Commit | Line | Data |
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75ba64d6 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e | 7 | * This library is free software; you can redistribute it and/or |
53befeb7 NJ |
8 | * modify it under the terms of the GNU Lesser General Public License |
9 | * as published by the Free Software Foundation; either version 3 of | |
10 | * the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
53befeb7 NJ |
12 | * This library is distributed in the hope that it will be useful, but |
13 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |
73be1d9e MV |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
53befeb7 NJ |
19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
20 | * 02110-1301 USA | |
73be1d9e | 21 | */ |
1bbd0b84 | 22 | |
0f2d19dd | 23 | \f |
ca46fb90 | 24 | /* General assumptions: |
ca46fb90 RB |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
c7218482 | 28 | * XXX What about infinities? They are equal to their own floor! -mhw |
f92e85f7 | 29 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
30 | */ |
31 | ||
32 | /* TODO: | |
33 | ||
34 | - see if special casing bignums and reals in integer-exponent when | |
35 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
36 | ||
37 | - look in to better short-circuiting of common cases in | |
38 | integer-expt and elsewhere. | |
39 | ||
40 | - see if direct mpz operations can help in ash and elsewhere. | |
41 | ||
42 | */ | |
0f2d19dd | 43 | |
dbb605f5 | 44 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
45 | # include <config.h> |
46 | #endif | |
47 | ||
bbec4602 LC |
48 | #include <verify.h> |
49 | ||
0f2d19dd | 50 | #include <math.h> |
fc194577 | 51 | #include <string.h> |
3f47e526 MG |
52 | #include <unicase.h> |
53 | #include <unictype.h> | |
f92e85f7 | 54 | |
8ab3d8a0 KR |
55 | #if HAVE_COMPLEX_H |
56 | #include <complex.h> | |
57 | #endif | |
58 | ||
a0599745 | 59 | #include "libguile/_scm.h" |
a0599745 MD |
60 | #include "libguile/feature.h" |
61 | #include "libguile/ports.h" | |
62 | #include "libguile/root.h" | |
63 | #include "libguile/smob.h" | |
64 | #include "libguile/strings.h" | |
864e7d42 | 65 | #include "libguile/bdw-gc.h" |
a0599745 MD |
66 | |
67 | #include "libguile/validate.h" | |
68 | #include "libguile/numbers.h" | |
1be6b49c | 69 | #include "libguile/deprecation.h" |
f4c627b3 | 70 | |
f92e85f7 MV |
71 | #include "libguile/eq.h" |
72 | ||
8ab3d8a0 KR |
73 | /* values per glibc, if not already defined */ |
74 | #ifndef M_LOG10E | |
75 | #define M_LOG10E 0.43429448190325182765 | |
76 | #endif | |
85bdb6ac MW |
77 | #ifndef M_LN2 |
78 | #define M_LN2 0.69314718055994530942 | |
79 | #endif | |
8ab3d8a0 KR |
80 | #ifndef M_PI |
81 | #define M_PI 3.14159265358979323846 | |
82 | #endif | |
83 | ||
cba521fe MW |
84 | /* FIXME: We assume that FLT_RADIX is 2 */ |
85 | verify (FLT_RADIX == 2); | |
86 | ||
e25f3727 AW |
87 | typedef scm_t_signed_bits scm_t_inum; |
88 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
89 | ||
7112615f MW |
90 | /* Tests to see if a C double is neither infinite nor a NaN. |
91 | TODO: if it's available, use C99's isfinite(x) instead */ | |
92 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
93 | ||
041fccf6 MW |
94 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
95 | of the infinity, but other platforms return a boolean only. */ | |
96 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
97 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
98 | ||
0f2d19dd | 99 | \f |
f4c627b3 | 100 | |
ca46fb90 RB |
101 | /* |
102 | Wonder if this might be faster for some of our code? A switch on | |
103 | the numtag would jump directly to the right case, and the | |
104 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
105 | ||
106 | #define SCM_I_NUMTAG_NOTNUM 0 | |
107 | #define SCM_I_NUMTAG_INUM 1 | |
108 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
109 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
110 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
111 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 112 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 113 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 114 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
115 | : SCM_I_NUMTAG_NOTNUM))) |
116 | */ | |
f92e85f7 | 117 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
118 | |
119 | ||
b57bf272 AW |
120 | /* Default to 1, because as we used to hard-code `free' as the |
121 | deallocator, we know that overriding these functions with | |
122 | instrumented `malloc' / `free' is OK. */ | |
123 | int scm_install_gmp_memory_functions = 1; | |
e7efe8e7 | 124 | static SCM flo0; |
ff62c168 | 125 | static SCM exactly_one_half; |
a5f6b751 | 126 | static SCM flo_log10e; |
e7efe8e7 | 127 | |
34d19ef6 | 128 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 129 | |
56e55ac7 | 130 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
131 | * printed or scm_string representation of an inexact number. |
132 | */ | |
0b799eea | 133 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 134 | |
b127c712 | 135 | |
ad79736c AW |
136 | #if !defined (HAVE_ASINH) |
137 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
138 | #endif | |
139 | #if !defined (HAVE_ACOSH) | |
140 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
141 | #endif | |
142 | #if !defined (HAVE_ATANH) | |
143 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
144 | #endif | |
145 | ||
18d78c5e MW |
146 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
147 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released | |
148 | in March 2006), mpz_cmp_d now handles infinities properly. */ | |
f8a8200b | 149 | #if 1 |
b127c712 | 150 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 151 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
152 | #else |
153 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
154 | #endif | |
155 | ||
f92e85f7 | 156 | |
4b26c03e | 157 | #if defined (GUILE_I) |
03976fee | 158 | #if defined HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
159 | |
160 | /* For an SCM object Z which is a complex number (ie. satisfies | |
161 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
162 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 163 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 164 | |
7a35784c | 165 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
166 | |
167 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 168 | static inline SCM |
8ab3d8a0 KR |
169 | scm_from_complex_double (complex double z) |
170 | { | |
171 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
172 | } | |
bca69a9f | 173 | |
8ab3d8a0 | 174 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 175 | #endif /* GUILE_I */ |
8ab3d8a0 | 176 | |
0f2d19dd JB |
177 | \f |
178 | ||
713a4259 | 179 | static mpz_t z_negative_one; |
ac0c002c DH |
180 | |
181 | \f | |
b57bf272 | 182 | |
864e7d42 LC |
183 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
184 | static void | |
6922d92f | 185 | finalize_bignum (void *ptr, void *data) |
864e7d42 LC |
186 | { |
187 | SCM bignum; | |
188 | ||
189 | bignum = PTR2SCM (ptr); | |
190 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
191 | } | |
192 | ||
b57bf272 AW |
193 | /* The next three functions (custom_libgmp_*) are passed to |
194 | mp_set_memory_functions (in GMP) so that memory used by the digits | |
195 | themselves is known to the garbage collector. This is needed so | |
196 | that GC will be run at appropriate times. Otherwise, a program which | |
197 | creates many large bignums would malloc a huge amount of memory | |
198 | before the GC runs. */ | |
199 | static void * | |
200 | custom_gmp_malloc (size_t alloc_size) | |
201 | { | |
202 | return scm_malloc (alloc_size); | |
203 | } | |
204 | ||
205 | static void * | |
206 | custom_gmp_realloc (void *old_ptr, size_t old_size, size_t new_size) | |
207 | { | |
208 | return scm_realloc (old_ptr, new_size); | |
209 | } | |
210 | ||
211 | static void | |
212 | custom_gmp_free (void *ptr, size_t size) | |
213 | { | |
214 | free (ptr); | |
215 | } | |
216 | ||
217 | ||
d017fcdf LC |
218 | /* Return a new uninitialized bignum. */ |
219 | static inline SCM | |
220 | make_bignum (void) | |
221 | { | |
222 | scm_t_bits *p; | |
223 | ||
224 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
225 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
226 | "bignum"); | |
227 | p[0] = scm_tc16_big; | |
228 | ||
75ba64d6 | 229 | scm_i_set_finalizer (p, finalize_bignum, NULL); |
864e7d42 | 230 | |
d017fcdf LC |
231 | return SCM_PACK (p); |
232 | } | |
ac0c002c | 233 | |
864e7d42 | 234 | |
189171c5 | 235 | SCM |
ca46fb90 RB |
236 | scm_i_mkbig () |
237 | { | |
238 | /* Return a newly created bignum. */ | |
d017fcdf | 239 | SCM z = make_bignum (); |
ca46fb90 RB |
240 | mpz_init (SCM_I_BIG_MPZ (z)); |
241 | return z; | |
242 | } | |
243 | ||
e25f3727 AW |
244 | static SCM |
245 | scm_i_inum2big (scm_t_inum x) | |
246 | { | |
247 | /* Return a newly created bignum initialized to X. */ | |
248 | SCM z = make_bignum (); | |
249 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
250 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
251 | #else | |
252 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
253 | mpz_*_si invocations in Guile. */ | |
254 | #error creation of mpz not implemented for this inum size | |
255 | #endif | |
256 | return z; | |
257 | } | |
258 | ||
189171c5 | 259 | SCM |
c71b0706 MV |
260 | scm_i_long2big (long x) |
261 | { | |
262 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 263 | SCM z = make_bignum (); |
c71b0706 MV |
264 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
265 | return z; | |
266 | } | |
267 | ||
189171c5 | 268 | SCM |
c71b0706 MV |
269 | scm_i_ulong2big (unsigned long x) |
270 | { | |
271 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 272 | SCM z = make_bignum (); |
c71b0706 MV |
273 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
274 | return z; | |
275 | } | |
276 | ||
189171c5 | 277 | SCM |
ca46fb90 RB |
278 | scm_i_clonebig (SCM src_big, int same_sign_p) |
279 | { | |
280 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 281 | SCM z = make_bignum (); |
ca46fb90 | 282 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
283 | if (!same_sign_p) |
284 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
285 | return z; |
286 | } | |
287 | ||
189171c5 | 288 | int |
ca46fb90 RB |
289 | scm_i_bigcmp (SCM x, SCM y) |
290 | { | |
291 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
292 | /* presume we already know x and y are bignums */ | |
293 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
294 | scm_remember_upto_here_2 (x, y); | |
295 | return result; | |
296 | } | |
297 | ||
189171c5 | 298 | SCM |
ca46fb90 RB |
299 | scm_i_dbl2big (double d) |
300 | { | |
301 | /* results are only defined if d is an integer */ | |
d017fcdf | 302 | SCM z = make_bignum (); |
ca46fb90 RB |
303 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
304 | return z; | |
305 | } | |
306 | ||
f92e85f7 MV |
307 | /* Convert a integer in double representation to a SCM number. */ |
308 | ||
189171c5 | 309 | SCM |
f92e85f7 MV |
310 | scm_i_dbl2num (double u) |
311 | { | |
312 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
313 | powers of 2, so there's no rounding when making "double" values | |
314 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
315 | get rounded on a 64-bit machine, hence the "+1". | |
316 | ||
317 | The use of floor() to force to an integer value ensures we get a | |
318 | "numerically closest" value without depending on how a | |
319 | double->long cast or how mpz_set_d will round. For reference, | |
320 | double->long probably follows the hardware rounding mode, | |
321 | mpz_set_d truncates towards zero. */ | |
322 | ||
323 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
324 | representable as a double? */ | |
325 | ||
326 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
327 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 328 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
329 | else |
330 | return scm_i_dbl2big (u); | |
331 | } | |
332 | ||
1eb6a33a MW |
333 | static SCM round_right_shift_exact_integer (SCM n, long count); |
334 | ||
335 | /* scm_i_big2dbl_2exp() is like frexp for bignums: it converts the | |
336 | bignum b into a normalized significand and exponent such that | |
337 | b = significand * 2^exponent and 1/2 <= abs(significand) < 1. | |
338 | The return value is the significand rounded to the closest | |
339 | representable double, and the exponent is placed into *expon_p. | |
340 | If b is zero, then the returned exponent and significand are both | |
341 | zero. */ | |
342 | ||
343 | static double | |
344 | scm_i_big2dbl_2exp (SCM b, long *expon_p) | |
ca46fb90 | 345 | { |
1eb6a33a MW |
346 | size_t bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); |
347 | size_t shift = 0; | |
089c9a59 KR |
348 | |
349 | if (bits > DBL_MANT_DIG) | |
350 | { | |
1eb6a33a MW |
351 | shift = bits - DBL_MANT_DIG; |
352 | b = round_right_shift_exact_integer (b, shift); | |
353 | if (SCM_I_INUMP (b)) | |
089c9a59 | 354 | { |
1eb6a33a MW |
355 | int expon; |
356 | double signif = frexp (SCM_I_INUM (b), &expon); | |
357 | *expon_p = expon + shift; | |
358 | return signif; | |
089c9a59 KR |
359 | } |
360 | } | |
361 | ||
1eb6a33a MW |
362 | { |
363 | long expon; | |
364 | double signif = mpz_get_d_2exp (&expon, SCM_I_BIG_MPZ (b)); | |
365 | scm_remember_upto_here_1 (b); | |
366 | *expon_p = expon + shift; | |
367 | return signif; | |
368 | } | |
369 | } | |
370 | ||
371 | /* scm_i_big2dbl() rounds to the closest representable double, | |
372 | in accordance with R5RS exact->inexact. */ | |
373 | double | |
374 | scm_i_big2dbl (SCM b) | |
375 | { | |
376 | long expon; | |
377 | double signif = scm_i_big2dbl_2exp (b, &expon); | |
378 | return ldexp (signif, expon); | |
ca46fb90 RB |
379 | } |
380 | ||
189171c5 | 381 | SCM |
ca46fb90 RB |
382 | scm_i_normbig (SCM b) |
383 | { | |
384 | /* convert a big back to a fixnum if it'll fit */ | |
385 | /* presume b is a bignum */ | |
386 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
387 | { | |
e25f3727 | 388 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 389 | if (SCM_FIXABLE (val)) |
d956fa6f | 390 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
391 | } |
392 | return b; | |
393 | } | |
f872b822 | 394 | |
f92e85f7 MV |
395 | static SCM_C_INLINE_KEYWORD SCM |
396 | scm_i_mpz2num (mpz_t b) | |
397 | { | |
398 | /* convert a mpz number to a SCM number. */ | |
399 | if (mpz_fits_slong_p (b)) | |
400 | { | |
e25f3727 | 401 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 402 | if (SCM_FIXABLE (val)) |
d956fa6f | 403 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
404 | } |
405 | ||
406 | { | |
d017fcdf | 407 | SCM z = make_bignum (); |
f92e85f7 MV |
408 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
409 | return z; | |
410 | } | |
411 | } | |
412 | ||
a285b18c MW |
413 | /* Make the ratio NUMERATOR/DENOMINATOR, where: |
414 | 1. NUMERATOR and DENOMINATOR are exact integers | |
415 | 2. NUMERATOR and DENOMINATOR are reduced to lowest terms: gcd(n,d) == 1 */ | |
cba42c93 | 416 | static SCM |
a285b18c | 417 | scm_i_make_ratio_already_reduced (SCM numerator, SCM denominator) |
f92e85f7 | 418 | { |
a285b18c MW |
419 | /* Flip signs so that the denominator is positive. */ |
420 | if (scm_is_false (scm_positive_p (denominator))) | |
f92e85f7 | 421 | { |
a285b18c | 422 | if (SCM_UNLIKELY (scm_is_eq (denominator, SCM_INUM0))) |
f92e85f7 | 423 | scm_num_overflow ("make-ratio"); |
a285b18c | 424 | else |
f92e85f7 | 425 | { |
a285b18c MW |
426 | numerator = scm_difference (numerator, SCM_UNDEFINED); |
427 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
f92e85f7 MV |
428 | } |
429 | } | |
a285b18c MW |
430 | |
431 | /* Check for the integer case */ | |
432 | if (scm_is_eq (denominator, SCM_INUM1)) | |
433 | return numerator; | |
434 | ||
435 | return scm_double_cell (scm_tc16_fraction, | |
436 | SCM_UNPACK (numerator), | |
437 | SCM_UNPACK (denominator), 0); | |
438 | } | |
439 | ||
440 | static SCM scm_exact_integer_quotient (SCM x, SCM y); | |
441 | ||
442 | /* Make the ratio NUMERATOR/DENOMINATOR */ | |
443 | static SCM | |
444 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
445 | #define FUNC_NAME "make-ratio" | |
446 | { | |
447 | /* Make sure the arguments are proper */ | |
448 | if (!SCM_LIKELY (SCM_I_INUMP (numerator) || SCM_BIGP (numerator))) | |
449 | SCM_WRONG_TYPE_ARG (1, numerator); | |
450 | else if (!SCM_LIKELY (SCM_I_INUMP (denominator) || SCM_BIGP (denominator))) | |
451 | SCM_WRONG_TYPE_ARG (2, denominator); | |
452 | else | |
f92e85f7 | 453 | { |
a285b18c MW |
454 | SCM the_gcd = scm_gcd (numerator, denominator); |
455 | if (!(scm_is_eq (the_gcd, SCM_INUM1))) | |
c60e130c | 456 | { |
a285b18c MW |
457 | /* Reduce to lowest terms */ |
458 | numerator = scm_exact_integer_quotient (numerator, the_gcd); | |
459 | denominator = scm_exact_integer_quotient (denominator, the_gcd); | |
f92e85f7 | 460 | } |
a285b18c | 461 | return scm_i_make_ratio_already_reduced (numerator, denominator); |
f92e85f7 | 462 | } |
f92e85f7 | 463 | } |
c60e130c | 464 | #undef FUNC_NAME |
f92e85f7 | 465 | |
98237784 MW |
466 | static mpz_t scm_i_divide2double_lo2b; |
467 | ||
468 | /* Return the double that is closest to the exact rational N/D, with | |
469 | ties rounded toward even mantissas. N and D must be exact | |
470 | integers. */ | |
471 | static double | |
472 | scm_i_divide2double (SCM n, SCM d) | |
473 | { | |
474 | int neg; | |
475 | mpz_t nn, dd, lo, hi, x; | |
476 | ssize_t e; | |
477 | ||
478 | if (SCM_I_INUMP (d)) | |
479 | { | |
480 | if (SCM_UNLIKELY (scm_is_eq (d, SCM_INUM0))) | |
481 | { | |
482 | if (scm_is_true (scm_positive_p (n))) | |
483 | return 1.0 / 0.0; | |
484 | else if (scm_is_true (scm_negative_p (n))) | |
485 | return -1.0 / 0.0; | |
486 | else | |
487 | return 0.0 / 0.0; | |
488 | } | |
489 | mpz_init_set_si (dd, SCM_I_INUM (d)); | |
490 | } | |
491 | else | |
492 | mpz_init_set (dd, SCM_I_BIG_MPZ (d)); | |
493 | ||
494 | if (SCM_I_INUMP (n)) | |
495 | mpz_init_set_si (nn, SCM_I_INUM (n)); | |
496 | else | |
497 | mpz_init_set (nn, SCM_I_BIG_MPZ (n)); | |
498 | ||
499 | neg = (mpz_sgn (nn) < 0) ^ (mpz_sgn (dd) < 0); | |
500 | mpz_abs (nn, nn); | |
501 | mpz_abs (dd, dd); | |
502 | ||
503 | /* Now we need to find the value of e such that: | |
504 | ||
505 | For e <= 0: | |
506 | b^{p-1} - 1/2b <= b^-e n / d < b^p - 1/2 [1A] | |
507 | (2 b^p - 1) <= 2 b b^-e n / d < (2 b^p - 1) b [2A] | |
508 | (2 b^p - 1) d <= 2 b b^-e n < (2 b^p - 1) d b [3A] | |
509 | ||
510 | For e >= 0: | |
511 | b^{p-1} - 1/2b <= n / b^e d < b^p - 1/2 [1B] | |
512 | (2 b^p - 1) <= 2 b n / b^e d < (2 b^p - 1) b [2B] | |
513 | (2 b^p - 1) d b^e <= 2 b n < (2 b^p - 1) d b b^e [3B] | |
514 | ||
515 | where: p = DBL_MANT_DIG | |
516 | b = FLT_RADIX (here assumed to be 2) | |
517 | ||
518 | After rounding, the mantissa must be an integer between b^{p-1} and | |
519 | (b^p - 1), except for subnormal numbers. In the inequations [1A] | |
520 | and [1B], the middle expression represents the mantissa *before* | |
521 | rounding, and therefore is bounded by the range of values that will | |
522 | round to a floating-point number with the exponent e. The upper | |
523 | bound is (b^p - 1 + 1/2) = (b^p - 1/2), and is exclusive because | |
524 | ties will round up to the next power of b. The lower bound is | |
525 | (b^{p-1} - 1/2b), and is inclusive because ties will round toward | |
526 | this power of b. Here we subtract 1/2b instead of 1/2 because it | |
527 | is in the range of the next smaller exponent, where the | |
528 | representable numbers are closer together by a factor of b. | |
529 | ||
530 | Inequations [2A] and [2B] are derived from [1A] and [1B] by | |
531 | multiplying by 2b, and in [3A] and [3B] we multiply by the | |
532 | denominator of the middle value to obtain integer expressions. | |
533 | ||
534 | In the code below, we refer to the three expressions in [3A] or | |
535 | [3B] as lo, x, and hi. If the number is normalizable, we will | |
536 | achieve the goal: lo <= x < hi */ | |
537 | ||
538 | /* Make an initial guess for e */ | |
539 | e = mpz_sizeinbase (nn, 2) - mpz_sizeinbase (dd, 2) - (DBL_MANT_DIG-1); | |
540 | if (e < DBL_MIN_EXP - DBL_MANT_DIG) | |
541 | e = DBL_MIN_EXP - DBL_MANT_DIG; | |
542 | ||
543 | /* Compute the initial values of lo, x, and hi | |
544 | based on the initial guess of e */ | |
545 | mpz_inits (lo, hi, x, NULL); | |
546 | mpz_mul_2exp (x, nn, 2 + ((e < 0) ? -e : 0)); | |
547 | mpz_mul (lo, dd, scm_i_divide2double_lo2b); | |
548 | if (e > 0) | |
549 | mpz_mul_2exp (lo, lo, e); | |
550 | mpz_mul_2exp (hi, lo, 1); | |
551 | ||
552 | /* Adjust e as needed to satisfy the inequality lo <= x < hi, | |
553 | (but without making e less then the minimum exponent) */ | |
554 | while (mpz_cmp (x, lo) < 0 && e > DBL_MIN_EXP - DBL_MANT_DIG) | |
555 | { | |
556 | mpz_mul_2exp (x, x, 1); | |
557 | e--; | |
558 | } | |
559 | while (mpz_cmp (x, hi) >= 0) | |
560 | { | |
561 | /* If we ever used lo's value again, | |
562 | we would need to double lo here. */ | |
563 | mpz_mul_2exp (hi, hi, 1); | |
564 | e++; | |
565 | } | |
566 | ||
567 | /* Now compute the rounded mantissa: | |
568 | n / b^e d (if e >= 0) | |
569 | n b^-e / d (if e <= 0) */ | |
570 | { | |
571 | int cmp; | |
572 | double result; | |
573 | ||
574 | if (e < 0) | |
575 | mpz_mul_2exp (nn, nn, -e); | |
576 | else | |
577 | mpz_mul_2exp (dd, dd, e); | |
578 | ||
579 | /* mpz does not directly support rounded right | |
580 | shifts, so we have to do it the hard way. | |
581 | For efficiency, we reuse lo and hi. | |
582 | hi == quotient, lo == remainder */ | |
583 | mpz_fdiv_qr (hi, lo, nn, dd); | |
584 | ||
585 | /* The fractional part of the unrounded mantissa would be | |
586 | remainder/dividend, i.e. lo/dd. So we have a tie if | |
587 | lo/dd = 1/2. Multiplying both sides by 2*dd yields the | |
588 | integer expression 2*lo = dd. Here we do that comparison | |
589 | to decide whether to round up or down. */ | |
590 | mpz_mul_2exp (lo, lo, 1); | |
591 | cmp = mpz_cmp (lo, dd); | |
592 | if (cmp > 0 || (cmp == 0 && mpz_odd_p (hi))) | |
593 | mpz_add_ui (hi, hi, 1); | |
594 | ||
595 | result = ldexp (mpz_get_d (hi), e); | |
596 | if (neg) | |
597 | result = -result; | |
598 | ||
599 | mpz_clears (nn, dd, lo, hi, x, NULL); | |
600 | return result; | |
601 | } | |
602 | } | |
603 | ||
f92e85f7 MV |
604 | double |
605 | scm_i_fraction2double (SCM z) | |
606 | { | |
98237784 MW |
607 | return scm_i_divide2double (SCM_FRACTION_NUMERATOR (z), |
608 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 MV |
609 | } |
610 | ||
2e274311 MW |
611 | static int |
612 | double_is_non_negative_zero (double x) | |
613 | { | |
614 | static double zero = 0.0; | |
615 | ||
616 | return !memcmp (&x, &zero, sizeof(double)); | |
617 | } | |
618 | ||
2519490c MW |
619 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
620 | (SCM x), | |
942e5b91 MG |
621 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
622 | "otherwise.") | |
1bbd0b84 | 623 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 624 | { |
41df63cf MW |
625 | if (SCM_INEXACTP (x)) |
626 | return SCM_BOOL_F; | |
627 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 628 | return SCM_BOOL_T; |
41df63cf | 629 | else |
2519490c | 630 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
631 | } |
632 | #undef FUNC_NAME | |
633 | ||
022dda69 MG |
634 | int |
635 | scm_is_exact (SCM val) | |
636 | { | |
637 | return scm_is_true (scm_exact_p (val)); | |
638 | } | |
41df63cf | 639 | |
2519490c | 640 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
641 | (SCM x), |
642 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
643 | "else.") | |
644 | #define FUNC_NAME s_scm_inexact_p | |
645 | { | |
646 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 647 | return SCM_BOOL_T; |
41df63cf | 648 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 649 | return SCM_BOOL_F; |
41df63cf | 650 | else |
2519490c | 651 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 652 | } |
1bbd0b84 | 653 | #undef FUNC_NAME |
0f2d19dd | 654 | |
022dda69 MG |
655 | int |
656 | scm_is_inexact (SCM val) | |
657 | { | |
658 | return scm_is_true (scm_inexact_p (val)); | |
659 | } | |
4219f20d | 660 | |
2519490c | 661 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 662 | (SCM n), |
942e5b91 MG |
663 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
664 | "otherwise.") | |
1bbd0b84 | 665 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 666 | { |
e11e83f3 | 667 | if (SCM_I_INUMP (n)) |
0aacf84e | 668 | { |
e25f3727 | 669 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 670 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
671 | } |
672 | else if (SCM_BIGP (n)) | |
673 | { | |
674 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
675 | scm_remember_upto_here_1 (n); | |
73e4de09 | 676 | return scm_from_bool (odd_p); |
0aacf84e | 677 | } |
f92e85f7 MV |
678 | else if (SCM_REALP (n)) |
679 | { | |
2519490c MW |
680 | double val = SCM_REAL_VALUE (n); |
681 | if (DOUBLE_IS_FINITE (val)) | |
682 | { | |
683 | double rem = fabs (fmod (val, 2.0)); | |
684 | if (rem == 1.0) | |
685 | return SCM_BOOL_T; | |
686 | else if (rem == 0.0) | |
687 | return SCM_BOOL_F; | |
688 | } | |
f92e85f7 | 689 | } |
2519490c | 690 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 691 | } |
1bbd0b84 | 692 | #undef FUNC_NAME |
0f2d19dd | 693 | |
4219f20d | 694 | |
2519490c | 695 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 696 | (SCM n), |
942e5b91 MG |
697 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
698 | "otherwise.") | |
1bbd0b84 | 699 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 700 | { |
e11e83f3 | 701 | if (SCM_I_INUMP (n)) |
0aacf84e | 702 | { |
e25f3727 | 703 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 704 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
705 | } |
706 | else if (SCM_BIGP (n)) | |
707 | { | |
708 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
709 | scm_remember_upto_here_1 (n); | |
73e4de09 | 710 | return scm_from_bool (even_p); |
0aacf84e | 711 | } |
f92e85f7 MV |
712 | else if (SCM_REALP (n)) |
713 | { | |
2519490c MW |
714 | double val = SCM_REAL_VALUE (n); |
715 | if (DOUBLE_IS_FINITE (val)) | |
716 | { | |
717 | double rem = fabs (fmod (val, 2.0)); | |
718 | if (rem == 1.0) | |
719 | return SCM_BOOL_F; | |
720 | else if (rem == 0.0) | |
721 | return SCM_BOOL_T; | |
722 | } | |
f92e85f7 | 723 | } |
2519490c | 724 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 725 | } |
1bbd0b84 | 726 | #undef FUNC_NAME |
0f2d19dd | 727 | |
2519490c MW |
728 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
729 | (SCM x), | |
10391e06 AW |
730 | "Return @code{#t} if the real number @var{x} is neither\n" |
731 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
732 | #define FUNC_NAME s_scm_finite_p |
733 | { | |
734 | if (SCM_REALP (x)) | |
735 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 736 | else if (scm_is_real (x)) |
7112615f MW |
737 | return SCM_BOOL_T; |
738 | else | |
2519490c | 739 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
740 | } |
741 | #undef FUNC_NAME | |
742 | ||
2519490c MW |
743 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
744 | (SCM x), | |
745 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
746 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
747 | #define FUNC_NAME s_scm_inf_p |
748 | { | |
b1092b3a | 749 | if (SCM_REALP (x)) |
2e65b52f | 750 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 751 | else if (scm_is_real (x)) |
7351e207 | 752 | return SCM_BOOL_F; |
10391e06 | 753 | else |
2519490c | 754 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
755 | } |
756 | #undef FUNC_NAME | |
757 | ||
2519490c MW |
758 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
759 | (SCM x), | |
10391e06 AW |
760 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
761 | "or @code{#f} otherwise.") | |
7351e207 MV |
762 | #define FUNC_NAME s_scm_nan_p |
763 | { | |
10391e06 AW |
764 | if (SCM_REALP (x)) |
765 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
766 | else if (scm_is_real (x)) | |
7351e207 | 767 | return SCM_BOOL_F; |
10391e06 | 768 | else |
2519490c | 769 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
770 | } |
771 | #undef FUNC_NAME | |
772 | ||
773 | /* Guile's idea of infinity. */ | |
774 | static double guile_Inf; | |
775 | ||
776 | /* Guile's idea of not a number. */ | |
777 | static double guile_NaN; | |
778 | ||
779 | static void | |
780 | guile_ieee_init (void) | |
781 | { | |
7351e207 MV |
782 | /* Some version of gcc on some old version of Linux used to crash when |
783 | trying to make Inf and NaN. */ | |
784 | ||
240a27d2 KR |
785 | #ifdef INFINITY |
786 | /* C99 INFINITY, when available. | |
787 | FIXME: The standard allows for INFINITY to be something that overflows | |
788 | at compile time. We ought to have a configure test to check for that | |
789 | before trying to use it. (But in practice we believe this is not a | |
790 | problem on any system guile is likely to target.) */ | |
791 | guile_Inf = INFINITY; | |
56a3dcd4 | 792 | #elif defined HAVE_DINFINITY |
240a27d2 | 793 | /* OSF */ |
7351e207 | 794 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 795 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
796 | #else |
797 | double tmp = 1e+10; | |
798 | guile_Inf = tmp; | |
799 | for (;;) | |
800 | { | |
801 | guile_Inf *= 1e+10; | |
802 | if (guile_Inf == tmp) | |
803 | break; | |
804 | tmp = guile_Inf; | |
805 | } | |
806 | #endif | |
807 | ||
240a27d2 KR |
808 | #ifdef NAN |
809 | /* C99 NAN, when available */ | |
810 | guile_NaN = NAN; | |
56a3dcd4 | 811 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
812 | { |
813 | /* OSF */ | |
814 | extern unsigned int DQNAN[2]; | |
815 | guile_NaN = (*((double *)(DQNAN))); | |
816 | } | |
7351e207 MV |
817 | #else |
818 | guile_NaN = guile_Inf / guile_Inf; | |
819 | #endif | |
7351e207 MV |
820 | } |
821 | ||
822 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
823 | (void), | |
824 | "Return Inf.") | |
825 | #define FUNC_NAME s_scm_inf | |
826 | { | |
827 | static int initialized = 0; | |
828 | if (! initialized) | |
829 | { | |
830 | guile_ieee_init (); | |
831 | initialized = 1; | |
832 | } | |
55f26379 | 833 | return scm_from_double (guile_Inf); |
7351e207 MV |
834 | } |
835 | #undef FUNC_NAME | |
836 | ||
837 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
838 | (void), | |
839 | "Return NaN.") | |
840 | #define FUNC_NAME s_scm_nan | |
841 | { | |
842 | static int initialized = 0; | |
0aacf84e | 843 | if (!initialized) |
7351e207 MV |
844 | { |
845 | guile_ieee_init (); | |
846 | initialized = 1; | |
847 | } | |
55f26379 | 848 | return scm_from_double (guile_NaN); |
7351e207 MV |
849 | } |
850 | #undef FUNC_NAME | |
851 | ||
4219f20d | 852 | |
a48d60b1 MD |
853 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
854 | (SCM x), | |
855 | "Return the absolute value of @var{x}.") | |
2519490c | 856 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 857 | { |
e11e83f3 | 858 | if (SCM_I_INUMP (x)) |
0aacf84e | 859 | { |
e25f3727 | 860 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
861 | if (xx >= 0) |
862 | return x; | |
863 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 864 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 865 | else |
e25f3727 | 866 | return scm_i_inum2big (-xx); |
4219f20d | 867 | } |
9b9ef10c MW |
868 | else if (SCM_LIKELY (SCM_REALP (x))) |
869 | { | |
870 | double xx = SCM_REAL_VALUE (x); | |
871 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
872 | if (xx < 0.0) | |
873 | return scm_from_double (-xx); | |
874 | /* Handle signed zeroes properly */ | |
875 | else if (SCM_UNLIKELY (xx == 0.0)) | |
876 | return flo0; | |
877 | else | |
878 | return x; | |
879 | } | |
0aacf84e MD |
880 | else if (SCM_BIGP (x)) |
881 | { | |
882 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
883 | if (sgn < 0) | |
884 | return scm_i_clonebig (x, 0); | |
885 | else | |
886 | return x; | |
4219f20d | 887 | } |
f92e85f7 MV |
888 | else if (SCM_FRACTIONP (x)) |
889 | { | |
73e4de09 | 890 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 891 | return x; |
a285b18c MW |
892 | return scm_i_make_ratio_already_reduced |
893 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
894 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 895 | } |
0aacf84e | 896 | else |
a48d60b1 | 897 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 898 | } |
a48d60b1 | 899 | #undef FUNC_NAME |
0f2d19dd | 900 | |
4219f20d | 901 | |
2519490c MW |
902 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
903 | (SCM x, SCM y), | |
904 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
905 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 906 | { |
495a39c4 | 907 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 908 | { |
495a39c4 | 909 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 910 | return scm_truncate_quotient (x, y); |
0aacf84e | 911 | else |
2519490c | 912 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 913 | } |
0aacf84e | 914 | else |
2519490c | 915 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 916 | } |
2519490c | 917 | #undef FUNC_NAME |
0f2d19dd | 918 | |
2519490c MW |
919 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
920 | (SCM x, SCM y), | |
921 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
922 | "@lisp\n" | |
923 | "(remainder 13 4) @result{} 1\n" | |
924 | "(remainder -13 4) @result{} -1\n" | |
925 | "@end lisp") | |
926 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 927 | { |
495a39c4 | 928 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 929 | { |
495a39c4 | 930 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 931 | return scm_truncate_remainder (x, y); |
0aacf84e | 932 | else |
2519490c | 933 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 934 | } |
0aacf84e | 935 | else |
2519490c | 936 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 937 | } |
2519490c | 938 | #undef FUNC_NAME |
0f2d19dd | 939 | |
89a7e495 | 940 | |
2519490c MW |
941 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
942 | (SCM x, SCM y), | |
943 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
944 | "@lisp\n" | |
945 | "(modulo 13 4) @result{} 1\n" | |
946 | "(modulo -13 4) @result{} 3\n" | |
947 | "@end lisp") | |
948 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 949 | { |
495a39c4 | 950 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 951 | { |
495a39c4 | 952 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 953 | return scm_floor_remainder (x, y); |
0aacf84e | 954 | else |
2519490c | 955 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 956 | } |
0aacf84e | 957 | else |
2519490c | 958 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 959 | } |
2519490c | 960 | #undef FUNC_NAME |
0f2d19dd | 961 | |
a285b18c MW |
962 | /* Return the exact integer q such that n = q*d, for exact integers n |
963 | and d, where d is known in advance to divide n evenly (with zero | |
964 | remainder). For large integers, this can be computed more | |
965 | efficiently than when the remainder is unknown. */ | |
966 | static SCM | |
967 | scm_exact_integer_quotient (SCM n, SCM d) | |
968 | #define FUNC_NAME "exact-integer-quotient" | |
969 | { | |
970 | if (SCM_LIKELY (SCM_I_INUMP (n))) | |
971 | { | |
972 | scm_t_inum nn = SCM_I_INUM (n); | |
973 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
974 | { | |
975 | scm_t_inum dd = SCM_I_INUM (d); | |
976 | if (SCM_UNLIKELY (dd == 0)) | |
977 | scm_num_overflow ("exact-integer-quotient"); | |
978 | else | |
979 | { | |
980 | scm_t_inum qq = nn / dd; | |
981 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
982 | return SCM_I_MAKINUM (qq); | |
983 | else | |
984 | return scm_i_inum2big (qq); | |
985 | } | |
986 | } | |
987 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
988 | { | |
989 | /* n is an inum and d is a bignum. Given that d is known to | |
990 | divide n evenly, there are only two possibilities: n is 0, | |
991 | or else n is fixnum-min and d is abs(fixnum-min). */ | |
992 | if (nn == 0) | |
993 | return SCM_INUM0; | |
994 | else | |
995 | return SCM_I_MAKINUM (-1); | |
996 | } | |
997 | else | |
998 | SCM_WRONG_TYPE_ARG (2, d); | |
999 | } | |
1000 | else if (SCM_LIKELY (SCM_BIGP (n))) | |
1001 | { | |
1002 | if (SCM_LIKELY (SCM_I_INUMP (d))) | |
1003 | { | |
1004 | scm_t_inum dd = SCM_I_INUM (d); | |
1005 | if (SCM_UNLIKELY (dd == 0)) | |
1006 | scm_num_overflow ("exact-integer-quotient"); | |
1007 | else if (SCM_UNLIKELY (dd == 1)) | |
1008 | return n; | |
1009 | else | |
1010 | { | |
1011 | SCM q = scm_i_mkbig (); | |
1012 | if (dd > 0) | |
1013 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), dd); | |
1014 | else | |
1015 | { | |
1016 | mpz_divexact_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), -dd); | |
1017 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1018 | } | |
1019 | scm_remember_upto_here_1 (n); | |
1020 | return scm_i_normbig (q); | |
1021 | } | |
1022 | } | |
1023 | else if (SCM_LIKELY (SCM_BIGP (d))) | |
1024 | { | |
1025 | SCM q = scm_i_mkbig (); | |
1026 | mpz_divexact (SCM_I_BIG_MPZ (q), | |
1027 | SCM_I_BIG_MPZ (n), | |
1028 | SCM_I_BIG_MPZ (d)); | |
1029 | scm_remember_upto_here_2 (n, d); | |
1030 | return scm_i_normbig (q); | |
1031 | } | |
1032 | else | |
1033 | SCM_WRONG_TYPE_ARG (2, d); | |
1034 | } | |
1035 | else | |
1036 | SCM_WRONG_TYPE_ARG (1, n); | |
1037 | } | |
1038 | #undef FUNC_NAME | |
1039 | ||
5fbf680b MW |
1040 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
1041 | two-valued functions. It is called from primitive generics that take | |
1042 | two arguments and return two values, when the core procedure is | |
1043 | unable to handle the given argument types. If there are GOOPS | |
1044 | methods for this primitive generic, it dispatches to GOOPS and, if | |
1045 | successful, expects two values to be returned, which are placed in | |
1046 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
1047 | wrong-type-arg exception. | |
1048 | ||
1049 | FIXME: This obviously belongs somewhere else, but until we decide on | |
1050 | the right API, it is here as a static function, because it is needed | |
1051 | by the *_divide functions below. | |
1052 | */ | |
1053 | static void | |
1054 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
1055 | const char *subr, SCM *rp1, SCM *rp2) | |
1056 | { | |
1057 | if (SCM_UNPACK (gf)) | |
1058 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
1059 | else | |
1060 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
1061 | } | |
1062 | ||
a8da6d93 MW |
1063 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
1064 | (SCM x, SCM y), | |
1065 | "Return the integer @var{q} such that\n" | |
1066 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1067 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1068 | "@lisp\n" | |
1069 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1070 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1071 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1072 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1073 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1074 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1075 | "@end lisp") | |
ff62c168 MW |
1076 | #define FUNC_NAME s_scm_euclidean_quotient |
1077 | { | |
a8da6d93 MW |
1078 | if (scm_is_false (scm_negative_p (y))) |
1079 | return scm_floor_quotient (x, y); | |
ff62c168 | 1080 | else |
a8da6d93 | 1081 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
1082 | } |
1083 | #undef FUNC_NAME | |
1084 | ||
a8da6d93 MW |
1085 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
1086 | (SCM x, SCM y), | |
1087 | "Return the real number @var{r} such that\n" | |
1088 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1089 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1090 | "for some integer @var{q}.\n" | |
1091 | "@lisp\n" | |
1092 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1093 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1094 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1095 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1096 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1097 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1098 | "@end lisp") | |
ff62c168 MW |
1099 | #define FUNC_NAME s_scm_euclidean_remainder |
1100 | { | |
a8da6d93 MW |
1101 | if (scm_is_false (scm_negative_p (y))) |
1102 | return scm_floor_remainder (x, y); | |
ff62c168 | 1103 | else |
a8da6d93 | 1104 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
1105 | } |
1106 | #undef FUNC_NAME | |
1107 | ||
a8da6d93 MW |
1108 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
1109 | (SCM x, SCM y), | |
1110 | "Return the integer @var{q} and the real number @var{r}\n" | |
1111 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1112 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1113 | "@lisp\n" | |
1114 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1115 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1116 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1117 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1118 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1119 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1120 | "@end lisp") | |
5fbf680b MW |
1121 | #define FUNC_NAME s_scm_i_euclidean_divide |
1122 | { | |
a8da6d93 MW |
1123 | if (scm_is_false (scm_negative_p (y))) |
1124 | return scm_i_floor_divide (x, y); | |
1125 | else | |
1126 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
1127 | } |
1128 | #undef FUNC_NAME | |
1129 | ||
5fbf680b MW |
1130 | void |
1131 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 1132 | { |
a8da6d93 MW |
1133 | if (scm_is_false (scm_negative_p (y))) |
1134 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 1135 | else |
a8da6d93 | 1136 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
1137 | } |
1138 | ||
8f9da340 MW |
1139 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
1140 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
1141 | ||
1142 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
1143 | (SCM x, SCM y), | |
1144 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1145 | "@lisp\n" | |
1146 | "(floor-quotient 123 10) @result{} 12\n" | |
1147 | "(floor-quotient 123 -10) @result{} -13\n" | |
1148 | "(floor-quotient -123 10) @result{} -13\n" | |
1149 | "(floor-quotient -123 -10) @result{} 12\n" | |
1150 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1151 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1152 | "@end lisp") | |
1153 | #define FUNC_NAME s_scm_floor_quotient | |
1154 | { | |
1155 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1156 | { | |
1157 | scm_t_inum xx = SCM_I_INUM (x); | |
1158 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1159 | { | |
1160 | scm_t_inum yy = SCM_I_INUM (y); | |
1161 | scm_t_inum xx1 = xx; | |
1162 | scm_t_inum qq; | |
1163 | if (SCM_LIKELY (yy > 0)) | |
1164 | { | |
1165 | if (SCM_UNLIKELY (xx < 0)) | |
1166 | xx1 = xx - yy + 1; | |
1167 | } | |
1168 | else if (SCM_UNLIKELY (yy == 0)) | |
1169 | scm_num_overflow (s_scm_floor_quotient); | |
1170 | else if (xx > 0) | |
1171 | xx1 = xx - yy - 1; | |
1172 | qq = xx1 / yy; | |
1173 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1174 | return SCM_I_MAKINUM (qq); | |
1175 | else | |
1176 | return scm_i_inum2big (qq); | |
1177 | } | |
1178 | else if (SCM_BIGP (y)) | |
1179 | { | |
1180 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1181 | scm_remember_upto_here_1 (y); | |
1182 | if (sign > 0) | |
1183 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1184 | else | |
1185 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1186 | } | |
1187 | else if (SCM_REALP (y)) | |
1188 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1189 | else if (SCM_FRACTIONP (y)) | |
1190 | return scm_i_exact_rational_floor_quotient (x, y); | |
1191 | else | |
1192 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1193 | s_scm_floor_quotient); | |
1194 | } | |
1195 | else if (SCM_BIGP (x)) | |
1196 | { | |
1197 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1198 | { | |
1199 | scm_t_inum yy = SCM_I_INUM (y); | |
1200 | if (SCM_UNLIKELY (yy == 0)) | |
1201 | scm_num_overflow (s_scm_floor_quotient); | |
1202 | else if (SCM_UNLIKELY (yy == 1)) | |
1203 | return x; | |
1204 | else | |
1205 | { | |
1206 | SCM q = scm_i_mkbig (); | |
1207 | if (yy > 0) | |
1208 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1209 | else | |
1210 | { | |
1211 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1212 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1213 | } | |
1214 | scm_remember_upto_here_1 (x); | |
1215 | return scm_i_normbig (q); | |
1216 | } | |
1217 | } | |
1218 | else if (SCM_BIGP (y)) | |
1219 | { | |
1220 | SCM q = scm_i_mkbig (); | |
1221 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1222 | SCM_I_BIG_MPZ (x), | |
1223 | SCM_I_BIG_MPZ (y)); | |
1224 | scm_remember_upto_here_2 (x, y); | |
1225 | return scm_i_normbig (q); | |
1226 | } | |
1227 | else if (SCM_REALP (y)) | |
1228 | return scm_i_inexact_floor_quotient | |
1229 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1230 | else if (SCM_FRACTIONP (y)) | |
1231 | return scm_i_exact_rational_floor_quotient (x, y); | |
1232 | else | |
1233 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1234 | s_scm_floor_quotient); | |
1235 | } | |
1236 | else if (SCM_REALP (x)) | |
1237 | { | |
1238 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1239 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1240 | return scm_i_inexact_floor_quotient | |
