |
5021 | "Return the number of bits in integer @var{n}. If integer is\n" |
5022 | "positive, the 1-bits in its binary representation are counted.\n" | |
5023 | "If negative, the 0-bits in its two's-complement binary\n" | |
5024 | "representation are counted. If 0, 0 is returned.\n" | |
5025 | "\n" | |
b380b885 MD |
5026 | "@lisp\n" |
5027 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
5028 | " @result{} 4\n" |
5029 | "(logcount 0)\n" | |
5030 | " @result{} 0\n" | |
5031 | "(logcount -2)\n" | |
5032 | " @result{} 1\n" | |
5033 | "@end lisp") | |
5034 | #define FUNC_NAME s_scm_logcount | |
5035 | { | |
e11e83f3 | 5036 | if (SCM_I_INUMP (n)) |
f872b822 | 5037 | { |
e25f3727 AW |
5038 | unsigned long c = 0; |
5039 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
5040 | if (nn < 0) |
5041 | nn = -1 - nn; | |
5042 | while (nn) | |
5043 | { | |
5044 | c += scm_logtab[15 & nn]; | |
5045 | nn >>= 4; | |
5046 | } | |
d956fa6f | 5047 | return SCM_I_MAKINUM (c); |
f872b822 | 5048 | } |
ca46fb90 | 5049 | else if (SCM_BIGP (n)) |
f872b822 | 5050 | { |
ca46fb90 | 5051 | unsigned long count; |
713a4259 KR |
5052 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
5053 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 5054 | else |
713a4259 KR |
5055 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
5056 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5057 | return SCM_I_MAKINUM (count); |
f872b822 | 5058 | } |
ca46fb90 RB |
5059 | else |
5060 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 5061 | } |
ca46fb90 | 5062 | #undef FUNC_NAME |
0f2d19dd JB |
5063 | |
5064 | ||
ca46fb90 RB |
5065 | static const char scm_ilentab[] = { |
5066 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
5067 | }; | |
5068 | ||
0f2d19dd | 5069 | |
ca46fb90 RB |
5070 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
5071 | (SCM n), | |
5072 | "Return the number of bits necessary to represent @var{n}.\n" | |
5073 | "\n" | |
5074 | "@lisp\n" | |
5075 | "(integer-length #b10101010)\n" | |
5076 | " @result{} 8\n" | |
5077 | "(integer-length 0)\n" | |
5078 | " @result{} 0\n" | |
5079 | "(integer-length #b1111)\n" | |
5080 | " @result{} 4\n" | |
5081 | "@end lisp") | |
5082 | #define FUNC_NAME s_scm_integer_length | |
5083 | { | |
e11e83f3 | 5084 | if (SCM_I_INUMP (n)) |
0aacf84e | 5085 | { |
e25f3727 | 5086 | unsigned long c = 0; |
0aacf84e | 5087 | unsigned int l = 4; |
e25f3727 | 5088 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
5089 | if (nn < 0) |
5090 | nn = -1 - nn; | |
5091 | while (nn) | |
5092 | { | |
5093 | c += 4; | |
5094 | l = scm_ilentab [15 & nn]; | |
5095 | nn >>= 4; | |
5096 | } | |
d956fa6f | 5097 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
5098 | } |
5099 | else if (SCM_BIGP (n)) | |
5100 | { | |
5101 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
5102 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
5103 | 1 too big, so check for that and adjust. */ | |
5104 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
5105 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
5106 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
5107 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
5108 | size--; | |
5109 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5110 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
5111 | } |
5112 | else | |
ca46fb90 | 5113 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5114 | } |
5115 | #undef FUNC_NAME | |
0f2d19dd JB |
5116 | |
5117 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5118 | #define SCM_MAX_DBL_PREC 60 |
5119 | #define SCM_MAX_DBL_RADIX 36 | |
5120 | ||
5121 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
5122 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
5123 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
5124 | ||
5125 | static | |
5126 | void init_dblprec(int *prec, int radix) { | |
5127 | /* determine floating point precision by adding successively | |
5128 | smaller increments to 1.0 until it is considered == 1.0 */ | |
5129 | double f = ((double)1.0)/radix; | |
5130 | double fsum = 1.0 + f; | |
5131 | ||
5132 | *prec = 0; | |
5133 | while (fsum != 1.0) | |
5134 | { | |
5135 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
5136 | fsum = 1.0; | |
5137 | else | |
5138 | { | |
5139 | f /= radix; | |
5140 | fsum = f + 1.0; | |
5141 | } | |
5142 | } | |
5143 | (*prec) -= 1; | |
5144 | } | |
5145 | ||
5146 | static | |
5147 | void init_fx_radix(double *fx_list, int radix) | |
5148 | { | |
5149 | /* initialize a per-radix list of tolerances. When added | |
5150 | to a number < 1.0, we can determine if we should raund | |
5151 | up and quit converting a number to a string. */ | |
5152 | int i; | |
5153 | fx_list[0] = 0.0; | |
5154 | fx_list[1] = 0.5; | |
5155 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
5156 | fx_list[i] = (fx_list[i-1] / radix); | |
5157 | } | |
5158 | ||
5159 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5160 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5161 | |
1be6b49c | 5162 | static size_t |
0b799eea | 5163 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5164 | { |
0b799eea MV |
5165 | int efmt, dpt, d, i, wp; |
5166 | double *fx; | |
5167 | #ifdef DBL_MIN_10_EXP | |
5168 | double f_cpy; | |
5169 | int exp_cpy; | |
5170 | #endif /* DBL_MIN_10_EXP */ | |
5171 | size_t ch = 0; | |
5172 | int exp = 0; | |
5173 | ||
5174 | if(radix < 2 || | |
5175 | radix > SCM_MAX_DBL_RADIX) | |
5176 | { | |
5177 | /* revert to existing behavior */ | |
5178 | radix = 10; | |
5179 | } | |
5180 | ||
5181 | wp = scm_dblprec[radix-2]; | |
5182 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5183 | |
f872b822 | 5184 | if (f == 0.0) |
abb7e44d MV |
5185 | { |
5186 | #ifdef HAVE_COPYSIGN | |
5187 | double sgn = copysign (1.0, f); | |
5188 | ||
5189 | if (sgn < 0.0) | |
5190 | a[ch++] = '-'; | |
5191 | #endif | |
abb7e44d MV |
5192 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5193 | } | |
7351e207 | 5194 | |
2e65b52f | 5195 | if (isinf (f)) |
7351e207 MV |
5196 | { |
5197 | if (f < 0) | |
5198 | strcpy (a, "-inf.0"); | |
5199 | else | |
5200 | strcpy (a, "+inf.0"); | |
5201 | return ch+6; | |
5202 | } | |
2e65b52f | 5203 | else if (isnan (f)) |
7351e207 MV |
5204 | { |
5205 | strcpy (a, "+nan.0"); | |
5206 | return ch+6; | |
5207 | } | |
5208 | ||
f872b822 MD |
5209 | if (f < 0.0) |
5210 | { | |
5211 | f = -f; | |
5212 | a[ch++] = '-'; | |
5213 | } | |
7351e207 | 5214 | |
f872b822 MD |
5215 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5216 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5217 | /* just do the checking...if it passes, we do the conversion for our |
5218 | radix again below */ | |
5219 | f_cpy = f; | |
5220 | exp_cpy = exp; | |
5221 | ||
5222 | while (f_cpy < 1.0) | |
f872b822 | 5223 | { |
0b799eea MV |
5224 | f_cpy *= 10.0; |
5225 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5226 | { |
5227 | a[ch++] = '#'; | |
5228 | a[ch++] = '.'; | |
5229 | a[ch++] = '#'; | |
5230 | return ch; | |
5231 | } | |
f872b822 | 5232 | } |
0b799eea | 5233 | while (f_cpy > 10.0) |
f872b822 | 5234 | { |
0b799eea MV |
5235 | f_cpy *= 0.10; |
5236 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5237 | { |
5238 | a[ch++] = '#'; | |
5239 | a[ch++] = '.'; | |
5240 | a[ch++] = '#'; | |
5241 | return ch; | |
5242 | } | |
f872b822 | 5243 | } |
0b799eea MV |
5244 | #endif |
5245 | ||
f872b822 MD |
5246 | while (f < 1.0) |
5247 | { | |
0b799eea | 5248 | f *= radix; |
f872b822 MD |
5249 | exp--; |
5250 | } | |
0b799eea | 5251 | while (f > radix) |
f872b822 | 5252 | { |
0b799eea | 5253 | f /= radix; |
f872b822 MD |
5254 | exp++; |
5255 | } | |
0b799eea MV |
5256 | |
5257 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5258 | { |
5259 | f = 1.0; | |
5260 | exp++; | |
5261 | } | |
0f2d19dd | 5262 | zero: |
0b799eea MV |
5263 | #ifdef ENGNOT |
5264 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 5265 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
5266 | exp -= dpt++; |
5267 | efmt = 1; | |
f872b822 MD |
5268 | #else |
5269 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 5270 | if (!efmt) |
cda139a7 MD |
5271 | { |
5272 | if (exp < 0) | |
5273 | { | |
5274 | a[ch++] = '0'; | |
5275 | a[ch++] = '.'; | |
5276 | dpt = exp; | |
f872b822 MD |
5277 | while (++dpt) |
5278 | a[ch++] = '0'; | |
cda139a7 MD |
5279 | } |
5280 | else | |
f872b822 | 5281 | dpt = exp + 1; |
cda139a7 | 5282 | } |
0f2d19dd JB |
5283 | else |
5284 | dpt = 1; | |
f872b822 MD |
5285 | #endif |
5286 | ||
5287 | do | |
5288 | { | |
5289 | d = f; | |
5290 | f -= d; | |
0b799eea | 5291 | a[ch++] = number_chars[d]; |
f872b822 MD |
5292 | if (f < fx[wp]) |
5293 | break; | |
5294 | if (f + fx[wp] >= 1.0) | |
5295 | { | |
0b799eea | 5296 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5297 | break; |
5298 | } | |
0b799eea | 5299 | f *= radix; |
f872b822 MD |
5300 | if (!(--dpt)) |
5301 | a[ch++] = '.'; | |
0f2d19dd | 5302 | } |
f872b822 | 5303 | while (wp--); |
0f2d19dd JB |
5304 | |
5305 | if (dpt > 0) | |
cda139a7 | 5306 | { |
f872b822 | 5307 | #ifndef ENGNOT |
cda139a7 MD |
5308 | if ((dpt > 4) && (exp > 6)) |
5309 | { | |
f872b822 | 5310 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 5311 | for (i = ch++; i > d; i--) |
f872b822 | 5312 | a[i] = a[i - 1]; |
cda139a7 MD |
5313 | a[d] = '.'; |
5314 | efmt = 1; | |
5315 | } | |
5316 | else | |
f872b822 | 5317 | #endif |
cda139a7 | 5318 | { |
f872b822 MD |
5319 | while (--dpt) |
5320 | a[ch++] = '0'; | |
cda139a7 MD |
5321 | a[ch++] = '.'; |
5322 | } | |
5323 | } | |
f872b822 MD |
5324 | if (a[ch - 1] == '.') |
5325 | a[ch++] = '0'; /* trailing zero */ | |
5326 | if (efmt && exp) | |
5327 | { | |
5328 | a[ch++] = 'e'; | |
5329 | if (exp < 0) | |
5330 | { | |
5331 | exp = -exp; | |
5332 | a[ch++] = '-'; | |
5333 | } | |
0b799eea MV |
5334 | for (i = radix; i <= exp; i *= radix); |
5335 | for (i /= radix; i; i /= radix) | |
f872b822 | 5336 | { |
0b799eea | 5337 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5338 | exp %= i; |
5339 | } | |
0f2d19dd | 5340 | } |
0f2d19dd JB |
5341 | return ch; |
5342 | } | |
5343 | ||
7a1aba42 MV |
5344 | |
5345 | static size_t | |
5346 | icmplx2str (double real, double imag, char *str, int radix) | |
5347 | { | |
5348 | size_t i; | |
c7218482 | 5349 | double sgn; |
7a1aba42 MV |
5350 | |
5351 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5352 | #ifdef HAVE_COPYSIGN |
5353 | sgn = copysign (1.0, imag); | |
5354 | #else | |
5355 | sgn = imag; | |
5356 | #endif | |
5357 | /* Don't output a '+' for negative numbers or for Inf and | |
5358 | NaN. They will provide their own sign. */ | |
5359 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5360 | str[i++] = '+'; | |
5361 | i += idbl2str (imag, &str[i], radix); | |
5362 | str[i++] = 'i'; | |
7a1aba42 MV |
5363 | return i; |
5364 | } | |
5365 | ||
1be6b49c | 5366 | static size_t |
0b799eea | 5367 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5368 | { |
1be6b49c | 5369 | size_t i; |
3c9a524f | 5370 | if (SCM_REALP (flt)) |
0b799eea | 5371 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5372 | else |
7a1aba42 MV |
5373 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5374 | str, radix); | |
0f2d19dd JB |
5375 | return i; |
5376 | } | |
0f2d19dd | 5377 | |
2881e77b | 5378 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5379 | characters in the result. |
5380 | rad is output base | |
5381 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5382 | size_t |
2881e77b MV |
5383 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5384 | { | |
5385 | if (num < 0) | |
5386 | { | |
5387 | *p++ = '-'; | |
5388 | return scm_iuint2str (-num, rad, p) + 1; | |
5389 | } | |
5390 | else | |
5391 | return scm_iuint2str (num, rad, p); | |
5392 | } | |
5393 | ||
5394 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5395 | characters in the result. | |
5396 | rad is output base | |
5397 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5398 | size_t | |
5399 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5400 | { |
1be6b49c ML |
5401 | size_t j = 1; |
5402 | size_t i; | |
2881e77b | 5403 | scm_t_uintmax n = num; |
5c11cc9d | 5404 | |
a6f3af16 AW |
5405 | if (rad < 2 || rad > 36) |
5406 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5407 | ||
f872b822 | 5408 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5409 | j++; |
5410 | ||
5411 | i = j; | |
2881e77b | 5412 | n = num; |
f872b822 MD |
5413 | while (i--) |
5414 | { | |
5c11cc9d GH |
5415 | int d = n % rad; |
5416 | ||
f872b822 | 5417 | n /= rad; |
a6f3af16 | 5418 | p[i] = number_chars[d]; |
f872b822 | 5419 | } |
0f2d19dd JB |
5420 | return j; |
5421 | } | |
5422 | ||
a1ec6916 | 5423 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5424 | (SCM n, SCM radix), |
5425 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5426 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5427 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5428 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5429 | { |
1bbd0b84 | 5430 | int base; |
98cb6e75 | 5431 | |
0aacf84e | 5432 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5433 | base = 10; |
0aacf84e | 5434 | else |
5efd3c7d | 5435 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5436 | |
e11e83f3 | 5437 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5438 | { |
5439 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5440 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5441 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5442 | } |
5443 | else if (SCM_BIGP (n)) | |
5444 | { | |
5445 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
d88f5323 AW |
5446 | size_t len = strlen (str); |
5447 | void (*freefunc) (void *, size_t); | |
5448 | SCM ret; | |
5449 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
0aacf84e | 5450 | scm_remember_upto_here_1 (n); |
d88f5323 AW |
5451 | ret = scm_from_latin1_stringn (str, len); |
5452 | freefunc (str, len + 1); | |
5453 | return ret; | |
0aacf84e | 5454 | } |
f92e85f7 MV |
5455 | else if (SCM_FRACTIONP (n)) |
5456 | { | |
f92e85f7 | 5457 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5458 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5459 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5460 | } | |
0aacf84e MD |
5461 | else if (SCM_INEXACTP (n)) |
5462 | { | |
5463 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5464 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5465 | } |
5466 | else | |
bb628794 | 5467 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5468 | } |
1bbd0b84 | 5469 | #undef FUNC_NAME |
0f2d19dd JB |
5470 | |
5471 | ||
ca46fb90 RB |
5472 | /* These print routines used to be stubbed here so that scm_repl.c |
5473 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5474 | |
0f2d19dd | 5475 | int |
e81d98ec | 5476 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5477 | { |
56e55ac7 | 5478 | char num_buf[FLOBUFLEN]; |
0b799eea | 5479 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5480 | return !0; |
5481 | } | |
5482 | ||
b479fe9a MV |
5483 | void |
5484 | scm_i_print_double (double val, SCM port) | |
5485 | { | |
5486 | char num_buf[FLOBUFLEN]; | |
5487 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5488 | } | |
5489 | ||
f3ae5d60 | 5490 | int |
e81d98ec | 5491 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5492 | |
f3ae5d60 | 5493 | { |
56e55ac7 | 5494 | char num_buf[FLOBUFLEN]; |
0b799eea | 5495 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5496 | return !0; |
5497 | } | |
1cc91f1b | 5498 | |
7a1aba42 MV |
5499 | void |
5500 | scm_i_print_complex (double real, double imag, SCM port) | |
5501 | { | |
5502 | char num_buf[FLOBUFLEN]; | |
5503 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5504 | } | |
5505 | ||
f92e85f7 MV |
5506 | int |
5507 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5508 | { | |
5509 | SCM str; | |
f92e85f7 | 5510 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5511 | scm_display (str, port); |
f92e85f7 MV |
5512 | scm_remember_upto_here_1 (str); |
5513 | return !0; | |
5514 | } | |
5515 | ||
0f2d19dd | 5516 | int |
e81d98ec | 5517 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5518 | { |
ca46fb90 | 5519 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
b57bf272 AW |
5520 | size_t len = strlen (str); |
5521 | void (*freefunc) (void *, size_t); | |
5522 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
ca46fb90 | 5523 | scm_remember_upto_here_1 (exp); |
b57bf272 AW |
5524 | scm_lfwrite (str, len, port); |
5525 | freefunc (str, len + 1); | |
0f2d19dd JB |
5526 | return !0; |
5527 | } | |
5528 | /*** END nums->strs ***/ | |
5529 | ||
3c9a524f | 5530 | |
0f2d19dd | 5531 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5532 | |
3c9a524f DH |
5533 | /* The following functions implement the conversion from strings to numbers. |
5534 | * The implementation somehow follows the grammar for numbers as it is given | |
5535 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5536 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5537 | * points should be noted about the implementation: | |
bc3d34f5 | 5538 | * |
3c9a524f DH |
5539 | * * Each function keeps a local index variable 'idx' that points at the |
5540 | * current position within the parsed string. The global index is only | |
5541 | * updated if the function could parse the corresponding syntactic unit | |
5542 | * successfully. | |
bc3d34f5 | 5543 | * |
3c9a524f | 5544 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5545 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5546 | * | |
3c9a524f DH |
5547 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5548 | * Only if these fixnums would overflow, the result variables are updated | |
5549 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5550 | * the temporary variables holding the fixnums are cleared, and the process | |
5551 | * starts over again. If for example fixnums were able to store five decimal | |
5552 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5553 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5554 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5555 | * |
5556 | * Notes on the handling of exactness specifiers: | |
5557 | * | |
5558 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5559 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5560 | * written in rectangular form, exactness specifiers are applied to the | |
5561 | * real and imaginary parts before calling scm_make_rectangular. For | |
5562 | * complex numbers written in polar form, exactness specifiers are applied | |
5563 | * to the magnitude and angle before calling scm_make_polar. | |
5564 | * | |
5565 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5566 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5567 | * the entire number, and applies to both components of a complex number. | |
5568 | * "#e" causes each component to be made exact, and "#i" causes each | |
5569 | * component to be made inexact. If no forced exactness specifier is | |
5570 | * present, then the exactness of each component is determined | |
5571 | * independently by the presence or absence of a decimal point or hash mark | |
5572 | * within that component. If a decimal point or hash mark is present, the | |
5573 | * component is made inexact, otherwise it is made exact. | |
5574 | * | |
5575 | * After the exactness specifiers have been applied to each component, they | |
5576 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5577 | * the final result. Note that this will result in a real number if the | |
5578 | * imaginary part, magnitude, or angle is an exact 0. | |
5579 | * | |
5580 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5581 | * | |
5582 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5583 | */ |
5584 | ||
5585 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5586 | ||
5587 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5588 | ||
a6f3af16 AW |
5589 | /* Caller is responsible for checking that the return value is in range |
5590 | for the given radix, which should be <= 36. */ | |
5591 | static unsigned int | |
5592 | char_decimal_value (scm_t_uint32 c) | |
5593 | { | |
5594 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5595 | that's certainly above any valid decimal, so we take advantage of | |
5596 | that to elide some tests. */ | |
5597 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5598 | ||
5599 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5600 | hexadecimals. */ | |
5601 | if (d >= 10U) | |
5602 | { | |
5603 | c = uc_tolower (c); | |
5604 | if (c >= (scm_t_uint32) 'a') | |
5605 | d = c - (scm_t_uint32)'a' + 10U; | |
5606 | } | |
5607 | return d; | |
5608 | } | |
3c9a524f | 5609 | |
91db4a37 LC |
5610 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5611 | in base RADIX. Upon success, return the unsigned integer and update | |
5612 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5613 | static SCM |
3f47e526 | 5614 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5615 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5616 | { |
3c9a524f DH |
5617 | unsigned int idx = *p_idx; |
5618 | unsigned int hash_seen = 0; | |
5619 | scm_t_bits shift = 1; | |
5620 | scm_t_bits add = 0; | |
5621 | unsigned int digit_value; | |
5622 | SCM result; | |
5623 | char c; | |
3f47e526 | 5624 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5625 | |
5626 | if (idx == len) | |
5627 | return SCM_BOOL_F; | |
2a8fecee | 5628 | |
3f47e526 | 5629 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5630 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5631 | if (digit_value >= radix) |
5632 | return SCM_BOOL_F; | |
5633 | ||
5634 | idx++; | |
d956fa6f | 5635 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5636 | while (idx != len) |
f872b822 | 5637 | { |
3f47e526 | 5638 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5639 | if (c == '#') |
3c9a524f DH |
5640 | { |
5641 | hash_seen = 1; | |
5642 | digit_value = 0; | |
5643 | } | |
a6f3af16 AW |
5644 | else if (hash_seen) |
5645 | break; | |
3c9a524f | 5646 | else |
a6f3af16 AW |
5647 | { |
5648 | digit_value = char_decimal_value (c); | |
5649 | /* This check catches non-decimals in addition to out-of-range | |
5650 | decimals. */ | |
5651 | if (digit_value >= radix) | |
5652 | break; | |
5653 | } | |
3c9a524f DH |
5654 | |
5655 | idx++; | |
5656 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5657 | { | |
d956fa6f | 5658 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5659 | if (add > 0) |
d956fa6f | 5660 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5661 | |