1241 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1242 | else | |
1243 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1244 | s_scm_floor_quotient); | |
1245 | } | |
1246 | else if (SCM_FRACTIONP (x)) | |
1247 | { | |
1248 | if (SCM_REALP (y)) | |
1249 | return scm_i_inexact_floor_quotient | |
1250 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1251 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1252 | return scm_i_exact_rational_floor_quotient (x, y); | |
1253 | else | |
1254 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1255 | s_scm_floor_quotient); | |
1256 | } | |
1257 | else | |
1258 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1259 | s_scm_floor_quotient); | |
1260 | } | |
1261 | #undef FUNC_NAME | |
1262 | ||
1263 | static SCM | |
1264 | scm_i_inexact_floor_quotient (double x, double y) | |
1265 | { | |
1266 | if (SCM_UNLIKELY (y == 0)) | |
1267 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1268 | else | |
1269 | return scm_from_double (floor (x / y)); | |
1270 | } | |
1271 | ||
1272 | static SCM | |
1273 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1274 | { | |
1275 | return scm_floor_quotient | |
1276 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1277 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1278 | } | |
1279 | ||
1280 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1281 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1282 | ||
1283 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1284 | (SCM x, SCM y), | |
1285 | "Return the real number @var{r} such that\n" | |
1286 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1287 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1288 | "@lisp\n" | |
1289 | "(floor-remainder 123 10) @result{} 3\n" | |
1290 | "(floor-remainder 123 -10) @result{} -7\n" | |
1291 | "(floor-remainder -123 10) @result{} 7\n" | |
1292 | "(floor-remainder -123 -10) @result{} -3\n" | |
1293 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1294 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1295 | "@end lisp") | |
1296 | #define FUNC_NAME s_scm_floor_remainder | |
1297 | { | |
1298 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1299 | { | |
1300 | scm_t_inum xx = SCM_I_INUM (x); | |
1301 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1302 | { | |
1303 | scm_t_inum yy = SCM_I_INUM (y); | |
1304 | if (SCM_UNLIKELY (yy == 0)) | |
1305 | scm_num_overflow (s_scm_floor_remainder); | |
1306 | else | |
1307 | { | |
1308 | scm_t_inum rr = xx % yy; | |
1309 | int needs_adjustment; | |
1310 | ||
1311 | if (SCM_LIKELY (yy > 0)) | |
1312 | needs_adjustment = (rr < 0); | |
1313 | else | |
1314 | needs_adjustment = (rr > 0); | |
1315 | ||
1316 | if (needs_adjustment) | |
1317 | rr += yy; | |
1318 | return SCM_I_MAKINUM (rr); | |
1319 | } | |
1320 | } | |
1321 | else if (SCM_BIGP (y)) | |
1322 | { | |
1323 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1324 | scm_remember_upto_here_1 (y); | |
1325 | if (sign > 0) | |
1326 | { | |
1327 | if (xx < 0) | |
1328 | { | |
1329 | SCM r = scm_i_mkbig (); | |
1330 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1331 | scm_remember_upto_here_1 (y); | |
1332 | return scm_i_normbig (r); | |
1333 | } | |
1334 | else | |
1335 | return x; | |
1336 | } | |
1337 | else if (xx <= 0) | |
1338 | return x; | |
1339 | else | |
1340 | { | |
1341 | SCM r = scm_i_mkbig (); | |
1342 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1343 | scm_remember_upto_here_1 (y); | |
1344 | return scm_i_normbig (r); | |
1345 | } | |
1346 | } | |
1347 | else if (SCM_REALP (y)) | |
1348 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1349 | else if (SCM_FRACTIONP (y)) | |
1350 | return scm_i_exact_rational_floor_remainder (x, y); | |
1351 | else | |
1352 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1353 | s_scm_floor_remainder); | |
1354 | } | |
1355 | else if (SCM_BIGP (x)) | |
1356 | { | |
1357 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1358 | { | |
1359 | scm_t_inum yy = SCM_I_INUM (y); | |
1360 | if (SCM_UNLIKELY (yy == 0)) | |
1361 | scm_num_overflow (s_scm_floor_remainder); | |
1362 | else | |
1363 | { | |
1364 | scm_t_inum rr; | |
1365 | if (yy > 0) | |
1366 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1367 | else | |
1368 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1369 | scm_remember_upto_here_1 (x); | |
1370 | return SCM_I_MAKINUM (rr); | |
1371 | } | |
1372 | } | |
1373 | else if (SCM_BIGP (y)) | |
1374 | { | |
1375 | SCM r = scm_i_mkbig (); | |
1376 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1377 | SCM_I_BIG_MPZ (x), | |
1378 | SCM_I_BIG_MPZ (y)); | |
1379 | scm_remember_upto_here_2 (x, y); | |
1380 | return scm_i_normbig (r); | |
1381 | } | |
1382 | else if (SCM_REALP (y)) | |
1383 | return scm_i_inexact_floor_remainder | |
1384 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1385 | else if (SCM_FRACTIONP (y)) | |
1386 | return scm_i_exact_rational_floor_remainder (x, y); | |
1387 | else | |
1388 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1389 | s_scm_floor_remainder); | |
1390 | } | |
1391 | else if (SCM_REALP (x)) | |
1392 | { | |
1393 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1394 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1395 | return scm_i_inexact_floor_remainder | |
1396 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1397 | else | |
1398 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1399 | s_scm_floor_remainder); | |
1400 | } | |
1401 | else if (SCM_FRACTIONP (x)) | |
1402 | { | |
1403 | if (SCM_REALP (y)) | |
1404 | return scm_i_inexact_floor_remainder | |
1405 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1406 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1407 | return scm_i_exact_rational_floor_remainder (x, y); | |
1408 | else | |
1409 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1410 | s_scm_floor_remainder); | |
1411 | } | |
1412 | else | |
1413 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1414 | s_scm_floor_remainder); | |
1415 | } | |
1416 | #undef FUNC_NAME | |
1417 | ||
1418 | static SCM | |
1419 | scm_i_inexact_floor_remainder (double x, double y) | |
1420 | { | |
1421 | /* Although it would be more efficient to use fmod here, we can't | |
1422 | because it would in some cases produce results inconsistent with | |
1423 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1424 | close). In particular, when x is very close to a multiple of y, | |
1425 | then r might be either 0.0 or y, but those two cases must | |
1426 | correspond to different choices of q. If r = 0.0 then q must be | |
1427 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1428 | and remainder chooses the other, it would be bad. */ | |
1429 | if (SCM_UNLIKELY (y == 0)) | |
1430 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1431 | else | |
1432 | return scm_from_double (x - y * floor (x / y)); | |
1433 | } | |
1434 | ||
1435 | static SCM | |
1436 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1437 | { | |
1438 | SCM xd = scm_denominator (x); | |
1439 | SCM yd = scm_denominator (y); | |
1440 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1441 | scm_product (scm_numerator (y), xd)); | |
1442 | return scm_divide (r1, scm_product (xd, yd)); | |
1443 | } | |
1444 | ||
1445 | ||
1446 | static void scm_i_inexact_floor_divide (double x, double y, | |
1447 | SCM *qp, SCM *rp); | |
1448 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1449 | SCM *qp, SCM *rp); | |
1450 | ||
1451 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1452 | (SCM x, SCM y), | |
1453 | "Return the integer @var{q} and the real number @var{r}\n" | |
1454 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1455 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1456 | "@lisp\n" | |
1457 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1458 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1459 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1460 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1461 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1462 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1463 | "@end lisp") | |
1464 | #define FUNC_NAME s_scm_i_floor_divide | |
1465 | { | |
1466 | SCM q, r; | |
1467 | ||
1468 | scm_floor_divide(x, y, &q, &r); | |
1469 | return scm_values (scm_list_2 (q, r)); | |
1470 | } | |
1471 | #undef FUNC_NAME | |
1472 | ||
1473 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1474 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1475 | ||
1476 | void | |
1477 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1478 | { | |
1479 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1480 | { | |
1481 | scm_t_inum xx = SCM_I_INUM (x); | |
1482 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1483 | { | |
1484 | scm_t_inum yy = SCM_I_INUM (y); | |
1485 | if (SCM_UNLIKELY (yy == 0)) | |
1486 | scm_num_overflow (s_scm_floor_divide); | |
1487 | else | |
1488 | { | |
1489 | scm_t_inum qq = xx / yy; | |
1490 | scm_t_inum rr = xx % yy; | |
1491 | int needs_adjustment; | |
1492 | ||
1493 | if (SCM_LIKELY (yy > 0)) | |
1494 | needs_adjustment = (rr < 0); | |
1495 | else | |
1496 | needs_adjustment = (rr > 0); | |
1497 | ||
1498 | if (needs_adjustment) | |
1499 | { | |
1500 | rr += yy; | |
1501 | qq--; | |
1502 | } | |
1503 | ||
1504 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1505 | *qp = SCM_I_MAKINUM (qq); | |
1506 | else | |
1507 | *qp = scm_i_inum2big (qq); | |
1508 | *rp = SCM_I_MAKINUM (rr); | |
1509 | } | |
1510 | return; | |
1511 | } | |
1512 | else if (SCM_BIGP (y)) | |
1513 | { | |
1514 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1515 | scm_remember_upto_here_1 (y); | |
1516 | if (sign > 0) | |
1517 | { | |
1518 | if (xx < 0) | |
1519 | { | |
1520 | SCM r = scm_i_mkbig (); | |
1521 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1522 | scm_remember_upto_here_1 (y); | |
1523 | *qp = SCM_I_MAKINUM (-1); | |
1524 | *rp = scm_i_normbig (r); | |
1525 | } | |
1526 | else | |
1527 | { | |
1528 | *qp = SCM_INUM0; | |
1529 | *rp = x; | |
1530 | } | |
1531 | } | |
1532 | else if (xx <= 0) | |
1533 | { | |
1534 | *qp = SCM_INUM0; | |
1535 | *rp = x; | |
1536 | } | |
1537 | else | |
1538 | { | |
1539 | SCM r = scm_i_mkbig (); | |
1540 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1541 | scm_remember_upto_here_1 (y); | |
1542 | *qp = SCM_I_MAKINUM (-1); | |
1543 | *rp = scm_i_normbig (r); | |
1544 | } | |
1545 | return; | |
1546 | } | |
1547 | else if (SCM_REALP (y)) | |
1548 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1549 | else if (SCM_FRACTIONP (y)) | |
1550 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1551 | else | |
1552 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1553 | s_scm_floor_divide, qp, rp); | |
1554 | } | |
1555 | else if (SCM_BIGP (x)) | |
1556 | { | |
1557 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1558 | { | |
1559 | scm_t_inum yy = SCM_I_INUM (y); | |
1560 | if (SCM_UNLIKELY (yy == 0)) | |
1561 | scm_num_overflow (s_scm_floor_divide); | |
1562 | else | |
1563 | { | |
1564 | SCM q = scm_i_mkbig (); | |
1565 | SCM r = scm_i_mkbig (); | |
1566 | if (yy > 0) | |
1567 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1568 | SCM_I_BIG_MPZ (x), yy); | |
1569 | else | |
1570 | { | |
1571 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1572 | SCM_I_BIG_MPZ (x), -yy); | |
1573 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1574 | } | |
1575 | scm_remember_upto_here_1 (x); | |
1576 | *qp = scm_i_normbig (q); | |
1577 | *rp = scm_i_normbig (r); | |
1578 | } | |
1579 | return; | |
1580 | } | |
1581 | else if (SCM_BIGP (y)) | |
1582 | { | |
1583 | SCM q = scm_i_mkbig (); | |
1584 | SCM r = scm_i_mkbig (); | |
1585 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1586 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1587 | scm_remember_upto_here_2 (x, y); | |
1588 | *qp = scm_i_normbig (q); | |
1589 | *rp = scm_i_normbig (r); | |
1590 | return; | |
1591 | } | |
1592 | else if (SCM_REALP (y)) | |
1593 | return scm_i_inexact_floor_divide | |
1594 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1595 | else if (SCM_FRACTIONP (y)) | |
1596 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1597 | else | |
1598 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1599 | s_scm_floor_divide, qp, rp); | |
1600 | } | |
1601 | else if (SCM_REALP (x)) | |
1602 | { | |
1603 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1604 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1605 | return scm_i_inexact_floor_divide | |
1606 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1607 | else | |
1608 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1609 | s_scm_floor_divide, qp, rp); | |
1610 | } | |
1611 | else if (SCM_FRACTIONP (x)) | |
1612 | { | |
1613 | if (SCM_REALP (y)) | |
1614 | return scm_i_inexact_floor_divide | |
1615 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1616 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1617 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1618 | else | |
1619 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1620 | s_scm_floor_divide, qp, rp); | |
1621 | } | |
1622 | else | |
1623 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1624 | s_scm_floor_divide, qp, rp); | |
1625 | } | |
1626 | ||
1627 | static void | |
1628 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1629 | { | |
1630 | if (SCM_UNLIKELY (y == 0)) | |
1631 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1632 | else | |
1633 | { | |
1634 | double q = floor (x / y); | |
1635 | double r = x - q * y; | |
1636 | *qp = scm_from_double (q); | |
1637 | *rp = scm_from_double (r); | |
1638 | } | |
1639 | } | |
1640 | ||
1641 | static void | |
1642 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1643 | { | |
1644 | SCM r1; | |
1645 | SCM xd = scm_denominator (x); | |
1646 | SCM yd = scm_denominator (y); | |
1647 | ||
1648 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1649 | scm_product (scm_numerator (y), xd), | |
1650 | qp, &r1); | |
1651 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1652 | } | |
1653 | ||
1654 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1655 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1656 | ||
1657 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1658 | (SCM x, SCM y), | |
1659 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1660 | "@lisp\n" | |
1661 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1662 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1663 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1664 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1665 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1666 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1667 | "@end lisp") | |
1668 | #define FUNC_NAME s_scm_ceiling_quotient | |
1669 | { | |
1670 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1671 | { | |
1672 | scm_t_inum xx = SCM_I_INUM (x); | |
1673 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1674 | { | |
1675 | scm_t_inum yy = SCM_I_INUM (y); | |
1676 | if (SCM_UNLIKELY (yy == 0)) | |
1677 | scm_num_overflow (s_scm_ceiling_quotient); | |
1678 | else | |
1679 | { | |
1680 | scm_t_inum xx1 = xx; | |
1681 | scm_t_inum qq; | |
1682 | if (SCM_LIKELY (yy > 0)) | |
1683 | { | |
1684 | if (SCM_LIKELY (xx >= 0)) | |
1685 | xx1 = xx + yy - 1; | |
1686 | } | |
8f9da340 MW |
1687 | else if (xx < 0) |
1688 | xx1 = xx + yy + 1; | |
1689 | qq = xx1 / yy; | |
1690 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1691 | return SCM_I_MAKINUM (qq); | |
1692 | else | |
1693 | return scm_i_inum2big (qq); | |
1694 | } | |
1695 | } | |
1696 | else if (SCM_BIGP (y)) | |
1697 | { | |
1698 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1699 | scm_remember_upto_here_1 (y); | |
1700 | if (SCM_LIKELY (sign > 0)) | |
1701 | { | |
1702 | if (SCM_LIKELY (xx > 0)) | |
1703 | return SCM_INUM1; | |
1704 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1705 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1706 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1707 | { | |
1708 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1709 | scm_remember_upto_here_1 (y); | |
1710 | return SCM_I_MAKINUM (-1); | |
1711 | } | |
1712 | else | |
1713 | return SCM_INUM0; | |
1714 | } | |
1715 | else if (xx >= 0) | |
1716 | return SCM_INUM0; | |
1717 | else | |
1718 | return SCM_INUM1; | |
1719 | } | |
1720 | else if (SCM_REALP (y)) | |
1721 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1722 | else if (SCM_FRACTIONP (y)) | |
1723 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1724 | else | |
1725 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1726 | s_scm_ceiling_quotient); | |
1727 | } | |
1728 | else if (SCM_BIGP (x)) | |
1729 | { | |
1730 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1731 | { | |
1732 | scm_t_inum yy = SCM_I_INUM (y); | |
1733 | if (SCM_UNLIKELY (yy == 0)) | |
1734 | scm_num_overflow (s_scm_ceiling_quotient); | |
1735 | else if (SCM_UNLIKELY (yy == 1)) | |
1736 | return x; | |
1737 | else | |
1738 | { | |
1739 | SCM q = scm_i_mkbig (); | |
1740 | if (yy > 0) | |
1741 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1742 | else | |
1743 | { | |
1744 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1745 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1746 | } | |
1747 | scm_remember_upto_here_1 (x); | |
1748 | return scm_i_normbig (q); | |
1749 | } | |
1750 | } | |
1751 | else if (SCM_BIGP (y)) | |
1752 | { | |
1753 | SCM q = scm_i_mkbig (); | |
1754 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1755 | SCM_I_BIG_MPZ (x), | |
1756 | SCM_I_BIG_MPZ (y)); | |
1757 | scm_remember_upto_here_2 (x, y); | |
1758 | return scm_i_normbig (q); | |
1759 | } | |
1760 | else if (SCM_REALP (y)) | |
1761 | return scm_i_inexact_ceiling_quotient | |
1762 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1763 | else if (SCM_FRACTIONP (y)) | |
1764 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1765 | else | |
1766 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1767 | s_scm_ceiling_quotient); | |
1768 | } | |
1769 | else if (SCM_REALP (x)) | |
1770 | { | |
1771 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1772 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1773 | return scm_i_inexact_ceiling_quotient | |
1774 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1775 | else | |
1776 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1777 | s_scm_ceiling_quotient); | |
1778 | } | |
1779 | else if (SCM_FRACTIONP (x)) | |
1780 | { | |
1781 | if (SCM_REALP (y)) | |
1782 | return scm_i_inexact_ceiling_quotient | |
1783 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1784 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1785 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1786 | else | |
1787 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1788 | s_scm_ceiling_quotient); | |
1789 | } | |
1790 | else | |
1791 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1792 | s_scm_ceiling_quotient); | |
1793 | } | |
1794 | #undef FUNC_NAME | |
1795 | ||
1796 | static SCM | |
1797 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1798 | { | |
1799 | if (SCM_UNLIKELY (y == 0)) | |
1800 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1801 | else | |
1802 | return scm_from_double (ceil (x / y)); | |
1803 | } | |
1804 | ||
1805 | static SCM | |
1806 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1807 | { | |
1808 | return scm_ceiling_quotient | |
1809 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1810 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1811 | } | |
1812 | ||
1813 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1814 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1815 | ||
1816 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1817 | (SCM x, SCM y), | |
1818 | "Return the real number @var{r} such that\n" | |
1819 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1820 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1821 | "@lisp\n" | |
1822 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1823 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1824 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1825 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1826 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1827 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1828 | "@end lisp") | |
1829 | #define FUNC_NAME s_scm_ceiling_remainder | |
1830 | { | |
1831 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1832 | { | |
1833 | scm_t_inum xx = SCM_I_INUM (x); | |
1834 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1835 | { | |
1836 | scm_t_inum yy = SCM_I_INUM (y); | |
1837 | if (SCM_UNLIKELY (yy == 0)) | |
1838 | scm_num_overflow (s_scm_ceiling_remainder); | |
1839 | else | |
1840 | { | |
1841 | scm_t_inum rr = xx % yy; | |
1842 | int needs_adjustment; | |
1843 | ||
1844 | if (SCM_LIKELY (yy > 0)) | |
1845 | needs_adjustment = (rr > 0); | |
1846 | else | |
1847 | needs_adjustment = (rr < 0); | |
1848 | ||
1849 | if (needs_adjustment) | |
1850 | rr -= yy; | |
1851 | return SCM_I_MAKINUM (rr); | |
1852 | } | |
1853 | } | |
1854 | else if (SCM_BIGP (y)) | |
1855 | { | |
1856 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1857 | scm_remember_upto_here_1 (y); | |
1858 | if (SCM_LIKELY (sign > 0)) | |
1859 | { | |
1860 | if (SCM_LIKELY (xx > 0)) | |
1861 | { | |
1862 | SCM r = scm_i_mkbig (); | |
1863 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1864 | scm_remember_upto_here_1 (y); | |
1865 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1866 | return scm_i_normbig (r); | |
1867 | } | |
1868 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1869 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1870 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1871 | { | |
1872 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1873 | scm_remember_upto_here_1 (y); | |
1874 | return SCM_INUM0; | |
1875 | } | |
1876 | else | |
1877 | return x; | |
1878 | } | |
1879 | else if (xx >= 0) | |
1880 | return x; | |
1881 | else | |
1882 | { | |
1883 | SCM r = scm_i_mkbig (); | |
1884 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1885 | scm_remember_upto_here_1 (y); | |
1886 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1887 | return scm_i_normbig (r); | |
1888 | } | |
1889 | } | |
1890 | else if (SCM_REALP (y)) | |
1891 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1892 | else if (SCM_FRACTIONP (y)) | |
1893 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1894 | else | |
1895 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1896 | s_scm_ceiling_remainder); | |
1897 | } | |
1898 | else if (SCM_BIGP (x)) | |
1899 | { | |
1900 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1901 | { | |
1902 | scm_t_inum yy = SCM_I_INUM (y); | |
1903 | if (SCM_UNLIKELY (yy == 0)) | |
1904 | scm_num_overflow (s_scm_ceiling_remainder); | |
1905 | else | |
1906 | { | |
1907 | scm_t_inum rr; | |
1908 | if (yy > 0) | |
1909 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1910 | else | |
1911 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1912 | scm_remember_upto_here_1 (x); | |
1913 | return SCM_I_MAKINUM (rr); | |
1914 | } | |
1915 | } | |
1916 | else if (SCM_BIGP (y)) | |
1917 | { | |
1918 | SCM r = scm_i_mkbig (); | |
1919 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1920 | SCM_I_BIG_MPZ (x), | |
1921 | SCM_I_BIG_MPZ (y)); | |
1922 | scm_remember_upto_here_2 (x, y); | |
1923 | return scm_i_normbig (r); | |
1924 | } | |
1925 | else if (SCM_REALP (y)) | |
1926 | return scm_i_inexact_ceiling_remainder | |
1927 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1928 | else if (SCM_FRACTIONP (y)) | |
1929 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1930 | else | |
1931 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1932 | s_scm_ceiling_remainder); | |
1933 | } | |
1934 | else if (SCM_REALP (x)) | |
1935 | { | |
1936 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1937 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1938 | return scm_i_inexact_ceiling_remainder | |
1939 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1940 | else | |
1941 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1942 | s_scm_ceiling_remainder); | |
1943 | } | |
1944 | else if (SCM_FRACTIONP (x)) | |
1945 | { | |
1946 | if (SCM_REALP (y)) | |
1947 | return scm_i_inexact_ceiling_remainder | |
1948 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1949 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1950 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1951 | else | |
1952 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1953 | s_scm_ceiling_remainder); | |
1954 | } | |
1955 | else | |
1956 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1957 | s_scm_ceiling_remainder); | |
1958 | } | |
1959 | #undef FUNC_NAME | |
1960 | ||
1961 | static SCM | |
1962 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1963 | { | |
1964 | /* Although it would be more efficient to use fmod here, we can't | |
1965 | because it would in some cases produce results inconsistent with | |
1966 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1967 | close). In particular, when x is very close to a multiple of y, | |
1968 | then r might be either 0.0 or -y, but those two cases must | |
1969 | correspond to different choices of q. If r = 0.0 then q must be | |
1970 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1971 | and remainder chooses the other, it would be bad. */ | |
1972 | if (SCM_UNLIKELY (y == 0)) | |
1973 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1974 | else | |
1975 | return scm_from_double (x - y * ceil (x / y)); | |
1976 | } | |
1977 | ||
1978 | static SCM | |
1979 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1980 | { | |
1981 | SCM xd = scm_denominator (x); | |
1982 | SCM yd = scm_denominator (y); | |
1983 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1984 | scm_product (scm_numerator (y), xd)); | |
1985 | return scm_divide (r1, scm_product (xd, yd)); | |
1986 | } | |
1987 | ||
1988 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1989 | SCM *qp, SCM *rp); | |
1990 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1991 | SCM *qp, SCM *rp); | |
1992 | ||
1993 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1994 | (SCM x, SCM y), | |
1995 | "Return the integer @var{q} and the real number @var{r}\n" | |
1996 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1997 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1998 | "@lisp\n" | |
1999 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
2000 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
2001 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
2002 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
2003 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2004 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2005 | "@end lisp") | |
2006 | #define FUNC_NAME s_scm_i_ceiling_divide | |
2007 | { | |
2008 | SCM q, r; | |
2009 | ||
2010 | scm_ceiling_divide(x, y, &q, &r); | |
2011 | return scm_values (scm_list_2 (q, r)); | |
2012 | } | |
2013 | #undef FUNC_NAME | |
2014 | ||
2015 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
2016 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
2017 | ||
2018 | void | |
2019 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2020 | { | |
2021 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2022 | { | |
2023 | scm_t_inum xx = SCM_I_INUM (x); | |
2024 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2025 | { | |
2026 | scm_t_inum yy = SCM_I_INUM (y); | |
2027 | if (SCM_UNLIKELY (yy == 0)) | |
2028 | scm_num_overflow (s_scm_ceiling_divide); | |
2029 | else | |
2030 | { | |
2031 | scm_t_inum qq = xx / yy; | |
2032 | scm_t_inum rr = xx % yy; | |
2033 | int needs_adjustment; | |
2034 | ||
2035 | if (SCM_LIKELY (yy > 0)) | |
2036 | needs_adjustment = (rr > 0); | |
2037 | else | |
2038 | needs_adjustment = (rr < 0); | |
2039 | ||
2040 | if (needs_adjustment) | |
2041 | { | |
2042 | rr -= yy; | |
2043 | qq++; | |
2044 | } | |
2045 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2046 | *qp = SCM_I_MAKINUM (qq); | |
2047 | else | |
2048 | *qp = scm_i_inum2big (qq); | |
2049 | *rp = SCM_I_MAKINUM (rr); | |
2050 | } | |
2051 | return; | |
2052 | } | |
2053 | else if (SCM_BIGP (y)) | |
2054 | { | |
2055 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2056 | scm_remember_upto_here_1 (y); | |
2057 | if (SCM_LIKELY (sign > 0)) | |
2058 | { | |
2059 | if (SCM_LIKELY (xx > 0)) | |
2060 | { | |
2061 | SCM r = scm_i_mkbig (); | |
2062 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2063 | scm_remember_upto_here_1 (y); | |
2064 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2065 | *qp = SCM_INUM1; | |
2066 | *rp = scm_i_normbig (r); | |
2067 | } | |
2068 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2069 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2070 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2071 | { | |
2072 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2073 | scm_remember_upto_here_1 (y); | |
2074 | *qp = SCM_I_MAKINUM (-1); | |
2075 | *rp = SCM_INUM0; | |
2076 | } | |
2077 | else | |
2078 | { | |
2079 | *qp = SCM_INUM0; | |
2080 | *rp = x; | |
2081 | } | |
2082 | } | |
2083 | else if (xx >= 0) | |
2084 | { | |
2085 | *qp = SCM_INUM0; | |
2086 | *rp = x; | |
2087 | } | |
2088 | else | |
2089 | { | |
2090 | SCM r = scm_i_mkbig (); | |
2091 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2092 | scm_remember_upto_here_1 (y); | |
2093 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2094 | *qp = SCM_INUM1; | |
2095 | *rp = scm_i_normbig (r); | |
2096 | } | |
2097 | return; | |
2098 | } | |
2099 | else if (SCM_REALP (y)) | |
2100 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2101 | else if (SCM_FRACTIONP (y)) | |
2102 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2103 | else | |
2104 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2105 | s_scm_ceiling_divide, qp, rp); | |
2106 | } | |
2107 | else if (SCM_BIGP (x)) | |
2108 | { | |
2109 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2110 | { | |
2111 | scm_t_inum yy = SCM_I_INUM (y); | |
2112 | if (SCM_UNLIKELY (yy == 0)) | |
2113 | scm_num_overflow (s_scm_ceiling_divide); | |
2114 | else | |
2115 | { | |
2116 | SCM q = scm_i_mkbig (); | |
2117 | SCM r = scm_i_mkbig (); | |
2118 | if (yy > 0) | |
2119 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2120 | SCM_I_BIG_MPZ (x), yy); | |
2121 | else | |
2122 | { | |
2123 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2124 | SCM_I_BIG_MPZ (x), -yy); | |
2125 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2126 | } | |
2127 | scm_remember_upto_here_1 (x); | |
2128 | *qp = scm_i_normbig (q); | |
2129 | *rp = scm_i_normbig (r); | |
2130 | } | |
2131 | return; | |
2132 | } | |
2133 | else if (SCM_BIGP (y)) | |
2134 | { | |
2135 | SCM q = scm_i_mkbig (); | |
2136 | SCM r = scm_i_mkbig (); | |
2137 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2138 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2139 | scm_remember_upto_here_2 (x, y); | |
2140 | *qp = scm_i_normbig (q); | |
2141 | *rp = scm_i_normbig (r); | |
2142 | return; | |
2143 | } | |
2144 | else if (SCM_REALP (y)) | |
2145 | return scm_i_inexact_ceiling_divide | |
2146 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2147 | else if (SCM_FRACTIONP (y)) | |
2148 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2149 | else | |
2150 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2151 | s_scm_ceiling_divide, qp, rp); | |
2152 | } | |
2153 | else if (SCM_REALP (x)) | |
2154 | { | |
2155 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2156 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2157 | return scm_i_inexact_ceiling_divide | |
2158 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2159 | else | |
2160 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2161 | s_scm_ceiling_divide, qp, rp); | |
2162 | } | |
2163 | else if (SCM_FRACTIONP (x)) | |
2164 | { | |
2165 | if (SCM_REALP (y)) | |
2166 | return scm_i_inexact_ceiling_divide | |
2167 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2168 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2169 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2170 | else | |
2171 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2172 | s_scm_ceiling_divide, qp, rp); | |
2173 | } | |
2174 | else | |
2175 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2176 | s_scm_ceiling_divide, qp, rp); | |
2177 | } | |
2178 | ||
2179 | static void | |
2180 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2181 | { | |
2182 | if (SCM_UNLIKELY (y == 0)) | |
2183 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2184 | else | |
2185 | { | |
2186 | double q = ceil (x / y); | |
2187 | double r = x - q * y; | |
2188 | *qp = scm_from_double (q); | |
2189 | *rp = scm_from_double (r); | |
2190 | } | |
2191 | } | |
2192 | ||
2193 | static void | |
2194 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2195 | { | |
2196 | SCM r1; | |
2197 | SCM xd = scm_denominator (x); | |
2198 | SCM yd = scm_denominator (y); | |
2199 | ||
2200 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2201 | scm_product (scm_numerator (y), xd), | |
2202 | qp, &r1); | |
2203 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2204 | } | |
2205 | ||
2206 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2207 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2208 | ||
2209 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2210 | (SCM x, SCM y), | |
2211 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2212 | "@lisp\n" | |
2213 | "(truncate-quotient 123 10) @result{} 12\n" | |
2214 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2215 | "(truncate-quotient -123 10) @result{} -12\n" | |
2216 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2217 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2218 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2219 | "@end lisp") | |
2220 | #define FUNC_NAME s_scm_truncate_quotient | |
2221 | { | |
2222 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2223 | { | |
2224 | scm_t_inum xx = SCM_I_INUM (x); | |
2225 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2226 | { | |
2227 | scm_t_inum yy = SCM_I_INUM (y); | |
2228 | if (SCM_UNLIKELY (yy == 0)) | |
2229 | scm_num_overflow (s_scm_truncate_quotient); | |
2230 | else | |
2231 | { | |
2232 | scm_t_inum qq = xx / yy; | |
2233 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2234 | return SCM_I_MAKINUM (qq); | |
2235 | else | |
2236 | return scm_i_inum2big (qq); | |
2237 | } | |
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_I_MAKINUM (-1); | |
2248 | } | |
2249 | else | |
2250 | return SCM_INUM0; | |
2251 | } | |
2252 | else if (SCM_REALP (y)) | |
2253 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2254 | else if (SCM_FRACTIONP (y)) | |
2255 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2256 | else | |
2257 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2258 | s_scm_truncate_quotient); | |
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_quotient); | |
2267 | else if (SCM_UNLIKELY (yy == 1)) | |
2268 | return x; | |
2269 | else | |
2270 | { | |
2271 | SCM q = scm_i_mkbig (); | |
2272 | if (yy > 0) | |
2273 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2274 | else | |
2275 | { | |
2276 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2277 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2278 | } | |
2279 | scm_remember_upto_here_1 (x); | |
2280 | return scm_i_normbig (q); | |
2281 | } | |
2282 | } | |
2283 | else if (SCM_BIGP (y)) | |
2284 | { | |
2285 | SCM q = scm_i_mkbig (); | |
2286 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2287 | SCM_I_BIG_MPZ (x), | |
2288 | SCM_I_BIG_MPZ (y)); | |
2289 | scm_remember_upto_here_2 (x, y); | |
2290 | return scm_i_normbig (q); | |
2291 | } | |
2292 | else if (SCM_REALP (y)) | |
2293 | return scm_i_inexact_truncate_quotient | |
2294 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2295 | else if (SCM_FRACTIONP (y)) | |
2296 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2297 | else | |
2298 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2299 | s_scm_truncate_quotient); | |
2300 | } | |
2301 | else if (SCM_REALP (x)) | |
2302 | { | |
2303 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2304 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2305 | return scm_i_inexact_truncate_quotient | |
2306 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2307 | else | |
2308 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2309 | s_scm_truncate_quotient); | |
2310 | } | |
2311 | else if (SCM_FRACTIONP (x)) | |
2312 | { | |
2313 | if (SCM_REALP (y)) | |
2314 | return scm_i_inexact_truncate_quotient | |
2315 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2316 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2317 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2318 | else | |
2319 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2320 | s_scm_truncate_quotient); | |
2321 | } | |
2322 | else | |
2323 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2324 | s_scm_truncate_quotient); | |
2325 | } | |
2326 | #undef FUNC_NAME | |
2327 | ||
2328 | static SCM | |
2329 | scm_i_inexact_truncate_quotient (double x, double y) | |
2330 | { | |
2331 | if (SCM_UNLIKELY (y == 0)) | |
2332 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2333 | else | |
c251ab63 | 2334 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2335 | } |
2336 | ||
2337 | static SCM | |
2338 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2339 | { | |
2340 | return scm_truncate_quotient | |
2341 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2342 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2343 | } | |
2344 | ||
2345 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2346 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2347 | ||
2348 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2349 | (SCM x, SCM y), | |
2350 | "Return the real number @var{r} such that\n" | |
2351 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2352 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2353 | "@lisp\n" | |
2354 | "(truncate-remainder 123 10) @result{} 3\n" | |
2355 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2356 | "(truncate-remainder -123 10) @result{} -3\n" | |
2357 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2358 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2359 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2360 | "@end lisp") | |
2361 | #define FUNC_NAME s_scm_truncate_remainder | |
2362 | { | |
2363 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2364 | { | |
2365 | scm_t_inum xx = SCM_I_INUM (x); | |
2366 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2367 | { | |
2368 | scm_t_inum yy = SCM_I_INUM (y); | |
2369 | if (SCM_UNLIKELY (yy == 0)) | |
2370 | scm_num_overflow (s_scm_truncate_remainder); | |
2371 | else | |
2372 | return SCM_I_MAKINUM (xx % yy); | |
2373 | } | |
2374 | else if (SCM_BIGP (y)) | |
2375 | { | |
2376 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2377 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2378 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2379 | { | |
2380 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2381 | scm_remember_upto_here_1 (y); | |
2382 | return SCM_INUM0; | |
2383 | } | |
2384 | else | |
2385 | return x; | |
2386 | } | |
2387 | else if (SCM_REALP (y)) | |
2388 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2389 | else if (SCM_FRACTIONP (y)) | |
2390 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2391 | else | |
2392 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2393 | s_scm_truncate_remainder); | |
2394 | } | |
2395 | else if (SCM_BIGP (x)) | |
2396 | { | |
2397 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2398 | { | |
2399 | scm_t_inum yy = SCM_I_INUM (y); | |
2400 | if (SCM_UNLIKELY (yy == 0)) | |
2401 | scm_num_overflow (s_scm_truncate_remainder); | |
2402 | else | |
2403 | { | |
2404 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2405 | (yy > 0) ? yy : -yy) | |
2406 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2407 | scm_remember_upto_here_1 (x); | |
2408 | return SCM_I_MAKINUM (rr); | |
2409 | } | |
2410 | } | |
2411 | else if (SCM_BIGP (y)) | |
2412 | { | |
2413 | SCM r = scm_i_mkbig (); | |
2414 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2415 | SCM_I_BIG_MPZ (x), | |
2416 | SCM_I_BIG_MPZ (y)); | |
2417 | scm_remember_upto_here_2 (x, y); | |
2418 | return scm_i_normbig (r); | |
2419 | } | |
2420 | else if (SCM_REALP (y)) | |
2421 | return scm_i_inexact_truncate_remainder | |
2422 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2423 | else if (SCM_FRACTIONP (y)) | |
2424 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2425 | else | |
2426 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2427 | s_scm_truncate_remainder); | |
2428 | } | |
2429 | else if (SCM_REALP (x)) | |
2430 | { | |
2431 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2432 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2433 | return scm_i_inexact_truncate_remainder | |
2434 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2435 | else | |
2436 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2437 | s_scm_truncate_remainder); | |
2438 | } | |
2439 | else if (SCM_FRACTIONP (x)) | |
2440 | { | |
2441 | if (SCM_REALP (y)) | |
2442 | return scm_i_inexact_truncate_remainder | |
2443 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2444 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2445 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2446 | else | |
2447 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2448 | s_scm_truncate_remainder); | |
2449 | } | |
2450 | else | |
2451 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2452 | s_scm_truncate_remainder); | |
2453 | } | |
2454 | #undef FUNC_NAME | |
2455 | ||
2456 | static SCM | |
2457 | scm_i_inexact_truncate_remainder (double x, double y) | |
2458 | { | |
2459 | /* Although it would be more efficient to use fmod here, we can't | |
2460 | because it would in some cases produce results inconsistent with | |
2461 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2462 | close). In particular, when x is very close to a multiple of y, | |
2463 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2464 | correspond to different choices of q. If quotient chooses one and | |
2465 | remainder chooses the other, it would be bad. */ | |
2466 | if (SCM_UNLIKELY (y == 0)) | |
2467 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2468 | else | |
c251ab63 | 2469 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2470 | } |
2471 | ||
2472 | static SCM | |
2473 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2474 | { | |
2475 | SCM xd = scm_denominator (x); | |
2476 | SCM yd = scm_denominator (y); | |
2477 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2478 | scm_product (scm_numerator (y), xd)); | |
2479 | return scm_divide (r1, scm_product (xd, yd)); | |
2480 | } | |
2481 | ||
2482 | ||
2483 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2484 | SCM *qp, SCM *rp); | |
2485 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2486 | SCM *qp, SCM *rp); | |
2487 | ||
2488 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2489 | (SCM x, SCM y), | |
2490 | "Return the integer @var{q} and the real number @var{r}\n" | |
2491 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2492 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2493 | "@lisp\n" | |
2494 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2495 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2496 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2497 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2498 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2499 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2500 | "@end lisp") | |
2501 | #define FUNC_NAME s_scm_i_truncate_divide | |
2502 | { | |
2503 | SCM q, r; | |
2504 | ||
2505 | scm_truncate_divide(x, y, &q, &r); | |
2506 | return scm_values (scm_list_2 (q, r)); | |
2507 | } | |
2508 | #undef FUNC_NAME | |
2509 | ||
2510 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2511 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2512 | ||
2513 | void | |
2514 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2515 | { | |
2516 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2517 | { | |
2518 | scm_t_inum xx = SCM_I_INUM (x); | |
2519 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2520 | { | |
2521 | scm_t_inum yy = SCM_I_INUM (y); | |
2522 | if (SCM_UNLIKELY (yy == 0)) | |
2523 | scm_num_overflow (s_scm_truncate_divide); | |
2524 | else | |
2525 | { | |
2526 | scm_t_inum qq = xx / yy; | |
2527 | scm_t_inum rr = xx % yy; | |
2528 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2529 | *qp = SCM_I_MAKINUM (qq); | |
2530 | else | |
2531 | *qp = scm_i_inum2big (qq); | |
2532 | *rp = SCM_I_MAKINUM (rr); | |
2533 | } | |
2534 | return; | |
2535 | } | |
2536 | else if (SCM_BIGP (y)) | |
2537 | { | |
2538 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2539 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2540 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2541 | { | |
2542 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2543 | scm_remember_upto_here_1 (y); | |
2544 | *qp = SCM_I_MAKINUM (-1); | |
2545 | *rp = SCM_INUM0; | |
2546 | } | |
2547 | else | |
2548 | { | |
2549 | *qp = SCM_INUM0; | |
2550 | *rp = x; | |
2551 | } | |
2552 | return; | |
2553 | } | |
2554 | else if (SCM_REALP (y)) | |
2555 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2556 | else if (SCM_FRACTIONP (y)) | |