5662 | shift = radix; | |
5663 | add = digit_value; | |
5664 | } | |
5665 | else | |
5666 | { | |
5667 | shift = shift * radix; | |
5668 | add = add * radix + digit_value; | |
5669 | } | |
5670 | }; | |
5671 | ||
5672 | if (shift > 1) | |
d956fa6f | 5673 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5674 | if (add > 0) |
d956fa6f | 5675 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5676 | |
5677 | *p_idx = idx; | |
5678 | if (hash_seen) | |
5679 | *p_exactness = INEXACT; | |
5680 | ||
5681 | return result; | |
2a8fecee JB |
5682 | } |
5683 | ||
5684 | ||
3c9a524f DH |
5685 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5686 | * covers the parts of the rules that start at a potential point. The value | |
5687 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5688 | * in variable result. The content of *p_exactness indicates, whether a hash |
5689 | * has already been seen in the digits before the point. | |
3c9a524f | 5690 | */ |
1cc91f1b | 5691 | |
3f47e526 | 5692 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5693 | |
5694 | static SCM | |
3f47e526 | 5695 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5696 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5697 | { |
3c9a524f DH |
5698 | unsigned int idx = *p_idx; |
5699 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5700 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5701 | |
5702 | if (idx == len) | |
79d34f68 | 5703 | return result; |
3c9a524f | 5704 | |
3f47e526 | 5705 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5706 | { |
5707 | scm_t_bits shift = 1; | |
5708 | scm_t_bits add = 0; | |
5709 | unsigned int digit_value; | |
cff5fa33 | 5710 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5711 | |
5712 | idx++; | |
5713 | while (idx != len) | |
5714 | { | |
3f47e526 MG |
5715 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5716 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5717 | { |
5718 | if (x == INEXACT) | |
5719 | return SCM_BOOL_F; | |
5720 | else | |
5721 | digit_value = DIGIT2UINT (c); | |
5722 | } | |
5723 | else if (c == '#') | |
5724 | { | |
5725 | x = INEXACT; | |
5726 | digit_value = 0; | |
5727 | } | |
5728 | else | |
5729 | break; | |
5730 | ||
5731 | idx++; | |
5732 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5733 | { | |
d956fa6f MV |
5734 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5735 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5736 | if (add > 0) |
d956fa6f | 5737 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5738 | |
5739 | shift = 10; | |
5740 | add = digit_value; | |
5741 | } | |
5742 | else | |
5743 | { | |
5744 | shift = shift * 10; | |
5745 | add = add * 10 + digit_value; | |
5746 | } | |
5747 | }; | |
5748 | ||
5749 | if (add > 0) | |
5750 | { | |
d956fa6f MV |
5751 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5752 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5753 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5754 | } |
5755 | ||
d8592269 | 5756 | result = scm_divide (result, big_shift); |
79d34f68 | 5757 | |
3c9a524f DH |
5758 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5759 | x = INEXACT; | |
f872b822 | 5760 | } |
3c9a524f | 5761 | |
3c9a524f | 5762 | if (idx != len) |
f872b822 | 5763 | { |
3c9a524f DH |
5764 | int sign = 1; |
5765 | unsigned int start; | |
3f47e526 | 5766 | scm_t_wchar c; |
3c9a524f DH |
5767 | int exponent; |
5768 | SCM e; | |
5769 | ||
5770 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5771 | ||
3f47e526 | 5772 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5773 | { |
3c9a524f DH |
5774 | case 'd': case 'D': |
5775 | case 'e': case 'E': | |
5776 | case 'f': case 'F': | |
5777 | case 'l': case 'L': | |
5778 | case 's': case 'S': | |
5779 | idx++; | |
ee0ddd21 AW |
5780 | if (idx == len) |
5781 | return SCM_BOOL_F; | |
5782 | ||
3c9a524f | 5783 | start = idx; |
3f47e526 | 5784 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5785 | if (c == '-') |
5786 | { | |
5787 | idx++; | |
ee0ddd21 AW |
5788 | if (idx == len) |
5789 | return SCM_BOOL_F; | |
5790 | ||
3c9a524f | 5791 | sign = -1; |
3f47e526 | 5792 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5793 | } |
5794 | else if (c == '+') | |
5795 | { | |
5796 | idx++; | |
ee0ddd21 AW |
5797 | if (idx == len) |
5798 | return SCM_BOOL_F; | |
5799 | ||
3c9a524f | 5800 | sign = 1; |
3f47e526 | 5801 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5802 | } |
5803 | else | |
5804 | sign = 1; | |
5805 | ||
3f47e526 | 5806 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5807 | return SCM_BOOL_F; |
5808 | ||
5809 | idx++; | |
5810 | exponent = DIGIT2UINT (c); | |
5811 | while (idx != len) | |
f872b822 | 5812 | { |
3f47e526 MG |
5813 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5814 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5815 | { |
5816 | idx++; | |
5817 | if (exponent <= SCM_MAXEXP) | |
5818 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5819 | } | |
5820 | else | |
5821 | break; | |
f872b822 | 5822 | } |
3c9a524f DH |
5823 | |
5824 | if (exponent > SCM_MAXEXP) | |
f872b822 | 5825 | { |
3c9a524f | 5826 | size_t exp_len = idx - start; |
3f47e526 | 5827 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5828 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5829 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5830 | } |
3c9a524f | 5831 | |
d956fa6f | 5832 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5833 | if (sign == 1) |
5834 | result = scm_product (result, e); | |
5835 | else | |
6ebecdeb | 5836 | result = scm_divide (result, e); |
3c9a524f DH |
5837 | |
5838 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5839 | x = INEXACT; | |
5840 | ||
f872b822 | 5841 | break; |
3c9a524f | 5842 | |
f872b822 | 5843 | default: |
3c9a524f | 5844 | break; |
f872b822 | 5845 | } |
0f2d19dd | 5846 | } |
3c9a524f DH |
5847 | |
5848 | *p_idx = idx; | |
5849 | if (x == INEXACT) | |
5850 | *p_exactness = x; | |
5851 | ||
5852 | return result; | |
0f2d19dd | 5853 | } |
0f2d19dd | 5854 | |
3c9a524f DH |
5855 | |
5856 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5857 | ||
5858 | static SCM | |
3f47e526 | 5859 | mem2ureal (SCM mem, unsigned int *p_idx, |
929d11b2 MW |
5860 | unsigned int radix, enum t_exactness forced_x, |
5861 | int allow_inf_or_nan) | |
0f2d19dd | 5862 | { |
3c9a524f | 5863 | unsigned int idx = *p_idx; |
164d2481 | 5864 | SCM result; |
3f47e526 | 5865 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5866 | |
40f89215 NJ |
5867 | /* Start off believing that the number will be exact. This changes |
5868 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5869 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5870 | |
3c9a524f DH |
5871 | if (idx == len) |
5872 | return SCM_BOOL_F; | |
5873 | ||
929d11b2 MW |
5874 | if (allow_inf_or_nan && forced_x != EXACT && idx+5 <= len) |
5875 | switch (scm_i_string_ref (mem, idx)) | |
5876 | { | |
5877 | case 'i': case 'I': | |
5878 | switch (scm_i_string_ref (mem, idx + 1)) | |
5879 | { | |
5880 | case 'n': case 'N': | |
5881 | switch (scm_i_string_ref (mem, idx + 2)) | |
5882 | { | |
5883 | case 'f': case 'F': | |
5884 | if (scm_i_string_ref (mem, idx + 3) == '.' | |
5885 | && scm_i_string_ref (mem, idx + 4) == '0') | |
5886 | { | |
5887 | *p_idx = idx+5; | |
5888 | return scm_inf (); | |
5889 | } | |
5890 | } | |
5891 | } | |
5892 | case 'n': case 'N': | |
5893 | switch (scm_i_string_ref (mem, idx + 1)) | |
5894 | { | |
5895 | case 'a': case 'A': | |
5896 | switch (scm_i_string_ref (mem, idx + 2)) | |
5897 | { | |
5898 | case 'n': case 'N': | |
5899 | if (scm_i_string_ref (mem, idx + 3) == '.') | |
5900 | { | |
5901 | /* Cobble up the fractional part. We might want to | |
5902 | set the NaN's mantissa from it. */ | |
5903 | idx += 4; | |
5904 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), | |
5905 | SCM_INUM0)) | |
5906 | { | |
5f237d6e | 5907 | #if SCM_ENABLE_DEPRECATED == 1 |
929d11b2 MW |
5908 | scm_c_issue_deprecation_warning |
5909 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5f237d6e | 5910 | #else |
929d11b2 | 5911 | return SCM_BOOL_F; |
5f237d6e | 5912 | #endif |
929d11b2 | 5913 | } |
5f237d6e | 5914 | |
929d11b2 MW |
5915 | *p_idx = idx; |
5916 | return scm_nan (); | |
5917 | } | |
5918 | } | |
5919 | } | |
5920 | } | |
7351e207 | 5921 | |
3f47e526 | 5922 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5923 | { |
5924 | if (radix != 10) | |
5925 | return SCM_BOOL_F; | |
5926 | else if (idx + 1 == len) | |
5927 | return SCM_BOOL_F; | |
3f47e526 | 5928 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
5929 | return SCM_BOOL_F; |
5930 | else | |
cff5fa33 | 5931 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 5932 | p_idx, &implicit_x); |
f872b822 | 5933 | } |
3c9a524f DH |
5934 | else |
5935 | { | |
3c9a524f | 5936 | SCM uinteger; |
3c9a524f | 5937 | |
9d427b2c | 5938 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5939 | if (scm_is_false (uinteger)) |
3c9a524f DH |
5940 | return SCM_BOOL_F; |
5941 | ||
5942 | if (idx == len) | |
5943 | result = uinteger; | |
3f47e526 | 5944 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 5945 | { |
3c9a524f DH |
5946 | SCM divisor; |
5947 | ||
5948 | idx++; | |
ee0ddd21 AW |
5949 | if (idx == len) |
5950 | return SCM_BOOL_F; | |
3c9a524f | 5951 | |
9d427b2c | 5952 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
929d11b2 | 5953 | if (scm_is_false (divisor) || scm_is_eq (divisor, SCM_INUM0)) |
3c9a524f DH |
5954 | return SCM_BOOL_F; |
5955 | ||
f92e85f7 | 5956 | /* both are int/big here, I assume */ |
cba42c93 | 5957 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 5958 | } |
3c9a524f DH |
5959 | else if (radix == 10) |
5960 | { | |
9d427b2c | 5961 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 5962 | if (scm_is_false (result)) |
3c9a524f DH |
5963 | return SCM_BOOL_F; |
5964 | } | |
5965 | else | |
5966 | result = uinteger; | |
5967 | ||
5968 | *p_idx = idx; | |
f872b822 | 5969 | } |
164d2481 | 5970 | |
9d427b2c MW |
5971 | switch (forced_x) |
5972 | { | |
5973 | case EXACT: | |
5974 | if (SCM_INEXACTP (result)) | |
5975 | return scm_inexact_to_exact (result); | |
5976 | else | |
5977 | return result; | |
5978 | case INEXACT: | |
5979 | if (SCM_INEXACTP (result)) | |
5980 | return result; | |
5981 | else | |
5982 | return scm_exact_to_inexact (result); | |
5983 | case NO_EXACTNESS: | |
5984 | if (implicit_x == INEXACT) | |
5985 | { | |
5986 | if (SCM_INEXACTP (result)) | |
5987 | return result; | |
5988 | else | |
5989 | return scm_exact_to_inexact (result); | |
5990 | } | |
5991 | else | |
5992 | return result; | |
5993 | } | |
164d2481 | 5994 | |
9d427b2c MW |
5995 | /* We should never get here */ |
5996 | scm_syserror ("mem2ureal"); | |
3c9a524f | 5997 | } |
0f2d19dd | 5998 | |
0f2d19dd | 5999 | |
3c9a524f | 6000 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 6001 | |
3c9a524f | 6002 | static SCM |
3f47e526 | 6003 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 6004 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 6005 | { |
3f47e526 | 6006 | scm_t_wchar c; |
3c9a524f DH |
6007 | int sign = 0; |
6008 | SCM ureal; | |
3f47e526 | 6009 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6010 | |
6011 | if (idx == len) | |
6012 | return SCM_BOOL_F; | |
6013 | ||
3f47e526 | 6014 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6015 | if (c == '+') |
6016 | { | |
6017 | idx++; | |
6018 | sign = 1; | |
6019 | } | |
6020 | else if (c == '-') | |
6021 | { | |
6022 | idx++; | |
6023 | sign = -1; | |
0f2d19dd | 6024 | } |
0f2d19dd | 6025 | |
3c9a524f DH |
6026 | if (idx == len) |
6027 | return SCM_BOOL_F; | |
6028 | ||
929d11b2 | 6029 | ureal = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6030 | if (scm_is_false (ureal)) |
f872b822 | 6031 | { |
3c9a524f DH |
6032 | /* input must be either +i or -i */ |
6033 | ||
6034 | if (sign == 0) | |
6035 | return SCM_BOOL_F; | |
6036 | ||
3f47e526 MG |
6037 | if (scm_i_string_ref (mem, idx) == 'i' |
6038 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 6039 | { |
3c9a524f DH |
6040 | idx++; |
6041 | if (idx != len) | |
6042 | return SCM_BOOL_F; | |
6043 | ||
cff5fa33 | 6044 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 6045 | } |
3c9a524f DH |
6046 | else |
6047 | return SCM_BOOL_F; | |
0f2d19dd | 6048 | } |
3c9a524f DH |
6049 | else |
6050 | { | |
73e4de09 | 6051 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 6052 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 6053 | |
3c9a524f DH |
6054 | if (idx == len) |
6055 | return ureal; | |
6056 | ||
3f47e526 | 6057 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 6058 | switch (c) |
f872b822 | 6059 | { |
3c9a524f DH |
6060 | case 'i': case 'I': |
6061 | /* either +<ureal>i or -<ureal>i */ | |
6062 | ||
6063 | idx++; | |
6064 | if (sign == 0) | |
6065 | return SCM_BOOL_F; | |
6066 | if (idx != len) | |
6067 | return SCM_BOOL_F; | |
cff5fa33 | 6068 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
6069 | |
6070 | case '@': | |
6071 | /* polar input: <real>@<real>. */ | |
6072 | ||
6073 | idx++; | |
6074 | if (idx == len) | |
6075 | return SCM_BOOL_F; | |
6076 | else | |
f872b822 | 6077 | { |
3c9a524f DH |
6078 | int sign; |
6079 | SCM angle; | |
6080 | SCM result; | |
6081 | ||
3f47e526 | 6082 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6083 | if (c == '+') |
6084 | { | |
6085 | idx++; | |
ee0ddd21 AW |
6086 | if (idx == len) |
6087 | return SCM_BOOL_F; | |
3c9a524f DH |
6088 | sign = 1; |
6089 | } | |
6090 | else if (c == '-') | |
6091 | { | |
6092 | idx++; | |
ee0ddd21 AW |
6093 | if (idx == len) |
6094 | return SCM_BOOL_F; | |
3c9a524f DH |
6095 | sign = -1; |
6096 | } | |
6097 | else | |
929d11b2 | 6098 | sign = 0; |
3c9a524f | 6099 | |
929d11b2 | 6100 | angle = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6101 | if (scm_is_false (angle)) |
3c9a524f DH |
6102 | return SCM_BOOL_F; |
6103 | if (idx != len) | |
6104 | return SCM_BOOL_F; | |
6105 | ||
73e4de09 | 6106 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
6107 | angle = scm_difference (angle, SCM_UNDEFINED); |
6108 | ||
6109 | result = scm_make_polar (ureal, angle); | |
6110 | return result; | |
f872b822 | 6111 | } |
3c9a524f DH |
6112 | case '+': |
6113 | case '-': | |
6114 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 6115 | |
3c9a524f DH |
6116 | idx++; |
6117 | if (idx == len) | |
6118 | return SCM_BOOL_F; | |
6119 | else | |
6120 | { | |
6121 | int sign = (c == '+') ? 1 : -1; | |
929d11b2 | 6122 | SCM imag = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
0f2d19dd | 6123 | |
73e4de09 | 6124 | if (scm_is_false (imag)) |
d956fa6f | 6125 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 6126 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 6127 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 6128 | |
3c9a524f DH |
6129 | if (idx == len) |
6130 | return SCM_BOOL_F; | |
3f47e526 MG |
6131 | if (scm_i_string_ref (mem, idx) != 'i' |
6132 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 6133 | return SCM_BOOL_F; |
0f2d19dd | 6134 | |
3c9a524f DH |
6135 | idx++; |
6136 | if (idx != len) | |
6137 | return SCM_BOOL_F; | |
0f2d19dd | 6138 | |
1fe5e088 | 6139 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6140 | } |
6141 | default: | |
6142 | return SCM_BOOL_F; | |
6143 | } | |
6144 | } | |
0f2d19dd | 6145 | } |
0f2d19dd JB |
6146 | |
6147 | ||
3c9a524f DH |
6148 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6149 | ||
6150 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6151 | |
0f2d19dd | 6152 | SCM |
3f47e526 | 6153 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6154 | { |
3c9a524f DH |
6155 | unsigned int idx = 0; |
6156 | unsigned int radix = NO_RADIX; | |
6157 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6158 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6159 | |
6160 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6161 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6162 | { |
3f47e526 | 6163 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6164 | { |
6165 | case 'b': case 'B': | |
6166 | if (radix != NO_RADIX) | |
6167 | return SCM_BOOL_F; | |
6168 | radix = DUAL; | |
6169 | break; | |
6170 | case 'd': case 'D': | |
6171 | if (radix != NO_RADIX) | |
6172 | return SCM_BOOL_F; | |
6173 | radix = DEC; | |
6174 | break; | |
6175 | case 'i': case 'I': | |
6176 | if (forced_x != NO_EXACTNESS) | |
6177 | return SCM_BOOL_F; | |
6178 | forced_x = INEXACT; | |
6179 | break; | |
6180 | case 'e': case 'E': | |
6181 | if (forced_x != NO_EXACTNESS) | |
6182 | return SCM_BOOL_F; | |
6183 | forced_x = EXACT; | |
6184 | break; | |
6185 | case 'o': case 'O': | |
6186 | if (radix != NO_RADIX) | |
6187 | return SCM_BOOL_F; | |
6188 | radix = OCT; | |
6189 | break; | |
6190 | case 'x': case 'X': | |
6191 | if (radix != NO_RADIX) | |
6192 | return SCM_BOOL_F; | |
6193 | radix = HEX; | |
6194 | break; | |
6195 | default: | |
f872b822 | 6196 | return SCM_BOOL_F; |
3c9a524f DH |
6197 | } |
6198 | idx += 2; | |
6199 | } | |
6200 | ||
6201 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6202 | if (radix == NO_RADIX) | |
9d427b2c | 6203 | radix = default_radix; |
f872b822 | 6204 | |
9d427b2c | 6205 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6206 | } |
6207 | ||
3f47e526 MG |
6208 | SCM |
6209 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6210 | unsigned int default_radix) | |
6211 | { | |
6212 | SCM str = scm_from_locale_stringn (mem, len); | |
6213 | ||
6214 | return scm_i_string_to_number (str, default_radix); | |
6215 | } | |
6216 | ||
0f2d19dd | 6217 | |
a1ec6916 | 6218 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6219 | (SCM string, SCM radix), |
1e6808ea | 6220 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6221 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6222 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6223 | "is a default radix that may be overridden by an explicit radix\n" | |
6224 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6225 | "supplied, then the default radix is 10. If string is not a\n" | |
6226 | "syntactically valid notation for a number, then\n" | |
6227 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6228 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6229 | { |
6230 | SCM answer; | |
5efd3c7d | 6231 | unsigned int base; |
a6d9e5ab | 6232 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6233 | |
6234 | if (SCM_UNBNDP (radix)) | |
6235 | base = 10; | |
6236 | else | |
6237 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6238 | ||
3f47e526 | 6239 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6240 | scm_remember_upto_here_1 (string); |
6241 | return answer; | |
0f2d19dd | 6242 | } |
1bbd0b84 | 6243 | #undef FUNC_NAME |
3c9a524f DH |
6244 | |
6245 | ||
0f2d19dd JB |
6246 | /*** END strs->nums ***/ |
6247 | ||
5986c47d | 6248 | |
8507ec80 MV |
6249 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6250 | (SCM x), | |
6251 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6252 | "otherwise.") | |
6253 | #define FUNC_NAME s_scm_number_p | |
6254 | { | |
6255 | return scm_from_bool (SCM_NUMBERP (x)); | |
6256 | } | |
6257 | #undef FUNC_NAME | |
6258 | ||
6259 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6260 | (SCM x), |
942e5b91 | 6261 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6262 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6263 | "values form subsets of the set of complex numbers, i. e. the\n" |
6264 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6265 | "rational or integer number.") | |
8507ec80 | 6266 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6267 | { |
8507ec80 MV |
6268 | /* all numbers are complex. */ |
6269 | return scm_number_p (x); | |
0f2d19dd | 6270 | } |
1bbd0b84 | 6271 | #undef FUNC_NAME |
0f2d19dd | 6272 | |
f92e85f7 MV |
6273 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6274 | (SCM x), | |
6275 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6276 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6277 | "the set of real numbers, i. e. the predicate will also be\n" | |
6278 | "fulfilled if @var{x} is an integer number.") | |
6279 | #define FUNC_NAME s_scm_real_p | |
6280 | { | |
c960e556 MW |
6281 | return scm_from_bool |
6282 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6283 | } |
6284 | #undef FUNC_NAME | |
6285 | ||
6286 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6287 | (SCM x), |
942e5b91 | 6288 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6289 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6290 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6291 | "fulfilled if @var{x} is an integer number.") |
6292 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6293 | { |
c960e556 | 6294 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6295 | return SCM_BOOL_T; |
6296 | else if (SCM_REALP (x)) | |
c960e556 MW |
6297 | /* due to their limited precision, finite floating point numbers are |
6298 | rational as well. (finite means neither infinity nor a NaN) */ | |
6299 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6300 | else |
bb628794 | 6301 | return SCM_BOOL_F; |
0f2d19dd | 6302 | } |
1bbd0b84 | 6303 | #undef FUNC_NAME |
0f2d19dd | 6304 | |
a1ec6916 | 6305 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6306 | (SCM x), |
942e5b91 MG |
6307 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6308 | "else.") | |
1bbd0b84 | 6309 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6310 | { |
c960e556 | 6311 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6312 | return SCM_BOOL_T; |
c960e556 MW |
6313 | else if (SCM_REALP (x)) |
6314 | { | |
6315 | double val = SCM_REAL_VALUE (x); | |
6316 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6317 | } | |
6318 | else | |
8e43ed5d | 6319 | return SCM_BOOL_F; |
0f2d19dd | 6320 | } |
1bbd0b84 | 6321 | #undef FUNC_NAME |
0f2d19dd JB |
6322 | |
6323 | ||
8a1f4f98 AW |
6324 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6325 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6326 | (SCM x, SCM y, SCM rest), | |
6327 | "Return @code{#t} if all parameters are numerically equal.") | |
6328 | #define FUNC_NAME s_scm_i_num_eq_p | |
6329 | { | |
6330 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6331 | return SCM_BOOL_T; | |
6332 | while (!scm_is_null (rest)) | |
6333 | { | |
6334 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6335 | return SCM_BOOL_F; | |
6336 | x = y; | |
6337 | y = scm_car (rest); | |
6338 | rest = scm_cdr (rest); | |
6339 | } | |
6340 | return scm_num_eq_p (x, y); | |
6341 | } | |
6342 | #undef FUNC_NAME | |