2557 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2558 | else | |
2559 | return two_valued_wta_dispatch_2 | |
2560 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2561 | s_scm_truncate_divide, qp, rp); | |
2562 | } | |
2563 | else if (SCM_BIGP (x)) | |
2564 | { | |
2565 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2566 | { | |
2567 | scm_t_inum yy = SCM_I_INUM (y); | |
2568 | if (SCM_UNLIKELY (yy == 0)) | |
2569 | scm_num_overflow (s_scm_truncate_divide); | |
2570 | else | |
2571 | { | |
2572 | SCM q = scm_i_mkbig (); | |
2573 | scm_t_inum rr; | |
2574 | if (yy > 0) | |
2575 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2576 | SCM_I_BIG_MPZ (x), yy); | |
2577 | else | |
2578 | { | |
2579 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2580 | SCM_I_BIG_MPZ (x), -yy); | |
2581 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2582 | } | |
2583 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2584 | scm_remember_upto_here_1 (x); | |
2585 | *qp = scm_i_normbig (q); | |
2586 | *rp = SCM_I_MAKINUM (rr); | |
2587 | } | |
2588 | return; | |
2589 | } | |
2590 | else if (SCM_BIGP (y)) | |
2591 | { | |
2592 | SCM q = scm_i_mkbig (); | |
2593 | SCM r = scm_i_mkbig (); | |
2594 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2595 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2596 | scm_remember_upto_here_2 (x, y); | |
2597 | *qp = scm_i_normbig (q); | |
2598 | *rp = scm_i_normbig (r); | |
2599 | } | |
2600 | else if (SCM_REALP (y)) | |
2601 | return scm_i_inexact_truncate_divide | |
2602 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2603 | else if (SCM_FRACTIONP (y)) | |
2604 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2605 | else | |
2606 | return two_valued_wta_dispatch_2 | |
2607 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2608 | s_scm_truncate_divide, qp, rp); | |
2609 | } | |
2610 | else if (SCM_REALP (x)) | |
2611 | { | |
2612 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2613 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2614 | return scm_i_inexact_truncate_divide | |
2615 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2616 | else | |
2617 | return two_valued_wta_dispatch_2 | |
2618 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2619 | s_scm_truncate_divide, qp, rp); | |
2620 | } | |
2621 | else if (SCM_FRACTIONP (x)) | |
2622 | { | |
2623 | if (SCM_REALP (y)) | |
2624 | return scm_i_inexact_truncate_divide | |
2625 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2626 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2627 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2628 | else | |
2629 | return two_valued_wta_dispatch_2 | |
2630 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2631 | s_scm_truncate_divide, qp, rp); | |
2632 | } | |
2633 | else | |
2634 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2635 | s_scm_truncate_divide, qp, rp); | |
2636 | } | |
2637 | ||
2638 | static void | |
2639 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2640 | { | |
2641 | if (SCM_UNLIKELY (y == 0)) | |
2642 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2643 | else | |
2644 | { | |
c15fe499 MW |
2645 | double q = trunc (x / y); |
2646 | double r = x - q * y; | |
8f9da340 MW |
2647 | *qp = scm_from_double (q); |
2648 | *rp = scm_from_double (r); | |
2649 | } | |
2650 | } | |
2651 | ||
2652 | static void | |
2653 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2654 | { | |
2655 | SCM r1; | |
2656 | SCM xd = scm_denominator (x); | |
2657 | SCM yd = scm_denominator (y); | |
2658 | ||
2659 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2660 | scm_product (scm_numerator (y), xd), | |
2661 | qp, &r1); | |
2662 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2663 | } | |
2664 | ||
ff62c168 MW |
2665 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2666 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2667 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2668 | |
8f9da340 MW |
2669 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2670 | (SCM x, SCM y), | |
2671 | "Return the integer @var{q} such that\n" | |
2672 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2673 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2674 | "@lisp\n" | |
2675 | "(centered-quotient 123 10) @result{} 12\n" | |
2676 | "(centered-quotient 123 -10) @result{} -12\n" | |
2677 | "(centered-quotient -123 10) @result{} -12\n" | |
2678 | "(centered-quotient -123 -10) @result{} 12\n" | |
2679 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2680 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2681 | "@end lisp") | |
2682 | #define FUNC_NAME s_scm_centered_quotient | |
2683 | { | |
2684 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2685 | { | |
2686 | scm_t_inum xx = SCM_I_INUM (x); | |
2687 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2688 | { | |
2689 | scm_t_inum yy = SCM_I_INUM (y); | |
2690 | if (SCM_UNLIKELY (yy == 0)) | |
2691 | scm_num_overflow (s_scm_centered_quotient); | |
2692 | else | |
2693 | { | |
2694 | scm_t_inum qq = xx / yy; | |
2695 | scm_t_inum rr = xx % yy; | |
2696 | if (SCM_LIKELY (xx > 0)) | |
2697 | { | |
2698 | if (SCM_LIKELY (yy > 0)) | |
2699 | { | |
2700 | if (rr >= (yy + 1) / 2) | |
2701 | qq++; | |
2702 | } | |
2703 | else | |
2704 | { | |
2705 | if (rr >= (1 - yy) / 2) | |
2706 | qq--; | |
2707 | } | |
2708 | } | |
2709 | else | |
2710 | { | |
2711 | if (SCM_LIKELY (yy > 0)) | |
2712 | { | |
2713 | if (rr < -yy / 2) | |
2714 | qq--; | |
2715 | } | |
2716 | else | |
2717 | { | |
2718 | if (rr < yy / 2) | |
2719 | qq++; | |
2720 | } | |
2721 | } | |
2722 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2723 | return SCM_I_MAKINUM (qq); | |
2724 | else | |
2725 | return scm_i_inum2big (qq); | |
2726 | } | |
2727 | } | |
2728 | else if (SCM_BIGP (y)) | |
2729 | { | |
2730 | /* Pass a denormalized bignum version of x (even though it | |
2731 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2732 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2733 | } | |
2734 | else if (SCM_REALP (y)) | |
2735 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2736 | else if (SCM_FRACTIONP (y)) | |
2737 | return scm_i_exact_rational_centered_quotient (x, y); | |
2738 | else | |
2739 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2740 | s_scm_centered_quotient); | |
2741 | } | |
2742 | else if (SCM_BIGP (x)) | |
2743 | { | |
2744 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2745 | { | |
2746 | scm_t_inum yy = SCM_I_INUM (y); | |
2747 | if (SCM_UNLIKELY (yy == 0)) | |
2748 | scm_num_overflow (s_scm_centered_quotient); | |
2749 | else if (SCM_UNLIKELY (yy == 1)) | |
2750 | return x; | |
2751 | else | |
2752 | { | |
2753 | SCM q = scm_i_mkbig (); | |
2754 | scm_t_inum rr; | |
2755 | /* Arrange for rr to initially be non-positive, | |
2756 | because that simplifies the test to see | |
2757 | if it is within the needed bounds. */ | |
2758 | if (yy > 0) | |
2759 | { | |
2760 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2761 | SCM_I_BIG_MPZ (x), yy); | |
2762 | scm_remember_upto_here_1 (x); | |
2763 | if (rr < -yy / 2) | |
2764 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2765 | SCM_I_BIG_MPZ (q), 1); | |
2766 | } | |
2767 | else | |
2768 | { | |
2769 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2770 | SCM_I_BIG_MPZ (x), -yy); | |
2771 | scm_remember_upto_here_1 (x); | |
2772 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2773 | if (rr < yy / 2) | |
2774 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2775 | SCM_I_BIG_MPZ (q), 1); | |
2776 | } | |
2777 | return scm_i_normbig (q); | |
2778 | } | |
2779 | } | |
2780 | else if (SCM_BIGP (y)) | |
2781 | return scm_i_bigint_centered_quotient (x, y); | |
2782 | else if (SCM_REALP (y)) | |
2783 | return scm_i_inexact_centered_quotient | |
2784 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2785 | else if (SCM_FRACTIONP (y)) | |
2786 | return scm_i_exact_rational_centered_quotient (x, y); | |
2787 | else | |
2788 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2789 | s_scm_centered_quotient); | |
2790 | } | |
2791 | else if (SCM_REALP (x)) | |
2792 | { | |
2793 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2794 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2795 | return scm_i_inexact_centered_quotient | |
2796 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2797 | else | |
2798 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2799 | s_scm_centered_quotient); | |
2800 | } | |
2801 | else if (SCM_FRACTIONP (x)) | |
2802 | { | |
2803 | if (SCM_REALP (y)) | |
2804 | return scm_i_inexact_centered_quotient | |
2805 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2806 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2807 | return scm_i_exact_rational_centered_quotient (x, y); | |
2808 | else | |
2809 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2810 | s_scm_centered_quotient); | |
2811 | } | |
2812 | else | |
2813 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2814 | s_scm_centered_quotient); | |
2815 | } | |
2816 | #undef FUNC_NAME | |
2817 | ||
2818 | static SCM | |
2819 | scm_i_inexact_centered_quotient (double x, double y) | |
2820 | { | |
2821 | if (SCM_LIKELY (y > 0)) | |
2822 | return scm_from_double (floor (x/y + 0.5)); | |
2823 | else if (SCM_LIKELY (y < 0)) | |
2824 | return scm_from_double (ceil (x/y - 0.5)); | |
2825 | else if (y == 0) | |
2826 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2827 | else | |
2828 | return scm_nan (); | |
2829 | } | |
2830 | ||
2831 | /* Assumes that both x and y are bigints, though | |
2832 | x might be able to fit into a fixnum. */ | |
2833 | static SCM | |
2834 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2835 | { | |
2836 | SCM q, r, min_r; | |
2837 | ||
2838 | /* Note that x might be small enough to fit into a | |
2839 | fixnum, so we must not let it escape into the wild */ | |
2840 | q = scm_i_mkbig (); | |
2841 | r = scm_i_mkbig (); | |
2842 | ||
2843 | /* min_r will eventually become -abs(y)/2 */ | |
2844 | min_r = scm_i_mkbig (); | |
2845 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2846 | SCM_I_BIG_MPZ (y), 1); | |
2847 | ||
2848 | /* Arrange for rr to initially be non-positive, | |
2849 | because that simplifies the test to see | |
2850 | if it is within the needed bounds. */ | |
2851 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2852 | { | |
2853 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2854 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2855 | scm_remember_upto_here_2 (x, y); | |
2856 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2857 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2858 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2859 | SCM_I_BIG_MPZ (q), 1); | |
2860 | } | |
2861 | else | |
2862 | { | |
2863 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2864 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2865 | scm_remember_upto_here_2 (x, y); | |
2866 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2867 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2868 | SCM_I_BIG_MPZ (q), 1); | |
2869 | } | |
2870 | scm_remember_upto_here_2 (r, min_r); | |
2871 | return scm_i_normbig (q); | |
2872 | } | |
2873 | ||
2874 | static SCM | |
2875 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2876 | { | |
2877 | return scm_centered_quotient | |
2878 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2879 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2880 | } | |
2881 | ||
2882 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2883 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2884 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2885 | ||
2886 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2887 | (SCM x, SCM y), | |
2888 | "Return the real number @var{r} such that\n" | |
2889 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2890 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2891 | "for some integer @var{q}.\n" | |
2892 | "@lisp\n" | |
2893 | "(centered-remainder 123 10) @result{} 3\n" | |
2894 | "(centered-remainder 123 -10) @result{} 3\n" | |
2895 | "(centered-remainder -123 10) @result{} -3\n" | |
2896 | "(centered-remainder -123 -10) @result{} -3\n" | |
2897 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2898 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2899 | "@end lisp") | |
2900 | #define FUNC_NAME s_scm_centered_remainder | |
2901 | { | |
2902 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2903 | { | |
2904 | scm_t_inum xx = SCM_I_INUM (x); | |
2905 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2906 | { | |
2907 | scm_t_inum yy = SCM_I_INUM (y); | |
2908 | if (SCM_UNLIKELY (yy == 0)) | |
2909 | scm_num_overflow (s_scm_centered_remainder); | |
2910 | else | |
2911 | { | |
2912 | scm_t_inum rr = xx % yy; | |
2913 | if (SCM_LIKELY (xx > 0)) | |
2914 | { | |
2915 | if (SCM_LIKELY (yy > 0)) | |
2916 | { | |
2917 | if (rr >= (yy + 1) / 2) | |
2918 | rr -= yy; | |
2919 | } | |
2920 | else | |
2921 | { | |
2922 | if (rr >= (1 - yy) / 2) | |
2923 | rr += yy; | |
2924 | } | |
2925 | } | |
2926 | else | |
2927 | { | |
2928 | if (SCM_LIKELY (yy > 0)) | |
2929 | { | |
2930 | if (rr < -yy / 2) | |
2931 | rr += yy; | |
2932 | } | |
2933 | else | |
2934 | { | |
2935 | if (rr < yy / 2) | |
2936 | rr -= yy; | |
2937 | } | |
2938 | } | |
2939 | return SCM_I_MAKINUM (rr); | |
2940 | } | |
2941 | } | |
2942 | else if (SCM_BIGP (y)) | |
2943 | { | |
2944 | /* Pass a denormalized bignum version of x (even though it | |
2945 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2946 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2947 | } | |
2948 | else if (SCM_REALP (y)) | |
2949 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2950 | else if (SCM_FRACTIONP (y)) | |
2951 | return scm_i_exact_rational_centered_remainder (x, y); | |
2952 | else | |
2953 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2954 | s_scm_centered_remainder); | |
2955 | } | |
2956 | else if (SCM_BIGP (x)) | |
2957 | { | |
2958 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2959 | { | |
2960 | scm_t_inum yy = SCM_I_INUM (y); | |
2961 | if (SCM_UNLIKELY (yy == 0)) | |
2962 | scm_num_overflow (s_scm_centered_remainder); | |
2963 | else | |
2964 | { | |
2965 | scm_t_inum rr; | |
2966 | /* Arrange for rr to initially be non-positive, | |
2967 | because that simplifies the test to see | |
2968 | if it is within the needed bounds. */ | |
2969 | if (yy > 0) | |
2970 | { | |
2971 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2972 | scm_remember_upto_here_1 (x); | |
2973 | if (rr < -yy / 2) | |
2974 | rr += yy; | |
2975 | } | |
2976 | else | |
2977 | { | |
2978 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2979 | scm_remember_upto_here_1 (x); | |
2980 | if (rr < yy / 2) | |
2981 | rr -= yy; | |
2982 | } | |
2983 | return SCM_I_MAKINUM (rr); | |
2984 | } | |
2985 | } | |
2986 | else if (SCM_BIGP (y)) | |
2987 | return scm_i_bigint_centered_remainder (x, y); | |
2988 | else if (SCM_REALP (y)) | |
2989 | return scm_i_inexact_centered_remainder | |
2990 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2991 | else if (SCM_FRACTIONP (y)) | |
2992 | return scm_i_exact_rational_centered_remainder (x, y); | |
2993 | else | |
2994 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2995 | s_scm_centered_remainder); | |
2996 | } | |
2997 | else if (SCM_REALP (x)) | |
2998 | { | |
2999 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3000 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3001 | return scm_i_inexact_centered_remainder | |
3002 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
3003 | else | |
3004 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3005 | s_scm_centered_remainder); | |
3006 | } | |
3007 | else if (SCM_FRACTIONP (x)) | |
3008 | { | |
3009 | if (SCM_REALP (y)) | |
3010 | return scm_i_inexact_centered_remainder | |
3011 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
3012 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3013 | return scm_i_exact_rational_centered_remainder (x, y); | |
3014 | else | |
3015 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3016 | s_scm_centered_remainder); | |
3017 | } | |
3018 | else | |
3019 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
3020 | s_scm_centered_remainder); | |
3021 | } | |
3022 | #undef FUNC_NAME | |
3023 | ||
3024 | static SCM | |
3025 | scm_i_inexact_centered_remainder (double x, double y) | |
3026 | { | |
3027 | double q; | |
3028 | ||
3029 | /* Although it would be more efficient to use fmod here, we can't | |
3030 | because it would in some cases produce results inconsistent with | |
3031 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
3032 | close). In particular, when x-y/2 is very close to a multiple of | |
3033 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
3034 | two cases must correspond to different choices of q. If quotient | |
3035 | chooses one and remainder chooses the other, it would be bad. */ | |
3036 | if (SCM_LIKELY (y > 0)) | |
3037 | q = floor (x/y + 0.5); | |
3038 | else if (SCM_LIKELY (y < 0)) | |
3039 | q = ceil (x/y - 0.5); | |
3040 | else if (y == 0) | |
3041 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
3042 | else | |
3043 | return scm_nan (); | |
3044 | return scm_from_double (x - q * y); | |
3045 | } | |
3046 | ||
3047 | /* Assumes that both x and y are bigints, though | |
3048 | x might be able to fit into a fixnum. */ | |
3049 | static SCM | |
3050 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
3051 | { | |
3052 | SCM r, min_r; | |
3053 | ||
3054 | /* Note that x might be small enough to fit into a | |
3055 | fixnum, so we must not let it escape into the wild */ | |
3056 | r = scm_i_mkbig (); | |
3057 | ||
3058 | /* min_r will eventually become -abs(y)/2 */ | |
3059 | min_r = scm_i_mkbig (); | |
3060 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3061 | SCM_I_BIG_MPZ (y), 1); | |
3062 | ||
3063 | /* Arrange for rr to initially be non-positive, | |
3064 | because that simplifies the test to see | |
3065 | if it is within the needed bounds. */ | |
3066 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3067 | { | |
3068 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
3069 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3070 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3071 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3072 | mpz_add (SCM_I_BIG_MPZ (r), | |
3073 | SCM_I_BIG_MPZ (r), | |
3074 | SCM_I_BIG_MPZ (y)); | |
3075 | } | |
3076 | else | |
3077 | { | |
3078 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
3079 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3080 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3081 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3082 | SCM_I_BIG_MPZ (r), | |
3083 | SCM_I_BIG_MPZ (y)); | |
3084 | } | |
3085 | scm_remember_upto_here_2 (x, y); | |
3086 | return scm_i_normbig (r); | |
3087 | } | |
3088 | ||
3089 | static SCM | |
3090 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
3091 | { | |
3092 | SCM xd = scm_denominator (x); | |
3093 | SCM yd = scm_denominator (y); | |
3094 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
3095 | scm_product (scm_numerator (y), xd)); | |
3096 | return scm_divide (r1, scm_product (xd, yd)); | |
3097 | } | |
3098 | ||
3099 | ||
3100 | static void scm_i_inexact_centered_divide (double x, double y, | |
3101 | SCM *qp, SCM *rp); | |
3102 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3103 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
3104 | SCM *qp, SCM *rp); | |
3105 | ||
3106 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
3107 | (SCM x, SCM y), | |
3108 | "Return the integer @var{q} and the real number @var{r}\n" | |
3109 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
3110 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
3111 | "@lisp\n" | |
3112 | "(centered/ 123 10) @result{} 12 and 3\n" | |
3113 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
3114 | "(centered/ -123 10) @result{} -12 and -3\n" | |
3115 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
3116 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3117 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
3118 | "@end lisp") | |
3119 | #define FUNC_NAME s_scm_i_centered_divide | |
3120 | { | |
3121 | SCM q, r; | |
3122 | ||
3123 | scm_centered_divide(x, y, &q, &r); | |
3124 | return scm_values (scm_list_2 (q, r)); | |
3125 | } | |
3126 | #undef FUNC_NAME | |
3127 | ||
3128 | #define s_scm_centered_divide s_scm_i_centered_divide | |
3129 | #define g_scm_centered_divide g_scm_i_centered_divide | |
3130 | ||
3131 | void | |
3132 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3133 | { | |
3134 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3135 | { | |
3136 | scm_t_inum xx = SCM_I_INUM (x); | |
3137 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3138 | { | |
3139 | scm_t_inum yy = SCM_I_INUM (y); | |
3140 | if (SCM_UNLIKELY (yy == 0)) | |
3141 | scm_num_overflow (s_scm_centered_divide); | |
3142 | else | |
3143 | { | |
3144 | scm_t_inum qq = xx / yy; | |
3145 | scm_t_inum rr = xx % yy; | |
3146 | if (SCM_LIKELY (xx > 0)) | |
3147 | { | |
3148 | if (SCM_LIKELY (yy > 0)) | |
3149 | { | |
3150 | if (rr >= (yy + 1) / 2) | |
3151 | { qq++; rr -= yy; } | |
3152 | } | |
3153 | else | |
3154 | { | |
3155 | if (rr >= (1 - yy) / 2) | |
3156 | { qq--; rr += yy; } | |
3157 | } | |
3158 | } | |
3159 | else | |
3160 | { | |
3161 | if (SCM_LIKELY (yy > 0)) | |
3162 | { | |
3163 | if (rr < -yy / 2) | |
3164 | { qq--; rr += yy; } | |
3165 | } | |
3166 | else | |
3167 | { | |
3168 | if (rr < yy / 2) | |
3169 | { qq++; rr -= yy; } | |
3170 | } | |
3171 | } | |
3172 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3173 | *qp = SCM_I_MAKINUM (qq); | |
3174 | else | |
3175 | *qp = scm_i_inum2big (qq); | |
3176 | *rp = SCM_I_MAKINUM (rr); | |
3177 | } | |
3178 | return; | |
3179 | } | |
3180 | else if (SCM_BIGP (y)) | |
3181 | { | |
3182 | /* Pass a denormalized bignum version of x (even though it | |
3183 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3184 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3185 | } | |
3186 | else if (SCM_REALP (y)) | |
3187 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3188 | else if (SCM_FRACTIONP (y)) | |
3189 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3190 | else | |
3191 | return two_valued_wta_dispatch_2 | |
3192 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3193 | s_scm_centered_divide, qp, rp); | |
3194 | } | |
3195 | else if (SCM_BIGP (x)) | |
3196 | { | |
3197 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3198 | { | |
3199 | scm_t_inum yy = SCM_I_INUM (y); | |
3200 | if (SCM_UNLIKELY (yy == 0)) | |
3201 | scm_num_overflow (s_scm_centered_divide); | |
3202 | else | |
3203 | { | |
3204 | SCM q = scm_i_mkbig (); | |
3205 | scm_t_inum rr; | |
3206 | /* Arrange for rr to initially be non-positive, | |
3207 | because that simplifies the test to see | |
3208 | if it is within the needed bounds. */ | |
3209 | if (yy > 0) | |
3210 | { | |
3211 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3212 | SCM_I_BIG_MPZ (x), yy); | |
3213 | scm_remember_upto_here_1 (x); | |
3214 | if (rr < -yy / 2) | |
3215 | { | |
3216 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3217 | SCM_I_BIG_MPZ (q), 1); | |
3218 | rr += yy; | |
3219 | } | |
3220 | } | |
3221 | else | |
3222 | { | |
3223 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3224 | SCM_I_BIG_MPZ (x), -yy); | |
3225 | scm_remember_upto_here_1 (x); | |
3226 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3227 | if (rr < yy / 2) | |
3228 | { | |
3229 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3230 | SCM_I_BIG_MPZ (q), 1); | |
3231 | rr -= yy; | |
3232 | } | |
3233 | } | |
3234 | *qp = scm_i_normbig (q); | |
3235 | *rp = SCM_I_MAKINUM (rr); | |
3236 | } | |
3237 | return; | |
3238 | } | |
3239 | else if (SCM_BIGP (y)) | |
3240 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3241 | else if (SCM_REALP (y)) | |
3242 | return scm_i_inexact_centered_divide | |
3243 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3244 | else if (SCM_FRACTIONP (y)) | |
3245 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3246 | else | |
3247 | return two_valued_wta_dispatch_2 | |
3248 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3249 | s_scm_centered_divide, qp, rp); | |
3250 | } | |
3251 | else if (SCM_REALP (x)) | |
3252 | { | |
3253 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3254 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3255 | return scm_i_inexact_centered_divide | |
3256 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3257 | else | |
3258 | return two_valued_wta_dispatch_2 | |
3259 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3260 | s_scm_centered_divide, qp, rp); | |
3261 | } | |
3262 | else if (SCM_FRACTIONP (x)) | |
3263 | { | |
3264 | if (SCM_REALP (y)) | |
3265 | return scm_i_inexact_centered_divide | |
3266 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3267 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3268 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3269 | else | |
3270 | return two_valued_wta_dispatch_2 | |
3271 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3272 | s_scm_centered_divide, qp, rp); | |
3273 | } | |
3274 | else | |
3275 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3276 | s_scm_centered_divide, qp, rp); | |
3277 | } | |
3278 | ||
3279 | static void | |
3280 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3281 | { | |
3282 | double q, r; | |
3283 | ||
3284 | if (SCM_LIKELY (y > 0)) | |
3285 | q = floor (x/y + 0.5); | |
3286 | else if (SCM_LIKELY (y < 0)) | |
3287 | q = ceil (x/y - 0.5); | |
3288 | else if (y == 0) | |
3289 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3290 | else | |
3291 | q = guile_NaN; | |
3292 | r = x - q * y; | |
3293 | *qp = scm_from_double (q); | |
3294 | *rp = scm_from_double (r); | |
3295 | } | |
3296 | ||
3297 | /* Assumes that both x and y are bigints, though | |
3298 | x might be able to fit into a fixnum. */ | |
3299 | static void | |
3300 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3301 | { | |
3302 | SCM q, r, min_r; | |
3303 | ||
3304 | /* Note that x might be small enough to fit into a | |
3305 | fixnum, so we must not let it escape into the wild */ | |
3306 | q = scm_i_mkbig (); | |
3307 | r = scm_i_mkbig (); | |
3308 | ||
3309 | /* min_r will eventually become -abs(y/2) */ | |
3310 | min_r = scm_i_mkbig (); | |
3311 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3312 | SCM_I_BIG_MPZ (y), 1); | |
3313 | ||
3314 | /* Arrange for rr to initially be non-positive, | |
3315 | because that simplifies the test to see | |
3316 | if it is within the needed bounds. */ | |
3317 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3318 | { | |
3319 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3320 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3321 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3322 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3323 | { | |
3324 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3325 | SCM_I_BIG_MPZ (q), 1); | |
3326 | mpz_add (SCM_I_BIG_MPZ (r), | |
3327 | SCM_I_BIG_MPZ (r), | |
3328 | SCM_I_BIG_MPZ (y)); | |
3329 | } | |
3330 | } | |
3331 | else | |
3332 | { | |
3333 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3334 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3335 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3336 | { | |
3337 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3338 | SCM_I_BIG_MPZ (q), 1); | |
3339 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3340 | SCM_I_BIG_MPZ (r), | |
3341 | SCM_I_BIG_MPZ (y)); | |
3342 | } | |
3343 | } | |
3344 | scm_remember_upto_here_2 (x, y); | |
3345 | *qp = scm_i_normbig (q); | |
3346 | *rp = scm_i_normbig (r); | |
3347 | } | |
3348 | ||
3349 | static void | |
3350 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3351 | { | |
3352 | SCM r1; | |
3353 | SCM xd = scm_denominator (x); | |
3354 | SCM yd = scm_denominator (y); | |
3355 | ||
3356 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3357 | scm_product (scm_numerator (y), xd), | |
3358 | qp, &r1); | |
3359 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3360 | } | |
3361 | ||
3362 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3363 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3364 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3365 | ||
3366 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3367 | (SCM x, SCM y), |
8f9da340 MW |
3368 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3369 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3370 | "@lisp\n" |
8f9da340 MW |
3371 | "(round-quotient 123 10) @result{} 12\n" |
3372 | "(round-quotient 123 -10) @result{} -12\n" | |
3373 | "(round-quotient -123 10) @result{} -12\n" | |
3374 | "(round-quotient -123 -10) @result{} 12\n" | |
3375 | "(round-quotient 125 10) @result{} 12\n" | |
3376 | "(round-quotient 127 10) @result{} 13\n" | |
3377 | "(round-quotient 135 10) @result{} 14\n" | |
3378 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3379 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3380 | "@end lisp") |
8f9da340 | 3381 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3382 | { |
3383 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3384 | { | |
4a46bc2a | 3385 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3386 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3387 | { | |
3388 | scm_t_inum yy = SCM_I_INUM (y); | |
3389 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3390 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3391 | else |
3392 | { | |
ff62c168 | 3393 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3394 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3395 | scm_t_inum ay = yy; |
3396 | scm_t_inum r2 = 2 * rr; | |
3397 | ||
3398 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3399 | { |
8f9da340 MW |
3400 | ay = -ay; |
3401 | r2 = -r2; | |
3402 | } | |
3403 | ||
3404 | if (qq & 1L) | |
3405 | { | |
3406 | if (r2 >= ay) | |
3407 | qq++; | |
3408 | else if (r2 <= -ay) | |
3409 | qq--; | |
ff62c168 MW |
3410 | } |
3411 | else | |
3412 | { | |
8f9da340 MW |
3413 | if (r2 > ay) |
3414 | qq++; | |
3415 | else if (r2 < -ay) | |
3416 | qq--; | |
ff62c168 | 3417 | } |
4a46bc2a MW |
3418 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3419 | return SCM_I_MAKINUM (qq); | |
3420 | else | |
3421 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3422 | } |
3423 | } | |
3424 | else if (SCM_BIGP (y)) | |
3425 | { | |
3426 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3427 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3428 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3429 | } |
3430 | else if (SCM_REALP (y)) | |
8f9da340 | 3431 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3432 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3433 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3434 | else |
8f9da340 MW |
3435 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3436 | s_scm_round_quotient); | |
ff62c168 MW |
3437 | } |
3438 | else if (SCM_BIGP (x)) | |
3439 | { | |
3440 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3441 | { | |
3442 | scm_t_inum yy = SCM_I_INUM (y); | |
3443 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3444 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3445 | else if (SCM_UNLIKELY (yy == 1)) |
3446 | return x; | |
ff62c168 MW |
3447 | else |
3448 | { | |
3449 | SCM q = scm_i_mkbig (); | |
3450 | scm_t_inum rr; | |
8f9da340 MW |
3451 | int needs_adjustment; |
3452 | ||
ff62c168 MW |
3453 | if (yy > 0) |
3454 | { | |
8f9da340 MW |
3455 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3456 | SCM_I_BIG_MPZ (x), yy); | |
3457 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3458 | needs_adjustment = (2*rr >= yy); | |
3459 | else | |
3460 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3461 | } |
3462 | else | |
3463 | { | |
3464 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3465 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3466 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3467 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3468 | needs_adjustment = (2*rr <= yy); | |
3469 | else | |
3470 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3471 | } |
8f9da340 MW |
3472 | scm_remember_upto_here_1 (x); |
3473 | if (needs_adjustment) | |
3474 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3475 | return scm_i_normbig (q); |
3476 | } | |
3477 | } | |
3478 | else if (SCM_BIGP (y)) | |
8f9da340 | 3479 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3480 | else if (SCM_REALP (y)) |
8f9da340 | 3481 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3482 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3483 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3484 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3485 | else |
8f9da340 MW |
3486 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3487 | s_scm_round_quotient); | |
ff62c168 MW |
3488 | } |
3489 | else if (SCM_REALP (x)) | |
3490 | { | |
3491 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3492 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3493 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3494 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3495 | else | |
8f9da340 MW |
3496 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3497 | s_scm_round_quotient); | |
ff62c168 MW |
3498 | } |
3499 | else if (SCM_FRACTIONP (x)) | |
3500 | { | |
3501 | if (SCM_REALP (y)) | |
8f9da340 | 3502 | return scm_i_inexact_round_quotient |
ff62c168 | 3503 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3504 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3505 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3506 | else |
8f9da340 MW |
3507 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3508 | s_scm_round_quotient); | |
ff62c168 MW |
3509 | } |
3510 | else | |
8f9da340 MW |
3511 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3512 | s_scm_round_quotient); | |
ff62c168 MW |
3513 | } |
3514 | #undef FUNC_NAME | |
3515 | ||
3516 | static SCM | |
8f9da340 | 3517 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3518 | { |
8f9da340 MW |
3519 | if (SCM_UNLIKELY (y == 0)) |
3520 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3521 | else |
8f9da340 | 3522 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3523 | } |
3524 | ||
3525 | /* Assumes that both x and y are bigints, though | |
3526 | x might be able to fit into a fixnum. */ | |
3527 | static SCM | |
8f9da340 | 3528 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3529 | { |
8f9da340 MW |
3530 | SCM q, r, r2; |
3531 | int cmp, needs_adjustment; | |
ff62c168 MW |
3532 | |
3533 | /* Note that x might be small enough to fit into a | |
3534 | fixnum, so we must not let it escape into the wild */ | |
3535 | q = scm_i_mkbig (); | |
3536 | r = scm_i_mkbig (); | |
8f9da340 | 3537 | r2 = scm_i_mkbig (); |
ff62c168 | 3538 | |
8f9da340 MW |
3539 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3540 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3541 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3542 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3543 | |
8f9da340 MW |
3544 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3545 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3546 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3547 | else |
8f9da340 MW |
3548 | needs_adjustment = (cmp > 0); |
3549 | scm_remember_upto_here_2 (r2, y); | |
3550 | ||
3551 | if (needs_adjustment) | |
3552 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3553 | ||
ff62c168 MW |
3554 | return scm_i_normbig (q); |
3555 | } | |
3556 | ||
ff62c168 | 3557 | static SCM |
8f9da340 | 3558 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3559 | { |
8f9da340 | 3560 | return scm_round_quotient |
03ddd15b MW |
3561 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3562 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3563 | } |
3564 | ||
8f9da340 MW |
3565 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3566 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3567 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3568 | |
8f9da340 | 3569 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3570 | (SCM x, SCM y), |
3571 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3572 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3573 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3574 | "nearest integer, with ties going to the nearest\n" | |
3575 | "even integer.\n" | |
ff62c168 | 3576 | "@lisp\n" |
8f9da340 MW |
3577 | "(round-remainder 123 10) @result{} 3\n" |
3578 | "(round-remainder 123 -10) @result{} 3\n" | |
3579 | "(round-remainder -123 10) @result{} -3\n" | |
3580 | "(round-remainder -123 -10) @result{} -3\n" | |
3581 | "(round-remainder 125 10) @result{} 5\n" | |
3582 | "(round-remainder 127 10) @result{} -3\n" | |
3583 | "(round-remainder 135 10) @result{} -5\n" | |
3584 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3585 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3586 | "@end lisp") |
8f9da340 | 3587 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3588 | { |
3589 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3590 | { | |
4a46bc2a | 3591 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3592 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3593 | { | |
3594 | scm_t_inum yy = SCM_I_INUM (y); | |
3595 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3596 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3597 | else |
3598 | { | |
8f9da340 | 3599 | scm_t_inum qq = xx / yy; |
ff62c168 | 3600 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3601 | scm_t_inum ay = yy; |
3602 | scm_t_inum r2 = 2 * rr; | |
3603 | ||
3604 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3605 | { |
8f9da340 MW |
3606 | ay = -ay; |
3607 | r2 = -r2; | |
3608 | } | |
3609 | ||
3610 | if (qq & 1L) | |
3611 | { | |
3612 | if (r2 >= ay) | |
3613 | rr -= yy; | |
3614 | else if (r2 <= -ay) | |
3615 | rr += yy; | |
ff62c168 MW |
3616 | } |
3617 | else | |
3618 | { | |
8f9da340 MW |
3619 | if (r2 > ay) |
3620 | rr -= yy; | |
3621 | else if (r2 < -ay) | |
3622 | rr += yy; | |
ff62c168 MW |
3623 | } |
3624 | return SCM_I_MAKINUM (rr); | |
3625 | } | |
3626 | } | |
3627 | else if (SCM_BIGP (y)) | |
3628 | { | |
3629 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3630 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3631 | return scm_i_bigint_round_remainder | |
3632 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3633 | } |
3634 | else if (SCM_REALP (y)) | |
8f9da340 | 3635 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3636 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3637 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3638 | else |
8f9da340 MW |
3639 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3640 | s_scm_round_remainder); | |
ff62c168 MW |
3641 | } |
3642 | else if (SCM_BIGP (x)) | |
3643 | { | |
3644 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3645 | { | |
3646 | scm_t_inum yy = SCM_I_INUM (y); | |
3647 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3648 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3649 | else |
3650 | { | |
8f9da340 | 3651 | SCM q = scm_i_mkbig (); |
ff62c168 | 3652 | scm_t_inum rr; |
8f9da340 MW |
3653 | int needs_adjustment; |
3654 | ||
ff62c168 MW |
3655 | if (yy > 0) |
3656 | { | |
8f9da340 MW |
3657 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3658 | SCM_I_BIG_MPZ (x), yy); | |
3659 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3660 | needs_adjustment = (2*rr >= yy); | |
3661 | else | |
3662 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3663 | } |
3664 | else | |
3665 | { | |
8f9da340 MW |
3666 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3667 | SCM_I_BIG_MPZ (x), -yy); | |
3668 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3669 | needs_adjustment = (2*rr <= yy); | |
3670 | else | |
3671 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3672 | } |
8f9da340 MW |
3673 | scm_remember_upto_here_2 (x, q); |
3674 | if (needs_adjustment) | |
3675 | rr -= yy; | |
ff62c168 MW |
3676 | return SCM_I_MAKINUM (rr); |
3677 | } | |
3678 | } | |
3679 | else if (SCM_BIGP (y)) | |
8f9da340 | 3680 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3681 | else if (SCM_REALP (y)) |
8f9da340 | 3682 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3683 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3684 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3685 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3686 | else |
8f9da340 MW |
3687 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3688 | s_scm_round_remainder); | |
ff62c168 MW |
3689 | } |
3690 | else if (SCM_REALP (x)) | |
3691 | { | |
3692 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3693 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3694 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3695 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3696 | else | |
8f9da340 MW |
3697 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3698 | s_scm_round_remainder); | |
ff62c168 MW |
3699 | } |
3700 | else if (SCM_FRACTIONP (x)) | |
3701 | { | |
3702 | if (SCM_REALP (y)) | |
8f9da340 | 3703 | return scm_i_inexact_round_remainder |
ff62c168 | 3704 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3705 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3706 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3707 | else |
8f9da340 MW |
3708 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3709 | s_scm_round_remainder); | |
ff62c168 MW |
3710 | } |
3711 | else | |
8f9da340 MW |
3712 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3713 | s_scm_round_remainder); | |
ff62c168 MW |
3714 | } |
3715 | #undef FUNC_NAME | |
3716 | ||
3717 | static SCM | |
8f9da340 | 3718 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3719 | { |
ff62c168 MW |
3720 | /* Although it would be more efficient to use fmod here, we can't |
3721 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3722 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3723 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3724 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3725 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3726 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3727 | |
3728 | if (SCM_UNLIKELY (y == 0)) | |
3729 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3730 | else |
8f9da340 MW |
3731 | { |
3732 | double q = scm_c_round (x / y); | |
3733 | return scm_from_double (x - q * y); | |
3734 | } | |
ff62c168 MW |
3735 | } |
3736 | ||
3737 | /* Assumes that both x and y are bigints, though | |
3738 | x might be able to fit into a fixnum. */ | |
3739 | static SCM | |
8f9da340 | 3740 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3741 | { |
8f9da340 MW |
3742 | SCM q, r, r2; |
3743 | int cmp, needs_adjustment; | |
ff62c168 MW |
3744 | |
3745 | /* Note that x might be small enough to fit into a | |
3746 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3747 | q = scm_i_mkbig (); |
ff62c168 | 3748 | r = scm_i_mkbig (); |
8f9da340 | 3749 | r2 = scm_i_mkbig (); |
ff62c168 | 3750 | |
8f9da340 MW |
3751 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3752 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3753 | scm_remember_upto_here_1 (x); | |
3754 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3755 | |
8f9da340 MW |
3756 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3757 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3758 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3759 | else |
8f9da340 MW |
3760 | needs_adjustment = (cmp > 0); |
3761 | scm_remember_upto_here_2 (q, r2); | |
3762 | ||
3763 | if (needs_adjustment) | |
3764 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3765 | ||
3766 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3767 | return scm_i_normbig (r); |
3768 | } | |
3769 | ||
ff62c168 | 3770 | static SCM |
8f9da340 | 3771 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3772 | { |
03ddd15b MW |
3773 | SCM xd = scm_denominator (x); |
3774 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3775 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3776 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3777 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3778 | } |
3779 | ||
3780 | ||
8f9da340 MW |
3781 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3782 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3783 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3784 | |
8f9da340 | 3785 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3786 | (SCM x, SCM y), |
3787 | "Return the integer @var{q} and the real number @var{r}\n" | |
3788 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3789 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3790 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3791 | "@lisp\n" |
8f9da340 MW |
3792 | "(round/ 123 10) @result{} 12 and 3\n" |
3793 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3794 | "(round/ -123 10) @result{} -12 and -3\n" | |
3795 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3796 | "(round/ 125 10) @result{} 12 and 5\n" | |
3797 | "(round/ 127 10) @result{} 13 and -3\n" | |
3798 | "(round/ 135 10) @result{} 14 and -5\n" | |
3799 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3800 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3801 | "@end lisp") |
8f9da340 | 3802 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3803 | { |
3804 | SCM q, r; | |
3805 | ||