0f2d19dd | 6343 | SCM |
6e8d25a6 | 6344 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6345 | { |
d8b95e27 | 6346 | again: |
e11e83f3 | 6347 | if (SCM_I_INUMP (x)) |
0aacf84e | 6348 | { |
e25f3727 | 6349 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6350 | if (SCM_I_INUMP (y)) |
0aacf84e | 6351 | { |
e25f3727 | 6352 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6353 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6354 | } |
6355 | else if (SCM_BIGP (y)) | |
6356 | return SCM_BOOL_F; | |
6357 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6358 | { |
6359 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6360 | to a double and compare. | |
6361 | ||
6362 | But on a 64-bit system an inum is bigger than a double and | |
6363 | casting it to a double (call that dxx) will round. dxx is at | |
6364 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6365 | an integer and fits a long. So we cast yy to a long and | |
6366 | compare with plain xx. | |
6367 | ||
6368 | An alternative (for any size system actually) would be to check | |
6369 | yy is an integer (with floor) and is in range of an inum | |
6370 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6371 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6372 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6373 | |
6374 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6375 | return scm_from_bool ((double) xx == yy |
6376 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6377 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6378 | } |
0aacf84e | 6379 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6380 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6381 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6382 | else if (SCM_FRACTIONP (y)) |
6383 | return SCM_BOOL_F; | |
0aacf84e | 6384 | else |
8a1f4f98 | 6385 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6386 | } |
0aacf84e MD |
6387 | else if (SCM_BIGP (x)) |
6388 | { | |
e11e83f3 | 6389 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6390 | return SCM_BOOL_F; |
6391 | else if (SCM_BIGP (y)) | |
6392 | { | |
6393 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6394 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6395 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6396 | } |
6397 | else if (SCM_REALP (y)) | |
6398 | { | |
6399 | int cmp; | |
2e65b52f | 6400 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6401 | return SCM_BOOL_F; |
6402 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6403 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6404 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6405 | } |
6406 | else if (SCM_COMPLEXP (y)) | |
6407 | { | |
6408 | int cmp; | |
6409 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6410 | return SCM_BOOL_F; | |
2e65b52f | 6411 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6412 | return SCM_BOOL_F; |
6413 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6414 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6415 | return scm_from_bool (0 == cmp); |
0aacf84e | 6416 | } |
f92e85f7 MV |
6417 | else if (SCM_FRACTIONP (y)) |
6418 | return SCM_BOOL_F; | |
0aacf84e | 6419 | else |
8a1f4f98 | 6420 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6421 | } |
0aacf84e MD |
6422 | else if (SCM_REALP (x)) |
6423 | { | |
e8c5b1f2 | 6424 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6425 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6426 | { |
6427 | /* see comments with inum/real above */ | |
e25f3727 | 6428 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6429 | return scm_from_bool (xx == (double) yy |
6430 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6431 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6432 | } |
0aacf84e MD |
6433 | else if (SCM_BIGP (y)) |
6434 | { | |
6435 | int cmp; | |
2e65b52f | 6436 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6437 | return SCM_BOOL_F; |
6438 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6439 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6440 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6441 | } |
6442 | else if (SCM_REALP (y)) | |
73e4de09 | 6443 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6444 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6445 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6446 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6447 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6448 | { |
6449 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6450 | if (isnan (xx)) |
d8b95e27 | 6451 | return SCM_BOOL_F; |
2e65b52f | 6452 | if (isinf (xx)) |
73e4de09 | 6453 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6454 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6455 | goto again; | |
6456 | } | |
0aacf84e | 6457 | else |
8a1f4f98 | 6458 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6459 | } |
0aacf84e MD |
6460 | else if (SCM_COMPLEXP (x)) |
6461 | { | |
e11e83f3 MV |
6462 | if (SCM_I_INUMP (y)) |
6463 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6464 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6465 | else if (SCM_BIGP (y)) | |
6466 | { | |
6467 | int cmp; | |
6468 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6469 | return SCM_BOOL_F; | |
2e65b52f | 6470 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6471 | return SCM_BOOL_F; |
6472 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6473 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6474 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6475 | } |
6476 | else if (SCM_REALP (y)) | |
73e4de09 | 6477 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6478 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6479 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6480 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6481 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6482 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6483 | { |
6484 | double xx; | |
6485 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6486 | return SCM_BOOL_F; | |
6487 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6488 | if (isnan (xx)) |
d8b95e27 | 6489 | return SCM_BOOL_F; |
2e65b52f | 6490 | if (isinf (xx)) |
73e4de09 | 6491 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6492 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6493 | goto again; | |
6494 | } | |
f92e85f7 | 6495 | else |
8a1f4f98 | 6496 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6497 | } |
6498 | else if (SCM_FRACTIONP (x)) | |
6499 | { | |
e11e83f3 | 6500 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6501 | return SCM_BOOL_F; |
6502 | else if (SCM_BIGP (y)) | |
6503 | return SCM_BOOL_F; | |
6504 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6505 | { |
6506 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6507 | if (isnan (yy)) |
d8b95e27 | 6508 | return SCM_BOOL_F; |
2e65b52f | 6509 | if (isinf (yy)) |
73e4de09 | 6510 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6511 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6512 | goto again; | |
6513 | } | |
f92e85f7 | 6514 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6515 | { |
6516 | double yy; | |
6517 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6518 | return SCM_BOOL_F; | |
6519 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6520 | if (isnan (yy)) |
d8b95e27 | 6521 | return SCM_BOOL_F; |
2e65b52f | 6522 | if (isinf (yy)) |
73e4de09 | 6523 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6524 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6525 | goto again; | |
6526 | } | |
f92e85f7 MV |
6527 | else if (SCM_FRACTIONP (y)) |
6528 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6529 | else |
8a1f4f98 | 6530 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6531 | } |
0aacf84e | 6532 | else |
8a1f4f98 | 6533 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6534 | } |
6535 | ||
6536 | ||
a5f0b599 KR |
6537 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6538 | done are good for inums, but for bignums an answer can almost always be | |
6539 | had by just examining a few high bits of the operands, as done by GMP in | |
6540 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6541 | of the float exponent to take into account. */ | |
6542 | ||
8c93b597 | 6543 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6544 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6545 | (SCM x, SCM y, SCM rest), | |
6546 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6547 | "increasing.") | |
6548 | #define FUNC_NAME s_scm_i_num_less_p | |
6549 | { | |
6550 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6551 | return SCM_BOOL_T; | |
6552 | while (!scm_is_null (rest)) | |
6553 | { | |
6554 | if (scm_is_false (scm_less_p (x, y))) | |
6555 | return SCM_BOOL_F; | |
6556 | x = y; | |
6557 | y = scm_car (rest); | |
6558 | rest = scm_cdr (rest); | |
6559 | } | |
6560 | return scm_less_p (x, y); | |
6561 | } | |
6562 | #undef FUNC_NAME | |
0f2d19dd | 6563 | SCM |
6e8d25a6 | 6564 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6565 | { |
a5f0b599 | 6566 | again: |
e11e83f3 | 6567 | if (SCM_I_INUMP (x)) |
0aacf84e | 6568 | { |
e25f3727 | 6569 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6570 | if (SCM_I_INUMP (y)) |
0aacf84e | 6571 | { |
e25f3727 | 6572 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6573 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6574 | } |
6575 | else if (SCM_BIGP (y)) | |
6576 | { | |
6577 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6578 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6579 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6580 | } |
6581 | else if (SCM_REALP (y)) | |
73e4de09 | 6582 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6583 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6584 | { |
6585 | /* "x < a/b" becomes "x*b < a" */ | |
6586 | int_frac: | |
6587 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6588 | y = SCM_FRACTION_NUMERATOR (y); | |
6589 | goto again; | |
6590 | } | |
0aacf84e | 6591 | else |
8a1f4f98 | 6592 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6593 | } |
0aacf84e MD |
6594 | else if (SCM_BIGP (x)) |
6595 | { | |
e11e83f3 | 6596 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6597 | { |
6598 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6599 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6600 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6601 | } |
6602 | else if (SCM_BIGP (y)) | |
6603 | { | |
6604 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6605 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6606 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6607 | } |
6608 | else if (SCM_REALP (y)) | |
6609 | { | |
6610 | int cmp; | |
2e65b52f | 6611 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6612 | return SCM_BOOL_F; |
6613 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6614 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6615 | return scm_from_bool (cmp < 0); |
0aacf84e | 6616 | } |
f92e85f7 | 6617 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6618 | goto int_frac; |
0aacf84e | 6619 | else |
8a1f4f98 | 6620 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6621 | } |
0aacf84e MD |
6622 | else if (SCM_REALP (x)) |
6623 | { | |
e11e83f3 MV |
6624 | if (SCM_I_INUMP (y)) |
6625 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6626 | else if (SCM_BIGP (y)) |
6627 | { | |
6628 | int cmp; | |
2e65b52f | 6629 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6630 | return SCM_BOOL_F; |
6631 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6632 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6633 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6634 | } |
6635 | else if (SCM_REALP (y)) | |
73e4de09 | 6636 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6637 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6638 | { |
6639 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6640 | if (isnan (xx)) |
a5f0b599 | 6641 | return SCM_BOOL_F; |
2e65b52f | 6642 | if (isinf (xx)) |
73e4de09 | 6643 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6644 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6645 | goto again; | |
6646 | } | |
f92e85f7 | 6647 | else |
8a1f4f98 | 6648 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6649 | } |
6650 | else if (SCM_FRACTIONP (x)) | |
6651 | { | |
e11e83f3 | 6652 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6653 | { |
6654 | /* "a/b < y" becomes "a < y*b" */ | |
6655 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6656 | x = SCM_FRACTION_NUMERATOR (x); | |
6657 | goto again; | |
6658 | } | |
f92e85f7 | 6659 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6660 | { |
6661 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6662 | if (isnan (yy)) |
a5f0b599 | 6663 | return SCM_BOOL_F; |
2e65b52f | 6664 | if (isinf (yy)) |
73e4de09 | 6665 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6666 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6667 | goto again; | |
6668 | } | |
f92e85f7 | 6669 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6670 | { |
6671 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6672 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6673 | SCM_FRACTION_DENOMINATOR (y)); | |
6674 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6675 | SCM_FRACTION_DENOMINATOR (x)); | |
6676 | x = new_x; | |
6677 | y = new_y; | |
6678 | goto again; | |
6679 | } | |
0aacf84e | 6680 | else |
8a1f4f98 | 6681 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6682 | } |
0aacf84e | 6683 | else |
8a1f4f98 | 6684 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6685 | } |
6686 | ||
6687 | ||
8a1f4f98 AW |
6688 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6689 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6690 | (SCM x, SCM y, SCM rest), | |
6691 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6692 | "decreasing.") | |
6693 | #define FUNC_NAME s_scm_i_num_gr_p | |
6694 | { | |
6695 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6696 | return SCM_BOOL_T; | |
6697 | while (!scm_is_null (rest)) | |
6698 | { | |
6699 | if (scm_is_false (scm_gr_p (x, y))) | |
6700 | return SCM_BOOL_F; | |
6701 | x = y; | |
6702 | y = scm_car (rest); | |
6703 | rest = scm_cdr (rest); | |
6704 | } | |
6705 | return scm_gr_p (x, y); | |
6706 | } | |
6707 | #undef FUNC_NAME | |
6708 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6709 | SCM |
6710 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6711 | { |
c76b1eaf | 6712 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6713 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6714 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6715 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6716 | else |
6717 | return scm_less_p (y, x); | |
0f2d19dd | 6718 | } |
1bbd0b84 | 6719 | #undef FUNC_NAME |
0f2d19dd JB |
6720 | |
6721 | ||
8a1f4f98 AW |
6722 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6723 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6724 | (SCM x, SCM y, SCM rest), | |
6725 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6726 | "non-decreasing.") | |
6727 | #define FUNC_NAME s_scm_i_num_leq_p | |
6728 | { | |
6729 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6730 | return SCM_BOOL_T; | |
6731 | while (!scm_is_null (rest)) | |
6732 | { | |
6733 | if (scm_is_false (scm_leq_p (x, y))) | |
6734 | return SCM_BOOL_F; | |
6735 | x = y; | |
6736 | y = scm_car (rest); | |
6737 | rest = scm_cdr (rest); | |
6738 | } | |
6739 | return scm_leq_p (x, y); | |
6740 | } | |
6741 | #undef FUNC_NAME | |
6742 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6743 | SCM |
6744 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6745 | { |
c76b1eaf | 6746 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6747 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6748 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6749 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6750 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6751 | return SCM_BOOL_F; |
c76b1eaf | 6752 | else |
73e4de09 | 6753 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6754 | } |
1bbd0b84 | 6755 | #undef FUNC_NAME |
0f2d19dd JB |
6756 | |
6757 | ||
8a1f4f98 AW |
6758 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6759 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6760 | (SCM x, SCM y, SCM rest), | |
6761 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6762 | "non-increasing.") | |
6763 | #define FUNC_NAME s_scm_i_num_geq_p | |
6764 | { | |
6765 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6766 | return SCM_BOOL_T; | |
6767 | while (!scm_is_null (rest)) | |
6768 | { | |
6769 | if (scm_is_false (scm_geq_p (x, y))) | |
6770 | return SCM_BOOL_F; | |
6771 | x = y; | |
6772 | y = scm_car (rest); | |
6773 | rest = scm_cdr (rest); | |
6774 | } | |
6775 | return scm_geq_p (x, y); | |
6776 | } | |
6777 | #undef FUNC_NAME | |
6778 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6779 | SCM |
6780 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6781 | { |
c76b1eaf | 6782 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6783 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6784 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6785 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6786 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6787 | return SCM_BOOL_F; |
c76b1eaf | 6788 | else |
73e4de09 | 6789 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6790 | } |
1bbd0b84 | 6791 | #undef FUNC_NAME |
0f2d19dd JB |
6792 | |
6793 | ||
2519490c MW |
6794 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6795 | (SCM z), | |
6796 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6797 | "zero.") | |
6798 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6799 | { |
e11e83f3 | 6800 | if (SCM_I_INUMP (z)) |
bc36d050 | 6801 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6802 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6803 | return SCM_BOOL_F; |
0aacf84e | 6804 | else if (SCM_REALP (z)) |
73e4de09 | 6805 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6806 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6807 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6808 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6809 | else if (SCM_FRACTIONP (z)) |
6810 | return SCM_BOOL_F; | |
0aacf84e | 6811 | else |
2519490c | 6812 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6813 | } |
2519490c | 6814 | #undef FUNC_NAME |
0f2d19dd JB |
6815 | |
6816 | ||
2519490c MW |
6817 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6818 | (SCM x), | |
6819 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6820 | "zero.") | |
6821 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6822 | { |
e11e83f3 MV |
6823 | if (SCM_I_INUMP (x)) |
6824 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6825 | else if (SCM_BIGP (x)) |
6826 | { | |
6827 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6828 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6829 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6830 | } |
6831 | else if (SCM_REALP (x)) | |
73e4de09 | 6832 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6833 | else if (SCM_FRACTIONP (x)) |
6834 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6835 | else |
2519490c | 6836 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6837 | } |
2519490c | 6838 | #undef FUNC_NAME |
0f2d19dd JB |
6839 | |
6840 | ||
2519490c MW |
6841 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6842 | (SCM x), | |
6843 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6844 | "zero.") | |
6845 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6846 | { |
e11e83f3 MV |
6847 | if (SCM_I_INUMP (x)) |
6848 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6849 | else if (SCM_BIGP (x)) |
6850 | { | |
6851 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6852 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6853 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6854 | } |
6855 | else if (SCM_REALP (x)) | |
73e4de09 | 6856 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6857 | else if (SCM_FRACTIONP (x)) |
6858 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6859 | else |
2519490c | 6860 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6861 | } |
2519490c | 6862 | #undef FUNC_NAME |
0f2d19dd JB |
6863 | |
6864 | ||
2a06f791 KR |
6865 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6866 | required by r5rs. On that basis, for exact/inexact combinations the | |
6867 | exact is converted to inexact to compare and possibly return. This is | |
6868 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6869 | its test, such trouble is not required for min and max. */ | |
6870 | ||
78d3deb1 AW |
6871 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6872 | (SCM x, SCM y, SCM rest), | |
6873 | "Return the maximum of all parameter values.") | |
6874 | #define FUNC_NAME s_scm_i_max | |
6875 | { | |
6876 | while (!scm_is_null (rest)) | |
6877 | { x = scm_max (x, y); | |
6878 | y = scm_car (rest); | |
6879 | rest = scm_cdr (rest); | |
6880 | } | |
6881 | return scm_max (x, y); | |
6882 | } | |
6883 | #undef FUNC_NAME | |
6884 | ||
6885 | #define s_max s_scm_i_max | |
6886 | #define g_max g_scm_i_max | |
6887 | ||
0f2d19dd | 6888 | SCM |
6e8d25a6 | 6889 | scm_max (SCM x, SCM y) |
0f2d19dd | 6890 | { |
0aacf84e MD |
6891 | if (SCM_UNBNDP (y)) |
6892 | { | |
6893 | if (SCM_UNBNDP (x)) | |
6894 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 6895 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6896 | return x; |
6897 | else | |
6898 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 6899 | } |
f4c627b3 | 6900 | |
e11e83f3 | 6901 | if (SCM_I_INUMP (x)) |
0aacf84e | 6902 | { |
e25f3727 | 6903 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6904 | if (SCM_I_INUMP (y)) |
0aacf84e | 6905 | { |
e25f3727 | 6906 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6907 | return (xx < yy) ? y : x; |
6908 | } | |
6909 | else if (SCM_BIGP (y)) | |
6910 | { | |
6911 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6912 | scm_remember_upto_here_1 (y); | |
6913 | return (sgn < 0) ? x : y; | |
6914 | } | |
6915 | else if (SCM_REALP (y)) | |
6916 | { | |
2e274311 MW |
6917 | double xxd = xx; |
6918 | double yyd = SCM_REAL_VALUE (y); | |
6919 | ||
6920 | if (xxd > yyd) | |
6921 | return scm_from_double (xxd); | |
6922 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
6923 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6924 | return y; | |
6925 | /* Handle signed zeroes properly */ | |
6926 | else if (xx == 0) | |
6927 | return flo0; | |
6928 | else | |
6929 | return y; | |
0aacf84e | 6930 | } |
f92e85f7 MV |
6931 | else if (SCM_FRACTIONP (y)) |
6932 | { | |
e4bc5d6c | 6933 | use_less: |
73e4de09 | 6934 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 6935 | } |
0aacf84e MD |
6936 | else |
6937 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6938 | } |
0aacf84e MD |
6939 | else if (SCM_BIGP (x)) |
6940 | { | |
e11e83f3 | 6941 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6942 | { |
6943 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6944 | scm_remember_upto_here_1 (x); | |
6945 | return (sgn < 0) ? y : x; | |
6946 | } | |
6947 | else if (SCM_BIGP (y)) | |
6948 | { | |
6949 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6950 | scm_remember_upto_here_2 (x, y); | |
6951 | return (cmp > 0) ? x : y; | |
6952 | } | |
6953 | else if (SCM_REALP (y)) | |
6954 | { | |
2a06f791 KR |
6955 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
6956 | double xx, yy; | |
6957 | big_real: | |
6958 | xx = scm_i_big2dbl (x); | |
6959 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6960 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 6961 | } |
f92e85f7 MV |
6962 | else if (SCM_FRACTIONP (y)) |
6963 | { | |
e4bc5d6c | 6964 | goto use_less; |
f92e85f7 | 6965 | } |
0aacf84e MD |
6966 | else |
6967 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 6968 | } |
0aacf84e MD |
6969 | else if (SCM_REALP (x)) |
6970 | { | |
e11e83f3 | 6971 | if (SCM_I_INUMP (y)) |
0aacf84e | 6972 | { |
2e274311 MW |
6973 | scm_t_inum yy = SCM_I_INUM (y); |
6974 | double xxd = SCM_REAL_VALUE (x); | |
6975 | double yyd = yy; | |
6976 | ||
6977 | if (yyd > xxd) | |
6978 | return scm_from_double (yyd); | |
6979 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
6980 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6981 | return x; | |
6982 | /* Handle signed zeroes properly */ | |
6983 | else if (yy == 0) | |
6984 | return flo0; | |
6985 | else | |
6986 | return x; | |
0aacf84e MD |
6987 | } |
6988 | else if (SCM_BIGP (y)) | |
6989 | { | |
b6f8f763 | 6990 | SCM_SWAP (x, y); |
2a06f791 | 6991 | goto big_real; |
0aacf84e MD |
6992 | } |
6993 | else if (SCM_REALP (y)) | |
6994 | { | |
0aacf84e | 6995 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6996 | double yy = SCM_REAL_VALUE (y); |
6997 | ||
6998 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
6999 | if (xx > yy) | |
7000 | return x; | |
7001 | else if (SCM_LIKELY (xx < yy)) | |
7002 | return y; | |
7003 | /* If neither (xx > yy) nor (xx < yy), then | |
7004 | either they're equal or one is a NaN */ | |
7005 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7006 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 7007 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7008 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7009 | /* xx == yy, but handle signed zeroes properly */ |
7010 | else if (double_is_non_negative_zero (yy)) | |
7011 | return y; | |
7012 | else | |
7013 | return x; | |
0aacf84e | 7014 | } |
f92e85f7 MV |
7015 | else if (SCM_FRACTIONP (y)) |
7016 | { | |
7017 | double yy = scm_i_fraction2double (y); | |
7018 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7019 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
7020 | } |
7021 | else | |
7022 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
7023 | } | |
7024 | else if (SCM_FRACTIONP (x)) | |
7025 | { | |
e11e83f3 | 7026 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7027 | { |
e4bc5d6c | 7028 | goto use_less; |
f92e85f7 MV |
7029 | } |
7030 | else if (SCM_BIGP (y)) | |
7031 | { | |
e4bc5d6c | 7032 | goto use_less; |
f92e85f7 MV |
7033 | } |
7034 | else if (SCM_REALP (y)) | |
7035 | { | |
7036 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7037 | /* if y==NaN then ">" is false, so we return the NaN y */ |
7038 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7039 | } |
7040 | else if (SCM_FRACTIONP (y)) | |
7041 | { | |
e4bc5d6c | 7042 | goto use_less; |
f92e85f7 | 7043 | } |
0aacf84e MD |
7044 | else |
7045 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7046 | } |
0aacf84e | 7047 | else |
f4c627b3 | 7048 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
7049 | } |
7050 | ||
7051 | ||
78d3deb1 AW |
7052 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
7053 | (SCM x, SCM y, SCM rest), | |
7054 | "Return the minimum of all parameter values.") | |
7055 | #define FUNC_NAME s_scm_i_min | |
7056 | { | |
7057 | while (!scm_is_null (rest)) | |
7058 | { x = scm_min (x, y); | |
7059 | y = scm_car (rest); | |
7060 | rest = scm_cdr (rest); | |
7061 | } | |
7062 | return scm_min (x, y); | |
7063 | } | |
7064 | #undef FUNC_NAME | |
7065 | ||
7066 | #define s_min s_scm_i_min | |
7067 | #define g_min g_scm_i_min | |
7068 | ||
0f2d19dd | 7069 | SCM |
6e8d25a6 | 7070 | scm_min (SCM x, SCM y) |
0f2d19dd | 7071 | { |
0aacf84e MD |
7072 | if (SCM_UNBNDP (y)) |
7073 | { | |
7074 | if (SCM_UNBNDP (x)) | |
7075 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 7076 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7077 | return x; |
7078 | else | |
7079 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 7080 | } |
f4c627b3 | 7081 | |
e11e83f3 | 7082 | if (SCM_I_INUMP (x)) |
0aacf84e | 7083 | { |
e25f3727 | 7084 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7085 | if (SCM_I_INUMP (y)) |
0aacf84e | 7086 | { |
e25f3727 | 7087 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7088 | return (xx < yy) ? x : y; |
7089 | } | |
7090 | else if (SCM_BIGP (y)) | |
7091 | { | |
7092 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7093 | scm_remember_upto_here_1 (y); | |
7094 | return (sgn < 0) ? y : x; | |
7095 | } | |
7096 | else if (SCM_REALP (y)) | |
7097 | { | |
7098 | double z = xx; | |
7099 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 7100 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 7101 | } |
f92e85f7 MV |
7102 | else if (SCM_FRACTIONP (y)) |
7103 | { | |
e4bc5d6c | 7104 | use_less: |
73e4de09 | 7105 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 7106 | } |
0aacf84e MD |
7107 | else |
7108 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7109 | } |
0aacf84e MD |
7110 | else if (SCM_BIGP (x)) |
7111 | { | |
e11e83f3 | 7112 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7113 | { |
7114 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7115 | scm_remember_upto_here_1 (x); | |
7116 | return (sgn < 0) ? x : y; | |
7117 | } | |
7118 | else if (SCM_BIGP (y)) | |
7119 | { | |
7120 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7121 | scm_remember_upto_here_2 (x, y); | |
7122 | return (cmp > 0) ? y : x; | |
7123 | } | |
7124 | else if (SCM_REALP (y)) | |
7125 | { | |
2a06f791 KR |
7126 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
7127 | double xx, yy; | |
7128 | big_real: | |
7129 | xx = scm_i_big2dbl (x); | |
7130 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7131 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 7132 | } |
f92e85f7 MV |
7133 | else if (SCM_FRACTIONP (y)) |
7134 | { | |
e4bc5d6c | 7135 | goto use_less; |
f92e85f7 | 7136 | } |
0aacf84e MD |
7137 | else |
7138 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 7139 | } |
0aacf84e MD |
7140 | else if (SCM_REALP (x)) |
7141 | { | |
e11e83f3 | 7142 | if (SCM_I_INUMP (y)) |
0aacf84e | 7143 | { |
e11e83f3 | 7144 | double z = SCM_I_INUM (y); |
0aacf84e | 7145 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7146 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7147 | } |
7148 | else if (SCM_BIGP (y)) | |
7149 | { | |
b6f8f763 | 7150 | SCM_SWAP (x, y); |
2a06f791 | 7151 | goto big_real; |
0aacf84e MD |
7152 | } |
7153 | else if (SCM_REALP (y)) | |
7154 | { | |
0aacf84e | 7155 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7156 | double yy = SCM_REAL_VALUE (y); |
7157 | ||
7158 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
7159 | if (xx < yy) | |
7160 | return x; | |
7161 | else if (SCM_LIKELY (xx > yy)) | |
7162 | return y; | |
7163 | /* If neither (xx < yy) nor (xx > yy), then | |
7164 | either they're equal or one is a NaN */ | |
7165 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7166 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 7167 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7168 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7169 | /* xx == yy, but handle signed zeroes properly */ |
7170 | else if (double_is_non_negative_zero (xx)) | |
7171 | return y; | |
7172 | else | |
7173 | return x; | |
0aacf84e | 7174 | } |
f92e85f7 MV |
7175 | else if (SCM_FRACTIONP (y)) |
7176 | { | |
7177 | double yy = scm_i_fraction2double (y); | |
7178 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7179 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7180 | } |
0aacf84e MD |
7181 | else |
7182 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7183 | } |
f92e85f7 MV |
7184 | else if (SCM_FRACTIONP (x)) |
7185 | { | |
e11e83f3 | 7186 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7187 | { |
e4bc5d6c | 7188 | goto use_less; |
f92e85f7 MV |
7189 | } |
7190 | else if (SCM_BIGP (y)) | |
7191 | { | |
e4bc5d6c | 7192 | goto use_less; |
f92e85f7 MV |
7193 | } |
7194 | else if (SCM_REALP (y)) | |
7195 | { | |
7196 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7197 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7198 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7199 | } |
7200 | else if (SCM_FRACTIONP (y)) | |
7201 | { | |
e4bc5d6c | 7202 | goto use_less; |
f92e85f7 MV |
7203 | } |
7204 | else | |
78d3deb1 | 7205 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7206 | } |
0aacf84e | 7207 | else |
f4c627b3 | 7208 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7209 | } |
7210 | ||
7211 | ||
8ccd24f7 AW |
7212 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7213 | (SCM x, SCM y, SCM rest), | |
7214 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7215 | "any parameters." ) | |
7216 | #define FUNC_NAME s_scm_i_sum | |
7217 | { | |
7218 | while (!scm_is_null (rest)) | |
7219 | { x = scm_sum (x, y); | |
7220 | y = scm_car (rest); | |
7221 | rest = scm_cdr (rest); | |
7222 | } | |
7223 | return scm_sum (x, y); | |
7224 | } | |
7225 | #undef FUNC_NAME | |
7226 | ||
7227 | #define s_sum s_scm_i_sum | |
7228 | #define g_sum g_scm_i_sum | |
7229 | ||
0f2d19dd | 7230 | SCM |
6e8d25a6 | 7231 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7232 | { |
9cc37597 | 7233 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7234 | { |
7235 | if (SCM_NUMBERP (x)) return x; | |
7236 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7237 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7238 | } |
c209c88e | 7239 | |
9cc37597 | 7240 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7241 | { |
9cc37597 | 7242 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7243 | { |
e25f3727 AW |
7244 | scm_t_inum xx = SCM_I_INUM (x); |
7245 | scm_t_inum yy = SCM_I_INUM (y); | |
7246 | scm_t_inum z = xx + yy; | |
7247 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7248 | } |
7249 | else if (SCM_BIGP (y)) | |
7250 | { | |
7251 | SCM_SWAP (x, y); | |
7252 | goto add_big_inum; | |
7253 | } | |
7254 | else if (SCM_REALP (y)) | |
7255 | { | |
e25f3727 | 7256 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7257 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7258 | } |
7259 | else if (SCM_COMPLEXP (y)) | |
7260 | { | |
e25f3727 | 7261 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7262 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7263 | SCM_COMPLEX_IMAG (y)); |
7264 | } | |
f92e85f7 | 7265 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7266 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7267 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7268 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7269 | else |
7270 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7271 | } else if (SCM_BIGP (x)) |
7272 | { | |
e11e83f3 | 7273 | if (SCM_I_INUMP (y)) |
0aacf84e | 7274 | { |
e25f3727 | 7275 | scm_t_inum inum; |
0aacf84e MD |
7276 | int bigsgn; |
7277 | add_big_inum: | |
e11e83f3 | 7278 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7279 | if (inum == 0) |
7280 | return x; | |
7281 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7282 | if (inum < 0) | |
7283 | { | |
7284 | SCM result = scm_i_mkbig (); | |
7285 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7286 | scm_remember_upto_here_1 (x); | |
7287 | /* we know the result will have to be a bignum */ | |
7288 | if (bigsgn == -1) | |
7289 | return result; | |
7290 | return scm_i_normbig (result); | |
7291 | } | |
7292 | else | |
7293 | { | |
7294 | SCM result = scm_i_mkbig (); | |
7295 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7296 | scm_remember_upto_here_1 (x); | |
7297 | /* we know the result will have to be a bignum */ | |
7298 | if (bigsgn == 1) | |
7299 | return result; | |
7300 | return scm_i_normbig (result); | |
7301 | } | |
7302 | } | |
7303 | else if (SCM_BIGP (y)) | |
7304 | { | |
7305 | SCM result = scm_i_mkbig (); | |
7306 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7307 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7308 | mpz_add (SCM_I_BIG_MPZ (result), | |
7309 | SCM_I_BIG_MPZ (x), | |
7310 | SCM_I_BIG_MPZ (y)); | |
7311 | scm_remember_upto_here_2 (x, y); | |
7312 | /* we know the result will have to be a bignum */ | |
7313 | if (sgn_x == sgn_y) | |
7314 | return result; | |
7315 | return scm_i_normbig (result); | |
7316 | } | |
7317 | else if (SCM_REALP (y)) | |
7318 | { | |
7319 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7320 | scm_remember_upto_here_1 (x); | |
55f26379 | 7321 | return scm_from_double (result); |
0aacf84e MD |
7322 | } |
7323 | else if (SCM_COMPLEXP (y)) | |
7324 | { | |
7325 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7326 | + SCM_COMPLEX_REAL (y)); | |
7327 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7328 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7329 | } |
f92e85f7 | 7330 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7331 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7332 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7333 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7334 | else |
7335 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7336 | } |
0aacf84e MD |
7337 | else if (SCM_REALP (x)) |
7338 | { | |
e11e83f3 | 7339 | if (SCM_I_INUMP (y)) |
55f26379 | 7340 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7341 | else if (SCM_BIGP (y)) |
7342 | { | |
7343 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7344 | scm_remember_upto_here_1 (y); | |
55f26379 | 7345 | return scm_from_double (result); |
0aacf84e MD |
7346 | } |
7347 | else if (SCM_REALP (y)) | |
55f26379 | 7348 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7349 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7350 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7351 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7352 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7353 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7354 | else |
7355 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7356 | } |
0aacf84e MD |
7357 | else if (SCM_COMPLEXP (x)) |
7358 | { | |
e11e83f3 | 7359 | if (SCM_I_INUMP (y)) |
8507ec80 | 7360 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7361 | SCM_COMPLEX_IMAG (x)); |
7362 | else if (SCM_BIGP (y)) | |
7363 | { | |
7364 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7365 | + SCM_COMPLEX_REAL (x)); | |
7366 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7367 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7368 | } |
7369 | else if (SCM_REALP (y)) | |
8507ec80 | 7370 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7371 | SCM_COMPLEX_IMAG (x)); |
7372 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7373 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7374 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7375 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7376 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7377 | SCM_COMPLEX_IMAG (x)); |
7378 | else | |
7379 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7380 | } | |
7381 | else if (SCM_FRACTIONP (x)) | |
7382 | { | |
e11e83f3 | 7383 | if (SCM_I_INUMP (y)) |
cba42c93 | 7384 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7385 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7386 | SCM_FRACTION_DENOMINATOR (x)); | |
7387 | else if (SCM_BIGP (y)) | |
cba42c93 | 7388 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7389 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7390 | SCM_FRACTION_DENOMINATOR (x)); | |
7391 | else if (SCM_REALP (y)) | |
55f26379 | 7392 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7393 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7394 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7395 | SCM_COMPLEX_IMAG (y)); |
7396 | else if (SCM_FRACTIONP (y)) | |
7397 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7398 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7399 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7400 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7401 | else |
7402 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7403 | } |
0aacf84e | 7404 | else |
98cb6e75 | 7405 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7406 | } |
7407 | ||
7408 | ||
40882e3d KR |
7409 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7410 | (SCM x), | |
7411 | "Return @math{@var{x}+1}.") | |
7412 | #define FUNC_NAME s_scm_oneplus | |
7413 | { | |
cff5fa33 | 7414 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7415 | } |
7416 | #undef FUNC_NAME | |
7417 | ||
7418 | ||
78d3deb1 AW |
7419 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7420 | (SCM x, SCM y, SCM rest), | |
7421 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7422 | "the sum of all but the first argument are subtracted from the first\n" | |
7423 | "argument.") | |
7424 | #define FUNC_NAME s_scm_i_difference | |
7425 | { | |
7426 | while (!scm_is_null (rest)) | |
7427 | { x = scm_difference (x, y); | |
7428 | y = scm_car (rest); | |
7429 | rest = scm_cdr (rest); | |
7430 | } | |
7431 | return scm_difference (x, y); | |
7432 | } | |
7433 | #undef FUNC_NAME | |
7434 | ||
7435 | #define s_difference s_scm_i_difference | |
7436 | #define g_difference g_scm_i_difference | |
7437 | ||
0f2d19dd | 7438 | SCM |
6e8d25a6 | 7439 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7440 | #define FUNC_NAME s_difference |
0f2d19dd | 7441 | { |
9cc37597 | 7442 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7443 | { |
7444 | if (SCM_UNBNDP (x)) | |
7445 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7446 | else | |
e11e83f3 | 7447 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7448 | { |
e25f3727 | 7449 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7450 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7451 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7452 | else |
e25f3727 | 7453 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7454 | } |
7455 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7456 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7457 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7458 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7459 | else if (SCM_REALP (x)) | |
55f26379 | 7460 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7461 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7462 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7463 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7464 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
7465 | return scm_i_make_ratio_already_reduced |
7466 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
7467 | SCM_FRACTION_DENOMINATOR (x)); | |
ca46fb90 RB |
7468 | else |
7469 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7470 | } |
ca46fb90 | 7471 | |
9cc37597 | 7472 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7473 | { |
9cc37597 | 7474 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7475 | { |
e25f3727 AW |
7476 | scm_t_inum xx = SCM_I_INUM (x); |
7477 | scm_t_inum yy = SCM_I_INUM (y); | |
7478 | scm_t_inum z = xx - yy; | |
0aacf84e | 7479 | if (SCM_FIXABLE (z)) |
d956fa6f | 7480 | return SCM_I_MAKINUM (z); |
0aacf84e | 7481 | else |
e25f3727 | 7482 | return scm_i_inum2big (z); |
0aacf84e MD |
7483 | } |
7484 | else if (SCM_BIGP (y)) | |
7485 | { | |
7486 | /* inum-x - big-y */ | |
e25f3727 | 7487 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7488 | |
0aacf84e | 7489 | if (xx == 0) |
b5c40589 MW |
7490 | { |
7491 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7492 | bignum, but negating that gives a fixnum. */ | |
7493 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7494 | } | |
0aacf84e MD |
7495 | else |
7496 | { | |
7497 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7498 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7499 | |
0aacf84e MD |
7500 | if (xx >= 0) |
7501 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7502 | else | |
7503 | { | |
7504 | /* x - y == -(y + -x) */ | |
7505 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7506 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7507 | } | |
7508 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7509 | |
0aacf84e MD |
7510 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7511 | /* we know the result will have to be a bignum */ | |
7512 | return result; | |
7513 | else | |
7514 | return scm_i_normbig (result); | |
7515 | } | |
7516 | } | |
7517 | else if (SCM_REALP (y)) | |
7518 | { | |
e25f3727 | 7519 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7520 | |
7521 | /* | |
7522 | * We need to handle x == exact 0 | |
7523 | * specially because R6RS states that: | |
7524 | * (- 0.0) ==> -0.0 and | |
7525 | * (- 0.0 0.0) ==> 0.0 | |
7526 | * and the scheme compiler changes | |
7527 | * (- 0.0) into (- 0 0.0) | |
7528 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7529 | * At the C level, (-x) is different than (0.0 - x). | |
7530 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7531 | */ | |
7532 | if (xx == 0) | |
7533 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7534 | else | |
7535 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7536 | } |
7537 | else if (SCM_COMPLEXP (y)) | |
7538 | { | |
e25f3727 | 7539 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7540 | |
7541 | /* We need to handle x == exact 0 specially. | |