8f9da340 | 3806 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3807 | return scm_values (scm_list_2 (q, r)); |
3808 | } | |
3809 | #undef FUNC_NAME | |
3810 | ||
8f9da340 MW |
3811 | #define s_scm_round_divide s_scm_i_round_divide |
3812 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3813 | |
3814 | void | |
8f9da340 | 3815 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3816 | { |
3817 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3818 | { | |
4a46bc2a | 3819 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3820 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3821 | { | |
3822 | scm_t_inum yy = SCM_I_INUM (y); | |
3823 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3824 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3825 | else |
3826 | { | |
ff62c168 | 3827 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3828 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3829 | scm_t_inum ay = yy; |
3830 | scm_t_inum r2 = 2 * rr; | |
3831 | ||
3832 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3833 | { |
8f9da340 MW |
3834 | ay = -ay; |
3835 | r2 = -r2; | |
3836 | } | |
3837 | ||
3838 | if (qq & 1L) | |
3839 | { | |
3840 | if (r2 >= ay) | |
3841 | { qq++; rr -= yy; } | |
3842 | else if (r2 <= -ay) | |
3843 | { qq--; rr += yy; } | |
ff62c168 MW |
3844 | } |
3845 | else | |
3846 | { | |
8f9da340 MW |
3847 | if (r2 > ay) |
3848 | { qq++; rr -= yy; } | |
3849 | else if (r2 < -ay) | |
3850 | { qq--; rr += yy; } | |
ff62c168 | 3851 | } |
4a46bc2a | 3852 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3853 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3854 | else |
5fbf680b MW |
3855 | *qp = scm_i_inum2big (qq); |
3856 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3857 | } |
5fbf680b | 3858 | return; |
ff62c168 MW |
3859 | } |
3860 | else if (SCM_BIGP (y)) | |
3861 | { | |
3862 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3863 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3864 | return scm_i_bigint_round_divide | |
3865 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3866 | } |
3867 | else if (SCM_REALP (y)) | |
8f9da340 | 3868 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3869 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3870 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3871 | else |
8f9da340 MW |
3872 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3873 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3874 | } |
3875 | else if (SCM_BIGP (x)) | |
3876 | { | |
3877 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3878 | { | |
3879 | scm_t_inum yy = SCM_I_INUM (y); | |
3880 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3881 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3882 | else |
3883 | { | |
3884 | SCM q = scm_i_mkbig (); | |
3885 | scm_t_inum rr; | |
8f9da340 MW |
3886 | int needs_adjustment; |
3887 | ||
ff62c168 MW |
3888 | if (yy > 0) |
3889 | { | |
8f9da340 MW |
3890 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3891 | SCM_I_BIG_MPZ (x), yy); | |
3892 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3893 | needs_adjustment = (2*rr >= yy); | |
3894 | else | |
3895 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3896 | } |
3897 | else | |
3898 | { | |
3899 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3900 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3901 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3902 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3903 | needs_adjustment = (2*rr <= yy); | |
3904 | else | |
3905 | needs_adjustment = (2*rr < yy); | |
3906 | } | |
3907 | scm_remember_upto_here_1 (x); | |
3908 | if (needs_adjustment) | |
3909 | { | |
3910 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3911 | rr -= yy; | |
ff62c168 | 3912 | } |
5fbf680b MW |
3913 | *qp = scm_i_normbig (q); |
3914 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3915 | } |
5fbf680b | 3916 | return; |
ff62c168 MW |
3917 | } |
3918 | else if (SCM_BIGP (y)) | |
8f9da340 | 3919 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3920 | else if (SCM_REALP (y)) |
8f9da340 | 3921 | return scm_i_inexact_round_divide |
5fbf680b | 3922 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3923 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3924 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3925 | else |
8f9da340 MW |
3926 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3927 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3928 | } |
3929 | else if (SCM_REALP (x)) | |
3930 | { | |
3931 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3932 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3933 | return scm_i_inexact_round_divide |
5fbf680b | 3934 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3935 | else |
8f9da340 MW |
3936 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3937 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3938 | } |
3939 | else if (SCM_FRACTIONP (x)) | |
3940 | { | |
3941 | if (SCM_REALP (y)) | |
8f9da340 | 3942 | return scm_i_inexact_round_divide |
5fbf680b | 3943 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3944 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3945 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3946 | else |
8f9da340 MW |
3947 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3948 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3949 | } |
3950 | else | |
8f9da340 MW |
3951 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3952 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3953 | } |
ff62c168 | 3954 | |
5fbf680b | 3955 | static void |
8f9da340 | 3956 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3957 | { |
8f9da340 MW |
3958 | if (SCM_UNLIKELY (y == 0)) |
3959 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3960 | else |
8f9da340 MW |
3961 | { |
3962 | double q = scm_c_round (x / y); | |
3963 | double r = x - q * y; | |
3964 | *qp = scm_from_double (q); | |
3965 | *rp = scm_from_double (r); | |
3966 | } | |
ff62c168 MW |
3967 | } |
3968 | ||
3969 | /* Assumes that both x and y are bigints, though | |
3970 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3971 | static void |
8f9da340 | 3972 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3973 | { |
8f9da340 MW |
3974 | SCM q, r, r2; |
3975 | int cmp, needs_adjustment; | |
ff62c168 MW |
3976 | |
3977 | /* Note that x might be small enough to fit into a | |
3978 | fixnum, so we must not let it escape into the wild */ | |
3979 | q = scm_i_mkbig (); | |
3980 | r = scm_i_mkbig (); | |
8f9da340 | 3981 | r2 = scm_i_mkbig (); |
ff62c168 | 3982 | |
8f9da340 MW |
3983 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3984 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3985 | scm_remember_upto_here_1 (x); | |
3986 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3987 | |
8f9da340 MW |
3988 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3989 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3990 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3991 | else |
8f9da340 MW |
3992 | needs_adjustment = (cmp > 0); |
3993 | ||
3994 | if (needs_adjustment) | |
ff62c168 | 3995 | { |
8f9da340 MW |
3996 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3997 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3998 | } |
8f9da340 MW |
3999 | |
4000 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
4001 | *qp = scm_i_normbig (q); |
4002 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
4003 | } |
4004 | ||
5fbf680b | 4005 | static void |
8f9da340 | 4006 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4007 | { |
03ddd15b MW |
4008 | SCM r1; |
4009 | SCM xd = scm_denominator (x); | |
4010 | SCM yd = scm_denominator (y); | |
4011 | ||
8f9da340 MW |
4012 | scm_round_divide (scm_product (scm_numerator (x), yd), |
4013 | scm_product (scm_numerator (y), xd), | |
4014 | qp, &r1); | |
03ddd15b | 4015 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
4016 | } |
4017 | ||
4018 | ||
78d3deb1 AW |
4019 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
4020 | (SCM x, SCM y, SCM rest), | |
4021 | "Return the greatest common divisor of all parameter values.\n" | |
4022 | "If called without arguments, 0 is returned.") | |
4023 | #define FUNC_NAME s_scm_i_gcd | |
4024 | { | |
4025 | while (!scm_is_null (rest)) | |
4026 | { x = scm_gcd (x, y); | |
4027 | y = scm_car (rest); | |
4028 | rest = scm_cdr (rest); | |
4029 | } | |
4030 | return scm_gcd (x, y); | |
4031 | } | |
4032 | #undef FUNC_NAME | |
4033 | ||
4034 | #define s_gcd s_scm_i_gcd | |
4035 | #define g_gcd g_scm_i_gcd | |
4036 | ||
0f2d19dd | 4037 | SCM |
6e8d25a6 | 4038 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 4039 | { |
a2dead1b | 4040 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
1dd79792 | 4041 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 4042 | |
a2dead1b | 4043 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4044 | { |
a2dead1b | 4045 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4046 | { |
e25f3727 AW |
4047 | scm_t_inum xx = SCM_I_INUM (x); |
4048 | scm_t_inum yy = SCM_I_INUM (y); | |
4049 | scm_t_inum u = xx < 0 ? -xx : xx; | |
4050 | scm_t_inum v = yy < 0 ? -yy : yy; | |
4051 | scm_t_inum result; | |
a2dead1b | 4052 | if (SCM_UNLIKELY (xx == 0)) |
0aacf84e | 4053 | result = v; |
a2dead1b | 4054 | else if (SCM_UNLIKELY (yy == 0)) |
0aacf84e MD |
4055 | result = u; |
4056 | else | |
4057 | { | |
a2dead1b | 4058 | int k = 0; |
0aacf84e | 4059 | /* Determine a common factor 2^k */ |
a2dead1b | 4060 | while (((u | v) & 1) == 0) |
0aacf84e | 4061 | { |
a2dead1b | 4062 | k++; |
0aacf84e MD |
4063 | u >>= 1; |
4064 | v >>= 1; | |
4065 | } | |
4066 | /* Now, any factor 2^n can be eliminated */ | |
a2dead1b MW |
4067 | if ((u & 1) == 0) |
4068 | while ((u & 1) == 0) | |
4069 | u >>= 1; | |
0aacf84e | 4070 | else |
a2dead1b MW |
4071 | while ((v & 1) == 0) |
4072 | v >>= 1; | |
4073 | /* Both u and v are now odd. Subtract the smaller one | |
4074 | from the larger one to produce an even number, remove | |
4075 | more factors of two, and repeat. */ | |
4076 | while (u != v) | |
0aacf84e | 4077 | { |
a2dead1b MW |
4078 | if (u > v) |
4079 | { | |
4080 | u -= v; | |
4081 | while ((u & 1) == 0) | |
4082 | u >>= 1; | |
4083 | } | |
4084 | else | |
4085 | { | |
4086 | v -= u; | |
4087 | while ((v & 1) == 0) | |
4088 | v >>= 1; | |
4089 | } | |
0aacf84e | 4090 | } |
a2dead1b | 4091 | result = u << k; |
0aacf84e MD |
4092 | } |
4093 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 4094 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4095 | : scm_i_inum2big (result)); |
ca46fb90 RB |
4096 | } |
4097 | else if (SCM_BIGP (y)) | |
4098 | { | |
0bff4dce KR |
4099 | SCM_SWAP (x, y); |
4100 | goto big_inum; | |
ca46fb90 RB |
4101 | } |
4102 | else | |
4103 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 4104 | } |
ca46fb90 RB |
4105 | else if (SCM_BIGP (x)) |
4106 | { | |
e11e83f3 | 4107 | if (SCM_I_INUMP (y)) |
ca46fb90 | 4108 | { |
e25f3727 AW |
4109 | scm_t_bits result; |
4110 | scm_t_inum yy; | |
0bff4dce | 4111 | big_inum: |
e11e83f3 | 4112 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
4113 | if (yy == 0) |
4114 | return scm_abs (x); | |
0aacf84e MD |
4115 | if (yy < 0) |
4116 | yy = -yy; | |
ca46fb90 RB |
4117 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
4118 | scm_remember_upto_here_1 (x); | |
0aacf84e | 4119 | return (SCM_POSFIXABLE (result) |
d956fa6f | 4120 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4121 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
4122 | } |
4123 | else if (SCM_BIGP (y)) | |
4124 | { | |
4125 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
4126 | mpz_gcd (SCM_I_BIG_MPZ (result), |
4127 | SCM_I_BIG_MPZ (x), | |
4128 | SCM_I_BIG_MPZ (y)); | |
4129 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
4130 | return scm_i_normbig (result); |
4131 | } | |
4132 | else | |
4133 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 4134 | } |
ca46fb90 | 4135 | else |
09fb7599 | 4136 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
4137 | } |
4138 | ||
78d3deb1 AW |
4139 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
4140 | (SCM x, SCM y, SCM rest), | |
4141 | "Return the least common multiple of the arguments.\n" | |
4142 | "If called without arguments, 1 is returned.") | |
4143 | #define FUNC_NAME s_scm_i_lcm | |
4144 | { | |
4145 | while (!scm_is_null (rest)) | |
4146 | { x = scm_lcm (x, y); | |
4147 | y = scm_car (rest); | |
4148 | rest = scm_cdr (rest); | |
4149 | } | |
4150 | return scm_lcm (x, y); | |
4151 | } | |
4152 | #undef FUNC_NAME | |
4153 | ||
4154 | #define s_lcm s_scm_i_lcm | |
4155 | #define g_lcm g_scm_i_lcm | |
4156 | ||
0f2d19dd | 4157 | SCM |
6e8d25a6 | 4158 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4159 | { |
ca46fb90 RB |
4160 | if (SCM_UNBNDP (n2)) |
4161 | { | |
4162 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
4163 | return SCM_I_MAKINUM (1L); |
4164 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 4165 | } |
09fb7599 | 4166 | |
e11e83f3 | 4167 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 4168 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 4169 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 4170 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 4171 | |
e11e83f3 | 4172 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 4173 | { |
e11e83f3 | 4174 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4175 | { |
4176 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4177 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4178 | return d; |
4179 | else | |
4180 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4181 | } | |
4182 | else | |
4183 | { | |
4184 | /* inum n1, big n2 */ | |
4185 | inumbig: | |
4186 | { | |
4187 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4188 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4189 | if (nn1 == 0) return SCM_INUM0; |
4190 | if (nn1 < 0) nn1 = - nn1; | |
4191 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4192 | scm_remember_upto_here_1 (n2); | |
4193 | return result; | |
4194 | } | |
4195 | } | |
4196 | } | |
4197 | else | |
4198 | { | |
4199 | /* big n1 */ | |
e11e83f3 | 4200 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4201 | { |
4202 | SCM_SWAP (n1, n2); | |
4203 | goto inumbig; | |
4204 | } | |
4205 | else | |
4206 | { | |
4207 | SCM result = scm_i_mkbig (); | |
4208 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4209 | SCM_I_BIG_MPZ (n1), | |
4210 | SCM_I_BIG_MPZ (n2)); | |
4211 | scm_remember_upto_here_2(n1, n2); | |
4212 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4213 | return result; | |
4214 | } | |
f872b822 | 4215 | } |
0f2d19dd JB |
4216 | } |
4217 | ||
8a525303 GB |
4218 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4219 | ||
4220 | Logand: | |
4221 | X Y Result Method: | |
4222 | (len) | |
4223 | + + + x (map digit:logand X Y) | |
4224 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4225 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4226 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4227 | ||
4228 | Logior: | |
4229 | X Y Result Method: | |
4230 | ||
4231 | + + + (map digit:logior X Y) | |
4232 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4233 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4234 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4235 | ||
4236 | Logxor: | |
4237 | X Y Result Method: | |
4238 | ||
4239 | + + + (map digit:logxor X Y) | |
4240 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4241 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4242 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4243 | ||
4244 | Logtest: | |
4245 | X Y Result | |
4246 | ||
4247 | + + (any digit:logand X Y) | |
4248 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4249 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4250 | - - #t | |
4251 | ||
4252 | */ | |
4253 | ||
78d3deb1 AW |
4254 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4255 | (SCM x, SCM y, SCM rest), | |
4256 | "Return the bitwise AND of the integer arguments.\n\n" | |
4257 | "@lisp\n" | |
4258 | "(logand) @result{} -1\n" | |
4259 | "(logand 7) @result{} 7\n" | |
4260 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4261 | "@end lisp") | |
4262 | #define FUNC_NAME s_scm_i_logand | |
4263 | { | |
4264 | while (!scm_is_null (rest)) | |
4265 | { x = scm_logand (x, y); | |
4266 | y = scm_car (rest); | |
4267 | rest = scm_cdr (rest); | |
4268 | } | |
4269 | return scm_logand (x, y); | |
4270 | } | |
4271 | #undef FUNC_NAME | |
4272 | ||
4273 | #define s_scm_logand s_scm_i_logand | |
4274 | ||
4275 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4276 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4277 | { |
e25f3727 | 4278 | scm_t_inum nn1; |
9a00c9fc | 4279 | |
0aacf84e MD |
4280 | if (SCM_UNBNDP (n2)) |
4281 | { | |
4282 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4283 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4284 | else if (!SCM_NUMBERP (n1)) |
4285 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4286 | else if (SCM_NUMBERP (n1)) | |
4287 | return n1; | |
4288 | else | |
4289 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4290 | } |
09fb7599 | 4291 | |
e11e83f3 | 4292 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4293 | { |
e11e83f3 MV |
4294 | nn1 = SCM_I_INUM (n1); |
4295 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4296 | { |
e25f3727 | 4297 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4298 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4299 | } |
4300 | else if SCM_BIGP (n2) | |
4301 | { | |
4302 | intbig: | |
2e16a342 | 4303 | if (nn1 == 0) |
0aacf84e MD |
4304 | return SCM_INUM0; |
4305 | { | |
4306 | SCM result_z = scm_i_mkbig (); | |
4307 | mpz_t nn1_z; | |
4308 | mpz_init_set_si (nn1_z, nn1); | |
4309 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4310 | scm_remember_upto_here_1 (n2); | |
4311 | mpz_clear (nn1_z); | |
4312 | return scm_i_normbig (result_z); | |
4313 | } | |
4314 | } | |
4315 | else | |
4316 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4317 | } | |
4318 | else if (SCM_BIGP (n1)) | |
4319 | { | |
e11e83f3 | 4320 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4321 | { |
4322 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4323 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4324 | goto intbig; |
4325 | } | |
4326 | else if (SCM_BIGP (n2)) | |
4327 | { | |
4328 | SCM result_z = scm_i_mkbig (); | |
4329 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4330 | SCM_I_BIG_MPZ (n1), | |
4331 | SCM_I_BIG_MPZ (n2)); | |
4332 | scm_remember_upto_here_2 (n1, n2); | |
4333 | return scm_i_normbig (result_z); | |
4334 | } | |
4335 | else | |
4336 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4337 | } |
0aacf84e | 4338 | else |
09fb7599 | 4339 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4340 | } |
1bbd0b84 | 4341 | #undef FUNC_NAME |
0f2d19dd | 4342 | |
09fb7599 | 4343 | |
78d3deb1 AW |
4344 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4345 | (SCM x, SCM y, SCM rest), | |
4346 | "Return the bitwise OR of the integer arguments.\n\n" | |
4347 | "@lisp\n" | |
4348 | "(logior) @result{} 0\n" | |
4349 | "(logior 7) @result{} 7\n" | |
4350 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4351 | "@end lisp") | |
4352 | #define FUNC_NAME s_scm_i_logior | |
4353 | { | |
4354 | while (!scm_is_null (rest)) | |
4355 | { x = scm_logior (x, y); | |
4356 | y = scm_car (rest); | |
4357 | rest = scm_cdr (rest); | |
4358 | } | |
4359 | return scm_logior (x, y); | |
4360 | } | |
4361 | #undef FUNC_NAME | |
4362 | ||
4363 | #define s_scm_logior s_scm_i_logior | |
4364 | ||
4365 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4366 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4367 | { |
e25f3727 | 4368 | scm_t_inum nn1; |
9a00c9fc | 4369 | |
0aacf84e MD |
4370 | if (SCM_UNBNDP (n2)) |
4371 | { | |
4372 | if (SCM_UNBNDP (n1)) | |
4373 | return SCM_INUM0; | |
4374 | else if (SCM_NUMBERP (n1)) | |
4375 | return n1; | |
4376 | else | |
4377 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4378 | } |
09fb7599 | 4379 | |
e11e83f3 | 4380 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4381 | { |
e11e83f3 MV |
4382 | nn1 = SCM_I_INUM (n1); |
4383 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4384 | { |
e11e83f3 | 4385 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4386 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4387 | } |
4388 | else if (SCM_BIGP (n2)) | |
4389 | { | |
4390 | intbig: | |
4391 | if (nn1 == 0) | |
4392 | return n2; | |
4393 | { | |
4394 | SCM result_z = scm_i_mkbig (); | |
4395 | mpz_t nn1_z; | |
4396 | mpz_init_set_si (nn1_z, nn1); | |
4397 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4398 | scm_remember_upto_here_1 (n2); | |
4399 | mpz_clear (nn1_z); | |
9806de0d | 4400 | return scm_i_normbig (result_z); |
0aacf84e MD |
4401 | } |
4402 | } | |
4403 | else | |
4404 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4405 | } | |
4406 | else if (SCM_BIGP (n1)) | |
4407 | { | |
e11e83f3 | 4408 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4409 | { |
4410 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4411 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4412 | goto intbig; |
4413 | } | |
4414 | else if (SCM_BIGP (n2)) | |
4415 | { | |
4416 | SCM result_z = scm_i_mkbig (); | |
4417 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4418 | SCM_I_BIG_MPZ (n1), | |
4419 | SCM_I_BIG_MPZ (n2)); | |
4420 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4421 | return scm_i_normbig (result_z); |
0aacf84e MD |
4422 | } |
4423 | else | |
4424 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4425 | } |
0aacf84e | 4426 | else |
09fb7599 | 4427 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4428 | } |
1bbd0b84 | 4429 | #undef FUNC_NAME |
0f2d19dd | 4430 | |
09fb7599 | 4431 | |
78d3deb1 AW |
4432 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4433 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4434 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4435 | "set in the result if it is set in an odd number of arguments.\n" | |
4436 | "@lisp\n" | |
4437 | "(logxor) @result{} 0\n" | |
4438 | "(logxor 7) @result{} 7\n" | |
4439 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4440 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4441 | "@end lisp") |
78d3deb1 AW |
4442 | #define FUNC_NAME s_scm_i_logxor |
4443 | { | |
4444 | while (!scm_is_null (rest)) | |
4445 | { x = scm_logxor (x, y); | |
4446 | y = scm_car (rest); | |
4447 | rest = scm_cdr (rest); | |
4448 | } | |
4449 | return scm_logxor (x, y); | |
4450 | } | |
4451 | #undef FUNC_NAME | |
4452 | ||
4453 | #define s_scm_logxor s_scm_i_logxor | |
4454 | ||
4455 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4456 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4457 | { |
e25f3727 | 4458 | scm_t_inum nn1; |
9a00c9fc | 4459 | |
0aacf84e MD |
4460 | if (SCM_UNBNDP (n2)) |
4461 | { | |
4462 | if (SCM_UNBNDP (n1)) | |
4463 | return SCM_INUM0; | |
4464 | else if (SCM_NUMBERP (n1)) | |
4465 | return n1; | |
4466 | else | |
4467 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4468 | } |
09fb7599 | 4469 | |
e11e83f3 | 4470 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4471 | { |
e11e83f3 MV |
4472 | nn1 = SCM_I_INUM (n1); |
4473 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4474 | { |
e25f3727 | 4475 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4476 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4477 | } |
4478 | else if (SCM_BIGP (n2)) | |
4479 | { | |
4480 | intbig: | |
4481 | { | |
4482 | SCM result_z = scm_i_mkbig (); | |
4483 | mpz_t nn1_z; | |
4484 | mpz_init_set_si (nn1_z, nn1); | |
4485 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4486 | scm_remember_upto_here_1 (n2); | |
4487 | mpz_clear (nn1_z); | |
4488 | return scm_i_normbig (result_z); | |
4489 | } | |
4490 | } | |
4491 | else | |
4492 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4493 | } | |
4494 | else if (SCM_BIGP (n1)) | |
4495 | { | |
e11e83f3 | 4496 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4497 | { |
4498 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4499 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4500 | goto intbig; |
4501 | } | |
4502 | else if (SCM_BIGP (n2)) | |
4503 | { | |
4504 | SCM result_z = scm_i_mkbig (); | |
4505 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4506 | SCM_I_BIG_MPZ (n1), | |
4507 | SCM_I_BIG_MPZ (n2)); | |
4508 | scm_remember_upto_here_2 (n1, n2); | |
4509 | return scm_i_normbig (result_z); | |
4510 | } | |
4511 | else | |
4512 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4513 | } |
0aacf84e | 4514 | else |
09fb7599 | 4515 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4516 | } |
1bbd0b84 | 4517 | #undef FUNC_NAME |
0f2d19dd | 4518 | |
09fb7599 | 4519 | |
a1ec6916 | 4520 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4521 | (SCM j, SCM k), |
ba6e7231 KR |
4522 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4523 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4524 | "without actually calculating the @code{logand}, just testing\n" | |
4525 | "for non-zero.\n" | |
4526 | "\n" | |
1e6808ea | 4527 | "@lisp\n" |
b380b885 MD |
4528 | "(logtest #b0100 #b1011) @result{} #f\n" |
4529 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4530 | "@end lisp") |
1bbd0b84 | 4531 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4532 | { |
e25f3727 | 4533 | scm_t_inum nj; |
9a00c9fc | 4534 | |
e11e83f3 | 4535 | if (SCM_I_INUMP (j)) |
0aacf84e | 4536 | { |
e11e83f3 MV |
4537 | nj = SCM_I_INUM (j); |
4538 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4539 | { |
e25f3727 | 4540 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4541 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4542 | } |
4543 | else if (SCM_BIGP (k)) | |
4544 | { | |
4545 | intbig: | |
4546 | if (nj == 0) | |
4547 | return SCM_BOOL_F; | |
4548 | { | |
4549 | SCM result; | |
4550 | mpz_t nj_z; | |
4551 | mpz_init_set_si (nj_z, nj); | |
4552 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4553 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4554 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4555 | mpz_clear (nj_z); |
4556 | return result; | |
4557 | } | |
4558 | } | |
4559 | else | |
4560 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4561 | } | |
4562 | else if (SCM_BIGP (j)) | |
4563 | { | |
e11e83f3 | 4564 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4565 | { |
4566 | SCM_SWAP (j, k); | |
e11e83f3 | 4567 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4568 | goto intbig; |
4569 | } | |
4570 | else if (SCM_BIGP (k)) | |
4571 | { | |
4572 | SCM result; | |
4573 | mpz_t result_z; | |
4574 | mpz_init (result_z); | |
4575 | mpz_and (result_z, | |
4576 | SCM_I_BIG_MPZ (j), | |
4577 | SCM_I_BIG_MPZ (k)); | |
4578 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4579 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4580 | mpz_clear (result_z); |
4581 | return result; | |
4582 | } | |
4583 | else | |
4584 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4585 | } | |
4586 | else | |
4587 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4588 | } |
1bbd0b84 | 4589 | #undef FUNC_NAME |
0f2d19dd | 4590 | |
c1bfcf60 | 4591 | |
a1ec6916 | 4592 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4593 | (SCM index, SCM j), |
ba6e7231 KR |
4594 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4595 | "@var{index} starts from 0 for the least significant bit.\n" | |
4596 | "\n" | |
1e6808ea | 4597 | "@lisp\n" |
b380b885 MD |
4598 | "(logbit? 0 #b1101) @result{} #t\n" |
4599 | "(logbit? 1 #b1101) @result{} #f\n" | |
4600 | "(logbit? 2 #b1101) @result{} #t\n" | |
4601 | "(logbit? 3 #b1101) @result{} #t\n" | |
4602 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4603 | "@end lisp") |
1bbd0b84 | 4604 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4605 | { |
78166ad5 | 4606 | unsigned long int iindex; |
5efd3c7d | 4607 | iindex = scm_to_ulong (index); |
78166ad5 | 4608 | |
e11e83f3 | 4609 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4610 | { |
4611 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4612 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4613 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4614 | } |
0aacf84e MD |
4615 | else if (SCM_BIGP (j)) |
4616 | { | |
4617 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4618 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4619 | return scm_from_bool (val); |
0aacf84e MD |
4620 | } |
4621 | else | |
78166ad5 | 4622 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4623 | } |
1bbd0b84 | 4624 | #undef FUNC_NAME |
0f2d19dd | 4625 | |
78166ad5 | 4626 | |
a1ec6916 | 4627 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4628 | (SCM n), |
4d814788 | 4629 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4630 | "argument.\n" |
4631 | "\n" | |
b380b885 MD |
4632 | "@lisp\n" |
4633 | "(number->string (lognot #b10000000) 2)\n" | |
4634 | " @result{} \"-10000001\"\n" | |
4635 | "(number->string (lognot #b0) 2)\n" | |
4636 | " @result{} \"-1\"\n" | |
1e6808ea | 4637 | "@end lisp") |
1bbd0b84 | 4638 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4639 | { |
e11e83f3 | 4640 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4641 | /* No overflow here, just need to toggle all the bits making up the inum. |
4642 | Enhancement: No need to strip the tag and add it back, could just xor | |
4643 | a block of 1 bits, if that worked with the various debug versions of | |
4644 | the SCM typedef. */ | |
e11e83f3 | 4645 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4646 | |
4647 | } else if (SCM_BIGP (n)) { | |
4648 | SCM result = scm_i_mkbig (); | |
4649 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4650 | scm_remember_upto_here_1 (n); | |
4651 | return result; | |
4652 | ||
4653 | } else { | |
4654 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4655 | } | |
0f2d19dd | 4656 | } |
1bbd0b84 | 4657 | #undef FUNC_NAME |
0f2d19dd | 4658 | |
518b7508 KR |
4659 | /* returns 0 if IN is not an integer. OUT must already be |
4660 | initialized. */ | |
4661 | static int | |
4662 | coerce_to_big (SCM in, mpz_t out) | |
4663 | { | |
4664 | if (SCM_BIGP (in)) | |
4665 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4666 | else if (SCM_I_INUMP (in)) |
4667 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4668 | else |
4669 | return 0; | |
4670 | ||
4671 | return 1; | |
4672 | } | |
4673 | ||
d885e204 | 4674 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4675 | (SCM n, SCM k, SCM m), |
4676 | "Return @var{n} raised to the integer exponent\n" | |
4677 | "@var{k}, modulo @var{m}.\n" | |
4678 | "\n" | |
4679 | "@lisp\n" | |
4680 | "(modulo-expt 2 3 5)\n" | |
4681 | " @result{} 3\n" | |
4682 | "@end lisp") | |
d885e204 | 4683 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4684 | { |
4685 | mpz_t n_tmp; | |
4686 | mpz_t k_tmp; | |
4687 | mpz_t m_tmp; | |
4688 | ||
4689 | /* There are two classes of error we might encounter -- | |
4690 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4691 | and | |
4692 | 2) wrong-type errors, which of course we'll report by calling | |
4693 | SCM_WRONG_TYPE_ARG. | |
4694 | We don't report those errors immediately, however; instead we do | |
4695 | some cleanup first. These variables tell us which error (if | |
4696 | any) we should report after cleaning up. | |
4697 | */ | |
4698 | int report_overflow = 0; | |
4699 | ||
4700 | int position_of_wrong_type = 0; | |
4701 | SCM value_of_wrong_type = SCM_INUM0; | |
4702 | ||
4703 | SCM result = SCM_UNDEFINED; | |
4704 | ||
4705 | mpz_init (n_tmp); | |
4706 | mpz_init (k_tmp); | |
4707 | mpz_init (m_tmp); | |
4708 | ||
bc36d050 | 4709 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4710 | { |
4711 | report_overflow = 1; | |
4712 | goto cleanup; | |
4713 | } | |
4714 | ||
4715 | if (!coerce_to_big (n, n_tmp)) | |
4716 | { | |
4717 | value_of_wrong_type = n; | |
4718 | position_of_wrong_type = 1; | |
4719 | goto cleanup; | |
4720 | } | |
4721 | ||
4722 | if (!coerce_to_big (k, k_tmp)) | |
4723 | { | |
4724 | value_of_wrong_type = k; | |
4725 | position_of_wrong_type = 2; | |
4726 | goto cleanup; | |
4727 | } | |
4728 | ||
4729 | if (!coerce_to_big (m, m_tmp)) | |
4730 | { | |
4731 | value_of_wrong_type = m; | |
4732 | position_of_wrong_type = 3; | |
4733 | goto cleanup; | |
4734 | } | |
4735 | ||
4736 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4737 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4738 | doesn't exist (or is not unique). Since exceptions are hard to | |
4739 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4740 | a simple failure code, which is easy to handle. */ | |
4741 | ||
4742 | if (-1 == mpz_sgn (k_tmp)) | |
4743 | { | |
4744 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4745 | { | |
4746 | report_overflow = 1; | |
4747 | goto cleanup; | |
4748 | } | |
4749 | mpz_neg (k_tmp, k_tmp); | |
4750 | } | |
4751 | ||
4752 | result = scm_i_mkbig (); | |
4753 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4754 | n_tmp, | |
4755 | k_tmp, | |
4756 | m_tmp); | |
b7b8c575 KR |
4757 | |
4758 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4759 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4760 | ||
518b7508 KR |
4761 | cleanup: |
4762 | mpz_clear (m_tmp); | |
4763 | mpz_clear (k_tmp); | |
4764 | mpz_clear (n_tmp); | |
4765 | ||
4766 | if (report_overflow) | |
4767 | scm_num_overflow (FUNC_NAME); | |
4768 | ||
4769 | if (position_of_wrong_type) | |
4770 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4771 | value_of_wrong_type); | |
4772 | ||
4773 | return scm_i_normbig (result); | |
4774 | } | |
4775 | #undef FUNC_NAME | |
4776 | ||
a1ec6916 | 4777 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4778 | (SCM n, SCM k), |
ba6e7231 KR |
4779 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4780 | "exact integer, @var{n} can be any number.\n" | |
4781 | "\n" | |
2519490c MW |
4782 | "Negative @var{k} is supported, and results in\n" |
4783 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4784 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4785 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4786 | "\n" |
b380b885 | 4787 | "@lisp\n" |
ba6e7231 KR |
4788 | "(integer-expt 2 5) @result{} 32\n" |
4789 | "(integer-expt -3 3) @result{} -27\n" | |
4790 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4791 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4792 | "@end lisp") |
1bbd0b84 | 4793 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4794 | { |
e25f3727 | 4795 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4796 | SCM z_i2 = SCM_BOOL_F; |
4797 | int i2_is_big = 0; | |
d956fa6f | 4798 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4799 | |
bfe1f03a MW |
4800 | /* Specifically refrain from checking the type of the first argument. |
4801 | This allows us to exponentiate any object that can be multiplied. | |
4802 | If we must raise to a negative power, we must also be able to | |
4803 | take its reciprocal. */ | |
4804 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4805 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4806 | |
bfe1f03a MW |
4807 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4808 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4809 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4810 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4811 | /* The next check is necessary only because R6RS specifies different | |
4812 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4813 | we simply skip this case and move on. */ | |
4814 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4815 | { | |
4816 | /* k cannot be 0 at this point, because we | |
4817 | have already checked for that case above */ | |
4818 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4819 | return n; |
4820 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4821 | return scm_nan (); | |
4822 | } | |
a285b18c MW |
4823 | else if (SCM_FRACTIONP (n)) |
4824 | { | |
4825 | /* Optimize the fraction case by (a/b)^k ==> (a^k)/(b^k), to avoid | |
4826 | needless reduction of intermediate products to lowest terms. | |
4827 | If a and b have no common factors, then a^k and b^k have no | |
4828 | common factors. Use 'scm_i_make_ratio_already_reduced' to | |
4829 | construct the final result, so that no gcd computations are | |
4830 | needed to exponentiate a fraction. */ | |
4831 | if (scm_is_true (scm_positive_p (k))) | |
4832 | return scm_i_make_ratio_already_reduced | |
4833 | (scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k), | |
4834 | scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k)); | |
4835 | else | |
4836 | { | |
4837 | k = scm_difference (k, SCM_UNDEFINED); | |
4838 | return scm_i_make_ratio_already_reduced | |
4839 | (scm_integer_expt (SCM_FRACTION_DENOMINATOR (n), k), | |
4840 | scm_integer_expt (SCM_FRACTION_NUMERATOR (n), k)); | |
4841 | } | |
4842 | } | |
ca46fb90 | 4843 | |
e11e83f3 MV |
4844 | if (SCM_I_INUMP (k)) |
4845 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4846 | else if (SCM_BIGP (k)) |
4847 | { | |
4848 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4849 | scm_remember_upto_here_1 (k); |
4850 | i2_is_big = 1; | |
4851 | } | |
2830fd91 | 4852 | else |
ca46fb90 RB |
4853 | SCM_WRONG_TYPE_ARG (2, k); |
4854 | ||
4855 | if (i2_is_big) | |
f872b822 | 4856 | { |
ca46fb90 RB |
4857 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4858 | { | |
4859 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4860 | n = scm_divide (n, SCM_UNDEFINED); | |
4861 | } | |
4862 | while (1) | |
4863 | { | |
4864 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4865 | { | |
ca46fb90 RB |
4866 | return acc; |
4867 | } | |
4868 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4869 | { | |
ca46fb90 RB |
4870 | return scm_product (acc, n); |
4871 | } | |
4872 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4873 | acc = scm_product (acc, n); | |
4874 | n = scm_product (n, n); | |
4875 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4876 | } | |
f872b822 | 4877 | } |
ca46fb90 | 4878 | else |
f872b822 | 4879 | { |
ca46fb90 RB |
4880 | if (i2 < 0) |
4881 | { | |
4882 | i2 = -i2; | |
4883 | n = scm_divide (n, SCM_UNDEFINED); | |
4884 | } | |
4885 | while (1) | |
4886 | { | |
4887 | if (0 == i2) | |
4888 | return acc; | |
4889 | if (1 == i2) | |
4890 | return scm_product (acc, n); | |
4891 | if (i2 & 1) | |
4892 | acc = scm_product (acc, n); | |
4893 | n = scm_product (n, n); | |
4894 | i2 >>= 1; | |
4895 | } | |
f872b822 | 4896 | } |
0f2d19dd | 4897 | } |
1bbd0b84 | 4898 | #undef FUNC_NAME |
0f2d19dd | 4899 | |
e08a12b5 MW |
4900 | /* Efficiently compute (N * 2^COUNT), |
4901 | where N is an exact integer, and COUNT > 0. */ | |
4902 | static SCM | |
4903 | left_shift_exact_integer (SCM n, long count) | |
4904 | { | |
4905 | if (SCM_I_INUMP (n)) | |
4906 | { | |
4907 | scm_t_inum nn = SCM_I_INUM (n); | |
4908 | ||
4909 | /* Left shift of count >= SCM_I_FIXNUM_BIT-1 will always | |
4910 | overflow a non-zero fixnum. For smaller shifts we check the | |
4911 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4912 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4913 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - count)". */ | |
4914 | ||
4915 | if (nn == 0) | |
4916 | return n; | |
4917 | else if (count < SCM_I_FIXNUM_BIT-1 && | |
4918 | ((scm_t_bits) (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - count)) + 1) | |
4919 | <= 1)) | |
4920 | return SCM_I_MAKINUM (nn << count); | |
4921 | else | |
4922 | { | |
4923 | SCM result = scm_i_inum2big (nn); | |
4924 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
4925 | count); | |
4926 | return result; | |
4927 | } | |
4928 | } | |
4929 | else if (SCM_BIGP (n)) | |
4930 | { | |
4931 | SCM result = scm_i_mkbig (); | |
4932 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), count); | |
4933 | scm_remember_upto_here_1 (n); | |
4934 | return result; | |
4935 | } | |
4936 | else | |
4937 | scm_syserror ("left_shift_exact_integer"); | |
4938 | } | |
4939 | ||
4940 | /* Efficiently compute floor (N / 2^COUNT), | |
4941 | where N is an exact integer and COUNT > 0. */ | |
4942 | static SCM | |
4943 | floor_right_shift_exact_integer (SCM n, long count) | |
4944 | { | |
4945 | if (SCM_I_INUMP (n)) | |
4946 | { | |
4947 | scm_t_inum nn = SCM_I_INUM (n); | |
4948 | ||
4949 | if (count >= SCM_I_FIXNUM_BIT) | |
4950 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM (-1)); | |
4951 | else | |
4952 | return SCM_I_MAKINUM (SCM_SRS (nn, count)); | |
4953 | } | |
4954 | else if (SCM_BIGP (n)) | |
4955 | { | |
4956 | SCM result = scm_i_mkbig (); | |
4957 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4958 | count); | |
4959 | scm_remember_upto_here_1 (n); | |
4960 | return scm_i_normbig (result); | |
4961 | } | |
4962 | else | |
4963 | scm_syserror ("floor_right_shift_exact_integer"); | |
4964 | } | |
4965 | ||
4966 | /* Efficiently compute round (N / 2^COUNT), | |
4967 | where N is an exact integer and COUNT > 0. */ | |
4968 | static SCM | |
4969 | round_right_shift_exact_integer (SCM n, long count) | |
4970 | { | |
4971 | if (SCM_I_INUMP (n)) | |
4972 | { | |
4973 | if (count >= SCM_I_FIXNUM_BIT) | |
4974 | return SCM_INUM0; | |
4975 | else | |
4976 | { | |
4977 | scm_t_inum nn = SCM_I_INUM (n); | |
4978 | scm_t_inum qq = SCM_SRS (nn, count); | |
4979 | ||
4980 | if (0 == (nn & (1L << (count-1)))) | |
4981 | return SCM_I_MAKINUM (qq); /* round down */ | |
4982 | else if (nn & ((1L << (count-1)) - 1)) | |
4983 | return SCM_I_MAKINUM (qq + 1); /* round up */ | |
4984 | else | |
4985 | return SCM_I_MAKINUM ((~1L) & (qq + 1)); /* round to even */ | |
4986 | } | |
4987 | } | |
4988 | else if (SCM_BIGP (n)) | |
4989 | { | |
4990 | SCM q = scm_i_mkbig (); | |
4991 | ||
4992 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (n), count); | |
4993 | if (mpz_tstbit (SCM_I_BIG_MPZ (n), count-1) | |
4994 | && (mpz_odd_p (SCM_I_BIG_MPZ (q)) | |
4995 | || (mpz_scan1 (SCM_I_BIG_MPZ (n), 0) < count-1))) | |
4996 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
4997 | scm_remember_upto_here_1 (n); | |
4998 | return scm_i_normbig (q); | |
4999 | } | |
5000 | else | |
5001 | scm_syserror ("round_right_shift_exact_integer"); | |
5002 | } | |
5003 | ||
a1ec6916 | 5004 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
e08a12b5 MW |
5005 | (SCM n, SCM count), |
5006 | "Return @math{floor(@var{n} * 2^@var{count})}.\n" | |
5007 | "@var{n} and @var{count} must be exact integers.\n" | |
1e6808ea | 5008 | "\n" |
e08a12b5 MW |
5009 | "With @var{n} viewed as an infinite-precision twos-complement\n" |
5010 | "integer, @code{ash} means a left shift introducing zero bits\n" | |
5011 | "when @var{count} is positive, or a right shift dropping bits\n" | |
5012 | "when @var{count} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 5013 | "\n" |
b380b885 | 5014 | "@lisp\n" |
1e6808ea MG |
5015 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
5016 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
5017 | "\n" |
5018 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
5019 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 5020 | "@end lisp") |
1bbd0b84 | 5021 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 5022 | { |
e08a12b5 | 5023 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) |
788aca27 | 5024 | { |
e08a12b5 | 5025 | long bits_to_shift = scm_to_long (count); |
788aca27 KR |
5026 | |
5027 | if (bits_to_shift > 0) | |
e08a12b5 MW |
5028 | return left_shift_exact_integer (n, bits_to_shift); |
5029 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
5030 | return floor_right_shift_exact_integer (n, -bits_to_shift); | |
788aca27 | 5031 | else |
e08a12b5 | 5032 | return n; |
788aca27 | 5033 | } |
e08a12b5 MW |
5034 | else |
5035 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
5036 | } | |
5037 | #undef FUNC_NAME | |
788aca27 | 5038 | |
e08a12b5 MW |
5039 | SCM_DEFINE (scm_round_ash, "round-ash", 2, 0, 0, |
5040 | (SCM n, SCM count), | |
5041 | "Return @math{round(@var{n} * 2^@var{count})}.\n" | |
5042 | "@var{n} and @var{count} must be exact integers.\n" | |
5043 | "\n" | |
5044 | "With @var{n} viewed as an infinite-precision twos-complement\n" | |
5045 | "integer, @code{round-ash} means a left shift introducing zero\n" | |
5046 | "bits when @var{count} is positive, or a right shift rounding\n" | |
5047 | "to the nearest integer (with ties going to the nearest even\n" | |
5048 | "integer) when @var{count} is negative. This is a rounded\n" | |
5049 | "``arithmetic'' shift.\n" | |
5050 | "\n" | |
5051 | "@lisp\n" | |
5052 | "(number->string (round-ash #b1 3) 2) @result{} \"1000\"\n" | |
5053 | "(number->string (round-ash #b1010 -1) 2) @result{} \"101\"\n" | |
5054 | "(number->string (round-ash #b1010 -2) 2) @result{} \"10\"\n" | |
5055 | "(number->string (round-ash #b1011 -2) 2) @result{} \"11\"\n" | |
5056 | "(number->string (round-ash #b1101 -2) 2) @result{} \"11\"\n" | |
5057 | "(number->string (round-ash #b1110 -2) 2) @result{} \"100\"\n" | |
5058 | "@end lisp") | |
5059 | #define FUNC_NAME s_scm_round_ash | |
5060 | { | |
5061 | if (SCM_I_INUMP (n) || SCM_BIGP (n)) | |
5062 | { | |
5063 | long bits_to_shift = scm_to_long (count); | |
788aca27 | 5064 | |
e08a12b5 MW |
5065 | if (bits_to_shift > 0) |
5066 | return left_shift_exact_integer (n, bits_to_shift); | |
5067 | else if (SCM_LIKELY (bits_to_shift < 0)) | |
5068 | return round_right_shift_exact_integer (n, -bits_to_shift); | |
ca46fb90 | 5069 | else |
e08a12b5 | 5070 | return n; |
ca46fb90 RB |
5071 | } |
5072 | else | |
e08a12b5 | 5073 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5074 | } |
1bbd0b84 | 5075 | #undef FUNC_NAME |
0f2d19dd | 5076 | |
3c9f20f8 | 5077 | |