7542 | See the comment above (for SCM_REALP (y)) */ | |
7543 | if (xx == 0) | |
7544 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7545 | - SCM_COMPLEX_IMAG (y)); | |
7546 | else | |
7547 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7548 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7549 | } |
f92e85f7 MV |
7550 | else if (SCM_FRACTIONP (y)) |
7551 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7552 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7553 | SCM_FRACTION_NUMERATOR (y)), |
7554 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7555 | else |
7556 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7557 | } |
0aacf84e MD |
7558 | else if (SCM_BIGP (x)) |
7559 | { | |
e11e83f3 | 7560 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7561 | { |
7562 | /* big-x - inum-y */ | |
e25f3727 | 7563 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7564 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7565 | |
0aacf84e MD |
7566 | scm_remember_upto_here_1 (x); |
7567 | if (sgn_x == 0) | |
c71b0706 | 7568 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7569 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7570 | else |
7571 | { | |
7572 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7573 | |
708f22c6 KR |
7574 | if (yy >= 0) |
7575 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7576 | else | |
7577 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7578 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7579 | |
0aacf84e MD |
7580 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7581 | /* we know the result will have to be a bignum */ | |
7582 | return result; | |
7583 | else | |
7584 | return scm_i_normbig (result); | |
7585 | } | |
7586 | } | |
7587 | else if (SCM_BIGP (y)) | |
7588 | { | |
7589 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7590 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7591 | SCM result = scm_i_mkbig (); | |
7592 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7593 | SCM_I_BIG_MPZ (x), | |
7594 | SCM_I_BIG_MPZ (y)); | |
7595 | scm_remember_upto_here_2 (x, y); | |
7596 | /* we know the result will have to be a bignum */ | |
7597 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7598 | return result; | |
7599 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7600 | return result; | |
7601 | return scm_i_normbig (result); | |
7602 | } | |
7603 | else if (SCM_REALP (y)) | |
7604 | { | |
7605 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7606 | scm_remember_upto_here_1 (x); | |
55f26379 | 7607 | return scm_from_double (result); |
0aacf84e MD |
7608 | } |
7609 | else if (SCM_COMPLEXP (y)) | |
7610 | { | |
7611 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7612 | - SCM_COMPLEX_REAL (y)); | |
7613 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7614 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7615 | } |
f92e85f7 | 7616 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7617 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7618 | SCM_FRACTION_NUMERATOR (y)), |
7619 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7620 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7621 | } |
0aacf84e MD |
7622 | else if (SCM_REALP (x)) |
7623 | { | |
e11e83f3 | 7624 | if (SCM_I_INUMP (y)) |
55f26379 | 7625 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7626 | else if (SCM_BIGP (y)) |
7627 | { | |
7628 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7629 | scm_remember_upto_here_1 (x); | |
55f26379 | 7630 | return scm_from_double (result); |
0aacf84e MD |
7631 | } |
7632 | else if (SCM_REALP (y)) | |
55f26379 | 7633 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7634 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7635 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7636 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7637 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7638 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7639 | else |
7640 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7641 | } |
0aacf84e MD |
7642 | else if (SCM_COMPLEXP (x)) |
7643 | { | |
e11e83f3 | 7644 | if (SCM_I_INUMP (y)) |
8507ec80 | 7645 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7646 | SCM_COMPLEX_IMAG (x)); |
7647 | else if (SCM_BIGP (y)) | |
7648 | { | |
7649 | double real_part = (SCM_COMPLEX_REAL (x) | |
7650 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7651 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7652 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7653 | } |
7654 | else if (SCM_REALP (y)) | |
8507ec80 | 7655 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7656 | SCM_COMPLEX_IMAG (x)); |
7657 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7658 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7659 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7660 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7661 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7662 | SCM_COMPLEX_IMAG (x)); |
7663 | else | |
7664 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7665 | } | |
7666 | else if (SCM_FRACTIONP (x)) | |
7667 | { | |
e11e83f3 | 7668 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7669 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7670 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7671 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7672 | SCM_FRACTION_DENOMINATOR (x)); | |
7673 | else if (SCM_BIGP (y)) | |
cba42c93 | 7674 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7675 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7676 | SCM_FRACTION_DENOMINATOR (x)); | |
7677 | else if (SCM_REALP (y)) | |
55f26379 | 7678 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7679 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7680 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7681 | -SCM_COMPLEX_IMAG (y)); |
7682 | else if (SCM_FRACTIONP (y)) | |
7683 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7684 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7685 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7686 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7687 | else |
7688 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7689 | } |
0aacf84e | 7690 | else |
98cb6e75 | 7691 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7692 | } |
c05e97b7 | 7693 | #undef FUNC_NAME |
0f2d19dd | 7694 | |
ca46fb90 | 7695 | |
40882e3d KR |
7696 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7697 | (SCM x), | |
7698 | "Return @math{@var{x}-1}.") | |
7699 | #define FUNC_NAME s_scm_oneminus | |
7700 | { | |
cff5fa33 | 7701 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7702 | } |
7703 | #undef FUNC_NAME | |
7704 | ||
7705 | ||
78d3deb1 AW |
7706 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7707 | (SCM x, SCM y, SCM rest), | |
7708 | "Return the product of all arguments. If called without arguments,\n" | |
7709 | "1 is returned.") | |
7710 | #define FUNC_NAME s_scm_i_product | |
7711 | { | |
7712 | while (!scm_is_null (rest)) | |
7713 | { x = scm_product (x, y); | |
7714 | y = scm_car (rest); | |
7715 | rest = scm_cdr (rest); | |
7716 | } | |
7717 | return scm_product (x, y); | |
7718 | } | |
7719 | #undef FUNC_NAME | |
7720 | ||
7721 | #define s_product s_scm_i_product | |
7722 | #define g_product g_scm_i_product | |
7723 | ||
0f2d19dd | 7724 | SCM |
6e8d25a6 | 7725 | scm_product (SCM x, SCM y) |
0f2d19dd | 7726 | { |
9cc37597 | 7727 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7728 | { |
7729 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7730 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7731 | else if (SCM_NUMBERP (x)) |
7732 | return x; | |
7733 | else | |
7734 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7735 | } |
ca46fb90 | 7736 | |
9cc37597 | 7737 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7738 | { |
e25f3727 | 7739 | scm_t_inum xx; |
f4c627b3 | 7740 | |
5e791807 | 7741 | xinum: |
e11e83f3 | 7742 | xx = SCM_I_INUM (x); |
f4c627b3 | 7743 | |
0aacf84e MD |
7744 | switch (xx) |
7745 | { | |
5e791807 MW |
7746 | case 1: |
7747 | /* exact1 is the universal multiplicative identity */ | |
7748 | return y; | |
7749 | break; | |
7750 | case 0: | |
7751 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7752 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7753 | return SCM_INUM0; | |
7754 | /* if the other argument is inexact, the result is inexact, | |
7755 | and we must do the multiplication in order to handle | |
7756 | infinities and NaNs properly. */ | |
7757 | else if (SCM_REALP (y)) | |
7758 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7759 | else if (SCM_COMPLEXP (y)) | |
7760 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7761 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7762 | /* we've already handled inexact numbers, | |
7763 | so y must be exact, and we return exact0 */ | |
7764 | else if (SCM_NUMP (y)) | |
7765 | return SCM_INUM0; | |
7766 | else | |
7767 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7768 | break; | |
7769 | case -1: | |
b5c40589 | 7770 | /* |
5e791807 MW |
7771 | * This case is important for more than just optimization. |
7772 | * It handles the case of negating | |
b5c40589 MW |
7773 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7774 | * which is a bignum that must be changed back into a fixnum. | |
7775 | * Failure to do so will cause the following to return #f: | |
7776 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7777 | */ | |
b5c40589 MW |
7778 | return scm_difference(y, SCM_UNDEFINED); |
7779 | break; | |
0aacf84e | 7780 | } |
f4c627b3 | 7781 | |
9cc37597 | 7782 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7783 | { |
e25f3727 | 7784 | scm_t_inum yy = SCM_I_INUM (y); |
2355f017 MW |
7785 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
7786 | scm_t_int64 kk = xx * (scm_t_int64) yy; | |
7787 | if (SCM_FIXABLE (kk)) | |
7788 | return SCM_I_MAKINUM (kk); | |
7789 | #else | |
7790 | scm_t_inum axx = (xx > 0) ? xx : -xx; | |
7791 | scm_t_inum ayy = (yy > 0) ? yy : -yy; | |
7792 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) | |
7793 | return SCM_I_MAKINUM (xx * yy); | |
7794 | #endif | |
0aacf84e MD |
7795 | else |
7796 | { | |
e25f3727 | 7797 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7798 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7799 | return scm_i_normbig (result); | |
7800 | } | |
7801 | } | |
7802 | else if (SCM_BIGP (y)) | |
7803 | { | |
7804 | SCM result = scm_i_mkbig (); | |
7805 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7806 | scm_remember_upto_here_1 (y); | |
7807 | return result; | |
7808 | } | |
7809 | else if (SCM_REALP (y)) | |
55f26379 | 7810 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7811 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7812 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7813 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7814 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7815 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7816 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7817 | else |
7818 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7819 | } |
0aacf84e MD |
7820 | else if (SCM_BIGP (x)) |
7821 | { | |
e11e83f3 | 7822 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7823 | { |
7824 | SCM_SWAP (x, y); | |
5e791807 | 7825 | goto xinum; |
0aacf84e MD |
7826 | } |
7827 | else if (SCM_BIGP (y)) | |
7828 | { | |
7829 | SCM result = scm_i_mkbig (); | |
7830 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7831 | SCM_I_BIG_MPZ (x), | |
7832 | SCM_I_BIG_MPZ (y)); | |
7833 | scm_remember_upto_here_2 (x, y); | |
7834 | return result; | |
7835 | } | |
7836 | else if (SCM_REALP (y)) | |
7837 | { | |
7838 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7839 | scm_remember_upto_here_1 (x); | |
55f26379 | 7840 | return scm_from_double (result); |
0aacf84e MD |
7841 | } |
7842 | else if (SCM_COMPLEXP (y)) | |
7843 | { | |
7844 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7845 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7846 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7847 | z * SCM_COMPLEX_IMAG (y)); |
7848 | } | |
f92e85f7 | 7849 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7850 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7851 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7852 | else |
7853 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7854 | } |
0aacf84e MD |
7855 | else if (SCM_REALP (x)) |
7856 | { | |
e11e83f3 | 7857 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7858 | { |
7859 | SCM_SWAP (x, y); | |
7860 | goto xinum; | |
7861 | } | |
0aacf84e MD |
7862 | else if (SCM_BIGP (y)) |
7863 | { | |
7864 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7865 | scm_remember_upto_here_1 (y); | |
55f26379 | 7866 | return scm_from_double (result); |
0aacf84e MD |
7867 | } |
7868 | else if (SCM_REALP (y)) | |
55f26379 | 7869 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7870 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7871 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7872 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7873 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7874 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
7875 | else |
7876 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7877 | } |
0aacf84e MD |
7878 | else if (SCM_COMPLEXP (x)) |
7879 | { | |
e11e83f3 | 7880 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7881 | { |
7882 | SCM_SWAP (x, y); | |
7883 | goto xinum; | |
7884 | } | |
0aacf84e MD |
7885 | else if (SCM_BIGP (y)) |
7886 | { | |
7887 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7888 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7889 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7890 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7891 | } |
7892 | else if (SCM_REALP (y)) | |
8507ec80 | 7893 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
7894 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
7895 | else if (SCM_COMPLEXP (y)) | |
7896 | { | |
8507ec80 | 7897 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
7898 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
7899 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
7900 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
7901 | } | |
f92e85f7 MV |
7902 | else if (SCM_FRACTIONP (y)) |
7903 | { | |
7904 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 7905 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
7906 | yy * SCM_COMPLEX_IMAG (x)); |
7907 | } | |
7908 | else | |
7909 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7910 | } | |
7911 | else if (SCM_FRACTIONP (x)) | |
7912 | { | |
e11e83f3 | 7913 | if (SCM_I_INUMP (y)) |
cba42c93 | 7914 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7915 | SCM_FRACTION_DENOMINATOR (x)); |
7916 | else if (SCM_BIGP (y)) | |
cba42c93 | 7917 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7918 | SCM_FRACTION_DENOMINATOR (x)); |
7919 | else if (SCM_REALP (y)) | |
55f26379 | 7920 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
7921 | else if (SCM_COMPLEXP (y)) |
7922 | { | |
7923 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 7924 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7925 | xx * SCM_COMPLEX_IMAG (y)); |
7926 | } | |
7927 | else if (SCM_FRACTIONP (y)) | |
7928 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 7929 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7930 | SCM_FRACTION_NUMERATOR (y)), |
7931 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
7932 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7933 | else |
7934 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7935 | } |
0aacf84e | 7936 | else |
f4c627b3 | 7937 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
7938 | } |
7939 | ||
7351e207 MV |
7940 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
7941 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
7942 | #define ALLOW_DIVIDE_BY_ZERO | |
7943 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
7944 | #endif | |
0f2d19dd | 7945 | |
ba74ef4e MV |
7946 | /* The code below for complex division is adapted from the GNU |
7947 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
7948 | this copyright: */ | |
7949 | ||
7950 | /**************************************************************** | |
7951 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
7952 | ||
7953 | Permission to use, copy, modify, and distribute this software | |
7954 | and its documentation for any purpose and without fee is hereby | |
7955 | granted, provided that the above copyright notice appear in all | |
7956 | copies and that both that the copyright notice and this | |
7957 | permission notice and warranty disclaimer appear in supporting | |
7958 | documentation, and that the names of AT&T Bell Laboratories or | |
7959 | Bellcore or any of their entities not be used in advertising or | |
7960 | publicity pertaining to distribution of the software without | |
7961 | specific, written prior permission. | |
7962 | ||
7963 | AT&T and Bellcore disclaim all warranties with regard to this | |
7964 | software, including all implied warranties of merchantability | |
7965 | and fitness. In no event shall AT&T or Bellcore be liable for | |
7966 | any special, indirect or consequential damages or any damages | |
7967 | whatsoever resulting from loss of use, data or profits, whether | |
7968 | in an action of contract, negligence or other tortious action, | |
7969 | arising out of or in connection with the use or performance of | |
7970 | this software. | |
7971 | ****************************************************************/ | |
7972 | ||
78d3deb1 AW |
7973 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
7974 | (SCM x, SCM y, SCM rest), | |
7975 | "Divide the first argument by the product of the remaining\n" | |
7976 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
7977 | "returned.") | |
7978 | #define FUNC_NAME s_scm_i_divide | |
7979 | { | |
7980 | while (!scm_is_null (rest)) | |
7981 | { x = scm_divide (x, y); | |
7982 | y = scm_car (rest); | |
7983 | rest = scm_cdr (rest); | |
7984 | } | |
7985 | return scm_divide (x, y); | |
7986 | } | |
7987 | #undef FUNC_NAME | |
7988 | ||
7989 | #define s_divide s_scm_i_divide | |
7990 | #define g_divide g_scm_i_divide | |
7991 | ||
f92e85f7 | 7992 | static SCM |
78d3deb1 AW |
7993 | do_divide (SCM x, SCM y, int inexact) |
7994 | #define FUNC_NAME s_divide | |
0f2d19dd | 7995 | { |
f8de44c1 DH |
7996 | double a; |
7997 | ||
9cc37597 | 7998 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7999 | { |
8000 | if (SCM_UNBNDP (x)) | |
8001 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 8002 | else if (SCM_I_INUMP (x)) |
0aacf84e | 8003 | { |
e25f3727 | 8004 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
8005 | if (xx == 1 || xx == -1) |
8006 | return x; | |
7351e207 | 8007 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8008 | else if (xx == 0) |
8009 | scm_num_overflow (s_divide); | |
7351e207 | 8010 | #endif |
0aacf84e | 8011 | else |
f92e85f7 MV |
8012 | { |
8013 | if (inexact) | |
55f26379 | 8014 | return scm_from_double (1.0 / (double) xx); |
a285b18c | 8015 | else return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
f92e85f7 | 8016 | } |
0aacf84e MD |
8017 | } |
8018 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
8019 | { |
8020 | if (inexact) | |
55f26379 | 8021 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
a285b18c | 8022 | else return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
f92e85f7 | 8023 | } |
0aacf84e MD |
8024 | else if (SCM_REALP (x)) |
8025 | { | |
8026 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 8027 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8028 | if (xx == 0.0) |
8029 | scm_num_overflow (s_divide); | |
8030 | else | |
7351e207 | 8031 | #endif |
55f26379 | 8032 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
8033 | } |
8034 | else if (SCM_COMPLEXP (x)) | |
8035 | { | |
8036 | double r = SCM_COMPLEX_REAL (x); | |
8037 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 8038 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8039 | { |
8040 | double t = r / i; | |
8041 | double d = i * (1.0 + t * t); | |
8507ec80 | 8042 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
8043 | } |
8044 | else | |
8045 | { | |
8046 | double t = i / r; | |
8047 | double d = r * (1.0 + t * t); | |
8507ec80 | 8048 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
8049 | } |
8050 | } | |
f92e85f7 | 8051 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
8052 | return scm_i_make_ratio_already_reduced (SCM_FRACTION_DENOMINATOR (x), |
8053 | SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e MD |
8054 | else |
8055 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 8056 | } |
f8de44c1 | 8057 | |
9cc37597 | 8058 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8059 | { |
e25f3727 | 8060 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 8061 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8062 | { |
e25f3727 | 8063 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8064 | if (yy == 0) |
8065 | { | |
7351e207 | 8066 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8067 | scm_num_overflow (s_divide); |
7351e207 | 8068 | #else |
55f26379 | 8069 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 8070 | #endif |
0aacf84e MD |
8071 | } |
8072 | else if (xx % yy != 0) | |
f92e85f7 MV |
8073 | { |
8074 | if (inexact) | |
55f26379 | 8075 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 8076 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8077 | } |
0aacf84e MD |
8078 | else |
8079 | { | |
e25f3727 | 8080 | scm_t_inum z = xx / yy; |
0aacf84e | 8081 | if (SCM_FIXABLE (z)) |
d956fa6f | 8082 | return SCM_I_MAKINUM (z); |
0aacf84e | 8083 | else |
e25f3727 | 8084 | return scm_i_inum2big (z); |
0aacf84e | 8085 | } |
f872b822 | 8086 | } |
0aacf84e | 8087 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
8088 | { |
8089 | if (inexact) | |
55f26379 | 8090 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 8091 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8092 | } |
0aacf84e MD |
8093 | else if (SCM_REALP (y)) |
8094 | { | |
8095 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8096 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8097 | if (yy == 0.0) |
8098 | scm_num_overflow (s_divide); | |
8099 | else | |
7351e207 | 8100 | #endif |
55f26379 | 8101 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 8102 | } |
0aacf84e MD |