a1ec6916 | 5078 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 5079 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
5080 | "Return the integer composed of the @var{start} (inclusive)\n" |
5081 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
5082 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
5083 | "\n" | |
b380b885 MD |
5084 | "@lisp\n" |
5085 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
5086 | " @result{} \"1010\"\n" | |
5087 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
5088 | " @result{} \"10110\"\n" | |
5089 | "@end lisp") | |
1bbd0b84 | 5090 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 5091 | { |
7f848242 | 5092 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
5093 | istart = scm_to_ulong (start); |
5094 | iend = scm_to_ulong (end); | |
c1bfcf60 | 5095 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 5096 | |
7f848242 KR |
5097 | /* how many bits to keep */ |
5098 | bits = iend - istart; | |
5099 | ||
e11e83f3 | 5100 | if (SCM_I_INUMP (n)) |
0aacf84e | 5101 | { |
e25f3727 | 5102 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
5103 | |
5104 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 5105 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 5106 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 5107 | |
0aacf84e MD |
5108 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
5109 | { | |
5110 | /* Since we emulate two's complement encoded numbers, this | |
5111 | * special case requires us to produce a result that has | |
7f848242 | 5112 | * more bits than can be stored in a fixnum. |
0aacf84e | 5113 | */ |
e25f3727 | 5114 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
5115 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
5116 | bits); | |
5117 | return result; | |
0aacf84e | 5118 | } |
ac0c002c | 5119 | |
7f848242 | 5120 | /* mask down to requisite bits */ |
857ae6af | 5121 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 5122 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
5123 | } |
5124 | else if (SCM_BIGP (n)) | |
ac0c002c | 5125 | { |
7f848242 KR |
5126 | SCM result; |
5127 | if (bits == 1) | |
5128 | { | |
d956fa6f | 5129 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
5130 | } |
5131 | else | |
5132 | { | |
5133 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
5134 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
5135 | such bits into a ulong. */ | |
5136 | result = scm_i_mkbig (); | |
5137 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
5138 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
5139 | result = scm_i_normbig (result); | |
5140 | } | |
5141 | scm_remember_upto_here_1 (n); | |
5142 | return result; | |
ac0c002c | 5143 | } |
0aacf84e | 5144 | else |
78166ad5 | 5145 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5146 | } |
1bbd0b84 | 5147 | #undef FUNC_NAME |
0f2d19dd | 5148 | |
7f848242 | 5149 | |
e4755e5c JB |
5150 | static const char scm_logtab[] = { |
5151 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
5152 | }; | |
1cc91f1b | 5153 | |
a1ec6916 | 5154 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 5155 | (SCM n), |
1e6808ea MG |
5156 | "Return the number of bits in integer @var{n}. If integer is\n" |
5157 | "positive, the 1-bits in its binary representation are counted.\n" | |
5158 | "If negative, the 0-bits in its two's-complement binary\n" | |
5159 | "representation are counted. If 0, 0 is returned.\n" | |
5160 | "\n" | |
b380b885 MD |
5161 | "@lisp\n" |
5162 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
5163 | " @result{} 4\n" |
5164 | "(logcount 0)\n" | |
5165 | " @result{} 0\n" | |
5166 | "(logcount -2)\n" | |
5167 | " @result{} 1\n" | |
5168 | "@end lisp") | |
5169 | #define FUNC_NAME s_scm_logcount | |
5170 | { | |
e11e83f3 | 5171 | if (SCM_I_INUMP (n)) |
f872b822 | 5172 | { |
e25f3727 AW |
5173 | unsigned long c = 0; |
5174 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
5175 | if (nn < 0) |
5176 | nn = -1 - nn; | |
5177 | while (nn) | |
5178 | { | |
5179 | c += scm_logtab[15 & nn]; | |
5180 | nn >>= 4; | |
5181 | } | |
d956fa6f | 5182 | return SCM_I_MAKINUM (c); |
f872b822 | 5183 | } |
ca46fb90 | 5184 | else if (SCM_BIGP (n)) |
f872b822 | 5185 | { |
ca46fb90 | 5186 | unsigned long count; |
713a4259 KR |
5187 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
5188 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 5189 | else |
713a4259 KR |
5190 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
5191 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5192 | return SCM_I_MAKINUM (count); |
f872b822 | 5193 | } |
ca46fb90 RB |
5194 | else |
5195 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 5196 | } |
ca46fb90 | 5197 | #undef FUNC_NAME |
0f2d19dd JB |
5198 | |
5199 | ||
ca46fb90 RB |
5200 | static const char scm_ilentab[] = { |
5201 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
5202 | }; | |
5203 | ||
0f2d19dd | 5204 | |
ca46fb90 RB |
5205 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
5206 | (SCM n), | |
5207 | "Return the number of bits necessary to represent @var{n}.\n" | |
5208 | "\n" | |
5209 | "@lisp\n" | |
5210 | "(integer-length #b10101010)\n" | |
5211 | " @result{} 8\n" | |
5212 | "(integer-length 0)\n" | |
5213 | " @result{} 0\n" | |
5214 | "(integer-length #b1111)\n" | |
5215 | " @result{} 4\n" | |
5216 | "@end lisp") | |
5217 | #define FUNC_NAME s_scm_integer_length | |
5218 | { | |
e11e83f3 | 5219 | if (SCM_I_INUMP (n)) |
0aacf84e | 5220 | { |
e25f3727 | 5221 | unsigned long c = 0; |
0aacf84e | 5222 | unsigned int l = 4; |
e25f3727 | 5223 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
5224 | if (nn < 0) |
5225 | nn = -1 - nn; | |
5226 | while (nn) | |
5227 | { | |
5228 | c += 4; | |
5229 | l = scm_ilentab [15 & nn]; | |
5230 | nn >>= 4; | |
5231 | } | |
d956fa6f | 5232 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
5233 | } |
5234 | else if (SCM_BIGP (n)) | |
5235 | { | |
5236 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
5237 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
5238 | 1 too big, so check for that and adjust. */ | |
5239 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
5240 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
5241 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
5242 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
5243 | size--; | |
5244 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5245 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
5246 | } |
5247 | else | |
ca46fb90 | 5248 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5249 | } |
5250 | #undef FUNC_NAME | |
0f2d19dd JB |
5251 | |
5252 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5253 | #define SCM_MAX_DBL_RADIX 36 |
5254 | ||
0b799eea | 5255 | /* use this array as a way to generate a single digit */ |
9b5fcde6 | 5256 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5257 | |
1ea37620 MW |
5258 | static mpz_t dbl_minimum_normal_mantissa; |
5259 | ||
1be6b49c | 5260 | static size_t |
1ea37620 | 5261 | idbl2str (double dbl, char *a, int radix) |
0f2d19dd | 5262 | { |
1ea37620 | 5263 | int ch = 0; |
0b799eea | 5264 | |
1ea37620 MW |
5265 | if (radix < 2 || radix > SCM_MAX_DBL_RADIX) |
5266 | /* revert to existing behavior */ | |
5267 | radix = 10; | |
0f2d19dd | 5268 | |
1ea37620 | 5269 | if (isinf (dbl)) |
abb7e44d | 5270 | { |
1ea37620 MW |
5271 | strcpy (a, (dbl > 0.0) ? "+inf.0" : "-inf.0"); |
5272 | return 6; | |
abb7e44d | 5273 | } |
1ea37620 MW |
5274 | else if (dbl > 0.0) |
5275 | ; | |
5276 | else if (dbl < 0.0) | |
7351e207 | 5277 | { |
1ea37620 MW |
5278 | dbl = -dbl; |
5279 | a[ch++] = '-'; | |
7351e207 | 5280 | } |
1ea37620 | 5281 | else if (dbl == 0.0) |
7351e207 | 5282 | { |
1ea37620 MW |
5283 | if (!double_is_non_negative_zero (dbl)) |
5284 | a[ch++] = '-'; | |
5285 | strcpy (a + ch, "0.0"); | |
5286 | return ch + 3; | |
7351e207 | 5287 | } |
1ea37620 | 5288 | else if (isnan (dbl)) |
f872b822 | 5289 | { |
1ea37620 MW |
5290 | strcpy (a, "+nan.0"); |
5291 | return 6; | |
f872b822 | 5292 | } |
7351e207 | 5293 | |
1ea37620 MW |
5294 | /* Algorithm taken from "Printing Floating-Point Numbers Quickly and |
5295 | Accurately" by Robert G. Burger and R. Kent Dybvig */ | |
5296 | { | |
5297 | int e, k; | |
5298 | mpz_t f, r, s, mplus, mminus, hi, digit; | |
5299 | int f_is_even, f_is_odd; | |
5300 | int show_exp = 0; | |
5301 | ||
5302 | mpz_inits (f, r, s, mplus, mminus, hi, digit, NULL); | |
5303 | mpz_set_d (f, ldexp (frexp (dbl, &e), DBL_MANT_DIG)); | |
5304 | if (e < DBL_MIN_EXP) | |
5305 | { | |
5306 | mpz_tdiv_q_2exp (f, f, DBL_MIN_EXP - e); | |
5307 | e = DBL_MIN_EXP; | |
5308 | } | |
5309 | e -= DBL_MANT_DIG; | |
0b799eea | 5310 | |
1ea37620 MW |
5311 | f_is_even = !mpz_odd_p (f); |
5312 | f_is_odd = !f_is_even; | |
0b799eea | 5313 | |
1ea37620 MW |
5314 | /* Initialize r, s, mplus, and mminus according |
5315 | to Table 1 from the paper. */ | |
5316 | if (e < 0) | |
5317 | { | |
5318 | mpz_set_ui (mminus, 1); | |
5319 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0 | |
5320 | || e == DBL_MIN_EXP - DBL_MANT_DIG) | |
5321 | { | |
5322 | mpz_set_ui (mplus, 1); | |
5323 | mpz_mul_2exp (r, f, 1); | |
5324 | mpz_mul_2exp (s, mminus, 1 - e); | |
5325 | } | |
5326 | else | |
5327 | { | |
5328 | mpz_set_ui (mplus, 2); | |
5329 | mpz_mul_2exp (r, f, 2); | |
5330 | mpz_mul_2exp (s, mminus, 2 - e); | |
5331 | } | |
5332 | } | |
5333 | else | |
5334 | { | |
5335 | mpz_set_ui (mminus, 1); | |
5336 | mpz_mul_2exp (mminus, mminus, e); | |
5337 | if (mpz_cmp (f, dbl_minimum_normal_mantissa) != 0) | |
5338 | { | |
5339 | mpz_set (mplus, mminus); | |
5340 | mpz_mul_2exp (r, f, 1 + e); | |
5341 | mpz_set_ui (s, 2); | |
5342 | } | |
5343 | else | |
5344 | { | |
5345 | mpz_mul_2exp (mplus, mminus, 1); | |
5346 | mpz_mul_2exp (r, f, 2 + e); | |
5347 | mpz_set_ui (s, 4); | |
5348 | } | |
5349 | } | |
0b799eea | 5350 | |
1ea37620 MW |
5351 | /* Find the smallest k such that: |
5352 | (r + mplus) / s < radix^k (if f is even) | |
5353 | (r + mplus) / s <= radix^k (if f is odd) */ | |
f872b822 | 5354 | { |
1ea37620 MW |
5355 | /* IMPROVE-ME: Make an initial guess to speed this up */ |
5356 | mpz_add (hi, r, mplus); | |
5357 | k = 0; | |
5358 | while (mpz_cmp (hi, s) >= f_is_odd) | |
5359 | { | |
5360 | mpz_mul_ui (s, s, radix); | |
5361 | k++; | |
5362 | } | |
5363 | if (k == 0) | |
5364 | { | |
5365 | mpz_mul_ui (hi, hi, radix); | |
5366 | while (mpz_cmp (hi, s) < f_is_odd) | |
5367 | { | |
5368 | mpz_mul_ui (r, r, radix); | |
5369 | mpz_mul_ui (mplus, mplus, radix); | |
5370 | mpz_mul_ui (mminus, mminus, radix); | |
5371 | mpz_mul_ui (hi, hi, radix); | |
5372 | k--; | |
5373 | } | |
5374 | } | |
cda139a7 | 5375 | } |
f872b822 | 5376 | |
1ea37620 MW |
5377 | if (k >= 8 || k <= -3) |
5378 | { | |
5379 | /* Use scientific notation */ | |
5380 | show_exp = k - 1; | |
5381 | k = 1; | |
5382 | } | |
5383 | else if (k <= 0) | |
5384 | { | |
5385 | int i; | |
0f2d19dd | 5386 | |
1ea37620 MW |
5387 | /* Print leading zeroes */ |
5388 | a[ch++] = '0'; | |
5389 | a[ch++] = '.'; | |
5390 | for (i = 0; i > k; i--) | |
5391 | a[ch++] = '0'; | |
5392 | } | |
5393 | ||
5394 | for (;;) | |
5395 | { | |
5396 | int end_1_p, end_2_p; | |
5397 | int d; | |
5398 | ||
5399 | mpz_mul_ui (mplus, mplus, radix); | |
5400 | mpz_mul_ui (mminus, mminus, radix); | |
5401 | mpz_mul_ui (r, r, radix); | |
5402 | mpz_fdiv_qr (digit, r, r, s); | |
5403 | d = mpz_get_ui (digit); | |
5404 | ||
5405 | mpz_add (hi, r, mplus); | |
5406 | end_1_p = (mpz_cmp (r, mminus) < f_is_even); | |
5407 | end_2_p = (mpz_cmp (s, hi) < f_is_even); | |
5408 | if (end_1_p || end_2_p) | |
5409 | { | |
5410 | mpz_mul_2exp (r, r, 1); | |
5411 | if (!end_2_p) | |
5412 | ; | |
5413 | else if (!end_1_p) | |
5414 | d++; | |
5415 | else if (mpz_cmp (r, s) >= !(d & 1)) | |
5416 | d++; | |
5417 | a[ch++] = number_chars[d]; | |
5418 | if (--k == 0) | |
5419 | a[ch++] = '.'; | |
5420 | break; | |
5421 | } | |
5422 | else | |
5423 | { | |
5424 | a[ch++] = number_chars[d]; | |
5425 | if (--k == 0) | |
5426 | a[ch++] = '.'; | |
5427 | } | |
5428 | } | |
5429 | ||
5430 | if (k > 0) | |
5431 | { | |
5432 | for (; k > 0; k--) | |
5433 | a[ch++] = '0'; | |
5434 | a[ch++] = '.'; | |
5435 | } | |
5436 | ||
5437 | if (k == 0) | |
5438 | a[ch++] = '0'; | |
5439 | ||
5440 | if (show_exp) | |
5441 | { | |
5442 | a[ch++] = 'e'; | |
5443 | ch += scm_iint2str (show_exp, radix, a + ch); | |
5444 | } | |
5445 | ||
5446 | mpz_clears (f, r, s, mplus, mminus, hi, digit, NULL); | |
5447 | } | |
0f2d19dd JB |
5448 | return ch; |
5449 | } | |
5450 | ||
7a1aba42 MV |
5451 | |
5452 | static size_t | |
5453 | icmplx2str (double real, double imag, char *str, int radix) | |
5454 | { | |
5455 | size_t i; | |
c7218482 | 5456 | double sgn; |
7a1aba42 MV |
5457 | |
5458 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5459 | #ifdef HAVE_COPYSIGN |
5460 | sgn = copysign (1.0, imag); | |
5461 | #else | |
5462 | sgn = imag; | |
5463 | #endif | |
5464 | /* Don't output a '+' for negative numbers or for Inf and | |
5465 | NaN. They will provide their own sign. */ | |
5466 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5467 | str[i++] = '+'; | |
5468 | i += idbl2str (imag, &str[i], radix); | |
5469 | str[i++] = 'i'; | |
7a1aba42 MV |
5470 | return i; |
5471 | } | |
5472 | ||
1be6b49c | 5473 | static size_t |
0b799eea | 5474 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5475 | { |
1be6b49c | 5476 | size_t i; |
3c9a524f | 5477 | if (SCM_REALP (flt)) |
0b799eea | 5478 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5479 | else |
7a1aba42 MV |
5480 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5481 | str, radix); | |
0f2d19dd JB |
5482 | return i; |
5483 | } | |
0f2d19dd | 5484 | |
2881e77b | 5485 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5486 | characters in the result. |
5487 | rad is output base | |
5488 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5489 | size_t |
2881e77b MV |
5490 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5491 | { | |
5492 | if (num < 0) | |
5493 | { | |
5494 | *p++ = '-'; | |
5495 | return scm_iuint2str (-num, rad, p) + 1; | |
5496 | } | |
5497 | else | |
5498 | return scm_iuint2str (num, rad, p); | |
5499 | } | |
5500 | ||
5501 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5502 | characters in the result. | |
5503 | rad is output base | |
5504 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5505 | size_t | |
5506 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5507 | { |
1be6b49c ML |
5508 | size_t j = 1; |
5509 | size_t i; | |
2881e77b | 5510 | scm_t_uintmax n = num; |
5c11cc9d | 5511 | |
a6f3af16 AW |
5512 | if (rad < 2 || rad > 36) |
5513 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5514 | ||
f872b822 | 5515 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5516 | j++; |
5517 | ||
5518 | i = j; | |
2881e77b | 5519 | n = num; |
f872b822 MD |
5520 | while (i--) |
5521 | { | |
5c11cc9d GH |
5522 | int d = n % rad; |
5523 | ||
f872b822 | 5524 | n /= rad; |
a6f3af16 | 5525 | p[i] = number_chars[d]; |
f872b822 | 5526 | } |
0f2d19dd JB |
5527 | return j; |
5528 | } | |
5529 | ||
a1ec6916 | 5530 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5531 | (SCM n, SCM radix), |
5532 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5533 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5534 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5535 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5536 | { |
1bbd0b84 | 5537 | int base; |
98cb6e75 | 5538 | |
0aacf84e | 5539 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5540 | base = 10; |
0aacf84e | 5541 | else |
5efd3c7d | 5542 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5543 | |
e11e83f3 | 5544 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5545 | { |
5546 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5547 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5548 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5549 | } |
5550 | else if (SCM_BIGP (n)) | |
5551 | { | |
5552 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
d88f5323 AW |
5553 | size_t len = strlen (str); |
5554 | void (*freefunc) (void *, size_t); | |
5555 | SCM ret; | |
5556 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
0aacf84e | 5557 | scm_remember_upto_here_1 (n); |
d88f5323 AW |
5558 | ret = scm_from_latin1_stringn (str, len); |
5559 | freefunc (str, len + 1); | |
5560 | return ret; | |
0aacf84e | 5561 | } |
f92e85f7 MV |
5562 | else if (SCM_FRACTIONP (n)) |
5563 | { | |
f92e85f7 | 5564 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5565 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5566 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5567 | } | |
0aacf84e MD |
5568 | else if (SCM_INEXACTP (n)) |
5569 | { | |
5570 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5571 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5572 | } |
5573 | else | |
bb628794 | 5574 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5575 | } |
1bbd0b84 | 5576 | #undef FUNC_NAME |
0f2d19dd JB |
5577 | |
5578 | ||
ca46fb90 RB |
5579 | /* These print routines used to be stubbed here so that scm_repl.c |
5580 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5581 | |
0f2d19dd | 5582 | int |
e81d98ec | 5583 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5584 | { |
56e55ac7 | 5585 | char num_buf[FLOBUFLEN]; |
0b799eea | 5586 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5587 | return !0; |
5588 | } | |
5589 | ||
b479fe9a MV |
5590 | void |
5591 | scm_i_print_double (double val, SCM port) | |
5592 | { | |
5593 | char num_buf[FLOBUFLEN]; | |
5594 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5595 | } | |
5596 | ||
f3ae5d60 | 5597 | int |
e81d98ec | 5598 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5599 | |
f3ae5d60 | 5600 | { |
56e55ac7 | 5601 | char num_buf[FLOBUFLEN]; |
0b799eea | 5602 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5603 | return !0; |
5604 | } | |
1cc91f1b | 5605 | |
7a1aba42 MV |
5606 | void |
5607 | scm_i_print_complex (double real, double imag, SCM port) | |
5608 | { | |
5609 | char num_buf[FLOBUFLEN]; | |
5610 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5611 | } | |
5612 | ||
f92e85f7 MV |
5613 | int |
5614 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5615 | { | |
5616 | SCM str; | |
f92e85f7 | 5617 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5618 | scm_display (str, port); |
f92e85f7 MV |
5619 | scm_remember_upto_here_1 (str); |
5620 | return !0; | |
5621 | } | |
5622 | ||
0f2d19dd | 5623 | int |
e81d98ec | 5624 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5625 | { |
ca46fb90 | 5626 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
b57bf272 AW |
5627 | size_t len = strlen (str); |
5628 | void (*freefunc) (void *, size_t); | |
5629 | mp_get_memory_functions (NULL, NULL, &freefunc); | |
ca46fb90 | 5630 | scm_remember_upto_here_1 (exp); |
b57bf272 AW |
5631 | scm_lfwrite (str, len, port); |
5632 | freefunc (str, len + 1); | |
0f2d19dd JB |
5633 | return !0; |
5634 | } | |
5635 | /*** END nums->strs ***/ | |
5636 | ||
3c9a524f | 5637 | |
0f2d19dd | 5638 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5639 | |
3c9a524f DH |
5640 | /* The following functions implement the conversion from strings to numbers. |
5641 | * The implementation somehow follows the grammar for numbers as it is given | |
5642 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5643 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5644 | * points should be noted about the implementation: | |
bc3d34f5 | 5645 | * |
3c9a524f DH |
5646 | * * Each function keeps a local index variable 'idx' that points at the |
5647 | * current position within the parsed string. The global index is only | |
5648 | * updated if the function could parse the corresponding syntactic unit | |
5649 | * successfully. | |
bc3d34f5 | 5650 | * |
3c9a524f | 5651 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5652 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5653 | * | |
3c9a524f DH |
5654 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5655 | * Only if these fixnums would overflow, the result variables are updated | |
5656 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5657 | * the temporary variables holding the fixnums are cleared, and the process | |
5658 | * starts over again. If for example fixnums were able to store five decimal | |
5659 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5660 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5661 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5662 | * |
5663 | * Notes on the handling of exactness specifiers: | |
5664 | * | |
5665 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5666 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5667 | * written in rectangular form, exactness specifiers are applied to the | |
5668 | * real and imaginary parts before calling scm_make_rectangular. For | |
5669 | * complex numbers written in polar form, exactness specifiers are applied | |
5670 | * to the magnitude and angle before calling scm_make_polar. | |
5671 | * | |
5672 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5673 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5674 | * the entire number, and applies to both components of a complex number. | |
5675 | * "#e" causes each component to be made exact, and "#i" causes each | |
5676 | * component to be made inexact. If no forced exactness specifier is | |
5677 | * present, then the exactness of each component is determined | |
5678 | * independently by the presence or absence of a decimal point or hash mark | |
5679 | * within that component. If a decimal point or hash mark is present, the | |
5680 | * component is made inexact, otherwise it is made exact. | |
5681 | * | |
5682 | * After the exactness specifiers have been applied to each component, they | |
5683 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5684 | * the final result. Note that this will result in a real number if the | |
5685 | * imaginary part, magnitude, or angle is an exact 0. | |
5686 | * | |
5687 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5688 | * | |
5689 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5690 | */ |
5691 | ||
5692 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5693 | ||
5694 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5695 | ||
a6f3af16 AW |
5696 | /* Caller is responsible for checking that the return value is in range |
5697 | for the given radix, which should be <= 36. */ | |
5698 | static unsigned int | |
5699 | char_decimal_value (scm_t_uint32 c) | |
5700 | { | |
5701 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5702 | that's certainly above any valid decimal, so we take advantage of | |
5703 | that to elide some tests. */ | |
5704 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5705 | ||
5706 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5707 | hexadecimals. */ | |
5708 | if (d >= 10U) | |
5709 | { | |
5710 | c = uc_tolower (c); | |
5711 | if (c >= (scm_t_uint32) 'a') | |
5712 | d = c - (scm_t_uint32)'a' + 10U; | |
5713 | } | |
5714 | return d; | |
5715 | } | |
3c9a524f | 5716 | |
91db4a37 LC |
5717 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5718 | in base RADIX. Upon success, return the unsigned integer and update | |
5719 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5720 | static SCM |
3f47e526 | 5721 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5722 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5723 | { |
3c9a524f DH |
5724 | unsigned int idx = *p_idx; |
5725 | unsigned int hash_seen = 0; | |
5726 | scm_t_bits shift = 1; | |
5727 | scm_t_bits add = 0; | |
5728 | unsigned int digit_value; | |
5729 | SCM result; | |
5730 | char c; | |
3f47e526 | 5731 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5732 | |
5733 | if (idx == len) | |
5734 | return SCM_BOOL_F; | |
2a8fecee | 5735 | |
3f47e526 | 5736 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5737 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5738 | if (digit_value >= radix) |
5739 | return SCM_BOOL_F; | |
5740 | ||
5741 | idx++; | |
d956fa6f | 5742 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5743 | while (idx != len) |
f872b822 | 5744 | { |
3f47e526 | 5745 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5746 | if (c == '#') |
3c9a524f DH |
5747 | { |
5748 | hash_seen = 1; | |
5749 | digit_value = 0; | |
5750 | } | |
a6f3af16 AW |
5751 | else if (hash_seen) |
5752 | break; | |
3c9a524f | 5753 | else |
a6f3af16 AW |
5754 | { |
5755 | digit_value = char_decimal_value (c); | |
5756 | /* This check catches non-decimals in addition to out-of-range | |
5757 | decimals. */ | |
5758 | if (digit_value >= radix) | |
5759 | break; | |
5760 | } | |
3c9a524f DH |
5761 | |
5762 | idx++; | |
5763 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5764 | { | |
d956fa6f | 5765 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5766 | if (add > 0) |
d956fa6f | 5767 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5768 | |
5769 | shift = radix; | |
5770 | add = digit_value; | |
5771 | } | |
5772 | else | |
5773 | { | |
5774 | shift = shift * radix; | |
5775 | add = add * radix + digit_value; | |
5776 | } | |
5777 | }; | |
5778 | ||
5779 | if (shift > 1) | |
d956fa6f | 5780 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5781 | if (add > 0) |
d956fa6f | 5782 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5783 | |
5784 | *p_idx = idx; | |
5785 | if (hash_seen) | |
5786 | *p_exactness = INEXACT; | |
5787 | ||
5788 | return result; | |
2a8fecee JB |
5789 | } |
5790 | ||
5791 | ||
3c9a524f DH |
5792 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5793 | * covers the parts of the rules that start at a potential point. The value | |
5794 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5795 | * in variable result. The content of *p_exactness indicates, whether a hash |
5796 | * has already been seen in the digits before the point. | |
3c9a524f | 5797 | */ |
1cc91f1b | 5798 | |
3f47e526 | 5799 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5800 | |
5801 | static SCM | |
3f47e526 | 5802 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5803 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5804 | { |
3c9a524f DH |
5805 | unsigned int idx = *p_idx; |
5806 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5807 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5808 | |
5809 | if (idx == len) | |
79d34f68 | 5810 | return result; |
3c9a524f | 5811 | |
3f47e526 | 5812 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5813 | { |
5814 | scm_t_bits shift = 1; | |
5815 | scm_t_bits add = 0; | |
5816 | unsigned int digit_value; | |
cff5fa33 | 5817 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5818 | |
5819 | idx++; | |
5820 | while (idx != len) | |
5821 | { | |
3f47e526 MG |
5822 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5823 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5824 | { |
5825 | if (x == INEXACT) | |
5826 | return SCM_BOOL_F; | |
5827 | else | |
5828 | digit_value = DIGIT2UINT (c); | |
5829 | } | |
5830 | else if (c == '#') | |
5831 | { | |
5832 | x = INEXACT; | |
5833 | digit_value = 0; | |
5834 | } | |
5835 | else | |
5836 | break; | |
5837 | ||
5838 | idx++; | |
5839 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5840 | { | |
d956fa6f MV |
5841 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5842 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5843 | if (add > 0) |
d956fa6f | 5844 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5845 | |
5846 | shift = 10; | |
5847 | add = digit_value; | |
5848 | } | |
5849 | else | |
5850 | { | |
5851 | shift = shift * 10; | |
5852 | add = add * 10 + digit_value; | |
5853 | } | |
5854 | }; | |
5855 | ||
5856 | if (add > 0) | |
5857 | { | |
d956fa6f MV |
5858 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5859 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5860 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5861 | } |
5862 | ||
d8592269 | 5863 | result = scm_divide (result, big_shift); |
79d34f68 | 5864 | |
3c9a524f DH |
5865 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5866 | x = INEXACT; | |
f872b822 | 5867 | } |
3c9a524f | 5868 | |
3c9a524f | 5869 | if (idx != len) |
f872b822 | 5870 | { |
3c9a524f DH |
5871 | int sign = 1; |
5872 | unsigned int start; | |
3f47e526 | 5873 | scm_t_wchar c; |
3c9a524f DH |
5874 | int exponent; |
5875 | SCM e; | |
5876 | ||
5877 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5878 | ||
3f47e526 | 5879 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5880 | { |
3c9a524f DH |
5881 | case 'd': case 'D': |
5882 | case 'e': case 'E': | |
5883 | case 'f': case 'F': | |
5884 | case 'l': case 'L': | |
5885 | case 's': case 'S': | |
5886 | idx++; | |
ee0ddd21 AW |
5887 | if (idx == len) |
5888 | return SCM_BOOL_F; | |
5889 | ||
3c9a524f | 5890 | start = idx; |
3f47e526 | 5891 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5892 | if (c == '-') |
5893 | { | |
5894 | idx++; | |
ee0ddd21 AW |
5895 | if (idx == len) |
5896 | return SCM_BOOL_F; | |
5897 | ||
3c9a524f | 5898 | sign = -1; |
3f47e526 | 5899 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5900 | } |
5901 | else if (c == '+') | |
5902 | { | |
5903 | idx++; | |
ee0ddd21 AW |
5904 | if (idx == len) |
5905 | return SCM_BOOL_F; | |
5906 | ||
3c9a524f | 5907 | sign = 1; |
3f47e526 | 5908 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5909 | } |
5910 | else | |
5911 | sign = 1; | |
5912 | ||
3f47e526 | 5913 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5914 | return SCM_BOOL_F; |
5915 | ||
5916 | idx++; | |
5917 | exponent = DIGIT2UINT (c); | |
5918 | while (idx != len) | |
f872b822 | 5919 | { |
3f47e526 MG |
5920 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5921 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5922 | { |
5923 | idx++; | |
5924 | if (exponent <= SCM_MAXEXP) | |
5925 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5926 | } | |
5927 | else | |
5928 | break; | |
f872b822 | 5929 | } |
3c9a524f | 5930 | |
1ea37620 | 5931 | if (exponent > ((sign == 1) ? SCM_MAXEXP : SCM_MAXEXP + DBL_DIG + 1)) |
f872b822 | 5932 | { |
3c9a524f | 5933 | size_t exp_len = idx - start; |
3f47e526 | 5934 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5935 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5936 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5937 | } |
3c9a524f | 5938 | |
d956fa6f | 5939 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5940 | if (sign == 1) |
5941 | result = scm_product (result, e); | |
5942 | else | |
6ebecdeb | 5943 | result = scm_divide (result, e); |
3c9a524f DH |
5944 | |
5945 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5946 | x = INEXACT; | |
5947 | ||
f872b822 | 5948 | break; |
3c9a524f | 5949 | |
f872b822 | 5950 | default: |
3c9a524f | 5951 | break; |
f872b822 | 5952 | } |
0f2d19dd | 5953 | } |
3c9a524f DH |
5954 | |
5955 | *p_idx = idx; | |
5956 | if (x == INEXACT) | |
5957 | *p_exactness = x; | |
5958 | ||
5959 | return result; | |
0f2d19dd | 5960 | } |
0f2d19dd | 5961 | |
3c9a524f DH |
5962 | |
5963 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5964 | ||
5965 | static SCM | |
3f47e526 | 5966 | mem2ureal (SCM mem, unsigned int *p_idx, |
929d11b2 MW |
5967 | unsigned int radix, enum t_exactness forced_x, |
5968 | int allow_inf_or_nan) | |
0f2d19dd | 5969 | { |
3c9a524f | 5970 | unsigned int idx = *p_idx; |
164d2481 | 5971 | SCM result; |
3f47e526 | 5972 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5973 | |
40f89215 NJ |
5974 | /* Start off believing that the number will be exact. This changes |
5975 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5976 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5977 | |
3c9a524f DH |
5978 | if (idx == len) |
5979 | return SCM_BOOL_F; | |
5980 | ||
929d11b2 MW |
5981 | if (allow_inf_or_nan && forced_x != EXACT && idx+5 <= len) |
5982 | switch (scm_i_string_ref (mem, idx)) | |
5983 | { | |
5984 | case 'i': case 'I': | |
5985 | switch (scm_i_string_ref (mem, idx + 1)) | |
5986 | { | |
5987 | case 'n': case 'N': | |
5988 | switch (scm_i_string_ref (mem, idx + 2)) | |
5989 | { | |
5990 | case 'f': case 'F': | |
5991 | if (scm_i_string_ref (mem, idx + 3) == '.' | |
5992 | && scm_i_string_ref (mem, idx + 4) == '0') | |
5993 | { | |
5994 | *p_idx = idx+5; | |
5995 | return scm_inf (); | |
5996 | } | |
5997 | } | |
5998 | } | |
5999 | case 'n': case 'N': | |
6000 | switch (scm_i_string_ref (mem, idx + 1)) | |
6001 | { | |
6002 | case 'a': case 'A': | |
6003 | switch (scm_i_string_ref (mem, idx + 2)) | |
6004 | { | |
6005 | case 'n': case 'N': | |
6006 | if (scm_i_string_ref (mem, idx + 3) == '.') | |
6007 | { | |
6008 | /* Cobble up the fractional part. We might want to | |
6009 | set the NaN's mantissa from it. */ | |
6010 | idx += 4; | |
6011 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), | |
6012 | SCM_INUM0)) | |
6013 | { | |
5f237d6e | 6014 | #if SCM_ENABLE_DEPRECATED == 1 |
929d11b2 MW |
6015 | scm_c_issue_deprecation_warning |
6016 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5f237d6e | 6017 | #else |
929d11b2 | 6018 | return SCM_BOOL_F; |
5f237d6e | 6019 | #endif |
929d11b2 | 6020 | } |
5f237d6e | 6021 | |
929d11b2 MW |
6022 | *p_idx = idx; |
6023 | return scm_nan (); | |
6024 | } | |
6025 | } | |
6026 | } | |
6027 | } | |
7351e207 | 6028 | |
3f47e526 | 6029 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
6030 | { |
6031 | if (radix != 10) | |
6032 | return SCM_BOOL_F; | |
6033 | else if (idx + 1 == len) | |
6034 | return SCM_BOOL_F; | |
3f47e526 | 6035 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
6036 | return SCM_BOOL_F; |
6037 | else | |
cff5fa33 | 6038 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 6039 | p_idx, &implicit_x); |
f872b822 | 6040 | } |
3c9a524f DH |
6041 | else |
6042 | { | |
3c9a524f | 6043 | SCM uinteger; |
3c9a524f | 6044 | |
9d427b2c | 6045 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 6046 | if (scm_is_false (uinteger)) |
3c9a524f DH |
6047 | return SCM_BOOL_F; |
6048 | ||
6049 | if (idx == len) | |
6050 | result = uinteger; | |
3f47e526 | 6051 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 6052 | { |
3c9a524f DH |
6053 | SCM divisor; |
6054 | ||
6055 | idx++; | |
ee0ddd21 AW |
6056 | if (idx == len) |
6057 | return SCM_BOOL_F; | |
3c9a524f | 6058 | |
9d427b2c | 6059 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
929d11b2 | 6060 | if (scm_is_false (divisor) || scm_is_eq (divisor, SCM_INUM0)) |
3c9a524f DH |
6061 | return SCM_BOOL_F; |
6062 | ||
f92e85f7 | 6063 | /* both are int/big here, I assume */ |
cba42c93 | 6064 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 6065 | } |
3c9a524f DH |
6066 | else if (radix == 10) |
6067 | { | |
9d427b2c | 6068 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 6069 | if (scm_is_false (result)) |
3c9a524f DH |
6070 | return SCM_BOOL_F; |
6071 | } | |
6072 | else | |
6073 | result = uinteger; | |
6074 | ||
6075 | *p_idx = idx; | |
f872b822 | 6076 | } |
164d2481 | 6077 | |
9d427b2c MW |
6078 | switch (forced_x) |
6079 | { | |
6080 | case EXACT: | |
6081 | if (SCM_INEXACTP (result)) | |
6082 | return scm_inexact_to_exact (result); | |
6083 | else | |
6084 | return result; | |
6085 | case INEXACT: | |
6086 | if (SCM_INEXACTP (result)) | |
6087 | return result; | |
6088 | else | |
6089 | return scm_exact_to_inexact (result); | |
6090 | case NO_EXACTNESS: | |
6091 | if (implicit_x == INEXACT) | |
6092 | { | |
6093 | if (SCM_INEXACTP (result)) | |
6094 | return result; | |
6095 | else | |
6096 | return scm_exact_to_inexact (result); | |
6097 | } | |
6098 | else | |
6099 | return result; | |
6100 | } | |
164d2481 | 6101 | |
9d427b2c MW |
6102 | /* We should never get here */ |
6103 | scm_syserror ("mem2ureal"); | |
3c9a524f | 6104 | } |
0f2d19dd | 6105 | |
0f2d19dd | 6106 | |
3c9a524f | 6107 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 6108 | |
3c9a524f | 6109 | static SCM |
3f47e526 | 6110 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 6111 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 6112 | { |
3f47e526 | 6113 | scm_t_wchar c; |
3c9a524f DH |
6114 | int sign = 0; |
6115 | SCM ureal; | |
3f47e526 | 6116 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6117 | |
6118 | if (idx == len) | |
6119 | return SCM_BOOL_F; | |
6120 | ||
3f47e526 | 6121 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6122 | if (c == '+') |
6123 | { | |
6124 | idx++; | |
6125 | sign = 1; | |
6126 | } | |
6127 | else if (c == '-') | |
6128 | { | |
6129 | idx++; | |
6130 | sign = -1; | |
0f2d19dd | 6131 | } |
0f2d19dd | 6132 | |
3c9a524f DH |
6133 | if (idx == len) |
6134 | return SCM_BOOL_F; | |
6135 | ||
929d11b2 | 6136 | ureal = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6137 | if (scm_is_false (ureal)) |
f872b822 | 6138 | { |
3c9a524f DH |
6139 | /* input must be either +i or -i */ |
6140 | ||
6141 | if (sign == 0) | |
6142 | return SCM_BOOL_F; | |
6143 | ||
3f47e526 MG |
6144 | if (scm_i_string_ref (mem, idx) == 'i' |
6145 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 6146 | { |
3c9a524f DH |
6147 | idx++; |
6148 | if (idx != len) | |
6149 | return SCM_BOOL_F; | |
6150 | ||
cff5fa33 | 6151 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 6152 | } |
3c9a524f DH |
6153 | else |
6154 | return SCM_BOOL_F; | |
0f2d19dd | 6155 | } |
3c9a524f DH |
6156 | else |
6157 | { | |
73e4de09 | 6158 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 6159 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 6160 | |
3c9a524f DH |
6161 | if (idx == len) |
6162 | return ureal; | |
6163 | ||
3f47e526 | 6164 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 6165 | switch (c) |
f872b822 | 6166 | { |
3c9a524f DH |
6167 | case 'i': case 'I': |
6168 | /* either +<ureal>i or -<ureal>i */ | |
6169 | ||
6170 | idx++; | |
6171 | if (sign == 0) | |
6172 | return SCM_BOOL_F; | |
6173 | if (idx != len) | |
6174 | return SCM_BOOL_F; | |
cff5fa33 | 6175 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
6176 | |
6177 | case '@': | |
6178 | /* polar input: <real>@<real>. */ | |
6179 | ||
6180 | idx++; | |
6181 | if (idx == len) | |
6182 | return SCM_BOOL_F; | |
6183 | else | |
f872b822 | 6184 | { |
3c9a524f DH |
6185 | int sign; |
6186 | SCM angle; | |
6187 | SCM result; | |
6188 | ||
3f47e526 | 6189 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6190 | if (c == '+') |
6191 | { | |
6192 | idx++; | |
ee0ddd21 AW |
6193 | if (idx == len) |
6194 | return SCM_BOOL_F; | |
3c9a524f DH |
6195 | sign = 1; |
6196 | } | |
6197 | else if (c == '-') | |
6198 | { | |
6199 | idx++; | |
ee0ddd21 AW |
6200 | if (idx == len) |
6201 | return SCM_BOOL_F; | |
3c9a524f DH |
6202 | sign = -1; |
6203 | } | |
6204 | else | |
929d11b2 | 6205 | sign = 0; |
3c9a524f | 6206 | |
929d11b2 | 6207 | angle = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
73e4de09 | 6208 | if (scm_is_false (angle)) |
3c9a524f DH |
6209 | return SCM_BOOL_F; |
6210 | if (idx != len) | |
6211 | return SCM_BOOL_F; | |
6212 | ||
73e4de09 | 6213 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
6214 | angle = scm_difference (angle, SCM_UNDEFINED); |
6215 | ||
6216 | result = scm_make_polar (ureal, angle); | |
6217 | return result; | |
f872b822 | 6218 | } |
3c9a524f DH |
6219 | case '+': |
6220 | case '-': | |
6221 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 6222 | |
3c9a524f DH |
6223 | idx++; |
6224 | if (idx == len) | |
6225 | return SCM_BOOL_F; | |
6226 | else | |
6227 | { | |
6228 | int sign = (c == '+') ? 1 : -1; | |
929d11b2 | 6229 | SCM imag = mem2ureal (mem, &idx, radix, forced_x, sign != 0); |
0f2d19dd | 6230 | |
73e4de09 | 6231 | if (scm_is_false (imag)) |
d956fa6f | 6232 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 6233 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 6234 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 6235 | |
3c9a524f DH |
6236 | if (idx == len) |
6237 | return SCM_BOOL_F; | |
3f47e526 MG |
6238 | if (scm_i_string_ref (mem, idx) != 'i' |
6239 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 6240 | return SCM_BOOL_F; |
0f2d19dd | 6241 | |
3c9a524f DH |
6242 | idx++; |
6243 | if (idx != len) | |
6244 | return SCM_BOOL_F; | |
0f2d19dd | 6245 | |
1fe5e088 | 6246 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6247 | } |
6248 | default: | |
6249 | return SCM_BOOL_F; | |
6250 | } | |
6251 | } | |
0f2d19dd | 6252 | } |
0f2d19dd JB |
6253 | |
6254 | ||
3c9a524f DH |
6255 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6256 | ||
6257 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6258 | |
0f2d19dd | 6259 | SCM |
3f47e526 | 6260 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6261 | { |
3c9a524f DH |
6262 | unsigned int idx = 0; |
6263 | unsigned int radix = NO_RADIX; | |
6264 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6265 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6266 | |
6267 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6268 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6269 | { |
3f47e526 | 6270 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6271 | { |
6272 | case 'b': case 'B': | |
6273 | if (radix != NO_RADIX) | |
6274 | return SCM_BOOL_F; | |
6275 | radix = DUAL; | |
6276 | break; | |
6277 | case 'd': case 'D': | |
6278 | if (radix != NO_RADIX) | |
6279 | return SCM_BOOL_F; | |
6280 | radix = DEC; | |
6281 | break; | |
6282 | case 'i': case 'I': | |
6283 | if (forced_x != NO_EXACTNESS) | |
6284 | return SCM_BOOL_F; | |
6285 | forced_x = INEXACT; | |
6286 | break; | |
6287 | case 'e': case 'E': | |
6288 | if (forced_x != NO_EXACTNESS) | |
6289 | return SCM_BOOL_F; | |
6290 | forced_x = EXACT; | |
6291 | break; | |
6292 | case 'o': case 'O': | |
6293 | if (radix != NO_RADIX) | |
6294 | return SCM_BOOL_F; | |
6295 | radix = OCT; | |
6296 | break; | |
6297 | case 'x': case 'X': | |
6298 | if (radix != NO_RADIX) | |
6299 | return SCM_BOOL_F; | |
6300 | radix = HEX; | |
6301 | break; | |
6302 | default: | |
f872b822 | 6303 | return SCM_BOOL_F; |
3c9a524f DH |
6304 | } |
6305 | idx += 2; | |
6306 | } | |
6307 | ||
6308 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6309 | if (radix == NO_RADIX) | |
9d427b2c | 6310 | radix = default_radix; |
f872b822 | 6311 | |
9d427b2c | 6312 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6313 | } |
6314 | ||
3f47e526 MG |
6315 | SCM |
6316 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6317 | unsigned int default_radix) | |
6318 | { | |
6319 | SCM str = scm_from_locale_stringn (mem, len); | |
6320 | ||
6321 | return scm_i_string_to_number (str, default_radix); | |
6322 | } | |
6323 | ||
0f2d19dd | 6324 | |
a1ec6916 | 6325 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6326 | (SCM string, SCM radix), |
1e6808ea | 6327 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6328 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6329 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6330 | "is a default radix that may be overridden by an explicit radix\n" | |
6331 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6332 | "supplied, then the default radix is 10. If string is not a\n" | |
6333 | "syntactically valid notation for a number, then\n" | |
6334 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6335 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6336 | { |
6337 | SCM answer; | |
5efd3c7d | 6338 | unsigned int base; |
a6d9e5ab | 6339 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6340 | |
6341 | if (SCM_UNBNDP (radix)) | |
6342 | base = 10; | |
6343 | else | |
6344 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6345 | ||
3f47e526 | 6346 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6347 | scm_remember_upto_here_1 (string); |
6348 | return answer; | |
0f2d19dd | 6349 | } |
1bbd0b84 | 6350 | #undef FUNC_NAME |
3c9a524f DH |
6351 | |
6352 | ||
0f2d19dd JB |
6353 | /*** END strs->nums ***/ |
6354 | ||
5986c47d | 6355 | |
8507ec80 MV |
6356 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6357 | (SCM x), | |
6358 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6359 | "otherwise.") | |
6360 | #define FUNC_NAME s_scm_number_p | |
6361 | { | |
6362 | return scm_from_bool (SCM_NUMBERP (x)); | |
6363 | } | |
6364 | #undef FUNC_NAME | |
6365 | ||
6366 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6367 | (SCM x), |
942e5b91 | 6368 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6369 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6370 | "values form subsets of the set of complex numbers, i. e. the\n" |
6371 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6372 | "rational or integer number.") | |
8507ec80 | 6373 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6374 | { |
8507ec80 MV |
6375 | /* all numbers are complex. */ |
6376 | return scm_number_p (x); | |
0f2d19dd | 6377 | } |
1bbd0b84 | 6378 | #undef FUNC_NAME |
0f2d19dd | 6379 | |
f92e85f7 MV |
6380 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6381 | (SCM x), | |
6382 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6383 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6384 | "the set of real numbers, i. e. the predicate will also be\n" | |
6385 | "fulfilled if @var{x} is an integer number.") | |
6386 | #define FUNC_NAME s_scm_real_p | |
6387 | { | |
c960e556 MW |
6388 | return scm_from_bool |
6389 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6390 | } |
6391 | #undef FUNC_NAME | |
6392 | ||
6393 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6394 | (SCM x), |
942e5b91 | 6395 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6396 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6397 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6398 | "fulfilled if @var{x} is an integer number.") |
6399 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6400 | { |
c960e556 | 6401 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6402 | return SCM_BOOL_T; |
6403 | else if (SCM_REALP (x)) | |
c960e556 MW |
6404 | /* due to their limited precision, finite floating point numbers are |
6405 | rational as well. (finite means neither infinity nor a NaN) */ | |
6406 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6407 | else |
bb628794 | 6408 | return SCM_BOOL_F; |
0f2d19dd | 6409 | } |
1bbd0b84 | 6410 | #undef FUNC_NAME |
0f2d19dd | 6411 | |
a1ec6916 | 6412 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6413 | (SCM x), |
942e5b91 MG |
6414 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6415 | "else.") | |
1bbd0b84 | 6416 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6417 | { |
c960e556 | 6418 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6419 | return SCM_BOOL_T; |
c960e556 MW |
6420 | else if (SCM_REALP (x)) |
6421 | { | |
6422 | double val = SCM_REAL_VALUE (x); | |
6423 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6424 | } | |
6425 | else | |
8e43ed5d | 6426 | return SCM_BOOL_F; |
0f2d19dd | 6427 | } |
1bbd0b84 | 6428 | #undef FUNC_NAME |
0f2d19dd JB |
6429 | |
6430 | ||
8a1f4f98 AW |
6431 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6432 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6433 | (SCM x, SCM y, SCM rest), | |
6434 | "Return @code{#t} if all parameters are numerically equal.") | |
6435 | #define FUNC_NAME s_scm_i_num_eq_p | |
6436 | { | |
6437 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6438 | return SCM_BOOL_T; | |
6439 | while (!scm_is_null (rest)) | |
6440 | { | |
6441 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6442 | return SCM_BOOL_F; | |
6443 | x = y; | |
6444 | y = scm_car (rest); | |
6445 | rest = scm_cdr (rest); | |
6446 | } | |
6447 | return scm_num_eq_p (x, y); | |
6448 | } | |
6449 | #undef FUNC_NAME | |
0f2d19dd | 6450 | SCM |
6e8d25a6 | 6451 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6452 | { |
d8b95e27 | 6453 | again: |
e11e83f3 | 6454 | if (SCM_I_INUMP (x)) |
0aacf84e | 6455 | { |
e25f3727 | 6456 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6457 | if (SCM_I_INUMP (y)) |
0aacf84e | 6458 | { |
e25f3727 | 6459 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6460 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6461 | } |
6462 | else if (SCM_BIGP (y)) | |
6463 | return SCM_BOOL_F; | |
6464 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6465 | { |
6466 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6467 | to a double and compare. | |
6468 | ||
6469 | But on a 64-bit system an inum is bigger than a double and | |
6470 | casting it to a double (call that dxx) will round. dxx is at | |
6471 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6472 | an integer and fits a long. So we cast yy to a long and | |
6473 | compare with plain xx. | |
6474 | ||
6475 | An alternative (for any size system actually) would be to check | |
6476 | yy is an integer (with floor) and is in range of an inum | |
6477 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6478 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6479 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6480 | |
6481 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6482 | return scm_from_bool ((double) xx == yy |
6483 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6484 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6485 | } |
0aacf84e | 6486 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6487 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6488 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6489 | else if (SCM_FRACTIONP (y)) |
6490 | return SCM_BOOL_F; | |
0aacf84e | 6491 | else |
8a1f4f98 | 6492 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6493 | } |
0aacf84e MD |
6494 | else if (SCM_BIGP (x)) |
6495 | { | |
e11e83f3 | 6496 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6497 | return SCM_BOOL_F; |
6498 | else if (SCM_BIGP (y)) | |
6499 | { | |
6500 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6501 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6502 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6503 | } |
6504 | else if (SCM_REALP (y)) | |
6505 | { | |
6506 | int cmp; | |
2e65b52f | 6507 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6508 | return SCM_BOOL_F; |
6509 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6510 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6511 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6512 | } |
6513 | else if (SCM_COMPLEXP (y)) | |
6514 | { | |
6515 | int cmp; | |
6516 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6517 | return SCM_BOOL_F; | |
2e65b52f | 6518 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6519 | return SCM_BOOL_F; |
6520 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6521 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6522 | return scm_from_bool (0 == cmp); |
0aacf84e | 6523 | } |
f92e85f7 MV |
6524 | else if (SCM_FRACTIONP (y)) |
6525 | return SCM_BOOL_F; | |
0aacf84e | 6526 | else |
8a1f4f98 | 6527 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6528 | } |
0aacf84e MD |
6529 | else if (SCM_REALP (x)) |
6530 | { | |
e8c5b1f2 | 6531 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6532 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6533 | { |
6534 | /* see comments with inum/real above */ | |
e25f3727 | 6535 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6536 | return scm_from_bool (xx == (double) yy |
6537 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6538 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6539 | } |
0aacf84e MD |
6540 | else if (SCM_BIGP (y)) |
6541 | { | |
6542 | int cmp; | |
2e65b52f | 6543 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6544 | return SCM_BOOL_F; |
6545 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6546 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6547 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6548 | } |
6549 | else if (SCM_REALP (y)) | |
73e4de09 | 6550 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6551 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6552 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6553 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6554 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6555 | { |
6556 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6557 | if (isnan (xx)) |
d8b95e27 | 6558 | return SCM_BOOL_F; |
2e65b52f | 6559 | if (isinf (xx)) |
73e4de09 | 6560 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6561 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6562 | goto again; | |
6563 | } | |
0aacf84e | 6564 | else |
8a1f4f98 | 6565 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6566 | } |
0aacf84e MD |
6567 | else if (SCM_COMPLEXP (x)) |
6568 | { | |
e11e83f3 MV |
6569 | if (SCM_I_INUMP (y)) |
6570 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6571 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6572 | else if (SCM_BIGP (y)) | |
6573 | { | |
6574 | int cmp; | |
6575 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6576 | return SCM_BOOL_F; | |
2e65b52f | 6577 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6578 | return SCM_BOOL_F; |
6579 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6580 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6581 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6582 | } |
6583 | else if (SCM_REALP (y)) | |
73e4de09 | 6584 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6585 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6586 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6587 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6588 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6589 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6590 | { |
6591 | double xx; | |
6592 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6593 | return SCM_BOOL_F; | |
6594 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6595 | if (isnan (xx)) |
d8b95e27 | 6596 | return SCM_BOOL_F; |
2e65b52f | 6597 | if (isinf (xx)) |
73e4de09 | 6598 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6599 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6600 | goto again; | |
6601 | } | |
f92e85f7 | 6602 | else |
8a1f4f98 | 6603 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6604 | } |
6605 | else if (SCM_FRACTIONP (x)) | |
6606 | { | |
e11e83f3 | 6607 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6608 | return SCM_BOOL_F; |
6609 | else if (SCM_BIGP (y)) | |
6610 | return SCM_BOOL_F; | |
6611 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6612 | { |
6613 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6614 | if (isnan (yy)) |
d8b95e27 | 6615 | return SCM_BOOL_F; |
2e65b52f | 6616 | if (isinf (yy)) |
73e4de09 | 6617 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6618 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6619 | goto again; | |
6620 | } | |
f92e85f7 | 6621 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6622 | { |
6623 | double yy; | |
6624 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6625 | return SCM_BOOL_F; | |
6626 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6627 | if (isnan (yy)) |
d8b95e27 | 6628 | return SCM_BOOL_F; |
2e65b52f | 6629 | if (isinf (yy)) |
73e4de09 | 6630 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6631 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6632 | goto again; | |
6633 | } | |
f92e85f7 MV |
6634 | else if (SCM_FRACTIONP (y)) |
6635 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6636 | else |
8a1f4f98 | 6637 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6638 | } |
0aacf84e | 6639 | else |
8a1f4f98 | 6640 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6641 | } |
6642 | ||
6643 | ||
a5f0b599 KR |
6644 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6645 | done are good for inums, but for bignums an answer can almost always be | |
6646 | had by just examining a few high bits of the operands, as done by GMP in | |
6647 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6648 | of the float exponent to take into account. */ | |
6649 | ||
8c93b597 | 6650 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6651 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6652 | (SCM x, SCM y, SCM rest), | |
6653 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6654 | "increasing.") | |
6655 | #define FUNC_NAME s_scm_i_num_less_p | |
6656 | { | |
6657 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6658 | return SCM_BOOL_T; | |
6659 | while (!scm_is_null (rest)) | |
6660 | { | |
6661 | if (scm_is_false (scm_less_p (x, y))) | |
6662 | return SCM_BOOL_F; | |
6663 | x = y; | |
6664 | y = scm_car (rest); | |
6665 | rest = scm_cdr (rest); | |
6666 | } | |
6667 | return scm_less_p (x, y); | |
6668 | } | |
6669 | #undef FUNC_NAME | |
0f2d19dd | 6670 | SCM |
6e8d25a6 | 6671 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6672 | { |
a5f0b599 | 6673 | again: |
e11e83f3 | 6674 | if (SCM_I_INUMP (x)) |
0aacf84e | 6675 | { |
e25f3727 | 6676 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6677 | if (SCM_I_INUMP (y)) |
0aacf84e | 6678 | { |
e25f3727 | 6679 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6680 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6681 | } |
6682 | else if (SCM_BIGP (y)) | |
6683 | { | |
6684 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6685 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6686 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6687 | } |
6688 | else if (SCM_REALP (y)) | |
73e4de09 | 6689 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6690 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6691 | { |
6692 | /* "x < a/b" becomes "x*b < a" */ | |
6693 | int_frac: | |
6694 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6695 | y = SCM_FRACTION_NUMERATOR (y); | |
6696 | goto again; | |
6697 | } | |
0aacf84e | 6698 | else |
8a1f4f98 | 6699 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6700 | } |
0aacf84e MD |
6701 | else if (SCM_BIGP (x)) |
6702 | { | |
e11e83f3 | 6703 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6704 | { |
6705 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6706 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6707 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6708 | } |
6709 | else if (SCM_BIGP (y)) | |
6710 | { | |
6711 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6712 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6713 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6714 | } |
6715 | else if (SCM_REALP (y)) | |
6716 | { | |
6717 | int cmp; | |
2e65b52f | 6718 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6719 | return SCM_BOOL_F; |
6720 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6721 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6722 | return scm_from_bool (cmp < 0); |
0aacf84e | 6723 | } |
f92e85f7 | 6724 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6725 | goto int_frac; |
0aacf84e | 6726 | else |
8a1f4f98 | 6727 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6728 | } |
0aacf84e MD |
6729 | else if (SCM_REALP (x)) |
6730 | { | |
e11e83f3 MV |
6731 | if (SCM_I_INUMP (y)) |
6732 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6733 | else if (SCM_BIGP (y)) |
6734 | { | |
6735 | int cmp; | |
2e65b52f | 6736 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6737 | return SCM_BOOL_F; |
6738 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6739 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6740 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6741 | } |
6742 | else if (SCM_REALP (y)) | |
73e4de09 | 6743 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6744 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6745 | { |
6746 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6747 | if (isnan (xx)) |
a5f0b599 | 6748 | return SCM_BOOL_F; |
2e65b52f | 6749 | if (isinf (xx)) |
73e4de09 | 6750 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6751 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6752 | goto again; | |
6753 | } | |
f92e85f7 | 6754 | else |
8a1f4f98 | 6755 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6756 | } |
6757 | else if (SCM_FRACTIONP (x)) | |
6758 | { | |
e11e83f3 | 6759 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6760 | { |
6761 | /* "a/b < y" becomes "a < y*b" */ | |
6762 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6763 | x = SCM_FRACTION_NUMERATOR (x); | |
6764 | goto again; | |
6765 | } | |
f92e85f7 | 6766 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6767 | { |
6768 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6769 | if (isnan (yy)) |
a5f0b599 | 6770 | return SCM_BOOL_F; |
2e65b52f | 6771 | if (isinf (yy)) |
73e4de09 | 6772 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6773 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6774 | goto again; | |
6775 | } | |
f92e85f7 | 6776 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6777 | { |
6778 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6779 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6780 | SCM_FRACTION_DENOMINATOR (y)); | |
6781 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6782 | SCM_FRACTION_DENOMINATOR (x)); | |
6783 | x = new_x; | |
6784 | y = new_y; | |
6785 | goto again; | |
6786 | } | |
0aacf84e | 6787 | else |
8a1f4f98 | 6788 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6789 | } |
0aacf84e | 6790 | else |
8a1f4f98 | 6791 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6792 | } |
6793 | ||
6794 | ||
8a1f4f98 AW |
6795 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6796 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6797 | (SCM x, SCM y, SCM rest), | |
6798 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6799 | "decreasing.") | |
6800 | #define FUNC_NAME s_scm_i_num_gr_p | |
6801 | { | |
6802 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6803 | return SCM_BOOL_T; | |
6804 | while (!scm_is_null (rest)) | |
6805 | { | |
6806 | if (scm_is_false (scm_gr_p (x, y))) | |
6807 | return SCM_BOOL_F; | |
6808 | x = y; | |
6809 | y = scm_car (rest); | |
6810 | rest = scm_cdr (rest); | |
6811 | } | |
6812 | return scm_gr_p (x, y); | |
6813 | } | |
6814 | #undef FUNC_NAME | |
6815 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6816 | SCM |
6817 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6818 | { |
c76b1eaf | 6819 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6820 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6821 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6822 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6823 | else |
6824 | return scm_less_p (y, x); | |
0f2d19dd | 6825 | } |
1bbd0b84 | 6826 | #undef FUNC_NAME |
0f2d19dd JB |
6827 | |
6828 | ||
8a1f4f98 AW |
6829 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6830 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6831 | (SCM x, SCM y, SCM rest), | |
6832 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6833 | "non-decreasing.") | |
6834 | #define FUNC_NAME s_scm_i_num_leq_p | |
6835 | { | |
6836 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6837 | return SCM_BOOL_T; | |
6838 | while (!scm_is_null (rest)) | |
6839 | { | |
6840 | if (scm_is_false (scm_leq_p (x, y))) | |
6841 | return SCM_BOOL_F; | |
6842 | x = y; | |
6843 | y = scm_car (rest); | |
6844 | rest = scm_cdr (rest); | |
6845 | } | |
6846 | return scm_leq_p (x, y); | |
6847 | } | |
6848 | #undef FUNC_NAME | |
6849 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6850 | SCM |
6851 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6852 | { |
c76b1eaf | 6853 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6854 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6855 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6856 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6857 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6858 | return SCM_BOOL_F; |
c76b1eaf | 6859 | else |
73e4de09 | 6860 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6861 | } |
1bbd0b84 | 6862 | #undef FUNC_NAME |
0f2d19dd JB |
6863 | |
6864 | ||
8a1f4f98 AW |
6865 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6866 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6867 | (SCM x, SCM y, SCM rest), | |
6868 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6869 | "non-increasing.") | |
6870 | #define FUNC_NAME s_scm_i_num_geq_p | |
6871 | { | |
6872 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6873 | return SCM_BOOL_T; | |
6874 | while (!scm_is_null (rest)) | |
6875 | { | |
6876 | if (scm_is_false (scm_geq_p (x, y))) | |
6877 | return SCM_BOOL_F; | |
6878 | x = y; | |
6879 | y = scm_car (rest); | |
6880 | rest = scm_cdr (rest); | |
6881 | } | |
6882 | return scm_geq_p (x, y); | |
6883 | } | |
6884 | #undef FUNC_NAME | |
6885 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6886 | SCM |
6887 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6888 | { |
c76b1eaf | 6889 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6890 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6891 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6892 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6893 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6894 | return SCM_BOOL_F; |
c76b1eaf | 6895 | else |
73e4de09 | 6896 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6897 | } |
1bbd0b84 | 6898 | #undef FUNC_NAME |
0f2d19dd JB |
6899 | |
6900 | ||
2519490c MW |
6901 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6902 | (SCM z), | |
6903 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6904 | "zero.") | |
6905 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6906 | { |
e11e83f3 | 6907 | if (SCM_I_INUMP (z)) |
bc36d050 | 6908 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6909 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6910 | return SCM_BOOL_F; |
0aacf84e | 6911 | else if (SCM_REALP (z)) |
73e4de09 | 6912 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6913 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6914 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6915 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6916 | else if (SCM_FRACTIONP (z)) |
6917 | return SCM_BOOL_F; | |
0aacf84e | 6918 | else |
2519490c | 6919 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6920 | } |
2519490c | 6921 | #undef FUNC_NAME |
0f2d19dd JB |
6922 | |
6923 | ||
2519490c MW |
6924 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6925 | (SCM x), | |
6926 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6927 | "zero.") | |
6928 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6929 | { |
e11e83f3 MV |
6930 | if (SCM_I_INUMP (x)) |
6931 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6932 | else if (SCM_BIGP (x)) |
6933 | { | |
6934 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6935 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6936 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6937 | } |
6938 | else if (SCM_REALP (x)) | |
73e4de09 | 6939 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6940 | else if (SCM_FRACTIONP (x)) |
6941 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6942 | else |
2519490c | 6943 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6944 | } |
2519490c | 6945 | #undef FUNC_NAME |
0f2d19dd JB |
6946 | |
6947 | ||
2519490c MW |
6948 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6949 | (SCM x), | |
6950 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6951 | "zero.") | |
6952 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6953 | { |
e11e83f3 MV |
6954 | if (SCM_I_INUMP (x)) |
6955 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6956 | else if (SCM_BIGP (x)) |
6957 | { | |
6958 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6959 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6960 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6961 | } |
6962 | else if (SCM_REALP (x)) | |
73e4de09 | 6963 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6964 | else if (SCM_FRACTIONP (x)) |
6965 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6966 | else |
2519490c | 6967 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6968 | } |
2519490c | 6969 | #undef FUNC_NAME |
0f2d19dd JB |
6970 | |
6971 | ||
2a06f791 KR |
6972 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6973 | required by r5rs. On that basis, for exact/inexact combinations the | |
6974 | exact is converted to inexact to compare and possibly return. This is | |
6975 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6976 | its test, such trouble is not required for min and max. */ | |
6977 | ||
78d3deb1 AW |
6978 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6979 | (SCM x, SCM y, SCM rest), | |
6980 | "Return the maximum of all parameter values.") | |
6981 | #define FUNC_NAME s_scm_i_max | |
6982 | { | |
6983 | while (!scm_is_null (rest)) | |
6984 | { x = scm_max (x, y); | |
6985 | y = scm_car (rest); | |
6986 | rest = scm_cdr (rest); | |
6987 | } | |
6988 | return scm_max (x, y); | |
6989 | } | |
6990 | #undef FUNC_NAME | |
6991 | ||
6992 | #define s_max s_scm_i_max | |
6993 | #define g_max g_scm_i_max | |
6994 | ||
0f2d19dd | 6995 | SCM |
6e8d25a6 | 6996 | scm_max (SCM x, SCM y) |
0f2d19dd | 6997 | { |
0aacf84e MD |
6998 | if (SCM_UNBNDP (y)) |
6999 | { | |
7000 | if (SCM_UNBNDP (x)) | |
7001 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 7002 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7003 | return x; |
7004 | else | |
7005 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 7006 | } |
f4c627b3 | 7007 | |
e11e83f3 | 7008 | if (SCM_I_INUMP (x)) |
0aacf84e | 7009 | { |
e25f3727 | 7010 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7011 | if (SCM_I_INUMP (y)) |
0aacf84e | 7012 | { |
e25f3727 | 7013 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7014 | return (xx < yy) ? y : x; |
7015 | } | |
7016 | else if (SCM_BIGP (y)) | |
7017 | { | |
7018 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7019 | scm_remember_upto_here_1 (y); | |
7020 | return (sgn < 0) ? x : y; | |
7021 | } | |
7022 | else if (SCM_REALP (y)) | |
7023 | { | |
2e274311 MW |
7024 | double xxd = xx; |
7025 | double yyd = SCM_REAL_VALUE (y); | |
7026 | ||
7027 | if (xxd > yyd) | |
7028 | return scm_from_double (xxd); | |
7029 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
7030 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7031 | return y; | |
7032 | /* Handle signed zeroes properly */ | |
7033 | else if (xx == 0) | |
7034 | return flo0; | |
7035 | else | |
7036 | return y; | |
0aacf84e | 7037 | } |
f92e85f7 MV |
7038 | else if (SCM_FRACTIONP (y)) |
7039 | { | |
e4bc5d6c | 7040 | use_less: |
73e4de09 | 7041 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 7042 | } |
0aacf84e MD |
7043 | else |
7044 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7045 | } |
0aacf84e MD |
7046 | else if (SCM_BIGP (x)) |
7047 | { | |
e11e83f3 | 7048 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7049 | { |
7050 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7051 | scm_remember_upto_here_1 (x); | |
7052 | return (sgn < 0) ? y : x; | |
7053 | } | |
7054 | else if (SCM_BIGP (y)) | |
7055 | { | |
7056 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7057 | scm_remember_upto_here_2 (x, y); | |
7058 | return (cmp > 0) ? x : y; | |
7059 | } | |
7060 | else if (SCM_REALP (y)) | |
7061 | { | |
2a06f791 KR |
7062 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
7063 | double xx, yy; | |
7064 | big_real: | |
7065 | xx = scm_i_big2dbl (x); | |
7066 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7067 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 7068 | } |
f92e85f7 MV |
7069 | else if (SCM_FRACTIONP (y)) |
7070 | { | |
e4bc5d6c | 7071 | goto use_less; |
f92e85f7 | 7072 | } |
0aacf84e MD |
7073 | else |
7074 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 7075 | } |
0aacf84e MD |
7076 | else if (SCM_REALP (x)) |
7077 | { | |
e11e83f3 | 7078 | if (SCM_I_INUMP (y)) |
0aacf84e | 7079 | { |
2e274311 MW |
7080 | scm_t_inum yy = SCM_I_INUM (y); |
7081 | double xxd = SCM_REAL_VALUE (x); | |
7082 | double yyd = yy; | |
7083 | ||
7084 | if (yyd > xxd) | |
7085 | return scm_from_double (yyd); | |
7086 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
7087 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7088 | return x; | |
7089 | /* Handle signed zeroes properly */ | |
7090 | else if (yy == 0) | |
7091 | return flo0; | |
7092 | else | |
7093 | return x; | |
0aacf84e MD |
7094 | } |
7095 | else if (SCM_BIGP (y)) | |
7096 | { | |
b6f8f763 | 7097 | SCM_SWAP (x, y); |
2a06f791 | 7098 | goto big_real; |
0aacf84e MD |
7099 | } |
7100 | else if (SCM_REALP (y)) | |
7101 | { | |
0aacf84e | 7102 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7103 | double yy = SCM_REAL_VALUE (y); |
7104 | ||
7105 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
7106 | if (xx > yy) | |
7107 | return x; | |
7108 | else if (SCM_LIKELY (xx < yy)) | |
7109 | return y; | |
7110 | /* If neither (xx > yy) nor (xx < yy), then | |
7111 | either they're equal or one is a NaN */ | |
7112 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7113 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 7114 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7115 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7116 | /* xx == yy, but handle signed zeroes properly */ |
7117 | else if (double_is_non_negative_zero (yy)) | |
7118 | return y; | |
7119 | else | |
7120 | return x; | |
0aacf84e | 7121 | } |
f92e85f7 MV |
7122 | else if (SCM_FRACTIONP (y)) |
7123 | { | |
7124 | double yy = scm_i_fraction2double (y); | |
7125 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7126 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
7127 | } |
7128 | else | |
7129 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
7130 | } | |
7131 | else if (SCM_FRACTIONP (x)) | |
7132 | { | |
e11e83f3 | 7133 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7134 | { |
e4bc5d6c | 7135 | goto use_less; |
f92e85f7 MV |
7136 | } |
7137 | else if (SCM_BIGP (y)) | |
7138 | { | |
e4bc5d6c | 7139 | goto use_less; |
f92e85f7 MV |
7140 | } |
7141 | else if (SCM_REALP (y)) | |
7142 | { | |
7143 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7144 | /* if y==NaN then ">" is false, so we return the NaN y */ |
7145 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7146 | } |
7147 | else if (SCM_FRACTIONP (y)) | |
7148 | { | |
e4bc5d6c | 7149 | goto use_less; |
f92e85f7 | 7150 | } |
0aacf84e MD |
7151 | else |
7152 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7153 | } |
0aacf84e | 7154 | else |
f4c627b3 | 7155 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
7156 | } |
7157 | ||
7158 | ||
78d3deb1 AW |
7159 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
7160 | (SCM x, SCM y, SCM rest), | |
7161 | "Return the minimum of all parameter values.") | |
7162 | #define FUNC_NAME s_scm_i_min | |
7163 | { | |
7164 | while (!scm_is_null (rest)) | |
7165 | { x = scm_min (x, y); | |
7166 | y = scm_car (rest); | |
7167 | rest = scm_cdr (rest); | |
7168 | } | |
7169 | return scm_min (x, y); | |
7170 | } | |
7171 | #undef FUNC_NAME | |
7172 | ||
7173 | #define s_min s_scm_i_min | |
7174 | #define g_min g_scm_i_min | |
7175 | ||
0f2d19dd | 7176 | SCM |
6e8d25a6 | 7177 | scm_min (SCM x, SCM y) |
0f2d19dd | 7178 | { |
0aacf84e MD |
7179 | if (SCM_UNBNDP (y)) |
7180 | { | |
7181 | if (SCM_UNBNDP (x)) | |
7182 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 7183 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7184 | return x; |
7185 | else | |
7186 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 7187 | } |
f4c627b3 | 7188 | |
e11e83f3 | 7189 | if (SCM_I_INUMP (x)) |
0aacf84e | 7190 | { |
e25f3727 | 7191 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7192 | if (SCM_I_INUMP (y)) |
0aacf84e | 7193 | { |
e25f3727 | 7194 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7195 | return (xx < yy) ? x : y; |
7196 | } | |
7197 | else if (SCM_BIGP (y)) | |
7198 | { | |
7199 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7200 | scm_remember_upto_here_1 (y); | |
7201 | return (sgn < 0) ? y : x; | |
7202 | } | |
7203 | else if (SCM_REALP (y)) | |
7204 | { | |
7205 | double z = xx; | |
7206 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 7207 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 7208 | } |
f92e85f7 MV |
7209 | else if (SCM_FRACTIONP (y)) |
7210 | { | |
e4bc5d6c | 7211 | use_less: |
73e4de09 | 7212 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 7213 | } |
0aacf84e MD |
7214 | else |
7215 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7216 | } |
0aacf84e MD |
7217 | else if (SCM_BIGP (x)) |
7218 | { | |
e11e83f3 | 7219 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7220 | { |
7221 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7222 | scm_remember_upto_here_1 (x); | |
7223 | return (sgn < 0) ? x : y; | |
7224 | } | |
7225 | else if (SCM_BIGP (y)) | |
7226 | { | |
7227 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7228 | scm_remember_upto_here_2 (x, y); | |
7229 | return (cmp > 0) ? y : x; | |
7230 | } | |
7231 | else if (SCM_REALP (y)) | |
7232 | { | |
2a06f791 KR |
7233 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
7234 | double xx, yy; | |
7235 | big_real: | |
7236 | xx = scm_i_big2dbl (x); | |
7237 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7238 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 7239 | } |
f92e85f7 MV |
7240 | else if (SCM_FRACTIONP (y)) |
7241 | { | |
e4bc5d6c | 7242 | goto use_less; |
f92e85f7 | 7243 | } |
0aacf84e MD |
7244 | else |
7245 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 7246 | } |
0aacf84e MD |
7247 | else if (SCM_REALP (x)) |
7248 | { | |
e11e83f3 | 7249 | if (SCM_I_INUMP (y)) |
0aacf84e | 7250 | { |
e11e83f3 | 7251 | double z = SCM_I_INUM (y); |
0aacf84e | 7252 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7253 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7254 | } |
7255 | else if (SCM_BIGP (y)) | |
7256 | { | |
b6f8f763 | 7257 | SCM_SWAP (x, y); |
2a06f791 | 7258 | goto big_real; |
0aacf84e MD |
7259 | } |
7260 | else if (SCM_REALP (y)) | |
7261 | { | |
0aacf84e | 7262 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7263 | double yy = SCM_REAL_VALUE (y); |
7264 | ||
7265 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
7266 | if (xx < yy) | |
7267 | return x; | |
7268 | else if (SCM_LIKELY (xx > yy)) | |
7269 | return y; | |
7270 | /* If neither (xx < yy) nor (xx > yy), then | |
7271 | either they're equal or one is a NaN */ | |
7272 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7273 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 7274 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7275 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7276 | /* xx == yy, but handle signed zeroes properly */ |
7277 | else if (double_is_non_negative_zero (xx)) | |
7278 | return y; | |
7279 | else | |
7280 | return x; | |
0aacf84e | 7281 | } |
f92e85f7 MV |
7282 | else if (SCM_FRACTIONP (y)) |
7283 | { | |
7284 | double yy = scm_i_fraction2double (y); | |
7285 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7286 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7287 | } |
0aacf84e MD |
7288 | else |
7289 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7290 | } |
f92e85f7 MV |
7291 | else if (SCM_FRACTIONP (x)) |
7292 | { | |
e11e83f3 | 7293 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7294 | { |
e4bc5d6c | 7295 | goto use_less; |
f92e85f7 MV |
7296 | } |
7297 | else if (SCM_BIGP (y)) | |
7298 | { | |
e4bc5d6c | 7299 | goto use_less; |
f92e85f7 MV |
7300 | } |
7301 | else if (SCM_REALP (y)) | |
7302 | { | |
7303 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7304 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7305 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7306 | } |
7307 | else if (SCM_FRACTIONP (y)) | |
7308 | { | |
e4bc5d6c | 7309 | goto use_less; |
f92e85f7 MV |
7310 | } |
7311 | else | |
78d3deb1 | 7312 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7313 | } |
0aacf84e | 7314 | else |
f4c627b3 | 7315 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7316 | } |
7317 | ||
7318 | ||
8ccd24f7 AW |
7319 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7320 | (SCM x, SCM y, SCM rest), | |
7321 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7322 | "any parameters." ) | |
7323 | #define FUNC_NAME s_scm_i_sum | |
7324 | { | |
7325 | while (!scm_is_null (rest)) | |
7326 | { x = scm_sum (x, y); | |
7327 | y = scm_car (rest); | |
7328 | rest = scm_cdr (rest); | |
7329 | } | |
7330 | return scm_sum (x, y); | |
7331 | } | |
7332 | #undef FUNC_NAME | |
7333 | ||
7334 | #define s_sum s_scm_i_sum | |
7335 | #define g_sum g_scm_i_sum | |
7336 | ||
0f2d19dd | 7337 | SCM |
6e8d25a6 | 7338 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7339 | { |
9cc37597 | 7340 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7341 | { |
7342 | if (SCM_NUMBERP (x)) return x; | |
7343 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7344 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7345 | } |
c209c88e | 7346 | |
9cc37597 | 7347 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7348 | { |
9cc37597 | 7349 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7350 | { |
e25f3727 AW |
7351 | scm_t_inum xx = SCM_I_INUM (x); |
7352 | scm_t_inum yy = SCM_I_INUM (y); | |
7353 | scm_t_inum z = xx + yy; | |
7354 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7355 | } |
7356 | else if (SCM_BIGP (y)) | |
7357 | { | |
7358 | SCM_SWAP (x, y); | |
7359 | goto add_big_inum; | |
7360 | } | |
7361 | else if (SCM_REALP (y)) | |
7362 | { | |
e25f3727 | 7363 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7364 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7365 | } |
7366 | else if (SCM_COMPLEXP (y)) | |
7367 | { | |
e25f3727 | 7368 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7369 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7370 | SCM_COMPLEX_IMAG (y)); |
7371 | } | |
f92e85f7 | 7372 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7373 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7374 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7375 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7376 | else |
7377 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7378 | } else if (SCM_BIGP (x)) |
7379 | { | |
e11e83f3 | 7380 | if (SCM_I_INUMP (y)) |
0aacf84e | 7381 | { |
e25f3727 | 7382 | scm_t_inum inum; |
0aacf84e MD |
7383 | int bigsgn; |
7384 | add_big_inum: | |
e11e83f3 | 7385 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7386 | if (inum == 0) |
7387 | return x; | |
7388 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7389 | if (inum < 0) | |
7390 | { | |
7391 | SCM result = scm_i_mkbig (); | |
7392 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7393 | scm_remember_upto_here_1 (x); | |
7394 | /* we know the result will have to be a bignum */ | |
7395 | if (bigsgn == -1) | |
7396 | return result; | |
7397 | return scm_i_normbig (result); | |
7398 | } | |
7399 | else | |
7400 | { | |
7401 | SCM result = scm_i_mkbig (); | |
7402 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7403 | scm_remember_upto_here_1 (x); | |
7404 | /* we know the result will have to be a bignum */ | |
7405 | if (bigsgn == 1) | |
7406 | return result; | |
7407 | return scm_i_normbig (result); | |
7408 | } | |
7409 | } | |
7410 | else if (SCM_BIGP (y)) | |
7411 | { | |
7412 | SCM result = scm_i_mkbig (); | |
7413 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7414 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7415 | mpz_add (SCM_I_BIG_MPZ (result), | |
7416 | SCM_I_BIG_MPZ (x), | |
7417 | SCM_I_BIG_MPZ (y)); | |
7418 | scm_remember_upto_here_2 (x, y); | |
7419 | /* we know the result will have to be a bignum */ | |
7420 | if (sgn_x == sgn_y) | |
7421 | return result; | |
7422 | return scm_i_normbig (result); | |
7423 | } | |
7424 | else if (SCM_REALP (y)) | |
7425 | { | |
7426 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7427 | scm_remember_upto_here_1 (x); | |
55f26379 | 7428 | return scm_from_double (result); |
0aacf84e MD |
7429 | } |
7430 | else if (SCM_COMPLEXP (y)) | |
7431 | { | |
7432 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7433 | + SCM_COMPLEX_REAL (y)); | |
7434 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7435 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7436 | } |
f92e85f7 | 7437 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7438 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7439 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7440 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7441 | else |
7442 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7443 | } |
0aacf84e MD |
7444 | else if (SCM_REALP (x)) |
7445 | { | |
e11e83f3 | 7446 | if (SCM_I_INUMP (y)) |
55f26379 | 7447 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7448 | else if (SCM_BIGP (y)) |
7449 | { | |
7450 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7451 | scm_remember_upto_here_1 (y); | |
55f26379 | 7452 | return scm_from_double (result); |
0aacf84e MD |
7453 | } |
7454 | else if (SCM_REALP (y)) | |
55f26379 | 7455 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7456 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7457 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7458 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7459 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7460 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7461 | else |
7462 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7463 | } |
0aacf84e MD |
7464 | else if (SCM_COMPLEXP (x)) |
7465 | { | |
e11e83f3 | 7466 | if (SCM_I_INUMP (y)) |
8507ec80 | 7467 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7468 | SCM_COMPLEX_IMAG (x)); |
7469 | else if (SCM_BIGP (y)) | |
7470 | { | |
7471 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7472 | + SCM_COMPLEX_REAL (x)); | |
7473 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7474 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7475 | } |
7476 | else if (SCM_REALP (y)) | |
8507ec80 | 7477 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7478 | SCM_COMPLEX_IMAG (x)); |
7479 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7480 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7481 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7482 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7483 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7484 | SCM_COMPLEX_IMAG (x)); |
7485 | else | |
7486 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7487 | } | |
7488 | else if (SCM_FRACTIONP (x)) | |
7489 | { | |
e11e83f3 | 7490 | if (SCM_I_INUMP (y)) |
cba42c93 | 7491 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7492 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7493 | SCM_FRACTION_DENOMINATOR (x)); | |
7494 | else if (SCM_BIGP (y)) | |
cba42c93 | 7495 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7496 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7497 | SCM_FRACTION_DENOMINATOR (x)); | |
7498 | else if (SCM_REALP (y)) | |
55f26379 | 7499 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7500 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7501 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7502 | SCM_COMPLEX_IMAG (y)); |
7503 | else if (SCM_FRACTIONP (y)) | |
7504 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7505 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7506 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7507 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7508 | else |
7509 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7510 | } |
0aacf84e | 7511 | else |
98cb6e75 | 7512 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7513 | } |
7514 | ||
7515 | ||
40882e3d KR |
7516 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7517 | (SCM x), | |
7518 | "Return @math{@var{x}+1}.") | |
7519 | #define FUNC_NAME s_scm_oneplus | |
7520 | { | |
cff5fa33 | 7521 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7522 | } |
7523 | #undef FUNC_NAME | |
7524 | ||
7525 | ||
78d3deb1 AW |
7526 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7527 | (SCM x, SCM y, SCM rest), | |
7528 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7529 | "the sum of all but the first argument are subtracted from the first\n" | |
7530 | "argument.") | |
7531 | #define FUNC_NAME s_scm_i_difference | |
7532 | { | |
7533 | while (!scm_is_null (rest)) | |
7534 | { x = scm_difference (x, y); | |
7535 | y = scm_car (rest); | |
7536 | rest = scm_cdr (rest); | |
7537 | } | |
7538 | return scm_difference (x, y); | |
7539 | } | |
7540 | #undef FUNC_NAME | |
7541 | ||
7542 | #define s_difference s_scm_i_difference | |
7543 | #define g_difference g_scm_i_difference | |
7544 | ||
0f2d19dd | 7545 | SCM |
6e8d25a6 | 7546 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7547 | #define FUNC_NAME s_difference |
0f2d19dd | 7548 | { |
9cc37597 | 7549 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7550 | { |
7551 | if (SCM_UNBNDP (x)) | |
7552 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7553 | else | |
e11e83f3 | 7554 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7555 | { |
e25f3727 | 7556 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7557 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7558 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7559 | else |
e25f3727 | 7560 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7561 | } |
7562 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7563 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7564 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7565 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7566 | else if (SCM_REALP (x)) | |
55f26379 | 7567 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7568 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7569 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7570 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7571 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
7572 | return scm_i_make_ratio_already_reduced |
7573 | (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
7574 | SCM_FRACTION_DENOMINATOR (x)); | |
ca46fb90 RB |
7575 | else |
7576 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7577 | } |
ca46fb90 | 7578 | |
9cc37597 | 7579 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7580 | { |
9cc37597 | 7581 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7582 | { |
e25f3727 AW |
7583 | scm_t_inum xx = SCM_I_INUM (x); |
7584 | scm_t_inum yy = SCM_I_INUM (y); | |
7585 | scm_t_inum z = xx - yy; | |
0aacf84e | 7586 | if (SCM_FIXABLE (z)) |
d956fa6f | 7587 | return SCM_I_MAKINUM (z); |
0aacf84e | 7588 | else |
e25f3727 | 7589 | return scm_i_inum2big (z); |
0aacf84e MD |
7590 | } |
7591 | else if (SCM_BIGP (y)) | |
7592 | { | |
7593 | /* inum-x - big-y */ | |
e25f3727 | 7594 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7595 | |
0aacf84e | 7596 | if (xx == 0) |
b5c40589 MW |
7597 | { |
7598 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7599 | bignum, but negating that gives a fixnum. */ | |
7600 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7601 | } | |
0aacf84e MD |
7602 | else |
7603 | { | |
7604 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7605 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7606 | |
0aacf84e MD |
7607 | if (xx >= 0) |
7608 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7609 | else | |
7610 | { | |
7611 | /* x - y == -(y + -x) */ | |
7612 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7613 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7614 | } | |