8103 | else if (SCM_COMPLEXP (y)) |
8104 | { | |
8105 | a = xx; | |
8106 | complex_div: /* y _must_ be a complex number */ | |
8107 | { | |
8108 | double r = SCM_COMPLEX_REAL (y); | |
8109 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8110 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8111 | { |
8112 | double t = r / i; | |
8113 | double d = i * (1.0 + t * t); | |
8507ec80 | 8114 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
8115 | } |
8116 | else | |
8117 | { | |
8118 | double t = i / r; | |
8119 | double d = r * (1.0 + t * t); | |
8507ec80 | 8120 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
8121 | } |
8122 | } | |
8123 | } | |
f92e85f7 MV |
8124 | else if (SCM_FRACTIONP (y)) |
8125 | /* a / b/c = ac / b */ | |
cba42c93 | 8126 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8127 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8128 | else |
8129 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8130 | } |
0aacf84e MD |
8131 | else if (SCM_BIGP (x)) |
8132 | { | |
e11e83f3 | 8133 | if (SCM_I_INUMP (y)) |
0aacf84e | 8134 | { |
e25f3727 | 8135 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8136 | if (yy == 0) |
8137 | { | |
7351e207 | 8138 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8139 | scm_num_overflow (s_divide); |
7351e207 | 8140 | #else |
0aacf84e MD |
8141 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8142 | scm_remember_upto_here_1 (x); | |
8143 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8144 | #endif |
0aacf84e MD |
8145 | } |
8146 | else if (yy == 1) | |
8147 | return x; | |
8148 | else | |
8149 | { | |
8150 | /* FIXME: HMM, what are the relative performance issues here? | |
8151 | We need to test. Is it faster on average to test | |
8152 | divisible_p, then perform whichever operation, or is it | |
8153 | faster to perform the integer div opportunistically and | |
8154 | switch to real if there's a remainder? For now we take the | |
8155 | middle ground: test, then if divisible, use the faster div | |
8156 | func. */ | |
8157 | ||
e25f3727 | 8158 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8159 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8160 | ||
8161 | if (divisible_p) | |
8162 | { | |
8163 | SCM result = scm_i_mkbig (); | |
8164 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8165 | scm_remember_upto_here_1 (x); | |
8166 | if (yy < 0) | |
8167 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8168 | return scm_i_normbig (result); | |
8169 | } | |
8170 | else | |
f92e85f7 MV |
8171 | { |
8172 | if (inexact) | |
55f26379 | 8173 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 8174 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8175 | } |
0aacf84e MD |
8176 | } |
8177 | } | |
8178 | else if (SCM_BIGP (y)) | |
8179 | { | |
a4955a04 MW |
8180 | /* big_x / big_y */ |
8181 | if (inexact) | |
0aacf84e | 8182 | { |
a4955a04 MW |
8183 | /* It's easily possible for the ratio x/y to fit a double |
8184 | but one or both x and y be too big to fit a double, | |
8185 | hence the use of mpq_get_d rather than converting and | |
8186 | dividing. */ | |
8187 | mpq_t q; | |
8188 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
8189 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
8190 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
8191 | } |
8192 | else | |
8193 | { | |
a4955a04 MW |
8194 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8195 | SCM_I_BIG_MPZ (y)); | |
8196 | if (divisible_p) | |
8197 | { | |
8198 | SCM result = scm_i_mkbig (); | |
8199 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8200 | SCM_I_BIG_MPZ (x), | |
8201 | SCM_I_BIG_MPZ (y)); | |
8202 | scm_remember_upto_here_2 (x, y); | |
8203 | return scm_i_normbig (result); | |
8204 | } | |
8205 | else | |
8206 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8207 | } |
8208 | } | |
8209 | else if (SCM_REALP (y)) | |
8210 | { | |
8211 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8212 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8213 | if (yy == 0.0) |
8214 | scm_num_overflow (s_divide); | |
8215 | else | |
7351e207 | 8216 | #endif |
55f26379 | 8217 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8218 | } |
8219 | else if (SCM_COMPLEXP (y)) | |
8220 | { | |
8221 | a = scm_i_big2dbl (x); | |
8222 | goto complex_div; | |
8223 | } | |
f92e85f7 | 8224 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8225 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8226 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8227 | else |
8228 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8229 | } |
0aacf84e MD |
8230 | else if (SCM_REALP (x)) |
8231 | { | |
8232 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8233 | if (SCM_I_INUMP (y)) |
0aacf84e | 8234 | { |
e25f3727 | 8235 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8236 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8237 | if (yy == 0) |
8238 | scm_num_overflow (s_divide); | |
8239 | else | |
7351e207 | 8240 | #endif |
55f26379 | 8241 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8242 | } |
8243 | else if (SCM_BIGP (y)) | |
8244 | { | |
8245 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8246 | scm_remember_upto_here_1 (y); | |
55f26379 | 8247 | return scm_from_double (rx / dby); |
0aacf84e MD |
8248 | } |
8249 | else if (SCM_REALP (y)) | |
8250 | { | |
8251 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8252 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8253 | if (yy == 0.0) |
8254 | scm_num_overflow (s_divide); | |
8255 | else | |
7351e207 | 8256 | #endif |
55f26379 | 8257 | return scm_from_double (rx / yy); |
0aacf84e MD |
8258 | } |
8259 | else if (SCM_COMPLEXP (y)) | |
8260 | { | |
8261 | a = rx; | |
8262 | goto complex_div; | |
8263 | } | |
f92e85f7 | 8264 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8265 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8266 | else |
8267 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8268 | } |
0aacf84e MD |
8269 | else if (SCM_COMPLEXP (x)) |
8270 | { | |
8271 | double rx = SCM_COMPLEX_REAL (x); | |
8272 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8273 | if (SCM_I_INUMP (y)) |
0aacf84e | 8274 | { |
e25f3727 | 8275 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8276 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8277 | if (yy == 0) |
8278 | scm_num_overflow (s_divide); | |
8279 | else | |
7351e207 | 8280 | #endif |
0aacf84e MD |
8281 | { |
8282 | double d = yy; | |
8507ec80 | 8283 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8284 | } |
8285 | } | |
8286 | else if (SCM_BIGP (y)) | |
8287 | { | |
8288 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8289 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8290 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8291 | } |
8292 | else if (SCM_REALP (y)) | |
8293 | { | |
8294 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8295 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8296 | if (yy == 0.0) |
8297 | scm_num_overflow (s_divide); | |
8298 | else | |
7351e207 | 8299 | #endif |
8507ec80 | 8300 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8301 | } |
8302 | else if (SCM_COMPLEXP (y)) | |
8303 | { | |
8304 | double ry = SCM_COMPLEX_REAL (y); | |
8305 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8306 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8307 | { |
8308 | double t = ry / iy; | |
8309 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8310 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8311 | } |
8312 | else | |
8313 | { | |
8314 | double t = iy / ry; | |
8315 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8316 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8317 | } |
8318 | } | |
f92e85f7 MV |
8319 | else if (SCM_FRACTIONP (y)) |
8320 | { | |
8321 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8322 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8323 | } |
0aacf84e MD |
8324 | else |
8325 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8326 | } |
f92e85f7 MV |
8327 | else if (SCM_FRACTIONP (x)) |
8328 | { | |
e11e83f3 | 8329 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8330 | { |
e25f3727 | 8331 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8332 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8333 | if (yy == 0) | |
8334 | scm_num_overflow (s_divide); | |
8335 | else | |
8336 | #endif | |
cba42c93 | 8337 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8338 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8339 | } | |
8340 | else if (SCM_BIGP (y)) | |
8341 | { | |
cba42c93 | 8342 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8343 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8344 | } | |
8345 | else if (SCM_REALP (y)) | |
8346 | { | |
8347 | double yy = SCM_REAL_VALUE (y); | |
8348 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8349 | if (yy == 0.0) | |
8350 | scm_num_overflow (s_divide); | |
8351 | else | |
8352 | #endif | |
55f26379 | 8353 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8354 | } |
8355 | else if (SCM_COMPLEXP (y)) | |
8356 | { | |
8357 | a = scm_i_fraction2double (x); | |
8358 | goto complex_div; | |
8359 | } | |
8360 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8361 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8362 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8363 | else | |
8364 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8365 | } | |
0aacf84e | 8366 | else |
f8de44c1 | 8367 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8368 | } |
f92e85f7 MV |
8369 | |
8370 | SCM | |
8371 | scm_divide (SCM x, SCM y) | |
8372 | { | |
78d3deb1 | 8373 | return do_divide (x, y, 0); |
f92e85f7 MV |
8374 | } |
8375 | ||
8376 | static SCM scm_divide2real (SCM x, SCM y) | |
8377 | { | |
78d3deb1 | 8378 | return do_divide (x, y, 1); |
f92e85f7 | 8379 | } |
c05e97b7 | 8380 | #undef FUNC_NAME |
0f2d19dd | 8381 | |
fa605590 | 8382 | |
0f2d19dd | 8383 | double |
3101f40f | 8384 | scm_c_truncate (double x) |
0f2d19dd | 8385 | { |
fa605590 | 8386 | return trunc (x); |
0f2d19dd | 8387 | } |
0f2d19dd | 8388 | |
3101f40f MV |
8389 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8390 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8391 | Then half-way cases are identified and adjusted down if the | |
8392 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8393 | |
8394 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8395 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8396 | ||
8397 | An odd "result" value is identified with result/2 != floor(result/2). | |
8398 | This is done with plus_half, since that value is ready for use sooner in | |
8399 | a pipelined cpu, and we're already requiring plus_half == result. | |
8400 | ||
8401 | Note however that we need to be careful when x is big and already an | |
8402 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8403 | us to return such a value, incorrectly. For instance if the hardware is | |
8404 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8405 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8406 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8407 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8408 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8409 | ||
8410 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8411 | x is already an integer. If it is then clearly that's the desired result | |
8412 | already. And if it's not then the exponent must be small enough to allow | |
8413 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8414 | ||
0f2d19dd | 8415 | double |
3101f40f | 8416 | scm_c_round (double x) |
0f2d19dd | 8417 | { |
6187f48b KR |
8418 | double plus_half, result; |
8419 | ||
8420 | if (x == floor (x)) | |
8421 | return x; | |
8422 | ||
8423 | plus_half = x + 0.5; | |
8424 | result = floor (plus_half); | |
3101f40f | 8425 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8426 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8427 | ? result - 1 | |
8428 | : result); | |
0f2d19dd JB |
8429 | } |
8430 | ||
8b56bcec MW |
8431 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8432 | (SCM x), | |
8433 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8434 | #define FUNC_NAME s_scm_truncate_number |
8435 | { | |
8b56bcec MW |
8436 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8437 | return x; | |
8438 | else if (SCM_REALP (x)) | |
c251ab63 | 8439 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8440 | else if (SCM_FRACTIONP (x)) |
8441 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8442 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8443 | else |
8b56bcec MW |
8444 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8445 | s_scm_truncate_number); | |
f92e85f7 MV |
8446 | } |
8447 | #undef FUNC_NAME | |
8448 | ||
8b56bcec MW |
8449 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8450 | (SCM x), | |
8451 | "Round the number @var{x} towards the nearest integer. " | |
8452 | "When it is exactly halfway between two integers, " | |
8453 | "round towards the even one.") | |
f92e85f7 MV |
8454 | #define FUNC_NAME s_scm_round_number |
8455 | { | |
e11e83f3 | 8456 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8457 | return x; |
8458 | else if (SCM_REALP (x)) | |
3101f40f | 8459 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8460 | else if (SCM_FRACTIONP (x)) |
8461 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8462 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8463 | else |
8b56bcec MW |
8464 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8465 | s_scm_round_number); | |
f92e85f7 MV |
8466 | } |
8467 | #undef FUNC_NAME | |
8468 | ||
8469 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8470 | (SCM x), | |
8471 | "Round the number @var{x} towards minus infinity.") | |
8472 | #define FUNC_NAME s_scm_floor | |
8473 | { | |
e11e83f3 | 8474 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8475 | return x; |
8476 | else if (SCM_REALP (x)) | |
55f26379 | 8477 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8478 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8479 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8480 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8481 | else |
8482 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8483 | } | |
8484 | #undef FUNC_NAME | |
8485 | ||
8486 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8487 | (SCM x), | |
8488 | "Round the number @var{x} towards infinity.") | |
8489 | #define FUNC_NAME s_scm_ceiling | |
8490 | { | |
e11e83f3 | 8491 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8492 | return x; |
8493 | else if (SCM_REALP (x)) | |
55f26379 | 8494 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8495 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8496 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8497 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8498 | else |
8499 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8500 | } | |
8501 | #undef FUNC_NAME | |
0f2d19dd | 8502 | |
2519490c MW |
8503 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8504 | (SCM x, SCM y), | |
8505 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8506 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8507 | { |
01c7284a MW |
8508 | if (scm_is_integer (y)) |
8509 | { | |
8510 | if (scm_is_true (scm_exact_p (y))) | |
8511 | return scm_integer_expt (x, y); | |
8512 | else | |
8513 | { | |
8514 | /* Here we handle the case where the exponent is an inexact | |
8515 | integer. We make the exponent exact in order to use | |
8516 | scm_integer_expt, and thus avoid the spurious imaginary | |
8517 | parts that may result from round-off errors in the general | |
8518 | e^(y log x) method below (for example when squaring a large | |
8519 | negative number). In this case, we must return an inexact | |
8520 | result for correctness. We also make the base inexact so | |
8521 | that scm_integer_expt will use fast inexact arithmetic | |
8522 | internally. Note that making the base inexact is not | |
8523 | sufficient to guarantee an inexact result, because | |
8524 | scm_integer_expt will return an exact 1 when the exponent | |
8525 | is 0, even if the base is inexact. */ | |
8526 | return scm_exact_to_inexact | |
8527 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8528 | scm_inexact_to_exact (y))); | |
8529 | } | |
8530 | } | |
6fc4d012 AW |
8531 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8532 | { | |
8533 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8534 | } | |
2519490c | 8535 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8536 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8537 | else if (scm_is_complex (x)) |
8538 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8539 | else | |
8540 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8541 | } |
1bbd0b84 | 8542 | #undef FUNC_NAME |
0f2d19dd | 8543 | |
7f41099e MW |
8544 | /* sin/cos/tan/asin/acos/atan |
8545 | sinh/cosh/tanh/asinh/acosh/atanh | |
8546 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8547 | Written by Jerry D. Hedden, (C) FSF. | |
8548 | See the file `COPYING' for terms applying to this program. */ | |
8549 | ||
ad79736c AW |
8550 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8551 | (SCM z), | |
8552 | "Compute the sine of @var{z}.") | |
8553 | #define FUNC_NAME s_scm_sin | |
8554 | { | |
8deddc94 MW |
8555 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8556 | return z; /* sin(exact0) = exact0 */ | |
8557 | else if (scm_is_real (z)) | |
ad79736c AW |
8558 | return scm_from_double (sin (scm_to_double (z))); |
8559 | else if (SCM_COMPLEXP (z)) | |
8560 | { double x, y; | |
8561 | x = SCM_COMPLEX_REAL (z); | |
8562 | y = SCM_COMPLEX_IMAG (z); | |
8563 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8564 | cos (x) * sinh (y)); | |
8565 | } | |
8566 | else | |
8567 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8568 | } | |
8569 | #undef FUNC_NAME | |
0f2d19dd | 8570 | |
ad79736c AW |
8571 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8572 | (SCM z), | |
8573 | "Compute the cosine of @var{z}.") | |
8574 | #define FUNC_NAME s_scm_cos | |
8575 | { | |
8deddc94 MW |
8576 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8577 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8578 | else if (scm_is_real (z)) | |
ad79736c AW |
8579 | return scm_from_double (cos (scm_to_double (z))); |
8580 | else if (SCM_COMPLEXP (z)) | |
8581 | { double x, y; | |
8582 | x = SCM_COMPLEX_REAL (z); | |
8583 | y = SCM_COMPLEX_IMAG (z); | |
8584 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8585 | -sin (x) * sinh (y)); | |
8586 | } | |
8587 | else | |
8588 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8589 | } | |
8590 | #undef FUNC_NAME | |
8591 | ||
8592 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8593 | (SCM z), | |
8594 | "Compute the tangent of @var{z}.") | |
8595 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8596 | { |
8deddc94 MW |
8597 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8598 | return z; /* tan(exact0) = exact0 */ | |
8599 | else if (scm_is_real (z)) | |
ad79736c AW |
8600 | return scm_from_double (tan (scm_to_double (z))); |
8601 | else if (SCM_COMPLEXP (z)) | |
8602 | { double x, y, w; | |
8603 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8604 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8605 | w = cos (x) + cosh (y); | |
8606 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8607 | if (w == 0.0) | |
8608 | scm_num_overflow (s_scm_tan); | |
8609 | #endif | |
8610 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8611 | } | |
8612 | else | |
8613 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8614 | } | |
8615 | #undef FUNC_NAME | |
8616 | ||
8617 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8618 | (SCM z), | |
8619 | "Compute the hyperbolic sine of @var{z}.") | |
8620 | #define FUNC_NAME s_scm_sinh | |
8621 | { | |
8deddc94 MW |
8622 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8623 | return z; /* sinh(exact0) = exact0 */ | |
8624 | else if (scm_is_real (z)) | |
ad79736c AW |
8625 | return scm_from_double (sinh (scm_to_double (z))); |
8626 | else if (SCM_COMPLEXP (z)) | |
8627 | { double x, y; | |
8628 | x = SCM_COMPLEX_REAL (z); | |
8629 | y = SCM_COMPLEX_IMAG (z); | |
8630 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8631 | cosh (x) * sin (y)); | |
8632 | } | |
8633 | else | |
8634 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8635 | } | |
8636 | #undef FUNC_NAME | |
8637 | ||
8638 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8639 | (SCM z), | |
8640 | "Compute the hyperbolic cosine of @var{z}.") | |
8641 | #define FUNC_NAME s_scm_cosh | |
8642 | { | |
8deddc94 MW |
8643 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8644 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8645 | else if (scm_is_real (z)) | |
ad79736c AW |
8646 | return scm_from_double (cosh (scm_to_double (z))); |
8647 | else if (SCM_COMPLEXP (z)) | |
8648 | { double x, y; | |
8649 | x = SCM_COMPLEX_REAL (z); | |
8650 | y = SCM_COMPLEX_IMAG (z); | |
8651 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8652 | sinh (x) * sin (y)); | |
8653 | } | |
8654 | else | |
8655 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8656 | } | |
8657 | #undef FUNC_NAME | |
8658 | ||
8659 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8660 | (SCM z), | |
8661 | "Compute the hyperbolic tangent of @var{z}.") | |
8662 | #define FUNC_NAME s_scm_tanh | |
8663 | { | |
8deddc94 MW |
8664 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8665 | return z; /* tanh(exact0) = exact0 */ | |
8666 | else if (scm_is_real (z)) | |
ad79736c AW |
8667 | return scm_from_double (tanh (scm_to_double (z))); |
8668 | else if (SCM_COMPLEXP (z)) | |
8669 | { double x, y, w; | |
8670 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8671 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8672 | w = cosh (x) + cos (y); | |
8673 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8674 | if (w == 0.0) | |
8675 | scm_num_overflow (s_scm_tanh); | |
8676 | #endif | |
8677 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8678 | } | |
8679 | else | |
8680 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8681 | } | |
8682 | #undef FUNC_NAME | |
8683 | ||
8684 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8685 | (SCM z), | |
8686 | "Compute the arc sine of @var{z}.") | |
8687 | #define FUNC_NAME s_scm_asin | |
8688 | { | |
8deddc94 MW |
8689 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8690 | return z; /* asin(exact0) = exact0 */ | |
8691 | else if (scm_is_real (z)) | |
ad79736c AW |
8692 | { |
8693 | double w = scm_to_double (z); | |
8694 | if (w >= -1.0 && w <= 1.0) | |
8695 | return scm_from_double (asin (w)); | |
8696 | else | |
8697 | return scm_product (scm_c_make_rectangular (0, -1), | |
8698 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8699 | } | |
8700 | else if (SCM_COMPLEXP (z)) | |
8701 | { double x, y; | |
8702 | x = SCM_COMPLEX_REAL (z); | |
8703 | y = SCM_COMPLEX_IMAG (z); | |
8704 | return scm_product (scm_c_make_rectangular (0, -1), | |
8705 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8706 | } | |
8707 | else | |
8708 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8709 | } | |
8710 | #undef FUNC_NAME | |
8711 | ||
8712 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8713 | (SCM z), | |
8714 | "Compute the arc cosine of @var{z}.") | |
8715 | #define FUNC_NAME s_scm_acos | |
8716 | { | |
8deddc94 MW |
8717 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8718 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8719 | else if (scm_is_real (z)) | |
ad79736c AW |
8720 | { |
8721 | double w = scm_to_double (z); | |
8722 | if (w >= -1.0 && w <= 1.0) | |
8723 | return scm_from_double (acos (w)); | |
8724 | else | |
8725 | return scm_sum (scm_from_double (acos (0.0)), | |
8726 | scm_product (scm_c_make_rectangular (0, 1), | |
8727 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8728 | } | |
8729 | else if (SCM_COMPLEXP (z)) | |
8730 | { double x, y; | |
8731 | x = SCM_COMPLEX_REAL (z); | |
8732 | y = SCM_COMPLEX_IMAG (z); | |
8733 | return scm_sum (scm_from_double (acos (0.0)), | |
8734 | scm_product (scm_c_make_rectangular (0, 1), | |
8735 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8736 | } | |
8737 | else | |
8738 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8739 | } | |
8740 | #undef FUNC_NAME | |
8741 | ||
8742 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8743 | (SCM z, SCM y), | |
8744 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8745 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8746 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8747 | #define FUNC_NAME s_scm_atan | |
8748 | { | |
8749 | if (SCM_UNBNDP (y)) | |
8750 | { | |
8deddc94 MW |
8751 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8752 | return z; /* atan(exact0) = exact0 */ | |
8753 | else if (scm_is_real (z)) | |
ad79736c AW |
8754 | return scm_from_double (atan (scm_to_double (z))); |
8755 | else if (SCM_COMPLEXP (z)) | |
8756 | { | |
8757 | double v, w; | |
8758 | v = SCM_COMPLEX_REAL (z); | |
8759 | w = SCM_COMPLEX_IMAG (z); | |
8760 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8761 | scm_c_make_rectangular (v, w + 1.0))), | |
8762 | scm_c_make_rectangular (0, 2)); | |
8763 | } | |
8764 | else | |
18104cac | 8765 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8766 | } |
8767 | else if (scm_is_real (z)) | |
8768 | { | |
8769 | if (scm_is_real (y)) | |
8770 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8771 | else | |
8772 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8773 | } | |
8774 | else | |
8775 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8776 | } | |
8777 | #undef FUNC_NAME | |
8778 | ||
8779 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8780 | (SCM z), | |
8781 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8782 | #define FUNC_NAME s_scm_sys_asinh | |
8783 | { | |
8deddc94 MW |
8784 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8785 | return z; /* asinh(exact0) = exact0 */ | |
8786 | else if (scm_is_real (z)) | |
ad79736c AW |
8787 | return scm_from_double (asinh (scm_to_double (z))); |
8788 | else if (scm_is_number (z)) | |
8789 | return scm_log (scm_sum (z, | |
8790 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8791 | SCM_INUM1)))); |
ad79736c AW |
8792 | else |
8793 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8794 | } | |
8795 | #undef FUNC_NAME | |
8796 | ||
8797 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8798 | (SCM z), | |
8799 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8800 | #define FUNC_NAME s_scm_sys_acosh | |
8801 | { | |
8deddc94 MW |
8802 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8803 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8804 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8805 | return scm_from_double (acosh (scm_to_double (z))); |
8806 | else if (scm_is_number (z)) | |
8807 | return scm_log (scm_sum (z, | |
8808 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8809 | SCM_INUM1)))); |
ad79736c AW |
8810 | else |
8811 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8812 | } | |
8813 | #undef FUNC_NAME | |
8814 | ||
8815 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8816 | (SCM z), | |
8817 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8818 | #define FUNC_NAME s_scm_sys_atanh | |
8819 | { | |
8deddc94 MW |
8820 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8821 | return z; /* atanh(exact0) = exact0 */ | |
8822 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8823 | return scm_from_double (atanh (scm_to_double (z))); |
8824 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8825 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8826 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8827 | SCM_I_MAKINUM (2)); |
8828 | else | |
8829 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8830 | } |
1bbd0b84 | 8831 | #undef FUNC_NAME |
0f2d19dd | 8832 | |
8507ec80 MV |
8833 | SCM |
8834 | scm_c_make_rectangular (double re, double im) | |
8835 | { | |
c7218482 | 8836 | SCM z; |
03604fcf | 8837 | |
c7218482 MW |
8838 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8839 | "complex")); | |
8840 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8841 | SCM_COMPLEX_REAL (z) = re; | |
8842 | SCM_COMPLEX_IMAG (z) = im; | |
8843 | return z; | |
8507ec80 | 8844 | } |
0f2d19dd | 8845 | |
a1ec6916 | 8846 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 8847 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
8848 | "Return a complex number constructed of the given @var{real_part} " |
8849 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 8850 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8851 | { |
ad79736c AW |
8852 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8853 | SCM_ARG1, FUNC_NAME, "real"); | |
8854 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8855 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8856 | |
8857 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8858 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8859 | return real_part; | |
8860 | else | |
8861 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8862 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8863 | } |
1bbd0b84 | 8864 | #undef FUNC_NAME |
0f2d19dd | 8865 | |
8507ec80 MV |
8866 | SCM |
8867 | scm_c_make_polar (double mag, double ang) | |
8868 | { | |
8869 | double s, c; | |
5e647d08 LC |
8870 | |
8871 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8872 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8873 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8874 | details. */ | |
8875 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8876 | sincos (ang, &s, &c); |
8877 | #else | |
8878 | s = sin (ang); | |
8879 | c = cos (ang); | |
8880 | #endif | |
9d427b2c MW |
8881 | |
8882 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8883 | infinite, or perhaps simply too large to determine its value | |
8884 | mod 2*pi. However, we know something that the floating-point | |
8885 | implementation doesn't know: We know that s and c are finite. | |
8886 | Therefore, if the magnitude is zero, return a complex zero. | |
8887 | ||
8888 | The reason we check for the NaNs instead of using this case | |
8889 | whenever mag == 0.0 is because when the angle is known, we'd | |
8890 | like to return the correct kind of non-real complex zero: | |
8891 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8892 | on which quadrant the angle is in. | |
8893 | */ | |
8894 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8895 | return scm_c_make_rectangular (0.0, 0.0); | |
8896 | else | |
8897 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8898 | } |
0f2d19dd | 8899 | |
a1ec6916 | 8900 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8901 | (SCM mag, SCM ang), |
8902 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8903 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8904 | { |
c7218482 MW |
8905 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8906 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8907 | ||
8908 | /* If mag is exact0, return exact0 */ | |
8909 | if (scm_is_eq (mag, SCM_INUM0)) | |
8910 | return SCM_INUM0; | |
8911 | /* Return a real if ang is exact0 */ | |
8912 | else if (scm_is_eq (ang, SCM_INUM0)) | |
8913 | return mag; | |
8914 | else | |
8915 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 8916 | } |
1bbd0b84 | 8917 | #undef FUNC_NAME |
0f2d19dd JB |
8918 | |
8919 | ||
2519490c MW |
8920 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
8921 | (SCM z), | |
8922 | "Return the real part of the number @var{z}.") | |
8923 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 8924 | { |
2519490c | 8925 | if (SCM_COMPLEXP (z)) |
55f26379 | 8926 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 8927 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 8928 | return z; |
0aacf84e | 8929 | else |
2519490c | 8930 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 8931 | } |
2519490c | 8932 | #undef FUNC_NAME |
0f2d19dd JB |
8933 | |
8934 | ||
2519490c MW |
8935 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
8936 | (SCM z), | |
8937 | "Return the imaginary part of the number @var{z}.") | |
8938 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 8939 | { |
2519490c MW |
8940 | if (SCM_COMPLEXP (z)) |
8941 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 8942 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 8943 | return SCM_INUM0; |
0aacf84e | 8944 | else |
2519490c | 8945 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 8946 | } |
2519490c | 8947 | #undef FUNC_NAME |
0f2d19dd | 8948 | |
2519490c MW |
8949 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
8950 | (SCM z), | |
8951 | "Return the numerator of the number @var{z}.") | |
8952 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 8953 | { |
2519490c | 8954 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
8955 | return z; |
8956 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 8957 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
8958 | else if (SCM_REALP (z)) |
8959 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
8960 | else | |
2519490c | 8961 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 8962 | } |
2519490c | 8963 | #undef FUNC_NAME |
f92e85f7 MV |
8964 | |
8965 | ||
2519490c MW |
8966 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
8967 | (SCM z), | |
8968 | "Return the denominator of the number @var{z}.") | |
8969 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 8970 | { |
2519490c | 8971 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 8972 | return SCM_INUM1; |
f92e85f7 | 8973 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 8974 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
8975 | else if (SCM_REALP (z)) |
8976 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
8977 | else | |
2519490c | 8978 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 8979 | } |
2519490c | 8980 | #undef FUNC_NAME |
0f2d19dd | 8981 | |
2519490c MW |
8982 | |
8983 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
8984 | (SCM z), | |
8985 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
8986 | "@code{abs} for real arguments, but also allows complex numbers.") | |
8987 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 8988 | { |
e11e83f3 | 8989 | if (SCM_I_INUMP (z)) |
0aacf84e | 8990 | { |
e25f3727 | 8991 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
8992 | if (zz >= 0) |
8993 | return z; | |
8994 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 8995 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 8996 | else |
e25f3727 | 8997 | return scm_i_inum2big (-zz); |
5986c47d | 8998 | } |
0aacf84e MD |
8999 | else if (SCM_BIGP (z)) |
9000 | { | |
9001 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9002 | scm_remember_upto_here_1 (z); | |
9003 | if (sgn < 0) | |
9004 | return scm_i_clonebig (z, 0); | |
9005 | else | |
9006 | return z; | |
5986c47d | 9007 | } |
0aacf84e | 9008 | else if (SCM_REALP (z)) |
55f26379 | 9009 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 9010 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9011 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
9012 | else if (SCM_FRACTIONP (z)) |
9013 | { | |
73e4de09 | 9014 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 9015 | return z; |
a285b18c MW |
9016 | return scm_i_make_ratio_already_reduced |
9017 | (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), | |
9018 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 | 9019 | } |
0aacf84e | 9020 | else |
2519490c | 9021 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 9022 | } |
2519490c | 9023 | #undef FUNC_NAME |
0f2d19dd JB |
9024 | |
9025 | ||
2519490c MW |
9026 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
9027 | (SCM z), | |
9028 | "Return the angle of the complex number @var{z}.") | |
9029 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 9030 | { |
c8ae173e | 9031 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 9032 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
9033 | But if atan2 follows the floating point rounding mode, then the value |
9034 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 9035 | if (SCM_I_INUMP (z)) |
0aacf84e | 9036 | { |
e11e83f3 | 9037 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 9038 | return flo0; |
0aacf84e | 9039 | else |
55f26379 | 9040 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 9041 | } |
0aacf84e MD |
9042 | else if (SCM_BIGP (z)) |
9043 | { | |
9044 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9045 | scm_remember_upto_here_1 (z); | |
9046 | if (sgn < 0) | |
55f26379 | 9047 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 9048 | else |
e7efe8e7 | 9049 | return flo0; |
0f2d19dd | 9050 | } |
0aacf84e | 9051 | else if (SCM_REALP (z)) |
c8ae173e | 9052 | { |
10a97755 MW |
9053 | double x = SCM_REAL_VALUE (z); |
9054 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
e7efe8e7 | 9055 | return flo0; |
c8ae173e | 9056 | else |
55f26379 | 9057 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 9058 | } |
0aacf84e | 9059 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9060 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
9061 | else if (SCM_FRACTIONP (z)) |
9062 | { | |
73e4de09 | 9063 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 9064 | return flo0; |
55f26379 | 9065 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 9066 | } |
0aacf84e | 9067 | else |
2519490c | 9068 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 9069 | } |
2519490c | 9070 | #undef FUNC_NAME |
0f2d19dd JB |
9071 | |
9072 | ||
2519490c MW |
9073 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
9074 | (SCM z), | |
9075 | "Convert the number @var{z} to its inexact representation.\n") | |
9076 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 9077 | { |
e11e83f3 | 9078 | if (SCM_I_INUMP (z)) |
55f26379 | 9079 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 9080 | else if (SCM_BIGP (z)) |
55f26379 | 9081 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 9082 | else if (SCM_FRACTIONP (z)) |
55f26379 | 9083 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
9084 | else if (SCM_INEXACTP (z)) |
9085 | return z; | |
9086 | else | |
2519490c | 9087 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 9088 | } |
2519490c | 9089 | #undef FUNC_NAME |
3c9a524f DH |
9090 | |
9091 | ||
2519490c MW |
9092 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
9093 | (SCM z), | |
9094 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 9095 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 9096 | { |
c7218482 | 9097 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 9098 | return z; |
c7218482 | 9099 | else |
0aacf84e | 9100 | { |
c7218482 MW |
9101 | double val; |
9102 | ||
9103 | if (SCM_REALP (z)) | |
9104 | val = SCM_REAL_VALUE (z); | |
9105 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
9106 | val = SCM_COMPLEX_REAL (z); | |
9107 | else | |
9108 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
9109 | ||
9110 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 9111 | SCM_OUT_OF_RANGE (1, z); |
24475b86 MW |
9112 | else if (val == 0.0) |
9113 | return SCM_INUM0; | |
2be24db4 | 9114 | else |
f92e85f7 | 9115 | { |
24475b86 MW |
9116 | int expon; |
9117 | SCM numerator; | |
9118 | ||
9119 | numerator = scm_i_dbl2big (ldexp (frexp (val, &expon), | |
9120 | DBL_MANT_DIG)); | |
9121 | expon -= DBL_MANT_DIG; | |
9122 | if (expon < 0) | |
9123 | { | |
9124 | int shift = mpz_scan1 (SCM_I_BIG_MPZ (numerator), 0); | |
9125 | ||
9126 | if (shift > -expon) | |
9127 | shift = -expon; | |
9128 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (numerator), | |
9129 | SCM_I_BIG_MPZ (numerator), | |
9130 | shift); | |
9131 | expon += shift; | |
9132 | } | |
9133 | numerator = scm_i_normbig (numerator); | |
9134 | if (expon < 0) | |
9135 | return scm_i_make_ratio_already_reduced | |
9136 | (numerator, left_shift_exact_integer (SCM_INUM1, -expon)); | |
9137 | else if (expon > 0) | |
9138 | return left_shift_exact_integer (numerator, expon); | |
9139 | else | |
9140 | return numerator; | |
f92e85f7 | 9141 | } |
c2ff8ab0 | 9142 | } |
0f2d19dd | 9143 | } |
1bbd0b84 | 9144 | #undef FUNC_NAME |
0f2d19dd | 9145 | |
f92e85f7 | 9146 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
9147 | (SCM x, SCM eps), |
9148 | "Returns the @emph{simplest} rational number differing\n" | |
9149 | "from @var{x} by no more than @var{eps}.\n" | |
9150 | "\n" | |
9151 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9152 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9153 | "to use @code{inexact->exact} on the arguments.\n" | |
9154 | "\n" | |
9155 | "@lisp\n" | |
9156 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9157 | "@result{} 6/5\n" | |
9158 | "@end lisp") | |
f92e85f7 MV |
9159 | #define FUNC_NAME s_scm_rationalize |
9160 | { | |
605f6980 MW |
9161 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9162 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9163 | eps = scm_abs (eps); | |
9164 | if (scm_is_false (scm_positive_p (eps))) | |
9165 | { | |
9166 | /* eps is either zero or a NaN */ | |
9167 | if (scm_is_true (scm_nan_p (eps))) | |
9168 | return scm_nan (); | |
9169 | else if (SCM_INEXACTP (eps)) | |
9170 | return scm_exact_to_inexact (x); | |
9171 | else | |
9172 | return x; | |
9173 | } | |
9174 | else if (scm_is_false (scm_finite_p (eps))) | |
9175 | { | |
9176 | if (scm_is_true (scm_finite_p (x))) | |
9177 | return flo0; | |
9178 | else | |
9179 | return scm_nan (); | |
9180 | } | |
9181 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9182 | return x; |
605f6980 MW |
9183 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9184 | scm_ceiling (scm_difference (x, eps))))) | |
9185 | { | |
9186 | /* There's an integer within range; we want the one closest to zero */ | |
9187 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9188 | { | |
9189 | /* zero is within range */ | |
9190 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9191 | return flo0; | |
9192 | else | |
9193 | return SCM_INUM0; | |
9194 | } | |
9195 | else if (scm_is_true (scm_positive_p (x))) | |
9196 | return scm_ceiling (scm_difference (x, eps)); | |
9197 | else | |
9198 | return scm_floor (scm_sum (x, eps)); | |
9199 | } | |
9200 | else | |
f92e85f7 MV |
9201 | { |
9202 | /* Use continued fractions to find closest ratio. All | |
9203 | arithmetic is done with exact numbers. | |
9204 | */ | |
9205 | ||
9206 | SCM ex = scm_inexact_to_exact (x); | |
9207 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9208 | SCM tt = SCM_INUM1; |
9209 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9210 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9211 | SCM rx; |
9212 | int i = 0; | |
9213 | ||
f92e85f7 MV |
9214 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9215 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9216 | ||
9217 | /* We stop after a million iterations just to be absolutely sure | |
9218 | that we don't go into an infinite loop. The process normally | |
9219 | converges after less than a dozen iterations. | |
9220 | */ | |
9221 | ||
f92e85f7 MV |
9222 | while (++i < 1000000) |
9223 | { | |
9224 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9225 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9226 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9227 | scm_is_false | |
f92e85f7 | 9228 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9229 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9230 | { |
9231 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9232 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9233 | return scm_exact_to_inexact (res); |
9234 | else | |
9235 | return res; | |
9236 | } | |
f92e85f7 MV |
9237 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9238 | SCM_UNDEFINED); | |
9239 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9240 | a2 = a1; | |
9241 | b2 = b1; | |
9242 | a1 = a; | |
9243 | b1 = b; | |
9244 | } | |
9245 | scm_num_overflow (s_scm_rationalize); | |
9246 | } | |
f92e85f7 MV |
9247 | } |
9248 | #undef FUNC_NAME | |
9249 | ||
73e4de09 MV |
9250 | /* conversion functions */ |
9251 | ||
9252 | int | |
9253 | scm_is_integer (SCM val) | |
9254 | { | |
9255 | return scm_is_true (scm_integer_p (val)); | |
9256 | } | |
9257 | ||
9258 | int | |
9259 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9260 | { | |
e11e83f3 | 9261 | if (SCM_I_INUMP (val)) |
73e4de09 | 9262 | { |
e11e83f3 | 9263 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9264 | return n >= min && n <= max; |
9265 | } | |
9266 | else if (SCM_BIGP (val)) | |
9267 | { | |
9268 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9269 | return 0; | |
9270 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9271 | { |
9272 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9273 | { | |
9274 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9275 | return n >= min && n <= max; | |
9276 | } | |
9277 | else | |
9278 | return 0; | |
9279 | } | |