7615 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7616 | |
0aacf84e MD |
7617 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7618 | /* we know the result will have to be a bignum */ | |
7619 | return result; | |
7620 | else | |
7621 | return scm_i_normbig (result); | |
7622 | } | |
7623 | } | |
7624 | else if (SCM_REALP (y)) | |
7625 | { | |
e25f3727 | 7626 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7627 | |
7628 | /* | |
7629 | * We need to handle x == exact 0 | |
7630 | * specially because R6RS states that: | |
7631 | * (- 0.0) ==> -0.0 and | |
7632 | * (- 0.0 0.0) ==> 0.0 | |
7633 | * and the scheme compiler changes | |
7634 | * (- 0.0) into (- 0 0.0) | |
7635 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7636 | * At the C level, (-x) is different than (0.0 - x). | |
7637 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7638 | */ | |
7639 | if (xx == 0) | |
7640 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7641 | else | |
7642 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7643 | } |
7644 | else if (SCM_COMPLEXP (y)) | |
7645 | { | |
e25f3727 | 7646 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7647 | |
7648 | /* We need to handle x == exact 0 specially. | |
7649 | See the comment above (for SCM_REALP (y)) */ | |
7650 | if (xx == 0) | |
7651 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7652 | - SCM_COMPLEX_IMAG (y)); | |
7653 | else | |
7654 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7655 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7656 | } |
f92e85f7 MV |
7657 | else if (SCM_FRACTIONP (y)) |
7658 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7659 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7660 | SCM_FRACTION_NUMERATOR (y)), |
7661 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7662 | else |
7663 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7664 | } |
0aacf84e MD |
7665 | else if (SCM_BIGP (x)) |
7666 | { | |
e11e83f3 | 7667 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7668 | { |
7669 | /* big-x - inum-y */ | |
e25f3727 | 7670 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7671 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7672 | |
0aacf84e MD |
7673 | scm_remember_upto_here_1 (x); |
7674 | if (sgn_x == 0) | |
c71b0706 | 7675 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7676 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7677 | else |
7678 | { | |
7679 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7680 | |
708f22c6 KR |
7681 | if (yy >= 0) |
7682 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7683 | else | |
7684 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7685 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7686 | |
0aacf84e MD |
7687 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7688 | /* we know the result will have to be a bignum */ | |
7689 | return result; | |
7690 | else | |
7691 | return scm_i_normbig (result); | |
7692 | } | |
7693 | } | |
7694 | else if (SCM_BIGP (y)) | |
7695 | { | |
7696 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7697 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7698 | SCM result = scm_i_mkbig (); | |
7699 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7700 | SCM_I_BIG_MPZ (x), | |
7701 | SCM_I_BIG_MPZ (y)); | |
7702 | scm_remember_upto_here_2 (x, y); | |
7703 | /* we know the result will have to be a bignum */ | |
7704 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7705 | return result; | |
7706 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7707 | return result; | |
7708 | return scm_i_normbig (result); | |
7709 | } | |
7710 | else if (SCM_REALP (y)) | |
7711 | { | |
7712 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7713 | scm_remember_upto_here_1 (x); | |
55f26379 | 7714 | return scm_from_double (result); |
0aacf84e MD |
7715 | } |
7716 | else if (SCM_COMPLEXP (y)) | |
7717 | { | |
7718 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7719 | - SCM_COMPLEX_REAL (y)); | |
7720 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7721 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7722 | } |
f92e85f7 | 7723 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7724 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7725 | SCM_FRACTION_NUMERATOR (y)), |
7726 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7727 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7728 | } |
0aacf84e MD |
7729 | else if (SCM_REALP (x)) |
7730 | { | |
e11e83f3 | 7731 | if (SCM_I_INUMP (y)) |
55f26379 | 7732 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7733 | else if (SCM_BIGP (y)) |
7734 | { | |
7735 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7736 | scm_remember_upto_here_1 (x); | |
55f26379 | 7737 | return scm_from_double (result); |
0aacf84e MD |
7738 | } |
7739 | else if (SCM_REALP (y)) | |
55f26379 | 7740 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7741 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7742 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7743 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7744 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7745 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7746 | else |
7747 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7748 | } |
0aacf84e MD |
7749 | else if (SCM_COMPLEXP (x)) |
7750 | { | |
e11e83f3 | 7751 | if (SCM_I_INUMP (y)) |
8507ec80 | 7752 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7753 | SCM_COMPLEX_IMAG (x)); |
7754 | else if (SCM_BIGP (y)) | |
7755 | { | |
7756 | double real_part = (SCM_COMPLEX_REAL (x) | |
7757 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7758 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7759 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7760 | } |
7761 | else if (SCM_REALP (y)) | |
8507ec80 | 7762 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7763 | SCM_COMPLEX_IMAG (x)); |
7764 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7765 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7766 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7767 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7768 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7769 | SCM_COMPLEX_IMAG (x)); |
7770 | else | |
7771 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7772 | } | |
7773 | else if (SCM_FRACTIONP (x)) | |
7774 | { | |
e11e83f3 | 7775 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7776 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7777 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7778 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7779 | SCM_FRACTION_DENOMINATOR (x)); | |
7780 | else if (SCM_BIGP (y)) | |
cba42c93 | 7781 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7782 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7783 | SCM_FRACTION_DENOMINATOR (x)); | |
7784 | else if (SCM_REALP (y)) | |
55f26379 | 7785 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7786 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7787 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7788 | -SCM_COMPLEX_IMAG (y)); |
7789 | else if (SCM_FRACTIONP (y)) | |
7790 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7791 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7792 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7793 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7794 | else |
7795 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7796 | } |
0aacf84e | 7797 | else |
98cb6e75 | 7798 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7799 | } |
c05e97b7 | 7800 | #undef FUNC_NAME |
0f2d19dd | 7801 | |
ca46fb90 | 7802 | |
40882e3d KR |
7803 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7804 | (SCM x), | |
7805 | "Return @math{@var{x}-1}.") | |
7806 | #define FUNC_NAME s_scm_oneminus | |
7807 | { | |
cff5fa33 | 7808 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7809 | } |
7810 | #undef FUNC_NAME | |
7811 | ||
7812 | ||
78d3deb1 AW |
7813 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7814 | (SCM x, SCM y, SCM rest), | |
7815 | "Return the product of all arguments. If called without arguments,\n" | |
7816 | "1 is returned.") | |
7817 | #define FUNC_NAME s_scm_i_product | |
7818 | { | |
7819 | while (!scm_is_null (rest)) | |
7820 | { x = scm_product (x, y); | |
7821 | y = scm_car (rest); | |
7822 | rest = scm_cdr (rest); | |
7823 | } | |
7824 | return scm_product (x, y); | |
7825 | } | |
7826 | #undef FUNC_NAME | |
7827 | ||
7828 | #define s_product s_scm_i_product | |
7829 | #define g_product g_scm_i_product | |
7830 | ||
0f2d19dd | 7831 | SCM |
6e8d25a6 | 7832 | scm_product (SCM x, SCM y) |
0f2d19dd | 7833 | { |
9cc37597 | 7834 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7835 | { |
7836 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7837 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7838 | else if (SCM_NUMBERP (x)) |
7839 | return x; | |
7840 | else | |
7841 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7842 | } |
ca46fb90 | 7843 | |
9cc37597 | 7844 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7845 | { |
e25f3727 | 7846 | scm_t_inum xx; |
f4c627b3 | 7847 | |
5e791807 | 7848 | xinum: |
e11e83f3 | 7849 | xx = SCM_I_INUM (x); |
f4c627b3 | 7850 | |
0aacf84e MD |
7851 | switch (xx) |
7852 | { | |
5e791807 MW |
7853 | case 1: |
7854 | /* exact1 is the universal multiplicative identity */ | |
7855 | return y; | |
7856 | break; | |
7857 | case 0: | |
7858 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7859 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7860 | return SCM_INUM0; | |
7861 | /* if the other argument is inexact, the result is inexact, | |
7862 | and we must do the multiplication in order to handle | |
7863 | infinities and NaNs properly. */ | |
7864 | else if (SCM_REALP (y)) | |
7865 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7866 | else if (SCM_COMPLEXP (y)) | |
7867 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7868 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7869 | /* we've already handled inexact numbers, | |
7870 | so y must be exact, and we return exact0 */ | |
7871 | else if (SCM_NUMP (y)) | |
7872 | return SCM_INUM0; | |
7873 | else | |
7874 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7875 | break; | |
7876 | case -1: | |
b5c40589 | 7877 | /* |
5e791807 MW |
7878 | * This case is important for more than just optimization. |
7879 | * It handles the case of negating | |
b5c40589 MW |
7880 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7881 | * which is a bignum that must be changed back into a fixnum. | |
7882 | * Failure to do so will cause the following to return #f: | |
7883 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7884 | */ | |
b5c40589 MW |
7885 | return scm_difference(y, SCM_UNDEFINED); |
7886 | break; | |
0aacf84e | 7887 | } |
f4c627b3 | 7888 | |
9cc37597 | 7889 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7890 | { |
e25f3727 | 7891 | scm_t_inum yy = SCM_I_INUM (y); |
2355f017 MW |
7892 | #if SCM_I_FIXNUM_BIT < 32 && SCM_HAVE_T_INT64 |
7893 | scm_t_int64 kk = xx * (scm_t_int64) yy; | |
7894 | if (SCM_FIXABLE (kk)) | |
7895 | return SCM_I_MAKINUM (kk); | |
7896 | #else | |
7897 | scm_t_inum axx = (xx > 0) ? xx : -xx; | |
7898 | scm_t_inum ayy = (yy > 0) ? yy : -yy; | |
7899 | if (SCM_MOST_POSITIVE_FIXNUM / axx >= ayy) | |
7900 | return SCM_I_MAKINUM (xx * yy); | |
7901 | #endif | |
0aacf84e MD |
7902 | else |
7903 | { | |
e25f3727 | 7904 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7905 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7906 | return scm_i_normbig (result); | |
7907 | } | |
7908 | } | |
7909 | else if (SCM_BIGP (y)) | |
7910 | { | |
7911 | SCM result = scm_i_mkbig (); | |
7912 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7913 | scm_remember_upto_here_1 (y); | |
7914 | return result; | |
7915 | } | |
7916 | else if (SCM_REALP (y)) | |
55f26379 | 7917 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7918 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7919 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7920 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7921 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7922 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7923 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7924 | else |
7925 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7926 | } |
0aacf84e MD |
7927 | else if (SCM_BIGP (x)) |
7928 | { | |
e11e83f3 | 7929 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7930 | { |
7931 | SCM_SWAP (x, y); | |
5e791807 | 7932 | goto xinum; |
0aacf84e MD |
7933 | } |
7934 | else if (SCM_BIGP (y)) | |
7935 | { | |
7936 | SCM result = scm_i_mkbig (); | |
7937 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7938 | SCM_I_BIG_MPZ (x), | |
7939 | SCM_I_BIG_MPZ (y)); | |
7940 | scm_remember_upto_here_2 (x, y); | |
7941 | return result; | |
7942 | } | |
7943 | else if (SCM_REALP (y)) | |
7944 | { | |
7945 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7946 | scm_remember_upto_here_1 (x); | |
55f26379 | 7947 | return scm_from_double (result); |
0aacf84e MD |
7948 | } |
7949 | else if (SCM_COMPLEXP (y)) | |
7950 | { | |
7951 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7952 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7953 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7954 | z * SCM_COMPLEX_IMAG (y)); |
7955 | } | |
f92e85f7 | 7956 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7957 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7958 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7959 | else |
7960 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7961 | } |
0aacf84e MD |
7962 | else if (SCM_REALP (x)) |
7963 | { | |
e11e83f3 | 7964 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7965 | { |
7966 | SCM_SWAP (x, y); | |
7967 | goto xinum; | |
7968 | } | |
0aacf84e MD |
7969 | else if (SCM_BIGP (y)) |
7970 | { | |
7971 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7972 | scm_remember_upto_here_1 (y); | |
55f26379 | 7973 | return scm_from_double (result); |
0aacf84e MD |
7974 | } |
7975 | else if (SCM_REALP (y)) | |
55f26379 | 7976 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7977 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7978 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7979 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7980 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7981 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
7982 | else |
7983 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7984 | } |
0aacf84e MD |
7985 | else if (SCM_COMPLEXP (x)) |
7986 | { | |
e11e83f3 | 7987 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7988 | { |
7989 | SCM_SWAP (x, y); | |
7990 | goto xinum; | |
7991 | } | |
0aacf84e MD |
7992 | else if (SCM_BIGP (y)) |
7993 | { | |
7994 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7995 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7996 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7997 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7998 | } |
7999 | else if (SCM_REALP (y)) | |
8507ec80 | 8000 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
8001 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
8002 | else if (SCM_COMPLEXP (y)) | |
8003 | { | |
8507ec80 | 8004 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
8005 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
8006 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
8007 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
8008 | } | |
f92e85f7 MV |
8009 | else if (SCM_FRACTIONP (y)) |
8010 | { | |
8011 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8012 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
8013 | yy * SCM_COMPLEX_IMAG (x)); |
8014 | } | |
8015 | else | |
8016 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
8017 | } | |
8018 | else if (SCM_FRACTIONP (x)) | |
8019 | { | |
e11e83f3 | 8020 | if (SCM_I_INUMP (y)) |
cba42c93 | 8021 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8022 | SCM_FRACTION_DENOMINATOR (x)); |
8023 | else if (SCM_BIGP (y)) | |
cba42c93 | 8024 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8025 | SCM_FRACTION_DENOMINATOR (x)); |
8026 | else if (SCM_REALP (y)) | |
55f26379 | 8027 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
8028 | else if (SCM_COMPLEXP (y)) |
8029 | { | |
8030 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 8031 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
8032 | xx * SCM_COMPLEX_IMAG (y)); |
8033 | } | |
8034 | else if (SCM_FRACTIONP (y)) | |
8035 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 8036 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8037 | SCM_FRACTION_NUMERATOR (y)), |
8038 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
8039 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
8040 | else |
8041 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8042 | } |
0aacf84e | 8043 | else |
f4c627b3 | 8044 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
8045 | } |
8046 | ||
7351e207 MV |
8047 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
8048 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
8049 | #define ALLOW_DIVIDE_BY_ZERO | |
8050 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
8051 | #endif | |
0f2d19dd | 8052 | |
ba74ef4e MV |
8053 | /* The code below for complex division is adapted from the GNU |
8054 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
8055 | this copyright: */ | |
8056 | ||
8057 | /**************************************************************** | |
8058 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
8059 | ||
8060 | Permission to use, copy, modify, and distribute this software | |
8061 | and its documentation for any purpose and without fee is hereby | |
8062 | granted, provided that the above copyright notice appear in all | |
8063 | copies and that both that the copyright notice and this | |
8064 | permission notice and warranty disclaimer appear in supporting | |
8065 | documentation, and that the names of AT&T Bell Laboratories or | |
8066 | Bellcore or any of their entities not be used in advertising or | |
8067 | publicity pertaining to distribution of the software without | |
8068 | specific, written prior permission. | |
8069 | ||
8070 | AT&T and Bellcore disclaim all warranties with regard to this | |
8071 | software, including all implied warranties of merchantability | |
8072 | and fitness. In no event shall AT&T or Bellcore be liable for | |
8073 | any special, indirect or consequential damages or any damages | |
8074 | whatsoever resulting from loss of use, data or profits, whether | |
8075 | in an action of contract, negligence or other tortious action, | |
8076 | arising out of or in connection with the use or performance of | |
8077 | this software. | |
8078 | ****************************************************************/ | |
8079 | ||
78d3deb1 AW |
8080 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
8081 | (SCM x, SCM y, SCM rest), | |
8082 | "Divide the first argument by the product of the remaining\n" | |
8083 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
8084 | "returned.") | |
8085 | #define FUNC_NAME s_scm_i_divide | |
8086 | { | |
8087 | while (!scm_is_null (rest)) | |
8088 | { x = scm_divide (x, y); | |
8089 | y = scm_car (rest); | |
8090 | rest = scm_cdr (rest); | |
8091 | } | |
8092 | return scm_divide (x, y); | |
8093 | } | |
8094 | #undef FUNC_NAME | |
8095 | ||
8096 | #define s_divide s_scm_i_divide | |
8097 | #define g_divide g_scm_i_divide | |
8098 | ||
98237784 MW |
8099 | SCM |
8100 | scm_divide (SCM x, SCM y) | |
78d3deb1 | 8101 | #define FUNC_NAME s_divide |
0f2d19dd | 8102 | { |
f8de44c1 DH |
8103 | double a; |
8104 | ||
9cc37597 | 8105 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8106 | { |
8107 | if (SCM_UNBNDP (x)) | |
8108 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 8109 | else if (SCM_I_INUMP (x)) |
0aacf84e | 8110 | { |
e25f3727 | 8111 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
8112 | if (xx == 1 || xx == -1) |
8113 | return x; | |
7351e207 | 8114 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8115 | else if (xx == 0) |
8116 | scm_num_overflow (s_divide); | |
7351e207 | 8117 | #endif |
0aacf84e | 8118 | else |
98237784 | 8119 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8120 | } |
8121 | else if (SCM_BIGP (x)) | |
98237784 | 8122 | return scm_i_make_ratio_already_reduced (SCM_INUM1, x); |
0aacf84e MD |
8123 | else if (SCM_REALP (x)) |
8124 | { | |
8125 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 8126 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8127 | if (xx == 0.0) |
8128 | scm_num_overflow (s_divide); | |
8129 | else | |
7351e207 | 8130 | #endif |
55f26379 | 8131 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
8132 | } |
8133 | else if (SCM_COMPLEXP (x)) | |
8134 | { | |
8135 | double r = SCM_COMPLEX_REAL (x); | |
8136 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 8137 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8138 | { |
8139 | double t = r / i; | |
8140 | double d = i * (1.0 + t * t); | |
8507ec80 | 8141 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
8142 | } |
8143 | else | |
8144 | { | |
8145 | double t = i / r; | |
8146 | double d = r * (1.0 + t * t); | |
8507ec80 | 8147 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
8148 | } |
8149 | } | |
f92e85f7 | 8150 | else if (SCM_FRACTIONP (x)) |
a285b18c MW |
8151 | return scm_i_make_ratio_already_reduced (SCM_FRACTION_DENOMINATOR (x), |
8152 | SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e MD |
8153 | else |
8154 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 8155 | } |
f8de44c1 | 8156 | |
9cc37597 | 8157 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8158 | { |
e25f3727 | 8159 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 8160 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8161 | { |
e25f3727 | 8162 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8163 | if (yy == 0) |
8164 | { | |
7351e207 | 8165 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8166 | scm_num_overflow (s_divide); |
7351e207 | 8167 | #else |
55f26379 | 8168 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 8169 | #endif |
0aacf84e MD |
8170 | } |
8171 | else if (xx % yy != 0) | |
98237784 | 8172 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8173 | else |
8174 | { | |
e25f3727 | 8175 | scm_t_inum z = xx / yy; |
0aacf84e | 8176 | if (SCM_FIXABLE (z)) |
d956fa6f | 8177 | return SCM_I_MAKINUM (z); |
0aacf84e | 8178 | else |
e25f3727 | 8179 | return scm_i_inum2big (z); |
0aacf84e | 8180 | } |
f872b822 | 8181 | } |
0aacf84e | 8182 | else if (SCM_BIGP (y)) |
98237784 | 8183 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8184 | else if (SCM_REALP (y)) |
8185 | { | |
8186 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8187 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8188 | if (yy == 0.0) |
8189 | scm_num_overflow (s_divide); | |
8190 | else | |
7351e207 | 8191 | #endif |
98237784 MW |
8192 | /* FIXME: Precision may be lost here due to: |
8193 | (1) The cast from 'scm_t_inum' to 'double' | |
8194 | (2) Double rounding */ | |
55f26379 | 8195 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 8196 | } |
0aacf84e MD |
8197 | else if (SCM_COMPLEXP (y)) |
8198 | { | |
8199 | a = xx; | |
8200 | complex_div: /* y _must_ be a complex number */ | |
8201 | { | |
8202 | double r = SCM_COMPLEX_REAL (y); | |
8203 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8204 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8205 | { |
8206 | double t = r / i; | |
8207 | double d = i * (1.0 + t * t); | |
8507ec80 | 8208 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
8209 | } |
8210 | else | |
8211 | { | |
8212 | double t = i / r; | |
8213 | double d = r * (1.0 + t * t); | |
8507ec80 | 8214 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
8215 | } |
8216 | } | |
8217 | } | |
f92e85f7 MV |
8218 | else if (SCM_FRACTIONP (y)) |
8219 | /* a / b/c = ac / b */ | |
cba42c93 | 8220 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8221 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8222 | else |
8223 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8224 | } |
0aacf84e MD |
8225 | else if (SCM_BIGP (x)) |
8226 | { | |
e11e83f3 | 8227 | if (SCM_I_INUMP (y)) |
0aacf84e | 8228 | { |
e25f3727 | 8229 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8230 | if (yy == 0) |
8231 | { | |
7351e207 | 8232 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8233 | scm_num_overflow (s_divide); |
7351e207 | 8234 | #else |
0aacf84e MD |
8235 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8236 | scm_remember_upto_here_1 (x); | |
8237 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8238 | #endif |
0aacf84e MD |
8239 | } |
8240 | else if (yy == 1) | |
8241 | return x; | |
8242 | else | |
8243 | { | |
8244 | /* FIXME: HMM, what are the relative performance issues here? | |
8245 | We need to test. Is it faster on average to test | |
8246 | divisible_p, then perform whichever operation, or is it | |
8247 | faster to perform the integer div opportunistically and | |
8248 | switch to real if there's a remainder? For now we take the | |
8249 | middle ground: test, then if divisible, use the faster div | |
8250 | func. */ | |
8251 | ||
e25f3727 | 8252 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8253 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8254 | ||
8255 | if (divisible_p) | |
8256 | { | |
8257 | SCM result = scm_i_mkbig (); | |
8258 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8259 | scm_remember_upto_here_1 (x); | |
8260 | if (yy < 0) | |
8261 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8262 | return scm_i_normbig (result); | |
8263 | } | |
8264 | else | |
98237784 | 8265 | return scm_i_make_ratio (x, y); |
0aacf84e MD |
8266 | } |
8267 | } | |
8268 | else if (SCM_BIGP (y)) | |
8269 | { | |
98237784 MW |
8270 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8271 | SCM_I_BIG_MPZ (y)); | |
8272 | if (divisible_p) | |
8273 | { | |
8274 | SCM result = scm_i_mkbig (); | |
8275 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8276 | SCM_I_BIG_MPZ (x), | |
8277 | SCM_I_BIG_MPZ (y)); | |
8278 | scm_remember_upto_here_2 (x, y); | |
8279 | return scm_i_normbig (result); | |
8280 | } | |
8281 | else | |
8282 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8283 | } |
8284 | else if (SCM_REALP (y)) | |
8285 | { | |
8286 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8287 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8288 | if (yy == 0.0) |
8289 | scm_num_overflow (s_divide); | |
8290 | else | |
7351e207 | 8291 | #endif |
98237784 MW |
8292 | /* FIXME: Precision may be lost here due to: |
8293 | (1) scm_i_big2dbl (2) Double rounding */ | |
55f26379 | 8294 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8295 | } |
8296 | else if (SCM_COMPLEXP (y)) | |
8297 | { | |
8298 | a = scm_i_big2dbl (x); | |
8299 | goto complex_div; | |
8300 | } | |
f92e85f7 | 8301 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8302 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8303 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8304 | else |
8305 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8306 | } |
0aacf84e MD |
8307 | else if (SCM_REALP (x)) |
8308 | { | |
8309 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8310 | if (SCM_I_INUMP (y)) |
0aacf84e | 8311 | { |
e25f3727 | 8312 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8313 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8314 | if (yy == 0) |
8315 | scm_num_overflow (s_divide); | |
8316 | else | |
7351e207 | 8317 | #endif |
98237784 MW |
8318 | /* FIXME: Precision may be lost here due to: |
8319 | (1) The cast from 'scm_t_inum' to 'double' | |
8320 | (2) Double rounding */ | |
55f26379 | 8321 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8322 | } |
8323 | else if (SCM_BIGP (y)) | |
8324 | { | |
98237784 MW |
8325 | /* FIXME: Precision may be lost here due to: |
8326 | (1) The conversion from bignum to double | |
8327 | (2) Double rounding */ | |
0aacf84e MD |
8328 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8329 | scm_remember_upto_here_1 (y); | |
55f26379 | 8330 | return scm_from_double (rx / dby); |
0aacf84e MD |
8331 | } |
8332 | else if (SCM_REALP (y)) | |
8333 | { | |
8334 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8335 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8336 | if (yy == 0.0) |
8337 | scm_num_overflow (s_divide); | |
8338 | else | |
7351e207 | 8339 | #endif |
55f26379 | 8340 | return scm_from_double (rx / yy); |
0aacf84e MD |
8341 | } |
8342 | else if (SCM_COMPLEXP (y)) | |
8343 | { | |
8344 | a = rx; | |
8345 | goto complex_div; | |
8346 | } | |
f92e85f7 | 8347 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8348 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8349 | else |
8350 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8351 | } |
0aacf84e MD |
8352 | else if (SCM_COMPLEXP (x)) |
8353 | { | |
8354 | double rx = SCM_COMPLEX_REAL (x); | |
8355 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8356 | if (SCM_I_INUMP (y)) |
0aacf84e | 8357 | { |
e25f3727 | 8358 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8359 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8360 | if (yy == 0) |
8361 | scm_num_overflow (s_divide); | |
8362 | else | |
7351e207 | 8363 | #endif |
0aacf84e | 8364 | { |
98237784 MW |
8365 | /* FIXME: Precision may be lost here due to: |
8366 | (1) The conversion from 'scm_t_inum' to double | |
8367 | (2) Double rounding */ | |
0aacf84e | 8368 | double d = yy; |
8507ec80 | 8369 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8370 | } |
8371 | } | |
8372 | else if (SCM_BIGP (y)) | |
8373 | { | |
98237784 MW |
8374 | /* FIXME: Precision may be lost here due to: |
8375 | (1) The conversion from bignum to double | |
8376 | (2) Double rounding */ | |
0aacf84e MD |
8377 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); |
8378 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8379 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8380 | } |
8381 | else if (SCM_REALP (y)) | |
8382 | { | |
8383 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8384 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8385 | if (yy == 0.0) |
8386 | scm_num_overflow (s_divide); | |
8387 | else | |
7351e207 | 8388 | #endif |
8507ec80 | 8389 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8390 | } |
8391 | else if (SCM_COMPLEXP (y)) | |
8392 | { | |
8393 | double ry = SCM_COMPLEX_REAL (y); | |
8394 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8395 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8396 | { |
8397 | double t = ry / iy; | |
8398 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8399 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8400 | } |
8401 | else | |
8402 | { | |
8403 | double t = iy / ry; | |
8404 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8405 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8406 | } |
8407 | } | |
f92e85f7 MV |
8408 | else if (SCM_FRACTIONP (y)) |
8409 | { | |
98237784 MW |
8410 | /* FIXME: Precision may be lost here due to: |
8411 | (1) The conversion from fraction to double | |
8412 | (2) Double rounding */ | |
f92e85f7 | 8413 | double yy = scm_i_fraction2double (y); |
8507ec80 | 8414 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8415 | } |
0aacf84e MD |
8416 | else |
8417 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8418 | } |
f92e85f7 MV |
8419 | else if (SCM_FRACTIONP (x)) |
8420 | { | |
e11e83f3 | 8421 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8422 | { |
e25f3727 | 8423 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8424 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8425 | if (yy == 0) | |
8426 | scm_num_overflow (s_divide); | |
8427 | else | |
8428 | #endif | |
cba42c93 | 8429 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8430 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8431 | } |
8432 | else if (SCM_BIGP (y)) | |
8433 | { | |
cba42c93 | 8434 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
98237784 | 8435 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
f92e85f7 MV |
8436 | } |
8437 | else if (SCM_REALP (y)) | |
8438 | { | |
8439 | double yy = SCM_REAL_VALUE (y); | |
8440 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8441 | if (yy == 0.0) | |
8442 | scm_num_overflow (s_divide); | |
8443 | else | |
8444 | #endif | |
98237784 MW |
8445 | /* FIXME: Precision may be lost here due to: |
8446 | (1) The conversion from fraction to double | |
8447 | (2) Double rounding */ | |
55f26379 | 8448 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8449 | } |
8450 | else if (SCM_COMPLEXP (y)) | |
8451 | { | |
98237784 MW |
8452 | /* FIXME: Precision may be lost here due to: |
8453 | (1) The conversion from fraction to double | |
8454 | (2) Double rounding */ | |
f92e85f7 MV |
8455 | a = scm_i_fraction2double (x); |
8456 | goto complex_div; | |
8457 | } | |
8458 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8459 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
98237784 | 8460 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
f92e85f7 MV |
8461 | else |
8462 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8463 | } | |
0aacf84e | 8464 | else |
f8de44c1 | 8465 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8466 | } |
c05e97b7 | 8467 | #undef FUNC_NAME |
0f2d19dd | 8468 | |
fa605590 | 8469 | |
0f2d19dd | 8470 | double |
3101f40f | 8471 | scm_c_truncate (double x) |
0f2d19dd | 8472 | { |
fa605590 | 8473 | return trunc (x); |
0f2d19dd | 8474 | } |
0f2d19dd | 8475 | |
3101f40f MV |
8476 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8477 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8478 | Then half-way cases are identified and adjusted down if the | |
8479 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8480 | |
8481 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8482 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8483 | ||
8484 | An odd "result" value is identified with result/2 != floor(result/2). | |
8485 | This is done with plus_half, since that value is ready for use sooner in | |
8486 | a pipelined cpu, and we're already requiring plus_half == result. | |
8487 | ||
8488 | Note however that we need to be careful when x is big and already an | |
8489 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8490 | us to return such a value, incorrectly. For instance if the hardware is | |
8491 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8492 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8493 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8494 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8495 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8496 | ||
8497 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8498 | x is already an integer. If it is then clearly that's the desired result | |
8499 | already. And if it's not then the exponent must be small enough to allow | |
8500 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8501 | ||
0f2d19dd | 8502 | double |
3101f40f | 8503 | scm_c_round (double x) |
0f2d19dd | 8504 | { |
6187f48b KR |
8505 | double plus_half, result; |
8506 | ||
8507 | if (x == floor (x)) | |
8508 | return x; | |
8509 | ||
8510 | plus_half = x + 0.5; | |
8511 | result = floor (plus_half); | |
3101f40f | 8512 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8513 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8514 | ? result - 1 | |
8515 | : result); | |
0f2d19dd JB |
8516 | } |
8517 | ||
8b56bcec MW |
8518 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8519 | (SCM x), | |
8520 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8521 | #define FUNC_NAME s_scm_truncate_number |
8522 | { | |
8b56bcec MW |
8523 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8524 | return x; | |
8525 | else if (SCM_REALP (x)) | |
c251ab63 | 8526 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8527 | else if (SCM_FRACTIONP (x)) |
8528 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8529 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8530 | else |
8b56bcec MW |
8531 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8532 | s_scm_truncate_number); | |
f92e85f7 MV |
8533 | } |
8534 | #undef FUNC_NAME | |
8535 | ||
8b56bcec MW |
8536 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8537 | (SCM x), | |
8538 | "Round the number @var{x} towards the nearest integer. " | |
8539 | "When it is exactly halfway between two integers, " | |
8540 | "round towards the even one.") | |
f92e85f7 MV |
8541 | #define FUNC_NAME s_scm_round_number |
8542 | { | |
e11e83f3 | 8543 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8544 | return x; |
8545 | else if (SCM_REALP (x)) | |
3101f40f | 8546 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8547 | else if (SCM_FRACTIONP (x)) |
8548 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8549 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8550 | else |
8b56bcec MW |
8551 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8552 | s_scm_round_number); | |
f92e85f7 MV |
8553 | } |
8554 | #undef FUNC_NAME | |
8555 | ||
8556 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8557 | (SCM x), | |
8558 | "Round the number @var{x} towards minus infinity.") | |
8559 | #define FUNC_NAME s_scm_floor | |
8560 | { | |
e11e83f3 | 8561 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8562 | return x; |
8563 | else if (SCM_REALP (x)) | |
55f26379 | 8564 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8565 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8566 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8567 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8568 | else |
8569 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8570 | } | |
8571 | #undef FUNC_NAME | |
8572 | ||
8573 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8574 | (SCM x), | |
8575 | "Round the number @var{x} towards infinity.") | |
8576 | #define FUNC_NAME s_scm_ceiling | |
8577 | { | |
e11e83f3 | 8578 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8579 | return x; |
8580 | else if (SCM_REALP (x)) | |
55f26379 | 8581 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8582 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8583 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8584 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8585 | else |
8586 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8587 | } | |
8588 | #undef FUNC_NAME | |
0f2d19dd | 8589 | |
2519490c MW |
8590 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8591 | (SCM x, SCM y), | |
8592 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8593 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8594 | { |
01c7284a MW |
8595 | if (scm_is_integer (y)) |
8596 | { | |
8597 | if (scm_is_true (scm_exact_p (y))) | |
8598 | return scm_integer_expt (x, y); | |
8599 | else | |
8600 | { | |
8601 | /* Here we handle the case where the exponent is an inexact | |
8602 | integer. We make the exponent exact in order to use | |
8603 | scm_integer_expt, and thus avoid the spurious imaginary | |
8604 | parts that may result from round-off errors in the general | |
8605 | e^(y log x) method below (for example when squaring a large | |
8606 | negative number). In this case, we must return an inexact | |
8607 | result for correctness. We also make the base inexact so | |
8608 | that scm_integer_expt will use fast inexact arithmetic | |
8609 | internally. Note that making the base inexact is not | |
8610 | sufficient to guarantee an inexact result, because | |
8611 | scm_integer_expt will return an exact 1 when the exponent | |
8612 | is 0, even if the base is inexact. */ | |
8613 | return scm_exact_to_inexact | |
8614 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8615 | scm_inexact_to_exact (y))); | |
8616 | } | |
8617 | } | |
6fc4d012 AW |
8618 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8619 | { | |
8620 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8621 | } | |
2519490c | 8622 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8623 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8624 | else if (scm_is_complex (x)) |
8625 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8626 | else | |
8627 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8628 | } |
1bbd0b84 | 8629 | #undef FUNC_NAME |
0f2d19dd | 8630 | |
7f41099e MW |
8631 | /* sin/cos/tan/asin/acos/atan |
8632 | sinh/cosh/tanh/asinh/acosh/atanh | |
8633 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8634 | Written by Jerry D. Hedden, (C) FSF. | |
8635 | See the file `COPYING' for terms applying to this program. */ | |
8636 | ||
ad79736c AW |
8637 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8638 | (SCM z), | |
8639 | "Compute the sine of @var{z}.") | |
8640 | #define FUNC_NAME s_scm_sin | |
8641 | { | |
8deddc94 MW |
8642 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8643 | return z; /* sin(exact0) = exact0 */ | |
8644 | else if (scm_is_real (z)) | |
ad79736c AW |
8645 | return scm_from_double (sin (scm_to_double (z))); |
8646 | else if (SCM_COMPLEXP (z)) | |
8647 | { double x, y; | |
8648 | x = SCM_COMPLEX_REAL (z); | |
8649 | y = SCM_COMPLEX_IMAG (z); | |
8650 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8651 | cos (x) * sinh (y)); | |
8652 | } | |
8653 | else | |
8654 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8655 | } | |
8656 | #undef FUNC_NAME | |
0f2d19dd | 8657 | |
ad79736c AW |
8658 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8659 | (SCM z), | |
8660 | "Compute the cosine of @var{z}.") | |
8661 | #define FUNC_NAME s_scm_cos | |
8662 | { | |
8deddc94 MW |
8663 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8664 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8665 | else if (scm_is_real (z)) | |
ad79736c AW |
8666 | return scm_from_double (cos (scm_to_double (z))); |
8667 | else if (SCM_COMPLEXP (z)) | |
8668 | { double x, y; | |
8669 | x = SCM_COMPLEX_REAL (z); | |
8670 | y = SCM_COMPLEX_IMAG (z); | |
8671 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8672 | -sin (x) * sinh (y)); | |
8673 | } | |
8674 | else | |
8675 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8676 | } | |
8677 | #undef FUNC_NAME | |
8678 | ||
8679 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8680 | (SCM z), | |
8681 | "Compute the tangent of @var{z}.") | |
8682 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8683 | { |
8deddc94 MW |
8684 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8685 | return z; /* tan(exact0) = exact0 */ | |
8686 | else if (scm_is_real (z)) | |
ad79736c AW |
8687 | return scm_from_double (tan (scm_to_double (z))); |
8688 | else if (SCM_COMPLEXP (z)) | |
8689 | { double x, y, w; | |
8690 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8691 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8692 | w = cos (x) + cosh (y); | |
8693 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8694 | if (w == 0.0) | |
8695 | scm_num_overflow (s_scm_tan); | |
8696 | #endif | |
8697 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8698 | } | |
8699 | else | |
8700 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8701 | } | |
8702 | #undef FUNC_NAME | |
8703 | ||
8704 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8705 | (SCM z), | |
8706 | "Compute the hyperbolic sine of @var{z}.") | |
8707 | #define FUNC_NAME s_scm_sinh | |
8708 | { | |
8deddc94 MW |
8709 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8710 | return z; /* sinh(exact0) = exact0 */ | |
8711 | else if (scm_is_real (z)) | |
ad79736c AW |
8712 | return scm_from_double (sinh (scm_to_double (z))); |
8713 | else if (SCM_COMPLEXP (z)) | |
8714 | { double x, y; | |
8715 | x = SCM_COMPLEX_REAL (z); | |
8716 | y = SCM_COMPLEX_IMAG (z); | |
8717 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8718 | cosh (x) * sin (y)); | |
8719 | } | |
8720 | else | |
8721 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8722 | } | |
8723 | #undef FUNC_NAME | |
8724 | ||
8725 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8726 | (SCM z), | |
8727 | "Compute the hyperbolic cosine of @var{z}.") | |
8728 | #define FUNC_NAME s_scm_cosh | |
8729 | { | |
8deddc94 MW |
8730 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8731 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8732 | else if (scm_is_real (z)) | |
ad79736c AW |
8733 | return scm_from_double (cosh (scm_to_double (z))); |
8734 | else if (SCM_COMPLEXP (z)) | |
8735 | { double x, y; | |
8736 | x = SCM_COMPLEX_REAL (z); | |
8737 | y = SCM_COMPLEX_IMAG (z); | |
8738 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8739 | sinh (x) * sin (y)); | |
8740 | } | |
8741 | else | |
8742 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8743 | } | |
8744 | #undef FUNC_NAME | |
8745 | ||
8746 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8747 | (SCM z), | |
8748 | "Compute the hyperbolic tangent of @var{z}.") | |
8749 | #define FUNC_NAME s_scm_tanh | |
8750 | { | |
8deddc94 MW |
8751 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8752 | return z; /* tanh(exact0) = exact0 */ | |
8753 | else if (scm_is_real (z)) | |
ad79736c AW |
8754 | return scm_from_double (tanh (scm_to_double (z))); |
8755 | else if (SCM_COMPLEXP (z)) | |
8756 | { double x, y, w; | |
8757 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8758 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8759 | w = cosh (x) + cos (y); | |
8760 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8761 | if (w == 0.0) | |
8762 | scm_num_overflow (s_scm_tanh); | |
8763 | #endif | |
8764 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8765 | } | |