73e4de09 MV |
9280 | else |
9281 | { | |
d956fa6f MV |
9282 | scm_t_intmax n; |
9283 | size_t count; | |
73e4de09 | 9284 | |
d956fa6f MV |
9285 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9286 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9287 | return 0; | |
9288 | ||
9289 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9290 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9291 | |
d956fa6f | 9292 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9293 | { |
d956fa6f MV |
9294 | if (n < 0) |
9295 | return 0; | |
73e4de09 | 9296 | } |
73e4de09 MV |
9297 | else |
9298 | { | |
d956fa6f MV |
9299 | n = -n; |
9300 | if (n >= 0) | |
9301 | return 0; | |
73e4de09 | 9302 | } |
d956fa6f MV |
9303 | |
9304 | return n >= min && n <= max; | |
73e4de09 MV |
9305 | } |
9306 | } | |
73e4de09 MV |
9307 | else |
9308 | return 0; | |
9309 | } | |
9310 | ||
9311 | int | |
9312 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9313 | { | |
e11e83f3 | 9314 | if (SCM_I_INUMP (val)) |
73e4de09 | 9315 | { |
e11e83f3 | 9316 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9317 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9318 | } | |
9319 | else if (SCM_BIGP (val)) | |
9320 | { | |
9321 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9322 | return 0; | |
9323 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9324 | { |
9325 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9326 | { | |
9327 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9328 | return n >= min && n <= max; | |
9329 | } | |
9330 | else | |
9331 | return 0; | |
9332 | } | |
73e4de09 MV |
9333 | else |
9334 | { | |
d956fa6f MV |
9335 | scm_t_uintmax n; |
9336 | size_t count; | |
73e4de09 | 9337 | |
d956fa6f MV |
9338 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9339 | return 0; | |
73e4de09 | 9340 | |
d956fa6f MV |
9341 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9342 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9343 | return 0; |
d956fa6f MV |
9344 | |
9345 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9346 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9347 | |
d956fa6f | 9348 | return n >= min && n <= max; |
73e4de09 MV |
9349 | } |
9350 | } | |
73e4de09 MV |
9351 | else |
9352 | return 0; | |
9353 | } | |
9354 | ||
1713d319 MV |
9355 | static void |
9356 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9357 | { | |
9358 | scm_error (scm_out_of_range_key, | |
9359 | NULL, | |
9360 | "Value out of range ~S to ~S: ~S", | |
9361 | scm_list_3 (min, max, bad_val), | |
9362 | scm_list_1 (bad_val)); | |
9363 | } | |
9364 | ||
bfd7932e MV |
9365 | #define TYPE scm_t_intmax |
9366 | #define TYPE_MIN min | |
9367 | #define TYPE_MAX max | |
9368 | #define SIZEOF_TYPE 0 | |
9369 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9370 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9371 | #include "libguile/conv-integer.i.c" | |
9372 | ||
9373 | #define TYPE scm_t_uintmax | |
9374 | #define TYPE_MIN min | |
9375 | #define TYPE_MAX max | |
9376 | #define SIZEOF_TYPE 0 | |
9377 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9378 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9379 | #include "libguile/conv-uinteger.i.c" | |
9380 | ||
9381 | #define TYPE scm_t_int8 | |
9382 | #define TYPE_MIN SCM_T_INT8_MIN | |
9383 | #define TYPE_MAX SCM_T_INT8_MAX | |
9384 | #define SIZEOF_TYPE 1 | |
9385 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9386 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9387 | #include "libguile/conv-integer.i.c" | |
9388 | ||
9389 | #define TYPE scm_t_uint8 | |
9390 | #define TYPE_MIN 0 | |
9391 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9392 | #define SIZEOF_TYPE 1 | |
9393 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9394 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9395 | #include "libguile/conv-uinteger.i.c" | |
9396 | ||
9397 | #define TYPE scm_t_int16 | |
9398 | #define TYPE_MIN SCM_T_INT16_MIN | |
9399 | #define TYPE_MAX SCM_T_INT16_MAX | |
9400 | #define SIZEOF_TYPE 2 | |
9401 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9402 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9403 | #include "libguile/conv-integer.i.c" | |
9404 | ||
9405 | #define TYPE scm_t_uint16 | |
9406 | #define TYPE_MIN 0 | |
9407 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9408 | #define SIZEOF_TYPE 2 | |
9409 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9410 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9411 | #include "libguile/conv-uinteger.i.c" | |
9412 | ||
9413 | #define TYPE scm_t_int32 | |
9414 | #define TYPE_MIN SCM_T_INT32_MIN | |
9415 | #define TYPE_MAX SCM_T_INT32_MAX | |
9416 | #define SIZEOF_TYPE 4 | |
9417 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9418 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9419 | #include "libguile/conv-integer.i.c" | |
9420 | ||
9421 | #define TYPE scm_t_uint32 | |
9422 | #define TYPE_MIN 0 | |
9423 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9424 | #define SIZEOF_TYPE 4 | |
9425 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9426 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9427 | #include "libguile/conv-uinteger.i.c" | |
9428 | ||
904a78f1 MG |
9429 | #define TYPE scm_t_wchar |
9430 | #define TYPE_MIN (scm_t_int32)-1 | |
9431 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9432 | #define SIZEOF_TYPE 4 | |
9433 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9434 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9435 | #include "libguile/conv-integer.i.c" | |
9436 | ||
bfd7932e MV |
9437 | #define TYPE scm_t_int64 |
9438 | #define TYPE_MIN SCM_T_INT64_MIN | |
9439 | #define TYPE_MAX SCM_T_INT64_MAX | |
9440 | #define SIZEOF_TYPE 8 | |
9441 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9442 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9443 | #include "libguile/conv-integer.i.c" | |
9444 | ||
9445 | #define TYPE scm_t_uint64 | |
9446 | #define TYPE_MIN 0 | |
9447 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9448 | #define SIZEOF_TYPE 8 | |
9449 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9450 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9451 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9452 | |
cd036260 MV |
9453 | void |
9454 | scm_to_mpz (SCM val, mpz_t rop) | |
9455 | { | |
9456 | if (SCM_I_INUMP (val)) | |
9457 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9458 | else if (SCM_BIGP (val)) | |
9459 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9460 | else | |
9461 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9462 | } | |
9463 | ||
9464 | SCM | |
9465 | scm_from_mpz (mpz_t val) | |
9466 | { | |
9467 | return scm_i_mpz2num (val); | |
9468 | } | |
9469 | ||
73e4de09 MV |
9470 | int |
9471 | scm_is_real (SCM val) | |
9472 | { | |
9473 | return scm_is_true (scm_real_p (val)); | |
9474 | } | |
9475 | ||
55f26379 MV |
9476 | int |
9477 | scm_is_rational (SCM val) | |
9478 | { | |
9479 | return scm_is_true (scm_rational_p (val)); | |
9480 | } | |
9481 | ||
73e4de09 MV |
9482 | double |
9483 | scm_to_double (SCM val) | |
9484 | { | |
55f26379 MV |
9485 | if (SCM_I_INUMP (val)) |
9486 | return SCM_I_INUM (val); | |
9487 | else if (SCM_BIGP (val)) | |
9488 | return scm_i_big2dbl (val); | |
9489 | else if (SCM_FRACTIONP (val)) | |
9490 | return scm_i_fraction2double (val); | |
9491 | else if (SCM_REALP (val)) | |
9492 | return SCM_REAL_VALUE (val); | |
9493 | else | |
7a1aba42 | 9494 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9495 | } |
9496 | ||
9497 | SCM | |
9498 | scm_from_double (double val) | |
9499 | { | |
978c52d1 LC |
9500 | SCM z; |
9501 | ||
9502 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9503 | ||
9504 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9505 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9506 | |
55f26379 | 9507 | return z; |
73e4de09 MV |
9508 | } |
9509 | ||
220058a8 | 9510 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9511 | |
9512 | float | |
e25f3727 | 9513 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9514 | { |
220058a8 AW |
9515 | scm_c_issue_deprecation_warning |
9516 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9517 | ||
55f26379 MV |
9518 | if (SCM_BIGP (num)) |
9519 | { | |
9520 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9521 | if (!isinf (res)) |
55f26379 MV |
9522 | return res; |
9523 | else | |
9524 | scm_out_of_range (NULL, num); | |
9525 | } | |
9526 | else | |
9527 | return scm_to_double (num); | |
9528 | } | |
9529 | ||
9530 | double | |
e25f3727 | 9531 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9532 | { |
220058a8 AW |
9533 | scm_c_issue_deprecation_warning |
9534 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9535 | ||
55f26379 MV |
9536 | if (SCM_BIGP (num)) |
9537 | { | |
9538 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9539 | if (!isinf (res)) |
55f26379 MV |
9540 | return res; |
9541 | else | |
9542 | scm_out_of_range (NULL, num); | |
9543 | } | |
9544 | else | |
9545 | return scm_to_double (num); | |
9546 | } | |
9547 | ||
9548 | #endif | |
9549 | ||
8507ec80 MV |
9550 | int |
9551 | scm_is_complex (SCM val) | |
9552 | { | |
9553 | return scm_is_true (scm_complex_p (val)); | |
9554 | } | |
9555 | ||
9556 | double | |
9557 | scm_c_real_part (SCM z) | |
9558 | { | |
9559 | if (SCM_COMPLEXP (z)) | |
9560 | return SCM_COMPLEX_REAL (z); | |
9561 | else | |
9562 | { | |
9563 | /* Use the scm_real_part to get proper error checking and | |
9564 | dispatching. | |
9565 | */ | |
9566 | return scm_to_double (scm_real_part (z)); | |
9567 | } | |
9568 | } | |
9569 | ||
9570 | double | |
9571 | scm_c_imag_part (SCM z) | |
9572 | { | |
9573 | if (SCM_COMPLEXP (z)) | |
9574 | return SCM_COMPLEX_IMAG (z); | |
9575 | else | |
9576 | { | |
9577 | /* Use the scm_imag_part to get proper error checking and | |
9578 | dispatching. The result will almost always be 0.0, but not | |
9579 | always. | |
9580 | */ | |
9581 | return scm_to_double (scm_imag_part (z)); | |
9582 | } | |
9583 | } | |
9584 | ||
9585 | double | |
9586 | scm_c_magnitude (SCM z) | |
9587 | { | |
9588 | return scm_to_double (scm_magnitude (z)); | |
9589 | } | |
9590 | ||
9591 | double | |
9592 | scm_c_angle (SCM z) | |
9593 | { | |
9594 | return scm_to_double (scm_angle (z)); | |
9595 | } | |
9596 | ||
9597 | int | |
9598 | scm_is_number (SCM z) | |
9599 | { | |
9600 | return scm_is_true (scm_number_p (z)); | |
9601 | } | |
9602 | ||
8ab3d8a0 | 9603 | |
a5f6b751 MW |
9604 | /* Returns log(x * 2^shift) */ |
9605 | static SCM | |
9606 | log_of_shifted_double (double x, long shift) | |
9607 | { | |
9608 | double ans = log (fabs (x)) + shift * M_LN2; | |
9609 | ||
9610 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9611 | return scm_from_double (ans); | |
9612 | else | |
9613 | return scm_c_make_rectangular (ans, M_PI); | |
9614 | } | |
9615 | ||
85bdb6ac | 9616 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9617 | static SCM |
9618 | log_of_exact_integer (SCM n) | |
9619 | { | |
7f34acd8 MW |
9620 | if (SCM_I_INUMP (n)) |
9621 | return log_of_shifted_double (SCM_I_INUM (n), 0); | |
9622 | else if (SCM_BIGP (n)) | |
9623 | { | |
9624 | long expon; | |
9625 | double signif = scm_i_big2dbl_2exp (n, &expon); | |
9626 | return log_of_shifted_double (signif, expon); | |
9627 | } | |
9628 | else | |
9629 | scm_wrong_type_arg ("log_of_exact_integer", SCM_ARG1, n); | |
a5f6b751 MW |
9630 | } |
9631 | ||
9632 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9633 | static SCM | |
9634 | log_of_fraction (SCM n, SCM d) | |
9635 | { | |
9636 | long n_size = scm_to_long (scm_integer_length (n)); | |
9637 | long d_size = scm_to_long (scm_integer_length (d)); | |
9638 | ||
9639 | if (abs (n_size - d_size) > 1) | |
7f34acd8 MW |
9640 | return (scm_difference (log_of_exact_integer (n), |
9641 | log_of_exact_integer (d))); | |
a5f6b751 MW |
9642 | else if (scm_is_false (scm_negative_p (n))) |
9643 | return scm_from_double | |
9644 | (log1p (scm_to_double (scm_divide2real (scm_difference (n, d), d)))); | |
9645 | else | |
9646 | return scm_c_make_rectangular | |
9647 | (log1p (scm_to_double (scm_divide2real | |
9648 | (scm_difference (scm_abs (n), d), | |
9649 | d))), | |
9650 | M_PI); | |
9651 | } | |
9652 | ||
9653 | ||
8ab3d8a0 KR |
9654 | /* In the following functions we dispatch to the real-arg funcs like log() |
9655 | when we know the arg is real, instead of just handing everything to | |
9656 | clog() for instance. This is in case clog() doesn't optimize for a | |
9657 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9658 | well use it to go straight to the applicable C func. */ | |
9659 | ||
2519490c MW |
9660 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9661 | (SCM z), | |
9662 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9663 | #define FUNC_NAME s_scm_log |
9664 | { | |
9665 | if (SCM_COMPLEXP (z)) | |
9666 | { | |
03976fee AW |
9667 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9668 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9669 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9670 | #else | |
9671 | double re = SCM_COMPLEX_REAL (z); | |
9672 | double im = SCM_COMPLEX_IMAG (z); | |
9673 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9674 | atan2 (im, re)); | |
9675 | #endif | |
9676 | } | |
a5f6b751 MW |
9677 | else if (SCM_REALP (z)) |
9678 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9679 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9680 | { |
a5f6b751 MW |
9681 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9682 | if (scm_is_eq (z, SCM_INUM0)) | |
9683 | scm_num_overflow (s_scm_log); | |
9684 | #endif | |
9685 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9686 | } |
a5f6b751 MW |
9687 | else if (SCM_BIGP (z)) |
9688 | return log_of_exact_integer (z); | |
9689 | else if (SCM_FRACTIONP (z)) | |
9690 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9691 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9692 | else |
9693 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9694 | } |
9695 | #undef FUNC_NAME | |
9696 | ||
9697 | ||
2519490c MW |
9698 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9699 | (SCM z), | |
9700 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9701 | #define FUNC_NAME s_scm_log10 |
9702 | { | |
9703 | if (SCM_COMPLEXP (z)) | |
9704 | { | |
9705 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9706 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9707 | log10+hypot+atan2.) */ | |
f328f862 LC |
9708 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9709 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9710 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9711 | #else | |
9712 | double re = SCM_COMPLEX_REAL (z); | |
9713 | double im = SCM_COMPLEX_IMAG (z); | |
9714 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9715 | M_LOG10E * atan2 (im, re)); | |
9716 | #endif | |
9717 | } | |
a5f6b751 | 9718 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9719 | { |
a5f6b751 MW |
9720 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9721 | if (scm_is_eq (z, SCM_INUM0)) | |
9722 | scm_num_overflow (s_scm_log10); | |
9723 | #endif | |
9724 | { | |
9725 | double re = scm_to_double (z); | |
9726 | double l = log10 (fabs (re)); | |
9727 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9728 | return scm_from_double (l); | |
9729 | else | |
9730 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9731 | } | |
8ab3d8a0 | 9732 | } |
a5f6b751 MW |
9733 | else if (SCM_BIGP (z)) |
9734 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9735 | else if (SCM_FRACTIONP (z)) | |
9736 | return scm_product (flo_log10e, | |
9737 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9738 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9739 | else |
9740 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9741 | } |
9742 | #undef FUNC_NAME | |
9743 | ||
9744 | ||
2519490c MW |
9745 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9746 | (SCM z), | |
9747 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9748 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9749 | #define FUNC_NAME s_scm_exp |
9750 | { | |
9751 | if (SCM_COMPLEXP (z)) | |
9752 | { | |
93723f3d MW |
9753 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9754 | && defined (SCM_COMPLEX_VALUE) | |
9755 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); | |
9756 | #else | |
8ab3d8a0 KR |
9757 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), |
9758 | SCM_COMPLEX_IMAG (z)); | |
93723f3d | 9759 | #endif |
8ab3d8a0 | 9760 | } |
2519490c | 9761 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9762 | { |
9763 | /* When z is a negative bignum the conversion to double overflows, | |
9764 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9765 | return scm_from_double (exp (scm_to_double (z))); | |
9766 | } | |
2519490c MW |
9767 | else |
9768 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9769 | } |
9770 | #undef FUNC_NAME | |
9771 | ||
9772 | ||
882c8963 MW |
9773 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9774 | (SCM k), | |
9775 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9776 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9777 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9778 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9779 | "\n" | |
9780 | "@lisp\n" | |
9781 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9782 | "@end lisp") | |
9783 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9784 | { | |
9785 | SCM s, r; | |
9786 | ||
9787 | scm_exact_integer_sqrt (k, &s, &r); | |
9788 | return scm_values (scm_list_2 (s, r)); | |
9789 | } | |
9790 | #undef FUNC_NAME | |
9791 | ||
9792 | void | |
9793 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9794 | { | |
9795 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9796 | { | |
9797 | scm_t_inum kk = SCM_I_INUM (k); | |
9798 | scm_t_inum uu = kk; | |
9799 | scm_t_inum ss; | |
9800 | ||
9801 | if (SCM_LIKELY (kk > 0)) | |
9802 | { | |
9803 | do | |
9804 | { | |
9805 | ss = uu; | |
9806 | uu = (ss + kk/ss) / 2; | |
9807 | } while (uu < ss); | |
9808 | *sp = SCM_I_MAKINUM (ss); | |
9809 | *rp = SCM_I_MAKINUM (kk - ss*ss); | |
9810 | } | |
9811 | else if (SCM_LIKELY (kk == 0)) | |
9812 | *sp = *rp = SCM_INUM0; | |
9813 | else | |
9814 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9815 | "exact non-negative integer"); | |
9816 | } | |
9817 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9818 | { | |
9819 | SCM s, r; | |
9820 | ||
9821 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9822 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9823 | "exact non-negative integer"); | |
9824 | s = scm_i_mkbig (); | |
9825 | r = scm_i_mkbig (); | |
9826 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9827 | scm_remember_upto_here_1 (k); | |
9828 | *sp = scm_i_normbig (s); | |
9829 | *rp = scm_i_normbig (r); | |
9830 | } | |
9831 | else | |
9832 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9833 | "exact non-negative integer"); | |
9834 | } | |
9835 | ||
9836 | ||
2519490c MW |
9837 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9838 | (SCM z), | |
9839 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9840 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9841 | "is returned, or if that's zero then a positive imaginary part.\n" |
9842 | "Thus,\n" | |
9843 | "\n" | |
9844 | "@example\n" | |
9845 | "(sqrt 9.0) @result{} 3.0\n" | |
9846 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9847 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9848 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9849 | "@end example") | |
8ab3d8a0 KR |
9850 | #define FUNC_NAME s_scm_sqrt |
9851 | { | |
2519490c | 9852 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9853 | { |
f328f862 LC |
9854 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9855 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9856 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9857 | #else |
2519490c MW |
9858 | double re = SCM_COMPLEX_REAL (z); |
9859 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9860 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9861 | 0.5 * atan2 (im, re)); | |
9862 | #endif | |
9863 | } | |
2519490c | 9864 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9865 | { |
2519490c | 9866 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9867 | if (xx < 0) |
9868 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9869 | else | |
9870 | return scm_from_double (sqrt (xx)); | |
9871 | } | |
2519490c MW |
9872 | else |
9873 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
9874 | } |
9875 | #undef FUNC_NAME | |
9876 | ||
9877 | ||
9878 | ||
0f2d19dd JB |
9879 | void |
9880 | scm_init_numbers () | |
0f2d19dd | 9881 | { |
0b799eea MV |
9882 | int i; |
9883 | ||
b57bf272 AW |
9884 | if (scm_install_gmp_memory_functions) |
9885 | mp_set_memory_functions (custom_gmp_malloc, | |
9886 | custom_gmp_realloc, | |
9887 | custom_gmp_free); | |
9888 | ||
713a4259 KR |
9889 | mpz_init_set_si (z_negative_one, -1); |
9890 | ||
a261c0e9 DH |
9891 | /* It may be possible to tune the performance of some algorithms by using |
9892 | * the following constants to avoid the creation of bignums. Please, before | |
9893 | * using these values, remember the two rules of program optimization: | |
9894 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9895 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9896 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9897 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9898 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9899 | |
f3ae5d60 MD |
9900 | scm_add_feature ("complex"); |
9901 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9902 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9903 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea MV |
9904 | |
9905 | /* determine floating point precision */ | |
55f26379 | 9906 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
9907 | { |
9908 | init_dblprec(&scm_dblprec[i-2],i); | |
9909 | init_fx_radix(fx_per_radix[i-2],i); | |
9910 | } | |
f872b822 | 9911 | #ifdef DBL_DIG |
0b799eea | 9912 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 9913 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 9914 | #endif |
1be6b49c | 9915 | |
cff5fa33 | 9916 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 9917 | #include "libguile/numbers.x" |
0f2d19dd | 9918 | } |
89e00824 ML |
9919 | |
9920 | /* | |
9921 | Local Variables: | |
9922 | c-file-style: "gnu" | |
9923 | End: | |
9924 | */ |