8766 | else | |
8767 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8768 | } | |
8769 | #undef FUNC_NAME | |
8770 | ||
8771 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8772 | (SCM z), | |
8773 | "Compute the arc sine of @var{z}.") | |
8774 | #define FUNC_NAME s_scm_asin | |
8775 | { | |
8deddc94 MW |
8776 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8777 | return z; /* asin(exact0) = exact0 */ | |
8778 | else if (scm_is_real (z)) | |
ad79736c AW |
8779 | { |
8780 | double w = scm_to_double (z); | |
8781 | if (w >= -1.0 && w <= 1.0) | |
8782 | return scm_from_double (asin (w)); | |
8783 | else | |
8784 | return scm_product (scm_c_make_rectangular (0, -1), | |
8785 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8786 | } | |
8787 | else if (SCM_COMPLEXP (z)) | |
8788 | { double x, y; | |
8789 | x = SCM_COMPLEX_REAL (z); | |
8790 | y = SCM_COMPLEX_IMAG (z); | |
8791 | return scm_product (scm_c_make_rectangular (0, -1), | |
8792 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8793 | } | |
8794 | else | |
8795 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8796 | } | |
8797 | #undef FUNC_NAME | |
8798 | ||
8799 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8800 | (SCM z), | |
8801 | "Compute the arc cosine of @var{z}.") | |
8802 | #define FUNC_NAME s_scm_acos | |
8803 | { | |
8deddc94 MW |
8804 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8805 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8806 | else if (scm_is_real (z)) | |
ad79736c AW |
8807 | { |
8808 | double w = scm_to_double (z); | |
8809 | if (w >= -1.0 && w <= 1.0) | |
8810 | return scm_from_double (acos (w)); | |
8811 | else | |
8812 | return scm_sum (scm_from_double (acos (0.0)), | |
8813 | scm_product (scm_c_make_rectangular (0, 1), | |
8814 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8815 | } | |
8816 | else if (SCM_COMPLEXP (z)) | |
8817 | { double x, y; | |
8818 | x = SCM_COMPLEX_REAL (z); | |
8819 | y = SCM_COMPLEX_IMAG (z); | |
8820 | return scm_sum (scm_from_double (acos (0.0)), | |
8821 | scm_product (scm_c_make_rectangular (0, 1), | |
8822 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8823 | } | |
8824 | else | |
8825 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8826 | } | |
8827 | #undef FUNC_NAME | |
8828 | ||
8829 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8830 | (SCM z, SCM y), | |
8831 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8832 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8833 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8834 | #define FUNC_NAME s_scm_atan | |
8835 | { | |
8836 | if (SCM_UNBNDP (y)) | |
8837 | { | |
8deddc94 MW |
8838 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8839 | return z; /* atan(exact0) = exact0 */ | |
8840 | else if (scm_is_real (z)) | |
ad79736c AW |
8841 | return scm_from_double (atan (scm_to_double (z))); |
8842 | else if (SCM_COMPLEXP (z)) | |
8843 | { | |
8844 | double v, w; | |
8845 | v = SCM_COMPLEX_REAL (z); | |
8846 | w = SCM_COMPLEX_IMAG (z); | |
8847 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8848 | scm_c_make_rectangular (v, w + 1.0))), | |
8849 | scm_c_make_rectangular (0, 2)); | |
8850 | } | |
8851 | else | |
18104cac | 8852 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8853 | } |
8854 | else if (scm_is_real (z)) | |
8855 | { | |
8856 | if (scm_is_real (y)) | |
8857 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8858 | else | |
8859 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8860 | } | |
8861 | else | |
8862 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8863 | } | |
8864 | #undef FUNC_NAME | |
8865 | ||
8866 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8867 | (SCM z), | |
8868 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8869 | #define FUNC_NAME s_scm_sys_asinh | |
8870 | { | |
8deddc94 MW |
8871 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8872 | return z; /* asinh(exact0) = exact0 */ | |
8873 | else if (scm_is_real (z)) | |
ad79736c AW |
8874 | return scm_from_double (asinh (scm_to_double (z))); |
8875 | else if (scm_is_number (z)) | |
8876 | return scm_log (scm_sum (z, | |
8877 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8878 | SCM_INUM1)))); |
ad79736c AW |
8879 | else |
8880 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8881 | } | |
8882 | #undef FUNC_NAME | |
8883 | ||
8884 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8885 | (SCM z), | |
8886 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8887 | #define FUNC_NAME s_scm_sys_acosh | |
8888 | { | |
8deddc94 MW |
8889 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8890 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8891 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8892 | return scm_from_double (acosh (scm_to_double (z))); |
8893 | else if (scm_is_number (z)) | |
8894 | return scm_log (scm_sum (z, | |
8895 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8896 | SCM_INUM1)))); |
ad79736c AW |
8897 | else |
8898 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8899 | } | |
8900 | #undef FUNC_NAME | |
8901 | ||
8902 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8903 | (SCM z), | |
8904 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8905 | #define FUNC_NAME s_scm_sys_atanh | |
8906 | { | |
8deddc94 MW |
8907 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8908 | return z; /* atanh(exact0) = exact0 */ | |
8909 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8910 | return scm_from_double (atanh (scm_to_double (z))); |
8911 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8912 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8913 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8914 | SCM_I_MAKINUM (2)); |
8915 | else | |
8916 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8917 | } |
1bbd0b84 | 8918 | #undef FUNC_NAME |
0f2d19dd | 8919 | |
8507ec80 MV |
8920 | SCM |
8921 | scm_c_make_rectangular (double re, double im) | |
8922 | { | |
c7218482 | 8923 | SCM z; |
03604fcf | 8924 | |
c7218482 MW |
8925 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8926 | "complex")); | |
8927 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8928 | SCM_COMPLEX_REAL (z) = re; | |
8929 | SCM_COMPLEX_IMAG (z) = im; | |
8930 | return z; | |
8507ec80 | 8931 | } |
0f2d19dd | 8932 | |
a1ec6916 | 8933 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 | 8934 | (SCM real_part, SCM imaginary_part), |
b7e64f8b BT |
8935 | "Return a complex number constructed of the given @var{real_part} " |
8936 | "and @var{imaginary_part} parts.") | |
1bbd0b84 | 8937 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8938 | { |
ad79736c AW |
8939 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8940 | SCM_ARG1, FUNC_NAME, "real"); | |
8941 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8942 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8943 | |
8944 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8945 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8946 | return real_part; | |
8947 | else | |
8948 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8949 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8950 | } |
1bbd0b84 | 8951 | #undef FUNC_NAME |
0f2d19dd | 8952 | |
8507ec80 MV |
8953 | SCM |
8954 | scm_c_make_polar (double mag, double ang) | |
8955 | { | |
8956 | double s, c; | |
5e647d08 LC |
8957 | |
8958 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8959 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8960 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8961 | details. */ | |
8962 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8963 | sincos (ang, &s, &c); |
8964 | #else | |
8965 | s = sin (ang); | |
8966 | c = cos (ang); | |
8967 | #endif | |
9d427b2c MW |
8968 | |
8969 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8970 | infinite, or perhaps simply too large to determine its value | |
8971 | mod 2*pi. However, we know something that the floating-point | |
8972 | implementation doesn't know: We know that s and c are finite. | |
8973 | Therefore, if the magnitude is zero, return a complex zero. | |
8974 | ||
8975 | The reason we check for the NaNs instead of using this case | |
8976 | whenever mag == 0.0 is because when the angle is known, we'd | |
8977 | like to return the correct kind of non-real complex zero: | |
8978 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8979 | on which quadrant the angle is in. | |
8980 | */ | |
8981 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8982 | return scm_c_make_rectangular (0.0, 0.0); | |
8983 | else | |
8984 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8985 | } |
0f2d19dd | 8986 | |
a1ec6916 | 8987 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8988 | (SCM mag, SCM ang), |
8989 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8990 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8991 | { |
c7218482 MW |
8992 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8993 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8994 | ||
8995 | /* If mag is exact0, return exact0 */ | |
8996 | if (scm_is_eq (mag, SCM_INUM0)) | |
8997 | return SCM_INUM0; | |
8998 | /* Return a real if ang is exact0 */ | |
8999 | else if (scm_is_eq (ang, SCM_INUM0)) | |
9000 | return mag; | |
9001 | else | |
9002 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 9003 | } |
1bbd0b84 | 9004 | #undef FUNC_NAME |
0f2d19dd JB |
9005 | |
9006 | ||
2519490c MW |
9007 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
9008 | (SCM z), | |
9009 | "Return the real part of the number @var{z}.") | |
9010 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 9011 | { |
2519490c | 9012 | if (SCM_COMPLEXP (z)) |
55f26379 | 9013 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 9014 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 9015 | return z; |
0aacf84e | 9016 | else |
2519490c | 9017 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 9018 | } |
2519490c | 9019 | #undef FUNC_NAME |
0f2d19dd JB |
9020 | |
9021 | ||
2519490c MW |
9022 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
9023 | (SCM z), | |
9024 | "Return the imaginary part of the number @var{z}.") | |
9025 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 9026 | { |
2519490c MW |
9027 | if (SCM_COMPLEXP (z)) |
9028 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 9029 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 9030 | return SCM_INUM0; |
0aacf84e | 9031 | else |
2519490c | 9032 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 9033 | } |
2519490c | 9034 | #undef FUNC_NAME |
0f2d19dd | 9035 | |
2519490c MW |
9036 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
9037 | (SCM z), | |
9038 | "Return the numerator of the number @var{z}.") | |
9039 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 9040 | { |
2519490c | 9041 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
9042 | return z; |
9043 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 9044 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
9045 | else if (SCM_REALP (z)) |
9046 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
9047 | else | |
2519490c | 9048 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 9049 | } |
2519490c | 9050 | #undef FUNC_NAME |
f92e85f7 MV |
9051 | |
9052 | ||
2519490c MW |
9053 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
9054 | (SCM z), | |
9055 | "Return the denominator of the number @var{z}.") | |
9056 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 9057 | { |
2519490c | 9058 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 9059 | return SCM_INUM1; |
f92e85f7 | 9060 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 9061 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
9062 | else if (SCM_REALP (z)) |
9063 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
9064 | else | |
2519490c | 9065 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 9066 | } |
2519490c | 9067 | #undef FUNC_NAME |
0f2d19dd | 9068 | |
2519490c MW |
9069 | |
9070 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
9071 | (SCM z), | |
9072 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
9073 | "@code{abs} for real arguments, but also allows complex numbers.") | |
9074 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 9075 | { |
e11e83f3 | 9076 | if (SCM_I_INUMP (z)) |
0aacf84e | 9077 | { |
e25f3727 | 9078 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
9079 | if (zz >= 0) |
9080 | return z; | |
9081 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 9082 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 9083 | else |
e25f3727 | 9084 | return scm_i_inum2big (-zz); |
5986c47d | 9085 | } |
0aacf84e MD |
9086 | else if (SCM_BIGP (z)) |
9087 | { | |
9088 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9089 | scm_remember_upto_here_1 (z); | |
9090 | if (sgn < 0) | |
9091 | return scm_i_clonebig (z, 0); | |
9092 | else | |
9093 | return z; | |
5986c47d | 9094 | } |
0aacf84e | 9095 | else if (SCM_REALP (z)) |
55f26379 | 9096 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 9097 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9098 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
9099 | else if (SCM_FRACTIONP (z)) |
9100 | { | |
73e4de09 | 9101 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 9102 | return z; |
a285b18c MW |
9103 | return scm_i_make_ratio_already_reduced |
9104 | (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), | |
9105 | SCM_FRACTION_DENOMINATOR (z)); | |
f92e85f7 | 9106 | } |
0aacf84e | 9107 | else |
2519490c | 9108 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 9109 | } |
2519490c | 9110 | #undef FUNC_NAME |
0f2d19dd JB |
9111 | |
9112 | ||
2519490c MW |
9113 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
9114 | (SCM z), | |
9115 | "Return the angle of the complex number @var{z}.") | |
9116 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 9117 | { |
c8ae173e | 9118 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 9119 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
9120 | But if atan2 follows the floating point rounding mode, then the value |
9121 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 9122 | if (SCM_I_INUMP (z)) |
0aacf84e | 9123 | { |
e11e83f3 | 9124 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 9125 | return flo0; |
0aacf84e | 9126 | else |
55f26379 | 9127 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 9128 | } |
0aacf84e MD |
9129 | else if (SCM_BIGP (z)) |
9130 | { | |
9131 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9132 | scm_remember_upto_here_1 (z); | |
9133 | if (sgn < 0) | |
55f26379 | 9134 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 9135 | else |
e7efe8e7 | 9136 | return flo0; |
0f2d19dd | 9137 | } |
0aacf84e | 9138 | else if (SCM_REALP (z)) |
c8ae173e | 9139 | { |
10a97755 MW |
9140 | double x = SCM_REAL_VALUE (z); |
9141 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
e7efe8e7 | 9142 | return flo0; |
c8ae173e | 9143 | else |
55f26379 | 9144 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 9145 | } |
0aacf84e | 9146 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9147 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
9148 | else if (SCM_FRACTIONP (z)) |
9149 | { | |
73e4de09 | 9150 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 9151 | return flo0; |
55f26379 | 9152 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 9153 | } |
0aacf84e | 9154 | else |
2519490c | 9155 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 9156 | } |
2519490c | 9157 | #undef FUNC_NAME |
0f2d19dd JB |
9158 | |
9159 | ||
2519490c MW |
9160 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
9161 | (SCM z), | |
9162 | "Convert the number @var{z} to its inexact representation.\n") | |
9163 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 9164 | { |
e11e83f3 | 9165 | if (SCM_I_INUMP (z)) |
55f26379 | 9166 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 9167 | else if (SCM_BIGP (z)) |
55f26379 | 9168 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 9169 | else if (SCM_FRACTIONP (z)) |
55f26379 | 9170 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
9171 | else if (SCM_INEXACTP (z)) |
9172 | return z; | |
9173 | else | |
2519490c | 9174 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 9175 | } |
2519490c | 9176 | #undef FUNC_NAME |
3c9a524f DH |
9177 | |
9178 | ||
2519490c MW |
9179 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
9180 | (SCM z), | |
9181 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 9182 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 9183 | { |
c7218482 | 9184 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 9185 | return z; |
c7218482 | 9186 | else |
0aacf84e | 9187 | { |
c7218482 MW |
9188 | double val; |
9189 | ||
9190 | if (SCM_REALP (z)) | |
9191 | val = SCM_REAL_VALUE (z); | |
9192 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
9193 | val = SCM_COMPLEX_REAL (z); | |
9194 | else | |
9195 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
9196 | ||
9197 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 9198 | SCM_OUT_OF_RANGE (1, z); |
24475b86 MW |
9199 | else if (val == 0.0) |
9200 | return SCM_INUM0; | |
2be24db4 | 9201 | else |
f92e85f7 | 9202 | { |
24475b86 MW |
9203 | int expon; |
9204 | SCM numerator; | |
9205 | ||
9206 | numerator = scm_i_dbl2big (ldexp (frexp (val, &expon), | |
9207 | DBL_MANT_DIG)); | |
9208 | expon -= DBL_MANT_DIG; | |
9209 | if (expon < 0) | |
9210 | { | |
9211 | int shift = mpz_scan1 (SCM_I_BIG_MPZ (numerator), 0); | |
9212 | ||
9213 | if (shift > -expon) | |
9214 | shift = -expon; | |
9215 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (numerator), | |
9216 | SCM_I_BIG_MPZ (numerator), | |
9217 | shift); | |
9218 | expon += shift; | |
9219 | } | |
9220 | numerator = scm_i_normbig (numerator); | |
9221 | if (expon < 0) | |
9222 | return scm_i_make_ratio_already_reduced | |
9223 | (numerator, left_shift_exact_integer (SCM_INUM1, -expon)); | |
9224 | else if (expon > 0) | |
9225 | return left_shift_exact_integer (numerator, expon); | |
9226 | else | |
9227 | return numerator; | |
f92e85f7 | 9228 | } |
c2ff8ab0 | 9229 | } |
0f2d19dd | 9230 | } |
1bbd0b84 | 9231 | #undef FUNC_NAME |
0f2d19dd | 9232 | |
f92e85f7 | 9233 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
9234 | (SCM x, SCM eps), |
9235 | "Returns the @emph{simplest} rational number differing\n" | |
9236 | "from @var{x} by no more than @var{eps}.\n" | |
9237 | "\n" | |
9238 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9239 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9240 | "to use @code{inexact->exact} on the arguments.\n" | |
9241 | "\n" | |
9242 | "@lisp\n" | |
9243 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9244 | "@result{} 6/5\n" | |
9245 | "@end lisp") | |
f92e85f7 MV |
9246 | #define FUNC_NAME s_scm_rationalize |
9247 | { | |
605f6980 MW |
9248 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9249 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9250 | eps = scm_abs (eps); | |
9251 | if (scm_is_false (scm_positive_p (eps))) | |
9252 | { | |
9253 | /* eps is either zero or a NaN */ | |
9254 | if (scm_is_true (scm_nan_p (eps))) | |
9255 | return scm_nan (); | |
9256 | else if (SCM_INEXACTP (eps)) | |
9257 | return scm_exact_to_inexact (x); | |
9258 | else | |
9259 | return x; | |
9260 | } | |
9261 | else if (scm_is_false (scm_finite_p (eps))) | |
9262 | { | |
9263 | if (scm_is_true (scm_finite_p (x))) | |
9264 | return flo0; | |
9265 | else | |
9266 | return scm_nan (); | |
9267 | } | |
9268 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9269 | return x; |
605f6980 MW |
9270 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9271 | scm_ceiling (scm_difference (x, eps))))) | |
9272 | { | |
9273 | /* There's an integer within range; we want the one closest to zero */ | |
9274 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9275 | { | |
9276 | /* zero is within range */ | |
9277 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9278 | return flo0; | |
9279 | else | |
9280 | return SCM_INUM0; | |
9281 | } | |
9282 | else if (scm_is_true (scm_positive_p (x))) | |
9283 | return scm_ceiling (scm_difference (x, eps)); | |
9284 | else | |
9285 | return scm_floor (scm_sum (x, eps)); | |
9286 | } | |
9287 | else | |
f92e85f7 MV |
9288 | { |
9289 | /* Use continued fractions to find closest ratio. All | |
9290 | arithmetic is done with exact numbers. | |
9291 | */ | |
9292 | ||
9293 | SCM ex = scm_inexact_to_exact (x); | |
9294 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9295 | SCM tt = SCM_INUM1; |
9296 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9297 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9298 | SCM rx; |
9299 | int i = 0; | |
9300 | ||
f92e85f7 MV |
9301 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9302 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9303 | ||
9304 | /* We stop after a million iterations just to be absolutely sure | |
9305 | that we don't go into an infinite loop. The process normally | |
9306 | converges after less than a dozen iterations. | |
9307 | */ | |
9308 | ||
f92e85f7 MV |
9309 | while (++i < 1000000) |
9310 | { | |
9311 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9312 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9313 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9314 | scm_is_false | |
f92e85f7 | 9315 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9316 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9317 | { |
9318 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9319 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9320 | return scm_exact_to_inexact (res); |
9321 | else | |
9322 | return res; | |
9323 | } | |
f92e85f7 MV |
9324 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9325 | SCM_UNDEFINED); | |
9326 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9327 | a2 = a1; | |
9328 | b2 = b1; | |
9329 | a1 = a; | |
9330 | b1 = b; | |
9331 | } | |
9332 | scm_num_overflow (s_scm_rationalize); | |
9333 | } | |
f92e85f7 MV |
9334 | } |
9335 | #undef FUNC_NAME | |
9336 | ||
73e4de09 MV |
9337 | /* conversion functions */ |
9338 | ||
9339 | int | |
9340 | scm_is_integer (SCM val) | |
9341 | { | |
9342 | return scm_is_true (scm_integer_p (val)); | |
9343 | } | |
9344 | ||
9345 | int | |
9346 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9347 | { | |
e11e83f3 | 9348 | if (SCM_I_INUMP (val)) |
73e4de09 | 9349 | { |
e11e83f3 | 9350 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9351 | return n >= min && n <= max; |
9352 | } | |
9353 | else if (SCM_BIGP (val)) | |
9354 | { | |
9355 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9356 | return 0; | |
9357 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9358 | { |
9359 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9360 | { | |
9361 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9362 | return n >= min && n <= max; | |
9363 | } | |
9364 | else | |
9365 | return 0; | |
9366 | } | |
73e4de09 MV |
9367 | else |
9368 | { | |
d956fa6f MV |
9369 | scm_t_intmax n; |
9370 | size_t count; | |
73e4de09 | 9371 | |
d956fa6f MV |
9372 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9373 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9374 | return 0; | |
9375 | ||
9376 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9377 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9378 | |
d956fa6f | 9379 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9380 | { |
d956fa6f MV |
9381 | if (n < 0) |
9382 | return 0; | |
73e4de09 | 9383 | } |
73e4de09 MV |
9384 | else |
9385 | { | |
d956fa6f MV |
9386 | n = -n; |
9387 | if (n >= 0) | |
9388 | return 0; | |
73e4de09 | 9389 | } |
d956fa6f MV |
9390 | |
9391 | return n >= min && n <= max; | |
73e4de09 MV |
9392 | } |
9393 | } | |
73e4de09 MV |
9394 | else |
9395 | return 0; | |
9396 | } | |
9397 | ||
9398 | int | |
9399 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9400 | { | |
e11e83f3 | 9401 | if (SCM_I_INUMP (val)) |
73e4de09 | 9402 | { |
e11e83f3 | 9403 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9404 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9405 | } | |
9406 | else if (SCM_BIGP (val)) | |
9407 | { | |
9408 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9409 | return 0; | |
9410 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9411 | { |
9412 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9413 | { | |
9414 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9415 | return n >= min && n <= max; | |
9416 | } | |
9417 | else | |
9418 | return 0; | |
9419 | } | |
73e4de09 MV |
9420 | else |
9421 | { | |
d956fa6f MV |
9422 | scm_t_uintmax n; |
9423 | size_t count; | |
73e4de09 | 9424 | |
d956fa6f MV |
9425 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9426 | return 0; | |
73e4de09 | 9427 | |
d956fa6f MV |
9428 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9429 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9430 | return 0; |
d956fa6f MV |
9431 | |
9432 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9433 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9434 | |
d956fa6f | 9435 | return n >= min && n <= max; |
73e4de09 MV |
9436 | } |
9437 | } | |
73e4de09 MV |
9438 | else |
9439 | return 0; | |
9440 | } | |
9441 | ||
1713d319 MV |
9442 | static void |
9443 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9444 | { | |
9445 | scm_error (scm_out_of_range_key, | |
9446 | NULL, | |
9447 | "Value out of range ~S to ~S: ~S", | |
9448 | scm_list_3 (min, max, bad_val), | |
9449 | scm_list_1 (bad_val)); | |
9450 | } | |
9451 | ||
bfd7932e MV |
9452 | #define TYPE scm_t_intmax |
9453 | #define TYPE_MIN min | |
9454 | #define TYPE_MAX max | |
9455 | #define SIZEOF_TYPE 0 | |
9456 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9457 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9458 | #include "libguile/conv-integer.i.c" | |
9459 | ||
9460 | #define TYPE scm_t_uintmax | |
9461 | #define TYPE_MIN min | |
9462 | #define TYPE_MAX max | |
9463 | #define SIZEOF_TYPE 0 | |
9464 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9465 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9466 | #include "libguile/conv-uinteger.i.c" | |
9467 | ||
9468 | #define TYPE scm_t_int8 | |
9469 | #define TYPE_MIN SCM_T_INT8_MIN | |
9470 | #define TYPE_MAX SCM_T_INT8_MAX | |
9471 | #define SIZEOF_TYPE 1 | |
9472 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9473 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9474 | #include "libguile/conv-integer.i.c" | |
9475 | ||
9476 | #define TYPE scm_t_uint8 | |
9477 | #define TYPE_MIN 0 | |
9478 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9479 | #define SIZEOF_TYPE 1 | |
9480 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9481 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9482 | #include "libguile/conv-uinteger.i.c" | |
9483 | ||
9484 | #define TYPE scm_t_int16 | |
9485 | #define TYPE_MIN SCM_T_INT16_MIN | |
9486 | #define TYPE_MAX SCM_T_INT16_MAX | |
9487 | #define SIZEOF_TYPE 2 | |
9488 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9489 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9490 | #include "libguile/conv-integer.i.c" | |
9491 | ||
9492 | #define TYPE scm_t_uint16 | |
9493 | #define TYPE_MIN 0 | |
9494 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9495 | #define SIZEOF_TYPE 2 | |
9496 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9497 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9498 | #include "libguile/conv-uinteger.i.c" | |
9499 | ||
9500 | #define TYPE scm_t_int32 | |
9501 | #define TYPE_MIN SCM_T_INT32_MIN | |
9502 | #define TYPE_MAX SCM_T_INT32_MAX | |
9503 | #define SIZEOF_TYPE 4 | |
9504 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9505 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9506 | #include "libguile/conv-integer.i.c" | |
9507 | ||
9508 | #define TYPE scm_t_uint32 | |
9509 | #define TYPE_MIN 0 | |
9510 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9511 | #define SIZEOF_TYPE 4 | |
9512 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9513 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9514 | #include "libguile/conv-uinteger.i.c" | |
9515 | ||
904a78f1 MG |
9516 | #define TYPE scm_t_wchar |
9517 | #define TYPE_MIN (scm_t_int32)-1 | |
9518 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9519 | #define SIZEOF_TYPE 4 | |
9520 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9521 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9522 | #include "libguile/conv-integer.i.c" | |
9523 | ||
bfd7932e MV |
9524 | #define TYPE scm_t_int64 |
9525 | #define TYPE_MIN SCM_T_INT64_MIN | |
9526 | #define TYPE_MAX SCM_T_INT64_MAX | |
9527 | #define SIZEOF_TYPE 8 | |
9528 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9529 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9530 | #include "libguile/conv-integer.i.c" | |
9531 | ||
9532 | #define TYPE scm_t_uint64 | |
9533 | #define TYPE_MIN 0 | |
9534 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9535 | #define SIZEOF_TYPE 8 | |
9536 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9537 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9538 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9539 | |
cd036260 MV |
9540 | void |
9541 | scm_to_mpz (SCM val, mpz_t rop) | |
9542 | { | |
9543 | if (SCM_I_INUMP (val)) | |
9544 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9545 | else if (SCM_BIGP (val)) | |
9546 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9547 | else | |
9548 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9549 | } | |
9550 | ||
9551 | SCM | |
9552 | scm_from_mpz (mpz_t val) | |
9553 | { | |
9554 | return scm_i_mpz2num (val); | |
9555 | } | |
9556 | ||
73e4de09 MV |
9557 | int |
9558 | scm_is_real (SCM val) | |
9559 | { | |
9560 | return scm_is_true (scm_real_p (val)); | |
9561 | } | |
9562 | ||
55f26379 MV |
9563 | int |
9564 | scm_is_rational (SCM val) | |
9565 | { | |
9566 | return scm_is_true (scm_rational_p (val)); | |
9567 | } | |
9568 | ||
73e4de09 MV |
9569 | double |
9570 | scm_to_double (SCM val) | |
9571 | { | |
55f26379 MV |
9572 | if (SCM_I_INUMP (val)) |
9573 | return SCM_I_INUM (val); | |
9574 | else if (SCM_BIGP (val)) | |
9575 | return scm_i_big2dbl (val); | |
9576 | else if (SCM_FRACTIONP (val)) | |
9577 | return scm_i_fraction2double (val); | |
9578 | else if (SCM_REALP (val)) | |
9579 | return SCM_REAL_VALUE (val); | |
9580 | else | |
7a1aba42 | 9581 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9582 | } |
9583 | ||
9584 | SCM | |
9585 | scm_from_double (double val) | |
9586 | { | |
978c52d1 LC |
9587 | SCM z; |
9588 | ||
9589 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9590 | ||
9591 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9592 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9593 | |
55f26379 | 9594 | return z; |
73e4de09 MV |
9595 | } |
9596 | ||
220058a8 | 9597 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9598 | |
9599 | float | |
e25f3727 | 9600 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9601 | { |
220058a8 AW |
9602 | scm_c_issue_deprecation_warning |
9603 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9604 | ||
55f26379 MV |
9605 | if (SCM_BIGP (num)) |
9606 | { | |
9607 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9608 | if (!isinf (res)) |
55f26379 MV |
9609 | return res; |
9610 | else | |
9611 | scm_out_of_range (NULL, num); | |
9612 | } | |
9613 | else | |
9614 | return scm_to_double (num); | |
9615 | } | |
9616 | ||
9617 | double | |
e25f3727 | 9618 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9619 | { |
220058a8 AW |
9620 | scm_c_issue_deprecation_warning |
9621 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9622 | ||
55f26379 MV |
9623 | if (SCM_BIGP (num)) |
9624 | { | |
9625 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9626 | if (!isinf (res)) |
55f26379 MV |
9627 | return res; |
9628 | else | |
9629 | scm_out_of_range (NULL, num); | |
9630 | } | |
9631 | else | |
9632 | return scm_to_double (num); | |
9633 | } | |
9634 | ||
9635 | #endif | |
9636 | ||
8507ec80 MV |
9637 | int |
9638 | scm_is_complex (SCM val) | |
9639 | { | |
9640 | return scm_is_true (scm_complex_p (val)); | |
9641 | } | |
9642 | ||
9643 | double | |
9644 | scm_c_real_part (SCM z) | |
9645 | { | |
9646 | if (SCM_COMPLEXP (z)) | |
9647 | return SCM_COMPLEX_REAL (z); | |
9648 | else | |
9649 | { | |
9650 | /* Use the scm_real_part to get proper error checking and | |
9651 | dispatching. | |
9652 | */ | |
9653 | return scm_to_double (scm_real_part (z)); | |
9654 | } | |
9655 | } | |
9656 | ||
9657 | double | |
9658 | scm_c_imag_part (SCM z) | |
9659 | { | |
9660 | if (SCM_COMPLEXP (z)) | |
9661 | return SCM_COMPLEX_IMAG (z); | |
9662 | else | |
9663 | { | |
9664 | /* Use the scm_imag_part to get proper error checking and | |
9665 | dispatching. The result will almost always be 0.0, but not | |
9666 | always. | |
9667 | */ | |
9668 | return scm_to_double (scm_imag_part (z)); | |
9669 | } | |
9670 | } | |
9671 | ||
9672 | double | |
9673 | scm_c_magnitude (SCM z) | |
9674 | { | |
9675 | return scm_to_double (scm_magnitude (z)); | |
9676 | } | |
9677 | ||
9678 | double | |
9679 | scm_c_angle (SCM z) | |
9680 | { | |
9681 | return scm_to_double (scm_angle (z)); | |
9682 | } | |
9683 | ||
9684 | int | |
9685 | scm_is_number (SCM z) | |
9686 | { | |
9687 | return scm_is_true (scm_number_p (z)); | |
9688 | } | |
9689 | ||
8ab3d8a0 | 9690 | |
a5f6b751 MW |
9691 | /* Returns log(x * 2^shift) */ |
9692 | static SCM | |
9693 | log_of_shifted_double (double x, long shift) | |
9694 | { | |
9695 | double ans = log (fabs (x)) + shift * M_LN2; | |
9696 | ||
9697 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9698 | return scm_from_double (ans); | |
9699 | else | |
9700 | return scm_c_make_rectangular (ans, M_PI); | |
9701 | } | |
9702 | ||
85bdb6ac | 9703 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9704 | static SCM |
9705 | log_of_exact_integer (SCM n) | |
9706 | { | |
7f34acd8 MW |
9707 | if (SCM_I_INUMP (n)) |
9708 | return log_of_shifted_double (SCM_I_INUM (n), 0); | |
9709 | else if (SCM_BIGP (n)) | |
9710 | { | |
9711 | long expon; | |
9712 | double signif = scm_i_big2dbl_2exp (n, &expon); | |
9713 | return log_of_shifted_double (signif, expon); | |
9714 | } | |
9715 | else | |
9716 | scm_wrong_type_arg ("log_of_exact_integer", SCM_ARG1, n); | |
a5f6b751 MW |
9717 | } |
9718 | ||
9719 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9720 | static SCM | |
9721 | log_of_fraction (SCM n, SCM d) | |
9722 | { | |
9723 | long n_size = scm_to_long (scm_integer_length (n)); | |
9724 | long d_size = scm_to_long (scm_integer_length (d)); | |
9725 | ||
9726 | if (abs (n_size - d_size) > 1) | |
7f34acd8 MW |
9727 | return (scm_difference (log_of_exact_integer (n), |
9728 | log_of_exact_integer (d))); | |
a5f6b751 MW |
9729 | else if (scm_is_false (scm_negative_p (n))) |
9730 | return scm_from_double | |
98237784 | 9731 | (log1p (scm_i_divide2double (scm_difference (n, d), d))); |
a5f6b751 MW |
9732 | else |
9733 | return scm_c_make_rectangular | |
98237784 MW |
9734 | (log1p (scm_i_divide2double (scm_difference (scm_abs (n), d), |
9735 | d)), | |
a5f6b751 MW |
9736 | M_PI); |
9737 | } | |
9738 | ||
9739 | ||
8ab3d8a0 KR |
9740 | /* In the following functions we dispatch to the real-arg funcs like log() |
9741 | when we know the arg is real, instead of just handing everything to | |
9742 | clog() for instance. This is in case clog() doesn't optimize for a | |
9743 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9744 | well use it to go straight to the applicable C func. */ | |
9745 | ||
2519490c MW |
9746 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9747 | (SCM z), | |
9748 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9749 | #define FUNC_NAME s_scm_log |
9750 | { | |
9751 | if (SCM_COMPLEXP (z)) | |
9752 | { | |
03976fee AW |
9753 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9754 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9755 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9756 | #else | |
9757 | double re = SCM_COMPLEX_REAL (z); | |
9758 | double im = SCM_COMPLEX_IMAG (z); | |
9759 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9760 | atan2 (im, re)); | |
9761 | #endif | |
9762 | } | |
a5f6b751 MW |
9763 | else if (SCM_REALP (z)) |
9764 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9765 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9766 | { |
a5f6b751 MW |
9767 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9768 | if (scm_is_eq (z, SCM_INUM0)) | |
9769 | scm_num_overflow (s_scm_log); | |
9770 | #endif | |
9771 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9772 | } |
a5f6b751 MW |
9773 | else if (SCM_BIGP (z)) |
9774 | return log_of_exact_integer (z); | |
9775 | else if (SCM_FRACTIONP (z)) | |
9776 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9777 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9778 | else |
9779 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9780 | } |
9781 | #undef FUNC_NAME | |
9782 | ||
9783 | ||
2519490c MW |
9784 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9785 | (SCM z), | |
9786 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9787 | #define FUNC_NAME s_scm_log10 |
9788 | { | |
9789 | if (SCM_COMPLEXP (z)) | |
9790 | { | |
9791 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9792 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9793 | log10+hypot+atan2.) */ | |
f328f862 LC |
9794 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9795 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9796 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9797 | #else | |
9798 | double re = SCM_COMPLEX_REAL (z); | |
9799 | double im = SCM_COMPLEX_IMAG (z); | |
9800 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9801 | M_LOG10E * atan2 (im, re)); | |
9802 | #endif | |
9803 | } | |
a5f6b751 | 9804 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9805 | { |
a5f6b751 MW |
9806 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9807 | if (scm_is_eq (z, SCM_INUM0)) | |
9808 | scm_num_overflow (s_scm_log10); | |
9809 | #endif | |
9810 | { | |
9811 | double re = scm_to_double (z); | |
9812 | double l = log10 (fabs (re)); | |
9813 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9814 | return scm_from_double (l); | |
9815 | else | |
9816 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9817 | } | |
8ab3d8a0 | 9818 | } |
a5f6b751 MW |
9819 | else if (SCM_BIGP (z)) |
9820 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9821 | else if (SCM_FRACTIONP (z)) | |
9822 | return scm_product (flo_log10e, | |
9823 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9824 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9825 | else |
9826 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9827 | } |
9828 | #undef FUNC_NAME | |
9829 | ||
9830 | ||
2519490c MW |
9831 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9832 | (SCM z), | |
9833 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9834 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9835 | #define FUNC_NAME s_scm_exp |
9836 | { | |
9837 | if (SCM_COMPLEXP (z)) | |
9838 | { | |
93723f3d MW |
9839 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9840 | && defined (SCM_COMPLEX_VALUE) | |
9841 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); | |
9842 | #else | |
8ab3d8a0 KR |
9843 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), |
9844 | SCM_COMPLEX_IMAG (z)); | |
93723f3d | 9845 | #endif |
8ab3d8a0 | 9846 | } |
2519490c | 9847 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9848 | { |
9849 | /* When z is a negative bignum the conversion to double overflows, | |
9850 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9851 | return scm_from_double (exp (scm_to_double (z))); | |
9852 | } | |
2519490c MW |
9853 | else |
9854 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9855 | } |
9856 | #undef FUNC_NAME | |
9857 | ||
9858 | ||
882c8963 MW |
9859 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9860 | (SCM k), | |
9861 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9862 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9863 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9864 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9865 | "\n" | |
9866 | "@lisp\n" | |
9867 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9868 | "@end lisp") | |
9869 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9870 | { | |
9871 | SCM s, r; | |
9872 | ||
9873 | scm_exact_integer_sqrt (k, &s, &r); | |
9874 | return scm_values (scm_list_2 (s, r)); | |
9875 | } | |
9876 | #undef FUNC_NAME | |
9877 | ||
9878 | void | |
9879 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9880 | { | |
9881 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9882 | { | |
9883 | scm_t_inum kk = SCM_I_INUM (k); | |
9884 | scm_t_inum uu = kk; | |
9885 | scm_t_inum ss; | |
9886 | ||
9887 | if (SCM_LIKELY (kk > 0)) | |
9888 | { | |
9889 | do | |
9890 | { | |
9891 | ss = uu; | |
9892 | uu = (ss + kk/ss) / 2; | |
9893 | } while (uu < ss); | |
9894 | *sp = SCM_I_MAKINUM (ss); | |
9895 | *rp = SCM_I_MAKINUM (kk - ss*ss); | |
9896 | } | |
9897 | else if (SCM_LIKELY (kk == 0)) | |
9898 | *sp = *rp = SCM_INUM0; | |
9899 | else | |
9900 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9901 | "exact non-negative integer"); | |
9902 | } | |
9903 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9904 | { | |
9905 | SCM s, r; | |
9906 | ||
9907 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9908 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9909 | "exact non-negative integer"); | |
9910 | s = scm_i_mkbig (); | |
9911 | r = scm_i_mkbig (); | |
9912 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9913 | scm_remember_upto_here_1 (k); | |
9914 | *sp = scm_i_normbig (s); | |
9915 | *rp = scm_i_normbig (r); | |
9916 | } | |
9917 | else | |
9918 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9919 | "exact non-negative integer"); | |
9920 | } | |
9921 | ||
9922 | ||
2519490c MW |
9923 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9924 | (SCM z), | |
9925 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9926 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9927 | "is returned, or if that's zero then a positive imaginary part.\n" |
9928 | "Thus,\n" | |
9929 | "\n" | |
9930 | "@example\n" | |
9931 | "(sqrt 9.0) @result{} 3.0\n" | |
9932 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9933 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9934 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9935 | "@end example") | |
8ab3d8a0 KR |
9936 | #define FUNC_NAME s_scm_sqrt |
9937 | { | |
2519490c | 9938 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9939 | { |
f328f862 LC |
9940 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9941 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9942 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9943 | #else |
2519490c MW |
9944 | double re = SCM_COMPLEX_REAL (z); |
9945 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9946 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9947 | 0.5 * atan2 (im, re)); | |
9948 | #endif | |
9949 | } | |
2519490c | 9950 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9951 | { |
2519490c | 9952 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9953 | if (xx < 0) |
9954 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9955 | else | |
9956 | return scm_from_double (sqrt (xx)); | |
9957 | } | |
2519490c MW |
9958 | else |
9959 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
9960 | } |
9961 | #undef FUNC_NAME | |
9962 | ||
9963 | ||
9964 | ||
0f2d19dd JB |
9965 | void |
9966 | scm_init_numbers () | |
0f2d19dd | 9967 | { |
b57bf272 AW |
9968 | if (scm_install_gmp_memory_functions) |
9969 | mp_set_memory_functions (custom_gmp_malloc, | |
9970 | custom_gmp_realloc, | |
9971 | custom_gmp_free); | |
9972 | ||
713a4259 KR |
9973 | mpz_init_set_si (z_negative_one, -1); |
9974 | ||
a261c0e9 DH |
9975 | /* It may be possible to tune the performance of some algorithms by using |
9976 | * the following constants to avoid the creation of bignums. Please, before | |
9977 | * using these values, remember the two rules of program optimization: | |
9978 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9979 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9980 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9981 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9982 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9983 | |
f3ae5d60 MD |
9984 | scm_add_feature ("complex"); |
9985 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9986 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9987 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea | 9988 | |
cff5fa33 | 9989 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
98237784 MW |
9990 | |
9991 | { | |
9992 | /* Set scm_i_divide2double_lo2b to (2 b^p - 1) */ | |
9993 | mpz_init_set_ui (scm_i_divide2double_lo2b, 1); | |
9994 | mpz_mul_2exp (scm_i_divide2double_lo2b, | |
9995 | scm_i_divide2double_lo2b, | |
9996 | DBL_MANT_DIG + 1); /* 2 b^p */ | |
9997 | mpz_sub_ui (scm_i_divide2double_lo2b, scm_i_divide2double_lo2b, 1); | |
9998 | } | |
9999 | ||
1ea37620 MW |
10000 | { |
10001 | /* Set dbl_minimum_normal_mantissa to b^{p-1} */ | |
10002 | mpz_init_set_ui (dbl_minimum_normal_mantissa, 1); | |
10003 | mpz_mul_2exp (dbl_minimum_normal_mantissa, | |
10004 | dbl_minimum_normal_mantissa, | |
10005 | DBL_MANT_DIG - 1); | |
10006 | } | |
10007 | ||
a0599745 | 10008 | #include "libguile/numbers.x" |
0f2d19dd | 10009 | } |
89e00824 ML |
10010 | |
10011 | /* | |
10012 | Local Variables: | |
10013 | c-file-style: "gnu" | |
10014 | End: | |
10015 | */ |